| 1 | /* Common base code for the decNumber C Library. |
| 2 | Copyright (C) 2007 Free Software Foundation, Inc. |
| 3 | Contributed by IBM Corporation. Author Mike Cowlishaw. |
| 4 | |
| 5 | This file is part of GCC. |
| 6 | |
| 7 | GCC is free software; you can redistribute it and/or modify it under |
| 8 | the terms of the GNU General Public License as published by the Free |
| 9 | Software Foundation; either version 2, or (at your option) any later |
| 10 | version. |
| 11 | |
| 12 | In addition to the permissions in the GNU General Public License, |
| 13 | the Free Software Foundation gives you unlimited permission to link |
| 14 | the compiled version of this file into combinations with other |
| 15 | programs, and to distribute those combinations without any |
| 16 | restriction coming from the use of this file. (The General Public |
| 17 | License restrictions do apply in other respects; for example, they |
| 18 | cover modification of the file, and distribution when not linked |
| 19 | into a combine executable.) |
| 20 | |
| 21 | GCC is distributed in the hope that it will be useful, but WITHOUT ANY |
| 22 | WARRANTY; without even the implied warranty of MERCHANTABILITY or |
| 23 | FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
| 24 | for more details. |
| 25 | |
| 26 | You should have received a copy of the GNU General Public License |
| 27 | along with GCC; see the file COPYING. If not, write to the Free |
| 28 | Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA |
| 29 | 02110-1301, USA. */ |
| 30 | |
| 31 | /* ------------------------------------------------------------------ */ |
| 32 | /* decBasic.c -- common base code for Basic decimal types */ |
| 33 | /* ------------------------------------------------------------------ */ |
| 34 | /* This module comprises code that is shared between decDouble and */ |
| 35 | /* decQuad (but not decSingle). The main arithmetic operations are */ |
| 36 | /* here (Add, Subtract, Multiply, FMA, and Division operators). */ |
| 37 | /* */ |
| 38 | /* Unlike decNumber, parameterization takes place at compile time */ |
| 39 | /* rather than at runtime. The parameters are set in the decDouble.c */ |
| 40 | /* (etc.) files, which then include this one to produce the compiled */ |
| 41 | /* code. The functions here, therefore, are code shared between */ |
| 42 | /* multiple formats. */ |
| 43 | /* */ |
| 44 | /* This must be included after decCommon.c. */ |
| 45 | /* ------------------------------------------------------------------ */ |
| 46 | /* Names here refer to decFloat rather than to decDouble, etc., and */ |
| 47 | /* the functions are in strict alphabetical order. */ |
| 48 | |
| 49 | /* The compile-time flags SINGLE, DOUBLE, and QUAD are set up in */ |
| 50 | /* decCommon.c */ |
| 51 | #if !defined(QUAD) |
| 52 | #error decBasic.c must be included after decCommon.c |
| 53 | #endif |
| 54 | #if SINGLE |
| 55 | #error Routines in decBasic.c are for decDouble and decQuad only |
| 56 | #endif |
| 57 | |
| 58 | /* Private constants */ |
| 59 | #define DIVIDE 0x80000000 /* Divide operations [as flags] */ |
| 60 | #define REMAINDER 0x40000000 /* .. */ |
| 61 | #define DIVIDEINT 0x20000000 /* .. */ |
| 62 | #define REMNEAR 0x10000000 /* .. */ |
| 63 | |
| 64 | /* Private functions (local, used only by routines in this module) */ |
| 65 | static decFloat *decDivide(decFloat *, const decFloat *, |
| 66 | const decFloat *, decContext *, uInt); |
| 67 | static decFloat *decCanonical(decFloat *, const decFloat *); |
| 68 | static void decFiniteMultiply(bcdnum *, uByte *, const decFloat *, |
| 69 | const decFloat *); |
| 70 | static decFloat *decInfinity(decFloat *, const decFloat *); |
| 71 | static decFloat *decInvalid(decFloat *, decContext *); |
| 72 | static decFloat *decNaNs(decFloat *, const decFloat *, const decFloat *, |
| 73 | decContext *); |
| 74 | static Int decNumCompare(const decFloat *, const decFloat *, Flag); |
| 75 | static decFloat *decToIntegral(decFloat *, const decFloat *, decContext *, |
| 76 | enum rounding, Flag); |
| 77 | static uInt decToInt32(const decFloat *, decContext *, enum rounding, |
| 78 | Flag, Flag); |
| 79 | |
| 80 | /* ------------------------------------------------------------------ */ |
| 81 | /* decCanonical -- copy a decFloat, making canonical */ |
| 82 | /* */ |
| 83 | /* result gets the canonicalized df */ |
| 84 | /* df is the decFloat to copy and make canonical */ |
| 85 | /* returns result */ |
| 86 | /* */ |
| 87 | /* This is exposed via decFloatCanonical for Double and Quad only. */ |
| 88 | /* This works on specials, too; no error or exception is possible. */ |
| 89 | /* ------------------------------------------------------------------ */ |
| 90 | static decFloat * decCanonical(decFloat *result, const decFloat *df) { |
| 91 | uInt encode, precode, dpd; /* work */ |
| 92 | uInt inword, uoff, canon; /* .. */ |
| 93 | Int n; /* counter (down) */ |
| 94 | if (df!=result) *result=*df; /* effect copy if needed */ |
| 95 | if (DFISSPECIAL(result)) { |
| 96 | if (DFISINF(result)) return decInfinity(result, df); /* clean Infinity */ |
| 97 | /* is a NaN */ |
| 98 | DFWORD(result, 0)&=~ECONNANMASK; /* clear ECON except selector */ |
| 99 | if (DFISCCZERO(df)) return result; /* coefficient continuation is 0 */ |
| 100 | /* drop through to check payload */ |
| 101 | } |
| 102 | /* return quickly if the coefficient continuation is canonical */ |
| 103 | { /* declare block */ |
| 104 | #if DOUBLE |
| 105 | uInt sourhi=DFWORD(df, 0); |
| 106 | uInt sourlo=DFWORD(df, 1); |
| 107 | if (CANONDPDOFF(sourhi, 8) |
| 108 | && CANONDPDTWO(sourhi, sourlo, 30) |
| 109 | && CANONDPDOFF(sourlo, 20) |
| 110 | && CANONDPDOFF(sourlo, 10) |
| 111 | && CANONDPDOFF(sourlo, 0)) return result; |
| 112 | #elif QUAD |
| 113 | uInt sourhi=DFWORD(df, 0); |
| 114 | uInt sourmh=DFWORD(df, 1); |
| 115 | uInt sourml=DFWORD(df, 2); |
| 116 | uInt sourlo=DFWORD(df, 3); |
| 117 | if (CANONDPDOFF(sourhi, 4) |
| 118 | && CANONDPDTWO(sourhi, sourmh, 26) |
| 119 | && CANONDPDOFF(sourmh, 16) |
| 120 | && CANONDPDOFF(sourmh, 6) |
| 121 | && CANONDPDTWO(sourmh, sourml, 28) |
| 122 | && CANONDPDOFF(sourml, 18) |
| 123 | && CANONDPDOFF(sourml, 8) |
| 124 | && CANONDPDTWO(sourml, sourlo, 30) |
| 125 | && CANONDPDOFF(sourlo, 20) |
| 126 | && CANONDPDOFF(sourlo, 10) |
| 127 | && CANONDPDOFF(sourlo, 0)) return result; |
| 128 | #endif |
| 129 | } /* block */ |
| 130 | |
| 131 | /* Loop to repair a non-canonical coefficent, as needed */ |
| 132 | inword=DECWORDS-1; /* current input word */ |
| 133 | uoff=0; /* bit offset of declet */ |
| 134 | encode=DFWORD(result, inword); |
| 135 | for (n=DECLETS-1; n>=0; n--) { /* count down declets of 10 bits */ |
| 136 | dpd=encode>>uoff; |
| 137 | uoff+=10; |
| 138 | if (uoff>32) { /* crossed uInt boundary */ |
| 139 | inword--; |
| 140 | encode=DFWORD(result, inword); |
| 141 | uoff-=32; |
| 142 | dpd|=encode<<(10-uoff); /* get pending bits */ |
| 143 | } |
| 144 | dpd&=0x3ff; /* clear uninteresting bits */ |
| 145 | if (dpd<0x16e) continue; /* must be canonical */ |
| 146 | canon=BIN2DPD[DPD2BIN[dpd]]; /* determine canonical declet */ |
| 147 | if (canon==dpd) continue; /* have canonical declet */ |
| 148 | /* need to replace declet */ |
| 149 | if (uoff>=10) { /* all within current word */ |
| 150 | encode&=~(0x3ff<<(uoff-10)); /* clear the 10 bits ready for replace */ |
| 151 | encode|=canon<<(uoff-10); /* insert the canonical form */ |
| 152 | DFWORD(result, inword)=encode; /* .. and save */ |
| 153 | continue; |
| 154 | } |
| 155 | /* straddled words */ |
| 156 | precode=DFWORD(result, inword+1); /* get previous */ |
| 157 | precode&=0xffffffff>>(10-uoff); /* clear top bits */ |
| 158 | DFWORD(result, inword+1)=precode|(canon<<(32-(10-uoff))); |
| 159 | encode&=0xffffffff<<uoff; /* clear bottom bits */ |
| 160 | encode|=canon>>(10-uoff); /* insert canonical */ |
| 161 | DFWORD(result, inword)=encode; /* .. and save */ |
| 162 | } /* n */ |
| 163 | return result; |
| 164 | } /* decCanonical */ |
| 165 | |
| 166 | /* ------------------------------------------------------------------ */ |
| 167 | /* decDivide -- divide operations */ |
| 168 | /* */ |
| 169 | /* result gets the result of dividing dfl by dfr: */ |
| 170 | /* dfl is the first decFloat (lhs) */ |
| 171 | /* dfr is the second decFloat (rhs) */ |
| 172 | /* set is the context */ |
| 173 | /* op is the operation selector */ |
| 174 | /* returns result */ |
| 175 | /* */ |
| 176 | /* op is one of DIVIDE, REMAINDER, DIVIDEINT, or REMNEAR. */ |
| 177 | /* ------------------------------------------------------------------ */ |
| 178 | #define DIVCOUNT 0 /* 1 to instrument subtractions counter */ |
| 179 | #define DIVBASE BILLION /* the base used for divide */ |
| 180 | #define DIVOPLEN DECPMAX9 /* operand length ('digits' base 10**9) */ |
| 181 | #define DIVACCLEN (DIVOPLEN*3) /* accumulator length (ditto) */ |
| 182 | static decFloat * decDivide(decFloat *result, const decFloat *dfl, |
| 183 | const decFloat *dfr, decContext *set, uInt op) { |
| 184 | decFloat quotient; /* for remainders */ |
| 185 | bcdnum num; /* for final conversion */ |
| 186 | uInt acc[DIVACCLEN]; /* coefficent in base-billion .. */ |
| 187 | uInt div[DIVOPLEN]; /* divisor in base-billion .. */ |
| 188 | uInt quo[DIVOPLEN+1]; /* quotient in base-billion .. */ |
| 189 | uByte bcdacc[(DIVOPLEN+1)*9+2]; /* for quotient in BCD, +1, +1 */ |
| 190 | uInt *msua, *msud, *msuq; /* -> msu of acc, div, and quo */ |
| 191 | Int divunits, accunits; /* lengths */ |
| 192 | Int quodigits; /* digits in quotient */ |
| 193 | uInt *lsua, *lsuq; /* -> current acc and quo lsus */ |
| 194 | Int length, multiplier; /* work */ |
| 195 | uInt carry, sign; /* .. */ |
| 196 | uInt *ua, *ud, *uq; /* .. */ |
| 197 | uByte *ub; /* .. */ |
| 198 | uInt divtop; /* top unit of div adjusted for estimating */ |
| 199 | #if DIVCOUNT |
| 200 | static uInt maxcount=0; /* worst-seen subtractions count */ |
| 201 | uInt divcount=0; /* subtractions count [this divide] */ |
| 202 | #endif |
| 203 | |
| 204 | /* calculate sign */ |
| 205 | num.sign=(DFWORD(dfl, 0)^DFWORD(dfr, 0)) & DECFLOAT_Sign; |
| 206 | |
| 207 | if (DFISSPECIAL(dfl) || DFISSPECIAL(dfr)) { /* either is special? */ |
| 208 | /* NaNs are handled as usual */ |
| 209 | if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set); |
| 210 | /* one or two infinities */ |
| 211 | if (DFISINF(dfl)) { |
| 212 | if (DFISINF(dfr)) return decInvalid(result, set); /* Two infinities bad */ |
| 213 | if (op&(REMAINDER|REMNEAR)) return decInvalid(result, set); /* as is rem */ |
| 214 | /* Infinity/x is infinite and quiet, even if x=0 */ |
| 215 | DFWORD(result, 0)=num.sign; |
| 216 | return decInfinity(result, result); |
| 217 | } |
| 218 | /* must be x/Infinity -- remainders are lhs */ |
| 219 | if (op&(REMAINDER|REMNEAR)) return decCanonical(result, dfl); |
| 220 | /* divides: return zero with correct sign and exponent depending */ |
| 221 | /* on op (Etiny for divide, 0 for divideInt) */ |
| 222 | decFloatZero(result); |
| 223 | if (op==DIVIDEINT) DFWORD(result, 0)|=num.sign; /* add sign */ |
| 224 | else DFWORD(result, 0)=num.sign; /* zeros the exponent, too */ |
| 225 | return result; |
| 226 | } |
| 227 | /* next, handle zero operands (x/0 and 0/x) */ |
| 228 | if (DFISZERO(dfr)) { /* x/0 */ |
| 229 | if (DFISZERO(dfl)) { /* 0/0 is undefined */ |
| 230 | decFloatZero(result); |
| 231 | DFWORD(result, 0)=DECFLOAT_qNaN; |
| 232 | set->status|=DEC_Division_undefined; |
| 233 | return result; |
| 234 | } |
| 235 | if (op&(REMAINDER|REMNEAR)) return decInvalid(result, set); /* bad rem */ |
| 236 | set->status|=DEC_Division_by_zero; |
| 237 | DFWORD(result, 0)=num.sign; |
| 238 | return decInfinity(result, result); /* x/0 -> signed Infinity */ |
| 239 | } |
| 240 | num.exponent=GETEXPUN(dfl)-GETEXPUN(dfr); /* ideal exponent */ |
| 241 | if (DFISZERO(dfl)) { /* 0/x (x!=0) */ |
| 242 | /* if divide, result is 0 with ideal exponent; divideInt has */ |
| 243 | /* exponent=0, remainders give zero with lower exponent */ |
| 244 | if (op&DIVIDEINT) { |
| 245 | decFloatZero(result); |
| 246 | DFWORD(result, 0)|=num.sign; /* add sign */ |
| 247 | return result; |
| 248 | } |
| 249 | if (!(op&DIVIDE)) { /* a remainder */ |
| 250 | /* exponent is the minimum of the operands */ |
| 251 | num.exponent=MINI(GETEXPUN(dfl), GETEXPUN(dfr)); |
| 252 | /* if the result is zero the sign shall be sign of dfl */ |
| 253 | num.sign=DFWORD(dfl, 0)&DECFLOAT_Sign; |
| 254 | } |
| 255 | bcdacc[0]=0; |
| 256 | num.msd=bcdacc; /* -> 0 */ |
| 257 | num.lsd=bcdacc; /* .. */ |
| 258 | return decFinalize(result, &num, set); /* [divide may clamp exponent] */ |
| 259 | } /* 0/x */ |
| 260 | /* [here, both operands are known to be finite and non-zero] */ |
| 261 | |
| 262 | /* extract the operand coefficents into 'units' which are */ |
| 263 | /* base-billion; the lhs is high-aligned in acc and the msu of both */ |
| 264 | /* acc and div is at the right-hand end of array (offset length-1); */ |
| 265 | /* the quotient can need one more unit than the operands as digits */ |
| 266 | /* in it are not necessarily aligned neatly; further, the quotient */ |
| 267 | /* may not start accumulating until after the end of the initial */ |
| 268 | /* operand in acc if that is small (e.g., 1) so the accumulator */ |
| 269 | /* must have at least that number of units extra (at the ls end) */ |
| 270 | GETCOEFFBILL(dfl, acc+DIVACCLEN-DIVOPLEN); |
| 271 | GETCOEFFBILL(dfr, div); |
| 272 | /* zero the low uInts of acc */ |
| 273 | acc[0]=0; |
| 274 | acc[1]=0; |
| 275 | acc[2]=0; |
| 276 | acc[3]=0; |
| 277 | #if DOUBLE |
| 278 | #if DIVOPLEN!=2 |
| 279 | #error Unexpected Double DIVOPLEN |
| 280 | #endif |
| 281 | #elif QUAD |
| 282 | acc[4]=0; |
| 283 | acc[5]=0; |
| 284 | acc[6]=0; |
| 285 | acc[7]=0; |
| 286 | #if DIVOPLEN!=4 |
| 287 | #error Unexpected Quad DIVOPLEN |
| 288 | #endif |
| 289 | #endif |
| 290 | |
| 291 | /* set msu and lsu pointers */ |
| 292 | msua=acc+DIVACCLEN-1; /* [leading zeros removed below] */ |
| 293 | msuq=quo+DIVOPLEN; |
| 294 | /*[loop for div will terminate because operands are non-zero] */ |
| 295 | for (msud=div+DIVOPLEN-1; *msud==0;) msud--; |
| 296 | /* the initial least-significant unit of acc is set so acc appears */ |
| 297 | /* to have the same length as div. */ |
| 298 | /* This moves one position towards the least possible for each */ |
| 299 | /* iteration */ |
| 300 | divunits=(Int)(msud-div+1); /* precalculate */ |
| 301 | lsua=msua-divunits+1; /* initial working lsu of acc */ |
| 302 | lsuq=msuq; /* and of quo */ |
| 303 | |
| 304 | /* set up the estimator for the multiplier; this is the msu of div, */ |
| 305 | /* plus two bits from the unit below (if any) rounded up by one if */ |
| 306 | /* there are any non-zero bits or units below that [the extra two */ |
| 307 | /* bits makes for a much better estimate when the top unit is small] */ |
| 308 | divtop=*msud<<2; |
| 309 | if (divunits>1) { |
| 310 | uInt *um=msud-1; |
| 311 | uInt d=*um; |
| 312 | if (d>=750000000) {divtop+=3; d-=750000000;} |
| 313 | else if (d>=500000000) {divtop+=2; d-=500000000;} |
| 314 | else if (d>=250000000) {divtop++; d-=250000000;} |
| 315 | if (d) divtop++; |
| 316 | else for (um--; um>=div; um--) if (*um) { |
| 317 | divtop++; |
| 318 | break; |
| 319 | } |
| 320 | } /* >1 unit */ |
| 321 | |
| 322 | #if DECTRACE |
| 323 | {Int i; |
| 324 | printf("----- div="); |
| 325 | for (i=divunits-1; i>=0; i--) printf("%09ld ", (LI)div[i]); |
| 326 | printf("\n");} |
| 327 | #endif |
| 328 | |
| 329 | /* now collect up to DECPMAX+1 digits in the quotient (this may */ |
| 330 | /* need OPLEN+1 uInts if unaligned) */ |
| 331 | quodigits=0; /* no digits yet */ |
| 332 | for (;; lsua--) { /* outer loop -- each input position */ |
| 333 | #if DECCHECK |
| 334 | if (lsua<acc) { |
| 335 | printf("Acc underrun...\n"); |
| 336 | break; |
| 337 | } |
| 338 | #endif |
| 339 | #if DECTRACE |
| 340 | printf("Outer: quodigits=%ld acc=", (LI)quodigits); |
| 341 | for (ua=msua; ua>=lsua; ua--) printf("%09ld ", (LI)*ua); |
| 342 | printf("\n"); |
| 343 | #endif |
| 344 | *lsuq=0; /* default unit result is 0 */ |
| 345 | for (;;) { /* inner loop -- calculate quotient unit */ |
| 346 | /* strip leading zero units from acc (either there initially or */ |
| 347 | /* from subtraction below); this may strip all if exactly 0 */ |
| 348 | for (; *msua==0 && msua>=lsua;) msua--; |
| 349 | accunits=(Int)(msua-lsua+1); /* [maybe 0] */ |
| 350 | /* subtraction is only necessary and possible if there are as */ |
| 351 | /* least as many units remaining in acc for this iteration as */ |
| 352 | /* there are in div */ |
| 353 | if (accunits<divunits) { |
| 354 | if (accunits==0) msua++; /* restore */ |
| 355 | break; |
| 356 | } |
| 357 | |
| 358 | /* If acc is longer than div then subtraction is definitely */ |
| 359 | /* possible (as msu of both is non-zero), but if they are the */ |
| 360 | /* same length a comparison is needed. */ |
| 361 | /* If a subtraction is needed then a good estimate of the */ |
| 362 | /* multiplier for the subtraction is also needed in order to */ |
| 363 | /* minimise the iterations of this inner loop because the */ |
| 364 | /* subtractions needed dominate division performance. */ |
| 365 | if (accunits==divunits) { |
| 366 | /* compare the high divunits of acc and div: */ |
| 367 | /* acc<div: this quotient unit is unchanged; subtraction */ |
| 368 | /* will be possible on the next iteration */ |
| 369 | /* acc==div: quotient gains 1, set acc=0 */ |
| 370 | /* acc>div: subtraction necessary at this position */ |
| 371 | for (ud=msud, ua=msua; ud>div; ud--, ua--) if (*ud!=*ua) break; |
| 372 | /* [now at first mismatch or lsu] */ |
| 373 | if (*ud>*ua) break; /* next time... */ |
| 374 | if (*ud==*ua) { /* all compared equal */ |
| 375 | *lsuq+=1; /* increment result */ |
| 376 | msua=lsua; /* collapse acc units */ |
| 377 | *msua=0; /* .. to a zero */ |
| 378 | break; |
| 379 | } |
| 380 | |
| 381 | /* subtraction necessary; estimate multiplier [see above] */ |
| 382 | /* if both *msud and *msua are small it is cost-effective to */ |
| 383 | /* bring in part of the following units (if any) to get a */ |
| 384 | /* better estimate (assume some other non-zero in div) */ |
| 385 | #define DIVLO 1000000U |
| 386 | #define DIVHI (DIVBASE/DIVLO) |
| 387 | #if DECUSE64 |
| 388 | if (divunits>1) { |
| 389 | /* there cannot be a *(msud-2) for DECDOUBLE so next is */ |
| 390 | /* an exact calculation unless DECQUAD (which needs to */ |
| 391 | /* assume bits out there if divunits>2) */ |
| 392 | uLong mul=(uLong)*msua * DIVBASE + *(msua-1); |
| 393 | uLong div=(uLong)*msud * DIVBASE + *(msud-1); |
| 394 | #if QUAD |
| 395 | if (divunits>2) div++; |
| 396 | #endif |
| 397 | mul/=div; |
| 398 | multiplier=(Int)mul; |
| 399 | } |
| 400 | else multiplier=*msua/(*msud); |
| 401 | #else |
| 402 | if (divunits>1 && *msua<DIVLO && *msud<DIVLO) { |
| 403 | multiplier=(*msua*DIVHI + *(msua-1)/DIVLO) |
| 404 | /(*msud*DIVHI + *(msud-1)/DIVLO +1); |
| 405 | } |
| 406 | else multiplier=(*msua<<2)/divtop; |
| 407 | #endif |
| 408 | } |
| 409 | else { /* accunits>divunits */ |
| 410 | /* msud is one unit 'lower' than msua, so estimate differently */ |
| 411 | #if DECUSE64 |
| 412 | uLong mul; |
| 413 | /* as before, bring in extra digits if possible */ |
| 414 | if (divunits>1 && *msua<DIVLO && *msud<DIVLO) { |
| 415 | mul=((uLong)*msua * DIVHI * DIVBASE) + *(msua-1) * DIVHI |
| 416 | + *(msua-2)/DIVLO; |
| 417 | mul/=(*msud*DIVHI + *(msud-1)/DIVLO +1); |
| 418 | } |
| 419 | else if (divunits==1) { |
| 420 | mul=(uLong)*msua * DIVBASE + *(msua-1); |
| 421 | mul/=*msud; /* no more to the right */ |
| 422 | } |
| 423 | else { |
| 424 | mul=(uLong)(*msua) * (uInt)(DIVBASE<<2) + (*(msua-1)<<2); |
| 425 | mul/=divtop; /* [divtop already allows for sticky bits] */ |
| 426 | } |
| 427 | multiplier=(Int)mul; |
| 428 | #else |
| 429 | multiplier=*msua * ((DIVBASE<<2)/divtop); |
| 430 | #endif |
| 431 | } |
| 432 | if (multiplier==0) multiplier=1; /* marginal case */ |
| 433 | *lsuq+=multiplier; |
| 434 | |
| 435 | #if DIVCOUNT |
| 436 | /* printf("Multiplier: %ld\n", (LI)multiplier); */ |
| 437 | divcount++; |
| 438 | #endif |
| 439 | |
| 440 | /* Carry out the subtraction acc-(div*multiplier); for each */ |
| 441 | /* unit in div, do the multiply, split to units (see */ |
| 442 | /* decFloatMultiply for the algorithm), and subtract from acc */ |
| 443 | #define DIVMAGIC 2305843009U /* 2**61/10**9 */ |
| 444 | #define DIVSHIFTA 29 |
| 445 | #define DIVSHIFTB 32 |
| 446 | carry=0; |
| 447 | for (ud=div, ua=lsua; ud<=msud; ud++, ua++) { |
| 448 | uInt lo, hop; |
| 449 | #if DECUSE64 |
| 450 | uLong sub=(uLong)multiplier*(*ud)+carry; |
| 451 | if (sub<DIVBASE) { |
| 452 | carry=0; |
| 453 | lo=(uInt)sub; |
| 454 | } |
| 455 | else { |
| 456 | hop=(uInt)(sub>>DIVSHIFTA); |
| 457 | carry=(uInt)(((uLong)hop*DIVMAGIC)>>DIVSHIFTB); |
| 458 | /* the estimate is now in hi; now calculate sub-hi*10**9 */ |
| 459 | /* to get the remainder (which will be <DIVBASE)) */ |
| 460 | lo=(uInt)sub; |
| 461 | lo-=carry*DIVBASE; /* low word of result */ |
| 462 | if (lo>=DIVBASE) { |
| 463 | lo-=DIVBASE; /* correct by +1 */ |
| 464 | carry++; |
| 465 | } |
| 466 | } |
| 467 | #else /* 32-bit */ |
| 468 | uInt hi; |
| 469 | /* calculate multiplier*(*ud) into hi and lo */ |
| 470 | LONGMUL32HI(hi, *ud, multiplier); /* get the high word */ |
| 471 | lo=multiplier*(*ud); /* .. and the low */ |
| 472 | lo+=carry; /* add the old hi */ |
| 473 | carry=hi+(lo<carry); /* .. with any carry */ |
| 474 | if (carry || lo>=DIVBASE) { /* split is needed */ |
| 475 | hop=(carry<<3)+(lo>>DIVSHIFTA); /* hi:lo/2**29 */ |
| 476 | LONGMUL32HI(carry, hop, DIVMAGIC); /* only need the high word */ |
| 477 | /* [DIVSHIFTB is 32, so carry can be used directly] */ |
| 478 | /* the estimate is now in carry; now calculate hi:lo-est*10**9; */ |
| 479 | /* happily the top word of the result is irrelevant because it */ |
| 480 | /* will always be zero so this needs only one multiplication */ |
| 481 | lo-=(carry*DIVBASE); |
| 482 | /* the correction here will be at most +1; do it */ |
| 483 | if (lo>=DIVBASE) { |
| 484 | lo-=DIVBASE; |
