1/* ------------------------------------------------------------------ */ 2/* Decimal Number arithmetic module */ 3/* ------------------------------------------------------------------ */ 4/* Copyright (c) IBM Corporation, 2000-2012. 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 20/* Modified version, for use from within ICU. 21 * Renamed public functions, to avoid an unwanted export of the 22 * standard names from the ICU library. 23 * 24 * Use ICU's uprv_malloc() and uprv_free() 25 * 26 * Revert comment syntax to plain C 27 * 28 * Remove a few compiler warnings. 29 */ 30 31/* This module comprises the routines for arbitrary-precision General */ 32/* Decimal Arithmetic as defined in the specification which may be */ 33/* found on the General Decimal Arithmetic pages. It implements both */ 34/* the full ('extended') arithmetic and the simpler ('subset') */ 35/* arithmetic. */ 36/* */ 37/* Usage notes: */ 38/* */ 39/* 1. This code is ANSI C89 except: */ 40/* */ 41/* a) C99 line comments (double forward slash) are used. (Most C */ 42/* compilers accept these. If yours does not, a simple script */ 43/* can be used to convert them to ANSI C comments.) */ 44/* */ 45/* b) Types from C99 stdint.h are used. If you do not have this */ 46/* header file, see the User's Guide section of the decNumber */ 47/* documentation; this lists the necessary definitions. */ 48/* */ 49/* c) If DECDPUN>4 or DECUSE64=1, the C99 64-bit int64_t and */ 50/* uint64_t types may be used. To avoid these, set DECUSE64=0 */ 51/* and DECDPUN<=4 (see documentation). */ 52/* */ 53/* The code also conforms to C99 restrictions; in particular, */ 54/* strict aliasing rules are observed. */ 55/* */ 56/* 2. The decNumber format which this library uses is optimized for */ 57/* efficient processing of relatively short numbers; in particular */ 58/* it allows the use of fixed sized structures and minimizes copy */ 59/* and move operations. It does, however, support arbitrary */ 60/* precision (up to 999,999,999 digits) and arbitrary exponent */ 61/* range (Emax in the range 0 through 999,999,999 and Emin in the */ 62/* range -999,999,999 through 0). Mathematical functions (for */ 63/* example decNumberExp) as identified below are restricted more */ 64/* tightly: digits, emax, and -emin in the context must be <= */ 65/* DEC_MAX_MATH (999999), and their operand(s) must be within */ 66/* these bounds. */ 67/* */ 68/* 3. Logical functions are further restricted; their operands must */ 69/* be finite, positive, have an exponent of zero, and all digits */ 70/* must be either 0 or 1. The result will only contain digits */ 71/* which are 0 or 1 (and will have exponent=0 and a sign of 0). */ 72/* */ 73/* 4. Operands to operator functions are never modified unless they */ 74/* are also specified to be the result number (which is always */ 75/* permitted). Other than that case, operands must not overlap. */ 76/* */ 77/* 5. Error handling: the type of the error is ORed into the status */ 78/* flags in the current context (decContext structure). The */ 79/* SIGFPE signal is then raised if the corresponding trap-enabler */ 80/* flag in the decContext is set (is 1). */ 81/* */ 82/* It is the responsibility of the caller to clear the status */ 83/* flags as required. */ 84/* */ 85/* The result of any routine which returns a number will always */ 86/* be a valid number (which may be a special value, such as an */ 87/* Infinity or NaN). */ 88/* */ 89/* 6. The decNumber format is not an exchangeable concrete */ 90/* representation as it comprises fields which may be machine- */ 91/* dependent (packed or unpacked, or special length, for example). */ 92/* Canonical conversions to and from strings are provided; other */ 93/* conversions are available in separate modules. */ 94/* */ 95/* 7. Normally, input operands are assumed to be valid. Set DECCHECK */ 96/* to 1 for extended operand checking (including NULL operands). */ 97/* Results are undefined if a badly-formed structure (or a NULL */ 98/* pointer to a structure) is provided, though with DECCHECK */ 99/* enabled the operator routines are protected against exceptions. */ 100/* (Except if the result pointer is NULL, which is unrecoverable.) */ 101/* */ 102/* However, the routines will never cause exceptions if they are */ 103/* given well-formed operands, even if the value of the operands */ 104/* is inappropriate for the operation and DECCHECK is not set. */ 105/* (Except for SIGFPE, as and where documented.) */ 106/* */ 107/* 8. Subset arithmetic is available only if DECSUBSET is set to 1. */ 108/* ------------------------------------------------------------------ */ 109/* Implementation notes for maintenance of this module: */ 110/* */ 111/* 1. Storage leak protection: Routines which use malloc are not */ 112/* permitted to use return for fastpath or error exits (i.e., */ 113/* they follow strict structured programming conventions). */ 114/* Instead they have a do{}while(0); construct surrounding the */ 115/* code which is protected -- break may be used to exit this. */ 116/* Other routines can safely use the return statement inline. */ 117/* */ 118/* Storage leak accounting can be enabled using DECALLOC. */ 119/* */ 120/* 2. All loops use the for(;;) construct. Any do construct does */ 121/* not loop; it is for allocation protection as just described. */ 122/* */ 123/* 3. Setting status in the context must always be the very last */ 124/* action in a routine, as non-0 status may raise a trap and hence */ 125/* the call to set status may not return (if the handler uses long */ 126/* jump). Therefore all cleanup must be done first. In general, */ 127/* to achieve this status is accumulated and is only applied just */ 128/* before return by calling decContextSetStatus (via decStatus). */ 129/* */ 130/* Routines which allocate storage cannot, in general, use the */ 131/* 'top level' routines which could cause a non-returning */ 132/* transfer of control. The decXxxxOp routines are safe (do not */ 133/* call decStatus even if traps are set in the context) and should */ 134/* be used instead (they are also a little faster). */ 135/* */ 136/* 4. Exponent checking is minimized by allowing the exponent to */ 137/* grow outside its limits during calculations, provided that */ 138/* the decFinalize function is called later. Multiplication and */ 139/* division, and intermediate calculations in exponentiation, */ 140/* require more careful checks because of the risk of 31-bit */ 141/* overflow (the most negative valid exponent is -1999999997, for */ 142/* a 999999999-digit number with adjusted exponent of -999999999). */ 143/* */ 144/* 5. Rounding is deferred until finalization of results, with any */ 145/* 'off to the right' data being represented as a single digit */ 146/* residue (in the range -1 through 9). This avoids any double- */ 147/* rounding when more than one shortening takes place (for */ 148/* example, when a result is subnormal). */ 149/* */ 150/* 6. The digits count is allowed to rise to a multiple of DECDPUN */ 151/* during many operations, so whole Units are handled and exact */ 152/* accounting of digits is not needed. The correct digits value */ 153/* is found by decGetDigits, which accounts for leading zeros. */ 154/* This must be called before any rounding if the number of digits */ 155/* is not known exactly. */ 156/* */ 157/* 7. The multiply-by-reciprocal 'trick' is used for partitioning */ 158/* numbers up to four digits, using appropriate constants. This */ 159/* is not useful for longer numbers because overflow of 32 bits */ 160/* would lead to 4 multiplies, which is almost as expensive as */ 161/* a divide (unless a floating-point or 64-bit multiply is */ 162/* assumed to be available). */ 163/* */ 164/* 8. Unusual abbreviations that may be used in the commentary: */ 165/* lhs -- left hand side (operand, of an operation) */ 166/* lsd -- least significant digit (of coefficient) */ 167/* lsu -- least significant Unit (of coefficient) */ 168/* msd -- most significant digit (of coefficient) */ 169/* msi -- most significant item (in an array) */ 170/* msu -- most significant Unit (of coefficient) */ 171/* rhs -- right hand side (operand, of an operation) */ 172/* +ve -- positive */ 173/* -ve -- negative */ 174/* ** -- raise to the power */ 175/* ------------------------------------------------------------------ */ 176 177#include <stdlib.h> /* for malloc, free, etc. */ 178/* #include <stdio.h> */ /* for printf [if needed] */ 179#include <string.h> /* for strcpy */ 180#include <ctype.h> /* for lower */ 181#include "cmemory.h" /* for uprv_malloc, etc., in ICU */ 182#include "decNumber.h" /* base number library */ 183#include "decNumberLocal.h" /* decNumber local types, etc. */ 184 185/* Constants */ 186/* Public lookup table used by the D2U macro */ 187const uByte d2utable[DECMAXD2U+1]=D2UTABLE; 188 189#define DECVERB 1 /* set to 1 for verbose DECCHECK */ 190#define powers DECPOWERS /* old internal name */ 191 192/* Local constants */ 193#define DIVIDE 0x80 /* Divide operators */ 194#define REMAINDER 0x40 /* .. */ 195#define DIVIDEINT 0x20 /* .. */ 196#define REMNEAR 0x10 /* .. */ 197#define COMPARE 0x01 /* Compare operators */ 198#define COMPMAX 0x02 /* .. */ 199#define COMPMIN 0x03 /* .. */ 200#define COMPTOTAL 0x04 /* .. */ 201#define COMPNAN 0x05 /* .. [NaN processing] */ 202#define COMPSIG 0x06 /* .. [signaling COMPARE] */ 203#define COMPMAXMAG 0x07 /* .. */ 204#define COMPMINMAG 0x08 /* .. */ 205 206#define DEC_sNaN 0x40000000 /* local status: sNaN signal */ 207#define BADINT (Int)0x80000000 /* most-negative Int; error indicator */ 208/* Next two indicate an integer >= 10**6, and its parity (bottom bit) */ 209#define BIGEVEN (Int)0x80000002 210#define BIGODD (Int)0x80000003 211 212static Unit uarrone[1]={1}; /* Unit array of 1, used for incrementing */ 213 214/* Granularity-dependent code */ 215#if DECDPUN<=4 216 #define eInt Int /* extended integer */ 217 #define ueInt uInt /* unsigned extended integer */ 218 /* Constant multipliers for divide-by-power-of five using reciprocal */ 219 /* multiply, after removing powers of 2 by shifting, and final shift */ 220 /* of 17 [we only need up to **4] */ 221 static const uInt multies[]={131073, 26215, 5243, 1049, 210}; 222 /* QUOT10 -- macro to return the quotient of unit u divided by 10**n */ 223 #define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17) 224#else 225 /* For DECDPUN>4 non-ANSI-89 64-bit types are needed. */ 226 #if !DECUSE64 227 #error decNumber.c: DECUSE64 must be 1 when DECDPUN>4 228 #endif 229 #define eInt Long /* extended integer */ 230 #define ueInt uLong /* unsigned extended integer */ 231#endif 232 233/* Local routines */ 234static decNumber * decAddOp(decNumber *, const decNumber *, const decNumber *, 235 decContext *, uByte, uInt *); 236static Flag decBiStr(const char *, const char *, const char *); 237static uInt decCheckMath(const decNumber *, decContext *, uInt *); 238static void decApplyRound(decNumber *, decContext *, Int, uInt *); 239static Int decCompare(const decNumber *lhs, const decNumber *rhs, Flag); 240static decNumber * decCompareOp(decNumber *, const decNumber *, 241 const decNumber *, decContext *, 242 Flag, uInt *); 243static void decCopyFit(decNumber *, const decNumber *, decContext *, 244 Int *, uInt *); 245static decNumber * decDecap(decNumber *, Int); 246static decNumber * decDivideOp(decNumber *, const decNumber *, 247 const decNumber *, decContext *, Flag, uInt *); 248static decNumber * decExpOp(decNumber *, const decNumber *, 249 decContext *, uInt *); 250static void decFinalize(decNumber *, decContext *, Int *, uInt *); 251static Int decGetDigits(Unit *, Int); 252static Int decGetInt(const decNumber *); 253static decNumber * decLnOp(decNumber *, const decNumber *, 254 decContext *, uInt *); 255static decNumber * decMultiplyOp(decNumber *, const decNumber *, 256 const decNumber *, decContext *, 257 uInt *); 258static decNumber * decNaNs(decNumber *, const decNumber *, 259 const decNumber *, decContext *, uInt *); 260static decNumber * decQuantizeOp(decNumber *, const decNumber *, 261 const decNumber *, decContext *, Flag, 262 uInt *); 263static void decReverse(Unit *, Unit *); 264static void decSetCoeff(decNumber *, decContext *, const Unit *, 265 Int, Int *, uInt *); 266static void decSetMaxValue(decNumber *, decContext *); 267static void decSetOverflow(decNumber *, decContext *, uInt *); 268static void decSetSubnormal(decNumber *, decContext *, Int *, uInt *); 269static Int decShiftToLeast(Unit *, Int, Int); 270static Int decShiftToMost(Unit *, Int, Int); 271static void decStatus(decNumber *, uInt, decContext *); 272static void decToString(const decNumber *, char[], Flag); 273static decNumber * decTrim(decNumber *, decContext *, Flag, Flag, Int *); 274static Int decUnitAddSub(const Unit *, Int, const Unit *, Int, Int, 275 Unit *, Int); 276static Int decUnitCompare(const Unit *, Int, const Unit *, Int, Int); 277 278#if !DECSUBSET 279/* decFinish == decFinalize when no subset arithmetic needed */ 280#define decFinish(a,b,c,d) decFinalize(a,b,c,d) 281#else 282static void decFinish(decNumber *, decContext *, Int *, uInt *); 283static decNumber * decRoundOperand(const decNumber *, decContext *, uInt *); 284#endif 285 286/* Local macros */ 287/* masked special-values bits */ 288#define SPECIALARG (rhs->bits & DECSPECIAL) 289#define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL) 290 291/* For use in ICU */ 292#define malloc(a) uprv_malloc(a) 293#define free(a) uprv_free(a) 294 295/* Diagnostic macros, etc. */ 296#if DECALLOC 