github.com/matrixorigin/matrixone@v0.7.0/cgo/external/decNumber/decimal128.c (about) 1 /* ------------------------------------------------------------------ */ 2 /* Decimal 128-bit format module */ 3 /* ------------------------------------------------------------------ */ 4 /* Copyright (c) IBM Corporation, 2000, 2008. All rights reserved. */ 5 /* */ 6 /* This software is made available under the terms of the */ 7 /* ICU License -- ICU 1.8.1 and later. */ 8 /* */ 9 /* The description and User's Guide ("The decNumber C Library") for */ 10 /* this software is called decNumber.pdf. This document is */ 11 /* available, together with arithmetic and format specifications, */ 12 /* testcases, and Web links, on the General Decimal Arithmetic page. */ 13 /* */ 14 /* Please send comments, suggestions, and corrections to the author: */ 15 /* mfc@uk.ibm.com */ 16 /* Mike Cowlishaw, IBM Fellow */ 17 /* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ 18 /* ------------------------------------------------------------------ */ 19 /* This module comprises the routines for decimal128 format numbers. */ 20 /* Conversions are supplied to and from decNumber and String. */ 21 /* */ 22 /* This is used when decNumber provides operations, either for all */ 23 /* operations or as a proxy between decNumber and decSingle. */ 24 /* */ 25 /* Error handling is the same as decNumber (qv.). */ 26 /* ------------------------------------------------------------------ */ 27 #include <string.h> // [for memset/memcpy] 28 #include <stdio.h> // [for printf] 29 30 #define DECNUMDIGITS 34 // make decNumbers with space for 34 31 #include "decNumber.h" // base number library 32 #include "decNumberLocal.h" // decNumber local types, etc. 33 #include "decimal128.h" // our primary include 34 35 /* Utility routines and tables [in decimal64.c] */ 36 // DPD2BIN and the reverse are renamed to prevent link-time conflict 37 // if decQuad is also built in the same executable 38 #define DPD2BIN DPD2BINx 39 #define BIN2DPD BIN2DPDx 40 extern const uInt COMBEXP[32], COMBMSD[32]; 41 extern const uShort DPD2BIN[1024]; 42 extern const uShort BIN2DPD[1000]; // [not used] 43 extern const uByte BIN2CHAR[4001]; 44 45 extern void decDigitsFromDPD(decNumber *, const uInt *, Int); 46 extern void decDigitsToDPD(const decNumber *, uInt *, Int); 47 48 #if DECTRACE || DECCHECK 49 void decimal128Show(const decimal128 *); // for debug 50 extern void decNumberShow(const decNumber *); // .. 51 #endif 52 53 /* Useful macro */ 54 // Clear a structure (e.g., a decNumber) 55 #define DEC_clear(d) memset(d, 0, sizeof(*d)) 56 57 /* ------------------------------------------------------------------ */ 58 /* decimal128FromNumber -- convert decNumber to decimal128 */ 59 /* */ 60 /* ds is the target decimal128 */ 61 /* dn is the source number (assumed valid) */ 62 /* set is the context, used only for reporting errors */ 63 /* */ 64 /* The set argument is used only for status reporting and for the */ 65 /* rounding mode (used if the coefficient is more than DECIMAL128_Pmax*/ 66 /* digits or an overflow is detected). If the exponent is out of the */ 67 /* valid range then Overflow or Underflow will be raised. */ 68 /* After Underflow a subnormal result is possible. */ 69 /* */ 70 /* DEC_Clamped is set if the number has to be 'folded down' to fit, */ 71 /* by reducing its exponent and multiplying the coefficient by a */ 72 /* power of ten, or if the exponent on a zero had to be clamped. */ 73 /* ------------------------------------------------------------------ */ 74 decimal128 * decimal128FromNumber(decimal128 *d128, const decNumber *dn, 75 decContext *set) { 76 uInt status=0; // status accumulator 77 Int ae; // adjusted exponent 78 decNumber dw; // work 79 decContext dc; // .. 