| 485 | carry++; |
| 486 | } |
| 487 | } |
| 488 | #endif |
| 489 | if (lo>*ua) { /* borrow needed */ |
| 490 | *ua+=DIVBASE; |
| 491 | carry++; |
| 492 | } |
| 493 | *ua-=lo; |
| 494 | } /* ud loop */ |
| 495 | if (carry) *ua-=carry; /* accdigits>divdigits [cannot borrow] */ |
| 496 | } /* inner loop */ |
| 497 | |
| 498 | /* the outer loop terminates when there is either an exact result */ |
| 499 | /* or enough digits; first update the quotient digit count and */ |
| 500 | /* pointer (if any significant digits) */ |
| 501 | #if DECTRACE |
| 502 | if (*lsuq || quodigits) printf("*lsuq=%09ld\n", (LI)*lsuq); |
| 503 | #endif |
| 504 | if (quodigits) { |
| 505 | quodigits+=9; /* had leading unit earlier */ |
| 506 | lsuq--; |
| 507 | if (quodigits>DECPMAX+1) break; /* have enough */ |
| 508 | } |
| 509 | else if (*lsuq) { /* first quotient digits */ |
| 510 | const uInt *pow; |
| 511 | for (pow=DECPOWERS; *lsuq>=*pow; pow++) quodigits++; |
| 512 | lsuq--; |
| 513 | /* [cannot have >DECPMAX+1 on first unit] */ |
| 514 | } |
| 515 | |
| 516 | if (*msua!=0) continue; /* not an exact result */ |
| 517 | /* acc is zero iff used all of original units and zero down to lsua */ |
| 518 | /* (must also continue to original lsu for correct quotient length) */ |
| 519 | if (lsua>acc+DIVACCLEN-DIVOPLEN) continue; |
| 520 | for (; msua>lsua && *msua==0;) msua--; |
| 521 | if (*msua==0 && msua==lsua) break; |
| 522 | } /* outer loop */ |
| 523 | |
| 524 | /* all of the original operand in acc has been covered at this point */ |
| 525 | /* quotient now has at least DECPMAX+2 digits */ |
| 526 | /* *msua is now non-0 if inexact and sticky bits */ |
| 527 | /* lsuq is one below the last uint of the quotient */ |
| 528 | lsuq++; /* set -> true lsu of quo */ |
| 529 | if (*msua) *lsuq|=1; /* apply sticky bit */ |
| 530 | |
| 531 | /* quo now holds the (unrounded) quotient in base-billion; one */ |
| 532 | /* base-billion 'digit' per uInt. */ |
| 533 | #if DECTRACE |
| 534 | printf("DivQuo:"); |
| 535 | for (uq=msuq; uq>=lsuq; uq--) printf(" %09ld", (LI)*uq); |
| 536 | printf("\n"); |
| 537 | #endif |
| 538 | |
| 539 | /* Now convert to BCD for rounding and cleanup, starting from the */ |
| 540 | /* most significant end [offset by one into bcdacc to leave room */ |
| 541 | /* for a possible carry digit if rounding for REMNEAR is needed] */ |
| 542 | for (uq=msuq, ub=bcdacc+1; uq>=lsuq; uq--, ub+=9) { |
| 543 | uInt top, mid, rem; /* work */ |
| 544 | if (*uq==0) { /* no split needed */ |
| 545 | UINTAT(ub)=0; /* clear 9 BCD8s */ |
| 546 | UINTAT(ub+4)=0; /* .. */ |
| 547 | *(ub+8)=0; /* .. */ |
| 548 | continue; |
| 549 | } |
| 550 | /* *uq is non-zero -- split the base-billion digit into */ |
| 551 | /* hi, mid, and low three-digits */ |
| 552 | #define divsplit9 1000000 /* divisor */ |
| 553 | #define divsplit6 1000 /* divisor */ |
| 554 | /* The splitting is done by simple divides and remainders, */ |
| 555 | /* assuming the compiler will optimize these [GCC does] */ |
| 556 | top=*uq/divsplit9; |
| 557 | rem=*uq%divsplit9; |
| 558 | mid=rem/divsplit6; |
| 559 | rem=rem%divsplit6; |
| 560 | /* lay out the nine BCD digits (plus one unwanted byte) */ |
| 561 | UINTAT(ub) =UINTAT(&BIN2BCD8[top*4]); |
| 562 | UINTAT(ub+3)=UINTAT(&BIN2BCD8[mid*4]); |
| 563 | UINTAT(ub+6)=UINTAT(&BIN2BCD8[rem*4]); |
| 564 | } /* BCD conversion loop */ |
| 565 | ub--; /* -> lsu */ |
| 566 | |
| 567 | /* complete the bcdnum; quodigits is correct, so the position of */ |
| 568 | /* the first non-zero is known */ |
| 569 | num.msd=bcdacc+1+(msuq-lsuq+1)*9-quodigits; |
| 570 | num.lsd=ub; |
| 571 | |
| 572 | /* make exponent adjustments, etc */ |
| 573 | if (lsua<acc+DIVACCLEN-DIVOPLEN) { /* used extra digits */ |
| 574 | num.exponent-=(Int)((acc+DIVACCLEN-DIVOPLEN-lsua)*9); |
| 575 | /* if the result was exact then there may be up to 8 extra */ |
| 576 | /* trailing zeros in the overflowed quotient final unit */ |
| 577 | if (*msua==0) { |
| 578 | for (; *ub==0;) ub--; /* drop zeros */ |
| 579 | num.exponent+=(Int)(num.lsd-ub); /* and adjust exponent */ |
| 580 | num.lsd=ub; |
| 581 | } |
| 582 | } /* adjustment needed */ |
| 583 | |
| 584 | #if DIVCOUNT |
| 585 | if (divcount>maxcount) { /* new high-water nark */ |
| 586 | maxcount=divcount; |
| 587 | printf("DivNewMaxCount: %ld\n", (LI)maxcount); |
| 588 | } |
| 589 | #endif |
| 590 | |
| 591 | if (op&DIVIDE) return decFinalize(result, &num, set); /* all done */ |
| 592 | |
| 593 | /* Is DIVIDEINT or a remainder; there is more to do -- first form */ |
| 594 | /* the integer (this is done 'after the fact', unlike as in */ |
| 595 | /* decNumber, so as not to tax DIVIDE) */ |
| 596 | |
| 597 | /* The first non-zero digit will be in the first 9 digits, known */ |
| 598 | /* from quodigits and num.msd, so there is always space for DECPMAX */ |
| 599 | /* digits */ |
| 600 | |
| 601 | length=(Int)(num.lsd-num.msd+1); |
| 602 | /*printf("Length exp: %ld %ld\n", (LI)length, (LI)num.exponent); */ |
| 603 | |
| 604 | if (length+num.exponent>DECPMAX) { /* cannot fit */ |
| 605 | decFloatZero(result); |
| 606 | DFWORD(result, 0)=DECFLOAT_qNaN; |
| 607 | set->status|=DEC_Division_impossible; |
| 608 | return result; |
| 609 | } |
| 610 | |
| 611 | if (num.exponent>=0) { /* already an int, or need pad zeros */ |
| 612 | for (ub=num.lsd+1; ub<=num.lsd+num.exponent; ub++) *ub=0; |
| 613 | num.lsd+=num.exponent; |
| 614 | } |
| 615 | else { /* too long: round or truncate needed */ |
| 616 | Int drop=-num.exponent; |
| 617 | if (!(op&REMNEAR)) { /* simple truncate */ |
| 618 | num.lsd-=drop; |
| 619 | if (num.lsd<num.msd) { /* truncated all */ |
| 620 | num.lsd=num.msd; /* make 0 */ |
| 621 | *num.lsd=0; /* .. [sign still relevant] */ |
| 622 | } |
| 623 | } |
| 624 | else { /* round to nearest even [sigh] */ |
| 625 | /* round-to-nearest, in-place; msd is at or to right of bcdacc+1 */ |
| 626 | /* (this is a special case of Quantize -- q.v. for commentary) */ |
| 627 | uByte *roundat; /* -> re-round digit */ |
| 628 | uByte reround; /* reround value */ |
| 629 | *(num.msd-1)=0; /* in case of left carry, or make 0 */ |
| 630 | if (drop<length) roundat=num.lsd-drop+1; |
| 631 | else if (drop==length) roundat=num.msd; |
| 632 | else roundat=num.msd-1; /* [-> 0] */ |
| 633 | reround=*roundat; |
| 634 | for (ub=roundat+1; ub<=num.lsd; ub++) { |
| 635 | if (*ub!=0) { |
| 636 | reround=DECSTICKYTAB[reround]; |
| 637 | break; |
| 638 | } |
| 639 | } /* check stickies */ |
| 640 | if (roundat>num.msd) num.lsd=roundat-1; |
| 641 | else { |
| 642 | num.msd--; /* use the 0 .. */ |
| 643 | num.lsd=num.msd; /* .. at the new MSD place */ |
| 644 | } |
| 645 | if (reround!=0) { /* discarding non-zero */ |
| 646 | uInt bump=0; |
| 647 | /* rounding is DEC_ROUND_HALF_EVEN always */ |
| 648 | if (reround>5) bump=1; /* >0.5 goes up */ |
| 649 | else if (reround==5) /* exactly 0.5000 .. */ |
| 650 | bump=*(num.lsd) & 0x01; /* .. up iff [new] lsd is odd */ |
| 651 | if (bump!=0) { /* need increment */ |
| 652 | /* increment the coefficient; this might end up with 1000... */ |
| 653 | ub=num.lsd; |
| 654 | for (; UINTAT(ub-3)==0x09090909; ub-=4) UINTAT(ub-3)=0; |
| 655 | for (; *ub==9; ub--) *ub=0; /* at most 3 more */ |
| 656 | *ub+=1; |
| 657 | if (ub<num.msd) num.msd--; /* carried */ |
| 658 | } /* bump needed */ |
| 659 | } /* reround!=0 */ |
| 660 | } /* remnear */ |
| 661 | } /* round or truncate needed */ |
| 662 | num.exponent=0; /* all paths */ |
| 663 | /*decShowNum(&num, "int"); */ |
| 664 | |
| 665 | if (op&DIVIDEINT) return decFinalize(result, &num, set); /* all done */ |
| 666 | |
| 667 | /* Have a remainder to calculate */ |
| 668 | decFinalize("ient, &num, set); /* lay out the integer so far */ |
| 669 | DFWORD("ient, 0)^=DECFLOAT_Sign; /* negate it */ |
| 670 | sign=DFWORD(dfl, 0); /* save sign of dfl */ |
| 671 | decFloatFMA(result, "ient, dfr, dfl, set); |
| 672 | if (!DFISZERO(result)) return result; |
| 673 | /* if the result is zero the sign shall be sign of dfl */ |
| 674 | DFWORD("ient, 0)=sign; /* construct decFloat of sign */ |
| 675 | return decFloatCopySign(result, result, "ient); |
| 676 | } /* decDivide */ |
| 677 | |
| 678 | /* ------------------------------------------------------------------ */ |
| 679 | /* decFiniteMultiply -- multiply two finite decFloats */ |
| 680 | /* */ |
| 681 | /* num gets the result of multiplying dfl and dfr */ |
| 682 | /* bcdacc .. with the coefficient in this array */ |
| 683 | /* dfl is the first decFloat (lhs) */ |
| 684 | /* dfr is the second decFloat (rhs) */ |
| 685 | /* */ |
| 686 | /* This effects the multiplication of two decFloats, both known to be */ |
| 687 | /* finite, leaving the result in a bcdnum ready for decFinalize (for */ |
| 688 | /* use in Multiply) or in a following addition (FMA). */ |
| 689 | /* */ |
| 690 | /* bcdacc must have space for at least DECPMAX9*18+1 bytes. */ |
| 691 | /* No error is possible and no status is set. */ |
| 692 | /* ------------------------------------------------------------------ */ |
| 693 | /* This routine has two separate implementations of the core */ |
| 694 | /* multiplication; both using base-billion. One uses only 32-bit */ |
| 695 | /* variables (Ints and uInts) or smaller; the other uses uLongs (for */ |
| 696 | /* multiplication and addition only). Both implementations cover */ |
| 697 | /* both arithmetic sizes (DOUBLE and QUAD) in order to allow timing */ |
| 698 | /* comparisons. In any one compilation only one implementation for */ |
| 699 | /* each size can be used, and if DECUSE64 is 0 then use of the 32-bit */ |
| 700 | /* version is forced. */ |
| 701 | /* */ |
| 702 | /* Historical note: an earlier version of this code also supported the */ |
| 703 | /* 256-bit format and has been preserved. That is somewhat trickier */ |
| 704 | /* during lazy carry splitting because the initial quotient estimate */ |
| 705 | /* (est) can exceed 32 bits. */ |
| 706 | |
| 707 | #define MULTBASE BILLION /* the base used for multiply */ |
| 708 | #define MULOPLEN DECPMAX9 /* operand length ('digits' base 10**9) */ |
| 709 | #define MULACCLEN (MULOPLEN*2) /* accumulator length (ditto) */ |
| 710 | #define LEADZEROS (MULACCLEN*9 - DECPMAX*2) /* leading zeros always */ |
| 711 | |
| 712 | /* Assertions: exponent not too large and MULACCLEN is a multiple of 4 */ |
| 713 | #if DECEMAXD>9 |
| 714 | #error Exponent may overflow when doubled for Multiply |
| 715 | #endif |
| 716 | #if MULACCLEN!=(MULACCLEN/4)*4 |
| 717 | /* This assumption is used below only for initialization */ |
| 718 | #error MULACCLEN is not a multiple of 4 |
| 719 | #endif |
| 720 | |
| 721 | static void decFiniteMultiply(bcdnum *num, uByte *bcdacc, |
| 722 | const decFloat *dfl, const decFloat *dfr) { |
| 723 | uInt bufl[MULOPLEN]; /* left coefficient (base-billion) */ |
| 724 | uInt bufr[MULOPLEN]; /* right coefficient (base-billion) */ |
| 725 | uInt *ui, *uj; /* work */ |
| 726 | uByte *ub; /* .. */ |
| 727 | |
| 728 | #if DECUSE64 |
| 729 | uLong accl[MULACCLEN]; /* lazy accumulator (base-billion+) */ |
| 730 | uLong *pl; /* work -> lazy accumulator */ |
| 731 | uInt acc[MULACCLEN]; /* coefficent in base-billion .. */ |
| 732 | #else |
| 733 | uInt acc[MULACCLEN*2]; /* accumulator in base-billion .. */ |
| 734 | #endif |
| 735 | uInt *pa; /* work -> accumulator */ |
| 736 | /*printf("Base10**9: OpLen=%d MulAcclen=%d\n", OPLEN, MULACCLEN); */ |
| 737 | |
| 738 | /* Calculate sign and exponent */ |
| 739 | num->sign=(DFWORD(dfl, 0)^DFWORD(dfr, 0)) & DECFLOAT_Sign; |
| 740 | num->exponent=GETEXPUN(dfl)+GETEXPUN(dfr); /* [see assertion above] */ |
| 741 | |
| 742 | /* Extract the coefficients and prepare the accumulator */ |
| 743 | /* the coefficients of the operands are decoded into base-billion */ |
| 744 | /* numbers in uInt arrays (bufl and bufr, LSD at offset 0) of the */ |
| 745 | /* appropriate size. */ |
| 746 | GETCOEFFBILL(dfl, bufl); |
| 747 | GETCOEFFBILL(dfr, bufr); |
| 748 | #if DECTRACE && 0 |
| 749 | printf("CoeffbL:"); |
| 750 | for (ui=bufl+MULOPLEN-1; ui>=bufl; ui--) printf(" %08lx", (LI)*ui); |
| 751 | printf("\n"); |
| 752 | printf("CoeffbR:"); |
| 753 | for (uj=bufr+MULOPLEN-1; uj>=bufr; uj--) printf(" %08lx", (LI)*uj); |
| 754 | printf("\n"); |
| 755 | #endif |
| 756 | |
| 757 | /* start the 64-bit/32-bit differing paths... */ |
| 758 | #if DECUSE64 |
| 759 | |
| 760 | /* zero the accumulator */ |
| 761 | #if MULACCLEN==4 |
| 762 | accl[0]=0; accl[1]=0; accl[2]=0; accl[3]=0; |
| 763 | #else /* use a loop */ |
| 764 | /* MULACCLEN is a multiple of four, asserted above */ |
| 765 | for (pl=accl; pl<accl+MULACCLEN; pl+=4) { |
| 766 | *pl=0; *(pl+1)=0; *(pl+2)=0; *(pl+3)=0;/* [reduce overhead] */ |
| 767 | } /* pl */ |
| 768 | #endif |
| 769 | |
| 770 | /* Effect the multiplication */ |
| 771 | /* The multiplcation proceeds using MFC's lazy-carry resolution */ |
| 772 | /* algorithm from decNumber. First, the multiplication is */ |
| 773 | /* effected, allowing accumulation of the partial products (which */ |
| 774 | /* are in base-billion at each column position) into 64 bits */ |
| 775 | /* without resolving back to base=billion after each addition. */ |
| 776 | /* These 64-bit numbers (which may contain up to 19 decimal digits) */ |
| 777 | /* are then split using the Clark & Cowlishaw algorithm (see below). */ |
| 778 | /* [Testing for 0 in the inner loop is not really a 'win'] */ |
| 779 | for (ui=bufr; ui<bufr+MULOPLEN; ui++) { /* over each item in rhs */ |
| 780 | if (*ui==0) continue; /* product cannot affect result */ |
| 781 | pl=accl+(ui-bufr); /* where to add the lhs */ |
| 782 | for (uj=bufl; uj<bufl+MULOPLEN; uj++, pl++) { /* over each item in lhs */ |
| 783 | /* if (*uj==0) continue; // product cannot affect result */ |
| 784 | *pl+=((uLong)*ui)*(*uj); |
| 785 | } /* uj */ |
| 786 | } /* ui */ |
| 787 | |
| 788 | /* The 64-bit carries must now be resolved; this means that a */ |
| 789 | /* quotient/remainder has to be calculated for base-billion (1E+9). */ |
| 790 | /* For this, Clark & Cowlishaw's quotient estimation approach (also */ |
| 791 | /* used in decNumber) is needed, because 64-bit divide is generally */ |
| 792 | /* extremely slow on 32-bit machines, and may be slower than this */ |
| 793 | /* approach even on 64-bit machines. This algorithm splits X */ |
| 794 | /* using: */ |
| 795 | /* */ |
| 796 | /* magic=2**(A+B)/1E+9; // 'magic number' */ |
| 797 | /* hop=X/2**A; // high order part of X (by shift) */ |
| 798 | /* est=magic*hop/2**B // quotient estimate (may be low by 1) */ |
| 799 | /* */ |
| 800 | /* A and B are quite constrained; hop and magic must fit in 32 bits, */ |
| 801 | /* and 2**(A+B) must be as large as possible (which is 2**61 if */ |
| 802 | /* magic is to fit). Further, maxX increases with the length of */ |
| 803 | /* the operands (and hence the number of partial products */ |
| 804 | /* accumulated); maxX is OPLEN*(10**18), which is up to 19 digits. */ |
| 805 | /* */ |
| 806 | /* It can be shown that when OPLEN is 2 then the maximum error in */ |
| 807 | /* the estimated quotient is <1, but for larger maximum x the */ |
| 808 | /* maximum error is above 1 so a correction that is >1 may be */ |
| 809 | /* needed. Values of A and B are chosen to satisfy the constraints */ |
| 810 | /* just mentioned while minimizing the maximum error (and hence the */ |
| 811 | /* maximum correction), as shown in the following table: */ |
| 812 | /* */ |
| 813 | /* Type OPLEN A B maxX maxError maxCorrection */ |
| 814 | /* --------------------------------------------------------- */ |
| 815 | /* DOUBLE 2 29 32 <2*10**18 0.63 1 */ |
| 816 | /* QUAD 4 30 31 <4*10**18 1.17 2 */ |
| 817 | /* */ |
| 818 | /* In the OPLEN==2 case there is most choice, but the value for B */ |
| 819 | /* of 32 has a big advantage as then the calculation of the */ |
| 820 | /* estimate requires no shifting; the compiler can extract the high */ |
| 821 | /* word directly after multiplying magic*hop. */ |
| 822 | #define MULMAGIC 2305843009U /* 2**61/10**9 [both cases] */ |
| 823 | #if DOUBLE |
| 824 | #define MULSHIFTA 29 |
| 825 | #define MULSHIFTB 32 |
| 826 | #elif QUAD |
| 827 | #define MULSHIFTA 30 |
| 828 | #define MULSHIFTB 31 |
| 829 | #else |
| 830 | #error Unexpected type |
| 831 | #endif |
| 832 | |
| 833 | #if DECTRACE |
| 834 | printf("MulAccl:"); |
| 835 | for (pl=accl+MULACCLEN-1; pl>=accl; pl--) |
| 836 | printf(" %08lx:%08lx", (LI)(*pl>>32), (LI)(*pl&0xffffffff)); |
| 837 | printf("\n"); |
| 838 | #endif |
| 839 | |
| 840 | for (pl=accl, pa=acc; pl<accl+MULACCLEN; pl++, pa++) { /* each column position */ |
| 841 | uInt lo, hop; /* work */ |
| 842 | uInt est; /* cannot exceed 4E+9 */ |
| 843 | if (*pl>MULTBASE) { |
| 844 | /* *pl holds a binary number which needs to be split */ |
| 845 | hop=(uInt)(*pl>>MULSHIFTA); |
| 846 | est=(uInt)(((uLong)hop*MULMAGIC)>>MULSHIFTB); |
| 847 | /* the estimate is now in est; now calculate hi:lo-est*10**9; */ |
| 848 | /* happily the top word of the result is irrelevant because it */ |
| 849 | /* will always be zero so this needs only one multiplication */ |
| 850 | lo=(uInt)(*pl-((uLong)est*MULTBASE)); /* low word of result */ |
| 851 | /* If QUAD, the correction here could be +2 */ |
| 852 | if (lo>=MULTBASE) { |
| 853 | lo-=MULTBASE; /* correct by +1 */ |
| 854 | est++; |
| 855 | #if QUAD |
| 856 | /* may need to correct by +2 */ |
| 857 | if (lo>=MULTBASE) { |
| 858 | lo-=MULTBASE; |
| 859 | est++; |
| 860 | } |
| 861 | #endif |
| 862 | } |
| 863 | /* finally place lo as the new coefficient 'digit' and add est to */ |
| 864 | /* the next place up [this is safe because this path is never */ |
| 865 | /* taken on the final iteration as *pl will fit] */ |
| 866 | *pa=lo; |
| 867 | *(pl+1)+=est; |
| 868 | } /* *pl needed split */ |
| 869 | else { /* *pl<MULTBASE */ |
| 870 | *pa=(uInt)*pl; /* just copy across */ |
| 871 | } |
| 872 | } /* pl loop */ |
| 873 | |
| 874 | #else /* 32-bit */ |
| 875 | for (pa=acc;; pa+=4) { /* zero the accumulator */ |
| 876 | *pa=0; *(pa+1)=0; *(pa+2)=0; *(pa+3)=0; /* [reduce overhead] */ |
| 877 | if (pa==acc+MULACCLEN*2-4) break; /* multiple of 4 asserted */ |
| 878 | } /* pa */ |
| 879 | |
| 880 | /* Effect the multiplication */ |
| 881 | /* uLongs are not available (and in particular, there is no uLong */ |
| 882 | /* divide) but it is still possible to use MFC's lazy-carry */ |
| 883 | /* resolution algorithm from decNumber. First, the multiplication */ |
| 884 | /* is effected, allowing accumulation of the partial products */ |
| 885 | /* (which are in base-billion at each column position) into 64 bits */ |
| 886 | /* [with the high-order 32 bits in each position being held at */ |
| 887 | /* offset +ACCLEN from the low-order 32 bits in the accumulator]. */ |
| 888 | /* These 64-bit numbers (which may contain up to 19 decimal digits) */ |
| 889 | /* are then split using the Clark & Cowlishaw algorithm (see */ |
| 890 | /* below). */ |
| 891 | for (ui=bufr;; ui++) { /* over each item in rhs */ |
| 892 | uInt hi, lo; /* words of exact multiply result */ |
| 893 | pa=acc+(ui-bufr); /* where to add the lhs */ |
| 894 | for (uj=bufl;; uj++, pa++) { /* over each item in lhs */ |
| 895 | LONGMUL32HI(hi, *ui, *uj); /* calculate product of digits */ |
| 896 | lo=(*ui)*(*uj); /* .. */ |
| 897 | *pa+=lo; /* accumulate low bits and .. */ |
| 898 | *(pa+MULACCLEN)+=hi+(*pa<lo); /* .. high bits with any carry */ |
| 899 | if (uj==bufl+MULOPLEN-1) break; |
| 900 | } |
| 901 | if (ui==bufr+MULOPLEN-1) break; |
| 902 | } |
| 903 | |
| 904 | /* The 64-bit carries must now be resolved; this means that a */ |
| 905 | /* quotient/remainder has to be calculated for base-billion (1E+9). */ |
| 906 | /* For this, Clark & Cowlishaw's quotient estimation approach (also */ |
| 907 | /* used in decNumber) is needed, because 64-bit divide is generally */ |
| 908 | /* extremely slow on 32-bit machines. This algorithm splits X */ |
| 909 | /* using: */ |
| 910 | /* */ |
| 911 | /* magic=2**(A+B)/1E+9; // 'magic number' */ |
| 912 | /* hop=X/2**A; // high order part of X (by shift) */ |
| 913 | /* est=magic*hop/2**B // quotient estimate (may be low by 1) */ |
| 914 | /* */ |
| 915 | /* A and B are quite constrained; hop and magic must fit in 32 bits, */ |
| 916 | /* and 2**(A+B) must be as large as possible (which is 2**61 if */ |
| 917 | /* magic is to fit). Further, maxX increases with the length of */ |
| 918 | /* the operands (and hence the number of partial products */ |
| 919 | /* accumulated); maxX is OPLEN*(10**18), which is up to 19 digits. */ |
| 920 | /* */ |
| 921 | /* It can be shown that when OPLEN is 2 then the maximum error in */ |
| 922 | /* the estimated quotient is <1, but for larger maximum x the */ |
| 923 | /* maximum error is above 1 so a correction that is >1 may be */ |
| 924 | /* needed. Values of A and B are chosen to satisfy the constraints */ |
| 925 | /* just mentioned while minimizing the maximum error (and hence the */ |
| 926 | /* maximum correction), as shown in the following table: */ |
| 927 | /* */ |
| 928 | /* Type OPLEN A B maxX maxError maxCorrection */ |
| 929 | /* --------------------------------------------------------- */ |
| 930 | /* DOUBLE 2 29 32 <2*10**18 0.63 1 */ |
| 931 | /* QUAD 4 30 31 <4*10**18 1.17 2 */ |
| 932 | /* */ |
| 933 | /* In the OPLEN==2 case there is most choice, but the value for B */ |
| 934 | /* of 32 has a big advantage as then the calculation of the */ |
| 935 | /* estimate requires no shifting; the high word is simply */ |
| 936 | /* calculated from multiplying magic*hop. */ |
| 937 | #define MULMAGIC 2305843009U /* 2**61/10**9 [both cases] */ |
| 938 | #if DOUBLE |
| 939 | #define MULSHIFTA 29 |
| 940 | #define MULSHIFTB 32 |
| 941 | #elif QUAD |
| 942 | #define MULSHIFTA 30 |
| 943 | #define MULSHIFTB 31 |
| 944 | #else |
| 945 | #error Unexpected type |
| 946 | #endif |
| 947 | |
| 948 | #if DECTRACE |
| 949 | printf("MulHiLo:"); |
| 950 | for (pa=acc+MULACCLEN-1; pa>=acc; pa--) |
| 951 | printf(" %08lx:%08lx", (LI)*(pa+MULACCLEN), (LI)*pa); |
| 952 | printf("\n"); |
| 953 | #endif |
| 954 | |
| 955 | for (pa=acc;; pa++) { /* each low uInt */ |
| 956 | uInt hi, lo; /* words of exact multiply result */ |
| 957 | uInt hop, estlo; /* work */ |