297/* Handle malloc/free accounting. If enabled, our accountable routines */ 298/* are used; otherwise the code just goes straight to the system malloc */ 299/* and free routines. */ 300#define malloc(a) decMalloc(a) 301#define free(a) decFree(a) 302#define DECFENCE 0x5a /* corruption detector */ 303/* 'Our' malloc and free: */ 304static void *decMalloc(size_t); 305static void decFree(void *); 306uInt decAllocBytes=0; /* count of bytes allocated */ 307/* Note that DECALLOC code only checks for storage buffer overflow. */ 308/* To check for memory leaks, the decAllocBytes variable must be */ 309/* checked to be 0 at appropriate times (e.g., after the test */ 310/* harness completes a set of tests). This checking may be unreliable */ 311/* if the testing is done in a multi-thread environment. */ 312#endif 313 314#if DECCHECK 315/* Optional checking routines. Enabling these means that decNumber */ 316/* and decContext operands to operator routines are checked for */ 317/* correctness. This roughly doubles the execution time of the */ 318/* fastest routines (and adds 600+ bytes), so should not normally be */ 319/* used in 'production'. */ 320/* decCheckInexact is used to check that inexact results have a full */ 321/* complement of digits (where appropriate -- this is not the case */ 322/* for Quantize, for example) */ 323#define DECUNRESU ((decNumber *)(void *)0xffffffff) 324#define DECUNUSED ((const decNumber *)(void *)0xffffffff) 325#define DECUNCONT ((decContext *)(void *)(0xffffffff)) 326static Flag decCheckOperands(decNumber *, const decNumber *, 327 const decNumber *, decContext *); 328static Flag decCheckNumber(const decNumber *); 329static void decCheckInexact(const decNumber *, decContext *); 330#endif 331 332#if DECTRACE || DECCHECK 333/* Optional trace/debugging routines (may or may not be used) */ 334void decNumberShow(const decNumber *); /* displays the components of a number */ 335static void decDumpAr(char, const Unit *, Int); 336#endif 337 338/* ================================================================== */ 339/* Conversions */ 340/* ================================================================== */ 341 342/* ------------------------------------------------------------------ */ 343/* from-int32 -- conversion from Int or uInt */ 344/* */ 345/* dn is the decNumber to receive the integer */ 346/* in or uin is the integer to be converted */ 347/* returns dn */ 348/* */ 349/* No error is possible. */ 350/* ------------------------------------------------------------------ */ 351U_CAPI decNumber * U_EXPORT2 uprv_decNumberFromInt32(decNumber *dn, Int in) { 352 uInt unsig; 353 if (in>=0) unsig=in; 354 else { /* negative (possibly BADINT) */ 355 if (in==BADINT) unsig=(uInt)1073741824*2; /* special case */ 356 else unsig=-in; /* invert */ 357 } 358 /* in is now positive */ 359 uprv_decNumberFromUInt32(dn, unsig); 360 if (in<0) dn->bits=DECNEG; /* sign needed */ 361 return dn; 362 } /* decNumberFromInt32 */ 363 364U_CAPI decNumber * U_EXPORT2 uprv_decNumberFromUInt32(decNumber *dn, uInt uin) { 365 Unit *up; /* work pointer */ 366 uprv_decNumberZero(dn); /* clean */ 367 if (uin==0) return dn; /* [or decGetDigits bad call] */ 368 for (up=dn->lsu; uin>0; up++) { 369 *up=(Unit)(uin%(DECDPUNMAX+1)); 370 uin=uin/(DECDPUNMAX+1); 371 } 372 dn->digits=decGetDigits(dn->lsu, up-dn->lsu); 373 return dn; 374 } /* decNumberFromUInt32 */ 375 376/* ------------------------------------------------------------------ */ 377/* to-int32 -- conversion to Int or uInt */ 378/* */ 379/* dn is the decNumber to convert */ 380/* set is the context for reporting errors */ 381/* returns the converted decNumber, or 0 if Invalid is set */ 382/* */ 383/* Invalid is set if the decNumber does not have exponent==0 or if */ 384/* it is a NaN, Infinite, or out-of-range. */ 385/* ------------------------------------------------------------------ */ 386U_CAPI Int U_EXPORT2 uprv_decNumberToInt32(const decNumber *dn, decContext *set) { 387 #if DECCHECK 388 if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; 389 #endif 390 391 /* special or too many digits, or bad exponent */ 392 if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; /* bad */ 393 else { /* is a finite integer with 10 or fewer digits */ 394 Int d; /* work */ 395 const Unit *up; /* .. */ 396 uInt hi=0, lo; /* .. */ 397 up=dn->lsu; /* -> lsu */ 398 lo=*up; /* get 1 to 9 digits */ 399 #if DECDPUN>1 /* split to higher */ 400 hi=lo/10; 401 lo=lo%10; 402 #endif 403 up++; 404 /* collect remaining Units, if any, into hi */ 405 for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1]; 406 /* now low has the lsd, hi the remainder */ 407 if (hi>214748364 || (hi==214748364 && lo>7)) { /* out of range? */ 408 /* most-negative is a reprieve */ 409 if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000; 410 /* bad -- drop through */ 411 } 412 else { /* in-range always */ 413 Int i=X10(hi)+lo; 414 if (dn->bits&DECNEG) return -i; 415 return i; 416 } 417 } /* integer */ 418 uprv_decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */ 419 return 0; 420 } /* decNumberToInt32 */ 421 422U_CAPI uInt U_EXPORT2 uprv_decNumberToUInt32(const decNumber *dn, decContext *set) { 423 #if DECCHECK 424 if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; 425 #endif 426 /* special or too many digits, or bad exponent, or negative (<0) */ 427 if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0 428 || (dn->bits&DECNEG && !ISZERO(dn))); /* bad */ 429 else { /* is a finite integer with 10 or fewer digits */ 430 Int d; /* work */ 431 const Unit *up; /* .. */ 432 uInt hi=0, lo; /* .. */ 433 up=dn->lsu; /* -> lsu */ 434 lo=*up; /* get 1 to 9 digits */ 435 #if DECDPUN>1 /* split to higher */ 436 hi=lo/10; 437 lo=lo%10; 438 #endif 439 up++; 440 /* collect remaining Units, if any, into hi */ 441 for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1]; 442 443 /* now low has the lsd, hi the remainder */ 444 if (hi>429496729 || (hi==429496729 && lo>5)) ; /* no reprieve possible */ 445 else return X10(hi)+lo; 446 } /* integer */ 447 uprv_decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */ 448 return 0; 449 } /* decNumberToUInt32 */ 450 451/* ------------------------------------------------------------------ */ 452/* to-scientific-string -- conversion to numeric string */ 453/* to-engineering-string -- conversion to numeric string */ 454/* */ 455/* decNumberToString(dn, string); */ 456/* decNumberToEngString(dn, string); */ 457/* */ 458/* dn is the decNumber to convert */ 459/* string is the string where the result will be laid out */ 460/* */ 461/* string must be at least dn->digits+14 characters long */ 462/* */ 463/* No error is possible, and no status can be set. */ 464/* ------------------------------------------------------------------ */ 