250206.1 · 972772153f3d6905c7e6a2bad7b7e3b4706185a1
Move oniguruma and decNumber to vendor directory (#3234)
reading declarations
@@ -1,9 +1,7 @@ .gitattributes export-ignore .gitignore export-ignore * text=auto eol=lf--# vendored files-src/decNumber/** linguist-vendored+vendor/** linguist-vendored # generated files src/lexer.[ch] linguist-generated=true
@@ -1,3 +1,3 @@-[submodule "modules/oniguruma"]- path = modules/oniguruma+[submodule "vendor/oniguruma"]+ path = vendor/oniguruma url = https://github.com/kkos/oniguruma.git
@@ -5,16 +5,16 @@ LIBJQ_INCS = src/builtin.h src/bytecode.h src/compile.h \ src/exec_stack.h src/jq_parser.h src/jv_alloc.h src/jv_dtoa.h \ src/jv_unicode.h src/jv_utf8_tables.h src/lexer.l src/libm.h \ src/linker.h src/locfile.h src/opcode_list.h src/parser.y \- src/util.h src/decNumber/decContext.h src/decNumber/decNumber.h \- src/decNumber/decNumberLocal.h src/jv_dtoa_tsd.h src/jv_thread.h \- src/jv_private.h+ src/util.h src/jv_dtoa_tsd.h src/jv_thread.h src/jv_private.h \+ vendor/decNumber/decContext.h vendor/decNumber/decNumber.h \+ vendor/decNumber/decNumberLocal.h LIBJQ_SRC = src/builtin.c src/bytecode.c src/compile.c src/execute.c \ src/jq_test.c src/jv.c src/jv_alloc.c src/jv_aux.c \ src/jv_dtoa.c src/jv_file.c src/jv_parse.c src/jv_print.c \ src/jv_unicode.c src/linker.c src/locfile.c src/util.c \- src/decNumber/decContext.c src/decNumber/decNumber.c \ src/jv_dtoa_tsd.c \+ vendor/decNumber/decContext.c vendor/decNumber/decNumber.c \ ${LIBJQ_INCS} ### C build options@@ -69,7 +69,7 @@ if ENABLE_UBSAN AM_CFLAGS += -fsanitize=undefined endif -AM_CPPFLAGS = -I$(srcdir)/src+AM_CPPFLAGS = -I$(srcdir)/src -I$(srcdir)/vendor ### Running tests under Valgrind @@ -176,8 +176,8 @@ CLEANFILES += jq.1 ### Build oniguruma if BUILD_ONIGURUMA-libjq_la_LIBADD += modules/oniguruma/src/.libs/libonig.la-SUBDIRS = modules/oniguruma+libjq_la_LIBADD += vendor/oniguruma/src/.libs/libonig.la+SUBDIRS = vendor/oniguruma endif AM_CFLAGS += $(onig_CFLAGS)
@@ -277,10 +277,10 @@ AS_IF([test "x$with_oniguruma" != xno], [ AC_MSG_NOTICE([Oniguruma was not found. Will use the packaged oniguruma.]) ]) ])- AS_IF([test "x$build_oniguruma" = xyes && test -f "${srcdir}/modules/oniguruma/configure.ac" ], [- onig_CFLAGS="-I${srcdir}/modules/oniguruma/src"- onig_LDFLAGS="-L${srcdir}/modules/oniguruma/src -Wl,-rpath,${libdir}"- AC_CONFIG_SUBDIRS([modules/oniguruma])+ AS_IF([test "x$build_oniguruma" = xyes && test -f "${srcdir}/vendor/oniguruma/configure.ac" ], [+ onig_CFLAGS="-I${srcdir}/vendor/oniguruma/src"+ onig_LDFLAGS="-L${srcdir}/vendor/oniguruma/src -Wl,-rpath,${libdir}"+ AC_CONFIG_SUBDIRS([vendor/oniguruma]) AC_DEFINE([HAVE_LIBONIG],1,[Define to 1 if the system includes libonig]) ]) CFLAGS="$save_CFLAGS"
modules/oniguruma
@@ -1 +0,0 @@-Subproject commit d2f1a14ced5d5d461acac0da0d477ab240a7ab5f
src/decNumber/ICU-license.html
@@ -1,45 +0,0 @@-<html> - -<head> -<meta http-equiv="Content-Type" content="text/html; charset=us-ascii"></meta> -<title>ICU License - ICU 1.8.1 and later</title> -</head> - -<body> -<h1>ICU License - ICU 1.8.1 and later</h1> -<pre> -COPYRIGHT AND PERMISSION NOTICE - -Copyright (c) 1995-2005 International Business Machines Corporation and others -All rights reserved. - -Permission is hereby granted, free of charge, to any person obtaining a -copy of this software and associated documentation files (the -"Software"), to deal in the Software without restriction, including -without limitation the rights to use, copy, modify, merge, publish, -distribute, and/or sell copies of the Software, and to permit persons -to whom the Software is furnished to do so, provided that the above -copyright notice(s) and this permission notice appear in all copies of -the Software and that both the above copyright notice(s) and this -permission notice appear in supporting documentation. - -THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS -OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF -MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT -OF THIRD PARTY RIGHTS. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR -HOLDERS INCLUDED IN THIS NOTICE BE LIABLE FOR ANY CLAIM, OR ANY SPECIAL -INDIRECT OR CONSEQUENTIAL DAMAGES, OR ANY DAMAGES WHATSOEVER RESULTING -FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, -NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION -WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. - -Except as contained in this notice, the name of a copyright holder -shall not be used in advertising or otherwise to promote the sale, use -or other dealings in this Software without prior written authorization -of the copyright holder. - --------------------------------------------------------------------------------- -All trademarks and registered trademarks mentioned herein are the property of their respective owners. -</pre> -</body> -</html>
src/decNumber/decBasic.c
@@ -1,3908 +0,0 @@-/* ------------------------------------------------------------------ */ -/* decBasic.c -- common base code for Basic decimal types */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is included in the package as decNumber.pdf. This */ -/* document is also available in HTML, together with specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ -/* This module comprises code that is shared between decDouble and */ -/* decQuad (but not decSingle). The main arithmetic operations are */ -/* here (Add, Subtract, Multiply, FMA, and Division operators). */ -/* */ -/* Unlike decNumber, parameterization takes place at compile time */ -/* rather than at runtime. The parameters are set in the decDouble.c */ -/* (etc.) files, which then include this one to produce the compiled */ -/* code. The functions here, therefore, are code shared between */ -/* multiple formats. */ -/* */ -/* This must be included after decCommon.c. */ -/* ------------------------------------------------------------------ */ -// Names here refer to decFloat rather than to decDouble, etc., and -// the functions are in strict alphabetical order. - -// The compile-time flags SINGLE, DOUBLE, and QUAD are set up in -// decCommon.c -#if !defined(QUAD) - #error decBasic.c must be included after decCommon.c -#endif -#if SINGLE - #error Routines in decBasic.c are for decDouble and decQuad only -#endif - -/* Private constants */ -#define DIVIDE 0x80000000 // Divide operations [as flags] -#define REMAINDER 0x40000000 // .. -#define DIVIDEINT 0x20000000 // .. -#define REMNEAR 0x10000000 // .. - -/* Private functions (local, used only by routines in this module) */ -static decFloat *decDivide(decFloat *, const decFloat *, - const decFloat *, decContext *, uInt); -static decFloat *decCanonical(decFloat *, const decFloat *); -static void decFiniteMultiply(bcdnum *, uByte *, const decFloat *, - const decFloat *); -static decFloat *decInfinity(decFloat *, const decFloat *); -static decFloat *decInvalid(decFloat *, decContext *); -static decFloat *decNaNs(decFloat *, const decFloat *, const decFloat *, - decContext *); -static Int decNumCompare(const decFloat *, const decFloat *, Flag); -static decFloat *decToIntegral(decFloat *, const decFloat *, decContext *, - enum rounding, Flag); -static uInt decToInt32(const decFloat *, decContext *, enum rounding, - Flag, Flag); - -/* ------------------------------------------------------------------ */ -/* decCanonical -- copy a decFloat, making canonical */ -/* */ -/* result gets the canonicalized df */ -/* df is the decFloat to copy and make canonical */ -/* returns result */ -/* */ -/* This is exposed via decFloatCanonical for Double and Quad only. */ -/* This works on specials, too; no error or exception is possible. */ -/* ------------------------------------------------------------------ */ -static decFloat * decCanonical(decFloat *result, const decFloat *df) { - uInt encode, precode, dpd; // work - uInt inword, uoff, canon; // .. - Int n; // counter (down) - if (df!=result) *result=*df; // effect copy if needed - if (DFISSPECIAL(result)) { - if (DFISINF(result)) return decInfinity(result, df); // clean Infinity - // is a NaN - DFWORD(result, 0)&=~ECONNANMASK; // clear ECON except selector - if (DFISCCZERO(df)) return result; // coefficient continuation is 0 - // drop through to check payload - } - // return quickly if the coefficient continuation is canonical - { // declare block - #if DOUBLE - uInt sourhi=DFWORD(df, 0); - uInt sourlo=DFWORD(df, 1); - if (CANONDPDOFF(sourhi, 8) - && CANONDPDTWO(sourhi, sourlo, 30) - && CANONDPDOFF(sourlo, 20) - && CANONDPDOFF(sourlo, 10) - && CANONDPDOFF(sourlo, 0)) return result; - #elif QUAD - uInt sourhi=DFWORD(df, 0); - uInt sourmh=DFWORD(df, 1); - uInt sourml=DFWORD(df, 2); - uInt sourlo=DFWORD(df, 3); - if (CANONDPDOFF(sourhi, 4) - && CANONDPDTWO(sourhi, sourmh, 26) - && CANONDPDOFF(sourmh, 16) - && CANONDPDOFF(sourmh, 6) - && CANONDPDTWO(sourmh, sourml, 28) - && CANONDPDOFF(sourml, 18) - && CANONDPDOFF(sourml, 8) - && CANONDPDTWO(sourml, sourlo, 30) - && CANONDPDOFF(sourlo, 20) - && CANONDPDOFF(sourlo, 10) - && CANONDPDOFF(sourlo, 0)) return result; - #endif - } // block - - // Loop to repair a non-canonical coefficent, as needed - inword=DECWORDS-1; // current input word - uoff=0; // bit offset of declet - encode=DFWORD(result, inword); - for (n=DECLETS-1; n>=0; n--) { // count down declets of 10 bits - dpd=encode>>uoff; - uoff+=10; - if (uoff>32) { // crossed uInt boundary - inword--; - encode=DFWORD(result, inword); - uoff-=32; - dpd|=encode<<(10-uoff); // get pending bits - } - dpd&=0x3ff; // clear uninteresting bits - if (dpd<0x16e) continue; // must be canonical - canon=BIN2DPD[DPD2BIN[dpd]]; // determine canonical declet - if (canon==dpd) continue; // have canonical declet - // need to replace declet - if (uoff>=10) { // all within current word - encode&=~(0x3ff<<(uoff-10)); // clear the 10 bits ready for replace - encode|=canon<<(uoff-10); // insert the canonical form - DFWORD(result, inword)=encode; // .. and save - continue; - } - // straddled words - precode=DFWORD(result, inword+1); // get previous - precode&=0xffffffff>>(10-uoff); // clear top bits - DFWORD(result, inword+1)=precode|(canon<<(32-(10-uoff))); - encode&=0xffffffff<<uoff; // clear bottom bits - encode|=canon>>(10-uoff); // insert canonical - DFWORD(result, inword)=encode; // .. and save - } // n - return result; - } // decCanonical - -/* ------------------------------------------------------------------ */ -/* decDivide -- divide operations */ -/* */ -/* result gets the result of dividing dfl by dfr: */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs) */ -/* set is the context */ -/* op is the operation selector */ -/* returns result */ -/* */ -/* op is one of DIVIDE, REMAINDER, DIVIDEINT, or REMNEAR. */ -/* ------------------------------------------------------------------ */ -#define DIVCOUNT 0 // 1 to instrument subtractions counter -#define DIVBASE ((uInt)BILLION) // the base used for divide -#define DIVOPLEN DECPMAX9 // operand length ('digits' base 10**9) -#define DIVACCLEN (DIVOPLEN*3) // accumulator length (ditto) -static decFloat * decDivide(decFloat *result, const decFloat *dfl, - const decFloat *dfr, decContext *set, uInt op) { - decFloat quotient; // for remainders - bcdnum num; // for final conversion - uInt acc[DIVACCLEN]; // coefficent in base-billion .. - uInt div[DIVOPLEN]; // divisor in base-billion .. - uInt quo[DIVOPLEN+1]; // quotient in base-billion .. - uByte bcdacc[(DIVOPLEN+1)*9+2]; // for quotient in BCD, +1, +1 - uInt *msua, *msud, *msuq; // -> msu of acc, div, and quo - Int divunits, accunits; // lengths - Int quodigits; // digits in quotient - uInt *lsua, *lsuq; // -> current acc and quo lsus - Int length, multiplier; // work - uInt carry, sign; // .. - uInt *ua, *ud, *uq; // .. - uByte *ub; // .. - uInt uiwork; // for macros - uInt divtop; // top unit of div adjusted for estimating - #if DIVCOUNT - static uInt maxcount=0; // worst-seen subtractions count - uInt divcount=0; // subtractions count [this divide] - #endif - - // calculate sign - num.sign=(DFWORD(dfl, 0)^DFWORD(dfr, 0)) & DECFLOAT_Sign; - - if (DFISSPECIAL(dfl) || DFISSPECIAL(dfr)) { // either is special? - // NaNs are handled as usual - if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set); - // one or two infinities - if (DFISINF(dfl)) { - if (DFISINF(dfr)) return decInvalid(result, set); // Two infinities bad - if (op&(REMAINDER|REMNEAR)) return decInvalid(result, set); // as is rem - // Infinity/x is infinite and quiet, even if x=0 - DFWORD(result, 0)=num.sign; - return decInfinity(result, result); - } - // must be x/Infinity -- remainders are lhs - if (op&(REMAINDER|REMNEAR)) return decCanonical(result, dfl); - // divides: return zero with correct sign and exponent depending - // on op (Etiny for divide, 0 for divideInt) - decFloatZero(result); - if (op==DIVIDEINT) DFWORD(result, 0)|=num.sign; // add sign - else DFWORD(result, 0)=num.sign; // zeros the exponent, too - return result; - } - // next, handle zero operands (x/0 and 0/x) - if (DFISZERO(dfr)) { // x/0 - if (DFISZERO(dfl)) { // 0/0 is undefined - decFloatZero(result); - DFWORD(result, 0)=DECFLOAT_qNaN; - set->status|=DEC_Division_undefined; - return result; - } - if (op&(REMAINDER|REMNEAR)) return decInvalid(result, set); // bad rem - set->status|=DEC_Division_by_zero; - DFWORD(result, 0)=num.sign; - return decInfinity(result, result); // x/0 -> signed Infinity - } - num.exponent=GETEXPUN(dfl)-GETEXPUN(dfr); // ideal exponent - if (DFISZERO(dfl)) { // 0/x (x!=0) - // if divide, result is 0 with ideal exponent; divideInt has - // exponent=0, remainders give zero with lower exponent - if (op&DIVIDEINT) { - decFloatZero(result); - DFWORD(result, 0)|=num.sign; // add sign - return result; - } - if (!(op&DIVIDE)) { // a remainder - // exponent is the minimum of the operands - num.exponent=MINI(GETEXPUN(dfl), GETEXPUN(dfr)); - // if the result is zero the sign shall be sign of dfl - num.sign=DFWORD(dfl, 0)&DECFLOAT_Sign; - } - bcdacc[0]=0; - num.msd=bcdacc; // -> 0 - num.lsd=bcdacc; // .. - return decFinalize(result, &num, set); // [divide may clamp exponent] - } // 0/x - // [here, both operands are known to be finite and non-zero] - - // extract the operand coefficents into 'units' which are - // base-billion; the lhs is high-aligned in acc and the msu of both - // acc and div is at the right-hand end of array (offset length-1); - // the quotient can need one more unit than the operands as digits - // in it are not necessarily aligned neatly; further, the quotient - // may not start accumulating until after the end of the initial - // operand in acc if that is small (e.g., 1) so the accumulator - // must have at least that number of units extra (at the ls end) - GETCOEFFBILL(dfl, acc+DIVACCLEN-DIVOPLEN); - GETCOEFFBILL(dfr, div); - // zero the low uInts of acc - acc[0]=0; - acc[1]=0; - acc[2]=0; - acc[3]=0; - #if DOUBLE - #if DIVOPLEN!=2 - #error Unexpected Double DIVOPLEN - #endif - #elif QUAD - acc[4]=0; - acc[5]=0; - acc[6]=0; - acc[7]=0; - #if DIVOPLEN!=4 - #error Unexpected Quad DIVOPLEN - #endif - #endif - - // set msu and lsu pointers - msua=acc+DIVACCLEN-1; // [leading zeros removed below] - msuq=quo+DIVOPLEN; - //[loop for div will terminate because operands are non-zero] - for (msud=div+DIVOPLEN-1; *msud==0;) msud--; - // the initial least-significant unit of acc is set so acc appears - // to have the same length as div. - // This moves one position towards the least possible for each - // iteration - divunits=(Int)(msud-div+1); // precalculate - lsua=msua-divunits+1; // initial working lsu of acc - lsuq=msuq; // and of quo - - // set up the estimator for the multiplier; this is the msu of div, - // plus two bits from the unit below (if any) rounded up by one if - // there are any non-zero bits or units below that [the extra two - // bits makes for a much better estimate when the top unit is small] - divtop=*msud<<2; - if (divunits>1) { - uInt *um=msud-1; - uInt d=*um; - if (d>=750000000) {divtop+=3; d-=750000000;} - else if (d>=500000000) {divtop+=2; d-=500000000;} - else if (d>=250000000) {divtop++; d-=250000000;} - if (d) divtop++; - else for (um--; um>=div; um--) if (*um) { - divtop++; - break; - } - } // >1 unit - - #if DECTRACE - {Int i; - printf("----- div="); - for (i=divunits-1; i>=0; i--) printf("%09ld ", (LI)div[i]); - printf("\n");} - #endif - - // now collect up to DECPMAX+1 digits in the quotient (this may - // need OPLEN+1 uInts if unaligned) - quodigits=0; // no digits yet - for (;; lsua--) { // outer loop -- each input position - #if DECCHECK - if (lsua<acc) { - printf("Acc underrun...\n"); - break; - } - #endif - #if DECTRACE - printf("Outer: quodigits=%ld acc=", (LI)quodigits); - for (ua=msua; ua>=lsua; ua--) printf("%09ld ", (LI)*ua); - printf("\n"); - #endif - *lsuq=0; // default unit result is 0 - for (;;) { // inner loop -- calculate quotient unit - // strip leading zero units from acc (either there initially or - // from subtraction below); this may strip all if exactly 0 - for (; *msua==0 && msua>=lsua;) msua--; - accunits=(Int)(msua-lsua+1); // [maybe 0] - // subtraction is only necessary and possible if there are as - // least as many units remaining in acc for this iteration as - // there are in div - if (accunits<divunits) { - if (accunits==0) msua++; // restore - break; - } - - // If acc is longer than div then subtraction is definitely - // possible (as msu of both is non-zero), but if they are the - // same length a comparison is needed. - // If a subtraction is needed then a good estimate of the - // multiplier for the subtraction is also needed in order to - // minimise the iterations of this inner loop because the - // subtractions needed dominate division performance. - if (accunits==divunits) { - // compare the high divunits of acc and div: - // acc<div: this quotient unit is unchanged; subtraction - // will be possible on the next iteration - // acc==div: quotient gains 1, set acc=0 - // acc>div: subtraction necessary at this position - for (ud=msud, ua=msua; ud>div; ud--, ua--) if (*ud!=*ua) break; - // [now at first mismatch or lsu] - if (*ud>*ua) break; // next time... - if (*ud==*ua) { // all compared equal - *lsuq+=1; // increment result - msua=lsua; // collapse acc units - *msua=0; // .. to a zero - break; - } - - // subtraction necessary; estimate multiplier [see above] - // if both *msud and *msua are small it is cost-effective to - // bring in part of the following units (if any) to get a - // better estimate (assume some other non-zero in div) - #define DIVLO 1000000U - #define DIVHI (DIVBASE/DIVLO) - #if DECUSE64 - if (divunits>1) { - // there cannot be a *(msud-2) for DECDOUBLE so next is - // an exact calculation unless DECQUAD (which needs to - // assume bits out there if divunits>2) - uLong mul=(uLong)*msua * DIVBASE + *(msua-1); - uLong div=(uLong)*msud * DIVBASE + *(msud-1); - #if QUAD - if (divunits>2) div++; - #endif - mul/=div; - multiplier=(Int)mul; - } - else multiplier=*msua/(*msud); - #else - if (divunits>1 && *msua<DIVLO && *msud<DIVLO) { - multiplier=(*msua*DIVHI + *(msua-1)/DIVLO) - /(*msud*DIVHI + *(msud-1)/DIVLO +1); - } - else multiplier=(*msua<<2)/divtop; - #endif - } - else { // accunits>divunits - // msud is one unit 'lower' than msua, so estimate differently - #if DECUSE64 - uLong mul; - // as before, bring in extra digits if possible - if (divunits>1 && *msua<DIVLO && *msud<DIVLO) { - mul=((uLong)*msua * DIVHI * DIVBASE) + *(msua-1) * DIVHI - + *(msua-2)/DIVLO; - mul/=(*msud*DIVHI + *(msud-1)/DIVLO +1); - } - else if (divunits==1) { - mul=(uLong)*msua * DIVBASE + *(msua-1); - mul/=*msud; // no more to the right - } - else { - mul=(uLong)(*msua) * (uInt)(DIVBASE<<2) - + (*(msua-1)<<2); - mul/=divtop; // [divtop already allows for sticky bits] - } - multiplier=(Int)mul; - #else - multiplier=*msua * ((DIVBASE<<2)/divtop); - #endif - } - if (multiplier==0) multiplier=1; // marginal case - *lsuq+=multiplier; - - #if DIVCOUNT - // printf("Multiplier: %ld\n", (LI)multiplier); - divcount++; - #endif - - // Carry out the subtraction acc-(div*multiplier); for each - // unit in div, do the multiply, split to units (see - // decFloatMultiply for the algorithm), and subtract from acc - #define DIVMAGIC 2305843009U // 2**61/10**9 - #define DIVSHIFTA 29 - #define DIVSHIFTB 32 - carry=0; - for (ud=div, ua=lsua; ud<=msud; ud++, ua++) { - uInt lo, hop; - #if DECUSE64 - uLong sub=(uLong)multiplier*(*ud)+carry; - if (sub<DIVBASE) { - carry=0; - lo=(uInt)sub; - } - else { - hop=(uInt)(sub>>DIVSHIFTA); - carry=(uInt)(((uLong)hop*DIVMAGIC)>>DIVSHIFTB); - // the estimate is now in hi; now calculate sub-hi*10**9 - // to get the remainder (which will be <DIVBASE)) - lo=(uInt)sub; - lo-=carry*DIVBASE; // low word of result - if (lo>=DIVBASE) { - lo-=DIVBASE; // correct by +1 - carry++; - } - } - #else // 32-bit - uInt hi; - // calculate multiplier*(*ud) into hi and lo - LONGMUL32HI(hi, *ud, multiplier); // get the high word - lo=multiplier*(*ud); // .. and the low - lo+=carry; // add the old hi - carry=hi+(lo<carry); // .. with any carry - if (carry || lo>=DIVBASE) { // split is needed - hop=(carry<<3)+(lo>>DIVSHIFTA); // hi:lo/2**29 - LONGMUL32HI(carry, hop, DIVMAGIC); // only need the high word - // [DIVSHIFTB is 32, so carry can be used directly] - // the estimate is now in carry; now calculate hi:lo-est*10**9; - // happily the top word of the result is irrelevant because it - // will always be zero so this needs only one multiplication - lo-=(carry*DIVBASE); - // the correction here will be at most +1; do it - if (lo>=DIVBASE) { - lo-=DIVBASE; - carry++; - } - } - #endif - if (lo>*ua) { // borrow needed - *ua+=DIVBASE; - carry++; - } - *ua-=lo; - } // ud loop - if (carry) *ua-=carry; // accdigits>divdigits [cannot borrow] - } // inner loop - - // the outer loop terminates when there is either an exact result - // or enough digits; first update the quotient digit count and - // pointer (if any significant digits) - #if DECTRACE - if (*lsuq || quodigits) printf("*lsuq=%09ld\n", (LI)*lsuq); - #endif - if (quodigits) { - quodigits+=9; // had leading unit earlier - lsuq--; - if (quodigits>DECPMAX+1) break; // have enough - } - else if (*lsuq) { // first quotient digits - const uInt *pow; - for (pow=DECPOWERS; *lsuq>=*pow; pow++) quodigits++; - lsuq--; - // [cannot have >DECPMAX+1 on first unit] - } - - if (*msua!=0) continue; // not an exact result - // acc is zero iff used all of original units and zero down to lsua - // (must also continue to original lsu for correct quotient length) - if (lsua>acc+DIVACCLEN-DIVOPLEN) continue; - for (; msua>lsua && *msua==0;) msua--; - if (*msua==0 && msua==lsua) break; - } // outer loop - - // all of the original operand in acc has been covered at this point - // quotient now has at least DECPMAX+2 digits - // *msua is now non-0 if inexact and sticky bits - // lsuq is one below the last uint of the quotient - lsuq++; // set -> true lsu of quo - if (*msua) *lsuq|=1; // apply sticky bit - - // quo now holds the (unrounded) quotient in base-billion; one - // base-billion 'digit' per uInt. - #if DECTRACE - printf("DivQuo:"); - for (uq=msuq; uq>=lsuq; uq--) printf(" %09ld", (LI)*uq); - printf("\n"); - #endif - - // Now convert to BCD for rounding and cleanup, starting from the - // most significant end [offset by one into bcdacc to leave room - // for a possible carry digit if rounding for REMNEAR is needed] - for (uq=msuq, ub=bcdacc+1; uq>=lsuq; uq--, ub+=9) { - uInt top, mid, rem; // work - if (*uq==0) { // no split needed - UBFROMUI(ub, 0); // clear 9 BCD8s - UBFROMUI(ub+4, 0); // .. - *(ub+8)=0; // .. - continue; - } - // *uq is non-zero -- split the base-billion digit into - // hi, mid, and low three-digits - #define divsplit9 1000000 // divisor - #define divsplit6 1000 // divisor - // The splitting is done by simple divides and remainders, - // assuming the compiler will optimize these [GCC does] - top=*uq/divsplit9; - rem=*uq%divsplit9; - mid=rem/divsplit6; - rem=rem%divsplit6; - // lay out the nine BCD digits (plus one unwanted byte) - UBFROMUI(ub, UBTOUI(&BIN2BCD8[top*4])); - UBFROMUI(ub+3, UBTOUI(&BIN2BCD8[mid*4])); - UBFROMUI(ub+6, UBTOUI(&BIN2BCD8[rem*4])); - } // BCD conversion loop - ub--; // -> lsu - - // complete the bcdnum; quodigits is correct, so the position of - // the first non-zero is known - num.msd=bcdacc+1+(msuq-lsuq+1)*9-quodigits; - num.lsd=ub; - - // make exponent adjustments, etc - if (lsua<acc+DIVACCLEN-DIVOPLEN) { // used extra digits - num.exponent-=(Int)((acc+DIVACCLEN-DIVOPLEN-lsua)*9); - // if the result was exact then there may be up to 8 extra - // trailing zeros in the overflowed quotient final unit - if (*msua==0) { - for (; *ub==0;) ub--; // drop zeros - num.exponent+=(Int)(num.lsd-ub); // and adjust exponent - num.lsd=ub; - } - } // adjustment needed - - #if DIVCOUNT - if (divcount>maxcount) { // new high-water nark - maxcount=divcount; - printf("DivNewMaxCount: %ld\n", (LI)maxcount); - } - #endif - - if (op&DIVIDE) return decFinalize(result, &num, set); // all done - - // Is DIVIDEINT or a remainder; there is more to do -- first form - // the integer (this is done 'after the fact', unlike as in - // decNumber, so as not to tax DIVIDE) - - // The first non-zero digit will be in the first 9 digits, known - // from quodigits and num.msd, so there is always space for DECPMAX - // digits - - length=(Int)(num.lsd-num.msd+1); - //printf("Length exp: %ld %ld\n", (LI)length, (LI)num.exponent); - - if (length+num.exponent>DECPMAX) { // cannot fit - decFloatZero(result); - DFWORD(result, 0)=DECFLOAT_qNaN; - set->status|=DEC_Division_impossible; - return result; - } - - if (num.exponent>=0) { // already an int, or need pad zeros - for (ub=num.lsd+1; ub<=num.lsd+num.exponent; ub++) *ub=0; - num.lsd+=num.exponent; - } - else { // too long: round or truncate needed - Int drop=-num.exponent; - if (!(op&REMNEAR)) { // simple truncate - num.lsd-=drop; - if (num.lsd<num.msd) { // truncated all - num.lsd=num.msd; // make 0 - *num.lsd=0; // .. [sign still relevant] - } - } - else { // round to nearest even [sigh] - // round-to-nearest, in-place; msd is at or to right of bcdacc+1 - // (this is a special case of Quantize -- q.v. for commentary) - uByte *roundat; // -> re-round digit - uByte reround; // reround value - *(num.msd-1)=0; // in case of left carry, or make 0 - if (drop<length) roundat=num.lsd-drop+1; - else if (drop==length) roundat=num.msd; - else roundat=num.msd-1; // [-> 0] - reround=*roundat; - for (ub=roundat+1; ub<=num.lsd; ub++) { - if (*ub!=0) { - reround=DECSTICKYTAB[reround]; - break; - } - } // check stickies - if (roundat>num.msd) num.lsd=roundat-1; - else { - num.msd--; // use the 0 .. - num.lsd=num.msd; // .. at the new MSD place - } - if (reround!=0) { // discarding non-zero - uInt bump=0; - // rounding is DEC_ROUND_HALF_EVEN always - if (reround>5) bump=1; // >0.5 goes up - else if (reround==5) // exactly 0.5000 .. - bump=*(num.lsd) & 0x01; // .. up iff [new] lsd is odd - if (bump!=0) { // need increment - // increment the coefficient; this might end up with 1000... - ub=num.lsd; - for (; UBTOUI(ub-3)==0x09090909; ub-=4) UBFROMUI(ub-3, 0); - for (; *ub==9; ub--) *ub=0; // at most 3 more - *ub+=1; - if (ub<num.msd) num.msd--; // carried - } // bump needed - } // reround!=0 - } // remnear - } // round or truncate needed - num.exponent=0; // all paths - //decShowNum(&num, "int"); - - if (op&DIVIDEINT) return decFinalize(result, &num, set); // all done - - // Have a remainder to calculate - decFinalize("ient, &num, set); // lay out the integer so far - DFWORD("ient, 0)^=DECFLOAT_Sign; // negate it - sign=DFWORD(dfl, 0); // save sign of dfl - decFloatFMA(result, "ient, dfr, dfl, set); - if (!DFISZERO(result)) return result; - // if the result is zero the sign shall be sign of dfl - DFWORD("ient, 0)=sign; // construct decFloat of sign - return decFloatCopySign(result, result, "ient); - } // decDivide - -/* ------------------------------------------------------------------ */ -/* decFiniteMultiply -- multiply two finite decFloats */ -/* */ -/* num gets the result of multiplying dfl and dfr */ -/* bcdacc .. with the coefficient in this array */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs) */ -/* */ -/* This effects the multiplication of two decFloats, both known to be */ -/* finite, leaving the result in a bcdnum ready for decFinalize (for */ -/* use in Multiply) or in a following addition (FMA). */ -/* */ -/* bcdacc must have space for at least DECPMAX9*18+1 bytes. */ -/* No error is possible and no status is set. */ -/* ------------------------------------------------------------------ */ -// This routine has two separate implementations of the core -// multiplication; both using base-billion. One uses only 32-bit -// variables (Ints and uInts) or smaller; the other uses uLongs (for -// multiplication and addition only). Both implementations cover -// both arithmetic sizes (DOUBLE and QUAD) in order to allow timing -// comparisons. In any one compilation only one implementation for -// each size can be used, and if DECUSE64 is 0 then use of the 32-bit -// version is forced. -// -// Historical note: an earlier version of this code also supported the -// 256-bit format and has been preserved. That is somewhat trickier -// during lazy carry splitting because the initial quotient estimate -// (est) can exceed 32 bits. - -#define MULTBASE ((uInt)BILLION) // the base used for multiply -#define MULOPLEN DECPMAX9 // operand length ('digits' base 10**9) -#define MULACCLEN (MULOPLEN*2) // accumulator length (ditto) -#define LEADZEROS (MULACCLEN*9 - DECPMAX*2) // leading zeros always - -// Assertions: exponent not too large and MULACCLEN is a multiple of 4 -#if DECEMAXD>9 - #error Exponent may overflow when doubled for Multiply -#endif -#if MULACCLEN!=(MULACCLEN/4)*4 - // This assumption is used below only for initialization - #error MULACCLEN is not a multiple of 4 -#endif - -static void decFiniteMultiply(bcdnum *num, uByte *bcdacc, - const decFloat *dfl, const decFloat *dfr) { - uInt bufl[MULOPLEN]; // left coefficient (base-billion) - uInt bufr[MULOPLEN]; // right coefficient (base-billion) - uInt *ui, *uj; // work - uByte *ub; // .. - uInt uiwork; // for macros - - #if DECUSE64 - uLong accl[MULACCLEN]; // lazy accumulator (base-billion+) - uLong *pl; // work -> lazy accumulator - uInt acc[MULACCLEN]; // coefficent in base-billion .. - #else - uInt acc[MULACCLEN*2]; // accumulator in base-billion .. - #endif - uInt *pa; // work -> accumulator - //printf("Base10**9: OpLen=%d MulAcclen=%d\n", OPLEN, MULACCLEN); - - /* Calculate sign and exponent */ - num->sign=(DFWORD(dfl, 0)^DFWORD(dfr, 0)) & DECFLOAT_Sign; - num->exponent=GETEXPUN(dfl)+GETEXPUN(dfr); // [see assertion above] - - /* Extract the coefficients and prepare the accumulator */ - // the coefficients of the operands are decoded into base-billion - // numbers in uInt arrays (bufl and bufr, LSD at offset 0) of the - // appropriate size. - GETCOEFFBILL(dfl, bufl); - GETCOEFFBILL(dfr, bufr); - #if DECTRACE && 0 - printf("CoeffbL:"); - for (ui=bufl+MULOPLEN-1; ui>=bufl; ui--) printf(" %08lx", (LI)*ui); - printf("\n"); - printf("CoeffbR:"); - for (uj=bufr+MULOPLEN-1; uj>=bufr; uj--) printf(" %08lx", (LI)*uj); - printf("\n"); - #endif - - // start the 64-bit/32-bit differing paths... -#if DECUSE64 - - // zero the accumulator - #if MULACCLEN==4 - accl[0]=0; accl[1]=0; accl[2]=0; accl[3]=0; - #else // use a loop - // MULACCLEN is a multiple of four, asserted above - for (pl=accl; pl<accl+MULACCLEN; pl+=4) { - *pl=0; *(pl+1)=0; *(pl+2)=0; *(pl+3)=0;// [reduce overhead] - } // pl - #endif - - /* Effect the multiplication */ - // The multiplication proceeds using MFC's lazy-carry resolution - // algorithm from decNumber. First, the multiplication is - // effected, allowing accumulation of the partial products (which - // are in base-billion at each column position) into 64 bits - // without resolving back to base=billion after each addition. - // These 64-bit numbers (which may contain up to 19 decimal digits) - // are then split using the Clark & Cowlishaw algorithm (see below). - // [Testing for 0 in the inner loop is not really a 'win'] - for (ui=bufr; ui<bufr+MULOPLEN; ui++) { // over each item in rhs - if (*ui==0) continue; // product cannot affect result - pl=accl+(ui-bufr); // where to add the lhs - for (uj=bufl; uj<bufl+MULOPLEN; uj++, pl++) { // over each item in lhs - // if (*uj==0) continue; // product cannot affect result - *pl+=((uLong)*ui)*(*uj); - } // uj - } // ui - - // The 64-bit carries must now be resolved; this means that a - // quotient/remainder has to be calculated for base-billion (1E+9). - // For this, Clark & Cowlishaw's quotient estimation approach (also - // used in decNumber) is needed, because 64-bit divide is generally - // extremely slow on 32-bit machines, and may be slower than this - // approach even on 64-bit machines. This algorithm splits X - // using: - // - // magic=2**(A+B)/1E+9; // 'magic number' - // hop=X/2**A; // high order part of X (by shift) - // est=magic*hop/2**B // quotient estimate (may be low by 1) - // - // A and B are quite constrained; hop and magic must fit in 32 bits, - // and 2**(A+B) must be as large as possible (which is 2**61 if - // magic is to fit). Further, maxX increases with the length of - // the operands (and hence the number of partial products - // accumulated); maxX is OPLEN*(10**18), which is up to 19 digits. - // - // It can be shown that when OPLEN is 2 then the maximum error in - // the estimated quotient is <1, but for larger maximum x the - // maximum error is above 1 so a correction that is >1 may be - // needed. Values of A and B are chosen to satisfy the constraints - // just mentioned while minimizing the maximum error (and hence the - // maximum correction), as shown in the following table: - // - // Type OPLEN A B maxX maxError maxCorrection - // --------------------------------------------------------- - // DOUBLE 2 29 32 <2*10**18 0.63 1 - // QUAD 4 30 31 <4*10**18 1.17 2 - // - // In the OPLEN==2 case there is most choice, but the value for B - // of 32 has a big advantage as then the calculation of the - // estimate requires no shifting; the compiler can extract the high - // word directly after multiplying magic*hop. - #define MULMAGIC 2305843009U // 2**61/10**9 [both cases] - #if DOUBLE - #define MULSHIFTA 29 - #define MULSHIFTB 32 - #elif QUAD - #define MULSHIFTA 30 - #define MULSHIFTB 31 - #else - #error Unexpected type - #endif - - #if DECTRACE - printf("MulAccl:"); - for (pl=accl+MULACCLEN-1; pl>=accl; pl--) - printf(" %08lx:%08lx", (LI)(*pl>>32), (LI)(*pl&0xffffffff)); - printf("\n"); - #endif - - for (pl=accl, pa=acc; pl<accl+MULACCLEN; pl++, pa++) { // each column position - uInt lo, hop; // work - uInt est; // cannot exceed 4E+9 - if (*pl>=MULTBASE) { - // *pl holds a binary number which needs to be split - hop=(uInt)(*pl>>MULSHIFTA); - est=(uInt)(((uLong)hop*MULMAGIC)>>MULSHIFTB); - // the estimate is now in est; now calculate hi:lo-est*10**9; - // happily the top word of the result is irrelevant because it - // will always be zero so this needs only one multiplication - lo=(uInt)(*pl-((uLong)est*MULTBASE)); // low word of result - // If QUAD, the correction here could be +2 - if (lo>=MULTBASE) { - lo-=MULTBASE; // correct by +1 - est++; - #if QUAD - // may need to correct by +2 - if (lo>=MULTBASE) { - lo-=MULTBASE; - est++; - } - #endif - } - // finally place lo as the new coefficient 'digit' and add est to - // the next place up [this is safe because this path is never - // taken on the final iteration as *pl will fit] - *pa=lo; - *(pl+1)+=est; - } // *pl needed split - else { // *pl<MULTBASE - *pa=(uInt)*pl; // just copy across - } - } // pl loop - -#else // 32-bit - for (pa=acc;; pa+=4) { // zero the accumulator - *pa=0; *(pa+1)=0; *(pa+2)=0; *(pa+3)=0; // [reduce overhead] - if (pa==acc+MULACCLEN*2-4) break; // multiple of 4 asserted - } // pa - - /* Effect the multiplication */ - // uLongs are not available (and in particular, there is no uLong - // divide) but it is still possible to use MFC's lazy-carry - // resolution algorithm from decNumber. First, the multiplication - // is effected, allowing accumulation of the partial products - // (which are in base-billion at each column position) into 64 bits - // [with the high-order 32 bits in each position being held at - // offset +ACCLEN from the low-order 32 bits in the accumulator]. - // These 64-bit numbers (which may contain up to 19 decimal digits) - // are then split using the Clark & Cowlishaw algorithm (see - // below). - for (ui=bufr;; ui++) { // over each item in rhs - uInt hi, lo; // words of exact multiply result - pa=acc+(ui-bufr); // where to add the lhs - for (uj=bufl;; uj++, pa++) { // over each item in lhs - LONGMUL32HI(hi, *ui, *uj); // calculate product of digits - lo=(*ui)*(*uj); // .. - *pa+=lo; // accumulate low bits and .. - *(pa+MULACCLEN)+=hi+(*pa<lo); // .. high bits with any carry - if (uj==bufl+MULOPLEN-1) break; - } - if (ui==bufr+MULOPLEN-1) break; - } - - // The 64-bit carries must now be resolved; this means that a - // quotient/remainder has to be calculated for base-billion (1E+9). - // For this, Clark & Cowlishaw's quotient estimation approach (also - // used in decNumber) is needed, because 64-bit divide is generally - // extremely slow on 32-bit machines. This algorithm splits X - // using: - // - // magic=2**(A+B)/1E+9; // 'magic number' - // hop=X/2**A; // high order part of X (by shift) - // est=magic*hop/2**B // quotient estimate (may be low by 1) - // - // A and B are quite constrained; hop and magic must fit in 32 bits, - // and 2**(A+B) must be as large as possible (which is 2**61 if - // magic is to fit). Further, maxX increases with the length of - // the operands (and hence the number of partial products - // accumulated); maxX is OPLEN*(10**18), which is up to 19 digits. - // - // It can be shown that when OPLEN is 2 then the maximum error in - // the estimated quotient is <1, but for larger maximum x the - // maximum error is above 1 so a correction that is >1 may be - // needed. Values of A and B are chosen to satisfy the constraints - // just mentioned while minimizing the maximum error (and hence the - // maximum correction), as shown in the following table: - // - // Type OPLEN A B maxX maxError maxCorrection - // --------------------------------------------------------- - // DOUBLE 2 29 32 <2*10**18 0.63 1 - // QUAD 4 30 31 <4*10**18 1.17 2 - // - // In the OPLEN==2 case there is most choice, but the value for B - // of 32 has a big advantage as then the calculation of the - // estimate requires no shifting; the high word is simply - // calculated from multiplying magic*hop. - #define MULMAGIC 2305843009U // 2**61/10**9 [both cases] - #if DOUBLE - #define MULSHIFTA 29 - #define MULSHIFTB 32 - #elif QUAD - #define MULSHIFTA 30 - #define MULSHIFTB 31 - #else - #error Unexpected type - #endif - - #if DECTRACE - printf("MulHiLo:"); - for (pa=acc+MULACCLEN-1; pa>=acc; pa--) - printf(" %08lx:%08lx", (LI)*(pa+MULACCLEN), (LI)*pa); - printf("\n"); - #endif - - for (pa=acc;; pa++) { // each low uInt - uInt hi, lo; // words of exact multiply result - uInt hop, estlo; // work - #if QUAD - uInt esthi; // .. - #endif - - lo=*pa; - hi=*(pa+MULACCLEN); // top 32 bits - // hi and lo now hold a binary number which needs to be split - - #if DOUBLE - hop=(hi<<3)+(lo>>MULSHIFTA); // hi:lo/2**29 - LONGMUL32HI(estlo, hop, MULMAGIC);// only need the high word - // [MULSHIFTB is 32, so estlo can be used directly] - // the estimate is now in estlo; now calculate hi:lo-est*10**9; - // happily the top word of the result is irrelevant because it - // will always be zero so this needs only one multiplication - lo-=(estlo*MULTBASE); - // esthi=0; // high word is ignored below - // the correction here will be at most +1; do it - if (lo>=MULTBASE) { - lo-=MULTBASE; - estlo++; - } - #elif QUAD - hop=(hi<<2)+(lo>>MULSHIFTA); // hi:lo/2**30 - LONGMUL32HI(esthi, hop, MULMAGIC);// shift will be 31 .. - estlo=hop*MULMAGIC; // .. so low word needed - estlo=(esthi<<1)+(estlo>>MULSHIFTB); // [just the top bit] - // esthi=0; // high word is ignored below - lo-=(estlo*MULTBASE); // as above - // the correction here could be +1 or +2 - if (lo>=MULTBASE) { - lo-=MULTBASE; - estlo++; - } - if (lo>=MULTBASE) { - lo-=MULTBASE; - estlo++; - } - #else - #error Unexpected type - #endif - - // finally place lo as the new accumulator digit and add est to - // the next place up; this latter add could cause a carry of 1 - // to the high word of the next place - *pa=lo; - *(pa+1)+=estlo; - // esthi is always 0 for DOUBLE and QUAD so this is skipped - // *(pa+1+MULACCLEN)+=esthi; - if (*(pa+1)<estlo) *(pa+1+MULACCLEN)+=1; // carry - if (pa==acc+MULACCLEN-2) break; // [MULACCLEN-1 will never need split] - } // pa loop -#endif - - // At this point, whether using the 64-bit or the 32-bit paths, the - // accumulator now holds the (unrounded) result in base-billion; - // one base-billion 'digit' per uInt. - #if DECTRACE - printf("MultAcc:"); - for (pa=acc+MULACCLEN-1; pa>=acc; pa--) printf(" %09ld", (LI)*pa); - printf("\n"); - #endif - - // Now convert to BCD for rounding and cleanup, starting from the - // most significant end - pa=acc+MULACCLEN-1; - if (*pa!=0) num->msd=bcdacc+LEADZEROS;// drop known lead zeros - else { // >=1 word of leading zeros - num->msd=bcdacc; // known leading zeros are gone - pa--; // skip first word .. - for (; *pa==0; pa--) if (pa==acc) break; // .. and any more leading 0s - } - for (ub=bcdacc;; pa--, ub+=9) { - if (*pa!=0) { // split(s) needed - uInt top, mid, rem; // work - // *pa is non-zero -- split the base-billion acc digit into - // hi, mid, and low three-digits - #define mulsplit9 1000000 // divisor - #define mulsplit6 1000 // divisor - // The splitting is done by simple divides and remainders, - // assuming the compiler will optimize these where useful - // [GCC does] - top=*pa/mulsplit9; - rem=*pa%mulsplit9; - mid=rem/mulsplit6; - rem=rem%mulsplit6; - // lay out the nine BCD digits (plus one unwanted byte) - UBFROMUI(ub, UBTOUI(&BIN2BCD8[top*4])); - UBFROMUI(ub+3, UBTOUI(&BIN2BCD8[mid*4])); - UBFROMUI(ub+6, UBTOUI(&BIN2BCD8[rem*4])); - } - else { // *pa==0 - UBFROMUI(ub, 0); // clear 9 BCD8s - UBFROMUI(ub+4, 0); // .. - *(ub+8)=0; // .. - } - if (pa==acc) break; - } // BCD conversion loop - - num->lsd=ub+8; // complete the bcdnum .. - - #if DECTRACE - decShowNum(num, "postmult"); - decFloatShow(dfl, "dfl"); - decFloatShow(dfr, "dfr"); - #endif - return; - } // decFiniteMultiply - -/* ------------------------------------------------------------------ */ -/* decFloatAbs -- absolute value, heeding NaNs, etc. */ -/* */ -/* result gets the canonicalized df with sign 0 */ -/* df is the decFloat to abs */ -/* set is the context */ -/* returns result */ -/* */ -/* This has the same effect as decFloatPlus unless df is negative, */ -/* in which case it has the same effect as decFloatMinus. The */ -/* effect is also the same as decFloatCopyAbs except that NaNs are */ -/* handled normally (the sign of a NaN is not affected, and an sNaN */ -/* will signal) and the result will be canonical. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatAbs(decFloat *result, const decFloat *df, - decContext *set) { - if (DFISNAN(df)) return decNaNs(result, df, NULL, set); - decCanonical(result, df); // copy and check - DFBYTE(result, 0)&=~0x80; // zero sign bit - return result; - } // decFloatAbs - -/* ------------------------------------------------------------------ */ -/* decFloatAdd -- add two decFloats */ -/* */ -/* result gets the result of adding dfl and dfr: */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs) */ -/* set is the context */ -/* returns result */ -/* */ -/* ------------------------------------------------------------------ */ -#if QUAD -// Table for testing MSDs for fastpath elimination; returns the MSD of -// a decDouble or decQuad (top 6 bits tested) ignoring the sign. -// Infinities return -32 and NaNs return -128 so that summing the two -// MSDs also allows rapid tests for the Specials (see code below). -const Int DECTESTMSD[64]={ - 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, - 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 8, 9, -32, -128, - 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, - 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 8, 9, -32, -128}; -#else -// The table for testing MSDs is shared between the modules -extern const Int DECTESTMSD[64]; -#endif - -decFloat * decFloatAdd(decFloat *result, - const decFloat *dfl, const decFloat *dfr, - decContext *set) { - bcdnum num; // for final conversion - Int bexpl, bexpr; // left and right biased exponents - uByte *ub, *us, *ut; // work - uInt uiwork; // for macros - #if QUAD - uShort uswork; // .. - #endif - - uInt sourhil, sourhir; // top words from source decFloats - // [valid only through end of - // fastpath code -- before swap] - uInt diffsign; // non-zero if signs differ - uInt carry; // carry: 0 or 1 before add loop - Int overlap; // coefficient overlap (if full) - Int summ; // sum of the MSDs - // the following buffers hold coefficients with various alignments - // (see commentary and diagrams below) - uByte acc[4+2+DECPMAX*3+8]; - uByte buf[4+2+DECPMAX*2]; - uByte *umsd, *ulsd; // local MSD and LSD pointers - - #if DECLITEND - #define CARRYPAT 0x01000000 // carry=1 pattern - #else - #define CARRYPAT 0x00000001 // carry=1 pattern - #endif - - /* Start decoding the arguments */ - // The initial exponents are placed into the opposite Ints to - // that which might be expected; there are two sets of data to - // keep track of (each decFloat and the corresponding exponent), - // and this scheme means that at the swap point (after comparing - // exponents) only one pair of words needs to be swapped - // whichever path is taken (thereby minimising worst-case path). - // The calculated exponents will be nonsense when the arguments are - // Special, but are not used in that path - sourhil=DFWORD(dfl, 0); // LHS top word - summ=DECTESTMSD[sourhil>>26]; // get first MSD for testing - bexpr=DECCOMBEXP[sourhil>>26]; // get exponent high bits (in place) - bexpr+=GETECON(dfl); // .. + continuation - - sourhir=DFWORD(dfr, 0); // RHS top word - summ+=DECTESTMSD[sourhir>>26]; // sum MSDs for testing - bexpl=DECCOMBEXP[sourhir>>26]; - bexpl+=GETECON(dfr); - - // here bexpr has biased exponent from lhs, and vice versa - - diffsign=(sourhil^sourhir)&DECFLOAT_Sign; - - // now determine whether to take a fast path or the full-function - // slow path. The slow path must be taken when: - // -- both numbers are finite, and: - // the exponents are different, or - // the signs are different, or - // the sum of the MSDs is >8 (hence might overflow) - // specialness and the sum of the MSDs can be tested at once using - // the summ value just calculated, so the test for specials is no - // longer on the worst-case path (as of 3.60) - - if (summ<=8) { // MSD+MSD is good, or there is a special - if (summ<0) { // there is a special - // Inf+Inf would give -64; Inf+finite is -32 or higher - if (summ<-64) return decNaNs(result, dfl, dfr, set); // one or two NaNs - // two infinities with different signs is invalid - if (summ==-64 && diffsign) return decInvalid(result, set); - if (DFISINF(dfl)) return decInfinity(result, dfl); // LHS is infinite - return decInfinity(result, dfr); // RHS must be Inf - } - // Here when both arguments are finite; fast path is possible - // (currently only for aligned and same-sign) - if (bexpr==bexpl && !diffsign) { - uInt tac[DECLETS+1]; // base-1000 coefficient - uInt encode; // work - - // Get one coefficient as base-1000 and add the other - GETCOEFFTHOU(dfl, tac); // least-significant goes to [0] - ADDCOEFFTHOU(dfr, tac); - // here the sum of the MSDs (plus any carry) will be <10 due to - // the fastpath test earlier - - // construct the result; low word is the same for both formats - encode =BIN2DPD[tac[0]]; - encode|=BIN2DPD[tac[1]]<<10; - encode|=BIN2DPD[tac[2]]<<20; - encode|=BIN2DPD[tac[3]]<<30; - DFWORD(result, (DECBYTES/4)-1)=encode; - - // collect next two declets (all that remains, for Double) - encode =BIN2DPD[tac[3]]>>2; - encode|=BIN2DPD[tac[4]]<<8; - - #if QUAD - // complete and lay out middling words - encode|=BIN2DPD[tac[5]]<<18; - encode|=BIN2DPD[tac[6]]<<28; - DFWORD(result, 2)=encode; - - encode =BIN2DPD[tac[6]]>>4; - encode|=BIN2DPD[tac[7]]<<6; - encode|=BIN2DPD[tac[8]]<<16; - encode|=BIN2DPD[tac[9]]<<26; - DFWORD(result, 1)=encode; - - // and final two declets - encode =BIN2DPD[tac[9]]>>6; - encode|=BIN2DPD[tac[10]]<<4; - #endif - - // add exponent continuation and sign (from either argument) - encode|=sourhil & (ECONMASK | DECFLOAT_Sign); - - // create lookup index = MSD + top two bits of biased exponent <<4 - tac[DECLETS]|=(bexpl>>DECECONL)<<4; - encode|=DECCOMBFROM[tac[DECLETS]]; // add constructed combination field - DFWORD(result, 0)=encode; // complete - - // decFloatShow(result, ">"); - return result; - } // fast path OK - // drop through to slow path - } // low sum or Special(s) - - /* Slow path required -- arguments are finite and might overflow, */ - /* or require alignment, or might have different signs */ - - // now swap either exponents or argument pointers - if (bexpl<=bexpr) { - // original left is bigger - Int bexpswap=bexpl; - bexpl=bexpr; - bexpr=bexpswap; - // printf("left bigger\n"); - } - else { - const decFloat *dfswap=dfl; - dfl=dfr; - dfr=dfswap; - // printf("right bigger\n"); - } - // [here dfl and bexpl refer to the datum with the larger exponent, - // of if the exponents are equal then the original LHS argument] - - // if lhs is zero then result will be the rhs (now known to have - // the smaller exponent), which also may need to be tested for zero - // for the weird IEEE 754 sign rules - if (DFISZERO(dfl)) { - decCanonical(result, dfr); // clean copy - // "When the sum of two operands with opposite signs is - // exactly zero, the sign of that sum shall be '+' in all - // rounding modes except round toward -Infinity, in which - // mode that sign shall be '-'." - if (diffsign && DFISZERO(result)) { - DFWORD(result, 0)&=~DECFLOAT_Sign; // assume sign 0 - if (set->round==DEC_ROUND_FLOOR) DFWORD(result, 0)|=DECFLOAT_Sign; - } - return result; - } // numfl is zero - // [here, LHS is non-zero; code below assumes that] - - // Coefficients layout during the calculations to follow: - // - // Overlap case: - // +------------------------------------------------+ - // acc: |0000| coeffa | tail B | | - // +------------------------------------------------+ - // buf: |0000| pad0s | coeffb | | - // +------------------------------------------------+ - // - // Touching coefficients or gap: - // +------------------------------------------------+ - // acc: |0000| coeffa | gap | coeffb | - // +------------------------------------------------+ - // [buf not used or needed; gap clamped to Pmax] - - // lay out lhs coefficient into accumulator; this starts at acc+4 - // for decDouble or acc+6 for decQuad so the LSD is word- - // aligned; the top word gap is there only in case a carry digit - // is prefixed after the add -- it does not need to be zeroed - #if DOUBLE - #define COFF 4 // offset into acc - #elif QUAD - UBFROMUS(acc+4, 0); // prefix 00 - #define COFF 6 // offset into acc - #endif - - GETCOEFF(dfl, acc+COFF); // decode from decFloat - ulsd=acc+COFF+DECPMAX-1; - umsd=acc+4; // [having this here avoids - - #if DECTRACE - {bcdnum tum; - tum.msd=umsd; - tum.lsd=ulsd; - tum.exponent=bexpl-DECBIAS; - tum.sign=DFWORD(dfl, 0) & DECFLOAT_Sign; - decShowNum(&tum, "dflx");} - #endif - - // if signs differ, take ten's complement of lhs (here the - // coefficient is subtracted from all-nines; the 1 is added during - // the later add cycle -- zeros to the right do not matter because - // the complement of zero is zero); these are fixed-length inverts - // where the lsd is known to be at a 4-byte boundary (so no borrow - // possible) - carry=0; // assume no carry - if (diffsign) { - carry=CARRYPAT; // for +1 during add - UBFROMUI(acc+ 4, 0x09090909-UBTOUI(acc+ 4)); - UBFROMUI(acc+ 8, 0x09090909-UBTOUI(acc+ 8)); - UBFROMUI(acc+12, 0x09090909-UBTOUI(acc+12)); - UBFROMUI(acc+16, 0x09090909-UBTOUI(acc+16)); - #if QUAD - UBFROMUI(acc+20, 0x09090909-UBTOUI(acc+20)); - UBFROMUI(acc+24, 0x09090909-UBTOUI(acc+24)); - UBFROMUI(acc+28, 0x09090909-UBTOUI(acc+28)); - UBFROMUI(acc+32, 0x09090909-UBTOUI(acc+32)); - UBFROMUI(acc+36, 0x09090909-UBTOUI(acc+36)); - #endif - } // diffsign - - // now process the rhs coefficient; if it cannot overlap lhs then - // it can be put straight into acc (with an appropriate gap, if - // needed) because no actual addition will be needed (except - // possibly to complete ten's complement) - overlap=DECPMAX-(bexpl-bexpr); - #if DECTRACE - printf("exps: %ld %ld\n", (LI)(bexpl-DECBIAS), (LI)(bexpr-DECBIAS)); - printf("Overlap=%ld carry=%08lx\n", (LI)overlap, (LI)carry); - #endif - - if (overlap<=0) { // no overlap possible - uInt gap; // local work - // since a full addition is not needed, a ten's complement - // calculation started above may need to be completed - if (carry) { - for (ub=ulsd; *ub==9; ub--) *ub=0; - *ub+=1; - carry=0; // taken care of - } - // up to DECPMAX-1 digits of the final result can extend down - // below the LSD of the lhs, so if the gap is >DECPMAX then the - // rhs will be simply sticky bits. In this case the gap is - // clamped to DECPMAX and the exponent adjusted to suit [this is - // safe because the lhs is non-zero]. - gap=-overlap; - if (gap>DECPMAX) { - bexpr+=gap-1; - gap=DECPMAX; - } - ub=ulsd+gap+1; // where MSD will go - // Fill the gap with 0s; note that there is no addition to do - ut=acc+COFF+DECPMAX; // start of gap - for (; ut<ub; ut+=4) UBFROMUI(ut, 0); // mind the gap - if (overlap<-DECPMAX) { // gap was > DECPMAX - *ub=(uByte)(!DFISZERO(dfr)); // make sticky digit - } - else { // need full coefficient - GETCOEFF(dfr, ub); // decode from decFloat - ub+=DECPMAX-1; // new LSD... - } - ulsd=ub; // save new LSD - } // no overlap possible - - else { // overlap>0 - // coefficients overlap (perhaps completely, although also - // perhaps only where zeros) - if (overlap==DECPMAX) { // aligned - ub=buf+COFF; // where msd will go - #if QUAD - UBFROMUS(buf+4, 0); // clear quad's 00 - #endif - GETCOEFF(dfr, ub); // decode from decFloat - } - else { // unaligned - ub=buf+COFF+DECPMAX-overlap; // where MSD will go - // Fill the prefix gap with 0s; 8 will cover most common - // unalignments, so start with direct assignments (a loop is - // then used for any remaining -- the loop (and the one in a - // moment) is not then on the critical path because the number - // of additions is reduced by (at least) two in this case) - UBFROMUI(buf+4, 0); // [clears decQuad 00 too] - UBFROMUI(buf+8, 0); - if (ub>buf+12) { - ut=buf+12; // start any remaining - for (; ut<ub; ut+=4) UBFROMUI(ut, 0); // fill them - } - GETCOEFF(dfr, ub); // decode from decFloat - - // now move tail of rhs across to main acc; again use direct - // copies for 8 digits-worth - UBFROMUI(acc+COFF+DECPMAX, UBTOUI(buf+COFF+DECPMAX)); - UBFROMUI(acc+COFF+DECPMAX+4, UBTOUI(buf+COFF+DECPMAX+4)); - if (buf+COFF+DECPMAX+8<ub+DECPMAX) { - us=buf+COFF+DECPMAX+8; // source - ut=acc+COFF+DECPMAX+8; // target - for (; us<ub+DECPMAX; us+=4, ut+=4) UBFROMUI(ut, UBTOUI(us)); - } - } // unaligned - - ulsd=acc+(ub-buf+DECPMAX-1); // update LSD pointer - - // Now do the add of the non-tail; this is all nicely aligned, - // and is over a multiple of four digits (because for Quad two - // zero digits were added on the left); words in both acc and - // buf (buf especially) will often be zero - // [byte-by-byte add, here, is about 15% slower total effect than - // the by-fours] - - // Now effect the add; this is harder on a little-endian - // machine as the inter-digit carry cannot use the usual BCD - // addition trick because the bytes are loaded in the wrong order - // [this loop could be unrolled, but probably scarcely worth it] - - ut=acc+COFF+DECPMAX-4; // target LSW (acc) - us=buf+COFF+DECPMAX-4; // source LSW (buf, to add to acc) - - #if !DECLITEND - for (; ut>=acc+4; ut-=4, us-=4) { // big-endian add loop - // bcd8 add - carry+=UBTOUI(us); // rhs + carry - if (carry==0) continue; // no-op - carry+=UBTOUI(ut); // lhs - // Big-endian BCD adjust (uses internal carry) - carry+=0x76f6f6f6; // note top nibble not all bits - // apply BCD adjust and save - UBFROMUI(ut, (carry & 0x0f0f0f0f) - ((carry & 0x60606060)>>4)); - carry>>=31; // true carry was at far left - } // add loop - #else - for (; ut>=acc+4; ut-=4, us-=4) { // little-endian add loop - // bcd8 add - carry+=UBTOUI(us); // rhs + carry - if (carry==0) continue; // no-op [common if unaligned] - carry+=UBTOUI(ut); // lhs - // Little-endian BCD adjust; inter-digit carry must be manual - // because the lsb from the array will be in the most-significant - // byte of carry - carry+=0x76767676; // note no inter-byte carries - carry+=(carry & 0x80000000)>>15; - carry+=(carry & 0x00800000)>>15; - carry+=(carry & 0x00008000)>>15; - carry-=(carry & 0x60606060)>>4; // BCD adjust back - UBFROMUI(ut, carry & 0x0f0f0f0f); // clear debris and save - // here, final carry-out bit is at 0x00000080; move it ready - // for next word-add (i.e., to 0x01000000) - carry=(carry & 0x00000080)<<17; - } // add loop - #endif - - #if DECTRACE - {bcdnum tum; - printf("Add done, carry=%08lx, diffsign=%ld\n", (LI)carry, (LI)diffsign); - tum.msd=umsd; // acc+4; - tum.lsd=ulsd; - tum.exponent=0; - tum.sign=0; - decShowNum(&tum, "dfadd");} - #endif - } // overlap possible - - // ordering here is a little strange in order to have slowest path - // first in GCC asm listing - if (diffsign) { // subtraction - if (!carry) { // no carry out means RHS<LHS - // borrowed -- take ten's complement - // sign is lhs sign - num.sign=DFWORD(dfl, 0) & DECFLOAT_Sign; - - // invert the coefficient first by fours, then add one; space - // at the end of the buffer ensures the by-fours is always - // safe, but lsd+1 must be cleared to prevent a borrow - // if big-endian - #if !DECLITEND - *(ulsd+1)=0; - #endif - // there are always at least four coefficient words - UBFROMUI(umsd, 0x09090909-UBTOUI(umsd)); - UBFROMUI(umsd+4, 0x09090909-UBTOUI(umsd+4)); - UBFROMUI(umsd+8, 0x09090909-UBTOUI(umsd+8)); - UBFROMUI(umsd+12, 0x09090909-UBTOUI(umsd+12)); - #if DOUBLE - #define BNEXT 16 - #elif QUAD - UBFROMUI(umsd+16, 0x09090909-UBTOUI(umsd+16)); - UBFROMUI(umsd+20, 0x09090909-UBTOUI(umsd+20)); - UBFROMUI(umsd+24, 0x09090909-UBTOUI(umsd+24)); - UBFROMUI(umsd+28, 0x09090909-UBTOUI(umsd+28)); - UBFROMUI(umsd+32, 0x09090909-UBTOUI(umsd+32)); - #define BNEXT 36 - #endif - if (ulsd>=umsd+BNEXT) { // unaligned - // eight will handle most unaligments for Double; 16 for Quad - UBFROMUI(umsd+BNEXT, 0x09090909-UBTOUI(umsd+BNEXT)); - UBFROMUI(umsd+BNEXT+4, 0x09090909-UBTOUI(umsd+BNEXT+4)); - #if DOUBLE - #define BNEXTY (BNEXT+8) - #elif QUAD - UBFROMUI(umsd+BNEXT+8, 0x09090909-UBTOUI(umsd+BNEXT+8)); - UBFROMUI(umsd+BNEXT+12, 0x09090909-UBTOUI(umsd+BNEXT+12)); - #define BNEXTY (BNEXT+16) - #endif - if (ulsd>=umsd+BNEXTY) { // very unaligned - ut=umsd+BNEXTY; // -> continue - for (;;ut+=4) { - UBFROMUI(ut, 0x09090909-UBTOUI(ut)); // invert four digits - if (ut>=ulsd-3) break; // all done - } - } - } - // complete the ten's complement by adding 1 - for (ub=ulsd; *ub==9; ub--) *ub=0; - *ub+=1; - } // borrowed - - else { // carry out means RHS>=LHS - num.sign=DFWORD(dfr, 0) & DECFLOAT_Sign; - // all done except for the special IEEE 754 exact-zero-result - // rule (see above); while testing for zero, strip leading - // zeros (which will save decFinalize doing it) (this is in - // diffsign path, so carry impossible and true umsd is - // acc+COFF) - - // Check the initial coefficient area using the fast macro; - // this will often be all that needs to be done (as on the - // worst-case path when the subtraction was aligned and - // full-length) - if (ISCOEFFZERO(acc+COFF)) { - umsd=acc+COFF+DECPMAX-1; // so far, so zero - if (ulsd>umsd) { // more to check - umsd++; // to align after checked area - for (; UBTOUI(umsd)==0 && umsd+3<ulsd;) umsd+=4; - for (; *umsd==0 && umsd<ulsd;) umsd++; - } - if (*umsd==0) { // must be true zero (and diffsign) - num.sign=0; // assume + - if (set->round==DEC_ROUND_FLOOR) num.sign=DECFLOAT_Sign; - } - } - // [else was not zero, might still have leading zeros] - } // subtraction gave positive result - } // diffsign - - else { // same-sign addition - num.sign=DFWORD(dfl, 0)&DECFLOAT_Sign; - #if DOUBLE - if (carry) { // only possible with decDouble - *(acc+3)=1; // [Quad has leading 00] - umsd=acc+3; - } - #endif - } // same sign - - num.msd=umsd; // set MSD .. - num.lsd=ulsd; // .. and LSD - num.exponent=bexpr-DECBIAS; // set exponent to smaller, unbiassed - - #if DECTRACE - decFloatShow(dfl, "dfl"); - decFloatShow(dfr, "dfr"); - decShowNum(&num, "postadd"); - #endif - return decFinalize(result, &num, set); // round, check, and lay out - } // decFloatAdd - -/* ------------------------------------------------------------------ */ -/* decFloatAnd -- logical digitwise AND of two decFloats */ -/* */ -/* result gets the result of ANDing dfl and dfr */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs) */ -/* set is the context */ -/* returns result, which will be canonical with sign=0 */ -/* */ -/* The operands must be positive, finite with exponent q=0, and */ -/* comprise just zeros and ones; if not, Invalid operation results. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatAnd(decFloat *result, - const decFloat *dfl, const decFloat *dfr, - decContext *set) { - if (!DFISUINT01(dfl) || !DFISUINT01(dfr) - || !DFISCC01(dfl) || !DFISCC01(dfr)) return decInvalid(result, set); - // the operands are positive finite integers (q=0) with just 0s and 1s - #if DOUBLE - DFWORD(result, 0)=ZEROWORD - |((DFWORD(dfl, 0) & DFWORD(dfr, 0))&0x04009124); - DFWORD(result, 1)=(DFWORD(dfl, 1) & DFWORD(dfr, 1))&0x49124491; - #elif QUAD - DFWORD(result, 0)=ZEROWORD - |((DFWORD(dfl, 0) & DFWORD(dfr, 0))&0x04000912); - DFWORD(result, 1)=(DFWORD(dfl, 1) & DFWORD(dfr, 1))&0x44912449; - DFWORD(result, 2)=(DFWORD(dfl, 2) & DFWORD(dfr, 2))&0x12449124; - DFWORD(result, 3)=(DFWORD(dfl, 3) & DFWORD(dfr, 3))&0x49124491; - #endif - return result; - } // decFloatAnd - -/* ------------------------------------------------------------------ */ -/* decFloatCanonical -- copy a decFloat, making canonical */ -/* */ -/* result gets the canonicalized df */ -/* df is the decFloat to copy and make canonical */ -/* returns result */ -/* */ -/* This works on specials, too; no error or exception is possible. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatCanonical(decFloat *result, const decFloat *df) { - return decCanonical(result, df); - } // decFloatCanonical - -/* ------------------------------------------------------------------ */ -/* decFloatClass -- return the class of a decFloat */ -/* */ -/* df is the decFloat to test */ -/* returns the decClass that df falls into */ -/* ------------------------------------------------------------------ */ -enum decClass decFloatClass(const decFloat *df) { - Int exp; // exponent - if (DFISSPECIAL(df)) { - if (DFISQNAN(df)) return DEC_CLASS_QNAN; - if (DFISSNAN(df)) return DEC_CLASS_SNAN; - // must be an infinity - if (DFISSIGNED(df)) return DEC_CLASS_NEG_INF; - return DEC_CLASS_POS_INF; - } - if (DFISZERO(df)) { // quite common - if (DFISSIGNED(df)) return DEC_CLASS_NEG_ZERO; - return DEC_CLASS_POS_ZERO; - } - // is finite and non-zero; similar code to decFloatIsNormal, here - // [this could be speeded up slightly by in-lining decFloatDigits] - exp=GETEXPUN(df) // get unbiased exponent .. - +decFloatDigits(df)-1; // .. and make adjusted exponent - if (exp>=DECEMIN) { // is normal - if (DFISSIGNED(df)) return DEC_CLASS_NEG_NORMAL; - return DEC_CLASS_POS_NORMAL; - } - // is subnormal - if (DFISSIGNED(df)) return DEC_CLASS_NEG_SUBNORMAL; - return DEC_CLASS_POS_SUBNORMAL; - } // decFloatClass - -/* ------------------------------------------------------------------ */ -/* decFloatClassString -- return the class of a decFloat as a string */ -/* */ -/* df is the decFloat to test */ -/* returns a constant string describing the class df falls into */ -/* ------------------------------------------------------------------ */ -const char *decFloatClassString(const decFloat *df) { - enum decClass eclass=decFloatClass(df); - if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN; - if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN; - if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ; - if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ; - if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS; - if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS; - if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI; - if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI; - if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN; - if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN; - return DEC_ClassString_UN; // Unknown - } // decFloatClassString - -/* ------------------------------------------------------------------ */ -/* decFloatCompare -- compare two decFloats; quiet NaNs allowed */ -/* */ -/* result gets the result of comparing dfl and dfr */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs) */ -/* set is the context */ -/* returns result, which may be -1, 0, 1, or NaN (Unordered) */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatCompare(decFloat *result, - const decFloat *dfl, const decFloat *dfr, - decContext *set) { - Int comp; // work - // NaNs are handled as usual - if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set); - // numeric comparison needed - comp=decNumCompare(dfl, dfr, 0); - decFloatZero(result); - if (comp==0) return result; - DFBYTE(result, DECBYTES-1)=0x01; // LSD=1 - if (comp<0) DFBYTE(result, 0)|=0x80; // set sign bit - return result; - } // decFloatCompare - -/* ------------------------------------------------------------------ */ -/* decFloatCompareSignal -- compare two decFloats; all NaNs signal */ -/* */ -/* result gets the result of comparing dfl and dfr */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs) */ -/* set is the context */ -/* returns result, which may be -1, 0, 1, or NaN (Unordered) */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatCompareSignal(decFloat *result, - const decFloat *dfl, const decFloat *dfr, - decContext *set) { - Int comp; // work - // NaNs are handled as usual, except that all NaNs signal - if (DFISNAN(dfl) || DFISNAN(dfr)) { - set->status|=DEC_Invalid_operation; - return decNaNs(result, dfl, dfr, set); - } - // numeric comparison needed - comp=decNumCompare(dfl, dfr, 0); - decFloatZero(result); - if (comp==0) return result; - DFBYTE(result, DECBYTES-1)=0x01; // LSD=1 - if (comp<0) DFBYTE(result, 0)|=0x80; // set sign bit - return result; - } // decFloatCompareSignal - -/* ------------------------------------------------------------------ */ -/* decFloatCompareTotal -- compare two decFloats with total ordering */ -/* */ -/* result gets the result of comparing dfl and dfr */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs) */ -/* returns result, which may be -1, 0, or 1 */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatCompareTotal(decFloat *result, - const decFloat *dfl, const decFloat *dfr) { - Int comp; // work - uInt uiwork; // for macros - #if QUAD - uShort uswork; // .. - #endif - if (DFISNAN(dfl) || DFISNAN(dfr)) { - Int nanl, nanr; // work - // morph NaNs to +/- 1 or 2, leave numbers as 0 - nanl=DFISSNAN(dfl)+DFISQNAN(dfl)*2; // quiet > signalling - if (DFISSIGNED(dfl)) nanl=-nanl; - nanr=DFISSNAN(dfr)+DFISQNAN(dfr)*2; - if (DFISSIGNED(dfr)) nanr=-nanr; - if (nanl>nanr) comp=+1; - else if (nanl<nanr) comp=-1; - else { // NaNs are the same type and sign .. must compare payload - // buffers need +2 for QUAD - uByte bufl[DECPMAX+4]; // for LHS coefficient + foot - uByte bufr[DECPMAX+4]; // for RHS coefficient + foot - uByte *ub, *uc; // work - Int sigl; // signum of LHS - sigl=(DFISSIGNED(dfl) ? -1 : +1); - - // decode the coefficients - // (shift both right two if Quad to make a multiple of four) - #if QUAD - UBFROMUS(bufl, 0); - UBFROMUS(bufr, 0); - #endif - GETCOEFF(dfl, bufl+QUAD*2); // decode from decFloat - GETCOEFF(dfr, bufr+QUAD*2); // .. - // all multiples of four, here - comp=0; // assume equal - for (ub=bufl, uc=bufr; ub<bufl+DECPMAX+QUAD*2; ub+=4, uc+=4) { - uInt ui=UBTOUI(ub); - if (ui==UBTOUI(uc)) continue; // so far so same - // about to find a winner; go by bytes in case little-endian - for (;; ub++, uc++) { - if (*ub==*uc) continue; - if (*ub>*uc) comp=sigl; // difference found - else comp=-sigl; // .. - break; - } - } - } // same NaN type and sign - } - else { - // numeric comparison needed - comp=decNumCompare(dfl, dfr, 1); // total ordering - } - decFloatZero(result); - if (comp==0) return result; - DFBYTE(result, DECBYTES-1)=0x01; // LSD=1 - if (comp<0) DFBYTE(result, 0)|=0x80; // set sign bit - return result; - } // decFloatCompareTotal - -/* ------------------------------------------------------------------ */ -/* decFloatCompareTotalMag -- compare magnitudes with total ordering */ -/* */ -/* result gets the result of comparing abs(dfl) and abs(dfr) */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs) */ -/* returns result, which may be -1, 0, or 1 */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatCompareTotalMag(decFloat *result, - const decFloat *dfl, const decFloat *dfr) { - decFloat a, b; // for copy if needed - // copy and redirect signed operand(s) - if (DFISSIGNED(dfl)) { - decFloatCopyAbs(&a, dfl); - dfl=&a; - } - if (DFISSIGNED(dfr)) { - decFloatCopyAbs(&b, dfr); - dfr=&b; - } - return decFloatCompareTotal(result, dfl, dfr); - } // decFloatCompareTotalMag - -/* ------------------------------------------------------------------ */ -/* decFloatCopy -- copy a decFloat as-is */ -/* */ -/* result gets the copy of dfl */ -/* dfl is the decFloat to copy */ -/* returns result */ -/* */ -/* This is a bitwise operation; no errors or exceptions are possible. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatCopy(decFloat *result, const decFloat *dfl) { - if (dfl!=result) *result=*dfl; // copy needed - return result; - } // decFloatCopy - -/* ------------------------------------------------------------------ */ -/* decFloatCopyAbs -- copy a decFloat as-is and set sign bit to 0 */ -/* */ -/* result gets the copy of dfl with sign bit 0 */ -/* dfl is the decFloat to copy */ -/* returns result */ -/* */ -/* This is a bitwise operation; no errors or exceptions are possible. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatCopyAbs(decFloat *result, const decFloat *dfl) { - if (dfl!=result) *result=*dfl; // copy needed - DFBYTE(result, 0)&=~0x80; // zero sign bit - return result; - } // decFloatCopyAbs - -/* ------------------------------------------------------------------ */ -/* decFloatCopyNegate -- copy a decFloat as-is with inverted sign bit */ -/* */ -/* result gets the copy of dfl with sign bit inverted */ -/* dfl is the decFloat to copy */ -/* returns result */ -/* */ -/* This is a bitwise operation; no errors or exceptions are possible. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatCopyNegate(decFloat *result, const decFloat *dfl) { - if (dfl!=result) *result=*dfl; // copy needed - DFBYTE(result, 0)^=0x80; // invert sign bit - return result; - } // decFloatCopyNegate - -/* ------------------------------------------------------------------ */ -/* decFloatCopySign -- copy a decFloat with the sign of another */ -/* */ -/* result gets the result of copying dfl with the sign of dfr */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs) */ -/* returns result */ -/* */ -/* This is a bitwise operation; no errors or exceptions are possible. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatCopySign(decFloat *result, - const decFloat *dfl, const decFloat *dfr) { - uByte sign=(uByte)(DFBYTE(dfr, 0)&0x80); // save sign bit - if (dfl!=result) *result=*dfl; // copy needed - DFBYTE(result, 0)&=~0x80; // clear sign .. - DFBYTE(result, 0)=(uByte)(DFBYTE(result, 0)|sign); // .. and set saved - return result; - } // decFloatCopySign - -/* ------------------------------------------------------------------ */ -/* decFloatDigits -- return the number of digits in a decFloat */ -/* */ -/* df is the decFloat to investigate */ -/* returns the number of significant digits in the decFloat; a */ -/* zero coefficient returns 1 as does an infinity (a NaN returns */ -/* the number of digits in the payload) */ -/* ------------------------------------------------------------------ */ -// private macro to extract a declet according to provided formula -// (form), and if it is non-zero then return the calculated digits -// depending on the declet number (n), where n=0 for the most -// significant declet; uses uInt dpd for work -#define dpdlenchk(n, form) dpd=(form)&0x3ff; \ - if (dpd) return (DECPMAX-1-3*(n))-(3-DPD2BCD8[dpd*4+3]) -// next one is used when it is known that the declet must be -// non-zero, or is the final zero declet -#define dpdlendun(n, form) dpd=(form)&0x3ff; \ - if (dpd==0) return 1; \ - return (DECPMAX-1-3*(n))-(3-DPD2BCD8[dpd*4+3]) - -uInt decFloatDigits(const decFloat *df) { - uInt dpd; // work - uInt sourhi=DFWORD(df, 0); // top word from source decFloat - #if QUAD - uInt sourmh, sourml; - #endif - uInt sourlo; - - if (DFISINF(df)) return 1; - // A NaN effectively has an MSD of 0; otherwise if non-zero MSD - // then the coefficient is full-length - if (!DFISNAN(df) && DECCOMBMSD[sourhi>>26]) return DECPMAX; - - #if DOUBLE - if (sourhi&0x0003ffff) { // ends in first - dpdlenchk(0, sourhi>>8); - sourlo=DFWORD(df, 1); - dpdlendun(1, (sourhi<<2) | (sourlo>>30)); - } // [cannot drop through] - sourlo=DFWORD(df, 1); // sourhi not involved now - if (sourlo&0xfff00000) { // in one of first two - dpdlenchk(1, sourlo>>30); // very rare - dpdlendun(2, sourlo>>20); - } // [cannot drop through] - dpdlenchk(3, sourlo>>10); - dpdlendun(4, sourlo); - // [cannot drop through] - - #elif QUAD - if (sourhi&0x00003fff) { // ends in first - dpdlenchk(0, sourhi>>4); - sourmh=DFWORD(df, 1); - dpdlendun(1, ((sourhi)<<6) | (sourmh>>26)); - } // [cannot drop through] - sourmh=DFWORD(df, 1); - if (sourmh) { - dpdlenchk(1, sourmh>>26); - dpdlenchk(2, sourmh>>16); - dpdlenchk(3, sourmh>>6); - sourml=DFWORD(df, 2); - dpdlendun(4, ((sourmh)<<4) | (sourml>>28)); - } // [cannot drop through] - sourml=DFWORD(df, 2); - if (sourml) { - dpdlenchk(4, sourml>>28); - dpdlenchk(5, sourml>>18); - dpdlenchk(6, sourml>>8); - sourlo=DFWORD(df, 3); - dpdlendun(7, ((sourml)<<2) | (sourlo>>30)); - } // [cannot drop through] - sourlo=DFWORD(df, 3); - if (sourlo&0xfff00000) { // in one of first two - dpdlenchk(7, sourlo>>30); // very rare - dpdlendun(8, sourlo>>20); - } // [cannot drop through] - dpdlenchk(9, sourlo>>10); - dpdlendun(10, sourlo); - // [cannot drop through] - #endif - } // decFloatDigits - -/* ------------------------------------------------------------------ */ -/* decFloatDivide -- divide a decFloat by another */ -/* */ -/* result gets the result of dividing dfl by dfr: */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs) */ -/* set is the context */ -/* returns result */ -/* */ -/* ------------------------------------------------------------------ */ -// This is just a wrapper. -decFloat * decFloatDivide(decFloat *result, - const decFloat *dfl, const decFloat *dfr, - decContext *set) { - return decDivide(result, dfl, dfr, set, DIVIDE); - } // decFloatDivide - -/* ------------------------------------------------------------------ */ -/* decFloatDivideInteger -- integer divide a decFloat by another */ -/* */ -/* result gets the result of dividing dfl by dfr: */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs) */ -/* set is the context */ -/* returns result */ -/* */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatDivideInteger(decFloat *result, - const decFloat *dfl, const decFloat *dfr, - decContext *set) { - return decDivide(result, dfl, dfr, set, DIVIDEINT); - } // decFloatDivideInteger - -/* ------------------------------------------------------------------ */ -/* decFloatFMA -- multiply and add three decFloats, fused */ -/* */ -/* result gets the result of (dfl*dfr)+dff with a single rounding */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs) */ -/* dff is the final decFloat (fhs) */ -/* set is the context */ -/* returns result */ -/* */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatFMA(decFloat *result, const decFloat *dfl, - const decFloat *dfr, const decFloat *dff, - decContext *set) { - - // The accumulator has the bytes needed for FiniteMultiply, plus - // one byte to the left in case of carry, plus DECPMAX+2 to the - // right for the final addition (up to full fhs + round & sticky) - #define FMALEN (ROUNDUP4(1+ (DECPMAX9*18+1) +DECPMAX+2)) - uByte acc[FMALEN]; // for multiplied coefficient in BCD - // .. and for final result - bcdnum mul; // for multiplication result - bcdnum fin; // for final operand, expanded - uByte coe[ROUNDUP4(DECPMAX)]; // dff coefficient in BCD - bcdnum *hi, *lo; // bcdnum with higher/lower exponent - uInt diffsign; // non-zero if signs differ - uInt hipad; // pad digit for hi if needed - Int padding; // excess exponent - uInt carry; // +1 for ten's complement and during add - uByte *ub, *uh, *ul; // work - uInt uiwork; // for macros - - // handle all the special values [any special operand leads to a - // special result] - if (DFISSPECIAL(dfl) || DFISSPECIAL(dfr) || DFISSPECIAL(dff)) { - decFloat proxy; // multiplication result proxy - // NaNs are handled as usual, giving priority to sNaNs - if (DFISSNAN(dfl) || DFISSNAN(dfr)) return decNaNs(result, dfl, dfr, set); - if (DFISSNAN(dff)) return decNaNs(result, dff, NULL, set); - if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set); - if (DFISNAN(dff)) return decNaNs(result, dff, NULL, set); - // One or more of the three is infinite - // infinity times zero is bad - decFloatZero(&proxy); - if (DFISINF(dfl)) { - if (DFISZERO(dfr)) return decInvalid(result, set); - decInfinity(&proxy, &proxy); - } - else if (DFISINF(dfr)) { - if (DFISZERO(dfl)) return decInvalid(result, set); - decInfinity(&proxy, &proxy); - } - // compute sign of multiplication and place in proxy - DFWORD(&proxy, 0)|=(DFWORD(dfl, 0)^DFWORD(dfr, 0))&DECFLOAT_Sign; - if (!DFISINF(dff)) return decFloatCopy(result, &proxy); - // dff is Infinite - if (!DFISINF(&proxy)) return decInfinity(result, dff); - // both sides of addition are infinite; different sign is bad - if ((DFWORD(dff, 0)&DECFLOAT_Sign)!=(DFWORD(&proxy, 0)&DECFLOAT_Sign)) - return decInvalid(result, set); - return decFloatCopy(result, &proxy); - } - - /* Here when all operands are finite */ - - // First multiply dfl*dfr - decFiniteMultiply(&mul, acc+1, dfl, dfr); - // The multiply is complete, exact and unbounded, and described in - // mul with the coefficient held in acc[1...] - - // now add in dff; the algorithm is essentially the same as - // decFloatAdd, but the code is different because the code there - // is highly optimized for adding two numbers of the same size - fin.exponent=GETEXPUN(dff); // get dff exponent and sign - fin.sign=DFWORD(dff, 0)&DECFLOAT_Sign; - diffsign=mul.sign^fin.sign; // note if signs differ - fin.msd=coe; - fin.lsd=coe+DECPMAX-1; - GETCOEFF(dff, coe); // extract the coefficient - - // now set hi and lo so that hi points to whichever of mul and fin - // has the higher exponent and lo points to the other [don't care, - // if the same]. One coefficient will be in acc, the other in coe. - if (mul.exponent>=fin.exponent) { - hi=&mul; - lo=&fin; - } - else { - hi=&fin; - lo=&mul; - } - - // remove leading zeros on both operands; this will save time later - // and make testing for zero trivial (tests are safe because acc - // and coe are rounded up to uInts) - for (; UBTOUI(hi->msd)==0 && hi->msd+3<hi->lsd;) hi->msd+=4; - for (; *hi->msd==0 && hi->msd<hi->lsd;) hi->msd++; - for (; UBTOUI(lo->msd)==0 && lo->msd+3<lo->lsd;) lo->msd+=4; - for (; *lo->msd==0 && lo->msd<lo->lsd;) lo->msd++; - - // if hi is zero then result will be lo (which has the smaller - // exponent), which also may need to be tested for zero for the - // weird IEEE 754 sign rules - if (*hi->msd==0) { // hi is zero - // "When the sum of two operands with opposite signs is - // exactly zero, the sign of that sum shall be '+' in all - // rounding modes except round toward -Infinity, in which - // mode that sign shall be '-'." - if (diffsign) { - if (*lo->msd==0) { // lo is zero - lo->sign=0; - if (set->round==DEC_ROUND_FLOOR) lo->sign=DECFLOAT_Sign; - } // diffsign && lo=0 - } // diffsign - return decFinalize(result, lo, set); // may need clamping - } // numfl is zero - // [here, both are minimal length and hi is non-zero] - // (if lo is zero then padding with zeros may be needed, below) - - // if signs differ, take the ten's complement of hi (zeros to the - // right do not matter because the complement of zero is zero); the - // +1 is done later, as part of the addition, inserted at the - // correct digit - hipad=0; - carry=0; - if (diffsign) { - hipad=9; - carry=1; - // exactly the correct number of digits must be inverted - for (uh=hi->msd; uh<hi->lsd-3; uh+=4) UBFROMUI(uh, 0x09090909-UBTOUI(uh)); - for (; uh<=hi->lsd; uh++) *uh=(uByte)(0x09-*uh); - } - - // ready to add; note that hi has no leading zeros so gap - // calculation does not have to be as pessimistic as in decFloatAdd - // (this is much more like the arbitrary-precision algorithm in - // Rexx and decNumber) - - // padding is the number of zeros that would need to be added to hi - // for its lsd to be aligned with the lsd of lo - padding=hi->exponent-lo->exponent; - // printf("FMA pad %ld\n", (LI)padding); - - // the result of the addition will be built into the accumulator, - // starting from the far right; this could be either hi or lo, and - // will be aligned - ub=acc+FMALEN-1; // where lsd of result will go - ul=lo->lsd; // lsd of rhs - - if (padding!=0) { // unaligned - // if the msd of lo is more than DECPMAX+2 digits to the right of - // the original msd of hi then it can be reduced to a single - // digit at the right place, as it stays clear of hi digits - // [it must be DECPMAX+2 because during a subtraction the msd - // could become 0 after a borrow from 1.000 to 0.9999...] - - Int hilen=(Int)(hi->lsd-hi->msd+1); // length of hi - Int lolen=(Int)(lo->lsd-lo->msd+1); // and of lo - - if (hilen+padding-lolen > DECPMAX+2) { // can reduce lo to single - // make sure it is virtually at least DECPMAX from hi->msd, at - // least to right of hi->lsd (in case of destructive subtract), - // and separated by at least two digits from either of those - // (the tricky DOUBLE case is when hi is a 1 that will become a - // 0.9999... by subtraction: - // hi: 1 E+16 - // lo: .................1000000000000000 E-16 - // which for the addition pads to: - // hi: 1000000000000000000 E-16 - // lo: .................1000000000000000 E-16 - Int newexp=MINI(hi->exponent, hi->exponent+hilen-DECPMAX)-3; - - // printf("FMA reduce: %ld\n", (LI)reduce); - lo->lsd=lo->msd; // to single digit [maybe 0] - lo->exponent=newexp; // new lowest exponent - padding=hi->exponent-lo->exponent; // recalculate - ul=lo->lsd; // .. and repoint - } - - // padding is still > 0, but will fit in acc (less leading carry slot) - #if DECCHECK - if (padding<=0) printf("FMA low padding: %ld\n", (LI)padding); - if (hilen+padding+1>FMALEN) - printf("FMA excess hilen+padding: %ld+%ld \n", (LI)hilen, (LI)padding); - // printf("FMA padding: %ld\n", (LI)padding); - #endif - - // padding digits can now be set in the result; one or more of - // these will come from lo; others will be zeros in the gap - for (; ul-3>=lo->msd && padding>3; padding-=4, ul-=4, ub-=4) { - UBFROMUI(ub-3, UBTOUI(ul-3)); // [cannot overlap] - } - for (; ul>=lo->msd && padding>0; padding--, ul--, ub--) *ub=*ul; - for (;padding>0; padding--, ub--) *ub=0; // mind the gap - } - - // addition now complete to the right of the rightmost digit of hi - uh=hi->lsd; - - // dow do the add from hi->lsd to the left - // [bytewise, because either operand can run out at any time] - // carry was set up depending on ten's complement above - // first assume both operands have some digits - for (;; ub--) { - if (uh<hi->msd || ul<lo->msd) break; - *ub=(uByte)(carry+(*uh--)+(*ul--)); - carry=0; - if (*ub<10) continue; - *ub-=10; - carry=1; - } // both loop - - if (ul<lo->msd) { // to left of lo - for (;; ub--) { - if (uh<hi->msd) break; - *ub=(uByte)(carry+(*uh--)); // [+0] - carry=0; - if (*ub<10) continue; - *ub-=10; - carry=1; - } // hi loop - } - else { // to left of hi - for (;; ub--) { - if (ul<lo->msd) break; - *ub=(uByte)(carry+hipad+(*ul--)); - carry=0; - if (*ub<10) continue; - *ub-=10; - carry=1; - } // lo loop - } - - // addition complete -- now handle carry, borrow, etc. - // use lo to set up the num (its exponent is already correct, and - // sign usually is) - lo->msd=ub+1; - lo->lsd=acc+FMALEN-1; - // decShowNum(lo, "lo"); - if (!diffsign) { // same-sign addition - if (carry) { // carry out - *ub=1; // place the 1 .. - lo->msd--; // .. and update - } - } // same sign - else { // signs differed (subtraction) - if (!carry) { // no carry out means hi<lo - // borrowed -- take ten's complement of the right digits - lo->sign=hi->sign; // sign is lhs sign - for (ul=lo->msd; ul<lo->lsd-3; ul+=4) UBFROMUI(ul, 0x09090909-UBTOUI(ul)); - for (; ul<=lo->lsd; ul++) *ul=(uByte)(0x09-*ul); // [leaves ul at lsd+1] - // complete the ten's complement by adding 1 [cannot overrun] - for (ul--; *ul==9; ul--) *ul=0; - *ul+=1; - } // borrowed - else { // carry out means hi>=lo - // sign to use is lo->sign - // all done except for the special IEEE 754 exact-zero-result - // rule (see above); while testing for zero, strip leading - // zeros (which will save decFinalize doing it) - for (; UBTOUI(lo->msd)==0 && lo->msd+3<lo->lsd;) lo->msd+=4; - for (; *lo->msd==0 && lo->msd<lo->lsd;) lo->msd++; - if (*lo->msd==0) { // must be true zero (and diffsign) - lo->sign=0; // assume + - if (set->round==DEC_ROUND_FLOOR) lo->sign=DECFLOAT_Sign; - } - // [else was not zero, might still have leading zeros] - } // subtraction gave positive result - } // diffsign - - #if DECCHECK - // assert no left underrun - if (lo->msd<acc) { - printf("FMA underrun by %ld \n", (LI)(acc-lo->msd)); - } - #endif - - return decFinalize(result, lo, set); // round, check, and lay out - } // decFloatFMA - -/* ------------------------------------------------------------------ */ -/* decFloatFromInt -- initialise a decFloat from an Int */ -/* */ -/* result gets the converted Int */ -/* n is the Int to convert */ -/* returns result */ -/* */ -/* The result is Exact; no errors or exceptions are possible. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatFromInt32(decFloat *result, Int n) { - uInt u=(uInt)n; // copy as bits - uInt encode; // work - DFWORD(result, 0)=ZEROWORD; // always - #if QUAD - DFWORD(result, 1)=0; - DFWORD(result, 2)=0; - #endif - if (n<0) { // handle -n with care - // [This can be done without the test, but is then slightly slower] - u=(~u)+1; - DFWORD(result, 0)|=DECFLOAT_Sign; - } - // Since the maximum value of u now is 2**31, only the low word of - // result is affected - encode=BIN2DPD[u%1000]; - u/=1000; - encode|=BIN2DPD[u%1000]<<10; - u/=1000; - encode|=BIN2DPD[u%1000]<<20; - u/=1000; // now 0, 1, or 2 - encode|=u<<30; - DFWORD(result, DECWORDS-1)=encode; - return result; - } // decFloatFromInt32 - -/* ------------------------------------------------------------------ */ -/* decFloatFromUInt -- initialise a decFloat from a uInt */ -/* */ -/* result gets the converted uInt */ -/* n is the uInt to convert */ -/* returns result */ -/* */ -/* The result is Exact; no errors or exceptions are possible. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatFromUInt32(decFloat *result, uInt u) { - uInt encode; // work - DFWORD(result, 0)=ZEROWORD; // always - #if QUAD - DFWORD(result, 1)=0; - DFWORD(result, 2)=0; - #endif - encode=BIN2DPD[u%1000]; - u/=1000; - encode|=BIN2DPD[u%1000]<<10; - u/=1000; - encode|=BIN2DPD[u%1000]<<20; - u/=1000; // now 0 -> 4 - encode|=u<<30; - DFWORD(result, DECWORDS-1)=encode; - DFWORD(result, DECWORDS-2)|=u>>2; // rarely non-zero - return result; - } // decFloatFromUInt32 - -/* ------------------------------------------------------------------ */ -/* decFloatInvert -- logical digitwise INVERT of a decFloat */ -/* */ -/* result gets the result of INVERTing df */ -/* df is the decFloat to invert */ -/* set is the context */ -/* returns result, which will be canonical with sign=0 */ -/* */ -/* The operand must be positive, finite with exponent q=0, and */ -/* comprise just zeros and ones; if not, Invalid operation results. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatInvert(decFloat *result, const decFloat *df, - decContext *set) { - uInt sourhi=DFWORD(df, 0); // top word of dfs - - if (!DFISUINT01(df) || !DFISCC01(df)) return decInvalid(result, set); - // the operand is a finite integer (q=0) - #if DOUBLE - DFWORD(result, 0)=ZEROWORD|((~sourhi)&0x04009124); - DFWORD(result, 1)=(~DFWORD(df, 1)) &0x49124491; - #elif QUAD - DFWORD(result, 0)=ZEROWORD|((~sourhi)&0x04000912); - DFWORD(result, 1)=(~DFWORD(df, 1)) &0x44912449; - DFWORD(result, 2)=(~DFWORD(df, 2)) &0x12449124; - DFWORD(result, 3)=(~DFWORD(df, 3)) &0x49124491; - #endif - return result; - } // decFloatInvert - -/* ------------------------------------------------------------------ */ -/* decFloatIs -- decFloat tests (IsSigned, etc.) */ -/* */ -/* df is the decFloat to test */ -/* returns 0 or 1 in a uInt */ -/* */ -/* Many of these could be macros, but having them as real functions */ -/* is a little cleaner (and they can be referred to here by the */ -/* generic names) */ -/* ------------------------------------------------------------------ */ -uInt decFloatIsCanonical(const decFloat *df) { - if (DFISSPECIAL(df)) { - if (DFISINF(df)) { - if (DFWORD(df, 0)&ECONMASK) return 0; // exponent continuation - if (!DFISCCZERO(df)) return 0; // coefficient continuation - return 1; - } - // is a NaN - if (DFWORD(df, 0)&ECONNANMASK) return 0; // exponent continuation - if (DFISCCZERO(df)) return 1; // coefficient continuation - // drop through to check payload - } - { // declare block - #if DOUBLE - uInt sourhi=DFWORD(df, 0); - uInt sourlo=DFWORD(df, 1); - if (CANONDPDOFF(sourhi, 8) - && CANONDPDTWO(sourhi, sourlo, 30) - && CANONDPDOFF(sourlo, 20) - && CANONDPDOFF(sourlo, 10) - && CANONDPDOFF(sourlo, 0)) return 1; - #elif QUAD - uInt sourhi=DFWORD(df, 0); - uInt sourmh=DFWORD(df, 1); - uInt sourml=DFWORD(df, 2); - uInt sourlo=DFWORD(df, 3); - if (CANONDPDOFF(sourhi, 4) - && CANONDPDTWO(sourhi, sourmh, 26) - && CANONDPDOFF(sourmh, 16) - && CANONDPDOFF(sourmh, 6) - && CANONDPDTWO(sourmh, sourml, 28) - && CANONDPDOFF(sourml, 18) - && CANONDPDOFF(sourml, 8) - && CANONDPDTWO(sourml, sourlo, 30) - && CANONDPDOFF(sourlo, 20) - && CANONDPDOFF(sourlo, 10) - && CANONDPDOFF(sourlo, 0)) return 1; - #endif - } // block - return 0; // a declet is non-canonical - } - -uInt decFloatIsFinite(const decFloat *df) { - return !DFISSPECIAL(df); - } -uInt decFloatIsInfinite(const decFloat *df) { - return DFISINF(df); - } -uInt decFloatIsInteger(const decFloat *df) { - return DFISINT(df); - } -uInt decFloatIsLogical(const decFloat *df) { - return DFISUINT01(df) & DFISCC01(df); - } -uInt decFloatIsNaN(const decFloat *df) { - return DFISNAN(df); - } -uInt decFloatIsNegative(const decFloat *df) { - return DFISSIGNED(df) && !DFISZERO(df) && !DFISNAN(df); - } -uInt decFloatIsNormal(const decFloat *df) { - Int exp; // exponent - if (DFISSPECIAL(df)) return 0; - if (DFISZERO(df)) return 0; - // is finite and non-zero - exp=GETEXPUN(df) // get unbiased exponent .. - +decFloatDigits(df)-1; // .. and make adjusted exponent - return (exp>=DECEMIN); // < DECEMIN is subnormal - } -uInt decFloatIsPositive(const decFloat *df) { - return !DFISSIGNED(df) && !DFISZERO(df) && !DFISNAN(df); - } -uInt decFloatIsSignaling(const decFloat *df) { - return DFISSNAN(df); - } -uInt decFloatIsSignalling(const decFloat *df) { - return DFISSNAN(df); - } -uInt decFloatIsSigned(const decFloat *df) { - return DFISSIGNED(df); - } -uInt decFloatIsSubnormal(const decFloat *df) { - if (DFISSPECIAL(df)) return 0; - // is finite - if (decFloatIsNormal(df)) return 0; - // it is <Nmin, but could be zero - if (DFISZERO(df)) return 0; - return 1; // is subnormal - } -uInt decFloatIsZero(const decFloat *df) { - return DFISZERO(df); - } // decFloatIs... - -/* ------------------------------------------------------------------ */ -/* decFloatLogB -- return adjusted exponent, by 754 rules */ -/* */ -/* result gets the adjusted exponent as an integer, or a NaN etc. */ -/* df is the decFloat to be examined */ -/* set is the context */ -/* returns result */ -/* */ -/* Notable cases: */ -/* A<0 -> Use |A| */ -/* A=0 -> -Infinity (Division by zero) */ -/* A=Infinite -> +Infinity (Exact) */ -/* A=1 exactly -> 0 (Exact) */ -/* NaNs are propagated as usual */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatLogB(decFloat *result, const decFloat *df, - decContext *set) { - Int ae; // adjusted exponent - if (DFISNAN(df)) return decNaNs(result, df, NULL, set); - if (DFISINF(df)) { - DFWORD(result, 0)=0; // need +ve - return decInfinity(result, result); // canonical +Infinity - } - if (DFISZERO(df)) { - set->status|=DEC_Division_by_zero; // as per 754 - DFWORD(result, 0)=DECFLOAT_Sign; // make negative - return decInfinity(result, result); // canonical -Infinity - } - ae=GETEXPUN(df) // get unbiased exponent .. - +decFloatDigits(df)-1; // .. and make adjusted exponent - // ae has limited range (3 digits for DOUBLE and 4 for QUAD), so - // it is worth using a special case of decFloatFromInt32 - DFWORD(result, 0)=ZEROWORD; // always - if (ae<0) { - DFWORD(result, 0)|=DECFLOAT_Sign; // -0 so far - ae=-ae; - } - #if DOUBLE - DFWORD(result, 1)=BIN2DPD[ae]; // a single declet - #elif QUAD - DFWORD(result, 1)=0; - DFWORD(result, 2)=0; - DFWORD(result, 3)=(ae/1000)<<10; // is <10, so need no DPD encode - DFWORD(result, 3)|=BIN2DPD[ae%1000]; - #endif - return result; - } // decFloatLogB - -/* ------------------------------------------------------------------ */ -/* decFloatMax -- return maxnum of two operands */ -/* */ -/* result gets the chosen decFloat */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs) */ -/* set is the context */ -/* returns result */ -/* */ -/* If just one operand is a quiet NaN it is ignored. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatMax(decFloat *result, - const decFloat *dfl, const decFloat *dfr, - decContext *set) { - Int comp; - if (DFISNAN(dfl)) { - // sNaN or both NaNs leads to normal NaN processing - if (DFISNAN(dfr) || DFISSNAN(dfl)) return decNaNs(result, dfl, dfr, set); - return decCanonical(result, dfr); // RHS is numeric - } - if (DFISNAN(dfr)) { - // sNaN leads to normal NaN processing (both NaN handled above) - if (DFISSNAN(dfr)) return decNaNs(result, dfl, dfr, set); - return decCanonical(result, dfl); // LHS is numeric - } - // Both operands are numeric; numeric comparison needed -- use - // total order for a well-defined choice (and +0 > -0) - comp=decNumCompare(dfl, dfr, 1); - if (comp>=0) return decCanonical(result, dfl); - return decCanonical(result, dfr); - } // decFloatMax - -/* ------------------------------------------------------------------ */ -/* decFloatMaxMag -- return maxnummag of two operands */ -/* */ -/* result gets the chosen decFloat */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs) */ -/* set is the context */ -/* returns result */ -/* */ -/* Returns according to the magnitude comparisons if both numeric and */ -/* unequal, otherwise returns maxnum */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatMaxMag(decFloat *result, - const decFloat *dfl, const decFloat *dfr, - decContext *set) { - Int comp; - decFloat absl, absr; - if (DFISNAN(dfl) || DFISNAN(dfr)) return decFloatMax(result, dfl, dfr, set); - - decFloatCopyAbs(&absl, dfl); - decFloatCopyAbs(&absr, dfr); - comp=decNumCompare(&absl, &absr, 0); - if (comp>0) return decCanonical(result, dfl); - if (comp<0) return decCanonical(result, dfr); - return decFloatMax(result, dfl, dfr, set); - } // decFloatMaxMag - -/* ------------------------------------------------------------------ */ -/* decFloatMin -- return minnum of two operands */ -/* */ -/* result gets the chosen decFloat */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs) */ -/* set is the context */ -/* returns result */ -/* */ -/* If just one operand is a quiet NaN it is ignored. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatMin(decFloat *result, - const decFloat *dfl, const decFloat *dfr, - decContext *set) { - Int comp; - if (DFISNAN(dfl)) { - // sNaN or both NaNs leads to normal NaN processing - if (DFISNAN(dfr) || DFISSNAN(dfl)) return decNaNs(result, dfl, dfr, set); - return decCanonical(result, dfr); // RHS is numeric - } - if (DFISNAN(dfr)) { - // sNaN leads to normal NaN processing (both NaN handled above) - if (DFISSNAN(dfr)) return decNaNs(result, dfl, dfr, set); - return decCanonical(result, dfl); // LHS is numeric - } - // Both operands are numeric; numeric comparison needed -- use - // total order for a well-defined choice (and +0 > -0) - comp=decNumCompare(dfl, dfr, 1); - if (comp<=0) return decCanonical(result, dfl); - return decCanonical(result, dfr); - } // decFloatMin - -/* ------------------------------------------------------------------ */ -/* decFloatMinMag -- return minnummag of two operands */ -/* */ -/* result gets the chosen decFloat */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs) */ -/* set is the context */ -/* returns result */ -/* */ -/* Returns according to the magnitude comparisons if both numeric and */ -/* unequal, otherwise returns minnum */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatMinMag(decFloat *result, - const decFloat *dfl, const decFloat *dfr, - decContext *set) { - Int comp; - decFloat absl, absr; - if (DFISNAN(dfl) || DFISNAN(dfr)) return decFloatMin(result, dfl, dfr, set); - - decFloatCopyAbs(&absl, dfl); - decFloatCopyAbs(&absr, dfr); - comp=decNumCompare(&absl, &absr, 0); - if (comp<0) return decCanonical(result, dfl); - if (comp>0) return decCanonical(result, dfr); - return decFloatMin(result, dfl, dfr, set); - } // decFloatMinMag - -/* ------------------------------------------------------------------ */ -/* decFloatMinus -- negate value, heeding NaNs, etc. */ -/* */ -/* result gets the canonicalized 0-df */ -/* df is the decFloat to minus */ -/* set is the context */ -/* returns result */ -/* */ -/* This has the same effect as 0-df where the exponent of the zero is */ -/* the same as that of df (if df is finite). */ -/* The effect is also the same as decFloatCopyNegate except that NaNs */ -/* are handled normally (the sign of a NaN is not affected, and an */ -/* sNaN will signal), the result is canonical, and zero gets sign 0. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatMinus(decFloat *result, const decFloat *df, - decContext *set) { - if (DFISNAN(df)) return decNaNs(result, df, NULL, set); - decCanonical(result, df); // copy and check - if (DFISZERO(df)) DFBYTE(result, 0)&=~0x80; // turn off sign bit - else DFBYTE(result, 0)^=0x80; // flip sign bit - return result; - } // decFloatMinus - -/* ------------------------------------------------------------------ */ -/* decFloatMultiply -- multiply two decFloats */ -/* */ -/* result gets the result of multiplying dfl and dfr: */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs) */ -/* set is the context */ -/* returns result */ -/* */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatMultiply(decFloat *result, - const decFloat *dfl, const decFloat *dfr, - decContext *set) { - bcdnum num; // for final conversion - uByte bcdacc[DECPMAX9*18+1]; // for coefficent in BCD - - if (DFISSPECIAL(dfl) || DFISSPECIAL(dfr)) { // either is special? - // NaNs are handled as usual - if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set); - // infinity times zero is bad - if (DFISINF(dfl) && DFISZERO(dfr)) return decInvalid(result, set); - if (DFISINF(dfr) && DFISZERO(dfl)) return decInvalid(result, set); - // both infinite; return canonical infinity with computed sign - DFWORD(result, 0)=DFWORD(dfl, 0)^DFWORD(dfr, 0); // compute sign - return decInfinity(result, result); - } - - /* Here when both operands are finite */ - decFiniteMultiply(&num, bcdacc, dfl, dfr); - return decFinalize(result, &num, set); // round, check, and lay out - } // decFloatMultiply - -/* ------------------------------------------------------------------ */ -/* decFloatNextMinus -- next towards -Infinity */ -/* */ -/* result gets the next lesser decFloat */ -/* dfl is the decFloat to start with */ -/* set is the context */ -/* returns result */ -/* */ -/* This is 754 nextdown; Invalid is the only status possible (from */ -/* an sNaN). */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatNextMinus(decFloat *result, const decFloat *dfl, - decContext *set) { - decFloat delta; // tiny increment - uInt savestat; // saves status - enum rounding saveround; // .. and mode - - // +Infinity is the special case - if (DFISINF(dfl) && !DFISSIGNED(dfl)) { - DFSETNMAX(result); - return result; // [no status to set] - } - // other cases are effected by sutracting a tiny delta -- this - // should be done in a wider format as the delta is unrepresentable - // here (but can be done with normal add if the sign of zero is - // treated carefully, because no Inexactitude is interesting); - // rounding to -Infinity then pushes the result to next below - decFloatZero(&delta); // set up tiny delta - DFWORD(&delta, DECWORDS-1)=1; // coefficient=1 - DFWORD(&delta, 0)=DECFLOAT_Sign; // Sign=1 + biased exponent=0 - // set up for the directional round - saveround=set->round; // save mode - set->round=DEC_ROUND_FLOOR; // .. round towards -Infinity - savestat=set->status; // save status - decFloatAdd(result, dfl, &delta, set); - // Add rules mess up the sign when going from +Ntiny to 0 - if (DFISZERO(result)) DFWORD(result, 0)^=DECFLOAT_Sign; // correct - set->status&=DEC_Invalid_operation; // preserve only sNaN status - set->status|=savestat; // restore pending flags - set->round=saveround; // .. and mode - return result; - } // decFloatNextMinus - -/* ------------------------------------------------------------------ */ -/* decFloatNextPlus -- next towards +Infinity */ -/* */ -/* result gets the next larger decFloat */ -/* dfl is the decFloat to start with */ -/* set is the context */ -/* returns result */ -/* */ -/* This is 754 nextup; Invalid is the only status possible (from */ -/* an sNaN). */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatNextPlus(decFloat *result, const decFloat *dfl, - decContext *set) { - uInt savestat; // saves status - enum rounding saveround; // .. and mode - decFloat delta; // tiny increment - - // -Infinity is the special case - if (DFISINF(dfl) && DFISSIGNED(dfl)) { - DFSETNMAX(result); - DFWORD(result, 0)|=DECFLOAT_Sign; // make negative - return result; // [no status to set] - } - // other cases are effected by sutracting a tiny delta -- this - // should be done in a wider format as the delta is unrepresentable - // here (but can be done with normal add if the sign of zero is - // treated carefully, because no Inexactitude is interesting); - // rounding to +Infinity then pushes the result to next above - decFloatZero(&delta); // set up tiny delta - DFWORD(&delta, DECWORDS-1)=1; // coefficient=1 - DFWORD(&delta, 0)=0; // Sign=0 + biased exponent=0 - // set up for the directional round - saveround=set->round; // save mode - set->round=DEC_ROUND_CEILING; // .. round towards +Infinity - savestat=set->status; // save status - decFloatAdd(result, dfl, &delta, set); - // Add rules mess up the sign when going from -Ntiny to -0 - if (DFISZERO(result)) DFWORD(result, 0)^=DECFLOAT_Sign; // correct - set->status&=DEC_Invalid_operation; // preserve only sNaN status - set->status|=savestat; // restore pending flags - set->round=saveround; // .. and mode - return result; - } // decFloatNextPlus - -/* ------------------------------------------------------------------ */ -/* decFloatNextToward -- next towards a decFloat */ -/* */ -/* result gets the next decFloat */ -/* dfl is the decFloat to start with */ -/* dfr is the decFloat to move toward */ -/* set is the context */ -/* returns result */ -/* */ -/* This is 754-1985 nextafter, as modified during revision (dropped */ -/* from 754-2008); status may be set unless the result is a normal */ -/* number. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatNextToward(decFloat *result, - const decFloat *dfl, const decFloat *dfr, - decContext *set) { - decFloat delta; // tiny increment or decrement - decFloat pointone; // 1e-1 - uInt savestat; // saves status - enum rounding saveround; // .. and mode - uInt deltatop; // top word for delta - Int comp; // work - - if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set); - // Both are numeric, so Invalid no longer a possibility - comp=decNumCompare(dfl, dfr, 0); - if (comp==0) return decFloatCopySign(result, dfl, dfr); // equal - // unequal; do NextPlus or NextMinus but with different status rules - - if (comp<0) { // lhs<rhs, do NextPlus, see above for commentary - if (DFISINF(dfl) && DFISSIGNED(dfl)) { // -Infinity special case - DFSETNMAX(result); - DFWORD(result, 0)|=DECFLOAT_Sign; - return result; - } - saveround=set->round; // save mode - set->round=DEC_ROUND_CEILING; // .. round towards +Infinity - deltatop=0; // positive delta - } - else { // lhs>rhs, do NextMinus, see above for commentary - if (DFISINF(dfl) && !DFISSIGNED(dfl)) { // +Infinity special case - DFSETNMAX(result); - return result; - } - saveround=set->round; // save mode - set->round=DEC_ROUND_FLOOR; // .. round towards -Infinity - deltatop=DECFLOAT_Sign; // negative delta - } - savestat=set->status; // save status - // Here, Inexact is needed where appropriate (and hence Underflow, - // etc.). Therefore the tiny delta which is otherwise - // unrepresentable (see NextPlus and NextMinus) is constructed - // using the multiplication of FMA. - decFloatZero(&delta); // set up tiny delta - DFWORD(&delta, DECWORDS-1)=1; // coefficient=1 - DFWORD(&delta, 0)=deltatop; // Sign + biased exponent=0 - decFloatFromString(&pointone, "1E-1", set); // set up multiplier - decFloatFMA(result, &delta, &pointone, dfl, set); - // [Delta is truly tiny, so no need to correct sign of zero] - // use new status unless the result is normal - if (decFloatIsNormal(result)) set->status=savestat; // else goes forward - set->round=saveround; // restore mode - return result; - } // decFloatNextToward - -/* ------------------------------------------------------------------ */ -/* decFloatOr -- logical digitwise OR of two decFloats */ -/* */ -/* result gets the result of ORing dfl and dfr */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs) */ -/* set is the context */ -/* returns result, which will be canonical with sign=0 */ -/* */ -/* The operands must be positive, finite with exponent q=0, and */ -/* comprise just zeros and ones; if not, Invalid operation results. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatOr(decFloat *result, - const decFloat *dfl, const decFloat *dfr, - decContext *set) { - if (!DFISUINT01(dfl) || !DFISUINT01(dfr) - || !DFISCC01(dfl) || !DFISCC01(dfr)) return decInvalid(result, set); - // the operands are positive finite integers (q=0) with just 0s and 1s - #if DOUBLE - DFWORD(result, 0)=ZEROWORD - |((DFWORD(dfl, 0) | DFWORD(dfr, 0))&0x04009124); - DFWORD(result, 1)=(DFWORD(dfl, 1) | DFWORD(dfr, 1))&0x49124491; - #elif QUAD - DFWORD(result, 0)=ZEROWORD - |((DFWORD(dfl, 0) | DFWORD(dfr, 0))&0x04000912); - DFWORD(result, 1)=(DFWORD(dfl, 1) | DFWORD(dfr, 1))&0x44912449; - DFWORD(result, 2)=(DFWORD(dfl, 2) | DFWORD(dfr, 2))&0x12449124; - DFWORD(result, 3)=(DFWORD(dfl, 3) | DFWORD(dfr, 3))&0x49124491; - #endif - return result; - } // decFloatOr - -/* ------------------------------------------------------------------ */ -/* decFloatPlus -- add value to 0, heeding NaNs, etc. */ -/* */ -/* result gets the canonicalized 0+df */ -/* df is the decFloat to plus */ -/* set is the context */ -/* returns result */ -/* */ -/* This has the same effect as 0+df where the exponent of the zero is */ -/* the same as that of df (if df is finite). */ -/* The effect is also the same as decFloatCopy except that NaNs */ -/* are handled normally (the sign of a NaN is not affected, and an */ -/* sNaN will signal), the result is canonical, and zero gets sign 0. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatPlus(decFloat *result, const decFloat *df, - decContext *set) { - if (DFISNAN(df)) return decNaNs(result, df, NULL, set); - decCanonical(result, df); // copy and check - if (DFISZERO(df)) DFBYTE(result, 0)&=~0x80; // turn off sign bit - return result; - } // decFloatPlus - -/* ------------------------------------------------------------------ */ -/* decFloatQuantize -- quantize a decFloat */ -/* */ -/* result gets the result of quantizing dfl to match dfr */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs), which sets the exponent */ -/* set is the context */ -/* returns result */ -/* */ -/* Unless there is an error or the result is infinite, the exponent */ -/* of result is guaranteed to be the same as that of dfr. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatQuantize(decFloat *result, - const decFloat *dfl, const decFloat *dfr, - decContext *set) { - Int explb, exprb; // left and right biased exponents - uByte *ulsd; // local LSD pointer - uByte *ub, *uc; // work - Int drop; // .. - uInt dpd; // .. - uInt encode; // encoding accumulator - uInt sourhil, sourhir; // top words from source decFloats - uInt uiwork; // for macros - #if QUAD - uShort uswork; // .. - #endif - // the following buffer holds the coefficient for manipulation - uByte buf[4+DECPMAX*3+2*QUAD]; // + space for zeros to left or right - #if DECTRACE - bcdnum num; // for trace displays - #endif - - /* Start decoding the arguments */ - sourhil=DFWORD(dfl, 0); // LHS top word - explb=DECCOMBEXP[sourhil>>26]; // get exponent high bits (in place) - sourhir=DFWORD(dfr, 0); // RHS top word - exprb=DECCOMBEXP[sourhir>>26]; - - if (EXPISSPECIAL(explb | exprb)) { // either is special? - // NaNs are handled as usual - if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set); - // one infinity but not both is bad - if (DFISINF(dfl)!=DFISINF(dfr)) return decInvalid(result, set); - // both infinite; return canonical infinity with sign of LHS - return decInfinity(result, dfl); - } - - /* Here when both arguments are finite */ - // complete extraction of the exponents [no need to unbias] - explb+=GETECON(dfl); // + continuation - exprb+=GETECON(dfr); // .. - - // calculate the number of digits to drop from the coefficient - drop=exprb-explb; // 0 if nothing to do - if (drop==0) return decCanonical(result, dfl); // return canonical - - // the coefficient is needed; lay it out into buf, offset so zeros - // can be added before or after as needed -- an extra heading is - // added so can safely pad Quad DECPMAX-1 zeros to the left by - // fours - #define BUFOFF (buf+4+DECPMAX) - GETCOEFF(dfl, BUFOFF); // decode from decFloat - // [now the msd is at BUFOFF and the lsd is at BUFOFF+DECPMAX-1] - - #if DECTRACE - num.msd=BUFOFF; - num.lsd=BUFOFF+DECPMAX-1; - num.exponent=explb-DECBIAS; - num.sign=sourhil & DECFLOAT_Sign; - decShowNum(&num, "dfl"); - #endif - - if (drop>0) { // [most common case] - // (this code is very similar to that in decFloatFinalize, but - // has many differences so is duplicated here -- so any changes - // may need to be made there, too) - uByte *roundat; // -> re-round digit - uByte reround; // reround value - // printf("Rounding; drop=%ld\n", (LI)drop); - - // there is at least one zero needed to the left, in all but one - // exceptional (all-nines) case, so place four zeros now; this is - // needed almost always and makes rounding all-nines by fours safe - UBFROMUI(BUFOFF-4, 0); - - // Three cases here: - // 1. new LSD is in coefficient (almost always) - // 2. new LSD is digit to left of coefficient (so MSD is - // round-for-reround digit) - // 3. new LSD is to left of case 2 (whole coefficient is sticky) - // Note that leading zeros can safely be treated as useful digits - - // [duplicate check-stickies code to save a test] - // [by-digit check for stickies as runs of zeros are rare] - if (drop<DECPMAX) { // NB lengths not addresses - roundat=BUFOFF+DECPMAX-drop; - reround=*roundat; - for (ub=roundat+1; ub<BUFOFF+DECPMAX; ub++) { - if (*ub!=0) { // non-zero to be discarded - reround=DECSTICKYTAB[reround]; // apply sticky bit - break; // [remainder don't-care] - } - } // check stickies - ulsd=roundat-1; // set LSD - } - else { // edge case - if (drop==DECPMAX) { - roundat=BUFOFF; - reround=*roundat; - } - else { - roundat=BUFOFF-1; - reround=0; - } - for (ub=roundat+1; ub<BUFOFF+DECPMAX; ub++) { - if (*ub!=0) { // non-zero to be discarded - reround=DECSTICKYTAB[reround]; // apply sticky bit - break; // [remainder don't-care] - } - } // check stickies - *BUFOFF=0; // make a coefficient of 0 - ulsd=BUFOFF; // .. at the MSD place - } - - if (reround!=0) { // discarding non-zero - uInt bump=0; - set->status|=DEC_Inexact; - - // next decide whether to increment the coefficient - if (set->round==DEC_ROUND_HALF_EVEN) { // fastpath slowest case - if (reround>5) bump=1; // >0.5 goes up - else if (reround==5) // exactly 0.5000 .. - bump=*ulsd & 0x01; // .. up iff [new] lsd is odd - } // r-h-e - else switch (set->round) { - case DEC_ROUND_DOWN: { - // no change - break;} // r-d - case DEC_ROUND_HALF_DOWN: { - if (reround>5) bump=1; - break;} // r-h-d - case DEC_ROUND_HALF_UP: { - if (reround>=5) bump=1; - break;} // r-h-u - case DEC_ROUND_UP: { - if (reround>0) bump=1; - break;} // r-u - case DEC_ROUND_CEILING: { - // same as _UP for positive numbers, and as _DOWN for negatives - if (!(sourhil&DECFLOAT_Sign) && reround>0) bump=1; - break;} // r-c - case DEC_ROUND_FLOOR: { - // same as _UP for negative numbers, and as _DOWN for positive - // [negative reround cannot occur on 0] - if (sourhil&DECFLOAT_Sign && reround>0) bump=1; - break;} // r-f - case DEC_ROUND_05UP: { - if (reround>0) { // anything out there is 'sticky' - // bump iff lsd=0 or 5; this cannot carry so it could be - // effected immediately with no bump -- but the code - // is clearer if this is done the same way as the others - if (*ulsd==0 || *ulsd==5) bump=1; - } - break;} // r-r - default: { // e.g., DEC_ROUND_MAX - set->status|=DEC_Invalid_context; - #if DECCHECK - printf("Unknown rounding mode: %ld\n", (LI)set->round); - #endif - break;} - } // switch (not r-h-e) - // printf("ReRound: %ld bump: %ld\n", (LI)reround, (LI)bump); - - if (bump!=0) { // need increment - // increment the coefficient; this could give 1000... (after - // the all nines case) - ub=ulsd; - for (; UBTOUI(ub-3)==0x09090909; ub-=4) UBFROMUI(ub-3, 0); - // now at most 3 digits left to non-9 (usually just the one) - for (; *ub==9; ub--) *ub=0; - *ub+=1; - // [the all-nines case will have carried one digit to the - // left of the original MSD -- just where it is needed] - } // bump needed - } // inexact rounding - - // now clear zeros to the left so exactly DECPMAX digits will be - // available in the coefficent -- the first word to the left was - // cleared earlier for safe carry; now add any more needed - if (drop>4) { - UBFROMUI(BUFOFF-8, 0); // must be at least 5 - for (uc=BUFOFF-12; uc>ulsd-DECPMAX-3; uc-=4) UBFROMUI(uc, 0); - } - } // need round (drop>0) - - else { // drop<0; padding with -drop digits is needed - // This is the case where an error can occur if the padded - // coefficient will not fit; checking for this can be done in the - // same loop as padding for zeros if the no-hope and zero cases - // are checked first - if (-drop>DECPMAX-1) { // cannot fit unless 0 - if (!ISCOEFFZERO(BUFOFF)) return decInvalid(result, set); - // a zero can have any exponent; just drop through and use it - ulsd=BUFOFF+DECPMAX-1; - } - else { // padding will fit (but may still be too long) - // final-word mask depends on endianess - #if DECLITEND - static const uInt dmask[]={0, 0x000000ff, 0x0000ffff, 0x00ffffff}; - #else - static const uInt dmask[]={0, 0xff000000, 0xffff0000, 0xffffff00}; - #endif - // note that here zeros to the right are added by fours, so in - // the Quad case this could write 36 zeros if the coefficient has - // fewer than three significant digits (hence the +2*QUAD for buf) - for (uc=BUFOFF+DECPMAX;; uc+=4) { - UBFROMUI(uc, 0); - if (UBTOUI(uc-DECPMAX)!=0) { // could be bad - // if all four digits should be zero, definitely bad - if (uc<=BUFOFF+DECPMAX+(-drop)-4) - return decInvalid(result, set); - // must be a 1- to 3-digit sequence; check more carefully - if ((UBTOUI(uc-DECPMAX)&dmask[(-drop)%4])!=0) - return decInvalid(result, set); - break; // no need for loop end test - } - if (uc>=BUFOFF+DECPMAX+(-drop)-4) break; // done - } - ulsd=BUFOFF+DECPMAX+(-drop)-1; - } // pad and check leading zeros - } // drop<0 - - #if DECTRACE - num.msd=ulsd-DECPMAX+1; - num.lsd=ulsd; - num.exponent=explb-DECBIAS; - num.sign=sourhil & DECFLOAT_Sign; - decShowNum(&num, "res"); - #endif - - /*------------------------------------------------------------------*/ - /* At this point the result is DECPMAX digits, ending at ulsd, so */ - /* fits the encoding exactly; there is no possibility of error */ - /*------------------------------------------------------------------*/ - encode=((exprb>>DECECONL)<<4) + *(ulsd-DECPMAX+1); // make index - encode=DECCOMBFROM[encode]; // indexed by (0-2)*16+msd - // the exponent continuation can be extracted from the original RHS - encode|=sourhir & ECONMASK; - encode|=sourhil&DECFLOAT_Sign; // add the sign from LHS - - // finally encode the coefficient - // private macro to encode a declet; this version can be used - // because all coefficient digits exist - #define getDPD3q(dpd, n) ub=ulsd-(3*(n))-2; \ - dpd=BCD2DPD[(*ub*256)+(*(ub+1)*16)+*(ub+2)]; - - #if DOUBLE - getDPD3q(dpd, 4); encode|=dpd<<8; - getDPD3q(dpd, 3); encode|=dpd>>2; - DFWORD(result, 0)=encode; - encode=dpd<<30; - getDPD3q(dpd, 2); encode|=dpd<<20; - getDPD3q(dpd, 1); encode|=dpd<<10; - getDPD3q(dpd, 0); encode|=dpd; - DFWORD(result, 1)=encode; - - #elif QUAD - getDPD3q(dpd,10); encode|=dpd<<4; - getDPD3q(dpd, 9); encode|=dpd>>6; - DFWORD(result, 0)=encode; - encode=dpd<<26; - getDPD3q(dpd, 8); encode|=dpd<<16; - getDPD3q(dpd, 7); encode|=dpd<<6; - getDPD3q(dpd, 6); encode|=dpd>>4; - DFWORD(result, 1)=encode; - encode=dpd<<28; - getDPD3q(dpd, 5); encode|=dpd<<18; - getDPD3q(dpd, 4); encode|=dpd<<8; - getDPD3q(dpd, 3); encode|=dpd>>2; - DFWORD(result, 2)=encode; - encode=dpd<<30; - getDPD3q(dpd, 2); encode|=dpd<<20; - getDPD3q(dpd, 1); encode|=dpd<<10; - getDPD3q(dpd, 0); encode|=dpd; - DFWORD(result, 3)=encode; - #endif - return result; - } // decFloatQuantize - -/* ------------------------------------------------------------------ */ -/* decFloatReduce -- reduce finite coefficient to minimum length */ -/* */ -/* result gets the reduced decFloat */ -/* df is the source decFloat */ -/* set is the context */ -/* returns result, which will be canonical */ -/* */ -/* This removes all possible trailing zeros from the coefficient; */ -/* some may remain when the number is very close to Nmax. */ -/* Special values are unchanged and no status is set unless df=sNaN. */ -/* Reduced zero has an exponent q=0. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatReduce(decFloat *result, const decFloat *df, - decContext *set) { - bcdnum num; // work - uByte buf[DECPMAX], *ub; // coefficient and pointer - if (df!=result) *result=*df; // copy, if needed - if (DFISNAN(df)) return decNaNs(result, df, NULL, set); // sNaN - // zeros and infinites propagate too - if (DFISINF(df)) return decInfinity(result, df); // canonical - if (DFISZERO(df)) { - uInt sign=DFWORD(df, 0)&DECFLOAT_Sign; - decFloatZero(result); - DFWORD(result, 0)|=sign; - return result; // exponent dropped, sign OK - } - // non-zero finite - GETCOEFF(df, buf); - ub=buf+DECPMAX-1; // -> lsd - if (*ub) return result; // no trailing zeros - for (ub--; *ub==0;) ub--; // terminates because non-zero - // *ub is the first non-zero from the right - num.sign=DFWORD(df, 0)&DECFLOAT_Sign; // set up number... - num.exponent=GETEXPUN(df)+(Int)(buf+DECPMAX-1-ub); // adjusted exponent - num.msd=buf; - num.lsd=ub; - return decFinalize(result, &num, set); - } // decFloatReduce - -/* ------------------------------------------------------------------ */ -/* decFloatRemainder -- integer divide and return remainder */ -/* */ -/* result gets the remainder of dividing dfl by dfr: */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs) */ -/* set is the context */ -/* returns result */ -/* */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatRemainder(decFloat *result, - const decFloat *dfl, const decFloat *dfr, - decContext *set) { - return decDivide(result, dfl, dfr, set, REMAINDER); - } // decFloatRemainder - -/* ------------------------------------------------------------------ */ -/* decFloatRemainderNear -- integer divide to nearest and remainder */ -/* */ -/* result gets the remainder of dividing dfl by dfr: */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs) */ -/* set is the context */ -/* returns result */ -/* */ -/* This is the IEEE remainder, where the nearest integer is used. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatRemainderNear(decFloat *result, - const decFloat *dfl, const decFloat *dfr, - decContext *set) { - return decDivide(result, dfl, dfr, set, REMNEAR); - } // decFloatRemainderNear - -/* ------------------------------------------------------------------ */ -/* decFloatRotate -- rotate the coefficient of a decFloat left/right */ -/* */ -/* result gets the result of rotating dfl */ -/* dfl is the source decFloat to rotate */ -/* dfr is the count of digits to rotate, an integer (with q=0) */ -/* set is the context */ -/* returns result */ -/* */ -/* The digits of the coefficient of dfl are rotated to the left (if */ -/* dfr is positive) or to the right (if dfr is negative) without */ -/* adjusting the exponent or the sign of dfl. */ -/* */ -/* dfr must be in the range -DECPMAX through +DECPMAX. */ -/* NaNs are propagated as usual. An infinite dfl is unaffected (but */ -/* dfr must be valid). No status is set unless dfr is invalid or an */ -/* operand is an sNaN. The result is canonical. */ -/* ------------------------------------------------------------------ */ -#define PHALF (ROUNDUP(DECPMAX/2, 4)) // half length, rounded up -decFloat * decFloatRotate(decFloat *result, - const decFloat *dfl, const decFloat *dfr, - decContext *set) { - Int rotate; // dfr as an Int - uByte buf[DECPMAX+PHALF]; // coefficient + half - uInt digits, savestat; // work - bcdnum num; // .. - uByte *ub; // .. - - if (DFISNAN(dfl)||DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set); - if (!DFISINT(dfr)) return decInvalid(result, set); - digits=decFloatDigits(dfr); // calculate digits - if (digits>2) return decInvalid(result, set); // definitely out of range - rotate=DPD2BIN[DFWORD(dfr, DECWORDS-1)&0x3ff]; // is in bottom declet - if (rotate>DECPMAX) return decInvalid(result, set); // too big - // [from here on no error or status change is possible] - if (DFISINF(dfl)) return decInfinity(result, dfl); // canonical - // handle no-rotate cases - if (rotate==0 || rotate==DECPMAX) return decCanonical(result, dfl); - // a real rotate is needed: 0 < rotate < DECPMAX - // reduce the rotation to no more than half to reduce copying later - // (for QUAD in fact half + 2 digits) - if (DFISSIGNED(dfr)) rotate=-rotate; - if (abs(rotate)>PHALF) { - if (rotate<0) rotate=DECPMAX+rotate; - else rotate=rotate-DECPMAX; - } - // now lay out the coefficient, leaving room to the right or the - // left depending on the direction of rotation - ub=buf; - if (rotate<0) ub+=PHALF; // rotate right, so space to left - GETCOEFF(dfl, ub); - // copy half the digits to left or right, and set num.msd - if (rotate<0) { - memcpy(buf, buf+DECPMAX, PHALF); - num.msd=buf+PHALF+rotate; - } - else { - memcpy(buf+DECPMAX, buf, PHALF); - num.msd=buf+rotate; - } - // fill in rest of num - num.lsd=num.msd+DECPMAX-1; - num.sign=DFWORD(dfl, 0)&DECFLOAT_Sign; - num.exponent=GETEXPUN(dfl); - savestat=set->status; // record - decFinalize(result, &num, set); - set->status=savestat; // restore - return result; - } // decFloatRotate - -/* ------------------------------------------------------------------ */ -/* decFloatSameQuantum -- test decFloats for same quantum */ -/* */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs) */ -/* returns 1 if the operands have the same quantum, 0 otherwise */ -/* */ -/* No error is possible and no status results. */ -/* ------------------------------------------------------------------ */ -uInt decFloatSameQuantum(const decFloat *dfl, const decFloat *dfr) { - if (DFISSPECIAL(dfl) || DFISSPECIAL(dfr)) { - if (DFISNAN(dfl) && DFISNAN(dfr)) return 1; - if (DFISINF(dfl) && DFISINF(dfr)) return 1; - return 0; // any other special mixture gives false - } - if (GETEXP(dfl)==GETEXP(dfr)) return 1; // biased exponents match - return 0; - } // decFloatSameQuantum - -/* ------------------------------------------------------------------ */ -/* decFloatScaleB -- multiply by a power of 10, as per 754 */ -/* */ -/* result gets the result of the operation */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs), am integer (with q=0) */ -/* set is the context */ -/* returns result */ -/* */ -/* This computes result=dfl x 10**dfr where dfr is an integer in the */ -/* range +/-2*(emax+pmax), typically resulting from LogB. */ -/* Underflow and Overflow (with Inexact) may occur. NaNs propagate */ -/* as usual. */ -/* ------------------------------------------------------------------ */ -#define SCALEBMAX 2*(DECEMAX+DECPMAX) // D=800, Q=12356 -decFloat * decFloatScaleB(decFloat *result, - const decFloat *dfl, const decFloat *dfr, - decContext *set) { - uInt digits; // work - Int expr; // dfr as an Int - - if (DFISNAN(dfl)||DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set); - if (!DFISINT(dfr)) return decInvalid(result, set); - digits=decFloatDigits(dfr); // calculate digits - - #if DOUBLE - if (digits>3) return decInvalid(result, set); // definitely out of range - expr=DPD2BIN[DFWORD(dfr, 1)&0x3ff]; // must be in bottom declet - #elif QUAD - if (digits>5) return decInvalid(result, set); // definitely out of range - expr=DPD2BIN[DFWORD(dfr, 3)&0x3ff] // in bottom 2 declets .. - +DPD2BIN[(DFWORD(dfr, 3)>>10)&0x3ff]*1000; // .. - #endif - if (expr>SCALEBMAX) return decInvalid(result, set); // oops - // [from now on no error possible] - if (DFISINF(dfl)) return decInfinity(result, dfl); // canonical - if (DFISSIGNED(dfr)) expr=-expr; - // dfl is finite and expr is valid - *result=*dfl; // copy to target - return decFloatSetExponent(result, set, GETEXPUN(result)+expr); - } // decFloatScaleB - -/* ------------------------------------------------------------------ */ -/* decFloatShift -- shift the coefficient of a decFloat left or right */ -/* */ -/* result gets the result of shifting dfl */ -/* dfl is the source decFloat to shift */ -/* dfr is the count of digits to shift, an integer (with q=0) */ -/* set is the context */ -/* returns result */ -/* */ -/* The digits of the coefficient of dfl are shifted to the left (if */ -/* dfr is positive) or to the right (if dfr is negative) without */ -/* adjusting the exponent or the sign of dfl. */ -/* */ -/* dfr must be in the range -DECPMAX through +DECPMAX. */ -/* NaNs are propagated as usual. An infinite dfl is unaffected (but */ -/* dfr must be valid). No status is set unless dfr is invalid or an */ -/* operand is an sNaN. The result is canonical. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatShift(decFloat *result, - const decFloat *dfl, const decFloat *dfr, - decContext *set) { - Int shift; // dfr as an Int - uByte buf[DECPMAX*2]; // coefficient + padding - uInt digits, savestat; // work - bcdnum num; // .. - uInt uiwork; // for macros - - if (DFISNAN(dfl)||DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set); - if (!DFISINT(dfr)) return decInvalid(result, set); - digits=decFloatDigits(dfr); // calculate digits - if (digits>2) return decInvalid(result, set); // definitely out of range - shift=DPD2BIN[DFWORD(dfr, DECWORDS-1)&0x3ff]; // is in bottom declet - if (shift>DECPMAX) return decInvalid(result, set); // too big - // [from here on no error or status change is possible] - - if (DFISINF(dfl)) return decInfinity(result, dfl); // canonical - // handle no-shift and all-shift (clear to zero) cases - if (shift==0) return decCanonical(result, dfl); - if (shift==DECPMAX) { // zero with sign - uByte sign=(uByte)(DFBYTE(dfl, 0)&0x80); // save sign bit - decFloatZero(result); // make +0 - DFBYTE(result, 0)=(uByte)(DFBYTE(result, 0)|sign); // and set sign - // [cannot safely use CopySign] - return result; - } - // a real shift is needed: 0 < shift < DECPMAX - num.sign=DFWORD(dfl, 0)&DECFLOAT_Sign; - num.exponent=GETEXPUN(dfl); - num.msd=buf; - GETCOEFF(dfl, buf); - if (DFISSIGNED(dfr)) { // shift right - // edge cases are taken care of, so this is easy - num.lsd=buf+DECPMAX-shift-1; - } - else { // shift left -- zero padding needed to right - UBFROMUI(buf+DECPMAX, 0); // 8 will handle most cases - UBFROMUI(buf+DECPMAX+4, 0); // .. - if (shift>8) memset(buf+DECPMAX+8, 0, 8+QUAD*18); // all other cases - num.msd+=shift; - num.lsd=num.msd+DECPMAX-1; - } - savestat=set->status; // record - decFinalize(result, &num, set); - set->status=savestat; // restore - return result; - } // decFloatShift - -/* ------------------------------------------------------------------ */ -/* decFloatSubtract -- subtract a decFloat from another */ -/* */ -/* result gets the result of subtracting dfr from dfl: */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs) */ -/* set is the context */ -/* returns result */ -/* */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatSubtract(decFloat *result, - const decFloat *dfl, const decFloat *dfr, - decContext *set) { - decFloat temp; - // NaNs must propagate without sign change - if (DFISNAN(dfr)) return decFloatAdd(result, dfl, dfr, set); - temp=*dfr; // make a copy - DFBYTE(&temp, 0)^=0x80; // flip sign - return decFloatAdd(result, dfl, &temp, set); // and add to the lhs - } // decFloatSubtract - -/* ------------------------------------------------------------------ */ -/* decFloatToInt -- round to 32-bit binary integer (4 flavours) */ -/* */ -/* df is the decFloat to round */ -/* set is the context */ -/* round is the rounding mode to use */ -/* returns a uInt or an Int, rounded according to the name */ -/* */ -/* Invalid will always be signaled if df is a NaN, is Infinite, or is */ -/* outside the range of the target; Inexact will not be signaled for */ -/* simple rounding unless 'Exact' appears in the name. */ -/* ------------------------------------------------------------------ */ -uInt decFloatToUInt32(const decFloat *df, decContext *set, - enum rounding round) { - return decToInt32(df, set, round, 0, 1);} - -uInt decFloatToUInt32Exact(const decFloat *df, decContext *set, - enum rounding round) { - return decToInt32(df, set, round, 1, 1);} - -Int decFloatToInt32(const decFloat *df, decContext *set, - enum rounding round) { - return (Int)decToInt32(df, set, round, 0, 0);} - -Int decFloatToInt32Exact(const decFloat *df, decContext *set, - enum rounding round) { - return (Int)decToInt32(df, set, round, 1, 0);} - -/* ------------------------------------------------------------------ */ -/* decFloatToIntegral -- round to integral value (two flavours) */ -/* */ -/* result gets the result */ -/* df is the decFloat to round */ -/* set is the context */ -/* round is the rounding mode to use */ -/* returns result */ -/* */ -/* No exceptions, even Inexact, are raised except for sNaN input, or */ -/* if 'Exact' appears in the name. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatToIntegralValue(decFloat *result, const decFloat *df, - decContext *set, enum rounding round) { - return decToIntegral(result, df, set, round, 0);} - -decFloat * decFloatToIntegralExact(decFloat *result, const decFloat *df, - decContext *set) { - return decToIntegral(result, df, set, set->round, 1);} - -/* ------------------------------------------------------------------ */ -/* decFloatXor -- logical digitwise XOR of two decFloats */ -/* */ -/* result gets the result of XORing dfl and dfr */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs) */ -/* set is the context */ -/* returns result, which will be canonical with sign=0 */ -/* */ -/* The operands must be positive, finite with exponent q=0, and */ -/* comprise just zeros and ones; if not, Invalid operation results. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatXor(decFloat *result, - const decFloat *dfl, const decFloat *dfr, - decContext *set) { - if (!DFISUINT01(dfl) || !DFISUINT01(dfr) - || !DFISCC01(dfl) || !DFISCC01(dfr)) return decInvalid(result, set); - // the operands are positive finite integers (q=0) with just 0s and 1s - #if DOUBLE - DFWORD(result, 0)=ZEROWORD - |((DFWORD(dfl, 0) ^ DFWORD(dfr, 0))&0x04009124); - DFWORD(result, 1)=(DFWORD(dfl, 1) ^ DFWORD(dfr, 1))&0x49124491; - #elif QUAD - DFWORD(result, 0)=ZEROWORD - |((DFWORD(dfl, 0) ^ DFWORD(dfr, 0))&0x04000912); - DFWORD(result, 1)=(DFWORD(dfl, 1) ^ DFWORD(dfr, 1))&0x44912449; - DFWORD(result, 2)=(DFWORD(dfl, 2) ^ DFWORD(dfr, 2))&0x12449124; - DFWORD(result, 3)=(DFWORD(dfl, 3) ^ DFWORD(dfr, 3))&0x49124491; - #endif - return result; - } // decFloatXor - -/* ------------------------------------------------------------------ */ -/* decInvalid -- set Invalid_operation result */ -/* */ -/* result gets a canonical NaN */ -/* set is the context */ -/* returns result */ -/* */ -/* status has Invalid_operation added */ -/* ------------------------------------------------------------------ */ -static decFloat *decInvalid(decFloat *result, decContext *set) { - decFloatZero(result); - DFWORD(result, 0)=DECFLOAT_qNaN; - set->status|=DEC_Invalid_operation; - return result; - } // decInvalid - -/* ------------------------------------------------------------------ */ -/* decInfinity -- set canonical Infinity with sign from a decFloat */ -/* */ -/* result gets a canonical Infinity */ -/* df is source decFloat (only the sign is used) */ -/* returns result */ -/* */ -/* df may be the same as result */ -/* ------------------------------------------------------------------ */ -static decFloat *decInfinity(decFloat *result, const decFloat *df) { - uInt sign=DFWORD(df, 0); // save source signword - decFloatZero(result); // clear everything - DFWORD(result, 0)=DECFLOAT_Inf | (sign & DECFLOAT_Sign); - return result; - } // decInfinity - -/* ------------------------------------------------------------------ */ -/* decNaNs -- handle NaN argument(s) */ -/* */ -/* result gets the result of handling dfl and dfr, one or both of */ -/* which is a NaN */ -/* dfl is the first decFloat (lhs) */ -/* dfr is the second decFloat (rhs) -- may be NULL for a single- */ -/* operand operation */ -/* set is the context */ -/* returns result */ -/* */ -/* Called when one or both operands is a NaN, and propagates the */ -/* appropriate result to res. When an sNaN is found, it is changed */ -/* to a qNaN and Invalid operation is set. */ -/* ------------------------------------------------------------------ */ -static decFloat *decNaNs(decFloat *result, - const decFloat *dfl, const decFloat *dfr, - decContext *set) { - // handle sNaNs first - if (dfr!=NULL && DFISSNAN(dfr) && !DFISSNAN(dfl)) dfl=dfr; // use RHS - if (DFISSNAN(dfl)) { - decCanonical(result, dfl); // propagate canonical sNaN - DFWORD(result, 0)&=~(DECFLOAT_qNaN ^ DECFLOAT_sNaN); // quiet - set->status|=DEC_Invalid_operation; - return result; - } - // one or both is a quiet NaN - if (!DFISNAN(dfl)) dfl=dfr; // RHS must be NaN, use it - return decCanonical(result, dfl); // propagate canonical qNaN - } // decNaNs - -/* ------------------------------------------------------------------ */ -/* decNumCompare -- numeric comparison of two decFloats */ -/* */ -/* dfl is the left-hand decFloat, which is not a NaN */ -/* dfr is the right-hand decFloat, which is not a NaN */ -/* tot is 1 for total order compare, 0 for simple numeric */ -/* returns -1, 0, or +1 for dfl<dfr, dfl=dfr, dfl>dfr */ -/* */ -/* No error is possible; status and mode are unchanged. */ -/* ------------------------------------------------------------------ */ -static Int decNumCompare(const decFloat *dfl, const decFloat *dfr, Flag tot) { - Int sigl, sigr; // LHS and RHS non-0 signums - Int shift; // shift needed to align operands - uByte *ub, *uc; // work - uInt uiwork; // for macros - // buffers +2 if Quad (36 digits), need double plus 4 for safe padding - uByte bufl[DECPMAX*2+QUAD*2+4]; // for LHS coefficient + padding - uByte bufr[DECPMAX*2+QUAD*2+4]; // for RHS coefficient + padding - - sigl=1; - if (DFISSIGNED(dfl)) { - if (!DFISSIGNED(dfr)) { // -LHS +RHS - if (DFISZERO(dfl) && DFISZERO(dfr) && !tot) return 0; - return -1; // RHS wins - } - sigl=-1; - } - if (DFISSIGNED(dfr)) { - if (!DFISSIGNED(dfl)) { // +LHS -RHS - if (DFISZERO(dfl) && DFISZERO(dfr) && !tot) return 0; - return +1; // LHS wins - } - } - - // signs are the same; operand(s) could be zero - sigr=-sigl; // sign to return if abs(RHS) wins - - if (DFISINF(dfl)) { - if (DFISINF(dfr)) return 0; // both infinite & same sign - return sigl; // inf > n - } - if (DFISINF(dfr)) return sigr; // n < inf [dfl is finite] - - // here, both are same sign and finite; calculate their offset - shift=GETEXP(dfl)-GETEXP(dfr); // [0 means aligned] - // [bias can be ignored -- the absolute exponent is not relevant] - - if (DFISZERO(dfl)) { - if (!DFISZERO(dfr)) return sigr; // LHS=0, RHS!=0 - // both are zero, return 0 if both same exponent or numeric compare - if (shift==0 || !tot) return 0; - if (shift>0) return sigl; - return sigr; // [shift<0] - } - else { // LHS!=0 - if (DFISZERO(dfr)) return sigl; // LHS!=0, RHS=0 - } - // both are known to be non-zero at this point - - // if the exponents are so different that the coefficients do not - // overlap (by even one digit) then a full comparison is not needed - if (abs(shift)>=DECPMAX) { // no overlap - // coefficients are known to be non-zero - if (shift>0) return sigl; - return sigr; // [shift<0] - } - - // decode the coefficients - // (shift both right two if Quad to make a multiple of four) - #if QUAD - UBFROMUI(bufl, 0); - UBFROMUI(bufr, 0); - #endif - GETCOEFF(dfl, bufl+QUAD*2); // decode from decFloat - GETCOEFF(dfr, bufr+QUAD*2); // .. - if (shift==0) { // aligned; common and easy - // all multiples of four, here - for (ub=bufl, uc=bufr; ub<bufl+DECPMAX+QUAD*2; ub+=4, uc+=4) { - uInt ui=UBTOUI(ub); - if (ui==UBTOUI(uc)) continue; // so far so same - // about to find a winner; go by bytes in case little-endian - for (;; ub++, uc++) { - if (*ub>*uc) return sigl; // difference found - if (*ub<*uc) return sigr; // .. - } - } - } // aligned - else if (shift>0) { // lhs to left - ub=bufl; // RHS pointer - // pad bufl so right-aligned; most shifts will fit in 8 - UBFROMUI(bufl+DECPMAX+QUAD*2, 0); // add eight zeros - UBFROMUI(bufl+DECPMAX+QUAD*2+4, 0); // .. - if (shift>8) { - // more than eight; fill the rest, and also worth doing the - // lead-in by fours - uByte *up; // work - uByte *upend=bufl+DECPMAX+QUAD*2+shift; - for (up=bufl+DECPMAX+QUAD*2+8; up<upend; up+=4) UBFROMUI(up, 0); - // [pads up to 36 in all for Quad] - for (;; ub+=4) { - if (UBTOUI(ub)!=0) return sigl; - if (ub+4>bufl+shift-4) break; - } - } - // check remaining leading digits - for (; ub<bufl+shift; ub++) if (*ub!=0) return sigl; - // now start the overlapped part; bufl has been padded, so the - // comparison can go for the full length of bufr, which is a - // multiple of 4 bytes - for (uc=bufr; ; uc+=4, ub+=4) { - uInt ui=UBTOUI(ub); - if (ui!=UBTOUI(uc)) { // mismatch found - for (;; uc++, ub++) { // check from left [little-endian?] - if (*ub>*uc) return sigl; // difference found - if (*ub<*uc) return sigr; // .. - } - } // mismatch - if (uc==bufr+QUAD*2+DECPMAX-4) break; // all checked - } - } // shift>0 - - else { // shift<0) .. RHS is to left of LHS; mirror shift>0 - uc=bufr; // RHS pointer - // pad bufr so right-aligned; most shifts will fit in 8 - UBFROMUI(bufr+DECPMAX+QUAD*2, 0); // add eight zeros - UBFROMUI(bufr+DECPMAX+QUAD*2+4, 0); // .. - if (shift<-8) { - // more than eight; fill the rest, and also worth doing the - // lead-in by fours - uByte *up; // work - uByte *upend=bufr+DECPMAX+QUAD*2-shift; - for (up=bufr+DECPMAX+QUAD*2+8; up<upend; up+=4) UBFROMUI(up, 0); - // [pads up to 36 in all for Quad] - for (;; uc+=4) { - if (UBTOUI(uc)!=0) return sigr; - if (uc+4>bufr-shift-4) break; - } - } - // check remaining leading digits - for (; uc<bufr-shift; uc++) if (*uc!=0) return sigr; - // now start the overlapped part; bufr has been padded, so the - // comparison can go for the full length of bufl, which is a - // multiple of 4 bytes - for (ub=bufl; ; ub+=4, uc+=4) { - uInt ui=UBTOUI(ub); - if (ui!=UBTOUI(uc)) { // mismatch found - for (;; ub++, uc++) { // check from left [little-endian?] - if (*ub>*uc) return sigl; // difference found - if (*ub<*uc) return sigr; // .. - } - } // mismatch - if (ub==bufl+QUAD*2+DECPMAX-4) break; // all checked - } - } // shift<0 - - // Here when compare equal - if (!tot) return 0; // numerically equal - // total ordering .. exponent matters - if (shift>0) return sigl; // total order by exponent - if (shift<0) return sigr; // .. - return 0; - } // decNumCompare - -/* ------------------------------------------------------------------ */ -/* decToInt32 -- local routine to effect ToInteger conversions */ -/* */ -/* df is the decFloat to convert */ -/* set is the context */ -/* rmode is the rounding mode to use */ -/* exact is 1 if Inexact should be signalled */ -/* unsign is 1 if the result a uInt, 0 if an Int (cast to uInt) */ -/* returns 32-bit result as a uInt */ -/* */ -/* Invalid is set is df is a NaN, is infinite, or is out-of-range; in */ -/* these cases 0 is returned. */ -/* ------------------------------------------------------------------ */ -static uInt decToInt32(const decFloat *df, decContext *set, - enum rounding rmode, Flag exact, Flag unsign) { - Int exp; // exponent - uInt sourhi, sourpen, sourlo; // top word from source decFloat .. - uInt hi, lo; // .. penultimate, least, etc. - decFloat zero, result; // work - Int i; // .. - - /* Start decoding the argument */ - sourhi=DFWORD(df, 0); // top word - exp=DECCOMBEXP[sourhi>>26]; // get exponent high bits (in place) - if (EXPISSPECIAL(exp)) { // is special? - set->status|=DEC_Invalid_operation; // signal - return 0; - } - - /* Here when the argument is finite */ - if (GETEXPUN(df)==0) result=*df; // already a true integer - else { // need to round to integer - enum rounding saveround; // saver - uInt savestatus; // .. - saveround=set->round; // save rounding mode .. - savestatus=set->status; // .. and status - set->round=rmode; // set mode - decFloatZero(&zero); // make 0E+0 - set->status=0; // clear - decFloatQuantize(&result, df, &zero, set); // [this may fail] - set->round=saveround; // restore rounding mode .. - if (exact) set->status|=savestatus; // include Inexact - else set->status=savestatus; // .. or just original status - } - - // only the last four declets of the coefficient can contain - // non-zero; check for others (and also NaN or Infinity from the - // Quantize) first (see DFISZERO for explanation): - // decFloatShow(&result, "sofar"); - #if DOUBLE - if ((DFWORD(&result, 0)&0x1c03ff00)!=0 - || (DFWORD(&result, 0)&0x60000000)==0x60000000) { - #elif QUAD - if ((DFWORD(&result, 2)&0xffffff00)!=0 - || DFWORD(&result, 1)!=0 - || (DFWORD(&result, 0)&0x1c003fff)!=0 - || (DFWORD(&result, 0)&0x60000000)==0x60000000) { - #endif - set->status|=DEC_Invalid_operation; // Invalid or out of range - return 0; - } - // get last twelve digits of the coefficent into hi & ho, base - // 10**9 (see GETCOEFFBILL): - sourlo=DFWORD(&result, DECWORDS-1); - lo=DPD2BIN0[sourlo&0x3ff] - +DPD2BINK[(sourlo>>10)&0x3ff] - +DPD2BINM[(sourlo>>20)&0x3ff]; - sourpen=DFWORD(&result, DECWORDS-2); - hi=DPD2BIN0[((sourpen<<2) | (sourlo>>30))&0x3ff]; - - // according to request, check range carefully - if (unsign) { - if (hi>4 || (hi==4 && lo>294967295) || (hi+lo!=0 && DFISSIGNED(&result))) { - set->status|=DEC_Invalid_operation; // out of range - return 0; - } - return hi*BILLION+lo; - } - // signed - if (hi>2 || (hi==2 && lo>147483647)) { - // handle the usual edge case - if (lo==147483648 && hi==2 && DFISSIGNED(&result)) return 0x80000000; - set->status|=DEC_Invalid_operation; // truly out of range - return 0; - } - i=hi*BILLION+lo; - if (DFISSIGNED(&result)) i=-i; - return (uInt)i; - } // decToInt32 - -/* ------------------------------------------------------------------ */ -/* decToIntegral -- local routine to effect ToIntegral value */ -/* */ -/* result gets the result */ -/* df is the decFloat to round */ -/* set is the context */ -/* rmode is the rounding mode to use */ -/* exact is 1 if Inexact should be signalled */ -/* returns result */ -/* ------------------------------------------------------------------ */ -static decFloat * decToIntegral(decFloat *result, const decFloat *df, - decContext *set, enum rounding rmode, - Flag exact) { - Int exp; // exponent - uInt sourhi; // top word from source decFloat - enum rounding saveround; // saver - uInt savestatus; // .. - decFloat zero; // work - - /* Start decoding the argument */ - sourhi=DFWORD(df, 0); // top word - exp=DECCOMBEXP[sourhi>>26]; // get exponent high bits (in place) - - if (EXPISSPECIAL(exp)) { // is special? - // NaNs are handled as usual - if (DFISNAN(df)) return decNaNs(result, df, NULL, set); - // must be infinite; return canonical infinity with sign of df - return decInfinity(result, df); - } - - /* Here when the argument is finite */ - // complete extraction of the exponent - exp+=GETECON(df)-DECBIAS; // .. + continuation and unbias - - if (exp>=0) return decCanonical(result, df); // already integral - - saveround=set->round; // save rounding mode .. - savestatus=set->status; // .. and status - set->round=rmode; // set mode - decFloatZero(&zero); // make 0E+0 - decFloatQuantize(result, df, &zero, set); // 'integrate'; cannot fail - set->round=saveround; // restore rounding mode .. - if (!exact) set->status=savestatus; // .. and status, unless exact - return result; - } // decToIntegral
src/decNumber/decCommon.c
@@ -1,1835 +0,0 @@-/* ------------------------------------------------------------------ */ -/* decCommon.c -- common code for all three fixed-size types */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is included in the package as decNumber.pdf. This */ -/* document is also available in HTML, together with specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ -/* This module comprises code that is shared between all the formats */ -/* (decSingle, decDouble, and decQuad); it includes set and extract */ -/* of format components, widening, narrowing, and string conversions. */ -/* */ -/* Unlike decNumber, parameterization takes place at compile time */ -/* rather than at runtime. The parameters are set in the decDouble.c */ -/* (etc.) files, which then include this one to produce the compiled */ -/* code. The functions here, therefore, are code shared between */ -/* multiple formats. */ -/* ------------------------------------------------------------------ */ -// Names here refer to decFloat rather than to decDouble, etc., and -// the functions are in strict alphabetical order. -// Constants, tables, and debug function(s) are included only for QUAD -// (which will always be compiled if DOUBLE or SINGLE are used). -// -// Whenever a decContext is used, only the status may be set (using -// OR) or the rounding mode read; all other fields are ignored and -// untouched. - -// names for simpler testing and default context -#if DECPMAX==7 - #define SINGLE 1 - #define DOUBLE 0 - #define QUAD 0 - #define DEFCONTEXT DEC_INIT_DECIMAL32 -#elif DECPMAX==16 - #define SINGLE 0 - #define DOUBLE 1 - #define QUAD 0 - #define DEFCONTEXT DEC_INIT_DECIMAL64 -#elif DECPMAX==34 - #define SINGLE 0 - #define DOUBLE 0 - #define QUAD 1 - #define DEFCONTEXT DEC_INIT_DECIMAL128 -#else - #error Unexpected DECPMAX value -#endif - -/* Assertions */ - -#if DECPMAX!=7 && DECPMAX!=16 && DECPMAX!=34 - #error Unexpected Pmax (DECPMAX) value for this module -#endif - -// Assert facts about digit characters, etc. -#if ('9'&0x0f)!=9 - #error This module assumes characters are of the form 0b....nnnn - // where .... are don't care 4 bits and nnnn is 0000 through 1001 -#endif -#if ('9'&0xf0)==('.'&0xf0) - #error This module assumes '.' has a different mask than a digit -#endif - -// Assert ToString lay-out conditions -#if DECSTRING<DECPMAX+9 - #error ToString needs at least 8 characters for lead-in and dot -#endif -#if DECPMAX+DECEMAXD+5 > DECSTRING - #error Exponent form can be too long for ToString to lay out safely -#endif -#if DECEMAXD > 4 - #error Exponent form is too long for ToString to lay out - // Note: code for up to 9 digits exists in archives [decOct] -#endif - -/* Private functions used here and possibly in decBasic.c, etc. */ -static decFloat * decFinalize(decFloat *, bcdnum *, decContext *); -static Flag decBiStr(const char *, const char *, const char *); - -/* Macros and private tables; those which are not format-dependent */ -/* are only included if decQuad is being built. */ - -/* ------------------------------------------------------------------ */ -/* Combination field lookup tables (uInts to save measurable work) */ -/* */ -/* DECCOMBEXP - 2 most-significant-bits of exponent (00, 01, or */ -/* 10), shifted left for format, or DECFLOAT_Inf/NaN */ -/* DECCOMBWEXP - The same, for the next-wider format (unless QUAD) */ -/* DECCOMBMSD - 4-bit most-significant-digit */ -/* [0 if the index is a special (Infinity or NaN)] */ -/* DECCOMBFROM - 5-bit combination field from EXP top bits and MSD */ -/* (placed in uInt so no shift is needed) */ -/* */ -/* DECCOMBEXP, DECCOMBWEXP, and DECCOMBMSD are indexed by the sign */ -/* and 5-bit combination field (0-63, the second half of the table */ -/* identical to the first half) */ -/* DECCOMBFROM is indexed by expTopTwoBits*16 + msd */ -/* */ -/* DECCOMBMSD and DECCOMBFROM are not format-dependent and so are */ -/* only included once, when QUAD is being built */ -/* ------------------------------------------------------------------ */ -static const uInt DECCOMBEXP[64]={ - 0, 0, 0, 0, 0, 0, 0, 0, - 1<<DECECONL, 1<<DECECONL, 1<<DECECONL, 1<<DECECONL, - 1<<DECECONL, 1<<DECECONL, 1<<DECECONL, 1<<DECECONL, - 2<<DECECONL, 2<<DECECONL, 2<<DECECONL, 2<<DECECONL, - 2<<DECECONL, 2<<DECECONL, 2<<DECECONL, 2<<DECECONL, - 0, 0, 1<<DECECONL, 1<<DECECONL, - 2<<DECECONL, 2<<DECECONL, DECFLOAT_Inf, DECFLOAT_NaN, - 0, 0, 0, 0, 0, 0, 0, 0, - 1<<DECECONL, 1<<DECECONL, 1<<DECECONL, 1<<DECECONL, - 1<<DECECONL, 1<<DECECONL, 1<<DECECONL, 1<<DECECONL, - 2<<DECECONL, 2<<DECECONL, 2<<DECECONL, 2<<DECECONL, - 2<<DECECONL, 2<<DECECONL, 2<<DECECONL, 2<<DECECONL, - 0, 0, 1<<DECECONL, 1<<DECECONL, - 2<<DECECONL, 2<<DECECONL, DECFLOAT_Inf, DECFLOAT_NaN}; -#if !QUAD -static const uInt DECCOMBWEXP[64]={ - 0, 0, 0, 0, 0, 0, 0, 0, - 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, - 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, - 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, - 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, - 0, 0, 1<<DECWECONL, 1<<DECWECONL, - 2<<DECWECONL, 2<<DECWECONL, DECFLOAT_Inf, DECFLOAT_NaN, - 0, 0, 0, 0, 0, 0, 0, 0, - 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, - 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, - 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, - 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, - 0, 0, 1<<DECWECONL, 1<<DECWECONL, - 2<<DECWECONL, 2<<DECWECONL, DECFLOAT_Inf, DECFLOAT_NaN}; -#endif - -#if QUAD -const uInt DECCOMBMSD[64]={ - 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, - 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 8, 9, 0, 0, - 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, - 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 8, 9, 0, 0}; - -const uInt DECCOMBFROM[48]={ - 0x00000000, 0x04000000, 0x08000000, 0x0C000000, 0x10000000, 0x14000000, - 0x18000000, 0x1C000000, 0x60000000, 0x64000000, 0x00000000, 0x00000000, - 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x20000000, 0x24000000, - 0x28000000, 0x2C000000, 0x30000000, 0x34000000, 0x38000000, 0x3C000000, - 0x68000000, 0x6C000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, - 0x00000000, 0x00000000, 0x40000000, 0x44000000, 0x48000000, 0x4C000000, - 0x50000000, 0x54000000, 0x58000000, 0x5C000000, 0x70000000, 0x74000000, - 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000}; - -/* ------------------------------------------------------------------ */ -/* Request and include the tables to use for conversions */ -/* ------------------------------------------------------------------ */ -#define DEC_BCD2DPD 1 // 0-0x999 -> DPD -#define DEC_BIN2DPD 1 // 0-999 -> DPD -#define DEC_BIN2BCD8 1 // 0-999 -> ddd, len -#define DEC_DPD2BCD8 1 // DPD -> ddd, len -#define DEC_DPD2BIN 1 // DPD -> 0-999 -#define DEC_DPD2BINK 1 // DPD -> 0-999000 -#define DEC_DPD2BINM 1 // DPD -> 0-999000000 -#include "decDPD.h" // source of the lookup tables - -#endif - -/* ----------------------------------------------------------------- */ -/* decBiStr -- compare string with pairwise options */ -/* */ -/* targ is the string to compare */ -/* str1 is one of the strings to compare against (length may be 0) */ -/* str2 is the other; it must be the same length as str1 */ -/* */ -/* returns 1 if strings compare equal, (that is, targ is the same */ -/* length as str1 and str2, and each character of targ is in one */ -/* of str1 or str2 in the corresponding position), or 0 otherwise */ -/* */ -/* This is used for generic caseless compare, including the awkward */ -/* case of the Turkish dotted and dotless Is. Use as (for example): */ -/* if (decBiStr(test, "mike", "MIKE")) ... */ -/* ----------------------------------------------------------------- */ -static Flag decBiStr(const char *targ, const char *str1, const char *str2) { - for (;;targ++, str1++, str2++) { - if (*targ!=*str1 && *targ!=*str2) return 0; - // *targ has a match in one (or both, if terminator) - if (*targ=='\0') break; - } // forever - return 1; - } // decBiStr - -/* ------------------------------------------------------------------ */ -/* decFinalize -- adjust and store a final result */ -/* */ -/* df is the decFloat format number which gets the final result */ -/* num is the descriptor of the number to be checked and encoded */ -/* [its values, including the coefficient, may be modified] */ -/* set is the context to use */ -/* returns df */ -/* */ -/* The num descriptor may point to a bcd8 string of any length; this */ -/* string may have leading insignificant zeros. If it has more than */ -/* DECPMAX digits then the final digit can be a round-for-reround */ -/* digit (i.e., it may include a sticky bit residue). */ -/* */ -/* The exponent (q) may be one of the codes for a special value and */ -/* can be up to 999999999 for conversion from string. */ -/* */ -/* No error is possible, but Inexact, Underflow, and/or Overflow may */ -/* be set. */ -/* ------------------------------------------------------------------ */ -// Constant whose size varies with format; also the check for surprises -static uByte allnines[DECPMAX]= -#if SINGLE - {9, 9, 9, 9, 9, 9, 9}; -#elif DOUBLE - {9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9}; -#elif QUAD - {9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, - 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9}; -#endif - -static decFloat * decFinalize(decFloat *df, bcdnum *num, - decContext *set) { - uByte *ub; // work - uInt dpd; // .. - uInt uiwork; // for macros - uByte *umsd=num->msd; // local copy - uByte *ulsd=num->lsd; // .. - uInt encode; // encoding accumulator - Int length; // coefficient length - - #if DECCHECK - Int clen=ulsd-umsd+1; - #if QUAD - #define COEXTRA 2 // extra-long coefficent - #else - #define COEXTRA 0 - #endif - if (clen<1 || clen>DECPMAX*3+2+COEXTRA) - printf("decFinalize: suspect coefficient [length=%ld]\n", (LI)clen); - if (num->sign!=0 && num->sign!=DECFLOAT_Sign) - printf("decFinalize: bad sign [%08lx]\n", (LI)num->sign); - if (!EXPISSPECIAL(num->exponent) - && (num->exponent>1999999999 || num->exponent<-1999999999)) - printf("decFinalize: improbable exponent [%ld]\n", (LI)num->exponent); - // decShowNum(num, "final"); - #endif - - // A special will have an 'exponent' which is very positive and a - // coefficient < DECPMAX - length=(uInt)(ulsd-umsd+1); // coefficient length - - if (!NUMISSPECIAL(num)) { - Int drop; // digits to be dropped - // skip leading insignificant zeros to calculate an exact length - // [this is quite expensive] - if (*umsd==0) { - for (; umsd+3<ulsd && UBTOUI(umsd)==0;) umsd+=4; - for (; *umsd==0 && umsd<ulsd;) umsd++; - length=ulsd-umsd+1; // recalculate - } - drop=MAXI(length-DECPMAX, DECQTINY-num->exponent); - // drop can now be > digits for bottom-clamp (subnormal) cases - if (drop>0) { // rounding needed - // (decFloatQuantize has very similar code to this, so any - // changes may need to be made there, too) - uByte *roundat; // -> re-round digit - uByte reround; // reround value - // printf("Rounding; drop=%ld\n", (LI)drop); - - num->exponent+=drop; // always update exponent - - // Three cases here: - // 1. new LSD is in coefficient (almost always) - // 2. new LSD is digit to left of coefficient (so MSD is - // round-for-reround digit) - // 3. new LSD is to left of case 2 (whole coefficient is sticky) - // [duplicate check-stickies code to save a test] - // [by-digit check for stickies as runs of zeros are rare] - if (drop<length) { // NB lengths not addresses - roundat=umsd+length-drop; - reround=*roundat; - for (ub=roundat+1; ub<=ulsd; ub++) { - if (*ub!=0) { // non-zero to be discarded - reround=DECSTICKYTAB[reround]; // apply sticky bit - break; // [remainder don't-care] - } - } // check stickies - ulsd=roundat-1; // new LSD - } - else { // edge case - if (drop==length) { - roundat=umsd; - reround=*roundat; - } - else { - roundat=umsd-1; - reround=0; - } - for (ub=roundat+1; ub<=ulsd; ub++) { - if (*ub!=0) { // non-zero to be discarded - reround=DECSTICKYTAB[reround]; // apply sticky bit - break; // [remainder don't-care] - } - } // check stickies - *umsd=0; // coefficient is a 0 - ulsd=umsd; // .. - } - - if (reround!=0) { // discarding non-zero - uInt bump=0; - set->status|=DEC_Inexact; - // if adjusted exponent [exp+digits-1] is < EMIN then num is - // subnormal -- so raise Underflow - if (num->exponent<DECEMIN && (num->exponent+(ulsd-umsd+1)-1)<DECEMIN) - set->status|=DEC_Underflow; - - // next decide whether increment of the coefficient is needed - if (set->round==DEC_ROUND_HALF_EVEN) { // fastpath slowest case - if (reround>5) bump=1; // >0.5 goes up - else if (reround==5) // exactly 0.5000 .. - bump=*ulsd & 0x01; // .. up iff [new] lsd is odd - } // r-h-e - else switch (set->round) { - case DEC_ROUND_DOWN: { - // no change - break;} // r-d - case DEC_ROUND_HALF_DOWN: { - if (reround>5) bump=1; - break;} // r-h-d - case DEC_ROUND_HALF_UP: { - if (reround>=5) bump=1; - break;} // r-h-u - case DEC_ROUND_UP: { - if (reround>0) bump=1; - break;} // r-u - case DEC_ROUND_CEILING: { - // same as _UP for positive numbers, and as _DOWN for negatives - if (!num->sign && reround>0) bump=1; - break;} // r-c - case DEC_ROUND_FLOOR: { - // same as _UP for negative numbers, and as _DOWN for positive - // [negative reround cannot occur on 0] - if (num->sign && reround>0) bump=1; - break;} // r-f - case DEC_ROUND_05UP: { - if (reround>0) { // anything out there is 'sticky' - // bump iff lsd=0 or 5; this cannot carry so it could be - // effected immediately with no bump -- but the code - // is clearer if this is done the same way as the others - if (*ulsd==0 || *ulsd==5) bump=1; - } - break;} // r-r - default: { // e.g., DEC_ROUND_MAX - set->status|=DEC_Invalid_context; - #if DECCHECK - printf("Unknown rounding mode: %ld\n", (LI)set->round); - #endif - break;} - } // switch (not r-h-e) - // printf("ReRound: %ld bump: %ld\n", (LI)reround, (LI)bump); - - if (bump!=0) { // need increment - // increment the coefficient; this might end up with 1000... - // (after the all nines case) - ub=ulsd; - for(; ub-3>=umsd && UBTOUI(ub-3)==0x09090909; ub-=4) { - UBFROMUI(ub-3, 0); // to 00000000 - } - // [note ub could now be to left of msd, and it is not safe - // to write to the left of the msd] - // now at most 3 digits left to non-9 (usually just the one) - for (; ub>=umsd; *ub=0, ub--) { - if (*ub==9) continue; // carry - *ub+=1; - break; - } - if (ub<umsd) { // had all-nines - *umsd=1; // coefficient to 1000... - // usually the 1000... coefficient can be used as-is - if ((ulsd-umsd+1)==DECPMAX) { - num->exponent++; - } - else { - // if coefficient is shorter than Pmax then num is - // subnormal, so extend it; this is safe as drop>0 - // (or, if the coefficient was supplied above, it could - // not be 9); this may make the result normal. - ulsd++; - *ulsd=0; - // [exponent unchanged] - #if DECCHECK - if (num->exponent!=DECQTINY) // sanity check - printf("decFinalize: bad all-nines extend [^%ld, %ld]\n", - (LI)num->exponent, (LI)(ulsd-umsd+1)); - #endif - } // subnormal extend - } // had all-nines - } // bump needed - } // inexact rounding - - length=ulsd-umsd+1; // recalculate (may be <DECPMAX) - } // need round (drop>0) - - // The coefficient will now fit and has final length unless overflow - // decShowNum(num, "rounded"); - - // if exponent is >=emax may have to clamp, overflow, or fold-down - if (num->exponent>DECEMAX-(DECPMAX-1)) { // is edge case - // printf("overflow checks...\n"); - if (*ulsd==0 && ulsd==umsd) { // have zero - num->exponent=DECEMAX-(DECPMAX-1); // clamp to max - } - else if ((num->exponent+length-1)>DECEMAX) { // > Nmax - // Overflow -- these could go straight to encoding, here, but - // instead num is adjusted to keep the code cleaner - Flag needmax=0; // 1 for finite result - set->status|=(DEC_Overflow | DEC_Inexact); - switch (set->round) { - case DEC_ROUND_DOWN: { - needmax=1; // never Infinity - break;} // r-d - case DEC_ROUND_05UP: { - needmax=1; // never Infinity - break;} // r-05 - case DEC_ROUND_CEILING: { - if (num->sign) needmax=1; // Infinity iff non-negative - break;} // r-c - case DEC_ROUND_FLOOR: { - if (!num->sign) needmax=1; // Infinity iff negative - break;} // r-f - default: break; // Infinity in all other cases - } - if (!needmax) { // easy .. set Infinity - num->exponent=DECFLOAT_Inf; - *umsd=0; // be clean: coefficient to 0 - ulsd=umsd; // .. - } - else { // return Nmax - umsd=allnines; // use constant array - ulsd=allnines+DECPMAX-1; - num->exponent=DECEMAX-(DECPMAX-1); - } - } - else { // no overflow but non-zero and may have to fold-down - Int shift=num->exponent-(DECEMAX-(DECPMAX-1)); - if (shift>0) { // fold-down needed - // fold down needed; must copy to buffer in order to pad - // with zeros safely; fortunately this is not the worst case - // path because cannot have had a round - uByte buffer[ROUNDUP(DECPMAX+3, 4)]; // [+3 allows uInt padding] - uByte *s=umsd; // source - uByte *t=buffer; // safe target - uByte *tlsd=buffer+(ulsd-umsd)+shift; // target LSD - // printf("folddown shift=%ld\n", (LI)shift); - for (; s<=ulsd; s+=4, t+=4) UBFROMUI(t, UBTOUI(s)); - for (t=tlsd-shift+1; t<=tlsd; t+=4) UBFROMUI(t, 0); // pad 0s - num->exponent-=shift; - umsd=buffer; - ulsd=tlsd; - } - } // fold-down? - length=ulsd-umsd+1; // recalculate length - } // high-end edge case - } // finite number - - /*------------------------------------------------------------------*/ - /* At this point the result will properly fit the decFloat */ - /* encoding, and it can be encoded with no possibility of error */ - /*------------------------------------------------------------------*/ - // Following code does not alter coefficient (could be allnines array) - - // fast path possible when DECPMAX digits - if (length==DECPMAX) { - return decFloatFromBCD(df, num->exponent, umsd, num->sign); - } // full-length - - // slower path when not a full-length number; must care about length - // [coefficient length here will be < DECPMAX] - if (!NUMISSPECIAL(num)) { // is still finite - // encode the combination field and exponent continuation - uInt uexp=(uInt)(num->exponent+DECBIAS); // biased exponent - uInt code=(uexp>>DECECONL)<<4; // top two bits of exp - // [msd==0] - // look up the combination field and make high word - encode=DECCOMBFROM[code]; // indexed by (0-2)*16+msd - encode|=(uexp<<(32-6-DECECONL)) & 0x03ffffff; // exponent continuation - } - else encode=num->exponent; // special [already in word] - encode|=num->sign; // add sign - - // private macro to extract a declet, n (where 0<=n<DECLETS and 0 - // refers to the declet from the least significant three digits) - // and put the corresponding DPD code into dpd. Access to umsd and - // ulsd (pointers to the most and least significant digit of the - // variable-length coefficient) is assumed, along with use of a - // working pointer, uInt *ub. - // As not full-length then chances are there are many leading zeros - // [and there may be a partial triad] - #define getDPDt(dpd, n) ub=ulsd-(3*(n))-2; \ - if (ub<umsd-2) dpd=0; \ - else if (ub>=umsd) dpd=BCD2DPD[(*ub*256)+(*(ub+1)*16)+*(ub+2)]; \ - else {dpd=*(ub+2); if (ub+1==umsd) dpd+=*(ub+1)*16; dpd=BCD2DPD[dpd];} - - // place the declets in the encoding words and copy to result (df), - // according to endianness; in all cases complete the sign word - // first - #if DECPMAX==7 - getDPDt(dpd, 1); - encode|=dpd<<10; - getDPDt(dpd, 0); - encode|=dpd; - DFWORD(df, 0)=encode; // just the one word - - #elif DECPMAX==16 - getDPDt(dpd, 4); encode|=dpd<<8; - getDPDt(dpd, 3); encode|=dpd>>2; - DFWORD(df, 0)=encode; - encode=dpd<<30; - getDPDt(dpd, 2); encode|=dpd<<20; - getDPDt(dpd, 1); encode|=dpd<<10; - getDPDt(dpd, 0); encode|=dpd; - DFWORD(df, 1)=encode; - - #elif DECPMAX==34 - getDPDt(dpd,10); encode|=dpd<<4; - getDPDt(dpd, 9); encode|=dpd>>6; - DFWORD(df, 0)=encode; - - encode=dpd<<26; - getDPDt(dpd, 8); encode|=dpd<<16; - getDPDt(dpd, 7); encode|=dpd<<6; - getDPDt(dpd, 6); encode|=dpd>>4; - DFWORD(df, 1)=encode; - - encode=dpd<<28; - getDPDt(dpd, 5); encode|=dpd<<18; - getDPDt(dpd, 4); encode|=dpd<<8; - getDPDt(dpd, 3); encode|=dpd>>2; - DFWORD(df, 2)=encode; - - encode=dpd<<30; - getDPDt(dpd, 2); encode|=dpd<<20; - getDPDt(dpd, 1); encode|=dpd<<10; - getDPDt(dpd, 0); encode|=dpd; - DFWORD(df, 3)=encode; - #endif - - // printf("Status: %08lx\n", (LI)set->status); - // decFloatShow(df, "final2"); - return df; - } // decFinalize - -/* ------------------------------------------------------------------ */ -/* decFloatFromBCD -- set decFloat from exponent, BCD8, and sign */ -/* */ -/* df is the target decFloat */ -/* exp is the in-range unbiased exponent, q, or a special value in */ -/* the form returned by decFloatGetExponent */ -/* bcdar holds DECPMAX digits to set the coefficient from, one */ -/* digit in each byte (BCD8 encoding); the first (MSD) is ignored */ -/* if df is a NaN; all are ignored if df is infinite. */ -/* All bytes must be in 0-9; results are undefined otherwise. */ -/* sig is DECFLOAT_Sign to set the sign bit, 0 otherwise */ -/* returns df, which will be canonical */ -/* */ -/* No error is possible, and no status will be set. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatFromBCD(decFloat *df, Int exp, const uByte *bcdar, - Int sig) { - uInt encode, dpd; // work - const uByte *ub; // .. - - if (EXPISSPECIAL(exp)) encode=exp|sig;// specials already encoded - else { // is finite - // encode the combination field and exponent continuation - uInt uexp=(uInt)(exp+DECBIAS); // biased exponent - uInt code=(uexp>>DECECONL)<<4; // top two bits of exp - code+=bcdar[0]; // add msd - // look up the combination field and make high word - encode=DECCOMBFROM[code]|sig; // indexed by (0-2)*16+msd - encode|=(uexp<<(32-6-DECECONL)) & 0x03ffffff; // exponent continuation - } - - // private macro to extract a declet, n (where 0<=n<DECLETS and 0 - // refers to the declet from the least significant three digits) - // and put the corresponding DPD code into dpd. - // Use of a working pointer, uInt *ub, is assumed. - - #define getDPDb(dpd, n) ub=bcdar+DECPMAX-1-(3*(n))-2; \ - dpd=BCD2DPD[(*ub*256)+(*(ub+1)*16)+*(ub+2)]; - - // place the declets in the encoding words and copy to result (df), - // according to endianness; in all cases complete the sign word - // first - #if DECPMAX==7 - getDPDb(dpd, 1); - encode|=dpd<<10; - getDPDb(dpd, 0); - encode|=dpd; - DFWORD(df, 0)=encode; // just the one word - - #elif DECPMAX==16 - getDPDb(dpd, 4); encode|=dpd<<8; - getDPDb(dpd, 3); encode|=dpd>>2; - DFWORD(df, 0)=encode; - encode=dpd<<30; - getDPDb(dpd, 2); encode|=dpd<<20; - getDPDb(dpd, 1); encode|=dpd<<10; - getDPDb(dpd, 0); encode|=dpd; - DFWORD(df, 1)=encode; - - #elif DECPMAX==34 - getDPDb(dpd,10); encode|=dpd<<4; - getDPDb(dpd, 9); encode|=dpd>>6; - DFWORD(df, 0)=encode; - - encode=dpd<<26; - getDPDb(dpd, 8); encode|=dpd<<16; - getDPDb(dpd, 7); encode|=dpd<<6; - getDPDb(dpd, 6); encode|=dpd>>4; - DFWORD(df, 1)=encode; - - encode=dpd<<28; - getDPDb(dpd, 5); encode|=dpd<<18; - getDPDb(dpd, 4); encode|=dpd<<8; - getDPDb(dpd, 3); encode|=dpd>>2; - DFWORD(df, 2)=encode; - - encode=dpd<<30; - getDPDb(dpd, 2); encode|=dpd<<20; - getDPDb(dpd, 1); encode|=dpd<<10; - getDPDb(dpd, 0); encode|=dpd; - DFWORD(df, 3)=encode; - #endif - // decFloatShow(df, "fromB"); - return df; - } // decFloatFromBCD - -/* ------------------------------------------------------------------ */ -/* decFloatFromPacked -- set decFloat from exponent and packed BCD */ -/* */ -/* df is the target decFloat */ -/* exp is the in-range unbiased exponent, q, or a special value in */ -/* the form returned by decFloatGetExponent */ -/* packed holds DECPMAX packed decimal digits plus a sign nibble */ -/* (all 6 codes are OK); the first (MSD) is ignored if df is a NaN */ -/* and all except sign are ignored if df is infinite. For DOUBLE */ -/* and QUAD the first (pad) nibble is also ignored in all cases. */ -/* All coefficient nibbles must be in 0-9 and sign in A-F; results */ -/* are undefined otherwise. */ -/* returns df, which will be canonical */ -/* */ -/* No error is possible, and no status will be set. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatFromPacked(decFloat *df, Int exp, const uByte *packed) { - uByte bcdar[DECPMAX+2]; // work [+1 for pad, +1 for sign] - const uByte *ip; // .. - uByte *op; // .. - Int sig=0; // sign - - // expand coefficient and sign to BCDAR - #if SINGLE - op=bcdar+1; // no pad digit - #else - op=bcdar; // first (pad) digit ignored - #endif - for (ip=packed; ip<packed+((DECPMAX+2)/2); ip++) { - *op++=*ip>>4; - *op++=(uByte)(*ip&0x0f); // [final nibble is sign] - } - op--; // -> sign byte - if (*op==DECPMINUS || *op==DECPMINUSALT) sig=DECFLOAT_Sign; - - if (EXPISSPECIAL(exp)) { // Infinity or NaN - if (!EXPISINF(exp)) bcdar[1]=0; // a NaN: ignore MSD - else memset(bcdar+1, 0, DECPMAX); // Infinite: coefficient to 0 - } - return decFloatFromBCD(df, exp, bcdar+1, sig); - } // decFloatFromPacked - -/* ------------------------------------------------------------------ */ -/* decFloatFromPackedChecked -- set from exponent and packed; checked */ -/* */ -/* df is the target decFloat */ -/* exp is the in-range unbiased exponent, q, or a special value in */ -/* the form returned by decFloatGetExponent */ -/* packed holds DECPMAX packed decimal digits plus a sign nibble */ -/* (all 6 codes are OK); the first (MSD) must be 0 if df is a NaN */ -/* and all digits must be 0 if df is infinite. For DOUBLE and */ -/* QUAD the first (pad) nibble must be 0. */ -/* All coefficient nibbles must be in 0-9 and sign in A-F. */ -/* returns df, which will be canonical or NULL if any of the */ -/* requirements are not met (if this case df is unchanged); that */ -/* is, the input data must be as returned by decFloatToPacked, */ -/* except that all six sign codes are acccepted. */ -/* */ -/* No status will be set. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatFromPackedChecked(decFloat *df, Int exp, - const uByte *packed) { - uByte bcdar[DECPMAX+2]; // work [+1 for pad, +1 for sign] - const uByte *ip; // .. - uByte *op; // .. - Int sig=0; // sign - - // expand coefficient and sign to BCDAR - #if SINGLE - op=bcdar+1; // no pad digit - #else - op=bcdar; // first (pad) digit here - #endif - for (ip=packed; ip<packed+((DECPMAX+2)/2); ip++) { - *op=*ip>>4; - if (*op>9) return NULL; - op++; - *op=(uByte)(*ip&0x0f); // [final nibble is sign] - if (*op>9 && ip<packed+((DECPMAX+2)/2)-1) return NULL; - op++; - } - op--; // -> sign byte - if (*op<=9) return NULL; // bad sign - if (*op==DECPMINUS || *op==DECPMINUSALT) sig=DECFLOAT_Sign; - - #if !SINGLE - if (bcdar[0]!=0) return NULL; // bad pad nibble - #endif - - if (EXPISNAN(exp)) { // a NaN - if (bcdar[1]!=0) return NULL; // bad msd - } // NaN - else if (EXPISINF(exp)) { // is infinite - Int i; - for (i=0; i<DECPMAX; i++) { - if (bcdar[i+1]!=0) return NULL; // should be all zeros - } - } // infinity - else { // finite - // check the exponent is in range - if (exp>DECEMAX-DECPMAX+1) return NULL; - if (exp<DECEMIN-DECPMAX+1) return NULL; - } - return decFloatFromBCD(df, exp, bcdar+1, sig); - } // decFloatFromPacked - -/* ------------------------------------------------------------------ */ -/* decFloatFromString -- conversion from numeric string */ -/* */ -/* result is the decFloat format number which gets the result of */ -/* the conversion */ -/* *string is the character string which should contain a valid */ -/* number (which may be a special value), \0-terminated */ -/* If there are too many significant digits in the */ -/* coefficient it will be rounded. */ -/* set is the context */ -/* returns result */ -/* */ -/* The length of the coefficient and the size of the exponent are */ -/* checked by this routine, so the correct error (Underflow or */ -/* Overflow) can be reported or rounding applied, as necessary. */ -/* */ -/* There is no limit to the coefficient length for finite inputs; */ -/* NaN payloads must be integers with no more than DECPMAX-1 digits. */ -/* Exponents may have up to nine significant digits. */ -/* */ -/* If bad syntax is detected, the result will be a quiet NaN. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatFromString(decFloat *result, const char *string, - decContext *set) { - Int digits; // count of digits in coefficient - const char *dotchar=NULL; // where dot was found [NULL if none] - const char *cfirst=string; // -> first character of decimal part - const char *c; // work - uByte *ub; // .. - uInt uiwork; // for macros - bcdnum num; // collects data for finishing - uInt error=DEC_Conversion_syntax; // assume the worst - uByte buffer[ROUNDUP(DECSTRING+11, 8)]; // room for most coefficents, - // some common rounding, +3, & pad - #if DECTRACE - // printf("FromString %s ...\n", string); - #endif - - for(;;) { // once-only 'loop' - num.sign=0; // assume non-negative - num.msd=buffer; // MSD is here always - - // detect and validate the coefficient, including any leading, - // trailing, or embedded '.' - // [could test four-at-a-time here (saving 10% for decQuads), - // but that risks storage violation because the position of the - // terminator is unknown] - for (c=string;; c++) { // -> input character - if (((unsigned)(*c-'0'))<=9) continue; // '0' through '9' is good - if (*c=='\0') break; // most common non-digit - if (*c=='.') { - if (dotchar!=NULL) break; // not first '.' - dotchar=c; // record offset into decimal part - continue;} - if (c==string) { // first in string... - if (*c=='-') { // valid - sign - cfirst++; - num.sign=DECFLOAT_Sign; - continue;} - if (*c=='+') { // valid + sign - cfirst++; - continue;} - } - // *c is not a digit, terminator, or a valid +, -, or '.' - break; - } // c loop - - digits=(uInt)(c-cfirst); // digits (+1 if a dot) - - if (digits>0) { // had digits and/or dot - const char *clast=c-1; // note last coefficient char position - Int exp=0; // exponent accumulator - if (*c!='\0') { // something follows the coefficient - uInt edig; // unsigned work - // had some digits and more to come; expect E[+|-]nnn now - const char *firstexp; // exponent first non-zero - if (*c!='E' && *c!='e') break; - c++; // to (optional) sign - if (*c=='-' || *c=='+') c++; // step over sign (c=clast+2) - if (*c=='\0') break; // no digits! (e.g., '1.2E') - for (; *c=='0';) c++; // skip leading zeros [even last] - firstexp=c; // remember start [maybe '\0'] - // gather exponent digits - edig=(uInt)*c-(uInt)'0'; - if (edig<=9) { // [check not bad or terminator] - exp+=edig; // avoid initial X10 - c++; - for (;; c++) { - edig=(uInt)*c-(uInt)'0'; - if (edig>9) break; - exp=exp*10+edig; - } - } - // if not now on the '\0', *c must not be a digit - if (*c!='\0') break; - - // (this next test must be after the syntax checks) - // if definitely more than the possible digits for format then - // the exponent may have wrapped, so simply set it to a certain - // over/underflow value - if (c>firstexp+DECEMAXD) exp=DECEMAX*2; - if (*(clast+2)=='-') exp=-exp; // was negative - } // exponent part - - if (dotchar!=NULL) { // had a '.' - digits--; // remove from digits count - if (digits==0) break; // was dot alone: bad syntax - exp-=(Int)(clast-dotchar); // adjust exponent - // [the '.' can now be ignored] - } - num.exponent=exp; // exponent is good; store it - - // Here when whole string has been inspected and syntax is good - // cfirst->first digit or dot, clast->last digit or dot - error=0; // no error possible now - - // if the number of digits in the coefficient will fit in buffer - // then it can simply be converted to bcd8 and copied -- decFinalize - // will take care of leading zeros and rounding; the buffer is big - // enough for all canonical coefficients, including 0.00000nn... - ub=buffer; - if (digits<=(Int)(sizeof(buffer)-3)) { // [-3 allows by-4s copy] - c=cfirst; - if (dotchar!=NULL) { // a dot to worry about - if (*(c+1)=='.') { // common canonical case - *ub++=(uByte)(*c-'0'); // copy leading digit - c+=2; // prepare to handle rest - } - else for (; c<=clast;) { // '.' could be anywhere - // as usual, go by fours when safe; NB it has been asserted - // that a '.' does not have the same mask as a digit - if (c<=clast-3 // safe for four - && (UBTOUI(c)&0xf0f0f0f0)==CHARMASK) { // test four - UBFROMUI(ub, UBTOUI(c)&0x0f0f0f0f); // to BCD8 - ub+=4; - c+=4; - continue; - } - if (*c=='.') { // found the dot - c++; // step over it .. - break; // .. and handle the rest - } - *ub++=(uByte)(*c++-'0'); - } - } // had dot - // Now no dot; do this by fours (where safe) - for (; c<=clast-3; c+=4, ub+=4) UBFROMUI(ub, UBTOUI(c)&0x0f0f0f0f); - for (; c<=clast; c++, ub++) *ub=(uByte)(*c-'0'); - num.lsd=buffer+digits-1; // record new LSD - } // fits - - else { // too long for buffer - // [This is a rare and unusual case; arbitrary-length input] - // strip leading zeros [but leave final 0 if all 0's] - if (*cfirst=='.') cfirst++; // step past dot at start - if (*cfirst=='0') { // [cfirst always -> digit] - for (; cfirst<clast; cfirst++) { - if (*cfirst!='0') { // non-zero found - if (*cfirst=='.') continue; // [ignore] - break; // done - } - digits--; // 0 stripped - } // cfirst - } // at least one leading 0 - - // the coefficient is now as short as possible, but may still - // be too long; copy up to Pmax+1 digits to the buffer, then - // just record any non-zeros (set round-for-reround digit) - for (c=cfirst; c<=clast && ub<=buffer+DECPMAX; c++) { - // (see commentary just above) - if (c<=clast-3 // safe for four - && (UBTOUI(c)&0xf0f0f0f0)==CHARMASK) { // four digits - UBFROMUI(ub, UBTOUI(c)&0x0f0f0f0f); // to BCD8 - ub+=4; - c+=3; // [will become 4] - continue; - } - if (*c=='.') continue; // [ignore] - *ub++=(uByte)(*c-'0'); - } - ub--; // -> LSD - for (; c<=clast; c++) { // inspect remaining chars - if (*c!='0') { // sticky bit needed - if (*c=='.') continue; // [ignore] - *ub=DECSTICKYTAB[*ub]; // update round-for-reround - break; // no need to look at more - } - } - num.lsd=ub; // record LSD - // adjust exponent for dropped digits - num.exponent+=digits-(Int)(ub-buffer+1); - } // too long for buffer - } // digits and/or dot - - else { // no digits or dot were found - // only Infinities and NaNs are allowed, here - if (*c=='\0') break; // nothing there is bad - buffer[0]=0; // default a coefficient of 0 - num.lsd=buffer; // .. - if (decBiStr(c, "infinity", "INFINITY") - || decBiStr(c, "inf", "INF")) num.exponent=DECFLOAT_Inf; - else { // should be a NaN - num.exponent=DECFLOAT_qNaN; // assume quiet NaN - if (*c=='s' || *c=='S') { // probably an sNaN - num.exponent=DECFLOAT_sNaN; // effect the 's' - c++; // and step over it - } - if (*c!='N' && *c!='n') break; // check caseless "NaN" - c++; - if (*c!='a' && *c!='A') break; // .. - c++; - if (*c!='N' && *c!='n') break; // .. - c++; - // now either nothing, or nnnn payload (no dots), expected - // -> start of integer, and skip leading 0s [including plain 0] - for (cfirst=c; *cfirst=='0';) cfirst++; - if (*cfirst!='\0') { // not empty or all-0, payload - // payload found; check all valid digits and copy to buffer as bcd8 - ub=buffer; - for (c=cfirst;; c++, ub++) { - if ((unsigned)(*c-'0')>9) break; // quit if not 0-9 - if (c-cfirst==DECPMAX-1) break; // too many digits - *ub=(uByte)(*c-'0'); // good bcd8 - } - if (*c!='\0') break; // not all digits, or too many - num.lsd=ub-1; // record new LSD - } - } // NaN or sNaN - error=0; // syntax is OK - } // digits=0 (special expected) - break; // drop out - } // [for(;;) once-loop] - - // decShowNum(&num, "fromStr"); - - if (error!=0) { - set->status|=error; - num.exponent=DECFLOAT_qNaN; // set up quiet NaN - num.sign=0; // .. with 0 sign - buffer[0]=0; // .. and coefficient - num.lsd=buffer; // .. - // decShowNum(&num, "oops"); - } - - // decShowNum(&num, "dffs"); - decFinalize(result, &num, set); // round, check, and lay out - // decFloatShow(result, "fromString"); - return result; - } // decFloatFromString - -/* ------------------------------------------------------------------ */ -/* decFloatFromWider -- conversion from next-wider format */ -/* */ -/* result is the decFloat format number which gets the result of */ -/* the conversion */ -/* wider is the decFloatWider format number which will be narrowed */ -/* set is the context */ -/* returns result */ -/* */ -/* Narrowing can cause rounding, overflow, etc., but not Invalid */ -/* operation (sNaNs are copied and do not signal). */ -/* ------------------------------------------------------------------ */ -// narrow-to is not possible for decQuad format numbers; simply omit -#if !QUAD -decFloat * decFloatFromWider(decFloat *result, const decFloatWider *wider, - decContext *set) { - bcdnum num; // collects data for finishing - uByte bcdar[DECWPMAX]; // room for wider coefficient - uInt widerhi=DFWWORD(wider, 0); // top word - Int exp; - - GETWCOEFF(wider, bcdar); - - num.msd=bcdar; // MSD is here always - num.lsd=bcdar+DECWPMAX-1; // LSD is here always - num.sign=widerhi&0x80000000; // extract sign [DECFLOAT_Sign=Neg] - - // decode the wider combination field to exponent - exp=DECCOMBWEXP[widerhi>>26]; // decode from wider combination field - // if it is a special there's nothing to do unless sNaN; if it's - // finite then add the (wider) exponent continuation and unbias - if (EXPISSPECIAL(exp)) exp=widerhi&0x7e000000; // include sNaN selector - else exp+=GETWECON(wider)-DECWBIAS; - num.exponent=exp; - - // decShowNum(&num, "dffw"); - return decFinalize(result, &num, set);// round, check, and lay out - } // decFloatFromWider -#endif - -/* ------------------------------------------------------------------ */ -/* decFloatGetCoefficient -- get coefficient as BCD8 */ -/* */ -/* df is the decFloat from which to extract the coefficient */ -/* bcdar is where DECPMAX bytes will be written, one BCD digit in */ -/* each byte (BCD8 encoding); if df is a NaN the first byte will */ -/* be zero, and if it is infinite they will all be zero */ -/* returns the sign of the coefficient (DECFLOAT_Sign if negative, */ -/* 0 otherwise) */ -/* */ -/* No error is possible, and no status will be set. If df is a */ -/* special value the array is set to zeros (for Infinity) or to the */ -/* payload of a qNaN or sNaN. */ -/* ------------------------------------------------------------------ */ -Int decFloatGetCoefficient(const decFloat *df, uByte *bcdar) { - if (DFISINF(df)) memset(bcdar, 0, DECPMAX); - else { - GETCOEFF(df, bcdar); // use macro - if (DFISNAN(df)) bcdar[0]=0; // MSD needs correcting - } - return GETSIGN(df); - } // decFloatGetCoefficient - -/* ------------------------------------------------------------------ */ -/* decFloatGetExponent -- get unbiased exponent */ -/* */ -/* df is the decFloat from which to extract the exponent */ -/* returns the exponent, q. */ -/* */ -/* No error is possible, and no status will be set. If df is a */ -/* special value the first seven bits of the decFloat are returned, */ -/* left adjusted and with the first (sign) bit set to 0 (followed by */ -/* 25 0 bits). e.g., -sNaN would return 0x7e000000 (DECFLOAT_sNaN). */ -/* ------------------------------------------------------------------ */ -Int decFloatGetExponent(const decFloat *df) { - if (DFISSPECIAL(df)) return DFWORD(df, 0)&0x7e000000; - return GETEXPUN(df); - } // decFloatGetExponent - -/* ------------------------------------------------------------------ */ -/* decFloatSetCoefficient -- set coefficient from BCD8 */ -/* */ -/* df is the target decFloat (and source of exponent/special value) */ -/* bcdar holds DECPMAX digits to set the coefficient from, one */ -/* digit in each byte (BCD8 encoding); the first (MSD) is ignored */ -/* if df is a NaN; all are ignored if df is infinite. */ -/* sig is DECFLOAT_Sign to set the sign bit, 0 otherwise */ -/* returns df, which will be canonical */ -/* */ -/* No error is possible, and no status will be set. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatSetCoefficient(decFloat *df, const uByte *bcdar, - Int sig) { - uInt exp; // for exponent - uByte bcdzero[DECPMAX]; // for infinities - - // Exponent/special code is extracted from df - if (DFISSPECIAL(df)) { - exp=DFWORD(df, 0)&0x7e000000; - if (DFISINF(df)) { - memset(bcdzero, 0, DECPMAX); - return decFloatFromBCD(df, exp, bcdzero, sig); - } - } - else exp=GETEXPUN(df); - return decFloatFromBCD(df, exp, bcdar, sig); - } // decFloatSetCoefficient - -/* ------------------------------------------------------------------ */ -/* decFloatSetExponent -- set exponent or special value */ -/* */ -/* df is the target decFloat (and source of coefficient/payload) */ -/* set is the context for reporting status */ -/* exp is the unbiased exponent, q, or a special value in the form */ -/* returned by decFloatGetExponent */ -/* returns df, which will be canonical */ -/* */ -/* No error is possible, but Overflow or Underflow might occur. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatSetExponent(decFloat *df, decContext *set, Int exp) { - uByte bcdcopy[DECPMAX]; // for coefficient - bcdnum num; // work - num.exponent=exp; - num.sign=decFloatGetCoefficient(df, bcdcopy); // extract coefficient - if (DFISSPECIAL(df)) { // MSD or more needs correcting - if (DFISINF(df)) memset(bcdcopy, 0, DECPMAX); - bcdcopy[0]=0; - } - num.msd=bcdcopy; - num.lsd=bcdcopy+DECPMAX-1; - return decFinalize(df, &num, set); - } // decFloatSetExponent - -/* ------------------------------------------------------------------ */ -/* decFloatRadix -- returns the base (10) */ -/* */ -/* df is any decFloat of this format */ -/* ------------------------------------------------------------------ */ -uInt decFloatRadix(const decFloat *df) { - if (df) return 10; // to placate compiler - return 10; - } // decFloatRadix - -/* The following function is not available if DECPRINT=0 */ -#if DECPRINT -/* ------------------------------------------------------------------ */ -/* decFloatShow -- printf a decFloat in hexadecimal and decimal */ -/* df is the decFloat to show */ -/* tag is a tag string displayed with the number */ -/* */ -/* This is a debug aid; the precise format of the string may change. */ -/* ------------------------------------------------------------------ */ -void decFloatShow(const decFloat *df, const char *tag) { - char hexbuf[DECBYTES*2+DECBYTES/4+1]; // NB blank after every fourth - char buff[DECSTRING]; // for value in decimal - Int i, j=0; - - for (i=0; i<DECBYTES; i++) { - #if DECLITEND - sprintf(&hexbuf[j], "%02x", df->bytes[DECBYTES-1-i]); - #else - sprintf(&hexbuf[j], "%02x", df->bytes[i]); - #endif - j+=2; - // the next line adds blank (and terminator) after final pair, too - if ((i+1)%4==0) {strcpy(&hexbuf[j], " "); j++;} - } - decFloatToString(df, buff); - printf(">%s> %s [big-endian] %s\n", tag, hexbuf, buff); - return; - } // decFloatShow -#endif - -/* ------------------------------------------------------------------ */ -/* decFloatToBCD -- get sign, exponent, and BCD8 from a decFloat */ -/* */ -/* df is the source decFloat */ -/* exp will be set to the unbiased exponent, q, or to a special */ -/* value in the form returned by decFloatGetExponent */ -/* bcdar is where DECPMAX bytes will be written, one BCD digit in */ -/* each byte (BCD8 encoding); if df is a NaN the first byte will */ -/* be zero, and if it is infinite they will all be zero */ -/* returns the sign of the coefficient (DECFLOAT_Sign if negative, */ -/* 0 otherwise) */ -/* */ -/* No error is possible, and no status will be set. */ -/* ------------------------------------------------------------------ */ -Int decFloatToBCD(const decFloat *df, Int *exp, uByte *bcdar) { - if (DFISINF(df)) { - memset(bcdar, 0, DECPMAX); - *exp=DFWORD(df, 0)&0x7e000000; - } - else { - GETCOEFF(df, bcdar); // use macro - if (DFISNAN(df)) { - bcdar[0]=0; // MSD needs correcting - *exp=DFWORD(df, 0)&0x7e000000; - } - else { // finite - *exp=GETEXPUN(df); - } - } - return GETSIGN(df); - } // decFloatToBCD - -/* ------------------------------------------------------------------ */ -/* decFloatToEngString -- conversion to numeric string, engineering */ -/* */ -/* df is the decFloat format number to convert */ -/* string is the string where the result will be laid out */ -/* */ -/* string must be at least DECPMAX+9 characters (the worst case is */ -/* "-0.00000nnn...nnn\0", which is as long as the exponent form when */ -/* DECEMAXD<=4); this condition is asserted above */ -/* */ -/* No error is possible, and no status will be set */ -/* ------------------------------------------------------------------ */ -char * decFloatToEngString(const decFloat *df, char *string){ - uInt msd; // coefficient MSD - Int exp; // exponent top two bits or full - uInt comb; // combination field - char *cstart; // coefficient start - char *c; // output pointer in string - char *s, *t; // .. (source, target) - Int pre, e; // work - const uByte *u; // .. - uInt uiwork; // for macros [one compiler needs - // volatile here to avoid bug, but - // that doubles execution time] - - // Source words; macro handles endianness - uInt sourhi=DFWORD(df, 0); // word with sign - #if DECPMAX==16 - uInt sourlo=DFWORD(df, 1); - #elif DECPMAX==34 - uInt sourmh=DFWORD(df, 1); - uInt sourml=DFWORD(df, 2); - uInt sourlo=DFWORD(df, 3); - #endif - - c=string; // where result will go - if (((Int)sourhi)<0) *c++='-'; // handle sign - comb=sourhi>>26; // sign+combination field - msd=DECCOMBMSD[comb]; // decode the combination field - exp=DECCOMBEXP[comb]; // .. - - if (EXPISSPECIAL(exp)) { // special - if (exp==DECFLOAT_Inf) { // infinity - strcpy(c, "Inf"); - strcpy(c+3, "inity"); - return string; // easy - } - if (sourhi&0x02000000) *c++='s'; // sNaN - strcpy(c, "NaN"); // complete word - c+=3; // step past - // quick exit if the payload is zero - #if DECPMAX==7 - if ((sourhi&0x000fffff)==0) return string; - #elif DECPMAX==16 - if (sourlo==0 && (sourhi&0x0003ffff)==0) return string; - #elif DECPMAX==34 - if (sourlo==0 && sourml==0 && sourmh==0 - && (sourhi&0x00003fff)==0) return string; - #endif - // otherwise drop through to add integer; set correct exp etc. - exp=0; msd=0; // setup for following code - } - else { // complete exponent; top two bits are in place - exp+=GETECON(df)-DECBIAS; // .. + continuation and unbias - } - - /* convert the digits of the significand to characters */ - cstart=c; // save start of coefficient - if (msd) *c++=(char)('0'+(char)msd); // non-zero most significant digit - - // Decode the declets. After extracting each declet, it is - // decoded to a 4-uByte sequence by table lookup; the four uBytes - // are the three encoded BCD8 digits followed by a 1-byte length - // (significant digits, except that 000 has length 0). This allows - // us to left-align the first declet with non-zero content, then - // the remaining ones are full 3-char length. Fixed-length copies - // are used because variable-length memcpy causes a subroutine call - // in at least two compilers. (The copies are length 4 for speed - // and are safe because the last item in the array is of length - // three and has the length byte following.) - #define dpd2char(dpdin) u=&DPD2BCD8[((dpdin)&0x3ff)*4]; \ - if (c!=cstart) {UBFROMUI(c, UBTOUI(u)|CHARMASK); c+=3;} \ - else if (*(u+3)) { \ - UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); c+=*(u+3);} - - #if DECPMAX==7 - dpd2char(sourhi>>10); // declet 1 - dpd2char(sourhi); // declet 2 - - #elif DECPMAX==16 - dpd2char(sourhi>>8); // declet 1 - dpd2char((sourhi<<2) | (sourlo>>30)); // declet 2 - dpd2char(sourlo>>20); // declet 3 - dpd2char(sourlo>>10); // declet 4 - dpd2char(sourlo); // declet 5 - - #elif DECPMAX==34 - dpd2char(sourhi>>4); // declet 1 - dpd2char((sourhi<<6) | (sourmh>>26)); // declet 2 - dpd2char(sourmh>>16); // declet 3 - dpd2char(sourmh>>6); // declet 4 - dpd2char((sourmh<<4) | (sourml>>28)); // declet 5 - dpd2char(sourml>>18); // declet 6 - dpd2char(sourml>>8); // declet 7 - dpd2char((sourml<<2) | (sourlo>>30)); // declet 8 - dpd2char(sourlo>>20); // declet 9 - dpd2char(sourlo>>10); // declet 10 - dpd2char(sourlo); // declet 11 - #endif - - if (c==cstart) *c++='0'; // all zeros, empty -- make "0" - - if (exp==0) { // integer or NaN case -- easy - *c='\0'; // terminate - return string; - } - /* non-0 exponent */ - - e=0; // assume no E - pre=(Int)(c-cstart)+exp; // length+exp [c->LSD+1] - // [here, pre-exp is the digits count (==1 for zero)] - - if (exp>0 || pre<-5) { // need exponential form - e=pre-1; // calculate E value - pre=1; // assume one digit before '.' - if (e!=0) { // engineering: may need to adjust - Int adj; // adjustment - // The C remainder operator is undefined for negative numbers, so - // a positive remainder calculation must be used here - if (e<0) { - adj=(-e)%3; - if (adj!=0) adj=3-adj; - } - else { // e>0 - adj=e%3; - } - e=e-adj; - // if dealing with zero still produce an exponent which is a - // multiple of three, as expected, but there will only be the - // one zero before the E, still. Otherwise note the padding. - if (!DFISZERO(df)) pre+=adj; - else { // is zero - if (adj!=0) { // 0.00Esnn needed - e=e+3; - pre=-(2-adj); - } - } // zero - } // engineering adjustment - } // exponential form - // printf("e=%ld pre=%ld exp=%ld\n", (LI)e, (LI)pre, (LI)exp); - - /* modify the coefficient, adding 0s, '.', and E+nn as needed */ - if (pre>0) { // ddd.ddd (plain), perhaps with E - // or dd00 padding for engineering - char *dotat=cstart+pre; - if (dotat<c) { // if embedded dot needed... - // move by fours; there must be space for junk at the end - // because there is still space for exponent - s=dotat+ROUNDDOWN4(c-dotat); // source - t=s+1; // target - // open the gap [cannot use memcpy] - for (; s>=dotat; s-=4, t-=4) UBFROMUI(t, UBTOUI(s)); - *dotat='.'; - c++; // length increased by one - } // need dot? - else for (; c<dotat; c++) *c='0'; // pad for engineering - } // pre>0 - else { - /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (may have - E, but only for 0.00E+3 kind of case -- with plenty of spare - space in this case */ - pre=-pre+2; // gap width, including "0." - t=cstart+ROUNDDOWN4(c-cstart)+pre; // preferred first target point - // backoff if too far to the right - if (t>string+DECSTRING-5) t=string+DECSTRING-5; // adjust to fit - // now shift the entire coefficient to the right, being careful not - // to access to the left of string [cannot use memcpy] - for (s=t-pre; s>=string; s-=4, t-=4) UBFROMUI(t, UBTOUI(s)); - // for Quads and Singles there may be a character or two left... - s+=3; // where next would come from - for(; s>=cstart; s--, t--) *(t+3)=*(s); - // now have fill 0. through 0.00000; use overlaps to avoid tests - if (pre>=4) { - memcpy(cstart+pre-4, "0000", 4); - memcpy(cstart, "0.00", 4); - } - else { // 2 or 3 - *(cstart+pre-1)='0'; - memcpy(cstart, "0.", 2); - } - c+=pre; // to end - } - - // finally add the E-part, if needed; it will never be 0, and has - // a maximum length of 3 or 4 digits (asserted above) - if (e!=0) { - memcpy(c, "E+", 2); // starts with E, assume + - c++; - if (e<0) { - *c='-'; // oops, need '-' - e=-e; // uInt, please - } - c++; - // Three-character exponents are easy; 4-character a little trickier - #if DECEMAXD<=3 - u=&BIN2BCD8[e*4]; // -> 3 digits + length byte - // copy fixed 4 characters [is safe], starting at non-zero - // and with character mask to convert BCD to char - UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); - c+=*(u+3); // bump pointer appropriately - #elif DECEMAXD==4 - if (e<1000) { // 3 (or fewer) digits case - u=&BIN2BCD8[e*4]; // -> 3 digits + length byte - UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); // [as above] - c+=*(u+3); // bump pointer appropriately - } - else { // 4-digits - Int thou=((e>>3)*1049)>>17; // e/1000 - Int rem=e-(1000*thou); // e%1000 - *c++=(char)('0'+(char)thou); // the thousands digit - u=&BIN2BCD8[rem*4]; // -> 3 digits + length byte - UBFROMUI(c, UBTOUI(u)|CHARMASK);// copy fixed 3+1 characters [is safe] - c+=3; // bump pointer, always 3 digits - } - #endif - } - *c='\0'; // terminate - //printf("res %s\n", string); - return string; - } // decFloatToEngString - -/* ------------------------------------------------------------------ */ -/* decFloatToPacked -- convert decFloat to Packed decimal + exponent */ -/* */ -/* df is the source decFloat */ -/* exp will be set to the unbiased exponent, q, or to a special */ -/* value in the form returned by decFloatGetExponent */ -/* packed is where DECPMAX nibbles will be written with the sign as */ -/* final nibble (0x0c for +, 0x0d for -); a NaN has a first nibble */ -/* of zero, and an infinity is all zeros. decDouble and decQuad */ -/* have a additional leading zero nibble, leading to result */ -/* lengths of 4, 9, and 18 bytes. */ -/* returns the sign of the coefficient (DECFLOAT_Sign if negative, */ -/* 0 otherwise) */ -/* */ -/* No error is possible, and no status will be set. */ -/* ------------------------------------------------------------------ */ -Int decFloatToPacked(const decFloat *df, Int *exp, uByte *packed) { - uByte bcdar[DECPMAX+2]; // work buffer - uByte *ip=bcdar, *op=packed; // work pointers - if (DFISINF(df)) { - memset(bcdar, 0, DECPMAX+2); - *exp=DECFLOAT_Inf; - } - else { - GETCOEFF(df, bcdar+1); // use macro - if (DFISNAN(df)) { - bcdar[1]=0; // MSD needs clearing - *exp=DFWORD(df, 0)&0x7e000000; - } - else { // finite - *exp=GETEXPUN(df); - } - } - // now pack; coefficient currently at bcdar+1 - #if SINGLE - ip++; // ignore first byte - #else - *ip=0; // need leading zero - #endif - // set final byte to Packed BCD sign value - bcdar[DECPMAX+1]=(DFISSIGNED(df) ? DECPMINUS : DECPPLUS); - // pack an even number of bytes... - for (; op<packed+((DECPMAX+2)/2); op++, ip+=2) { - *op=(uByte)((*ip<<4)+*(ip+1)); - } - return (bcdar[DECPMAX+1]==DECPMINUS ? DECFLOAT_Sign : 0); - } // decFloatToPacked - -/* ------------------------------------------------------------------ */ -/* decFloatToString -- conversion to numeric string */ -/* */ -/* df is the decFloat format number to convert */ -/* string is the string where the result will be laid out */ -/* */ -/* string must be at least DECPMAX+9 characters (the worst case is */ -/* "-0.00000nnn...nnn\0", which is as long as the exponent form when */ -/* DECEMAXD<=4); this condition is asserted above */ -/* */ -/* No error is possible, and no status will be set */ -/* ------------------------------------------------------------------ */ -char * decFloatToString(const decFloat *df, char *string){ - uInt msd; // coefficient MSD - Int exp; // exponent top two bits or full - uInt comb; // combination field - char *cstart; // coefficient start - char *c; // output pointer in string - char *s, *t; // .. (source, target) - Int pre, e; // work - const uByte *u; // .. - uInt uiwork; // for macros [one compiler needs - // volatile here to avoid bug, but - // that doubles execution time] - - // Source words; macro handles endianness - uInt sourhi=DFWORD(df, 0); // word with sign - #if DECPMAX==16 - uInt sourlo=DFWORD(df, 1); - #elif DECPMAX==34 - uInt sourmh=DFWORD(df, 1); - uInt sourml=DFWORD(df, 2); - uInt sourlo=DFWORD(df, 3); - #endif - - c=string; // where result will go - if (((Int)sourhi)<0) *c++='-'; // handle sign - comb=sourhi>>26; // sign+combination field - msd=DECCOMBMSD[comb]; // decode the combination field - exp=DECCOMBEXP[comb]; // .. - - if (!EXPISSPECIAL(exp)) { // finite - // complete exponent; top two bits are in place - exp+=GETECON(df)-DECBIAS; // .. + continuation and unbias - } - else { // IS special - if (exp==DECFLOAT_Inf) { // infinity - strcpy(c, "Infinity"); - return string; // easy - } - if (sourhi&0x02000000) *c++='s'; // sNaN - strcpy(c, "NaN"); // complete word - c+=3; // step past - // quick exit if the payload is zero - #if DECPMAX==7 - if ((sourhi&0x000fffff)==0) return string; - #elif DECPMAX==16 - if (sourlo==0 && (sourhi&0x0003ffff)==0) return string; - #elif DECPMAX==34 - if (sourlo==0 && sourml==0 && sourmh==0 - && (sourhi&0x00003fff)==0) return string; - #endif - // otherwise drop through to add integer; set correct exp etc. - exp=0; msd=0; // setup for following code - } - - /* convert the digits of the significand to characters */ - cstart=c; // save start of coefficient - if (msd) *c++=(char)('0'+(char)msd); // non-zero most significant digit - - // Decode the declets. After extracting each declet, it is - // decoded to a 4-uByte sequence by table lookup; the four uBytes - // are the three encoded BCD8 digits followed by a 1-byte length - // (significant digits, except that 000 has length 0). This allows - // us to left-align the first declet with non-zero content, then - // the remaining ones are full 3-char length. Fixed-length copies - // are used because variable-length memcpy causes a subroutine call - // in at least two compilers. (The copies are length 4 for speed - // and are safe because the last item in the array is of length - // three and has the length byte following.) - #define dpd2char(dpdin) u=&DPD2BCD8[((dpdin)&0x3ff)*4]; \ - if (c!=cstart) {UBFROMUI(c, UBTOUI(u)|CHARMASK); c+=3;} \ - else if (*(u+3)) { \ - UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); c+=*(u+3);} - - #if DECPMAX==7 - dpd2char(sourhi>>10); // declet 1 - dpd2char(sourhi); // declet 2 - - #elif DECPMAX==16 - dpd2char(sourhi>>8); // declet 1 - dpd2char((sourhi<<2) | (sourlo>>30)); // declet 2 - dpd2char(sourlo>>20); // declet 3 - dpd2char(sourlo>>10); // declet 4 - dpd2char(sourlo); // declet 5 - - #elif DECPMAX==34 - dpd2char(sourhi>>4); // declet 1 - dpd2char((sourhi<<6) | (sourmh>>26)); // declet 2 - dpd2char(sourmh>>16); // declet 3 - dpd2char(sourmh>>6); // declet 4 - dpd2char((sourmh<<4) | (sourml>>28)); // declet 5 - dpd2char(sourml>>18); // declet 6 - dpd2char(sourml>>8); // declet 7 - dpd2char((sourml<<2) | (sourlo>>30)); // declet 8 - dpd2char(sourlo>>20); // declet 9 - dpd2char(sourlo>>10); // declet 10 - dpd2char(sourlo); // declet 11 - #endif - - if (c==cstart) *c++='0'; // all zeros, empty -- make "0" - - //[This fast path is valid but adds 3-5 cycles to worst case length] - //if (exp==0) { // integer or NaN case -- easy - // *c='\0'; // terminate - // return string; - // } - - e=0; // assume no E - pre=(Int)(c-cstart)+exp; // length+exp [c->LSD+1] - // [here, pre-exp is the digits count (==1 for zero)] - - if (exp>0 || pre<-5) { // need exponential form - e=pre-1; // calculate E value - pre=1; // assume one digit before '.' - } // exponential form - - /* modify the coefficient, adding 0s, '.', and E+nn as needed */ - if (pre>0) { // ddd.ddd (plain), perhaps with E - char *dotat=cstart+pre; - if (dotat<c) { // if embedded dot needed... - // [memmove is a disaster, here] - // move by fours; there must be space for junk at the end - // because exponent is still possible - s=dotat+ROUNDDOWN4(c-dotat); // source - t=s+1; // target - // open the gap [cannot use memcpy] - for (; s>=dotat; s-=4, t-=4) UBFROMUI(t, UBTOUI(s)); - *dotat='.'; - c++; // length increased by one - } // need dot? - - // finally add the E-part, if needed; it will never be 0, and has - // a maximum length of 3 or 4 digits (asserted above) - if (e!=0) { - memcpy(c, "E+", 2); // starts with E, assume + - c++; - if (e<0) { - *c='-'; // oops, need '-' - e=-e; // uInt, please - } - c++; - // Three-character exponents are easy; 4-character a little trickier - #if DECEMAXD<=3 - u=&BIN2BCD8[e*4]; // -> 3 digits + length byte - // copy fixed 4 characters [is safe], starting at non-zero - // and with character mask to convert BCD to char - UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); - c+=*(u+3); // bump pointer appropriately - #elif DECEMAXD==4 - if (e<1000) { // 3 (or fewer) digits case - u=&BIN2BCD8[e*4]; // -> 3 digits + length byte - UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); // [as above] - c+=*(u+3); // bump pointer appropriately - } - else { // 4-digits - Int thou=((e>>3)*1049)>>17; // e/1000 - Int rem=e-(1000*thou); // e%1000 - *c++=(char)('0'+(char)thou); // the thousands digit - u=&BIN2BCD8[rem*4]; // -> 3 digits + length byte - UBFROMUI(c, UBTOUI(u)|CHARMASK); // copy fixed 3+1 characters [is safe] - c+=3; // bump pointer, always 3 digits - } - #endif - } - *c='\0'; // add terminator - //printf("res %s\n", string); - return string; - } // pre>0 - - /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */ - // Surprisingly, this is close to being the worst-case path, so the - // shift is done by fours; this is a little tricky because the - // rightmost character to be written must not be beyond where the - // rightmost terminator could be -- so backoff to not touch - // terminator position if need be (this can make exact alignments - // for full Doubles, but in some cases needs care not to access too - // far to the left) - - pre=-pre+2; // gap width, including "0." - t=cstart+ROUNDDOWN4(c-cstart)+pre; // preferred first target point - // backoff if too far to the right - if (t>string+DECSTRING-5) t=string+DECSTRING-5; // adjust to fit - // now shift the entire coefficient to the right, being careful not - // to access to the left of string [cannot use memcpy] - for (s=t-pre; s>=string; s-=4, t-=4) UBFROMUI(t, UBTOUI(s)); - // for Quads and Singles there may be a character or two left... - s+=3; // where next would come from - for(; s>=cstart; s--, t--) *(t+3)=*(s); - // now have fill 0. through 0.00000; use overlaps to avoid tests - if (pre>=4) { - memcpy(cstart+pre-4, "0000", 4); - memcpy(cstart, "0.00", 4); - } - else { // 2 or 3 - *(cstart+pre-1)='0'; - memcpy(cstart, "0.", 2); - } - *(c+pre)='\0'; // terminate - return string; - } // decFloatToString - -/* ------------------------------------------------------------------ */ -/* decFloatToWider -- conversion to next-wider format */ -/* */ -/* source is the decFloat format number which gets the result of */ -/* the conversion */ -/* wider is the decFloatWider format number which will be narrowed */ -/* returns wider */ -/* */ -/* Widening is always exact; no status is set (sNaNs are copied and */ -/* do not signal). The result will be canonical if the source is, */ -/* and may or may not be if the source is not. */ -/* ------------------------------------------------------------------ */ -// widening is not possible for decQuad format numbers; simply omit -#if !QUAD -decFloatWider * decFloatToWider(const decFloat *source, decFloatWider *wider) { - uInt msd; - - /* Construct and copy the sign word */ - if (DFISSPECIAL(source)) { - // copy sign, combination, and first bit of exponent (sNaN selector) - DFWWORD(wider, 0)=DFWORD(source, 0)&0xfe000000; - msd=0; - } - else { // is finite number - uInt exp=GETEXPUN(source)+DECWBIAS; // get unbiased exponent and rebias - uInt code=(exp>>DECWECONL)<<29; // set two bits of exp [msd=0] - code|=(exp<<(32-6-DECWECONL)) & 0x03ffffff; // add exponent continuation - code|=DFWORD(source, 0)&0x80000000; // add sign - DFWWORD(wider, 0)=code; // .. and place top word in wider - msd=GETMSD(source); // get source coefficient MSD [0-9] - } - /* Copy the coefficient and clear any 'unused' words to left */ - #if SINGLE - DFWWORD(wider, 1)=(DFWORD(source, 0)&0x000fffff)|(msd<<20); - #elif DOUBLE - DFWWORD(wider, 2)=(DFWORD(source, 0)&0x0003ffff)|(msd<<18); - DFWWORD(wider, 3)=DFWORD(source, 1); - DFWWORD(wider, 1)=0; - #endif - return wider; - } // decFloatToWider -#endif - -/* ------------------------------------------------------------------ */ -/* decFloatVersion -- return package version string */ -/* */ -/* returns a constant string describing this package */ -/* ------------------------------------------------------------------ */ -const char *decFloatVersion(void) { - return DECVERSION; - } // decFloatVersion - -/* ------------------------------------------------------------------ */ -/* decFloatZero -- set to canonical (integer) zero */ -/* */ -/* df is the decFloat format number to integer +0 (q=0, c=+0) */ -/* returns df */ -/* */ -/* No error is possible, and no status can be set. */ -/* ------------------------------------------------------------------ */ -decFloat * decFloatZero(decFloat *df){ - DFWORD(df, 0)=ZEROWORD; // set appropriate top word - #if DOUBLE || QUAD - DFWORD(df, 1)=0; - #if QUAD - DFWORD(df, 2)=0; - DFWORD(df, 3)=0; - #endif - #endif - // decFloatShow(df, "zero"); - return df; - } // decFloatZero - -/* ------------------------------------------------------------------ */ -/* Private generic function (not format-specific) for development use */ -/* ------------------------------------------------------------------ */ -// This is included once only, for all to use -#if QUAD && (DECCHECK || DECTRACE) - /* ---------------------------------------------------------------- */ - /* decShowNum -- display bcd8 number in debug form */ - /* */ - /* num is the bcdnum to display */ - /* tag is a string to label the display */ - /* ---------------------------------------------------------------- */ - void decShowNum(const bcdnum *num, const char *tag) { - const char *csign="+"; // sign character - uByte *ub; // work - uInt uiwork; // for macros - if (num->sign==DECFLOAT_Sign) csign="-"; - - printf(">%s> ", tag); - if (num->exponent==DECFLOAT_Inf) printf("%sInfinity", csign); - else if (num->exponent==DECFLOAT_qNaN) printf("%sqNaN", csign); - else if (num->exponent==DECFLOAT_sNaN) printf("%ssNaN", csign); - else { // finite - char qbuf[10]; // for right-aligned q - char *c; // work - const uByte *u; // .. - Int e=num->exponent; // .. exponent - strcpy(qbuf, "q="); - c=&qbuf[2]; // where exponent will go - // lay out the exponent - if (e<0) { - *c++='-'; // add '-' - e=-e; // uInt, please - } - #if DECEMAXD>4 - #error Exponent form is too long for ShowNum to lay out - #endif - if (e==0) *c++='0'; // 0-length case - else if (e<1000) { // 3 (or fewer) digits case - u=&BIN2BCD8[e*4]; // -> 3 digits + length byte - UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); // [as above] - c+=*(u+3); // bump pointer appropriately - } - else { // 4-digits - Int thou=((e>>3)*1049)>>17; // e/1000 - Int rem=e-(1000*thou); // e%1000 - *c++=(char)('0'+(char)thou); // the thousands digit - u=&BIN2BCD8[rem*4]; // -> 3 digits + length byte - UBFROMUI(c, UBTOUI(u)|CHARMASK); // copy fixed 3+1 characters [is safe] - c+=3; // bump pointer, always 3 digits - } - *c='\0'; // add terminator - printf("%7s c=%s", qbuf, csign); - } - - if (!EXPISSPECIAL(num->exponent) || num->msd!=num->lsd || *num->lsd!=0) { - for (ub=num->msd; ub<=num->lsd; ub++) { // coefficient... - printf("%1x", *ub); - if ((num->lsd-ub)%3==0 && ub!=num->lsd) printf(" "); // 4-space - } - } - printf("\n"); - } // decShowNum -#endif
src/decNumber/decContext.c
@@ -1,437 +0,0 @@-/* ------------------------------------------------------------------ */ -/* Decimal Context module */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2009. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is called decNumber.pdf. This document is */ -/* available, together with arithmetic and format specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ -/* This module comprises the routines for handling arithmetic */ -/* context structures. */ -/* ------------------------------------------------------------------ */ - -#include <string.h> // for strcmp -#include <stdio.h> // for printf if DECCHECK -#include "decContext.h" // context and base types -#include "decNumberLocal.h" // decNumber local types, etc. - -/* compile-time endian tester [assumes sizeof(Int)>1] */ -static const Int mfcone=1; // constant 1 -static const Flag *mfctop=(const Flag *)&mfcone; // -> top byte -#define LITEND *mfctop // named flag; 1=little-endian - -/* ------------------------------------------------------------------ */ -/* round-for-reround digits */ -/* ------------------------------------------------------------------ */ -const uByte DECSTICKYTAB[10]={1,1,2,3,4,6,6,7,8,9}; /* used if sticky */ - -/* ------------------------------------------------------------------ */ -/* Powers of ten (powers[n]==10**n, 0<=n<=9) */ -/* ------------------------------------------------------------------ */ -const uInt DECPOWERS[10]={1, 10, 100, 1000, 10000, 100000, 1000000, - 10000000, 100000000, 1000000000}; - -/* ------------------------------------------------------------------ */ -/* decContextClearStatus -- clear bits in current status */ -/* */ -/* context is the context structure to be queried */ -/* mask indicates the bits to be cleared (the status bit that */ -/* corresponds to each 1 bit in the mask is cleared) */ -/* returns context */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -decContext *decContextClearStatus(decContext *context, uInt mask) { - context->status&=~mask; - return context; - } // decContextClearStatus - -/* ------------------------------------------------------------------ */ -/* decContextDefault -- initialize a context structure */ -/* */ -/* context is the structure to be initialized */ -/* kind selects the required set of default values, one of: */ -/* DEC_INIT_BASE -- select ANSI X3-274 defaults */ -/* DEC_INIT_DECIMAL32 -- select IEEE 754 defaults, 32-bit */ -/* DEC_INIT_DECIMAL64 -- select IEEE 754 defaults, 64-bit */ -/* DEC_INIT_DECIMAL128 -- select IEEE 754 defaults, 128-bit */ -/* For any other value a valid context is returned, but with */ -/* Invalid_operation set in the status field. */ -/* returns a context structure with the appropriate initial values. */ -/* ------------------------------------------------------------------ */ -decContext * decContextDefault(decContext *context, Int kind) { - // set defaults... - context->digits=9; // 9 digits - context->emax=DEC_MAX_EMAX; // 9-digit exponents - context->emin=DEC_MIN_EMIN; // .. balanced - context->round=DEC_ROUND_HALF_UP; // 0.5 rises - context->traps=DEC_Errors; // all but informational - context->status=0; // cleared - context->clamp=0; // no clamping - #if DECSUBSET - context->extended=0; // cleared - #endif - switch (kind) { - case DEC_INIT_BASE: - // [use defaults] - break; - case DEC_INIT_DECIMAL32: - context->digits=7; // digits - context->emax=96; // Emax - context->emin=-95; // Emin - context->round=DEC_ROUND_HALF_EVEN; // 0.5 to nearest even - context->traps=0; // no traps set - context->clamp=1; // clamp exponents - #if DECSUBSET - context->extended=1; // set - #endif - break; - case DEC_INIT_DECIMAL64: - context->digits=16; // digits - context->emax=384; // Emax - context->emin=-383; // Emin - context->round=DEC_ROUND_HALF_EVEN; // 0.5 to nearest even - context->traps=0; // no traps set - context->clamp=1; // clamp exponents - #if DECSUBSET - context->extended=1; // set - #endif - break; - case DEC_INIT_DECIMAL128: - context->digits=34; // digits - context->emax=6144; // Emax - context->emin=-6143; // Emin - context->round=DEC_ROUND_HALF_EVEN; // 0.5 to nearest even - context->traps=0; // no traps set - context->clamp=1; // clamp exponents - #if DECSUBSET - context->extended=1; // set - #endif - break; - - default: // invalid Kind - // use defaults, and .. - decContextSetStatus(context, DEC_Invalid_operation); // trap - } - - return context;} // decContextDefault - -/* ------------------------------------------------------------------ */ -/* decContextGetRounding -- return current rounding mode */ -/* */ -/* context is the context structure to be queried */ -/* returns the rounding mode */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -enum rounding decContextGetRounding(decContext *context) { - return context->round; - } // decContextGetRounding - -/* ------------------------------------------------------------------ */ -/* decContextGetStatus -- return current status */ -/* */ -/* context is the context structure to be queried */ -/* returns status */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -uInt decContextGetStatus(decContext *context) { - return context->status; - } // decContextGetStatus - -/* ------------------------------------------------------------------ */ -/* decContextRestoreStatus -- restore bits in current status */ -/* */ -/* context is the context structure to be updated */ -/* newstatus is the source for the bits to be restored */ -/* mask indicates the bits to be restored (the status bit that */ -/* corresponds to each 1 bit in the mask is set to the value of */ -/* the correspnding bit in newstatus) */ -/* returns context */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -decContext *decContextRestoreStatus(decContext *context, - uInt newstatus, uInt mask) { - context->status&=~mask; // clear the selected bits - context->status|=(mask&newstatus); // or in the new bits - return context; - } // decContextRestoreStatus - -/* ------------------------------------------------------------------ */ -/* decContextSaveStatus -- save bits in current status */ -/* */ -/* context is the context structure to be queried */ -/* mask indicates the bits to be saved (the status bits that */ -/* correspond to each 1 bit in the mask are saved) */ -/* returns the AND of the mask and the current status */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -uInt decContextSaveStatus(decContext *context, uInt mask) { - return context->status&mask; - } // decContextSaveStatus - -/* ------------------------------------------------------------------ */ -/* decContextSetRounding -- set current rounding mode */ -/* */ -/* context is the context structure to be updated */ -/* newround is the value which will replace the current mode */ -/* returns context */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -decContext *decContextSetRounding(decContext *context, - enum rounding newround) { - context->round=newround; - return context; - } // decContextSetRounding - -/* ------------------------------------------------------------------ */ -/* decContextSetStatus -- set status and raise trap if appropriate */ -/* */ -/* context is the context structure to be updated */ -/* status is the DEC_ exception code */ -/* returns the context structure */ -/* */ -/* Control may never return from this routine, if there is a signal */ -/* handler and it takes a long jump. */ -/* ------------------------------------------------------------------ */ -decContext * decContextSetStatus(decContext *context, uInt status) { - context->status|=status; - if (status & context->traps) raise(SIGFPE); - return context;} // decContextSetStatus - -/* ------------------------------------------------------------------ */ -/* decContextSetStatusFromString -- set status from a string + trap */ -/* */ -/* context is the context structure to be updated */ -/* string is a string exactly equal to one that might be returned */ -/* by decContextStatusToString */ -/* */ -/* The status bit corresponding to the string is set, and a trap */ -/* is raised if appropriate. */ -/* */ -/* returns the context structure, unless the string is equal to */ -/* DEC_Condition_MU or is not recognized. In these cases NULL is */ -/* returned. */ -/* ------------------------------------------------------------------ */ -decContext * decContextSetStatusFromString(decContext *context, - const char *string) { - if (strcmp(string, DEC_Condition_CS)==0) - return decContextSetStatus(context, DEC_Conversion_syntax); - if (strcmp(string, DEC_Condition_DZ)==0) - return decContextSetStatus(context, DEC_Division_by_zero); - if (strcmp(string, DEC_Condition_DI)==0) - return decContextSetStatus(context, DEC_Division_impossible); - if (strcmp(string, DEC_Condition_DU)==0) - return decContextSetStatus(context, DEC_Division_undefined); - if (strcmp(string, DEC_Condition_IE)==0) - return decContextSetStatus(context, DEC_Inexact); - if (strcmp(string, DEC_Condition_IS)==0) - return decContextSetStatus(context, DEC_Insufficient_storage); - if (strcmp(string, DEC_Condition_IC)==0) - return decContextSetStatus(context, DEC_Invalid_context); - if (strcmp(string, DEC_Condition_IO)==0) - return decContextSetStatus(context, DEC_Invalid_operation); - #if DECSUBSET - if (strcmp(string, DEC_Condition_LD)==0) - return decContextSetStatus(context, DEC_Lost_digits); - #endif - if (strcmp(string, DEC_Condition_OV)==0) - return decContextSetStatus(context, DEC_Overflow); - if (strcmp(string, DEC_Condition_PA)==0) - return decContextSetStatus(context, DEC_Clamped); - if (strcmp(string, DEC_Condition_RO)==0) - return decContextSetStatus(context, DEC_Rounded); - if (strcmp(string, DEC_Condition_SU)==0) - return decContextSetStatus(context, DEC_Subnormal); - if (strcmp(string, DEC_Condition_UN)==0) - return decContextSetStatus(context, DEC_Underflow); - if (strcmp(string, DEC_Condition_ZE)==0) - return context; - return NULL; // Multiple status, or unknown - } // decContextSetStatusFromString - -/* ------------------------------------------------------------------ */ -/* decContextSetStatusFromStringQuiet -- set status from a string */ -/* */ -/* context is the context structure to be updated */ -/* string is a string exactly equal to one that might be returned */ -/* by decContextStatusToString */ -/* */ -/* The status bit corresponding to the string is set; no trap is */ -/* raised. */ -/* */ -/* returns the context structure, unless the string is equal to */ -/* DEC_Condition_MU or is not recognized. In these cases NULL is */ -/* returned. */ -/* ------------------------------------------------------------------ */ -decContext * decContextSetStatusFromStringQuiet(decContext *context, - const char *string) { - if (strcmp(string, DEC_Condition_CS)==0) - return decContextSetStatusQuiet(context, DEC_Conversion_syntax); - if (strcmp(string, DEC_Condition_DZ)==0) - return decContextSetStatusQuiet(context, DEC_Division_by_zero); - if (strcmp(string, DEC_Condition_DI)==0) - return decContextSetStatusQuiet(context, DEC_Division_impossible); - if (strcmp(string, DEC_Condition_DU)==0) - return decContextSetStatusQuiet(context, DEC_Division_undefined); - if (strcmp(string, DEC_Condition_IE)==0) - return decContextSetStatusQuiet(context, DEC_Inexact); - if (strcmp(string, DEC_Condition_IS)==0) - return decContextSetStatusQuiet(context, DEC_Insufficient_storage); - if (strcmp(string, DEC_Condition_IC)==0) - return decContextSetStatusQuiet(context, DEC_Invalid_context); - if (strcmp(string, DEC_Condition_IO)==0) - return decContextSetStatusQuiet(context, DEC_Invalid_operation); - #if DECSUBSET - if (strcmp(string, DEC_Condition_LD)==0) - return decContextSetStatusQuiet(context, DEC_Lost_digits); - #endif - if (strcmp(string, DEC_Condition_OV)==0) - return decContextSetStatusQuiet(context, DEC_Overflow); - if (strcmp(string, DEC_Condition_PA)==0) - return decContextSetStatusQuiet(context, DEC_Clamped); - if (strcmp(string, DEC_Condition_RO)==0) - return decContextSetStatusQuiet(context, DEC_Rounded); - if (strcmp(string, DEC_Condition_SU)==0) - return decContextSetStatusQuiet(context, DEC_Subnormal); - if (strcmp(string, DEC_Condition_UN)==0) - return decContextSetStatusQuiet(context, DEC_Underflow); - if (strcmp(string, DEC_Condition_ZE)==0) - return context; - return NULL; // Multiple status, or unknown - } // decContextSetStatusFromStringQuiet - -/* ------------------------------------------------------------------ */ -/* decContextSetStatusQuiet -- set status without trap */ -/* */ -/* context is the context structure to be updated */ -/* status is the DEC_ exception code */ -/* returns the context structure */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -decContext * decContextSetStatusQuiet(decContext *context, uInt status) { - context->status|=status; - return context;} // decContextSetStatusQuiet - -/* ------------------------------------------------------------------ */ -/* decContextStatusToString -- convert status flags to a string */ -/* */ -/* context is a context with valid status field */ -/* */ -/* returns a constant string describing the condition. If multiple */ -/* (or no) flags are set, a generic constant message is returned. */ -/* ------------------------------------------------------------------ */ -const char *decContextStatusToString(const decContext *context) { - Int status=context->status; - - // test the five IEEE first, as some of the others are ambiguous when - // DECEXTFLAG=0 - if (status==DEC_Invalid_operation ) return DEC_Condition_IO; - if (status==DEC_Division_by_zero ) return DEC_Condition_DZ; - if (status==DEC_Overflow ) return DEC_Condition_OV; - if (status==DEC_Underflow ) return DEC_Condition_UN; - if (status==DEC_Inexact ) return DEC_Condition_IE; - - if (status==DEC_Division_impossible ) return DEC_Condition_DI; - if (status==DEC_Division_undefined ) return DEC_Condition_DU; - if (status==DEC_Rounded ) return DEC_Condition_RO; - if (status==DEC_Clamped ) return DEC_Condition_PA; - if (status==DEC_Subnormal ) return DEC_Condition_SU; - if (status==DEC_Conversion_syntax ) return DEC_Condition_CS; - if (status==DEC_Insufficient_storage ) return DEC_Condition_IS; - if (status==DEC_Invalid_context ) return DEC_Condition_IC; - #if DECSUBSET - if (status==DEC_Lost_digits ) return DEC_Condition_LD; - #endif - if (status==0 ) return DEC_Condition_ZE; - return DEC_Condition_MU; // Multiple errors - } // decContextStatusToString - -/* ------------------------------------------------------------------ */ -/* decContextTestEndian -- test whether DECLITEND is set correctly */ -/* */ -/* quiet is 1 to suppress message; 0 otherwise */ -/* returns 0 if DECLITEND is correct */ -/* 1 if DECLITEND is incorrect and should be 1 */ -/* -1 if DECLITEND is incorrect and should be 0 */ -/* */ -/* A message is displayed if the return value is not 0 and quiet==0. */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -Int decContextTestEndian(Flag quiet) { - Int res=0; // optimist - uInt dle=(uInt)DECLITEND; // unsign - if (dle>1) dle=1; // ensure 0 or 1 - - if (LITEND!=DECLITEND) { - if (!quiet) { // always refer to this - #if DECPRINT - const char *adj; - if (LITEND) adj="little"; - else adj="big"; - printf("Warning: DECLITEND is set to %d, but this computer appears to be %s-endian\n", - DECLITEND, adj); - #endif - } - res=(Int)LITEND-dle; - } - return res; - } // decContextTestEndian - -/* ------------------------------------------------------------------ */ -/* decContextTestSavedStatus -- test bits in saved status */ -/* */ -/* oldstatus is the status word to be tested */ -/* mask indicates the bits to be tested (the oldstatus bits that */ -/* correspond to each 1 bit in the mask are tested) */ -/* returns 1 if any of the tested bits are 1, or 0 otherwise */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -uInt decContextTestSavedStatus(uInt oldstatus, uInt mask) { - return (oldstatus&mask)!=0; - } // decContextTestSavedStatus - -/* ------------------------------------------------------------------ */ -/* decContextTestStatus -- test bits in current status */ -/* */ -/* context is the context structure to be updated */ -/* mask indicates the bits to be tested (the status bits that */ -/* correspond to each 1 bit in the mask are tested) */ -/* returns 1 if any of the tested bits are 1, or 0 otherwise */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -uInt decContextTestStatus(decContext *context, uInt mask) { - return (context->status&mask)!=0; - } // decContextTestStatus - -/* ------------------------------------------------------------------ */ -/* decContextZeroStatus -- clear all status bits */ -/* */ -/* context is the context structure to be updated */ -/* returns context */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -decContext *decContextZeroStatus(decContext *context) { - context->status=0; - return context; - } // decContextZeroStatus -
src/decNumber/decContext.h
@@ -1,254 +0,0 @@-/* ------------------------------------------------------------------ */ -/* Decimal Context module header */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is called decNumber.pdf. This document is */ -/* available, together with arithmetic and format specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ -/* */ -/* Context variables must always have valid values: */ -/* */ -/* status -- [any bits may be cleared, but not set, by user] */ -/* round -- must be one of the enumerated rounding modes */ -/* */ -/* The following variables are implied for fixed size formats (i.e., */ -/* they are ignored) but should still be set correctly in case used */ -/* with decNumber functions: */ -/* */ -/* clamp -- must be either 0 or 1 */ -/* digits -- must be in the range 1 through 999999999 */ -/* emax -- must be in the range 0 through 999999999 */ -/* emin -- must be in the range 0 through -999999999 */ -/* extended -- must be either 0 or 1 [present only if DECSUBSET] */ -/* traps -- only defined bits may be set */ -/* */ -/* ------------------------------------------------------------------ */ - -#if !defined(DECCONTEXT) - #define DECCONTEXT - #define DECCNAME "decContext" /* Short name */ - #define DECCFULLNAME "Decimal Context Descriptor" /* Verbose name */ - #define DECCAUTHOR "Mike Cowlishaw" /* Who to blame */ - - #if !defined(int32_t) - #include <stdint.h> /* C99 standard integers */ - #endif - #include <stdio.h> /* for printf, etc. */ - #include <signal.h> /* for traps */ - - /* Extended flags setting -- set this to 0 to use only IEEE flags */ - #if !defined(DECEXTFLAG) - #define DECEXTFLAG 1 /* 1=enable extended flags */ - #endif - - /* Conditional code flag -- set this to 0 for best performance */ - #if !defined(DECSUBSET) - #define DECSUBSET 0 /* 1=enable subset arithmetic */ - #endif - - /* Context for operations, with associated constants */ - enum rounding { - DEC_ROUND_CEILING, /* round towards +infinity */ - DEC_ROUND_UP, /* round away from 0 */ - DEC_ROUND_HALF_UP, /* 0.5 rounds up */ - DEC_ROUND_HALF_EVEN, /* 0.5 rounds to nearest even */ - DEC_ROUND_HALF_DOWN, /* 0.5 rounds down */ - DEC_ROUND_DOWN, /* round towards 0 (truncate) */ - DEC_ROUND_FLOOR, /* round towards -infinity */ - DEC_ROUND_05UP, /* round for reround */ - DEC_ROUND_MAX /* enum must be less than this */ - }; - #define DEC_ROUND_DEFAULT DEC_ROUND_HALF_EVEN; - - typedef struct { - int32_t digits; /* working precision */ - int32_t emax; /* maximum positive exponent */ - int32_t emin; /* minimum negative exponent */ - enum rounding round; /* rounding mode */ - uint32_t traps; /* trap-enabler flags */ - uint32_t status; /* status flags */ - uint8_t clamp; /* flag: apply IEEE exponent clamp */ - #if DECSUBSET - uint8_t extended; /* flag: special-values allowed */ - #endif - } decContext; - - /* Maxima and Minima for context settings */ - #define DEC_MAX_DIGITS 999999999 - #define DEC_MIN_DIGITS 1 - #define DEC_MAX_EMAX 999999999 - #define DEC_MIN_EMAX 0 - #define DEC_MAX_EMIN 0 - #define DEC_MIN_EMIN -999999999 - #define DEC_MAX_MATH 999999 /* max emax, etc., for math funcs. */ - - /* Classifications for decimal numbers, aligned with 754 (note that */ - /* 'normal' and 'subnormal' are meaningful only with a decContext */ - /* or a fixed size format). */ - enum decClass { - DEC_CLASS_SNAN, - DEC_CLASS_QNAN, - DEC_CLASS_NEG_INF, - DEC_CLASS_NEG_NORMAL, - DEC_CLASS_NEG_SUBNORMAL, - DEC_CLASS_NEG_ZERO, - DEC_CLASS_POS_ZERO, - DEC_CLASS_POS_SUBNORMAL, - DEC_CLASS_POS_NORMAL, - DEC_CLASS_POS_INF - }; - /* Strings for the decClasses */ - #define DEC_ClassString_SN "sNaN" - #define DEC_ClassString_QN "NaN" - #define DEC_ClassString_NI "-Infinity" - #define DEC_ClassString_NN "-Normal" - #define DEC_ClassString_NS "-Subnormal" - #define DEC_ClassString_NZ "-Zero" - #define DEC_ClassString_PZ "+Zero" - #define DEC_ClassString_PS "+Subnormal" - #define DEC_ClassString_PN "+Normal" - #define DEC_ClassString_PI "+Infinity" - #define DEC_ClassString_UN "Invalid" - - /* Trap-enabler and Status flags (exceptional conditions), and */ - /* their names. The top byte is reserved for internal use */ - #if DECEXTFLAG - /* Extended flags */ - #define DEC_Conversion_syntax 0x00000001 - #define DEC_Division_by_zero 0x00000002 - #define DEC_Division_impossible 0x00000004 - #define DEC_Division_undefined 0x00000008 - #define DEC_Insufficient_storage 0x00000010 /* [when malloc fails] */ - #define DEC_Inexact 0x00000020 - #define DEC_Invalid_context 0x00000040 - #define DEC_Invalid_operation 0x00000080 - #if DECSUBSET - #define DEC_Lost_digits 0x00000100 - #endif - #define DEC_Overflow 0x00000200 - #define DEC_Clamped 0x00000400 - #define DEC_Rounded 0x00000800 - #define DEC_Subnormal 0x00001000 - #define DEC_Underflow 0x00002000 - #else - /* IEEE flags only */ - #define DEC_Conversion_syntax 0x00000010 - #define DEC_Division_by_zero 0x00000002 - #define DEC_Division_impossible 0x00000010 - #define DEC_Division_undefined 0x00000010 - #define DEC_Insufficient_storage 0x00000010 /* [when malloc fails] */ - #define DEC_Inexact 0x00000001 - #define DEC_Invalid_context 0x00000010 - #define DEC_Invalid_operation 0x00000010 - #if DECSUBSET - #define DEC_Lost_digits 0x00000000 - #endif - #define DEC_Overflow 0x00000008 - #define DEC_Clamped 0x00000000 - #define DEC_Rounded 0x00000000 - #define DEC_Subnormal 0x00000000 - #define DEC_Underflow 0x00000004 - #endif - - /* IEEE 754 groupings for the flags */ - /* [DEC_Clamped, DEC_Lost_digits, DEC_Rounded, and DEC_Subnormal */ - /* are not in IEEE 754] */ - #define DEC_IEEE_754_Division_by_zero (DEC_Division_by_zero) - #if DECSUBSET - #define DEC_IEEE_754_Inexact (DEC_Inexact | DEC_Lost_digits) - #else - #define DEC_IEEE_754_Inexact (DEC_Inexact) - #endif - #define DEC_IEEE_754_Invalid_operation (DEC_Conversion_syntax | \ - DEC_Division_impossible | \ - DEC_Division_undefined | \ - DEC_Insufficient_storage | \ - DEC_Invalid_context | \ - DEC_Invalid_operation) - #define DEC_IEEE_754_Overflow (DEC_Overflow) - #define DEC_IEEE_754_Underflow (DEC_Underflow) - - /* flags which are normally errors (result is qNaN, infinite, or 0) */ - #define DEC_Errors (DEC_IEEE_754_Division_by_zero | \ - DEC_IEEE_754_Invalid_operation | \ - DEC_IEEE_754_Overflow | DEC_IEEE_754_Underflow) - /* flags which cause a result to become qNaN */ - #define DEC_NaNs DEC_IEEE_754_Invalid_operation - - /* flags which are normally for information only (finite results) */ - #if DECSUBSET - #define DEC_Information (DEC_Clamped | DEC_Rounded | DEC_Inexact \ - | DEC_Lost_digits) - #else - #define DEC_Information (DEC_Clamped | DEC_Rounded | DEC_Inexact) - #endif - - /* IEEE 854 names (for compatibility with older decNumber versions) */ - #define DEC_IEEE_854_Division_by_zero DEC_IEEE_754_Division_by_zero - #define DEC_IEEE_854_Inexact DEC_IEEE_754_Inexact - #define DEC_IEEE_854_Invalid_operation DEC_IEEE_754_Invalid_operation - #define DEC_IEEE_854_Overflow DEC_IEEE_754_Overflow - #define DEC_IEEE_854_Underflow DEC_IEEE_754_Underflow - - /* Name strings for the exceptional conditions */ - #define DEC_Condition_CS "Conversion syntax" - #define DEC_Condition_DZ "Division by zero" - #define DEC_Condition_DI "Division impossible" - #define DEC_Condition_DU "Division undefined" - #define DEC_Condition_IE "Inexact" - #define DEC_Condition_IS "Insufficient storage" - #define DEC_Condition_IC "Invalid context" - #define DEC_Condition_IO "Invalid operation" - #if DECSUBSET - #define DEC_Condition_LD "Lost digits" - #endif - #define DEC_Condition_OV "Overflow" - #define DEC_Condition_PA "Clamped" - #define DEC_Condition_RO "Rounded" - #define DEC_Condition_SU "Subnormal" - #define DEC_Condition_UN "Underflow" - #define DEC_Condition_ZE "No status" - #define DEC_Condition_MU "Multiple status" - #define DEC_Condition_Length 21 /* length of the longest string, */ - /* including terminator */ - - /* Initialization descriptors, used by decContextDefault */ - #define DEC_INIT_BASE 0 - #define DEC_INIT_DECIMAL32 32 - #define DEC_INIT_DECIMAL64 64 - #define DEC_INIT_DECIMAL128 128 - /* Synonyms */ - #define DEC_INIT_DECSINGLE DEC_INIT_DECIMAL32 - #define DEC_INIT_DECDOUBLE DEC_INIT_DECIMAL64 - #define DEC_INIT_DECQUAD DEC_INIT_DECIMAL128 - - /* decContext routines */ - extern decContext * decContextClearStatus(decContext *, uint32_t); - extern decContext * decContextDefault(decContext *, int32_t); - extern enum rounding decContextGetRounding(decContext *); - extern uint32_t decContextGetStatus(decContext *); - extern decContext * decContextRestoreStatus(decContext *, uint32_t, uint32_t); - extern uint32_t decContextSaveStatus(decContext *, uint32_t); - extern decContext * decContextSetRounding(decContext *, enum rounding); - extern decContext * decContextSetStatus(decContext *, uint32_t); - extern decContext * decContextSetStatusFromString(decContext *, const char *); - extern decContext * decContextSetStatusFromStringQuiet(decContext *, const char *); - extern decContext * decContextSetStatusQuiet(decContext *, uint32_t); - extern const char * decContextStatusToString(const decContext *); - extern int32_t decContextTestEndian(uint8_t); - extern uint32_t decContextTestSavedStatus(uint32_t, uint32_t); - extern uint32_t decContextTestStatus(decContext *, uint32_t); - extern decContext * decContextZeroStatus(decContext *); - -#endif
src/decNumber/decDPD.h
@@ -1,1185 +0,0 @@-/* ------------------------------------------------------------------------ */ -/* Binary Coded Decimal and Densely Packed Decimal conversion lookup tables */ -/* [Automatically generated -- do not edit. 2008.06.21] */ -/* ------------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2008. All rights reserved. */ -/* ------------------------------------------------------------------------ */ -/* For details, see DPDecimal.html on the General Decimal Arithmetic page. */ -/* */ -/* This include file defines several DPD and BCD conversion tables: */ -/* */ -/* uint16_t BCD2DPD[2458]; -- BCD -> DPD (0x999 => 2457) */ -/* uint16_t BIN2DPD[1000]; -- Bin -> DPD (999 => 2457) */ -/* uint8_t BIN2CHAR[4001]; -- Bin -> CHAR (999 => '\3' '9' '9' '9') */ -/* uint8_t BIN2BCD8[4000]; -- Bin -> bytes (999 => 9 9 9 3) */ -/* uint16_t DPD2BCD[1024]; -- DPD -> BCD (0x3FF => 0x999) */ -/* uint16_t DPD2BIN[1024]; -- DPD -> BIN (0x3FF => 999) */ -/* uint32_t DPD2BINK[1024]; -- DPD -> BIN * 1000 (0x3FF => 999000) */ -/* uint32_t DPD2BINM[1024]; -- DPD -> BIN * 1E+6 (0x3FF => 999000000) */ -/* uint8_t DPD2BCD8[4096]; -- DPD -> bytes (x3FF => 9 9 9 3) */ -/* */ -/* In all cases the result (10 bits or 12 bits, or binary) is right-aligned */ -/* in the table entry. BIN2CHAR entries are a single byte length (0 for */ -/* value 0) followed by three digit characters; a trailing terminator is */ -/* included to allow 4-char moves always. BIN2BCD8 and DPD2BCD8 entries */ -/* are similar with the three BCD8 digits followed by a one-byte length */ -/* (again, length=0 for value 0). */ -/* */ -/* To use a table, its name, prefixed with DEC_, must be defined with a */ -/* value of 1 before this header file is included. For example: */ -/* #define DEC_BCD2DPD 1 */ -/* This mechanism allows software to only include tables that are needed. */ -/* ------------------------------------------------------------------------ */ - -#if defined(DEC_BCD2DPD) && DEC_BCD2DPD==1 && !defined(DECBCD2DPD) -#define DECBCD2DPD - -const uint16_t BCD2DPD[2458]={ 0, 1, 2, 3, 4, 5, 6, 7, - 8, 9, 0, 0, 0, 0, 0, 0, 16, 17, 18, 19, 20, - 21, 22, 23, 24, 25, 0, 0, 0, 0, 0, 0, 32, 33, - 34, 35, 36, 37, 38, 39, 40, 41, 0, 0, 0, 0, 0, - 0, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 0, 0, - 0, 0, 0, 0, 64, 65, 66, 67, 68, 69, 70, 71, 72, - 73, 0, 0, 0, 0, 0, 0, 80, 81, 82, 83, 84, 85, - 86, 87, 88, 89, 0, 0, 0, 0, 0, 0, 96, 97, 98, - 99, 100, 101, 102, 103, 104, 105, 0, 0, 0, 0, 0, 0, - 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 0, 0, 0, - 0, 0, 0, 10, 11, 42, 43, 74, 75, 106, 107, 78, 79, - 0, 0, 0, 0, 0, 0, 26, 27, 58, 59, 90, 91, 122, - 123, 94, 95, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 0, 0, - 0, 0, 0, 0, 144, 145, 146, 147, 148, 149, 150, 151, 152, - 153, 0, 0, 0, 0, 0, 0, 160, 161, 162, 163, 164, 165, - 166, 167, 168, 169, 0, 0, 0, 0, 0, 0, 176, 177, 178, - 179, 180, 181, 182, 183, 184, 185, 0, 0, 0, 0, 0, 0, - 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 0, 0, 0, - 0, 0, 0, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, - 0, 0, 0, 0, 0, 0, 224, 225, 226, 227, 228, 229, 230, - 231, 232, 233, 0, 0, 0, 0, 0, 0, 240, 241, 242, 243, - 244, 245, 246, 247, 248, 249, 0, 0, 0, 0, 0, 0, 138, - 139, 170, 171, 202, 203, 234, 235, 206, 207, 0, 0, 0, 0, - 0, 0, 154, 155, 186, 187, 218, 219, 250, 251, 222, 223, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 256, 257, 258, - 259, 260, 261, 262, 263, 264, 265, 0, 0, 0, 0, 0, 0, - 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 0, 0, 0, - 0, 0, 0, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, - 0, 0, 0, 0, 0, 0, 304, 305, 306, 307, 308, 309, 310, - 311, 312, 313, 0, 0, 0, 0, 0, 0, 320, 321, 322, 323, - 324, 325, 326, 327, 328, 329, 0, 0, 0, 0, 0, 0, 336, - 337, 338, 339, 340, 341, 342, 343, 344, 345, 0, 0, 0, 0, - 0, 0, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 0, - 0, 0, 0, 0, 0, 368, 369, 370, 371, 372, 373, 374, 375, - 376, 377, 0, 0, 0, 0, 0, 0, 266, 267, 298, 299, 330, - 331, 362, 363, 334, 335, 0, 0, 0, 0, 0, 0, 282, 283, - 314, 315, 346, 347, 378, 379, 350, 351, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 384, 385, 386, 387, 388, 389, 390, - 391, 392, 393, 0, 0, 0, 0, 0, 0, 400, 401, 402, 403, - 404, 405, 406, 407, 408, 409, 0, 0, 0, 0, 0, 0, 416, - 417, 418, 419, 420, 421, 422, 423, 424, 425, 0, 0, 0, 0, - 0, 0, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 0, - 0, 0, 0, 0, 0, 448, 449, 450, 451, 452, 453, 454, 455, - 456, 457, 0, 0, 0, 0, 0, 0, 464, 465, 466, 467, 468, - 469, 470, 471, 472, 473, 0, 0, 0, 0, 0, 0, 480, 481, - 482, 483, 484, 485, 486, 487, 488, 489, 0, 0, 0, 0, 0, - 0, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 0, 0, - 0, 0, 0, 0, 394, 395, 426, 427, 458, 459, 490, 491, 462, - 463, 0, 0, 0, 0, 0, 0, 410, 411, 442, 443, 474, 475, - 506, 507, 478, 479, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 0, - 0, 0, 0, 0, 0, 528, 529, 530, 531, 532, 533, 534, 535, - 536, 537, 0, 0, 0, 0, 0, 0, 544, 545, 546, 547, 548, - 549, 550, 551, 552, 553, 0, 0, 0, 0, 0, 0, 560, 561, - 562, 563, 564, 565, 566, 567, 568, 569, 0, 0, 0, 0, 0, - 0, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 0, 0, - 0, 0, 0, 0, 592, 593, 594, 595, 596, 597, 598, 599, 600, - 601, 0, 0, 0, 0, 0, 0, 608, 609, 610, 611, 612, 613, - 614, 615, 616, 617, 0, 0, 0, 0, 0, 0, 624, 625, 626, - 627, 628, 629, 630, 631, 632, 633, 0, 0, 0, 0, 0, 0, - 522, 523, 554, 555, 586, 587, 618, 619, 590, 591, 0, 0, 0, - 0, 0, 0, 538, 539, 570, 571, 602, 603, 634, 635, 606, 607, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 640, 641, - 642, 643, 644, 645, 646, 647, 648, 649, 0, 0, 0, 0, 0, - 0, 656, 657, 658, 659, 660, 661, 662, 663, 664, 665, 0, 0, - 0, 0, 0, 0, 672, 673, 674, 675, 676, 677, 678, 679, 680, - 681, 0, 0, 0, 0, 0, 0, 688, 689, 690, 691, 692, 693, - 694, 695, 696, 697, 0, 0, 0, 0, 0, 0, 704, 705, 706, - 707, 708, 709, 710, 711, 712, 713, 0, 0, 0, 0, 0, 0, - 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 0, 0, 0, - 0, 0, 0, 736, 737, 738, 739, 740, 741, 742, 743, 744, 745, - 0, 0, 0, 0, 0, 0, 752, 753, 754, 755, 756, 757, 758, - 759, 760, 761, 0, 0, 0, 0, 0, 0, 650, 651, 682, 683, - 714, 715, 746, 747, 718, 719, 0, 0, 0, 0, 0, 0, 666, - 667, 698, 699, 730, 731, 762, 763, 734, 735, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 768, 769, 770, 771, 772, 773, - 774, 775, 776, 777, 0, 0, 0, 0, 0, 0, 784, 785, 786, - 787, 788, 789, 790, 791, 792, 793, 0, 0, 0, 0, 0, 0, - 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 0, 0, 0, - 0, 0, 0, 816, 817, 818, 819, 820, 821, 822, 823, 824, 825, - 0, 0, 0, 0, 0, 0, 832, 833, 834, 835, 836, 837, 838, - 839, 840, 841, 0, 0, 0, 0, 0, 0, 848, 849, 850, 851, - 852, 853, 854, 855, 856, 857, 0, 0, 0, 0, 0, 0, 864, - 865, 866, 867, 868, 869, 870, 871, 872, 873, 0, 0, 0, 0, - 0, 0, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 0, - 0, 0, 0, 0, 0, 778, 779, 810, 811, 842, 843, 874, 875, - 846, 847, 0, 0, 0, 0, 0, 0, 794, 795, 826, 827, 858, - 859, 890, 891, 862, 863, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 896, 897, 898, 899, 900, 901, 902, 903, 904, 905, - 0, 0, 0, 0, 0, 0, 912, 913, 914, 915, 916, 917, 918, - 919, 920, 921, 0, 0, 0, 0, 0, 0, 928, 929, 930, 931, - 932, 933, 934, 935, 936, 937, 0, 0, 0, 0, 0, 0, 944, - 945, 946, 947, 948, 949, 950, 951, 952, 953, 0, 0, 0, 0, - 0, 0, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 0, - 0, 0, 0, 0, 0, 976, 977, 978, 979, 980, 981, 982, 983, - 984, 985, 0, 0, 0, 0, 0, 0, 992, 993, 994, 995, 996, - 997, 998, 999, 1000, 1001, 0, 0, 0, 0, 0, 0, 1008, 1009, - 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 0, 0, 0, 0, 0, - 0, 906, 907, 938, 939, 970, 971, 1002, 1003, 974, 975, 0, 0, - 0, 0, 0, 0, 922, 923, 954, 955, 986, 987, 1018, 1019, 990, - 991, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, - 13, 268, 269, 524, 525, 780, 781, 46, 47, 0, 0, 0, 0, - 0, 0, 28, 29, 284, 285, 540, 541, 796, 797, 62, 63, 0, - 0, 0, 0, 0, 0, 44, 45, 300, 301, 556, 557, 812, 813, - 302, 303, 0, 0, 0, 0, 0, 0, 60, 61, 316, 317, 572, - 573, 828, 829, 318, 319, 0, 0, 0, 0, 0, 0, 76, 77, - 332, 333, 588, 589, 844, 845, 558, 559, 0, 0, 0, 0, 0, - 0, 92, 93, 348, 349, 604, 605, 860, 861, 574, 575, 0, 0, - 0, 0, 0, 0, 108, 109, 364, 365, 620, 621, 876, 877, 814, - 815, 0, 0, 0, 0, 0, 0, 124, 125, 380, 381, 636, 637, - 892, 893, 830, 831, 0, 0, 0, 0, 0, 0, 14, 15, 270, - 271, 526, 527, 782, 783, 110, 111, 0, 0, 0, 0, 0, 0, - 30, 31, 286, 287, 542, 543, 798, 799, 126, 127, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 140, 141, 396, 397, 652, - 653, 908, 909, 174, 175, 0, 0, 0, 0, 0, 0, 156, 157, - 412, 413, 668, 669, 924, 925, 190, 191, 0, 0, 0, 0, 0, - 0, 172, 173, 428, 429, 684, 685, 940, 941, 430, 431, 0, 0, - 0, 0, 0, 0, 188, 189, 444, 445, 700, 701, 956, 957, 446, - 447, 0, 0, 0, 0, 0, 0, 204, 205, 460, 461, 716, 717, - 972, 973, 686, 687, 0, 0, 0, 0, 0, 0, 220, 221, 476, - 477, 732, 733, 988, 989, 702, 703, 0, 0, 0, 0, 0, 0, - 236, 237, 492, 493, 748, 749, 1004, 1005, 942, 943, 0, 0, 0, - 0, 0, 0, 252, 253, 508, 509, 764, 765, 1020, 1021, 958, 959, - 0, 0, 0, 0, 0, 0, 142, 143, 398, 399, 654, 655, 910, - 911, 238, 239, 0, 0, 0, 0, 0, 0, 158, 159, 414, 415, - 670, 671, 926, 927, 254, 255}; -#endif - -#if defined(DEC_DPD2BCD) && DEC_DPD2BCD==1 && !defined(DECDPD2BCD) -#define DECDPD2BCD - -const uint16_t DPD2BCD[1024]={ 0, 1, 2, 3, 4, 5, 6, 7, - 8, 9, 128, 129, 2048, 2049, 2176, 2177, 16, 17, 18, 19, 20, - 21, 22, 23, 24, 25, 144, 145, 2064, 2065, 2192, 2193, 32, 33, - 34, 35, 36, 37, 38, 39, 40, 41, 130, 131, 2080, 2081, 2056, - 2057, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 146, 147, - 2096, 2097, 2072, 2073, 64, 65, 66, 67, 68, 69, 70, 71, 72, - 73, 132, 133, 2112, 2113, 136, 137, 80, 81, 82, 83, 84, 85, - 86, 87, 88, 89, 148, 149, 2128, 2129, 152, 153, 96, 97, 98, - 99, 100, 101, 102, 103, 104, 105, 134, 135, 2144, 2145, 2184, 2185, - 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 150, 151, 2160, - 2161, 2200, 2201, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, - 384, 385, 2304, 2305, 2432, 2433, 272, 273, 274, 275, 276, 277, 278, - 279, 280, 281, 400, 401, 2320, 2321, 2448, 2449, 288, 289, 290, 291, - 292, 293, 294, 295, 296, 297, 386, 387, 2336, 2337, 2312, 2313, 304, - 305, 306, 307, 308, 309, 310, 311, 312, 313, 402, 403, 2352, 2353, - 2328, 2329, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 388, - 389, 2368, 2369, 392, 393, 336, 337, 338, 339, 340, 341, 342, 343, - 344, 345, 404, 405, 2384, 2385, 408, 409, 352, 353, 354, 355, 356, - 357, 358, 359, 360, 361, 390, 391, 2400, 2401, 2440, 2441, 368, 369, - 370, 371, 372, 373, 374, 375, 376, 377, 406, 407, 2416, 2417, 2456, - 2457, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 640, 641, - 2050, 2051, 2178, 2179, 528, 529, 530, 531, 532, 533, 534, 535, 536, - 537, 656, 657, 2066, 2067, 2194, 2195, 544, 545, 546, 547, 548, 549, - 550, 551, 552, 553, 642, 643, 2082, 2083, 2088, 2089, 560, 561, 562, - 563, 564, 565, 566, 567, 568, 569, 658, 659, 2098, 2099, 2104, 2105, - 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 644, 645, 2114, - 2115, 648, 649, 592, 593, 594, 595, 596, 597, 598, 599, 600, 601, - 660, 661, 2130, 2131, 664, 665, 608, 609, 610, 611, 612, 613, 614, - 615, 616, 617, 646, 647, 2146, 2147, 2184, 2185, 624, 625, 626, 627, - 628, 629, 630, 631, 632, 633, 662, 663, 2162, 2163, 2200, 2201, 768, - 769, 770, 771, 772, 773, 774, 775, 776, 777, 896, 897, 2306, 2307, - 2434, 2435, 784, 785, 786, 787, 788, 789, 790, 791, 792, 793, 912, - 913, 2322, 2323, 2450, 2451, 800, 801, 802, 803, 804, 805, 806, 807, - 808, 809, 898, 899, 2338, 2339, 2344, 2345, 816, 817, 818, 819, 820, - 821, 822, 823, 824, 825, 914, 915, 2354, 2355, 2360, 2361, 832, 833, - 834, 835, 836, 837, 838, 839, 840, 841, 900, 901, 2370, 2371, 904, - 905, 848, 849, 850, 851, 852, 853, 854, 855, 856, 857, 916, 917, - 2386, 2387, 920, 921, 864, 865, 866, 867, 868, 869, 870, 871, 872, - 873, 902, 903, 2402, 2403, 2440, 2441, 880, 881, 882, 883, 884, 885, - 886, 887, 888, 889, 918, 919, 2418, 2419, 2456, 2457, 1024, 1025, 1026, - 1027, 1028, 1029, 1030, 1031, 1032, 1033, 1152, 1153, 2052, 2053, 2180, 2181, - 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 1168, 1169, 2068, - 2069, 2196, 2197, 1056, 1057, 1058, 1059, 1060, 1061, 1062, 1063, 1064, 1065, - 1154, 1155, 2084, 2085, 2120, 2121, 1072, 1073, 1074, 1075, 1076, 1077, 1078, - 1079, 1080, 1081, 1170, 1171, 2100, 2101, 2136, 2137, 1088, 1089, 1090, 1091, - 1092, 1093, 1094, 1095, 1096, 1097, 1156, 1157, 2116, 2117, 1160, 1161, 1104, - 1105, 1106, 1107, 1108, 1109, 1110, 1111, 1112, 1113, 1172, 1173, 2132, 2133, - 1176, 1177, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 1158, - 1159, 2148, 2149, 2184, 2185, 1136, 1137, 1138, 1139, 1140, 1141, 1142, 1143, - 1144, 1145, 1174, 1175, 2164, 2165, 2200, 2201, 1280, 1281, 1282, 1283, 1284, - 1285, 1286, 1287, 1288, 1289, 1408, 1409, 2308, 2309, 2436, 2437, 1296, 1297, - 1298, 1299, 1300, 1301, 1302, 1303, 1304, 1305, 1424, 1425, 2324, 2325, 2452, - 2453, 1312, 1313, 1314, 1315, 1316, 1317, 1318, 1319, 1320, 1321, 1410, 1411, - 2340, 2341, 2376, 2377, 1328, 1329, 1330, 1331, 1332, 1333, 1334, 1335, 1336, - 1337, 1426, 1427, 2356, 2357, 2392, 2393, 1344, 1345, 1346, 1347, 1348, 1349, - 1350, 1351, 1352, 1353, 1412, 1413, 2372, 2373, 1416, 1417, 1360, 1361, 1362, - 1363, 1364, 1365, 1366, 1367, 1368, 1369, 1428, 1429, 2388, 2389, 1432, 1433, - 1376, 1377, 1378, 1379, 1380, 1381, 1382, 1383, 1384, 1385, 1414, 1415, 2404, - 2405, 2440, 2441, 1392, 1393, 1394, 1395, 1396, 1397, 1398, 1399, 1400, 1401, - 1430, 1431, 2420, 2421, 2456, 2457, 1536, 1537, 1538, 1539, 1540, 1541, 1542, - 1543, 1544, 1545, 1664, 1665, 2054, 2055, 2182, 2183, 1552, 1553, 1554, 1555, - 1556, 1557, 1558, 1559, 1560, 1561, 1680, 1681, 2070, 2071, 2198, 2199, 1568, - 1569, 1570, 1571, 1572, 1573, 1574, 1575, 1576, 1577, 1666, 1667, 2086, 2087, - 2152, 2153, 1584, 1585, 1586, 1587, 1588, 1589, 1590, 1591, 1592, 1593, 1682, - 1683, 2102, 2103, 2168, 2169, 1600, 1601, 1602, 1603, 1604, 1605, 1606, 1607, - 1608, 1609, 1668, 1669, 2118, 2119, 1672, 1673, 1616, 1617, 1618, 1619, 1620, - 1621, 1622, 1623, 1624, 1625, 1684, 1685, 2134, 2135, 1688, 1689, 1632, 1633, - 1634, 1635, 1636, 1637, 1638, 1639, 1640, 1641, 1670, 1671, 2150, 2151, 2184, - 2185, 1648, 1649, 1650, 1651, 1652, 1653, 1654, 1655, 1656, 1657, 1686, 1687, - 2166, 2167, 2200, 2201, 1792, 1793, 1794, 1795, 1796, 1797, 1798, 1799, 1800, - 1801, 1920, 1921, 2310, 2311, 2438, 2439, 1808, 1809, 1810, 1811, 1812, 1813, - 1814, 1815, 1816, 1817, 1936, 1937, 2326, 2327, 2454, 2455, 1824, 1825, 1826, - 1827, 1828, 1829, 1830, 1831, 1832, 1833, 1922, 1923, 2342, 2343, 2408, 2409, - 1840, 1841, 1842, 1843, 1844, 1845, 1846, 1847, 1848, 1849, 1938, 1939, 2358, - 2359, 2424, 2425, 1856, 1857, 1858, 1859, 1860, 1861, 1862, 1863, 1864, 1865, - 1924, 1925, 2374, 2375, 1928, 1929, 1872, 1873, 1874, 1875, 1876, 1877, 1878, - 1879, 1880, 1881, 1940, 1941, 2390, 2391, 1944, 1945, 1888, 1889, 1890, 1891, - 1892, 1893, 1894, 1895, 1896, 1897, 1926, 1927, 2406, 2407, 2440, 2441, 1904, - 1905, 1906, 1907, 1908, 1909, 1910, 1911, 1912, 1913, 1942, 1943, 2422, 2423, - 2456, 2457}; -#endif - -#if defined(DEC_BIN2DPD) && DEC_BIN2DPD==1 && !defined(DECBIN2DPD) -#define DECBIN2DPD - -const uint16_t BIN2DPD[1000]={ 0, 1, 2, 3, 4, 5, 6, 7, - 8, 9, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 32, - 33, 34, 35, 36, 37, 38, 39, 40, 41, 48, 49, 50, 51, - 52, 53, 54, 55, 56, 57, 64, 65, 66, 67, 68, 69, 70, - 71, 72, 73, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, - 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 112, 113, 114, - 115, 116, 117, 118, 119, 120, 121, 10, 11, 42, 43, 74, 75, - 106, 107, 78, 79, 26, 27, 58, 59, 90, 91, 122, 123, 94, - 95, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 144, 145, - 146, 147, 148, 149, 150, 151, 152, 153, 160, 161, 162, 163, 164, - 165, 166, 167, 168, 169, 176, 177, 178, 179, 180, 181, 182, 183, - 184, 185, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 208, - 209, 210, 211, 212, 213, 214, 215, 216, 217, 224, 225, 226, 227, - 228, 229, 230, 231, 232, 233, 240, 241, 242, 243, 244, 245, 246, - 247, 248, 249, 138, 139, 170, 171, 202, 203, 234, 235, 206, 207, - 154, 155, 186, 187, 218, 219, 250, 251, 222, 223, 256, 257, 258, - 259, 260, 261, 262, 263, 264, 265, 272, 273, 274, 275, 276, 277, - 278, 279, 280, 281, 288, 289, 290, 291, 292, 293, 294, 295, 296, - 297, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 320, 321, - 322, 323, 324, 325, 326, 327, 328, 329, 336, 337, 338, 339, 340, - 341, 342, 343, 344, 345, 352, 353, 354, 355, 356, 357, 358, 359, - 360, 361, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 266, - 267, 298, 299, 330, 331, 362, 363, 334, 335, 282, 283, 314, 315, - 346, 347, 378, 379, 350, 351, 384, 385, 386, 387, 388, 389, 390, - 391, 392, 393, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, - 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 432, 433, 434, - 435, 436, 437, 438, 439, 440, 441, 448, 449, 450, 451, 452, 453, - 454, 455, 456, 457, 464, 465, 466, 467, 468, 469, 470, 471, 472, - 473, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 496, 497, - 498, 499, 500, 501, 502, 503, 504, 505, 394, 395, 426, 427, 458, - 459, 490, 491, 462, 463, 410, 411, 442, 443, 474, 475, 506, 507, - 478, 479, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 528, - 529, 530, 531, 532, 533, 534, 535, 536, 537, 544, 545, 546, 547, - 548, 549, 550, 551, 552, 553, 560, 561, 562, 563, 564, 565, 566, - 567, 568, 569, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, - 592, 593, 594, 595, 596, 597, 598, 599, 600, 601, 608, 609, 610, - 611, 612, 613, 614, 615, 616, 617, 624, 625, 626, 627, 628, 629, - 630, 631, 632, 633, 522, 523, 554, 555, 586, 587, 618, 619, 590, - 591, 538, 539, 570, 571, 602, 603, 634, 635, 606, 607, 640, 641, - 642, 643, 644, 645, 646, 647, 648, 649, 656, 657, 658, 659, 660, - 661, 662, 663, 664, 665, 672, 673, 674, 675, 676, 677, 678, 679, - 680, 681, 688, 689, 690, 691, 692, 693, 694, 695, 696, 697, 704, - 705, 706, 707, 708, 709, 710, 711, 712, 713, 720, 721, 722, 723, - 724, 725, 726, 727, 728, 729, 736, 737, 738, 739, 740, 741, 742, - 743, 744, 745, 752, 753, 754, 755, 756, 757, 758, 759, 760, 761, - 650, 651, 682, 683, 714, 715, 746, 747, 718, 719, 666, 667, 698, - 699, 730, 731, 762, 763, 734, 735, 768, 769, 770, 771, 772, 773, - 774, 775, 776, 777, 784, 785, 786, 787, 788, 789, 790, 791, 792, - 793, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 816, 817, - 818, 819, 820, 821, 822, 823, 824, 825, 832, 833, 834, 835, 836, - 837, 838, 839, 840, 841, 848, 849, 850, 851, 852, 853, 854, 855, - 856, 857, 864, 865, 866, 867, 868, 869, 870, 871, 872, 873, 880, - 881, 882, 883, 884, 885, 886, 887, 888, 889, 778, 779, 810, 811, - 842, 843, 874, 875, 846, 847, 794, 795, 826, 827, 858, 859, 890, - 891, 862, 863, 896, 897, 898, 899, 900, 901, 902, 903, 904, 905, - 912, 913, 914, 915, 916, 917, 918, 919, 920, 921, 928, 929, 930, - 931, 932, 933, 934, 935, 936, 937, 944, 945, 946, 947, 948, 949, - 950, 951, 952, 953, 960, 961, 962, 963, 964, 965, 966, 967, 968, - 969, 976, 977, 978, 979, 980, 981, 982, 983, 984, 985, 992, 993, - 994, 995, 996, 997, 998, 999, 1000, 1001, 1008, 1009, 1010, 1011, 1012, - 1013, 1014, 1015, 1016, 1017, 906, 907, 938, 939, 970, 971, 1002, 1003, - 974, 975, 922, 923, 954, 955, 986, 987, 1018, 1019, 990, 991, 12, - 13, 268, 269, 524, 525, 780, 781, 46, 47, 28, 29, 284, 285, - 540, 541, 796, 797, 62, 63, 44, 45, 300, 301, 556, 557, 812, - 813, 302, 303, 60, 61, 316, 317, 572, 573, 828, 829, 318, 319, - 76, 77, 332, 333, 588, 589, 844, 845, 558, 559, 92, 93, 348, - 349, 604, 605, 860, 861, 574, 575, 108, 109, 364, 365, 620, 621, - 876, 877, 814, 815, 124, 125, 380, 381, 636, 637, 892, 893, 830, - 831, 14, 15, 270, 271, 526, 527, 782, 783, 110, 111, 30, 31, - 286, 287, 542, 543, 798, 799, 126, 127, 140, 141, 396, 397, 652, - 653, 908, 909, 174, 175, 156, 157, 412, 413, 668, 669, 924, 925, - 190, 191, 172, 173, 428, 429, 684, 685, 940, 941, 430, 431, 188, - 189, 444, 445, 700, 701, 956, 957, 446, 447, 204, 205, 460, 461, - 716, 717, 972, 973, 686, 687, 220, 221, 476, 477, 732, 733, 988, - 989, 702, 703, 236, 237, 492, 493, 748, 749, 1004, 1005, 942, 943, - 252, 253, 508, 509, 764, 765, 1020, 1021, 958, 959, 142, 143, 398, - 399, 654, 655, 910, 911, 238, 239, 158, 159, 414, 415, 670, 671, - 926, 927, 254, 255}; -#endif - -#if defined(DEC_DPD2BIN) && DEC_DPD2BIN==1 && !defined(DECDPD2BIN) -#define DECDPD2BIN - -const uint16_t DPD2BIN[1024]={ 0, 1, 2, 3, 4, 5, 6, 7, - 8, 9, 80, 81, 800, 801, 880, 881, 10, 11, 12, 13, 14, - 15, 16, 17, 18, 19, 90, 91, 810, 811, 890, 891, 20, 21, - 22, 23, 24, 25, 26, 27, 28, 29, 82, 83, 820, 821, 808, - 809, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 92, 93, - 830, 831, 818, 819, 40, 41, 42, 43, 44, 45, 46, 47, 48, - 49, 84, 85, 840, 841, 88, 89, 50, 51, 52, 53, 54, 55, - 56, 57, 58, 59, 94, 95, 850, 851, 98, 99, 60, 61, 62, - 63, 64, 65, 66, 67, 68, 69, 86, 87, 860, 861, 888, 889, - 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 96, 97, 870, - 871, 898, 899, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, - 180, 181, 900, 901, 980, 981, 110, 111, 112, 113, 114, 115, 116, - 117, 118, 119, 190, 191, 910, 911, 990, 991, 120, 121, 122, 123, - 124, 125, 126, 127, 128, 129, 182, 183, 920, 921, 908, 909, 130, - 131, 132, 133, 134, 135, 136, 137, 138, 139, 192, 193, 930, 931, - 918, 919, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 184, - 185, 940, 941, 188, 189, 150, 151, 152, 153, 154, 155, 156, 157, - 158, 159, 194, 195, 950, 951, 198, 199, 160, 161, 162, 163, 164, - 165, 166, 167, 168, 169, 186, 187, 960, 961, 988, 989, 170, 171, - 172, 173, 174, 175, 176, 177, 178, 179, 196, 197, 970, 971, 998, - 999, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 280, 281, - 802, 803, 882, 883, 210, 211, 212, 213, 214, 215, 216, 217, 218, - 219, 290, 291, 812, 813, 892, 893, 220, 221, 222, 223, 224, 225, - 226, 227, 228, 229, 282, 283, 822, 823, 828, 829, 230, 231, 232, - 233, 234, 235, 236, 237, 238, 239, 292, 293, 832, 833, 838, 839, - 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 284, 285, 842, - 843, 288, 289, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, - 294, 295, 852, 853, 298, 299, 260, 261, 262, 263, 264, 265, 266, - 267, 268, 269, 286, 287, 862, 863, 888, 889, 270, 271, 272, 273, - 274, 275, 276, 277, 278, 279, 296, 297, 872, 873, 898, 899, 300, - 301, 302, 303, 304, 305, 306, 307, 308, 309, 380, 381, 902, 903, - 982, 983, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 390, - 391, 912, 913, 992, 993, 320, 321, 322, 323, 324, 325, 326, 327, - 328, 329, 382, 383, 922, 923, 928, 929, 330, 331, 332, 333, 334, - 335, 336, 337, 338, 339, 392, 393, 932, 933, 938, 939, 340, 341, - 342, 343, 344, 345, 346, 347, 348, 349, 384, 385, 942, 943, 388, - 389, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 394, 395, - 952, 953, 398, 399, 360, 361, 362, 363, 364, 365, 366, 367, 368, - 369, 386, 387, 962, 963, 988, 989, 370, 371, 372, 373, 374, 375, - 376, 377, 378, 379, 396, 397, 972, 973, 998, 999, 400, 401, 402, - 403, 404, 405, 406, 407, 408, 409, 480, 481, 804, 805, 884, 885, - 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 490, 491, 814, - 815, 894, 895, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, - 482, 483, 824, 825, 848, 849, 430, 431, 432, 433, 434, 435, 436, - 437, 438, 439, 492, 493, 834, 835, 858, 859, 440, 441, 442, 443, - 444, 445, 446, 447, 448, 449, 484, 485, 844, 845, 488, 489, 450, - 451, 452, 453, 454, 455, 456, 457, 458, 459, 494, 495, 854, 855, - 498, 499, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 486, - 487, 864, 865, 888, 889, 470, 471, 472, 473, 474, 475, 476, 477, - 478, 479, 496, 497, 874, 875, 898, 899, 500, 501, 502, 503, 504, - 505, 506, 507, 508, 509, 580, 581, 904, 905, 984, 985, 510, 511, - 512, 513, 514, 515, 516, 517, 518, 519, 590, 591, 914, 915, 994, - 995, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 582, 583, - 924, 925, 948, 949, 530, 531, 532, 533, 534, 535, 536, 537, 538, - 539, 592, 593, 934, 935, 958, 959, 540, 541, 542, 543, 544, 545, - 546, 547, 548, 549, 584, 585, 944, 945, 588, 589, 550, 551, 552, - 553, 554, 555, 556, 557, 558, 559, 594, 595, 954, 955, 598, 599, - 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 586, 587, 964, - 965, 988, 989, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, - 596, 597, 974, 975, 998, 999, 600, 601, 602, 603, 604, 605, 606, - 607, 608, 609, 680, 681, 806, 807, 886, 887, 610, 611, 612, 613, - 614, 615, 616, 617, 618, 619, 690, 691, 816, 817, 896, 897, 620, - 621, 622, 623, 624, 625, 626, 627, 628, 629, 682, 683, 826, 827, - 868, 869, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 692, - 693, 836, 837, 878, 879, 640, 641, 642, 643, 644, 645, 646, 647, - 648, 649, 684, 685, 846, 847, 688, 689, 650, 651, 652, 653, 654, - 655, 656, 657, 658, 659, 694, 695, 856, 857, 698, 699, 660, 661, - 662, 663, 664, 665, 666, 667, 668, 669, 686, 687, 866, 867, 888, - 889, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 696, 697, - 876, 877, 898, 899, 700, 701, 702, 703, 704, 705, 706, 707, 708, - 709, 780, 781, 906, 907, 986, 987, 710, 711, 712, 713, 714, 715, - 716, 717, 718, 719, 790, 791, 916, 917, 996, 997, 720, 721, 722, - 723, 724, 725, 726, 727, 728, 729, 782, 783, 926, 927, 968, 969, - 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 792, 793, 936, - 937, 978, 979, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, - 784, 785, 946, 947, 788, 789, 750, 751, 752, 753, 754, 755, 756, - 757, 758, 759, 794, 795, 956, 957, 798, 799, 760, 761, 762, 763, - 764, 765, 766, 767, 768, 769, 786, 787, 966, 967, 988, 989, 770, - 771, 772, 773, 774, 775, 776, 777, 778, 779, 796, 797, 976, 977, - 998, 999}; -#endif - -#if defined(DEC_DPD2BINK) && DEC_DPD2BINK==1 && !defined(DECDPD2BINK) -#define DECDPD2BINK - -const uint32_t DPD2BINK[1024]={ 0, 1000, 2000, 3000, 4000, 5000, - 6000, 7000, 8000, 9000, 80000, 81000, 800000, 801000, 880000, 881000, - 10000, 11000, 12000, 13000, 14000, 15000, 16000, 17000, 18000, 19000, - 90000, 91000, 810000, 811000, 890000, 891000, 20000, 21000, 22000, 23000, - 24000, 25000, 26000, 27000, 28000, 29000, 82000, 83000, 820000, 821000, - 808000, 809000, 30000, 31000, 32000, 33000, 34000, 35000, 36000, 37000, - 38000, 39000, 92000, 93000, 830000, 831000, 818000, 819000, 40000, 41000, - 42000, 43000, 44000, 45000, 46000, 47000, 48000, 49000, 84000, 85000, - 840000, 841000, 88000, 89000, 50000, 51000, 52000, 53000, 54000, 55000, - 56000, 57000, 58000, 59000, 94000, 95000, 850000, 851000, 98000, 99000, - 60000, 61000, 62000, 63000, 64000, 65000, 66000, 67000, 68000, 69000, - 86000, 87000, 860000, 861000, 888000, 889000, 70000, 71000, 72000, 73000, - 74000, 75000, 76000, 77000, 78000, 79000, 96000, 97000, 870000, 871000, - 898000, 899000, 100000, 101000, 102000, 103000, 104000, 105000, 106000, 107000, - 108000, 109000, 180000, 181000, 900000, 901000, 980000, 981000, 110000, 111000, - 112000, 113000, 114000, 115000, 116000, 117000, 118000, 119000, 190000, 191000, - 910000, 911000, 990000, 991000, 120000, 121000, 122000, 123000, 124000, 125000, - 126000, 127000, 128000, 129000, 182000, 183000, 920000, 921000, 908000, 909000, - 130000, 131000, 132000, 133000, 134000, 135000, 136000, 137000, 138000, 139000, - 192000, 193000, 930000, 931000, 918000, 919000, 140000, 141000, 142000, 143000, - 144000, 145000, 146000, 147000, 148000, 149000, 184000, 185000, 940000, 941000, - 188000, 189000, 150000, 151000, 152000, 153000, 154000, 155000, 156000, 157000, - 158000, 159000, 194000, 195000, 950000, 951000, 198000, 199000, 160000, 161000, - 162000, 163000, 164000, 165000, 166000, 167000, 168000, 169000, 186000, 187000, - 960000, 961000, 988000, 989000, 170000, 171000, 172000, 173000, 174000, 175000, - 176000, 177000, 178000, 179000, 196000, 197000, 970000, 971000, 998000, 999000, - 200000, 201000, 202000, 203000, 204000, 205000, 206000, 207000, 208000, 209000, - 280000, 281000, 802000, 803000, 882000, 883000, 210000, 211000, 212000, 213000, - 214000, 215000, 216000, 217000, 218000, 219000, 290000, 291000, 812000, 813000, - 892000, 893000, 220000, 221000, 222000, 223000, 224000, 225000, 226000, 227000, - 228000, 229000, 282000, 283000, 822000, 823000, 828000, 829000, 230000, 231000, - 232000, 233000, 234000, 235000, 236000, 237000, 238000, 239000, 292000, 293000, - 832000, 833000, 838000, 839000, 240000, 241000, 242000, 243000, 244000, 245000, - 246000, 247000, 248000, 249000, 284000, 285000, 842000, 843000, 288000, 289000, - 250000, 251000, 252000, 253000, 254000, 255000, 256000, 257000, 258000, 259000, - 294000, 295000, 852000, 853000, 298000, 299000, 260000, 261000, 262000, 263000, - 264000, 265000, 266000, 267000, 268000, 269000, 286000, 287000, 862000, 863000, - 888000, 889000, 270000, 271000, 272000, 273000, 274000, 275000, 276000, 277000, - 278000, 279000, 296000, 297000, 872000, 873000, 898000, 899000, 300000, 301000, - 302000, 303000, 304000, 305000, 306000, 307000, 308000, 309000, 380000, 381000, - 902000, 903000, 982000, 983000, 310000, 311000, 312000, 313000, 314000, 315000, - 316000, 317000, 318000, 319000, 390000, 391000, 912000, 913000, 992000, 993000, - 320000, 321000, 322000, 323000, 324000, 325000, 326000, 327000, 328000, 329000, - 382000, 383000, 922000, 923000, 928000, 929000, 330000, 331000, 332000, 333000, - 334000, 335000, 336000, 337000, 338000, 339000, 392000, 393000, 932000, 933000, - 938000, 939000, 340000, 341000, 342000, 343000, 344000, 345000, 346000, 347000, - 348000, 349000, 384000, 385000, 942000, 943000, 388000, 389000, 350000, 351000, - 352000, 353000, 354000, 355000, 356000, 357000, 358000, 359000, 394000, 395000, - 952000, 953000, 398000, 399000, 360000, 361000, 362000, 363000, 364000, 365000, - 366000, 367000, 368000, 369000, 386000, 387000, 962000, 963000, 988000, 989000, - 370000, 371000, 372000, 373000, 374000, 375000, 376000, 377000, 378000, 379000, - 396000, 397000, 972000, 973000, 998000, 999000, 400000, 401000, 402000, 403000, - 404000, 405000, 406000, 407000, 408000, 409000, 480000, 481000, 804000, 805000, - 884000, 885000, 410000, 411000, 412000, 413000, 414000, 415000, 416000, 417000, - 418000, 419000, 490000, 491000, 814000, 815000, 894000, 895000, 420000, 421000, - 422000, 423000, 424000, 425000, 426000, 427000, 428000, 429000, 482000, 483000, - 824000, 825000, 848000, 849000, 430000, 431000, 432000, 433000, 434000, 435000, - 436000, 437000, 438000, 439000, 492000, 493000, 834000, 835000, 858000, 859000, - 440000, 441000, 442000, 443000, 444000, 445000, 446000, 447000, 448000, 449000, - 484000, 485000, 844000, 845000, 488000, 489000, 450000, 451000, 452000, 453000, - 454000, 455000, 456000, 457000, 458000, 459000, 494000, 495000, 854000, 855000, - 498000, 499000, 460000, 461000, 462000, 463000, 464000, 465000, 466000, 467000, - 468000, 469000, 486000, 487000, 864000, 865000, 888000, 889000, 470000, 471000, - 472000, 473000, 474000, 475000, 476000, 477000, 478000, 479000, 496000, 497000, - 874000, 875000, 898000, 899000, 500000, 501000, 502000, 503000, 504000, 505000, - 506000, 507000, 508000, 509000, 580000, 581000, 904000, 905000, 984000, 985000, - 510000, 511000, 512000, 513000, 514000, 515000, 516000, 517000, 518000, 519000, - 590000, 591000, 914000, 915000, 994000, 995000, 520000, 521000, 522000, 523000, - 524000, 525000, 526000, 527000, 528000, 529000, 582000, 583000, 924000, 925000, - 948000, 949000, 530000, 531000, 532000, 533000, 534000, 535000, 536000, 537000, - 538000, 539000, 592000, 593000, 934000, 935000, 958000, 959000, 540000, 541000, - 542000, 543000, 544000, 545000, 546000, 547000, 548000, 549000, 584000, 585000, - 944000, 945000, 588000, 589000, 550000, 551000, 552000, 553000, 554000, 555000, - 556000, 557000, 558000, 559000, 594000, 595000, 954000, 955000, 598000, 599000, - 560000, 561000, 562000, 563000, 564000, 565000, 566000, 567000, 568000, 569000, - 586000, 587000, 964000, 965000, 988000, 989000, 570000, 571000, 572000, 573000, - 574000, 575000, 576000, 577000, 578000, 579000, 596000, 597000, 974000, 975000, - 998000, 999000, 600000, 601000, 602000, 603000, 604000, 605000, 606000, 607000, - 608000, 609000, 680000, 681000, 806000, 807000, 886000, 887000, 610000, 611000, - 612000, 613000, 614000, 615000, 616000, 617000, 618000, 619000, 690000, 691000, - 816000, 817000, 896000, 897000, 620000, 621000, 622000, 623000, 624000, 625000, - 626000, 627000, 628000, 629000, 682000, 683000, 826000, 827000, 868000, 869000, - 630000, 631000, 632000, 633000, 634000, 635000, 636000, 637000, 638000, 639000, - 692000, 693000, 836000, 837000, 878000, 879000, 640000, 641000, 642000, 643000, - 644000, 645000, 646000, 647000, 648000, 649000, 684000, 685000, 846000, 847000, - 688000, 689000, 650000, 651000, 652000, 653000, 654000, 655000, 656000, 657000, - 658000, 659000, 694000, 695000, 856000, 857000, 698000, 699000, 660000, 661000, - 662000, 663000, 664000, 665000, 666000, 667000, 668000, 669000, 686000, 687000, - 866000, 867000, 888000, 889000, 670000, 671000, 672000, 673000, 674000, 675000, - 676000, 677000, 678000, 679000, 696000, 697000, 876000, 877000, 898000, 899000, - 700000, 701000, 702000, 703000, 704000, 705000, 706000, 707000, 708000, 709000, - 780000, 781000, 906000, 907000, 986000, 987000, 710000, 711000, 712000, 713000, - 714000, 715000, 716000, 717000, 718000, 719000, 790000, 791000, 916000, 917000, - 996000, 997000, 720000, 721000, 722000, 723000, 724000, 725000, 726000, 727000, - 728000, 729000, 782000, 783000, 926000, 927000, 968000, 969000, 730000, 731000, - 732000, 733000, 734000, 735000, 736000, 737000, 738000, 739000, 792000, 793000, - 936000, 937000, 978000, 979000, 740000, 741000, 742000, 743000, 744000, 745000, - 746000, 747000, 748000, 749000, 784000, 785000, 946000, 947000, 788000, 789000, - 750000, 751000, 752000, 753000, 754000, 755000, 756000, 757000, 758000, 759000, - 794000, 795000, 956000, 957000, 798000, 799000, 760000, 761000, 762000, 763000, - 764000, 765000, 766000, 767000, 768000, 769000, 786000, 787000, 966000, 967000, - 988000, 989000, 770000, 771000, 772000, 773000, 774000, 775000, 776000, 777000, - 778000, 779000, 796000, 797000, 976000, 977000, 998000, 999000}; -#endif - -#if defined(DEC_DPD2BINM) && DEC_DPD2BINM==1 && !defined(DECDPD2BINM) -#define DECDPD2BINM - -const uint32_t DPD2BINM[1024]={0, 1000000, 2000000, 3000000, 4000000, - 5000000, 6000000, 7000000, 8000000, 9000000, 80000000, 81000000, - 800000000, 801000000, 880000000, 881000000, 10000000, 11000000, 12000000, - 13000000, 14000000, 15000000, 16000000, 17000000, 18000000, 19000000, - 90000000, 91000000, 810000000, 811000000, 890000000, 891000000, 20000000, - 21000000, 22000000, 23000000, 24000000, 25000000, 26000000, 27000000, - 28000000, 29000000, 82000000, 83000000, 820000000, 821000000, 808000000, - 809000000, 30000000, 31000000, 32000000, 33000000, 34000000, 35000000, - 36000000, 37000000, 38000000, 39000000, 92000000, 93000000, 830000000, - 831000000, 818000000, 819000000, 40000000, 41000000, 42000000, 43000000, - 44000000, 45000000, 46000000, 47000000, 48000000, 49000000, 84000000, - 85000000, 840000000, 841000000, 88000000, 89000000, 50000000, 51000000, - 52000000, 53000000, 54000000, 55000000, 56000000, 57000000, 58000000, - 59000000, 94000000, 95000000, 850000000, 851000000, 98000000, 99000000, - 60000000, 61000000, 62000000, 63000000, 64000000, 65000000, 66000000, - 67000000, 68000000, 69000000, 86000000, 87000000, 860000000, 861000000, - 888000000, 889000000, 70000000, 71000000, 72000000, 73000000, 74000000, - 75000000, 76000000, 77000000, 78000000, 79000000, 96000000, 97000000, - 870000000, 871000000, 898000000, 899000000, 100000000, 101000000, 102000000, - 103000000, 104000000, 105000000, 106000000, 107000000, 108000000, 109000000, - 180000000, 181000000, 900000000, 901000000, 980000000, 981000000, 110000000, - 111000000, 112000000, 113000000, 114000000, 115000000, 116000000, 117000000, - 118000000, 119000000, 190000000, 191000000, 910000000, 911000000, 990000000, - 991000000, 120000000, 121000000, 122000000, 123000000, 124000000, 125000000, - 126000000, 127000000, 128000000, 129000000, 182000000, 183000000, 920000000, - 921000000, 908000000, 909000000, 130000000, 131000000, 132000000, 133000000, - 134000000, 135000000, 136000000, 137000000, 138000000, 139000000, 192000000, - 193000000, 930000000, 931000000, 918000000, 919000000, 140000000, 141000000, - 142000000, 143000000, 144000000, 145000000, 146000000, 147000000, 148000000, - 149000000, 184000000, 185000000, 940000000, 941000000, 188000000, 189000000, - 150000000, 151000000, 152000000, 153000000, 154000000, 155000000, 156000000, - 157000000, 158000000, 159000000, 194000000, 195000000, 950000000, 951000000, - 198000000, 199000000, 160000000, 161000000, 162000000, 163000000, 164000000, - 165000000, 166000000, 167000000, 168000000, 169000000, 186000000, 187000000, - 960000000, 961000000, 988000000, 989000000, 170000000, 171000000, 172000000, - 173000000, 174000000, 175000000, 176000000, 177000000, 178000000, 179000000, - 196000000, 197000000, 970000000, 971000000, 998000000, 999000000, 200000000, - 201000000, 202000000, 203000000, 204000000, 205000000, 206000000, 207000000, - 208000000, 209000000, 280000000, 281000000, 802000000, 803000000, 882000000, - 883000000, 210000000, 211000000, 212000000, 213000000, 214000000, 215000000, - 216000000, 217000000, 218000000, 219000000, 290000000, 291000000, 812000000, - 813000000, 892000000, 893000000, 220000000, 221000000, 222000000, 223000000, - 224000000, 225000000, 226000000, 227000000, 228000000, 229000000, 282000000, - 283000000, 822000000, 823000000, 828000000, 829000000, 230000000, 231000000, - 232000000, 233000000, 234000000, 235000000, 236000000, 237000000, 238000000, - 239000000, 292000000, 293000000, 832000000, 833000000, 838000000, 839000000, - 240000000, 241000000, 242000000, 243000000, 244000000, 245000000, 246000000, - 247000000, 248000000, 249000000, 284000000, 285000000, 842000000, 843000000, - 288000000, 289000000, 250000000, 251000000, 252000000, 253000000, 254000000, - 255000000, 256000000, 257000000, 258000000, 259000000, 294000000, 295000000, - 852000000, 853000000, 298000000, 299000000, 260000000, 261000000, 262000000, - 263000000, 264000000, 265000000, 266000000, 267000000, 268000000, 269000000, - 286000000, 287000000, 862000000, 863000000, 888000000, 889000000, 270000000, - 271000000, 272000000, 273000000, 274000000, 275000000, 276000000, 277000000, - 278000000, 279000000, 296000000, 297000000, 872000000, 873000000, 898000000, - 899000000, 300000000, 301000000, 302000000, 303000000, 304000000, 305000000, - 306000000, 307000000, 308000000, 309000000, 380000000, 381000000, 902000000, - 903000000, 982000000, 983000000, 310000000, 311000000, 312000000, 313000000, - 314000000, 315000000, 316000000, 317000000, 318000000, 319000000, 390000000, - 391000000, 912000000, 913000000, 992000000, 993000000, 320000000, 321000000, - 322000000, 323000000, 324000000, 325000000, 326000000, 327000000, 328000000, - 329000000, 382000000, 383000000, 922000000, 923000000, 928000000, 929000000, - 330000000, 331000000, 332000000, 333000000, 334000000, 335000000, 336000000, - 337000000, 338000000, 339000000, 392000000, 393000000, 932000000, 933000000, - 938000000, 939000000, 340000000, 341000000, 342000000, 343000000, 344000000, - 345000000, 346000000, 347000000, 348000000, 349000000, 384000000, 385000000, - 942000000, 943000000, 388000000, 389000000, 350000000, 351000000, 352000000, - 353000000, 354000000, 355000000, 356000000, 357000000, 358000000, 359000000, - 394000000, 395000000, 952000000, 953000000, 398000000, 399000000, 360000000, - 361000000, 362000000, 363000000, 364000000, 365000000, 366000000, 367000000, - 368000000, 369000000, 386000000, 387000000, 962000000, 963000000, 988000000, - 989000000, 370000000, 371000000, 372000000, 373000000, 374000000, 375000000, - 376000000, 377000000, 378000000, 379000000, 396000000, 397000000, 972000000, - 973000000, 998000000, 999000000, 400000000, 401000000, 402000000, 403000000, - 404000000, 405000000, 406000000, 407000000, 408000000, 409000000, 480000000, - 481000000, 804000000, 805000000, 884000000, 885000000, 410000000, 411000000, - 412000000, 413000000, 414000000, 415000000, 416000000, 417000000, 418000000, - 419000000, 490000000, 491000000, 814000000, 815000000, 894000000, 895000000, - 420000000, 421000000, 422000000, 423000000, 424000000, 425000000, 426000000, - 427000000, 428000000, 429000000, 482000000, 483000000, 824000000, 825000000, - 848000000, 849000000, 430000000, 431000000, 432000000, 433000000, 434000000, - 435000000, 436000000, 437000000, 438000000, 439000000, 492000000, 493000000, - 834000000, 835000000, 858000000, 859000000, 440000000, 441000000, 442000000, - 443000000, 444000000, 445000000, 446000000, 447000000, 448000000, 449000000, - 484000000, 485000000, 844000000, 845000000, 488000000, 489000000, 450000000, - 451000000, 452000000, 453000000, 454000000, 455000000, 456000000, 457000000, - 458000000, 459000000, 494000000, 495000000, 854000000, 855000000, 498000000, - 499000000, 460000000, 461000000, 462000000, 463000000, 464000000, 465000000, - 466000000, 467000000, 468000000, 469000000, 486000000, 487000000, 864000000, - 865000000, 888000000, 889000000, 470000000, 471000000, 472000000, 473000000, - 474000000, 475000000, 476000000, 477000000, 478000000, 479000000, 496000000, - 497000000, 874000000, 875000000, 898000000, 899000000, 500000000, 501000000, - 502000000, 503000000, 504000000, 505000000, 506000000, 507000000, 508000000, - 509000000, 580000000, 581000000, 904000000, 905000000, 984000000, 985000000, - 510000000, 511000000, 512000000, 513000000, 514000000, 515000000, 516000000, - 517000000, 518000000, 519000000, 590000000, 591000000, 914000000, 915000000, - 994000000, 995000000, 520000000, 521000000, 522000000, 523000000, 524000000, - 525000000, 526000000, 527000000, 528000000, 529000000, 582000000, 583000000, - 924000000, 925000000, 948000000, 949000000, 530000000, 531000000, 532000000, - 533000000, 534000000, 535000000, 536000000, 537000000, 538000000, 539000000, - 592000000, 593000000, 934000000, 935000000, 958000000, 959000000, 540000000, - 541000000, 542000000, 543000000, 544000000, 545000000, 546000000, 547000000, - 548000000, 549000000, 584000000, 585000000, 944000000, 945000000, 588000000, - 589000000, 550000000, 551000000, 552000000, 553000000, 554000000, 555000000, - 556000000, 557000000, 558000000, 559000000, 594000000, 595000000, 954000000, - 955000000, 598000000, 599000000, 560000000, 561000000, 562000000, 563000000, - 564000000, 565000000, 566000000, 567000000, 568000000, 569000000, 586000000, - 587000000, 964000000, 965000000, 988000000, 989000000, 570000000, 571000000, - 572000000, 573000000, 574000000, 575000000, 576000000, 577000000, 578000000, - 579000000, 596000000, 597000000, 974000000, 975000000, 998000000, 999000000, - 600000000, 601000000, 602000000, 603000000, 604000000, 605000000, 606000000, - 607000000, 608000000, 609000000, 680000000, 681000000, 806000000, 