80 uInt comb, exp; // .. 81 uInt uiwork; // for macros 82 uInt targar[4]={0,0,0,0}; // target 128-bit 83 #define targhi targar[3] // name the word with the sign 84 #define targmh targar[2] // name the words 85 #define targml targar[1] // .. 86 #define targlo targar[0] // .. 87 88 // If the number has too many digits, or the exponent could be 89 // out of range then reduce the number under the appropriate 90 // constraints. This could push the number to Infinity or zero, 91 // so this check and rounding must be done before generating the 92 // decimal128] 93 ae=dn->exponent+dn->digits-1; // [0 if special] 94 if (dn->digits>DECIMAL128_Pmax // too many digits 95 || ae>DECIMAL128_Emax // likely overflow 96 || ae<DECIMAL128_Emin) { // likely underflow 97 decContextDefault(&dc, DEC_INIT_DECIMAL128); // [no traps] 98 dc.round=set->round; // use supplied rounding 99 decNumberPlus(&dw, dn, &dc); // (round and check) 100 // [this changes -0 to 0, so enforce the sign...] 101 dw.bits|=dn->bits&DECNEG; 102 status=dc.status; // save status 103 dn=&dw; // use the work number 104 } // maybe out of range 105 106 if (dn->bits&DECSPECIAL) { // a special value 107 if (dn->bits&DECINF) targhi=DECIMAL_Inf<<24; 108 else { // sNaN or qNaN 109 if ((*dn->lsu!=0 || dn->digits>1) // non-zero coefficient 110 && (dn->digits<DECIMAL128_Pmax)) { // coefficient fits 111 decDigitsToDPD(dn, targar, 0); 112 } 113 if (dn->bits&DECNAN) targhi|=DECIMAL_NaN<<24; 114 else targhi|=DECIMAL_sNaN<<24; 115 } // a NaN 116 } // special 117 118 else { // is finite 119 if (decNumberIsZero(dn)) { // is a zero 120 // set and clamp exponent 121 if (dn->exponent<-DECIMAL128_Bias) { 122 exp=0; // low clamp 123 status|=DEC_Clamped; 124 } 125 else { 126 exp=dn->exponent+DECIMAL128_Bias; // bias exponent 127 if (exp>DECIMAL128_Ehigh) { // top clamp 128 exp=DECIMAL128_Ehigh; 129 status|=DEC_Clamped; 130 } 131 } 132 comb=(exp>>9) & 0x18; // msd=0, exp top 2 bits .. 133 } 134 else { // non-zero finite number 135 uInt msd; // work 136 Int pad=0; // coefficient pad digits 137 138 // the dn is known to fit, but it may need to be padded 139 exp=(uInt)(dn->exponent+DECIMAL128_Bias); // bias exponent 140 if (exp>DECIMAL128_Ehigh) { // fold-down case 141 pad=exp-DECIMAL128_Ehigh; 142 exp=DECIMAL128_Ehigh; // [to maximum] 143 status|=DEC_Clamped; 144 } 145 146 // [fastpath for common case is not a win, here] 147 decDigitsToDPD(dn, targar, pad); 148 // save and clear the top digit 149 msd=targhi>>14; 150 targhi&=0x00003fff; 151 152 // create the combination field 153 if (msd>=8) comb=0x18 | ((exp>>11) & 0x06) | (msd & 0x01); 154 else comb=((exp>>9) & 0x18) | msd; 155 } 156 targhi|=comb<<26; // add combination field .. 157 targhi|=(exp&0xfff)<<14; // .. and exponent continuation 158 } // finite 159 160 if (dn->bits&DECNEG) targhi|=0x80000000; // add sign bit 161 162 // now write to storage; this is endian 163 if (DECLITEND) { 164 // lo -> hi 165 UBFROMUI(d128->bytes, targlo); 166 UBFROMUI(d128->bytes+4, targml); 167 UBFROMUI(d128->bytes+8, targmh); 168 UBFROMUI(d128->bytes+12, targhi); 169 } 170 else { 171 // hi -> lo 172 UBFROMUI(d128->bytes, targhi); 173 UBFROMUI(d128->bytes+4, targmh); 174 UBFROMUI(d128->bytes+8, targml); 175 UBFROMUI(d128->bytes+12, targlo); 176 } 177 178 if (status!