465U_CAPI char * U_EXPORT2 uprv_decNumberToString(const decNumber *dn, char *string){ 466 decToString(dn, string, 0); 467 return string; 468 } /* DecNumberToString */ 469 470U_CAPI char * U_EXPORT2 uprv_decNumberToEngString(const decNumber *dn, char *string){ 471 decToString(dn, string, 1); 472 return string; 473 } /* DecNumberToEngString */ 474 475/* ------------------------------------------------------------------ */ 476/* to-number -- conversion from numeric string */ 477/* */ 478/* decNumberFromString -- convert string to decNumber */ 479/* dn -- the number structure to fill */ 480/* chars[] -- the string to convert ('\0' terminated) */ 481/* set -- the context used for processing any error, */ 482/* determining the maximum precision available */ 483/* (set.digits), determining the maximum and minimum */ 484/* exponent (set.emax and set.emin), determining if */ 485/* extended values are allowed, and checking the */ 486/* rounding mode if overflow occurs or rounding is */ 487/* needed. */ 488/* */ 489/* The length of the coefficient and the size of the exponent are */ 490/* checked by this routine, so the correct error (Underflow or */ 491/* Overflow) can be reported or rounding applied, as necessary. */ 492/* */ 493/* If bad syntax is detected, the result will be a quiet NaN. */ 494/* ------------------------------------------------------------------ */ 495U_CAPI decNumber * U_EXPORT2 uprv_decNumberFromString(decNumber *dn, const char chars[], 496 decContext *set) { 497 Int exponent=0; /* working exponent [assume 0] */ 498 uByte bits=0; /* working flags [assume +ve] */ 499 Unit *res; /* where result will be built */ 500 Unit resbuff[SD2U(DECBUFFER+9)];/* local buffer in case need temporary */ 501 /* [+9 allows for ln() constants] */ 502 Unit *allocres=NULL; /* -> allocated result, iff allocated */ 503 Int d=0; /* count of digits found in decimal part */ 504 const char *dotchar=NULL; /* where dot was found */ 505 const char *cfirst=chars; /* -> first character of decimal part */ 506 const char *last=NULL; /* -> last digit of decimal part */ 507 const char *c; /* work */ 508 Unit *up; /* .. */ 509 #if DECDPUN>1 510 Int cut, out; /* .. */ 511 #endif 512 Int residue; /* rounding residue */ 513 uInt status=0; /* error code */ 514 515 #if DECCHECK 516 if (decCheckOperands(DECUNRESU, DECUNUSED, DECUNUSED, set)) 517 return uprv_decNumberZero(dn); 518 #endif 519 520 do { /* status & malloc protection */ 521 for (c=chars;; c++) { /* -> input character */ 522 if (*c>='0' && *c<='9') { /* test for Arabic digit */ 523 last=c; 524 d++; /* count of real digits */ 525 continue; /* still in decimal part */ 526 } 527 if (*c=='.' && dotchar==NULL) { /* first '.' */ 528 dotchar=c; /* record offset into decimal part */ 529 if (c==cfirst) cfirst++; /* first digit must follow */ 530 continue;} 531 if (c==chars) { /* first in string... */ 532 if (*c=='-') { /* valid - sign */ 533 cfirst++; 534 bits=DECNEG; 535 continue;} 536 if (*c=='+') { /* valid + sign */ 537 cfirst++; 538 continue;} 539 } 540 /* *c is not a digit, or a valid +, -, or '.' */ 541 break; 542 } /* c */ 543 544 if (last==NULL) { /* no digits yet */ 545 status=DEC_Conversion_syntax;/* assume the worst */ 546 if (*c=='\0') break; /* and no more to come... */ 547 #if DECSUBSET 548 /* if subset then infinities and NaNs are not allowed */ 549 if (!set->extended) break; /* hopeless */ 550 #endif 551 /* Infinities and NaNs are possible, here */ 552 if (dotchar!=NULL) break; /* .. unless had a dot */ 553 uprv_decNumberZero(dn); /* be optimistic */ 554 if (decBiStr(c, "infinity", "INFINITY") 555 || decBiStr(c, "inf", "INF")) { 556 dn->bits=bits | DECINF; 557 status=0; /* is OK */ 558 break; /* all done */ 559 } 560 /* a NaN expected */ 561 /* 2003.09.10 NaNs are now permitted to have a sign */ 562 dn->bits=bits | DECNAN; /* assume simple NaN */ 563 if (*c=='s' || *c=='S') { /* looks like an sNaN */ 564 c++; 565 dn->bits=bits | DECSNAN; 566 } 567 if (*c!='n' && *c!='N') break; /* check caseless "NaN" */ 568 c++; 569 if (*c!='a' && *c!='A') break; /* .. */ 570 c++; 571 if (*c!='n' && *c!='N') break; /* .. */ 572 c++; 573 /* now either nothing, or nnnn payload, expected */ 574 /* -> start of integer and skip leading 0s [including plain 0] */ 575 for (cfirst=c; *cfirst=='0';) cfirst++; 576 if (*cfirst=='\0') { /* "NaN" or "sNaN", maybe with all 0s */ 577 status=0; /* it's good */ 578 break; /* .. */ 579 } 580 /* something other than 0s; setup last and d as usual [no dots] */ 581 for (c=cfirst;; c++, d++) { 582 if (*c<'0' || *c>'9') break; /* test for Arabic digit */ 583 last=c; 584 } 585 if (*c!='\0') break; /* not all digits */ 586 if (d>set->digits-1) { 587 /* [NB: payload in a decNumber can be full length unless */ 588 /* clamped, in which case can only be digits-1] */ 589 if (set->clamp) break; 590 if (d>set->digits) break; 591 } /* too many digits? */ 592 /* good; drop through to convert the integer to coefficient */ 593 status=0; /* syntax is OK */ 594 bits=dn->bits; /* for copy-back */ 595 } /* last==NULL */ 596 597 else if (*c!='\0') { /* more to process... */ 598 /* had some digits; exponent is only valid sequence now */ 599 Flag nege; /* 1=negative exponent */ 600 const char *firstexp; /* -> first significant exponent digit */ 601 status=DEC_Conversion_syntax;/* assume the worst */ 602 if (*c!='e' && *c!='E') break; 603 /* Found 'e' or 'E' -- now process explicit exponent */ 604 /* 1998.07.11: sign no longer required */ 605 nege=0; 606 c++; /* to (possible) sign */ 607 if (*c=='-') {nege=1; c++;} 608 else if (*c=='+') c++; 609 if (*c=='\0') break; 610 611 for (; *c=='0' && *(c+1)!='\0';) c++; /* strip insignificant zeros */ 612 firstexp=c; /* save exponent digit place */ 613 for (; ;c++) { 614 if (*c<'0' || *c>'9') break; /* not a digit */ 615 exponent=X10(exponent)+(Int)*c-(Int)'0'; 616 } /* c */ 617 /* if not now on a '\0', *c must not be a digit */ 618 if (*c!='\0') break; 619 620 /* (this next test must be after the syntax checks) */ 621 /* if it was too long the exponent may have wrapped, so check */ 622 /* carefully and set it to a certain overflow if wrap possible */ 623 if (c>=firstexp+9+1) { 624 if (c>firstexp+9+1 || *firstexp>'1') exponent=DECNUMMAXE*2; 625 /* [up to 1999999999 is OK, for example 1E-1000000998] */ 626 } 627 if (nege) exponent=-exponent; /* was negative */ 628 status=0; /* is OK */ 629 } /* stuff after digits */ 630 631 /* Here when whole string has been inspected; syntax is good */ 632 /* cfirst->first digit (never dot), last->last digit (ditto) */ 633 634 /* strip leading zeros/dot [leave final 0 if all 0's] */ 635 if (*cfirst=='0') { /* [cfirst has stepped over .] */ 636 for (c=cfirst; c<last; c++, cfirst++) { 637 if (*c=='.') continue; /* ignore dots */ 638 if (*c!