| 958 | #if QUAD |
| 959 | uInt esthi; /* .. */ |
| 960 | #endif |
| 961 | |
| 962 | lo=*pa; |
| 963 | hi=*(pa+MULACCLEN); /* top 32 bits */ |
| 964 | /* hi and lo now hold a binary number which needs to be split */ |
| 965 | |
| 966 | #if DOUBLE |
| 967 | hop=(hi<<3)+(lo>>MULSHIFTA); /* hi:lo/2**29 */ |
| 968 | LONGMUL32HI(estlo, hop, MULMAGIC);/* only need the high word */ |
| 969 | /* [MULSHIFTB is 32, so estlo can be used directly] */ |
| 970 | /* the estimate is now in estlo; now calculate hi:lo-est*10**9; */ |
| 971 | /* happily the top word of the result is irrelevant because it */ |
| 972 | /* will always be zero so this needs only one multiplication */ |
| 973 | lo-=(estlo*MULTBASE); |
| 974 | /* esthi=0; // high word is ignored below */ |
| 975 | /* the correction here will be at most +1; do it */ |
| 976 | if (lo>=MULTBASE) { |
| 977 | lo-=MULTBASE; |
| 978 | estlo++; |
| 979 | } |
| 980 | #elif QUAD |
| 981 | hop=(hi<<2)+(lo>>MULSHIFTA); /* hi:lo/2**30 */ |
| 982 | LONGMUL32HI(esthi, hop, MULMAGIC);/* shift will be 31 .. */ |
| 983 | estlo=hop*MULMAGIC; /* .. so low word needed */ |
| 984 | estlo=(esthi<<1)+(estlo>>MULSHIFTB); /* [just the top bit] */ |
| 985 | /* esthi=0; // high word is ignored below */ |
| 986 | lo-=(estlo*MULTBASE); /* as above */ |
| 987 | /* the correction here could be +1 or +2 */ |
| 988 | if (lo>=MULTBASE) { |
| 989 | lo-=MULTBASE; |
| 990 | estlo++; |
| 991 | } |
| 992 | if (lo>=MULTBASE) { |
| 993 | lo-=MULTBASE; |
| 994 | estlo++; |
| 995 | } |
| 996 | #else |
| 997 | #error Unexpected type |
| 998 | #endif |
| 999 | |
| 1000 | /* finally place lo as the new accumulator digit and add est to */ |
| 1001 | /* the next place up; this latter add could cause a carry of 1 */ |
| 1002 | /* to the high word of the next place */ |
| 1003 | *pa=lo; |
| 1004 | *(pa+1)+=estlo; |
| 1005 | /* esthi is always 0 for DOUBLE and QUAD so this is skipped */ |
| 1006 | /* *(pa+1+MULACCLEN)+=esthi; */ |
| 1007 | if (*(pa+1)<estlo) *(pa+1+MULACCLEN)+=1; /* carry */ |
| 1008 | if (pa==acc+MULACCLEN-2) break; /* [MULACCLEN-1 will never need split] */ |
| 1009 | } /* pa loop */ |
| 1010 | #endif |
| 1011 | |
| 1012 | /* At this point, whether using the 64-bit or the 32-bit paths, the */ |
| 1013 | /* accumulator now holds the (unrounded) result in base-billion; */ |
| 1014 | /* one base-billion 'digit' per uInt. */ |
| 1015 | #if DECTRACE |
| 1016 | printf("MultAcc:"); |
| 1017 | for (pa=acc+MULACCLEN-1; pa>=acc; pa--) printf(" %09ld", (LI)*pa); |
| 1018 | printf("\n"); |
| 1019 | #endif |
| 1020 | |
| 1021 | /* Now convert to BCD for rounding and cleanup, starting from the */ |
| 1022 | /* most significant end */ |
| 1023 | pa=acc+MULACCLEN-1; |
| 1024 | if (*pa!=0) num->msd=bcdacc+LEADZEROS;/* drop known lead zeros */ |
| 1025 | else { /* >=1 word of leading zeros */ |
| 1026 | num->msd=bcdacc; /* known leading zeros are gone */ |
| 1027 | pa--; /* skip first word .. */ |
| 1028 | for (; *pa==0; pa--) if (pa==acc) break; /* .. and any more leading 0s */ |
| 1029 | } |
| 1030 | for (ub=bcdacc;; pa--, ub+=9) { |
| 1031 | if (*pa!=0) { /* split(s) needed */ |
| 1032 | uInt top, mid, rem; /* work */ |
| 1033 | /* *pa is non-zero -- split the base-billion acc digit into */ |
| 1034 | /* hi, mid, and low three-digits */ |
| 1035 | #define mulsplit9 1000000 /* divisor */ |
| 1036 | #define mulsplit6 1000 /* divisor */ |
| 1037 | /* The splitting is done by simple divides and remainders, */ |
| 1038 | /* assuming the compiler will optimize these where useful */ |
| 1039 | /* [GCC does] */ |
| 1040 | top=*pa/mulsplit9; |
| 1041 | rem=*pa%mulsplit9; |
| 1042 | mid=rem/mulsplit6; |
| 1043 | rem=rem%mulsplit6; |
| 1044 | /* lay out the nine BCD digits (plus one unwanted byte) */ |
| 1045 | UINTAT(ub) =UINTAT(&BIN2BCD8[top*4]); |
| 1046 | UINTAT(ub+3)=UINTAT(&BIN2BCD8[mid*4]); |
| 1047 | UINTAT(ub+6)=UINTAT(&BIN2BCD8[rem*4]); |
| 1048 | } |
| 1049 | else { /* *pa==0 */ |
| 1050 | UINTAT(ub)=0; /* clear 9 BCD8s */ |
| 1051 | UINTAT(ub+4)=0; /* .. */ |
| 1052 | *(ub+8)=0; /* .. */ |
| 1053 | } |
| 1054 | if (pa==acc) break; |
| 1055 | } /* BCD conversion loop */ |
| 1056 | |
| 1057 | num->lsd=ub+8; /* complete the bcdnum .. */ |
| 1058 | |
| 1059 | #if DECTRACE |
| 1060 | decShowNum(num, "postmult"); |
| 1061 | decFloatShow(dfl, "dfl"); |
| 1062 | decFloatShow(dfr, "dfr"); |
| 1063 | #endif |
| 1064 | return; |
| 1065 | } /* decFiniteMultiply */ |
| 1066 | |
| 1067 | /* ------------------------------------------------------------------ */ |
| 1068 | /* decFloatAbs -- absolute value, heeding NaNs, etc. */ |
| 1069 | /* */ |
| 1070 | /* result gets the canonicalized df with sign 0 */ |
| 1071 | /* df is the decFloat to abs */ |
| 1072 | /* set is the context */ |
| 1073 | /* returns result */ |
| 1074 | /* */ |
| 1075 | /* This has the same effect as decFloatPlus unless df is negative, */ |
| 1076 | /* in which case it has the same effect as decFloatMinus. The */ |
| 1077 | /* effect is also the same as decFloatCopyAbs except that NaNs are */ |
| 1078 | /* handled normally (the sign of a NaN is not affected, and an sNaN */ |
| 1079 | /* will signal) and the result will be canonical. */ |
| 1080 | /* ------------------------------------------------------------------ */ |
| 1081 | decFloat * decFloatAbs(decFloat *result, const decFloat *df, |
| 1082 | decContext *set) { |
| 1083 | if (DFISNAN(df)) return decNaNs(result, df, NULL, set); |
| 1084 | decCanonical(result, df); /* copy and check */ |
| 1085 | DFBYTE(result, 0)&=~0x80; /* zero sign bit */ |
| 1086 | return result; |
| 1087 | } /* decFloatAbs */ |
| 1088 | |
| 1089 | /* ------------------------------------------------------------------ */ |
| 1090 | /* decFloatAdd -- add two decFloats */ |
| 1091 | /* */ |
| 1092 | /* result gets the result of adding dfl and dfr: */ |
| 1093 | /* dfl is the first decFloat (lhs) */ |
| 1094 | /* dfr is the second decFloat (rhs) */ |
| 1095 | /* set is the context */ |
| 1096 | /* returns result */ |
| 1097 | /* */ |
| 1098 | /* ------------------------------------------------------------------ */ |
| 1099 | decFloat * decFloatAdd(decFloat *result, |
| 1100 | const decFloat *dfl, const decFloat *dfr, |
| 1101 | decContext *set) { |
| 1102 | bcdnum num; /* for final conversion */ |
| 1103 | Int expl, expr; /* left and right exponents */ |
| 1104 | uInt *ui, *uj; /* work */ |
| 1105 | uByte *ub; /* .. */ |
| 1106 | |
| 1107 | uInt sourhil, sourhir; /* top words from source decFloats */ |
| 1108 | /* [valid only until specials */ |
| 1109 | /* handled or exponents decoded] */ |
| 1110 | uInt diffsign; /* non-zero if signs differ */ |
| 1111 | uInt carry; /* carry: 0 or 1 before add loop */ |
| 1112 | Int overlap; /* coefficient overlap (if full) */ |
| 1113 | /* the following buffers hold coefficients with various alignments */ |
| 1114 | /* (see commentary and diagrams below) */ |
| 1115 | uByte acc[4+2+DECPMAX*3+8]; |
| 1116 | uByte buf[4+2+DECPMAX*2]; |
| 1117 | uByte *umsd, *ulsd; /* local MSD and LSD pointers */ |
| 1118 | |
| 1119 | #if DECLITEND |
| 1120 | #define CARRYPAT 0x01000000 /* carry=1 pattern */ |
| 1121 | #else |
| 1122 | #define CARRYPAT 0x00000001 /* carry=1 pattern */ |
| 1123 | #endif |
| 1124 | |
| 1125 | /* Start decoding the arguments */ |
| 1126 | /* the initial exponents are placed into the opposite Ints to */ |
| 1127 | /* that which might be expected; there are two sets of data to */ |
| 1128 | /* keep track of (each decFloat and the corresponding exponent), */ |
| 1129 | /* and this scheme means that at the swap point (after comparing */ |
| 1130 | /* exponents) only one pair of words needs to be swapped */ |
| 1131 | /* whichever path is taken (thereby minimising worst-case path) */ |
| 1132 | sourhil=DFWORD(dfl, 0); /* LHS top word */ |
| 1133 | expr=DECCOMBEXP[sourhil>>26]; /* get exponent high bits (in place) */ |
| 1134 | sourhir=DFWORD(dfr, 0); /* RHS top word */ |
| 1135 | expl=DECCOMBEXP[sourhir>>26]; |
| 1136 | |
| 1137 | diffsign=(sourhil^sourhir)&DECFLOAT_Sign; |
| 1138 | |
| 1139 | if (EXPISSPECIAL(expl | expr)) { /* either is special? */ |
| 1140 | if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set); |
| 1141 | /* one or two infinities */ |
| 1142 | /* two infinities with different signs is invalid */ |
| 1143 | if (diffsign && DFISINF(dfl) && DFISINF(dfr)) |
| 1144 | return decInvalid(result, set); |
| 1145 | if (DFISINF(dfl)) return decInfinity(result, dfl); /* LHS is infinite */ |
| 1146 | return decInfinity(result, dfr); /* RHS must be Infinite */ |
| 1147 | } |
| 1148 | |
| 1149 | /* Here when both arguments are finite */ |
| 1150 | |
| 1151 | /* complete exponent gathering (keeping swapped) */ |
| 1152 | expr+=GETECON(dfl)-DECBIAS; /* .. + continuation and unbias */ |
| 1153 | expl+=GETECON(dfr)-DECBIAS; |
| 1154 | /* here expr has exponent from lhs, and vice versa */ |
| 1155 | |
| 1156 | /* now swap either exponents or argument pointers */ |
| 1157 | if (expl<=expr) { |
| 1158 | /* original left is bigger */ |
| 1159 | Int expswap=expl; |
| 1160 | expl=expr; |
| 1161 | expr=expswap; |
| 1162 | /* printf("left bigger\n"); */ |
| 1163 | } |
| 1164 | else { |
| 1165 | const decFloat *dfswap=dfl; |
| 1166 | dfl=dfr; |
| 1167 | dfr=dfswap; |
| 1168 | /* printf("right bigger\n"); */ |
| 1169 | } |
| 1170 | /* [here dfl and expl refer to the datum with the larger exponent, */ |
| 1171 | /* of if the exponents are equal then the original LHS argument] */ |
| 1172 | |
| 1173 | /* if lhs is zero then result will be the rhs (now known to have */ |
| 1174 | /* the smaller exponent), which also may need to be tested for zero */ |
| 1175 | /* for the weird IEEE 754 sign rules */ |
| 1176 | if (DFISZERO(dfl)) { |
| 1177 | decCanonical(result, dfr); /* clean copy */ |
| 1178 | /* "When the sum of two operands with opposite signs is */ |
| 1179 | /* exactly zero, the sign of that sum shall be '+' in all */ |
| 1180 | /* rounding modes except round toward -Infinity, in which */ |
| 1181 | /* mode that sign shall be '-'." */ |
| 1182 | if (diffsign && DFISZERO(result)) { |
| 1183 | DFWORD(result, 0)&=~DECFLOAT_Sign; /* assume sign 0 */ |
| 1184 | if (set->round==DEC_ROUND_FLOOR) DFWORD(result, 0)|=DECFLOAT_Sign; |
| 1185 | } |
| 1186 | return result; |
| 1187 | } /* numfl is zero */ |
| 1188 | /* [here, LHS is non-zero; code below assumes that] */ |
| 1189 | |
| 1190 | /* Coefficients layout during the calculations to follow: */ |
| 1191 | /* */ |
| 1192 | /* Overlap case: */ |
| 1193 | /* +------------------------------------------------+ */ |
| 1194 | /* acc: |0000| coeffa | tail B | | */ |
| 1195 | /* +------------------------------------------------+ */ |
| 1196 | /* buf: |0000| pad0s | coeffb | | */ |
| 1197 | /* +------------------------------------------------+ */ |
| 1198 | /* */ |
| 1199 | /* Touching coefficients or gap: */ |
| 1200 | /* +------------------------------------------------+ */ |
| 1201 | /* acc: |0000| coeffa | gap | coeffb | */ |
| 1202 | /* +------------------------------------------------+ */ |
| 1203 | /* [buf not used or needed; gap clamped to Pmax] */ |
| 1204 | |
| 1205 | /* lay out lhs coefficient into accumulator; this starts at acc+4 */ |
| 1206 | /* for decDouble or acc+6 for decQuad so the LSD is word- */ |
| 1207 | /* aligned; the top word gap is there only in case a carry digit */ |
| 1208 | /* is prefixed after the add -- it does not need to be zeroed */ |
| 1209 | #if DOUBLE |
| 1210 | #define COFF 4 /* offset into acc */ |
| 1211 | #elif QUAD |
| 1212 | USHORTAT(acc+4)=0; /* prefix 00 */ |
| 1213 | #define COFF 6 /* offset into acc */ |
| 1214 | #endif |
| 1215 | |
| 1216 | GETCOEFF(dfl, acc+COFF); /* decode from decFloat */ |
| 1217 | ulsd=acc+COFF+DECPMAX-1; |
| 1218 | umsd=acc+4; /* [having this here avoids */ |
| 1219 | /* weird GCC optimizer failure] */ |
| 1220 | #if DECTRACE |
| 1221 | {bcdnum tum; |
| 1222 | tum.msd=umsd; |
| 1223 | tum.lsd=ulsd; |
| 1224 | tum.exponent=expl; |
| 1225 | tum.sign=DFWORD(dfl, 0) & DECFLOAT_Sign; |
| 1226 | decShowNum(&tum, "dflx");} |
| 1227 | #endif |
| 1228 | |
| 1229 | /* if signs differ, take ten's complement of lhs (here the */ |
| 1230 | /* coefficient is subtracted from all-nines; the 1 is added during */ |
| 1231 | /* the later add cycle -- zeros to the right do not matter because */ |
| 1232 | /* the complement of zero is zero); these are fixed-length inverts */ |
| 1233 | /* where the lsd is known to be at a 4-byte boundary (so no borrow */ |
| 1234 | /* possible) */ |
| 1235 | carry=0; /* assume no carry */ |
| 1236 | if (diffsign) { |
| 1237 | carry=CARRYPAT; /* for +1 during add */ |
| 1238 | UINTAT(acc+ 4)=0x09090909-UINTAT(acc+ 4); |
| 1239 | UINTAT(acc+ 8)=0x09090909-UINTAT(acc+ 8); |
| 1240 | UINTAT(acc+12)=0x09090909-UINTAT(acc+12); |
| 1241 | UINTAT(acc+16)=0x09090909-UINTAT(acc+16); |
| 1242 | #if QUAD |
| 1243 | UINTAT(acc+20)=0x09090909-UINTAT(acc+20); |
| 1244 | UINTAT(acc+24)=0x09090909-UINTAT(acc+24); |
| 1245 | UINTAT(acc+28)=0x09090909-UINTAT(acc+28); |
| 1246 | UINTAT(acc+32)=0x09090909-UINTAT(acc+32); |
| 1247 | UINTAT(acc+36)=0x09090909-UINTAT(acc+36); |
| 1248 | #endif |
| 1249 | } /* diffsign */ |
| 1250 | |
| 1251 | /* now process the rhs coefficient; if it cannot overlap lhs then */ |
| 1252 | /* it can be put straight into acc (with an appropriate gap, if */ |
| 1253 | /* needed) because no actual addition will be needed (except */ |
| 1254 | /* possibly to complete ten's complement) */ |
| 1255 | overlap=DECPMAX-(expl-expr); |
| 1256 | #if DECTRACE |
| 1257 | printf("exps: %ld %ld\n", (LI)expl, (LI)expr); |
| 1258 | printf("Overlap=%ld carry=%08lx\n", (LI)overlap, (LI)carry); |
| 1259 | #endif |
| 1260 | |
| 1261 | if (overlap<=0) { /* no overlap possible */ |
| 1262 | uInt gap; /* local work */ |
| 1263 | /* since a full addition is not needed, a ten's complement */ |
| 1264 | /* calculation started above may need to be completed */ |
| 1265 | if (carry) { |
| 1266 | for (ub=ulsd; *ub==9; ub--) *ub=0; |
| 1267 | *ub+=1; |
| 1268 | carry=0; /* taken care of */ |
| 1269 | } |
| 1270 | /* up to DECPMAX-1 digits of the final result can extend down */ |
| 1271 | /* below the LSD of the lhs, so if the gap is >DECPMAX then the */ |
| 1272 | /* rhs will be simply sticky bits. In this case the gap is */ |
| 1273 | /* clamped to DECPMAX and the exponent adjusted to suit [this is */ |
| 1274 | /* safe because the lhs is non-zero]. */ |
| 1275 | gap=-overlap; |
| 1276 | if (gap>DECPMAX) { |
| 1277 | expr+=gap-1; |
| 1278 | gap=DECPMAX; |
| 1279 | } |
| 1280 | ub=ulsd+gap+1; /* where MSD will go */ |
| 1281 | /* Fill the gap with 0s; note that there is no addition to do */ |
| 1282 | ui=&UINTAT(acc+COFF+DECPMAX); /* start of gap */ |
| 1283 | for (; ui<&UINTAT(ub); ui++) *ui=0; /* mind the gap */ |
| 1284 | if (overlap<-DECPMAX) { /* gap was > DECPMAX */ |
| 1285 | *ub=(uByte)(!DFISZERO(dfr)); /* make sticky digit */ |
| 1286 | } |
| 1287 | else { /* need full coefficient */ |
| 1288 | GETCOEFF(dfr, ub); /* decode from decFloat */ |
| 1289 | ub+=DECPMAX-1; /* new LSD... */ |
| 1290 | } |
| 1291 | ulsd=ub; /* save new LSD */ |
| 1292 | } /* no overlap possible */ |
| 1293 | |
| 1294 | else { /* overlap>0 */ |
| 1295 | /* coefficients overlap (perhaps completely, although also */ |
| 1296 | /* perhaps only where zeros) */ |
| 1297 | ub=buf+COFF+DECPMAX-overlap; /* where MSD will go */ |
| 1298 | /* Fill the prefix gap with 0s; 8 will cover most common */ |
| 1299 | /* unalignments, so start with direct assignments (a loop is */ |
| 1300 | /* then used for any remaining -- the loop (and the one in a */ |
| 1301 | /* moment) is not then on the critical path because the number */ |
| 1302 | /* of additions is reduced by (at least) two in this case) */ |
| 1303 | UINTAT(buf+4)=0; /* [clears decQuad 00 too] */ |
| 1304 | UINTAT(buf+8)=0; |
| 1305 | if (ub>buf+12) { |
| 1306 | ui=&UINTAT(buf+12); /* start of any remaining */ |
| 1307 | for (; ui<&UINTAT(ub); ui++) *ui=0; /* fill them */ |
| 1308 | } |
| 1309 | GETCOEFF(dfr, ub); /* decode from decFloat */ |
| 1310 | |
| 1311 | /* now move tail of rhs across to main acc; again use direct */ |
| 1312 | /* assignment for 8 digits-worth */ |
| 1313 | UINTAT(acc+COFF+DECPMAX)=UINTAT(buf+COFF+DECPMAX); |
| 1314 | UINTAT(acc+COFF+DECPMAX+4)=UINTAT(buf+COFF+DECPMAX+4); |
| 1315 | if (buf+COFF+DECPMAX+8<ub+DECPMAX) { |
| 1316 | uj=&UINTAT(buf+COFF+DECPMAX+8); /* source */ |
| 1317 | ui=&UINTAT(acc+COFF+DECPMAX+8); /* target */ |
| 1318 | for (; uj<&UINTAT(ub+DECPMAX); ui++, uj++) *ui=*uj; |
| 1319 | } |
| 1320 | |
| 1321 | ulsd=acc+(ub-buf+DECPMAX-1); /* update LSD pointer */ |
| 1322 | |
| 1323 | /* now do the add of the non-tail; this is all nicely aligned, */ |
| 1324 | /* and is over a multiple of four digits (because for Quad two */ |
| 1325 | /* two 0 digits were added on the left); words in both acc and */ |
| 1326 | /* buf (buf especially) will often be zero */ |
| 1327 | /* [byte-by-byte add, here, is about 15% slower than the by-fours] */ |
| 1328 | |
| 1329 | /* Now effect the add; this is harder on a little-endian */ |
| 1330 | /* machine as the inter-digit carry cannot use the usual BCD */ |
| 1331 | /* addition trick because the bytes are loaded in the wrong order */ |
| 1332 | /* [this loop could be unrolled, but probably scarcely worth it] */ |
| 1333 | |
| 1334 | ui=&UINTAT(acc+COFF+DECPMAX-4); /* target LSW (acc) */ |
| 1335 | uj=&UINTAT(buf+COFF+DECPMAX-4); /* source LSW (buf, to add to acc) */ |
| 1336 | |
| 1337 | #if !DECLITEND |
| 1338 | for (; ui>=&UINTAT(acc+4); ui--, uj--) { |
| 1339 | /* bcd8 add */ |
| 1340 | carry+=*uj; /* rhs + carry */ |
| 1341 | if (carry==0) continue; /* no-op */ |
| 1342 | carry+=*ui; /* lhs */ |
| 1343 | /* Big-endian BCD adjust (uses internal carry) */ |
| 1344 | carry+=0x76f6f6f6; /* note top nibble not all bits */ |
| 1345 | *ui=(carry & 0x0f0f0f0f) - ((carry & 0x60606060)>>4); /* BCD adjust */ |
| 1346 | carry>>=31; /* true carry was at far left */ |
| 1347 | } /* add loop */ |
| 1348 | #else |
| 1349 | for (; ui>=&UINTAT(acc+4); ui--, uj--) { |
| 1350 | /* bcd8 add */ |
| 1351 | carry+=*uj; /* rhs + carry */ |
| 1352 | if (carry==0) continue; /* no-op [common if unaligned] */ |
| 1353 | carry+=*ui; /* lhs */ |
| 1354 | /* Little-endian BCD adjust; inter-digit carry must be manual */ |
| 1355 | /* because the lsb from the array will be in the most-significant */ |
| 1356 | /* byte of carry */ |
| 1357 | carry+=0x76767676; /* note no inter-byte carries */ |
| 1358 | carry+=(carry & 0x80000000)>>15; |
| 1359 | carry+=(carry & 0x00800000)>>15; |
| 1360 | carry+=(carry & 0x00008000)>>15; |
| 1361 | carry-=(carry & 0x60606060)>>4; /* BCD adjust back */ |
| 1362 | *ui=carry & 0x0f0f0f0f; /* clear debris and save */ |
| 1363 | /* here, final carry-out bit is at 0x00000080; move it ready */ |
| 1364 | /* for next word-add (i.e., to 0x01000000) */ |
| 1365 | carry=(carry & 0x00000080)<<17; |
| 1366 | } /* add loop */ |
| 1367 | #endif |
| 1368 | #if DECTRACE |
| 1369 | {bcdnum tum; |
| 1370 | printf("Add done, carry=%08lx, diffsign=%ld\n", (LI)carry, (LI)diffsign); |
| 1371 | tum.msd=umsd; /* acc+4; */ |
| 1372 | tum.lsd=ulsd; |
| 1373 | tum.exponent=0; |
| 1374 | tum.sign=0; |
| 1375 | decShowNum(&tum, "dfadd");} |
| 1376 | #endif |
| 1377 | } /* overlap possible */ |
| 1378 | |
| 1379 | /* ordering here is a little strange in order to have slowest path */ |
| 1380 | /* first in GCC asm listing */ |
| 1381 | if (diffsign) { /* subtraction */ |
| 1382 | if (!carry) { /* no carry out means RHS<LHS */ |
| 1383 | /* borrowed -- take ten's complement */ |
| 1384 | /* sign is lhs sign */ |
| 1385 | num.sign=DFWORD(dfl, 0) & DECFLOAT_Sign; |
| 1386 | |
| 1387 | /* invert the coefficient first by fours, then add one; space */ |
| 1388 | /* at the end of the buffer ensures the by-fours is always */ |
| 1389 | /* safe, but lsd+1 must be cleared to prevent a borrow */ |
| 1390 | /* if big-endian */ |
| 1391 | #if !DECLITEND |
| 1392 | *(ulsd+1)=0; |
| 1393 | #endif |
| 1394 | /* there are always at least four coefficient words */ |
| 1395 | UINTAT(umsd) =0x09090909-UINTAT(umsd); |
| 1396 | UINTAT(umsd+4) =0x09090909-UINTAT(umsd+4); |
| 1397 | UINTAT(umsd+8) =0x09090909-UINTAT(umsd+8); |
| 1398 | UINTAT(umsd+12)=0x09090909-UINTAT(umsd+12); |
| 1399 | #if DOUBLE |
| 1400 | #define BNEXT 16 |
| 1401 | #elif QUAD |
| 1402 | UINTAT(umsd+16)=0x09090909-UINTAT(umsd+16); |
| 1403 | UINTAT(umsd+20)=0x09090909-UINTAT(umsd+20); |
| 1404 | UINTAT(umsd+24)=0x09090909-UINTAT(umsd+24); |
| 1405 | UINTAT(umsd+28)=0x09090909-UINTAT(umsd+28); |
| 1406 | UINTAT(umsd+32)=0x09090909-UINTAT(umsd+32); |
| 1407 | #define BNEXT 36 |
| 1408 | #endif |
| 1409 | if (ulsd>=umsd+BNEXT) { /* unaligned */ |
| 1410 | /* eight will handle most unaligments for Double; 16 for Quad */ |
| 1411 | UINTAT(umsd+BNEXT)=0x09090909-UINTAT(umsd+BNEXT); |
| 1412 | UINTAT(umsd+BNEXT+4)=0x09090909-UINTAT(umsd+BNEXT+4); |
| 1413 | #if DOUBLE |
| 1414 | #define BNEXTY (BNEXT+8) |
| 1415 | #elif QUAD |
| 1416 | UINTAT(umsd+BNEXT+8)=0x09090909-UINTAT(umsd+BNEXT+8); |
| 1417 | UINTAT(umsd+BNEXT+12)=0x09090909-UINTAT(umsd+BNEXT+12); |
| 1418 | #define BNEXTY (BNEXT+16) |
| 1419 | #endif |
| 1420 | if (ulsd>=umsd+BNEXTY) { /* very unaligned */ |
| 1421 | ui=&UINTAT(umsd+BNEXTY); /* -> continue */ |
| 1422 | for (;;ui++) { |
| 1423 | *ui=0x09090909-*ui; /* invert four digits */ |
| 1424 | if (ui>=&UINTAT(ulsd-3)) break; /* all done */ |
| 1425 | } |
| 1426 | } |
| 1427 | } |
| 1428 | /* complete the ten's complement by adding 1 */ |
| 1429 | for (ub=ulsd; *ub==9; ub--) *ub=0; |
| 1430 | *ub+=1; |
| 1431 | } /* borrowed */ |
| 1432 | |
| 1433 | else { /* carry out means RHS>=LHS */ |
| 1434 | num.sign=DFWORD(dfr, 0) & DECFLOAT_Sign; |
| 1435 | /* all done except for the special IEEE 754 exact-zero-result */ |
| 1436 | /* rule (see above); while testing for zero, strip leading */ |
| 1437 | /* zeros (which will save decFinalize doing it) (this is in */ |
| 1438 | /* diffsign path, so carry impossible and true umsd is */ |
| 1439 | /* acc+COFF) */ |
| 1440 | |
| 1441 | /* Check the initial coefficient area using the fast macro; */ |
| 1442 | /* this will often be all that needs to be done (as on the */ |