=0) decContextSetStatus(set, status); // pass on status 179 // decimal128Show(d128); 180 return d128; 181 } // decimal128FromNumber 182 183 /* ------------------------------------------------------------------ */ 184 /* decimal128ToNumber -- convert decimal128 to decNumber */ 185 /* d128 is the source decimal128 */ 186 /* dn is the target number, with appropriate space */ 187 /* No error is possible. */ 188 /* ------------------------------------------------------------------ */ 189 decNumber * decimal128ToNumber(const decimal128 *d128, decNumber *dn) { 190 uInt msd; // coefficient MSD 191 uInt exp; // exponent top two bits 192 uInt comb; // combination field 193 Int need; // work 194 uInt uiwork; // for macros 195 uInt sourar[4]; // source 128-bit 196 #define sourhi sourar[3] // name the word with the sign 197 #define sourmh sourar[2] // and the mid-high word 198 #define sourml sourar[1] // and the mod-low word 199 #define sourlo sourar[0] // and the lowest word 200 201 // load source from storage; this is endian 202 if (DECLITEND) { 203 sourlo=UBTOUI(d128->bytes ); // directly load the low int 204 sourml=UBTOUI(d128->bytes+4 ); // then the mid-low 205 sourmh=UBTOUI(d128->bytes+8 ); // then the mid-high 206 sourhi=UBTOUI(d128->bytes+12); // then the high int 207 } 208 else { 209 sourhi=UBTOUI(d128->bytes ); // directly load the high int 210 sourmh=UBTOUI(d128->bytes+4 ); // then the mid-high 211 sourml=UBTOUI(d128->bytes+8 ); // then the mid-low 212 sourlo=UBTOUI(d128->bytes+12); // then the low int 213 } 214 215 comb=(sourhi>>26)&0x1f; // combination field 216 217 decNumberZero(dn); // clean number 218 if (sourhi&0x80000000) dn->bits=DECNEG; // set sign if negative 219 220 msd=COMBMSD[comb]; // decode the combination field 221 exp=COMBEXP[comb]; // .. 222 223 if (exp==3) { // is a special 224 if (msd==0) { 225 dn->bits|=DECINF; 226 return dn; // no coefficient needed 227 } 228 else if (sourhi&0x02000000) dn->bits|=DECSNAN; 229 else dn->bits|=DECNAN; 230 msd=0; // no top digit 231 } 232 else { // is a finite number 233 dn->exponent=(exp<<12)+((sourhi>>14)&0xfff)-DECIMAL128_Bias; // unbiased 234 } 235 236 // get the coefficient 237 sourhi&=0x00003fff; // clean coefficient continuation 238 if (msd) { // non-zero msd 239 sourhi|=msd<<14; // prefix to coefficient 240 need=12; // process 12 declets 241 } 242 else { // msd=0 243 if (sourhi) need=11; // declets to process 244 else if (sourmh) need=10; 245 else if (sourml) need=7; 246 else if (sourlo) need=4; 247 else return dn; // easy: coefficient is 0 248 } //msd=0 249 250 decDigitsFromDPD(dn, sourar, need); // process declets 251 // decNumberShow(dn); 252 return dn; 253 } // decimal128ToNumber 254 255 /* ------------------------------------------------------------------ */ 256 /* to-scientific-string -- conversion to numeric string */ 257 /* to-engineering-string -- conversion to numeric string */ 258 /* */ 259 /* decimal128ToString(d128, string); */ 260 /* decimal128ToEngString(d128, string); */ 261 /* */ 262 /* d128 is the decimal128 format number to convert */ 263 /* string is the string where the result will be laid out */ 264 /* */ 265 /* string must be at least 24 characters */ 266 /* */ 267 /* No error is possible, and no status can be set. */ 268 /* ------------------------------------------------------------------ */ 269 char * decimal128ToEngString(const decimal128 *d128, char *string){ 270 decNumber dn; // work 271 decimal128ToNumber(d128, &dn); 272 decNumberToEngString(&dn, string); 273 return string; 274 } // decimal128ToEngString 275 276 char * decimal128ToString(const decimal128 *d128, char *string){ 277 uInt msd; // coefficient MSD 278 Int exp; // exponent top two bits or full 279 uInt comb; // combination field 280 char *cstart; // coefficient start 281 char *c; // output pointer in string 282 const uByte *u; // work 283 char *s, *t; // .. (source, target) 284 Int dpd; // .. 