='0') break; /* non-zero found */ 639 d--; /* 0 stripped */ 640 } /* c */ 641 #if DECSUBSET 642 /* make a rapid exit for easy zeros if !extended */ 643 if (*cfirst=='0' && !set->extended) { 644 uprv_decNumberZero(dn); /* clean result */ 645 break; /* [could be return] */ 646 } 647 #endif 648 } /* at least one leading 0 */ 649 650 /* Handle decimal point... */ 651 if (dotchar!=NULL && dotchar<last) /* non-trailing '.' found? */ 652 exponent-=(last-dotchar); /* adjust exponent */ 653 /* [we can now ignore the .] */ 654 655 /* OK, the digits string is good. Assemble in the decNumber, or in */ 656 /* a temporary units array if rounding is needed */ 657 if (d<=set->digits) res=dn->lsu; /* fits into supplied decNumber */ 658 else { /* rounding needed */ 659 Int needbytes=D2U(d)*sizeof(Unit);/* bytes needed */ 660 res=resbuff; /* assume use local buffer */ 661 if (needbytes>(Int)sizeof(resbuff)) { /* too big for local */ 662 allocres=(Unit *)malloc(needbytes); 663 if (allocres==NULL) {status|=DEC_Insufficient_storage; break;} 664 res=allocres; 665 } 666 } 667 /* res now -> number lsu, buffer, or allocated storage for Unit array */ 668 669 /* Place the coefficient into the selected Unit array */ 670 /* [this is often 70% of the cost of this function when DECDPUN>1] */ 671 #if DECDPUN>1 672 out=0; /* accumulator */ 673 up=res+D2U(d)-1; /* -> msu */ 674 cut=d-(up-res)*DECDPUN; /* digits in top unit */ 675 for (c=cfirst;; c++) { /* along the digits */ 676 if (*c=='.') continue; /* ignore '.' [don't decrement cut] */ 677 out=X10(out)+(Int)*c-(Int)'0'; 678 if (c==last) break; /* done [never get to trailing '.'] */ 679 cut--; 680 if (cut>0) continue; /* more for this unit */ 681 *up=(Unit)out; /* write unit */ 682 up--; /* prepare for unit below.. */ 683 cut=DECDPUN; /* .. */ 684 out=0; /* .. */ 685 } /* c */ 686 *up=(Unit)out; /* write lsu */ 687 688 #else 689 /* DECDPUN==1 */ 690 up=res; /* -> lsu */ 691 for (c=last; c>=cfirst; c--) { /* over each character, from least */ 692 if (*c=='.') continue; /* ignore . [don't step up] */ 693 *up=(Unit)((Int)*c-(Int)'0'); 694 up++; 695 } /* c */ 696 #endif 697 698 dn->bits=bits; 699 dn->exponent=exponent; 700 dn->digits=d; 701 702 /* if not in number (too long) shorten into the number */ 703 if (d>set->digits) { 704 residue=0; 705 decSetCoeff(dn, set, res, d, &residue, &status); 706 /* always check for overflow or subnormal and round as needed */ 707 decFinalize(dn, set, &residue, &status); 708 } 709 else { /* no rounding, but may still have overflow or subnormal */ 710 /* [these tests are just for performance; finalize repeats them] */ 711 if ((dn->exponent-1<set->emin-dn->digits) 712 || (dn->exponent-1>set->emax-set->digits)) { 713 residue=0; 714 decFinalize(dn, set, &residue, &status); 715 } 716 } 717 /* decNumberShow(dn); */ 718 } while(0); /* [for break] */ 719 720 if (allocres!=NULL) free(allocres); /* drop any storage used */ 721 if (status!=0) decStatus(dn, status, set); 722 return dn; 723 } /* decNumberFromString */ 724 725/* ================================================================== */ 726/* Operators */ 727/* ================================================================== */ 728 729/* ------------------------------------------------------------------ */ 730/* decNumberAbs -- absolute value operator */ 731/* */ 732/* This computes C = abs(A) */ 733/* */ 734/* res is C, the result. C may be A */ 735/* rhs is A */ 736/* set is the context */ 737/* */ 738/* See also decNumberCopyAbs for a quiet bitwise version of this. */ 739/* C must have space for set->digits digits. */ 740/* ------------------------------------------------------------------ */ 741/* This has the same effect as decNumberPlus unless A is negative, */ 742/* in which case it has the same effect as decNumberMinus. */ 743/* ------------------------------------------------------------------ */ 744U_CAPI decNumber * U_EXPORT2 uprv_decNumberAbs(decNumber *res, const decNumber *rhs, 745 decContext *set) { 746 decNumber dzero; /* for 0 */ 747 uInt status=0; /* accumulator */ 748 749 #if DECCHECK 750 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 751 #endif 752 753 uprv_decNumberZero(&dzero); /* set 0 */ 754 dzero.exponent=rhs->exponent; /* [no coefficient expansion] */ 755 decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status); 756 if (status!=0) decStatus(res, status, set); 757 #if DECCHECK 758 decCheckInexact(res, set); 759 #endif 760 return res; 761 } /* decNumberAbs */ 762 763/* ------------------------------------------------------------------ */ 764/* decNumberAdd -- add two Numbers */ 765/* */ 766/* This computes C = A + B */ 767/* */ 768/* res is C, the result. C may be A and/or B (e.g., X=X+X) */ 769/* lhs is A */ 770/* rhs is B */ 771/* set is the context */ 772/* */ 773/* C must have space for set->digits digits. */ 774/* ------------------------------------------------------------------ */ 775/* This just calls the routine shared with Subtract */ 776U_CAPI decNumber * U_EXPORT2 uprv_decNumberAdd(decNumber *res, const decNumber *lhs, 777 const decNumber *rhs, decContext *set) { 778 uInt status=0; /* accumulator */ 779 decAddOp(res, lhs, rhs, set, 0, &status); 780 if (status!=0) decStatus(res, status, set); 781 #if DECCHECK 782 decCheckInexact(res, set); 783 #endif 784 return res; 785 } /* decNumberAdd */ 786 787/* ------------------------------------------------------------------ */ 788/* decNumberAnd -- AND two Numbers, digitwise */ 789/* */ 790/* This computes C = A & B */ 791/* */ 792/* res is C, the result. C may be A and/or B (e.g., X=X&X) */ 793/* lhs is A */ 794/* rhs is B */ 795/* set is the context (used for result length and error report) */ 796/* */ 797/* C must have space for set->digits digits. */ 798/* */ 799/* Logical function restrictions apply (see above); a NaN is */ 800/* returned with Invalid_operation if a restriction is violated. */ 801/* ------------------------------------------------------------------ */ 802U_CAPI decNumber * U_EXPORT2 uprv_decNumberAnd(decNumber *res, const decNumber *lhs, 803 const decNumber *rhs, decContext *set) { 804 const Unit *ua, *ub; /* -> operands */ 805 const Unit *msua, *msub; /* -> operand msus */ 806 Unit *uc, *msuc; /* -> result and its msu */ 807 Int msudigs; /* digits in res msu */ 808 #if DECCHECK 809 if (decCheckOperands(res, lhs, rhs, set)) return res; 810 #endif 811 812 if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) 813 || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { 814 decStatus(res, DEC_Invalid_operation, set); 815 return res; 816 } 817 818 /* operands are valid */ 819 ua=lhs->lsu; /* bottom-up */ 820 ub=rhs->lsu; /* .. */ 821 uc=res->lsu; /* .. */ 822 msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */ 823 msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */ 824 