1/* Decimal 64-bit format module for the decNumber C Library. 2 Copyright (C) 2005-2015 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 3, or (at your option) any later 10 version. 11 12 GCC is distributed in the hope that it will be useful, but WITHOUT ANY 13 WARRANTY; without even the implied warranty of MERCHANTABILITY or 14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 15 for more details. 16 17Under Section 7 of GPL version 3, you are granted additional 18permissions described in the GCC Runtime Library Exception, version 193.1, as published by the Free Software Foundation. 20 21You should have received a copy of the GNU General Public License and 22a copy of the GCC Runtime Library Exception along with this program; 23see the files COPYING3 and COPYING.RUNTIME respectively. If not, see 24<http://www.gnu.org/licenses/>. */ 25 26/* ------------------------------------------------------------------ */ 27/* Decimal 64-bit format module */ 28/* ------------------------------------------------------------------ */ 29/* This module comprises the routines for decimal64 format numbers. */ 30/* Conversions are supplied to and from decNumber and String. */ 31/* */ 32/* This is used when decNumber provides operations, either for all */ 33/* operations or as a proxy between decNumber and decSingle. */ 34/* */ 35/* Error handling is the same as decNumber (qv.). */ 36/* ------------------------------------------------------------------ */ 37#include <string.h> /* [for memset/memcpy] */ 38#include <stdio.h> /* [for printf] */ 39 40#include "dconfig.h" /* GCC definitions */ 41#define DECNUMDIGITS 16 /* make decNumbers with space for 16 */ 42#include "decNumber.h" /* base number library */ 43#include "decNumberLocal.h" /* decNumber local types, etc. */ 44#include "decimal64.h" /* our primary include */ 45 46/* Utility routines and tables [in decimal64.c]; externs for C++ */ 47extern const uInt COMBEXP[32], COMBMSD[32]; 48extern const uShort DPD2BIN[1024]; 49extern const uShort BIN2DPD[1000]; 50extern const uByte BIN2CHAR[4001]; 51 52extern void decDigitsFromDPD(decNumber *, const uInt *, Int); 53extern void decDigitsToDPD(const decNumber *, uInt *, Int); 54 55#if DECTRACE || DECCHECK 56void decimal64Show(const decimal64 *); /* for debug */ 57extern void decNumberShow(const decNumber *); /* .. */ 58#endif 59 60/* Useful macro */ 61/* Clear a structure (e.g., a decNumber) */ 62#define DEC_clear(d) memset(d, 0, sizeof(*d)) 63 64/* define and include the tables to use for conversions */ 65#define DEC_BIN2CHAR 1 66#define DEC_DPD2BIN 1 67#define DEC_BIN2DPD 1 /* used for all sizes */ 68#include "decDPD.h" /* lookup tables */ 69 70/* ------------------------------------------------------------------ */ 71/* decimal64FromNumber -- convert decNumber to decimal64 */ 72/* */ 73/* ds is the target decimal64 */ 74/* dn is the source number (assumed valid) */ 75/* set is the context, used only for reporting errors */ 76/* */ 77/* The set argument is used only for status reporting and for the */ 78/* rounding mode (used if the coefficient is more than DECIMAL64_Pmax */ 79/* digits or an overflow is detected). If the exponent is out of the */ 80/* valid range then Overflow or Underflow will be raised. */ 81/* After Underflow a subnormal result is possible. */ 82/* */ 83/* DEC_Clamped is set if the number has to be 'folded down' to fit, */ 84/* by reducing its exponent and multiplying the coefficient by a */ 85/* power of ten, or if the exponent on a zero had to be clamped. */ 86/* ------------------------------------------------------------------ */ 87decimal64 * decimal64FromNumber(decimal64 *d64, const decNumber *dn, 88 decContext *set) { 89 uInt status=0; /* status accumulator */ 90 Int ae; /* adjusted exponent */ 91 decNumber dw; /* work */ 92 decContext dc; /* .. */ 93 uInt comb, exp; /* .. */ 94 uInt uiwork; /* for macros */ 95 uInt targar[2]={0, 0}; /* target 64-bit */ 96 #define targhi targar[1] /* name the word with