285 Int pre, e; // .. 286 uInt uiwork; // for macros 287 288 uInt sourar[4]; // source 128-bit 289 #define sourhi sourar[3] // name the word with the sign 290 #define sourmh sourar[2] // and the mid-high word 291 #define sourml sourar[1] // and the mod-low word 292 #define sourlo sourar[0] // and the lowest word 293 294 // load source from storage; this is endian 295 if (DECLITEND) { 296 sourlo=UBTOUI(d128->bytes ); // directly load the low int 297 sourml=UBTOUI(d128->bytes+4 ); // then the mid-low 298 sourmh=UBTOUI(d128->bytes+8 ); // then the mid-high 299 sourhi=UBTOUI(d128->bytes+12); // then the high int 300 } 301 else { 302 sourhi=UBTOUI(d128->bytes ); // directly load the high int 303 sourmh=UBTOUI(d128->bytes+4 ); // then the mid-high 304 sourml=UBTOUI(d128->bytes+8 ); // then the mid-low 305 sourlo=UBTOUI(d128->bytes+12); // then the low int 306 } 307 308 c=string; // where result will go 309 if (((Int)sourhi)<0) *c++='-'; // handle sign 310 311 comb=(sourhi>>26)&0x1f; // combination field 312 msd=COMBMSD[comb]; // decode the combination field 313 exp=COMBEXP[comb]; // .. 314 315 if (exp==3) { 316 if (msd==0) { // infinity 317 strcpy(c, "Inf"); 318 strcpy(c+3, "inity"); 319 return string; // easy 320 } 321 if (sourhi&0x02000000) *c++='s'; // sNaN 322 strcpy(c, "NaN"); // complete word 323 c+=3; // step past 324 if (sourlo==0 && sourml==0 && sourmh==0 325 && (sourhi&0x0003ffff)==0) return string; // zero payload 326 // otherwise drop through to add integer; set correct exp 327 exp=0; msd=0; // setup for following code 328 } 329 else exp=(exp<<12)+((sourhi>>14)&0xfff)-DECIMAL128_Bias; // unbiased 330 331 // convert 34 digits of significand to characters 332 cstart=c; // save start of coefficient 333 if (msd) *c++='0'+(char)msd; // non-zero most significant digit 334 335 // Now decode the declets. After extracting each one, it is 336 // decoded to binary and then to a 4-char sequence by table lookup; 337 // the 4-chars are a 1-char length (significant digits, except 000 338 // has length 0). This allows us to left-align the first declet 339 // with non-zero content, then remaining ones are full 3-char 340 // length. We use fixed-length memcpys because variable-length 341 // causes a subroutine call in GCC. (These are length 4 for speed 342 // and are safe because the array has an extra terminator byte.) 343 #define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4]; \ 344 if (c!=cstart) {memcpy(c, u+1, 4); c+=3;} \ 345 else if (*u) {memcpy(c, u+4-*u, 4); c+=*u;} 346 dpd=(sourhi>>4)&0x3ff; // declet 1 347 dpd2char; 348 dpd=((sourhi&0xf)<<6) | (sourmh>>26); // declet 2 349 dpd2char; 350 dpd=(sourmh>>16)&0x3ff; // declet 3 351 dpd2char; 352 dpd=(sourmh>>6)&0x3ff; // declet 4 353 dpd2char; 354 dpd=((sourmh&0x3f)<<4) | (sourml>>28); // declet 5 355 dpd2char; 356 dpd=(sourml>>18)&0x3ff; // declet 6 357 dpd2char; 358 dpd=(sourml>>8)&0x3ff; // declet 7 359 dpd2char; 360 dpd=((sourml&0xff)<<2) | (sourlo>>30); // declet 8 361 dpd2char; 362 dpd=(sourlo>>20)&0x3ff; // declet 9 363 dpd2char; 364 dpd=(sourlo>>10)&0x3ff; // declet 10 365 dpd2char; 366 dpd=(sourlo)&0x3ff; // declet 11 367 dpd2char; 368 369 if (c==cstart) *c++='0'; // all zeros -- make 0 370 371 if (exp==0) { // integer or NaN case -- easy 372 *c='\0'; // terminate 373 return string; 374 } 375 376 /* non-0 exponent */ 377 e=0; // assume no E 378 pre=c-cstart+exp; 379 // [here, pre-exp is the digits count (==1 for zero)] 380 if (exp>0 || pre<-5) { // need exponential form 381 e=pre-1; // calculate E value 382 pre=1; // assume one digit before '.' 