| 1443 | /* worst-case path when the subtraction was aligned and */ |
| 1444 | /* full-length) */ |
| 1445 | if (ISCOEFFZERO(acc+COFF)) { |
| 1446 | umsd=acc+COFF+DECPMAX-1; /* so far, so zero */ |
| 1447 | if (ulsd>umsd) { /* more to check */ |
| 1448 | umsd++; /* to align after checked area */ |
| 1449 | for (; UINTAT(umsd)==0 && umsd+3<ulsd;) umsd+=4; |
| 1450 | for (; *umsd==0 && umsd<ulsd;) umsd++; |
| 1451 | } |
| 1452 | if (*umsd==0) { /* must be true zero (and diffsign) */ |
| 1453 | num.sign=0; /* assume + */ |
| 1454 | if (set->round==DEC_ROUND_FLOOR) num.sign=DECFLOAT_Sign; |
| 1455 | } |
| 1456 | } |
| 1457 | /* [else was not zero, might still have leading zeros] */ |
| 1458 | } /* subtraction gave positive result */ |
| 1459 | } /* diffsign */ |
| 1460 | |
| 1461 | else { /* same-sign addition */ |
| 1462 | num.sign=DFWORD(dfl, 0)&DECFLOAT_Sign; |
| 1463 | #if DOUBLE |
| 1464 | if (carry) { /* only possible with decDouble */ |
| 1465 | *(acc+3)=1; /* [Quad has leading 00] */ |
| 1466 | umsd=acc+3; |
| 1467 | } |
| 1468 | #endif |
| 1469 | } /* same sign */ |
| 1470 | |
| 1471 | num.msd=umsd; /* set MSD .. */ |
| 1472 | num.lsd=ulsd; /* .. and LSD */ |
| 1473 | num.exponent=expr; /* set exponent to smaller */ |
| 1474 | |
| 1475 | #if DECTRACE |
| 1476 | decFloatShow(dfl, "dfl"); |
| 1477 | decFloatShow(dfr, "dfr"); |
| 1478 | decShowNum(&num, "postadd"); |
| 1479 | #endif |
| 1480 | return decFinalize(result, &num, set); /* round, check, and lay out */ |
| 1481 | } /* decFloatAdd */ |
| 1482 | |
| 1483 | /* ------------------------------------------------------------------ */ |
| 1484 | /* decFloatAnd -- logical digitwise AND of two decFloats */ |
| 1485 | /* */ |
| 1486 | /* result gets the result of ANDing dfl and dfr */ |
| 1487 | /* dfl is the first decFloat (lhs) */ |
| 1488 | /* dfr is the second decFloat (rhs) */ |
| 1489 | /* set is the context */ |
| 1490 | /* returns result, which will be canonical with sign=0 */ |
| 1491 | /* */ |
| 1492 | /* The operands must be positive, finite with exponent q=0, and */ |
| 1493 | /* comprise just zeros and ones; if not, Invalid operation results. */ |
| 1494 | /* ------------------------------------------------------------------ */ |
| 1495 | decFloat * decFloatAnd(decFloat *result, |
| 1496 | const decFloat *dfl, const decFloat *dfr, |
| 1497 | decContext *set) { |
| 1498 | if (!DFISUINT01(dfl) || !DFISUINT01(dfr) |
| 1499 | || !DFISCC01(dfl) || !DFISCC01(dfr)) return decInvalid(result, set); |
| 1500 | /* the operands are positive finite integers (q=0) with just 0s and 1s */ |
| 1501 | #if DOUBLE |
| 1502 | DFWORD(result, 0)=ZEROWORD |
| 1503 | |((DFWORD(dfl, 0) & DFWORD(dfr, 0))&0x04009124); |
| 1504 | DFWORD(result, 1)=(DFWORD(dfl, 1) & DFWORD(dfr, 1))&0x49124491; |
| 1505 | #elif QUAD |
| 1506 | DFWORD(result, 0)=ZEROWORD |
| 1507 | |((DFWORD(dfl, 0) & DFWORD(dfr, 0))&0x04000912); |
| 1508 | DFWORD(result, 1)=(DFWORD(dfl, 1) & DFWORD(dfr, 1))&0x44912449; |
| 1509 | DFWORD(result, 2)=(DFWORD(dfl, 2) & DFWORD(dfr, 2))&0x12449124; |
| 1510 | DFWORD(result, 3)=(DFWORD(dfl, 3) & DFWORD(dfr, 3))&0x49124491; |
| 1511 | #endif |
| 1512 | return result; |
| 1513 | } /* decFloatAnd */ |
| 1514 | |
| 1515 | /* ------------------------------------------------------------------ */ |
| 1516 | /* decFloatCanonical -- copy a decFloat, making canonical */ |
| 1517 | /* */ |
| 1518 | /* result gets the canonicalized df */ |
| 1519 | /* df is the decFloat to copy and make canonical */ |
| 1520 | /* returns result */ |
| 1521 | /* */ |
| 1522 | /* This works on specials, too; no error or exception is possible. */ |
| 1523 | /* ------------------------------------------------------------------ */ |
| 1524 | decFloat * decFloatCanonical(decFloat *result, const decFloat *df) { |
| 1525 | return decCanonical(result, df); |
| 1526 | } /* decFloatCanonical */ |
| 1527 | |
| 1528 | /* ------------------------------------------------------------------ */ |
| 1529 | /* decFloatClass -- return the class of a decFloat */ |
| 1530 | /* */ |
| 1531 | /* df is the decFloat to test */ |
| 1532 | /* returns the decClass that df falls into */ |
| 1533 | /* ------------------------------------------------------------------ */ |
| 1534 | enum decClass decFloatClass(const decFloat *df) { |
| 1535 | Int exp; /* exponent */ |
| 1536 | if (DFISSPECIAL(df)) { |
| 1537 | if (DFISQNAN(df)) return DEC_CLASS_QNAN; |
| 1538 | if (DFISSNAN(df)) return DEC_CLASS_SNAN; |
| 1539 | /* must be an infinity */ |
| 1540 | if (DFISSIGNED(df)) return DEC_CLASS_NEG_INF; |
| 1541 | return DEC_CLASS_POS_INF; |
| 1542 | } |
| 1543 | if (DFISZERO(df)) { /* quite common */ |
| 1544 | if (DFISSIGNED(df)) return DEC_CLASS_NEG_ZERO; |
| 1545 | return DEC_CLASS_POS_ZERO; |
| 1546 | } |
| 1547 | /* is finite and non-zero; similar code to decFloatIsNormal, here */ |
| 1548 | /* [this could be speeded up slightly by in-lining decFloatDigits] */ |
| 1549 | exp=GETEXPUN(df) /* get unbiased exponent .. */ |
| 1550 | +decFloatDigits(df)-1; /* .. and make adjusted exponent */ |
| 1551 | if (exp>=DECEMIN) { /* is normal */ |
| 1552 | if (DFISSIGNED(df)) return DEC_CLASS_NEG_NORMAL; |
| 1553 | return DEC_CLASS_POS_NORMAL; |
| 1554 | } |
| 1555 | /* is subnormal */ |
| 1556 | if (DFISSIGNED(df)) return DEC_CLASS_NEG_SUBNORMAL; |
| 1557 | return DEC_CLASS_POS_SUBNORMAL; |
| 1558 | } /* decFloatClass */ |
| 1559 | |
| 1560 | /* ------------------------------------------------------------------ */ |
| 1561 | /* decFloatClassString -- return the class of a decFloat as a string */ |
| 1562 | /* */ |
| 1563 | /* df is the decFloat to test */ |
| 1564 | /* returns a constant string describing the class df falls into */ |
| 1565 | /* ------------------------------------------------------------------ */ |
| 1566 | const char *decFloatClassString(const decFloat *df) { |
| 1567 | enum decClass eclass=decFloatClass(df); |
| 1568 | if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN; |
| 1569 | if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN; |
| 1570 | if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ; |
| 1571 | if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ; |
| 1572 | if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS; |
| 1573 | if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS; |
| 1574 | if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI; |
| 1575 | if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI; |
| 1576 | if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN; |
| 1577 | if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN; |
| 1578 | return DEC_ClassString_UN; /* Unknown */ |
| 1579 | } /* decFloatClassString */ |
| 1580 | |
| 1581 | /* ------------------------------------------------------------------ */ |
| 1582 | /* decFloatCompare -- compare two decFloats; quiet NaNs allowed */ |
| 1583 | /* */ |
| 1584 | /* result gets the result of comparing dfl and dfr */ |
| 1585 | /* dfl is the first decFloat (lhs) */ |
| 1586 | /* dfr is the second decFloat (rhs) */ |
| 1587 | /* set is the context */ |
| 1588 | /* returns result, which may be -1, 0, 1, or NaN (Unordered) */ |
| 1589 | /* ------------------------------------------------------------------ */ |
| 1590 | decFloat * decFloatCompare(decFloat *result, |
| 1591 | const decFloat *dfl, const decFloat *dfr, |
| 1592 | decContext *set) { |
| 1593 | Int comp; /* work */ |
| 1594 | /* NaNs are handled as usual */ |
| 1595 | if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set); |
| 1596 | /* numeric comparison needed */ |
| 1597 | comp=decNumCompare(dfl, dfr, 0); |
| 1598 | decFloatZero(result); |
| 1599 | if (comp==0) return result; |
| 1600 | DFBYTE(result, DECBYTES-1)=0x01; /* LSD=1 */ |
| 1601 | if (comp<0) DFBYTE(result, 0)|=0x80; /* set sign bit */ |
| 1602 | return result; |
| 1603 | } /* decFloatCompare */ |
| 1604 | |
| 1605 | /* ------------------------------------------------------------------ */ |
| 1606 | /* decFloatCompareSignal -- compare two decFloats; all NaNs signal */ |
| 1607 | /* */ |
| 1608 | /* result gets the result of comparing dfl and dfr */ |
| 1609 | /* dfl is the first decFloat (lhs) */ |
| 1610 | /* dfr is the second decFloat (rhs) */ |
| 1611 | /* set is the context */ |
| 1612 | /* returns result, which may be -1, 0, 1, or NaN (Unordered) */ |
| 1613 | /* ------------------------------------------------------------------ */ |
| 1614 | decFloat * decFloatCompareSignal(decFloat *result, |
| 1615 | const decFloat *dfl, const decFloat *dfr, |
| 1616 | decContext *set) { |
| 1617 | Int comp; /* work */ |
| 1618 | /* NaNs are handled as usual, except that all NaNs signal */ |
| 1619 | if (DFISNAN(dfl) || DFISNAN(dfr)) { |
| 1620 | set->status|=DEC_Invalid_operation; |
| 1621 | return decNaNs(result, dfl, dfr, set); |
| 1622 | } |
| 1623 | /* numeric comparison needed */ |
| 1624 | comp=decNumCompare(dfl, dfr, 0); |
| 1625 | decFloatZero(result); |
| 1626 | if (comp==0) return result; |
| 1627 | DFBYTE(result, DECBYTES-1)=0x01; /* LSD=1 */ |
| 1628 | if (comp<0) DFBYTE(result, 0)|=0x80; /* set sign bit */ |
| 1629 | return result; |
| 1630 | } /* decFloatCompareSignal */ |
| 1631 | |
| 1632 | /* ------------------------------------------------------------------ */ |
| 1633 | /* decFloatCompareTotal -- compare two decFloats with total ordering */ |
| 1634 | /* */ |
| 1635 | /* result gets the result of comparing dfl and dfr */ |
| 1636 | /* dfl is the first decFloat (lhs) */ |
| 1637 | /* dfr is the second decFloat (rhs) */ |
| 1638 | /* returns result, which may be -1, 0, or 1 */ |
| 1639 | /* ------------------------------------------------------------------ */ |
| 1640 | decFloat * decFloatCompareTotal(decFloat *result, |
| 1641 | const decFloat *dfl, const decFloat *dfr) { |
| 1642 | Int comp; /* work */ |
| 1643 | if (DFISNAN(dfl) || DFISNAN(dfr)) { |
| 1644 | Int nanl, nanr; /* work */ |
| 1645 | /* morph NaNs to +/- 1 or 2, leave numbers as 0 */ |
| 1646 | nanl=DFISSNAN(dfl)+DFISQNAN(dfl)*2; /* quiet > signalling */ |
| 1647 | if (DFISSIGNED(dfl)) nanl=-nanl; |
| 1648 | nanr=DFISSNAN(dfr)+DFISQNAN(dfr)*2; |
| 1649 | if (DFISSIGNED(dfr)) nanr=-nanr; |
| 1650 | if (nanl>nanr) comp=+1; |
| 1651 | else if (nanl<nanr) comp=-1; |
| 1652 | else { /* NaNs are the same type and sign .. must compare payload */ |
| 1653 | /* buffers need +2 for QUAD */ |
| 1654 | uByte bufl[DECPMAX+4]; /* for LHS coefficient + foot */ |
| 1655 | uByte bufr[DECPMAX+4]; /* for RHS coefficient + foot */ |
| 1656 | uByte *ub, *uc; /* work */ |
| 1657 | Int sigl; /* signum of LHS */ |
| 1658 | sigl=(DFISSIGNED(dfl) ? -1 : +1); |
| 1659 | |
| 1660 | /* decode the coefficients */ |
| 1661 | /* (shift both right two if Quad to make a multiple of four) */ |
| 1662 | #if QUAD |
| 1663 | USHORTAT(bufl)=0; |
| 1664 | USHORTAT(bufr)=0; |
| 1665 | #endif |
| 1666 | GETCOEFF(dfl, bufl+QUAD*2); /* decode from decFloat */ |
| 1667 | GETCOEFF(dfr, bufr+QUAD*2); /* .. */ |
| 1668 | /* all multiples of four, here */ |
| 1669 | comp=0; /* assume equal */ |
| 1670 | for (ub=bufl, uc=bufr; ub<bufl+DECPMAX+QUAD*2; ub+=4, uc+=4) { |
| 1671 | if (UINTAT(ub)==UINTAT(uc)) continue; /* so far so same */ |
| 1672 | /* about to find a winner; go by bytes in case little-endian */ |
| 1673 | for (;; ub++, uc++) { |
| 1674 | if (*ub==*uc) continue; |
| 1675 | if (*ub>*uc) comp=sigl; /* difference found */ |
| 1676 | else comp=-sigl; /* .. */ |
| 1677 | break; |
| 1678 | } |
| 1679 | } |
| 1680 | } /* same NaN type and sign */ |
| 1681 | } |
| 1682 | else { |
| 1683 | /* numeric comparison needed */ |
| 1684 | comp=decNumCompare(dfl, dfr, 1); /* total ordering */ |
| 1685 | } |
| 1686 | decFloatZero(result); |
| 1687 | if (comp==0) return result; |
| 1688 | DFBYTE(result, DECBYTES-1)=0x01; /* LSD=1 */ |
| 1689 | if (comp<0) DFBYTE(result, 0)|=0x80; /* set sign bit */ |
| 1690 | return result; |
| 1691 | } /* decFloatCompareTotal */ |
| 1692 | |
| 1693 | /* ------------------------------------------------------------------ */ |
| 1694 | /* decFloatCompareTotalMag -- compare magnitudes with total ordering */ |
| 1695 | /* */ |
| 1696 | /* result gets the result of comparing abs(dfl) and abs(dfr) */ |
| 1697 | /* dfl is the first decFloat (lhs) */ |
| 1698 | /* dfr is the second decFloat (rhs) */ |
| 1699 | /* returns result, which may be -1, 0, or 1 */ |
| 1700 | /* ------------------------------------------------------------------ */ |
| 1701 | decFloat * decFloatCompareTotalMag(decFloat *result, |
| 1702 | const decFloat *dfl, const decFloat *dfr) { |
| 1703 | decFloat a, b; /* for copy if needed */ |
| 1704 | /* copy and redirect signed operand(s) */ |
| 1705 | if (DFISSIGNED(dfl)) { |
| 1706 | decFloatCopyAbs(&a, dfl); |
| 1707 | dfl=&a; |
| 1708 | } |
| 1709 | if (DFISSIGNED(dfr)) { |
| 1710 | decFloatCopyAbs(&b, dfr); |
| 1711 | dfr=&b; |
| 1712 | } |
| 1713 | return decFloatCompareTotal(result, dfl, dfr); |
| 1714 | } /* decFloatCompareTotalMag */ |
| 1715 | |
| 1716 | /* ------------------------------------------------------------------ */ |
| 1717 | /* decFloatCopy -- copy a decFloat as-is */ |
| 1718 | /* */ |
| 1719 | /* result gets the copy of dfl */ |
| 1720 | /* dfl is the decFloat to copy */ |
| 1721 | /* returns result */ |
| 1722 | /* */ |
| 1723 | /* This is a bitwise operation; no errors or exceptions are possible. */ |
| 1724 | /* ------------------------------------------------------------------ */ |
| 1725 | decFloat * decFloatCopy(decFloat *result, const decFloat *dfl) { |
| 1726 | if (dfl!=result) *result=*dfl; /* copy needed */ |
| 1727 | return result; |
| 1728 | } /* decFloatCopy */ |
| 1729 | |
| 1730 | /* ------------------------------------------------------------------ */ |
| 1731 | /* decFloatCopyAbs -- copy a decFloat as-is and set sign bit to 0 */ |
| 1732 | /* */ |
| 1733 | /* result gets the copy of dfl with sign bit 0 */ |
| 1734 | /* dfl is the decFloat to copy */ |
| 1735 | /* returns result */ |
| 1736 | /* */ |
| 1737 | /* This is a bitwise operation; no errors or exceptions are possible. */ |
| 1738 | /* ------------------------------------------------------------------ */ |
| 1739 | decFloat * decFloatCopyAbs(decFloat *result, const decFloat *dfl) { |
| 1740 | if (dfl!=result) *result=*dfl; /* copy needed */ |
| 1741 | DFBYTE(result, 0)&=~0x80; /* zero sign bit */ |
| 1742 | return result; |
| 1743 | } /* decFloatCopyAbs */ |
| 1744 | |
| 1745 | /* ------------------------------------------------------------------ */ |
| 1746 | /* decFloatCopyNegate -- copy a decFloat as-is with inverted sign bit */ |
| 1747 | /* */ |
| 1748 | /* result gets the copy of dfl with sign bit inverted */ |
| 1749 | /* dfl is the decFloat to copy */ |
| 1750 | /* returns result */ |
| 1751 | /* */ |
| 1752 | /* This is a bitwise operation; no errors or exceptions are possible. */ |
| 1753 | /* ------------------------------------------------------------------ */ |
| 1754 | decFloat * decFloatCopyNegate(decFloat *result, const decFloat *dfl) { |
| 1755 | if (dfl!=result) *result=*dfl; /* copy needed */ |
| 1756 | DFBYTE(result, 0)^=0x80; /* invert sign bit */ |
| 1757 | return result; |
| 1758 | } /* decFloatCopyNegate */ |
| 1759 | |
| 1760 | /* ------------------------------------------------------------------ */ |
| 1761 | /* decFloatCopySign -- copy a decFloat with the sign of another */ |
| 1762 | /* */ |
| 1763 | /* result gets the result of copying dfl with the sign of dfr */ |
| 1764 | /* dfl is the first decFloat (lhs) */ |
| 1765 | /* dfr is the second decFloat (rhs) */ |
| 1766 | /* returns result */ |
| 1767 | /* */ |
| 1768 | /* This is a bitwise operation; no errors or exceptions are possible. */ |
| 1769 | /* ------------------------------------------------------------------ */ |
| 1770 | decFloat * decFloatCopySign(decFloat *result, |
| 1771 | const decFloat *dfl, const decFloat *dfr) { |
| 1772 | uByte sign=(uByte)(DFBYTE(dfr, 0)&0x80); /* save sign bit */ |
| 1773 | if (dfl!=result) *result=*dfl; /* copy needed */ |
| 1774 | DFBYTE(result, 0)&=~0x80; /* clear sign .. */ |
| 1775 | DFBYTE(result, 0)=(uByte)(DFBYTE(result, 0)|sign); /* .. and set saved */ |
| 1776 | return result; |
| 1777 | } /* decFloatCopySign */ |
| 1778 | |
| 1779 | /* ------------------------------------------------------------------ */ |
| 1780 | /* decFloatDigits -- return the number of digits in a decFloat */ |
| 1781 | /* */ |
| 1782 | /* df is the decFloat to investigate */ |
| 1783 | /* returns the number of significant digits in the decFloat; a */ |
| 1784 | /* zero coefficient returns 1 as does an infinity (a NaN returns */ |
| 1785 | /* the number of digits in the payload) */ |
| 1786 | /* ------------------------------------------------------------------ */ |
| 1787 | /* private macro to extract a declet according to provided formula */ |
| 1788 | /* (form), and if it is non-zero then return the calculated digits */ |
| 1789 | /* depending on the declet number (n), where n=0 for the most */ |
| 1790 | /* significant declet; uses uInt dpd for work */ |
| 1791 | #define dpdlenchk(n, form) {dpd=(form)&0x3ff; \ |
| 1792 | if (dpd) return (DECPMAX-1-3*(n))-(3-DPD2BCD8[dpd*4+3]);} |
| 1793 | /* next one is used when it is known that the declet must be */ |
| 1794 | /* non-zero, or is the final zero declet */ |
| 1795 | #define dpdlendun(n, form) {dpd=(form)&0x3ff; \ |
| 1796 | if (dpd==0) return 1; \ |
| 1797 | return (DECPMAX-1-3*(n))-(3-DPD2BCD8[dpd*4+3]);} |
| 1798 | |
| 1799 | uInt decFloatDigits(const decFloat *df) { |
| 1800 | uInt dpd; /* work */ |
| 1801 | uInt sourhi=DFWORD(df, 0); /* top word from source decFloat */ |
| 1802 | #if QUAD |
| 1803 | uInt sourmh, sourml; |
| 1804 | #endif |
| 1805 | uInt sourlo; |
| 1806 | |
| 1807 | if (DFISINF(df)) return 1; |
| 1808 | /* A NaN effectively has an MSD of 0; otherwise if non-zero MSD */ |
| 1809 | /* then the coefficient is full-length */ |
| 1810 | if (!DFISNAN(df) && DECCOMBMSD[sourhi>>26]) return DECPMAX; |
| 1811 | |
| 1812 | #if DOUBLE |
| 1813 | if (sourhi&0x0003ffff) { /* ends in first */ |
| 1814 | dpdlenchk(0, sourhi>>8); |
| 1815 | sourlo=DFWORD(df, 1); |
| 1816 | dpdlendun(1, (sourhi<<2) | (sourlo>>30)); |
| 1817 | } /* [cannot drop through] */ |
| 1818 | sourlo=DFWORD(df, 1); /* sourhi not involved now */ |
| 1819 | if (sourlo&0xfff00000) { /* in one of first two */ |
| 1820 | dpdlenchk(1, sourlo>>30); /* very rare */ |
| 1821 | dpdlendun(2, sourlo>>20); |
| 1822 | } /* [cannot drop through] */ |
| 1823 | dpdlenchk(3, sourlo>>10); |
| 1824 | dpdlendun(4, sourlo); |
| 1825 | /* [cannot drop through] */ |
| 1826 | |
| 1827 | #elif QUAD |
| 1828 | if (sourhi&0x00003fff) { /* ends in first */ |
| 1829 | dpdlenchk(0, sourhi>>4); |
| 1830 | sourmh=DFWORD(df, 1); |
| 1831 | dpdlendun(1, ((sourhi)<<6) | (sourmh>>26)); |
| 1832 | } /* [cannot drop through] */ |
| 1833 | sourmh=DFWORD(df, 1); |
| 1834 | if (sourmh) { |
| 1835 | dpdlenchk(1, sourmh>>26); |
| 1836 | dpdlenchk(2, sourmh>>16); |
| 1837 | dpdlenchk(3, sourmh>>6); |
| 1838 | sourml=DFWORD(df, 2); |
| 1839 | dpdlendun(4, ((sourmh)<<4) | (sourml>>28)); |
| 1840 | } /* [cannot drop through] */ |
| 1841 | sourml=DFWORD(df, 2); |
| 1842 | if (sourml) { |
| 1843 | dpdlenchk(4, sourml>>28); |
| 1844 | dpdlenchk(5, sourml>>18); |
| 1845 | dpdlenchk(6, sourml>>8); |
| 1846 | sourlo=DFWORD(df, 3); |
| 1847 | dpdlendun(7, ((sourml)<<2) | (sourlo>>30)); |
| 1848 | } /* [cannot drop through] */ |
| 1849 | sourlo=DFWORD(df, 3); |
| 1850 | if (sourlo&0xfff00000) { /* in one of first two */ |
| 1851 | dpdlenchk(7, sourlo>>30); /* very rare */ |
| 1852 | dpdlendun(8, sourlo>>20); |
| 1853 | } /* [cannot drop through] */ |
| 1854 | dpdlenchk(9, sourlo>>10); |
| 1855 | dpdlendun(10, sourlo); |
| 1856 | /* [cannot drop through] */ |
| 1857 | #endif |
| 1858 | } /* decFloatDigits */ |
| 1859 | |
| 1860 | /* ------------------------------------------------------------------ */ |
| 1861 | /* decFloatDivide -- divide a decFloat by another */ |
| 1862 | /* */ |
| 1863 | /* result gets the result of dividing dfl by dfr: */ |
| 1864 | /* dfl is the first decFloat (lhs) */ |
| 1865 | /* dfr is the second decFloat (rhs) */ |
| 1866 | /* set is the context */ |
| 1867 | /* returns result */ |
| 1868 | /* */ |
| 1869 | /* ------------------------------------------------------------------ */ |
| 1870 | /* This is just a wrapper. */ |
| 1871 | decFloat * decFloatDivide(decFloat *result, |
| 1872 | const decFloat *dfl, const decFloat *dfr, |
| 1873 | decContext *set) { |
| 1874 | return decDivide(result, dfl, dfr, set, DIVIDE); |
| 1875 | } /* decFloatDivide */ |
| 1876 | |
| 1877 | /* ------------------------------------------------------------------ */ |
| 1878 | /* decFloatDivideInteger -- integer divide a decFloat by another */ |
| 1879 | /* */ |
| 1880 | /* result gets the result of dividing dfl by dfr: */ |
| 1881 | /* dfl is the first decFloat (lhs) */ |
| 1882 | /* dfr is the second decFloat (rhs) */ |
| 1883 | /* set is the context */ |
| 1884 | /* returns result */ |
| 1885 | /* */ |
| 1886 | /* ------------------------------------------------------------------ */ |
| 1887 | decFloat * decFloatDivideInteger(decFloat *result, |
| 1888 | const decFloat *dfl, const decFloat *dfr, |
| 1889 | decContext *set) { |
| 1890 | return decDivide(result, dfl, dfr, set, DIVIDEINT); |
| 1891 | } /* decFloatDivideInteger */ |
| 1892 | |
| 1893 | /* ------------------------------------------------------------------ */ |
| 1894 | /* decFloatFMA -- multiply and add three decFloats, fused */ |
| 1895 | /* */ |
| 1896 | /* result gets the result of (dfl*dfr)+dff with a single rounding */ |
| 1897 | /* dfl is the first decFloat (lhs) */ |
| 1898 | /* dfr is the second decFloat (rhs) */ |
| 1899 | /* dff is the final decFloat (fhs) */ |
| 1900 | /* set is the context */ |
| 1901 | /* returns result */ |
| 1902 | /* */ |
| 1903 | /* ------------------------------------------------------------------ */ |
| 1904 | decFloat * decFloatFMA(decFloat *result, const decFloat *dfl, |
| 1905 | const decFloat *dfr, const decFloat *dff, |
| 1906 | decContext *set) { |
| 1907 | /* The accumulator has the bytes needed for FiniteMultiply, plus */ |
| 1908 | /* one byte to the left in case of carry, plus DECPMAX+2 to the */ |