the sign */ 97 #define targlo targar[0] /* and the other */ 98 99 /* If the number has too many digits, or the exponent could be */ 100 /* out of range then reduce the number under the appropriate */ 101 /* constraints. This could push the number to Infinity or zero, */ 102 /* so this check and rounding must be done before generating the */ 103 /* decimal64] */ 104 ae=dn->exponent+dn->digits-1; /* [0 if special] */ 105 if (dn->digits>DECIMAL64_Pmax /* too many digits */ 106 || ae>DECIMAL64_Emax /* likely overflow */ 107 || ae<DECIMAL64_Emin) { /* likely underflow */ 108 decContextDefault(&dc, DEC_INIT_DECIMAL64); /* [no traps] */ 109 dc.round=set->round; /* use supplied rounding */ 110 decNumberPlus(&dw, dn, &dc); /* (round and check) */ 111 /* [this changes -0 to 0, so enforce the sign...] */ 112 dw.bits|=dn->bits&DECNEG; 113 status=dc.status; /* save status */ 114 dn=&dw; /* use the work number */ 115 } /* maybe out of range */ 116 117 if (dn->bits&DECSPECIAL) { /* a special value */ 118 if (dn->bits&DECINF) targhi=DECIMAL_Inf<<24; 119 else { /* sNaN or qNaN */ 120 if ((*dn->lsu!=0 || dn->digits>1) /* non-zero coefficient */ 121 && (dn->digits<DECIMAL64_Pmax)) { /* coefficient fits */ 122 decDigitsToDPD(dn, targar, 0); 123 } 124 if (dn->bits&DECNAN) targhi|=DECIMAL_NaN<<24; 125 else targhi|=DECIMAL_sNaN<<24; 126 } /* a NaN */ 127 } /* special */ 128 129 else { /* is finite */ 130 if (decNumberIsZero(dn)) { /* is a zero */ 131 /* set and clamp exponent */ 132 if (dn->exponent<-DECIMAL64_Bias) { 133 exp=0; /* low clamp */ 134 status|=DEC_Clamped; 135 } 136 else { 137 exp=dn->exponent+DECIMAL64_Bias; /* bias exponent */ 138 if (exp>DECIMAL64_Ehigh) { /* top clamp */ 139 exp=DECIMAL64_Ehigh; 140 status|=DEC_Clamped; 141 } 142 } 143 comb=(exp>>5) & 0x18; /* msd=0, exp top 2 bits .. */ 144 } 145 else { /* non-zero finite number */ 146 uInt msd; /* work */ 147 Int pad=0; /* coefficient pad digits */ 148 149 /* the dn is known to fit, but it may need to be padded */ 150 exp=(uInt)(dn->exponent+DECIMAL64_Bias); /* bias exponent */ 151 if (exp>DECIMAL64_Ehigh) { /* fold-down case */ 152 pad=exp-DECIMAL64_Ehigh; 153 exp=DECIMAL64_Ehigh; /* [to maximum] */ 154 status|=DEC_Clamped; 155 } 156 157 /* fastpath common case */ 158 if (DECDPUN==3 && pad==0) { 159 uInt dpd[6]={0,0,0,0,0,0}; 160 uInt i; 161 Int d=dn->digits; 162 for (i=0; d>0; i++, d-=3) dpd[i]=BIN2DPD[dn->lsu[i]]; 163 targlo =dpd[0]; 164 targlo|=dpd[1]<<10; 165 targlo|=dpd[2]<<20; 166 if (dn->digits>6) { 167 targlo|=dpd[3]<<30; 168 targhi =dpd[3]>>2; 169 targhi|=dpd[4]<<8; 170 } 171 msd=dpd[5]; /* [did not really need conversion] */ 172 } 173 else { /* general case */ 174 decDigitsToDPD(dn, targar, pad); 175 /* save and clear the top digit */ 176 msd=targhi>>18; 177 targhi&=0x0003ffff; 178 } 179 180 /* create the combination field */ 181 if (msd>=8) comb=0x18 | ((exp>>7) & 0x06) | (msd & 0x01); 182 else comb=((exp>>5) & 0x18) | msd; 183 } 184 targhi|=comb<<26; /* add combination field .. */ 185 targhi|=(exp&0xff)<<18; /* .. and exponent continuation */ 186 } /* finite */ 187 188 if (dn->bits&DECNEG) targhi|=0x80000000; /* add sign bit */ 189 190 /* now write to storage; this is now always endian */ 191 if (DECLITEND) { 192 /* lo int then hi */ 193 UBFROMUI(d64->bytes, targar[0]); 194 UBFROMUI(d64->bytes+4, targar[1]); 195 } 196 else { 197 /* hi int then lo */ 198 UBFROMUI(d64->bytes, targar[1]); 199 UBFROMUI(d64->bytes+4, targar[0]); 200 } 201 202 if (status!