383 } // exponential form 384 385 /* modify the coefficient, adding 0s, '.', and E+nn as needed */ 386 s=c-1; // source (LSD) 387 if (pre>0) { // ddd.ddd (plain), perhaps with E 388 char *dotat=cstart+pre; 389 if (dotat<c) { // if embedded dot needed... 390 t=c; // target 391 for (; s>=dotat; s--, t--) *t=*s; // open the gap; leave t at gap 392 *t='.'; // insert the dot 393 c++; // length increased by one 394 } 395 396 // finally add the E-part, if needed; it will never be 0, and has 397 // a maximum length of 4 digits 398 if (e!=0) { 399 *c++='E'; // starts with E 400 *c++='+'; // assume positive 401 if (e<0) { 402 *(c-1)='-'; // oops, need '-' 403 e=-e; // uInt, please 404 } 405 if (e<1000) { // 3 (or fewer) digits case 406 u=&BIN2CHAR[e*4]; // -> length byte 407 memcpy(c, u+4-*u, 4); // copy fixed 4 characters [is safe] 408 c+=*u; // bump pointer appropriately 409 } 410 else { // 4-digits 411 Int thou=((e>>3)*1049)>>17; // e/1000 412 Int rem=e-(1000*thou); // e%1000 413 *c++='0'+(char)thou; 414 u=&BIN2CHAR[rem*4]; // -> length byte 415 memcpy(c, u+1, 4); // copy fixed 3+1 characters [is safe] 416 c+=3; // bump pointer, always 3 digits 417 } 418 } 419 *c='\0'; // add terminator 420 //printf("res %s\n", string); 421 return string; 422 } // pre>0 423 424 /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */ 425 t=c+1-pre; 426 *(t+1)='\0'; // can add terminator now 427 for (; s>=cstart; s--, t--) *t=*s; // shift whole coefficient right 428 c=cstart; 429 *c++='0'; // always starts with 0. 430 *c++='.'; 431 for (; pre<0; pre++) *c++='0'; // add any 0's after '.' 432 //printf("res %s\n", string); 433 return string; 434 } // decimal128ToString 435 436 /* ------------------------------------------------------------------ */ 437 /* to-number -- conversion from numeric string */ 438 /* */ 439 /* decimal128FromString(result, string, set); */ 440 /* */ 441 /* result is the decimal128 format number which gets the result of */ 442 /* the conversion */ 443 /* *string is the character string which should contain a valid */ 444 /* number (which may be a special value) */ 445 /* set is the context */ 446 /* */ 447 /* The context is supplied to this routine is used for error handling */ 448 /* (setting of status and traps) and for the rounding mode, only. */ 449 /* If an error occurs, the result will be a valid decimal128 NaN. */ 450 /* ------------------------------------------------------------------ */ 451 decimal128 * decimal128FromString(decimal128 *result, const char *string, 452 decContext *set) { 453 decContext dc; // work 454 decNumber dn; // .. 455 456 decContextDefault(&dc, DEC_INIT_DECIMAL128); // no traps, please 457 dc.round=set->round; // use supplied rounding 458 459 decNumberFromString(&dn, string, &dc); // will round if needed 460 decimal128FromNumber(result, &dn, &dc); 461 if (dc.status!