| 1909 | /* right for the final addition (up to full fhs + round & sticky) */ |
| 1910 | #define FMALEN (1+ (DECPMAX9*18) +DECPMAX+2) |
| 1911 | uByte acc[FMALEN]; /* for multiplied coefficient in BCD */ |
| 1912 | /* .. and for final result */ |
| 1913 | bcdnum mul; /* for multiplication result */ |
| 1914 | bcdnum fin; /* for final operand, expanded */ |
| 1915 | uByte coe[DECPMAX]; /* dff coefficient in BCD */ |
| 1916 | bcdnum *hi, *lo; /* bcdnum with higher/lower exponent */ |
| 1917 | uInt diffsign; /* non-zero if signs differ */ |
| 1918 | uInt hipad; /* pad digit for hi if needed */ |
| 1919 | Int padding; /* excess exponent */ |
| 1920 | uInt carry; /* +1 for ten's complement and during add */ |
| 1921 | uByte *ub, *uh, *ul; /* work */ |
| 1922 | |
| 1923 | /* handle all the special values [any special operand leads to a */ |
| 1924 | /* special result] */ |
| 1925 | if (DFISSPECIAL(dfl) || DFISSPECIAL(dfr) || DFISSPECIAL(dff)) { |
| 1926 | decFloat proxy; /* multiplication result proxy */ |
| 1927 | /* NaNs are handled as usual, giving priority to sNaNs */ |
| 1928 | if (DFISSNAN(dfl) || DFISSNAN(dfr)) return decNaNs(result, dfl, dfr, set); |
| 1929 | if (DFISSNAN(dff)) return decNaNs(result, dff, NULL, set); |
| 1930 | if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set); |
| 1931 | if (DFISNAN(dff)) return decNaNs(result, dff, NULL, set); |
| 1932 | /* One or more of the three is infinite */ |
| 1933 | /* infinity times zero is bad */ |
| 1934 | decFloatZero(&proxy); |
| 1935 | if (DFISINF(dfl)) { |
| 1936 | if (DFISZERO(dfr)) return decInvalid(result, set); |
| 1937 | decInfinity(&proxy, &proxy); |
| 1938 | } |
| 1939 | else if (DFISINF(dfr)) { |
| 1940 | if (DFISZERO(dfl)) return decInvalid(result, set); |
| 1941 | decInfinity(&proxy, &proxy); |
| 1942 | } |
| 1943 | /* compute sign of multiplication and place in proxy */ |
| 1944 | DFWORD(&proxy, 0)|=(DFWORD(dfl, 0)^DFWORD(dfr, 0))&DECFLOAT_Sign; |
| 1945 | if (!DFISINF(dff)) return decFloatCopy(result, &proxy); |
| 1946 | /* dff is Infinite */ |
| 1947 | if (!DFISINF(&proxy)) return decInfinity(result, dff); |
| 1948 | /* both sides of addition are infinite; different sign is bad */ |
| 1949 | if ((DFWORD(dff, 0)&DECFLOAT_Sign)!=(DFWORD(&proxy, 0)&DECFLOAT_Sign)) |
| 1950 | return decInvalid(result, set); |
| 1951 | return decFloatCopy(result, &proxy); |
| 1952 | } |
| 1953 | |
| 1954 | /* Here when all operands are finite */ |
| 1955 | |
| 1956 | /* First multiply dfl*dfr */ |
| 1957 | decFiniteMultiply(&mul, acc+1, dfl, dfr); |
| 1958 | /* The multiply is complete, exact and unbounded, and described in */ |
| 1959 | /* mul with the coefficient held in acc[1...] */ |
| 1960 | |
| 1961 | /* now add in dff; the algorithm is essentially the same as */ |
| 1962 | /* decFloatAdd, but the code is different because the code there */ |
| 1963 | /* is highly optimized for adding two numbers of the same size */ |
| 1964 | fin.exponent=GETEXPUN(dff); /* get dff exponent and sign */ |
| 1965 | fin.sign=DFWORD(dff, 0)&DECFLOAT_Sign; |
| 1966 | diffsign=mul.sign^fin.sign; /* note if signs differ */ |
| 1967 | fin.msd=coe; |
| 1968 | fin.lsd=coe+DECPMAX-1; |
| 1969 | GETCOEFF(dff, coe); /* extract the coefficient */ |
| 1970 | |
| 1971 | /* now set hi and lo so that hi points to whichever of mul and fin */ |
| 1972 | /* has the higher exponent and lo point to the other [don't care if */ |
| 1973 | /* the same] */ |
| 1974 | if (mul.exponent>=fin.exponent) { |
| 1975 | hi=&mul; |
| 1976 | lo=&fin; |
| 1977 | } |
| 1978 | else { |
| 1979 | hi=&fin; |
| 1980 | lo=&mul; |
| 1981 | } |
| 1982 | |
| 1983 | /* remove leading zeros on both operands; this will save time later */ |
| 1984 | /* and make testing for zero trivial */ |
| 1985 | for (; UINTAT(hi->msd)==0 && hi->msd+3<hi->lsd;) hi->msd+=4; |
| 1986 | for (; *hi->msd==0 && hi->msd<hi->lsd;) hi->msd++; |
| 1987 | for (; UINTAT(lo->msd)==0 && lo->msd+3<lo->lsd;) lo->msd+=4; |
| 1988 | for (; *lo->msd==0 && lo->msd<lo->lsd;) lo->msd++; |
| 1989 | |
| 1990 | /* if hi is zero then result will be lo (which has the smaller */ |
| 1991 | /* exponent), which also may need to be tested for zero for the */ |
| 1992 | /* weird IEEE 754 sign rules */ |
| 1993 | if (*hi->msd==0 && hi->msd==hi->lsd) { /* hi is zero */ |
| 1994 | /* "When the sum of two operands with opposite signs is */ |
| 1995 | /* exactly zero, the sign of that sum shall be '+' in all */ |
| 1996 | /* rounding modes except round toward -Infinity, in which */ |
| 1997 | /* mode that sign shall be '-'." */ |
| 1998 | if (diffsign) { |
| 1999 | if (*lo->msd==0 && lo->msd==lo->lsd) { /* lo is zero */ |
| 2000 | lo->sign=0; |
| 2001 | if (set->round==DEC_ROUND_FLOOR) lo->sign=DECFLOAT_Sign; |
| 2002 | } /* diffsign && lo=0 */ |
| 2003 | } /* diffsign */ |
| 2004 | return decFinalize(result, lo, set); /* may need clamping */ |
| 2005 | } /* numfl is zero */ |
| 2006 | /* [here, both are minimal length and hi is non-zero] */ |
| 2007 | |
| 2008 | /* if signs differ, take the ten's complement of hi (zeros to the */ |
| 2009 | /* right do not matter because the complement of zero is zero); */ |
| 2010 | /* the +1 is done later, as part of the addition, inserted at the */ |
| 2011 | /* correct digit */ |
| 2012 | hipad=0; |
| 2013 | carry=0; |
| 2014 | if (diffsign) { |
| 2015 | hipad=9; |
| 2016 | carry=1; |
| 2017 | /* exactly the correct number of digits must be inverted */ |
| 2018 | for (uh=hi->msd; uh<hi->lsd-3; uh+=4) UINTAT(uh)=0x09090909-UINTAT(uh); |
| 2019 | for (; uh<=hi->lsd; uh++) *uh=(uByte)(0x09-*uh); |
| 2020 | } |
| 2021 | |
| 2022 | /* ready to add; note that hi has no leading zeros so gap */ |
| 2023 | /* calculation does not have to be as pessimistic as in decFloatAdd */ |
| 2024 | /* (this is much more like the arbitrary-precision algorithm in */ |
| 2025 | /* Rexx and decNumber) */ |
| 2026 | |
| 2027 | /* padding is the number of zeros that would need to be added to hi */ |
| 2028 | /* for its lsd to be aligned with the lsd of lo */ |
| 2029 | padding=hi->exponent-lo->exponent; |
| 2030 | /* printf("FMA pad %ld\n", (LI)padding); */ |
| 2031 | |
| 2032 | /* the result of the addition will be built into the accumulator, */ |
| 2033 | /* starting from the far right; this could be either hi or lo */ |
| 2034 | ub=acc+FMALEN-1; /* where lsd of result will go */ |
| 2035 | ul=lo->lsd; /* lsd of rhs */ |
| 2036 | |
| 2037 | if (padding!=0) { /* unaligned */ |
| 2038 | /* if the msd of lo is more than DECPMAX+2 digits to the right of */ |
| 2039 | /* the original msd of hi then it can be reduced to a single */ |
| 2040 | /* digit at the right place, as it stays clear of hi digits */ |
| 2041 | /* [it must be DECPMAX+2 because during a subtraction the msd */ |
| 2042 | /* could become 0 after a borrow from 1.000 to 0.9999...] */ |
| 2043 | Int hilen=(Int)(hi->lsd-hi->msd+1); /* lengths */ |
| 2044 | Int lolen=(Int)(lo->lsd-lo->msd+1); /* .. */ |
| 2045 | Int newexp=MINI(hi->exponent, hi->exponent+hilen-DECPMAX)-3; |
| 2046 | Int reduce=newexp-lo->exponent; |
| 2047 | if (reduce>0) { /* [= case gives reduce=0 nop] */ |
| 2048 | /* printf("FMA reduce: %ld\n", (LI)reduce); */ |
| 2049 | if (reduce>=lolen) { /* eating all */ |
| 2050 | lo->lsd=lo->msd; /* reduce to single digit */ |
| 2051 | lo->exponent=newexp; /* [known to be non-zero] */ |
| 2052 | } |
| 2053 | else { /* < */ |
| 2054 | uByte *up=lo->lsd; |
| 2055 | lo->lsd=lo->lsd-reduce; |
| 2056 | if (*lo->lsd==0) /* could need sticky bit */ |
| 2057 | for (; up>lo->lsd; up--) { /* search discarded digits */ |
| 2058 | if (*up!=0) { /* found one... */ |
| 2059 | *lo->lsd=1; /* set sticky bit */ |
| 2060 | break; |
| 2061 | } |
| 2062 | } |
| 2063 | lo->exponent+=reduce; |
| 2064 | } |
| 2065 | padding=hi->exponent-lo->exponent; /* recalculate */ |
| 2066 | ul=lo->lsd; /* .. */ |
| 2067 | } /* maybe reduce */ |
| 2068 | /* padding is now <= DECPMAX+2 but still > 0; tricky DOUBLE case */ |
| 2069 | /* is when hi is a 1 that will become a 0.9999... by subtraction: */ |
| 2070 | /* hi: 1 E+16 */ |
| 2071 | /* lo: .................1000000000000000 E-16 */ |
| 2072 | /* which for the addition pads and reduces to: */ |
| 2073 | /* hi: 1000000000000000000 E-2 */ |
| 2074 | /* lo: .................1 E-2 */ |
| 2075 | #if DECCHECK |
| 2076 | if (padding>DECPMAX+2) printf("FMA excess padding: %ld\n", (LI)padding); |
| 2077 | if (padding<=0) printf("FMA low padding: %ld\n", (LI)padding); |
| 2078 | /* printf("FMA padding: %ld\n", (LI)padding); */ |
| 2079 | #endif |
| 2080 | /* padding digits can now be set in the result; one or more of */ |
| 2081 | /* these will come from lo; others will be zeros in the gap */ |
| 2082 | for (; ul>=lo->msd && padding>0; padding--, ul--, ub--) *ub=*ul; |
| 2083 | for (;padding>0; padding--, ub--) *ub=0; /* mind the gap */ |
| 2084 | } |
| 2085 | |
| 2086 | /* addition now complete to the right of the rightmost digit of hi */ |
| 2087 | uh=hi->lsd; |
| 2088 | |
| 2089 | /* carry was set up depending on ten's complement above; do the add... */ |
| 2090 | for (;; ub--) { |
| 2091 | uInt hid, lod; |
| 2092 | if (uh<hi->msd) { |
| 2093 | if (ul<lo->msd) break; |
| 2094 | hid=hipad; |
| 2095 | } |
| 2096 | else hid=*uh--; |
| 2097 | if (ul<lo->msd) lod=0; |
| 2098 | else lod=*ul--; |
| 2099 | *ub=(uByte)(carry+hid+lod); |
| 2100 | if (*ub<10) carry=0; |
| 2101 | else { |
| 2102 | *ub-=10; |
| 2103 | carry=1; |
| 2104 | } |
| 2105 | } /* addition loop */ |
| 2106 | |
| 2107 | /* addition complete -- now handle carry, borrow, etc. */ |
| 2108 | /* use lo to set up the num (its exponent is already correct, and */ |
| 2109 | /* sign usually is) */ |
| 2110 | lo->msd=ub+1; |
| 2111 | lo->lsd=acc+FMALEN-1; |
| 2112 | /* decShowNum(lo, "lo"); */ |
| 2113 | if (!diffsign) { /* same-sign addition */ |
| 2114 | if (carry) { /* carry out */ |
| 2115 | *ub=1; /* place the 1 .. */ |
| 2116 | lo->msd--; /* .. and update */ |
| 2117 | } |
| 2118 | } /* same sign */ |
| 2119 | else { /* signs differed (subtraction) */ |
| 2120 | if (!carry) { /* no carry out means hi<lo */ |
| 2121 | /* borrowed -- take ten's complement of the right digits */ |
| 2122 | lo->sign=hi->sign; /* sign is lhs sign */ |
| 2123 | for (ul=lo->msd; ul<lo->lsd-3; ul+=4) UINTAT(ul)=0x09090909-UINTAT(ul); |
| 2124 | for (; ul<=lo->lsd; ul++) *ul=(uByte)(0x09-*ul); /* [leaves ul at lsd+1] */ |
| 2125 | /* complete the ten's complement by adding 1 [cannot overrun] */ |
| 2126 | for (ul--; *ul==9; ul--) *ul=0; |
| 2127 | *ul+=1; |
| 2128 | } /* borrowed */ |
| 2129 | else { /* carry out means hi>=lo */ |
| 2130 | /* sign to use is lo->sign */ |
| 2131 | /* all done except for the special IEEE 754 exact-zero-result */ |
| 2132 | /* rule (see above); while testing for zero, strip leading */ |
| 2133 | /* zeros (which will save decFinalize doing it) */ |
| 2134 | for (; UINTAT(lo->msd)==0 && lo->msd+3<lo->lsd;) lo->msd+=4; |
| 2135 | for (; *lo->msd==0 && lo->msd<lo->lsd;) lo->msd++; |
| 2136 | if (*lo->msd==0) { /* must be true zero (and diffsign) */ |
| 2137 | lo->sign=0; /* assume + */ |
| 2138 | if (set->round==DEC_ROUND_FLOOR) lo->sign=DECFLOAT_Sign; |
| 2139 | } |
| 2140 | /* [else was not zero, might still have leading zeros] */ |
| 2141 | } /* subtraction gave positive result */ |
| 2142 | } /* diffsign */ |
| 2143 | |
| 2144 | return decFinalize(result, lo, set); /* round, check, and lay out */ |
| 2145 | } /* decFloatFMA */ |
| 2146 | |
| 2147 | /* ------------------------------------------------------------------ */ |
| 2148 | /* decFloatFromInt -- initialise a decFloat from an Int */ |
| 2149 | /* */ |
| 2150 | /* result gets the converted Int */ |
| 2151 | /* n is the Int to convert */ |
| 2152 | /* returns result */ |
| 2153 | /* */ |
| 2154 | /* The result is Exact; no errors or exceptions are possible. */ |
| 2155 | /* ------------------------------------------------------------------ */ |
| 2156 | decFloat * decFloatFromInt32(decFloat *result, Int n) { |
| 2157 | uInt u=(uInt)n; /* copy as bits */ |
| 2158 | uInt encode; /* work */ |
| 2159 | DFWORD(result, 0)=ZEROWORD; /* always */ |
| 2160 | #if QUAD |
| 2161 | DFWORD(result, 1)=0; |
| 2162 | DFWORD(result, 2)=0; |
| 2163 | #endif |
| 2164 | if (n<0) { /* handle -n with care */ |
| 2165 | /* [This can be done without the test, but is then slightly slower] */ |
| 2166 | u=(~u)+1; |
| 2167 | DFWORD(result, 0)|=DECFLOAT_Sign; |
| 2168 | } |
| 2169 | /* Since the maximum value of u now is 2**31, only the low word of */ |
| 2170 | /* result is affected */ |
| 2171 | encode=BIN2DPD[u%1000]; |
| 2172 | u/=1000; |
| 2173 | encode|=BIN2DPD[u%1000]<<10; |
| 2174 | u/=1000; |
| 2175 | encode|=BIN2DPD[u%1000]<<20; |
| 2176 | u/=1000; /* now 0, 1, or 2 */ |
| 2177 | encode|=u<<30; |
| 2178 | DFWORD(result, DECWORDS-1)=encode; |
| 2179 | return result; |
| 2180 | } /* decFloatFromInt32 */ |
| 2181 | |
| 2182 | /* ------------------------------------------------------------------ */ |
| 2183 | /* decFloatFromUInt -- initialise a decFloat from a uInt */ |
| 2184 | /* */ |
| 2185 | /* result gets the converted uInt */ |
| 2186 | /* n is the uInt to convert */ |
| 2187 | /* returns result */ |
| 2188 | /* */ |
| 2189 | /* The result is Exact; no errors or exceptions are possible. */ |
| 2190 | /* ------------------------------------------------------------------ */ |
| 2191 | decFloat * decFloatFromUInt32(decFloat *result, uInt u) { |
| 2192 | uInt encode; /* work */ |
| 2193 | DFWORD(result, 0)=ZEROWORD; /* always */ |
| 2194 | #if QUAD |
| 2195 | DFWORD(result, 1)=0; |
| 2196 | DFWORD(result, 2)=0; |
| 2197 | #endif |
| 2198 | encode=BIN2DPD[u%1000]; |
| 2199 | u/=1000; |
| 2200 | encode|=BIN2DPD[u%1000]<<10; |
| 2201 | u/=1000; |
| 2202 | encode|=BIN2DPD[u%1000]<<20; |
| 2203 | u/=1000; /* now 0 -> 4 */ |
| 2204 | encode|=u<<30; |
| 2205 | DFWORD(result, DECWORDS-1)=encode; |
| 2206 | DFWORD(result, DECWORDS-2)|=u>>2; /* rarely non-zero */ |
| 2207 | return result; |
| 2208 | } /* decFloatFromUInt32 */ |
| 2209 | |
| 2210 | /* ------------------------------------------------------------------ */ |
| 2211 | /* decFloatInvert -- logical digitwise INVERT of a decFloat */ |
| 2212 | /* */ |
| 2213 | /* result gets the result of INVERTing df */ |
| 2214 | /* df is the decFloat to invert */ |
| 2215 | /* set is the context */ |
| 2216 | /* returns result, which will be canonical with sign=0 */ |
| 2217 | /* */ |
| 2218 | /* The operand must be positive, finite with exponent q=0, and */ |
| 2219 | /* comprise just zeros and ones; if not, Invalid operation results. */ |
| 2220 | /* ------------------------------------------------------------------ */ |
| 2221 | decFloat * decFloatInvert(decFloat *result, const decFloat *df, |
| 2222 | decContext *set) { |
| 2223 | uInt sourhi=DFWORD(df, 0); /* top word of dfs */ |
| 2224 | |
| 2225 | if (!DFISUINT01(df) || !DFISCC01(df)) return decInvalid(result, set); |
| 2226 | /* the operand is a finite integer (q=0) */ |
| 2227 | #if DOUBLE |
| 2228 | DFWORD(result, 0)=ZEROWORD|((~sourhi)&0x04009124); |
| 2229 | DFWORD(result, 1)=(~DFWORD(df, 1)) &0x49124491; |
| 2230 | #elif QUAD |
| 2231 | DFWORD(result, 0)=ZEROWORD|((~sourhi)&0x04000912); |
| 2232 | DFWORD(result, 1)=(~DFWORD(df, 1)) &0x44912449; |
| 2233 | DFWORD(result, 2)=(~DFWORD(df, 2)) &0x12449124; |
| 2234 | DFWORD(result, 3)=(~DFWORD(df, 3)) &0x49124491; |
| 2235 | #endif |
| 2236 | return result; |
| 2237 | } /* decFloatInvert */ |
| 2238 | |
| 2239 | /* ------------------------------------------------------------------ */ |
| 2240 | /* decFloatIs -- decFloat tests (IsSigned, etc.) */ |
| 2241 | /* */ |
| 2242 | /* df is the decFloat to test */ |
| 2243 | /* returns 0 or 1 in an int32_t */ |
| 2244 | /* */ |
| 2245 | /* Many of these could be macros, but having them as real functions */ |
| 2246 | /* is a bit cleaner (and they can be referred to here by the generic */ |
| 2247 | /* names) */ |
| 2248 | /* ------------------------------------------------------------------ */ |
| 2249 | uInt decFloatIsCanonical(const decFloat *df) { |
| 2250 | if (DFISSPECIAL(df)) { |
| 2251 | if (DFISINF(df)) { |
| 2252 | if (DFWORD(df, 0)&ECONMASK) return 0; /* exponent continuation */ |
| 2253 | if (!DFISCCZERO(df)) return 0; /* coefficient continuation */ |
| 2254 | return 1; |
| 2255 | } |
| 2256 | /* is a NaN */ |
| 2257 | if (DFWORD(df, 0)&ECONNANMASK) return 0; /* exponent continuation */ |
| 2258 | if (DFISCCZERO(df)) return 1; /* coefficient continuation */ |
| 2259 | /* drop through to check payload */ |
| 2260 | } |
| 2261 | { /* declare block */ |
| 2262 | #if DOUBLE |
| 2263 | uInt sourhi=DFWORD(df, 0); |
| 2264 | uInt sourlo=DFWORD(df, 1); |
| 2265 | if (CANONDPDOFF(sourhi, 8) |
| 2266 | && CANONDPDTWO(sourhi, sourlo, 30) |
| 2267 | && CANONDPDOFF(sourlo, 20) |
| 2268 | && CANONDPDOFF(sourlo, 10) |
| 2269 | && CANONDPDOFF(sourlo, 0)) return 1; |
| 2270 | #elif QUAD |
| 2271 | uInt sourhi=DFWORD(df, 0); |
| 2272 | uInt sourmh=DFWORD(df, 1); |
| 2273 | uInt sourml=DFWORD(df, 2); |
| 2274 | uInt sourlo=DFWORD(df, 3); |
| 2275 | if (CANONDPDOFF(sourhi, 4) |
| 2276 | && CANONDPDTWO(sourhi, sourmh, 26) |
| 2277 | && CANONDPDOFF(sourmh, 16) |
| 2278 | && CANONDPDOFF(sourmh, 6) |
| 2279 | && CANONDPDTWO(sourmh, sourml, 28) |
| 2280 | && CANONDPDOFF(sourml, 18) |
| 2281 | && CANONDPDOFF(sourml, 8) |
| 2282 | && CANONDPDTWO(sourml, sourlo, 30) |
| 2283 | && CANONDPDOFF(sourlo, 20) |
| 2284 | && CANONDPDOFF(sourlo, 10) |
| 2285 | && CANONDPDOFF(sourlo, 0)) return 1; |
| 2286 | #endif |
| 2287 | } /* block */ |
| 2288 | return 0; /* a declet is non-canonical */ |
| 2289 | } |
| 2290 | |
| 2291 | uInt decFloatIsFinite(const decFloat *df) { |
| 2292 | return !DFISSPECIAL(df); |
| 2293 | } |
| 2294 | uInt decFloatIsInfinite(const decFloat *df) { |
| 2295 | return DFISINF(df); |
| 2296 | } |
| 2297 | uInt decFloatIsInteger(const decFloat *df) { |
| 2298 | return DFISINT(df); |
| 2299 | } |
| 2300 | uInt decFloatIsNaN(const decFloat *df) { |
| 2301 | return DFISNAN(df); |
| 2302 | } |
| 2303 | uInt decFloatIsNormal(const decFloat *df) { |
| 2304 | Int exp; /* exponent */ |
| 2305 | if (DFISSPECIAL(df)) return 0; |
| 2306 | if (DFISZERO(df)) return 0; |
| 2307 | /* is finite and non-zero */ |
| 2308 | exp=GETEXPUN(df) /* get unbiased exponent .. */ |
| 2309 | +decFloatDigits(df)-1; /* .. and make adjusted exponent */ |
| 2310 | return (exp>=DECEMIN); /* < DECEMIN is subnormal */ |
| 2311 | } |
| 2312 | uInt decFloatIsSignaling(const decFloat *df) { |
| 2313 | return DFISSNAN(df); |
| 2314 | } |
| 2315 | uInt decFloatIsSignalling(const decFloat *df) { |
| 2316 | return DFISSNAN(df); |
| 2317 | } |
| 2318 | uInt decFloatIsSigned(const decFloat *df) { |
| 2319 | return DFISSIGNED(df); |
| 2320 | } |
| 2321 | uInt decFloatIsSubnormal(const decFloat *df) { |
| 2322 | if (DFISSPECIAL(df)) return 0; |
| 2323 | /* is finite */ |
| 2324 | if (decFloatIsNormal(df)) return 0; |
| 2325 | /* it is <Nmin, but could be zero */ |
| 2326 | if (DFISZERO(df)) return 0; |
| 2327 | return 1; /* is subnormal */ |
| 2328 | } |
| 2329 | uInt decFloatIsZero(const decFloat *df) { |
| 2330 | return DFISZERO(df); |
| 2331 | } /* decFloatIs... */ |
| 2332 | |
| 2333 | /* ------------------------------------------------------------------ */ |
| 2334 | /* decFloatLogB -- return adjusted exponent, by 754r rules */ |
| 2335 | /* */ |
| 2336 | /* result gets the adjusted exponent as an integer, or a NaN etc. */ |
| 2337 | /* df is the decFloat to be examined */ |
| 2338 | /* set is the context */ |
| 2339 | /* returns result */ |
| 2340 | /* */ |
| 2341 | /* Notable cases: */ |
| 2342 | /* A<0 -> Use |A| */ |
| 2343 | /* A=0 -> -Infinity (Division by zero) */ |
| 2344 | /* A=Infinite -> +Infinity (Exact) */ |
| 2345 | /* A=1 exactly -> 0 (Exact) */ |
| 2346 | /* NaNs are propagated as usual */ |
| 2347 | /* ------------------------------------------------------------------ */ |
| 2348 | decFloat * decFloatLogB(decFloat *result, const decFloat *df, |
| 2349 | decContext *set) { |
| 2350 | Int ae; /* adjusted exponent */ |
| 2351 | if (DFISNAN(df)) return decNaNs(result, df, NULL, set); |
| 2352 | if (DFISINF(df)) { |
| 2353 | DFWORD(result, 0)=0; /* need +ve */ |
| 2354 | return decInfinity(result, result); /* canonical +Infinity */ |
| 2355 | } |
| 2356 | if (DFISZERO(df)) { |
| 2357 | set->status|=DEC_Division_by_zero; /* as per 754r */ |
| 2358 | DFWORD(result, 0)=DECFLOAT_Sign; /* make negative */ |
| 2359 | return decInfinity(result, result); /* canonical -Infinity */ |
| 2360 | } |
| 2361 | ae=GETEXPUN(df) /* get unbiased exponent .. */ |
| 2362 | +decFloatDigits(df)-1; /* .. and make adjusted exponent */ |
| 2363 | /* ae has limited range (3 digits for DOUBLE and 4 for QUAD), so */ |
| 2364 | /* it is worth using a special case of decFloatFromInt32 */ |
| 2365 | DFWORD(result, 0)=ZEROWORD; /* always */ |
| 2366 | if (ae<0) { |
| 2367 | DFWORD(result, 0)|=DECFLOAT_Sign; /* -0 so far */ |
| 2368 | ae=-ae; |
| 2369 | } |
| 2370 | #if DOUBLE |
| 2371 | DFWORD(result, 1)=BIN2DPD[ae]; /* a single declet */ |
| 2372 | #elif QUAD |
| 2373 | DFWORD(result, 1)=0; |
| 2374 | DFWORD(result, 2)=0; |
| 2375 | DFWORD(result, 3)=(ae/1000)<<10; /* is <10, so need no DPD encode */ |
| 2376 | DFWORD(result, 3)|=BIN2DPD[ae%1000]; |
| 2377 | #endif |
| 2378 | return result; |
| 2379 | } /* decFloatLogB */ |
| 2380 | |
| 2381 | /* ------------------------------------------------------------------ */ |
| 2382 | /* decFloatMax -- return maxnum of two operands */ |
| 2383 | /* */ |
| 2384 | /* result gets the chosen decFloat */ |
| 2385 | /* dfl is the first decFloat (lhs) */ |
| 2386 | /* dfr is the second decFloat (rhs) */ |
| 2387 | /* set is the context */ |
| 2388 | /* returns result */ |
| 2389 | /* */ |
| 2390 | /* If just one operand is a quiet NaN it is ignored. */ |
| 2391 | /* ------------------------------------------------------------------ */ |
| 2392 | decFloat * decFloatMax(decFloat *result, |
| 2393 | const decFloat *dfl, const decFloat *dfr, |
| 2394 | decContext *set) { |
| 2395 | Int comp; |
| 2396 | if (DFISNAN(dfl)) { |
| 2397 | /* sNaN or both NaNs leads to normal NaN processing */ |
| 2398 | if (DFISNAN(dfr) || DFISSNAN(dfl)) return decNaNs(result, dfl, dfr, set); |