=0) decContextSetStatus(set, status); /* pass on status */ 203 /* decimal64Show(d64); */ 204 return d64; 205 } /* decimal64FromNumber */ 206 207/* ------------------------------------------------------------------ */ 208/* decimal64ToNumber -- convert decimal64 to decNumber */ 209/* d64 is the source decimal64 */ 210/* dn is the target number, with appropriate space */ 211/* No error is possible. */ 212/* ------------------------------------------------------------------ */ 213decNumber * decimal64ToNumber(const decimal64 *d64, decNumber *dn) { 214 uInt msd; /* coefficient MSD */ 215 uInt exp; /* exponent top two bits */ 216 uInt comb; /* combination field */ 217 Int need; /* work */ 218 uInt uiwork; /* for macros */ 219 uInt sourar[2]; /* source 64-bit */ 220 #define sourhi sourar[1] /* name the word with the sign */ 221 #define sourlo sourar[0] /* and the lower word */ 222 223 /* load source from storage; this is endian */ 224 if (DECLITEND) { 225 sourlo=UBTOUI(d64->bytes ); /* directly load the low int */ 226 sourhi=UBTOUI(d64->bytes+4); /* then the high int */ 227 } 228 else { 229 sourhi=UBTOUI(d64->bytes ); /* directly load the high int */ 230 sourlo=UBTOUI(d64->bytes+4); /* then the low int */ 231 } 232 233 comb=(sourhi>>26)&0x1f; /* combination field */ 234 235 decNumberZero(dn); /* clean number */ 236 if (sourhi&0x80000000) dn->bits=DECNEG; /* set sign if negative */ 237 238 msd=COMBMSD[comb]; /* decode the combination field */ 239 exp=COMBEXP[comb]; /* .. */ 240 241 if (exp==3) { /* is a special */ 242 if (msd==0) { 243 dn->bits|=DECINF; 244 return dn; /* no coefficient needed */ 245 } 246 else if (sourhi&0x02000000) dn->bits|=DECSNAN; 247 else dn->bits|=DECNAN; 248 msd=0; /* no top digit */ 249 } 250 else { /* is a finite number */ 251 dn->exponent=(exp<<8)+((sourhi>>18)&0xff)-DECIMAL64_Bias; /* unbiased */ 252 } 253 254 /* get the coefficient */ 255 sourhi&=0x0003ffff; /* clean coefficient continuation */ 256 if (msd) { /* non-zero msd */ 257 sourhi|=msd<<18; /* prefix to coefficient */ 258 need=6; /* process 6 declets */ 259 } 260 else { /* msd=0 */ 261 if (!sourhi) { /* top word 0 */ 262 if (!sourlo) return dn; /* easy: coefficient is 0 */ 263 need=3; /* process at least 3 declets */ 264 if (sourlo&0xc0000000) need++; /* process 4 declets */ 265 /* [could reduce some more, here] */ 266 } 267 else { /* some bits in top word, msd=0 */ 268 need=4; /* process at least 4 declets */ 269 if (sourhi&0x0003ff00) need++; /* top declet!=0, process 5 */ 270 } 271 } /*msd=0 */ 272 273 decDigitsFromDPD(dn, sourar, need); /* process declets */ 274 return dn; 275 } /* decimal64ToNumber */ 276 277 278/* ------------------------------------------------------------------ */ 279/* to-scientific-string -- conversion to numeric string */ 280/* to-engineering-string -- conversion to numeric string */ 281/* */ 282/* decimal64ToString(d64, string); */ 283/* decimal64ToEngString(d64, string); */ 284/* */ 285/* d64 is the decimal64 format number to convert */ 286/* string is the string where the result will be laid out */ 287/* */ 288/* string must be at least 24 characters */ 289/* */ 290/* No error is possible, and no status can be set. */ 291/* ------------------------------------------------------------------ */ 292char * decimal64ToEngString(const decimal64 *d64, char *string){ 293 decNumber dn; /* work */ 294 decimal64ToNumber(d64, &dn); 295 decNumberToEngString(&dn, string); 296 return string; 297 } /* decimal64ToEngString */ 298 299char * decimal64ToString(const decimal64 *d64, char *string){ 300 uInt msd; /* coefficient MSD */ 301 Int exp; /* exponent top two bits or full */ 302 uInt comb; /* combination field */ 303 char *cstart; /* coefficient start */ 304 char *c; /* output pointer in string */ 305 const uByte *u; /* work */ 306 char *s, *t; /* .. (source, target) */ 307 Int dpd; /* .. */ 308 Int pre, e; /* .. */ 309 uInt uiwork; /* for macros */ 310 311 uInt sourar[2]; /* source 64-bit */ 312 #define sourhi sourar[1] /* name the word with the sign */ 313 #define sourlo sourar[0] /* and the lower word */ 314 315 /* load source from storage; this is endian */ 316 if (DECLITEND) { 317 sourlo=UBTOUI(d64->bytes ); /* directly load the low int */ 318 sourhi=UBTOUI(d64->bytes+4); /* then the high int */ 319 } 320 else { 321 sourhi=UBTOUI(d64->bytes ); /* directly load the high int */ 322 sourlo=UBTOUI(d64->bytes+4); /* then the low int */ 323 } 324 325 c=string; /* where result will go */ 326 if (((Int)sourhi)<0) *c++='-'; /* handle