=0) { // something happened 462 decContextSetStatus(set, dc.status); // .. pass it on 463 } 464 return result; 465 } // decimal128FromString 466 467 /* ------------------------------------------------------------------ */ 468 /* decimal128IsCanonical -- test whether encoding is canonical */ 469 /* d128 is the source decimal128 */ 470 /* returns 1 if the encoding of d128 is canonical, 0 otherwise */ 471 /* No error is possible. */ 472 /* ------------------------------------------------------------------ */ 473 uInt decimal128IsCanonical(const decimal128 *d128) { 474 decNumber dn; // work 475 decimal128 canon; // .. 476 decContext dc; // .. 477 decContextDefault(&dc, DEC_INIT_DECIMAL128); 478 decimal128ToNumber(d128, &dn); 479 decimal128FromNumber(&canon, &dn, &dc);// canon will now be canonical 480 return memcmp(d128, &canon, DECIMAL128_Bytes)==0; 481 } // decimal128IsCanonical 482 483 /* ------------------------------------------------------------------ */ 484 /* decimal128Canonical -- copy an encoding, ensuring it is canonical */ 485 /* d128 is the source decimal128 */ 486 /* result is the target (may be the same decimal128) */ 487 /* returns result */ 488 /* No error is possible. */ 489 /* ------------------------------------------------------------------ */ 490 decimal128 * decimal128Canonical(decimal128 *result, const decimal128 *d128) { 491 decNumber dn; // work 492 decContext dc; // .. 493 decContextDefault(&dc, DEC_INIT_DECIMAL128); 494 decimal128ToNumber(d128, &dn); 495 decimal128FromNumber(result, &dn, &dc);// result will now be canonical 496 return result; 497 } // decimal128Canonical 498 499 #if DECTRACE || DECCHECK 500 /* Macros for accessing decimal128 fields. These assume the argument 501 is a reference (pointer) to the decimal128 structure, and the 502 decimal128 is in network byte order (big-endian) */ 503 // Get sign 504 #define decimal128Sign(d) ((unsigned)(d)->bytes[0]>>7) 505 506 // Get combination field 507 #define decimal128Comb(d) (((d)->bytes[0] & 0x7c)>>2) 508 509 // Get exponent continuation [does not remove bias] 510 #define decimal128ExpCon(d) ((((d)->bytes[0] & 0x03)<<10) \ 511 | ((unsigned)(d)->bytes[1]<<2) \ 512 | ((unsigned)(d)->bytes[2]>>6)) 513 514 // Set sign [this assumes sign previously 0] 515 #define decimal128SetSign(d, b) { \ 516 (d)->bytes[0]|=((unsigned)(b)<<7);} 517 518 // Set exponent continuation [does not apply bias] 519 // This assumes range has been checked and exponent previously 0; 520 // type of exponent must be unsigned 521 #define decimal128SetExpCon(d, e) { \ 522 (d)->bytes[0]|=(uByte)((e)>>10); \ 523 (d)->bytes[1] =(uByte)(((e)&0x3fc)>>2); \ 524 (d)->bytes[2]|=(uByte)(((e)&0x03)<<6);} 525 526 /* ------------------------------------------------------------------ */ 527 /* decimal128Show -- display a decimal128 in hexadecimal [debug aid] */ 528 /* d128 -- the number to show */ 529 /* ------------------------------------------------------------------ */ 530 // Also shows sign/cob/expconfields extracted 531 void decimal128Show(const decimal128 *d128) { 532 char buf[DECIMAL128_Bytes*2+1]; 533 Int i, j=0; 534 535 if (DECLITEND) { 536 for (i=0; i<DECIMAL128_Bytes; i++, j+=2) { 537 sprintf(&buf[j], "%02x", d128->bytes[15-i]); 538 } 539 printf(" D128> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf, 540 d128->bytes[15]>>7, (d128->bytes[15]>>2)&0x1f, 541 ((d128->bytes[15]&0x3)<<10)|(d128->bytes[14]<<2)| 542 (d128->bytes[13]>>6)); 543 } 544 else { 545 for (i=0; i<DECIMAL128_Bytes; i++, j+=2) { 546 sprintf(&buf[j], "%02x", d128->bytes[i]); 547 } 548 printf(" D128> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf, 549 decimal128Sign(d128), decimal128Comb(d128), 550 decimal128ExpCon(d128)); 551 } 552 } // decimal128Show 553 #endif