807000000, - 886000000, 887000000, 610000000, 611000000, 612000000, 613000000, 614000000, - 615000000, 616000000, 617000000, 618000000, 619000000, 690000000, 691000000, - 816000000, 817000000, 896000000, 897000000, 620000000, 621000000, 622000000, - 623000000, 624000000, 625000000, 626000000, 627000000, 628000000, 629000000, - 682000000, 683000000, 826000000, 827000000, 868000000, 869000000, 630000000, - 631000000, 632000000, 633000000, 634000000, 635000000, 636000000, 637000000, - 638000000, 639000000, 692000000, 693000000, 836000000, 837000000, 878000000, - 879000000, 640000000, 641000000, 642000000, 643000000, 644000000, 645000000, - 646000000, 647000000, 648000000, 649000000, 684000000, 685000000, 846000000, - 847000000, 688000000, 689000000, 650000000, 651000000, 652000000, 653000000, - 654000000, 655000000, 656000000, 657000000, 658000000, 659000000, 694000000, - 695000000, 856000000, 857000000, 698000000, 699000000, 660000000, 661000000, - 662000000, 663000000, 664000000, 665000000, 666000000, 667000000, 668000000, - 669000000, 686000000, 687000000, 866000000, 867000000, 888000000, 889000000, - 670000000, 671000000, 672000000, 673000000, 674000000, 675000000, 676000000, - 677000000, 678000000, 679000000, 696000000, 697000000, 876000000, 877000000, - 898000000, 899000000, 700000000, 701000000, 702000000, 703000000, 704000000, - 705000000, 706000000, 707000000, 708000000, 709000000, 780000000, 781000000, - 906000000, 907000000, 986000000, 987000000, 710000000, 711000000, 712000000, - 713000000, 714000000, 715000000, 716000000, 717000000, 718000000, 719000000, - 790000000, 791000000, 916000000, 917000000, 996000000, 997000000, 720000000, - 721000000, 722000000, 723000000, 724000000, 725000000, 726000000, 727000000, - 728000000, 729000000, 782000000, 783000000, 926000000, 927000000, 968000000, - 969000000, 730000000, 731000000, 732000000, 733000000, 734000000, 735000000, - 736000000, 737000000, 738000000, 739000000, 792000000, 793000000, 936000000, - 937000000, 978000000, 979000000, 740000000, 741000000, 742000000, 743000000, - 744000000, 745000000, 746000000, 747000000, 748000000, 749000000, 784000000, - 785000000, 946000000, 947000000, 788000000, 789000000, 750000000, 751000000, - 752000000, 753000000, 754000000, 755000000, 756000000, 757000000, 758000000, - 759000000, 794000000, 795000000, 956000000, 957000000, 798000000, 799000000, - 760000000, 761000000, 762000000, 763000000, 764000000, 765000000, 766000000, - 767000000, 768000000, 769000000, 786000000, 787000000, 966000000, 967000000, - 988000000, 989000000, 770000000, 771000000, 772000000, 773000000, 774000000, - 775000000, 776000000, 777000000, 778000000, 779000000, 796000000, 797000000, - 976000000, 977000000, 998000000, 999000000}; -#endif - -#if defined(DEC_BIN2CHAR) && DEC_BIN2CHAR==1 && !defined(DECBIN2CHAR) -#define DECBIN2CHAR - -const uint8_t BIN2CHAR[4001]={ - '\0','0','0','0', '\1','0','0','1', '\1','0','0','2', '\1','0','0','3', '\1','0','0','4', - '\1','0','0','5', '\1','0','0','6', '\1','0','0','7', '\1','0','0','8', '\1','0','0','9', - '\2','0','1','0', '\2','0','1','1', '\2','0','1','2', '\2','0','1','3', '\2','0','1','4', - '\2','0','1','5', '\2','0','1','6', '\2','0','1','7', '\2','0','1','8', '\2','0','1','9', - '\2','0','2','0', '\2','0','2','1', '\2','0','2','2', '\2','0','2','3', '\2','0','2','4', - '\2','0','2','5', '\2','0','2','6', '\2','0','2','7', '\2','0','2','8', '\2','0','2','9', - '\2','0','3','0', '\2','0','3','1', '\2','0','3','2', '\2','0','3','3', '\2','0','3','4', - '\2','0','3','5', '\2','0','3','6', '\2','0','3','7', '\2','0','3','8', '\2','0','3','9', - '\2','0','4','0', '\2','0','4','1', '\2','0','4','2', '\2','0','4','3', '\2','0','4','4', - 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'\3','6','5','0', '\3','6','5','1', '\3','6','5','2', '\3','6','5','3', '\3','6','5','4', - '\3','6','5','5', '\3','6','5','6', '\3','6','5','7', '\3','6','5','8', '\3','6','5','9', - '\3','6','6','0', '\3','6','6','1', '\3','6','6','2', '\3','6','6','3', '\3','6','6','4', - '\3','6','6','5', '\3','6','6','6', '\3','6','6','7', '\3','6','6','8', '\3','6','6','9', - '\3','6','7','0', '\3','6','7','1', '\3','6','7','2', '\3','6','7','3', '\3','6','7','4', - '\3','6','7','5', '\3','6','7','6', '\3','6','7','7', '\3','6','7','8', '\3','6','7','9', - '\3','6','8','0', '\3','6','8','1', '\3','6','8','2', '\3','6','8','3', '\3','6','8','4', - '\3','6','8','5', '\3','6','8','6', '\3','6','8','7', '\3','6','8','8', '\3','6','8','9', - '\3','6','9','0', '\3','6','9','1', '\3','6','9','2', '\3','6','9','3', '\3','6','9','4', - '\3','6','9','5', '\3','6','9','6', '\3','6','9','7', '\3','6','9','8', '\3','6','9','9', - '\3','7','0','0', '\3','7','0','1', '\3','7','0','2', '\3','7','0','3', '\3','7','0','4', - '\3','7','0','5', '\3','7','0','6', '\3','7','0','7', '\3','7','0','8', '\3','7','0','9', - '\3','7','1','0', '\3','7','1','1', '\3','7','1','2', '\3','7','1','3', '\3','7','1','4', - '\3','7','1','5', '\3','7','1','6', '\3','7','1','7', '\3','7','1','8', '\3','7','1','9', - '\3','7','2','0', '\3','7','2','1', '\3','7','2','2', '\3','7','2','3', '\3','7','2','4', - '\3','7','2','5', '\3','7','2','6', '\3','7','2','7', '\3','7','2','8', '\3','7','2','9', - '\3','7','3','0', '\3','7','3','1', '\3','7','3','2', '\3','7','3','3', '\3','7','3','4', - '\3','7','3','5', '\3','7','3','6', '\3','7','3','7', '\3','7','3','8', '\3','7','3','9', - '\3','7','4','0', '\3','7','4','1', '\3','7','4','2', '\3','7','4','3', '\3','7','4','4', - '\3','7','4','5', '\3','7','4','6', '\3','7','4','7', '\3','7','4','8', '\3','7','4','9', - '\3','7','5','0', '\3','7','5','1', '\3','7','5','2', '\3','7','5','3', '\3','7','5','4', - '\3','7','5','5', '\3','7','5','6', '\3','7','5','7', '\3','7','5','8', '\3','7','5','9', - '\3','7','6','0', '\3','7','6','1', '\3','7','6','2', '\3','7','6','3', '\3','7','6','4', - '\3','7','6','5', '\3','7','6','6', '\3','7','6','7', '\3','7','6','8', '\3','7','6','9', - '\3','7','7','0', '\3','7','7','1', '\3','7','7','2', '\3','7','7','3', '\3','7','7','4', - '\3','7','7','5', '\3','7','7','6', '\3','7','7','7', '\3','7','7','8', '\3','7','7','9', - '\3','7','8','0', '\3','7','8','1', '\3','7','8','2', '\3','7','8','3', '\3','7','8','4', - '\3','7','8','5', '\3','7','8','6', '\3','7','8','7', '\3','7','8','8', '\3','7','8','9', - '\3','7','9','0', '\3','7','9','1', '\3','7','9','2', '\3','7','9','3', '\3','7','9','4', - '\3','7','9','5', '\3','7','9','6', '\3','7','9','7', '\3','7','9','8', '\3','7','9','9', - '\3','8','0','0', '\3','8','0','1', '\3','8','0','2', '\3','8','0','3', '\3','8','0','4', - '\3','8','0','5', '\3','8','0','6', '\3','8','0','7', '\3','8','0','8', '\3','8','0','9', - '\3','8','1','0', '\3','8','1','1', '\3','8','1','2', '\3','8','1','3', '\3','8','1','4', - '\3','8','1','5', '\3','8','1','6', '\3','8','1','7', '\3','8','1','8', '\3','8','1','9', - '\3','8','2','0', '\3','8','2','1', '\3','8','2','2', '\3','8','2','3', '\3','8','2','4', - '\3','8','2','5', '\3','8','2','6', '\3','8','2','7', '\3','8','2','8', '\3','8','2','9', - '\3','8','3','0', '\3','8','3','1', '\3','8','3','2', '\3','8','3','3', '\3','8','3','4', - '\3','8','3','5', '\3','8','3','6', '\3','8','3','7', '\3','8','3','8', '\3','8','3','9', - '\3','8','4','0', '\3','8','4','1', '\3','8','4','2', '\3','8','4','3', '\3','8','4','4', - '\3','8','4','5', '\3','8','4','6', '\3','8','4','7', '\3','8','4','8', '\3','8','4','9', - '\3','8','5','0', '\3','8','5','1', '\3','8','5','2', '\3','8','5','3', '\3','8','5','4', - '\3','8','5','5', '\3','8','5','6', '\3','8','5','7', '\3','8','5','8', '\3','8','5','9', - '\3','8','6','0', '\3','8','6','1', '\3','8','6','2', '\3','8','6','3', '\3','8','6','4', - '\3','8','6','5', '\3','8','6','6', '\3','8','6','7', '\3','8','6','8', '\3','8','6','9', - '\3','8','7','0', '\3','8','7','1', '\3','8','7','2', '\3','8','7','3', '\3','8','7','4', - '\3','8','7','5', '\3','8','7','6', '\3','8','7','7', '\3','8','7','8', '\3','8','7','9', - '\3','8','8','0', '\3','8','8','1', '\3','8','8','2', '\3','8','8','3', '\3','8','8','4', - '\3','8','8','5', '\3','8','8','6', '\3','8','8','7', '\3','8','8','8', '\3','8','8','9', - '\3','8','9','0', '\3','8','9','1', '\3','8','9','2', '\3','8','9','3', '\3','8','9','4', - '\3','8','9','5', '\3','8','9','6', '\3','8','9','7', '\3','8','9','8', '\3','8','9','9', - '\3','9','0','0', '\3','9','0','1', '\3','9','0','2', '\3','9','0','3', '\3','9','0','4', - '\3','9','0','5', '\3','9','0','6', '\3','9','0','7', '\3','9','0','8', '\3','9','0','9', - '\3','9','1','0', '\3','9','1','1', '\3','9','1','2', '\3','9','1','3', '\3','9','1','4', - '\3','9','1','5', '\3','9','1','6', '\3','9','1','7', '\3','9','1','8', '\3','9','1','9', - '\3','9','2','0', '\3','9','2','1', '\3','9','2','2', '\3','9','2','3', '\3','9','2','4', - '\3','9','2','5', '\3','9','2','6', '\3','9','2','7', '\3','9','2','8', '\3','9','2','9', - '\3','9','3','0', '\3','9','3','1', '\3','9','3','2', '\3','9','3','3', '\3','9','3','4', - '\3','9','3','5', '\3','9','3','6', '\3','9','3','7', '\3','9','3','8', '\3','9','3','9', - '\3','9','4','0', '\3','9','4','1', '\3','9','4','2', '\3','9','4','3', '\3','9','4','4', - '\3','9','4','5', '\3','9','4','6', '\3','9','4','7', '\3','9','4','8', '\3','9','4','9', - '\3','9','5','0', '\3','9','5','1', '\3','9','5','2', '\3','9','5','3', '\3','9','5','4', - '\3','9','5','5', '\3','9','5','6', '\3','9','5','7', '\3','9','5','8', '\3','9','5','9', - '\3','9','6','0', '\3','9','6','1', '\3','9','6','2', '\3','9','6','3', '\3','9','6','4', - '\3','9','6','5', '\3','9','6','6', '\3','9','6','7', '\3','9','6','8', '\3','9','6','9', - '\3','9','7','0', '\3','9','7','1', '\3','9','7','2', '\3','9','7','3', '\3','9','7','4', - '\3','9','7','5', '\3','9','7','6', '\3','9','7','7', '\3','9','7','8', '\3','9','7','9', - '\3','9','8','0', '\3','9','8','1', '\3','9','8','2', '\3','9','8','3', '\3','9','8','4', - '\3','9','8','5', '\3','9','8','6', '\3','9','8','7', '\3','9','8','8', '\3','9','8','9', - '\3','9','9','0', '\3','9','9','1', '\3','9','9','2', '\3','9','9','3', '\3','9','9','4', - '\3','9','9','5', '\3','9','9','6', '\3','9','9','7', '\3','9','9','8', '\3','9','9','9', '\0'}; -#endif - -#if defined(DEC_DPD2BCD8) && DEC_DPD2BCD8==1 && !defined(DECDPD2BCD8) -#define DECDPD2BCD8 - -const uint8_t DPD2BCD8[4096]={ - 0,0,0,0, 0,0,1,1, 0,0,2,1, 0,0,3,1, 0,0,4,1, 0,0,5,1, 0,0,6,1, 0,0,7,1, 0,0,8,1, - 0,0,9,1, 0,8,0,2, 0,8,1,2, 8,0,0,3, 8,0,1,3, 8,8,0,3, 8,8,1,3, 0,1,0,2, 0,1,1,2, - 0,1,2,2, 0,1,3,2, 0,1,4,2, 0,1,5,2, 0,1,6,2, 0,1,7,2, 0,1,8,2, 0,1,9,2, 0,9,0,2, - 0,9,1,2, 8,1,0,3, 8,1,1,3, 8,9,0,3, 8,9,1,3, 0,2,0,2, 0,2,1,2, 0,2,2,2, 0,2,3,2, - 0,2,4,2, 0,2,5,2, 0,2,6,2, 0,2,7,2, 0,2,8,2, 0,2,9,2, 0,8,2,2, 0,8,3,2, 8,2,0,3, - 8,2,1,3, 8,0,8,3, 8,0,9,3, 0,3,0,2, 0,3,1,2, 0,3,2,2, 0,3,3,2, 0,3,4,2, 0,3,5,2, - 0,3,6,2, 0,3,7,2, 0,3,8,2, 0,3,9,2, 0,9,2,2, 0,9,3,2, 8,3,0,3, 8,3,1,3, 8,1,8,3, - 8,1,9,3, 0,4,0,2, 0,4,1,2, 0,4,2,2, 0,4,3,2, 0,4,4,2, 0,4,5,2, 0,4,6,2, 0,4,7,2, - 0,4,8,2, 0,4,9,2, 0,8,4,2, 0,8,5,2, 8,4,0,3, 8,4,1,3, 0,8,8,2, 0,8,9,2, 0,5,0,2, - 0,5,1,2, 0,5,2,2, 0,5,3,2, 0,5,4,2, 0,5,5,2, 0,5,6,2, 0,5,7,2, 0,5,8,2, 0,5,9,2, - 0,9,4,2, 0,9,5,2, 8,5,0,3, 8,5,1,3, 0,9,8,2, 0,9,9,2, 0,6,0,2, 0,6,1,2, 0,6,2,2, - 0,6,3,2, 0,6,4,2, 0,6,5,2, 0,6,6,2, 0,6,7,2, 0,6,8,2, 0,6,9,2, 0,8,6,2, 0,8,7,2, - 8,6,0,3, 8,6,1,3, 8,8,8,3, 8,8,9,3, 0,7,0,2, 0,7,1,2, 0,7,2,2, 0,7,3,2, 0,7,4,2, - 0,7,5,2, 0,7,6,2, 0,7,7,2, 0,7,8,2, 0,7,9,2, 0,9,6,2, 0,9,7,2, 8,7,0,3, 8,7,1,3, - 8,9,8,3, 8,9,9,3, 1,0,0,3, 1,0,1,3, 1,0,2,3, 1,0,3,3, 1,0,4,3, 1,0,5,3, 1,0,6,3, - 1,0,7,3, 1,0,8,3, 1,0,9,3, 1,8,0,3, 1,8,1,3, 9,0,0,3, 9,0,1,3, 9,8,0,3, 9,8,1,3, - 1,1,0,3, 1,1,1,3, 1,1,2,3, 1,1,3,3, 1,1,4,3, 1,1,5,3, 1,1,6,3, 1,1,7,3, 1,1,8,3, - 1,1,9,3, 1,9,0,3, 1,9,1,3, 9,1,0,3, 9,1,1,3, 9,9,0,3, 9,9,1,3, 1,2,0,3, 1,2,1,3, - 1,2,2,3, 1,2,3,3, 1,2,4,3, 1,2,5,3, 1,2,6,3, 1,2,7,3, 1,2,8,3, 1,2,9,3, 1,8,2,3, - 1,8,3,3, 9,2,0,3, 9,2,1,3, 9,0,8,3, 9,0,9,3, 1,3,0,3, 1,3,1,3, 1,3,2,3, 1,3,3,3, - 1,3,4,3, 1,3,5,3, 1,3,6,3, 1,3,7,3, 1,3,8,3, 1,3,9,3, 1,9,2,3, 1,9,3,3, 9,3,0,3, - 9,3,1,3, 9,1,8,3, 9,1,9,3, 1,4,0,3, 1,4,1,3, 1,4,2,3, 1,4,3,3, 1,4,4,3, 1,4,5,3, - 1,4,6,3, 1,4,7,3, 1,4,8,3, 1,4,9,3, 1,8,4,3, 1,8,5,3, 9,4,0,3, 9,4,1,3, 1,8,8,3, - 1,8,9,3, 1,5,0,3, 1,5,1,3, 1,5,2,3, 1,5,3,3, 1,5,4,3, 1,5,5,3, 1,5,6,3, 1,5,7,3, - 1,5,8,3, 1,5,9,3, 1,9,4,3, 1,9,5,3, 9,5,0,3, 9,5,1,3, 1,9,8,3, 1,9,9,3, 1,6,0,3, - 1,6,1,3, 1,6,2,3, 1,6,3,3, 1,6,4,3, 1,6,5,3, 1,6,6,3, 1,6,7,3, 1,6,8,3, 1,6,9,3, - 1,8,6,3, 1,8,7,3, 9,6,0,3, 9,6,1,3, 9,8,8,3, 9,8,9,3, 1,7,0,3, 1,7,1,3, 1,7,2,3, - 1,7,3,3, 1,7,4,3, 1,7,5,3, 1,7,6,3, 1,7,7,3, 1,7,8,3, 1,7,9,3, 1,9,6,3, 1,9,7,3, - 9,7,0,3, 9,7,1,3, 9,9,8,3, 9,9,9,3, 2,0,0,3, 2,0,1,3, 2,0,2,3, 2,0,3,3, 2,0,4,3, - 2,0,5,3, 2,0,6,3, 2,0,7,3, 2,0,8,3, 2,0,9,3, 2,8,0,3, 2,8,1,3, 8,0,2,3, 8,0,3,3, - 8,8,2,3, 8,8,3,3, 2,1,0,3, 2,1,1,3, 2,1,2,3, 2,1,3,3, 2,1,4,3, 2,1,5,3, 2,1,6,3, - 2,1,7,3, 2,1,8,3, 2,1,9,3, 2,9,0,3, 2,9,1,3, 8,1,2,3, 8,1,3,3, 8,9,2,3, 8,9,3,3, - 2,2,0,3, 2,2,1,3, 2,2,2,3, 2,2,3,3, 2,2,4,3, 2,2,5,3, 2,2,6,3, 2,2,7,3, 2,2,8,3, - 2,2,9,3, 2,8,2,3, 2,8,3,3, 8,2,2,3, 8,2,3,3, 8,2,8,3, 8,2,9,3, 2,3,0,3, 2,3,1,3, - 2,3,2,3, 2,3,3,3, 2,3,4,3, 2,3,5,3, 2,3,6,3, 2,3,7,3, 2,3,8,3, 2,3,9,3, 2,9,2,3, - 2,9,3,3, 8,3,2,3, 8,3,3,3, 8,3,8,3, 8,3,9,3, 2,4,0,3, 2,4,1,3, 2,4,2,3, 2,4,3,3, - 2,4,4,3, 2,4,5,3, 2,4,6,3, 2,4,7,3, 2,4,8,3, 2,4,9,3, 2,8,4,3, 2,8,5,3, 8,4,2,3, - 8,4,3,3, 2,8,8,3, 2,8,9,3, 2,5,0,3, 2,5,1,3, 2,5,2,3, 2,5,3,3, 2,5,4,3, 2,5,5,3, - 2,5,6,3, 2,5,7,3, 2,5,8,3, 2,5,9,3, 2,9,4,3, 2,9,5,3, 8,5,2,3, 8,5,3,3, 2,9,8,3, - 2,9,9,3, 2,6,0,3, 2,6,1,3, 2,6,2,3, 2,6,3,3, 2,6,4,3, 2,6,5,3, 2,6,6,3, 2,6,7,3, - 2,6,8,3, 2,6,9,3, 2,8,6,3, 2,8,7,3, 8,6,2,3, 8,6,3,3, 8,8,8,3, 8,8,9,3, 2,7,0,3, - 2,7,1,3, 2,7,2,3, 2,7,3,3, 2,7,4,3, 2,7,5,3, 2,7,6,3, 2,7,7,3, 2,7,8,3, 2,7,9,3, - 2,9,6,3, 2,9,7,3, 8,7,2,3, 8,7,3,3, 8,9,8,3, 8,9,9,3, 3,0,0,3, 3,0,1,3, 3,0,2,3, - 3,0,3,3, 3,0,4,3, 3,0,5,3, 3,0,6,3, 3,0,7,3, 3,0,8,3, 3,0,9,3, 3,8,0,3, 3,8,1,3, - 9,0,2,3, 9,0,3,3, 9,8,2,3, 9,8,3,3, 3,1,0,3, 3,1,1,3, 3,1,2,3, 3,1,3,3, 3,1,4,3, - 3,1,5,3, 3,1,6,3, 3,1,7,3, 3,1,8,3, 3,1,9,3, 3,9,0,3, 3,9,1,3, 9,1,2,3, 9,1,3,3, - 9,9,2,3, 9,9,3,3, 3,2,0,3, 3,2,1,3, 3,2,2,3, 3,2,3,3, 3,2,4,3, 3,2,5,3, 3,2,6,3, - 3,2,7,3, 3,2,8,3, 3,2,9,3, 3,8,2,3, 3,8,3,3, 9,2,2,3, 9,2,3,3, 9,2,8,3, 9,2,9,3, - 3,3,0,3, 3,3,1,3, 3,3,2,3, 3,3,3,3, 3,3,4,3, 3,3,5,3, 3,3,6,3, 3,3,7,3, 3,3,8,3, - 3,3,9,3, 3,9,2,3, 3,9,3,3, 9,3,2,3, 9,3,3,3, 9,3,8,3, 9,3,9,3, 3,4,0,3, 3,4,1,3, - 3,4,2,3, 3,4,3,3, 3,4,4,3, 3,4,5,3, 3,4,6,3, 3,4,7,3, 3,4,8,3, 3,4,9,3, 3,8,4,3, - 3,8,5,3, 9,4,2,3, 9,4,3,3, 3,8,8,3, 3,8,9,3, 3,5,0,3, 3,5,1,3, 3,5,2,3, 3,5,3,3, - 3,5,4,3, 3,5,5,3, 3,5,6,3, 3,5,7,3, 3,5,8,3, 3,5,9,3, 3,9,4,3, 3,9,5,3, 9,5,2,3, - 9,5,3,3, 3,9,8,3, 3,9,9,3, 3,6,0,3, 3,6,1,3, 3,6,2,3, 3,6,3,3, 3,6,4,3, 3,6,5,3, - 3,6,6,3, 3,6,7,3, 3,6,8,3, 3,6,9,3, 3,8,6,3, 3,8,7,3, 9,6,2,3, 9,6,3,3, 9,8,8,3, - 9,8,9,3, 3,7,0,3, 3,7,1,3, 3,7,2,3, 3,7,3,3, 3,7,4,3, 3,7,5,3, 3,7,6,3, 3,7,7,3, - 3,7,8,3, 3,7,9,3, 3,9,6,3, 3,9,7,3, 9,7,2,3, 9,7,3,3, 9,9,8,3, 9,9,9,3, 4,0,0,3, - 4,0,1,3, 4,0,2,3, 4,0,3,3, 4,0,4,3, 4,0,5,3, 4,0,6,3, 4,0,7,3, 4,0,8,3, 4,0,9,3, - 4,8,0,3, 4,8,1,3, 8,0,4,3, 8,0,5,3, 8,8,4,3, 8,8,5,3, 4,1,0,3, 4,1,1,3, 4,1,2,3, - 4,1,3,3, 4,1,4,3, 4,1,5,3, 4,1,6,3, 4,1,7,3, 4,1,8,3, 4,1,9,3, 4,9,0,3, 4,9,1,3, - 8,1,4,3, 8,1,5,3, 8,9,4,3, 8,9,5,3, 4,2,0,3, 4,2,1,3, 4,2,2,3, 4,2,3,3, 4,2,4,3, - 4,2,5,3, 4,2,6,3, 4,2,7,3, 4,2,8,3, 4,2,9,3, 4,8,2,3, 4,8,3,3, 8,2,4,3, 8,2,5,3, - 8,4,8,3, 8,4,9,3, 4,3,0,3, 4,3,1,3, 4,3,2,3, 4,3,3,3, 4,3,4,3, 4,3,5,3, 4,3,6,3, - 4,3,7,3, 4,3,8,3, 4,3,9,3, 4,9,2,3, 4,9,3,3, 8,3,4,3, 8,3,5,3, 8,5,8,3, 8,5,9,3, - 4,4,0,3, 4,4,1,3, 4,4,2,3, 4,4,3,3, 4,4,4,3, 4,4,5,3, 4,4,6,3, 4,4,7,3, 4,4,8,3, - 4,4,9,3, 4,8,4,3, 4,8,5,3, 8,4,4,3, 8,4,5,3, 4,8,8,3, 4,8,9,3, 4,5,0,3, 4,5,1,3, - 4,5,2,3, 4,5,3,3, 4,5,4,3, 4,5,5,3, 4,5,6,3, 4,5,7,3, 4,5,8,3, 4,5,9,3, 4,9,4,3, - 4,9,5,3, 8,5,4,3, 8,5,5,3, 4,9,8,3, 4,9,9,3, 4,6,0,3, 4,6,1,3, 4,6,2,3, 4,6,3,3, - 4,6,4,3, 4,6,5,3, 4,6,6,3, 4,6,7,3, 4,6,8,3, 4,6,9,3, 4,8,6,3, 4,8,7,3, 8,6,4,3, - 8,6,5,3, 8,8,8,3, 8,8,9,3, 4,7,0,3, 4,7,1,3, 4,7,2,3, 4,7,3,3, 4,7,4,3, 4,7,5,3, - 4,7,6,3, 4,7,7,3, 4,7,8,3, 4,7,9,3, 4,9,6,3, 4,9,7,3, 8,7,4,3, 8,7,5,3, 8,9,8,3, - 8,9,9,3, 5,0,0,3, 5,0,1,3, 5,0,2,3, 5,0,3,3, 5,0,4,3, 5,0,5,3, 5,0,6,3, 5,0,7,3, - 5,0,8,3, 5,0,9,3, 5,8,0,3, 5,8,1,3, 9,0,4,3, 9,0,5,3, 9,8,4,3, 9,8,5,3, 5,1,0,3, - 5,1,1,3, 5,1,2,3, 5,1,3,3, 5,1,4,3, 5,1,5,3, 5,1,6,3, 5,1,7,3, 5,1,8,3, 5,1,9,3, - 5,9,0,3, 5,9,1,3, 9,1,4,3, 9,1,5,3, 9,9,4,3, 9,9,5,3, 5,2,0,3, 5,2,1,3, 5,2,2,3, - 5,2,3,3, 5,2,4,3, 5,2,5,3, 5,2,6,3, 5,2,7,3, 5,2,8,3, 5,2,9,3, 5,8,2,3, 5,8,3,3, - 9,2,4,3, 9,2,5,3, 9,4,8,3, 9,4,9,3, 5,3,0,3, 5,3,1,3, 5,3,2,3, 5,3,3,3, 5,3,4,3, - 5,3,5,3, 5,3,6,3, 5,3,7,3, 5,3,8,3, 5,3,9,3, 5,9,2,3, 5,9,3,3, 9,3,4,3, 9,3,5,3, - 9,5,8,3, 9,5,9,3, 5,4,0,3, 5,4,1,3, 5,4,2,3, 5,4,3,3, 5,4,4,3, 5,4,5,3, 5,4,6,3, - 5,4,7,3, 5,4,8,3, 5,4,9,3, 5,8,4,3, 5,8,5,3, 9,4,4,3, 9,4,5,3, 5,8,8,3, 5,8,9,3, - 5,5,0,3, 5,5,1,3, 5,5,2,3, 5,5,3,3, 5,5,4,3, 5,5,5,3, 5,5,6,3, 5,5,7,3, 5,5,8,3, - 5,5,9,3, 5,9,4,3, 5,9,5,3, 9,5,4,3, 9,5,5,3, 5,9,8,3, 5,9,9,3, 5,6,0,3, 5,6,1,3, - 5,6,2,3, 5,6,3,3, 5,6,4,3, 5,6,5,3, 5,6,6,3, 5,6,7,3, 5,6,8,3, 5,6,9,3, 5,8,6,3, - 5,8,7,3, 9,6,4,3, 9,6,5,3, 9,8,8,3, 9,8,9,3, 5,7,0,3, 5,7,1,3, 5,7,2,3, 5,7,3,3, - 5,7,4,3, 5,7,5,3, 5,7,6,3, 5,7,7,3, 5,7,8,3, 5,7,9,3, 5,9,6,3, 5,9,7,3, 9,7,4,3, - 9,7,5,3, 9,9,8,3, 9,9,9,3, 6,0,0,3, 6,0,1,3, 6,0,2,3, 6,0,3,3, 6,0,4,3, 6,0,5,3, - 6,0,6,3, 6,0,7,3, 6,0,8,3, 6,0,9,3, 6,8,0,3, 6,8,1,3, 8,0,6,3, 8,0,7,3, 8,8,6,3, - 8,8,7,3, 6,1,0,3, 6,1,1,3, 6,1,2,3, 6,1,3,3, 6,1,4,3, 6,1,5,3, 6,1,6,3, 6,1,7,3, - 6,1,8,3, 6,1,9,3, 6,9,0,3, 6,9,1,3, 8,1,6,3, 8,1,7,3, 8,9,6,3, 8,9,7,3, 6,2,0,3, - 6,2,1,3, 6,2,2,3, 6,2,3,3, 6,2,4,3, 6,2,5,3, 6,2,6,3, 6,2,7,3, 6,2,8,3, 6,2,9,3, - 6,8,2,3, 6,8,3,3, 8,2,6,3, 8,2,7,3, 8,6,8,3, 8,6,9,3, 6,3,0,3, 6,3,1,3, 6,3,2,3, - 6,3,3,3, 6,3,4,3, 6,3,5,3, 6,3,6,3, 6,3,7,3, 6,3,8,3, 6,3,9,3, 6,9,2,3, 6,9,3,3, - 8,3,6,3, 8,3,7,3, 8,7,8,3, 8,7,9,3, 6,4,0,3, 6,4,1,3, 6,4,2,3, 6,4,3,3, 6,4,4,3, - 6,4,5,3, 6,4,6,3, 6,4,7,3, 6,4,8,3, 6,4,9,3, 6,8,4,3, 6,8,5,3, 8,4,6,3, 8,4,7,3, - 6,8,8,3, 6,8,9,3, 6,5,0,3, 6,5,1,3, 6,5,2,3, 6,5,3,3, 6,5,4,3, 6,5,5,3, 6,5,6,3, - 6,5,7,3, 6,5,8,3, 6,5,9,3, 6,9,4,3, 6,9,5,3, 8,5,6,3, 8,5,7,3, 6,9,8,3, 6,9,9,3, - 6,6,0,3, 6,6,1,3, 6,6,2,3, 6,6,3,3, 6,6,4,3, 6,6,5,3, 6,6,6,3, 6,6,7,3, 6,6,8,3, - 6,6,9,3, 6,8,6,3, 6,8,7,3, 8,6,6,3, 8,6,7,3, 8,8,8,3, 8,8,9,3, 6,7,0,3, 6,7,1,3, - 6,7,2,3, 6,7,3,3, 6,7,4,3, 6,7,5,3, 6,7,6,3, 6,7,7,3, 6,7,8,3, 6,7,9,3, 6,9,6,3, - 6,9,7,3, 8,7,6,3, 8,7,7,3, 8,9,8,3, 8,9,9,3, 7,0,0,3, 7,0,1,3, 7,0,2,3, 7,0,3,3, - 7,0,4,3, 7,0,5,3, 7,0,6,3, 7,0,7,3, 7,0,8,3, 7,0,9,3, 7,8,0,3, 7,8,1,3, 9,0,6,3, - 9,0,7,3, 9,8,6,3, 9,8,7,3, 7,1,0,3, 7,1,1,3, 7,1,2,3, 7,1,3,3, 7,1,4,3, 7,1,5,3, - 7,1,6,3, 7,1,7,3, 7,1,8,3, 7,1,9,3, 7,9,0,3, 7,9,1,3, 9,1,6,3, 9,1,7,3, 9,9,6,3, - 9,9,7,3, 7,2,0,3, 7,2,1,3, 7,2,2,3, 7,2,3,3, 7,2,4,3, 7,2,5,3, 7,2,6,3, 7,2,7,3, - 7,2,8,3, 7,2,9,3, 7,8,2,3, 7,8,3,3, 9,2,6,3, 9,2,7,3, 9,6,8,3, 9,6,9,3, 7,3,0,3, - 7,3,1,3, 7,3,2,3, 7,3,3,3, 7,3,4,3, 7,3,5,3, 7,3,6,3, 7,3,7,3, 7,3,8,3, 7,3,9,3, - 7,9,2,3, 7,9,3,3, 9,3,6,3, 9,3,7,3, 9,7,8,3, 9,7,9,3, 7,4,0,3, 7,4,1,3, 7,4,2,3, - 7,4,3,3, 7,4,4,3, 7,4,5,3, 7,4,6,3, 7,4,7,3, 7,4,8,3, 7,4,9,3, 7,8,4,3, 7,8,5,3, - 9,4,6,3, 9,4,7,3, 7,8,8,3, 7,8,9,3, 7,5,0,3, 7,5,1,3, 7,5,2,3, 7,5,3,3, 7,5,4,3, - 7,5,5,3, 7,5,6,3, 7,5,7,3, 7,5,8,3, 7,5,9,3, 7,9,4,3, 7,9,5,3, 9,5,6,3, 9,5,7,3, - 7,9,8,3, 7,9,9,3, 7,6,0,3, 7,6,1,3, 7,6,2,3, 7,6,3,3, 7,6,4,3, 7,6,5,3, 7,6,6,3, - 7,6,7,3, 7,6,8,3, 7,6,9,3, 7,8,6,3, 7,8,7,3, 9,6,6,3, 9,6,7,3, 9,8,8,3, 9,8,9,3, - 7,7,0,3, 7,7,1,3, 7,7,2,3, 7,7,3,3, 7,7,4,3, 7,7,5,3, 7,7,6,3, 7,7,7,3, 7,7,8,3, - 7,7,9,3, 7,9,6,3, 7,9,7,3, 9,7,6,3, 9,7,7,3, 9,9,8,3, 9,9,9,3}; -#endif - -#if defined(DEC_BIN2BCD8) && DEC_BIN2BCD8==1 && !defined(DECBIN2BCD8) -#define DECBIN2BCD8 - -const uint8_t BIN2BCD8[4000]={ - 0,0,0,0, 0,0,1,1, 0,0,2,1, 0,0,3,1, 0,0,4,1, 0,0,5,1, 0,0,6,1, 0,0,7,1, 0,0,8,1, - 0,0,9,1, 0,1,0,2, 0,1,1,2, 0,1,2,2, 0,1,3,2, 0,1,4,2, 0,1,5,2, 0,1,6,2, 0,1,7,2, - 0,1,8,2, 0,1,9,2, 0,2,0,2, 0,2,1,2, 0,2,2,2, 0,2,3,2, 0,2,4,2, 0,2,5,2, 0,2,6,2, - 0,2,7,2, 0,2,8,2, 0,2,9,2, 0,3,0,2, 0,3,1,2, 0,3,2,2, 0,3,3,2, 0,3,4,2, 0,3,5,2, - 0,3,6,2, 0,3,7,2, 0,3,8,2, 0,3,9,2, 0,4,0,2, 0,4,1,2, 0,4,2,2, 0,4,3,2, 0,4,4,2, - 0,4,5,2, 0,4,6,2, 0,4,7,2, 0,4,8,2, 0,4,9,2, 0,5,0,2, 0,5,1,2, 0,5,2,2, 0,5,3,2, - 0,5,4,2, 0,5,5,2, 0,5,6,2, 0,5,7,2, 0,5,8,2, 0,5,9,2, 0,6,0,2, 0,6,1,2, 0,6,2,2, - 0,6,3,2, 0,6,4,2, 0,6,5,2, 0,6,6,2, 0,6,7,2, 0,6,8,2, 0,6,9,2, 0,7,0,2, 0,7,1,2, - 0,7,2,2, 0,7,3,2, 0,7,4,2, 0,7,5,2, 0,7,6,2, 0,7,7,2, 0,7,8,2, 0,7,9,2, 0,8,0,2, - 0,8,1,2, 0,8,2,2, 0,8,3,2, 0,8,4,2, 0,8,5,2, 0,8,6,2, 0,8,7,2, 0,8,8,2, 0,8,9,2, - 0,9,0,2, 0,9,1,2, 0,9,2,2, 0,9,3,2, 0,9,4,2, 0,9,5,2, 0,9,6,2, 0,9,7,2, 0,9,8,2, - 0,9,9,2, 1,0,0,3, 1,0,1,3, 1,0,2,3, 1,0,3,3, 1,0,4,3, 1,0,5,3, 1,0,6,3, 1,0,7,3, - 1,0,8,3, 1,0,9,3, 1,1,0,3, 1,1,1,3, 1,1,2,3, 1,1,3,3, 1,1,4,3, 1,1,5,3, 1,1,6,3, - 1,1,7,3, 1,1,8,3, 1,1,9,3, 1,2,0,3, 1,2,1,3, 1,2,2,3, 1,2,3,3, 1,2,4,3, 1,2,5,3, - 1,2,6,3, 1,2,7,3, 1,2,8,3, 1,2,9,3, 1,3,0,3, 1,3,1,3, 1,3,2,3, 1,3,3,3, 1,3,4,3, - 1,3,5,3, 1,3,6,3, 1,3,7,3, 1,3,8,3, 1,3,9,3, 1,4,0,3, 1,4,1,3, 1,4,2,3, 1,4,3,3, - 1,4,4,3, 1,4,5,3, 1,4,6,3, 1,4,7,3, 1,4,8,3, 1,4,9,3, 1,5,0,3, 1,5,1,3, 1,5,2,3, - 1,5,3,3, 1,5,4,3, 1,5,5,3, 1,5,6,3, 1,5,7,3, 1,5,8,3, 1,5,9,3, 1,6,0,3, 1,6,1,3, - 1,6,2,3, 1,6,3,3, 1,6,4,3, 1,6,5,3, 1,6,6,3, 1,6,7,3, 1,6,8,3, 1,6,9,3, 1,7,0,3, - 1,7,1,3, 1,7,2,3, 1,7,3,3, 1,7,4,3, 1,7,5,3, 1,7,6,3, 1,7,7,3, 1,7,8,3, 1,7,9,3, - 1,8,0,3, 1,8,1,3, 1,8,2,3, 1,8,3,3, 1,8,4,3, 1,8,5,3, 1,8,6,3, 1,8,7,3, 1,8,8,3, - 1,8,9,3, 1,9,0,3, 1,9,1,3, 1,9,2,3, 1,9,3,3, 1,9,4,3, 1,9,5,3, 1,9,6,3, 1,9,7,3, - 1,9,8,3, 1,9,9,3, 2,0,0,3, 2,0,1,3, 2,0,2,3, 2,0,3,3, 2,0,4,3, 2,0,5,3, 2,0,6,3, - 2,0,7,3, 2,0,8,3, 2,0,9,3, 2,1,0,3, 2,1,1,3, 2,1,2,3, 2,1,3,3, 2,1,4,3, 2,1,5,3, - 2,1,6,3, 2,1,7,3, 2,1,8,3, 2,1,9,3, 2,2,0,3, 2,2,1,3, 2,2,2,3, 2,2,3,3, 2,2,4,3, - 2,2,5,3, 2,2,6,3, 2,2,7,3, 2,2,8,3, 2,2,9,3, 2,3,0,3, 2,3,1,3, 2,3,2,3, 2,3,3,3, - 2,3,4,3, 2,3,5,3, 2,3,6,3, 2,3,7,3, 2,3,8,3, 2,3,9,3, 2,4,0,3, 2,4,1,3, 2,4,2,3, - 2,4,3,3, 2,4,4,3, 2,4,5,3, 2,4,6,3, 2,4,7,3, 2,4,8,3, 2,4,9,3, 2,5,0,3, 2,5,1,3, - 2,5,2,3, 2,5,3,3, 2,5,4,3, 2,5,5,3, 2,5,6,3, 2,5,7,3, 2,5,8,3, 2,5,9,3, 2,6,0,3, - 2,6,1,3, 2,6,2,3, 2,6,3,3, 2,6,4,3, 2,6,5,3, 2,6,6,3, 2,6,7,3, 2,6,8,3, 2,6,9,3, - 2,7,0,3, 2,7,1,3, 2,7,2,3, 2,7,3,3, 2,7,4,3, 2,7,5,3, 2,7,6,3, 2,7,7,3, 2,7,8,3, - 2,7,9,3, 2,8,0,3, 2,8,1,3, 2,8,2,3, 2,8,3,3, 2,8,4,3, 2,8,5,3, 2,8,6,3, 2,8,7,3, - 2,8,8,3, 2,8,9,3, 2,9,0,3, 2,9,1,3, 2,9,2,3, 2,9,3,3, 2,9,4,3, 2,9,5,3, 2,9,6,3, - 2,9,7,3, 2,9,8,3, 2,9,9,3, 3,0,0,3, 3,0,1,3, 3,0,2,3, 3,0,3,3, 3,0,4,3, 3,0,5,3, - 3,0,6,3, 3,0,7,3, 3,0,8,3, 3,0,9,3, 3,1,0,3, 3,1,1,3, 3,1,2,3, 3,1,3,3, 3,1,4,3, - 3,1,5,3, 3,1,6,3, 3,1,7,3, 3,1,8,3, 3,1,9,3, 3,2,0,3, 3,2,1,3, 3,2,2,3, 3,2,3,3, - 3,2,4,3, 3,2,5,3, 3,2,6,3, 3,2,7,3, 3,2,8,3, 3,2,9,3, 3,3,0,3, 3,3,1,3, 3,3,2,3, - 3,3,3,3, 3,3,4,3, 3,3,5,3, 3,3,6,3, 3,3,7,3, 3,3,8,3, 3,3,9,3, 3,4,0,3, 3,4,1,3, - 3,4,2,3, 3,4,3,3, 3,4,4,3, 3,4,5,3, 3,4,6,3, 3,4,7,3, 3,4,8,3, 3,4,9,3, 3,5,0,3, - 3,5,1,3, 3,5,2,3, 3,5,3,3, 3,5,4,3, 3,5,5,3, 3,5,6,3, 3,5,7,3, 3,5,8,3, 3,5,9,3, - 3,6,0,3, 3,6,1,3, 3,6,2,3, 3,6,3,3, 3,6,4,3, 3,6,5,3, 3,6,6,3, 3,6,7,3, 3,6,8,3, - 3,6,9,3, 3,7,0,3, 3,7,1,3, 3,7,2,3, 3,7,3,3, 3,7,4,3, 3,7,5,3, 3,7,6,3, 3,7,7,3, - 3,7,8,3, 3,7,9,3, 3,8,0,3, 3,8,1,3, 3,8,2,3, 3,8,3,3, 3,8,4,3, 3,8,5,3, 3,8,6,3, - 3,8,7,3, 3,8,8,3, 3,8,9,3, 3,9,0,3, 3,9,1,3, 3,9,2,3, 3,9,3,3, 3,9,4,3, 3,9,5,3, - 3,9,6,3, 3,9,7,3, 3,9,8,3, 3,9,9,3, 4,0,0,3, 4,0,1,3, 4,0,2,3, 4,0,3,3, 4,0,4,3, - 4,0,5,3, 4,0,6,3, 4,0,7,3, 4,0,8,3, 4,0,9,3, 4,1,0,3, 4,1,1,3, 4,1,2,3, 4,1,3,3, - 4,1,4,3, 4,1,5,3, 4,1,6,3, 4,1,7,3, 4,1,8,3, 4,1,9,3, 4,2,0,3, 4,2,1,3, 4,2,2,3, - 4,2,3,3, 4,2,4,3, 4,2,5,3, 4,2,6,3, 4,2,7,3, 4,2,8,3, 4,2,9,3, 4,3,0,3, 4,3,1,3, - 4,3,2,3, 4,3,3,3, 4,3,4,3, 4,3,5,3, 4,3,6,3, 4,3,7,3, 4,3,8,3, 4,3,9,3, 4,4,0,3, - 4,4,1,3, 4,4,2,3, 4,4,3,3, 4,4,4,3, 4,4,5,3, 4,4,6,3, 4,4,7,3, 4,4,8,3, 4,4,9,3, - 4,5,0,3, 4,5,1,3, 4,5,2,3, 4,5,3,3, 4,5,4,3, 4,5,5,3, 4,5,6,3, 4,5,7,3, 4,5,8,3, - 4,5,9,3, 4,6,0,3, 4,6,1,3, 4,6,2,3, 4,6,3,3, 4,6,4,3, 4,6,5,3, 4,6,6,3, 4,6,7,3, - 4,6,8,3, 4,6,9,3, 4,7,0,3, 4,7,1,3, 4,7,2,3, 4,7,3,3, 4,7,4,3, 4,7,5,3, 4,7,6,3, - 4,7,7,3, 4,7,8,3, 4,7,9,3, 4,8,0,3, 4,8,1,3, 4,8,2,3, 4,8,3,3, 4,8,4,3, 4,8,5,3, - 4,8,6,3, 4,8,7,3, 4,8,8,3, 4,8,9,3, 4,9,0,3, 4,9,1,3, 4,9,2,3, 4,9,3,3, 4,9,4,3, - 4,9,5,3, 4,9,6,3, 4,9,7,3, 4,9,8,3, 4,9,9,3, 5,0,0,3, 5,0,1,3, 5,0,2,3, 5,0,3,3, - 5,0,4,3, 5,0,5,3, 5,0,6,3, 5,0,7,3, 5,0,8,3, 5,0,9,3, 5,1,0,3, 5,1,1,3, 5,1,2,3, - 5,1,3,3, 5,1,4,3, 5,1,5,3, 5,1,6,3, 5,1,7,3, 5,1,8,3, 5,1,9,3, 5,2,0,3, 5,2,1,3, - 5,2,2,3, 5,2,3,3, 5,2,4,3, 5,2,5,3, 5,2,6,3, 5,2,7,3, 5,2,8,3, 5,2,9,3, 5,3,0,3, - 5,3,1,3, 5,3,2,3, 5,3,3,3, 5,3,4,3, 5,3,5,3, 5,3,6,3, 5,3,7,3, 5,3,8,3, 5,3,9,3, - 5,4,0,3, 5,4,1,3, 5,4,2,3, 5,4,3,3, 5,4,4,3, 5,4,5,3, 5,4,6,3, 5,4,7,3, 5,4,8,3, - 5,4,9,3, 5,5,0,3, 5,5,1,3, 5,5,2,3, 5,5,3,3, 5,5,4,3, 5,5,5,3, 5,5,6,3, 5,5,7,3, - 5,5,8,3, 5,5,9,3, 5,6,0,3, 5,6,1,3, 5,6,2,3, 5,6,3,3, 5,6,4,3, 5,6,5,3, 5,6,6,3, - 5,6,7,3, 5,6,8,3, 5,6,9,3, 5,7,0,3, 5,7,1,3, 5,7,2,3, 5,7,3,3, 5,7,4,3, 5,7,5,3, - 5,7,6,3, 5,7,7,3, 5,7,8,3, 5,7,9,3, 5,8,0,3, 5,8,1,3, 5,8,2,3, 5,8,3,3, 5,8,4,3, - 5,8,5,3, 5,8,6,3, 5,8,7,3, 5,8,8,3, 5,8,9,3, 5,9,0,3, 5,9,1,3, 5,9,2,3, 5,9,3,3, - 5,9,4,3, 5,9,5,3, 5,9,6,3, 5,9,7,3, 5,9,8,3, 5,9,9,3, 6,0,0,3, 6,0,1,3, 6,0,2,3, - 6,0,3,3, 6,0,4,3, 6,0,5,3, 6,0,6,3, 6,0,7,3, 6,0,8,3, 6,0,9,3, 6,1,0,3, 6,1,1,3, - 6,1,2,3, 6,1,3,3, 6,1,4,3, 6,1,5,3, 6,1,6,3, 6,1,7,3, 6,1,8,3, 6,1,9,3, 6,2,0,3, - 6,2,1,3, 6,2,2,3, 6,2,3,3, 6,2,4,3, 6,2,5,3, 6,2,6,3, 6,2,7,3, 6,2,8,3, 6,2,9,3, - 6,3,0,3, 6,3,1,3, 6,3,2,3, 6,3,3,3, 6,3,4,3, 6,3,5,3, 6,3,6,3, 6,3,7,3, 6,3,8,3, - 6,3,9,3, 6,4,0,3, 6,4,1,3, 6,4,2,3, 6,4,3,3, 6,4,4,3, 6,4,5,3, 6,4,6,3, 6,4,7,3, - 6,4,8,3, 6,4,9,3, 6,5,0,3, 6,5,1,3, 6,5,2,3, 6,5,3,3, 6,5,4,3, 6,5,5,3, 6,5,6,3, - 6,5,7,3, 6,5,8,3, 6,5,9,3, 6,6,0,3, 6,6,1,3, 6,6,2,3, 6,6,3,3, 6,6,4,3, 6,6,5,3, - 6,6,6,3, 6,6,7,3, 6,6,8,3, 6,6,9,3, 6,7,0,3, 6,7,1,3, 6,7,2,3, 6,7,3,3, 6,7,4,3, - 6,7,5,3, 6,7,6,3, 6,7,7,3, 6,7,8,3, 6,7,9,3, 6,8,0,3, 6,8,1,3, 6,8,2,3, 6,8,3,3, - 6,8,4,3, 6,8,5,3, 6,8,6,3, 6,8,7,3, 6,8,8,3, 6,8,9,3, 6,9,0,3, 6,9,1,3, 6,9,2,3, - 6,9,3,3, 6,9,4,3, 6,9,5,3, 6,9,6,3, 6,9,7,3, 6,9,8,3, 6,9,9,3, 7,0,0,3, 7,0,1,3, - 7,0,2,3, 7,0,3,3, 7,0,4,3, 7,0,5,3, 7,0,6,3, 7,0,7,3, 7,0,8,3, 7,0,9,3, 7,1,0,3, - 7,1,1,3, 7,1,2,3, 7,1,3,3, 7,1,4,3, 7,1,5,3, 7,1,6,3, 7,1,7,3, 7,1,8,3, 7,1,9,3, - 7,2,0,3, 7,2,1,3, 7,2,2,3, 7,2,3,3, 7,2,4,3, 7,2,5,3, 7,2,6,3, 7,2,7,3, 7,2,8,3, - 7,2,9,3, 7,3,0,3, 7,3,1,3, 7,3,2,3, 7,3,3,3, 7,3,4,3, 7,3,5,3, 7,3,6,3, 7,3,7,3, - 7,3,8,3, 7,3,9,3, 7,4,0,3, 7,4,1,3, 7,4,2,3, 7,4,3,3, 7,4,4,3, 7,4,5,3, 7,4,6,3, - 7,4,7,3, 7,4,8,3, 7,4,9,3, 7,5,0,3, 7,5,1,3, 7,5,2,3, 7,5,3,3, 7,5,4,3, 7,5,5,3, - 7,5,6,3, 7,5,7,3, 7,5,8,3, 7,5,9,3, 7,6,0,3, 7,6,1,3, 7,6,2,3, 7,6,3,3, 7,6,4,3, - 7,6,5,3, 7,6,6,3, 7,6,7,3, 7,6,8,3, 7,6,9,3, 7,7,0,3, 7,7,1,3, 7,7,2,3, 7,7,3,3, - 7,7,4,3, 7,7,5,3, 7,7,6,3, 7,7,7,3, 7,7,8,3, 7,7,9,3, 7,8,0,3, 7,8,1,3, 7,8,2,3, - 7,8,3,3, 7,8,4,3, 7,8,5,3, 7,8,6,3, 7,8,7,3, 7,8,8,3, 7,8,9,3, 7,9,0,3, 7,9,1,3, - 7,9,2,3, 7,9,3,3, 7,9,4,3, 7,9,5,3, 7,9,6,3, 7,9,7,3, 7,9,8,3, 7,9,9,3, 8,0,0,3, - 8,0,1,3, 8,0,2,3, 8,0,3,3, 8,0,4,3, 8,0,5,3, 8,0,6,3, 8,0,7,3, 8,0,8,3, 8,0,9,3, - 8,1,0,3, 8,1,1,3, 8,1,2,3, 8,1,3,3, 8,1,4,3, 8,1,5,3, 8,1,6,3, 8,1,7,3, 8,1,8,3, - 8,1,9,3, 8,2,0,3, 8,2,1,3, 8,2,2,3, 8,2,3,3, 8,2,4,3, 8,2,5,3, 8,2,6,3, 8,2,7,3, - 8,2,8,3, 8,2,9,3, 8,3,0,3, 8,3,1,3, 8,3,2,3, 8,3,3,3, 8,3,4,3, 8,3,5,3, 8,3,6,3, - 8,3,7,3, 8,3,8,3, 8,3,9,3, 8,4,0,3, 8,4,1,3, 8,4,2,3, 8,4,3,3, 8,4,4,3, 8,4,5,3, - 8,4,6,3, 8,4,7,3, 8,4,8,3, 8,4,9,3, 8,5,0,3, 8,5,1,3, 8,5,2,3, 8,5,3,3, 8,5,4,3, - 8,5,5,3, 8,5,6,3, 8,5,7,3, 8,5,8,3, 8,5,9,3, 8,6,0,3, 8,6,1,3, 8,6,2,3, 8,6,3,3, - 8,6,4,3, 8,6,5,3, 8,6,6,3, 8,6,7,3, 8,6,8,3, 8,6,9,3, 8,7,0,3, 8,7,1,3, 8,7,2,3, - 8,7,3,3, 8,7,4,3, 8,7,5,3, 8,7,6,3, 8,7,7,3, 8,7,8,3, 8,7,9,3, 8,8,0,3, 8,8,1,3, - 8,8,2,3, 8,8,3,3, 8,8,4,3, 8,8,5,3, 8,8,6,3, 8,8,7,3, 8,8,8,3, 8,8,9,3, 8,9,0,3, - 8,9,1,3, 8,9,2,3, 8,9,3,3, 8,9,4,3, 8,9,5,3, 8,9,6,3, 8,9,7,3, 8,9,8,3, 8,9,9,3, - 9,0,0,3, 9,0,1,3, 9,0,2,3, 9,0,3,3, 9,0,4,3, 9,0,5,3, 9,0,6,3, 9,0,7,3, 9,0,8,3, - 9,0,9,3, 9,1,0,3, 9,1,1,3, 9,1,2,3, 9,1,3,3, 9,1,4,3, 9,1,5,3, 9,1,6,3, 9,1,7,3, - 9,1,8,3, 9,1,9,3, 9,2,0,3, 9,2,1,3, 9,2,2,3, 9,2,3,3, 9,2,4,3, 9,2,5,3, 9,2,6,3, - 9,2,7,3, 9,2,8,3, 9,2,9,3, 9,3,0,3, 9,3,1,3, 9,3,2,3, 9,3,3,3, 9,3,4,3, 9,3,5,3, - 9,3,6,3, 9,3,7,3, 9,3,8,3, 9,3,9,3, 9,4,0,3, 9,4,1,3, 9,4,2,3, 9,4,3,3, 9,4,4,3, - 9,4,5,3, 9,4,6,3, 9,4,7,3, 9,4,8,3, 9,4,9,3, 9,5,0,3, 9,5,1,3, 9,5,2,3, 9,5,3,3, - 9,5,4,3, 9,5,5,3, 9,5,6,3, 9,5,7,3, 9,5,8,3, 9,5,9,3, 9,6,0,3, 9,6,1,3, 9,6,2,3, - 9,6,3,3, 9,6,4,3, 9,6,5,3, 9,6,6,3, 9,6,7,3, 9,6,8,3, 9,6,9,3, 9,7,0,3, 9,7,1,3, - 9,7,2,3, 9,7,3,3, 9,7,4,3, 9,7,5,3, 9,7,6,3, 9,7,7,3, 9,7,8,3, 9,7,9,3, 9,8,0,3, - 9,8,1,3, 9,8,2,3, 9,8,3,3, 9,8,4,3, 9,8,5,3, 9,8,6,3, 9,8,7,3, 9,8,8,3, 9,8,9,3, - 9,9,0,3, 9,9,1,3, 9,9,2,3, 9,9,3,3, 9,9,4,3, 9,9,5,3, 9,9,6,3, 9,9,7,3, 9,9,8,3, - 9,9,9,3}; -#endif -
src/decNumber/decDouble.c
@@ -1,140 +0,0 @@-/* ------------------------------------------------------------------ */ -/* decDouble.c -- decDouble operations module */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is included in the package as decNumber.pdf. This */ -/* document is also available in HTML, together with specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ -/* This module comprises decDouble operations (including conversions) */ -/* ------------------------------------------------------------------ */ - -#include "decContext.h" // public includes -#include "decDouble.h" // .. - -/* Constant mappings for shared code */ -#define DECPMAX DECDOUBLE_Pmax -#define DECEMIN DECDOUBLE_Emin -#define DECEMAX DECDOUBLE_Emax -#define DECEMAXD DECDOUBLE_EmaxD -#define DECBYTES DECDOUBLE_Bytes -#define DECSTRING DECDOUBLE_String -#define DECECONL DECDOUBLE_EconL -#define DECBIAS DECDOUBLE_Bias -#define DECLETS DECDOUBLE_Declets -#define DECQTINY (-DECDOUBLE_Bias) -// parameters of next-wider format -#define DECWBYTES DECQUAD_Bytes -#define DECWPMAX DECQUAD_Pmax -#define DECWECONL DECQUAD_EconL -#define DECWBIAS DECQUAD_Bias - -/* Type and function mappings for shared code */ -#define decFloat decDouble // Type name -#define decFloatWider decQuad // Type name - -// Utilities and conversions (binary results, extractors, etc.) -#define decFloatFromBCD decDoubleFromBCD -#define decFloatFromInt32 decDoubleFromInt32 -#define decFloatFromPacked decDoubleFromPacked -#define decFloatFromPackedChecked decDoubleFromPackedChecked -#define decFloatFromString decDoubleFromString -#define decFloatFromUInt32 decDoubleFromUInt32 -#define decFloatFromWider decDoubleFromWider -#define decFloatGetCoefficient decDoubleGetCoefficient -#define decFloatGetExponent decDoubleGetExponent -#define decFloatSetCoefficient decDoubleSetCoefficient -#define decFloatSetExponent decDoubleSetExponent -#define decFloatShow decDoubleShow -#define decFloatToBCD decDoubleToBCD -#define decFloatToEngString decDoubleToEngString -#define decFloatToInt32 decDoubleToInt32 -#define decFloatToInt32Exact decDoubleToInt32Exact -#define decFloatToPacked decDoubleToPacked -#define decFloatToString decDoubleToString -#define decFloatToUInt32 decDoubleToUInt32 -#define decFloatToUInt32Exact decDoubleToUInt32Exact -#define decFloatToWider decDoubleToWider -#define decFloatZero decDoubleZero - -// Computational (result is a decFloat) -#define decFloatAbs decDoubleAbs -#define decFloatAdd decDoubleAdd -#define decFloatAnd decDoubleAnd -#define decFloatDivide decDoubleDivide -#define decFloatDivideInteger decDoubleDivideInteger -#define decFloatFMA decDoubleFMA -#define decFloatInvert decDoubleInvert -#define decFloatLogB decDoubleLogB -#define decFloatMax decDoubleMax -#define decFloatMaxMag decDoubleMaxMag -#define decFloatMin decDoubleMin -#define decFloatMinMag decDoubleMinMag -#define decFloatMinus decDoubleMinus -#define decFloatMultiply decDoubleMultiply -#define decFloatNextMinus decDoubleNextMinus -#define decFloatNextPlus decDoubleNextPlus -#define decFloatNextToward decDoubleNextToward -#define decFloatOr decDoubleOr -#define decFloatPlus decDoublePlus -#define decFloatQuantize decDoubleQuantize -#define decFloatReduce decDoubleReduce -#define decFloatRemainder decDoubleRemainder -#define decFloatRemainderNear decDoubleRemainderNear -#define decFloatRotate decDoubleRotate -#define decFloatScaleB decDoubleScaleB -#define decFloatShift decDoubleShift -#define decFloatSubtract decDoubleSubtract -#define decFloatToIntegralValue decDoubleToIntegralValue -#define decFloatToIntegralExact decDoubleToIntegralExact -#define decFloatXor decDoubleXor - -// Comparisons -#define decFloatCompare decDoubleCompare -#define decFloatCompareSignal decDoubleCompareSignal -#define decFloatCompareTotal decDoubleCompareTotal -#define decFloatCompareTotalMag decDoubleCompareTotalMag - -// Copies -#define decFloatCanonical decDoubleCanonical -#define decFloatCopy decDoubleCopy -#define decFloatCopyAbs decDoubleCopyAbs -#define decFloatCopyNegate decDoubleCopyNegate -#define decFloatCopySign decDoubleCopySign - -// Non-computational -#define decFloatClass decDoubleClass -#define decFloatClassString decDoubleClassString -#define decFloatDigits decDoubleDigits -#define decFloatIsCanonical decDoubleIsCanonical -#define decFloatIsFinite decDoubleIsFinite -#define decFloatIsInfinite decDoubleIsInfinite -#define decFloatIsInteger decDoubleIsInteger -#define decFloatIsLogical decDoubleIsLogical -#define decFloatIsNaN decDoubleIsNaN -#define decFloatIsNegative decDoubleIsNegative -#define decFloatIsNormal decDoubleIsNormal -#define decFloatIsPositive decDoubleIsPositive -#define decFloatIsSignaling decDoubleIsSignaling -#define decFloatIsSignalling decDoubleIsSignalling -#define decFloatIsSigned decDoubleIsSigned -#define decFloatIsSubnormal decDoubleIsSubnormal -#define decFloatIsZero decDoubleIsZero -#define decFloatRadix decDoubleRadix -#define decFloatSameQuantum decDoubleSameQuantum -#define decFloatVersion decDoubleVersion - -#include "decNumberLocal.h" // local includes (need DECPMAX) -#include "decCommon.c" // non-arithmetic decFloat routines -#include "decBasic.c" // basic formats routines -
src/decNumber/decDouble.h
@@ -1,155 +0,0 @@-/* ------------------------------------------------------------------ */ -/* decDouble.h -- Decimal 64-bit format module header */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is included in the package as decNumber.pdf. This */ -/* document is also available in HTML, together with specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ - -#if !defined(DECDOUBLE) - #define DECDOUBLE - - #define DECDOUBLENAME "decimalDouble" /* Short name */ - #define DECDOUBLETITLE "Decimal 64-bit datum" /* Verbose name */ - #define DECDOUBLEAUTHOR "Mike Cowlishaw" /* Who to blame */ - - /* parameters for decDoubles */ - #define DECDOUBLE_Bytes 8 /* length */ - #define DECDOUBLE_Pmax 16 /* maximum precision (digits) */ - #define DECDOUBLE_Emin -383 /* minimum adjusted exponent */ - #define DECDOUBLE_Emax 384 /* maximum adjusted exponent */ - #define DECDOUBLE_EmaxD 3 /* maximum exponent digits */ - #define DECDOUBLE_Bias 398 /* bias for the exponent */ - #define DECDOUBLE_String 25 /* maximum string length, +1 */ - #define DECDOUBLE_EconL 8 /* exponent continuation length */ - #define DECDOUBLE_Declets 5 /* count of declets */ - /* highest biased exponent (Elimit-1) */ - #define DECDOUBLE_Ehigh (DECDOUBLE_Emax + DECDOUBLE_Bias - (DECDOUBLE_Pmax-1)) - - /* Required includes */ - #include "decContext.h" - #include "decQuad.h" - - /* The decDouble decimal 64-bit type, accessible by all sizes */ - typedef union { - uint8_t bytes[DECDOUBLE_Bytes]; /* fields: 1, 5, 8, 50 bits */ - uint16_t shorts[DECDOUBLE_Bytes/2]; - uint32_t words[DECDOUBLE_Bytes/4]; - #if DECUSE64 - uint64_t longs[DECDOUBLE_Bytes/8]; - #endif - } decDouble; - - /* ---------------------------------------------------------------- */ - /* Routines -- implemented as decFloat routines in common files */ - /* ---------------------------------------------------------------- */ - - /* Utilities and conversions, extractors, etc.) */ - extern decDouble * decDoubleFromBCD(decDouble *, int32_t, const uint8_t *, int32_t); - extern decDouble * decDoubleFromInt32(decDouble *, int32_t); - extern decDouble * decDoubleFromPacked(decDouble *, int32_t, const uint8_t *); - extern decDouble * decDoubleFromPackedChecked(decDouble *, int32_t, const uint8_t *); - extern decDouble * decDoubleFromString(decDouble *, const char *, decContext *); - extern decDouble * decDoubleFromUInt32(decDouble *, uint32_t); - extern decDouble * decDoubleFromWider(decDouble *, const decQuad *, decContext *); - extern int32_t decDoubleGetCoefficient(const decDouble *, uint8_t *); - extern int32_t decDoubleGetExponent(const decDouble *); - extern decDouble * decDoubleSetCoefficient(decDouble *, const uint8_t *, int32_t); - extern decDouble * decDoubleSetExponent(decDouble *, decContext *, int32_t); - extern void decDoubleShow(const decDouble *, const char *); - extern int32_t decDoubleToBCD(const decDouble *, int32_t *, uint8_t *); - extern char * decDoubleToEngString(const decDouble *, char *); - extern int32_t decDoubleToInt32(const decDouble *, decContext *, enum rounding); - extern int32_t decDoubleToInt32Exact(const decDouble *, decContext *, enum rounding); - extern int32_t decDoubleToPacked(const decDouble *, int32_t *, uint8_t *); - extern char * decDoubleToString(const decDouble *, char *); - extern uint32_t decDoubleToUInt32(const decDouble *, decContext *, enum rounding); - extern uint32_t decDoubleToUInt32Exact(const decDouble *, decContext *, enum rounding); - extern decQuad * decDoubleToWider(const decDouble *, decQuad *); - extern decDouble * decDoubleZero(decDouble *); - - /* Computational (result is a decDouble) */ - extern decDouble * decDoubleAbs(decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleAdd(decDouble *, const decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleAnd(decDouble *, const decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleDivide(decDouble *, const decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleDivideInteger(decDouble *, const decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleFMA(decDouble *, const decDouble *, const decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleInvert(decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleLogB(decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleMax(decDouble *, const decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleMaxMag(decDouble *, const decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleMin(decDouble *, const decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleMinMag(decDouble *, const decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleMinus(decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleMultiply(decDouble *, const decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleNextMinus(decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleNextPlus(decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleNextToward(decDouble *, const decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleOr(decDouble *, const decDouble *, const decDouble *, decContext *); - extern decDouble * decDoublePlus(decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleQuantize(decDouble *, const decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleReduce(decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleRemainder(decDouble *, const decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleRemainderNear(decDouble *, const decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleRotate(decDouble *, const decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleScaleB(decDouble *, const decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleShift(decDouble *, const decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleSubtract(decDouble *, const decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleToIntegralValue(decDouble *, const decDouble *, decContext *, enum rounding); - extern decDouble * decDoubleToIntegralExact(decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleXor(decDouble *, const decDouble *, const decDouble *, decContext *); - - /* Comparisons */ - extern decDouble * decDoubleCompare(decDouble *, const decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleCompareSignal(decDouble *, const decDouble *, const decDouble *, decContext *); - extern decDouble * decDoubleCompareTotal(decDouble *, const decDouble *, const decDouble *); - extern decDouble * decDoubleCompareTotalMag(decDouble *, const decDouble *, const decDouble *); - - /* Copies */ - extern decDouble * decDoubleCanonical(decDouble *, const decDouble *); - extern decDouble * decDoubleCopy(decDouble *, const decDouble *); - extern decDouble * decDoubleCopyAbs(decDouble *, const decDouble *); - extern decDouble * decDoubleCopyNegate(decDouble *, const decDouble *); - extern decDouble * decDoubleCopySign(decDouble *, const decDouble *, const decDouble *); - - /* Non-computational */ - extern enum decClass decDoubleClass(const decDouble *); - extern const char * decDoubleClassString(const decDouble *); - extern uint32_t decDoubleDigits(const decDouble *); - extern uint32_t decDoubleIsCanonical(const decDouble *); - extern uint32_t decDoubleIsFinite(const decDouble *); - extern uint32_t decDoubleIsInfinite(const decDouble *); - extern uint32_t decDoubleIsInteger(const decDouble *); - extern uint32_t decDoubleIsLogical(const decDouble *); - extern uint32_t decDoubleIsNaN(const decDouble *); - extern uint32_t decDoubleIsNegative(const decDouble *); - extern uint32_t decDoubleIsNormal(const decDouble *); - extern uint32_t decDoubleIsPositive(const decDouble *); - extern uint32_t decDoubleIsSignaling(const decDouble *); - extern uint32_t decDoubleIsSignalling(const decDouble *); - extern uint32_t decDoubleIsSigned(const decDouble *); - extern uint32_t decDoubleIsSubnormal(const decDouble *); - extern uint32_t decDoubleIsZero(const decDouble *); - extern uint32_t decDoubleRadix(const decDouble *); - extern uint32_t decDoubleSameQuantum(const decDouble *, const decDouble *); - extern const char * decDoubleVersion(void); - - /* decNumber conversions; these are implemented as macros so as not */ - /* to force a dependency on decimal64 and decNumber in decDouble. */ - /* decDoubleFromNumber returns a decimal64 * to avoid warnings. */ - #define decDoubleToNumber(dq, dn) decimal64ToNumber((decimal64 *)(dq), dn) - #define decDoubleFromNumber(dq, dn, set) decimal64FromNumber((decimal64 *)(dq), dn, set) - -#endif
src/decNumber/decNumber.c
@@ -1,8143 +0,0 @@-/* ------------------------------------------------------------------ */ -/* Decimal Number arithmetic module */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2009. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is called decNumber.pdf. This document is */ -/* available, together with arithmetic and format specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ -/* This module comprises the routines for arbitrary-precision General */ -/* Decimal Arithmetic as defined in the specification which may be */ -/* found on the General Decimal Arithmetic pages. It implements both */ -/* the full ('extended') arithmetic and the simpler ('subset') */ -/* arithmetic. */ -/* */ -/* Usage notes: */ -/* */ -/* 1. This code is ANSI C89 except: */ -/* */ -/* a) C99 line comments (double forward slash) are used. (Most C */ -/* compilers accept these. If yours does not, a simple script */ -/* can be used to convert them to ANSI C comments.) */ -/* */ -/* b) Types from C99 stdint.h are used. If you do not have this */ -/* header file, see the User's Guide section of the decNumber */ -/* documentation; this lists the necessary definitions. */ -/* */ -/* c) If DECDPUN>4 or DECUSE64=1, the C99 64-bit int64_t and */ -/* uint64_t types may be used. To avoid these, set DECUSE64=0 */ -/* and DECDPUN<=4 (see documentation). */ -/* */ -/* The code also conforms to C99 restrictions; in particular, */ -/* strict aliasing rules are observed. */ -/* */ -/* 2. The decNumber format which this library uses is optimized for */ -/* efficient processing of relatively short numbers; in particular */ -/* it allows the use of fixed sized structures and minimizes copy */ -/* and move operations. It does, however, support arbitrary */ -/* precision (up to 999,999,999 digits) and arbitrary exponent */ -/* range (Emax in the range 0 through 999,999,999 and Emin in the */ -/* range -999,999,999 through 0). Mathematical functions (for */ -/* example decNumberExp) as identified below are restricted more */ -/* tightly: digits, emax, and -emin in the context must be <= */ -/* DEC_MAX_MATH (999999), and their operand(s) must be within */ -/* these bounds. */ -/* */ -/* 3. Logical functions are further restricted; their operands must */ -/* be finite, positive, have an exponent of zero, and all digits */ -/* must be either 0 or 1. The result will only contain digits */ -/* which are 0 or 1 (and will have exponent=0 and a sign of 0). */ -/* */ -/* 4. Operands to operator functions are never modified unless they */ -/* are also specified to be the result number (which is always */ -/* permitted). Other than that case, operands must not overlap. */ -/* */ -/* 5. Error handling: the type of the error is ORed into the status */ -/* flags in the current context (decContext structure). The */ -/* SIGFPE signal is then raised if the corresponding trap-enabler */ -/* flag in the decContext is set (is 1). */ -/* */ -/* It is the responsibility of the caller to clear the status */ -/* flags as required. */ -/* */ -/* The result of any routine which returns a number will always */ -/* be a valid number (which may be a special value, such as an */ -/* Infinity or NaN). */ -/* */ -/* 6. The decNumber format is not an exchangeable concrete */ -/* representation as it comprises fields which may be machine- */ -/* dependent (packed or unpacked, or special length, for example). */ -/* Canonical conversions to and from strings are provided; other */ -/* conversions are available in separate modules. */ -/* */ -/* 7. Normally, input operands are assumed to be valid. Set DECCHECK */ -/* to 1 for extended operand checking (including NULL operands). */ -/* Results are undefined if a badly-formed structure (or a NULL */ -/* pointer to a structure) is provided, though with DECCHECK */ -/* enabled the operator routines are protected against exceptions. */ -/* (Except if the result pointer is NULL, which is unrecoverable.) */ -/* */ -/* However, the routines will never cause exceptions if they are */ -/* given well-formed operands, even if the value of the operands */ -/* is inappropriate for the operation and DECCHECK is not set. */ -/* (Except for SIGFPE, as and where documented.) */ -/* */ -/* 8. Subset arithmetic is available only if DECSUBSET is set to 1. */ -/* ------------------------------------------------------------------ */ -/* Implementation notes for maintenance of this module: */ -/* */ -/* 1. Storage leak protection: Routines which use malloc are not */ -/* permitted to use return for fastpath or error exits (i.e., */ -/* they follow strict structured programming conventions). */ -/* Instead they have a do{}while(0); construct surrounding the */ -/* code which is protected -- break may be used to exit this. */ -/* Other routines can safely use the return statement inline. */ -/* */ -/* Storage leak accounting can be enabled using DECALLOC. */ -/* */ -/* 2. All loops use the for(;;) construct. Any do construct does */ -/* not loop; it is for allocation protection as just described. */ -/* */ -/* 3. Setting status in the context must always be the very last */ -/* action in a routine, as non-0 status may raise a trap and hence */ -/* the call to set status may not return (if the handler uses long */ -/* jump). Therefore all cleanup must be done first. In general, */ -/* to achieve this status is accumulated and is only applied just */ -/* before return by calling decContextSetStatus (via decStatus). */ -/* */ -/* Routines which allocate storage cannot, in general, use the */ -/* 'top level' routines which could cause a non-returning */ -/* transfer of control. The decXxxxOp routines are safe (do not */ -/* call decStatus even if traps are set in the context) and should */ -/* be used instead (they are also a little faster). */ -/* */ -/* 4. Exponent checking is minimized by allowing the exponent to */ -/* grow outside its limits during calculations, provided that */ -/* the decFinalize function is called later. Multiplication and */ -/* division, and intermediate calculations in exponentiation, */ -/* require more careful checks because of the risk of 31-bit */ -/* overflow (the most negative valid exponent is -1999999997, for */ -/* a 999999999-digit number with adjusted exponent of -999999999). */ -/* */ -/* 5. Rounding is deferred until finalization of results, with any */ -/* 'off to the right' data being represented as a single digit */ -/* residue (in the range -1 through 9). This avoids any double- */ -/* rounding when more than one shortening takes place (for */ -/* example, when a result is subnormal). */ -/* */ -/* 6. The digits count is allowed to rise to a multiple of DECDPUN */ -/* during many operations, so whole Units are handled and exact */ -/* accounting of digits is not needed. The correct digits value */ -/* is found by decGetDigits, which accounts for leading zeros. */ -/* This must be called before any rounding if the number of digits */ -/* is not known exactly. */ -/* */ -/* 7. The multiply-by-reciprocal 'trick' is used for partitioning */ -/* numbers up to four digits, using appropriate constants. This */ -/* is not useful for longer numbers because overflow of 32 bits */ -/* would lead to 4 multiplies, which is almost as expensive as */ -/* a divide (unless a floating-point or 64-bit multiply is */ -/* assumed to be available). */ -/* */ -/* 8. Unusual abbreviations that may be used in the commentary: */ -/* lhs -- left hand side (operand, of an operation) */ -/* lsd -- least significant digit (of coefficient) */ -/* lsu -- least significant Unit (of coefficient) */ -/* msd -- most significant digit (of coefficient) */ -/* msi -- most significant item (in an array) */ -/* msu -- most significant Unit (of coefficient) */ -/* rhs -- right hand side (operand, of an operation) */ -/* +ve -- positive */ -/* -ve -- negative */ -/* ** -- raise to the power */ -/* ------------------------------------------------------------------ */ - -#include <stdlib.h> // for malloc, free, etc. -#include <stdio.h> // for printf [if needed] -#include <string.h> // for strcpy -#include <ctype.h> // for lower -#include "decNumber.h" // base number library -#include "decNumberLocal.h" // decNumber local types, etc. - -/* Constants */ -// Public lookup table used by the D2U macro -const uByte d2utable[DECMAXD2U+1]=D2UTABLE; - -#define DECVERB 1 // set to 1 for verbose DECCHECK -#define powers DECPOWERS // old internal name - -// Local constants -#define DIVIDE 0x80 // Divide operators -#define REMAINDER 0x40 // .. -#define DIVIDEINT 0x20 // .. -#define REMNEAR 0x10 // .. -#define COMPARE 0x01 // Compare operators -#define COMPMAX 0x02 // .. -#define COMPMIN 0x03 // .. -#define COMPTOTAL 0x04 // .. -#define COMPNAN 0x05 // .. [NaN processing] -#define COMPSIG 0x06 // .. [signaling COMPARE] -#define COMPMAXMAG 0x07 // .. -#define COMPMINMAG 0x08 // .. - -#define DEC_sNaN 0x40000000 // local status: sNaN signal -#define BADINT (Int)0x80000000 // most-negative Int; error indicator -// Next two indicate an integer >= 10**6, and its parity (bottom bit) -#define BIGEVEN (Int)0x80000002 -#define BIGODD (Int)0x80000003 - -static Unit uarrone[1]={1}; // Unit array of 1, used for incrementing - -/* Granularity-dependent code */ -#if DECDPUN<=4 - #define eInt Int // extended integer - #define ueInt uInt // unsigned extended integer - // Constant multipliers for divide-by-power-of five using reciprocal - // multiply, after removing powers of 2 by shifting, and final shift - // of 17 [we only need up to **4] - static const uInt multies[]={131073, 26215, 5243, 1049, 210}; - // QUOT10 -- macro to return the quotient of unit u divided by 10**n - #define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17) -#else - // For DECDPUN>4 non-ANSI-89 64-bit types are needed. - #if !DECUSE64 - #error decNumber.c: DECUSE64 must be 1 when DECDPUN>4 - #endif - #define eInt Long // extended integer - #define ueInt uLong // unsigned extended integer -#endif - -/* Local routines */ -static decNumber * decAddOp(decNumber *, const decNumber *, const decNumber *, - decContext *, uByte, uInt *); -static Flag decBiStr(const char *, const char *, const char *); -static uInt decCheckMath(const decNumber *, decContext *, uInt *); -static void decApplyRound(decNumber *, decContext *, Int, uInt *); -static Int decCompare(const decNumber *lhs, const decNumber *rhs, Flag); -static decNumber * decCompareOp(decNumber *, const decNumber *, - const decNumber *, decContext *, - Flag, uInt *); -static void decCopyFit(decNumber *, const decNumber *, decContext *, - Int *, uInt *); -static decNumber * decDecap(decNumber *, Int); -static decNumber * decDivideOp(decNumber *, const decNumber *, - const decNumber *, decContext *, Flag, uInt *); -static decNumber * decExpOp(decNumber *, const decNumber *, - decContext *, uInt *); -static void decFinalize(decNumber *, decContext *, Int *, uInt *); -static Int decGetDigits(Unit *, Int); -static Int decGetInt(const decNumber *); -static decNumber * decLnOp(decNumber *, const decNumber *, - decContext *, uInt *); -static decNumber * decMultiplyOp(decNumber *, const decNumber *, - const decNumber *, decContext *, - uInt *); -static decNumber * decNaNs(decNumber *, const decNumber *, - const decNumber *, decContext *, uInt *); -static decNumber * decQuantizeOp(decNumber *, const decNumber *, - const decNumber *, decContext *, Flag, - uInt *); -static void decReverse(Unit *, Unit *); -static void decSetCoeff(decNumber *, decContext *, const Unit *, - Int, Int *, uInt *); -static void decSetMaxValue(decNumber *, decContext *); -static void decSetOverflow(decNumber *, decContext *, uInt *); -static void decSetSubnormal(decNumber *, decContext *, Int *, uInt *); -static Int decShiftToLeast(Unit *, Int, Int); -static Int decShiftToMost(Unit *, Int, Int); -static void decStatus(decNumber *, uInt, decContext *); -static void decToString(const decNumber *, char[], Flag); -static decNumber * decTrim(decNumber *, decContext *, Flag, Flag, Int *); -static Int decUnitAddSub(const Unit *, Int, const Unit *, Int, Int, - Unit *, Int); -static Int decUnitCompare(const Unit *, Int, const Unit *, Int, Int); - -#if !DECSUBSET -/* decFinish == decFinalize when no subset arithmetic needed */ -#define decFinish(a,b,c,d) decFinalize(a,b,c,d) -#else -static void decFinish(decNumber *, decContext *, Int *, uInt *); -static decNumber * decRoundOperand(const decNumber *, decContext *, uInt *); -#endif - -/* Local macros */ -// masked special-values bits -#define SPECIALARG (rhs->bits & DECSPECIAL) -#define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL) - -/* Diagnostic macros, etc. */ -#if DECALLOC -// Handle malloc/free accounting. If enabled, our accountable routines -// are used; otherwise the code just goes straight to the system malloc -// and free routines. -#define malloc(a) decMalloc(a) -#define free(a) decFree(a) -#define DECFENCE 0x5a // corruption detector -// 'Our' malloc and free: -static void *decMalloc(size_t); -static void decFree(void *); -uInt decAllocBytes=0; // count of bytes allocated -// Note that DECALLOC code only checks for storage buffer overflow. -// To check for memory leaks, the decAllocBytes variable must be -// checked to be 0 at appropriate times (e.g., after the test -// harness completes a set of tests). This checking may be unreliable -// if the testing is done in a multi-thread environment. -#endif - -#if DECCHECK -// Optional checking routines. Enabling these means that decNumber -// and decContext operands to operator routines are checked for -// correctness. This roughly doubles the execution time of the -// fastest routines (and adds 600+ bytes), so should not normally be -// used in 'production'. -// decCheckInexact is used to check that inexact results have a full -// complement of digits (where appropriate -- this is not the case -// for Quantize, for example) -#define DECUNRESU ((decNumber *)(void *)0xffffffff) -#define DECUNUSED ((const decNumber *)(void *)0xffffffff) -#define DECUNCONT ((decContext *)(void *)(0xffffffff)) -static Flag decCheckOperands(decNumber *, const decNumber *, - const decNumber *, decContext *); -static Flag decCheckNumber(const decNumber *); -static void decCheckInexact(const decNumber *, decContext *); -#endif - -#if DECTRACE || DECCHECK -// Optional trace/debugging routines (may or may not be used) -void decNumberShow(const decNumber *); // displays the components of a number -static void decDumpAr(char, const Unit *, Int); -#endif - -/* ================================================================== */ -/* Conversions */ -/* ================================================================== */ - -/* ------------------------------------------------------------------ */ -/* from-int32 -- conversion from Int or uInt */ -/* */ -/* dn is the decNumber to receive the integer */ -/* in or uin is the integer to be converted */ -/* returns dn */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberFromInt32(decNumber *dn, Int in) { - uInt unsig; - if (in>=0) unsig=in; - else { // negative (possibly BADINT) - if (in==BADINT) unsig=(uInt)1073741824*2; // special case - else unsig=-in; // invert - } - // in is now positive - decNumberFromUInt32(dn, unsig); - if (in<0) dn->bits=DECNEG; // sign needed - return dn; - } // decNumberFromInt32 - -decNumber * decNumberFromUInt32(decNumber *dn, uInt uin) { - Unit *up; // work pointer - decNumberZero(dn); // clean - if (uin==0) return dn; // [or decGetDigits bad call] - for (up=dn->lsu; uin>0; up++) { - *up=(Unit)(uin%(DECDPUNMAX+1)); - uin=uin/(DECDPUNMAX+1); - } - dn->digits=decGetDigits(dn->lsu, up-dn->lsu); - return dn; - } // decNumberFromUInt32 - -/* ------------------------------------------------------------------ */ -/* to-int32 -- conversion to Int or uInt */ -/* */ -/* dn is the decNumber to convert */ -/* set is the context for reporting errors */ -/* returns the converted decNumber, or 0 if Invalid is set */ -/* */ -/* Invalid is set if the decNumber does not have exponent==0 or if */ -/* it is a NaN, Infinite, or out-of-range. */ -/* ------------------------------------------------------------------ */ -Int decNumberToInt32(const decNumber *dn, decContext *set) { - #if DECCHECK - if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; - #endif - - // special or too many digits, or bad exponent - if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; // bad - else { // is a finite integer with 10 or fewer digits - Int d; // work - const Unit *up; // .. - uInt hi=0, lo; // .. - up=dn->lsu; // -> lsu - lo=*up; // get 1 to 9 digits - #if DECDPUN>1 // split to higher - hi=lo/10; - lo=lo%10; - #endif - up++; - // collect remaining Units, if any, into hi - for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1]; - // now low has the lsd, hi the remainder - if (hi>214748364 || (hi==214748364 && lo>7)) { // out of range? - // most-negative is a reprieve - if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000; - // bad -- drop through - } - else { // in-range always - Int i=X10(hi)+lo; - if (dn->bits&DECNEG) return -i; - return i; - } - } // integer - decContextSetStatus(set, DEC_Invalid_operation); // [may not return] - return 0; - } // decNumberToInt32 - -uInt decNumberToUInt32(const decNumber *dn, decContext *set) { - #if DECCHECK - if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; - #endif - // special or too many digits, or bad exponent, or negative (<0) - if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0 - || (dn->bits&DECNEG && !ISZERO(dn))); // bad - else { // is a finite integer with 10 or fewer digits - Int d; // work - const Unit *up; // .. - uInt hi=0, lo; // .. - up=dn->lsu; // -> lsu - lo=*up; // get 1 to 9 digits - #if DECDPUN>1 // split to higher - hi=lo/10; - lo=lo%10; - #endif - up++; - // collect remaining Units, if any, into hi - for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1]; - - // now low has the lsd, hi the remainder - if (hi>429496729 || (hi==429496729 && lo>5)) ; // no reprieve possible - else return X10(hi)+lo; - } // integer - decContextSetStatus(set, DEC_Invalid_operation); // [may not return] - return 0; - } // decNumberToUInt32 - -/* ------------------------------------------------------------------ */ -/* to-scientific-string -- conversion to numeric string */ -/* to-engineering-string -- conversion to numeric string */ -/* */ -/* decNumberToString(dn, string); */ -/* decNumberToEngString(dn, string); */ -/* */ -/* dn is the decNumber to convert */ -/* string is the string where the result will be laid out */ -/* */ -/* string must be at least dn->digits+14 characters long */ -/* */ -/* No error is possible, and no status can be set. */ -/* ------------------------------------------------------------------ */ -char * decNumberToString(const decNumber *dn, char *string){ - decToString(dn, string, 0); - return string; - } // DecNumberToString - -char * decNumberToEngString(const decNumber *dn, char *string){ - decToString(dn, string, 1); - return string; - } // DecNumberToEngString - -/* ------------------------------------------------------------------ */ -/* to-number -- conversion from numeric string */ -/* */ -/* decNumberFromString -- convert string to decNumber */ -/* dn -- the number structure to fill */ -/* chars[] -- the string to convert ('\0' terminated) */ -/* set -- the context used for processing any error, */ -/* determining the maximum precision available */ -/* (set.digits), determining the maximum and minimum */ -/* exponent (set.emax and set.emin), determining if */ -/* extended values are allowed, and checking the */ -/* rounding mode if overflow occurs or rounding is */ -/* needed. */ -/* */ -/* The length of the coefficient and the size of the exponent are */ -/* checked by this routine, so the correct error (Underflow or */ -/* Overflow) can be reported or rounding applied, as necessary. */ -/* */ -/* If bad syntax is detected, the result will be a quiet NaN. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberFromString(decNumber *dn, const char chars[], - decContext *set) { - Int exponent=0; // working exponent [assume 0] - uByte bits=0; // working flags [assume +ve] - Unit *res; // where result will be built - Unit resbuff[SD2U(DECBUFFER+9)];// local buffer in case need temporary - // [+9 allows for ln() constants] - Unit *allocres=NULL; // -> allocated result, iff allocated - Int d=0; // count of digits found in decimal part - const char *dotchar=NULL; // where dot was found - const char *cfirst=chars; // -> first character of decimal part - const char *last=NULL; // -> last digit of decimal part - const char *c; // work - Unit *up; // .. - #if DECDPUN>1 - Int cut, out; // .. - #endif - Int residue; // rounding residue - uInt status=0; // error code - - #if DECCHECK - if (decCheckOperands(DECUNRESU, DECUNUSED, DECUNUSED, set)) - return decNumberZero(dn); - #endif - - do { // status & malloc protection - for (c=chars;; c++) { // -> input character - if (*c>='0' && *c<='9') { // test for Arabic digit - last=c; - d++; // count of real digits - continue; // still in decimal part - } - if (*c=='.' && dotchar==NULL) { // first '.' - dotchar=c; // record offset into decimal part - if (c==cfirst) cfirst++; // first digit must follow - continue;} - if (c==chars) { // first in string... - if (*c=='-') { // valid - sign - cfirst++; - bits=DECNEG; - continue;} - if (*c=='+') { // valid + sign - cfirst++; - continue;} - } - // *c is not a digit, or a valid +, -, or '.' - break; - } // c - - if (last==NULL) { // no digits yet - status=DEC_Conversion_syntax;// assume the worst - if (*c=='\0') break; // and no more to come... - #if DECSUBSET - // if subset then infinities and NaNs are not allowed - if (!set->extended) break; // hopeless - #endif - // Infinities and NaNs are possible, here - if (dotchar!=NULL) break; // .. unless had a dot - decNumberZero(dn); // be optimistic - if (decBiStr(c, "infinity", "INFINITY") - || decBiStr(c, "inf", "INF")) { - dn->bits=bits | DECINF; - status=0; // is OK - break; // all done - } - // a NaN expected - // 2003.09.10 NaNs are now permitted to have a sign - dn->bits=bits | DECNAN; // assume simple NaN - if (*c=='s' || *c=='S') { // looks like an sNaN - c++; - dn->bits=bits | DECSNAN; - } - if (*c!='n' && *c!='N') break; // check caseless "NaN" - c++; - if (*c!='a' && *c!='A') break; // .. - c++; - if (*c!='n' && *c!='N') break; // .. - c++; - // now either nothing, or nnnn payload, expected - // -> start of integer and skip leading 0s [including plain 0] - for (cfirst=c; *cfirst=='0';) cfirst++; - if (*cfirst=='\0') { // "NaN" or "sNaN", maybe with all 0s - status=0; // it's good - break; // .. - } - // something other than 0s; setup last and d as usual [no dots] - for (c=cfirst;; c++, d++) { - if (*c<'0' || *c>'9') break; // test for Arabic digit - last=c; - } - if (*c!='\0') break; // not all digits - if (d>set->digits-1) { - // [NB: payload in a decNumber can be full length unless - // clamped, in which case can only be digits-1] - if (set->clamp) break; - if (d>set->digits) break; - } // too many digits? - // good; drop through to convert the integer to coefficient - status=0; // syntax is OK - bits=dn->bits; // for copy-back - } // last==NULL - - else if (*c!='\0') { // more to process... - // had some digits; exponent is only valid sequence now - Flag nege; // 1=negative exponent - const char *firstexp; // -> first significant exponent digit - status=DEC_Conversion_syntax;// assume the worst - uInt expa=0; // accumulator for exponent - if (*c!='e' && *c!='E') break; - /* Found 'e' or 'E' -- now process explicit exponent */ - // 1998.07.11: sign no longer required - nege=0; - c++; // to (possible) sign - if (*c=='-') {nege=1; c++;} - else if (*c=='+') c++; - if (*c=='\0') break; - - for (; *c=='0' && *(c+1)!='\0';) c++; // strip insignificant zeros - firstexp=c; // save exponent digit place - for (; ;c++) { - if (*c<'0' || *c>'9') break; // not a digit - expa=X10(expa)+(Int)*c-(Int)'0'; - } // c - // if not now on a '\0', *c must not be a digit - if (*c!='\0') break; - - // (this next test must be after the syntax checks) - // if it was too long the exponent may have wrapped, so check - // carefully and set it to a certain overflow if wrap possible - if (c>=firstexp+9+1) { - if (c>firstexp+9+1 || *firstexp>'1') expa=DECNUMMAXE*2; - // [up to 1999999999 is OK, for example 1E-1000000998] - } - exponent=(Int)expa; // save exponent - if (nege) exponent=-exponent; // was negative - status=0; // is OK - } // stuff after digits - - // Here when whole string has been inspected; syntax is good - // cfirst->first digit (never dot), last->last digit (ditto) - - // strip leading zeros/dot [leave final 0 if all 0's] - if (*cfirst=='0') { // [cfirst has stepped over .] - for (c=cfirst; c<last; c++, cfirst++) { - if (*c=='.') continue; // ignore dots - if (*c!='0') break; // non-zero found - d--; // 0 stripped - } // c - #if DECSUBSET - // make a rapid exit for easy zeros if !extended - if (*cfirst=='0' && !set->extended) { - decNumberZero(dn); // clean result - break; // [could be return] - } - #endif - } // at least one leading 0 - - // Handle decimal point... - if (dotchar!=NULL && dotchar<last) // non-trailing '.' found? - exponent-=(last-dotchar); // adjust exponent - // [we can now ignore the .] - - // OK, the digits string is good. Assemble in the decNumber, or in - // a temporary units array if rounding is needed - if (d<=set->digits) res=dn->lsu; // fits into supplied decNumber - else { // rounding needed - Int needbytes=D2U(d)*sizeof(Unit);// bytes needed - res=resbuff; // assume use local buffer - if (needbytes>(Int)sizeof(resbuff)) { // too big for local - allocres=(Unit *)malloc(needbytes); - if (allocres==NULL) {status|=DEC_Insufficient_storage; break;} - res=allocres; - } - } - // res now -> number lsu, buffer, or allocated storage for Unit array - - // Place the coefficient into the selected Unit array - // [this is often 70% of the cost of this function when DECDPUN>1] - #if DECDPUN>1 - out=0; // accumulator - up=res+D2U(d)-1; // -> msu - cut=d-(up-res)*DECDPUN; // digits in top unit - for (c=cfirst;; c++) { // along the digits - if (*c=='.') continue; // ignore '.' [don't decrement cut] - out=X10(out)+(Int)*c-(Int)'0'; - if (c==last) break; // done [never get to trailing '.'] - cut--; - if (cut>0) continue; // more for this unit - *up=(Unit)out; // write unit - up--; // prepare for unit below.. - cut=DECDPUN; // .. - out=0; // .. - } // c - *up=(Unit)out; // write lsu - - #else - // DECDPUN==1 - up=res; // -> lsu - for (c=last; c>=cfirst; c--) { // over each character, from least - if (*c=='.') continue; // ignore . [don't step up] - *up=(Unit)((Int)*c-(Int)'0'); - up++; - } // c - #endif - - dn->bits=bits; - dn->exponent=exponent; - dn->digits=d; - - // if not in number (too long) shorten into the number - if (d>set->digits) { - residue=0; - decSetCoeff(dn, set, res, d, &residue, &status); - // always check for overflow or subnormal and round as needed - decFinalize(dn, set, &residue, &status); - } - else { // no rounding, but may still have overflow or subnormal - // [these tests are just for performance; finalize repeats them] - if ((dn->exponent-1<set->emin-dn->digits) - || (dn->exponent-1>set->emax-set->digits)) { - residue=0; - decFinalize(dn, set, &residue, &status); - } - } - // decNumberShow(dn); - } while(0); // [for break] - - if (allocres!=NULL) free(allocres); // drop any storage used - if (status!=0) decStatus(dn, status, set); - return dn; - } /* decNumberFromString */ - -/* ================================================================== */ -/* Operators */ -/* ================================================================== */ - -/* ------------------------------------------------------------------ */ -/* decNumberAbs -- absolute value operator */ -/* */ -/* This computes C = abs(A) */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context */ -/* */ -/* See also decNumberCopyAbs for a quiet bitwise version of this. */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -/* This has the same effect as decNumberPlus unless A is negative, */ -/* in which case it has the same effect as decNumberMinus. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberAbs(decNumber *res, const decNumber *rhs, - decContext *set) { - decNumber dzero; // for 0 - uInt status=0; // accumulator - - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - decNumberZero(&dzero); // set 0 - dzero.exponent=rhs->exponent; // [no coefficient expansion] - decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberAbs - -/* ------------------------------------------------------------------ */ -/* decNumberAdd -- add two Numbers */ -/* */ -/* This computes C = A + B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X+X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -/* This just calls the routine shared with Subtract */ -decNumber * decNumberAdd(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decAddOp(res, lhs, rhs, set, 0, &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberAdd - -/* ------------------------------------------------------------------ */ -/* decNumberAnd -- AND two Numbers, digitwise */ -/* */ -/* This computes C = A & B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X&X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context (used for result length and error report) */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* Logical function restrictions apply (see above); a NaN is */ -/* returned with Invalid_operation if a restriction is violated. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberAnd(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - const Unit *ua, *ub; // -> operands - const Unit *msua, *msub; // -> operand msus - Unit *uc, *msuc; // -> result and its msu - Int msudigs; // digits in res msu - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) - || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { - decStatus(res, DEC_Invalid_operation, set); - return res; - } - - // operands are valid - ua=lhs->lsu; // bottom-up - ub=rhs->lsu; // .. - uc=res->lsu; // .. - msua=ua+D2U(lhs->digits)-1; // -> msu of lhs - msub=ub+D2U(rhs->digits)-1; // -> msu of rhs - msuc=uc+D2U(set->digits)-1; // -> msu of result - msudigs=MSUDIGITS(set->digits); // [faster than remainder] - for (; uc<=msuc; ua++, ub++, uc++) { // Unit loop - Unit a, b; // extract units - if (ua>msua) a=0; - else a=*ua; - if (ub>msub) b=0; - else b=*ub; - *uc=0; // can now write back - if (a|b) { // maybe 1 bits to examine - Int i, j; - *uc=0; // can now write back - // This loop could be unrolled and/or use BIN2BCD tables - for (i=0; i<DECDPUN; i++) { - if (a&b&1) *uc=*uc+(Unit)powers[i]; // effect AND - j=a%10; - a=a/10; - j|=b%10; - b=b/10; - if (j>1) { - decStatus(res, DEC_Invalid_operation, set); - return res; - } - if (uc==msuc && i==msudigs-1) break; // just did final digit - } // each digit - } // both OK - } // each unit - // [here uc-1 is the msu of the result] - res->digits=decGetDigits(res->lsu, uc-res->lsu); - res->exponent=0; // integer - res->bits=0; // sign=0 - return res; // [no status to set] - } // decNumberAnd - -/* ------------------------------------------------------------------ */ -/* decNumberCompare -- compare two Numbers */ -/* */ -/* This computes C = A ? B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for one digit (or NaN). */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberCompare(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decCompareOp(res, lhs, rhs, set, COMPARE, &status); - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberCompare - -/* ------------------------------------------------------------------ */ -/* decNumberCompareSignal -- compare, signalling on all NaNs */ -/* */ -/* This computes C = A ? B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for one digit (or NaN). */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberCompareSignal(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decCompareOp(res, lhs, rhs, set, COMPSIG, &status); - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberCompareSignal - -/* ------------------------------------------------------------------ */ -/* decNumberCompareTotal -- compare two Numbers, using total ordering */ -/* */ -/* This computes C = A ? B, under total ordering */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for one digit; the result will always be one of */ -/* -1, 0, or 1. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberCompareTotal(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status); - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberCompareTotal - -/* ------------------------------------------------------------------ */ -/* decNumberCompareTotalMag -- compare, total ordering of magnitudes */ -/* */ -/* This computes C = |A| ? |B|, under total ordering */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for one digit; the result will always be one of */ -/* -1, 0, or 1. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberCompareTotalMag(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - uInt needbytes; // for space calculations - decNumber bufa[D2N(DECBUFFER+1)];// +1 in case DECBUFFER=0 - decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated - decNumber bufb[D2N(DECBUFFER+1)]; - decNumber *allocbufb=NULL; // -> allocated bufb, iff allocated - decNumber *a, *b; // temporary pointers - - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - do { // protect allocated storage - // if either is negative, take a copy and absolute - if (decNumberIsNegative(lhs)) { // lhs<0 - a=bufa; - needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit); - if (needbytes>sizeof(bufa)) { // need malloc space - allocbufa=(decNumber *)malloc(needbytes); - if (allocbufa==NULL) { // hopeless -- abandon - status|=DEC_Insufficient_storage; - break;} - a=allocbufa; // use the allocated space - } - decNumberCopy(a, lhs); // copy content - a->bits&=~DECNEG; // .. and clear the sign - lhs=a; // use copy from here on - } - if (decNumberIsNegative(rhs)) { // rhs<0 - b=bufb; - needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); - if (needbytes>sizeof(bufb)) { // need malloc space - allocbufb=(decNumber *)malloc(needbytes); - if (allocbufb==NULL) { // hopeless -- abandon - status|=DEC_Insufficient_storage; - break;} - b=allocbufb; // use the allocated space - } - decNumberCopy(b, rhs); // copy content - b->bits&=~DECNEG; // .. and clear the sign - rhs=b; // use copy from here on - } - decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status); - } while(0); // end protected - - if (allocbufa!=NULL) free(allocbufa); // drop any storage used - if (allocbufb!=NULL) free(allocbufb); // .. - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberCompareTotalMag - -/* ------------------------------------------------------------------ */ -/* decNumberDivide -- divide one number by another */ -/* */ -/* This computes C = A / B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X/X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberDivide(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decDivideOp(res, lhs, rhs, set, DIVIDE, &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberDivide - -/* ------------------------------------------------------------------ */ -/* decNumberDivideInteger -- divide and return integer quotient */ -/* */ -/* This computes C = A # B, where # is the integer divide operator */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X#X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberDivideInteger(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status); - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberDivideInteger - -/* ------------------------------------------------------------------ */ -/* decNumberExp -- exponentiation */ -/* */ -/* This computes C = exp(A) */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context; note that rounding mode has no effect */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* Mathematical function restrictions apply (see above); a NaN is */ -/* returned with Invalid_operation if a restriction is violated. */ -/* */ -/* Finite results will always be full precision and Inexact, except */ -/* when A is a zero or -Infinity (giving 1 or 0 respectively). */ -/* */ -/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ -/* almost always be correctly rounded, but may be up to 1 ulp in */ -/* error in rare cases. */ -/* ------------------------------------------------------------------ */ -/* This is a wrapper for decExpOp which can handle the slightly wider */ -/* (double) range needed by Ln (which has to be able to calculate */ -/* exp(-a) where a can be the tiniest number (Ntiny). */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberExp(decNumber *res, const decNumber *rhs, - decContext *set) { - uInt status=0; // accumulator - #if DECSUBSET - decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated - #endif - - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - // Check restrictions; these restrictions ensure that if h=8 (see - // decExpOp) then the result will either overflow or underflow to 0. - // Other math functions restrict the input range, too, for inverses. - // If not violated then carry out the operation. - if (!decCheckMath(rhs, set, &status)) do { // protect allocation - #if DECSUBSET - if (!set->extended) { - // reduce operand and set lostDigits status, as needed - if (rhs->digits>set->digits) { - allocrhs=decRoundOperand(rhs, set, &status); - if (allocrhs==NULL) break; - rhs=allocrhs; - } - } - #endif - decExpOp(res, rhs, set, &status); - } while(0); // end protected - - #if DECSUBSET - if (allocrhs !=NULL) free(allocrhs); // drop any storage used - #endif - // apply significant status - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberExp - -/* ------------------------------------------------------------------ */ -/* decNumberFMA -- fused multiply add */ -/* */ -/* This computes D = (A * B) + C with only one rounding */ -/* */ -/* res is D, the result. D may be A or B or C (e.g., X=FMA(X,X,X)) */ -/* lhs is A */ -/* rhs is B */ -/* fhs is C [far hand side] */ -/* set is the context */ -/* */ -/* Mathematical function restrictions apply (see above); a NaN is */ -/* returned with Invalid_operation if a restriction is violated. */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberFMA(decNumber *res, const decNumber *lhs, - const decNumber *rhs, const decNumber *fhs, - decContext *set) { - uInt status=0; // accumulator - decContext dcmul; // context for the multiplication - uInt needbytes; // for space calculations - decNumber bufa[D2N(DECBUFFER*2+1)]; - decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated - decNumber *acc; // accumulator pointer - decNumber dzero; // work - - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - if (decCheckOperands(res, fhs, DECUNUSED, set)) return res; - #endif - - do { // protect allocated storage - #if DECSUBSET - if (!set->extended) { // [undefined if subset] - status|=DEC_Invalid_operation; - break;} - #endif - // Check math restrictions [these ensure no overflow or underflow] - if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status)) - || (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status)) - || (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break; - // set up context for multiply - dcmul=*set; - dcmul.digits=lhs->digits+rhs->digits; // just enough - // [The above may be an over-estimate for subset arithmetic, but that's OK] - dcmul.emax=DEC_MAX_EMAX; // effectively unbounded .. - dcmul.emin=DEC_MIN_EMIN; // [thanks to Math restrictions] - // set up decNumber space to receive the result of the multiply - acc=bufa; // may fit - needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit); - if (needbytes>sizeof(bufa)) { // need malloc space - allocbufa=(decNumber *)malloc(needbytes); - if (allocbufa==NULL) { // hopeless -- abandon - status|=DEC_Insufficient_storage; - break;} - acc=allocbufa; // use the allocated space - } - // multiply with extended range and necessary precision - //printf("emin=%ld\n", dcmul.emin); - decMultiplyOp(acc, lhs, rhs, &dcmul, &status); - // Only Invalid operation (from sNaN or Inf * 0) is possible in - // status; if either is seen than ignore fhs (in case it is - // another sNaN) and set acc to NaN unless we had an sNaN - // [decMultiplyOp leaves that to caller] - // Note sNaN has to go through addOp to shorten payload if - // necessary - if ((status&DEC_Invalid_operation)!=0) { - if (!(status&DEC_sNaN)) { // but be true invalid - decNumberZero(res); // acc not yet set - res->bits=DECNAN; - break; - } - decNumberZero(&dzero); // make 0 (any non-NaN would do) - fhs=&dzero; // use that - } - #if DECCHECK - else { // multiply was OK - if (status!=0) printf("Status=%08lx after FMA multiply\n", (LI)status); - } - #endif - // add the third operand and result -> res, and all is done - decAddOp(res, acc, fhs, set, 0, &status); - } while(0); // end protected - - if (allocbufa!=NULL) free(allocbufa); // drop any storage used - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberFMA - -/* ------------------------------------------------------------------ */ -/* decNumberInvert -- invert a Number, digitwise */ -/* */ -/* This computes C = ~A */ -/* */ -/* res is C, the result. C may be A (e.g., X=~X) */ -/* rhs is A */ -/* set is the context (used for result length and error report) */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* Logical function restrictions apply (see above); a NaN is */ -/* returned with Invalid_operation if a restriction is violated. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberInvert(decNumber *res, const decNumber *rhs, - decContext *set) { - const Unit *ua, *msua; // -> operand and its msu - Unit *uc, *msuc; // -> result and its msu - Int msudigs; // digits in res msu - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { - decStatus(res, DEC_Invalid_operation, set); - return res; - } - // operand is valid - ua=rhs->lsu; // bottom-up - uc=res->lsu; // .. - msua=ua+D2U(rhs->digits)-1; // -> msu of rhs - msuc=uc+D2U(set->digits)-1; // -> msu of result - msudigs=MSUDIGITS(set->digits); // [faster than remainder] - for (; uc<=msuc; ua++, uc++) { // Unit loop - Unit a; // extract unit - Int i, j; // work - if (ua>msua) a=0; - else a=*ua; - *uc=0; // can now write back - // always need to examine all bits in rhs - // This loop could be unrolled and/or use BIN2BCD tables - for (i=0; i<DECDPUN; i++) { - if ((~a)&1) *uc=*uc+(Unit)powers[i]; // effect INVERT - j=a%10; - a=a/10; - if (j>1) { - decStatus(res, DEC_Invalid_operation, set); - return res; - } - if (uc==msuc && i==msudigs-1) break; // just did final digit - } // each digit - } // each unit - // [here uc-1 is the msu of the result] - res->digits=decGetDigits(res->lsu, uc-res->lsu); - res->exponent=0; // integer - res->bits=0; // sign=0 - return res; // [no status to set] - } // decNumberInvert - -/* ------------------------------------------------------------------ */ -/* decNumberLn -- natural logarithm */ -/* */ -/* This computes C = ln(A) */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context; note that rounding mode has no effect */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* Notable cases: */ -/* A<0 -> Invalid */ -/* A=0 -> -Infinity (Exact) */ -/* A=+Infinity -> +Infinity (Exact) */ -/* A=1 exactly -> 0 (Exact) */ -/* */ -/* Mathematical function restrictions apply (see above); a NaN is */ -/* returned with Invalid_operation if a restriction is violated. */ -/* */ -/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ -/* almost always be correctly rounded, but may be up to 1 ulp in */ -/* error in rare cases. */ -/* ------------------------------------------------------------------ */ -/* This is a wrapper for decLnOp which can handle the slightly wider */ -/* (+11) range needed by Ln, Log10, etc. (which may have to be able */ -/* to calculate at p+e+2). */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberLn(decNumber *res, const decNumber *rhs, - decContext *set) { - uInt status=0; // accumulator - #if DECSUBSET - decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated - #endif - - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - // Check restrictions; this is a math function; if not violated - // then carry out the operation. - if (!decCheckMath(rhs, set, &status)) do { // protect allocation - #if DECSUBSET - if (!set->extended) { - // reduce operand and set lostDigits status, as needed - if (rhs->digits>set->digits) { - allocrhs=decRoundOperand(rhs, set, &status); - if (allocrhs==NULL) break; - rhs=allocrhs; - } - // special check in subset for rhs=0 - if (ISZERO(rhs)) { // +/- zeros -> error - status|=DEC_Invalid_operation; - break;} - } // extended=0 - #endif - decLnOp(res, rhs, set, &status); - } while(0); // end protected - - #if DECSUBSET - if (allocrhs !=NULL) free(allocrhs); // drop any storage used - #endif - // apply significant status - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberLn - -/* ------------------------------------------------------------------ */ -/* decNumberLogB - get adjusted exponent, by 754 rules */ -/* */ -/* This computes C = adjustedexponent(A) */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context, used only for digits and status */ -/* */ -/* For an unrounded result, digits may need to be 10 (A might have */ -/* 10**9 digits and an exponent of +999999999, or one digit and an */ -/* exponent of -1999999999). */ -/* */ -/* This returns the adjusted exponent of A after (in theory) padding */ -/* with zeros on the right to set->digits digits while keeping the */ -/* same value. The exponent is not limited by emin/emax. */ -/* */ -/* Notable cases: */ -/* A<0 -> Use |A| */ -/* A=0 -> -Infinity (Division by zero) */ -/* A=Infinite -> +Infinity (Exact) */ -/* A=1 exactly -> 0 (Exact) */ -/* NaNs are propagated as usual */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberLogB(decNumber *res, const decNumber *rhs, - decContext *set) { - uInt status=0; // accumulator - - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - // NaNs as usual; Infinities return +Infinity; 0->oops - if (decNumberIsNaN(rhs)) decNaNs(res, rhs, NULL, set, &status); - else if (decNumberIsInfinite(rhs)) decNumberCopyAbs(res, rhs); - else if (decNumberIsZero(rhs)) { - decNumberZero(res); // prepare for Infinity - res->bits=DECNEG|DECINF; // -Infinity - status|=DEC_Division_by_zero; // as per 754 - } - else { // finite non-zero - Int ae=rhs->exponent+rhs->digits-1; // adjusted exponent - if (set->digits>=10) decNumberFromInt32(res, ae); // lay it out - else { - decNumber buft[D2N(10)]; // temporary number - decNumber *t=buft; // .. - decNumberFromInt32(t, ae); // lay it out - decNumberPlus(res, t, set); // round as necessary - } - } - - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberLogB - -/* ------------------------------------------------------------------ */ -/* decNumberLog10 -- logarithm in base 10 */ -/* */ -/* This computes C = log10(A) */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context; note that rounding mode has no effect */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* Notable cases: */ -/* A<0 -> Invalid */ -/* A=0 -> -Infinity (Exact) */ -/* A=+Infinity -> +Infinity (Exact) */ -/* A=10**n (if n is an integer) -> n (Exact) */ -/* */ -/* Mathematical function restrictions apply (see above); a NaN is */ -/* returned with Invalid_operation if a restriction is violated. */ -/* */ -/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ -/* almost always be correctly rounded, but may be up to 1 ulp in */ -/* error in rare cases. */ -/* ------------------------------------------------------------------ */ -/* This calculates ln(A)/ln(10) using appropriate precision. For */ -/* ln(A) this is the max(p, rhs->digits + t) + 3, where p is the */ -/* requested digits and t is the number of digits in the exponent */ -/* (maximum 6). For ln(10) it is p + 3; this is often handled by the */ -/* fastpath in decLnOp. The final division is done to the requested */ -/* precision. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberLog10(decNumber *res, const decNumber *rhs, - decContext *set) { - uInt status=0, ignore=0; // status accumulators - uInt needbytes; // for space calculations - Int p; // working precision - Int t; // digits in exponent of A - - // buffers for a and b working decimals - // (adjustment calculator, same size) - decNumber bufa[D2N(DECBUFFER+2)]; - decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated - decNumber *a=bufa; // temporary a - decNumber bufb[D2N(DECBUFFER+2)]; - decNumber *allocbufb=NULL; // -> allocated bufb, iff allocated - decNumber *b=bufb; // temporary b - decNumber bufw[D2N(10)]; // working 2-10 digit number - decNumber *w=bufw; // .. - #if DECSUBSET - decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated - #endif - - decContext aset; // working context - - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - // Check restrictions; this is a math function; if not violated - // then carry out the operation. - if (!decCheckMath(rhs, set, &status)) do { // protect malloc - #if DECSUBSET - if (!set->extended) { - // reduce operand and set lostDigits status, as needed - if (rhs->digits>set->digits) { - allocrhs=decRoundOperand(rhs, set, &status); - if (allocrhs==NULL) break; - rhs=allocrhs; - } - // special check in subset for rhs=0 - if (ISZERO(rhs)) { // +/- zeros -> error - status|=DEC_Invalid_operation; - break;} - } // extended=0 - #endif - - decContextDefault(&aset, DEC_INIT_DECIMAL64); // clean context - - // handle exact powers of 10; only check if +ve finite - if (!(rhs->bits&(DECNEG|DECSPECIAL)) && !ISZERO(rhs)) { - Int residue=0; // (no residue) - uInt copystat=0; // clean status - - // round to a single digit... - aset.digits=1; - decCopyFit(w, rhs, &aset, &residue, ©stat); // copy & shorten - // if exact and the digit is 1, rhs is a power of 10 - if (!(copystat&DEC_Inexact) && w->lsu[0]==1) { - // the exponent, conveniently, is the power of 10; making - // this the result needs a little care as it might not fit, - // so first convert it into the working number, and then move - // to res - decNumberFromInt32(w, w->exponent); - residue=0; - decCopyFit(res, w, set, &residue, &status); // copy & round - decFinish(res, set, &residue, &status); // cleanup/set flags - break; - } // not a power of 10 - } // not a candidate for exact - - // simplify the information-content calculation to use 'total - // number of digits in a, including exponent' as compared to the - // requested digits, as increasing this will only rarely cost an - // iteration in ln(a) anyway - t=6; // it can never be >6 - - // allocate space when needed... - p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3; - needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit); - if (needbytes>sizeof(bufa)) { // need malloc space - allocbufa=(decNumber *)malloc(needbytes); - if (allocbufa==NULL) { // hopeless -- abandon - status|=DEC_Insufficient_storage; - break;} - a=allocbufa; // use the allocated space - } - aset.digits=p; // as calculated - aset.emax=DEC_MAX_MATH; // usual bounds - aset.emin=-DEC_MAX_MATH; // .. - aset.clamp=0; // and no concrete format - decLnOp(a, rhs, &aset, &status); // a=ln(rhs) - - // skip the division if the result so far is infinite, NaN, or - // zero, or there was an error; note NaN from sNaN needs copy - if (status&DEC_NaNs && !