sign */ 327 328 comb=(sourhi>>26)&0x1f; /* combination field */ 329 msd=COMBMSD[comb]; /* decode the combination field */ 330 exp=COMBEXP[comb]; /* .. */ 331 332 if (exp==3) { 333 if (msd==0) { /* infinity */ 334 strcpy(c, "Inf"); 335 strcpy(c+3, "inity"); 336 return string; /* easy */ 337 } 338 if (sourhi&0x02000000) *c++='s'; /* sNaN */ 339 strcpy(c, "NaN"); /* complete word */ 340 c+=3; /* step past */ 341 if (sourlo==0 && (sourhi&0x0003ffff)==0) return string; /* zero payload */ 342 /* otherwise drop through to add integer; set correct exp */ 343 exp=0; msd=0; /* setup for following code */ 344 } 345 else exp=(exp<<8)+((sourhi>>18)&0xff)-DECIMAL64_Bias; 346 347 /* convert 16 digits of significand to characters */ 348 cstart=c; /* save start of coefficient */ 349 if (msd) *c++='0'+(char)msd; /* non-zero most significant digit */ 350 351 /* Now decode the declets. After extracting each one, it is */ 352 /* decoded to binary and then to a 4-char sequence by table lookup; */ 353 /* the 4-chars are a 1-char length (significant digits, except 000 */ 354 /* has length 0). This allows us to left-align the first declet */ 355 /* with non-zero content, then remaining ones are full 3-char */ 356 /* length. We use fixed-length memcpys because variable-length */ 357 /* causes a subroutine call in GCC. (These are length 4 for speed */ 358 /* and are safe because the array has an extra terminator byte.) */ 359 #define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4]; \ 360 if (c!=cstart) {memcpy(c, u+1, 4); c+=3;} \ 361 else if (*u) {memcpy(c, u+4-*u, 4); c+=*u;} 362 363 dpd=(sourhi>>8)&0x3ff; /* declet 1 */ 364 dpd2char; 365 dpd=((sourhi&0xff)<<2) | (sourlo>>30); /* declet 2 */ 366 dpd2char; 367 dpd=(sourlo>>20)&0x3ff; /* declet 3 */ 368 dpd2char; 369 dpd=(sourlo>>10)&0x3ff; /* declet 4 */ 370 dpd2char; 371 dpd=(sourlo)&0x3ff; /* declet 5 */ 372 dpd2char; 373 374 if (c==cstart) *c++='0'; /* all zeros -- make 0 */ 375 376 if (exp==0) { /* integer or NaN case -- easy */ 377 *c='\0'; /* terminate */ 378 return string; 379 } 380 381 /* non-0 exponent */ 382 e=0; /* assume no E */ 383 pre=c-cstart+exp; 384 /* [here, pre-exp is the digits count (==1 for zero)] */ 385 if (exp>0 || pre<-5) { /* need exponential form */ 386 e=pre-1; /* calculate E value */ 387 pre=1; /* assume one digit before '.' */ 388 } /* exponential form */ 389 390 /* modify the coefficient, adding 0s, '.', and E+nn as needed */ 391 s=c-1; /* source (LSD) */ 392 if (pre>0) { /* ddd.ddd (plain), perhaps with E */ 393 char *dotat=cstart+pre; 394 if (dotat<c) { /* if embedded dot needed... */ 395 t=c; /* target */ 396 for (; s>=dotat; s--, t--) *t=*s; /* open the gap; leave t at gap */ 397 *t='.'; /* insert the dot */ 398 c++; /* length increased by one */ 399 } 400 401 /* finally add the E-part, if needed; it will never be 0, and has */ 402 /* a maximum length of 3 digits */ 403 if (e!=0) { 404 *c++='E'; /* starts with E */ 405 *c++='+'; /* assume positive */ 406 if (e<0) { 407 *(c-1)='-'; /* oops, need '-' */ 408 e=-e; /* uInt, please */ 409 } 410 u=&BIN2CHAR[e*4]; /* -> length byte */ 411 memcpy(c, u+4-*u, 4); /* copy fixed 4 characters [is safe] */ 412 c+=*u; /* bump pointer appropriately */ 413 } 414 *c='\0'; /* add terminator */ 415 /*printf("res %s\n", string); */ 416 return string; 417 } /* pre>0 */ 418 419 /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */ 420 t=c+1-pre; 421 *(t+1)='\0'; /* can add terminator now */ 422 for (; s>=cstart; s--, t--) *t=*s; /* shift whole coefficient right */ 423 c=cstart; 424 *c++='0'; /* always starts with 0. */ 425 *c++='.'; 426 for (; pre<0; pre++) *c++='0'; /* add any 0's after '.' */ 427 /*printf("res %s\n", string); */ 428 return string; 429 } /* decimal64ToString */ 430 431/* ------------------------------------------------------------------ */ 432/* to-number -- conversion from numeric string */ 433/* */ 434/* decimal64FromString(result, string, set); */ 435/* */ 436/* result is the