| 2399 | return decCanonical(result, dfr); /* RHS is numeric */ |
| 2400 | } |
| 2401 | if (DFISNAN(dfr)) { |
| 2402 | /* sNaN leads to normal NaN processing (both NaN handled above) */ |
| 2403 | if (DFISSNAN(dfr)) return decNaNs(result, dfl, dfr, set); |
| 2404 | return decCanonical(result, dfl); /* LHS is numeric */ |
| 2405 | } |
| 2406 | /* Both operands are numeric; numeric comparison needed -- use */ |
| 2407 | /* total order for a well-defined choice (and +0 > -0) */ |
| 2408 | comp=decNumCompare(dfl, dfr, 1); |
| 2409 | if (comp>=0) return decCanonical(result, dfl); |
| 2410 | return decCanonical(result, dfr); |
| 2411 | } /* decFloatMax */ |
| 2412 | |
| 2413 | /* ------------------------------------------------------------------ */ |
| 2414 | /* decFloatMaxMag -- return maxnummag of two operands */ |
| 2415 | /* */ |
| 2416 | /* result gets the chosen decFloat */ |
| 2417 | /* dfl is the first decFloat (lhs) */ |
| 2418 | /* dfr is the second decFloat (rhs) */ |
| 2419 | /* set is the context */ |
| 2420 | /* returns result */ |
| 2421 | /* */ |
| 2422 | /* Returns according to the magnitude comparisons if both numeric and */ |
| 2423 | /* unequal, otherwise returns maxnum */ |
| 2424 | /* ------------------------------------------------------------------ */ |
| 2425 | decFloat * decFloatMaxMag(decFloat *result, |
| 2426 | const decFloat *dfl, const decFloat *dfr, |
| 2427 | decContext *set) { |
| 2428 | Int comp; |
| 2429 | decFloat absl, absr; |
| 2430 | if (DFISNAN(dfl) || DFISNAN(dfr)) return decFloatMax(result, dfl, dfr, set); |
| 2431 | |
| 2432 | decFloatCopyAbs(&absl, dfl); |
| 2433 | decFloatCopyAbs(&absr, dfr); |
| 2434 | comp=decNumCompare(&absl, &absr, 0); |
| 2435 | if (comp>0) return decCanonical(result, dfl); |
| 2436 | if (comp<0) return decCanonical(result, dfr); |
| 2437 | return decFloatMax(result, dfl, dfr, set); |
| 2438 | } /* decFloatMaxMag */ |
| 2439 | |
| 2440 | /* ------------------------------------------------------------------ */ |
| 2441 | /* decFloatMin -- return minnum of two operands */ |
| 2442 | /* */ |
| 2443 | /* result gets the chosen decFloat */ |
| 2444 | /* dfl is the first decFloat (lhs) */ |
| 2445 | /* dfr is the second decFloat (rhs) */ |
| 2446 | /* set is the context */ |
| 2447 | /* returns result */ |
| 2448 | /* */ |
| 2449 | /* If just one operand is a quiet NaN it is ignored. */ |
| 2450 | /* ------------------------------------------------------------------ */ |
| 2451 | decFloat * decFloatMin(decFloat *result, |
| 2452 | const decFloat *dfl, const decFloat *dfr, |
| 2453 | decContext *set) { |
| 2454 | Int comp; |
| 2455 | if (DFISNAN(dfl)) { |
| 2456 | /* sNaN or both NaNs leads to normal NaN processing */ |
| 2457 | if (DFISNAN(dfr) || DFISSNAN(dfl)) return decNaNs(result, dfl, dfr, set); |
| 2458 | return decCanonical(result, dfr); /* RHS is numeric */ |
| 2459 | } |
| 2460 | if (DFISNAN(dfr)) { |
| 2461 | /* sNaN leads to normal NaN processing (both NaN handled above) */ |
| 2462 | if (DFISSNAN(dfr)) return decNaNs(result, dfl, dfr, set); |
| 2463 | return decCanonical(result, dfl); /* LHS is numeric */ |
| 2464 | } |
| 2465 | /* Both operands are numeric; numeric comparison needed -- use */ |
| 2466 | /* total order for a well-defined choice (and +0 > -0) */ |
| 2467 | comp=decNumCompare(dfl, dfr, 1); |
| 2468 | if (comp<=0) return decCanonical(result, dfl); |
| 2469 | return decCanonical(result, dfr); |
| 2470 | } /* decFloatMin */ |
| 2471 | |
| 2472 | /* ------------------------------------------------------------------ */ |
| 2473 | /* decFloatMinMag -- return minnummag of two operands */ |
| 2474 | /* */ |
| 2475 | /* result gets the chosen decFloat */ |
| 2476 | /* dfl is the first decFloat (lhs) */ |
| 2477 | /* dfr is the second decFloat (rhs) */ |
| 2478 | /* set is the context */ |
| 2479 | /* returns result */ |
| 2480 | /* */ |
| 2481 | /* Returns according to the magnitude comparisons if both numeric and */ |
| 2482 | /* unequal, otherwise returns minnum */ |
| 2483 | /* ------------------------------------------------------------------ */ |
| 2484 | decFloat * decFloatMinMag(decFloat *result, |
| 2485 | const decFloat *dfl, const decFloat *dfr, |
| 2486 | decContext *set) { |
| 2487 | Int comp; |
| 2488 | decFloat absl, absr; |
| 2489 | if (DFISNAN(dfl) || DFISNAN(dfr)) return decFloatMin(result, dfl, dfr, set); |
| 2490 | |
| 2491 | decFloatCopyAbs(&absl, dfl); |
| 2492 | decFloatCopyAbs(&absr, dfr); |
| 2493 | comp=decNumCompare(&absl, &absr, 0); |
| 2494 | if (comp<0) return decCanonical(result, dfl); |
| 2495 | if (comp>0) return decCanonical(result, dfr); |
| 2496 | return decFloatMin(result, dfl, dfr, set); |
| 2497 | } /* decFloatMinMag */ |
| 2498 | |
| 2499 | /* ------------------------------------------------------------------ */ |
| 2500 | /* decFloatMinus -- negate value, heeding NaNs, etc. */ |
| 2501 | /* */ |
| 2502 | /* result gets the canonicalized 0-df */ |
| 2503 | /* df is the decFloat to minus */ |
| 2504 | /* set is the context */ |
| 2505 | /* returns result */ |
| 2506 | /* */ |
| 2507 | /* This has the same effect as 0-df where the exponent of the zero is */ |
| 2508 | /* the same as that of df (if df is finite). */ |
| 2509 | /* The effect is also the same as decFloatCopyNegate except that NaNs */ |
| 2510 | /* are handled normally (the sign of a NaN is not affected, and an */ |
| 2511 | /* sNaN will signal), the result is canonical, and zero gets sign 0. */ |
| 2512 | /* ------------------------------------------------------------------ */ |
| 2513 | decFloat * decFloatMinus(decFloat *result, const decFloat *df, |
| 2514 | decContext *set) { |
| 2515 | if (DFISNAN(df)) return decNaNs(result, df, NULL, set); |
| 2516 | decCanonical(result, df); /* copy and check */ |
| 2517 | if (DFISZERO(df)) DFBYTE(result, 0)&=~0x80; /* turn off sign bit */ |
| 2518 | else DFBYTE(result, 0)^=0x80; /* flip sign bit */ |
| 2519 | return result; |
| 2520 | } /* decFloatMinus */ |
| 2521 | |
| 2522 | /* ------------------------------------------------------------------ */ |
| 2523 | /* decFloatMultiply -- multiply two decFloats */ |
| 2524 | /* */ |
| 2525 | /* result gets the result of multiplying dfl and dfr: */ |
| 2526 | /* dfl is the first decFloat (lhs) */ |
| 2527 | /* dfr is the second decFloat (rhs) */ |
| 2528 | /* set is the context */ |
| 2529 | /* returns result */ |
| 2530 | /* */ |
| 2531 | /* ------------------------------------------------------------------ */ |
| 2532 | decFloat * decFloatMultiply(decFloat *result, |
| 2533 | const decFloat *dfl, const decFloat *dfr, |
| 2534 | decContext *set) { |
| 2535 | bcdnum num; /* for final conversion */ |
| 2536 | uByte bcdacc[DECPMAX9*18+1]; /* for coefficent in BCD */ |
| 2537 | |
| 2538 | if (DFISSPECIAL(dfl) || DFISSPECIAL(dfr)) { /* either is special? */ |
| 2539 | /* NaNs are handled as usual */ |
| 2540 | if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set); |
| 2541 | /* infinity times zero is bad */ |
| 2542 | if (DFISINF(dfl) && DFISZERO(dfr)) return decInvalid(result, set); |
| 2543 | if (DFISINF(dfr) && DFISZERO(dfl)) return decInvalid(result, set); |
| 2544 | /* both infinite; return canonical infinity with computed sign */ |
| 2545 | DFWORD(result, 0)=DFWORD(dfl, 0)^DFWORD(dfr, 0); /* compute sign */ |
| 2546 | return decInfinity(result, result); |
| 2547 | } |
| 2548 | |
| 2549 | /* Here when both operands are finite */ |
| 2550 | decFiniteMultiply(&num, bcdacc, dfl, dfr); |
| 2551 | return decFinalize(result, &num, set); /* round, check, and lay out */ |
| 2552 | } /* decFloatMultiply */ |
| 2553 | |
| 2554 | /* ------------------------------------------------------------------ */ |
| 2555 | /* decFloatNextMinus -- next towards -Infinity */ |
| 2556 | /* */ |
| 2557 | /* result gets the next lesser decFloat */ |
| 2558 | /* dfl is the decFloat to start with */ |
| 2559 | /* set is the context */ |
| 2560 | /* returns result */ |
| 2561 | /* */ |
| 2562 | /* This is 754r nextdown; Invalid is the only status possible (from */ |
| 2563 | /* an sNaN). */ |
| 2564 | /* ------------------------------------------------------------------ */ |
| 2565 | decFloat * decFloatNextMinus(decFloat *result, const decFloat *dfl, |
| 2566 | decContext *set) { |
| 2567 | decFloat delta; /* tiny increment */ |
| 2568 | uInt savestat; /* saves status */ |
| 2569 | enum rounding saveround; /* .. and mode */ |
| 2570 | |
| 2571 | /* +Infinity is the special case */ |
| 2572 | if (DFISINF(dfl) && !DFISSIGNED(dfl)) { |
| 2573 | DFSETNMAX(result); |
| 2574 | return result; /* [no status to set] */ |
| 2575 | } |
| 2576 | /* other cases are effected by sutracting a tiny delta -- this */ |
| 2577 | /* should be done in a wider format as the delta is unrepresentable */ |
| 2578 | /* here (but can be done with normal add if the sign of zero is */ |
| 2579 | /* treated carefully, because no Inexactitude is interesting); */ |
| 2580 | /* rounding to -Infinity then pushes the result to next below */ |
| 2581 | decFloatZero(&delta); /* set up tiny delta */ |
| 2582 | DFWORD(&delta, DECWORDS-1)=1; /* coefficient=1 */ |
| 2583 | DFWORD(&delta, 0)=DECFLOAT_Sign; /* Sign=1 + biased exponent=0 */ |
| 2584 | /* set up for the directional round */ |
| 2585 | saveround=set->round; /* save mode */ |
| 2586 | set->round=DEC_ROUND_FLOOR; /* .. round towards -Infinity */ |
| 2587 | savestat=set->status; /* save status */ |
| 2588 | decFloatAdd(result, dfl, &delta, set); |
| 2589 | /* Add rules mess up the sign when going from +Ntiny to 0 */ |
| 2590 | if (DFISZERO(result)) DFWORD(result, 0)^=DECFLOAT_Sign; /* correct */ |
| 2591 | set->status&=DEC_Invalid_operation; /* preserve only sNaN status */ |
| 2592 | set->status|=savestat; /* restore pending flags */ |
| 2593 | set->round=saveround; /* .. and mode */ |
| 2594 | return result; |
| 2595 | } /* decFloatNextMinus */ |
| 2596 | |
| 2597 | /* ------------------------------------------------------------------ */ |
| 2598 | /* decFloatNextPlus -- next towards +Infinity */ |
| 2599 | /* */ |
| 2600 | /* result gets the next larger decFloat */ |
| 2601 | /* dfl is the decFloat to start with */ |
| 2602 | /* set is the context */ |
| 2603 | /* returns result */ |
| 2604 | /* */ |
| 2605 | /* This is 754r nextup; Invalid is the only status possible (from */ |
| 2606 | /* an sNaN). */ |
| 2607 | /* ------------------------------------------------------------------ */ |
| 2608 | decFloat * decFloatNextPlus(decFloat *result, const decFloat *dfl, |
| 2609 | decContext *set) { |
| 2610 | uInt savestat; /* saves status */ |
| 2611 | enum rounding saveround; /* .. and mode */ |
| 2612 | decFloat delta; /* tiny increment */ |
| 2613 | |
| 2614 | /* -Infinity is the special case */ |
| 2615 | if (DFISINF(dfl) && DFISSIGNED(dfl)) { |
| 2616 | DFSETNMAX(result); |
| 2617 | DFWORD(result, 0)|=DECFLOAT_Sign; /* make negative */ |
| 2618 | return result; /* [no status to set] */ |
| 2619 | } |
| 2620 | /* other cases are effected by sutracting a tiny delta -- this */ |
| 2621 | /* should be done in a wider format as the delta is unrepresentable */ |
| 2622 | /* here (but can be done with normal add if the sign of zero is */ |
| 2623 | /* treated carefully, because no Inexactitude is interesting); */ |
| 2624 | /* rounding to +Infinity then pushes the result to next above */ |
| 2625 | decFloatZero(&delta); /* set up tiny delta */ |
| 2626 | DFWORD(&delta, DECWORDS-1)=1; /* coefficient=1 */ |
| 2627 | DFWORD(&delta, 0)=0; /* Sign=0 + biased exponent=0 */ |
| 2628 | /* set up for the directional round */ |
| 2629 | saveround=set->round; /* save mode */ |
| 2630 | set->round=DEC_ROUND_CEILING; /* .. round towards +Infinity */ |
| 2631 | savestat=set->status; /* save status */ |
| 2632 | decFloatAdd(result, dfl, &delta, set); |
| 2633 | /* Add rules mess up the sign when going from -Ntiny to -0 */ |
| 2634 | if (DFISZERO(result)) DFWORD(result, 0)^=DECFLOAT_Sign; /* correct */ |
| 2635 | set->status&=DEC_Invalid_operation; /* preserve only sNaN status */ |
| 2636 | set->status|=savestat; /* restore pending flags */ |
| 2637 | set->round=saveround; /* .. and mode */ |
| 2638 | return result; |
| 2639 | } /* decFloatNextPlus */ |
| 2640 | |
| 2641 | /* ------------------------------------------------------------------ */ |
| 2642 | /* decFloatNextToward -- next towards a decFloat */ |
| 2643 | /* */ |
| 2644 | /* result gets the next decFloat */ |
| 2645 | /* dfl is the decFloat to start with */ |
| 2646 | /* dfr is the decFloat to move toward */ |
| 2647 | /* set is the context */ |
| 2648 | /* returns result */ |
| 2649 | /* */ |
| 2650 | /* This is 754r nextafter; status may be set unless the result is a */ |
| 2651 | /* normal number. */ |
| 2652 | /* ------------------------------------------------------------------ */ |
| 2653 | decFloat * decFloatNextToward(decFloat *result, |
| 2654 | const decFloat *dfl, const decFloat *dfr, |
| 2655 | decContext *set) { |
| 2656 | decFloat delta; /* tiny increment or decrement */ |
| 2657 | decFloat pointone; /* 1e-1 */ |
| 2658 | uInt savestat; /* saves status */ |
| 2659 | enum rounding saveround; /* .. and mode */ |
| 2660 | uInt deltatop; /* top word for delta */ |
| 2661 | Int comp; /* work */ |
| 2662 | |
| 2663 | if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set); |
| 2664 | /* Both are numeric, so Invalid no longer a possibility */ |
| 2665 | comp=decNumCompare(dfl, dfr, 0); |
| 2666 | if (comp==0) return decFloatCopySign(result, dfl, dfr); /* equal */ |
| 2667 | /* unequal; do NextPlus or NextMinus but with different status rules */ |
| 2668 | |
| 2669 | if (comp<0) { /* lhs<rhs, do NextPlus, see above for commentary */ |
| 2670 | if (DFISINF(dfl) && DFISSIGNED(dfl)) { /* -Infinity special case */ |
| 2671 | DFSETNMAX(result); |
| 2672 | DFWORD(result, 0)|=DECFLOAT_Sign; |
| 2673 | return result; |
| 2674 | } |
| 2675 | saveround=set->round; /* save mode */ |
| 2676 | set->round=DEC_ROUND_CEILING; /* .. round towards +Infinity */ |
| 2677 | deltatop=0; /* positive delta */ |
| 2678 | } |
| 2679 | else { /* lhs>rhs, do NextMinus, see above for commentary */ |
| 2680 | if (DFISINF(dfl) && !DFISSIGNED(dfl)) { /* +Infinity special case */ |
| 2681 | DFSETNMAX(result); |
| 2682 | return result; |
| 2683 | } |
| 2684 | saveround=set->round; /* save mode */ |
| 2685 | set->round=DEC_ROUND_FLOOR; /* .. round towards -Infinity */ |
| 2686 | deltatop=DECFLOAT_Sign; /* negative delta */ |
| 2687 | } |
| 2688 | savestat=set->status; /* save status */ |
| 2689 | /* Here, Inexact is needed where appropriate (and hence Underflow, */ |
| 2690 | /* etc.). Therefore the tiny delta which is otherwise */ |
| 2691 | /* unrepresentable (see NextPlus and NextMinus) is constructed */ |
| 2692 | /* using the multiplication of FMA. */ |
| 2693 | decFloatZero(&delta); /* set up tiny delta */ |
| 2694 | DFWORD(&delta, DECWORDS-1)=1; /* coefficient=1 */ |
| 2695 | DFWORD(&delta, 0)=deltatop; /* Sign + biased exponent=0 */ |
| 2696 | decFloatFromString(&pointone, "1E-1", set); /* set up multiplier */ |
| 2697 | decFloatFMA(result, &delta, &pointone, dfl, set); |
| 2698 | /* [Delta is truly tiny, so no need to correct sign of zero] */ |
| 2699 | /* use new status unless the result is normal */ |
| 2700 | if (decFloatIsNormal(result)) set->status=savestat; /* else goes forward */ |
| 2701 | set->round=saveround; /* restore mode */ |
| 2702 | return result; |
| 2703 | } /* decFloatNextToward */ |
| 2704 | |
| 2705 | /* ------------------------------------------------------------------ */ |
| 2706 | /* decFloatOr -- logical digitwise OR of two decFloats */ |
| 2707 | /* */ |
| 2708 | /* result gets the result of ORing dfl and dfr */ |
| 2709 | /* dfl is the first decFloat (lhs) */ |
| 2710 | /* dfr is the second decFloat (rhs) */ |
| 2711 | /* set is the context */ |
| 2712 | /* returns result, which will be canonical with sign=0 */ |
| 2713 | /* */ |
| 2714 | /* The operands must be positive, finite with exponent q=0, and */ |
| 2715 | /* comprise just zeros and ones; if not, Invalid operation results. */ |
| 2716 | /* ------------------------------------------------------------------ */ |
| 2717 | decFloat * decFloatOr(decFloat *result, |
| 2718 | const decFloat *dfl, const decFloat *dfr, |
| 2719 | decContext *set) { |
| 2720 | if (!DFISUINT01(dfl) || !DFISUINT01(dfr) |
| 2721 | || !DFISCC01(dfl) || !DFISCC01(dfr)) return decInvalid(result, set); |
| 2722 | /* the operands are positive finite integers (q=0) with just 0s and 1s */ |
| 2723 | #if DOUBLE |
| 2724 | DFWORD(result, 0)=ZEROWORD |
| 2725 | |((DFWORD(dfl, 0) | DFWORD(dfr, 0))&0x04009124); |
| 2726 | DFWORD(result, 1)=(DFWORD(dfl, 1) | DFWORD(dfr, 1))&0x49124491; |
| 2727 | #elif QUAD |
| 2728 | DFWORD(result, 0)=ZEROWORD |
| 2729 | |((DFWORD(dfl, 0) | DFWORD(dfr, 0))&0x04000912); |
| 2730 | DFWORD(result, 1)=(DFWORD(dfl, 1) | DFWORD(dfr, 1))&0x44912449; |
| 2731 | DFWORD(result, 2)=(DFWORD(dfl, 2) | DFWORD(dfr, 2))&0x12449124; |
| 2732 | DFWORD(result, 3)=(DFWORD(dfl, 3) | DFWORD(dfr, 3))&0x49124491; |
| 2733 | #endif |
| 2734 | return result; |
| 2735 | } /* decFloatOr */ |
| 2736 | |
| 2737 | /* ------------------------------------------------------------------ */ |
| 2738 | /* decFloatPlus -- add value to 0, heeding NaNs, etc. */ |
| 2739 | /* */ |
| 2740 | /* result gets the canonicalized 0+df */ |
| 2741 | /* df is the decFloat to plus */ |
| 2742 | /* set is the context */ |
| 2743 | /* returns result */ |
| 2744 | /* */ |
| 2745 | /* This has the same effect as 0+df where the exponent of the zero is */ |
| 2746 | /* the same as that of df (if df is finite). */ |
| 2747 | /* The effect is also the same as decFloatCopy except that NaNs */ |
| 2748 | /* are handled normally (the sign of a NaN is not affected, and an */ |
| 2749 | /* sNaN will signal), the result is canonical, and zero gets sign 0. */ |
| 2750 | /* ------------------------------------------------------------------ */ |
| 2751 | decFloat * decFloatPlus(decFloat *result, const decFloat *df, |
| 2752 | decContext *set) { |
| 2753 | if (DFISNAN(df)) return decNaNs(result, df, NULL, set); |
| 2754 | decCanonical(result, df); /* copy and check */ |
| 2755 | if (DFISZERO(df)) DFBYTE(result, 0)&=~0x80; /* turn off sign bit */ |
| 2756 | return result; |
| 2757 | } /* decFloatPlus */ |
| 2758 | |
| 2759 | /* ------------------------------------------------------------------ */ |
| 2760 | /* decFloatQuantize -- quantize a decFloat */ |
| 2761 | /* */ |
| 2762 | /* result gets the result of quantizing dfl to match dfr */ |
| 2763 | /* dfl is the first decFloat (lhs) */ |
| 2764 | /* dfr is the second decFloat (rhs), which sets the exponent */ |
| 2765 | /* set is the context */ |
| 2766 | /* returns result */ |
| 2767 | /* */ |
| 2768 | /* Unless there is an error or the result is infinite, the exponent */ |
| 2769 | /* of result is guaranteed to be the same as that of dfr. */ |
| 2770 | /* ------------------------------------------------------------------ */ |
| 2771 | decFloat * decFloatQuantize(decFloat *result, |
| 2772 | const decFloat *dfl, const decFloat *dfr, |
| 2773 | decContext *set) { |
| 2774 | Int explb, exprb; /* left and right biased exponents */ |
| 2775 | uByte *ulsd; /* local LSD pointer */ |
| 2776 | uInt *ui; /* work */ |
| 2777 | uByte *ub; /* .. */ |
| 2778 | Int drop; /* .. */ |
| 2779 | uInt dpd; /* .. */ |
| 2780 | uInt encode; /* encoding accumulator */ |
| 2781 | uInt sourhil, sourhir; /* top words from source decFloats */ |
| 2782 | /* the following buffer holds the coefficient for manipulation */ |
| 2783 | uByte buf[4+DECPMAX*3]; /* + space for zeros to left or right */ |
| 2784 | #if DECTRACE |
| 2785 | bcdnum num; /* for trace displays */ |
| 2786 | #endif |
| 2787 | |
| 2788 | /* Start decoding the arguments */ |
| 2789 | sourhil=DFWORD(dfl, 0); /* LHS top word */ |
| 2790 | explb=DECCOMBEXP[sourhil>>26]; /* get exponent high bits (in place) */ |
| 2791 | sourhir=DFWORD(dfr, 0); /* RHS top word */ |
| 2792 | exprb=DECCOMBEXP[sourhir>>26]; |
| 2793 | |
| 2794 | if (EXPISSPECIAL(explb | exprb)) { /* either is special? */ |
| 2795 | /* NaNs are handled as usual */ |
| 2796 | if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set); |
| 2797 | /* one infinity but not both is bad */ |
| 2798 | if (DFISINF(dfl)!=DFISINF(dfr)) return decInvalid(result, set); |
| 2799 | /* both infinite; return canonical infinity with sign of LHS */ |
| 2800 | return decInfinity(result, dfl); |
| 2801 | } |
| 2802 | |
| 2803 | /* Here when both arguments are finite */ |
| 2804 | /* complete extraction of the exponents [no need to unbias] */ |
| 2805 | explb+=GETECON(dfl); /* + continuation */ |
| 2806 | exprb+=GETECON(dfr); /* .. */ |
| 2807 | |
| 2808 | /* calculate the number of digits to drop from the coefficient */ |
| 2809 | drop=exprb-explb; /* 0 if nothing to do */ |
| 2810 | if (drop==0) return decCanonical(result, dfl); /* return canonical */ |
| 2811 | |
| 2812 | /* the coefficient is needed; lay it out into buf, offset so zeros */ |
| 2813 | /* can be added before or after as needed -- an extra heading is */ |
| 2814 | /* added so can safely pad Quad DECPMAX-1 zeros to the left by */ |
| 2815 | /* fours */ |
| 2816 | #define BUFOFF (buf+4+DECPMAX) |
| 2817 | GETCOEFF(dfl, BUFOFF); /* decode from decFloat */ |
| 2818 | /* [now the msd is at BUFOFF and the lsd is at BUFOFF+DECPMAX-1] */ |
| 2819 | |
| 2820 | #if DECTRACE |
| 2821 | num.msd=BUFOFF; |
| 2822 | num.lsd=BUFOFF+DECPMAX-1; |
| 2823 | num.exponent=explb-DECBIAS; |
| 2824 | num.sign=sourhil & DECFLOAT_Sign; |
| 2825 | decShowNum(&num, "dfl"); |
| 2826 | #endif |
| 2827 | |
| 2828 | if (drop>0) { /* [most common case] */ |
| 2829 | /* (this code is very similar to that in decFloatFinalize, but */ |
| 2830 | /* has many differences so is duplicated here -- so any changes */ |
| 2831 | /* may need to be made there, too) */ |
| 2832 | uByte *roundat; /* -> re-round digit */ |
| 2833 | uByte reround; /* reround value */ |
| 2834 | /* printf("Rounding; drop=%ld\n", (LI)drop); */ |
| 2835 | |
| 2836 | /* there is at least one zero needed to the left, in all but one */ |
| 2837 | /* exceptional (all-nines) case, so place four zeros now; this is */ |