msuc=uc+D2U(set->digits)-1; /* -> msu of result */ 825 msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ 826 for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */ 827 Unit a, b; /* extract units */ 828 if (ua>msua) a=0; 829 else a=*ua; 830 if (ub>msub) b=0; 831 else b=*ub; 832 *uc=0; /* can now write back */ 833 if (a|b) { /* maybe 1 bits to examine */ 834 Int i, j; 835 *uc=0; /* can now write back */ 836 /* This loop could be unrolled and/or use BIN2BCD tables */ 837 for (i=0; i<DECDPUN; i++) { 838 if (a&b&1) *uc=*uc+(Unit)powers[i]; /* effect AND */ 839 j=a%10; 840 a=a/10; 841 j|=b%10; 842 b=b/10; 843 if (j>1) { 844 decStatus(res, DEC_Invalid_operation, set); 845 return res; 846 } 847 if (uc==msuc && i==msudigs-1) break; /* just did final digit */ 848 } /* each digit */ 849 } /* both OK */ 850 } /* each unit */ 851 /* [here uc-1 is the msu of the result] */ 852 res->digits=decGetDigits(res->lsu, uc-res->lsu); 853 res->exponent=0; /* integer */ 854 res->bits=0; /* sign=0 */ 855 return res; /* [no status to set] */ 856 } /* decNumberAnd */ 857 858/* ------------------------------------------------------------------ */ 859/* decNumberCompare -- compare two Numbers */ 860/* */ 861/* This computes C = A ? B */ 862/* */ 863/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ 864/* lhs is A */ 865/* rhs is B */ 866/* set is the context */ 867/* */ 868/* C must have space for one digit (or NaN). */ 869/* ------------------------------------------------------------------ */ 870U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompare(decNumber *res, const decNumber *lhs, 871 const decNumber *rhs, decContext *set) { 872 uInt status=0; /* accumulator */ 873 decCompareOp(res, lhs, rhs, set, COMPARE, &status); 874 if (status!=0) decStatus(res, status, set); 875 return res; 876 } /* decNumberCompare */ 877 878/* ------------------------------------------------------------------ */ 879/* decNumberCompareSignal -- compare, signalling on all NaNs */ 880/* */ 881/* This computes C = A ? B */ 882/* */ 883/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ 884/* lhs is A */ 885/* rhs is B */ 886/* set is the context */ 887/* */ 888/* C must have space for one digit (or NaN). */ 889/* ------------------------------------------------------------------ */ 890U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompareSignal(decNumber *res, const decNumber *lhs, 891 const decNumber *rhs, decContext *set) { 892 uInt status=0; /* accumulator */ 893 decCompareOp(res, lhs, rhs, set, COMPSIG, &status); 894 if (status!=0) decStatus(res, status, set); 895 return res; 896 } /* decNumberCompareSignal */ 897 898/* ------------------------------------------------------------------ */ 899/* decNumberCompareTotal -- compare two Numbers, using total ordering */ 900/* */ 901/* This computes C = A ? B, under total ordering */ 902/* */ 903/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ 904/* lhs is A */ 905/* rhs is B */ 906/* set is the context */ 907/* */ 908/* C must have space for one digit; the result will always be one of */ 909/* -1, 0, or 1. */ 910/* ------------------------------------------------------------------ */ 911U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompareTotal(decNumber *res, const decNumber *lhs, 912 const decNumber *rhs, decContext *set) { 913 uInt status=0; /* accumulator */ 914 decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status); 915 if (status!=0) decStatus(res, status, set); 916 return res; 917 } /* decNumberCompareTotal */ 918 919/* ------------------------------------------------------------------ */ 920/* decNumberCompareTotalMag -- compare, total ordering of magnitudes */ 921/* */ 922/* This computes C = |A| ? |B|, under total ordering */ 923/* */ 924/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ 925/* lhs is A */ 926/* rhs is B */ 927/* set is the context */ 928/* */ 929/* C must have space for one digit; the result will always be one of */ 930/* -1, 0, or 1. */ 931/* ------------------------------------------------------------------ */ 932U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompareTotalMag(decNumber *res, const decNumber *lhs, 933 const decNumber *rhs, decContext *set) { 934 uInt status=0; /* accumulator */ 935 uInt needbytes; /* for space calculations */ 936 decNumber bufa[D2N(DECBUFFER+1)];/* +1 in case DECBUFFER=0 */ 937 decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ 938 decNumber bufb[D2N(DECBUFFER+1)]; 939 decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */ 940 decNumber *a, *b; /* temporary pointers */ 941 942 #if DECCHECK 943 if (decCheckOperands(res, lhs, rhs, set)) return res; 944 #endif 945 946 do { /* protect allocated storage */ 947 /* if either is negative, take a copy and absolute */ 948 if (decNumberIsNegative(lhs)) { /* lhs<0 */ 949 a=bufa; 950 needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit); 951 if (needbytes>sizeof(bufa)) { /* need malloc space */ 952 allocbufa=(decNumber *)malloc(needbytes); 953 if (allocbufa==NULL) { /* hopeless -- abandon */ 954 status|=DEC_Insufficient_storage; 955 break;} 956 a=allocbufa; /* use the allocated space */ 957 } 958 uprv_decNumberCopy(a, lhs); /* copy content */ 959 a->bits&=~DECNEG; /* .. and clear the sign */ 960 lhs=a; /* use copy from here on */ 961 } 962 if (decNumberIsNegative(rhs)) { /* rhs<0 */ 963 b=bufb; 964 needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); 965 if (needbytes>sizeof(bufb)) { /* need malloc space */ 966 allocbufb=(decNumber *)malloc(needbytes); 967 if (allocbufb==NULL) { /* hopeless -- abandon */ 968 status|=DEC_Insufficient_storage; 969 break;} 970 b=allocbufb; /* use the allocated space */ 971 } 972 uprv_decNumberCopy(b, rhs); /* copy content */ 973 b->bits&=~DECNEG; /* .. and clear the sign */ 974 rhs=b; /* use copy from here on */ 975 } 976 decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status); 977 } while(0); /* end protected */ 978 979 if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ 980 if (allocbufb!=NULL) free(allocbufb); /* .. */ 981 if (status!=0) decStatus(res, status, set); 982 return res; 983 } /* decNumberCompareTotalMag */ 984 985/* ------------------------------------------------------------------ */ 986/* decNumberDivide -- divide one number by another */ 987/* */ 988/* This computes C = A / B */ 989/* */ 990/* res is C, the result. C may be A and/or B (e.g., X=X/X) */ 991/* lhs is A */ 992/* rhs is B */ 993/* set is the context */ 994/* */ 995/* C must have space for set->digits digits. */ 996/* ------------------------------------------------------------------ */ 997U_CAPI decNumber * U_EXPORT2 uprv_decNumberDivide(decNumber *res, const decNumber *lhs, 998 const decNumber *rhs, decContext *set) { 999 uInt status=0; /* accumulator */ 1000 decDivideOp(res, lhs, rhs, set, DIVIDE, &status); 1001 if (status!