decimal64 format number which gets the result of */ 437/* the conversion */ 438/* *string is the character string which should contain a valid */ 439/* number (which may be a special value) */ 440/* set is the context */ 441/* */ 442/* The context is supplied to this routine is used for error handling */ 443/* (setting of status and traps) and for the rounding mode, only. */ 444/* If an error occurs, the result will be a valid decimal64 NaN. */ 445/* ------------------------------------------------------------------ */ 446decimal64 * decimal64FromString(decimal64 *result, const char *string, 447 decContext *set) { 448 decContext dc; /* work */ 449 decNumber dn; /* .. */ 450 451 decContextDefault(&dc, DEC_INIT_DECIMAL64); /* no traps, please */ 452 dc.round=set->round; /* use supplied rounding */ 453 454 decNumberFromString(&dn, string, &dc); /* will round if needed */ 455 456 decimal64FromNumber(result, &dn, &dc); 457 if (dc.status!=0) { /* something happened */ 458 decContextSetStatus(set, dc.status); /* .. pass it on */ 459 } 460 return result; 461 } /* decimal64FromString */ 462 463/* ------------------------------------------------------------------ */ 464/* decimal64IsCanonical -- test whether encoding is canonical */ 465/* d64 is the source decimal64 */ 466/* returns 1 if the encoding of d64 is canonical, 0 otherwise */ 467/* No error is possible. */ 468/* ------------------------------------------------------------------ */ 469uInt decimal64IsCanonical(const decimal64 *d64) { 470 decNumber dn; /* work */ 471 decimal64 canon; /* .. */ 472 decContext dc; /* .. */ 473 decContextDefault(&dc, DEC_INIT_DECIMAL64); 474 decimal64ToNumber(d64, &dn); 475 decimal64FromNumber(&canon, &dn, &dc);/* canon will now be canonical */ 476 return memcmp(d64, &canon, DECIMAL64_Bytes)==0; 477 } /* decimal64IsCanonical */ 478 479/* ------------------------------------------------------------------ */ 480/* decimal64Canonical -- copy an encoding, ensuring it is canonical */ 481/* d64 is the source decimal64 */ 482/* result is the target (may be the same decimal64) */ 483/* returns result */ 484/* No error is possible. */ 485/* ------------------------------------------------------------------ */ 486decimal64 * decimal64Canonical(decimal64 *result, const decimal64 *d64) { 487 decNumber dn; /* work */ 488 decContext dc; /* .. */ 489 decContextDefault(&dc, DEC_INIT_DECIMAL64); 490 decimal64ToNumber(d64, &dn); 491 decimal64FromNumber(result, &dn, &dc);/* result will now be canonical */ 492 return result; 493 } /* decimal64Canonical */ 494 495#if DECTRACE || DECCHECK 496/* Macros for accessing decimal64 fields. These assume the 497 argument is a reference (pointer) to the decimal64 structure, 498 and the decimal64 is in network byte order (big-endian) */ 499/* Get sign */ 500#define decimal64Sign(d) ((unsigned)(d)->bytes[0]>>7) 501 502/* Get combination field */ 503#define decimal64Comb(d) (((d)->bytes[0] & 0x7c)>>2) 504 505/* Get exponent continuation [does not remove bias] */ 506#define decimal64ExpCon(d) ((((d)->bytes[0] & 0x03)<<6) \ 507 | ((unsigned)(d)->bytes[1]>>2)) 508 509/* Set sign [this assumes sign previously 0] */ 510#define decimal64SetSign(d, b) { \ 511 (d)->bytes[0]|=((unsigned)(b)<<7);} 512 513/* Set exponent continuation [does not apply bias] */ 514/* This assumes range has been checked and exponent previously 0; */ 515/* type of exponent must be unsigned */ 516#define decimal64SetExpCon(d, e) { \ 517 (d)->bytes[0]|=(uByte)((e)>>6); \ 518 (d)->bytes[1]|=(uByte)(((e)&0x3F)<<2);} 519 520/* ------------------------------------------------------------------ */ 521/* decimal64Show -- display a decimal64 in hexadecimal [debug aid] */ 522/* d64 -- the number to show */ 523/* ------------------------------------------------------------------ */ 524/* Also shows sign/cob/expconfields extracted */ 525void decimal64Show(const decimal64 *d64) { 526 char buf[DECIMAL64_Bytes*2+1]; 527 Int i, j=0; 528 529 if (DECLITEND) { 530 for (i=0; i<DECIMAL64_Bytes; i++, j+=2) { 531 sprintf(&buf[j], "%02x", d64->bytes[7-i]); 532 } 533 printf(" D64> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf, 534 d64->bytes[7]>>7, (d64->bytes[7]>>2)&0x1f, 535 ((d64->bytes[7]&0x3)<<6)| (d64->bytes[6]>>2)); 536 } 537 else { /* big-endian */ 538 for (i=0; i<DECIMAL64_Bytes; i++, j+=2) { 539 sprintf(&buf[j], "%02x", d64->bytes[i]); 540 } 541 printf(" D64> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf, 542 decimal64Sign(d64), decimal64Comb(d64), decimal64ExpCon(d64)); 543 } 544 } /* decimal64Show */ 545#endif 546 547/* ================================================================== */ 548/* Shared utility routines and tables */ 549/* ================================================================== */ 550/* define and include the conversion tables to use for shared code */ 551#if DECDPUN==3 552 #define DEC_DPD2BIN 1 553#else 554 #define DEC_DPD2BCD 1 555#endif 556#include "decDPD.h" /* lookup tables */ 557 558/* The maximum number of decNumberUnits needed for a working copy of */ 559/* the units array is the ceiling of digits/DECDPUN, where digits is */ 560/* the maximum number of digits in any of the formats for which this */ 561/* is used. decimal128.h must not be included in this module, so, as */ 562/* a very special case, that number is defined as a literal here. */ 563#define DECMAX754 34 564#define DECMAXUNITS ((DECMAX754+DECDPUN-1)/DECDPUN) 565 566/* ------------------------------------------------------------------ */ 567/* Combination field lookup tables (uInts to save measurable work) */ 568/* */ 569/* COMBEXP - 2-bit most-significant-bits of exponent */ 570/* [11 if an Infinity or NaN] */ 571/* COMBMSD - 4-bit most-significant-digit */ 572/* [0=Infinity, 1=NaN if COMBEXP=11] */ 573/* */ 574/* Both are indexed by the 5-bit combination field (0-31) */ 575/* ------------------------------------------------------------------ */ 576const uInt COMBEXP[32]={0, 0, 0, 0, 0, 0, 0, 0, 577 1, 1, 1, 1, 1, 1, 1, 1, 578 2, 2, 2, 2, 2, 2, 2, 2, 579 0, 0, 1, 1, 2, 2, 3, 3}; 580const uInt COMBMSD[32]={0, 1, 2, 3, 4, 5, 6, 7, 581 0, 1, 2, 3, 4, 5, 6, 7, 582 0, 1, 2, 3, 4, 5, 6, 7, 583 8, 9, 8, 9, 8, 9, 0, 1}; 584 585/* ------------------------------------------------------------------ */ 586/* decDigitsToDPD -- pack coefficient into DPD form */ 587/* */ 588/* dn is the source number (assumed valid, max DECMAX754 digits) */ 589/* targ is 1, 2, or 4-element uInt array, which the caller must */ 590/* have cleared to zeros */ 591/* shift is the number of 0 digits to add on the right (normally 0) */ 592/* */ 593/* The coefficient must be known small enough to fit. The full */ 594/* coefficient is copied, including the leading 'odd' digit. This */ 595/* digit is retrieved and packed into the combination field by the */ 596/* caller. */ 597/* */ 598/* The target uInts are altered only as necessary to receive the */ 599/* digits of the decNumber. When more than one uInt is needed, they */ 600/* are filled from left to right (that is, the uInt at offset 0 will */ 601/* end up with the least-significant digits). */ 602/* */ 603/* shift is used for 'fold-down' padding. */ 604/* */ 605/* No error is possible. */ 606/* ------------------------------------------------------------------ */ 607#if DECDPUN<=4 608/* Constant multipliers for divide-by-power-of five using reciprocal */ 609/* multiply, after removing powers of 2 by shifting, and final shift */ 610/* of 17 [we only need up to **4] */ 611static const uInt multies[]={131073, 26215, 5243, 1049, 210}; 612/* QUOT10 -- macro to return the quotient of unit u divided by 10**n */ 613#define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17) 614#endif 615void decDigitsToDPD(const decNumber *dn, uInt *targ, Int shift) { 616 Int cut; /* work */ 617 Int n; /* output bunch counter */ 618 Int digits=dn->digits; /* digit countdown */ 619 uInt dpd; /* densely packed decimal value */ 620 uInt bin; /* binary value 0-999 */ 621 uInt *uout=targ; /* -> current output uInt */ 622 uInt uoff=0; /* -> current output offset [from right] */ 623 const Unit *inu=dn->lsu; /* -> current input unit */ 624 Unit uar[DECMAXUNITS]; /* working copy of units, iff shifted */ 625 #if DECDPUN!