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/* 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 */
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