=0) decStatus(res, status, set); 1002 #if DECCHECK 1003 decCheckInexact(res, set); 1004 #endif 1005 return res; 1006 } /* decNumberDivide */ 1007 1008/* ------------------------------------------------------------------ */ 1009/* decNumberDivideInteger -- divide and return integer quotient */ 1010/* */ 1011/* This computes C = A # B, where # is the integer divide operator */ 1012/* */ 1013/* res is C, the result. C may be A and/or B (e.g., X=X#X) */ 1014/* lhs is A */ 1015/* rhs is B */ 1016/* set is the context */ 1017/* */ 1018/* C must have space for set->digits digits. */ 1019/* ------------------------------------------------------------------ */ 1020U_CAPI decNumber * U_EXPORT2 uprv_decNumberDivideInteger(decNumber *res, const decNumber *lhs, 1021 const decNumber *rhs, decContext *set) { 1022 uInt status=0; /* accumulator */ 1023 decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status); 1024 if (status!=0) decStatus(res, status, set); 1025 return res; 1026 } /* decNumberDivideInteger */ 1027 1028/* ------------------------------------------------------------------ */ 1029/* decNumberExp -- exponentiation */ 1030/* */ 1031/* This computes C = exp(A) */ 1032/* */ 1033/* res is C, the result. C may be A */ 1034/* rhs is A */ 1035/* set is the context; note that rounding mode has no effect */ 1036/* */ 1037/* C must have space for set->digits digits. */ 1038/* */ 1039/* Mathematical function restrictions apply (see above); a NaN is */ 1040/* returned with Invalid_operation if a restriction is violated. */ 1041/* */ 1042/* Finite results will always be full precision and Inexact, except */ 1043/* when A is a zero or -Infinity (giving 1 or 0 respectively). */ 1044/* */ 1045/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ 1046/* almost always be correctly rounded, but may be up to 1 ulp in */ 1047/* error in rare cases. */ 1048/* ------------------------------------------------------------------ */ 1049/* This is a wrapper for decExpOp which can handle the slightly wider */ 1050/* (double) range needed by Ln (which has to be able to calculate */ 1051/* exp(-a) where a can be the tiniest number (Ntiny). */ 1052/* ------------------------------------------------------------------ */ 1053U_CAPI decNumber * U_EXPORT2 uprv_decNumberExp(decNumber *res, const decNumber *rhs, 1054 decContext *set) { 1055 uInt status=0; /* accumulator */ 1056 #if DECSUBSET 1057 decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ 1058 #endif 1059 1060 #if DECCHECK 1061 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 1062 #endif 1063 1064 /* Check restrictions; these restrictions ensure that if h=8 (see */ 1065 /* decExpOp) then the result will either overflow or underflow to 0. */ 1066 /* Other math functions restrict the input range, too, for inverses. */ 1067 /* If not violated then carry out the operation. */ 1068 if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */ 1069 #if DECSUBSET 1070 if (!set->extended) { 1071 /* reduce operand and set lostDigits status, as needed */ 1072 if (rhs->digits>set->digits) { 1073 allocrhs=decRoundOperand(rhs, set, &status); 1074 if (allocrhs==NULL) break; 1075 rhs=allocrhs; 1076 } 1077 } 1078 #endif 1079 decExpOp(res, rhs, set, &status); 1080 } while(0); /* end protected */ 1081 1082 #if DECSUBSET 1083 if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */ 1084 #endif 1085 /* apply significant status */ 1086 if (status!=0) decStatus(res, status, set); 1087 #if DECCHECK 1088 decCheckInexact(res, set); 1089 #endif 1090 return res; 1091 } /* decNumberExp */ 1092 1093/* ------------------------------------------------------------------ */ 1094/* decNumberFMA -- fused multiply add */ 1095/* */ 1096/* This computes D = (A * B) + C with only one rounding */ 1097/* */ 1098/* res is D, the result. D may be A or B or C (e.g., X=FMA(X,X,X)) */ 1099/* lhs is A */ 1100/* rhs is B */ 1101/* fhs is C [far hand side] */ 1102/* set is the context */ 1103/* */ 1104/* Mathematical function restrictions apply (see above); a NaN is */ 1105/* returned with Invalid_operation if a restriction is violated. */ 1106/* */ 1107/* C must have space for set->digits digits. */ 1108/* ------------------------------------------------------------------ */ 1109U_CAPI decNumber * U_EXPORT2 uprv_decNumberFMA(decNumber *res, const decNumber *lhs, 1110 const decNumber *rhs, const decNumber *fhs, 1111 decContext *set) { 1112 uInt status=0; /* accumulator */ 1113 decContext dcmul; /* context for the multiplication */ 1114 uInt needbytes; /* for space calculations */ 1115 decNumber bufa[D2N(DECBUFFER*2+1)]; 1116 decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ 1117 decNumber *acc; /* accumulator pointer */ 1118 decNumber dzero; /* work */ 1119 1120 #if DECCHECK 1121 if (decCheckOperands(res, lhs, rhs, set)) return res; 1122 if (decCheckOperands(res, fhs, DECUNUSED, set)) return res; 1123 #endif 1124 1125 do { /* protect allocated storage */ 1126 #if DECSUBSET 1127 if (!set->extended) { /* [undefined if subset] */ 1128 status|=DEC_Invalid_operation; 1129 break;} 1130 #endif 1131 /* Check math restrictions [these ensure no overflow or underflow] */ 1132 if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status)) 1133 || (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status)) 1134 || (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break; 1135 /* set up context for multiply */ 1136 dcmul=*set; 1137 dcmul.digits=lhs->digits+rhs->digits; /* just enough */ 1138 /* [The above may be an over-estimate for subset arithmetic, but that's OK] */ 1139 dcmul.emax=DEC_MAX_EMAX; /* effectively unbounded .. */ 1140 dcmul.emin=DEC_MIN_EMIN; /* [thanks to Math restrictions] */ 1141 /* set up decNumber space to receive the result of the multiply */ 1142 acc=bufa; /* may fit */ 1143 needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit); 1144 if (needbytes>sizeof(bufa)) { /* need malloc space */ 1145 allocbufa=(decNumber *)malloc(needbytes); 1146 if (allocbufa==NULL) { /* hopeless -- abandon */ 1147 status|=DEC_Insufficient_storage; 1148 break;} 1149 acc=allocbufa; /* use the allocated space */ 1150 } 1151 /* multiply with extended range and necessary precision */ 1152 /*printf("emin=%ld\n", dcmul.emin); */ 1153 decMultiplyOp(acc, lhs, rhs, &dcmul, &status); 1154 /* Only Invalid operation (from sNaN or Inf * 0) is possible in */ 1155 /* status; if either is seen than ignore fhs (in case it is */ 1156 /* another sNaN) and set acc to NaN unless we had an sNaN */ 1157 /* [decMultiplyOp leaves that to caller] */ 1158 /* Note sNaN has to go through addOp to shorten payload if */ 1159 /* necessary */ 1160 if ((status&DEC_Invalid_operation)!=0) { 1161 if (!