=3 /* not fast path */ 626 Unit in; /* current unit */ 627 #endif 628 629 if (shift!=0) { /* shift towards most significant required */ 630 /* shift the units array to the left by pad digits and copy */ 631 /* [this code is a special case of decShiftToMost, which could */ 632 /* be used instead if exposed and the array were copied first] */ 633 const Unit *source; /* .. */ 634 Unit *target, *first; /* .. */ 635 uInt next=0; /* work */ 636 637 source=dn->lsu+D2U(digits)-1; /* where msu comes from */ 638 target=uar+D2U(digits)-1+D2U(shift);/* where upper part of first cut goes */ 639 cut=DECDPUN-MSUDIGITS(shift); /* where to slice */ 640 if (cut==0) { /* unit-boundary case */ 641 for (; source>=dn->lsu; source--, target--) *target=*source; 642 } 643 else { 644 first=uar+D2U(digits+shift)-1; /* where msu will end up */ 645 for (; source>=dn->lsu; source--, target--) { 646 /* split the source Unit and accumulate remainder for next */ 647 #if DECDPUN<=4 648 uInt quot=QUOT10(*source, cut); 649 uInt rem=*source-quot*DECPOWERS[cut]; 650 next+=quot; 651 #else 652 uInt rem=*source%DECPOWERS[cut]; 653 next+=*source/DECPOWERS[cut]; 654 #endif 655 if (target<=first) *target=(Unit)next; /* write to target iff valid */ 656 next=rem*DECPOWERS[DECDPUN-cut]; /* save remainder for next Unit */ 657 } 658 } /* shift-move */ 659 /* propagate remainder to one below and clear the rest */ 660 for (; target>=uar; target--) { 661 *target=(Unit)next; 662 next=0; 663 } 664 digits+=shift; /* add count (shift) of zeros added */ 665 inu=uar; /* use units in working array */ 666 } 667 668 /* now densely pack the coefficient into DPD declets */ 669 670 #if DECDPUN!=3 /* not fast path */ 671 in=*inu; /* current unit */ 672 cut=0; /* at lowest digit */ 673 bin=0; /* [keep compiler quiet] */ 674 #endif 675 676 for(n=0; digits>0; n++) { /* each output bunch */ 677 #if DECDPUN==3 /* fast path, 3-at-a-time */ 678 bin=*inu; /* 3 digits ready for convert */ 679 digits-=3; /* [may go negative] */ 680 inu++; /* may need another */ 681 682 #else /* must collect digit-by-digit */ 683 Unit dig; /* current digit */ 684 Int j; /* digit-in-declet count */ 685 for (j=0; j<3; j++) { 686 #if DECDPUN<=4 687 Unit temp=(Unit)((uInt)(in*6554)>>16); 688 dig=(Unit)(in-X10(temp)); 689 in=temp; 690 #else 691 dig=in%10; 692 in=in/10; 693 #endif 694 if (j==0) bin=dig; 695 else if (j==1) bin+=X10(dig); 696 else /* j==2 */ bin+=X100(dig); 697 digits--; 698 if (digits==0) break; /* [also protects *inu below] */ 699 cut++; 700 if (cut==DECDPUN) {inu++; in=*inu; cut=0;} 701 } 702 #endif 703 /* here there are 3 digits in bin, or have used all input digits */ 704 705 dpd=BIN2DPD[bin]; 706 707 /* write declet to uInt array */ 708 *uout|=dpd<<uoff; 709 uoff+=10; 710 if (uoff<32) continue; /* no uInt boundary cross */ 711 uout++; 712 uoff-=32; 713 *uout|=dpd>>(10-uoff); /* collect top bits */ 714 } /* n declets */ 715 return; 716 } /* decDigitsToDPD */ 717 718/* ------------------------------------------------------------------ */ 719/* decDigitsFromDPD -- unpack a format's coefficient */ 720/* */ 721/* dn is the target number, with 7, 16, or 34-digit space. */ 722/* sour is a 1, 2, or 4-element uInt array containing only declets */ 723/* declets is the number of (right-aligned) declets in sour to */ 724/* be processed. This may be 1 more than the obvious number in */ 725/* a format, as any top digit is prefixed to the coefficient */ 726/* continuation field. It also may be as small as 1, as the */ 727/* caller may pre-process leading zero declets. */ 728/* */ 729/* When doing the 'extra declet' case care is taken to avoid writing */ 730/* extra digits when there are leading zeros, as these could overflow */ 731/* the units array