| 2838 | /* needed almost always and makes rounding all-nines by fours safe */ |
| 2839 | UINTAT(BUFOFF-4)=0; |
| 2840 | |
| 2841 | /* Three cases here: */ |
| 2842 | /* 1. new LSD is in coefficient (almost always) */ |
| 2843 | /* 2. new LSD is digit to left of coefficient (so MSD is */ |
| 2844 | /* round-for-reround digit) */ |
| 2845 | /* 3. new LSD is to left of case 2 (whole coefficient is sticky) */ |
| 2846 | /* Note that leading zeros can safely be treated as useful digits */ |
| 2847 | |
| 2848 | /* [duplicate check-stickies code to save a test] */ |
| 2849 | /* [by-digit check for stickies as runs of zeros are rare] */ |
| 2850 | if (drop<DECPMAX) { /* NB lengths not addresses */ |
| 2851 | roundat=BUFOFF+DECPMAX-drop; |
| 2852 | reround=*roundat; |
| 2853 | for (ub=roundat+1; ub<BUFOFF+DECPMAX; ub++) { |
| 2854 | if (*ub!=0) { /* non-zero to be discarded */ |
| 2855 | reround=DECSTICKYTAB[reround]; /* apply sticky bit */ |
| 2856 | break; /* [remainder don't-care] */ |
| 2857 | } |
| 2858 | } /* check stickies */ |
| 2859 | ulsd=roundat-1; /* set LSD */ |
| 2860 | } |
| 2861 | else { /* edge case */ |
| 2862 | if (drop==DECPMAX) { |
| 2863 | roundat=BUFOFF; |
| 2864 | reround=*roundat; |
| 2865 | } |
| 2866 | else { |
| 2867 | roundat=BUFOFF-1; |
| 2868 | reround=0; |
| 2869 | } |
| 2870 | for (ub=roundat+1; ub<BUFOFF+DECPMAX; ub++) { |
| 2871 | if (*ub!=0) { /* non-zero to be discarded */ |
| 2872 | reround=DECSTICKYTAB[reround]; /* apply sticky bit */ |
| 2873 | break; /* [remainder don't-care] */ |
| 2874 | } |
| 2875 | } /* check stickies */ |
| 2876 | *BUFOFF=0; /* make a coefficient of 0 */ |
| 2877 | ulsd=BUFOFF; /* .. at the MSD place */ |
| 2878 | } |
| 2879 | |
| 2880 | if (reround!=0) { /* discarding non-zero */ |
| 2881 | uInt bump=0; |
| 2882 | set->status|=DEC_Inexact; |
| 2883 | |
| 2884 | /* next decide whether to increment the coefficient */ |
| 2885 | if (set->round==DEC_ROUND_HALF_EVEN) { /* fastpath slowest case */ |
| 2886 | if (reround>5) bump=1; /* >0.5 goes up */ |
| 2887 | else if (reround==5) /* exactly 0.5000 .. */ |
| 2888 | bump=*ulsd & 0x01; /* .. up iff [new] lsd is odd */ |
| 2889 | } /* r-h-e */ |
| 2890 | else switch (set->round) { |
| 2891 | case DEC_ROUND_DOWN: { |
| 2892 | /* no change */ |
| 2893 | break;} /* r-d */ |
| 2894 | case DEC_ROUND_HALF_DOWN: { |
| 2895 | if (reround>5) bump=1; |
| 2896 | break;} /* r-h-d */ |
| 2897 | case DEC_ROUND_HALF_UP: { |
| 2898 | if (reround>=5) bump=1; |
| 2899 | break;} /* r-h-u */ |
| 2900 | case DEC_ROUND_UP: { |
| 2901 | if (reround>0) bump=1; |
| 2902 | break;} /* r-u */ |
| 2903 | case DEC_ROUND_CEILING: { |
| 2904 | /* same as _UP for positive numbers, and as _DOWN for negatives */ |
| 2905 | if (!(sourhil&DECFLOAT_Sign) && reround>0) bump=1; |
| 2906 | break;} /* r-c */ |
| 2907 | case DEC_ROUND_FLOOR: { |
| 2908 | /* same as _UP for negative numbers, and as _DOWN for positive */ |
| 2909 | /* [negative reround cannot occur on 0] */ |
| 2910 | if (sourhil&DECFLOAT_Sign && reround>0) bump=1; |
| 2911 | break;} /* r-f */ |
| 2912 | case DEC_ROUND_05UP: { |
| 2913 | if (reround>0) { /* anything out there is 'sticky' */ |
| 2914 | /* bump iff lsd=0 or 5; this cannot carry so it could be */ |
| 2915 | /* effected immediately with no bump -- but the code */ |
| 2916 | /* is clearer if this is done the same way as the others */ |
| 2917 | if (*ulsd==0 || *ulsd==5) bump=1; |
| 2918 | } |
| 2919 | break;} /* r-r */ |
| 2920 | default: { /* e.g., DEC_ROUND_MAX */ |
| 2921 | set->status|=DEC_Invalid_context; |
| 2922 | #if DECCHECK |
| 2923 | printf("Unknown rounding mode: %ld\n", (LI)set->round); |
| 2924 | #endif |
| 2925 | break;} |
| 2926 | } /* switch (not r-h-e) */ |
| 2927 | /* printf("ReRound: %ld bump: %ld\n", (LI)reround, (LI)bump); */ |
| 2928 | |
| 2929 | if (bump!=0) { /* need increment */ |
| 2930 | /* increment the coefficient; this could give 1000... (after */ |
| 2931 | /* the all nines case) */ |
| 2932 | ub=ulsd; |
| 2933 | for (; UINTAT(ub-3)==0x09090909; ub-=4) UINTAT(ub-3)=0; |
| 2934 | /* now at most 3 digits left to non-9 (usually just the one) */ |
| 2935 | for (; *ub==9; ub--) *ub=0; |
| 2936 | *ub+=1; |
| 2937 | /* [the all-nines case will have carried one digit to the */ |
| 2938 | /* left of the original MSD -- just where it is needed] */ |
| 2939 | } /* bump needed */ |
| 2940 | } /* inexact rounding */ |
| 2941 | |
| 2942 | /* now clear zeros to the left so exactly DECPMAX digits will be */ |
| 2943 | /* available in the coefficent -- the first word to the left was */ |
| 2944 | /* cleared earlier for safe carry; now add any more needed */ |
| 2945 | if (drop>4) { |
| 2946 | UINTAT(BUFOFF-8)=0; /* must be at least 5 */ |
| 2947 | for (ui=&UINTAT(BUFOFF-12); ui>&UINTAT(ulsd-DECPMAX-3); ui--) *ui=0; |
| 2948 | } |
| 2949 | } /* need round (drop>0) */ |
| 2950 | |
| 2951 | else { /* drop<0; padding with -drop digits is needed */ |
| 2952 | /* This is the case where an error can occur if the padded */ |
| 2953 | /* coefficient will not fit; checking for this can be done in the */ |
| 2954 | /* same loop as padding for zeros if the no-hope and zero cases */ |
| 2955 | /* are checked first */ |
| 2956 | if (-drop>DECPMAX-1) { /* cannot fit unless 0 */ |
| 2957 | if (!ISCOEFFZERO(BUFOFF)) return decInvalid(result, set); |
| 2958 | /* a zero can have any exponent; just drop through and use it */ |
| 2959 | ulsd=BUFOFF+DECPMAX-1; |
| 2960 | } |
| 2961 | else { /* padding will fit (but may still be too long) */ |
| 2962 | /* final-word mask depends on endianess */ |
| 2963 | #if DECLITEND |
| 2964 | static const uInt dmask[]={0, 0x000000ff, 0x0000ffff, 0x00ffffff}; |
| 2965 | #else |
| 2966 | static const uInt dmask[]={0, 0xff000000, 0xffff0000, 0xffffff00}; |
| 2967 | #endif |
| 2968 | for (ui=&UINTAT(BUFOFF+DECPMAX);; ui++) { |
| 2969 | *ui=0; |
| 2970 | if (UINTAT(&UBYTEAT(ui)-DECPMAX)!=0) { /* could be bad */ |
| 2971 | /* if all four digits should be zero, definitely bad */ |
| 2972 | if (ui<=&UINTAT(BUFOFF+DECPMAX+(-drop)-4)) |
| 2973 | return decInvalid(result, set); |
| 2974 | /* must be a 1- to 3-digit sequence; check more carefully */ |
| 2975 | if ((UINTAT(&UBYTEAT(ui)-DECPMAX)&dmask[(-drop)%4])!=0) |
| 2976 | return decInvalid(result, set); |
| 2977 | break; /* no need for loop end test */ |
| 2978 | } |
| 2979 | if (ui>=&UINTAT(BUFOFF+DECPMAX+(-drop)-4)) break; /* done */ |
| 2980 | } |
| 2981 | ulsd=BUFOFF+DECPMAX+(-drop)-1; |
| 2982 | } /* pad and check leading zeros */ |
| 2983 | } /* drop<0 */ |
| 2984 | |
| 2985 | #if DECTRACE |
| 2986 | num.msd=ulsd-DECPMAX+1; |
| 2987 | num.lsd=ulsd; |
| 2988 | num.exponent=explb-DECBIAS; |
| 2989 | num.sign=sourhil & DECFLOAT_Sign; |
| 2990 | decShowNum(&num, "res"); |
| 2991 | #endif |
| 2992 | |
| 2993 | /*------------------------------------------------------------------*/ |
| 2994 | /* At this point the result is DECPMAX digits, ending at ulsd, so */ |
| 2995 | /* fits the encoding exactly; there is no possibility of error */ |
| 2996 | /*------------------------------------------------------------------*/ |
| 2997 | encode=((exprb>>DECECONL)<<4) + *(ulsd-DECPMAX+1); /* make index */ |
| 2998 | encode=DECCOMBFROM[encode]; /* indexed by (0-2)*16+msd */ |
| 2999 | /* the exponent continuation can be extracted from the original RHS */ |
| 3000 | encode|=sourhir & ECONMASK; |
| 3001 | encode|=sourhil&DECFLOAT_Sign; /* add the sign from LHS */ |
| 3002 | |
| 3003 | /* finally encode the coefficient */ |
| 3004 | /* private macro to encode a declet; this version can be used */ |
| 3005 | /* because all coefficient digits exist */ |
| 3006 | #define getDPD3q(dpd, n) ub=ulsd-(3*(n))-2; \ |
| 3007 | dpd=BCD2DPD[(*ub*256)+(*(ub+1)*16)+*(ub+2)]; |
| 3008 | |
| 3009 | #if DOUBLE |
| 3010 | getDPD3q(dpd, 4); encode|=dpd<<8; |
| 3011 | getDPD3q(dpd, 3); encode|=dpd>>2; |
| 3012 | DFWORD(result, 0)=encode; |
| 3013 | encode=dpd<<30; |
| 3014 | getDPD3q(dpd, 2); encode|=dpd<<20; |
| 3015 | getDPD3q(dpd, 1); encode|=dpd<<10; |
| 3016 | getDPD3q(dpd, 0); encode|=dpd; |
| 3017 | DFWORD(result, 1)=encode; |
| 3018 | |
| 3019 | #elif QUAD |
| 3020 | getDPD3q(dpd,10); encode|=dpd<<4; |
| 3021 | getDPD3q(dpd, 9); encode|=dpd>>6; |
| 3022 | DFWORD(result, 0)=encode; |
| 3023 | encode=dpd<<26; |
| 3024 | getDPD3q(dpd, 8); encode|=dpd<<16; |
| 3025 | getDPD3q(dpd, 7); encode|=dpd<<6; |
| 3026 | getDPD3q(dpd, 6); encode|=dpd>>4; |
| 3027 | DFWORD(result, 1)=encode; |
| 3028 | encode=dpd<<28; |
| 3029 | getDPD3q(dpd, 5); encode|=dpd<<18; |
| 3030 | getDPD3q(dpd, 4); encode|=dpd<<8; |
| 3031 | getDPD3q(dpd, 3); encode|=dpd>>2; |
| 3032 | DFWORD(result, 2)=encode; |
| 3033 | encode=dpd<<30; |
| 3034 | getDPD3q(dpd, 2); encode|=dpd<<20; |
| 3035 | getDPD3q(dpd, 1); encode|=dpd<<10; |
| 3036 | getDPD3q(dpd, 0); encode|=dpd; |
| 3037 | DFWORD(result, 3)=encode; |
| 3038 | #endif |
| 3039 | return result; |
| 3040 | } /* decFloatQuantize */ |
| 3041 | |
| 3042 | /* ------------------------------------------------------------------ */ |
| 3043 | /* decFloatReduce -- reduce finite coefficient to minimum length */ |
| 3044 | /* */ |
| 3045 | /* result gets the reduced decFloat */ |
| 3046 | /* df is the source decFloat */ |
| 3047 | /* set is the context */ |
| 3048 | /* returns result, which will be canonical */ |
| 3049 | /* */ |
| 3050 | /* This removes all possible trailing zeros from the coefficient; */ |
| 3051 | /* some may remain when the number is very close to Nmax. */ |
| 3052 | /* Special values are unchanged and no status is set unless df=sNaN. */ |
| 3053 | /* Reduced zero has an exponent q=0. */ |
| 3054 | /* ------------------------------------------------------------------ */ |
| 3055 | decFloat * decFloatReduce(decFloat *result, const decFloat *df, |
| 3056 | decContext *set) { |
| 3057 | bcdnum num; /* work */ |
| 3058 | uByte buf[DECPMAX], *ub; /* coefficient and pointer */ |
| 3059 | if (df!=result) *result=*df; /* copy, if needed */ |
| 3060 | if (DFISNAN(df)) return decNaNs(result, df, NULL, set); /* sNaN */ |
| 3061 | /* zeros and infinites propagate too */ |
| 3062 | if (DFISINF(df)) return decInfinity(result, df); /* canonical */ |
| 3063 | if (DFISZERO(df)) { |
| 3064 | uInt sign=DFWORD(df, 0)&DECFLOAT_Sign; |
| 3065 | decFloatZero(result); |
| 3066 | DFWORD(result, 0)|=sign; |
| 3067 | return result; /* exponent dropped, sign OK */ |
| 3068 | } |
| 3069 | /* non-zero finite */ |
| 3070 | GETCOEFF(df, buf); |
| 3071 | ub=buf+DECPMAX-1; /* -> lsd */ |
| 3072 | if (*ub) return result; /* no trailing zeros */ |
| 3073 | for (ub--; *ub==0;) ub--; /* terminates because non-zero */ |
| 3074 | /* *ub is the first non-zero from the right */ |
| 3075 | num.sign=DFWORD(df, 0)&DECFLOAT_Sign; /* set up number... */ |
| 3076 | num.exponent=GETEXPUN(df)+(Int)(buf+DECPMAX-1-ub); /* adjusted exponent */ |
| 3077 | num.msd=buf; |
| 3078 | num.lsd=ub; |
| 3079 | return decFinalize(result, &num, set); |
| 3080 | } /* decFloatReduce */ |
| 3081 | |
| 3082 | /* ------------------------------------------------------------------ */ |
| 3083 | /* decFloatRemainder -- integer divide and return remainder */ |
| 3084 | /* */ |
| 3085 | /* result gets the remainder of dividing dfl by dfr: */ |
| 3086 | /* dfl is the first decFloat (lhs) */ |
| 3087 | /* dfr is the second decFloat (rhs) */ |
| 3088 | /* set is the context */ |
| 3089 | /* returns result */ |
| 3090 | /* */ |
| 3091 | /* ------------------------------------------------------------------ */ |
| 3092 | decFloat * decFloatRemainder(decFloat *result, |
| 3093 | const decFloat *dfl, const decFloat *dfr, |
| 3094 | decContext *set) { |
| 3095 | return decDivide(result, dfl, dfr, set, REMAINDER); |
| 3096 | } /* decFloatRemainder */ |
| 3097 | |
| 3098 | /* ------------------------------------------------------------------ */ |
| 3099 | /* decFloatRemainderNear -- integer divide to nearest and remainder */ |
| 3100 | /* */ |
| 3101 | /* result gets the remainder of dividing dfl by dfr: */ |
| 3102 | /* dfl is the first decFloat (lhs) */ |
| 3103 | /* dfr is the second decFloat (rhs) */ |
| 3104 | /* set is the context */ |
| 3105 | /* returns result */ |
| 3106 | /* */ |
| 3107 | /* This is the IEEE remainder, where the nearest integer is used. */ |
| 3108 | /* ------------------------------------------------------------------ */ |
| 3109 | decFloat * decFloatRemainderNear(decFloat *result, |
| 3110 | const decFloat *dfl, const decFloat *dfr, |
| 3111 | decContext *set) { |
| 3112 | return decDivide(result, dfl, dfr, set, REMNEAR); |
| 3113 | } /* decFloatRemainderNear */ |
| 3114 | |
| 3115 | /* ------------------------------------------------------------------ */ |
| 3116 | /* decFloatRotate -- rotate the coefficient of a decFloat left/right */ |
| 3117 | /* */ |
| 3118 | /* result gets the result of rotating dfl */ |
| 3119 | /* dfl is the source decFloat to rotate */ |
| 3120 | /* dfr is the count of digits to rotate, an integer (with q=0) */ |
| 3121 | /* set is the context */ |
| 3122 | /* returns result */ |
| 3123 | /* */ |
| 3124 | /* The digits of the coefficient of dfl are rotated to the left (if */ |
| 3125 | /* dfr is positive) or to the right (if dfr is negative) without */ |
| 3126 | /* adjusting the exponent or the sign of dfl. */ |
| 3127 | /* */ |
| 3128 | /* dfr must be in the range -DECPMAX through +DECPMAX. */ |
| 3129 | /* NaNs are propagated as usual. An infinite dfl is unaffected (but */ |
| 3130 | /* dfr must be valid). No status is set unless dfr is invalid or an */ |
| 3131 | /* operand is an sNaN. The result is canonical. */ |
| 3132 | /* ------------------------------------------------------------------ */ |
| 3133 | #define PHALF (ROUNDUP(DECPMAX/2, 4)) /* half length, rounded up */ |
| 3134 | decFloat * decFloatRotate(decFloat *result, |
| 3135 | const decFloat *dfl, const decFloat *dfr, |
| 3136 | decContext *set) { |
| 3137 | Int rotate; /* dfr as an Int */ |
| 3138 | uByte buf[DECPMAX+PHALF]; /* coefficient + half */ |
| 3139 | uInt digits, savestat; /* work */ |
| 3140 | bcdnum num; /* .. */ |
| 3141 | uByte *ub; /* .. */ |
| 3142 | |
| 3143 | if (DFISNAN(dfl)||DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set); |
| 3144 | if (!DFISINT(dfr)) return decInvalid(result, set); |
| 3145 | digits=decFloatDigits(dfr); /* calculate digits */ |
| 3146 | if (digits>2) return decInvalid(result, set); /* definitely out of range */ |
| 3147 | rotate=DPD2BIN[DFWORD(dfr, DECWORDS-1)&0x3ff]; /* is in bottom declet */ |
| 3148 | if (rotate>DECPMAX) return decInvalid(result, set); /* too big */ |
| 3149 | /* [from here on no error or status change is possible] */ |
| 3150 | if (DFISINF(dfl)) return decInfinity(result, dfl); /* canonical */ |
| 3151 | /* handle no-rotate cases */ |
| 3152 | if (rotate==0 || rotate==DECPMAX) return decCanonical(result, dfl); |
| 3153 | /* a real rotate is needed: 0 < rotate < DECPMAX */ |
| 3154 | /* reduce the rotation to no more than half to reduce copying later */ |
| 3155 | /* (for QUAD in fact half + 2 digits) */ |
| 3156 | if (DFISSIGNED(dfr)) rotate=-rotate; |
| 3157 | if (abs(rotate)>PHALF) { |
| 3158 | if (rotate<0) rotate=DECPMAX+rotate; |
| 3159 | else rotate=rotate-DECPMAX; |
| 3160 | } |
| 3161 | /* now lay out the coefficient, leaving room to the right or the */ |
| 3162 | /* left depending on the direction of rotation */ |
| 3163 | ub=buf; |
| 3164 | if (rotate<0) ub+=PHALF; /* rotate right, so space to left */ |
| 3165 | GETCOEFF(dfl, ub); |
| 3166 | /* copy half the digits to left or right, and set num.msd */ |
| 3167 | if (rotate<0) { |
| 3168 | memcpy(buf, buf+DECPMAX, PHALF); |
| 3169 | num.msd=buf+PHALF+rotate; |
| 3170 | } |
| 3171 | else { |
| 3172 | memcpy(buf+DECPMAX, buf, PHALF); |
| 3173 | num.msd=buf+rotate; |
| 3174 | } |
| 3175 | /* fill in rest of num */ |
| 3176 | num.lsd=num.msd+DECPMAX-1; |
| 3177 | num.sign=DFWORD(dfl, 0)&DECFLOAT_Sign; |
| 3178 | num.exponent=GETEXPUN(dfl); |
| 3179 | savestat=set->status; /* record */ |
| 3180 | decFinalize(result, &num, set); |
| 3181 | set->status=savestat; /* restore */ |
| 3182 | return result; |
| 3183 | } /* decFloatRotate */ |
| 3184 | |
| 3185 | /* ------------------------------------------------------------------ */ |
| 3186 | /* decFloatSameQuantum -- test decFloats for same quantum */ |
| 3187 | /* */ |
| 3188 | /* dfl is the first decFloat (lhs) */ |
| 3189 | /* dfr is the second decFloat (rhs) */ |
| 3190 | /* returns 1 if the operands have the same quantum, 0 otherwise */ |
| 3191 | /* */ |
| 3192 | /* No error is possible and no status results. */ |
| 3193 | /* ------------------------------------------------------------------ */ |
| 3194 | uInt decFloatSameQuantum(const decFloat *dfl, const decFloat *dfr) { |
| 3195 | if (DFISSPECIAL(dfl) || DFISSPECIAL(dfr)) { |
| 3196 | if (DFISNAN(dfl) && DFISNAN(dfr)) return 1; |
| 3197 | if (DFISINF(dfl) && DFISINF(dfr)) return 1; |
| 3198 | return 0; /* any other special mixture gives false */ |
| 3199 | } |
| 3200 | if (GETEXP(dfl)==GETEXP(dfr)) return 1; /* biased exponents match */ |
| 3201 | return 0; |
| 3202 | } /* decFloatSameQuantum */ |
| 3203 | |
| 3204 | /* ------------------------------------------------------------------ */ |
| 3205 | /* decFloatScaleB -- multiply by a power of 10, as per 754r */ |
| 3206 | /* */ |
| 3207 | /* result gets the result of the operation */ |
| 3208 | /* dfl is the first decFloat (lhs) */ |
| 3209 | /* dfr is the second decFloat (rhs), am integer (with q=0) */ |
| 3210 | /* set is the context */ |
| 3211 | /* returns result */ |
| 3212 | /* */ |
| 3213 | /* This computes result=dfl x 10**dfr where dfr is an integer in the */ |
| 3214 | /* range +/-2*(emax+pmax), typically resulting from LogB. */ |
| 3215 | /* Underflow and Overflow (with Inexact) may occur. NaNs propagate */ |
| 3216 | /* as usual. */ |
| 3217 | /* ------------------------------------------------------------------ */ |
| 3218 | #define SCALEBMAX 2*(DECEMAX+DECPMAX) /* D=800, Q=12356 */ |
| 3219 | decFloat * decFloatScaleB(decFloat *result, |
| 3220 | const decFloat *dfl, const decFloat *dfr, |
| 3221 | decContext *set) { |
| 3222 | uInt digits; /* work */ |
| 3223 | Int expr; /* dfr as an Int */ |
| 3224 | |
| 3225 | if (DFISNAN(dfl)||DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set); |
| 3226 | if (!DFISINT(dfr)) return decInvalid(result, set); |
| 3227 | digits=decFloatDigits(dfr); /* calculate digits */ |
| 3228 | |
| 3229 | #if DOUBLE |
| 3230 | if (digits>3) return decInvalid(result, set); /* definitely out of range */ |
| 3231 | expr=DPD2BIN[DFWORD(dfr, 1)&0x3ff]; /* must be in bottom declet */ |
| 3232 | #elif QUAD |
| 3233 | if (digits>5) return decInvalid(result, set); /* definitely out of range */ |
| 3234 | expr=DPD2BIN[DFWORD(dfr, 3)&0x3ff] /* in bottom 2 declets .. */ |
| 3235 | +DPD2BIN[(DFWORD(dfr, 3)>>10)&0x3ff]*1000; /* .. */ |
| 3236 | #endif |
| 3237 | if (expr>SCALEBMAX) return decInvalid(result, set); /* oops */ |
| 3238 | /* [from now on no error possible] */ |
| 3239 | if (DFISINF(dfl)) return decInfinity(result, dfl); /* canonical */ |
| 3240 | if (DFISSIGNED(dfr)) expr=-expr; |
| 3241 | /* dfl is finite and expr is valid */ |
| 3242 | *result=*dfl; /* copy to target */ |
| 3243 | return decFloatSetExponent(result, set, GETEXPUN(result)+expr); |
| 3244 | } /* decFloatScaleB */ |
| 3245 | |
| 3246 | /* ------------------------------------------------------------------ */ |
| 3247 | /* decFloatShift -- shift the coefficient of a decFloat left or right */ |
| 3248 | /* */ |
| 3249 | /* result gets the result of shifting dfl */ |
| 3250 | /* dfl is the source decFloat to shift */ |
| 3251 | /* dfr is the count of digits to shift, an integer (with q=0) */ |
| 3252 | /* set is the context */ |
| 3253 | /* returns result */ |
| 3254 | /* */ |
| 3255 | /* The digits of the coefficient of dfl are shifted to the left (if */ |
| 3256 | /* dfr is positive) or to the right (if dfr is negative) without */ |
| 3257 | /* adjusting the exponent or the sign of dfl. */ |
| 3258 | /* */ |
| 3259 | /* dfr must be in the range -DECPMAX through +DECPMAX. */ |
| 3260 | /* NaNs are propagated as usual. An infinite dfl is unaffected (but */ |
| 3261 | /* dfr must be valid). No status is set unless dfr is invalid or an */ |
| 3262 | /* operand is an sNaN. The result is canonical. */ |
| 3263 | /* ------------------------------------------------------------------ */ |
| 3264 | decFloat * decFloatShift(decFloat *result, |
| 3265 | const decFloat *dfl, const decFloat *dfr, |
| 3266 | decContext *set) { |
| 3267 | Int shift; /* dfr as an Int */ |
| 3268 | uByte buf[DECPMAX*2]; /* coefficient + padding */ |
| 3269 | uInt digits, savestat; /* work */ |
| 3270 | bcdnum num; /* .. */ |
| 3271 | |
| 3272 | if (DFISNAN(dfl)||DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set); |
| 3273 | if (!DFISINT(dfr)) return decInvalid(result, set); |
| 3274 | digits=decFloatDigits(dfr); /* calculate digits */ |
| 3275 | if (digits>2) return decInvalid(result, set); /* definitely out of range */ |
| 3276 | shift=DPD2BIN[DFWORD(dfr, DECWORDS-1)&0x3ff]; /* is in bottom declet */ |
| 3277 | if (shift>DECPMAX) return decInvalid(result, set); /* too big */ |
| 3278 | /* [from here on no error or status change is possible] */ |
| 3279 | |
| 3280 | if (DFISINF(dfl)) return decInfinity(result, dfl); /* canonical */ |
| 3281 | /* handle no-shift and all-shift (clear to zero) cases */ |
| 3282 | if (shift==0) return decCanonical(result, dfl); |
| 3283 | if (shift==DECPMAX) { /* zero with sign */ |
| 3284 | uByte sign=(uByte)(DFBYTE(dfl, 0)&0x80); /* save sign bit */ |
| 3285 | decFloatZero(result); /* make +0 */ |
| 3286 | DFBYTE(result, 0)=(uByte)(DFBYTE(result, 0)|sign); /* and set sign */ |
| 3287 | /* [cannot safely use CopySign] */ |
| 3288 | return result; |
| 3289 | } |
| 3290 | /* a real shift is needed: 0 < shift < DECPMAX */ |
| 3291 | num.sign=DFWORD(dfl, 0)&DECFLOAT_Sign; |
| 3292 | num.exponent=GETEXPUN(dfl); |
| 3293 | num.msd=buf; |
| 3294 | GETCOEFF(dfl, buf); |
| 3295 | if (DFISSIGNED(dfr)) { /* shift right */ |
| 3296 | /* edge cases are taken care of, so this is easy */ |
| 3297 | num.lsd=buf+DECPMAX-shift-1; |
| 3298 | } |