(status&DEC_sNaN)) break; - if (a->bits&DECSPECIAL || ISZERO(a)) { - decNumberCopy(res, a); // [will fit] - break;} - - // for ln(10) an extra 3 digits of precision are needed - p=set->digits+3; - needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit); - if (needbytes>sizeof(bufb)) { // need malloc space - allocbufb=(decNumber *)malloc(needbytes); - if (allocbufb==NULL) { // hopeless -- abandon - status|=DEC_Insufficient_storage; - break;} - b=allocbufb; // use the allocated space - } - decNumberZero(w); // set up 10... - #if DECDPUN==1 - w->lsu[1]=1; w->lsu[0]=0; // .. - #else - w->lsu[0]=10; // .. - #endif - w->digits=2; // .. - - aset.digits=p; - decLnOp(b, w, &aset, &ignore); // b=ln(10) - - aset.digits=set->digits; // for final divide - decDivideOp(res, a, b, &aset, DIVIDE, &status); // into result - } while(0); // [for break] - - if (allocbufa!=NULL) free(allocbufa); // drop any storage used - if (allocbufb!=NULL) free(allocbufb); // .. - #if DECSUBSET - if (allocrhs !=NULL) free(allocrhs); // .. - #endif - // apply significant status - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberLog10 - -/* ------------------------------------------------------------------ */ -/* decNumberMax -- compare two Numbers and return the maximum */ -/* */ -/* This computes C = A ? B, returning the maximum by 754 rules */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberMax(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decCompareOp(res, lhs, rhs, set, COMPMAX, &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberMax - -/* ------------------------------------------------------------------ */ -/* decNumberMaxMag -- compare and return the maximum by magnitude */ -/* */ -/* This computes C = A ? B, returning the maximum by 754 rules */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberMaxMag(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decCompareOp(res, lhs, rhs, set, COMPMAXMAG, &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberMaxMag - -/* ------------------------------------------------------------------ */ -/* decNumberMin -- compare two Numbers and return the minimum */ -/* */ -/* This computes C = A ? B, returning the minimum by 754 rules */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberMin(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decCompareOp(res, lhs, rhs, set, COMPMIN, &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberMin - -/* ------------------------------------------------------------------ */ -/* decNumberMinMag -- compare and return the minimum by magnitude */ -/* */ -/* This computes C = A ? B, returning the minimum by 754 rules */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberMinMag(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decCompareOp(res, lhs, rhs, set, COMPMINMAG, &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberMinMag - -/* ------------------------------------------------------------------ */ -/* decNumberMinus -- prefix minus operator */ -/* */ -/* This computes C = 0 - A */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context */ -/* */ -/* See also decNumberCopyNegate for a quiet bitwise version of this. */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -/* Simply use AddOp for the subtract, which will do the necessary. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberMinus(decNumber *res, const decNumber *rhs, - decContext *set) { - decNumber dzero; - uInt status=0; // accumulator - - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - decNumberZero(&dzero); // make 0 - dzero.exponent=rhs->exponent; // [no coefficient expansion] - decAddOp(res, &dzero, rhs, set, DECNEG, &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberMinus - -/* ------------------------------------------------------------------ */ -/* decNumberNextMinus -- next towards -Infinity */ -/* */ -/* This computes C = A - infinitesimal, rounded towards -Infinity */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context */ -/* */ -/* This is a generalization of 754 NextDown. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberNextMinus(decNumber *res, const decNumber *rhs, - decContext *set) { - decNumber dtiny; // constant - decContext workset=*set; // work - uInt status=0; // accumulator - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - // +Infinity is the special case - if ((rhs->bits&(DECINF|DECNEG))==DECINF) { - decSetMaxValue(res, set); // is +ve - // there is no status to set - return res; - } - decNumberZero(&dtiny); // start with 0 - dtiny.lsu[0]=1; // make number that is .. - dtiny.exponent=DEC_MIN_EMIN-1; // .. smaller than tiniest - workset.round=DEC_ROUND_FLOOR; - decAddOp(res, rhs, &dtiny, &workset, DECNEG, &status); - status&=DEC_Invalid_operation|DEC_sNaN; // only sNaN Invalid please - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberNextMinus - -/* ------------------------------------------------------------------ */ -/* decNumberNextPlus -- next towards +Infinity */ -/* */ -/* This computes C = A + infinitesimal, rounded towards +Infinity */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context */ -/* */ -/* This is a generalization of 754 NextUp. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberNextPlus(decNumber *res, const decNumber *rhs, - decContext *set) { - decNumber dtiny; // constant - decContext workset=*set; // work - uInt status=0; // accumulator - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - // -Infinity is the special case - if ((rhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) { - decSetMaxValue(res, set); - res->bits=DECNEG; // negative - // there is no status to set - return res; - } - decNumberZero(&dtiny); // start with 0 - dtiny.lsu[0]=1; // make number that is .. - dtiny.exponent=DEC_MIN_EMIN-1; // .. smaller than tiniest - workset.round=DEC_ROUND_CEILING; - decAddOp(res, rhs, &dtiny, &workset, 0, &status); - status&=DEC_Invalid_operation|DEC_sNaN; // only sNaN Invalid please - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberNextPlus - -/* ------------------------------------------------------------------ */ -/* decNumberNextToward -- next towards rhs */ -/* */ -/* This computes C = A +/- infinitesimal, rounded towards */ -/* +/-Infinity in the direction of B, as per 754-1985 nextafter */ -/* modified during revision but dropped from 754-2008. */ -/* */ -/* res is C, the result. C may be A or B. */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* This is a generalization of 754-1985 NextAfter. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberNextToward(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - decNumber dtiny; // constant - decContext workset=*set; // work - Int result; // .. - uInt status=0; // accumulator - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { - decNaNs(res, lhs, rhs, set, &status); - } - else { // Is numeric, so no chance of sNaN Invalid, etc. - result=decCompare(lhs, rhs, 0); // sign matters - if (result==BADINT) status|=DEC_Insufficient_storage; // rare - else { // valid compare - if (result==0) decNumberCopySign(res, lhs, rhs); // easy - else { // differ: need NextPlus or NextMinus - uByte sub; // add or subtract - if (result<0) { // lhs<rhs, do nextplus - // -Infinity is the special case - if ((lhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) { - decSetMaxValue(res, set); - res->bits=DECNEG; // negative - return res; // there is no status to set - } - workset.round=DEC_ROUND_CEILING; - sub=0; // add, please - } // plus - else { // lhs>rhs, do nextminus - // +Infinity is the special case - if ((lhs->bits&(DECINF|DECNEG))==DECINF) { - decSetMaxValue(res, set); - return res; // there is no status to set - } - workset.round=DEC_ROUND_FLOOR; - sub=DECNEG; // subtract, please - } // minus - decNumberZero(&dtiny); // start with 0 - dtiny.lsu[0]=1; // make number that is .. - dtiny.exponent=DEC_MIN_EMIN-1; // .. smaller than tiniest - decAddOp(res, lhs, &dtiny, &workset, sub, &status); // + or - - // turn off exceptions if the result is a normal number - // (including Nmin), otherwise let all status through - if (decNumberIsNormal(res, set)) status=0; - } // unequal - } // compare OK - } // numeric - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberNextToward - -/* ------------------------------------------------------------------ */ -/* decNumberOr -- OR two Numbers, digitwise */ -/* */ -/* This computes C = A | B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X|X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context (used for result length and error report) */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* Logical function restrictions apply (see above); a NaN is */ -/* returned with Invalid_operation if a restriction is violated. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberOr(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - const Unit *ua, *ub; // -> operands - const Unit *msua, *msub; // -> operand msus - Unit *uc, *msuc; // -> result and its msu - Int msudigs; // digits in res msu - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) - || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { - decStatus(res, DEC_Invalid_operation, set); - return res; - } - // operands are valid - ua=lhs->lsu; // bottom-up - ub=rhs->lsu; // .. - uc=res->lsu; // .. - msua=ua+D2U(lhs->digits)-1; // -> msu of lhs - msub=ub+D2U(rhs->digits)-1; // -> msu of rhs - msuc=uc+D2U(set->digits)-1; // -> msu of result - msudigs=MSUDIGITS(set->digits); // [faster than remainder] - for (; uc<=msuc; ua++, ub++, uc++) { // Unit loop - Unit a, b; // extract units - if (ua>msua) a=0; - else a=*ua; - if (ub>msub) b=0; - else b=*ub; - *uc=0; // can now write back - if (a|b) { // maybe 1 bits to examine - Int i, j; - // This loop could be unrolled and/or use BIN2BCD tables - for (i=0; i<DECDPUN; i++) { - if ((a|b)&1) *uc=*uc+(Unit)powers[i]; // effect OR - j=a%10; - a=a/10; - j|=b%10; - b=b/10; - if (j>1) { - decStatus(res, DEC_Invalid_operation, set); - return res; - } - if (uc==msuc && i==msudigs-1) break; // just did final digit - } // each digit - } // non-zero - } // each unit - // [here uc-1 is the msu of the result] - res->digits=decGetDigits(res->lsu, uc-res->lsu); - res->exponent=0; // integer - res->bits=0; // sign=0 - return res; // [no status to set] - } // decNumberOr - -/* ------------------------------------------------------------------ */ -/* decNumberPlus -- prefix plus operator */ -/* */ -/* This computes C = 0 + A */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context */ -/* */ -/* See also decNumberCopy for a quiet bitwise version of this. */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -/* This simply uses AddOp; Add will take fast path after preparing A. */ -/* Performance is a concern here, as this routine is often used to */ -/* check operands and apply rounding and overflow/underflow testing. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberPlus(decNumber *res, const decNumber *rhs, - decContext *set) { - decNumber dzero; - uInt status=0; // accumulator - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - decNumberZero(&dzero); // make 0 - dzero.exponent=rhs->exponent; // [no coefficient expansion] - decAddOp(res, &dzero, rhs, set, 0, &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberPlus - -/* ------------------------------------------------------------------ */ -/* decNumberMultiply -- multiply two Numbers */ -/* */ -/* This computes C = A x B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X+X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberMultiply(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decMultiplyOp(res, lhs, rhs, set, &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberMultiply - -/* ------------------------------------------------------------------ */ -/* decNumberPower -- raise a number to a power */ -/* */ -/* This computes C = A ** B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X**X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* Mathematical function restrictions apply (see above); a NaN is */ -/* returned with Invalid_operation if a restriction is violated. */ -/* */ -/* However, if 1999999997<=B<=999999999 and B is an integer then the */ -/* restrictions on A and the context are relaxed to the usual bounds, */ -/* for compatibility with the earlier (integer power only) version */ -/* of this function. */ -/* */ -/* When B is an integer, the result may be exact, even if rounded. */ -/* */ -/* The final result is rounded according to the context; it will */ -/* almost always be correctly rounded, but may be up to 1 ulp in */ -/* error in rare cases. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberPower(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - #if DECSUBSET - decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated - decNumber *allocrhs=NULL; // .., rhs - #endif - decNumber *allocdac=NULL; // -> allocated acc buffer, iff used - decNumber *allocinv=NULL; // -> allocated 1/x buffer, iff used - Int reqdigits=set->digits; // requested DIGITS - Int n; // rhs in binary - Flag rhsint=0; // 1 if rhs is an integer - Flag useint=0; // 1 if can use integer calculation - Flag isoddint=0; // 1 if rhs is an integer and odd - Int i; // work - #if DECSUBSET - Int dropped; // .. - #endif - uInt needbytes; // buffer size needed - Flag seenbit; // seen a bit while powering - Int residue=0; // rounding residue - uInt status=0; // accumulators - uByte bits=0; // result sign if errors - decContext aset; // working context - decNumber dnOne; // work value 1... - // local accumulator buffer [a decNumber, with digits+elength+1 digits] - decNumber dacbuff[D2N(DECBUFFER+9)]; - decNumber *dac=dacbuff; // -> result accumulator - // same again for possible 1/lhs calculation - decNumber invbuff[D2N(DECBUFFER+9)]; - - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - do { // protect allocated storage - #if DECSUBSET - if (!set->extended) { // reduce operands and set status, as needed - if (lhs->digits>reqdigits) { - alloclhs=decRoundOperand(lhs, set, &status); - if (alloclhs==NULL) break; - lhs=alloclhs; - } - if (rhs->digits>reqdigits) { - allocrhs=decRoundOperand(rhs, set, &status); - if (allocrhs==NULL) break; - rhs=allocrhs; - } - } - #endif - // [following code does not require input rounding] - - // handle NaNs and rhs Infinity (lhs infinity is harder) - if (SPECIALARGS) { - if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { // NaNs - decNaNs(res, lhs, rhs, set, &status); - break;} - if (decNumberIsInfinite(rhs)) { // rhs Infinity - Flag rhsneg=rhs->bits&DECNEG; // save rhs sign - if (decNumberIsNegative(lhs) // lhs<0 - && !decNumberIsZero(lhs)) // .. - status|=DEC_Invalid_operation; - else { // lhs >=0 - decNumberZero(&dnOne); // set up 1 - dnOne.lsu[0]=1; - decNumberCompare(dac, lhs, &dnOne, set); // lhs ? 1 - decNumberZero(res); // prepare for 0/1/Infinity - if (decNumberIsNegative(dac)) { // lhs<1 - if (rhsneg) res->bits|=DECINF; // +Infinity [else is +0] - } - else if (dac->lsu[0]==0) { // lhs=1 - // 1**Infinity is inexact, so return fully-padded 1.0000 - Int shift=set->digits-1; - *res->lsu=1; // was 0, make int 1 - res->digits=decShiftToMost(res->lsu, 1, shift); - res->exponent=-shift; // make 1.0000... - status|=DEC_Inexact|DEC_Rounded; // deemed inexact - } - else { // lhs>1 - if (!rhsneg) res->bits|=DECINF; // +Infinity [else is +0] - } - } // lhs>=0 - break;} - // [lhs infinity drops through] - } // specials - - // Original rhs may be an integer that fits and is in range - n=decGetInt(rhs); - if (n!=BADINT) { // it is an integer - rhsint=1; // record the fact for 1**n - isoddint=(Flag)n&1; // [works even if big] - if (n!=BIGEVEN && n!=BIGODD) // can use integer path? - useint=1; // looks good - } - - if (decNumberIsNegative(lhs) // -x .. - && isoddint) bits=DECNEG; // .. to an odd power - - // handle LHS infinity - if (decNumberIsInfinite(lhs)) { // [NaNs already handled] - uByte rbits=rhs->bits; // save - decNumberZero(res); // prepare - if (n==0) *res->lsu=1; // [-]Inf**0 => 1 - else { - // -Inf**nonint -> error - if (!rhsint && decNumberIsNegative(lhs)) { - status|=DEC_Invalid_operation; // -Inf**nonint is error - break;} - if (!(rbits & DECNEG)) bits|=DECINF; // was not a **-n - // [otherwise will be 0 or -0] - res->bits=bits; - } - break;} - - // similarly handle LHS zero - if (decNumberIsZero(lhs)) { - if (n==0) { // 0**0 => Error - #if DECSUBSET - if (!set->extended) { // [unless subset] - decNumberZero(res); - *res->lsu=1; // return 1 - break;} - #endif - status|=DEC_Invalid_operation; - } - else { // 0**x - uByte rbits=rhs->bits; // save - if (rbits & DECNEG) { // was a 0**(-n) - #if DECSUBSET - if (!set->extended) { // [bad if subset] - status|=DEC_Invalid_operation; - break;} - #endif - bits|=DECINF; - } - decNumberZero(res); // prepare - // [otherwise will be 0 or -0] - res->bits=bits; - } - break;} - - // here both lhs and rhs are finite; rhs==0 is handled in the - // integer path. Next handle the non-integer cases - if (!useint) { // non-integral rhs - // any -ve lhs is bad, as is either operand or context out of - // bounds - if (decNumberIsNegative(lhs)) { - status|=DEC_Invalid_operation; - break;} - if (decCheckMath(lhs, set, &status) - || decCheckMath(rhs, set, &status)) break; // variable status - - decContextDefault(&aset, DEC_INIT_DECIMAL64); // clean context - aset.emax=DEC_MAX_MATH; // usual bounds - aset.emin=-DEC_MAX_MATH; // .. - aset.clamp=0; // and no concrete format - - // calculate the result using exp(ln(lhs)*rhs), which can - // all be done into the accumulator, dac. The precision needed - // is enough to contain the full information in the lhs (which - // is the total digits, including exponent), or the requested - // precision, if larger, + 4; 6 is used for the exponent - // maximum length, and this is also used when it is shorter - // than the requested digits as it greatly reduces the >0.5 ulp - // cases at little cost (because Ln doubles digits each - // iteration so a few extra digits rarely causes an extra - // iteration) - aset.digits=MAXI(lhs->digits, set->digits)+6+4; - } // non-integer rhs - - else { // rhs is in-range integer - if (n==0) { // x**0 = 1 - // (0**0 was handled above) - decNumberZero(res); // result=1 - *res->lsu=1; // .. - break;} - // rhs is a non-zero integer - if (n<0) n=-n; // use abs(n) - - aset=*set; // clone the context - aset.round=DEC_ROUND_HALF_EVEN; // internally use balanced - // calculate the working DIGITS - aset.digits=reqdigits+(rhs->digits+rhs->exponent)+2; - #if DECSUBSET - if (!set->extended) aset.digits--; // use classic precision - #endif - // it's an error if this is more than can be handled - if (aset.digits>DECNUMMAXP) {status|=DEC_Invalid_operation; break;} - } // integer path - - // aset.digits is the count of digits for the accumulator needed - // if accumulator is too long for local storage, then allocate - needbytes=sizeof(decNumber)+(D2U(aset.digits)-1)*sizeof(Unit); - // [needbytes also used below if 1/lhs needed] - if (needbytes>sizeof(dacbuff)) { - allocdac=(decNumber *)malloc(needbytes); - if (allocdac==NULL) { // hopeless -- abandon - status|=DEC_Insufficient_storage; - break;} - dac=allocdac; // use the allocated space - } - // here, aset is set up and accumulator is ready for use - - if (!useint) { // non-integral rhs - // x ** y; special-case x=1 here as it will otherwise always - // reduce to integer 1; decLnOp has a fastpath which detects - // the case of x=1 - decLnOp(dac, lhs, &aset, &status); // dac=ln(lhs) - // [no error possible, as lhs 0 already handled] - if (ISZERO(dac)) { // x==1, 1.0, etc. - // need to return fully-padded 1.0000 etc., but rhsint->1 - *dac->lsu=1; // was 0, make int 1 - if (!rhsint) { // add padding - Int shift=set->digits-1; - dac->digits=decShiftToMost(dac->lsu, 1, shift); - dac->exponent=-shift; // make 1.0000... - status|=DEC_Inexact|DEC_Rounded; // deemed inexact - } - } - else { - decMultiplyOp(dac, dac, rhs, &aset, &status); // dac=dac*rhs - decExpOp(dac, dac, &aset, &status); // dac=exp(dac) - } - // and drop through for final rounding - } // non-integer rhs - - else { // carry on with integer - decNumberZero(dac); // acc=1 - *dac->lsu=1; // .. - - // if a negative power the constant 1 is needed, and if not subset - // invert the lhs now rather than inverting the result later - if (decNumberIsNegative(rhs)) { // was a **-n [hence digits>0] - decNumber *inv=invbuff; // assume use fixed buffer - decNumberCopy(&dnOne, dac); // dnOne=1; [needed now or later] - #if DECSUBSET - if (set->extended) { // need to calculate 1/lhs - #endif - // divide lhs into 1, putting result in dac [dac=1/dac] - decDivideOp(dac, &dnOne, lhs, &aset, DIVIDE, &status); - // now locate or allocate space for the inverted lhs - if (needbytes>sizeof(invbuff)) { - allocinv=(decNumber *)malloc(needbytes); - if (allocinv==NULL) { // hopeless -- abandon - status|=DEC_Insufficient_storage; - break;} - inv=allocinv; // use the allocated space - } - // [inv now points to big-enough buffer or allocated storage] - decNumberCopy(inv, dac); // copy the 1/lhs - decNumberCopy(dac, &dnOne); // restore acc=1 - lhs=inv; // .. and go forward with new lhs - #if DECSUBSET - } - #endif - } - - // Raise-to-the-power loop... - seenbit=0; // set once a 1-bit is encountered - for (i=1;;i++){ // for each bit [top bit ignored] - // abandon if had overflow or terminal underflow - if (status & (DEC_Overflow|DEC_Underflow)) { // interesting? - if (status&DEC_Overflow || ISZERO(dac)) break; - } - // [the following two lines revealed an optimizer bug in a C++ - // compiler, with symptom: 5**3 -> 25, when n=n+n was used] - n=n<<1; // move next bit to testable position - if (n<0) { // top bit is set - seenbit=1; // OK, significant bit seen - decMultiplyOp(dac, dac, lhs, &aset, &status); // dac=dac*x - } - if (i==31) break; // that was the last bit - if (!seenbit) continue; // no need to square 1 - decMultiplyOp(dac, dac, dac, &aset, &status); // dac=dac*dac [square] - } /*i*/ // 32 bits - - // complete internal overflow or underflow processing - if (status & (DEC_Overflow|DEC_Underflow)) { - #if DECSUBSET - // If subset, and power was negative, reverse the kind of -erflow - // [1/x not yet done] - if (!set->extended && decNumberIsNegative(rhs)) { - if (status & DEC_Overflow) - status^=DEC_Overflow | DEC_Underflow | DEC_Subnormal; - else { // trickier -- Underflow may or may not be set - status&=~(DEC_Underflow | DEC_Subnormal); // [one or both] - status|=DEC_Overflow; - } - } - #endif - dac->bits=(dac->bits & ~DECNEG) | bits; // force correct sign - // round subnormals [to set.digits rather than aset.digits] - // or set overflow result similarly as required - decFinalize(dac, set, &residue, &status); - decNumberCopy(res, dac); // copy to result (is now OK length) - break; - } - - #if DECSUBSET - if (!set->extended && // subset math - decNumberIsNegative(rhs)) { // was a **-n [hence digits>0] - // so divide result into 1 [dac=1/dac] - decDivideOp(dac, &dnOne, dac, &aset, DIVIDE, &status); - } - #endif - } // rhs integer path - - // reduce result to the requested length and copy to result - decCopyFit(res, dac, set, &residue, &status); - decFinish(res, set, &residue, &status); // final cleanup - #if DECSUBSET - if (!set->extended) decTrim(res, set, 0, 1, &dropped); // trailing zeros - #endif - } while(0); // end protected - - if (allocdac!=NULL) free(allocdac); // drop any storage used - if (allocinv!=NULL) free(allocinv); // .. - #if DECSUBSET - if (alloclhs!=NULL) free(alloclhs); // .. - if (allocrhs!=NULL) free(allocrhs); // .. - #endif - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberPower - -/* ------------------------------------------------------------------ */ -/* decNumberQuantize -- force exponent to requested value */ -/* */ -/* This computes C = op(A, B), where op adjusts the coefficient */ -/* of C (by rounding or shifting) such that the exponent (-scale) */ -/* of C has exponent of B. The numerical value of C will equal A, */ -/* except for the effects of any rounding that occurred. */ -/* */ -/* res is C, the result. C may be A or B */ -/* lhs is A, the number to adjust */ -/* rhs is B, the number with exponent to match */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* Unless there is an error or the result is infinite, the exponent */ -/* after the operation is guaranteed to be equal to that of B. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberQuantize(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decQuantizeOp(res, lhs, rhs, set, 1, &status); - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberQuantize - -/* ------------------------------------------------------------------ */ -/* decNumberReduce -- remove trailing zeros */ -/* */ -/* This computes C = 0 + A, and normalizes the result */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -// Previously known as Normalize -decNumber * decNumberNormalize(decNumber *res, const decNumber *rhs, - decContext *set) { - return decNumberReduce(res, rhs, set); - } // decNumberNormalize - -decNumber * decNumberReduce(decNumber *res, const decNumber *rhs, - decContext *set) { - #if DECSUBSET - decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated - #endif - uInt status=0; // as usual - Int residue=0; // as usual - Int dropped; // work - - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - do { // protect allocated storage - #if DECSUBSET - if (!set->extended) { - // reduce operand and set lostDigits status, as needed - if (rhs->digits>set->digits) { - allocrhs=decRoundOperand(rhs, set, &status); - if (allocrhs==NULL) break; - rhs=allocrhs; - } - } - #endif - // [following code does not require input rounding] - - // Infinities copy through; NaNs need usual treatment - if (decNumberIsNaN(rhs)) { - decNaNs(res, rhs, NULL, set, &status); - break; - } - - // reduce result to the requested length and copy to result - decCopyFit(res, rhs, set, &residue, &status); // copy & round - decFinish(res, set, &residue, &status); // cleanup/set flags - decTrim(res, set, 1, 0, &dropped); // normalize in place - // [may clamp] - } while(0); // end protected - - #if DECSUBSET - if (allocrhs !=NULL) free(allocrhs); // .. - #endif - if (status!=0) decStatus(res, status, set);// then report status - return res; - } // decNumberReduce - -/* ------------------------------------------------------------------ */ -/* decNumberRescale -- force exponent to requested value */ -/* */ -/* This computes C = op(A, B), where op adjusts the coefficient */ -/* of C (by rounding or shifting) such that the exponent (-scale) */ -/* of C has the value B. The numerical value of C will equal A, */ -/* except for the effects of any rounding that occurred. */ -/* */ -/* res is C, the result. C may be A or B */ -/* lhs is A, the number to adjust */ -/* rhs is B, the requested exponent */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* Unless there is an error or the result is infinite, the exponent */ -/* after the operation is guaranteed to be equal to B. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberRescale(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decQuantizeOp(res, lhs, rhs, set, 0, &status); - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberRescale - -/* ------------------------------------------------------------------ */ -/* decNumberRemainder -- divide and return remainder */ -/* */ -/* This computes C = A % B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X%X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberRemainder(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decDivideOp(res, lhs, rhs, set, REMAINDER, &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberRemainder - -/* ------------------------------------------------------------------ */ -/* decNumberRemainderNear -- divide and return remainder from nearest */ -/* */ -/* This computes C = A % B, where % is the IEEE remainder operator */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X%X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberRemainderNear(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decDivideOp(res, lhs, rhs, set, REMNEAR, &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberRemainderNear - -/* ------------------------------------------------------------------ */ -/* decNumberRotate -- rotate the coefficient of a Number left/right */ -/* */ -/* This computes C = A rot B (in base ten and rotating set->digits */ -/* digits). */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=XrotX) */ -/* lhs is A */ -/* rhs is B, the number of digits to rotate (-ve to right) */ -/* set is the context */ -/* */ -/* The digits of the coefficient of A are rotated to the left (if B */ -/* is positive) or to the right (if B is negative) without adjusting */ -/* the exponent or the sign of A. If lhs->digits is less than */ -/* set->digits the coefficient is padded with zeros on the left */ -/* before the rotate. Any leading zeros in the result are removed */ -/* as usual. */ -/* */ -/* B must be an integer (q=0) and in the range -set->digits through */ -/* +set->digits. */ -/* C must have space for set->digits digits. */ -/* NaNs are propagated as usual. Infinities are unaffected (but */ -/* B must be valid). No status is set unless B is invalid or an */ -/* operand is an sNaN. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberRotate(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - Int rotate; // rhs as an Int - - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - // NaNs propagate as normal - if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) - decNaNs(res, lhs, rhs, set, &status); - // rhs must be an integer - else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) - status=DEC_Invalid_operation; - else { // both numeric, rhs is an integer - rotate=decGetInt(rhs); // [cannot fail] - if (rotate==BADINT // something bad .. - || rotate==BIGODD || rotate==BIGEVEN // .. very big .. - || abs(rotate)>set->digits) // .. or out of range - status=DEC_Invalid_operation; - else { // rhs is OK - decNumberCopy(res, lhs); - // convert -ve rotate to equivalent positive rotation - if (rotate<0) rotate=set->digits+rotate; - if (rotate!=0 && rotate!=set->digits // zero or full rotation - && !decNumberIsInfinite(res)) { // lhs was infinite - // left-rotate to do; 0 < rotate < set->digits - uInt units, shift; // work - uInt msudigits; // digits in result msu - Unit *msu=res->lsu+D2U(res->digits)-1; // current msu - Unit *msumax=res->lsu+D2U(set->digits)-1; // rotation msu - for (msu++; msu<=msumax; msu++) *msu=0; // ensure high units=0 - res->digits=set->digits; // now full-length - msudigits=MSUDIGITS(res->digits); // actual digits in msu - - // rotation here is done in-place, in three steps - // 1. shift all to least up to one unit to unit-align final - // lsd [any digits shifted out are rotated to the left, - // abutted to the original msd (which may require split)] - // - // [if there are no whole units left to rotate, the - // rotation is now complete] - // - // 2. shift to least, from below the split point only, so that - // the final msd is in the right place in its Unit [any - // digits shifted out will fit exactly in the current msu, - // left aligned, no split required] - // - // 3. rotate all the units by reversing left part, right - // part, and then whole - // - // example: rotate right 8 digits (2 units + 2), DECDPUN=3. - // - // start: 00a bcd efg hij klm npq - // - // 1a 000 0ab cde fgh|ijk lmn [pq saved] - // 1b 00p qab cde fgh|ijk lmn - // - // 2a 00p qab cde fgh|00i jkl [mn saved] - // 2b mnp qab cde fgh|00i jkl - // - // 3a fgh cde qab mnp|00i jkl - // 3b fgh cde qab mnp|jkl 00i - // 3c 00i jkl mnp qab cde fgh - - // Step 1: amount to shift is the partial right-rotate count - rotate=set->digits-rotate; // make it right-rotate - units=rotate/DECDPUN; // whole units to rotate - shift=rotate%DECDPUN; // left-over digits count - if (shift>0) { // not an exact number of units - uInt save=res->lsu[0]%powers[shift]; // save low digit(s) - decShiftToLeast(res->lsu, D2U(res->digits), shift); - if (shift>msudigits) { // msumax-1 needs >0 digits - uInt rem=save%powers[shift-msudigits];// split save - *msumax=(Unit)(save/powers[shift-msudigits]); // and insert - *(msumax-1)=*(msumax-1) - +(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); // .. - } - else { // all fits in msumax - *msumax=*msumax+(Unit)(save*powers[msudigits-shift]); // [maybe *1] - } - } // digits shift needed - - // If whole units to rotate... - if (units>0) { // some to do - // Step 2: the units to touch are the whole ones in rotate, - // if any, and the shift is DECDPUN-msudigits (which may be - // 0, again) - shift=DECDPUN-msudigits; - if (shift>0) { // not an exact number of units - uInt save=res->lsu[0]%powers[shift]; // save low digit(s) - decShiftToLeast(res->lsu, units, shift); - *msumax=*msumax+(Unit)(save*powers[msudigits]); - } // partial shift needed - - // Step 3: rotate the units array using triple reverse - // (reversing is easy and fast) - decReverse(res->lsu+units, msumax); // left part - decReverse(res->lsu, res->lsu+units-1); // right part - decReverse(res->lsu, msumax); // whole - } // whole units to rotate - // the rotation may have left an undetermined number of zeros - // on the left, so true length needs to be calculated - res->digits=decGetDigits(res->lsu, msumax-res->lsu+1); - } // rotate needed - } // rhs OK - } // numerics - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberRotate - -/* ------------------------------------------------------------------ */ -/* decNumberSameQuantum -- test for equal exponents */ -/* */ -/* res is the result number, which will contain either 0 or 1 */ -/* lhs is a number to test */ -/* rhs is the second (usually a pattern) */ -/* */ -/* No errors are possible and no context is needed. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberSameQuantum(decNumber *res, const decNumber *lhs, - const decNumber *rhs) { - Unit ret=0; // return value - - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, DECUNCONT)) return res; - #endif - - if (SPECIALARGS) { - if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1; - else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1; - // [anything else with a special gives 0] - } - else if (lhs->exponent==rhs->exponent) ret=1; - - decNumberZero(res); // OK to overwrite an operand now - *res->lsu=ret; - return res; - } // decNumberSameQuantum - -/* ------------------------------------------------------------------ */ -/* decNumberScaleB -- multiply by a power of 10 */ -/* */ -/* This computes C = A x 10**B where B is an integer (q=0) with */ -/* maximum magnitude 2*(emax+digits) */ -/* */ -/* res is C, the result. C may be A or B */ -/* lhs is A, the number to adjust */ -/* rhs is B, the requested power of ten to use */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* The result may underflow or overflow. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberScaleB(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - Int reqexp; // requested exponent change [B] - uInt status=0; // accumulator - Int residue; // work - - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - // Handle special values except lhs infinite - if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) - decNaNs(res, lhs, rhs, set, &status); - // rhs must be an integer - else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) - status=DEC_Invalid_operation; - else { - // lhs is a number; rhs is a finite with q==0 - reqexp=decGetInt(rhs); // [cannot fail] - // maximum range is larger than getInt can handle, so this is - // more restrictive than the specification - if (reqexp==BADINT // something bad .. - || reqexp==BIGODD || reqexp==BIGEVEN // it was huge - || (abs(reqexp)+1)/2>(set->digits+set->emax)) // .. or out of range - status=DEC_Invalid_operation; - else { // rhs is OK - decNumberCopy(res, lhs); // all done if infinite lhs - if (!decNumberIsInfinite(res)) { // prepare to scale - Int exp=res->exponent; // save for overflow test - res->exponent+=reqexp; // adjust the exponent - if (((exp^reqexp)>=0) // same sign ... - && ((exp^res->exponent)<0)) { // .. but result had different - // the calculation overflowed, so force right treatment - if (exp<0) res->exponent=DEC_MIN_EMIN-DEC_MAX_DIGITS; - else res->exponent=DEC_MAX_EMAX+1; - } - residue=0; - decFinalize(res, set, &residue, &status); // final check - } // finite LHS - } // rhs OK - } // rhs finite - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberScaleB - -/* ------------------------------------------------------------------ */ -/* decNumberShift -- shift the coefficient of a Number left or right */ -/* */ -/* This computes C = A << B or C = A >> -B (in base ten). */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X<<X) */ -/* lhs is A */ -/* rhs is B, the number of digits to shift (-ve to right) */ -/* set is the context */ -/* */ -/* The digits of the coefficient of A are shifted to the left (if B */ -/* is positive) or to the right (if B is negative) without adjusting */ -/* the exponent or the sign of A. */ -/* */ -/* B must be an integer (q=0) and in the range -set->digits through */ -/* +set->digits. */ -/* C must have space for set->digits digits. */ -/* NaNs are propagated as usual. Infinities are unaffected (but */ -/* B must be valid). No status is set unless B is invalid or an */ -/* operand is an sNaN. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberShift(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - Int shift; // rhs as an Int - - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - // NaNs propagate as normal - if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) - decNaNs(res, lhs, rhs, set, &status); - // rhs must be an integer - else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) - status=DEC_Invalid_operation; - else { // both numeric, rhs is an integer - shift=decGetInt(rhs); // [cannot fail] - if (shift==BADINT // something bad .. - || shift==BIGODD || shift==BIGEVEN // .. very big .. - || abs(shift)>set->digits) // .. or out of range - status=DEC_Invalid_operation; - else { // rhs is OK - decNumberCopy(res, lhs); - if (shift!=0 && !decNumberIsInfinite(res)) { // something to do - if (shift>0) { // to left - if (shift==set->digits) { // removing all - *res->lsu=0; // so place 0 - res->digits=1; // .. - } - else { // - // first remove leading digits if necessary - if (res->digits+shift>set->digits) { - decDecap(res, res->digits+shift-set->digits); - // that updated res->digits; may have gone to 1 (for a - // single digit or for zero - } - if (res->digits>1 || *res->lsu) // if non-zero.. - res->digits=decShiftToMost(res->lsu, res->digits, shift); - } // partial left - } // left - else { // to right - if (-shift>=res->digits) { // discarding all - *res->lsu=0; // so place 0 - res->digits=1; // .. - } - else { - decShiftToLeast(res->lsu, D2U(res->digits), -shift); - res->digits-=(-shift); - } - } // to right - } // non-0 non-Inf shift - } // rhs OK - } // numerics - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberShift - -/* ------------------------------------------------------------------ */ -/* decNumberSquareRoot -- square root operator */ -/* */ -/* This computes C = squareroot(A) */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context; note that rounding mode has no effect */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -/* This uses the following varying-precision algorithm in: */ -/* */ -/* Properly Rounded Variable Precision Square Root, T. E. Hull and */ -/* A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */ -/* pp229-237, ACM, September 1985. */ -/* */ -/* The square-root is calculated using Newton's method, after which */ -/* a check is made to ensure the result is correctly rounded. */ -/* */ -/* % [Reformatted original Numerical Turing source code follows.] */ -/* function sqrt(x : real) : real */ -/* % sqrt(x) returns the properly rounded approximation to the square */ -/* % root of x, in the precision of the calling environment, or it */ -/* % fails if x < 0. */ -/* % t e hull and a abrham, august, 1984 */ -/* if x <= 0 then */ -/* if x < 0 then */ -/* assert false */ -/* else */ -/* result 0 */ -/* end if */ -/* end if */ -/* var f := setexp(x, 0) % fraction part of x [0.1 <= x < 1] */ -/* var e := getexp(x) % exponent part of x */ -/* var approx : real */ -/* if e mod 2 = 0 then */ -/* approx := .259 + .819 * f % approx to root of f */ -/* else */ -/* f := f/l0 % adjustments */ -/* e := e + 1 % for odd */ -/* approx := .0819 + 2.59 * f % exponent */ -/* end if */ -/* */ -/* var p:= 3 */ -/* const maxp := currentprecision + 2 */ -/* loop */ -/* p := min(2*p - 2, maxp) % p = 4,6,10, . . . , maxp */ -/* precision p */ -/* approx := .5 * (approx + f/approx) */ -/* exit when p = maxp */ -/* end loop */ -/* */ -/* % approx is now within 1 ulp of the properly rounded square root */ -/* % of f; to ensure proper rounding, compare squares of (approx - */ -/* % l/2 ulp) and (approx + l/2 ulp) with f. */ -/* p := currentprecision */ -/* begin */ -/* precision p + 2 */ -/* const approxsubhalf := approx - setexp(.5, -p) */ -/* if mulru(approxsubhalf, approxsubhalf) > f then */ -/* approx := approx - setexp(.l, -p + 1) */ -/* else */ -/* const approxaddhalf := approx + setexp(.5, -p) */ -/* if mulrd(approxaddhalf, approxaddhalf) < f then */ -/* approx := approx + setexp(.l, -p + 1) */ -/* end if */ -/* end if */ -/* end */ -/* result setexp(approx, e div 2) % fix exponent */ -/* end sqrt */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberSquareRoot(decNumber *res, const decNumber *rhs, - decContext *set) { - decContext workset, approxset; // work contexts - decNumber dzero; // used for constant zero - Int maxp; // largest working precision - Int workp; // working precision - Int residue=0; // rounding residue - uInt status=0, ignore=0; // status accumulators - uInt rstatus; // .. - Int exp; // working exponent - Int ideal; // ideal (preferred) exponent - Int needbytes; // work - Int dropped; // .. - - #if DECSUBSET - decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated - #endif - // buffer for f [needs +1 in case DECBUFFER 0] - decNumber buff[D2N(DECBUFFER+1)]; - // buffer for a [needs +2 to match likely maxp] - decNumber bufa[D2N(DECBUFFER+2)]; - // buffer for temporary, b [must be same size as a] - decNumber bufb[D2N(DECBUFFER+2)]; - decNumber *allocbuff=NULL; // -> allocated buff, iff allocated - decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated - decNumber *allocbufb=NULL; // -> allocated bufb, iff allocated - decNumber *f=buff; // reduced fraction - decNumber *a=bufa; // approximation to result - decNumber *b=bufb; // intermediate result - // buffer for temporary variable, up to 3 digits - decNumber buft[D2N(3)]; - decNumber *t=buft; // up-to-3-digit constant or work - - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - do { // protect allocated storage - #if DECSUBSET - if (!set->extended) { - // reduce operand and set lostDigits status, as needed - if (rhs->digits>set->digits) { - allocrhs=decRoundOperand(rhs, set, &status); - if (allocrhs==NULL) break; - // [Note: 'f' allocation below could reuse this buffer if - // used, but as this is rare they are kept separate for clarity.] - rhs=allocrhs; - } - } - #endif - // [following code does not require input rounding] - - // handle infinities and NaNs - if (SPECIALARG) { - if (decNumberIsInfinite(rhs)) { // an infinity - if (decNumberIsNegative(rhs)) status|=DEC_Invalid_operation; - else decNumberCopy(res, rhs); // +Infinity - } - else decNaNs(res, rhs, NULL, set, &status); // a NaN - break; - } - - // calculate the ideal (preferred) exponent [floor(exp/2)] - // [It would be nicer to write: ideal=rhs->exponent>>1, but this - // generates a compiler warning. Generated code is the same.] - ideal=(rhs->exponent&~1)/2; // target - - // handle zeros - if (ISZERO(rhs)) { - decNumberCopy(res, rhs); // could be 0 or -0 - res->exponent=ideal; // use the ideal [safe] - // use decFinish to clamp any out-of-range exponent, etc. - decFinish(res, set, &residue, &status); - break; - } - - // any other -x is an oops - if (decNumberIsNegative(rhs)) { - status|=DEC_Invalid_operation; - break; - } - - // space is needed for three working variables - // f -- the same precision as the RHS, reduced to 0.01->0.99... - // a -- Hull's approximation -- precision, when assigned, is - // currentprecision+1 or the input argument precision, - // whichever is larger (+2 for use as temporary) - // b -- intermediate temporary result (same size as a) - // if any is too long for local storage, then allocate - workp=MAXI(set->digits+1, rhs->digits); // actual rounding precision - workp=MAXI(workp, 7); // at least 7 for low cases - maxp=workp+2; // largest working precision - - needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); - if (needbytes>(Int)sizeof(buff)) { - allocbuff=(decNumber *)malloc(needbytes); - if (allocbuff==NULL) { // hopeless -- abandon - status|=DEC_Insufficient_storage; - break;} - f=allocbuff; // use the allocated space - } - // a and b both need to be able to hold a maxp-length number - needbytes=sizeof(decNumber)+(D2U(maxp)-1)*sizeof(Unit); - if (needbytes>(Int)sizeof(bufa)) { // [same applies to b] - allocbufa=(decNumber *)malloc(needbytes); - allocbufb=(decNumber *)malloc(needbytes); - if (allocbufa==NULL || allocbufb==NULL) { // hopeless - status|=DEC_Insufficient_storage; - break;} - a=allocbufa; // use the allocated spaces - b=allocbufb; // .. - } - - // copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1 - decNumberCopy(f, rhs); - exp=f->exponent+f->digits; // adjusted to Hull rules - f->exponent=-(f->digits); // to range - - // set up working context - decContextDefault(&workset, DEC_INIT_DECIMAL64); - workset.emax=DEC_MAX_EMAX; - workset.emin=DEC_MIN_EMIN; - - // [Until further notice, no error is possible and status bits - // (Rounded, etc.) should be ignored, not accumulated.] - - // Calculate initial approximation, and allow for odd exponent - workset.digits=workp; // p for initial calculation - t->bits=0; t->digits=3; - a->bits=0; a->digits=3; - if ((exp & 1)==0) { // even exponent - // Set t=0.259, a=0.819 - t->exponent=-3; - a->exponent=-3; - #if DECDPUN>=3 - t->lsu[0]=259; - a->lsu[0]=819; - #elif DECDPUN==2 - t->lsu[0]=59; t->lsu[1]=2; - a->lsu[0]=19; a->lsu[1]=8; - #else - t->lsu[0]=9; t->lsu[1]=5; t->lsu[2]=2; - a->lsu[0]=9; a->lsu[1]=1; a->lsu[2]=8; - #endif - } - else { // odd exponent - // Set t=0.0819, a=2.59 - f->exponent--; // f=f/10 - exp++; // e=e+1 - t->exponent=-4; - a->exponent=-2; - #if DECDPUN>=3 - t->lsu[0]=819; - a->lsu[0]=259; - #elif DECDPUN==2 - t->lsu[0]=19; t->lsu[1]=8; - a->lsu[0]=59; a->lsu[1]=2; - #else - t->lsu[0]=9; t->lsu[1]=1; t->lsu[2]=8; - a->lsu[0]=9; a->lsu[1]=5; a->lsu[2]=2; - #endif - } - - decMultiplyOp(a, a, f, &workset, &ignore); // a=a*f - decAddOp(a, a, t, &workset, 0, &ignore); // ..+t - // [a is now the initial approximation for sqrt(f), calculated with - // currentprecision, which is also a's precision.] - - // the main calculation loop - decNumberZero(&dzero); // make 0 - decNumberZero(t); // set t = 0.5 - t->lsu[0]=5; // .. - t->exponent=-1; // .. - workset.digits=3; // initial p - for (; workset.digits<maxp;) { - // set p to min(2*p - 2, maxp) [hence 3; or: 4, 6, 10, ... , maxp] - workset.digits=MINI(workset.digits*2-2, maxp); - // a = 0.5 * (a + f/a) - // [calculated at p then rounded to currentprecision] - decDivideOp(b, f, a, &workset, DIVIDE, &ignore); // b=f/a - decAddOp(b, b, a, &workset, 0, &ignore); // b=b+a - decMultiplyOp(a, b, t, &workset, &ignore); // a=b*0.5 - } // loop - - // Here, 0.1 <= a < 1 [Hull], and a has maxp digits - // now reduce to length, etc.; this needs to be done with a - // having the correct exponent so as to handle subnormals - // correctly - approxset=*set; // get emin, emax, etc. - approxset.round=DEC_ROUND_HALF_EVEN; - a->exponent+=exp/2; // set correct exponent - rstatus=0; // clear status - residue=0; // .. and accumulator - decCopyFit(a, a, &approxset, &residue, &rstatus); // reduce (if needed) - decFinish(a, &approxset, &residue, &rstatus); // clean and finalize - - // Overflow was possible if the input exponent was out-of-range, - // in which case quit - if (rstatus&DEC_Overflow) { - status=rstatus; // use the status as-is - decNumberCopy(res, a); // copy to result - break; - } - - // Preserve status except Inexact/Rounded - status|=(rstatus & ~(DEC_Rounded|DEC_Inexact)); - - // Carry out the Hull correction - a->exponent-=exp/2; // back to 0.1->1 - - // a is now at final precision and within 1 ulp of the properly - // rounded square root of f; to ensure proper rounding, compare - // squares of (a - l/2 ulp) and (a + l/2 ulp) with f. - // Here workset.digits=maxp and t=0.5, and a->digits determines - // the ulp - workset.digits--; // maxp-1 is OK now - t->exponent=-a->digits-1; // make 0.5 ulp - decAddOp(b, a, t, &workset, DECNEG, &ignore); // b = a - 0.5 ulp - workset.round=DEC_ROUND_UP; - decMultiplyOp(b, b, b, &workset, &ignore); // b = mulru(b, b) - decCompareOp(b, f, b, &workset, COMPARE, &ignore); // b ? f, reversed - if (decNumberIsNegative(b)) { // f < b [i.e., b > f] - // this is the more common adjustment, though both are rare - t->exponent++; // make 1.0 ulp - t->lsu[0]=1; // .. - decAddOp(a, a, t, &workset, DECNEG, &ignore); // a = a - 1 ulp - // assign to approx [round to length] - approxset.emin-=exp/2; // adjust to match a - approxset.emax-=exp/2; - decAddOp(a, &dzero, a, &approxset, 0, &ignore); - } - else { - decAddOp(b, a, t, &workset, 0, &ignore); // b = a + 0.5 ulp - workset.round=DEC_ROUND_DOWN; - decMultiplyOp(b, b, b, &workset, &ignore); // b = mulrd(b, b) - decCompareOp(b, b, f, &workset, COMPARE, &ignore); // b ? f - if (decNumberIsNegative(b)) { // b < f - t->exponent++; // make 1.0 ulp - t->lsu[0]=1; // .. - decAddOp(a, a, t, &workset, 0, &ignore); // a = a + 1 ulp - // assign to approx [round to length] - approxset.emin-=exp/2; // adjust to match a - approxset.emax-=exp/2; - decAddOp(a, &dzero, a, &approxset, 0, &ignore); - } - } - // [no errors are possible in the above, and rounding/inexact during - // estimation are irrelevant, so status was not accumulated] - - // Here, 0.1 <= a < 1 (still), so adjust back - a->exponent+=exp/2; // set correct exponent - - // count droppable zeros [after any subnormal rounding] by - // trimming a copy - decNumberCopy(b, a); - decTrim(b, set, 1, 1, &dropped); // [drops trailing zeros] - - // Set Inexact and Rounded. The answer can only be exact if - // it is short enough so that squaring it could fit in workp - // digits, so this is the only (relatively rare) condition that - // a careful check is needed - if (b->digits*2-1 > workp) { // cannot fit - status|=DEC_Inexact|DEC_Rounded; - } - else { // could be exact/unrounded - uInt mstatus=0; // local status - decMultiplyOp(b, b, b, &workset, &mstatus); // try the multiply - if (mstatus&DEC_Overflow) { // result just won't fit - status|=DEC_Inexact|DEC_Rounded; - } - else { // plausible - decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); // b ? rhs - if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; // not equal - else { // is Exact - // here, dropped is the count of trailing zeros in 'a' - // use closest exponent to ideal... - Int todrop=ideal-a->exponent; // most that can be dropped - if (todrop<0) status|=DEC_Rounded; // ideally would add 0s - else { // unrounded - // there are some to drop, but emax may not allow all - Int maxexp=set->emax-set->digits+1; - Int maxdrop=maxexp-a->exponent; - if (todrop>maxdrop && set->clamp) { // apply clamping - todrop=maxdrop; - status|=DEC_Clamped; - } - if (dropped<todrop) { // clamp to those available - todrop=dropped; - status|=DEC_Clamped; - } - if (todrop>0) { // have some to drop - decShiftToLeast(a->lsu, D2U(a->digits), todrop); - a->exponent+=todrop; // maintain numerical value - a->digits-=todrop; // new length - } - } - } - } - } - - // double-check Underflow, as perhaps the result could not have - // been subnormal (initial argument too big), or it is now Exact - if (status&DEC_Underflow) { - Int ae=rhs->exponent+rhs->digits-1; // adjusted exponent - // check if truly subnormal - #if DECEXTFLAG // DEC_Subnormal too - if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow); - #else - if (ae>=set->emin*2) status&=~DEC_Underflow; - #endif - // check if truly inexact - if (!(status&DEC_Inexact)) status&=~DEC_Underflow; - } - - decNumberCopy(res, a); // a is now the result - } while(0); // end protected - - if (allocbuff!=NULL) free(allocbuff); // drop any storage used - if (allocbufa!=NULL) free(allocbufa); // .. - if (allocbufb!=NULL) free(allocbufb); // .. - #if DECSUBSET - if (allocrhs !=NULL) free(allocrhs); // .. - #endif - if (status!=0) decStatus(res, status, set);// then report status - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberSquareRoot - -/* ------------------------------------------------------------------ */ -/* decNumberSubtract -- subtract two Numbers */ -/* */ -/* This computes C = A - B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X-X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberSubtract(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - - decAddOp(res, lhs, rhs, set, DECNEG, &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberSubtract - -/* ------------------------------------------------------------------ */ -/* decNumberToIntegralExact -- round-to-integral-value with InExact */ -/* decNumberToIntegralValue -- round-to-integral-value */ -/* */ -/* res is the result */ -/* rhs is input number */ -/* set is the context */ -/* */ -/* res must have space for any value of rhs. */ -/* */ -/* This implements the IEEE special operators and therefore treats */ -/* special values as valid. For finite numbers it returns */ -/* rescale(rhs, 0) if rhs->exponent is <0. */ -/* Otherwise the result is rhs (so no error is possible, except for */ -/* sNaN). */ -/* */ -/* The context is used for rounding mode and status after sNaN, but */ -/* the digits setting is ignored. The Exact version will signal */ -/* Inexact if the result differs numerically from rhs; the other */ -/* never signals Inexact. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberToIntegralExact(decNumber *res, const decNumber *rhs, - decContext *set) { - decNumber dn; - decContext workset; // working context - uInt status=0; // accumulator - - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - // handle infinities and NaNs - if (SPECIALARG) { - if (decNumberIsInfinite(rhs)) decNumberCopy(res, rhs); // an Infinity - else decNaNs(res, rhs, NULL, set, &status); // a NaN - } - else { // finite - // have a finite number; no error possible (res must be big enough) - if (rhs->exponent>=0) return decNumberCopy(res, rhs); - // that was easy, but if negative exponent there is work to do... - workset=*set; // clone rounding, etc. - workset.digits=rhs->digits; // no length rounding - workset.traps=0; // no traps - decNumberZero(&dn); // make a number with exponent 0 - decNumberQuantize(res, rhs, &dn, &workset); - status|=workset.status; - } - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberToIntegralExact - -decNumber * decNumberToIntegralValue(decNumber *res, const decNumber *rhs, - decContext *set) { - decContext workset=*set; // working context - workset.traps=0; // no traps - decNumberToIntegralExact(res, rhs, &workset); - // this never affects set, except for sNaNs; NaN will have been set - // or propagated already, so no need to call decStatus - set->status|=workset.status&DEC_Invalid_operation; - return res; - } // decNumberToIntegralValue - -/* ------------------------------------------------------------------ */ -/* decNumberXor -- XOR two Numbers, digitwise */ -/* */ -/* This computes C = A ^ B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X^X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context (used for result length and error report) */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* Logical function restrictions apply (see above); a NaN is */ -/* returned with Invalid_operation if a restriction is violated. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberXor(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - const Unit *ua, *ub; // -> operands - const Unit *msua, *msub; // -> operand msus - Unit *uc, *msuc; // -> result and its msu - Int msudigs; // digits in res msu - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) - || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { - decStatus(res, DEC_Invalid_operation, set); - return res; - } - // operands are valid - ua=lhs->lsu; // bottom-up - ub=rhs->lsu; // .. - uc=res->lsu; // .. - msua=ua+D2U(lhs->digits)-1; // -> msu of lhs - msub=ub+D2U(rhs->digits)-1; // -> msu of rhs - msuc=uc+D2U(set->digits)-1; // -> msu of result - msudigs=MSUDIGITS(set->digits); // [faster than remainder] - for (; uc<=msuc; ua++, ub++, uc++) { // Unit loop - Unit a, b; // extract units - if (ua>msua) a=0; - else a=*ua; - if (ub>msub) b=0; - else b=*ub; - *uc=0; // can now write back - if (a|b) { // maybe 1 bits to examine - Int i, j; - // This loop could be unrolled and/or use BIN2BCD tables - for (i=0; i<DECDPUN; i++) { - if ((a^b)&1) *uc=*uc+(Unit)powers[i]; // effect XOR - j=a%10; - a=a/10; - j|=b%10; - b=b/10; - if (j>1) { - decStatus(res, DEC_Invalid_operation, set); - return res; - } - if (uc==msuc && i==msudigs-1) break; // just did final digit - } // each digit - } // non-zero - } // each unit - // [here uc-1 is the msu of the result] - res->digits=decGetDigits(res->lsu, uc-res->lsu); - res->exponent=0; // integer - res->bits=0; // sign=0 - return res; // [no status to set] - } // decNumberXor - - -/* ================================================================== */ -/* Utility routines */ -/* ================================================================== */ - -/* ------------------------------------------------------------------ */ -/* decNumberClass -- return the decClass of a decNumber */ -/* dn -- the decNumber to test */ -/* set -- the context to use for Emin */ -/* returns the decClass enum */ -/* ------------------------------------------------------------------ */ -enum decClass decNumberClass(const decNumber *dn, decContext *set) { - if (decNumberIsSpecial(dn)) { - if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN; - if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN; - // must be an infinity - if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF; - return DEC_CLASS_POS_INF; - } - // is finite - if (decNumberIsNormal(dn, set)) { // most common - if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL; - return DEC_CLASS_POS_NORMAL; - } - // is subnormal or zero - if (decNumberIsZero(dn)) { // most common - if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO; - return DEC_CLASS_POS_ZERO; - } - if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL; - return DEC_CLASS_POS_SUBNORMAL; - } // decNumberClass - -/* ------------------------------------------------------------------ */ -/* decNumberClassToString -- convert decClass to a string */ -/* */ -/* eclass is a valid decClass */ -/* returns a constant string describing the class (max 13+1 chars) */ -/* ------------------------------------------------------------------ */ -const char *decNumberClassToString(enum decClass eclass) { - if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN; - if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN; - if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ; - if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ; - if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS; - if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS; - if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI; - if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI; - if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN; - if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN; - return DEC_ClassString_UN; // Unknown - } // decNumberClassToString - -/* ------------------------------------------------------------------ */ -/* decNumberCopy -- copy a number */ -/* */ -/* dest is the target decNumber */ -/* src is the source decNumber */ -/* returns dest */ -/* */ -/* (dest==src is allowed and is a no-op) */ -/* All fields are updated as required. This is a utility operation, */ -/* so special values are unchanged and no error is possible. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberCopy(decNumber *dest, const decNumber *src) { - - #if DECCHECK - if (src==NULL) return decNumberZero(dest); - #endif - - if (dest==src) return dest; // no copy required - - // Use explicit assignments here as structure assignment could copy - // more than just the lsu (for small DECDPUN). This would not affect - // the value of the results, but could disturb test harness spill - // checking. - dest->bits=src->bits; - dest->exponent=src->exponent; - dest->digits=src->digits; - dest->lsu[0]=src->lsu[0]; - if (src->digits>DECDPUN) { // more Units to come - const Unit *smsup, *s; // work - Unit *d; // .. - // memcpy for the remaining Units would be safe as they cannot - // overlap. However, this explicit loop is faster in short cases. - d=dest->lsu+1; // -> first destination - smsup=src->lsu+D2U(src->digits); // -> source msu+1 - for (s=src->lsu+1; s<smsup; s++, d++) *d=*s; - } - return dest; - } // decNumberCopy - -/* ------------------------------------------------------------------ */ -/* decNumberCopyAbs -- quiet absolute value operator */ -/* */ -/* This sets C = abs(A) */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* */ -/* C must have space for set->digits digits. */ -/* No exception or error can occur; this is a quiet bitwise operation.*/ -/* See also decNumberAbs for a checking version of this. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberCopyAbs(decNumber *res, const decNumber *rhs) { - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; - #endif - decNumberCopy(res, rhs); - res->bits&=~DECNEG; // turn off sign - return res; - } // decNumberCopyAbs - -/* ------------------------------------------------------------------ */ -/* decNumberCopyNegate -- quiet negate value operator */ -/* */ -/* This sets C = negate(A) */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* */ -/* C must have space for set->digits digits. */ -/* No exception or error can occur; this is a quiet bitwise operation.*/ -/* See also decNumberMinus for a checking version of this. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberCopyNegate(decNumber *res, const decNumber *rhs) { - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; - #endif - decNumberCopy(res, rhs); - res->bits^=DECNEG; // invert the sign - return res; - } // decNumberCopyNegate - -/* ------------------------------------------------------------------ */ -/* decNumberCopySign -- quiet copy and set sign operator */ -/* */ -/* This sets C = A with the sign of B */ -/* */ -/* res is C, the result. C may be A */ -/* lhs is A */ -/* rhs is B */ -/* */ -/* C must have space for set->digits digits. */ -/* No exception or error can occur; this is a quiet bitwise operation.*/ -/* ------------------------------------------------------------------ */ -decNumber * decNumberCopySign(decNumber *res, const decNumber *lhs, - const decNumber *rhs) { - uByte sign; // rhs sign - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; - #endif - sign=rhs->bits & DECNEG; // save sign bit - decNumberCopy(res, lhs); - res->bits&=~DECNEG; // clear the sign - res->bits|=sign; // set from rhs - return res; - } // decNumberCopySign - -/* ------------------------------------------------------------------ */ -/* decNumberGetBCD -- get the coefficient in BCD8 */ -/* dn is the source decNumber */ -/* bcd is the uInt array that will receive dn->digits BCD bytes, */ -/* most-significant at offset 0 */ -/* returns bcd */ -/* */ -/* bcd must have at least dn->digits bytes. No error is possible; if */ -/* dn is a NaN or Infinite, digits must be 1 and the coefficient 0. */ -/* ------------------------------------------------------------------ */ -uByte * decNumberGetBCD(const decNumber *dn, uByte *bcd) { - uByte *ub=bcd+dn->digits-1; // -> lsd - const Unit *up=dn->lsu; // Unit pointer, -> lsu - - #if DECDPUN==1 // trivial simple copy - for (; ub>=bcd; ub--, up++) *ub=*up; - #else // chopping needed - uInt u=*up; // work - uInt cut=DECDPUN; // downcounter through unit - for (; ub>=bcd; ub--) { - *ub=(uByte)(u%10); // [*6554 trick inhibits, here] - u=u/10; - cut--; - if (cut>0) continue; // more in this unit - up++; - u=*up; - cut=DECDPUN; - } - #endif - return bcd; - } // decNumberGetBCD - -/* ------------------------------------------------------------------ */ -/* decNumberSetBCD -- set (replace) the coefficient from BCD8 */ -/* dn is the target decNumber */ -/* bcd is the uInt array that will source n BCD bytes, most- */ -/* significant at offset 0 */ -/* n is the number of digits in the source BCD array (bcd) */ -/* returns dn */ -/* */ -/* dn must have space for at least n digits. No error is possible; */ -/* if dn is a NaN, or Infinite, or is to become a zero, n must be 1 */ -/* and bcd[0] zero. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberSetBCD(decNumber *dn, const uByte *bcd, uInt n) { - Unit *up=dn->lsu+D2U(dn->digits)-1; // -> msu [target pointer] - const uByte *ub=bcd; // -> source msd - - #if DECDPUN==1 // trivial simple copy - for (; ub<bcd+n; ub++, up--) *up=*ub; - #else // some assembly needed - // calculate how many digits in msu, and hence first cut - Int cut=MSUDIGITS(n); // [faster than remainder] - for (;up>=dn->lsu; up--) { // each Unit from msu - *up=0; // will take <=DECDPUN digits - for (; cut>0; ub++, cut--) *up=X10(*up)+*ub; - cut=DECDPUN; // next Unit has all digits - } - #endif - dn->digits=n; // set digit count - return dn; - } // decNumberSetBCD - -/* ------------------------------------------------------------------ */ -/* decNumberIsNormal -- test normality of a decNumber */ -/* dn is the decNumber to test */ -/* set is the context to use for Emin */ -/* returns 1 if |dn| is finite and >=Nmin, 0 otherwise */ -/* ------------------------------------------------------------------ */ -Int decNumberIsNormal(const decNumber *dn, decContext *set) { - Int ae; // adjusted exponent - #if DECCHECK - if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; - #endif - - if (decNumberIsSpecial(dn)) return 0; // not finite - if (decNumberIsZero(dn)) return 0; // not non-zero - - ae=dn->exponent+dn->digits-1; // adjusted exponent - if (ae<set->emin) return 0; // is subnormal - return 1; - } // decNumberIsNormal - -/* ------------------------------------------------------------------ */ -/* decNumberIsSubnormal -- test subnormality of a decNumber */ -/* dn is the decNumber to test */ -/* set is the context to use for Emin */ -/* returns 1 if |dn| is finite, non-zero, and <Nmin, 0 otherwise */ -/* ------------------------------------------------------------------ */ -Int decNumberIsSubnormal(const decNumber *dn, decContext *set) { - Int ae; // adjusted exponent - #if DECCHECK - if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; - #endif - - if (decNumberIsSpecial(dn)) return 0; // not finite - if (decNumberIsZero(dn)) return 0; // not non-zero - - ae=dn->exponent+dn->digits-1; // adjusted exponent - if (ae<set->emin) return 1; // is subnormal - return 0; - } // decNumberIsSubnormal - -/* ------------------------------------------------------------------ */ -/* decNumberTrim -- remove insignificant zeros */ -/* */ -/* dn is the number to trim */ -/* returns dn */ -/* */ -/* All fields are updated as required. This is a utility operation, */ -/* so special values are unchanged and no error is possible. The */ -/* zeros are removed unconditionally. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberTrim(decNumber *dn) { - Int dropped; // work - decContext set; // .. - #if DECCHECK - if (decCheckOperands(DECUNRESU, DECUNUSED, dn, DECUNCONT)) return dn; - #endif - decContextDefault(&set, DEC_INIT_BASE); // clamp=0 - return decTrim(dn, &set, 0, 1, &dropped); - } // decNumberTrim - -/* ------------------------------------------------------------------ */ -/* decNumberVersion -- return the name and version of this module */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -const char * decNumberVersion(void) { - return DECVERSION; - } // decNumberVersion - -/* ------------------------------------------------------------------ */ -/* decNumberZero -- set a number to 0 */ -/* */ -/* dn is the number to set, with space for one digit */ -/* returns dn */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -// Memset is not used as it is much slower in some environments. -decNumber * decNumberZero(decNumber *dn) { - - #if DECCHECK - if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn; - #endif - - dn->bits=0; - dn->exponent=0; - dn->digits=1; - dn->lsu[0]=0; - return dn; - } // decNumberZero - -/* ================================================================== */ -/* Local routines */ -/* ================================================================== */ - -/* ------------------------------------------------------------------ */ -/* decToString -- lay out a number into a string */ -/* */ -/* dn is the number to lay out */ -/* string is where to lay out the number */ -/* eng is 1 if Engineering, 0 if Scientific */ -/* */ -/* string must be at least dn->digits+14 characters long */ -/* No error is possible. */ -/* */ -/* Note that this routine can generate a -0 or 0.000. These are */ -/* never generated in subset to-number or arithmetic, but can occur */ -/* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234). */ -/* ------------------------------------------------------------------ */ -// If DECCHECK is enabled the string "?" is returned if a number is -// invalid. -static void decToString(const decNumber *dn, char *string, Flag eng) { - Int exp=dn->exponent; // local copy - Int e; // E-part value - Int pre; // digits before the '.' - Int cut; // for counting digits in a Unit - char *c=string; // work [output pointer] - const Unit *up=dn->lsu+D2U(dn->digits)-1; // -> msu [input pointer] - uInt u, pow; // work - - #if DECCHECK - if (decCheckOperands(DECUNRESU, dn, DECUNUSED, DECUNCONT)) { - strcpy(string, "?"); - return;} - #endif - - if (decNumberIsNegative(dn)) { // Negatives get a minus - *c='-'; - c++; - } - if (dn->bits&DECSPECIAL) { // Is a special value - if (decNumberIsInfinite(dn)) { - strcpy(c, "Inf"); - strcpy(c+3, "inity"); - return;} - // a NaN - if (dn->bits&DECSNAN) { // signalling NaN - *c='s'; - c++; - } - strcpy(c, "NaN"); - c+=3; // step past - // if not a clean non-zero coefficient, that's all there is in a - // NaN string - if (exp!=0 || (*dn->lsu==0 && dn->digits==1)) return; - // [drop through to add integer] - } - - // calculate how many digits in msu, and hence first cut - cut=MSUDIGITS(dn->digits); // [faster than remainder] - cut--; // power of ten for digit - - if (exp==0) { // simple integer [common fastpath] - for (;up>=dn->lsu; up--) { // each Unit from msu - u=*up; // contains DECDPUN digits to lay out - for (; cut>=0; c++, cut--) TODIGIT(u, cut, c, pow); - cut=DECDPUN-1; // next Unit has all digits - } - *c='\0'; // terminate the string - return;} - - /* non-0 exponent -- assume plain form */ - pre=dn->digits+exp; // digits before '.' - e=0; // no E - if ((exp>0) || (pre<-5)) { // need exponential form - e=exp+dn->digits-1; // calculate E value - pre=1; // assume one digit before '.' - if (eng && (e!=0)) { // engineering: may need to adjust - Int adj; // adjustment - // The C remainder operator is undefined for negative numbers, so - // a positive remainder calculation must be used here - if (e<0) { - adj=(-e)%3; - if (adj!=0) adj=3-adj; - } - else { // e>0 - adj=e%3; - } - e=e-adj; - // if dealing with zero still produce an exponent which is a - // multiple of three, as expected, but there will only be the - // one zero before the E, still. Otherwise note the padding. - if (!ISZERO(dn)) pre+=adj; - else { // is zero - if (adj!=0) { // 0.00Esnn needed - e=e+3; - pre=-(2-adj); - } - } // zero - } // eng - } // need exponent - - /* lay out the digits of the coefficient, adding 0s and . as needed */ - u=*up; - if (pre>0) { // xxx.xxx or xx00 (engineering) form - Int n=pre; - for (; pre>0; pre--, c++, cut--) { - if (cut<0) { // need new Unit - if (up==dn->lsu) break; // out of input digits (pre>digits) - up--; - cut=DECDPUN-1; - u=*up; - } - TODIGIT(u, cut, c, pow); - } - if (n<dn->digits) { // more to come, after '.' - *c='.'; c++; - for (;; c++, cut--) { - if (cut<0) { // need new Unit - if (up==dn->lsu) break; // out of input digits - up--; - cut=DECDPUN-1; - u=*up; - } - TODIGIT(u, cut, c, pow); - } - } - else for (; pre>0; pre--, c++) *c='0'; // 0 padding (for engineering) needed - } - else { // 0.xxx or 0.000xxx form - *c='0'; c++; - *c='.'; c++; - for (; pre<0; pre++, c++) *c='0'; // add any 0's after '.' - for (; ; c++, cut--) { - if (cut<0) { // need new Unit - if (up==dn->lsu) break; // out of input digits - up--; - cut=DECDPUN-1; - u=*up; - } - TODIGIT(u, cut, c, pow); - } - } - - /* Finally add the E-part, if needed. It will never be 0, has a - base maximum and minimum of +999999999 through -999999999, but - could range down to -1999999998 for anormal numbers */ - if (e!=0) { - Flag had=0; // 1=had non-zero - *c='E'; c++; - *c='+'; c++; // assume positive - u=e; // .. - if (e<0) { - *(c-1)='-'; // oops, need - - u=-e; // uInt, please - } - // lay out the exponent [_itoa or equivalent is not ANSI C] - for (cut=9; cut>=0; cut--) { - TODIGIT(u, cut, c, pow); - if (*c=='0' && !had) continue; // skip leading zeros - had=1; // had non-0 - c++; // step for next - } // cut - } - *c='\0'; // terminate the string (all paths) - return; - } // decToString - -/* ------------------------------------------------------------------ */ -/* decAddOp -- add/subtract operation */ -/* */ -/* This computes C = A + B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X+X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* negate is DECNEG if rhs should be negated, or 0 otherwise */ -/* status accumulates status for the caller */ -/* */ -/* C must have space for set->digits digits. */ -/* Inexact in status must be 0 for correct Exact zero sign in result */ -/* ------------------------------------------------------------------ */ -/* If possible, the coefficient is calculated directly into C. */ -/* However, if: */ -/* -- a digits+1 calculation is needed because the numbers are */ -/* unaligned and span more than set->digits digits */ -/* -- a carry to digits+1 digits looks possible */ -/* -- C is the same as A or B, and the result would destructively */ -/* overlap the A or B coefficient */ -/* then the result must be calculated into a temporary buffer. In */ -/* this case a local (stack) buffer is used if possible, and only if */ -/* too long for that does malloc become the final resort. */ -/* */ -/* Misalignment is handled as follows: */ -/* Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp. */ -/* BPad: Apply the padding by a combination of shifting (whole */ -/* units) and multiplication (part units). */ -/* */ -/* Addition, especially x=x+1, is speed-critical. */ -/* The static buffer is larger than might be expected to allow for */ -/* calls from higher-level functions (notable exp). */ -/* ------------------------------------------------------------------ */ -static decNumber * decAddOp(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set, - uByte negate, uInt *status) { - #if DECSUBSET - decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated - decNumber *allocrhs=NULL; // .., rhs - #endif - Int rhsshift; // working shift (in Units) - Int maxdigits; // longest logical length - Int mult; // multiplier - Int residue; // rounding accumulator - uByte bits; // result bits - Flag diffsign; // non-0 if arguments have different sign - Unit *acc; // accumulator for result - Unit accbuff[SD2U(DECBUFFER*2+20)]; // local buffer [*2+20 reduces many - // allocations when called from - // other operations, notable exp] - Unit *allocacc=NULL; // -> allocated acc buffer, iff allocated - Int reqdigits=set->digits; // local copy; requested DIGITS - Int padding; // work - - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - do { // protect allocated storage - #if DECSUBSET - if (!set->extended) { - // reduce operands and set lostDigits status, as needed - if (lhs->digits>reqdigits) { - alloclhs=decRoundOperand(lhs, set, status); - if (alloclhs==NULL) break; - lhs=alloclhs; - } - if (rhs->digits>reqdigits) { - allocrhs=decRoundOperand(rhs, set, status); - if (allocrhs==NULL) break; - rhs=allocrhs; - } - } - #endif - // [following code does not require input rounding] - - // note whether signs differ [used all paths] - diffsign=(Flag)((lhs->bits^rhs->bits^negate)&DECNEG); - - // handle infinities and NaNs - if (SPECIALARGS) { // a special bit set - if (SPECIALARGS & (DECSNAN | DECNAN)) // a NaN - decNaNs(res, lhs, rhs, set, status); - else { // one or two infinities - if (decNumberIsInfinite(lhs)) { // LHS is infinity - // two infinities with different signs is invalid - if (decNumberIsInfinite(rhs) && diffsign) { - *status|=DEC_Invalid_operation; - break; - } - bits=lhs->bits & DECNEG; // get sign from LHS - } - else bits=(rhs->bits^negate) & DECNEG;// RHS must be Infinity - bits|=DECINF; - decNumberZero(res); - res->bits=bits; // set +/- infinity - } // an infinity - break; - } - - // Quick exit for add 0s; return the non-0, modified as need be - if (ISZERO(lhs)) { - Int adjust; // work - Int lexp=lhs->exponent; // save in case LHS==RES - bits=lhs->bits; // .. - residue=0; // clear accumulator - decCopyFit(res, rhs, set, &residue, status); // copy (as needed) - res->bits^=negate; // flip if rhs was negated - #if DECSUBSET - if (set->extended) { // exponents on zeros count - #endif - // exponent will be the lower of the two - adjust=lexp-res->exponent; // adjustment needed [if -ve] - if (ISZERO(res)) { // both 0: special IEEE 754 rules - if (adjust<0) res->exponent=lexp; // set exponent - // 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0 - if (diffsign) { - if (set->round!=DEC_ROUND_FLOOR) res->bits=0; - else res->bits=DECNEG; // preserve 0 sign - } - } - else { // non-0 res - if (adjust<0) { // 0-padding needed - if ((res->digits-adjust)>set->digits) { - adjust=res->digits-set->digits; // to fit exactly - *status|=DEC_Rounded; // [but exact] - } - res->digits=decShiftToMost(res->lsu, res->digits, -adjust); - res->exponent+=adjust; // set the exponent. - } - } // non-0 res - #if DECSUBSET - } // extended - #endif - decFinish(res, set, &residue, status); // clean and finalize - break;} - - if (ISZERO(rhs)) { // [lhs is non-zero] - Int adjust; // work - Int rexp=rhs->exponent; // save in case RHS==RES - bits=rhs->bits; // be clean - residue=0; // clear accumulator - decCopyFit(res, lhs, set, &residue, status); // copy (as needed) - #if DECSUBSET - if (set->extended) { // exponents on zeros count - #endif - // exponent will be the lower of the two - // [0-0 case handled above] - adjust=rexp-res->exponent; // adjustment needed [if -ve] - if (adjust<0) { // 0-padding needed - if ((res->digits-adjust)>set->digits) { - adjust=res->digits-set->digits; // to fit exactly - *status|=DEC_Rounded; // [but exact] - } - res->digits=decShiftToMost(res->lsu, res->digits, -adjust); - res->exponent+=adjust; // set the exponent. - } - #if DECSUBSET - } // extended - #endif - decFinish(res, set, &residue, status); // clean and finalize - break;} - - // [NB: both fastpath and mainpath code below assume these cases - // (notably 0-0) have already been handled] - - // calculate the padding needed to align the operands - padding=rhs->exponent-lhs->exponent; - - // Fastpath cases where the numbers are aligned and normal, the RHS - // is all in one unit, no operand rounding is needed, and no carry, - // lengthening, or borrow is needed - if (padding==0 - && rhs->digits<=DECDPUN - && rhs->exponent>=set->emin // [some normals drop through] - && rhs->exponent<=set->emax-set->digits+1 // [could clamp] - && rhs->digits<=reqdigits - && lhs->digits<=reqdigits) { - Int partial=*lhs->lsu; - if (!diffsign) { // adding - partial+=*rhs->lsu; - if ((partial<=DECDPUNMAX) // result fits in unit - && (lhs->digits>=DECDPUN || // .. and no digits-count change - partial<(Int)powers[lhs->digits])) { // .. - if (res!=lhs) decNumberCopy(res, lhs); // not in place - *res->lsu=(Unit)partial; // [copy could have overwritten RHS] - break; - } - // else drop out for careful add - } - else { // signs differ - partial-=*rhs->lsu; - if (partial>0) { // no borrow needed, and non-0 result - if (res!=lhs) decNumberCopy(res, lhs); // not in place - *res->lsu=(Unit)partial; - // this could have reduced digits [but result>0] - res->digits=decGetDigits(res->lsu, D2U(res->digits)); - break; - } - // else drop out for careful subtract - } - } - - // Now align (pad) the lhs or rhs so they can be added or - // subtracted, as necessary. If one number is much larger than - // the other (that is, if in plain form there is a least one - // digit between the lowest digit of one and the highest of the - // other) padding with up to DIGITS-1 trailing zeros may be - // needed; then apply rounding (as exotic rounding modes may be - // affected by the residue). - rhsshift=0; // rhs shift to left (padding) in Units - bits=lhs->bits; // assume sign is that of LHS - mult=1; // likely multiplier - - // [if padding==0 the operands are aligned; no padding is needed] - if (padding!=0) { - // some padding needed; always pad the RHS, as any required - // padding can then be effected by a simple combination of - // shifts and a multiply - Flag swapped=0; - if (padding<0) { // LHS needs the padding - const decNumber *t; - padding=-padding; // will be +ve - bits=(uByte)(rhs->bits^negate); // assumed sign is now that of RHS - t=lhs; lhs=rhs; rhs=t; - swapped=1; - } - - // If, after pad, rhs would be longer than lhs by digits+1 or - // more then lhs cannot affect the answer, except as a residue, - // so only need to pad up to a length of DIGITS+1. - if (rhs->digits+padding > lhs->digits+reqdigits+1) { - // The RHS is sufficient - // for residue use the relative sign indication... - Int shift=reqdigits-rhs->digits; // left shift needed - residue=1; // residue for rounding - if (diffsign) residue=-residue; // signs differ - // copy, shortening if necessary - decCopyFit(res, rhs, set, &residue, status); - // if it was already shorter, then need to pad with zeros - if (shift>0) { - res->digits=decShiftToMost(res->lsu, res->digits, shift); - res->exponent-=shift; // adjust the exponent. - } - // flip the result sign if unswapped and rhs was negated - if (!swapped) res->bits^=negate; - decFinish(res, set, &residue, status); // done - break;} - - // LHS digits may affect result - rhsshift=D2U(padding+1)-1; // this much by Unit shift .. - mult=powers[padding-(rhsshift*DECDPUN)]; // .. this by multiplication - } // padding needed - - if (diffsign) mult=-mult; // signs differ - - // determine the longer operand - maxdigits=rhs->digits+padding; // virtual length of RHS - if (lhs->digits>maxdigits) maxdigits=lhs->digits; - - // Decide on the result buffer to use; if possible place directly - // into result. - acc=res->lsu; // assume add direct to result - // If destructive overlap, or the number is too long, or a carry or - // borrow to DIGITS+1 might be possible, a buffer must be used. - // [Might be worth more sophisticated tests when maxdigits==reqdigits] - if ((maxdigits>=reqdigits) // is, or could be, too large - || (res==rhs && rhsshift>0)) { // destructive overlap - // buffer needed, choose it; units for maxdigits digits will be - // needed, +1 Unit for carry or borrow - Int need=D2U(maxdigits)+1; - acc=accbuff; // assume use local buffer - if (need*sizeof(Unit)>sizeof(accbuff)) { - // printf("malloc add %ld %ld\n", need, sizeof(accbuff)); - allocacc=(Unit *)malloc(need*sizeof(Unit)); - if (allocacc==NULL) { // hopeless -- abandon - *status|=DEC_Insufficient_storage; - break;} - acc=allocacc; - } - } - - res->bits=(uByte)(bits&DECNEG); // it's now safe to overwrite.. - res->exponent=lhs->exponent; // .. operands (even if aliased) - - #if DECTRACE - decDumpAr('A', lhs->lsu, D2U(lhs->digits)); - decDumpAr('B', rhs->lsu, D2U(rhs->digits)); - printf(" :h: %ld %ld\n", rhsshift, mult); - #endif - - // add [A+B*m] or subtract [A+B*(-m)] - res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits), - rhs->lsu, D2U(rhs->digits), - rhsshift, acc, mult) - *DECDPUN; // [units -> digits] - if (res->digits<0) { // borrowed... - res->digits=-res->digits; - res->bits^=DECNEG; // flip the sign - } - #if DECTRACE - decDumpAr('+', acc, D2U(res->digits)); - #endif - - // If a buffer was used the result must be copied back, possibly - // shortening. (If no buffer was used then the result must have - // fit, so can't need rounding and residue must be 0.) - residue=0; // clear accumulator - if (acc!=res->lsu) { - #if DECSUBSET - if (set->extended) { // round from first significant digit - #endif - // remove leading zeros that were added due to rounding up to - // integral Units -- before the test for rounding. - if (res->digits>reqdigits) - res->digits=decGetDigits(acc, D2U(res->digits)); - decSetCoeff(res, set, acc, res->digits, &residue, status); - #if DECSUBSET - } - else { // subset arithmetic rounds from original significant digit - // May have an underestimate. This only occurs when both - // numbers fit in DECDPUN digits and are padding with a - // negative multiple (-10, -100...) and the top digit(s) become - // 0. (This only matters when using X3.274 rules where the - // leading zero could be included in the rounding.) - if (res->digits<maxdigits) { - *(acc+D2U(res->digits))=0; // ensure leading 0 is there - res->digits=maxdigits; - } - else { - // remove leading zeros that added due to rounding up to - // integral Units (but only those in excess of the original - // maxdigits length, unless extended) before test for rounding. - if (res->digits>reqdigits) { - res->digits=decGetDigits(acc, D2U(res->digits)); - if (res->digits<maxdigits) res->digits=maxdigits; - } - } - decSetCoeff(res, set, acc, res->digits, &residue, status); - // Now apply rounding if needed before removing leading zeros. - // This is safe because subnormals are not a possibility - if (residue!=0) { - decApplyRound(res, set, residue, status); - residue=0; // did what needed to be done - } - } // subset - #endif - } // used buffer - - // strip leading zeros [these were left on in case of subset subtract] - res->digits=decGetDigits(res->lsu, D2U(res->digits)); - - // apply checks and rounding - decFinish(res, set, &residue, status); - - // "When the sum of two operands with opposite signs is exactly - // zero, the sign of that sum shall be '+' in all rounding modes - // except round toward -Infinity, in which mode that sign shall be - // '-'." [Subset zeros also never have '-', set by decFinish.] - if (ISZERO(res) && diffsign - #if DECSUBSET - && set->extended - #endif - && (*status&DEC_Inexact)==0) { - if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG; // sign - - else res->bits&=~DECNEG; // sign + - } - } while(0); // end protected - - if (allocacc!=NULL) free(allocacc); // drop any storage used - #if DECSUBSET - if (allocrhs!=NULL) free(allocrhs); // .. - if (alloclhs!=NULL) free(alloclhs); // .. - #endif - return res; - } // decAddOp - -/* ------------------------------------------------------------------ */ -/* decDivideOp -- division operation */ -/* */ -/* This routine performs the calculations for all four division */ -/* operators (divide, divideInteger, remainder, remainderNear). */ -/* */ -/* C=A op B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X/X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* op is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively. */ -/* status is the usual accumulator */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* ------------------------------------------------------------------ */ -/* The underlying algorithm of this routine is the same as in the */ -/* 1981 S/370 implementation, that is, non-restoring long division */ -/* with bi-unit (rather than bi-digit) estimation for each unit */ -/* multiplier. In this pseudocode overview, complications for the */ -/* Remainder operators and division residues for exact rounding are */ -/* omitted for clarity. */ -/* */ -/* Prepare operands and handle special values */ -/* Test for x/0 and then 0/x */ -/* Exp =Exp1 - Exp2 */ -/* Exp =Exp +len(var1) -len(var2) */ -/* Sign=Sign1 * Sign2 */ -/* Pad accumulator (Var1) to double-length with 0's (pad1) */ -/* Pad Var2 to same length as Var1 */ -/* msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round */ -/* have=0 */ -/* Do until (have=digits+1 OR residue=0) */ -/* if exp<0 then if integer divide/residue then leave */ -/* this_unit=0 */ -/* Do forever */ -/* compare numbers */ -/* if <0 then leave inner_loop */ -/* if =0 then (* quick exit without subtract *) do */ -/* this_unit=this_unit+1; output this_unit */ -/* leave outer_loop; end */ -/* Compare lengths of numbers (mantissae): */ -/* If same then tops2=msu2pair -- {units 1&2 of var2} */ -/* else tops2=msu2plus -- {0, unit 1 of var2} */ -/* tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */ -/* mult=tops1/tops2 -- Good and safe guess at divisor */ -/* if mult=0 then mult=1 */ -/* this_unit=this_unit+mult */ -/* subtract */ -/* end inner_loop */ -/* if have\=0 | this_unit\=0 then do */ -/* output this_unit */ -/* have=have+1; end */ -/* var2=var2/10 */ -/* exp=exp-1 */ -/* end outer_loop */ -/* exp=exp+1 -- set the proper exponent */ -/* if have=0 then generate answer=0 */ -/* Return (Result is defined by Var1) */ -/* */ -/* ------------------------------------------------------------------ */ -/* Two working buffers are needed during the division; one (digits+ */ -/* 1) to accumulate the result, and the other (up to 2*digits+1) for */ -/* long subtractions. These are acc and var1 respectively. */ -/* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/ -/* The static buffers may be larger than might be expected to allow */ -/* for calls from higher-level functions (notable exp). */ -/* ------------------------------------------------------------------ */ -static decNumber * decDivideOp(decNumber *res, - const decNumber *lhs, const decNumber *rhs, - decContext *set, Flag op, uInt *status) { - #if DECSUBSET - decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated - decNumber *allocrhs=NULL; // .., rhs - #endif - Unit accbuff[SD2U(DECBUFFER+DECDPUN+10)]; // local buffer - Unit *acc=accbuff; // -> accumulator array for result - Unit *allocacc=NULL; // -> allocated buffer, iff allocated - Unit *accnext; // -> where next digit will go - Int acclength; // length of acc needed [Units] - Int accunits; // count of units accumulated - Int accdigits; // count of digits accumulated - - Unit varbuff[SD2U(DECBUFFER*2+DECDPUN)]; // buffer for var1 - Unit *var1=varbuff; // -> var1 array for long subtraction - Unit *varalloc=NULL; // -> allocated buffer, iff used - Unit *msu1; // -> msu of var1 - - const Unit *var2; // -> var2 array - const Unit *msu2; // -> msu of var2 - Int msu2plus; // msu2 plus one [does not vary] - eInt msu2pair; // msu2 pair plus one [does not vary] - - Int var1units, var2units; // actual lengths - Int var2ulen; // logical length (units) - Int var1initpad=0; // var1 initial padding (digits) - Int maxdigits; // longest LHS or required acc length - Int mult; // multiplier for subtraction - Unit thisunit; // current unit being accumulated - Int residue; // for rounding - Int reqdigits=set->digits; // requested DIGITS - Int exponent; // working exponent - Int maxexponent=0; // DIVIDE maximum exponent if unrounded - uByte bits; // working sign - Unit *target; // work - const Unit *source; // .. - uInt const *pow; // .. - Int shift, cut; // .. - #if DECSUBSET - Int dropped; // work - #endif - - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - do { // protect allocated storage - #if DECSUBSET - if (!set->extended) { - // reduce operands and set lostDigits status, as needed - if (lhs->digits>reqdigits) { - alloclhs=decRoundOperand(lhs, set, status); - if (alloclhs==NULL) break; - lhs=alloclhs; - } - if (rhs->digits>reqdigits) { - allocrhs=decRoundOperand(rhs, set, status); - if (allocrhs==NULL) break; - rhs=allocrhs; - } - } - #endif - // [following code does not require input rounding] - - bits=(lhs->bits^rhs->bits)&DECNEG; // assumed sign for divisions - - // handle infinities and NaNs - if (SPECIALARGS) { // a special bit set - if (SPECIALARGS & (DECSNAN | DECNAN)) { // one or two NaNs - decNaNs(res, lhs, rhs, set, status); - break; - } - // one or two infinities - if (decNumberIsInfinite(lhs)) { // LHS (dividend) is infinite - if (decNumberIsInfinite(rhs) || // two infinities are invalid .. - op & (REMAINDER | REMNEAR)) { // as is remainder of infinity - *status|=DEC_Invalid_operation; - break; - } - // [Note that infinity/0 raises no exceptions] - decNumberZero(res); - res->bits=bits|DECINF; // set +/- infinity - break; - } - else { // RHS (divisor) is infinite - residue=0; - if (op&(REMAINDER|REMNEAR)) { - // result is [finished clone of] lhs - decCopyFit(res, lhs, set, &residue, status); - } - else { // a division - decNumberZero(res); - res->bits=bits; // set +/- zero - // for DIVIDEINT the exponent is always 0. For DIVIDE, result - // is a 0 with infinitely negative exponent, clamped to minimum - if (op&DIVIDE) { - res->exponent=set->emin-set->digits+1; - *status|=DEC_Clamped; - } - } - decFinish(res, set, &residue, status); - break; - } - } - - // handle 0 rhs (x/0) - if (ISZERO(rhs)) { // x/0 is always exceptional - if (ISZERO(lhs)) { - decNumberZero(res); // [after lhs test] - *status|=DEC_Division_undefined;// 0/0 will become NaN - } - else { - decNumberZero(res); - if (op&(REMAINDER|REMNEAR)) *status|=DEC_Invalid_operation; - else { - *status|=DEC_Division_by_zero; // x/0 - res->bits=bits|DECINF; // .. is +/- Infinity - } - } - break;} - - // handle 0 lhs (0/x) - if (ISZERO(lhs)) { // 0/x [x!