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Diffstat (limited to 'libdecnumber/decBasic.c')
| -rw-r--r-- | libdecnumber/decBasic.c | 3909 |
1 files changed, 3909 insertions, 0 deletions
diff --git a/libdecnumber/decBasic.c b/libdecnumber/decBasic.c new file mode 100644 index 000000000..75ce17bce --- /dev/null +++ b/libdecnumber/decBasic.c @@ -0,0 +1,3909 @@ +/* Common base code for the decNumber C Library. + Copyright (C) 2007, 2009 Free Software Foundation, Inc. + Contributed by IBM Corporation. Author Mike Cowlishaw. + + This file is part of GCC. + + GCC is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation; either version 3, or (at your option) any later + version. + + GCC is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or + FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +<http://www.gnu.org/licenses/>. */ + +/* ------------------------------------------------------------------ */ +/* decBasic.c -- common base code for Basic decimal types */ +/* ------------------------------------------------------------------ */ +/* 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 multiplcation 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 decFloatIsNaN(const decFloat *df) { + return 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 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 */ |