| 3299 | else { /* shift left -- zero padding needed to right */ |
| 3300 | UINTAT(buf+DECPMAX)=0; /* 8 will handle most cases */ |
| 3301 | UINTAT(buf+DECPMAX+4)=0; /* .. */ |
| 3302 | if (shift>8) memset(buf+DECPMAX+8, 0, 8+QUAD*18); /* all other cases */ |
| 3303 | num.msd+=shift; |
| 3304 | num.lsd=num.msd+DECPMAX-1; |
| 3305 | } |
| 3306 | savestat=set->status; /* record */ |
| 3307 | decFinalize(result, &num, set); |
| 3308 | set->status=savestat; /* restore */ |
| 3309 | return result; |
| 3310 | } /* decFloatShift */ |
| 3311 | |
| 3312 | /* ------------------------------------------------------------------ */ |
| 3313 | /* decFloatSubtract -- subtract a decFloat from another */ |
| 3314 | /* */ |
| 3315 | /* result gets the result of subtracting dfr from dfl: */ |
| 3316 | /* dfl is the first decFloat (lhs) */ |
| 3317 | /* dfr is the second decFloat (rhs) */ |
| 3318 | /* set is the context */ |
| 3319 | /* returns result */ |
| 3320 | /* */ |
| 3321 | /* ------------------------------------------------------------------ */ |
| 3322 | decFloat * decFloatSubtract(decFloat *result, |
| 3323 | const decFloat *dfl, const decFloat *dfr, |
| 3324 | decContext *set) { |
| 3325 | decFloat temp; |
| 3326 | /* NaNs must propagate without sign change */ |
| 3327 | if (DFISNAN(dfr)) return decFloatAdd(result, dfl, dfr, set); |
| 3328 | temp=*dfr; /* make a copy */ |
| 3329 | DFBYTE(&temp, 0)^=0x80; /* flip sign */ |
| 3330 | return decFloatAdd(result, dfl, &temp, set); /* and add to the lhs */ |
| 3331 | } /* decFloatSubtract */ |
| 3332 | |
| 3333 | /* ------------------------------------------------------------------ */ |
| 3334 | /* decFloatToInt -- round to 32-bit binary integer (4 flavours) */ |
| 3335 | /* */ |
| 3336 | /* df is the decFloat to round */ |
| 3337 | /* set is the context */ |
| 3338 | /* round is the rounding mode to use */ |
| 3339 | /* returns a uInt or an Int, rounded according to the name */ |
| 3340 | /* */ |
| 3341 | /* Invalid will always be signaled if df is a NaN, is Infinite, or is */ |
| 3342 | /* outside the range of the target; Inexact will not be signaled for */ |
| 3343 | /* simple rounding unless 'Exact' appears in the name. */ |
| 3344 | /* ------------------------------------------------------------------ */ |
| 3345 | uInt decFloatToUInt32(const decFloat *df, decContext *set, |
| 3346 | enum rounding round) { |
| 3347 | return decToInt32(df, set, round, 0, 1);} |
| 3348 | |
| 3349 | uInt decFloatToUInt32Exact(const decFloat *df, decContext *set, |
| 3350 | enum rounding round) { |
| 3351 | return decToInt32(df, set, round, 1, 1);} |
| 3352 | |
| 3353 | Int decFloatToInt32(const decFloat *df, decContext *set, |
| 3354 | enum rounding round) { |
| 3355 | return (Int)decToInt32(df, set, round, 0, 0);} |
| 3356 | |
| 3357 | Int decFloatToInt32Exact(const decFloat *df, decContext *set, |
| 3358 | enum rounding round) { |
| 3359 | return (Int)decToInt32(df, set, round, 1, 0);} |
| 3360 | |
| 3361 | /* ------------------------------------------------------------------ */ |
| 3362 | /* decFloatToIntegral -- round to integral value (two flavours) */ |
| 3363 | /* */ |
| 3364 | /* result gets the result */ |
| 3365 | /* df is the decFloat to round */ |
| 3366 | /* set is the context */ |
| 3367 | /* round is the rounding mode to use */ |
| 3368 | /* returns result */ |
| 3369 | /* */ |
| 3370 | /* No exceptions, even Inexact, are raised except for sNaN input, or */ |
| 3371 | /* if 'Exact' appears in the name. */ |
| 3372 | /* ------------------------------------------------------------------ */ |
| 3373 | decFloat * decFloatToIntegralValue(decFloat *result, const decFloat *df, |
| 3374 | decContext *set, enum rounding round) { |
| 3375 | return decToIntegral(result, df, set, round, 0);} |
| 3376 | |
| 3377 | decFloat * decFloatToIntegralExact(decFloat *result, const decFloat *df, |
| 3378 | decContext *set) { |
| 3379 | return decToIntegral(result, df, set, set->round, 1);} |
| 3380 | |
| 3381 | /* ------------------------------------------------------------------ */ |
| 3382 | /* decFloatXor -- logical digitwise XOR of two decFloats */ |
| 3383 | /* */ |
| 3384 | /* result gets the result of XORing dfl and dfr */ |
| 3385 | /* dfl is the first decFloat (lhs) */ |
| 3386 | /* dfr is the second decFloat (rhs) */ |
| 3387 | /* set is the context */ |
| 3388 | /* returns result, which will be canonical with sign=0 */ |
| 3389 | /* */ |
| 3390 | /* The operands must be positive, finite with exponent q=0, and */ |
| 3391 | /* comprise just zeros and ones; if not, Invalid operation results. */ |
| 3392 | /* ------------------------------------------------------------------ */ |
| 3393 | decFloat * decFloatXor(decFloat *result, |
| 3394 | const decFloat *dfl, const decFloat *dfr, |
| 3395 | decContext *set) { |
| 3396 | if (!DFISUINT01(dfl) || !DFISUINT01(dfr) |
| 3397 | || !DFISCC01(dfl) || !DFISCC01(dfr)) return decInvalid(result, set); |
| 3398 | /* the operands are positive finite integers (q=0) with just 0s and 1s */ |
| 3399 | #if DOUBLE |
| 3400 | DFWORD(result, 0)=ZEROWORD |
| 3401 | |((DFWORD(dfl, 0) ^ DFWORD(dfr, 0))&0x04009124); |
| 3402 | DFWORD(result, 1)=(DFWORD(dfl, 1) ^ DFWORD(dfr, 1))&0x49124491; |
| 3403 | #elif QUAD |
| 3404 | DFWORD(result, 0)=ZEROWORD |
| 3405 | |((DFWORD(dfl, 0) ^ DFWORD(dfr, 0))&0x04000912); |
| 3406 | DFWORD(result, 1)=(DFWORD(dfl, 1) ^ DFWORD(dfr, 1))&0x44912449; |
| 3407 | DFWORD(result, 2)=(DFWORD(dfl, 2) ^ DFWORD(dfr, 2))&0x12449124; |
| 3408 | DFWORD(result, 3)=(DFWORD(dfl, 3) ^ DFWORD(dfr, 3))&0x49124491; |
| 3409 | #endif |
| 3410 | return result; |
| 3411 | } /* decFloatXor */ |
| 3412 | |
| 3413 | /* ------------------------------------------------------------------ */ |
| 3414 | /* decInvalid -- set Invalid_operation result */ |
| 3415 | /* */ |
| 3416 | /* result gets a canonical NaN */ |
| 3417 | /* set is the context */ |
| 3418 | /* returns result */ |
| 3419 | /* */ |
| 3420 | /* status has Invalid_operation added */ |
| 3421 | /* ------------------------------------------------------------------ */ |
| 3422 | static decFloat *decInvalid(decFloat *result, decContext *set) { |
| 3423 | decFloatZero(result); |
| 3424 | DFWORD(result, 0)=DECFLOAT_qNaN; |
| 3425 | set->status|=DEC_Invalid_operation; |
| 3426 | return result; |
| 3427 | } /* decInvalid */ |
| 3428 | |
| 3429 | /* ------------------------------------------------------------------ */ |
| 3430 | /* decInfinity -- set canonical Infinity with sign from a decFloat */ |
| 3431 | /* */ |
| 3432 | /* result gets a canonical Infinity */ |
| 3433 | /* df is source decFloat (only the sign is used) */ |
| 3434 | /* returns result */ |
| 3435 | /* */ |
| 3436 | /* df may be the same as result */ |
| 3437 | /* ------------------------------------------------------------------ */ |
| 3438 | static decFloat *decInfinity(decFloat *result, const decFloat *df) { |
| 3439 | uInt sign=DFWORD(df, 0); /* save source signword */ |
| 3440 | decFloatZero(result); /* clear everything */ |
| 3441 | DFWORD(result, 0)=DECFLOAT_Inf | (sign & DECFLOAT_Sign); |
| 3442 | return result; |
| 3443 | } /* decInfinity */ |
| 3444 | |
| 3445 | /* ------------------------------------------------------------------ */ |
| 3446 | /* decNaNs -- handle NaN argument(s) */ |
| 3447 | /* */ |
| 3448 | /* result gets the result of handling dfl and dfr, one or both of */ |
| 3449 | /* which is a NaN */ |
| 3450 | /* dfl is the first decFloat (lhs) */ |
| 3451 | /* dfr is the second decFloat (rhs) -- may be NULL for a single- */ |
| 3452 | /* operand operation */ |
| 3453 | /* set is the context */ |
| 3454 | /* returns result */ |
| 3455 | /* */ |
| 3456 | /* Called when one or both operands is a NaN, and propagates the */ |
| 3457 | /* appropriate result to res. When an sNaN is found, it is changed */ |
| 3458 | /* to a qNaN and Invalid operation is set. */ |
| 3459 | /* ------------------------------------------------------------------ */ |
| 3460 | static decFloat *decNaNs(decFloat *result, |
| 3461 | const decFloat *dfl, const decFloat *dfr, |
| 3462 | decContext *set) { |
| 3463 | /* handle sNaNs first */ |
| 3464 | if (dfr!=NULL && DFISSNAN(dfr) && !DFISSNAN(dfl)) dfl=dfr; /* use RHS */ |
| 3465 | if (DFISSNAN(dfl)) { |
| 3466 | decCanonical(result, dfl); /* propagate canonical sNaN */ |
| 3467 | DFWORD(result, 0)&=~(DECFLOAT_qNaN ^ DECFLOAT_sNaN); /* quiet */ |
| 3468 | set->status|=DEC_Invalid_operation; |
| 3469 | return result; |
| 3470 | } |
| 3471 | /* one or both is a quiet NaN */ |
| 3472 | if (!DFISNAN(dfl)) dfl=dfr; /* RHS must be NaN, use it */ |
| 3473 | return decCanonical(result, dfl); /* propagate canonical qNaN */ |
| 3474 | } /* decNaNs */ |
| 3475 | |
| 3476 | /* ------------------------------------------------------------------ */ |
| 3477 | /* decNumCompare -- numeric comparison of two decFloats */ |
| 3478 | /* */ |
| 3479 | /* dfl is the left-hand decFloat, which is not a NaN */ |
| 3480 | /* dfr is the right-hand decFloat, which is not a NaN */ |
| 3481 | /* tot is 1 for total order compare, 0 for simple numeric */ |
| 3482 | /* returns -1, 0, or +1 for dfl<dfr, dfl=dfr, dfl>dfr */ |
| 3483 | /* */ |
| 3484 | /* No error is possible; status and mode are unchanged. */ |
| 3485 | /* ------------------------------------------------------------------ */ |
| 3486 | static Int decNumCompare(const decFloat *dfl, const decFloat *dfr, Flag tot) { |
| 3487 | Int sigl, sigr; /* LHS and RHS non-0 signums */ |
| 3488 | Int shift; /* shift needed to align operands */ |
| 3489 | uByte *ub, *uc; /* work */ |
| 3490 | /* buffers +2 if Quad (36 digits), need double plus 4 for safe padding */ |
| 3491 | uByte bufl[DECPMAX*2+QUAD*2+4]; /* for LHS coefficient + padding */ |
| 3492 | uByte bufr[DECPMAX*2+QUAD*2+4]; /* for RHS coefficient + padding */ |
| 3493 | |
| 3494 | sigl=1; |
| 3495 | if (DFISSIGNED(dfl)) { |
| 3496 | if (!DFISSIGNED(dfr)) { /* -LHS +RHS */ |
| 3497 | if (DFISZERO(dfl) && DFISZERO(dfr) && !tot) return 0; |
| 3498 | return -1; /* RHS wins */ |
| 3499 | } |
| 3500 | sigl=-1; |
| 3501 | } |
| 3502 | if (DFISSIGNED(dfr)) { |
| 3503 | if (!DFISSIGNED(dfl)) { /* +LHS -RHS */ |
| 3504 | if (DFISZERO(dfl) && DFISZERO(dfr) && !tot) return 0; |
| 3505 | return +1; /* LHS wins */ |
| 3506 | } |
| 3507 | } |
| 3508 | |
| 3509 | /* signs are the same; operand(s) could be zero */ |
| 3510 | sigr=-sigl; /* sign to return if abs(RHS) wins */ |
| 3511 | |
| 3512 | if (DFISINF(dfl)) { |
| 3513 | if (DFISINF(dfr)) return 0; /* both infinite & same sign */ |
| 3514 | return sigl; /* inf > n */ |
| 3515 | } |
| 3516 | if (DFISINF(dfr)) return sigr; /* n < inf [dfl is finite] */ |
| 3517 | |
| 3518 | /* here, both are same sign and finite; calculate their offset */ |
| 3519 | shift=GETEXP(dfl)-GETEXP(dfr); /* [0 means aligned] */ |
| 3520 | /* [bias can be ignored -- the absolute exponent is not relevant] */ |
| 3521 | |
| 3522 | if (DFISZERO(dfl)) { |
| 3523 | if (!DFISZERO(dfr)) return sigr; /* LHS=0, RHS!=0 */ |
| 3524 | /* both are zero, return 0 if both same exponent or numeric compare */ |
| 3525 | if (shift==0 || !tot) return 0; |
| 3526 | if (shift>0) return sigl; |
| 3527 | return sigr; /* [shift<0] */ |
| 3528 | } |
| 3529 | else { /* LHS!=0 */ |
| 3530 | if (DFISZERO(dfr)) return sigl; /* LHS!=0, RHS=0 */ |
| 3531 | } |
| 3532 | /* both are known to be non-zero at this point */ |
| 3533 | |
| 3534 | /* if the exponents are so different that the coefficients do not */ |
| 3535 | /* overlap (by even one digit) then a full comparison is not needed */ |
| 3536 | if (abs(shift)>=DECPMAX) { /* no overlap */ |
| 3537 | /* coefficients are known to be non-zero */ |
| 3538 | if (shift>0) return sigl; |
| 3539 | return sigr; /* [shift<0] */ |
| 3540 | } |
| 3541 | |
| 3542 | /* decode the coefficients */ |
| 3543 | /* (shift both right two if Quad to make a multiple of four) */ |
| 3544 | #if QUAD |
| 3545 | UINTAT(bufl)=0; |
| 3546 | UINTAT(bufr)=0; |
| 3547 | #endif |
| 3548 | GETCOEFF(dfl, bufl+QUAD*2); /* decode from decFloat */ |
| 3549 | GETCOEFF(dfr, bufr+QUAD*2); /* .. */ |
| 3550 | if (shift==0) { /* aligned; common and easy */ |
| 3551 | /* all multiples of four, here */ |
| 3552 | for (ub=bufl, uc=bufr; ub<bufl+DECPMAX+QUAD*2; ub+=4, uc+=4) { |
| 3553 | if (UINTAT(ub)==UINTAT(uc)) continue; /* so far so same */ |
| 3554 | /* about to find a winner; go by bytes in case little-endian */ |
| 3555 | for (;; ub++, uc++) { |
| 3556 | if (*ub>*uc) return sigl; /* difference found */ |
| 3557 | if (*ub<*uc) return sigr; /* .. */ |
| 3558 | } |
| 3559 | } |
| 3560 | } /* aligned */ |
| 3561 | else if (shift>0) { /* lhs to left */ |
| 3562 | ub=bufl; /* RHS pointer */ |
| 3563 | /* pad bufl so right-aligned; most shifts will fit in 8 */ |
| 3564 | UINTAT(bufl+DECPMAX+QUAD*2)=0; /* add eight zeros */ |
| 3565 | UINTAT(bufl+DECPMAX+QUAD*2+4)=0; /* .. */ |
| 3566 | if (shift>8) { |
| 3567 | /* more than eight; fill the rest, and also worth doing the */ |
| 3568 | /* lead-in by fours */ |
| 3569 | uByte *up; /* work */ |
| 3570 | uByte *upend=bufl+DECPMAX+QUAD*2+shift; |
| 3571 | for (up=bufl+DECPMAX+QUAD*2+8; up<upend; up+=4) UINTAT(up)=0; |
| 3572 | /* [pads up to 36 in all for Quad] */ |
| 3573 | for (;; ub+=4) { |
| 3574 | if (UINTAT(ub)!=0) return sigl; |
| 3575 | if (ub+4>bufl+shift-4) break; |
| 3576 | } |
| 3577 | } |
| 3578 | /* check remaining leading digits */ |
| 3579 | for (; ub<bufl+shift; ub++) if (*ub!=0) return sigl; |
| 3580 | /* now start the overlapped part; bufl has been padded, so the */ |
| 3581 | /* comparison can go for the full length of bufr, which is a */ |
| 3582 | /* multiple of 4 bytes */ |
| 3583 | for (uc=bufr; ; uc+=4, ub+=4) { |
| 3584 | if (UINTAT(uc)!=UINTAT(ub)) { /* mismatch found */ |
| 3585 | for (;; uc++, ub++) { /* check from left [little-endian?] */ |
| 3586 | if (*ub>*uc) return sigl; /* difference found */ |
| 3587 | if (*ub<*uc) return sigr; /* .. */ |
| 3588 | } |
| 3589 | } /* mismatch */ |
| 3590 | if (uc==bufr+QUAD*2+DECPMAX-4) break; /* all checked */ |
| 3591 | } |
| 3592 | } /* shift>0 */ |
| 3593 | |
| 3594 | else { /* shift<0) .. RHS is to left of LHS; mirror shift>0 */ |
| 3595 | uc=bufr; /* RHS pointer */ |
| 3596 | /* pad bufr so right-aligned; most shifts will fit in 8 */ |
| 3597 | UINTAT(bufr+DECPMAX+QUAD*2)=0; /* add eight zeros */ |
| 3598 | UINTAT(bufr+DECPMAX+QUAD*2+4)=0; /* .. */ |
| 3599 | if (shift<-8) { |
| 3600 | /* more than eight; fill the rest, and also worth doing the */ |
| 3601 | /* lead-in by fours */ |
| 3602 | uByte *up; /* work */ |
| 3603 | uByte *upend=bufr+DECPMAX+QUAD*2-shift; |
| 3604 | for (up=bufr+DECPMAX+QUAD*2+8; up<upend; up+=4) UINTAT(up)=0; |
| 3605 | /* [pads up to 36 in all for Quad] */ |
| 3606 | for (;; uc+=4) { |
| 3607 | if (UINTAT(uc)!=0) return sigr; |
| 3608 | if (uc+4>bufr-shift-4) break; |
| 3609 | } |
| 3610 | } |
| 3611 | /* check remaining leading digits */ |
| 3612 | for (; uc<bufr-shift; uc++) if (*uc!=0) return sigr; |
| 3613 | /* now start the overlapped part; bufr has been padded, so the */ |
| 3614 | /* comparison can go for the full length of bufl, which is a */ |
| 3615 | /* multiple of 4 bytes */ |
| 3616 | for (ub=bufl; ; ub+=4, uc+=4) { |
| 3617 | if (UINTAT(ub)!=UINTAT(uc)) { /* mismatch found */ |
| 3618 | for (;; ub++, uc++) { /* check from left [little-endian?] */ |
| 3619 | if (*ub>*uc) return sigl; /* difference found */ |
| 3620 | if (*ub<*uc) return sigr; /* .. */ |
| 3621 | } |
| 3622 | } /* mismatch */ |
| 3623 | if (ub==bufl+QUAD*2+DECPMAX-4) break; /* all checked */ |
| 3624 | } |
| 3625 | } /* shift<0 */ |
| 3626 | |
| 3627 | /* Here when compare equal */ |
| 3628 | if (!tot) return 0; /* numerically equal */ |
| 3629 | /* total ordering .. exponent matters */ |
| 3630 | if (shift>0) return sigl; /* total order by exponent */ |
| 3631 | if (shift<0) return sigr; /* .. */ |
| 3632 | return 0; |
| 3633 | } /* decNumCompare */ |
| 3634 | |
| 3635 | /* ------------------------------------------------------------------ */ |
| 3636 | /* decToInt32 -- local routine to effect ToInteger conversions */ |
| 3637 | /* */ |
| 3638 | /* df is the decFloat to convert */ |
| 3639 | /* set is the context */ |
| 3640 | /* rmode is the rounding mode to use */ |
| 3641 | /* exact is 1 if Inexact should be signalled */ |
| 3642 | /* unsign is 1 if the result a uInt, 0 if an Int (cast to uInt) */ |
| 3643 | /* returns 32-bit result as a uInt */ |
| 3644 | /* */ |
| 3645 | /* Invalid is set is df is a NaN, is infinite, or is out-of-range; in */ |
| 3646 | /* these cases 0 is returned. */ |
| 3647 | /* ------------------------------------------------------------------ */ |
| 3648 | static uInt decToInt32(const decFloat *df, decContext *set, |
| 3649 | enum rounding rmode, Flag exact, Flag unsign) { |
| 3650 | Int exp; /* exponent */ |
| 3651 | uInt sourhi, sourpen, sourlo; /* top word from source decFloat .. */ |
| 3652 | uInt hi, lo; /* .. penultimate, least, etc. */ |
| 3653 | decFloat zero, result; /* work */ |
| 3654 | Int i; /* .. */ |
| 3655 | |
| 3656 | /* Start decoding the argument */ |
| 3657 | sourhi=DFWORD(df, 0); /* top word */ |
| 3658 | exp=DECCOMBEXP[sourhi>>26]; /* get exponent high bits (in place) */ |
| 3659 | if (EXPISSPECIAL(exp)) { /* is special? */ |
| 3660 | set->status|=DEC_Invalid_operation; /* signal */ |
| 3661 | return 0; |
| 3662 | } |
| 3663 | |
| 3664 | /* Here when the argument is finite */ |
| 3665 | if (GETEXPUN(df)==0) result=*df; /* already a true integer */ |
| 3666 | else { /* need to round to integer */ |
| 3667 | enum rounding saveround; /* saver */ |
| 3668 | uInt savestatus; /* .. */ |
| 3669 | saveround=set->round; /* save rounding mode .. */ |
| 3670 | savestatus=set->status; /* .. and status */ |
| 3671 | set->round=rmode; /* set mode */ |
| 3672 | decFloatZero(&zero); /* make 0E+0 */ |
| 3673 | set->status=0; /* clear */ |
| 3674 | decFloatQuantize(&result, df, &zero, set); /* [this may fail] */ |
| 3675 | set->round=saveround; /* restore rounding mode .. */ |
| 3676 | if (exact) set->status|=savestatus; /* include Inexact */ |
| 3677 | else set->status=savestatus; /* .. or just original status */ |
| 3678 | } |
| 3679 | |
| 3680 | /* only the last four declets of the coefficient can contain */ |
| 3681 | /* non-zero; check for others (and also NaN or Infinity from the */ |
| 3682 | /* Quantize) first (see DFISZERO for explanation): */ |
| 3683 | /* decFloatShow(&result, "sofar"); */ |
| 3684 | #if DOUBLE |
| 3685 | if ((DFWORD(&result, 0)&0x1c03ff00)!=0 |
| 3686 | || (DFWORD(&result, 0)&0x60000000)==0x60000000) { |
| 3687 | #elif QUAD |
| 3688 | if ((DFWORD(&result, 2)&0xffffff00)!=0 |
| 3689 | || DFWORD(&result, 1)!=0 |
| 3690 | || (DFWORD(&result, 0)&0x1c003fff)!=0 |
| 3691 | || (DFWORD(&result, 0)&0x60000000)==0x60000000) { |
| 3692 | #endif |
| 3693 | set->status|=DEC_Invalid_operation; /* Invalid or out of range */ |
| 3694 | return 0; |
| 3695 | } |
| 3696 | /* get last twelve digits of the coefficent into hi & ho, base */ |
| 3697 | /* 10**9 (see GETCOEFFBILL): */ |
| 3698 | sourlo=DFWORD(&result, DECWORDS-1); |
| 3699 | lo=DPD2BIN0[sourlo&0x3ff] |
| 3700 | +DPD2BINK[(sourlo>>10)&0x3ff] |
| 3701 | +DPD2BINM[(sourlo>>20)&0x3ff]; |
| 3702 | sourpen=DFWORD(&result, DECWORDS-2); |
| 3703 | hi=DPD2BIN0[((sourpen<<2) | (sourlo>>30))&0x3ff]; |
| 3704 | |
| 3705 | /* according to request, check range carefully */ |
| 3706 | if (unsign) { |
| 3707 | if (hi>4 || (hi==4 && lo>294967295) || (hi+lo!=0 && DFISSIGNED(&result))) { |
| 3708 | set->status|=DEC_Invalid_operation; /* out of range */ |
| 3709 | return 0; |
| 3710 | } |
| 3711 | return hi*BILLION+lo; |
| 3712 | } |
| 3713 | /* signed */ |
| 3714 | if (hi>2 || (hi==2 && lo>147483647)) { |
| 3715 | /* handle the usual edge case */ |
| 3716 | if (lo==147483648 && hi==2 && DFISSIGNED(&result)) return 0x80000000; |
| 3717 | set->status|=DEC_Invalid_operation; /* truly out of range */ |
| 3718 | return 0; |
| 3719 | } |
| 3720 | i=hi*BILLION+lo; |
| 3721 | if (DFISSIGNED(&result)) i=-i; |
| 3722 | return (uInt)i; |
| 3723 | } /* decToInt32 */ |
| 3724 | |
| 3725 | /* ------------------------------------------------------------------ */ |
| 3726 | /* decToIntegral -- local routine to effect ToIntegral value */ |
| 3727 | /* */ |
| 3728 | /* result gets the result */ |
| 3729 | /* df is the decFloat to round */ |
| 3730 | /* set is the context */ |
| 3731 | /* rmode is the rounding mode to use */ |
| 3732 | /* exact is 1 if Inexact should be signalled */ |
| 3733 | /* returns result */ |
| 3734 | /* ------------------------------------------------------------------ */ |
| 3735 | static decFloat * decToIntegral(decFloat *result, const decFloat *df, |
| 3736 | decContext *set, enum rounding rmode, |
| 3737 | Flag exact) { |
| 3738 | Int exp; /* exponent */ |
| 3739 | uInt sourhi; /* top word from source decFloat */ |
| 3740 | enum rounding saveround; /* saver */ |
| 3741 | uInt savestatus; /* .. */ |
| 3742 | decFloat zero; /* work */ |
| 3743 | |
| 3744 | /* Start decoding the argument */ |
| 3745 | sourhi=DFWORD(df, 0); /* top word */ |
| 3746 | exp=DECCOMBEXP[sourhi>>26]; /* get exponent high bits (in place) */ |
| 3747 | |
| 3748 | if (EXPISSPECIAL(exp)) { /* is special? */ |
| 3749 | /* NaNs are handled as usual */ |
| 3750 | if (DFISNAN(df)) return decNaNs(result, df, NULL, set); |
| 3751 | /* must be infinite; return canonical infinity with sign of df */ |
| 3752 | return decInfinity(result, df); |
| 3753 | } |
| 3754 | |
| 3755 | /* Here when the argument is finite */ |
| 3756 | /* complete extraction of the exponent */ |
| 3757 | exp+=GETECON(df)-DECBIAS; /* .. + continuation and unbias */ |
| 3758 | |
| 3759 | if (exp>=0) return decCanonical(result, df); /* already integral */ |
| 3760 | |
| 3761 | saveround=set->round; /* save rounding mode .. */ |
| 3762 | savestatus=set->status; /* .. and status */ |
| 3763 | set->round=rmode; /* set mode */ |
| 3764 | decFloatZero(&zero); /* make 0E+0 */ |
| 3765 | decFloatQuantize(result, df, &zero, set); /* 'integrate'; cannot fail */ |
| 3766 | set->round=saveround; /* restore rounding mode .. */ |
| 3767 | if (!exact) set->status=savestatus; /* .. and status, unless exact */ |
| 3768 | return result; |
| 3769 | } /* decToIntegral */ |