=0] - #if DECSUBSET - if (!set->extended) decNumberZero(res); - else { - #endif - if (op&DIVIDE) { - residue=0; - exponent=lhs->exponent-rhs->exponent; // ideal exponent - decNumberCopy(res, lhs); // [zeros always fit] - res->bits=bits; // sign as computed - res->exponent=exponent; // exponent, too - decFinalize(res, set, &residue, status); // check exponent - } - else if (op&DIVIDEINT) { - decNumberZero(res); // integer 0 - res->bits=bits; // sign as computed - } - else { // a remainder - exponent=rhs->exponent; // [save in case overwrite] - decNumberCopy(res, lhs); // [zeros always fit] - if (exponent<res->exponent) res->exponent=exponent; // use lower - } - #if DECSUBSET - } - #endif - break;} - - // Precalculate exponent. This starts off adjusted (and hence fits - // in 31 bits) and becomes the usual unadjusted exponent as the - // division proceeds. The order of evaluation is important, here, - // to avoid wrap. - exponent=(lhs->exponent+lhs->digits)-(rhs->exponent+rhs->digits); - - // If the working exponent is -ve, then some quick exits are - // possible because the quotient is known to be <1 - // [for REMNEAR, it needs to be < -1, as -0.5 could need work] - if (exponent<0 && !(op==DIVIDE)) { - if (op&DIVIDEINT) { - decNumberZero(res); // integer part is 0 - #if DECSUBSET - if (set->extended) - #endif - res->bits=bits; // set +/- zero - break;} - // fastpath remainders so long as the lhs has the smaller - // (or equal) exponent - if (lhs->exponent<=rhs->exponent) { - if (op&REMAINDER || exponent<-1) { - // It is REMAINDER or safe REMNEAR; result is [finished - // clone of] lhs (r = x - 0*y) - residue=0; - decCopyFit(res, lhs, set, &residue, status); - decFinish(res, set, &residue, status); - break; - } - // [unsafe REMNEAR drops through] - } - } // fastpaths - - /* Long (slow) division is needed; roll up the sleeves... */ - - // The accumulator will hold the quotient of the division. - // If it needs to be too long for stack storage, then allocate. - acclength=D2U(reqdigits+DECDPUN); // in Units - if (acclength*sizeof(Unit)>sizeof(accbuff)) { - // printf("malloc dvacc %ld units\n", acclength); - allocacc=(Unit *)malloc(acclength*sizeof(Unit)); - if (allocacc==NULL) { // hopeless -- abandon - *status|=DEC_Insufficient_storage; - break;} - acc=allocacc; // use the allocated space - } - - // var1 is the padded LHS ready for subtractions. - // If it needs to be too long for stack storage, then allocate. - // The maximum units needed for var1 (long subtraction) is: - // Enough for - // (rhs->digits+reqdigits-1) -- to allow full slide to right - // or (lhs->digits) -- to allow for long lhs - // whichever is larger - // +1 -- for rounding of slide to right - // +1 -- for leading 0s - // +1 -- for pre-adjust if a remainder or DIVIDEINT - // [Note: unused units do not participate in decUnitAddSub data] - maxdigits=rhs->digits+reqdigits-1; - if (lhs->digits>maxdigits) maxdigits=lhs->digits; - var1units=D2U(maxdigits)+2; - // allocate a guard unit above msu1 for REMAINDERNEAR - if (!(op&DIVIDE)) var1units++; - if ((var1units+1)*sizeof(Unit)>sizeof(varbuff)) { - // printf("malloc dvvar %ld units\n", var1units+1); - varalloc=(Unit *)malloc((var1units+1)*sizeof(Unit)); - if (varalloc==NULL) { // hopeless -- abandon - *status|=DEC_Insufficient_storage; - break;} - var1=varalloc; // use the allocated space - } - - // Extend the lhs and rhs to full long subtraction length. The lhs - // is truly extended into the var1 buffer, with 0 padding, so a - // subtract in place is always possible. The rhs (var2) has - // virtual padding (implemented by decUnitAddSub). - // One guard unit was allocated above msu1 for rem=rem+rem in - // REMAINDERNEAR. - msu1=var1+var1units-1; // msu of var1 - source=lhs->lsu+D2U(lhs->digits)-1; // msu of input array - for (target=msu1; source>=lhs->lsu; source--, target--) *target=*source; - for (; target>=var1; target--) *target=0; - - // rhs (var2) is left-aligned with var1 at the start - var2ulen=var1units; // rhs logical length (units) - var2units=D2U(rhs->digits); // rhs actual length (units) - var2=rhs->lsu; // -> rhs array - msu2=var2+var2units-1; // -> msu of var2 [never changes] - // now set up the variables which will be used for estimating the - // multiplication factor. If these variables are not exact, add - // 1 to make sure that the multiplier is never overestimated. - msu2plus=*msu2; // it's value .. - if (var2units>1) msu2plus++; // .. +1 if any more - msu2pair=(eInt)*msu2*(DECDPUNMAX+1);// top two pair .. - if (var2units>1) { // .. [else treat 2nd as 0] - msu2pair+=*(msu2-1); // .. - if (var2units>2) msu2pair++; // .. +1 if any more - } - - // The calculation is working in units, which may have leading zeros, - // but the exponent was calculated on the assumption that they are - // both left-aligned. Adjust the exponent to compensate: add the - // number of leading zeros in var1 msu and subtract those in var2 msu. - // [This is actually done by counting the digits and negating, as - // lead1=DECDPUN-digits1, and similarly for lead2.] - for (pow=&powers[1]; *msu1>=*pow; pow++) exponent--; - for (pow=&powers[1]; *msu2>=*pow; pow++) exponent++; - - // Now, if doing an integer divide or remainder, ensure that - // the result will be Unit-aligned. To do this, shift the var1 - // accumulator towards least if need be. (It's much easier to - // do this now than to reassemble the residue afterwards, if - // doing a remainder.) Also ensure the exponent is not negative. - if (!(op&DIVIDE)) { - Unit *u; // work - // save the initial 'false' padding of var1, in digits - var1initpad=(var1units-D2U(lhs->digits))*DECDPUN; - // Determine the shift to do. - if (exponent<0) cut=-exponent; - else cut=DECDPUN-exponent%DECDPUN; - decShiftToLeast(var1, var1units, cut); - exponent+=cut; // maintain numerical value - var1initpad-=cut; // .. and reduce padding - // clean any most-significant units which were just emptied - for (u=msu1; cut>=DECDPUN; cut-=DECDPUN, u--) *u=0; - } // align - else { // is DIVIDE - maxexponent=lhs->exponent-rhs->exponent; // save - // optimization: if the first iteration will just produce 0, - // preadjust to skip it [valid for DIVIDE only] - if (*msu1<*msu2) { - var2ulen--; // shift down - exponent-=DECDPUN; // update the exponent - } - } - - // ---- start the long-division loops ------------------------------ - accunits=0; // no units accumulated yet - accdigits=0; // .. or digits - accnext=acc+acclength-1; // -> msu of acc [NB: allows digits+1] - for (;;) { // outer forever loop - thisunit=0; // current unit assumed 0 - // find the next unit - for (;;) { // inner forever loop - // strip leading zero units [from either pre-adjust or from - // subtract last time around]. Leave at least one unit. - for (; *msu1==0 && msu1>var1; msu1--) var1units--; - - if (var1units<var2ulen) break; // var1 too low for subtract - if (var1units==var2ulen) { // unit-by-unit compare needed - // compare the two numbers, from msu - const Unit *pv1, *pv2; - Unit v2; // units to compare - pv2=msu2; // -> msu - for (pv1=msu1; ; pv1--, pv2--) { - // v1=*pv1 -- always OK - v2=0; // assume in padding - if (pv2>=var2) v2=*pv2; // in range - if (*pv1!=v2) break; // no longer the same - if (pv1==var1) break; // done; leave pv1 as is - } - // here when all inspected or a difference seen - if (*pv1<v2) break; // var1 too low to subtract - if (*pv1==v2) { // var1 == var2 - // reach here if var1 and var2 are identical; subtraction - // would increase digit by one, and the residue will be 0 so - // the calculation is done; leave the loop with residue=0. - thisunit++; // as though subtracted - *var1=0; // set var1 to 0 - var1units=1; // .. - break; // from inner - } // var1 == var2 - // *pv1>v2. Prepare for real subtraction; the lengths are equal - // Estimate the multiplier (there's always a msu1-1)... - // Bring in two units of var2 to provide a good estimate. - mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2pair); - } // lengths the same - else { // var1units > var2ulen, so subtraction is safe - // The var2 msu is one unit towards the lsu of the var1 msu, - // so only one unit for var2 can be used. - mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2plus); - } - if (mult==0) mult=1; // must always be at least 1 - // subtraction needed; var1 is > var2 - thisunit=(Unit)(thisunit+mult); // accumulate - // subtract var1-var2, into var1; only the overlap needs - // processing, as this is an in-place calculation - shift=var2ulen-var2units; - #if DECTRACE - decDumpAr('1', &var1[shift], var1units-shift); - decDumpAr('2', var2, var2units); - printf("m=%ld\n", -mult); - #endif - decUnitAddSub(&var1[shift], var1units-shift, - var2, var2units, 0, - &var1[shift], -mult); - #if DECTRACE - decDumpAr('#', &var1[shift], var1units-shift); - #endif - // var1 now probably has leading zeros; these are removed at the - // top of the inner loop. - } // inner loop - - // The next unit has been calculated in full; unless it's a - // leading zero, add to acc - if (accunits!=0 || thisunit!=0) { // is first or non-zero - *accnext=thisunit; // store in accumulator - // account exactly for the new digits - if (accunits==0) { - accdigits++; // at least one - for (pow=&powers[1]; thisunit>=*pow; pow++) accdigits++; - } - else accdigits+=DECDPUN; - accunits++; // update count - accnext--; // ready for next - if (accdigits>reqdigits) break; // have enough digits - } - - // if the residue is zero, the operation is done (unless divide - // or divideInteger and still not enough digits yet) - if (*var1==0 && var1units==1) { // residue is 0 - if (op&(REMAINDER|REMNEAR)) break; - if ((op&DIVIDE) && (exponent<=maxexponent)) break; - // [drop through if divideInteger] - } - // also done enough if calculating remainder or integer - // divide and just did the last ('units') unit - if (exponent==0 && !(op&DIVIDE)) break; - - // to get here, var1 is less than var2, so divide var2 by the per- - // Unit power of ten and go for the next digit - var2ulen--; // shift down - exponent-=DECDPUN; // update the exponent - } // outer loop - - // ---- division is complete --------------------------------------- - // here: acc has at least reqdigits+1 of good results (or fewer - // if early stop), starting at accnext+1 (its lsu) - // var1 has any residue at the stopping point - // accunits is the number of digits collected in acc - if (accunits==0) { // acc is 0 - accunits=1; // show have a unit .. - accdigits=1; // .. - *accnext=0; // .. whose value is 0 - } - else accnext++; // back to last placed - // accnext now -> lowest unit of result - - residue=0; // assume no residue - if (op&DIVIDE) { - // record the presence of any residue, for rounding - if (*var1!=0 || var1units>1) residue=1; - else { // no residue - // Had an exact division; clean up spurious trailing 0s. - // There will be at most DECDPUN-1, from the final multiply, - // and then only if the result is non-0 (and even) and the - // exponent is 'loose'. - #if DECDPUN>1 - Unit lsu=*accnext; - if (!(lsu&0x01) && (lsu!=0)) { - // count the trailing zeros - Int drop=0; - for (;; drop++) { // [will terminate because lsu!=0] - if (exponent>=maxexponent) break; // don't chop real 0s - #if DECDPUN<=4 - if ((lsu-QUOT10(lsu, drop+1) - *powers[drop+1])!=0) break; // found non-0 digit - #else - if (lsu%powers[drop+1]!=0) break; // found non-0 digit - #endif - exponent++; - } - if (drop>0) { - accunits=decShiftToLeast(accnext, accunits, drop); - accdigits=decGetDigits(accnext, accunits); - accunits=D2U(accdigits); - // [exponent was adjusted in the loop] - } - } // neither odd nor 0 - #endif - } // exact divide - } // divide - else /* op!=DIVIDE */ { - // check for coefficient overflow - if (accdigits+exponent>reqdigits) { - *status|=DEC_Division_impossible; - break; - } - if (op & (REMAINDER|REMNEAR)) { - // [Here, the exponent will be 0, because var1 was adjusted - // appropriately.] - Int postshift; // work - Flag wasodd=0; // integer was odd - Unit *quotlsu; // for save - Int quotdigits; // .. - - bits=lhs->bits; // remainder sign is always as lhs - - // Fastpath when residue is truly 0 is worthwhile [and - // simplifies the code below] - if (*var1==0 && var1units==1) { // residue is 0 - Int exp=lhs->exponent; // save min(exponents) - if (rhs->exponent<exp) exp=rhs->exponent; - decNumberZero(res); // 0 coefficient - #if DECSUBSET - if (set->extended) - #endif - res->exponent=exp; // .. with proper exponent - res->bits=(uByte)(bits&DECNEG); // [cleaned] - decFinish(res, set, &residue, status); // might clamp - break; - } - // note if the quotient was odd - if (*accnext & 0x01) wasodd=1; // acc is odd - quotlsu=accnext; // save in case need to reinspect - quotdigits=accdigits; // .. - - // treat the residue, in var1, as the value to return, via acc - // calculate the unused zero digits. This is the smaller of: - // var1 initial padding (saved above) - // var2 residual padding, which happens to be given by: - postshift=var1initpad+exponent-lhs->exponent+rhs->exponent; - // [the 'exponent' term accounts for the shifts during divide] - if (var1initpad<postshift) postshift=var1initpad; - - // shift var1 the requested amount, and adjust its digits - var1units=decShiftToLeast(var1, var1units, postshift); - accnext=var1; - accdigits=decGetDigits(var1, var1units); - accunits=D2U(accdigits); - - exponent=lhs->exponent; // exponent is smaller of lhs & rhs - if (rhs->exponent<exponent) exponent=rhs->exponent; - - // Now correct the result if doing remainderNear; if it - // (looking just at coefficients) is > rhs/2, or == rhs/2 and - // the integer was odd then the result should be rem-rhs. - if (op&REMNEAR) { - Int compare, tarunits; // work - Unit *up; // .. - // calculate remainder*2 into the var1 buffer (which has - // 'headroom' of an extra unit and hence enough space) - // [a dedicated 'double' loop would be faster, here] - tarunits=decUnitAddSub(accnext, accunits, accnext, accunits, - 0, accnext, 1); - // decDumpAr('r', accnext, tarunits); - - // Here, accnext (var1) holds tarunits Units with twice the - // remainder's coefficient, which must now be compared to the - // RHS. The remainder's exponent may be smaller than the RHS's. - compare=decUnitCompare(accnext, tarunits, rhs->lsu, D2U(rhs->digits), - rhs->exponent-exponent); - if (compare==BADINT) { // deep trouble - *status|=DEC_Insufficient_storage; - break;} - - // now restore the remainder by dividing by two; the lsu - // is known to be even. - for (up=accnext; up<accnext+tarunits; up++) { - Int half; // half to add to lower unit - half=*up & 0x01; - *up/=2; // [shift] - if (!half) continue; - *(up-1)+=(DECDPUNMAX+1)/2; - } - // [accunits still describes the original remainder length] - - if (compare>0 || (compare==0 && wasodd)) { // adjustment needed - Int exp, expunits, exprem; // work - // This is effectively causing round-up of the quotient, - // so if it was the rare case where it was full and all - // nines, it would overflow and hence division-impossible - // should be raised - Flag allnines=0; // 1 if quotient all nines - if (quotdigits==reqdigits) { // could be borderline - for (up=quotlsu; ; up++) { - if (quotdigits>DECDPUN) { - if (*up!=DECDPUNMAX) break;// non-nines - } - else { // this is the last Unit - if (*up==powers[quotdigits]-1) allnines=1; - break; - } - quotdigits-=DECDPUN; // checked those digits - } // up - } // borderline check - if (allnines) { - *status|=DEC_Division_impossible; - break;} - - // rem-rhs is needed; the sign will invert. Again, var1 - // can safely be used for the working Units array. - exp=rhs->exponent-exponent; // RHS padding needed - // Calculate units and remainder from exponent. - expunits=exp/DECDPUN; - exprem=exp%DECDPUN; - // subtract [A+B*(-m)]; the result will always be negative - accunits=-decUnitAddSub(accnext, accunits, - rhs->lsu, D2U(rhs->digits), - expunits, accnext, -(Int)powers[exprem]); - accdigits=decGetDigits(accnext, accunits); // count digits exactly - accunits=D2U(accdigits); // and recalculate the units for copy - // [exponent is as for original remainder] - bits^=DECNEG; // flip the sign - } - } // REMNEAR - } // REMAINDER or REMNEAR - } // not DIVIDE - - // Set exponent and bits - res->exponent=exponent; - res->bits=(uByte)(bits&DECNEG); // [cleaned] - - // Now the coefficient. - decSetCoeff(res, set, accnext, accdigits, &residue, status); - - decFinish(res, set, &residue, status); // final cleanup - - #if DECSUBSET - // If a divide then strip trailing zeros if subset [after round] - if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, 1, &dropped); - #endif - } while(0); // end protected - - if (varalloc!=NULL) free(varalloc); // drop any storage used - if (allocacc!=NULL) free(allocacc); // .. - #if DECSUBSET - if (allocrhs!=NULL) free(allocrhs); // .. - if (alloclhs!=NULL) free(alloclhs); // .. - #endif - return res; - } // decDivideOp - -/* ------------------------------------------------------------------ */ -/* decMultiplyOp -- multiplication operation */ -/* */ -/* This routine performs the multiplication C=A x B. */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X*X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* status is the usual accumulator */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* ------------------------------------------------------------------ */ -/* 'Classic' multiplication is used rather than Karatsuba, as the */ -/* latter would give only a minor improvement for the short numbers */ -/* expected to be handled most (and uses much more memory). */ -/* */ -/* There are two major paths here: the general-purpose ('old code') */ -/* path which handles all DECDPUN values, and a fastpath version */ -/* which is used if 64-bit ints are available, DECDPUN<=4, and more */ -/* than two calls to decUnitAddSub would be made. */ -/* */ -/* The fastpath version lumps units together into 8-digit or 9-digit */ -/* chunks, and also uses a lazy carry strategy to minimise expensive */ -/* 64-bit divisions. The chunks are then broken apart again into */ -/* units for continuing processing. Despite this overhead, the */ -/* fastpath can speed up some 16-digit operations by 10x (and much */ -/* more for higher-precision calculations). */ -/* */ -/* A buffer always has to be used for the accumulator; in the */ -/* fastpath, buffers are also always needed for the chunked copies of */ -/* of the operand coefficients. */ -/* Static buffers are larger than needed just for multiply, to allow */ -/* for calls from other operations (notably exp). */ -/* ------------------------------------------------------------------ */ -#define FASTMUL (DECUSE64 && DECDPUN<5) -static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set, - uInt *status) { - Int accunits; // Units of accumulator in use - Int exponent; // work - Int residue=0; // rounding residue - uByte bits; // result sign - Unit *acc; // -> accumulator Unit array - Int needbytes; // size calculator - void *allocacc=NULL; // -> allocated accumulator, iff allocated - Unit accbuff[SD2U(DECBUFFER*4+1)]; // buffer (+1 for DECBUFFER==0, - // *4 for calls from other operations) - const Unit *mer, *mermsup; // work - Int madlength; // Units in multiplicand - Int shift; // Units to shift multiplicand by - - #if FASTMUL - // if DECDPUN is 1 or 3 work in base 10**9, otherwise - // (DECDPUN is 2 or 4) then work in base 10**8 - #if DECDPUN & 1 // odd - #define FASTBASE 1000000000 // base - #define FASTDIGS 9 // digits in base - #define FASTLAZY 18 // carry resolution point [1->18] - #else - #define FASTBASE 100000000 - #define FASTDIGS 8 - #define FASTLAZY 1844 // carry resolution point [1->1844] - #endif - // three buffers are used, two for chunked copies of the operands - // (base 10**8 or base 10**9) and one base 2**64 accumulator with - // lazy carry evaluation - uInt zlhibuff[(DECBUFFER*2+1)/8+1]; // buffer (+1 for DECBUFFER==0) - uInt *zlhi=zlhibuff; // -> lhs array - uInt *alloclhi=NULL; // -> allocated buffer, iff allocated - uInt zrhibuff[(DECBUFFER*2+1)/8+1]; // buffer (+1 for DECBUFFER==0) - uInt *zrhi=zrhibuff; // -> rhs array - uInt *allocrhi=NULL; // -> allocated buffer, iff allocated - uLong zaccbuff[(DECBUFFER*2+1)/4+2]; // buffer (+1 for DECBUFFER==0) - // [allocacc is shared for both paths, as only one will run] - uLong *zacc=zaccbuff; // -> accumulator array for exact result - #if DECDPUN==1 - Int zoff; // accumulator offset - #endif - uInt *lip, *rip; // item pointers - uInt *lmsi, *rmsi; // most significant items - Int ilhs, irhs, iacc; // item counts in the arrays - Int lazy; // lazy carry counter - uLong lcarry; // uLong carry - uInt carry; // carry (NB not uLong) - Int count; // work - const Unit *cup; // .. - Unit *up; // .. - uLong *lp; // .. - Int p; // .. - #endif - - #if DECSUBSET - decNumber *alloclhs=NULL; // -> allocated buffer, iff allocated - decNumber *allocrhs=NULL; // -> allocated buffer, iff allocated - #endif - - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - // precalculate result sign - bits=(uByte)((lhs->bits^rhs->bits)&DECNEG); - - // handle infinities and NaNs - if (SPECIALARGS) { // a special bit set - if (SPECIALARGS & (DECSNAN | DECNAN)) { // one or two NaNs - decNaNs(res, lhs, rhs, set, status); - return res;} - // one or two infinities; Infinity * 0 is invalid - if (((lhs->bits & DECINF)==0 && ISZERO(lhs)) - ||((rhs->bits & DECINF)==0 && ISZERO(rhs))) { - *status|=DEC_Invalid_operation; - return res;} - decNumberZero(res); - res->bits=bits|DECINF; // infinity - return res;} - - // For best speed, as in DMSRCN [the original Rexx numerics - // module], use the shorter number as the multiplier (rhs) and - // the longer as the multiplicand (lhs) to minimise the number of - // adds (partial products) - if (lhs->digits<rhs->digits) { // swap... - const decNumber *hold=lhs; - lhs=rhs; - rhs=hold; - } - - do { // protect allocated storage - #if DECSUBSET - if (!set->extended) { - // reduce operands and set lostDigits status, as needed - if (lhs->digits>set->digits) { - alloclhs=decRoundOperand(lhs, set, status); - if (alloclhs==NULL) break; - lhs=alloclhs; - } - if (rhs->digits>set->digits) { - allocrhs=decRoundOperand(rhs, set, status); - if (allocrhs==NULL) break; - rhs=allocrhs; - } - } - #endif - // [following code does not require input rounding] - - #if FASTMUL // fastpath can be used - // use the fast path if there are enough digits in the shorter - // operand to make the setup and takedown worthwhile - #define NEEDTWO (DECDPUN*2) // within two decUnitAddSub calls - if (rhs->digits>NEEDTWO) { // use fastpath... - // calculate the number of elements in each array - ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; // [ceiling] - irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; // .. - iacc=ilhs+irhs; - - // allocate buffers if required, as usual - needbytes=ilhs*sizeof(uInt); - if (needbytes>(Int)sizeof(zlhibuff)) { - alloclhi=(uInt *)malloc(needbytes); - zlhi=alloclhi;} - needbytes=irhs*sizeof(uInt); - if (needbytes>(Int)sizeof(zrhibuff)) { - allocrhi=(uInt *)malloc(needbytes); - zrhi=allocrhi;} - - // Allocating the accumulator space needs a special case when - // DECDPUN=1 because when converting the accumulator to Units - // after the multiplication each 8-byte item becomes 9 1-byte - // units. Therefore iacc extra bytes are needed at the front - // (rounded up to a multiple of 8 bytes), and the uLong - // accumulator starts offset the appropriate number of units - // to the right to avoid overwrite during the unchunking. - needbytes=iacc*sizeof(uLong); - #if DECDPUN==1 - zoff=(iacc+7)/8; // items to offset by - needbytes+=zoff*8; - #endif - if (needbytes>(Int)sizeof(zaccbuff)) { - allocacc=(uLong *)malloc(needbytes); - zacc=(uLong *)allocacc;} - if (zlhi==NULL||zrhi==NULL||zacc==NULL) { - *status|=DEC_Insufficient_storage; - break;} - - acc=(Unit *)zacc; // -> target Unit array - #if DECDPUN==1 - zacc+=zoff; // start uLong accumulator to right - #endif - - // assemble the chunked copies of the left and right sides - for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++) - for (p=0, *lip=0; p<FASTDIGS && count>0; - p+=DECDPUN, cup++, count-=DECDPUN) - *lip+=*cup*powers[p]; - lmsi=lip-1; // save -> msi - for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++) - for (p=0, *rip=0; p<FASTDIGS && count>0; - p+=DECDPUN, cup++, count-=DECDPUN) - *rip+=*cup*powers[p]; - rmsi=rip-1; // save -> msi - - // zero the accumulator - for (lp=zacc; lp<zacc+iacc; lp++) *lp=0; - - /* Start the multiplication */ - // Resolving carries can dominate the cost of accumulating the - // partial products, so this is only done when necessary. - // Each uLong item in the accumulator can hold values up to - // 2**64-1, and each partial product can be as large as - // (10**FASTDIGS-1)**2. When FASTDIGS=9, this can be added to - // itself 18.4 times in a uLong without overflowing, so during - // the main calculation resolution is carried out every 18th - // add -- every 162 digits. Similarly, when FASTDIGS=8, the - // partial products can be added to themselves 1844.6 times in - // a uLong without overflowing, so intermediate carry - // resolution occurs only every 14752 digits. Hence for common - // short numbers usually only the one final carry resolution - // occurs. - // (The count is set via FASTLAZY to simplify experiments to - // measure the value of this approach: a 35% improvement on a - // [34x34] multiply.) - lazy=FASTLAZY; // carry delay count - for (rip=zrhi; rip<=rmsi; rip++) { // over each item in rhs - lp=zacc+(rip-zrhi); // where to add the lhs - for (lip=zlhi; lip<=lmsi; lip++, lp++) { // over each item in lhs - *lp+=(uLong)(*lip)*(*rip); // [this should in-line] - } // lip loop - lazy--; - if (lazy>0 && rip!=rmsi) continue; - lazy=FASTLAZY; // reset delay count - // spin up the accumulator resolving overflows - for (lp=zacc; lp<zacc+iacc; lp++) { - if (*lp<FASTBASE) continue; // it fits - lcarry=*lp/FASTBASE; // top part [slow divide] - // lcarry can exceed 2**32-1, so check again; this check - // and occasional extra divide (slow) is well worth it, as - // it allows FASTLAZY to be increased to 18 rather than 4 - // in the FASTDIGS=9 case - if (lcarry<FASTBASE) carry=(uInt)lcarry; // [usual] - else { // two-place carry [fairly rare] - uInt carry2=(uInt)(lcarry/FASTBASE); // top top part - *(lp+2)+=carry2; // add to item+2 - *lp-=((uLong)FASTBASE*FASTBASE*carry2); // [slow] - carry=(uInt)(lcarry-((uLong)FASTBASE*carry2)); // [inline] - } - *(lp+1)+=carry; // add to item above [inline] - *lp-=((uLong)FASTBASE*carry); // [inline] - } // carry resolution - } // rip loop - - // The multiplication is complete; time to convert back into - // units. This can be done in-place in the accumulator and in - // 32-bit operations, because carries were resolved after the - // final add. This needs N-1 divides and multiplies for - // each item in the accumulator (which will become up to N - // units, where 2<=N<=9). - for (lp=zacc, up=acc; lp<zacc+iacc; lp++) { - uInt item=(uInt)*lp; // decapitate to uInt - for (p=0; p<FASTDIGS-DECDPUN; p+=DECDPUN, up++) { - uInt part=item/(DECDPUNMAX+1); - *up=(Unit)(item-(part*(DECDPUNMAX+1))); - item=part; - } // p - *up=(Unit)item; up++; // [final needs no division] - } // lp - accunits=up-acc; // count of units - } - else { // here to use units directly, without chunking ['old code'] - #endif - - // if accumulator will be too long for local storage, then allocate - acc=accbuff; // -> assume buffer for accumulator - needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit); - if (needbytes>(Int)sizeof(accbuff)) { - allocacc=(Unit *)malloc(needbytes); - if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;} - acc=(Unit *)allocacc; // use the allocated space - } - - /* Now the main long multiplication loop */ - // Unlike the equivalent in the IBM Java implementation, there - // is no advantage in calculating from msu to lsu. So, do it - // by the book, as it were. - // Each iteration calculates ACC=ACC+MULTAND*MULT - accunits=1; // accumulator starts at '0' - *acc=0; // .. (lsu=0) - shift=0; // no multiplicand shift at first - madlength=D2U(lhs->digits); // this won't change - mermsup=rhs->lsu+D2U(rhs->digits); // -> msu+1 of multiplier - - for (mer=rhs->lsu; mer<mermsup; mer++) { - // Here, *mer is the next Unit in the multiplier to use - // If non-zero [optimization] add it... - if (*mer!=0) accunits=decUnitAddSub(&acc[shift], accunits-shift, - lhs->lsu, madlength, 0, - &acc[shift], *mer) - + shift; - else { // extend acc with a 0; it will be used shortly - *(acc+accunits)=0; // [this avoids length of <=0 later] - accunits++; - } - // multiply multiplicand by 10**DECDPUN for next Unit to left - shift++; // add this for 'logical length' - } // n - #if FASTMUL - } // unchunked units - #endif - // common end-path - #if DECTRACE - decDumpAr('*', acc, accunits); // Show exact result - #endif - - // acc now contains the exact result of the multiplication, - // possibly with a leading zero unit; build the decNumber from - // it, noting if any residue - res->bits=bits; // set sign - res->digits=decGetDigits(acc, accunits); // count digits exactly - - // There can be a 31-bit wrap in calculating the exponent. - // This can only happen if both input exponents are negative and - // both their magnitudes are large. If there was a wrap, set a - // safe very negative exponent, from which decFinalize() will - // raise a hard underflow shortly. - exponent=lhs->exponent+rhs->exponent; // calculate exponent - if (lhs->exponent<0 && rhs->exponent<0 && exponent>0) - exponent=-2*DECNUMMAXE; // force underflow - res->exponent=exponent; // OK to overwrite now - - - // Set the coefficient. If any rounding, residue records - decSetCoeff(res, set, acc, res->digits, &residue, status); - decFinish(res, set, &residue, status); // final cleanup - } while(0); // end protected - - if (allocacc!=NULL) free(allocacc); // drop any storage used - #if DECSUBSET - if (allocrhs!=NULL) free(allocrhs); // .. - if (alloclhs!=NULL) free(alloclhs); // .. - #endif - #if FASTMUL - if (allocrhi!=NULL) free(allocrhi); // .. - if (alloclhi!=NULL) free(alloclhi); // .. - #endif - return res; - } // decMultiplyOp - -/* ------------------------------------------------------------------ */ -/* decExpOp -- effect exponentiation */ -/* */ -/* This computes C = exp(A) */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context; note that rounding mode has no effect */ -/* */ -/* C must have space for set->digits digits. status is updated but */ -/* not set. */ -/* */ -/* Restrictions: */ -/* */ -/* digits, emax, and -emin in the context must be less than */ -/* 2*DEC_MAX_MATH (1999998), and the rhs must be within these */ -/* bounds or a zero. This is an internal routine, so these */ -/* restrictions are contractual and not enforced. */ -/* */ -/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */ -/* almost always be correctly rounded, but may be up to 1 ulp in */ -/* error in rare cases. */ -/* */ -/* Finite results will always be full precision and Inexact, except */ -/* when A is a zero or -Infinity (giving 1 or 0 respectively). */ -/* ------------------------------------------------------------------ */ -/* This approach used here is similar to the algorithm described in */ -/* */ -/* Variable Precision Exponential Function, T. E. Hull and */ -/* A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */ -/* pp79-91, ACM, June 1986. */ -/* */ -/* with the main difference being that the iterations in the series */ -/* evaluation are terminated dynamically (which does not require the */ -/* extra variable-precision variables which are expensive in this */ -/* context). */ -/* */ -/* The error analysis in Hull & Abrham's paper applies except for the */ -/* round-off error accumulation during the series evaluation. This */ -/* code does not precalculate the number of iterations and so cannot */ -/* use Horner's scheme. Instead, the accumulation is done at double- */ -/* precision, which ensures that the additions of the terms are exact */ -/* and do not accumulate round-off (and any round-off errors in the */ -/* terms themselves move 'to the right' faster than they can */ -/* accumulate). This code also extends the calculation by allowing, */ -/* in the spirit of other decNumber operators, the input to be more */ -/* precise than the result (the precision used is based on the more */ -/* precise of the input or requested result). */ -/* */ -/* Implementation notes: */ -/* */ -/* 1. This is separated out as decExpOp so it can be called from */ -/* other Mathematical functions (notably Ln) with a wider range */ -/* than normal. In particular, it can handle the slightly wider */ -/* (double) range needed by Ln (which has to be able to calculate */ -/* exp(-x) where x can be the tiniest number (Ntiny). */ -/* */ -/* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop */ -/* iterations by approximately a third with additional (although */ -/* diminishing) returns as the range is reduced to even smaller */ -/* fractions. However, h (the power of 10 used to correct the */ -/* result at the end, see below) must be kept <=8 as otherwise */ -/* the final result cannot be computed. Hence the leverage is a */ -/* sliding value (8-h), where potentially the range is reduced */ -/* more for smaller values. */ -/* */ -/* The leverage that can be applied in this way is severely */ -/* limited by the cost of the raise-to-the power at the end, */ -/* which dominates when the number of iterations is small (less */ -/* than ten) or when rhs is short. As an example, the adjustment */ -/* x**10,000,000 needs 31 multiplications, all but one full-width. */ -/* */ -/* 3. The restrictions (especially precision) could be raised with */ -/* care, but the full decNumber range seems very hard within the */ -/* 32-bit limits. */ -/* */ -/* 4. The working precisions for the static buffers are twice the */ -/* obvious size to allow for calls from decNumberPower. */ -/* ------------------------------------------------------------------ */ -decNumber * decExpOp(decNumber *res, const decNumber *rhs, - decContext *set, uInt *status) { - uInt ignore=0; // working status - Int h; // adjusted exponent for 0.xxxx - Int p; // working precision - Int residue; // rounding residue - uInt needbytes; // for space calculations - const decNumber *x=rhs; // (may point to safe copy later) - decContext aset, tset, dset; // working contexts - Int comp; // work - - // the argument is often copied to normalize it, so (unusually) it - // is treated like other buffers, using DECBUFFER, +1 in case - // DECBUFFER is 0 - decNumber bufr[D2N(DECBUFFER*2+1)]; - decNumber *allocrhs=NULL; // non-NULL if rhs buffer allocated - - // the working precision will be no more than set->digits+8+1 - // so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER - // is 0 (and twice that for the accumulator) - - // buffer for t, term (working precision plus) - decNumber buft[D2N(DECBUFFER*2+9+1)]; - decNumber *allocbuft=NULL; // -> allocated buft, iff allocated - decNumber *t=buft; // term - // buffer for a, accumulator (working precision * 2), at least 9 - decNumber bufa[D2N(DECBUFFER*4+18+1)]; - decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated - decNumber *a=bufa; // accumulator - // decNumber for the divisor term; this needs at most 9 digits - // and so can be fixed size [16 so can use standard context] - decNumber bufd[D2N(16)]; - decNumber *d=bufd; // divisor - decNumber numone; // constant 1 - - #if DECCHECK - Int iterations=0; // for later sanity check - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - do { // protect allocated storage - if (SPECIALARG) { // handle infinities and NaNs - if (decNumberIsInfinite(rhs)) { // an infinity - if (decNumberIsNegative(rhs)) // -Infinity -> +0 - decNumberZero(res); - else decNumberCopy(res, rhs); // +Infinity -> self - } - else decNaNs(res, rhs, NULL, set, status); // a NaN - break;} - - if (ISZERO(rhs)) { // zeros -> exact 1 - decNumberZero(res); // make clean 1 - *res->lsu=1; // .. - break;} // [no status to set] - - // e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path - // positive and negative tiny cases which will result in inexact - // 1. This also allows the later add-accumulate to always be - // exact (because its length will never be more than twice the - // working precision). - // The comparator (tiny) needs just one digit, so use the - // decNumber d for it (reused as the divisor, etc., below); its - // exponent is such that if x is positive it will have - // set->digits-1 zeros between the decimal point and the digit, - // which is 4, and if x is negative one more zero there as the - // more precise result will be of the form 0.9999999 rather than - // 1.0000001. Hence, tiny will be 0.0000004 if digits=7 and x>0 - // or 0.00000004 if digits=7 and x<0. If RHS not larger than - // this then the result will be 1.000000 - decNumberZero(d); // clean - *d->lsu=4; // set 4 .. - d->exponent=-set->digits; // * 10**(-d) - if (decNumberIsNegative(rhs)) d->exponent--; // negative case - comp=decCompare(d, rhs, 1); // signless compare - if (comp==BADINT) { - *status|=DEC_Insufficient_storage; - break;} - if (comp>=0) { // rhs < d - Int shift=set->digits-1; - decNumberZero(res); // set 1 - *res->lsu=1; // .. - res->digits=decShiftToMost(res->lsu, 1, shift); - res->exponent=-shift; // make 1.0000... - *status|=DEC_Inexact | DEC_Rounded; // .. inexactly - break;} // tiny - - // set up the context to be used for calculating a, as this is - // used on both paths below - decContextDefault(&aset, DEC_INIT_DECIMAL64); - // accumulator bounds are as requested (could underflow) - aset.emax=set->emax; // usual bounds - aset.emin=set->emin; // .. - aset.clamp=0; // and no concrete format - - // calculate the adjusted (Hull & Abrham) exponent (where the - // decimal point is just to the left of the coefficient msd) - h=rhs->exponent+rhs->digits; - // if h>8 then 10**h cannot be calculated safely; however, when - // h=8 then exp(|rhs|) will be at least exp(1E+7) which is at - // least 6.59E+4342944, so (due to the restriction on Emax/Emin) - // overflow (or underflow to 0) is guaranteed -- so this case can - // be handled by simply forcing the appropriate excess - if (h>8) { // overflow/underflow - // set up here so Power call below will over or underflow to - // zero; set accumulator to either 2 or 0.02 - // [stack buffer for a is always big enough for this] - decNumberZero(a); - *a->lsu=2; // not 1 but < exp(1) - if (decNumberIsNegative(rhs)) a->exponent=-2; // make 0.02 - h=8; // clamp so 10**h computable - p=9; // set a working precision - } - else { // h<=8 - Int maxlever=(rhs->digits>8?1:0); - // [could/should increase this for precisions >40 or so, too] - - // if h is 8, cannot normalize to a lower upper limit because - // the final result will not be computable (see notes above), - // but leverage can be applied whenever h is less than 8. - // Apply as much as possible, up to a MAXLEVER digits, which - // sets the tradeoff against the cost of the later a**(10**h). - // As h is increased, the working precision below also - // increases to compensate for the "constant digits at the - // front" effect. - Int lever=MINI(8-h, maxlever); // leverage attainable - Int use=-rhs->digits-lever; // exponent to use for RHS - h+=lever; // apply leverage selected - if (h<0) { // clamp - use+=h; // [may end up subnormal] - h=0; - } - // Take a copy of RHS if it needs normalization (true whenever x>=1) - if (rhs->exponent!=use) { - decNumber *newrhs=bufr; // assume will fit on stack - needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); - if (needbytes>sizeof(bufr)) { // need malloc space - allocrhs=(decNumber *)malloc(needbytes); - if (allocrhs==NULL) { // hopeless -- abandon - *status|=DEC_Insufficient_storage; - break;} - newrhs=allocrhs; // use the allocated space - } - decNumberCopy(newrhs, rhs); // copy to safe space - newrhs->exponent=use; // normalize; now <1 - x=newrhs; // ready for use - // decNumberShow(x); - } - - // Now use the usual power series to evaluate exp(x). The - // series starts as 1 + x + x^2/2 ... so prime ready for the - // third term by setting the term variable t=x, the accumulator - // a=1, and the divisor d=2. - - // First determine the working precision. From Hull & Abrham - // this is set->digits+h+2. However, if x is 'over-precise' we - // need to allow for all its digits to potentially participate - // (consider an x where all the excess digits are 9s) so in - // this case use x->digits+h+2 - p=MAXI(x->digits, set->digits)+h+2; // [h<=8] - - // a and t are variable precision, and depend on p, so space - // must be allocated for them if necessary - - // the accumulator needs to be able to hold 2p digits so that - // the additions on the second and subsequent iterations are - // sufficiently exact. - needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit); - if (needbytes>sizeof(bufa)) { // need malloc space - allocbufa=(decNumber *)malloc(needbytes); - if (allocbufa==NULL) { // hopeless -- abandon - *status|=DEC_Insufficient_storage; - break;} - a=allocbufa; // use the allocated space - } - // the term needs to be able to hold p digits (which is - // guaranteed to be larger than x->digits, so the initial copy - // is safe); it may also be used for the raise-to-power - // calculation below, which needs an extra two digits - needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit); - if (needbytes>sizeof(buft)) { // need malloc space - allocbuft=(decNumber *)malloc(needbytes); - if (allocbuft==NULL) { // hopeless -- abandon - *status|=DEC_Insufficient_storage; - break;} - t=allocbuft; // use the allocated space - } - - decNumberCopy(t, x); // term=x - decNumberZero(a); *a->lsu=1; // accumulator=1 - decNumberZero(d); *d->lsu=2; // divisor=2 - decNumberZero(&numone); *numone.lsu=1; // constant 1 for increment - - // set up the contexts for calculating a, t, and d - decContextDefault(&tset, DEC_INIT_DECIMAL64); - dset=tset; - // accumulator bounds are set above, set precision now - aset.digits=p*2; // double - // term bounds avoid any underflow or overflow - tset.digits=p; - tset.emin=DEC_MIN_EMIN; // [emax is plenty] - // [dset.digits=16, etc., are sufficient] - - // finally ready to roll - for (;;) { - #if DECCHECK - iterations++; - #endif - // only the status from the accumulation is interesting - // [but it should remain unchanged after first add] - decAddOp(a, a, t, &aset, 0, status); // a=a+t - decMultiplyOp(t, t, x, &tset, &ignore); // t=t*x - decDivideOp(t, t, d, &tset, DIVIDE, &ignore); // t=t/d - // the iteration ends when the term cannot affect the result, - // if rounded to p digits, which is when its value is smaller - // than the accumulator by p+1 digits. There must also be - // full precision in a. - if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1)) - && (a->digits>=p)) break; - decAddOp(d, d, &numone, &dset, 0, &ignore); // d=d+1 - } // iterate - - #if DECCHECK - // just a sanity check; comment out test to show always - if (iterations>p+3) - printf("Exp iterations=%ld, status=%08lx, p=%ld, d=%ld\n", - (LI)iterations, (LI)*status, (LI)p, (LI)x->digits); - #endif - } // h<=8 - - // apply postconditioning: a=a**(10**h) -- this is calculated - // at a slightly higher precision than Hull & Abrham suggest - if (h>0) { - Int seenbit=0; // set once a 1-bit is seen - Int i; // counter - Int n=powers[h]; // always positive - aset.digits=p+2; // sufficient precision - // avoid the overhead and many extra digits of decNumberPower - // as all that is needed is the short 'multipliers' loop; here - // accumulate the answer into t - decNumberZero(t); *t->lsu=1; // acc=1 - for (i=1;;i++){ // for each bit [top bit ignored] - // abandon if have had overflow or terminal underflow - if (*status & (DEC_Overflow|DEC_Underflow)) { // interesting? - if (*status&DEC_Overflow || ISZERO(t)) break;} - n=n<<1; // move next bit to testable position - if (n<0) { // top bit is set - seenbit=1; // OK, have a significant bit - decMultiplyOp(t, t, a, &aset, status); // acc=acc*x - } - if (i==31) break; // that was the last bit - if (!seenbit) continue; // no need to square 1 - decMultiplyOp(t, t, t, &aset, status); // acc=acc*acc [square] - } /*i*/ // 32 bits - // decNumberShow(t); - a=t; // and carry on using t instead of a - } - - // Copy and round the result to res - residue=1; // indicate dirt to right .. - if (ISZERO(a)) residue=0; // .. unless underflowed to 0 - aset.digits=set->digits; // [use default rounding] - decCopyFit(res, a, &aset, &residue, status); // copy & shorten - decFinish(res, set, &residue, status); // cleanup/set flags - } while(0); // end protected - - if (allocrhs !=NULL) free(allocrhs); // drop any storage used - if (allocbufa!=NULL) free(allocbufa); // .. - if (allocbuft!=NULL) free(allocbuft); // .. - // [status is handled by caller] - return res; - } // decExpOp - -/* ------------------------------------------------------------------ */ -/* Initial-estimate natural logarithm table */ -/* */ -/* LNnn -- 90-entry 16-bit table for values from .10 through .99. */ -/* The result is a 4-digit encode of the coefficient (c=the */ -/* top 14 bits encoding 0-9999) and a 2-digit encode of the */ -/* exponent (e=the bottom 2 bits encoding 0-3) */ -/* */ -/* The resulting value is given by: */ -/* */ -/* v = -c * 10**(-e-3) */ -/* */ -/* where e and c are extracted from entry k = LNnn[x-10] */ -/* where x is truncated (NB) into the range 10 through 99, */ -/* and then c = k>>2 and e = k&3. */ -/* ------------------------------------------------------------------ */ -const uShort LNnn[90]={9016, 8652, 8316, 8008, 7724, 7456, 7208, - 6972, 6748, 6540, 6340, 6148, 5968, 5792, 5628, 5464, 5312, - 5164, 5020, 4884, 4748, 4620, 4496, 4376, 4256, 4144, 4032, - 39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629, - 29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837, - 22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321, - 15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717, - 10197, 9685, 9177, 8677, 8185, 7697, 7213, 6737, 6269, 5801, - 5341, 4889, 4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254, - 10130, 6046, 20055}; - -/* ------------------------------------------------------------------ */ -/* decLnOp -- effect natural logarithm */ -/* */ -/* This computes C = ln(A) */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context; note that rounding mode has no effect */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* Notable cases: */ -/* A<0 -> Invalid */ -/* A=0 -> -Infinity (Exact) */ -/* A=+Infinity -> +Infinity (Exact) */ -/* A=1 exactly -> 0 (Exact) */ -/* */ -/* Restrictions (as for Exp): */ -/* */ -/* digits, emax, and -emin in the context must be less than */ -/* DEC_MAX_MATH+11 (1000010), and the rhs must be within these */ -/* bounds or a zero. This is an internal routine, so these */ -/* restrictions are contractual and not enforced. */ -/* */ -/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */ -/* almost always be correctly rounded, but may be up to 1 ulp in */ -/* error in rare cases. */ -/* ------------------------------------------------------------------ */ -/* The result is calculated using Newton's method, with each */ -/* iteration calculating a' = a + x * exp(-a) - 1. See, for example, */ -/* Epperson 1989. */ -/* */ -/* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */ -/* This has to be calculated at the sum of the precision of x and the */ -/* working precision. */ -/* */ -/* Implementation notes: */ -/* */ -/* 1. This is separated out as decLnOp so it can be called from */ -/* other Mathematical functions (e.g., Log 10) with a wider range */ -/* than normal. In particular, it can handle the slightly wider */ -/* (+9+2) range needed by a power function. */ -/* */ -/* 2. The speed of this function is about 10x slower than exp, as */ -/* it typically needs 4-6 iterations for short numbers, and the */ -/* extra precision needed adds a squaring effect, twice. */ -/* */ -/* 3. Fastpaths are included for ln(10) and ln(2), up to length 40, */ -/* as these are common requests. ln(10) is used by log10(x). */ -/* */ -/* 4. An iteration might be saved by widening the LNnn table, and */ -/* would certainly save at least one if it were made ten times */ -/* bigger, too (for truncated fractions 0.100 through 0.999). */ -/* However, for most practical evaluations, at least four or five */ -/* iterations will be neede -- so this would only speed up by */ -/* 20-25% and that probably does not justify increasing the table */ -/* size. */ -/* */ -/* 5. The static buffers are larger than might be expected to allow */ -/* for calls from decNumberPower. */ -/* ------------------------------------------------------------------ */ -decNumber * decLnOp(decNumber *res, const decNumber *rhs, - decContext *set, uInt *status) { - uInt ignore=0; // working status accumulator - uInt needbytes; // for space calculations - Int residue; // rounding residue - Int r; // rhs=f*10**r [see below] - Int p; // working precision - Int pp; // precision for iteration - Int t; // work - - // buffers for a (accumulator, typically precision+2) and b - // (adjustment calculator, same size) - decNumber bufa[D2N(DECBUFFER+12)]; - decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated - decNumber *a=bufa; // accumulator/work - decNumber bufb[D2N(DECBUFFER*2+2)]; - decNumber *allocbufb=NULL; // -> allocated bufa, iff allocated - decNumber *b=bufb; // adjustment/work - - decNumber numone; // constant 1 - decNumber cmp; // work - decContext aset, bset; // working contexts - - #if DECCHECK - Int iterations=0; // for later sanity check - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - do { // protect allocated storage - if (SPECIALARG) { // handle infinities and NaNs - if (decNumberIsInfinite(rhs)) { // an infinity - if (decNumberIsNegative(rhs)) // -Infinity -> error - *status|=DEC_Invalid_operation; - else decNumberCopy(res, rhs); // +Infinity -> self - } - else decNaNs(res, rhs, NULL, set, status); // a NaN - break;} - - if (ISZERO(rhs)) { // +/- zeros -> -Infinity - decNumberZero(res); // make clean - res->bits=DECINF|DECNEG; // set - infinity - break;} // [no status to set] - - // Non-zero negatives are bad... - if (decNumberIsNegative(rhs)) { // -x -> error - *status|=DEC_Invalid_operation; - break;} - - // Here, rhs is positive, finite, and in range - - // lookaside fastpath code for ln(2) and ln(10) at common lengths - if (rhs->exponent==0 && set->digits<=40) { - #if DECDPUN==1 - if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { // ln(10) - #else - if (rhs->lsu[0]==10 && rhs->digits==2) { // ln(10) - #endif - aset=*set; aset.round=DEC_ROUND_HALF_EVEN; - #define LN10 "2.302585092994045684017991454684364207601" - decNumberFromString(res, LN10, &aset); - *status|=(DEC_Inexact | DEC_Rounded); // is inexact - break;} - if (rhs->lsu[0]==2 && rhs->digits==1) { // ln(2) - aset=*set; aset.round=DEC_ROUND_HALF_EVEN; - #define LN2 "0.6931471805599453094172321214581765680755" - decNumberFromString(res, LN2, &aset); - *status|=(DEC_Inexact | DEC_Rounded); - break;} - } // integer and short - - // Determine the working precision. This is normally the - // requested precision + 2, with a minimum of 9. However, if - // the rhs is 'over-precise' then allow for all its digits to - // potentially participate (consider an rhs where all the excess - // digits are 9s) so in this case use rhs->digits+2. - p=MAXI(rhs->digits, MAXI(set->digits, 7))+2; - - // Allocate space for the accumulator and the high-precision - // adjustment calculator, if necessary. The accumulator must - // be able to hold p digits, and the adjustment up to - // rhs->digits+p digits. They are also made big enough for 16 - // digits so that they can be used for calculating the initial - // estimate. - needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit); - if (needbytes>sizeof(bufa)) { // need malloc space - allocbufa=(decNumber *)malloc(needbytes); - if (allocbufa==NULL) { // hopeless -- abandon - *status|=DEC_Insufficient_storage; - break;} - a=allocbufa; // use the allocated space - } - pp=p+rhs->digits; - needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit); - if (needbytes>sizeof(bufb)) { // need malloc space - allocbufb=(decNumber *)malloc(needbytes); - if (allocbufb==NULL) { // hopeless -- abandon - *status|=DEC_Insufficient_storage; - break;} - b=allocbufb; // use the allocated space - } - - // Prepare an initial estimate in acc. Calculate this by - // considering the coefficient of x to be a normalized fraction, - // f, with the decimal point at far left and multiplied by - // 10**r. Then, rhs=f*10**r and 0.1<=f<1, and - // ln(x) = ln(f) + ln(10)*r - // Get the initial estimate for ln(f) from a small lookup - // table (see above) indexed by the first two digits of f, - // truncated. - - decContextDefault(&aset, DEC_INIT_DECIMAL64); // 16-digit extended - r=rhs->exponent+rhs->digits; // 'normalised' exponent - decNumberFromInt32(a, r); // a=r - decNumberFromInt32(b, 2302585); // b=ln(10) (2.302585) - b->exponent=-6; // .. - decMultiplyOp(a, a, b, &aset, &ignore); // a=a*b - // now get top two digits of rhs into b by simple truncate and - // force to integer - residue=0; // (no residue) - aset.digits=2; aset.round=DEC_ROUND_DOWN; - decCopyFit(b, rhs, &aset, &residue, &ignore); // copy & shorten - b->exponent=0; // make integer - t=decGetInt(b); // [cannot fail] - if (t<10) t=X10(t); // adjust single-digit b - t=LNnn[t-10]; // look up ln(b) - decNumberFromInt32(b, t>>2); // b=ln(b) coefficient - b->exponent=-(t&3)-3; // set exponent - b->bits=DECNEG; // ln(0.10)->ln(0.99) always -ve - aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; // restore - decAddOp(a, a, b, &aset, 0, &ignore); // acc=a+b - // the initial estimate is now in a, with up to 4 digits correct. - // When rhs is at or near Nmax the estimate will be low, so we - // will approach it from below, avoiding overflow when calling exp. - - decNumberZero(&numone); *numone.lsu=1; // constant 1 for adjustment - - // accumulator bounds are as requested (could underflow, but - // cannot overflow) - aset.emax=set->emax; - aset.emin=set->emin; - aset.clamp=0; // no concrete format - // set up a context to be used for the multiply and subtract - bset=aset; - bset.emax=DEC_MAX_MATH*2; // use double bounds for the - bset.emin=-DEC_MAX_MATH*2; // adjustment calculation - // [see decExpOp call below] - // for each iteration double the number of digits to calculate, - // up to a maximum of p - pp=9; // initial precision - // [initially 9 as then the sequence starts 7+2, 16+2, and - // 34+2, which is ideal for standard-sized numbers] - aset.digits=pp; // working context - bset.digits=pp+rhs->digits; // wider context - for (;;) { // iterate - #if DECCHECK - iterations++; - if (iterations>24) break; // consider 9 * 2**24 - #endif - // calculate the adjustment (exp(-a)*x-1) into b. This is a - // catastrophic subtraction but it really is the difference - // from 1 that is of interest. - // Use the internal entry point to Exp as it allows the double - // range for calculating exp(-a) when a is the tiniest subnormal. - a->bits^=DECNEG; // make -a - decExpOp(b, a, &bset, &ignore); // b=exp(-a) - a->bits^=DECNEG; // restore sign of a - // now multiply by rhs and subtract 1, at the wider precision - decMultiplyOp(b, b, rhs, &bset, &ignore); // b=b*rhs - decAddOp(b, b, &numone, &bset, DECNEG, &ignore); // b=b-1 - - // the iteration ends when the adjustment cannot affect the - // result by >=0.5 ulp (at the requested digits), which - // is when its value is smaller than the accumulator by - // set->digits+1 digits (or it is zero) -- this is a looser - // requirement than for Exp because all that happens to the - // accumulator after this is the final rounding (but note that - // there must also be full precision in a, or a=0). - - if (decNumberIsZero(b) || - (a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) { - if (a->digits==p) break; - if (decNumberIsZero(a)) { - decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); // rhs=1 ? - if (cmp.lsu[0]==0) a->exponent=0; // yes, exact 0 - else *status|=(DEC_Inexact | DEC_Rounded); // no, inexact - break; - } - // force padding if adjustment has gone to 0 before full length - if (decNumberIsZero(b)) b->exponent=a->exponent-p; - } - - // not done yet ... - decAddOp(a, a, b, &aset, 0, &ignore); // a=a+b for next estimate - if (pp==p) continue; // precision is at maximum - // lengthen the next calculation - pp=pp*2; // double precision - if (pp>p) pp=p; // clamp to maximum - aset.digits=pp; // working context - bset.digits=pp+rhs->digits; // wider context - } // Newton's iteration - - #if DECCHECK - // just a sanity check; remove the test to show always - if (iterations>24) - printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n", - (LI)iterations, (LI)*status, (LI)p, (LI)rhs->digits); - #endif - - // Copy and round the result to res - residue=1; // indicate dirt to right - if (ISZERO(a)) residue=0; // .. unless underflowed to 0 - aset.digits=set->digits; // [use default rounding] - decCopyFit(res, a, &aset, &residue, status); // copy & shorten - decFinish(res, set, &residue, status); // cleanup/set flags - } while(0); // end protected - - if (allocbufa!=NULL) free(allocbufa); // drop any storage used - if (allocbufb!=NULL) free(allocbufb); // .. - // [status is handled by caller] - return res; - } // decLnOp - -/* ------------------------------------------------------------------ */ -/* decQuantizeOp -- force exponent to requested value */ -/* */ -/* This computes C = op(A, B), where op adjusts the coefficient */ -/* of C (by rounding or shifting) such that the exponent (-scale) */ -/* of C has the value B or matches the exponent of B. */ -/* The numerical value of C will equal A, except for the effects of */ -/* any rounding that occurred. */ -/* */ -/* res is C, the result. C may be A or B */ -/* lhs is A, the number to adjust */ -/* rhs is B, the requested exponent */ -/* set is the context */ -/* quant is 1 for quantize or 0 for rescale */ -/* status is the status accumulator (this can be called without */ -/* risk of control loss) */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* Unless there is an error or the result is infinite, the exponent */ -/* after the operation is guaranteed to be that requested. */ -/* ------------------------------------------------------------------ */ -static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set, - Flag quant, uInt *status) { - #if DECSUBSET - decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated - decNumber *allocrhs=NULL; // .., rhs - #endif - const decNumber *inrhs=rhs; // save original rhs - Int reqdigits=set->digits; // requested DIGITS - Int reqexp; // requested exponent [-scale] - Int residue=0; // rounding residue - Int etiny=set->emin-(reqdigits-1); - - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - do { // protect allocated storage - #if DECSUBSET - if (!set->extended) { - // reduce operands and set lostDigits status, as needed - if (lhs->digits>reqdigits) { - alloclhs=decRoundOperand(lhs, set, status); - if (alloclhs==NULL) break; - lhs=alloclhs; - } - if (rhs->digits>reqdigits) { // [this only checks lostDigits] - allocrhs=decRoundOperand(rhs, set, status); - if (allocrhs==NULL) break; - rhs=allocrhs; - } - } - #endif - // [following code does not require input rounding] - - // Handle special values - if (SPECIALARGS) { - // NaNs get usual processing - if (SPECIALARGS & (DECSNAN | DECNAN)) - decNaNs(res, lhs, rhs, set, status); - // one infinity but not both is bad - else if ((lhs->bits ^ rhs->bits) & DECINF) - *status|=DEC_Invalid_operation; - // both infinity: return lhs - else decNumberCopy(res, lhs); // [nop if in place] - break; - } - - // set requested exponent - if (quant) reqexp=inrhs->exponent; // quantize -- match exponents - else { // rescale -- use value of rhs - // Original rhs must be an integer that fits and is in range, - // which could be from -1999999997 to +999999999, thanks to - // subnormals - reqexp=decGetInt(inrhs); // [cannot fail] - } - - #if DECSUBSET - if (!set->extended) etiny=set->emin; // no subnormals - #endif - - if (reqexp==BADINT // bad (rescale only) or .. - || reqexp==BIGODD || reqexp==BIGEVEN // very big (ditto) or .. - || (reqexp<etiny) // < lowest - || (reqexp>set->emax)) { // > emax - *status|=DEC_Invalid_operation; - break;} - - // the RHS has been processed, so it can be overwritten now if necessary - if (ISZERO(lhs)) { // zero coefficient unchanged - decNumberCopy(res, lhs); // [nop if in place] - res->exponent=reqexp; // .. just set exponent - #if DECSUBSET - if (!set->extended) res->bits=0; // subset specification; no -0 - #endif - } - else { // non-zero lhs - Int adjust=reqexp-lhs->exponent; // digit adjustment needed - // if adjusted coefficient will definitely not fit, give up now - if ((lhs->digits-adjust)>reqdigits) { - *status|=DEC_Invalid_operation; - break; - } - - if (adjust>0) { // increasing exponent - // this will decrease the length of the coefficient by adjust - // digits, and must round as it does so - decContext workset; // work - workset=*set; // clone rounding, etc. - workset.digits=lhs->digits-adjust; // set requested length - // [note that the latter can be <1, here] - decCopyFit(res, lhs, &workset, &residue, status); // fit to result - decApplyRound(res, &workset, residue, status); // .. and round - residue=0; // [used] - // If just rounded a 999s case, exponent will be off by one; - // adjust back (after checking space), if so. - if (res->exponent>reqexp) { - // re-check needed, e.g., for quantize(0.9999, 0.001) under - // set->digits==3 - if (res->digits==reqdigits) { // cannot shift by 1 - *status&=~(DEC_Inexact | DEC_Rounded); // [clean these] - *status|=DEC_Invalid_operation; - break; - } - res->digits=decShiftToMost(res->lsu, res->digits, 1); // shift - res->exponent--; // (re)adjust the exponent. - } - #if DECSUBSET - if (ISZERO(res) && !set->extended) res->bits=0; // subset; no -0 - #endif - } // increase - else /* adjust<=0 */ { // decreasing or = exponent - // this will increase the length of the coefficient by -adjust - // digits, by adding zero or more trailing zeros; this is - // already checked for fit, above - decNumberCopy(res, lhs); // [it will fit] - // if padding needed (adjust<0), add it now... - if (adjust<0) { - res->digits=decShiftToMost(res->lsu, res->digits, -adjust); - res->exponent+=adjust; // adjust the exponent - } - } // decrease - } // non-zero - - // Check for overflow [do not use Finalize in this case, as an - // overflow here is a "don't fit" situation] - if (res->exponent>set->emax-res->digits+1) { // too big - *status|=DEC_Invalid_operation; - break; - } - else { - decFinalize(res, set, &residue, status); // set subnormal flags - *status&=~DEC_Underflow; // suppress Underflow [as per 754] - } - } while(0); // end protected - - #if DECSUBSET - if (allocrhs!=NULL) free(allocrhs); // drop any storage used - if (alloclhs!=NULL) free(alloclhs); // .. - #endif - return res; - } // decQuantizeOp - -/* ------------------------------------------------------------------ */ -/* decCompareOp -- compare, min, or max two Numbers */ -/* */ -/* This computes C = A ? B and carries out one of four operations: */ -/* COMPARE -- returns the signum (as a number) giving the */ -/* result of a comparison unless one or both */ -/* operands is a NaN (in which case a NaN results) */ -/* COMPSIG -- as COMPARE except that a quiet NaN raises */ -/* Invalid operation. */ -/* COMPMAX -- returns the larger of the operands, using the */ -/* 754 maxnum operation */ -/* COMPMAXMAG -- ditto, comparing absolute values */ -/* COMPMIN -- the 754 minnum operation */ -/* COMPMINMAG -- ditto, comparing absolute values */ -/* COMTOTAL -- returns the signum (as a number) giving the */ -/* result of a comparison using 754 total ordering */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* op is the operation flag */ -/* status is the usual accumulator */ -/* */ -/* C must have space for one digit for COMPARE or set->digits for */ -/* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG. */ -/* ------------------------------------------------------------------ */ -/* The emphasis here is on speed for common cases, and avoiding */ -/* coefficient comparison if possible. */ -/* ------------------------------------------------------------------ */ -decNumber * decCompareOp(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set, - Flag op, uInt *status) { - #if DECSUBSET - decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated - decNumber *allocrhs=NULL; // .., rhs - #endif - Int result=0; // default result value - uByte merged; // work - - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - do { // protect allocated storage - #if DECSUBSET - if (!set->extended) { - // reduce operands and set lostDigits status, as needed - if (lhs->digits>set->digits) { - alloclhs=decRoundOperand(lhs, set, status); - if (alloclhs==NULL) {result=BADINT; break;} - lhs=alloclhs; - } - if (rhs->digits>set->digits) { - allocrhs=decRoundOperand(rhs, set, status); - if (allocrhs==NULL) {result=BADINT; break;} - rhs=allocrhs; - } - } - #endif - // [following code does not require input rounding] - - // If total ordering then handle differing signs 'up front' - if (op==COMPTOTAL) { // total ordering - if (decNumberIsNegative(lhs) & !decNumberIsNegative(rhs)) { - result=-1; - break; - } - if (!decNumberIsNegative(lhs) & decNumberIsNegative(rhs)) { - result=+1; - break; - } - } - - // handle NaNs specially; let infinities drop through - // This assumes sNaN (even just one) leads to NaN. - merged=(lhs->bits | rhs->bits) & (DECSNAN | DECNAN); - if (merged) { // a NaN bit set - if (op==COMPARE); // result will be NaN - else if (op==COMPSIG) // treat qNaN as sNaN - *status|=DEC_Invalid_operation | DEC_sNaN; - else if (op==COMPTOTAL) { // total ordering, always finite - // signs are known to be the same; compute the ordering here - // as if the signs are both positive, then invert for negatives - if (!decNumberIsNaN(lhs)) result=-1; - else if (!decNumberIsNaN(rhs)) result=+1; - // here if both NaNs - else if (decNumberIsSNaN(lhs) && decNumberIsQNaN(rhs)) result=-1; - else if (decNumberIsQNaN(lhs) && decNumberIsSNaN(rhs)) result=+1; - else { // both NaN or both sNaN - // now it just depends on the payload - result=decUnitCompare(lhs->lsu, D2U(lhs->digits), - rhs->lsu, D2U(rhs->digits), 0); - // [Error not possible, as these are 'aligned'] - } // both same NaNs - if (decNumberIsNegative(lhs)) result=-result; - break; - } // total order - - else if (merged & DECSNAN); // sNaN -> qNaN - else { // here if MIN or MAX and one or two quiet NaNs - // min or max -- 754 rules ignore single NaN - if (!decNumberIsNaN(lhs) || !decNumberIsNaN(rhs)) { - // just one NaN; force choice to be the non-NaN operand - op=COMPMAX; - if (lhs->bits & DECNAN) result=-1; // pick rhs - else result=+1; // pick lhs - break; - } - } // max or min - op=COMPNAN; // use special path - decNaNs(res, lhs, rhs, set, status); // propagate NaN - break; - } - // have numbers - if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1); - else result=decCompare(lhs, rhs, 0); // sign matters - } while(0); // end protected - - if (result==BADINT) *status|=DEC_Insufficient_storage; // rare - else { - if (op==COMPARE || op==COMPSIG ||op==COMPTOTAL) { // returning signum - if (op==COMPTOTAL && result==0) { - // operands are numerically equal or same NaN (and same sign, - // tested first); if identical, leave result 0 - if (lhs->exponent!=rhs->exponent) { - if (lhs->exponent<rhs->exponent) result=-1; - else result=+1; - if (decNumberIsNegative(lhs)) result=-result; - } // lexp!=rexp - } // total-order by exponent - decNumberZero(res); // [always a valid result] - if (result!=0) { // must be -1 or +1 - *res->lsu=1; - if (result<0) res->bits=DECNEG; - } - } - else if (op==COMPNAN); // special, drop through - else { // MAX or MIN, non-NaN result - Int residue=0; // rounding accumulator - // choose the operand for the result - const decNumber *choice; - if (result==0) { // operands are numerically equal - // choose according to sign then exponent (see 754) - uByte slhs=(lhs->bits & DECNEG); - uByte srhs=(rhs->bits & DECNEG); - #if DECSUBSET - if (!set->extended) { // subset: force left-hand - op=COMPMAX; - result=+1; - } - else - #endif - if (slhs!=srhs) { // signs differ - if (slhs) result=-1; // rhs is max - else result=+1; // lhs is max - } - else if (slhs && srhs) { // both negative - if (lhs->exponent<rhs->exponent) result=+1; - else result=-1; - // [if equal, use lhs, technically identical] - } - else { // both positive - if (lhs->exponent>rhs->exponent) result=+1; - else result=-1; - // [ditto] - } - } // numerically equal - // here result will be non-0; reverse if looking for MIN - if (op==COMPMIN || op==COMPMINMAG) result=-result; - choice=(result>0 ? lhs : rhs); // choose - // copy chosen to result, rounding if need be - decCopyFit(res, choice, set, &residue, status); - decFinish(res, set, &residue, status); - } - } - #if DECSUBSET - if (allocrhs!=NULL) free(allocrhs); // free any storage used - if (alloclhs!=NULL) free(alloclhs); // .. - #endif - return res; - } // decCompareOp - -/* ------------------------------------------------------------------ */ -/* decCompare -- compare two decNumbers by numerical value */ -/* */ -/* This routine compares A ? B without altering them. */ -/* */ -/* Arg1 is A, a decNumber which is not a NaN */ -/* Arg2 is B, a decNumber which is not a NaN */ -/* Arg3 is 1 for a sign-independent compare, 0 otherwise */ -/* */ -/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */ -/* (the only possible failure is an allocation error) */ -/* ------------------------------------------------------------------ */ -static Int decCompare(const decNumber *lhs, const decNumber *rhs, - Flag abs) { - Int result; // result value - Int sigr; // rhs signum - Int compare; // work - - result=1; // assume signum(lhs) - if (ISZERO(lhs)) result=0; - if (abs) { - if (ISZERO(rhs)) return result; // LHS wins or both 0 - // RHS is non-zero - if (result==0) return -1; // LHS is 0; RHS wins - // [here, both non-zero, result=1] - } - else { // signs matter - if (result && decNumberIsNegative(lhs)) result=-1; - sigr=1; // compute signum(rhs) - if (ISZERO(rhs)) sigr=0; - else if (decNumberIsNegative(rhs)) sigr=-1; - if (result > sigr) return +1; // L > R, return 1 - if (result < sigr) return -1; // L < R, return -1 - if (result==0) return 0; // both 0 - } - - // signums are the same; both are non-zero - if ((lhs->bits | rhs->bits) & DECINF) { // one or more infinities - if (decNumberIsInfinite(rhs)) { - if (decNumberIsInfinite(lhs)) result=0;// both infinite - else result=-result; // only rhs infinite - } - return result; - } - // must compare the coefficients, allowing for exponents - if (lhs->exponent>rhs->exponent) { // LHS exponent larger - // swap sides, and sign - const decNumber *temp=lhs; - lhs=rhs; - rhs=temp; - result=-result; - } - compare=decUnitCompare(lhs->lsu, D2U(lhs->digits), - rhs->lsu, D2U(rhs->digits), - rhs->exponent-lhs->exponent); - if (compare!=BADINT) compare*=result; // comparison succeeded - return compare; - } // decCompare - -/* ------------------------------------------------------------------ */ -/* decUnitCompare -- compare two >=0 integers in Unit arrays */ -/* */ -/* This routine compares A ? B*10**E where A and B are unit arrays */ -/* A is a plain integer */ -/* B has an exponent of E (which must be non-negative) */ -/* */ -/* Arg1 is A first Unit (lsu) */ -/* Arg2 is A length in Units */ -/* Arg3 is B first Unit (lsu) */ -/* Arg4 is B length in Units */ -/* Arg5 is E (0 if the units are aligned) */ -/* */ -/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */ -/* (the only possible failure is an allocation error, which can */ -/* only occur if E!=0) */ -/* ------------------------------------------------------------------ */ -static Int decUnitCompare(const Unit *a, Int alength, - const Unit *b, Int blength, Int exp) { - Unit *acc; // accumulator for result - Unit accbuff[SD2U(DECBUFFER*2+1)]; // local buffer - Unit *allocacc=NULL; // -> allocated acc buffer, iff allocated - Int accunits, need; // units in use or needed for acc - const Unit *l, *r, *u; // work - Int expunits, exprem, result; // .. - - if (exp==0) { // aligned; fastpath - if (alength>blength) return 1; - if (alength<blength) return -1; - // same number of units in both -- need unit-by-unit compare - l=a+alength-1; - r=b+alength-1; - for (;l>=a; l--, r--) { - if (*l>*r) return 1; - if (*l<*r) return -1; - } - return 0; // all units match - } // aligned - - // Unaligned. If one is >1 unit longer than the other, padded - // approximately, then can return easily - if (alength>blength+(Int)D2U(exp)) return 1; - if (alength+1<blength+(Int)D2U(exp)) return -1; - - // Need to do a real subtract. For this, a result buffer is needed - // even though only the sign is of interest. Its length needs - // to be the larger of alength and padded blength, +2 - need=blength+D2U(exp); // maximum real length of B - if (need<alength) need=alength; - need+=2; - acc=accbuff; // assume use local buffer - if (need*sizeof(Unit)>sizeof(accbuff)) { - allocacc=(Unit *)malloc(need*sizeof(Unit)); - if (allocacc==NULL) return BADINT; // hopeless -- abandon - acc=allocacc; - } - // Calculate units and remainder from exponent. - expunits=exp/DECDPUN; - exprem=exp%DECDPUN; - // subtract [A+B*(-m)] - accunits=decUnitAddSub(a, alength, b, blength, expunits, acc, - -(Int)powers[exprem]); - // [UnitAddSub result may have leading zeros, even on zero] - if (accunits<0) result=-1; // negative result - else { // non-negative result - // check units of the result before freeing any storage - for (u=acc; u<acc+accunits-1 && *u==0;) u++; - result=(*u==0 ? 0 : +1); - } - // clean up and return the result - if (allocacc!=NULL) free(allocacc); // drop any storage used - return result; - } // decUnitCompare - -/* ------------------------------------------------------------------ */ -/* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays */ -/* */ -/* This routine performs the calculation: */ -/* */ -/* C=A+(B*M) */ -/* */ -/* Where M is in the range -DECDPUNMAX through +DECDPUNMAX. */ -/* */ -/* A may be shorter or longer than B. */ -/* */ -/* Leading zeros are not removed after a calculation. The result is */ -/* either the same length as the longer of A and B (adding any */ -/* shift), or one Unit longer than that (if a Unit carry occurred). */ -/* */ -/* A and B content are not altered unless C is also A or B. */ -/* C may be the same array as A or B, but only if no zero padding is */ -/* requested (that is, C may be B only if bshift==0). */ -/* C is filled from the lsu; only those units necessary to complete */ -/* the calculation are referenced. */ -/* */ -/* Arg1 is A first Unit (lsu) */ -/* Arg2 is A length in Units */ -/* Arg3 is B first Unit (lsu) */ -/* Arg4 is B length in Units */ -/* Arg5 is B shift in Units (>=0; pads with 0 units if positive) */ -/* Arg6 is C first Unit (lsu) */ -/* Arg7 is M, the multiplier */ -/* */ -/* returns the count of Units written to C, which will be non-zero */ -/* and negated if the result is negative. That is, the sign of the */ -/* returned Int is the sign of the result (positive for zero) and */ -/* the absolute value of the Int is the count of Units. */ -/* */ -/* It is the caller's responsibility to make sure that C size is */ -/* safe, allowing space if necessary for a one-Unit carry. */ -/* */ -/* This routine is severely performance-critical; *any* change here */ -/* must be measured (timed) to assure no performance degradation. */ -/* In particular, trickery here tends to be counter-productive, as */ -/* increased complexity of code hurts register optimizations on */ -/* register-poor architectures. Avoiding divisions is nearly */ -/* always a Good Idea, however. */ -/* */ -/* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark */ -/* (IBM Warwick, UK) for some of the ideas used in this routine. */ -/* ------------------------------------------------------------------ */ -static Int decUnitAddSub(const Unit *a, Int alength, - const Unit *b, Int blength, Int bshift, - Unit *c, Int m) { - const Unit *alsu=a; // A lsu [need to remember it] - Unit *clsu=c; // C ditto - Unit *minC; // low water mark for C - Unit *maxC; // high water mark for C - eInt carry=0; // carry integer (could be Long) - Int add; // work - #if DECDPUN<=4 // myriadal, millenary, etc. - Int est; // estimated quotient - #endif - - #if DECTRACE - if (alength<1 || blength<1) - printf("decUnitAddSub: alen blen m %ld %ld [%ld]\n", alength, blength, m); - #endif - - maxC=c+alength; // A is usually the longer - minC=c+blength; // .. and B the shorter - if (bshift!=0) { // B is shifted; low As copy across - minC+=bshift; - // if in place [common], skip copy unless there's a gap [rare] - if (a==c && bshift<=alength) { - c+=bshift; - a+=bshift; - } - else for (; c<clsu+bshift; a++, c++) { // copy needed - if (a<alsu+alength) *c=*a; - else *c=0; - } - } - if (minC>maxC) { // swap - Unit *hold=minC; - minC=maxC; - maxC=hold; - } - - // For speed, do the addition as two loops; the first where both A - // and B contribute, and the second (if necessary) where only one or - // other of the numbers contribute. - // Carry handling is the same (i.e., duplicated) in each case. - for (; c<minC; c++) { - carry+=*a; - a++; - carry+=((eInt)*b)*m; // [special-casing m=1/-1 - b++; // here is not a win] - // here carry is new Unit of digits; it could be +ve or -ve - if ((ueInt)carry<=DECDPUNMAX) { // fastpath 0-DECDPUNMAX - *c=(Unit)carry; - carry=0; - continue; - } - #if DECDPUN==4 // use divide-by-multiply - if (carry>=0) { - est=(((ueInt)carry>>11)*53687)>>18; - *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder - carry=est; // likely quotient [89%] - if (*c<DECDPUNMAX+1) continue; // estimate was correct - carry++; - *c-=DECDPUNMAX+1; - continue; - } - // negative case - carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive - est=(((ueInt)carry>>11)*53687)>>18; - *c=(Unit)(carry-est*(DECDPUNMAX+1)); - carry=est-(DECDPUNMAX+1); // correctly negative - if (*c<DECDPUNMAX+1) continue; // was OK - carry++; - *c-=DECDPUNMAX+1; - #elif DECDPUN==3 - if (carry>=0) { - est=(((ueInt)carry>>3)*16777)>>21; - *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder - carry=est; // likely quotient [99%] - if (*c<DECDPUNMAX+1) continue; // estimate was correct - carry++; - *c-=DECDPUNMAX+1; - continue; - } - // negative case - carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive - est=(((ueInt)carry>>3)*16777)>>21; - *c=(Unit)(carry-est*(DECDPUNMAX+1)); - carry=est-(DECDPUNMAX+1); // correctly negative - if (*c<DECDPUNMAX+1) continue; // was OK - carry++; - *c-=DECDPUNMAX+1; - #elif DECDPUN<=2 - // Can use QUOT10 as carry <= 4 digits - if (carry>=0) { - est=QUOT10(carry, DECDPUN); - *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder - carry=est; // quotient - continue; - } - // negative case - carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive - est=QUOT10(carry, DECDPUN); - *c=(Unit)(carry-est*(DECDPUNMAX+1)); - carry=est-(DECDPUNMAX+1); // correctly negative - #else - // remainder operator is undefined if negative, so must test - if ((ueInt)carry<(DECDPUNMAX+1)*2) { // fastpath carry +1 - *c=(Unit)(carry-(DECDPUNMAX+1)); // [helps additions] - carry=1; - continue; - } - if (carry>=0) { - *c=(Unit)(carry%(DECDPUNMAX+1)); - carry=carry/(DECDPUNMAX+1); - continue; - } - // negative case - carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive - *c=(Unit)(carry%(DECDPUNMAX+1)); - carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1); - #endif - } // c - - // now may have one or other to complete - // [pretest to avoid loop setup/shutdown] - if (c<maxC) for (; c<maxC; c++) { - if (a<alsu+alength) { // still in A - carry+=*a; - a++; - } - else { // inside B - carry+=((eInt)*b)*m; - b++; - } - // here carry is new Unit of digits; it could be +ve or -ve and - // magnitude up to DECDPUNMAX squared - if ((ueInt)carry<=DECDPUNMAX) { // fastpath 0-DECDPUNMAX - *c=(Unit)carry; - carry=0; - continue; - } - // result for this unit is negative or >DECDPUNMAX - #if DECDPUN==4 // use divide-by-multiply - if (carry>=0) { - est=(((ueInt)carry>>11)*53687)>>18; - *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder - carry=est; // likely quotient [79.7%] - if (*c<DECDPUNMAX+1) continue; // estimate was correct - carry++; - *c-=DECDPUNMAX+1; - continue; - } - // negative case - carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive - est=(((ueInt)carry>>11)*53687)>>18; - *c=(Unit)(carry-est*(DECDPUNMAX+1)); - carry=est-(DECDPUNMAX+1); // correctly negative - if (*c<DECDPUNMAX+1) continue; // was OK - carry++; - *c-=DECDPUNMAX+1; - #elif DECDPUN==3 - if (carry>=0) { - est=(((ueInt)carry>>3)*16777)>>21; - *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder - carry=est; // likely quotient [99%] - if (*c<DECDPUNMAX+1) continue; // estimate was correct - carry++; - *c-=DECDPUNMAX+1; - continue; - } - // negative case - carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive - est=(((ueInt)carry>>3)*16777)>>21; - *c=(Unit)(carry-est*(DECDPUNMAX+1)); - carry=est-(DECDPUNMAX+1); // correctly negative - if (*c<DECDPUNMAX+1) continue; // was OK - carry++; - *c-=DECDPUNMAX+1; - #elif DECDPUN<=2 - if (carry>=0) { - est=QUOT10(carry, DECDPUN); - *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder - carry=est; // quotient - continue; - } - // negative case - carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive - est=QUOT10(carry, DECDPUN); - *c=(Unit)(carry-est*(DECDPUNMAX+1)); - carry=est-(DECDPUNMAX+1); // correctly negative - #else - if ((ueInt)carry<(DECDPUNMAX+1)*2){ // fastpath carry 1 - *c=(Unit)(carry-(DECDPUNMAX+1)); - carry=1; - continue; - } - // remainder operator is undefined if negative, so must test - if (carry>=0) { - *c=(Unit)(carry%(DECDPUNMAX+1)); - carry=carry/(DECDPUNMAX+1); - continue; - } - // negative case - carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive - *c=(Unit)(carry%(DECDPUNMAX+1)); - carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1); - #endif - } // c - - // OK, all A and B processed; might still have carry or borrow - // return number of Units in the result, negated if a borrow - if (carry==0) return c-clsu; // no carry, so no more to do - if (carry>0) { // positive carry - *c=(Unit)carry; // place as new unit - c++; // .. - return c-clsu; - } - // -ve carry: it's a borrow; complement needed - add=1; // temporary carry... - for (c=clsu; c<maxC; c++) { - add=DECDPUNMAX+add-*c; - if (add<=DECDPUNMAX) { - *c=(Unit)add; - add=0; - } - else { - *c=0; - add=1; - } - } - // add an extra unit iff it would be non-zero - #if DECTRACE - printf("UAS borrow: add %ld, carry %ld\n", add, carry); - #endif - if ((add-carry-1)!=0) { - *c=(Unit)(add-carry-1); - c++; // interesting, include it - } - return clsu-c; // -ve result indicates borrowed - } // decUnitAddSub - -/* ------------------------------------------------------------------ */ -/* decTrim -- trim trailing zeros or normalize */ -/* */ -/* dn is the number to trim or normalize */ -/* set is the context to use to check for clamp */ -/* all is 1 to remove all trailing zeros, 0 for just fraction ones */ -/* noclamp is 1 to unconditional (unclamped) trim */ -/* dropped returns the number of discarded trailing zeros */ -/* returns dn */ -/* */ -/* If clamp is set in the context then the number of zeros trimmed */ -/* may be limited if the exponent is high. */ -/* All fields are updated as required. This is a utility operation, */ -/* so special values are unchanged and no error is possible. */ -/* ------------------------------------------------------------------ */ -static decNumber * decTrim(decNumber *dn, decContext *set, Flag all, - Flag noclamp, Int *dropped) { - Int d, exp; // work - uInt cut; // .. - Unit *up; // -> current Unit - - #if DECCHECK - if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn; - #endif - - *dropped=0; // assume no zeros dropped - if ((dn->bits & DECSPECIAL) // fast exit if special .. - || (*dn->lsu & 0x01)) return dn; // .. or odd - if (ISZERO(dn)) { // .. or 0 - dn->exponent=0; // (sign is preserved) - return dn; - } - - // have a finite number which is even - exp=dn->exponent; - cut=1; // digit (1-DECDPUN) in Unit - up=dn->lsu; // -> current Unit - for (d=0; d<dn->digits-1; d++) { // [don't strip the final digit] - // slice by powers - #if DECDPUN<=4 - uInt quot=QUOT10(*up, cut); - if ((*up-quot*powers[cut])!=0) break; // found non-0 digit - #else - if (*up%powers[cut]!=0) break; // found non-0 digit - #endif - // have a trailing 0 - if (!all) { // trimming - // [if exp>0 then all trailing 0s are significant for trim] - if (exp<=0) { // if digit might be significant - if (exp==0) break; // then quit - exp++; // next digit might be significant - } - } - cut++; // next power - if (cut>DECDPUN) { // need new Unit - up++; - cut=1; - } - } // d - if (d==0) return dn; // none to drop - - // may need to limit drop if clamping - if (set->clamp && !noclamp) { - Int maxd=set->emax-set->digits+1-dn->exponent; - if (maxd<=0) return dn; // nothing possible - if (d>maxd) d=maxd; - } - - // effect the drop - decShiftToLeast(dn->lsu, D2U(dn->digits), d); - dn->exponent+=d; // maintain numerical value - dn->digits-=d; // new length - *dropped=d; // report the count - return dn; - } // decTrim - -/* ------------------------------------------------------------------ */ -/* decReverse -- reverse a Unit array in place */ -/* */ -/* ulo is the start of the array */ -/* uhi is the end of the array (highest Unit to include) */ -/* */ -/* The units ulo through uhi are reversed in place (if the number */ -/* of units is odd, the middle one is untouched). Note that the */ -/* digit(s) in each unit are unaffected. */ -/* ------------------------------------------------------------------ */ -static void decReverse(Unit *ulo, Unit *uhi) { - Unit temp; - for (; ulo<uhi; ulo++, uhi--) { - temp=*ulo; - *ulo=*uhi; - *uhi=temp; - } - return; - } // decReverse - -/* ------------------------------------------------------------------ */ -/* decShiftToMost -- shift digits in array towards most significant */ -/* */ -/* uar is the array */ -/* digits is the count of digits in use in the array */ -/* shift is the number of zeros to pad with (least significant); */ -/* it must be zero or positive */ -/* */ -/* returns the new length of the integer in the array, in digits */ -/* */ -/* No overflow is permitted (that is, the uar array must be known to */ -/* be large enough to hold the result, after shifting). */ -/* ------------------------------------------------------------------ */ -static Int decShiftToMost(Unit *uar, Int digits, Int shift) { - Unit *target, *source, *first; // work - Int cut; // odd 0's to add - uInt next; // work - - if (shift==0) return digits; // [fastpath] nothing to do - if ((digits+shift)<=DECDPUN) { // [fastpath] single-unit case - *uar=(Unit)(*uar*powers[shift]); - return digits+shift; - } - - next=0; // all paths - source=uar+D2U(digits)-1; // where msu comes from - target=source+D2U(shift); // where upper part of first cut goes - cut=DECDPUN-MSUDIGITS(shift); // where to slice - if (cut==0) { // unit-boundary case - for (; source>=uar; source--, target--) *target=*source; - } - else { - first=uar+D2U(digits+shift)-1; // where msu of source will end up - for (; source>=uar; source--, target--) { - // split the source Unit and accumulate remainder for next - #if DECDPUN<=4 - uInt quot=QUOT10(*source, cut); - uInt rem=*source-quot*powers[cut]; - next+=quot; - #else - uInt rem=*source%powers[cut]; - next+=*source/powers[cut]; - #endif - if (target<=first) *target=(Unit)next; // write to target iff valid - next=rem*powers[DECDPUN-cut]; // save remainder for next Unit - } - } // shift-move - - // propagate any partial unit to one below and clear the rest - for (; target>=uar; target--) { - *target=(Unit)next; - next=0; - } - return digits+shift; - } // decShiftToMost - -/* ------------------------------------------------------------------ */ -/* decShiftToLeast -- shift digits in array towards least significant */ -/* */ -/* uar is the array */ -/* units is length of the array, in units */ -/* shift is the number of digits to remove from the lsu end; it */ -/* must be zero or positive and <= than units*DECDPUN. */ -/* */ -/* returns the new length of the integer in the array, in units */ -/* */ -/* Removed digits are discarded (lost). Units not required to hold */ -/* the final result are unchanged. */ -/* ------------------------------------------------------------------ */ -static Int decShiftToLeast(Unit *uar, Int units, Int shift) { - Unit *target, *up; // work - Int cut, count; // work - Int quot, rem; // for division - - if (shift==0) return units; // [fastpath] nothing to do - if (shift==units*DECDPUN) { // [fastpath] little to do - *uar=0; // all digits cleared gives zero - return 1; // leaves just the one - } - - target=uar; // both paths - cut=MSUDIGITS(shift); - if (cut==DECDPUN) { // unit-boundary case; easy - up=uar+D2U(shift); - for (; up<uar+units; target++, up++) *target=*up; - return target-uar; - } - - // messier - up=uar+D2U(shift-cut); // source; correct to whole Units - count=units*DECDPUN-shift; // the maximum new length - #if DECDPUN<=4 - quot=QUOT10(*up, cut); - #else - quot=*up/powers[cut]; - #endif - for (; ; target++) { - *target=(Unit)quot; - count-=(DECDPUN-cut); - if (count<=0) break; - up++; - quot=*up; - #if DECDPUN<=4 - quot=QUOT10(quot, cut); - rem=*up-quot*powers[cut]; - #else - rem=quot%powers[cut]; - quot=quot/powers[cut]; - #endif - *target=(Unit)(*target+rem*powers[DECDPUN-cut]); - count-=cut; - if (count<=0) break; - } - return target-uar+1; - } // decShiftToLeast - -#if DECSUBSET -/* ------------------------------------------------------------------ */ -/* decRoundOperand -- round an operand [used for subset only] */ -/* */ -/* dn is the number to round (dn->digits is > set->digits) */ -/* set is the relevant context */ -/* status is the status accumulator */ -/* */ -/* returns an allocated decNumber with the rounded result. */ -/* */ -/* lostDigits and other status may be set by this. */ -/* */ -/* Since the input is an operand, it must not be modified. */ -/* Instead, return an allocated decNumber, rounded as required. */ -/* It is the caller's responsibility to free the allocated storage. */ -/* */ -/* If no storage is available then the result cannot be used, so NULL */ -/* is returned. */ -/* ------------------------------------------------------------------ */ -static decNumber *decRoundOperand(const decNumber *dn, decContext *set, - uInt *status) { - decNumber *res; // result structure - uInt newstatus=0; // status from round - Int residue=0; // rounding accumulator - - // Allocate storage for the returned decNumber, big enough for the - // length specified by the context - res=(decNumber *)malloc(sizeof(decNumber) - +(D2U(set->digits)-1)*sizeof(Unit)); - if (res==NULL) { - *status|=DEC_Insufficient_storage; - return NULL; - } - decCopyFit(res, dn, set, &residue, &newstatus); - decApplyRound(res, set, residue, &newstatus); - - // If that set Inexact then "lost digits" is raised... - if (newstatus & DEC_Inexact) newstatus|=DEC_Lost_digits; - *status|=newstatus; - return res; - } // decRoundOperand -#endif - -/* ------------------------------------------------------------------ */ -/* decCopyFit -- copy a number, truncating the coefficient if needed */ -/* */ -/* dest is the target decNumber */ -/* src is the source decNumber */ -/* set is the context [used for length (digits) and rounding mode] */ -/* residue is the residue accumulator */ -/* status contains the current status to be updated */ -/* */ -/* (dest==src is allowed and will be a no-op if fits) */ -/* All fields are updated as required. */ -/* ------------------------------------------------------------------ */ -static void decCopyFit(decNumber *dest, const decNumber *src, - decContext *set, Int *residue, uInt *status) { - dest->bits=src->bits; - dest->exponent=src->exponent; - decSetCoeff(dest, set, src->lsu, src->digits, residue, status); - } // decCopyFit - -/* ------------------------------------------------------------------ */ -/* decSetCoeff -- set the coefficient of a number */ -/* */ -/* dn is the number whose coefficient array is to be set. */ -/* It must have space for set->digits digits */ -/* set is the context [for size] */ -/* lsu -> lsu of the source coefficient [may be dn->lsu] */ -/* len is digits in the source coefficient [may be dn->digits] */ -/* residue is the residue accumulator. This has values as in */ -/* decApplyRound, and will be unchanged unless the */ -/* target size is less than len. In this case, the */ -/* coefficient is truncated and the residue is updated to */ -/* reflect the previous residue and the dropped digits. */ -/* status is the status accumulator, as usual */ -/* */ -/* The coefficient may already be in the number, or it can be an */ -/* external intermediate array. If it is in the number, lsu must == */ -/* dn->lsu and len must == dn->digits. */ -/* */ -/* Note that the coefficient length (len) may be < set->digits, and */ -/* in this case this merely copies the coefficient (or is a no-op */ -/* if dn->lsu==lsu). */ -/* */ -/* Note also that (only internally, from decQuantizeOp and */ -/* decSetSubnormal) the value of set->digits may be less than one, */ -/* indicating a round to left. This routine handles that case */ -/* correctly; caller ensures space. */ -/* */ -/* dn->digits, dn->lsu (and as required), and dn->exponent are */ -/* updated as necessary. dn->bits (sign) is unchanged. */ -/* */ -/* DEC_Rounded status is set if any digits are discarded. */ -/* DEC_Inexact status is set if any non-zero digits are discarded, or */ -/* incoming residue was non-0 (implies rounded) */ -/* ------------------------------------------------------------------ */ -// mapping array: maps 0-9 to canonical residues, so that a residue -// can be adjusted in the range [-1, +1] and achieve correct rounding -// 0 1 2 3 4 5 6 7 8 9 -static const uByte resmap[10]={0, 3, 3, 3, 3, 5, 7, 7, 7, 7}; -static void decSetCoeff(decNumber *dn, decContext *set, const Unit *lsu, - Int len, Int *residue, uInt *status) { - Int discard; // number of digits to discard - uInt cut; // cut point in Unit - const Unit *up; // work - Unit *target; // .. - Int count; // .. - #if DECDPUN<=4 - uInt temp; // .. - #endif - - discard=len-set->digits; // digits to discard - if (discard<=0) { // no digits are being discarded - if (dn->lsu!