when DECDPUN is not 3. */ 732/* */ 733/* The target uInts are used only as necessary to process declets */ 734/* declets into the decNumber. When more than one uInt is needed, */ 735/* they are used from left to right (that is, the uInt at offset 0 */ 736/* provides the least-significant digits). */ 737/* */ 738/* dn->digits is set, but not the sign or exponent. */ 739/* No error is possible [the redundant 888 codes are allowed]. */ 740/* ------------------------------------------------------------------ */ 741void decDigitsFromDPD(decNumber *dn, const uInt *sour, Int declets) { 742 743 uInt dpd; /* collector for 10 bits */ 744 Int n; /* counter */ 745 Unit *uout=dn->lsu; /* -> current output unit */ 746 Unit *last=uout; /* will be unit containing msd */ 747 const uInt *uin=sour; /* -> current input uInt */ 748 uInt uoff=0; /* -> current input offset [from right] */ 749 750 #if DECDPUN!=3 751 uInt bcd; /* BCD result */ 752 uInt nibble; /* work */ 753 Unit out=0; /* accumulator */ 754 Int cut=0; /* power of ten in current unit */ 755 #endif 756 #if DECDPUN>4 757 uInt const *pow; /* work */ 758 #endif 759 760 /* Expand the densely-packed integer, right to left */ 761 for (n=declets-1; n>=0; n--) { /* count down declets of 10 bits */ 762 dpd=*uin>>uoff; 763 uoff+=10; 764 if (uoff>32) { /* crossed uInt boundary */ 765 uin++; 766 uoff-=32; 767 dpd|=*uin<<(10-uoff); /* get waiting bits */ 768 } 769 dpd&=0x3ff; /* clear uninteresting bits */ 770 771 #if DECDPUN==3 772 if (dpd==0) *uout=0; 773 else { 774 *uout=DPD2BIN[dpd]; /* convert 10 bits to binary 0-999 */ 775 last=uout; /* record most significant unit */ 776 } 777 uout++; 778 } /* n */ 779 780 #else /* DECDPUN!=3 */ 781 if (dpd==0) { /* fastpath [e.g., leading zeros] */ 782 /* write out three 0 digits (nibbles); out may have digit(s) */ 783 cut++; 784 if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;} 785 if (n==0) break; /* [as below, works even if MSD=0] */ 786 cut++; 787 if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;} 788 cut++; 789 if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;} 790 continue; 791 } 792 793 bcd=DPD2BCD[dpd]; /* convert 10 bits to 12 bits BCD */ 794 795 /* now accumulate the 3 BCD nibbles into units */ 796 nibble=bcd & 0x00f; 797 if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]); 798 cut++; 799 if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;} 800 bcd>>=4; 801 802 /* if this is the last declet and the remaining nibbles in bcd */ 803 /* are 00 then process no more nibbles, because this could be */ 804 /* the 'odd' MSD declet and writing any more Units would then */ 805 /* overflow the unit array */ 806 if (n==0 && !bcd) break; 807 808 nibble=bcd & 0x00f; 809 if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]); 810 cut++; 811 if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;} 812 bcd>>=4; 813 814 nibble=bcd & 0x00f; 815 if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]); 816 cut++; 817 if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;} 818 } /* n */ 819 if (cut!=0) { /* some more left over */ 820 *uout=out; /* write out final unit */ 821 if (out) last=uout; /* and note if non-zero */ 822 } 823 #endif 824 825 /* here, last points to the most significant unit with digits; */ 826 /* inspect it to get the final digits count -- this is essentially */ 827 /* the same code as decGetDigits in decNumber.c */ 828 dn->digits=(last-dn->lsu)*DECDPUN+1; /* floor of digits, plus */ 829 /* must be at least 1 digit */ 830 #if DECDPUN>1 831 if (*last<10) return; /* common odd digit or 0 */ 832 dn->digits++; /* must be 2 at least */ 833 #if DECDPUN>2 834 if (*last<100) return; /* 10-99 */ 835 dn->digits++; /* must be 3 at least */ 836 #if DECDPUN>3 837 if (*last<1000) return; /* 100-999 */ 838 dn->digits++; /* must be 4 at least */ 839 #if DECDPUN>4 840 for (pow=&DECPOWERS[4]; *last>=*pow; pow++) dn->digits++; 841 #endif 842 #endif 843 #endif 844 #endif 845 return; 846 } /*decDigitsFromDPD */ 847