=lsu) { // copy needed - // copy the coefficient array to the result number; no shift needed - count=len; // avoids D2U - up=lsu; - for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN) - *target=*up; - dn->digits=len; // set the new length - } - // dn->exponent and residue are unchanged, record any inexactitude - if (*residue!=0) *status|=(DEC_Inexact | DEC_Rounded); - return; - } - - // some digits must be discarded ... - dn->exponent+=discard; // maintain numerical value - *status|=DEC_Rounded; // accumulate Rounded status - if (*residue>1) *residue=1; // previous residue now to right, so reduce - - if (discard>len) { // everything, +1, is being discarded - // guard digit is 0 - // residue is all the number [NB could be all 0s] - if (*residue<=0) { // not already positive - count=len; // avoids D2U - for (up=lsu; count>0; up++, count-=DECDPUN) if (*up!=0) { // found non-0 - *residue=1; - break; // no need to check any others - } - } - if (*residue!=0) *status|=DEC_Inexact; // record inexactitude - *dn->lsu=0; // coefficient will now be 0 - dn->digits=1; // .. - return; - } // total discard - - // partial discard [most common case] - // here, at least the first (most significant) discarded digit exists - - // spin up the number, noting residue during the spin, until get to - // the Unit with the first discarded digit. When reach it, extract - // it and remember its position - count=0; - for (up=lsu;; up++) { - count+=DECDPUN; - if (count>=discard) break; // full ones all checked - if (*up!=0) *residue=1; - } // up - - // here up -> Unit with first discarded digit - cut=discard-(count-DECDPUN)-1; - if (cut==DECDPUN-1) { // unit-boundary case (fast) - Unit half=(Unit)powers[DECDPUN]>>1; - // set residue directly - if (*up>=half) { - if (*up>half) *residue=7; - else *residue+=5; // add sticky bit - } - else { // <half - if (*up!=0) *residue=3; // [else is 0, leave as sticky bit] - } - if (set->digits<=0) { // special for Quantize/Subnormal :-( - *dn->lsu=0; // .. result is 0 - dn->digits=1; // .. - } - else { // shift to least - count=set->digits; // now digits to end up with - dn->digits=count; // set the new length - up++; // move to next - // on unit boundary, so shift-down copy loop is simple - for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN) - *target=*up; - } - } // unit-boundary case - - else { // discard digit is in low digit(s), and not top digit - uInt discard1; // first discarded digit - uInt quot, rem; // for divisions - if (cut==0) quot=*up; // is at bottom of unit - else /* cut>0 */ { // it's not at bottom of unit - #if DECDPUN<=4 - quot=QUOT10(*up, cut); - rem=*up-quot*powers[cut]; - #else - rem=*up%powers[cut]; - quot=*up/powers[cut]; - #endif - if (rem!=0) *residue=1; - } - // discard digit is now at bottom of quot - #if DECDPUN<=4 - temp=(quot*6554)>>16; // fast /10 - // Vowels algorithm here not a win (9 instructions) - discard1=quot-X10(temp); - quot=temp; - #else - discard1=quot%10; - quot=quot/10; - #endif - // here, discard1 is the guard digit, and residue is everything - // else [use mapping array to accumulate residue safely] - *residue+=resmap[discard1]; - cut++; // update cut - // here: up -> Unit of the array with bottom digit - // cut is the division point for each Unit - // quot holds the uncut high-order digits for the current unit - if (set->digits<=0) { // special for Quantize/Subnormal :-( - *dn->lsu=0; // .. result is 0 - dn->digits=1; // .. - } - else { // shift to least needed - count=set->digits; // now digits to end up with - dn->digits=count; // set the new length - // shift-copy the coefficient array to the result number - for (target=dn->lsu; ; target++) { - *target=(Unit)quot; - count-=(DECDPUN-cut); - if (count<=0) break; - up++; - quot=*up; - #if DECDPUN<=4 - quot=QUOT10(quot, cut); - rem=*up-quot*powers[cut]; - #else - rem=quot%powers[cut]; - quot=quot/powers[cut]; - #endif - *target=(Unit)(*target+rem*powers[DECDPUN-cut]); - count-=cut; - if (count<=0) break; - } // shift-copy loop - } // shift to least - } // not unit boundary - - if (*residue!=0) *status|=DEC_Inexact; // record inexactitude - return; - } // decSetCoeff - -/* ------------------------------------------------------------------ */ -/* decApplyRound -- apply pending rounding to a number */ -/* */ -/* dn is the number, with space for set->digits digits */ -/* set is the context [for size and rounding mode] */ -/* residue indicates pending rounding, being any accumulated */ -/* guard and sticky information. It may be: */ -/* 6-9: rounding digit is >5 */ -/* 5: rounding digit is exactly half-way */ -/* 1-4: rounding digit is <5 and >0 */ -/* 0: the coefficient is exact */ -/* -1: as 1, but the hidden digits are subtractive, that */ -/* is, of the opposite sign to dn. In this case the */ -/* coefficient must be non-0. This case occurs when */ -/* subtracting a small number (which can be reduced to */ -/* a sticky bit); see decAddOp. */ -/* status is the status accumulator, as usual */ -/* */ -/* This routine applies rounding while keeping the length of the */ -/* coefficient constant. The exponent and status are unchanged */ -/* except if: */ -/* */ -/* -- the coefficient was increased and is all nines (in which */ -/* case Overflow could occur, and is handled directly here so */ -/* the caller does not need to re-test for overflow) */ -/* */ -/* -- the coefficient was decreased and becomes all nines (in which */ -/* case Underflow could occur, and is also handled directly). */ -/* */ -/* All fields in dn are updated as required. */ -/* */ -/* ------------------------------------------------------------------ */ -static void decApplyRound(decNumber *dn, decContext *set, Int residue, - uInt *status) { - Int bump; // 1 if coefficient needs to be incremented - // -1 if coefficient needs to be decremented - - if (residue==0) return; // nothing to apply - - bump=0; // assume a smooth ride - - // now decide whether, and how, to round, depending on mode - switch (set->round) { - case DEC_ROUND_05UP: { // round zero or five up (for reround) - // This is the same as DEC_ROUND_DOWN unless there is a - // positive residue and the lsd of dn is 0 or 5, in which case - // it is bumped; when residue is <0, the number is therefore - // bumped down unless the final digit was 1 or 6 (in which - // case it is bumped down and then up -- a no-op) - Int lsd5=*dn->lsu%5; // get lsd and quintate - if (residue<0 && lsd5!=1) bump=-1; - else if (residue>0 && lsd5==0) bump=1; - // [bump==1 could be applied directly; use common path for clarity] - break;} // r-05 - - case DEC_ROUND_DOWN: { - // no change, except if negative residue - if (residue<0) bump=-1; - break;} // r-d - - case DEC_ROUND_HALF_DOWN: { - if (residue>5) bump=1; - break;} // r-h-d - - case DEC_ROUND_HALF_EVEN: { - if (residue>5) bump=1; // >0.5 goes up - else if (residue==5) { // exactly 0.5000... - // 0.5 goes up iff [new] lsd is odd - if (*dn->lsu & 0x01) bump=1; - } - break;} // r-h-e - - case DEC_ROUND_HALF_UP: { - if (residue>=5) bump=1; - break;} // r-h-u - - case DEC_ROUND_UP: { - if (residue>0) bump=1; - break;} // r-u - - case DEC_ROUND_CEILING: { - // same as _UP for positive numbers, and as _DOWN for negatives - // [negative residue cannot occur on 0] - if (decNumberIsNegative(dn)) { - if (residue<0) bump=-1; - } - else { - if (residue>0) bump=1; - } - break;} // r-c - - case DEC_ROUND_FLOOR: { - // same as _UP for negative numbers, and as _DOWN for positive - // [negative residue cannot occur on 0] - if (!decNumberIsNegative(dn)) { - if (residue<0) bump=-1; - } - else { - if (residue>0) bump=1; - } - break;} // r-f - - default: { // e.g., DEC_ROUND_MAX - *status|=DEC_Invalid_context; - #if DECTRACE || (DECCHECK && DECVERB) - printf("Unknown rounding mode: %d\n", set->round); - #endif - break;} - } // switch - - // now bump the number, up or down, if need be - if (bump==0) return; // no action required - - // Simply use decUnitAddSub unless bumping up and the number is - // all nines. In this special case set to 100... explicitly - // and adjust the exponent by one (as otherwise could overflow - // the array) - // Similarly handle all-nines result if bumping down. - if (bump>0) { - Unit *up; // work - uInt count=dn->digits; // digits to be checked - for (up=dn->lsu; ; up++) { - if (count<=DECDPUN) { - // this is the last Unit (the msu) - if (*up!=powers[count]-1) break; // not still 9s - // here if it, too, is all nines - *up=(Unit)powers[count-1]; // here 999 -> 100 etc. - for (up=up-1; up>=dn->lsu; up--) *up=0; // others all to 0 - dn->exponent++; // and bump exponent - // [which, very rarely, could cause Overflow...] - if ((dn->exponent+dn->digits)>set->emax+1) { - decSetOverflow(dn, set, status); - } - return; // done - } - // a full unit to check, with more to come - if (*up!=DECDPUNMAX) break; // not still 9s - count-=DECDPUN; - } // up - } // bump>0 - else { // -1 - // here checking for a pre-bump of 1000... (leading 1, all - // other digits zero) - Unit *up, *sup; // work - uInt count=dn->digits; // digits to be checked - for (up=dn->lsu; ; up++) { - if (count<=DECDPUN) { - // this is the last Unit (the msu) - if (*up!=powers[count-1]) break; // not 100.. - // here if have the 1000... case - sup=up; // save msu pointer - *up=(Unit)powers[count]-1; // here 100 in msu -> 999 - // others all to all-nines, too - for (up=up-1; up>=dn->lsu; up--) *up=(Unit)powers[DECDPUN]-1; - dn->exponent--; // and bump exponent - - // iff the number was at the subnormal boundary (exponent=etiny) - // then the exponent is now out of range, so it will in fact get - // clamped to etiny and the final 9 dropped. - // printf(">> emin=%d exp=%d sdig=%d\n", set->emin, - // dn->exponent, set->digits); - if (dn->exponent+1==set->emin-set->digits+1) { - if (count==1 && dn->digits==1) *sup=0; // here 9 -> 0[.9] - else { - *sup=(Unit)powers[count-1]-1; // here 999.. in msu -> 99.. - dn->digits--; - } - dn->exponent++; - *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded; - } - return; // done - } - - // a full unit to check, with more to come - if (*up!=0) break; // not still 0s - count-=DECDPUN; - } // up - - } // bump<0 - - // Actual bump needed. Do it. - decUnitAddSub(dn->lsu, D2U(dn->digits), uarrone, 1, 0, dn->lsu, bump); - } // decApplyRound - -#if DECSUBSET -/* ------------------------------------------------------------------ */ -/* decFinish -- finish processing a number */ -/* */ -/* dn is the number */ -/* set is the context */ -/* residue is the rounding accumulator (as in decApplyRound) */ -/* status is the accumulator */ -/* */ -/* This finishes off the current number by: */ -/* 1. If not extended: */ -/* a. Converting a zero result to clean '0' */ -/* b. Reducing positive exponents to 0, if would fit in digits */ -/* 2. Checking for overflow and subnormals (always) */ -/* Note this is just Finalize when no subset arithmetic. */ -/* All fields are updated as required. */ -/* ------------------------------------------------------------------ */ -static void decFinish(decNumber *dn, decContext *set, Int *residue, - uInt *status) { - if (!set->extended) { - if ISZERO(dn) { // value is zero - dn->exponent=0; // clean exponent .. - dn->bits=0; // .. and sign - return; // no error possible - } - if (dn->exponent>=0) { // non-negative exponent - // >0; reduce to integer if possible - if (set->digits >= (dn->exponent+dn->digits)) { - dn->digits=decShiftToMost(dn->lsu, dn->digits, dn->exponent); - dn->exponent=0; - } - } - } // !extended - - decFinalize(dn, set, residue, status); - } // decFinish -#endif - -/* ------------------------------------------------------------------ */ -/* decFinalize -- final check, clamp, and round of a number */ -/* */ -/* dn is the number */ -/* set is the context */ -/* residue is the rounding accumulator (as in decApplyRound) */ -/* status is the status accumulator */ -/* */ -/* This finishes off the current number by checking for subnormal */ -/* results, applying any pending rounding, checking for overflow, */ -/* and applying any clamping. */ -/* Underflow and overflow conditions are raised as appropriate. */ -/* All fields are updated as required. */ -/* ------------------------------------------------------------------ */ -static void decFinalize(decNumber *dn, decContext *set, Int *residue, - uInt *status) { - Int shift; // shift needed if clamping - Int tinyexp=set->emin-dn->digits+1; // precalculate subnormal boundary - - // Must be careful, here, when checking the exponent as the - // adjusted exponent could overflow 31 bits [because it may already - // be up to twice the expected]. - - // First test for subnormal. This must be done before any final - // round as the result could be rounded to Nmin or 0. - if (dn->exponent<=tinyexp) { // prefilter - Int comp; - decNumber nmin; - // A very nasty case here is dn == Nmin and residue<0 - if (dn->exponent<tinyexp) { - // Go handle subnormals; this will apply round if needed. - decSetSubnormal(dn, set, residue, status); - return; - } - // Equals case: only subnormal if dn=Nmin and negative residue - decNumberZero(&nmin); - nmin.lsu[0]=1; - nmin.exponent=set->emin; - comp=decCompare(dn, &nmin, 1); // (signless compare) - if (comp==BADINT) { // oops - *status|=DEC_Insufficient_storage; // abandon... - return; - } - if (*residue<0 && comp==0) { // neg residue and dn==Nmin - decApplyRound(dn, set, *residue, status); // might force down - decSetSubnormal(dn, set, residue, status); - return; - } - } - - // now apply any pending round (this could raise overflow). - if (*residue!=0) decApplyRound(dn, set, *residue, status); - - // Check for overflow [redundant in the 'rare' case] or clamp - if (dn->exponent<=set->emax-set->digits+1) return; // neither needed - - - // here when might have an overflow or clamp to do - if (dn->exponent>set->emax-dn->digits+1) { // too big - decSetOverflow(dn, set, status); - return; - } - // here when the result is normal but in clamp range - if (!set->clamp) return; - - // here when need to apply the IEEE exponent clamp (fold-down) - shift=dn->exponent-(set->emax-set->digits+1); - - // shift coefficient (if non-zero) - if (!ISZERO(dn)) { - dn->digits=decShiftToMost(dn->lsu, dn->digits, shift); - } - dn->exponent-=shift; // adjust the exponent to match - *status|=DEC_Clamped; // and record the dirty deed - return; - } // decFinalize - -/* ------------------------------------------------------------------ */ -/* decSetOverflow -- set number to proper overflow value */ -/* */ -/* dn is the number (used for sign [only] and result) */ -/* set is the context [used for the rounding mode, etc.] */ -/* status contains the current status to be updated */ -/* */ -/* This sets the sign of a number and sets its value to either */ -/* Infinity or the maximum finite value, depending on the sign of */ -/* dn and the rounding mode, following IEEE 754 rules. */ -/* ------------------------------------------------------------------ */ -static void decSetOverflow(decNumber *dn, decContext *set, uInt *status) { - Flag needmax=0; // result is maximum finite value - uByte sign=dn->bits&DECNEG; // clean and save sign bit - - if (ISZERO(dn)) { // zero does not overflow magnitude - Int emax=set->emax; // limit value - if (set->clamp) emax-=set->digits-1; // lower if clamping - if (dn->exponent>emax) { // clamp required - dn->exponent=emax; - *status|=DEC_Clamped; - } - return; - } - - decNumberZero(dn); - switch (set->round) { - case DEC_ROUND_DOWN: { - needmax=1; // never Infinity - break;} // r-d - case DEC_ROUND_05UP: { - needmax=1; // never Infinity - break;} // r-05 - case DEC_ROUND_CEILING: { - if (sign) needmax=1; // Infinity if non-negative - break;} // r-c - case DEC_ROUND_FLOOR: { - if (!sign) needmax=1; // Infinity if negative - break;} // r-f - default: break; // Infinity in all other cases - } - if (needmax) { - decSetMaxValue(dn, set); - dn->bits=sign; // set sign - } - else dn->bits=sign|DECINF; // Value is +/-Infinity - *status|=DEC_Overflow | DEC_Inexact | DEC_Rounded; - } // decSetOverflow - -/* ------------------------------------------------------------------ */ -/* decSetMaxValue -- set number to +Nmax (maximum normal value) */ -/* */ -/* dn is the number to set */ -/* set is the context [used for digits and emax] */ -/* */ -/* This sets the number to the maximum positive value. */ -/* ------------------------------------------------------------------ */ -static void decSetMaxValue(decNumber *dn, decContext *set) { - Unit *up; // work - Int count=set->digits; // nines to add - dn->digits=count; - // fill in all nines to set maximum value - for (up=dn->lsu; ; up++) { - if (count>DECDPUN) *up=DECDPUNMAX; // unit full o'nines - else { // this is the msu - *up=(Unit)(powers[count]-1); - break; - } - count-=DECDPUN; // filled those digits - } // up - dn->bits=0; // + sign - dn->exponent=set->emax-set->digits+1; - } // decSetMaxValue - -/* ------------------------------------------------------------------ */ -/* decSetSubnormal -- process value whose exponent is <Emin */ -/* */ -/* dn is the number (used as input as well as output; it may have */ -/* an allowed subnormal value, which may need to be rounded) */ -/* set is the context [used for the rounding mode] */ -/* residue is any pending residue */ -/* status contains the current status to be updated */ -/* */ -/* If subset mode, set result to zero and set Underflow flags. */ -/* */ -/* Value may be zero with a low exponent; this does not set Subnormal */ -/* but the exponent will be clamped to Etiny. */ -/* */ -/* Otherwise ensure exponent is not out of range, and round as */ -/* necessary. Underflow is set if the result is Inexact. */ -/* ------------------------------------------------------------------ */ -static void decSetSubnormal(decNumber *dn, decContext *set, Int *residue, - uInt *status) { - decContext workset; // work - Int etiny, adjust; // .. - - #if DECSUBSET - // simple set to zero and 'hard underflow' for subset - if (!set->extended) { - decNumberZero(dn); - // always full overflow - *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded; - return; - } - #endif - - // Full arithmetic -- allow subnormals, rounded to minimum exponent - // (Etiny) if needed - etiny=set->emin-(set->digits-1); // smallest allowed exponent - - if ISZERO(dn) { // value is zero - // residue can never be non-zero here - #if DECCHECK - if (*residue!=0) { - printf("++ Subnormal 0 residue %ld\n", (LI)*residue); - *status|=DEC_Invalid_operation; - } - #endif - if (dn->exponent<etiny) { // clamp required - dn->exponent=etiny; - *status|=DEC_Clamped; - } - return; - } - - *status|=DEC_Subnormal; // have a non-zero subnormal - adjust=etiny-dn->exponent; // calculate digits to remove - if (adjust<=0) { // not out of range; unrounded - // residue can never be non-zero here, except in the Nmin-residue - // case (which is a subnormal result), so can take fast-path here - // it may already be inexact (from setting the coefficient) - if (*status&DEC_Inexact) *status|=DEC_Underflow; - return; - } - - // adjust>0, so need to rescale the result so exponent becomes Etiny - // [this code is similar to that in rescale] - workset=*set; // clone rounding, etc. - workset.digits=dn->digits-adjust; // set requested length - workset.emin-=adjust; // and adjust emin to match - // [note that the latter can be <1, here, similar to Rescale case] - decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status); - decApplyRound(dn, &workset, *residue, status); - - // Use 754 default rule: Underflow is set iff Inexact - // [independent of whether trapped] - if (*status&DEC_Inexact) *status|=DEC_Underflow; - - // if rounded up a 999s case, exponent will be off by one; adjust - // back if so [it will fit, because it was shortened earlier] - if (dn->exponent>etiny) { - dn->digits=decShiftToMost(dn->lsu, dn->digits, 1); - dn->exponent--; // (re)adjust the exponent. - } - - // if rounded to zero, it is by definition clamped... - if (ISZERO(dn)) *status|=DEC_Clamped; - } // decSetSubnormal - -/* ------------------------------------------------------------------ */ -/* decCheckMath - check entry conditions for a math function */ -/* */ -/* This checks the context and the operand */ -/* */ -/* rhs is the operand to check */ -/* set is the context to check */ -/* status is unchanged if both are good */ -/* */ -/* returns non-zero if status is changed, 0 otherwise */ -/* */ -/* Restrictions enforced: */ -/* */ -/* digits, emax, and -emin in the context must be less than */ -/* DEC_MAX_MATH (999999), and A must be within these bounds if */ -/* non-zero. Invalid_operation is set in the status if a */ -/* restriction is violated. */ -/* ------------------------------------------------------------------ */ -static uInt decCheckMath(const decNumber *rhs, decContext *set, - uInt *status) { - uInt save=*status; // record - if (set->digits>DEC_MAX_MATH - || set->emax>DEC_MAX_MATH - || -set->emin>DEC_MAX_MATH) *status|=DEC_Invalid_context; - else if ((rhs->digits>DEC_MAX_MATH - || rhs->exponent+rhs->digits>DEC_MAX_MATH+1 - || rhs->exponent+rhs->digits<2*(1-DEC_MAX_MATH)) - && !ISZERO(rhs)) *status|=DEC_Invalid_operation; - return (*status!=save); - } // decCheckMath - -/* ------------------------------------------------------------------ */ -/* decGetInt -- get integer from a number */ -/* */ -/* dn is the number [which will not be altered] */ -/* */ -/* returns one of: */ -/* BADINT if there is a non-zero fraction */ -/* the converted integer */ -/* BIGEVEN if the integer is even and magnitude > 2*10**9 */ -/* BIGODD if the integer is odd and magnitude > 2*10**9 */ -/* */ -/* This checks and gets a whole number from the input decNumber. */ -/* The sign can be determined from dn by the caller when BIGEVEN or */ -/* BIGODD is returned. */ -/* ------------------------------------------------------------------ */ -static Int decGetInt(const decNumber *dn) { - Int theInt; // result accumulator - const Unit *up; // work - Int got; // digits (real or not) processed - Int ilength=dn->digits+dn->exponent; // integral length - Flag neg=decNumberIsNegative(dn); // 1 if -ve - - // The number must be an integer that fits in 10 digits - // Assert, here, that 10 is enough for any rescale Etiny - #if DEC_MAX_EMAX > 999999999 - #error GetInt may need updating [for Emax] - #endif - #if DEC_MIN_EMIN < -999999999 - #error GetInt may need updating [for Emin] - #endif - if (ISZERO(dn)) return 0; // zeros are OK, with any exponent - - up=dn->lsu; // ready for lsu - theInt=0; // ready to accumulate - if (dn->exponent>=0) { // relatively easy - // no fractional part [usual]; allow for positive exponent - got=dn->exponent; - } - else { // -ve exponent; some fractional part to check and discard - Int count=-dn->exponent; // digits to discard - // spin up whole units until reach the Unit with the unit digit - for (; count>=DECDPUN; up++) { - if (*up!=0) return BADINT; // non-zero Unit to discard - count-=DECDPUN; - } - if (count==0) got=0; // [a multiple of DECDPUN] - else { // [not multiple of DECDPUN] - Int rem; // work - // slice off fraction digits and check for non-zero - #if DECDPUN<=4 - theInt=QUOT10(*up, count); - rem=*up-theInt*powers[count]; - #else - rem=*up%powers[count]; // slice off discards - theInt=*up/powers[count]; - #endif - if (rem!=0) return BADINT; // non-zero fraction - // it looks good - got=DECDPUN-count; // number of digits so far - up++; // ready for next - } - } - // now it's known there's no fractional part - - // tricky code now, to accumulate up to 9.3 digits - if (got==0) {theInt=*up; got+=DECDPUN; up++;} // ensure lsu is there - - if (ilength<11) { - Int save=theInt; - // collect any remaining unit(s) - for (; got<ilength; up++) { - theInt+=*up*powers[got]; - got+=DECDPUN; - } - if (ilength==10) { // need to check for wrap - if (theInt/(Int)powers[got-DECDPUN]!=(Int)*(up-1)) ilength=11; - // [that test also disallows the BADINT result case] - else if (neg && theInt>1999999997) ilength=11; - else if (!neg && theInt>999999999) ilength=11; - if (ilength==11) theInt=save; // restore correct low bit - } - } - - if (ilength>10) { // too big - if (theInt&1) return BIGODD; // bottom bit 1 - return BIGEVEN; // bottom bit 0 - } - - if (neg) theInt=-theInt; // apply sign - return theInt; - } // decGetInt - -/* ------------------------------------------------------------------ */ -/* decDecap -- decapitate the coefficient of a number */ -/* */ -/* dn is the number to be decapitated */ -/* drop is the number of digits to be removed from the left of dn; */ -/* this must be <= dn->digits (if equal, the coefficient is */ -/* set to 0) */ -/* */ -/* Returns dn; dn->digits will be <= the initial digits less drop */ -/* (after removing drop digits there may be leading zero digits */ -/* which will also be removed). Only dn->lsu and dn->digits change. */ -/* ------------------------------------------------------------------ */ -static decNumber *decDecap(decNumber *dn, Int drop) { - Unit *msu; // -> target cut point - Int cut; // work - if (drop>=dn->digits) { // losing the whole thing - #if DECCHECK - if (drop>dn->digits) - printf("decDecap called with drop>digits [%ld>%ld]\n", - (LI)drop, (LI)dn->digits); - #endif - dn->lsu[0]=0; - dn->digits=1; - return dn; - } - msu=dn->lsu+D2U(dn->digits-drop)-1; // -> likely msu - cut=MSUDIGITS(dn->digits-drop); // digits to be in use in msu - if (cut!=DECDPUN) *msu%=powers[cut]; // clear left digits - // that may have left leading zero digits, so do a proper count... - dn->digits=decGetDigits(dn->lsu, msu-dn->lsu+1); - return dn; - } // decDecap - -/* ------------------------------------------------------------------ */ -/* decBiStr -- compare string with pairwise options */ -/* */ -/* targ is the string to compare */ -/* str1 is one of the strings to compare against (length may be 0) */ -/* str2 is the other; it must be the same length as str1 */ -/* */ -/* returns 1 if strings compare equal, (that is, it is the same */ -/* length as str1 and str2, and each character of targ is in either */ -/* str1 or str2 in the corresponding position), or 0 otherwise */ -/* */ -/* This is used for generic caseless compare, including the awkward */ -/* case of the Turkish dotted and dotless Is. Use as (for example): */ -/* if (decBiStr(test, "mike", "MIKE")) ... */ -/* ------------------------------------------------------------------ */ -static Flag decBiStr(const char *targ, const char *str1, const char *str2) { - for (;;targ++, str1++, str2++) { - if (*targ!=*str1 && *targ!=*str2) return 0; - // *targ has a match in one (or both, if terminator) - if (*targ=='\0') break; - } // forever - return 1; - } // decBiStr - -/* ------------------------------------------------------------------ */ -/* decNaNs -- handle NaN operand or operands */ -/* */ -/* res is the result number */ -/* lhs is the first operand */ -/* rhs is the second operand, or NULL if none */ -/* context is used to limit payload length */ -/* status contains the current status */ -/* returns res in case convenient */ -/* */ -/* Called when one or both operands is a NaN, and propagates the */ -/* appropriate result to res. When an sNaN is found, it is changed */ -/* to a qNaN and Invalid operation is set. */ -/* ------------------------------------------------------------------ */ -static decNumber * decNaNs(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set, - uInt *status) { - // This decision tree ends up with LHS being the source pointer, - // and status updated if need be - if (lhs->bits & DECSNAN) - *status|=DEC_Invalid_operation | DEC_sNaN; - else if (rhs==NULL); - else if (rhs->bits & DECSNAN) { - lhs=rhs; - *status|=DEC_Invalid_operation | DEC_sNaN; - } - else if (lhs->bits & DECNAN); - else lhs=rhs; - - // propagate the payload - if (lhs->digits<=set->digits) decNumberCopy(res, lhs); // easy - else { // too long - const Unit *ul; - Unit *ur, *uresp1; - // copy safe number of units, then decapitate - res->bits=lhs->bits; // need sign etc. - uresp1=res->lsu+D2U(set->digits); - for (ur=res->lsu, ul=lhs->lsu; ur<uresp1; ur++, ul++) *ur=*ul; - res->digits=D2U(set->digits)*DECDPUN; - // maybe still too long - if (res->digits>set->digits) decDecap(res, res->digits-set->digits); - } - - res->bits&=~DECSNAN; // convert any sNaN to NaN, while - res->bits|=DECNAN; // .. preserving sign - res->exponent=0; // clean exponent - // [coefficient was copied/decapitated] - return res; - } // decNaNs - -/* ------------------------------------------------------------------ */ -/* decStatus -- apply non-zero status */ -/* */ -/* dn is the number to set if error */ -/* status contains the current status (not yet in context) */ -/* set is the context */ -/* */ -/* If the status is an error status, the number is set to a NaN, */ -/* unless the error was an overflow, divide-by-zero, or underflow, */ -/* in which case the number will have already been set. */ -/* */ -/* The context status is then updated with the new status. Note that */ -/* this may raise a signal, so control may never return from this */ -/* routine (hence resources must be recovered before it is called). */ -/* ------------------------------------------------------------------ */ -static void decStatus(decNumber *dn, uInt status, decContext *set) { - if (status & DEC_NaNs) { // error status -> NaN - // if cause was an sNaN, clear and propagate [NaN is already set up] - if (status & DEC_sNaN) status&=~DEC_sNaN; - else { - decNumberZero(dn); // other error: clean throughout - dn->bits=DECNAN; // and make a quiet NaN - } - } - decContextSetStatus(set, status); // [may not return] - return; - } // decStatus - -/* ------------------------------------------------------------------ */ -/* decGetDigits -- count digits in a Units array */ -/* */ -/* uar is the Unit array holding the number (this is often an */ -/* accumulator of some sort) */ -/* len is the length of the array in units [>=1] */ -/* */ -/* returns the number of (significant) digits in the array */ -/* */ -/* All leading zeros are excluded, except the last if the array has */ -/* only zero Units. */ -/* ------------------------------------------------------------------ */ -// This may be called twice during some operations. -static Int decGetDigits(Unit *uar, Int len) { - Unit *up=uar+(len-1); // -> msu - Int digits=(len-1)*DECDPUN+1; // possible digits excluding msu - #if DECDPUN>4 - uInt const *pow; // work - #endif - // (at least 1 in final msu) - #if DECCHECK - if (len<1) printf("decGetDigits called with len<1 [%ld]\n", (LI)len); - #endif - - for (; up>=uar; up--) { - if (*up==0) { // unit is all 0s - if (digits==1) break; // a zero has one digit - digits-=DECDPUN; // adjust for 0 unit - continue;} - // found the first (most significant) non-zero Unit - #if DECDPUN>1 // not done yet - if (*up<10) break; // is 1-9 - digits++; - #if DECDPUN>2 // not done yet - if (*up<100) break; // is 10-99 - digits++; - #if DECDPUN>3 // not done yet - if (*up<1000) break; // is 100-999 - digits++; - #if DECDPUN>4 // count the rest ... - for (pow=&powers[4]; *up>=*pow; pow++) digits++; - #endif - #endif - #endif - #endif - break; - } // up - return digits; - } // decGetDigits - -#if DECTRACE | DECCHECK -/* ------------------------------------------------------------------ */ -/* decNumberShow -- display a number [debug aid] */ -/* dn is the number to show */ -/* */ -/* Shows: sign, exponent, coefficient (msu first), digits */ -/* or: sign, special-value */ -/* ------------------------------------------------------------------ */ -// this is public so other modules can use it -void decNumberShow(const decNumber *dn) { - const Unit *up; // work - uInt u, d; // .. - Int cut; // .. - char isign='+'; // main sign - if (dn==NULL) { - printf("NULL\n"); - return;} - if (decNumberIsNegative(dn)) isign='-'; - printf(" >> %c ", isign); - if (dn->bits&DECSPECIAL) { // Is a special value - if (decNumberIsInfinite(dn)) printf("Infinity"); - else { // a NaN - if (dn->bits&DECSNAN) printf("sNaN"); // signalling NaN - else printf("NaN"); - } - // if coefficient and exponent are 0, no more to do - if (dn->exponent==0 && dn->digits==1 && *dn->lsu==0) { - printf("\n"); - return;} - // drop through to report other information - printf(" "); - } - - // now carefully display the coefficient - up=dn->lsu+D2U(dn->digits)-1; // msu - printf("%ld", (LI)*up); - for (up=up-1; up>=dn->lsu; up--) { - u=*up; - printf(":"); - for (cut=DECDPUN-1; cut>=0; cut--) { - d=u/powers[cut]; - u-=d*powers[cut]; - printf("%ld", (LI)d); - } // cut - } // up - if (dn->exponent!=0) { - char esign='+'; - if (dn->exponent<0) esign='-'; - printf(" E%c%ld", esign, (LI)abs(dn->exponent)); - } - printf(" [%ld]\n", (LI)dn->digits); - } // decNumberShow -#endif - -#if DECTRACE || DECCHECK -/* ------------------------------------------------------------------ */ -/* decDumpAr -- display a unit array [debug/check aid] */ -/* name is a single-character tag name */ -/* ar is the array to display */ -/* len is the length of the array in Units */ -/* ------------------------------------------------------------------ */ -static void decDumpAr(char name, const Unit *ar, Int len) { - Int i; - const char *spec; - #if DECDPUN==9 - spec="%09d "; - #elif DECDPUN==8 - spec="%08d "; - #elif DECDPUN==7 - spec="%07d "; - #elif DECDPUN==6 - spec="%06d "; - #elif DECDPUN==5 - spec="%05d "; - #elif DECDPUN==4 - spec="%04d "; - #elif DECDPUN==3 - spec="%03d "; - #elif DECDPUN==2 - spec="%02d "; - #else - spec="%d "; - #endif - printf(" :%c: ", name); - for (i=len-1; i>=0; i--) { - if (i==len-1) printf("%ld ", (LI)ar[i]); - else printf(spec, ar[i]); - } - printf("\n"); - return;} -#endif - -#if DECCHECK -/* ------------------------------------------------------------------ */ -/* decCheckOperands -- check operand(s) to a routine */ -/* res is the result structure (not checked; it will be set to */ -/* quiet NaN if error found (and it is not NULL)) */ -/* lhs is the first operand (may be DECUNRESU) */ -/* rhs is the second (may be DECUNUSED) */ -/* set is the context (may be DECUNCONT) */ -/* returns 0 if both operands, and the context are clean, or 1 */ -/* otherwise (in which case the context will show an error, */ -/* unless NULL). Note that res is not cleaned; caller should */ -/* handle this so res=NULL case is safe. */ -/* The caller is expected to abandon immediately if 1 is returned. */ -/* ------------------------------------------------------------------ */ -static Flag decCheckOperands(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - Flag bad=0; - if (set==NULL) { // oops; hopeless - #if DECTRACE || DECVERB - printf("Reference to context is NULL.\n"); - #endif - bad=1; - return 1;} - else if (set!=DECUNCONT - && (set->digits<1 || set->round>=DEC_ROUND_MAX)) { - bad=1; - #if DECTRACE || DECVERB - printf("Bad context [digits=%ld round=%ld].\n", - (LI)set->digits, (LI)set->round); - #endif - } - else { - if (res==NULL) { - bad=1; - #if DECTRACE - // this one not DECVERB as standard tests include NULL - printf("Reference to result is NULL.\n"); - #endif - } - if (!bad && lhs!=DECUNUSED) bad=(decCheckNumber(lhs)); - if (!bad && rhs!=DECUNUSED) bad=(decCheckNumber(rhs)); - } - if (bad) { - if (set!=DECUNCONT) decContextSetStatus(set, DEC_Invalid_operation); - if (res!=DECUNRESU && res!=NULL) { - decNumberZero(res); - res->bits=DECNAN; // qNaN - } - } - return bad; - } // decCheckOperands - -/* ------------------------------------------------------------------ */ -/* decCheckNumber -- check a number */ -/* dn is the number to check */ -/* returns 0 if the number is clean, or 1 otherwise */ -/* */ -/* The number is considered valid if it could be a result from some */ -/* operation in some valid context. */ -/* ------------------------------------------------------------------ */ -static Flag decCheckNumber(const decNumber *dn) { - const Unit *up; // work - uInt maxuint; // .. - Int ae, d, digits; // .. - Int emin, emax; // .. - - if (dn==NULL) { // hopeless - #if DECTRACE - // this one not DECVERB as standard tests include NULL - printf("Reference to decNumber is NULL.\n"); - #endif - return 1;} - - // check special values - if (dn->bits & DECSPECIAL) { - if (dn->exponent!=0) { - #if DECTRACE || DECVERB - printf("Exponent %ld (not 0) for a special value [%02x].\n", - (LI)dn->exponent, dn->bits); - #endif - return 1;} - - // 2003.09.08: NaNs may now have coefficients, so next tests Inf only - if (decNumberIsInfinite(dn)) { - if (dn->digits!=1) { - #if DECTRACE || DECVERB - printf("Digits %ld (not 1) for an infinity.\n", (LI)dn->digits); - #endif - return 1;} - if (*dn->lsu!=0) { - #if DECTRACE || DECVERB - printf("LSU %ld (not 0) for an infinity.\n", (LI)*dn->lsu); - #endif - decDumpAr('I', dn->lsu, D2U(dn->digits)); - return 1;} - } // Inf - // 2002.12.26: negative NaNs can now appear through proposed IEEE - // concrete formats (decimal64, etc.). - return 0; - } - - // check the coefficient - if (dn->digits<1 || dn->digits>DECNUMMAXP) { - #if DECTRACE || DECVERB - printf("Digits %ld in number.\n", (LI)dn->digits); - #endif - return 1;} - - d=dn->digits; - - for (up=dn->lsu; d>0; up++) { - if (d>DECDPUN) maxuint=DECDPUNMAX; - else { // reached the msu - maxuint=powers[d]-1; - if (dn->digits>1 && *up<powers[d-1]) { - #if DECTRACE || DECVERB - printf("Leading 0 in number.\n"); - decNumberShow(dn); - #endif - return 1;} - } - if (*up>maxuint) { - #if DECTRACE || DECVERB - printf("Bad Unit [%08lx] in %ld-digit number at offset %ld [maxuint %ld].\n", - (LI)*up, (LI)dn->digits, (LI)(up-dn->lsu), (LI)maxuint); - #endif - return 1;} - d-=DECDPUN; - } - - // check the exponent. Note that input operands can have exponents - // which are out of the set->emin/set->emax and set->digits range - // (just as they can have more digits than set->digits). - ae=dn->exponent+dn->digits-1; // adjusted exponent - emax=DECNUMMAXE; - emin=DECNUMMINE; - digits=DECNUMMAXP; - if (ae<emin-(digits-1)) { - #if DECTRACE || DECVERB - printf("Adjusted exponent underflow [%ld].\n", (LI)ae); - decNumberShow(dn); - #endif - return 1;} - if (ae>+emax) { - #if DECTRACE || DECVERB - printf("Adjusted exponent overflow [%ld].\n", (LI)ae); - decNumberShow(dn); - #endif - return 1;} - - return 0; // it's OK - } // decCheckNumber - -/* ------------------------------------------------------------------ */ -/* decCheckInexact -- check a normal finite inexact result has digits */ -/* dn is the number to check */ -/* set is the context (for status and precision) */ -/* sets Invalid operation, etc., if some digits are missing */ -/* [this check is not made for DECSUBSET compilation or when */ -/* subnormal is not set] */ -/* ------------------------------------------------------------------ */ -static void decCheckInexact(const decNumber *dn, decContext *set) { - #if !DECSUBSET && DECEXTFLAG - if ((set->status & (DEC_Inexact|DEC_Subnormal))==DEC_Inexact - && (set->digits!=dn->digits) && !(dn->bits & DECSPECIAL)) { - #if DECTRACE || DECVERB - printf("Insufficient digits [%ld] on normal Inexact result.\n", - (LI)dn->digits); - decNumberShow(dn); - #endif - decContextSetStatus(set, DEC_Invalid_operation); - } - #else - // next is a noop for quiet compiler - if (dn!=NULL && dn->digits==0) set->status|=DEC_Invalid_operation; - #endif - return; - } // decCheckInexact -#endif - -#if DECALLOC -#undef malloc -#undef free -/* ------------------------------------------------------------------ */ -/* decMalloc -- accountable allocation routine */ -/* n is the number of bytes to allocate */ -/* */ -/* Semantics is the same as the stdlib malloc routine, but bytes */ -/* allocated are accounted for globally, and corruption fences are */ -/* added before and after the 'actual' storage. */ -/* ------------------------------------------------------------------ */ -/* This routine allocates storage with an extra twelve bytes; 8 are */ -/* at the start and hold: */ -/* 0-3 the original length requested */ -/* 4-7 buffer corruption detection fence (DECFENCE, x4) */ -/* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */ -/* ------------------------------------------------------------------ */ -static void *decMalloc(size_t n) { - uInt size=n+12; // true size - void *alloc; // -> allocated storage - uByte *b, *b0; // work - uInt uiwork; // for macros - - alloc=malloc(size); // -> allocated storage - if (alloc==NULL) return NULL; // out of strorage - b0=(uByte *)alloc; // as bytes - decAllocBytes+=n; // account for storage - UBFROMUI(alloc, n); // save n - // printf(" alloc ++ dAB: %ld (%ld)\n", (LI)decAllocBytes, (LI)n); - for (b=b0+4; b<b0+8; b++) *b=DECFENCE; - for (b=b0+n+8; b<b0+n+12; b++) *b=DECFENCE; - return b0+8; // -> play area - } // decMalloc - -/* ------------------------------------------------------------------ */ -/* decFree -- accountable free routine */ -/* alloc is the storage to free */ -/* */ -/* Semantics is the same as the stdlib malloc routine, except that */ -/* the global storage accounting is updated and the fences are */ -/* checked to ensure that no routine has written 'out of bounds'. */ -/* ------------------------------------------------------------------ */ -/* This routine first checks that the fences have not been corrupted. */ -/* It then frees the storage using the 'truw' storage address (that */ -/* is, offset by 8). */ -/* ------------------------------------------------------------------ */ -static void decFree(void *alloc) { - uInt n; // original length - uByte *b, *b0; // work - uInt uiwork; // for macros - - if (alloc==NULL) return; // allowed; it's a nop - b0=(uByte *)alloc; // as bytes - b0-=8; // -> true start of storage - n=UBTOUI(b0); // lift length - for (b=b0+4; b<b0+8; b++) if (*b!=DECFENCE) - printf("=== Corrupt byte [%02x] at offset %d from %ld ===\n", *b, - b-b0-8, (LI)b0); - for (b=b0+n+8; b<b0+n+12; b++) if (*b!=DECFENCE) - printf("=== Corrupt byte [%02x] at offset +%d from %ld, n=%ld ===\n", *b, - b-b0-8, (LI)b0, (LI)n); - free(b0); // drop the storage - decAllocBytes-=n; // account for storage - // printf(" free -- dAB: %d (%d)\n", decAllocBytes, -n); - } // decFree -#define malloc(a) decMalloc(a) -#define free(a) decFree(a) -#endif
src/decNumber/decNumber.h
@@ -1,182 +0,0 @@-/* ------------------------------------------------------------------ */ -/* Decimal Number arithmetic module header */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is called decNumber.pdf. This document is */ -/* available, together with arithmetic and format specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ - -#if !defined(DECNUMBER) - #define DECNUMBER - #define DECNAME "decNumber" /* Short name */ - #define DECFULLNAME "Decimal Number Module" /* Verbose name */ - #define DECAUTHOR "Mike Cowlishaw" /* Who to blame */ - - #if !defined(DECCONTEXT) - #include "decContext.h" - #endif - - /* Bit settings for decNumber.bits */ - #define DECNEG 0x80 /* Sign; 1=negative, 0=positive or zero */ - #define DECINF 0x40 /* 1=Infinity */ - #define DECNAN 0x20 /* 1=NaN */ - #define DECSNAN 0x10 /* 1=sNaN */ - /* The remaining bits are reserved; they must be 0 */ - #define DECSPECIAL (DECINF|DECNAN|DECSNAN) /* any special value */ - - /* Define the decNumber data structure. The size and shape of the */ - /* units array in the structure is determined by the following */ - /* constant. This must not be changed without recompiling the */ - /* decNumber library modules. */ - - #define DECDPUN 3 /* DECimal Digits Per UNit [must be >0 */ - /* and <10; 3 or powers of 2 are best]. */ - - /* DECNUMDIGITS is the default number of digits that can be held in */ - /* the structure. If undefined, 1 is assumed and it is assumed */ - /* that the structure will be immediately followed by extra space, */ - /* as required. DECNUMDIGITS is always >0. */ - #if !defined(DECNUMDIGITS) - #define DECNUMDIGITS 1 - #endif - - /* The size (integer data type) of each unit is determined by the */ - /* number of digits it will hold. */ - #if DECDPUN<=2 - #define decNumberUnit uint8_t - #elif DECDPUN<=4 - #define decNumberUnit uint16_t - #else - #define decNumberUnit uint32_t - #endif - /* The number of units needed is ceil(DECNUMDIGITS/DECDPUN) */ - #define DECNUMUNITS ((DECNUMDIGITS+DECDPUN-1)/DECDPUN) - - /* The data structure... */ - typedef struct { - int32_t digits; /* Count of digits in the coefficient; >0 */ - int32_t exponent; /* Unadjusted exponent, unbiased, in */ - /* range: -1999999997 through 999999999 */ - uint8_t bits; /* Indicator bits (see above) */ - /* Coefficient, from least significant unit */ - decNumberUnit lsu[DECNUMUNITS]; - } decNumber; - - /* Notes: */ - /* 1. If digits is > DECDPUN then there will one or more */ - /* decNumberUnits immediately following the first element of lsu.*/ - /* These contain the remaining (more significant) digits of the */ - /* number, and may be in the lsu array, or may be guaranteed by */ - /* some other mechanism (such as being contained in another */ - /* structure, or being overlaid on dynamically allocated */ - /* storage). */ - /* */ - /* Each integer of the coefficient (except potentially the last) */ - /* contains DECDPUN digits (e.g., a value in the range 0 through */ - /* 99999999 if DECDPUN is 8, or 0 through 999 if DECDPUN is 3). */ - /* */ - /* 2. A decNumber converted to a string may need up to digits+14 */ - /* characters. The worst cases (non-exponential and exponential */ - /* formats) are -0.00000{9...}# and -9.{9...}E+999999999# */ - /* (where # is '\0') */ - - - /* ---------------------------------------------------------------- */ - /* decNumber public functions and macros */ - /* ---------------------------------------------------------------- */ - /* Conversions */ - decNumber * decNumberFromInt32(decNumber *, int32_t); - decNumber * decNumberFromUInt32(decNumber *, uint32_t); - decNumber * decNumberFromString(decNumber *, const char *, decContext *); - char * decNumberToString(const decNumber *, char *); - char * decNumberToEngString(const decNumber *, char *); - uint32_t decNumberToUInt32(const decNumber *, decContext *); - int32_t decNumberToInt32(const decNumber *, decContext *); - uint8_t * decNumberGetBCD(const decNumber *, uint8_t *); - decNumber * decNumberSetBCD(decNumber *, const uint8_t *, uint32_t); - - /* Operators and elementary functions */ - decNumber * decNumberAbs(decNumber *, const decNumber *, decContext *); - decNumber * decNumberAdd(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberAnd(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberCompare(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberCompareSignal(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberCompareTotal(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberCompareTotalMag(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberDivide(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberDivideInteger(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberExp(decNumber *, const decNumber *, decContext *); - decNumber * decNumberFMA(decNumber *, const decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberInvert(decNumber *, const decNumber *, decContext *); - decNumber * decNumberLn(decNumber *, const decNumber *, decContext *); - decNumber * decNumberLogB(decNumber *, const decNumber *, decContext *); - decNumber * decNumberLog10(decNumber *, const decNumber *, decContext *); - decNumber * decNumberMax(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberMaxMag(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberMin(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberMinMag(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberMinus(decNumber *, const decNumber *, decContext *); - decNumber * decNumberMultiply(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberNormalize(decNumber *, const decNumber *, decContext *); - decNumber * decNumberOr(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberPlus(decNumber *, const decNumber *, decContext *); - decNumber * decNumberPower(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberQuantize(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberReduce(decNumber *, const decNumber *, decContext *); - decNumber * decNumberRemainder(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberRemainderNear(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberRescale(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberRotate(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberSameQuantum(decNumber *, const decNumber *, const decNumber *); - decNumber * decNumberScaleB(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberShift(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberSquareRoot(decNumber *, const decNumber *, decContext *); - decNumber * decNumberSubtract(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberToIntegralExact(decNumber *, const decNumber *, decContext *); - decNumber * decNumberToIntegralValue(decNumber *, const decNumber *, decContext *); - decNumber * decNumberXor(decNumber *, const decNumber *, const decNumber *, decContext *); - - /* Utilities */ - enum decClass decNumberClass(const decNumber *, decContext *); - const char * decNumberClassToString(enum decClass); - decNumber * decNumberCopy(decNumber *, const decNumber *); - decNumber * decNumberCopyAbs(decNumber *, const decNumber *); - decNumber * decNumberCopyNegate(decNumber *, const decNumber *); - decNumber * decNumberCopySign(decNumber *, const decNumber *, const decNumber *); - decNumber * decNumberNextMinus(decNumber *, const decNumber *, decContext *); - decNumber * decNumberNextPlus(decNumber *, const decNumber *, decContext *); - decNumber * decNumberNextToward(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberTrim(decNumber *); - const char * decNumberVersion(void); - decNumber * decNumberZero(decNumber *); - - /* Functions for testing decNumbers (normality depends on context) */ - int32_t decNumberIsNormal(const decNumber *, decContext *); - int32_t decNumberIsSubnormal(const decNumber *, decContext *); - - /* Macros for testing decNumber *dn */ - #define decNumberIsCanonical(dn) (1) /* All decNumbers are saintly */ - #define decNumberIsFinite(dn) (((dn)->bits&DECSPECIAL)==0) - #define decNumberIsInfinite(dn) (((dn)->bits&DECINF)!=0) - #define decNumberIsNaN(dn) (((dn)->bits&(DECNAN|DECSNAN))!=0) - #define decNumberIsNegative(dn) (((dn)->bits&DECNEG)!=0) - #define decNumberIsQNaN(dn) (((dn)->bits&(DECNAN))!=0) - #define decNumberIsSNaN(dn) (((dn)->bits&(DECSNAN))!=0) - #define decNumberIsSpecial(dn) (((dn)->bits&DECSPECIAL)!=0) - #define decNumberIsZero(dn) (*(dn)->lsu==0 \ - && (dn)->digits==1 \ - && (((dn)->bits&DECSPECIAL)==0)) - #define decNumberRadix(dn) (10) - -#endif
src/decNumber/decNumberLocal.h
@@ -1,757 +0,0 @@-/* ------------------------------------------------------------------ */ -/* decNumber package local type, tuning, and macro definitions */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is called decNumber.pdf. This document is */ -/* available, together with arithmetic and format specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ -/* This header file is included by all modules in the decNumber */ -/* library, and contains local type definitions, tuning parameters, */ -/* etc. It should not need to be used by application programs. */ -/* decNumber.h or one of decDouble (etc.) must be included first. */ -/* ------------------------------------------------------------------ */ - -#if !defined(DECNUMBERLOC) - #define DECNUMBERLOC - #define DECVERSION "decNumber 3.68" /* Package Version [16 max.] */ - #define DECNLAUTHOR "Mike Cowlishaw" /* Who to blame */ - - #include <stdlib.h> /* for abs */ - #include <string.h> /* for memset, strcpy */ - - /* Conditional code flag -- set this to match hardware platform */ - #if !defined(DECLITEND) - #define DECLITEND 1 /* 1=little-endian, 0=big-endian */ - #endif - - /* Conditional code flag -- set this to 1 for best performance */ - #if !defined(DECUSE64) - #define DECUSE64 1 /* 1=use int64s, 0=int32 & smaller only */ - #endif - - /* Conditional code flag -- set this to 0 to exclude printf calls */ - #if !defined(DECPRINT) - #define DECPRINT 1 /* 1=allow printf calls; 0=no printf */ - #endif - - /* Conditional check flags -- set these to 0 for best performance */ - #if !defined(DECCHECK) - #define DECCHECK 0 /* 1 to enable robust checking */ - #endif - #if !defined(DECALLOC) - #define DECALLOC 0 /* 1 to enable memory accounting */ - #endif - #if !defined(DECTRACE) - #define DECTRACE 0 /* 1 to trace certain internals, etc. */ - #endif - - /* Tuning parameter for decNumber (arbitrary precision) module */ - #if !defined(DECBUFFER) - #define DECBUFFER 36 /* Size basis for local buffers. This */ - /* should be a common maximum precision */ - /* rounded up to a multiple of 4; must */ - /* be zero or positive. */ - #endif - - - /* ---------------------------------------------------------------- */ - /* Check parameter dependencies */ - /* ---------------------------------------------------------------- */ - #if DECCHECK & !DECPRINT - #error DECCHECK needs DECPRINT to be useful - #endif - #if DECALLOC & !DECPRINT - #error DECALLOC needs DECPRINT to be useful - #endif - #if DECTRACE & !DECPRINT - #error DECTRACE needs DECPRINT to be useful - #endif - - /* ---------------------------------------------------------------- */ - /* Definitions for all modules (general-purpose) */ - /* ---------------------------------------------------------------- */ - - /* Local names for common types -- for safety, decNumber modules do */ - /* not use int or long directly. */ - #define Flag uint8_t - #define Byte int8_t - #define uByte uint8_t - #define Short int16_t - #define uShort uint16_t - #define Int int32_t - #define uInt uint32_t - #define Unit decNumberUnit - #if DECUSE64 - #define Long int64_t - #define uLong uint64_t - #endif - - /* Development-use definitions */ - typedef long int LI; /* for printf arguments only */ - #define DECNOINT 0 /* 1 to check no internal use of 'int' */ - /* or stdint types */ - #if DECNOINT - /* if these interfere with your C includes, do not set DECNOINT */ - #define int ? /* enable to ensure that plain C 'int' */ - #define long ?? /* .. or 'long' types are not used */ - #endif - - /* Shared lookup tables */ - extern const uByte DECSTICKYTAB[10]; /* re-round digits if sticky */ - extern const uInt DECPOWERS[10]; /* powers of ten table */ - /* The following are included from decDPD.h */ - extern const uShort DPD2BIN[1024]; /* DPD -> 0-999 */ - extern const uShort BIN2DPD[1000]; /* 0-999 -> DPD */ - extern const uInt DPD2BINK[1024]; /* DPD -> 0-999000 */ - extern const uInt DPD2BINM[1024]; /* DPD -> 0-999000000 */ - extern const uByte DPD2BCD8[4096]; /* DPD -> ddd + len */ - extern const uByte BIN2BCD8[4000]; /* 0-999 -> ddd + len */ - extern const uShort BCD2DPD[2458]; /* 0-0x999 -> DPD (0x999=2457)*/ - - /* LONGMUL32HI -- set w=(u*v)>>32, where w, u, and v are uInts */ - /* (that is, sets w to be the high-order word of the 64-bit result; */ - /* the low-order word is simply u*v.) */ - /* This version is derived from Knuth via Hacker's Delight; */ - /* it seems to optimize better than some others tried */ - #define LONGMUL32HI(w, u, v) { \ - uInt u0, u1, v0, v1, w0, w1, w2, t; \ - u0=u & 0xffff; u1=u>>16; \ - v0=v & 0xffff; v1=v>>16; \ - w0=u0*v0; \ - t=u1*v0 + (w0>>16); \ - w1=t & 0xffff; w2=t>>16; \ - w1=u0*v1 + w1; \ - (w)=u1*v1 + w2 + (w1>>16);} - - /* ROUNDUP -- round an integer up to a multiple of n */ - #define ROUNDUP(i, n) ((((i)+(n)-1)/n)*n) - #define ROUNDUP4(i) (((i)+3)&~3) /* special for n=4 */ - - /* ROUNDDOWN -- round an integer down to a multiple of n */ - #define ROUNDDOWN(i, n) (((i)/n)*n) - #define ROUNDDOWN4(i) ((i)&~3) /* special for n=4 */ - - /* References to multi-byte sequences under different sizes; these */ - /* require locally declared variables, but do not violate strict */ - /* aliasing or alignment (as did the UINTAT simple cast to uInt). */ - /* Variables needed are uswork, uiwork, etc. [so do not use at same */ - /* level in an expression, e.g., UBTOUI(x)==UBTOUI(y) may fail]. */ - - /* Return a uInt, etc., from bytes starting at a char* or uByte* */ - #define UBTOUS(b) (memcpy((void *)&uswork, b, 2), uswork) - #define UBTOUI(b) (memcpy((void *)&uiwork, b, 4), uiwork) - - /* Store a uInt, etc., into bytes starting at a char* or uByte*. */ - /* Returns i, evaluated, for convenience; has to use uiwork because */ - /* i may be an expression. */ - #define UBFROMUS(b, i) (uswork=(i), memcpy(b, (void *)&uswork, 2), uswork) - #define UBFROMUI(b, i) (uiwork=(i), memcpy(b, (void *)&uiwork, 4), uiwork) - - /* X10 and X100 -- multiply integer i by 10 or 100 */ - /* [shifts are usually faster than multiply; could be conditional] */ - #define X10(i) (((i)<<1)+((i)<<3)) - #define X100(i) (((i)<<2)+((i)<<5)+((i)<<6)) - - /* MAXI and MINI -- general max & min (not in ANSI) for integers */ - #define MAXI(x,y) ((x)<(y)?(y):(x)) - #define MINI(x,y) ((x)>(y)?(y):(x)) - - /* Useful constants */ - #define BILLION 1000000000 /* 10**9 */ - /* CHARMASK: 0x30303030 for ASCII/UTF8; 0xF0F0F0F0 for EBCDIC */ - #define CHARMASK ((((((((uInt)'0')<<8)+'0')<<8)+'0')<<8)+'0') - - - /* ---------------------------------------------------------------- */ - /* Definitions for arbitary-precision modules (only valid after */ - /* decNumber.h has been included) */ - /* ---------------------------------------------------------------- */ - - /* Limits and constants */ - #define DECNUMMAXP 999999999 /* maximum precision code can handle */ - #define DECNUMMAXE 999999999 /* maximum adjusted exponent ditto */ - #define DECNUMMINE -999999999 /* minimum adjusted exponent ditto */ - #if (DECNUMMAXP != DEC_MAX_DIGITS) - #error Maximum digits mismatch - #endif - #if (DECNUMMAXE != DEC_MAX_EMAX) - #error Maximum exponent mismatch - #endif - #if (DECNUMMINE != DEC_MIN_EMIN) - #error Minimum exponent mismatch - #endif - - /* Set DECDPUNMAX -- the maximum integer that fits in DECDPUN */ - /* digits, and D2UTABLE -- the initializer for the D2U table */ - #if DECDPUN==1 - #define DECDPUNMAX 9 - #define D2UTABLE {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17, \ - 18,19,20,21,22,23,24,25,26,27,28,29,30,31,32, \ - 33,34,35,36,37,38,39,40,41,42,43,44,45,46,47, \ - 48,49} - #elif DECDPUN==2 - #define DECDPUNMAX 99 - #define D2UTABLE {0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10, \ - 11,11,12,12,13,13,14,14,15,15,16,16,17,17,18, \ - 18,19,19,20,20,21,21,22,22,23,23,24,24,25} - #elif DECDPUN==3 - #define DECDPUNMAX 999 - #define D2UTABLE {0,1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7, \ - 8,8,8,9,9,9,10,10,10,11,11,11,12,12,12,13,13, \ - 13,14,14,14,15,15,15,16,16,16,17} - #elif DECDPUN==4 - #define DECDPUNMAX 9999 - #define D2UTABLE {0,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6, \ - 6,6,6,7,7,7,7,8,8,8,8,9,9,9,9,10,10,10,10,11, \ - 11,11,11,12,12,12,12,13} - #elif DECDPUN==5 - #define DECDPUNMAX 99999 - #define D2UTABLE {0,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,5, \ - 5,5,5,5,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,9,9,9, \ - 9,9,10,10,10,10} - #elif DECDPUN==6 - #define DECDPUNMAX 999999 - #define D2UTABLE {0,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4, \ - 4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8, \ - 8,8,8,8,8,9} - #elif DECDPUN==7 - #define DECDPUNMAX 9999999 - #define D2UTABLE {0,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3, \ - 4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,6,7, \ - 7,7,7,7,7,7} - #elif DECDPUN==8 - #define DECDPUNMAX 99999999 - #define D2UTABLE {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3, \ - 3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6, \ - 6,6,6,6,6,7} - #elif DECDPUN==9 - #define DECDPUNMAX 999999999 - #define D2UTABLE {0,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3, \ - 3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5, \ - 5,5,6,6,6,6} - #elif defined(DECDPUN) - #error DECDPUN must be in the range 1-9 - #endif - - /* ----- Shared data (in decNumber.c) ----- */ - /* Public lookup table used by the D2U macro (see below) */ - #define DECMAXD2U 49 - extern const uByte d2utable[DECMAXD2U+1]; - - /* ----- Macros ----- */ - /* ISZERO -- return true if decNumber dn is a zero */ - /* [performance-critical in some situations] */ - #define ISZERO(dn) decNumberIsZero(dn) /* now just a local name */ - - /* D2U -- return the number of Units needed to hold d digits */ - /* (runtime version, with table lookaside for small d) */ - #if DECDPUN==8 - #define D2U(d) ((unsigned)((d)<=DECMAXD2U?d2utable[d]:((d)+7)>>3)) - #elif DECDPUN==4 - #define D2U(d) ((unsigned)((d)<=DECMAXD2U?d2utable[d]:((d)+3)>>2)) - #else - #define D2U(d) ((d)<=DECMAXD2U?d2utable[d]:((d)+DECDPUN-1)/DECDPUN) - #endif - /* SD2U -- static D2U macro (for compile-time calculation) */ - #define SD2U(d) (((d)+DECDPUN-1)/DECDPUN) - - /* MSUDIGITS -- returns digits in msu, from digits, calculated */ - /* using D2U */ - #define MSUDIGITS(d) ((d)-(D2U(d)-1)*DECDPUN) - - /* D2N -- return the number of decNumber structs that would be */ - /* needed to contain that number of digits (and the initial */ - /* decNumber struct) safely. Note that one Unit is included in the */ - /* initial structure. Used for allocating space that is aligned on */ - /* a decNumber struct boundary. */ - #define D2N(d) \ - ((((SD2U(d)-1)*sizeof(Unit))+sizeof(decNumber)*2-1)/sizeof(decNumber)) - - /* TODIGIT -- macro to remove the leading digit from the unsigned */ - /* integer u at column cut (counting from the right, LSD=0) and */ - /* place it as an ASCII character into the character pointed to by */ - /* c. Note that cut must be <= 9, and the maximum value for u is */ - /* 2,000,000,000 (as is needed for negative exponents of */ - /* subnormals). The unsigned integer pow is used as a temporary */ - /* variable. */ - #define TODIGIT(u, cut, c, pow) { \ - *(c)='0'; \ - pow=DECPOWERS[cut]*2; \ - if ((u)>pow) { \ - pow*=4; \ - if ((u)>=pow) {(u)-=pow; *(c)+=8;} \ - pow/=2; \ - if ((u)>=pow) {(u)-=pow; *(c)+=4;} \ - pow/=2; \ - } \ - if ((u)>=pow) {(u)-=pow; *(c)+=2;} \ - pow/=2; \ - if ((u)>=pow) {(u)-=pow; *(c)+=1;} \ - } - - /* ---------------------------------------------------------------- */ - /* Definitions for fixed-precision modules (only valid after */ - /* decSingle.h, decDouble.h, or decQuad.h has been included) */ - /* ---------------------------------------------------------------- */ - - /* bcdnum -- a structure describing a format-independent finite */ - /* number, whose coefficient is a string of bcd8 uBytes */ - typedef struct { - uByte *msd; /* -> most significant digit */ - uByte *lsd; /* -> least ditto */ - uInt sign; /* 0=positive, DECFLOAT_Sign=negative */ - Int exponent; /* Unadjusted signed exponent (q), or */ - /* DECFLOAT_NaN etc. for a special */ - } bcdnum; - - /* Test if exponent or bcdnum exponent must be a special, etc. */ - #define EXPISSPECIAL(exp) ((exp)>=DECFLOAT_MinSp) - #define EXPISINF(exp) (exp==DECFLOAT_Inf) - #define EXPISNAN(exp) (exp==DECFLOAT_qNaN || exp==DECFLOAT_sNaN) - #define NUMISSPECIAL(num) (EXPISSPECIAL((num)->exponent)) - - /* Refer to a 32-bit word or byte in a decFloat (df) by big-endian */ - /* (array) notation (the 0 word or byte contains the sign bit), */ - /* automatically adjusting for endianness; similarly address a word */ - /* in the next-wider format (decFloatWider, or dfw) */ - #define DECWORDS (DECBYTES/4) - #define DECWWORDS (DECWBYTES/4) - #if DECLITEND - #define DFBYTE(df, off) ((df)->bytes[DECBYTES-1-(off)]) - #define DFWORD(df, off) ((df)->words[DECWORDS-1-(off)]) - #define DFWWORD(dfw, off) ((dfw)->words[DECWWORDS-1-(off)]) - #else - #define DFBYTE(df, off) ((df)->bytes[off]) - #define DFWORD(df, off) ((df)->words[off]) - #define DFWWORD(dfw, off) ((dfw)->words[off]) - #endif - - /* Tests for sign or specials, directly on DECFLOATs */ - #define DFISSIGNED(df) ((DFWORD(df, 0)&0x80000000)!=0) - #define DFISSPECIAL(df) ((DFWORD(df, 0)&0x78000000)==0x78000000) - #define DFISINF(df) ((DFWORD(df, 0)&0x7c000000)==0x78000000) - #define DFISNAN(df) ((DFWORD(df, 0)&0x7c000000)==0x7c000000) - #define DFISQNAN(df) ((DFWORD(df, 0)&0x7e000000)==0x7c000000) - #define DFISSNAN(df) ((DFWORD(df, 0)&0x7e000000)==0x7e000000) - - /* Shared lookup tables */ - extern const uInt DECCOMBMSD[64]; /* Combination field -> MSD */ - extern const uInt DECCOMBFROM[48]; /* exp+msd -> Combination */ - - /* Private generic (utility) routine */ - #if DECCHECK || DECTRACE - extern void decShowNum(const bcdnum *, const char *); - #endif - - /* Format-dependent macros and constants */ - #if defined(DECPMAX) - - /* Useful constants */ - #define DECPMAX9 (ROUNDUP(DECPMAX, 9)/9) /* 'Pmax' in 10**9s */ - /* Top words for a zero */ - #define SINGLEZERO 0x22500000 - #define DOUBLEZERO 0x22380000 - #define QUADZERO 0x22080000 - /* [ZEROWORD is defined to be one of these in the DFISZERO macro] */ - - /* Format-dependent common tests: */ - /* DFISZERO -- test for (any) zero */ - /* DFISCCZERO -- test for coefficient continuation being zero */ - /* DFISCC01 -- test for coefficient contains only 0s and 1s */ - /* DFISINT -- test for finite and exponent q=0 */ - /* DFISUINT01 -- test for sign=0, finite, exponent q=0, and */ - /* MSD=0 or 1 */ - /* ZEROWORD is also defined here. */ - /* */ - /* In DFISZERO the first test checks the least-significant word */ - /* (most likely to be non-zero); the penultimate tests MSD and */ - /* DPDs in the signword, and the final test excludes specials and */ - /* MSD>7. DFISINT similarly has to allow for the two forms of */ - /* MSD codes. DFISUINT01 only has to allow for one form of MSD */ - /* code. */ - #if DECPMAX==7 - #define ZEROWORD SINGLEZERO - /* [test macros not needed except for Zero] */ - #define DFISZERO(df) ((DFWORD(df, 0)&0x1c0fffff)==0 \ - && (DFWORD(df, 0)&0x60000000)!=0x60000000) - #elif DECPMAX==16 - #define ZEROWORD DOUBLEZERO - #define DFISZERO(df) ((DFWORD(df, 1)==0 \ - && (DFWORD(df, 0)&0x1c03ffff)==0 \ - && (DFWORD(df, 0)&0x60000000)!=0x60000000)) - #define DFISINT(df) ((DFWORD(df, 0)&0x63fc0000)==0x22380000 \ - ||(DFWORD(df, 0)&0x7bfc0000)==0x6a380000) - #define DFISUINT01(df) ((DFWORD(df, 0)&0xfbfc0000)==0x22380000) - #define DFISCCZERO(df) (DFWORD(df, 1)==0 \ - && (DFWORD(df, 0)&0x0003ffff)==0) - #define DFISCC01(df) ((DFWORD(df, 0)&~0xfffc9124)==0 \ - && (DFWORD(df, 1)&~0x49124491)==0) - #elif DECPMAX==34 - #define ZEROWORD QUADZERO - #define DFISZERO(df) ((DFWORD(df, 3)==0 \ - && DFWORD(df, 2)==0 \ - && DFWORD(df, 1)==0 \ - && (DFWORD(df, 0)&0x1c003fff)==0 \ - && (DFWORD(df, 0)&0x60000000)!=0x60000000)) - #define DFISINT(df) ((DFWORD(df, 0)&0x63ffc000)==0x22080000 \ - ||(DFWORD(df, 0)&0x7bffc000)==0x6a080000) - #define DFISUINT01(df) ((DFWORD(df, 0)&0xfbffc000)==0x22080000) - #define DFISCCZERO(df) (DFWORD(df, 3)==0 \ - && DFWORD(df, 2)==0 \ - && DFWORD(df, 1)==0 \ - && (DFWORD(df, 0)&0x00003fff)==0) - - #define DFISCC01(df) ((DFWORD(df, 0)&~0xffffc912)==0 \ - && (DFWORD(df, 1)&~0x44912449)==0 \ - && (DFWORD(df, 2)&~0x12449124)==0 \ - && (DFWORD(df, 3)&~0x49124491)==0) - #endif - - /* Macros to test if a certain 10 bits of a uInt or pair of uInts */ - /* are a canonical declet [higher or lower bits are ignored]. */ - /* declet is at offset 0 (from the right) in a uInt: */ - #define CANONDPD(dpd) (((dpd)&0x300)==0 || ((dpd)&0x6e)!=0x6e) - /* declet is at offset k (a multiple of 2) in a uInt: */ - #define CANONDPDOFF(dpd, k) (((dpd)&(0x300<<(k)))==0 \ - || ((dpd)&(((uInt)0x6e)<<(k)))!=(((uInt)0x6e)<<(k))) - /* declet is at offset k (a multiple of 2) in a pair of uInts: */ - /* [the top 2 bits will always be in the more-significant uInt] */ - #define CANONDPDTWO(hi, lo, k) (((hi)&(0x300>>(32-(k))))==0 \ - || ((hi)&(0x6e>>(32-(k))))!=(0x6e>>(32-(k))) \ - || ((lo)&(((uInt)0x6e)<<(k)))!=(((uInt)0x6e)<<(k))) - - /* Macro to test whether a full-length (length DECPMAX) BCD8 */ - /* coefficient, starting at uByte u, is all zeros */ - /* Test just the LSWord first, then the remainder as a sequence */ - /* of tests in order to avoid same-level use of UBTOUI */ - #if DECPMAX==7 - #define ISCOEFFZERO(u) ( \ - UBTOUI((u)+DECPMAX-4)==0 \ - && UBTOUS((u)+DECPMAX-6)==0 \ - && *(u)==0) - #elif DECPMAX==16 - #define ISCOEFFZERO(u) ( \ - UBTOUI((u)+DECPMAX-4)==0 \ - && UBTOUI((u)+DECPMAX-8)==0 \ - && UBTOUI((u)+DECPMAX-12)==0 \ - && UBTOUI(u)==0) - #elif DECPMAX==34 - #define ISCOEFFZERO(u) ( \ - UBTOUI((u)+DECPMAX-4)==0 \ - && UBTOUI((u)+DECPMAX-8)==0 \ - && UBTOUI((u)+DECPMAX-12)==0 \ - && UBTOUI((u)+DECPMAX-16)==0 \ - && UBTOUI((u)+DECPMAX-20)==0 \ - && UBTOUI((u)+DECPMAX-24)==0 \ - && UBTOUI((u)+DECPMAX-28)==0 \ - && UBTOUI((u)+DECPMAX-32)==0 \ - && UBTOUS(u)==0) - #endif - - /* Macros and masks for the sign, exponent continuation, and MSD */ - /* Get the sign as DECFLOAT_Sign or 0 */ - #define GETSIGN(df) (DFWORD(df, 0)&0x80000000) - /* Get the exponent continuation from a decFloat *df as an Int */ - #define GETECON(df) ((Int)((DFWORD((df), 0)&0x03ffffff)>>(32-6-DECECONL))) - /* Ditto, from the next-wider format */ - #define GETWECON(df) ((Int)((DFWWORD((df), 0)&0x03ffffff)>>(32-6-DECWECONL))) - /* Get the biased exponent similarly */ - #define GETEXP(df) ((Int)(DECCOMBEXP[DFWORD((df), 0)>>26]+GETECON(df))) - /* Get the unbiased exponent similarly */ - #define GETEXPUN(df) ((Int)GETEXP(df)-DECBIAS) - /* Get the MSD similarly (as uInt) */ - #define GETMSD(df) (DECCOMBMSD[DFWORD((df), 0)>>26]) - - /* Compile-time computes of the exponent continuation field masks */ - /* full exponent continuation field: */ - #define ECONMASK ((0x03ffffff>>(32-6-DECECONL))<<(32-6-DECECONL)) - /* same, not including its first digit (the qNaN/sNaN selector): */ - #define ECONNANMASK ((0x01ffffff>>(32-6-DECECONL))<<(32-6-DECECONL)) - - /* Macros to decode the coefficient in a finite decFloat *df into */ - /* a BCD string (uByte *bcdin) of length DECPMAX uBytes. */ - - /* In-line sequence to convert least significant 10 bits of uInt */ - /* dpd to three BCD8 digits starting at uByte u. Note that an */ - /* extra byte is written to the right of the three digits because */ - /* four bytes are moved at a time for speed; the alternative */ - /* macro moves exactly three bytes (usually slower). */ - #define dpd2bcd8(u, dpd) memcpy(u, &DPD2BCD8[((dpd)&0x3ff)*4], 4) - #define dpd2bcd83(u, dpd) memcpy(u, &DPD2BCD8[((dpd)&0x3ff)*4], 3) - - /* Decode the declets. After extracting each one, it is decoded */ - /* to BCD8 using a table lookup (also used for variable-length */ - /* decode). Each DPD decode is 3 bytes BCD8 plus a one-byte */ - /* length which is not used, here). Fixed-length 4-byte moves */ - /* are fast, however, almost everywhere, and so are used except */ - /* for the final three bytes (to avoid overrun). The code below */ - /* is 36 instructions for Doubles and about 70 for Quads, even */ - /* on IA32. */ - - /* Two macros are defined for each format: */ - /* GETCOEFF extracts the coefficient of the current format */ - /* GETWCOEFF extracts the coefficient of the next-wider format. */ - /* The latter is a copy of the next-wider GETCOEFF using DFWWORD. */ - - #if DECPMAX==7 - #define GETCOEFF(df, bcd) { \ - uInt sourhi=DFWORD(df, 0); \ - *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \ - dpd2bcd8(bcd+1, sourhi>>10); \ - dpd2bcd83(bcd+4, sourhi);} - #define GETWCOEFF(df, bcd) { \ - uInt sourhi=DFWWORD(df, 0); \ - uInt sourlo=DFWWORD(df, 1); \ - *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \ - dpd2bcd8(bcd+1, sourhi>>8); \ - dpd2bcd8(bcd+4, (sourhi<<2) | (sourlo>>30)); \ - dpd2bcd8(bcd+7, sourlo>>20); \ - dpd2bcd8(bcd+10, sourlo>>10); \ - dpd2bcd83(bcd+13, sourlo);} - - #elif DECPMAX==16 - #define GETCOEFF(df, bcd) { \ - uInt sourhi=DFWORD(df, 0); \ - uInt sourlo=DFWORD(df, 1); \ - *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \ - dpd2bcd8(bcd+1, sourhi>>8); \ - dpd2bcd8(bcd+4, (sourhi<<2) | (sourlo>>30)); \ - dpd2bcd8(bcd+7, sourlo>>20); \ - dpd2bcd8(bcd+10, sourlo>>10); \ - dpd2bcd83(bcd+13, sourlo);} - #define GETWCOEFF(df, bcd) { \ - uInt sourhi=DFWWORD(df, 0); \ - uInt sourmh=DFWWORD(df, 1); \ - uInt sourml=DFWWORD(df, 2); \ - uInt sourlo=DFWWORD(df, 3); \ - *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \ - dpd2bcd8(bcd+1, sourhi>>4); \ - dpd2bcd8(bcd+4, ((sourhi)<<6) | (sourmh>>26)); \ - dpd2bcd8(bcd+7, sourmh>>16); \ - dpd2bcd8(bcd+10, sourmh>>6); \ - dpd2bcd8(bcd+13, ((sourmh)<<4) | (sourml>>28)); \ - dpd2bcd8(bcd+16, sourml>>18); \ - dpd2bcd8(bcd+19, sourml>>8); \ - dpd2bcd8(bcd+22, ((sourml)<<2) | (sourlo>>30)); \ - dpd2bcd8(bcd+25, sourlo>>20); \ - dpd2bcd8(bcd+28, sourlo>>10); \ - dpd2bcd83(bcd+31, sourlo);} - - #elif DECPMAX==34 - #define GETCOEFF(df, bcd) { \ - uInt sourhi=DFWORD(df, 0); \ - uInt sourmh=DFWORD(df, 1); \ - uInt sourml=DFWORD(df, 2); \ - uInt sourlo=DFWORD(df, 3); \ - *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \ - dpd2bcd8(bcd+1, sourhi>>4); \ - dpd2bcd8(bcd+4, ((sourhi)<<6) | (sourmh>>26)); \ - dpd2bcd8(bcd+7, sourmh>>16); \ - dpd2bcd8(bcd+10, sourmh>>6); \ - dpd2bcd8(bcd+13, ((sourmh)<<4) | (sourml>>28)); \ - dpd2bcd8(bcd+16, sourml>>18); \ - dpd2bcd8(bcd+19, sourml>>8); \ - dpd2bcd8(bcd+22, ((sourml)<<2) | (sourlo>>30)); \ - dpd2bcd8(bcd+25, sourlo>>20); \ - dpd2bcd8(bcd+28, sourlo>>10); \ - dpd2bcd83(bcd+31, sourlo);} - - #define GETWCOEFF(df, bcd) {??} /* [should never be used] */ - #endif - - /* Macros to decode the coefficient in a finite decFloat *df into */ - /* a base-billion uInt array, with the least-significant */ - /* 0-999999999 'digit' at offset 0. */ - - /* Decode the declets. After extracting each one, it is decoded */ - /* to binary using a table lookup. Three tables are used; one */ - /* the usual DPD to binary, the other two pre-multiplied by 1000 */ - /* and 1000000 to avoid multiplication during decode. These */ - /* tables can also be used for multiplying up the MSD as the DPD */ - /* code for 0 through 9 is the identity. */ - #define DPD2BIN0 DPD2BIN /* for prettier code */ - - #if DECPMAX==7 - #define GETCOEFFBILL(df, buf) { \ - uInt sourhi=DFWORD(df, 0); \ - (buf)[0]=DPD2BIN0[sourhi&0x3ff] \ - +DPD2BINK[(sourhi>>10)&0x3ff] \ - +DPD2BINM[DECCOMBMSD[sourhi>>26]];} - - #elif DECPMAX==16 - #define GETCOEFFBILL(df, buf) { \ - uInt sourhi, sourlo; \ - sourlo=DFWORD(df, 1); \ - (buf)[0]=DPD2BIN0[sourlo&0x3ff] \ - +DPD2BINK[(sourlo>>10)&0x3ff] \ - +DPD2BINM[(sourlo>>20)&0x3ff]; \ - sourhi=DFWORD(df, 0); \ - (buf)[1]=DPD2BIN0[((sourhi<<2) | (sourlo>>30))&0x3ff] \ - +DPD2BINK[(sourhi>>8)&0x3ff] \ - +DPD2BINM[DECCOMBMSD[sourhi>>26]];} - - #elif DECPMAX==34 - #define GETCOEFFBILL(df, buf) { \ - uInt sourhi, sourmh, sourml, sourlo; \ - sourlo=DFWORD(df, 3); \ - (buf)[0]=DPD2BIN0[sourlo&0x3ff] \ - +DPD2BINK[(sourlo>>10)&0x3ff] \ - +DPD2BINM[(sourlo>>20)&0x3ff]; \ - sourml=DFWORD(df, 2); \ - (buf)[1]=DPD2BIN0[((sourml<<2) | (sourlo>>30))&0x3ff] \ - +DPD2BINK[(sourml>>8)&0x3ff] \ - +DPD2BINM[(sourml>>18)&0x3ff]; \ - sourmh=DFWORD(df, 1); \ - (buf)[2]=DPD2BIN0[((sourmh<<4) | (sourml>>28))&0x3ff] \ - +DPD2BINK[(sourmh>>6)&0x3ff] \ - +DPD2BINM[(sourmh>>16)&0x3ff]; \ - sourhi=DFWORD(df, 0); \ - (buf)[3]=DPD2BIN0[((sourhi<<6) | (sourmh>>26))&0x3ff] \ - +DPD2BINK[(sourhi>>4)&0x3ff] \ - +DPD2BINM[DECCOMBMSD[sourhi>>26]];} - - #endif - - /* Macros to decode the coefficient in a finite decFloat *df into */ - /* a base-thousand uInt array (of size DECLETS+1, to allow for */ - /* the MSD), with the least-significant 0-999 'digit' at offset 0.*/ - - /* Decode the declets. After extracting each one, it is decoded */ - /* to binary using a table lookup. */ - #if DECPMAX==7 - #define GETCOEFFTHOU(df, buf) { \ - uInt sourhi=DFWORD(df, 0); \ - (buf)[0]=DPD2BIN[sourhi&0x3ff]; \ - (buf)[1]=DPD2BIN[(sourhi>>10)&0x3ff]; \ - (buf)[2]=DECCOMBMSD[sourhi>>26];} - - #elif DECPMAX==16 - #define GETCOEFFTHOU(df, buf) { \ - uInt sourhi, sourlo; \ - sourlo=DFWORD(df, 1); \ - (buf)[0]=DPD2BIN[sourlo&0x3ff]; \ - (buf)[1]=DPD2BIN[(sourlo>>10)&0x3ff]; \ - (buf)[2]=DPD2BIN[(sourlo>>20)&0x3ff]; \ - sourhi=DFWORD(df, 0); \ - (buf)[3]=DPD2BIN[((sourhi<<2) | (sourlo>>30))&0x3ff]; \ - (buf)[4]=DPD2BIN[(sourhi>>8)&0x3ff]; \ - (buf)[5]=DECCOMBMSD[sourhi>>26];} - - #elif DECPMAX==34 - #define GETCOEFFTHOU(df, buf) { \ - uInt sourhi, sourmh, sourml, sourlo; \ - sourlo=DFWORD(df, 3); \ - (buf)[0]=DPD2BIN[sourlo&0x3ff]; \ - (buf)[1]=DPD2BIN[(sourlo>>10)&0x3ff]; \ - (buf)[2]=DPD2BIN[(sourlo>>20)&0x3ff]; \ - sourml=DFWORD(df, 2); \ - (buf)[3]=DPD2BIN[((sourml<<2) | (sourlo>>30))&0x3ff]; \ - (buf)[4]=DPD2BIN[(sourml>>8)&0x3ff]; \ - (buf)[5]=DPD2BIN[(sourml>>18)&0x3ff]; \ - sourmh=DFWORD(df, 1); \ - (buf)[6]=DPD2BIN[((sourmh<<4) | (sourml>>28))&0x3ff]; \ - (buf)[7]=DPD2BIN[(sourmh>>6)&0x3ff]; \ - (buf)[8]=DPD2BIN[(sourmh>>16)&0x3ff]; \ - sourhi=DFWORD(df, 0); \ - (buf)[9]=DPD2BIN[((sourhi<<6) | (sourmh>>26))&0x3ff]; \ - (buf)[10]=DPD2BIN[(sourhi>>4)&0x3ff]; \ - (buf)[11]=DECCOMBMSD[sourhi>>26];} - #endif - - - /* Macros to decode the coefficient in a finite decFloat *df and */ - /* add to a base-thousand uInt array (as for GETCOEFFTHOU). */ - /* After the addition then most significant 'digit' in the array */ - /* might have a value larger then 10 (with a maximum of 19). */ - #if DECPMAX==7 - #define ADDCOEFFTHOU(df, buf) { \ - uInt sourhi=DFWORD(df, 0); \ - (buf)[0]+=DPD2BIN[sourhi&0x3ff]; \ - if (buf[0]>999) {buf[0]-=1000; buf[1]++;} \ - (buf)[1]+=DPD2BIN[(sourhi>>10)&0x3ff]; \ - if (buf[1]>999) {buf[1]-=1000; buf[2]++;} \ - (buf)[2]+=DECCOMBMSD[sourhi>>26];} - - #elif DECPMAX==16 - #define ADDCOEFFTHOU(df, buf) { \ - uInt sourhi, sourlo; \ - sourlo=DFWORD(df, 1); \ - (buf)[0]+=DPD2BIN[sourlo&0x3ff]; \ - if (buf[0]>999) {buf[0]-=1000; buf[1]++;} \ - (buf)[1]+=DPD2BIN[(sourlo>>10)&0x3ff]; \ - if (buf[1]>999) {buf[1]-=1000; buf[2]++;} \ - (buf)[2]+=DPD2BIN[(sourlo>>20)&0x3ff]; \ - if (buf[2]>999) {buf[2]-=1000; buf[3]++;} \ - sourhi=DFWORD(df, 0); \ - (buf)[3]+=DPD2BIN[((sourhi<<2) | (sourlo>>30))&0x3ff]; \ - if (buf[3]>999) {buf[3]-=1000; buf[4]++;} \ - (buf)[4]+=DPD2BIN[(sourhi>>8)&0x3ff]; \ - if (buf[4]>999) {buf[4]-=1000; buf[5]++;} \ - (buf)[5]+=DECCOMBMSD[sourhi>>26];} - - #elif DECPMAX==34 - #define ADDCOEFFTHOU(df, buf) { \ - uInt sourhi, sourmh, sourml, sourlo; \ - sourlo=DFWORD(df, 3); \ - (buf)[0]+=DPD2BIN[sourlo&0x3ff]; \ - if (buf[0]>999) {buf[0]-=1000; buf[1]++;} \ - (buf)[1]+=DPD2BIN[(sourlo>>10)&0x3ff]; \ - if (buf[1]>999) {buf[1]-=1000; buf[2]++;} \ - (buf)[2]+=DPD2BIN[(sourlo>>20)&0x3ff]; \ - if (buf[2]>999) {buf[2]-=1000; buf[3]++;} \ - sourml=DFWORD(df, 2); \ - (buf)[3]+=DPD2BIN[((sourml<<2) | (sourlo>>30))&0x3ff]; \ - if (buf[3]>999) {buf[3]-=1000; buf[4]++;} \ - (buf)[4]+=DPD2BIN[(sourml>>8)&0x3ff]; \ - if (buf[4]>999) {buf[4]-=1000; buf[5]++;} \ - (buf)[5]+=DPD2BIN[(sourml>>18)&0x3ff]; \ - if (buf[5]>999) {buf[5]-=1000; buf[6]++;} \ - sourmh=DFWORD(df, 1); \ - (buf)[6]+=DPD2BIN[((sourmh<<4) | (sourml>>28))&0x3ff]; \ - if (buf[6]>999) {buf[6]-=1000; buf[7]++;} \ - (buf)[7]+=DPD2BIN[(sourmh>>6)&0x3ff]; \ - if (buf[7]>999) {buf[7]-=1000; buf[8]++;} \ - (buf)[8]+=DPD2BIN[(sourmh>>16)&0x3ff]; \ - if (buf[8]>999) {buf[8]-=1000; buf[9]++;} \ - sourhi=DFWORD(df, 0); \ - (buf)[9]+=DPD2BIN[((sourhi<<6) | (sourmh>>26))&0x3ff]; \ - if (buf[9]>999) {buf[9]-=1000; buf[10]++;} \ - (buf)[10]+=DPD2BIN[(sourhi>>4)&0x3ff]; \ - if (buf[10]>999) {buf[10]-=1000; buf[11]++;} \ - (buf)[11]+=DECCOMBMSD[sourhi>>26];} - #endif - - - /* Set a decFloat to the maximum positive finite number (Nmax) */ - #if DECPMAX==7 - #define DFSETNMAX(df) \ - {DFWORD(df, 0)=0x77f3fcff;} - #elif DECPMAX==16 - #define DFSETNMAX(df) \ - {DFWORD(df, 0)=0x77fcff3f; \ - DFWORD(df, 1)=0xcff3fcff;} - #elif DECPMAX==34 - #define DFSETNMAX(df) \ - {DFWORD(df, 0)=0x77ffcff3; \ - DFWORD(df, 1)=0xfcff3fcf; \ - DFWORD(df, 2)=0xf3fcff3f; \ - DFWORD(df, 3)=0xcff3fcff;} - #endif - - /* [end of format-dependent macros and constants] */ - #endif - -#else - #error decNumberLocal included more than once -#endif
src/decNumber/decPacked.c
@@ -1,220 +0,0 @@-/* ------------------------------------------------------------------ */ -/* Packed Decimal conversion module */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2002. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is called decNumber.pdf. This document is */ -/* available, together with arithmetic and format specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ -/* This module comprises the routines for Packed Decimal format */ -/* numbers. Conversions are supplied to and from decNumber, which in */ -/* turn supports: */ -/* conversions to and from string */ -/* arithmetic routines */ -/* utilities. */ -/* Conversions from decNumber to and from densely packed decimal */ -/* formats are provided by the decimal32 through decimal128 modules. */ -/* ------------------------------------------------------------------ */ - -#include <string.h> // for NULL -#include "decNumber.h" // base number library -#include "decPacked.h" // packed decimal -#include "decNumberLocal.h" // decNumber local types, etc. - -/* ------------------------------------------------------------------ */ -/* decPackedFromNumber -- convert decNumber to BCD Packed Decimal */ -/* */ -/* bcd is the BCD bytes */ -/* length is the length of the BCD array */ -/* scale is the scale result */ -/* dn is the decNumber */ -/* returns bcd, or NULL if error */ -/* */ -/* The number is converted to a BCD packed decimal byte array, */ -/* right aligned in the bcd array, whose length is indicated by the */ -/* second parameter. The final 4-bit nibble in the array will be a */ -/* sign nibble, C (1100) for + and D (1101) for -. Unused bytes and */ -/* nibbles to the left of the number are set to 0. */ -/* */ -/* scale is set to the scale of the number (this is the exponent, */ -/* negated). To force the number to a specified scale, first use the */ -/* decNumberRescale routine, which will round and change the exponent */ -/* as necessary. */ -/* */ -/* If there is an error (that is, the decNumber has too many digits */ -/* to fit in length bytes, or it is a NaN or Infinity), NULL is */ -/* returned and the bcd and scale results are unchanged. Otherwise */ -/* bcd is returned. */ -/* ------------------------------------------------------------------ */ -uByte * decPackedFromNumber(uByte *bcd, Int length, Int *scale, - const decNumber *dn) { - const Unit *up=dn->lsu; // Unit array pointer - uByte obyte, *out; // current output byte, and where it goes - Int indigs=dn->digits; // digits processed - uInt cut=DECDPUN; // downcounter per Unit - uInt u=*up; // work - uInt nib; // .. - #if DECDPUN<=4 - uInt temp; // .. - #endif - - if (dn->digits>length*2-1 // too long .. - ||(dn->bits & DECSPECIAL)) return NULL; // .. or special -- hopeless - - if (dn->bits&DECNEG) obyte=DECPMINUS; // set the sign .. - else obyte=DECPPLUS; - *scale=-dn->exponent; // .. and scale - - // loop from lowest (rightmost) byte - out=bcd+length-1; // -> final byte - for (; out>=bcd; out--) { - if (indigs>0) { - if (cut==0) { - up++; - u=*up; - cut=DECDPUN; - } - #if DECDPUN<=4 - temp=(u*6554)>>16; // fast /10 - nib=u-X10(temp); - u=temp; - #else - nib=u%10; // cannot use *6554 trick :-( - u=u/10; - #endif - obyte|=(nib<<4); - indigs--; - cut--; - } - *out=obyte; - obyte=0; // assume 0 - if (indigs>0) { - if (cut==0) { - up++; - u=*up; - cut=DECDPUN; - } - #if DECDPUN<=4 - temp=(u*6554)>>16; // as above - obyte=(uByte)(u-X10(temp)); - u=temp; - #else - obyte=(uByte)(u%10); - u=u/10; - #endif - indigs--; - cut--; - } - } // loop - - return bcd; - } // decPackedFromNumber - -/* ------------------------------------------------------------------ */ -/* decPackedToNumber -- convert BCD Packed Decimal to a decNumber */ -/* */ -/* bcd is the BCD bytes */ -/* length is the length of the BCD array */ -/* scale is the scale associated with the BCD integer */ -/* dn is the decNumber [with space for length*2 digits] */ -/* returns dn, or NULL if error */ -/* */ -/* The BCD packed decimal byte array, together with an associated */ -/* scale, is converted to a decNumber. The BCD array is assumed full */ -/* of digits, and must be ended by a 4-bit sign nibble in the least */ -/* significant four bits of the final byte. */ -/* */ -/* The scale is used (negated) as the exponent of the decNumber. */ -/* Note that zeros may have a sign and/or a scale. */ -/* */ -/* The decNumber structure is assumed to have sufficient space to */ -/* hold the converted number (that is, up to length*2-1 digits), so */ -/* no error is possible unless the adjusted exponent is out of range, */ -/* no sign nibble was found, or a sign nibble was found before the */ -/* final nibble. In these error cases, NULL is returned and the */ -/* decNumber will be 0. */ -/* ------------------------------------------------------------------ */ -decNumber * decPackedToNumber(const uByte *bcd, Int length, - const Int *scale, decNumber *dn) { - const uByte *last=bcd+length-1; // -> last byte - const uByte *first; // -> first non-zero byte - uInt nib; // work nibble - Unit *up=dn->lsu; // output pointer - Int digits; // digits count - Int cut=0; // phase of output - - decNumberZero(dn); // default result - last=&bcd[length-1]; - nib=*last & 0x0f; // get the sign - if (nib==DECPMINUS || nib==DECPMINUSALT) dn->bits=DECNEG; - else if (nib<=9) return NULL; // not a sign nibble - - // skip leading zero bytes [final byte is always non-zero, due to sign] - for (first=bcd; *first==0;) first++; - digits=(last-first)*2+1; // calculate digits .. - if ((*first & 0xf0)==0) digits--; // adjust for leading zero nibble - if (digits!=0) dn->digits=digits; // count of actual digits [if 0, - // leave as 1] - - // check the adjusted exponent; note that scale could be unbounded - dn->exponent=-*scale; // set the exponent - if (*scale>=0) { // usual case - if ((dn->digits-*scale-1)<-DECNUMMAXE) { // underflow - decNumberZero(dn); - return NULL;} - } - else { // -ve scale; +ve exponent - // need to be careful to avoid wrap, here, also BADINT case - if ((*scale<-DECNUMMAXE) // overflow even without digits - || ((dn->digits-*scale-1)>DECNUMMAXE)) { // overflow - decNumberZero(dn); - return NULL;} - } - if (digits==0) return dn; // result was zero - - // copy the digits to the number's units, starting at the lsu - // [unrolled] - for (;;) { // forever - // left nibble first - nib=(unsigned)(*last & 0xf0)>>4; - // got a digit, in nib - if (nib>9) {decNumberZero(dn); return NULL;} - - if (cut==0) *up=(Unit)nib; - else *up=(Unit)(*up+nib*DECPOWERS[cut]); - digits--; - if (digits==0) break; // got them all - cut++; - if (cut==DECDPUN) { - up++; - cut=0; - } - last--; // ready for next - nib=*last & 0x0f; // get right nibble - if (nib>9) {decNumberZero(dn); return NULL;} - - // got a digit, in nib - if (cut==0) *up=(Unit)nib; - else *up=(Unit)(*up+nib*DECPOWERS[cut]); - digits--; - if (digits==0) break; // got them all - cut++; - if (cut==DECDPUN) { - up++; - cut=0; - } - } // forever - - return dn; - } // decPackedToNumber -
src/decNumber/decPacked.h
@@ -1,52 +0,0 @@-/* ------------------------------------------------------------------ */ -/* Packed Decimal conversion module header */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2005. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is called decNumber.pdf. This document is */ -/* available, together with arithmetic and format specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ - -#if !defined(DECPACKED) - #define DECPACKED - #define DECPNAME "decPacked" /* Short name */ - #define DECPFULLNAME "Packed Decimal conversions" /* Verbose name */ - #define DECPAUTHOR "Mike Cowlishaw" /* Who to blame */ - - #define DECPACKED_DefP 32 /* default precision */ - - #ifndef DECNUMDIGITS - #define DECNUMDIGITS DECPACKED_DefP /* size if not already defined*/ - #endif - #include "decNumber.h" /* context and number library */ - - /* Sign nibble constants */ - #if !defined(DECPPLUSALT) - #define DECPPLUSALT 0x0A /* alternate plus nibble */ - #define DECPMINUSALT 0x0B /* alternate minus nibble */ - #define DECPPLUS 0x0C /* preferred plus nibble */ - #define DECPMINUS 0x0D /* preferred minus nibble */ - #define DECPPLUSALT2 0x0E /* alternate plus nibble */ - #define DECPUNSIGNED 0x0F /* alternate plus nibble (unsigned) */ - #endif - - /* ---------------------------------------------------------------- */ - /* decPacked public routines */ - /* ---------------------------------------------------------------- */ - /* Conversions */ - uint8_t * decPackedFromNumber(uint8_t *, int32_t, int32_t *, - const decNumber *); - decNumber * decPackedToNumber(const uint8_t *, int32_t, const int32_t *, - decNumber *); - -#endif
src/decNumber/decQuad.c
@@ -1,135 +0,0 @@-/* ------------------------------------------------------------------ */ -/* decQuad.c -- decQuad operations module */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is included in the package as decNumber.pdf. This */ -/* document is also available in HTML, together with specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ -/* This module comprises decQuad operations (including conversions) */ -/* ------------------------------------------------------------------ */ - - -/* Constant mappings for shared code */ -#define DECPMAX DECQUAD_Pmax -#define DECEMIN DECQUAD_Emin -#define DECEMAX DECQUAD_Emax -#define DECEMAXD DECQUAD_EmaxD -#define DECBYTES DECQUAD_Bytes -#define DECSTRING DECQUAD_String -#define DECECONL DECQUAD_EconL -#define DECBIAS DECQUAD_Bias -#define DECLETS DECQUAD_Declets -#define DECQTINY (-DECQUAD_Bias) - -/* Type and function mappings for shared code */ -#define decFloat decQuad // Type name - -// Utilities and conversions (binary results, extractors, etc.) -#define decFloatFromBCD decQuadFromBCD -#define decFloatFromInt32 decQuadFromInt32 -#define decFloatFromPacked decQuadFromPacked -#define decFloatFromPackedChecked decQuadFromPackedChecked -#define decFloatFromString decQuadFromString -#define decFloatFromUInt32 decQuadFromUInt32 -#define decFloatFromWider decQuadFromWider -#define decFloatGetCoefficient decQuadGetCoefficient -#define decFloatGetExponent decQuadGetExponent -#define decFloatSetCoefficient decQuadSetCoefficient -#define decFloatSetExponent decQuadSetExponent -#define decFloatShow decQuadShow -#define decFloatToBCD decQuadToBCD -#define decFloatToEngString decQuadToEngString -#define decFloatToInt32 decQuadToInt32 -#define decFloatToInt32Exact decQuadToInt32Exact -#define decFloatToPacked decQuadToPacked -#define decFloatToString decQuadToString -#define decFloatToUInt32 decQuadToUInt32 -#define decFloatToUInt32Exact decQuadToUInt32Exact -#define decFloatToWider decQuadToWider -#define decFloatZero decQuadZero - -// Computational (result is a decFloat) -#define decFloatAbs decQuadAbs -#define decFloatAdd decQuadAdd -#define decFloatAnd decQuadAnd -#define decFloatDivide decQuadDivide -#define decFloatDivideInteger decQuadDivideInteger -#define decFloatFMA decQuadFMA -#define decFloatInvert decQuadInvert -#define decFloatLogB decQuadLogB -#define decFloatMax decQuadMax -#define decFloatMaxMag decQuadMaxMag -#define decFloatMin decQuadMin -#define decFloatMinMag decQuadMinMag -#define decFloatMinus decQuadMinus -#define decFloatMultiply decQuadMultiply -#define decFloatNextMinus decQuadNextMinus -#define decFloatNextPlus decQuadNextPlus -#define decFloatNextToward decQuadNextToward -#define decFloatOr decQuadOr -#define decFloatPlus decQuadPlus -#define decFloatQuantize decQuadQuantize -#define decFloatReduce decQuadReduce -#define decFloatRemainder decQuadRemainder -#define decFloatRemainderNear decQuadRemainderNear -#define decFloatRotate decQuadRotate -#define decFloatScaleB decQuadScaleB -#define decFloatShift decQuadShift -#define decFloatSubtract decQuadSubtract -#define decFloatToIntegralValue decQuadToIntegralValue -#define decFloatToIntegralExact decQuadToIntegralExact -#define decFloatXor decQuadXor - -// Comparisons -#define decFloatCompare decQuadCompare -#define decFloatCompareSignal decQuadCompareSignal -#define decFloatCompareTotal decQuadCompareTotal -#define decFloatCompareTotalMag decQuadCompareTotalMag - -// Copies -#define decFloatCanonical decQuadCanonical -#define decFloatCopy decQuadCopy -#define decFloatCopyAbs decQuadCopyAbs -#define decFloatCopyNegate decQuadCopyNegate -#define decFloatCopySign decQuadCopySign - -// Non-computational -#define decFloatClass decQuadClass -#define decFloatClassString decQuadClassString -#define decFloatDigits decQuadDigits -#define decFloatIsCanonical decQuadIsCanonical -#define decFloatIsFinite decQuadIsFinite -#define decFloatIsInfinite decQuadIsInfinite -#define decFloatIsInteger decQuadIsInteger -#define decFloatIsLogical decQuadIsLogical -#define decFloatIsNaN decQuadIsNaN -#define decFloatIsNegative decQuadIsNegative -#define decFloatIsNormal decQuadIsNormal -#define decFloatIsPositive decQuadIsPositive -#define decFloatIsSignaling decQuadIsSignaling -#define decFloatIsSignalling decQuadIsSignalling -#define decFloatIsSigned decQuadIsSigned -#define decFloatIsSubnormal decQuadIsSubnormal -#define decFloatIsZero decQuadIsZero -#define decFloatRadix decQuadRadix -#define decFloatSameQuantum decQuadSameQuantum -#define decFloatVersion decQuadVersion - -/* And now the code itself */ -#include "decContext.h" // public includes -#include "decQuad.h" // .. -#include "decNumberLocal.h" // local includes (need DECPMAX) -#include "decCommon.c" // non-arithmetic decFloat routines -#include "decBasic.c" // basic formats routines -
src/decNumber/decQuad.h
@@ -1,177 +0,0 @@-/* ------------------------------------------------------------------ */ -/* decQuad.h -- Decimal 128-bit format module header */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is included in the package as decNumber.pdf. This */ -/* document is also available in HTML, together with specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ -/* This include file is always included by decSingle and decDouble, */ -/* and therefore also holds useful constants used by all three. */ - -#if !defined(DECQUAD) - #define DECQUAD - - #define DECQUADNAME "decimalQuad" /* Short name */ - #define DECQUADTITLE "Decimal 128-bit datum" /* Verbose name */ - #define DECQUADAUTHOR "Mike Cowlishaw" /* Who to blame */ - - /* parameters for decQuads */ - #define DECQUAD_Bytes 16 /* length */ - #define DECQUAD_Pmax 34 /* maximum precision (digits) */ - #define DECQUAD_Emin -6143 /* minimum adjusted exponent */ - #define DECQUAD_Emax 6144 /* maximum adjusted exponent */ - #define DECQUAD_EmaxD 4 /* maximum exponent digits */ - #define DECQUAD_Bias 6176 /* bias for the exponent */ - #define DECQUAD_String 43 /* maximum string length, +1 */ - #define DECQUAD_EconL 12 /* exponent continuation length */ - #define DECQUAD_Declets 11 /* count of declets */ - /* highest biased exponent (Elimit-1) */ - #define DECQUAD_Ehigh (DECQUAD_Emax + DECQUAD_Bias - (DECQUAD_Pmax-1)) - - /* Required include */ - #include "decContext.h" - - /* The decQuad decimal 128-bit type, accessible by all sizes */ - typedef union { - uint8_t bytes[DECQUAD_Bytes]; /* fields: 1, 5, 12, 110 bits */ - uint16_t shorts[DECQUAD_Bytes/2]; - uint32_t words[DECQUAD_Bytes/4]; - #if DECUSE64 - uint64_t longs[DECQUAD_Bytes/8]; - #endif - } decQuad; - - /* ---------------------------------------------------------------- */ - /* Shared constants */ - /* ---------------------------------------------------------------- */ - - /* sign and special values [top 32-bits; last two bits are don't-care - for Infinity on input, last bit don't-care for NaNs] */ - #define DECFLOAT_Sign 0x80000000 /* 1 00000 00 Sign */ - #define DECFLOAT_NaN 0x7c000000 /* 0 11111 00 NaN generic */ - #define DECFLOAT_qNaN 0x7c000000 /* 0 11111 00 qNaN */ - #define DECFLOAT_sNaN 0x7e000000 /* 0 11111 10 sNaN */ - #define DECFLOAT_Inf 0x78000000 /* 0 11110 00 Infinity */ - #define DECFLOAT_MinSp 0x78000000 /* minimum special value */ - /* [specials are all >=MinSp] */ - /* Sign nibble constants */ - #if !defined(DECPPLUSALT) - #define DECPPLUSALT 0x0A /* alternate plus nibble */ - #define DECPMINUSALT 0x0B /* alternate minus nibble */ - #define DECPPLUS 0x0C /* preferred plus nibble */ - #define DECPMINUS 0x0D /* preferred minus nibble */ - #define DECPPLUSALT2 0x0E /* alternate plus nibble */ - #define DECPUNSIGNED 0x0F /* alternate plus nibble (unsigned) */ - #endif - - /* ---------------------------------------------------------------- */ - /* Routines -- implemented as decFloat routines in common files */ - /* ---------------------------------------------------------------- */ - - /* Utilities and conversions, extractors, etc.) */ - extern decQuad * decQuadFromBCD(decQuad *, int32_t, const uint8_t *, int32_t); - extern decQuad * decQuadFromInt32(decQuad *, int32_t); - extern decQuad * decQuadFromPacked(decQuad *, int32_t, const uint8_t *); - extern decQuad * decQuadFromPackedChecked(decQuad *, int32_t, const uint8_t *); - extern decQuad * decQuadFromString(decQuad *, const char *, decContext *); - extern decQuad * decQuadFromUInt32(decQuad *, uint32_t); - extern int32_t decQuadGetCoefficient(const decQuad *, uint8_t *); - extern int32_t decQuadGetExponent(const decQuad *); - extern decQuad * decQuadSetCoefficient(decQuad *, const uint8_t *, int32_t); - extern decQuad * decQuadSetExponent(decQuad *, decContext *, int32_t); - extern void decQuadShow(const decQuad *, const char *); - extern int32_t decQuadToBCD(const decQuad *, int32_t *, uint8_t *); - extern char * decQuadToEngString(const decQuad *, char *); - extern int32_t decQuadToInt32(const decQuad *, decContext *, enum rounding); - extern int32_t decQuadToInt32Exact(const decQuad *, decContext *, enum rounding); - extern int32_t decQuadToPacked(const decQuad *, int32_t *, uint8_t *); - extern char * decQuadToString(const decQuad *, char *); - extern uint32_t decQuadToUInt32(const decQuad *, decContext *, enum rounding); - extern uint32_t decQuadToUInt32Exact(const decQuad *, decContext *, enum rounding); - extern decQuad * decQuadZero(decQuad *); - - /* Computational (result is a decQuad) */ - extern decQuad * decQuadAbs(decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadAdd(decQuad *, const decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadAnd(decQuad *, const decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadDivide(decQuad *, const decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadDivideInteger(decQuad *, const decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadFMA(decQuad *, const decQuad *, const decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadInvert(decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadLogB(decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadMax(decQuad *, const decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadMaxMag(decQuad *, const decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadMin(decQuad *, const decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadMinMag(decQuad *, const decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadMinus(decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadMultiply(decQuad *, const decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadNextMinus(decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadNextPlus(decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadNextToward(decQuad *, const decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadOr(decQuad *, const decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadPlus(decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadQuantize(decQuad *, const decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadReduce(decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadRemainder(decQuad *, const decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadRemainderNear(decQuad *, const decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadRotate(decQuad *, const decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadScaleB(decQuad *, const decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadShift(decQuad *, const decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadSubtract(decQuad *, const decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadToIntegralValue(decQuad *, const decQuad *, decContext *, enum rounding); - extern decQuad * decQuadToIntegralExact(decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadXor(decQuad *, const decQuad *, const decQuad *, decContext *); - - /* Comparisons */ - extern decQuad * decQuadCompare(decQuad *, const decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadCompareSignal(decQuad *, const decQuad *, const decQuad *, decContext *); - extern decQuad * decQuadCompareTotal(decQuad *, const decQuad *, const decQuad *); - extern decQuad * decQuadCompareTotalMag(decQuad *, const decQuad *, const decQuad *); - - /* Copies */ - extern decQuad * decQuadCanonical(decQuad *, const decQuad *); - extern decQuad * decQuadCopy(decQuad *, const decQuad *); - extern decQuad * decQuadCopyAbs(decQuad *, const decQuad *); - extern decQuad * decQuadCopyNegate(decQuad *, const decQuad *); - extern decQuad * decQuadCopySign(decQuad *, const decQuad *, const decQuad *); - - /* Non-computational */ - extern enum decClass decQuadClass(const decQuad *); - extern const char * decQuadClassString(const decQuad *); - extern uint32_t decQuadDigits(const decQuad *); - extern uint32_t decQuadIsCanonical(const decQuad *); - extern uint32_t decQuadIsFinite(const decQuad *); - extern uint32_t decQuadIsInteger(const decQuad *); - extern uint32_t decQuadIsLogical(const decQuad *); - extern uint32_t decQuadIsInfinite(const decQuad *); - extern uint32_t decQuadIsNaN(const decQuad *); - extern uint32_t decQuadIsNegative(const decQuad *); - extern uint32_t decQuadIsNormal(const decQuad *); - extern uint32_t decQuadIsPositive(const decQuad *); - extern uint32_t decQuadIsSignaling(const decQuad *); - extern uint32_t decQuadIsSignalling(const decQuad *); - extern uint32_t decQuadIsSigned(const decQuad *); - extern uint32_t decQuadIsSubnormal(const decQuad *); - extern uint32_t decQuadIsZero(const decQuad *); - extern uint32_t decQuadRadix(const decQuad *); - extern uint32_t decQuadSameQuantum(const decQuad *, const decQuad *); - extern const char * decQuadVersion(void); - - /* decNumber conversions; these are implemented as macros so as not */ - /* to force a dependency on decimal128 and decNumber in decQuad. */ - /* decQuadFromNumber returns a decimal128 * to avoid warnings. */ - #define decQuadToNumber(dq, dn) decimal128ToNumber((decimal128 *)(dq), dn) - #define decQuadFromNumber(dq, dn, set) decimal128FromNumber((decimal128 *)(dq), dn, set) - -#endif
src/decNumber/decSingle.c
@@ -1,71 +0,0 @@-/* ------------------------------------------------------------------ */ -/* decSingle.c -- decSingle operations module */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2008. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is included in the package as decNumber.pdf. This */ -/* document is also available in HTML, together with specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ -/* This module comprises decSingle operations (including conversions) */ -/* ------------------------------------------------------------------ */ - -#include "decContext.h" // public includes -#include "decSingle.h" // public includes - -/* Constant mappings for shared code */ -#define DECPMAX DECSINGLE_Pmax -#define DECEMIN DECSINGLE_Emin -#define DECEMAX DECSINGLE_Emax -#define DECEMAXD DECSINGLE_EmaxD -#define DECBYTES DECSINGLE_Bytes -#define DECSTRING DECSINGLE_String -#define DECECONL DECSINGLE_EconL -#define DECBIAS DECSINGLE_Bias -#define DECLETS DECSINGLE_Declets -#define DECQTINY (-DECSINGLE_Bias) -// parameters of next-wider format -#define DECWBYTES DECDOUBLE_Bytes -#define DECWPMAX DECDOUBLE_Pmax -#define DECWECONL DECDOUBLE_EconL -#define DECWBIAS DECDOUBLE_Bias - -/* Type and function mappings for shared code */ -#define decFloat decSingle // Type name -#define decFloatWider decDouble // Type name - -// Utility (binary results, extractors, etc.) -#define decFloatFromBCD decSingleFromBCD -#define decFloatFromPacked decSingleFromPacked -#define decFloatFromPackedChecked decSingleFromPackedChecked -#define decFloatFromString decSingleFromString -#define decFloatFromWider decSingleFromWider -#define decFloatGetCoefficient decSingleGetCoefficient -#define decFloatGetExponent decSingleGetExponent -#define decFloatSetCoefficient decSingleSetCoefficient -#define decFloatSetExponent decSingleSetExponent -#define decFloatShow decSingleShow -#define decFloatToBCD decSingleToBCD -#define decFloatToEngString decSingleToEngString -#define decFloatToPacked decSingleToPacked -#define decFloatToString decSingleToString -#define decFloatToWider decSingleToWider -#define decFloatZero decSingleZero - -// Non-computational -#define decFloatRadix decSingleRadix -#define decFloatVersion decSingleVersion - -#include "decNumberLocal.h" // local includes (need DECPMAX) -#include "decCommon.c" // non-basic decFloat routines -// [Do not include decBasic.c for decimal32] -
src/decNumber/decSingle.h
@@ -1,86 +0,0 @@-/* ------------------------------------------------------------------ */ -/* decSingle.h -- Decimal 32-bit format module header */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2008. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is included in the package as decNumber.pdf. This */ -/* document is also available in HTML, together with specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ - -#if !defined(DECSINGLE) - #define DECSINGLE - - #define DECSINGLENAME "decSingle" /* Short name */ - #define DECSINGLETITLE "Decimal 32-bit datum" /* Verbose name */ - #define DECSINGLEAUTHOR "Mike Cowlishaw" /* Who to blame */ - - /* parameters for decSingles */ - #define DECSINGLE_Bytes 4 /* length */ - #define DECSINGLE_Pmax 7 /* maximum precision (digits) */ - #define DECSINGLE_Emin -95 /* minimum adjusted exponent */ - #define DECSINGLE_Emax 96 /* maximum adjusted exponent */ - #define DECSINGLE_EmaxD 3 /* maximum exponent digits */ - #define DECSINGLE_Bias 101 /* bias for the exponent */ - #define DECSINGLE_String 16 /* maximum string length, +1 */ - #define DECSINGLE_EconL 6 /* exponent continuation length */ - #define DECSINGLE_Declets 2 /* count of declets */ - /* highest biased exponent (Elimit-1) */ - #define DECSINGLE_Ehigh (DECSINGLE_Emax + DECSINGLE_Bias - (DECSINGLE_Pmax-1)) - - /* Required includes */ - #include "decContext.h" - #include "decQuad.h" - #include "decDouble.h" - - /* The decSingle decimal 32-bit type, accessible by all sizes */ - typedef union { - uint8_t bytes[DECSINGLE_Bytes]; /* fields: 1, 5, 6, 20 bits */ - uint16_t shorts[DECSINGLE_Bytes/2]; - uint32_t words[DECSINGLE_Bytes/4]; - } decSingle; - - /* ---------------------------------------------------------------- */ - /* Routines -- implemented as decFloat routines in common files */ - /* ---------------------------------------------------------------- */ - - /* Utilities (binary argument(s) or result, extractors, etc.) */ - extern decSingle * decSingleFromBCD(decSingle *, int32_t, const uint8_t *, int32_t); - extern decSingle * decSingleFromPacked(decSingle *, int32_t, const uint8_t *); - extern decSingle * decSingleFromPackedChecked(decSingle *, int32_t, const uint8_t *); - extern decSingle * decSingleFromString(decSingle *, const char *, decContext *); - extern decSingle * decSingleFromWider(decSingle *, const decDouble *, decContext *); - extern int32_t decSingleGetCoefficient(const decSingle *, uint8_t *); - extern int32_t decSingleGetExponent(const decSingle *); - extern decSingle * decSingleSetCoefficient(decSingle *, const uint8_t *, int32_t); - extern decSingle * decSingleSetExponent(decSingle *, decContext *, int32_t); - extern void decSingleShow(const decSingle *, const char *); - extern int32_t decSingleToBCD(const decSingle *, int32_t *, uint8_t *); - extern char * decSingleToEngString(const decSingle *, char *); - extern int32_t decSingleToPacked(const decSingle *, int32_t *, uint8_t *); - extern char * decSingleToString(const decSingle *, char *); - extern decDouble * decSingleToWider(const decSingle *, decDouble *); - extern decSingle * decSingleZero(decSingle *); - - /* (No Arithmetic routines for decSingle) */ - - /* Non-computational */ - extern uint32_t decSingleRadix(const decSingle *); - extern const char * decSingleVersion(void); - - /* decNumber conversions; these are implemented as macros so as not */ - /* to force a dependency on decimal32 and decNumber in decSingle. */ - /* decSingleFromNumber returns a decimal32 * to avoid warnings. */ - #define decSingleToNumber(dq, dn) decimal32ToNumber((decimal32 *)(dq), dn) - #define decSingleFromNumber(dq, dn, set) decimal32FromNumber((decimal32 *)(dq), dn, set) - -#endif
src/decNumber/decimal128.c
@@ -1,553 +0,0 @@-/* ------------------------------------------------------------------ */ -/* Decimal 128-bit format module */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2008. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is called decNumber.pdf. This document is */ -/* available, together with arithmetic and format specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ -/* This module comprises the routines for decimal128 format numbers. */ -/* Conversions are supplied to and from decNumber and String. */ -/* */ -/* This is used when decNumber provides operations, either for all */ -/* operations or as a proxy between decNumber and decSingle. */ -/* */ -/* Error handling is the same as decNumber (qv.). */ -/* ------------------------------------------------------------------ */ -#include <string.h> // [for memset/memcpy] -#include <stdio.h> // [for printf] - -#define DECNUMDIGITS 34 // make decNumbers with space for 34 -#include "decNumber.h" // base number library -#include "decNumberLocal.h" // decNumber local types, etc. -#include "decimal128.h" // our primary include - -/* Utility routines and tables [in decimal64.c] */ -// DPD2BIN and the reverse are renamed to prevent link-time conflict -// if decQuad is also built in the same executable -#define DPD2BIN DPD2BINx -#define BIN2DPD BIN2DPDx -extern const uInt COMBEXP[32], COMBMSD[32]; -extern const uShort DPD2BIN[1024]; -extern const uShort BIN2DPD[1000]; // [not used] -extern const uByte BIN2CHAR[4001]; - -extern void decDigitsFromDPD(decNumber *, const uInt *, Int); -extern void decDigitsToDPD(const decNumber *, uInt *, Int); - -#if DECTRACE || DECCHECK -void decimal128Show(const decimal128 *); // for debug -extern void decNumberShow(const decNumber *); // .. -#endif - -/* Useful macro */ -// Clear a structure (e.g., a decNumber) -#define DEC_clear(d) memset(d, 0, sizeof(*d)) - -/* ------------------------------------------------------------------ */ -/* decimal128FromNumber -- convert decNumber to decimal128 */ -/* */ -/* ds is the target decimal128 */ -/* dn is the source number (assumed valid) */ -/* set is the context, used only for reporting errors */ -/* */ -/* The set argument is used only for status reporting and for the */ -/* rounding mode (used if the coefficient is more than DECIMAL128_Pmax*/ -/* digits or an overflow is detected). If the exponent is out of the */ -/* valid range then Overflow or Underflow will be raised. */ -/* After Underflow a subnormal result is possible. */ -/* */ -/* DEC_Clamped is set if the number has to be 'folded down' to fit, */ -/* by reducing its exponent and multiplying the coefficient by a */ -/* power of ten, or if the exponent on a zero had to be clamped. */ -/* ------------------------------------------------------------------ */ -decimal128 * decimal128FromNumber(decimal128 *d128, const decNumber *dn, - decContext *set) { - uInt status=0; // status accumulator - Int ae; // adjusted exponent - decNumber dw; // work - decContext dc; // .. - uInt comb, exp; // .. - uInt uiwork; // for macros - uInt targar[4]={0,0,0,0}; // target 128-bit - #define targhi targar[3] // name the word with the sign - #define targmh targar[2] // name the words - #define targml targar[1] // .. - #define targlo targar[0] // .. - - // If the number has too many digits, or the exponent could be - // out of range then reduce the number under the appropriate - // constraints. This could push the number to Infinity or zero, - // so this check and rounding must be done before generating the - // decimal128] - ae=dn->exponent+dn->digits-1; // [0 if special] - if (dn->digits>DECIMAL128_Pmax // too many digits - || ae>DECIMAL128_Emax // likely overflow - || ae<DECIMAL128_Emin) { // likely underflow - decContextDefault(&dc, DEC_INIT_DECIMAL128); // [no traps] - dc.round=set->round; // use supplied rounding - decNumberPlus(&dw, dn, &dc); // (round and check) - // [this changes -0 to 0, so enforce the sign...] - dw.bits|=dn->bits&DECNEG; - status=dc.status; // save status - dn=&dw; // use the work number - } // maybe out of range - - if (dn->bits&DECSPECIAL) { // a special value - if (dn->bits&DECINF) targhi=DECIMAL_Inf<<24; - else { // sNaN or qNaN - if ((*dn->lsu!=0 || dn->digits>1) // non-zero coefficient - && (dn->digits<DECIMAL128_Pmax)) { // coefficient fits - decDigitsToDPD(dn, targar, 0); - } - if (dn->bits&DECNAN) targhi|=DECIMAL_NaN<<24; - else targhi|=DECIMAL_sNaN<<24; - } // a NaN - } // special - - else { // is finite - if (decNumberIsZero(dn)) { // is a zero - // set and clamp exponent - if (dn->exponent<-DECIMAL128_Bias) { - exp=0; // low clamp - status|=DEC_Clamped; - } - else { - exp=dn->exponent+DECIMAL128_Bias; // bias exponent - if (exp>DECIMAL128_Ehigh) { // top clamp - exp=DECIMAL128_Ehigh; - status|=DEC_Clamped; - } - } - comb=(exp>>9) & 0x18; // msd=0, exp top 2 bits .. - } - else { // non-zero finite number - uInt msd; // work - Int pad=0; // coefficient pad digits - - // the dn is known to fit, but it may need to be padded - exp=(uInt)(dn->exponent+DECIMAL128_Bias); // bias exponent - if (exp>DECIMAL128_Ehigh) { // fold-down case - pad=exp-DECIMAL128_Ehigh; - exp=DECIMAL128_Ehigh; // [to maximum] - status|=DEC_Clamped; - } - - // [fastpath for common case is not a win, here] - decDigitsToDPD(dn, targar, pad); - // save and clear the top digit - msd=targhi>>14; - targhi&=0x00003fff; - - // create the combination field - if (msd>=8) comb=0x18 | ((exp>>11) & 0x06) | (msd & 0x01); - else comb=((exp>>9) & 0x18) | msd; - } - targhi|=comb<<26; // add combination field .. - targhi|=(exp&0xfff)<<14; // .. and exponent continuation - } // finite - - if (dn->bits&DECNEG) targhi|=0x80000000; // add sign bit - - // now write to storage; this is endian - if (DECLITEND) { - // lo -> hi - UBFROMUI(d128->bytes, targlo); - UBFROMUI(d128->bytes+4, targml); - UBFROMUI(d128->bytes+8, targmh); - UBFROMUI(d128->bytes+12, targhi); - } - else { - // hi -> lo - UBFROMUI(d128->bytes, targhi); - UBFROMUI(d128->bytes+4, targmh); - UBFROMUI(d128->bytes+8, targml); - UBFROMUI(d128->bytes+12, targlo); - } - - if (status!=0) decContextSetStatus(set, status); // pass on status - // decimal128Show(d128); - return d128; - } // decimal128FromNumber - -/* ------------------------------------------------------------------ */ -/* decimal128ToNumber -- convert decimal128 to decNumber */ -/* d128 is the source decimal128 */ -/* dn is the target number, with appropriate space */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -decNumber * decimal128ToNumber(const decimal128 *d128, decNumber *dn) { - uInt msd; // coefficient MSD - uInt exp; // exponent top two bits - uInt comb; // combination field - Int need; // work - uInt uiwork; // for macros - uInt sourar[4]; // source 128-bit - #define sourhi sourar[3] // name the word with the sign - #define sourmh sourar[2] // and the mid-high word - #define sourml sourar[1] // and the mod-low word - #define sourlo sourar[0] // and the lowest word - - // load source from storage; this is endian - if (DECLITEND) { - sourlo=UBTOUI(d128->bytes ); // directly load the low int - sourml=UBTOUI(d128->bytes+4 ); // then the mid-low - sourmh=UBTOUI(d128->bytes+8 ); // then the mid-high - sourhi=UBTOUI(d128->bytes+12); // then the high int - } - else { - sourhi=UBTOUI(d128->bytes ); // directly load the high int - sourmh=UBTOUI(d128->bytes+4 ); // then the mid-high - sourml=UBTOUI(d128->bytes+8 ); // then the mid-low - sourlo=UBTOUI(d128->bytes+12); // then the low int - } - - comb=(sourhi>>26)&0x1f; // combination field - - decNumberZero(dn); // clean number - if (sourhi&0x80000000) dn->bits=DECNEG; // set sign if negative - - msd=COMBMSD[comb]; // decode the combination field - exp=COMBEXP[comb]; // .. - - if (exp==3) { // is a special - if (msd==0) { - dn->bits|=DECINF; - return dn; // no coefficient needed - } - else if (sourhi&0x02000000) dn->bits|=DECSNAN; - else dn->bits|=DECNAN; - msd=0; // no top digit - } - else { // is a finite number - dn->exponent=(exp<<12)+((sourhi>>14)&0xfff)-DECIMAL128_Bias; // unbiased - } - - // get the coefficient - sourhi&=0x00003fff; // clean coefficient continuation - if (msd) { // non-zero msd - sourhi|=msd<<14; // prefix to coefficient - need=12; // process 12 declets - } - else { // msd=0 - if (sourhi) need=11; // declets to process - else if (sourmh) need=10; - else if (sourml) need=7; - else if (sourlo) need=4; - else return dn; // easy: coefficient is 0 - } //msd=0 - - decDigitsFromDPD(dn, sourar, need); // process declets - // decNumberShow(dn); - return dn; - } // decimal128ToNumber - -/* ------------------------------------------------------------------ */ -/* to-scientific-string -- conversion to numeric string */ -/* to-engineering-string -- conversion to numeric string */ -/* */ -/* decimal128ToString(d128, string); */ -/* decimal128ToEngString(d128, string); */ -/* */ -/* d128 is the decimal128 format number to convert */ -/* string is the string where the result will be laid out */ -/* */ -/* string must be at least 24 characters */ -/* */ -/* No error is possible, and no status can be set. */ -/* ------------------------------------------------------------------ */ -char * decimal128ToEngString(const decimal128 *d128, char *string){ - decNumber dn; // work - decimal128ToNumber(d128, &dn); - decNumberToEngString(&dn, string); - return string; - } // decimal128ToEngString - -char * decimal128ToString(const decimal128 *d128, char *string){ - uInt msd; // coefficient MSD - Int exp; // exponent top two bits or full - uInt comb; // combination field - char *cstart; // coefficient start - char *c; // output pointer in string - const uByte *u; // work - char *s, *t; // .. (source, target) - Int dpd; // .. - Int pre, e; // .. - uInt uiwork; // for macros - - uInt sourar[4]; // source 128-bit - #define sourhi sourar[3] // name the word with the sign - #define sourmh sourar[2] // and the mid-high word - #define sourml sourar[1] // and the mod-low word - #define sourlo sourar[0] // and the lowest word - - // load source from storage; this is endian - if (DECLITEND) { - sourlo=UBTOUI(d128->bytes ); // directly load the low int - sourml=UBTOUI(d128->bytes+4 ); // then the mid-low - sourmh=UBTOUI(d128->bytes+8 ); // then the mid-high - sourhi=UBTOUI(d128->bytes+12); // then the high int - } - else { - sourhi=UBTOUI(d128->bytes ); // directly load the high int - sourmh=UBTOUI(d128->bytes+4 ); // then the mid-high - sourml=UBTOUI(d128->bytes+8 ); // then the mid-low - sourlo=UBTOUI(d128->bytes+12); // then the low int - } - - c=string; // where result will go - if (((Int)sourhi)<0) *c++='-'; // handle sign - - comb=(sourhi>>26)&0x1f; // combination field - msd=COMBMSD[comb]; // decode the combination field - exp=COMBEXP[comb]; // .. - - if (exp==3) { - if (msd==0) { // infinity - strcpy(c, "Inf"); - strcpy(c+3, "inity"); - return string; // easy - } - if (sourhi&0x02000000) *c++='s'; // sNaN - strcpy(c, "NaN"); // complete word - c+=3; // step past - if (sourlo==0 && sourml==0 && sourmh==0 - && (sourhi&0x0003ffff)==0) return string; // zero payload - // otherwise drop through to add integer; set correct exp - exp=0; msd=0; // setup for following code - } - else exp=(exp<<12)+((sourhi>>14)&0xfff)-DECIMAL128_Bias; // unbiased - - // convert 34 digits of significand to characters - cstart=c; // save start of coefficient - if (msd) *c++='0'+(char)msd; // non-zero most significant digit - - // Now decode the declets. After extracting each one, it is - // decoded to binary and then to a 4-char sequence by table lookup; - // the 4-chars are a 1-char length (significant digits, except 000 - // has length 0). This allows us to left-align the first declet - // with non-zero content, then remaining ones are full 3-char - // length. We use fixed-length memcpys because variable-length - // causes a subroutine call in GCC. (These are length 4 for speed - // and are safe because the array has an extra terminator byte.) - #define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4]; \ - if (c!=cstart) {memcpy(c, u+1, 4); c+=3;} \ - else if (*u) {memcpy(c, u+4-*u, 4); c+=*u;} - dpd=(sourhi>>4)&0x3ff; // declet 1 - dpd2char; - dpd=((sourhi&0xf)<<6) | (sourmh>>26); // declet 2 - dpd2char; - dpd=(sourmh>>16)&0x3ff; // declet 3 - dpd2char; - dpd=(sourmh>>6)&0x3ff; // declet 4 - dpd2char; - dpd=((sourmh&0x3f)<<4) | (sourml>>28); // declet 5 - dpd2char; - dpd=(sourml>>18)&0x3ff; // declet 6 - dpd2char; - dpd=(sourml>>8)&0x3ff; // declet 7 - dpd2char; - dpd=((sourml&0xff)<<2) | (sourlo>>30); // declet 8 - dpd2char; - dpd=(sourlo>>20)&0x3ff; // declet 9 - dpd2char; - dpd=(sourlo>>10)&0x3ff; // declet 10 - dpd2char; - dpd=(sourlo)&0x3ff; // declet 11 - dpd2char; - - if (c==cstart) *c++='0'; // all zeros -- make 0 - - if (exp==0) { // integer or NaN case -- easy - *c='\0'; // terminate - return string; - } - - /* non-0 exponent */ - e=0; // assume no E - pre=c-cstart+exp; - // [here, pre-exp is the digits count (==1 for zero)] - if (exp>0 || pre<-5) { // need exponential form - e=pre-1; // calculate E value - pre=1; // assume one digit before '.' - } // exponential form - - /* modify the coefficient, adding 0s, '.', and E+nn as needed */ - s=c-1; // source (LSD) - if (pre>0) { // ddd.ddd (plain), perhaps with E - char *dotat=cstart+pre; - if (dotat<c) { // if embedded dot needed... - t=c; // target - for (; s>=dotat; s--, t--) *t=*s; // open the gap; leave t at gap - *t='.'; // insert the dot - c++; // length increased by one - } - - // finally add the E-part, if needed; it will never be 0, and has - // a maximum length of 4 digits - if (e!=0) { - *c++='E'; // starts with E - *c++='+'; // assume positive - if (e<0) { - *(c-1)='-'; // oops, need '-' - e=-e; // uInt, please - } - if (e<1000) { // 3 (or fewer) digits case - u=&BIN2CHAR[e*4]; // -> length byte - memcpy(c, u+4-*u, 4); // copy fixed 4 characters [is safe] - c+=*u; // bump pointer appropriately - } - else { // 4-digits - Int thou=((e>>3)*1049)>>17; // e/1000 - Int rem=e-(1000*thou); // e%1000 - *c++='0'+(char)thou; - u=&BIN2CHAR[rem*4]; // -> length byte - memcpy(c, u+1, 4); // copy fixed 3+1 characters [is safe] - c+=3; // bump pointer, always 3 digits - } - } - *c='\0'; // add terminator - //printf("res %s\n", string); - return string; - } // pre>0 - - /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */ - t=c+1-pre; - *(t+1)='\0'; // can add terminator now - for (; s>=cstart; s--, t--) *t=*s; // shift whole coefficient right - c=cstart; - *c++='0'; // always starts with 0. - *c++='.'; - for (; pre<0; pre++) *c++='0'; // add any 0's after '.' - //printf("res %s\n", string); - return string; - } // decimal128ToString - -/* ------------------------------------------------------------------ */ -/* to-number -- conversion from numeric string */ -/* */ -/* decimal128FromString(result, string, set); */ -/* */ -/* result is the decimal128 format number which gets the result of */ -/* the conversion */ -/* *string is the character string which should contain a valid */ -/* number (which may be a special value) */ -/* set is the context */ -/* */ -/* The context is supplied to this routine is used for error handling */ -/* (setting of status and traps) and for the rounding mode, only. */ -/* If an error occurs, the result will be a valid decimal128 NaN. */ -/* ------------------------------------------------------------------ */ -decimal128 * decimal128FromString(decimal128 *result, const char *string, - decContext *set) { - decContext dc; // work - decNumber dn; // .. - - decContextDefault(&dc, DEC_INIT_DECIMAL128); // no traps, please - dc.round=set->round; // use supplied rounding - - decNumberFromString(&dn, string, &dc); // will round if needed - decimal128FromNumber(result, &dn, &dc); - if (dc.status!=0) { // something happened - decContextSetStatus(set, dc.status); // .. pass it on - } - return result; - } // decimal128FromString - -/* ------------------------------------------------------------------ */ -/* decimal128IsCanonical -- test whether encoding is canonical */ -/* d128 is the source decimal128 */ -/* returns 1 if the encoding of d128 is canonical, 0 otherwise */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -uInt decimal128IsCanonical(const decimal128 *d128) { - decNumber dn; // work - decimal128 canon; // .. - decContext dc; // .. - decContextDefault(&dc, DEC_INIT_DECIMAL128); - decimal128ToNumber(d128, &dn); - decimal128FromNumber(&canon, &dn, &dc);// canon will now be canonical - return memcmp(d128, &canon, DECIMAL128_Bytes)==0; - } // decimal128IsCanonical - -/* ------------------------------------------------------------------ */ -/* decimal128Canonical -- copy an encoding, ensuring it is canonical */ -/* d128 is the source decimal128 */ -/* result is the target (may be the same decimal128) */ -/* returns result */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -decimal128 * decimal128Canonical(decimal128 *result, const decimal128 *d128) { - decNumber dn; // work - decContext dc; // .. - decContextDefault(&dc, DEC_INIT_DECIMAL128); - decimal128ToNumber(d128, &dn); - decimal128FromNumber(result, &dn, &dc);// result will now be canonical - return result; - } // decimal128Canonical - -#if DECTRACE || DECCHECK -/* Macros for accessing decimal128 fields. These assume the argument - is a reference (pointer) to the decimal128 structure, and the - decimal128 is in network byte order (big-endian) */ -// Get sign -#define decimal128Sign(d) ((unsigned)(d)->bytes[0]>>7) - -// Get combination field -#define decimal128Comb(d) (((d)->bytes[0] & 0x7c)>>2) - -// Get exponent continuation [does not remove bias] -#define decimal128ExpCon(d) ((((d)->bytes[0] & 0x03)<<10) \ - | ((unsigned)(d)->bytes[1]<<2) \ - | ((unsigned)(d)->bytes[2]>>6)) - -// Set sign [this assumes sign previously 0] -#define decimal128SetSign(d, b) { \ - (d)->bytes[0]|=((unsigned)(b)<<7);} - -// Set exponent continuation [does not apply bias] -// This assumes range has been checked and exponent previously 0; -// type of exponent must be unsigned -#define decimal128SetExpCon(d, e) { \ - (d)->bytes[0]|=(uByte)((e)>>10); \ - (d)->bytes[1] =(uByte)(((e)&0x3fc)>>2); \ - (d)->bytes[2]|=(uByte)(((e)&0x03)<<6);} - -/* ------------------------------------------------------------------ */ -/* decimal128Show -- display a decimal128 in hexadecimal [debug aid] */ -/* d128 -- the number to show */ -/* ------------------------------------------------------------------ */ -// Also shows sign/cob/expconfields extracted -void decimal128Show(const decimal128 *d128) { - char buf[DECIMAL128_Bytes*2+1]; - Int i, j=0; - - if (DECLITEND) { - for (i=0; i<DECIMAL128_Bytes; i++, j+=2) { - sprintf(&buf[j], "%02x", d128->bytes[15-i]); - } - printf(" D128> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf, - d128->bytes[15]>>7, (d128->bytes[15]>>2)&0x1f, - ((d128->bytes[15]&0x3)<<10)|(d128->bytes[14]<<2)| - (d128->bytes[13]>>6)); - } - else { - for (i=0; i<DECIMAL128_Bytes; i++, j+=2) { - sprintf(&buf[j], "%02x", d128->bytes[i]); - } - printf(" D128> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf, - decimal128Sign(d128), decimal128Comb(d128), - decimal128ExpCon(d128)); - } - } // decimal128Show -#endif
src/decNumber/decimal128.h
@@ -1,81 +0,0 @@-/* ------------------------------------------------------------------ */ -/* Decimal 128-bit format module header */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2005. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is called decNumber.pdf. This document is */ -/* available, together with arithmetic and format specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ - -#if !defined(DECIMAL128) - #define DECIMAL128 - #define DEC128NAME "decimal128" /* Short name */ - #define DEC128FULLNAME "Decimal 128-bit Number" /* Verbose name */ - #define DEC128AUTHOR "Mike Cowlishaw" /* Who to blame */ - - /* parameters for decimal128s */ - #define DECIMAL128_Bytes 16 /* length */ - #define DECIMAL128_Pmax 34 /* maximum precision (digits) */ - #define DECIMAL128_Emax 6144 /* maximum adjusted exponent */ - #define DECIMAL128_Emin -6143 /* minimum adjusted exponent */ - #define DECIMAL128_Bias 6176 /* bias for the exponent */ - #define DECIMAL128_String 43 /* maximum string length, +1 */ - #define DECIMAL128_EconL 12 /* exp. continuation length */ - /* highest biased exponent (Elimit-1) */ - #define DECIMAL128_Ehigh (DECIMAL128_Emax+DECIMAL128_Bias-DECIMAL128_Pmax+1) - - /* check enough digits, if pre-defined */ - #if defined(DECNUMDIGITS) - #if (DECNUMDIGITS<DECIMAL128_Pmax) - #error decimal128.h needs pre-defined DECNUMDIGITS>=34 for safe use - #endif - #endif - - #ifndef DECNUMDIGITS - #define DECNUMDIGITS DECIMAL128_Pmax /* size if not already defined*/ - #endif - #ifndef DECNUMBER - #include "decNumber.h" /* context and number library */ - #endif - - /* Decimal 128-bit type, accessible by bytes */ - typedef struct { - uint8_t bytes[DECIMAL128_Bytes]; /* decimal128: 1, 5, 12, 110 bits*/ - } decimal128; - - /* special values [top byte excluding sign bit; last two bits are */ - /* don't-care for Infinity on input, last bit don't-care for NaN] */ - #if !defined(DECIMAL_NaN) - #define DECIMAL_NaN 0x7c /* 0 11111 00 NaN */ - #define DECIMAL_sNaN 0x7e /* 0 11111 10 sNaN */ - #define DECIMAL_Inf 0x78 /* 0 11110 00 Infinity */ - #endif - - /* ---------------------------------------------------------------- */ - /* Routines */ - /* ---------------------------------------------------------------- */ - /* String conversions */ - decimal128 * decimal128FromString(decimal128 *, const char *, decContext *); - char * decimal128ToString(const decimal128 *, char *); - char * decimal128ToEngString(const decimal128 *, char *); - - /* decNumber conversions */ - decimal128 * decimal128FromNumber(decimal128 *, const decNumber *, - decContext *); - decNumber * decimal128ToNumber(const decimal128 *, decNumber *); - - /* Format-dependent utilities */ - uint32_t decimal128IsCanonical(const decimal128 *); - decimal128 * decimal128Canonical(decimal128 *, const decimal128 *); - -#endif
src/decNumber/decimal32.c
@@ -1,476 +0,0 @@-/* ------------------------------------------------------------------ */ -/* Decimal 32-bit format module */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2008. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is called decNumber.pdf. This document is */ -/* available, together with arithmetic and format specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ -/* This module comprises the routines for decimal32 format numbers. */ -/* Conversions are supplied to and from decNumber and String. */ -/* */ -/* This is used when decNumber provides operations, either for all */ -/* operations or as a proxy between decNumber and decSingle. */ -/* */ -/* Error handling is the same as decNumber (qv.). */ -/* ------------------------------------------------------------------ */ -#include <string.h> // [for memset/memcpy] -#include <stdio.h> // [for printf] - -#define DECNUMDIGITS 7 // make decNumbers with space for 7 -#include "decNumber.h" // base number library -#include "decNumberLocal.h" // decNumber local types, etc. -#include "decimal32.h" // our primary include - -/* Utility tables and routines [in decimal64.c] */ -// DPD2BIN and the reverse are renamed to prevent link-time conflict -// if decQuad is also built in the same executable -#define DPD2BIN DPD2BINx -#define BIN2DPD BIN2DPDx -extern const uInt COMBEXP[32], COMBMSD[32]; -extern const uShort DPD2BIN[1024]; -extern const uShort BIN2DPD[1000]; -extern const uByte BIN2CHAR[4001]; - -extern void decDigitsToDPD(const decNumber *, uInt *, Int); -extern void decDigitsFromDPD(decNumber *, const uInt *, Int); - -#if DECTRACE || DECCHECK -void decimal32Show(const decimal32 *); // for debug -extern void decNumberShow(const decNumber *); // .. -#endif - -/* Useful macro */ -// Clear a structure (e.g., a decNumber) -#define DEC_clear(d) memset(d, 0, sizeof(*d)) - -/* ------------------------------------------------------------------ */ -/* decimal32FromNumber -- convert decNumber to decimal32 */ -/* */ -/* ds is the target decimal32 */ -/* dn is the source number (assumed valid) */ -/* set is the context, used only for reporting errors */ -/* */ -/* The set argument is used only for status reporting and for the */ -/* rounding mode (used if the coefficient is more than DECIMAL32_Pmax */ -/* digits or an overflow is detected). If the exponent is out of the */ -/* valid range then Overflow or Underflow will be raised. */ -/* After Underflow a subnormal result is possible. */ -/* */ -/* DEC_Clamped is set if the number has to be 'folded down' to fit, */ -/* by reducing its exponent and multiplying the coefficient by a */ -/* power of ten, or if the exponent on a zero had to be clamped. */ -/* ------------------------------------------------------------------ */ -decimal32 * decimal32FromNumber(decimal32 *d32, const decNumber *dn, - decContext *set) { - uInt status=0; // status accumulator - Int ae; // adjusted exponent - decNumber dw; // work - decContext dc; // .. - uInt comb, exp; // .. - uInt uiwork; // for macros - uInt targ=0; // target 32-bit - - // If the number has too many digits, or the exponent could be - // out of range then reduce the number under the appropriate - // constraints. This could push the number to Infinity or zero, - // so this check and rounding must be done before generating the - // decimal32] - ae=dn->exponent+dn->digits-1; // [0 if special] - if (dn->digits>DECIMAL32_Pmax // too many digits - || ae>DECIMAL32_Emax // likely overflow - || ae<DECIMAL32_Emin) { // likely underflow - decContextDefault(&dc, DEC_INIT_DECIMAL32); // [no traps] - dc.round=set->round; // use supplied rounding - decNumberPlus(&dw, dn, &dc); // (round and check) - // [this changes -0 to 0, so enforce the sign...] - dw.bits|=dn->bits&DECNEG; - status=dc.status; // save status - dn=&dw; // use the work number - } // maybe out of range - - if (dn->bits&DECSPECIAL) { // a special value - if (dn->bits&DECINF) targ=DECIMAL_Inf<<24; - else { // sNaN or qNaN - if ((*dn->lsu!=0 || dn->digits>1) // non-zero coefficient - && (dn->digits<DECIMAL32_Pmax)) { // coefficient fits - decDigitsToDPD(dn, &targ, 0); - } - if (dn->bits&DECNAN) targ|=DECIMAL_NaN<<24; - else targ|=DECIMAL_sNaN<<24; - } // a NaN - } // special - - else { // is finite - if (decNumberIsZero(dn)) { // is a zero - // set and clamp exponent - if (dn->exponent<-DECIMAL32_Bias) { - exp=0; // low clamp - status|=DEC_Clamped; - } - else { - exp=dn->exponent+DECIMAL32_Bias; // bias exponent - if (exp>DECIMAL32_Ehigh) { // top clamp - exp=DECIMAL32_Ehigh; - status|=DEC_Clamped; - } - } - comb=(exp>>3) & 0x18; // msd=0, exp top 2 bits .. - } - else { // non-zero finite number - uInt msd; // work - Int pad=0; // coefficient pad digits - - // the dn is known to fit, but it may need to be padded - exp=(uInt)(dn->exponent+DECIMAL32_Bias); // bias exponent - if (exp>DECIMAL32_Ehigh) { // fold-down case - pad=exp-DECIMAL32_Ehigh; - exp=DECIMAL32_Ehigh; // [to maximum] - status|=DEC_Clamped; - } - - // fastpath common case - if (DECDPUN==3 && pad==0) { - targ=BIN2DPD[dn->lsu[0]]; - if (dn->digits>3) targ|=(uInt)(BIN2DPD[dn->lsu[1]])<<10; - msd=(dn->digits==7 ? dn->lsu[2] : 0); - } - else { // general case - decDigitsToDPD(dn, &targ, pad); - // save and clear the top digit - msd=targ>>20; - targ&=0x000fffff; - } - - // create the combination field - if (msd>=8) comb=0x18 | ((exp>>5) & 0x06) | (msd & 0x01); - else comb=((exp>>3) & 0x18) | msd; - } - targ|=comb<<26; // add combination field .. - targ|=(exp&0x3f)<<20; // .. and exponent continuation - } // finite - - if (dn->bits&DECNEG) targ|=0x80000000; // add sign bit - - // now write to storage; this is endian - UBFROMUI(d32->bytes, targ); // directly store the int - - if (status!=0) decContextSetStatus(set, status); // pass on status - // decimal32Show(d32); - return d32; - } // decimal32FromNumber - -/* ------------------------------------------------------------------ */ -/* decimal32ToNumber -- convert decimal32 to decNumber */ -/* d32 is the source decimal32 */ -/* dn is the target number, with appropriate space */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -decNumber * decimal32ToNumber(const decimal32 *d32, decNumber *dn) { - uInt msd; // coefficient MSD - uInt exp; // exponent top two bits - uInt comb; // combination field - uInt sour; // source 32-bit - uInt uiwork; // for macros - - // load source from storage; this is endian - sour=UBTOUI(d32->bytes); // directly load the int - - comb=(sour>>26)&0x1f; // combination field - - decNumberZero(dn); // clean number - if (sour&0x80000000) dn->bits=DECNEG; // set sign if negative - - msd=COMBMSD[comb]; // decode the combination field - exp=COMBEXP[comb]; // .. - - if (exp==3) { // is a special - if (msd==0) { - dn->bits|=DECINF; - return dn; // no coefficient needed - } - else if (sour&0x02000000) dn->bits|=DECSNAN; - else dn->bits|=DECNAN; - msd=0; // no top digit - } - else { // is a finite number - dn->exponent=(exp<<6)+((sour>>20)&0x3f)-DECIMAL32_Bias; // unbiased - } - - // get the coefficient - sour&=0x000fffff; // clean coefficient continuation - if (msd) { // non-zero msd - sour|=msd<<20; // prefix to coefficient - decDigitsFromDPD(dn, &sour, 3); // process 3 declets - return dn; - } - // msd=0 - if (!sour) return dn; // easy: coefficient is 0 - if (sour&0x000ffc00) // need 2 declets? - decDigitsFromDPD(dn, &sour, 2); // process 2 declets - else - decDigitsFromDPD(dn, &sour, 1); // process 1 declet - return dn; - } // decimal32ToNumber - -/* ------------------------------------------------------------------ */ -/* to-scientific-string -- conversion to numeric string */ -/* to-engineering-string -- conversion to numeric string */ -/* */ -/* decimal32ToString(d32, string); */ -/* decimal32ToEngString(d32, string); */ -/* */ -/* d32 is the decimal32 format number to convert */ -/* string is the string where the result will be laid out */ -/* */ -/* string must be at least 24 characters */ -/* */ -/* No error is possible, and no status can be set. */ -/* ------------------------------------------------------------------ */ -char * decimal32ToEngString(const decimal32 *d32, char *string){ - decNumber dn; // work - decimal32ToNumber(d32, &dn); - decNumberToEngString(&dn, string); - return string; - } // decimal32ToEngString - -char * decimal32ToString(const decimal32 *d32, char *string){ - uInt msd; // coefficient MSD - Int exp; // exponent top two bits or full - uInt comb; // combination field - char *cstart; // coefficient start - char *c; // output pointer in string - const uByte *u; // work - char *s, *t; // .. (source, target) - Int dpd; // .. - Int pre, e; // .. - uInt uiwork; // for macros - uInt sour; // source 32-bit - - // load source from storage; this is endian - sour=UBTOUI(d32->bytes); // directly load the int - - c=string; // where result will go - if (((Int)sour)<0) *c++='-'; // handle sign - - comb=(sour>>26)&0x1f; // combination field - msd=COMBMSD[comb]; // decode the combination field - exp=COMBEXP[comb]; // .. - - if (exp==3) { - if (msd==0) { // infinity - strcpy(c, "Inf"); - strcpy(c+3, "inity"); - return string; // easy - } - if (sour&0x02000000) *c++='s'; // sNaN - strcpy(c, "NaN"); // complete word - c+=3; // step past - if ((sour&0x000fffff)==0) return string; // zero payload - // otherwise drop through to add integer; set correct exp - exp=0; msd=0; // setup for following code - } - else exp=(exp<<6)+((sour>>20)&0x3f)-DECIMAL32_Bias; // unbiased - - // convert 7 digits of significand to characters - cstart=c; // save start of coefficient - if (msd) *c++='0'+(char)msd; // non-zero most significant digit - - // Now decode the declets. After extracting each one, it is - // decoded to binary and then to a 4-char sequence by table lookup; - // the 4-chars are a 1-char length (significant digits, except 000 - // has length 0). This allows us to left-align the first declet - // with non-zero content, then remaining ones are full 3-char - // length. We use fixed-length memcpys because variable-length - // causes a subroutine call in GCC. (These are length 4 for speed - // and are safe because the array has an extra terminator byte.) - #define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4]; \ - if (c!=cstart) {memcpy(c, u+1, 4); c+=3;} \ - else if (*u) {memcpy(c, u+4-*u, 4); c+=*u;} - - dpd=(sour>>10)&0x3ff; // declet 1 - dpd2char; - dpd=(sour)&0x3ff; // declet 2 - dpd2char; - - if (c==cstart) *c++='0'; // all zeros -- make 0 - - if (exp==0) { // integer or NaN case -- easy - *c='\0'; // terminate - return string; - } - - /* non-0 exponent */ - e=0; // assume no E - pre=c-cstart+exp; - // [here, pre-exp is the digits count (==1 for zero)] - if (exp>0 || pre<-5) { // need exponential form - e=pre-1; // calculate E value - pre=1; // assume one digit before '.' - } // exponential form - - /* modify the coefficient, adding 0s, '.', and E+nn as needed */ - s=c-1; // source (LSD) - if (pre>0) { // ddd.ddd (plain), perhaps with E - char *dotat=cstart+pre; - if (dotat<c) { // if embedded dot needed... - t=c; // target - for (; s>=dotat; s--, t--) *t=*s; // open the gap; leave t at gap - *t='.'; // insert the dot - c++; // length increased by one - } - - // finally add the E-part, if needed; it will never be 0, and has - // a maximum length of 3 digits (E-101 case) - if (e!=0) { - *c++='E'; // starts with E - *c++='+'; // assume positive - if (e<0) { - *(c-1)='-'; // oops, need '-' - e=-e; // uInt, please - } - u=&BIN2CHAR[e*4]; // -> length byte - memcpy(c, u+4-*u, 4); // copy fixed 4 characters [is safe] - c+=*u; // bump pointer appropriately - } - *c='\0'; // add terminator - //printf("res %s\n", string); - return string; - } // pre>0 - - /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */ - t=c+1-pre; - *(t+1)='\0'; // can add terminator now - for (; s>=cstart; s--, t--) *t=*s; // shift whole coefficient right - c=cstart; - *c++='0'; // always starts with 0. - *c++='.'; - for (; pre<0; pre++) *c++='0'; // add any 0's after '.' - //printf("res %s\n", string); - return string; - } // decimal32ToString - -/* ------------------------------------------------------------------ */ -/* to-number -- conversion from numeric string */ -/* */ -/* decimal32FromString(result, string, set); */ -/* */ -/* result is the decimal32 format number which gets the result of */ -/* the conversion */ -/* *string is the character string which should contain a valid */ -/* number (which may be a special value) */ -/* set is the context */ -/* */ -/* The context is supplied to this routine is used for error handling */ -/* (setting of status and traps) and for the rounding mode, only. */ -/* If an error occurs, the result will be a valid decimal32 NaN. */ -/* ------------------------------------------------------------------ */ -decimal32 * decimal32FromString(decimal32 *result, const char *string, - decContext *set) { - decContext dc; // work - decNumber dn; // .. - - decContextDefault(&dc, DEC_INIT_DECIMAL32); // no traps, please - dc.round=set->round; // use supplied rounding - - decNumberFromString(&dn, string, &dc); // will round if needed - decimal32FromNumber(result, &dn, &dc); - if (dc.status!=0) { // something happened - decContextSetStatus(set, dc.status); // .. pass it on - } - return result; - } // decimal32FromString - -/* ------------------------------------------------------------------ */ -/* decimal32IsCanonical -- test whether encoding is canonical */ -/* d32 is the source decimal32 */ -/* returns 1 if the encoding of d32 is canonical, 0 otherwise */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -uInt decimal32IsCanonical(const decimal32 *d32) { - decNumber dn; // work - decimal32 canon; // .. - decContext dc; // .. - decContextDefault(&dc, DEC_INIT_DECIMAL32); - decimal32ToNumber(d32, &dn); - decimal32FromNumber(&canon, &dn, &dc);// canon will now be canonical - return memcmp(d32, &canon, DECIMAL32_Bytes)==0; - } // decimal32IsCanonical - -/* ------------------------------------------------------------------ */ -/* decimal32Canonical -- copy an encoding, ensuring it is canonical */ -/* d32 is the source decimal32 */ -/* result is the target (may be the same decimal32) */ -/* returns result */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -decimal32 * decimal32Canonical(decimal32 *result, const decimal32 *d32) { - decNumber dn; // work - decContext dc; // .. - decContextDefault(&dc, DEC_INIT_DECIMAL32); - decimal32ToNumber(d32, &dn); - decimal32FromNumber(result, &dn, &dc);// result will now be canonical - return result; - } // decimal32Canonical - -#if DECTRACE || DECCHECK -/* Macros for accessing decimal32 fields. These assume the argument - is a reference (pointer) to the decimal32 structure, and the - decimal32 is in network byte order (big-endian) */ -// Get sign -#define decimal32Sign(d) ((unsigned)(d)->bytes[0]>>7) - -// Get combination field -#define decimal32Comb(d) (((d)->bytes[0] & 0x7c)>>2) - -// Get exponent continuation [does not remove bias] -#define decimal32ExpCon(d) ((((d)->bytes[0] & 0x03)<<4) \ - | ((unsigned)(d)->bytes[1]>>4)) - -// Set sign [this assumes sign previously 0] -#define decimal32SetSign(d, b) { \ - (d)->bytes[0]|=((unsigned)(b)<<7);} - -// Set exponent continuation [does not apply bias] -// This assumes range has been checked and exponent previously 0; -// type of exponent must be unsigned -#define decimal32SetExpCon(d, e) { \ - (d)->bytes[0]|=(uByte)((e)>>4); \ - (d)->bytes[1]|=(uByte)(((e)&0x0F)<<4);} - -/* ------------------------------------------------------------------ */ -/* decimal32Show -- display a decimal32 in hexadecimal [debug aid] */ -/* d32 -- the number to show */ -/* ------------------------------------------------------------------ */ -// Also shows sign/cob/expconfields extracted - valid bigendian only -void decimal32Show(const decimal32 *d32) { - char buf[DECIMAL32_Bytes*2+1]; - Int i, j=0; - - if (DECLITEND) { - for (i=0; i<DECIMAL32_Bytes; i++, j+=2) { - sprintf(&buf[j], "%02x", d32->bytes[3-i]); - } - printf(" D32> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf, - d32->bytes[3]>>7, (d32->bytes[3]>>2)&0x1f, - ((d32->bytes[3]&0x3)<<4)| (d32->bytes[2]>>4)); - } - else { - for (i=0; i<DECIMAL32_Bytes; i++, j+=2) { - sprintf(&buf[j], "%02x", d32->bytes[i]); - } - printf(" D32> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf, - decimal32Sign(d32), decimal32Comb(d32), decimal32ExpCon(d32)); - } - } // decimal32Show -#endif
src/decNumber/decimal32.h
@@ -1,81 +0,0 @@-/* ------------------------------------------------------------------ */ -/* Decimal 32-bit format module header */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2006. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is called decNumber.pdf. This document is */ -/* available, together with arithmetic and format specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ - -#if !defined(DECIMAL32) - #define DECIMAL32 - #define DEC32NAME "decimal32" /* Short name */ - #define DEC32FULLNAME "Decimal 32-bit Number" /* Verbose name */ - #define DEC32AUTHOR "Mike Cowlishaw" /* Who to blame */ - - /* parameters for decimal32s */ - #define DECIMAL32_Bytes 4 /* length */ - #define DECIMAL32_Pmax 7 /* maximum precision (digits) */ - #define DECIMAL32_Emax 96 /* maximum adjusted exponent */ - #define DECIMAL32_Emin -95 /* minimum adjusted exponent */ - #define DECIMAL32_Bias 101 /* bias for the exponent */ - #define DECIMAL32_String 15 /* maximum string length, +1 */ - #define DECIMAL32_EconL 6 /* exp. continuation length */ - /* highest biased exponent (Elimit-1) */ - #define DECIMAL32_Ehigh (DECIMAL32_Emax+DECIMAL32_Bias-DECIMAL32_Pmax+1) - - /* check enough digits, if pre-defined */ - #if defined(DECNUMDIGITS) - #if (DECNUMDIGITS<DECIMAL32_Pmax) - #error decimal32.h needs pre-defined DECNUMDIGITS>=7 for safe use - #endif - #endif - - #ifndef DECNUMDIGITS - #define DECNUMDIGITS DECIMAL32_Pmax /* size if not already defined*/ - #endif - #ifndef DECNUMBER - #include "decNumber.h" /* context and number library */ - #endif - - /* Decimal 32-bit type, accessible by bytes */ - typedef struct { - uint8_t bytes[DECIMAL32_Bytes]; /* decimal32: 1, 5, 6, 20 bits*/ - } decimal32; - - /* special values [top byte excluding sign bit; last two bits are */ - /* don't-care for Infinity on input, last bit don't-care for NaN] */ - #if !defined(DECIMAL_NaN) - #define DECIMAL_NaN 0x7c /* 0 11111 00 NaN */ - #define DECIMAL_sNaN 0x7e /* 0 11111 10 sNaN */ - #define DECIMAL_Inf 0x78 /* 0 11110 00 Infinity */ - #endif - - /* ---------------------------------------------------------------- */ - /* Routines */ - /* ---------------------------------------------------------------- */ - /* String conversions */ - decimal32 * decimal32FromString(decimal32 *, const char *, decContext *); - char * decimal32ToString(const decimal32 *, char *); - char * decimal32ToEngString(const decimal32 *, char *); - - /* decNumber conversions */ - decimal32 * decimal32FromNumber(decimal32 *, const decNumber *, - decContext *); - decNumber * decimal32ToNumber(const decimal32 *, decNumber *); - - /* Format-dependent utilities */ - uint32_t decimal32IsCanonical(const decimal32 *); - decimal32 * decimal32Canonical(decimal32 *, const decimal32 *); - -#endif
src/decNumber/decimal64.c
@@ -1,839 +0,0 @@-/* ------------------------------------------------------------------ */ -/* Decimal 64-bit format module */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2009. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is called decNumber.pdf. This document is */ -/* available, together with arithmetic and format specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ -/* This module comprises the routines for decimal64 format numbers. */ -/* Conversions are supplied to and from decNumber and String. */ -/* */ -/* This is used when decNumber provides operations, either for all */ -/* operations or as a proxy between decNumber and decSingle. */ -/* */ -/* Error handling is the same as decNumber (qv.). */ -/* ------------------------------------------------------------------ */ -#include <string.h> // [for memset/memcpy] -#include <stdio.h> // [for printf] - -#define DECNUMDIGITS 16 // make decNumbers with space for 16 -#include "decNumber.h" // base number library -#include "decNumberLocal.h" // decNumber local types, etc. -#include "decimal64.h" // our primary include - -/* Utility routines and tables [in decimal64.c]; externs for C++ */ -// DPD2BIN and the reverse are renamed to prevent link-time conflict -// if decQuad is also built in the same executable -#define DPD2BIN DPD2BINx -#define BIN2DPD BIN2DPDx -extern const uInt COMBEXP[32], COMBMSD[32]; -extern const uShort DPD2BIN[1024]; -extern const uShort BIN2DPD[1000]; -extern const uByte BIN2CHAR[4001]; - -extern void decDigitsFromDPD(decNumber *, const uInt *, Int); -extern void decDigitsToDPD(const decNumber *, uInt *, Int); - -#if DECTRACE || DECCHECK -void decimal64Show(const decimal64 *); // for debug -extern void decNumberShow(const decNumber *); // .. -#endif - -/* Useful macro */ -// Clear a structure (e.g., a decNumber) -#define DEC_clear(d) memset(d, 0, sizeof(*d)) - -/* define and include the tables to use for conversions */ -#define DEC_BIN2CHAR 1 -#define DEC_DPD2BIN 1 -#define DEC_BIN2DPD 1 // used for all sizes -#include "decDPD.h" // lookup tables - -/* ------------------------------------------------------------------ */ -/* decimal64FromNumber -- convert decNumber to decimal64 */ -/* */ -/* ds is the target decimal64 */ -/* dn is the source number (assumed valid) */ -/* set is the context, used only for reporting errors */ -/* */ -/* The set argument is used only for status reporting and for the */ -/* rounding mode (used if the coefficient is more than DECIMAL64_Pmax */ -/* digits or an overflow is detected). If the exponent is out of the */ -/* valid range then Overflow or Underflow will be raised. */ -/* After Underflow a subnormal result is possible. */ -/* */ -/* DEC_Clamped is set if the number has to be 'folded down' to fit, */ -/* by reducing its exponent and multiplying the coefficient by a */ -/* power of ten, or if the exponent on a zero had to be clamped. */ -/* ------------------------------------------------------------------ */ -decimal64 * decimal64FromNumber(decimal64 *d64, const decNumber *dn, - decContext *set) { - uInt status=0; // status accumulator - Int ae; // adjusted exponent - decNumber dw; // work - decContext dc; // .. - uInt comb, exp; // .. - uInt uiwork; // for macros - uInt targar[2]={0, 0}; // target 64-bit - #define targhi targar[1] // name the word with the sign - #define targlo targar[0] // and the other - - // If the number has too many digits, or the exponent could be - // out of range then reduce the number under the appropriate - // constraints. This could push the number to Infinity or zero, - // so this check and rounding must be done before generating the - // decimal64] - ae=dn->exponent+dn->digits-1; // [0 if special] - if (dn->digits>DECIMAL64_Pmax // too many digits - || ae>DECIMAL64_Emax // likely overflow - || ae<DECIMAL64_Emin) { // likely underflow - decContextDefault(&dc, DEC_INIT_DECIMAL64); // [no traps] - dc.round=set->round; // use supplied rounding - decNumberPlus(&dw, dn, &dc); // (round and check) - // [this changes -0 to 0, so enforce the sign...] - dw.bits|=dn->bits&DECNEG; - status=dc.status; // save status - dn=&dw; // use the work number - } // maybe out of range - - if (dn->bits&DECSPECIAL) { // a special value - if (dn->bits&DECINF) targhi=DECIMAL_Inf<<24; - else { // sNaN or qNaN - if ((*dn->lsu!=0 || dn->digits>1) // non-zero coefficient - && (dn->digits<DECIMAL64_Pmax)) { // coefficient fits - decDigitsToDPD(dn, targar, 0); - } - if (dn->bits&DECNAN) targhi|=DECIMAL_NaN<<24; - else targhi|=DECIMAL_sNaN<<24; - } // a NaN - } // special - - else { // is finite - if (decNumberIsZero(dn)) { // is a zero - // set and clamp exponent - if (dn->exponent<-DECIMAL64_Bias) { - exp=0; // low clamp - status|=DEC_Clamped; - } - else { - exp=dn->exponent+DECIMAL64_Bias; // bias exponent - if (exp>DECIMAL64_Ehigh) { // top clamp - exp=DECIMAL64_Ehigh; - status|=DEC_Clamped; - } - } - comb=(exp>>5) & 0x18; // msd=0, exp top 2 bits .. - } - else { // non-zero finite number - uInt msd; // work - Int pad=0; // coefficient pad digits - - // the dn is known to fit, but it may need to be padded - exp=(uInt)(dn->exponent+DECIMAL64_Bias); // bias exponent - if (exp>DECIMAL64_Ehigh) { // fold-down case - pad=exp-DECIMAL64_Ehigh; - exp=DECIMAL64_Ehigh; // [to maximum] - status|=DEC_Clamped; - } - - // fastpath common case - if (DECDPUN==3 && pad==0) { - uInt dpd[6]={0,0,0,0,0,0}; - uInt i; - Int d=dn->digits; - for (i=0; d>0; i++, d-=3) dpd[i]=BIN2DPD[dn->lsu[i]]; - targlo =dpd[0]; - targlo|=dpd[1]<<10; - targlo|=dpd[2]<<20; - if (dn->digits>6) { - targlo|=dpd[3]<<30; - targhi =dpd[3]>>2; - targhi|=dpd[4]<<8; - } - msd=dpd[5]; // [did not really need conversion] - } - else { // general case - decDigitsToDPD(dn, targar, pad); - // save and clear the top digit - msd=targhi>>18; - targhi&=0x0003ffff; - } - - // create the combination field - if (msd>=8) comb=0x18 | ((exp>>7) & 0x06) | (msd & 0x01); - else comb=((exp>>5) & 0x18) | msd; - } - targhi|=comb<<26; // add combination field .. - targhi|=(exp&0xff)<<18; // .. and exponent continuation - } // finite - - if (dn->bits&DECNEG) targhi|=0x80000000; // add sign bit - - // now write to storage; this is now always endian - if (DECLITEND) { - // lo int then hi - UBFROMUI(d64->bytes, targar[0]); - UBFROMUI(d64->bytes+4, targar[1]); - } - else { - // hi int then lo - UBFROMUI(d64->bytes, targar[1]); - UBFROMUI(d64->bytes+4, targar[0]); - } - - if (status!=0) decContextSetStatus(set, status); // pass on status - // decimal64Show(d64); - return d64; - } // decimal64FromNumber - -/* ------------------------------------------------------------------ */ -/* decimal64ToNumber -- convert decimal64 to decNumber */ -/* d64 is the source decimal64 */ -/* dn is the target number, with appropriate space */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -decNumber * decimal64ToNumber(const decimal64 *d64, decNumber *dn) { - uInt msd; // coefficient MSD - uInt exp; // exponent top two bits - uInt comb; // combination field - Int need; // work - uInt uiwork; // for macros - uInt sourar[2]; // source 64-bit - #define sourhi sourar[1] // name the word with the sign - #define sourlo sourar[0] // and the lower word - - // load source from storage; this is endian - if (DECLITEND) { - sourlo=UBTOUI(d64->bytes ); // directly load the low int - sourhi=UBTOUI(d64->bytes+4); // then the high int - } - else { - sourhi=UBTOUI(d64->bytes ); // directly load the high int - sourlo=UBTOUI(d64->bytes+4); // then the low int - } - - comb=(sourhi>>26)&0x1f; // combination field - - decNumberZero(dn); // clean number - if (sourhi&0x80000000) dn->bits=DECNEG; // set sign if negative - - msd=COMBMSD[comb]; // decode the combination field - exp=COMBEXP[comb]; // .. - - if (exp==3) { // is a special - if (msd==0) { - dn->bits|=DECINF; - return dn; // no coefficient needed - } - else if (sourhi&0x02000000) dn->bits|=DECSNAN; - else dn->bits|=DECNAN; - msd=0; // no top digit - } - else { // is a finite number - dn->exponent=(exp<<8)+((sourhi>>18)&0xff)-DECIMAL64_Bias; // unbiased - } - - // get the coefficient - sourhi&=0x0003ffff; // clean coefficient continuation - if (msd) { // non-zero msd - sourhi|=msd<<18; // prefix to coefficient - need=6; // process 6 declets - } - else { // msd=0 - if (!sourhi) { // top word 0 - if (!sourlo) return dn; // easy: coefficient is 0 - need=3; // process at least 3 declets - if (sourlo&0xc0000000) need++; // process 4 declets - // [could reduce some more, here] - } - else { // some bits in top word, msd=0 - need=4; // process at least 4 declets - if (sourhi&0x0003ff00) need++; // top declet!=0, process 5 - } - } //msd=0 - - decDigitsFromDPD(dn, sourar, need); // process declets - return dn; - } // decimal64ToNumber - - -/* ------------------------------------------------------------------ */ -/* to-scientific-string -- conversion to numeric string */ -/* to-engineering-string -- conversion to numeric string */ -/* */ -/* decimal64ToString(d64, string); */ -/* decimal64ToEngString(d64, string); */ -/* */ -/* d64 is the decimal64 format number to convert */ -/* string is the string where the result will be laid out */ -/* */ -/* string must be at least 24 characters */ -/* */ -/* No error is possible, and no status can be set. */ -/* ------------------------------------------------------------------ */ -char * decimal64ToEngString(const decimal64 *d64, char *string){ - decNumber dn; // work - decimal64ToNumber(d64, &dn); - decNumberToEngString(&dn, string); - return string; - } // decimal64ToEngString - -char * decimal64ToString(const decimal64 *d64, char *string){ - uInt msd; // coefficient MSD - Int exp; // exponent top two bits or full - uInt comb; // combination field - char *cstart; // coefficient start - char *c; // output pointer in string - const uByte *u; // work - char *s, *t; // .. (source, target) - Int dpd; // .. - Int pre, e; // .. - uInt uiwork; // for macros - - uInt sourar[2]; // source 64-bit - #define sourhi sourar[1] // name the word with the sign - #define sourlo sourar[0] // and the lower word - - // load source from storage; this is endian - if (DECLITEND) { - sourlo=UBTOUI(d64->bytes ); // directly load the low int - sourhi=UBTOUI(d64->bytes+4); // then the high int - } - else { - sourhi=UBTOUI(d64->bytes ); // directly load the high int - sourlo=UBTOUI(d64->bytes+4); // then the low int - } - - c=string; // where result will go - if (((Int)sourhi)<0) *c++='-'; // handle sign - - comb=(sourhi>>26)&0x1f; // combination field - msd=COMBMSD[comb]; // decode the combination field - exp=COMBEXP[comb]; // .. - - if (exp==3) { - if (msd==0) { // infinity - strcpy(c, "Inf"); - strcpy(c+3, "inity"); - return string; // easy - } - if (sourhi&0x02000000) *c++='s'; // sNaN - strcpy(c, "NaN"); // complete word - c+=3; // step past - if (sourlo==0 && (sourhi&0x0003ffff)==0) return string; // zero payload - // otherwise drop through to add integer; set correct exp - exp=0; msd=0; // setup for following code - } - else exp=(exp<<8)+((sourhi>>18)&0xff)-DECIMAL64_Bias; - - // convert 16 digits of significand to characters - cstart=c; // save start of coefficient - if (msd) *c++='0'+(char)msd; // non-zero most significant digit - - // Now decode the declets. After extracting each one, it is - // decoded to binary and then to a 4-char sequence by table lookup; - // the 4-chars are a 1-char length (significant digits, except 000 - // has length 0). This allows us to left-align the first declet - // with non-zero content, then remaining ones are full 3-char - // length. We use fixed-length memcpys because variable-length - // causes a subroutine call in GCC. (These are length 4 for speed - // and are safe because the array has an extra terminator byte.) - #define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4]; \ - if (c!=cstart) {memcpy(c, u+1, 4); c+=3;} \ - else if (*u) {memcpy(c, u+4-*u, 4); c+=*u;} - - dpd=(sourhi>>8)&0x3ff; // declet 1 - dpd2char; - dpd=((sourhi&0xff)<<2) | (sourlo>>30); // declet 2 - dpd2char; - dpd=(sourlo>>20)&0x3ff; // declet 3 - dpd2char; - dpd=(sourlo>>10)&0x3ff; // declet 4 - dpd2char; - dpd=(sourlo)&0x3ff; // declet 5 - dpd2char; - - if (c==cstart) *c++='0'; // all zeros -- make 0 - - if (exp==0) { // integer or NaN case -- easy - *c='\0'; // terminate - return string; - } - - /* non-0 exponent */ - e=0; // assume no E - pre=c-cstart+exp; - // [here, pre-exp is the digits count (==1 for zero)] - if (exp>0 || pre<-5) { // need exponential form - e=pre-1; // calculate E value - pre=1; // assume one digit before '.' - } // exponential form - - /* modify the coefficient, adding 0s, '.', and E+nn as needed */ - s=c-1; // source (LSD) - if (pre>0) { // ddd.ddd (plain), perhaps with E - char *dotat=cstart+pre; - if (dotat<c) { // if embedded dot needed... - t=c; // target - for (; s>=dotat; s--, t--) *t=*s; // open the gap; leave t at gap - *t='.'; // insert the dot - c++; // length increased by one - } - - // finally add the E-part, if needed; it will never be 0, and has - // a maximum length of 3 digits - if (e!=0) { - *c++='E'; // starts with E - *c++='+'; // assume positive - if (e<0) { - *(c-1)='-'; // oops, need '-' - e=-e; // uInt, please - } - u=&BIN2CHAR[e*4]; // -> length byte - memcpy(c, u+4-*u, 4); // copy fixed 4 characters [is safe] - c+=*u; // bump pointer appropriately - } - *c='\0'; // add terminator - //printf("res %s\n", string); - return string; - } // pre>0 - - /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */ - t=c+1-pre; - *(t+1)='\0'; // can add terminator now - for (; s>=cstart; s--, t--) *t=*s; // shift whole coefficient right - c=cstart; - *c++='0'; // always starts with 0. - *c++='.'; - for (; pre<0; pre++) *c++='0'; // add any 0's after '.' - //printf("res %s\n", string); - return string; - } // decimal64ToString - -/* ------------------------------------------------------------------ */ -/* to-number -- conversion from numeric string */ -/* */ -/* decimal64FromString(result, string, set); */ -/* */ -/* result is the decimal64 format number which gets the result of */ -/* the conversion */ -/* *string is the character string which should contain a valid */ -/* number (which may be a special value) */ -/* set is the context */ -/* */ -/* The context is supplied to this routine is used for error handling */ -/* (setting of status and traps) and for the rounding mode, only. */ -/* If an error occurs, the result will be a valid decimal64 NaN. */ -/* ------------------------------------------------------------------ */ -decimal64 * decimal64FromString(decimal64 *result, const char *string, - decContext *set) { - decContext dc; // work - decNumber dn; // .. - - decContextDefault(&dc, DEC_INIT_DECIMAL64); // no traps, please - dc.round=set->round; // use supplied rounding - - decNumberFromString(&dn, string, &dc); // will round if needed - - decimal64FromNumber(result, &dn, &dc); - if (dc.status!=0) { // something happened - decContextSetStatus(set, dc.status); // .. pass it on - } - return result; - } // decimal64FromString - -/* ------------------------------------------------------------------ */ -/* decimal64IsCanonical -- test whether encoding is canonical */ -/* d64 is the source decimal64 */ -/* returns 1 if the encoding of d64 is canonical, 0 otherwise */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -uInt decimal64IsCanonical(const decimal64 *d64) { - decNumber dn; // work - decimal64 canon; // .. - decContext dc; // .. - decContextDefault(&dc, DEC_INIT_DECIMAL64); - decimal64ToNumber(d64, &dn); - decimal64FromNumber(&canon, &dn, &dc);// canon will now be canonical - return memcmp(d64, &canon, DECIMAL64_Bytes)==0; - } // decimal64IsCanonical - -/* ------------------------------------------------------------------ */ -/* decimal64Canonical -- copy an encoding, ensuring it is canonical */ -/* d64 is the source decimal64 */ -/* result is the target (may be the same decimal64) */ -/* returns result */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -decimal64 * decimal64Canonical(decimal64 *result, const decimal64 *d64) { - decNumber dn; // work - decContext dc; // .. - decContextDefault(&dc, DEC_INIT_DECIMAL64); - decimal64ToNumber(d64, &dn); - decimal64FromNumber(result, &dn, &dc);// result will now be canonical - return result; - } // decimal64Canonical - -#if DECTRACE || DECCHECK -/* Macros for accessing decimal64 fields. These assume the - argument is a reference (pointer) to the decimal64 structure, - and the decimal64 is in network byte order (big-endian) */ -// Get sign -#define decimal64Sign(d) ((unsigned)(d)->bytes[0]>>7) - -// Get combination field -#define decimal64Comb(d) (((d)->bytes[0] & 0x7c)>>2) - -// Get exponent continuation [does not remove bias] -#define decimal64ExpCon(d) ((((d)->bytes[0] & 0x03)<<6) \ - | ((unsigned)(d)->bytes[1]>>2)) - -// Set sign [this assumes sign previously 0] -#define decimal64SetSign(d, b) { \ - (d)->bytes[0]|=((unsigned)(b)<<7);} - -// Set exponent continuation [does not apply bias] -// This assumes range has been checked and exponent previously 0; -// type of exponent must be unsigned -#define decimal64SetExpCon(d, e) { \ - (d)->bytes[0]|=(uByte)((e)>>6); \ - (d)->bytes[1]|=(uByte)(((e)&0x3F)<<2);} - -/* ------------------------------------------------------------------ */ -/* decimal64Show -- display a decimal64 in hexadecimal [debug aid] */ -/* d64 -- the number to show */ -/* ------------------------------------------------------------------ */ -// Also shows sign/cob/expconfields extracted -void decimal64Show(const decimal64 *d64) { - char buf[DECIMAL64_Bytes*2+1]; - Int i, j=0; - - if (DECLITEND) { - for (i=0; i<DECIMAL64_Bytes; i++, j+=2) { - sprintf(&buf[j], "%02x", d64->bytes[7-i]); - } - printf(" D64> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf, - d64->bytes[7]>>7, (d64->bytes[7]>>2)&0x1f, - ((d64->bytes[7]&0x3)<<6)| (d64->bytes[6]>>2)); - } - else { // big-endian - for (i=0; i<DECIMAL64_Bytes; i++, j+=2) { - sprintf(&buf[j], "%02x", d64->bytes[i]); - } - printf(" D64> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf, - decimal64Sign(d64), decimal64Comb(d64), decimal64ExpCon(d64)); - } - } // decimal64Show -#endif - -/* ================================================================== */ -/* Shared utility routines and tables */ -/* ================================================================== */ -// define and include the conversion tables to use for shared code -#if DECDPUN==3 - #define DEC_DPD2BIN 1 -#else - #define DEC_DPD2BCD 1 -#endif -#include "decDPD.h" // lookup tables - -// The maximum number of decNumberUnits needed for a working copy of -// the units array is the ceiling of digits/DECDPUN, where digits is -// the maximum number of digits in any of the formats for which this -// is used. decimal128.h must not be included in this module, so, as -// a very special case, that number is defined as a literal here. -#define DECMAX754 34 -#define DECMAXUNITS ((DECMAX754+DECDPUN-1)/DECDPUN) - -/* ------------------------------------------------------------------ */ -/* Combination field lookup tables (uInts to save measurable work) */ -/* */ -/* COMBEXP - 2-bit most-significant-bits of exponent */ -/* [11 if an Infinity or NaN] */ -/* COMBMSD - 4-bit most-significant-digit */ -/* [0=Infinity, 1=NaN if COMBEXP=11] */ -/* */ -/* Both are indexed by the 5-bit combination field (0-31) */ -/* ------------------------------------------------------------------ */ -const uInt COMBEXP[32]={0, 0, 0, 0, 0, 0, 0, 0, - 1, 1, 1, 1, 1, 1, 1, 1, - 2, 2, 2, 2, 2, 2, 2, 2, - 0, 0, 1, 1, 2, 2, 3, 3}; -const uInt COMBMSD[32]={0, 1, 2, 3, 4, 5, 6, 7, - 0, 1, 2, 3, 4, 5, 6, 7, - 0, 1, 2, 3, 4, 5, 6, 7, - 8, 9, 8, 9, 8, 9, 0, 1}; - -/* ------------------------------------------------------------------ */ -/* decDigitsToDPD -- pack coefficient into DPD form */ -/* */ -/* dn is the source number (assumed valid, max DECMAX754 digits) */ -/* targ is 1, 2, or 4-element uInt array, which the caller must */ -/* have cleared to zeros */ -/* shift is the number of 0 digits to add on the right (normally 0) */ -/* */ -/* The coefficient must be known small enough to fit. The full */ -/* coefficient is copied, including the leading 'odd' digit. This */ -/* digit is retrieved and packed into the combination field by the */ -/* caller. */ -/* */ -/* The target uInts are altered only as necessary to receive the */ -/* digits of the decNumber. When more than one uInt is needed, they */ -/* are filled from left to right (that is, the uInt at offset 0 will */ -/* end up with the least-significant digits). */ -/* */ -/* shift is used for 'fold-down' padding. */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -#if DECDPUN<=4 -// Constant multipliers for divide-by-power-of five using reciprocal -// multiply, after removing powers of 2 by shifting, and final shift -// of 17 [we only need up to **4] -static const uInt multies[]={131073, 26215, 5243, 1049, 210}; -// QUOT10 -- macro to return the quotient of unit u divided by 10**n -#define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17) -#endif -void decDigitsToDPD(const decNumber *dn, uInt *targ, Int shift) { - Int cut; // work - Int n; // output bunch counter - Int digits=dn->digits; // digit countdown - uInt dpd; // densely packed decimal value - uInt bin; // binary value 0-999 - uInt *uout=targ; // -> current output uInt - uInt uoff=0; // -> current output offset [from right] - const Unit *inu=dn->lsu; // -> current input unit - Unit uar[DECMAXUNITS]; // working copy of units, iff shifted - #if DECDPUN!=3 // not fast path - Unit in; // current unit - #endif - - if (shift!=0) { // shift towards most significant required - // shift the units array to the left by pad digits and copy - // [this code is a special case of decShiftToMost, which could - // be used instead if exposed and the array were copied first] - const Unit *source; // .. - Unit *target, *first; // .. - uInt next=0; // work - - source=dn->lsu+D2U(digits)-1; // where msu comes from - target=uar+D2U(digits)-1+D2U(shift);// where upper part of first cut goes - cut=DECDPUN-MSUDIGITS(shift); // where to slice - if (cut==0) { // unit-boundary case - for (; source>=dn->lsu; source--, target--) *target=*source; - } - else { - first=uar+D2U(digits+shift)-1; // where msu will end up - for (; source>=dn->lsu; source--, target--) { - // split the source Unit and accumulate remainder for next - #if DECDPUN<=4 - uInt quot=QUOT10(*source, cut); - uInt rem=*source-quot*DECPOWERS[cut]; - next+=quot; - #else - uInt rem=*source%DECPOWERS[cut]; - next+=*source/DECPOWERS[cut]; - #endif - if (target<=first) *target=(Unit)next; // write to target iff valid - next=rem*DECPOWERS[DECDPUN-cut]; // save remainder for next Unit - } - } // shift-move - // propagate remainder to one below and clear the rest - for (; target>=uar; target--) { - *target=(Unit)next; - next=0; - } - digits+=shift; // add count (shift) of zeros added - inu=uar; // use units in working array - } - - /* now densely pack the coefficient into DPD declets */ - - #if DECDPUN!=3 // not fast path - in=*inu; // current unit - cut=0; // at lowest digit - bin=0; // [keep compiler quiet] - #endif - - for(n=0; digits>0; n++) { // each output bunch - #if DECDPUN==3 // fast path, 3-at-a-time - bin=*inu; // 3 digits ready for convert - digits-=3; // [may go negative] - inu++; // may need another - - #else // must collect digit-by-digit - Unit dig; // current digit - Int j; // digit-in-declet count - for (j=0; j<3; j++) { - #if DECDPUN<=4 - Unit temp=(Unit)((uInt)(in*6554)>>16); - dig=(Unit)(in-X10(temp)); - in=temp; - #else - dig=in%10; - in=in/10; - #endif - if (j==0) bin=dig; - else if (j==1) bin+=X10(dig); - else /* j==2 */ bin+=X100(dig); - digits--; - if (digits==0) break; // [also protects *inu below] - cut++; - if (cut==DECDPUN) {inu++; in=*inu; cut=0;} - } - #endif - // here there are 3 digits in bin, or have used all input digits - - dpd=BIN2DPD[bin]; - - // write declet to uInt array - *uout|=dpd<<uoff; - uoff+=10; - if (uoff<32) continue; // no uInt boundary cross - uout++; - uoff-=32; - *uout|=dpd>>(10-uoff); // collect top bits - } // n declets - return; - } // decDigitsToDPD - -/* ------------------------------------------------------------------ */ -/* decDigitsFromDPD -- unpack a format's coefficient */ -/* */ -/* dn is the target number, with 7, 16, or 34-digit space. */ -/* sour is a 1, 2, or 4-element uInt array containing only declets */ -/* declets is the number of (right-aligned) declets in sour to */ -/* be processed. This may be 1 more than the obvious number in */ -/* a format, as any top digit is prefixed to the coefficient */ -/* continuation field. It also may be as small as 1, as the */ -/* caller may pre-process leading zero declets. */ -/* */ -/* When doing the 'extra declet' case care is taken to avoid writing */ -/* extra digits when there are leading zeros, as these could overflow */ -/* the units array when DECDPUN is not 3. */ -/* */ -/* The target uInts are used only as necessary to process declets */ -/* declets into the decNumber. When more than one uInt is needed, */ -/* they are used from left to right (that is, the uInt at offset 0 */ -/* provides the least-significant digits). */ -/* */ -/* dn->digits is set, but not the sign or exponent. */ -/* No error is possible [the redundant 888 codes are allowed]. */ -/* ------------------------------------------------------------------ */ -void decDigitsFromDPD(decNumber *dn, const uInt *sour, Int declets) { - - uInt dpd; // collector for 10 bits - Int n; // counter - Unit *uout=dn->lsu; // -> current output unit - Unit *last=uout; // will be unit containing msd - const uInt *uin=sour; // -> current input uInt - uInt uoff=0; // -> current input offset [from right] - - #if DECDPUN!=3 - uInt bcd; // BCD result - uInt nibble; // work - Unit out=0; // accumulator - Int cut=0; // power of ten in current unit - #endif - #if DECDPUN>4 - uInt const *pow; // work - #endif - - // Expand the densely-packed integer, right to left - for (n=declets-1; n>=0; n--) { // count down declets of 10 bits - dpd=*uin>>uoff; - uoff+=10; - if (uoff>32) { // crossed uInt boundary - uin++; - uoff-=32; // [if using this code for wider, check this] - dpd|=*uin<<(10-uoff); // get waiting bits - } - dpd&=0x3ff; // clear uninteresting bits - - #if DECDPUN==3 - if (dpd==0) *uout=0; - else { - *uout=DPD2BIN[dpd]; // convert 10 bits to binary 0-999 - last=uout; // record most significant unit - } - uout++; - } // n - - #else // DECDPUN!=3 - if (dpd==0) { // fastpath [e.g., leading zeros] - // write out three 0 digits (nibbles); out may have digit(s) - cut++; - if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;} - if (n==0) break; // [as below, works even if MSD=0] - cut++; - if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;} - cut++; - if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;} - continue; - } - - bcd=DPD2BCD[dpd]; // convert 10 bits to 12 bits BCD - - // now accumulate the 3 BCD nibbles into units - nibble=bcd & 0x00f; - if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]); - cut++; - if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;} - bcd>>=4; - - // if this is the last declet and the remaining nibbles in bcd - // are 00 then process no more nibbles, because this could be - // the 'odd' MSD declet and writing any more Units would then - // overflow the unit array - if (n==0 && !bcd) break; - - nibble=bcd & 0x00f; - if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]); - cut++; - if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;} - bcd>>=4; - - nibble=bcd & 0x00f; - if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]); - cut++; - if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;} - } // n - if (cut!=0) { // some more left over - *uout=out; // write out final unit - if (out) last=uout; // and note if non-zero - } - #endif - - // here, last points to the most significant unit with digits; - // inspect it to get the final digits count -- this is essentially - // the same code as decGetDigits in decNumber.c - dn->digits=(last-dn->lsu)*DECDPUN+1; // floor of digits, plus - // must be at least 1 digit - #if DECDPUN>1 - if (*last<10) return; // common odd digit or 0 - dn->digits++; // must be 2 at least - #if DECDPUN>2 - if (*last<100) return; // 10-99 - dn->digits++; // must be 3 at least - #if DECDPUN>3 - if (*last<1000) return; // 100-999 - dn->digits++; // must be 4 at least - #if DECDPUN>4 - for (pow=&DECPOWERS[4]; *last>=*pow; pow++) dn->digits++; - #endif - #endif - #endif - #endif - return; - } //decDigitsFromDPD
src/decNumber/decimal64.h
@@ -1,83 +0,0 @@-/* ------------------------------------------------------------------ */ -/* Decimal 64-bit format module header */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2005. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is called decNumber.pdf. This document is */ -/* available, together with arithmetic and format specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ - -#if !defined(DECIMAL64) - #define DECIMAL64 - #define DEC64NAME "decimal64" /* Short name */ - #define DEC64FULLNAME "Decimal 64-bit Number" /* Verbose name */ - #define DEC64AUTHOR "Mike Cowlishaw" /* Who to blame */ - - - /* parameters for decimal64s */ - #define DECIMAL64_Bytes 8 /* length */ - #define DECIMAL64_Pmax 16 /* maximum precision (digits) */ - #define DECIMAL64_Emax 384 /* maximum adjusted exponent */ - #define DECIMAL64_Emin -383 /* minimum adjusted exponent */ - #define DECIMAL64_Bias 398 /* bias for the exponent */ - #define DECIMAL64_String 24 /* maximum string length, +1 */ - #define DECIMAL64_EconL 8 /* exp. continuation length */ - /* highest biased exponent (Elimit-1) */ - #define DECIMAL64_Ehigh (DECIMAL64_Emax+DECIMAL64_Bias-DECIMAL64_Pmax+1) - - /* check enough digits, if pre-defined */ - #if defined(DECNUMDIGITS) - #if (DECNUMDIGITS<DECIMAL64_Pmax) - #error decimal64.h needs pre-defined DECNUMDIGITS>=16 for safe use - #endif - #endif - - - #ifndef DECNUMDIGITS - #define DECNUMDIGITS DECIMAL64_Pmax /* size if not already defined*/ - #endif - #ifndef DECNUMBER - #include "decNumber.h" /* context and number library */ - #endif - - /* Decimal 64-bit type, accessible by bytes */ - typedef struct { - uint8_t bytes[DECIMAL64_Bytes]; /* decimal64: 1, 5, 8, 50 bits*/ - } decimal64; - - /* special values [top byte excluding sign bit; last two bits are */ - /* don't-care for Infinity on input, last bit don't-care for NaN] */ - #if !defined(DECIMAL_NaN) - #define DECIMAL_NaN 0x7c /* 0 11111 00 NaN */ - #define DECIMAL_sNaN 0x7e /* 0 11111 10 sNaN */ - #define DECIMAL_Inf 0x78 /* 0 11110 00 Infinity */ - #endif - - /* ---------------------------------------------------------------- */ - /* Routines */ - /* ---------------------------------------------------------------- */ - /* String conversions */ - decimal64 * decimal64FromString(decimal64 *, const char *, decContext *); - char * decimal64ToString(const decimal64 *, char *); - char * decimal64ToEngString(const decimal64 *, char *); - - /* decNumber conversions */ - decimal64 * decimal64FromNumber(decimal64 *, const decNumber *, - decContext *); - decNumber * decimal64ToNumber(const decimal64 *, decNumber *); - - /* Format-dependent utilities */ - uint32_t decimal64IsCanonical(const decimal64 *); - decimal64 * decimal64Canonical(decimal64 *, const decimal64 *); - -#endif
src/decNumber/decnumber.pdf
src/decNumber/example1.c
@@ -1,38 +0,0 @@-/* ------------------------------------------------------------------ */ -/* Decimal Number Library Demonstration program */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2001, 2007. All rights reserved. */ -/* ----------------------------------------------------------------+- */ -/* right margin -->| */ - -// example1.c -- convert the first two argument words to decNumber, -// add them together, and display the result - -#define DECNUMDIGITS 34 // work with up to 34 digits -#include "decNumber.h" // base number library -#include <stdio.h> // for printf - -int main(int argc, char *argv[]) { - decNumber a, b; // working numbers - decContext set; // working context - char string[DECNUMDIGITS+14]; // conversion buffer - - decContextTestEndian(0); // warn if DECLITEND is wrong - - if (argc<3) { // not enough words - printf("Please supply two numbers to add.\n"); - return 1; - } - decContextDefault(&set, DEC_INIT_BASE); // initialize - set.traps=0; // no traps, thank you - set.digits=DECNUMDIGITS; // set precision - - decNumberFromString(&a, argv[1], &set); - decNumberFromString(&b, argv[2], &set); - - decNumberAdd(&a, &a, &b, &set); // a=a+b - decNumberToString(&a, string); - - printf("%s + %s => %s\n", argv[1], argv[2], string); - return 0; - } // main
src/decNumber/example2.c
@@ -1,52 +0,0 @@-/* ------------------------------------------------------------------ */ -/* Decimal Number Library Demonstration program */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2001. All rights reserved. */ -/* ----------------------------------------------------------------+- */ -/* right margin -->| */ - -// example2.c -- calculate compound interest -// Arguments are investment, rate (%), and years - -#define DECNUMDIGITS 38 // work with up to 38 digits -#include "decNumber.h" // base number library -#include <stdio.h> // for printf - -int main(int argc, char *argv[]) { - int need=3; - if (argc<need+1) { // not enough words - printf("Please supply %d number(s).\n", need); - return 1; - } - - { // excerpt for User's Guide starts here--------------------------| - decNumber one, mtwo, hundred; // constants - decNumber start, rate, years; // parameters - decNumber total; // result - decContext set; // working context - char string[DECNUMDIGITS+14]; // conversion buffer - - decContextDefault(&set, DEC_INIT_BASE); // initialize - set.traps=0; // no traps - set.digits=25; // precision 25 - decNumberFromString(&one, "1", &set); // set constants - decNumberFromString(&mtwo, "-2", &set); - decNumberFromString(&hundred, "100", &set); - - decNumberFromString(&start, argv[1], &set); // parameter words - decNumberFromString(&rate, argv[2], &set); - decNumberFromString(&years, argv[3], &set); - - decNumberDivide(&rate, &rate, &hundred, &set); // rate=rate/100 - decNumberAdd(&rate, &rate, &one, &set); // rate=rate+1 - decNumberPower(&rate, &rate, &years, &set); // rate=rate^years - decNumberMultiply(&total, &rate, &start, &set); // total=rate*start - decNumberRescale(&total, &total, &mtwo, &set); // two digits please - - decNumberToString(&total, string); - printf("%s at %s%% for %s years => %s\n", - argv[1], argv[2], argv[3], string); - - } //---------------------------------------------------------------| - return 0; - } // main
src/decNumber/example3.c
@@ -1,64 +0,0 @@-/* ------------------------------------------------------------------ */ -/* Decimal Number Library Demonstration program */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2001. All rights reserved. */ -/* ----------------------------------------------------------------+- */ -/* right margin -->| */ - -// example3.c -- calculate compound interest, passive checking -// Arguments are investment, rate (%), and years - -#define DECNUMDIGITS 38 // work with up to 38 digits -#include "decNumber.h" // base number library -#include <stdio.h> // for printf - -int main(int argc, char *argv[]) { - int need=3; - if (argc<need+1) { // not enough words - printf("Please supply %d number(s).\n", need); - return 1; - } - - { // start of Example 2 segment - decNumber one, mtwo, hundred; // constants - decNumber start, rate, years; // parameters - decNumber total; // result - decContext set; // working context - char string[DECNUMDIGITS+14]; // conversion buffer - - decContextDefault(&set, DEC_INIT_BASE); // initialize - set.traps=0; // no traps - set.digits=25; // precision 25 - decNumberFromString(&one, "1", &set); // set constants - decNumberFromString(&mtwo, "-2", &set); - decNumberFromString(&hundred, "100", &set); - -// [snip... - decNumberFromString(&start, argv[1], &set); // parameter words - decNumberFromString(&rate, argv[2], &set); - decNumberFromString(&years, argv[3], &set); - if (set.status & DEC_Errors) { - printf("An input argument word was invalid [%s]\n", - decContextStatusToString(&set)); - return 1; - } - decNumberDivide(&rate, &rate, &hundred, &set); // rate=rate/100 - decNumberAdd(&rate, &rate, &one, &set); // rate=rate+1 - decNumberPower(&rate, &rate, &years, &set); // rate=rate^years - decNumberMultiply(&total, &rate, &start, &set); // total=rate*start - decNumberRescale(&total, &total, &mtwo, &set); // two digits please - if (set.status & DEC_Errors) { - set.status &= DEC_Errors; // keep only errors - printf("Result could not be calculated [%s]\n", - decContextStatusToString(&set)); - return 1; - } -// ...snip] - - decNumberToString(&total, string); - printf("%s at %s%% for %s years => %s\n", - argv[1], argv[2], argv[3], string); - - } //---------------------------------------------------------------| - return 0; - } // main
src/decNumber/example4.c
@@ -1,61 +0,0 @@-/* ------------------------------------------------------------------ */ -/* Decimal Number Library Demonstration program */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2001. All rights reserved. */ -/* ----------------------------------------------------------------+- */ -/* right margin -->| */ - -// example4.c -- add two numbers, active error handling -// Arguments are two numbers - -#define DECNUMDIGITS 38 // work with up to 38 digits -#include "decNumber.h" // base number library -#include <stdio.h> // for printf - -// [snip... -#include <signal.h> // signal handling -#include <setjmp.h> // setjmp/longjmp - -jmp_buf preserve; // stack snapshot - -void signalHandler(int); // prototype for GCC -void signalHandler(int sig) { - signal(SIGFPE, signalHandler); // re-enable - longjmp(preserve, sig); // branch to preserved point - } -// ...snip] -int main(int argc, char *argv[]) { - decNumber a, b; // working numbers
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