(status&DEC_sNaN)) { /* but be true invalid */ 1162 uprv_decNumberZero(res); /* acc not yet set */ 1163 res->bits=DECNAN; 1164 break; 1165 } 1166 uprv_decNumberZero(&dzero); /* make 0 (any non-NaN would do) */ 1167 fhs=&dzero; /* use that */ 1168 } 1169 #if DECCHECK 1170 else { /* multiply was OK */ 1171 if (status!=0) printf("Status=%08lx after FMA multiply\n", (LI)status); 1172 } 1173 #endif 1174 /* add the third operand and result -> res, and all is done */ 1175 decAddOp(res, acc, fhs, set, 0, &status); 1176 } while(0); /* end protected */ 1177 1178 if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ 1179 if (status!=0) decStatus(res, status, set); 1180 #if DECCHECK 1181 decCheckInexact(res, set); 1182 #endif 1183 return res; 1184 } /* decNumberFMA */ 1185 1186/* ------------------------------------------------------------------ */ 1187/* decNumberInvert -- invert a Number, digitwise */ 1188/* */ 1189/* This computes C = ~A */ 1190/* */ 1191/* res is C, the result. C may be A (e.g., X=~X) */ 1192/* rhs is A */ 1193/* set is the context (used for result length and error report) */ 1194/* */ 1195/* C must have space for set->digits digits. */ 1196/* */ 1197/* Logical function restrictions apply (see above); a NaN is */ 1198/* returned with Invalid_operation if a restriction is violated. */ 1199/* ------------------------------------------------------------------ */ 1200U_CAPI decNumber * U_EXPORT2 uprv_decNumberInvert(decNumber *res, const decNumber *rhs, 1201 decContext *set) { 1202 const Unit *ua, *msua; /* -> operand and its msu */ 1203 Unit *uc, *msuc; /* -> result and its msu */ 1204 Int msudigs; /* digits in res msu */ 1205 #if DECCHECK 1206 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 1207 #endif 1208 1209 if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { 1210 decStatus(res, DEC_Invalid_operation, set); 1211 return res; 1212 } 1213 /* operand is valid */ 1214 ua=rhs->lsu; /* bottom-up */ 1215 uc=res->lsu; /* .. */ 1216 msua=ua+D2U(rhs->digits)-1; /* -> msu of rhs */ 1217 msuc=uc+D2U(set->digits)-1; /* -> msu of result */ 1218 msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ 1219 for (; uc<=msuc; ua++, uc++) { /* Unit loop */ 1220 Unit a; /* extract unit */ 1221 Int i, j; /* work */ 1222 if (ua>msua) a=0; 1223 else a=*ua; 1224 *uc=0; /* can now write back */ 1225 /* always need to examine all bits in rhs */ 1226 /* This loop could be unrolled and/or use BIN2BCD tables */ 1227 for (i=0; i<DECDPUN; i++) { 1228 if ((~a)&1) *uc=*uc+(Unit)powers[i]; /* effect INVERT */ 1229 j=a%10; 1230 a=a/10; 1231 if (j>1) { 1232 decStatus(res, DEC_Invalid_operation, set); 1233 return res; 1234 } 1235 if (uc==msuc && i==msudigs-1) break; /* just did final digit */ 1236 } /* each digit */ 1237 } /* each unit */ 1238 /* [here uc-1 is the msu of the result] */ 1239 res->digits=decGetDigits(res->lsu, uc-res->lsu); 1240 res->exponent=0; /* integer */ 1241 res->bits=0; /* sign=0 */ 1242 return res; /* [no status to set] */ 1243 } /* decNumberInvert */ 1244 1245/* ------------------------------------------------------------------ */ 1246/* decNumberLn -- natural logarithm */ 1247/* */ 1248/* This computes C = ln(A) */ 1249/* */ 1250/* res is C, the result. C may be A */ 1251/* rhs is A */ 1252/* set is the context; note that rounding mode has no effect */ 1253/* */ 1254/* C must have space for set->digits digits. */ 1255/* */ 1256/* Notable cases: */ 1257/* A<0 -> Invalid */ 1258/* A=0 -> -Infinity (Exact) */ 1259/* A=+Infinity -> +Infinity (Exact) */ 1260/* A=1 exactly -> 0 (Exact) */ 1261/* */ 1262/* Mathematical function restrictions apply (see above); a NaN is */ 1263/* returned with Invalid_operation if a restriction is violated. */ 1264/* */ 1265/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ 1266/* almost always be correctly rounded, but may be up to 1 ulp in */ 1267/* error in rare cases. */ 1268/* ------------------------------------------------------------------ */ 1269/* This is a wrapper for decLnOp which can handle the slightly wider */ 1270/* (+11) range needed by Ln, Log10, etc. (which may have to be able */ 1271/* to calculate at p+e+2). */ 1272/* ------------------------------------------------------------------ */ 1273U_CAPI decNumber * U_EXPORT2 uprv_decNumberLn(decNumber *res, const decNumber *rhs, 1274 decContext *set) { 1275 uInt status=0; /* accumulator */ 1276 #if DECSUBSET 1277 decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ 1278 #endif 1279 1280 #if DECCHECK 1281 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 1282 #endif 1283 1284 /* Check restrictions; this is a math function; if not violated */ 1285 /* then carry out the operation. */ 1286 if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */ 1287 #if DECSUBSET 1288 if (!set->extended) { 1289 /* reduce operand and set lostDigits status, as needed */ 1290 if (rhs->digits>set->digits) { 1291 allocrhs=decRoundOperand(rhs, set, &status); 1292 if (allocrhs==NULL) break; 1293 rhs=allocrhs; 1294 } 1295 /* special check in subset for rhs=0 */ 1296 if (ISZERO(rhs)) { /* +/- zeros -> error */ 1297 status|=DEC_Invalid_operation; 1298 break;} 1299 } /* extended=0 */ 1300 #endif 1301 decLnOp(res, rhs, set, &status); 1302 } while(0); /* end protected */ 1303 1304 #if DECSUBSET 1305 if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */ 1306 #endif 1307 /* apply significant status */ 1308 if (status!=0) decStatus(res, status, set); 1309 #if DECCHECK 1310 decCheckInexact(res, set); 1311 #endif 1312 return res; 1313 } /* decNumberLn */ 1314 1315/* ------------------------------------------------------------------ */ 1316/* decNumberLogB - get adjusted exponent, by 754 rules */ 1317/* */ 1318/* This computes C = adjustedexponent(A) */ 1319/* */ 1320/* res is C, the result. C may be A */ 1321/* rhs is A */ 1322/* set is the context, used only for digits and status */ 1323/* */ 1324/* C must have space for 10 digits (A might have 10**9 digits and */ 1325/* an exponent of +999999999, or one digit and an exponent of */ 1326/* -1999999999). */ 1327/* */ 1328/* This returns the adjusted exponent of A after (in theory) padding */ 1329/* with zeros on the right to set->digits digits while keeping the */ 1330/* same value. The exponent is not limited by emin/emax. */ 1331/* */ 1332/* Notable cases: */ 1333/* A<0 -> Use |A| */ 1334/* A=0 -> -Infinity (Division by zero) */ 1335/* A=Infinite -> +Infinity (Exact) */ 1336/* A=1 exactly -> 0 (Exact) */ 1337/* NaNs are propagated as usual */ 1338/* ------------------------------------------------------------------ */ 1339U_CAPI decNumber * U_EXPORT2 uprv_decNumberLogB(decNumber *res, const decNumber *rhs, 1340 decContext *set) { 1341 uInt status=0; /* accumulator */ 1342 1343 #if DECCHECK 1344 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 1345 #endif 1346 1347 /* NaNs as usual; Infinities return +Infinity; 0->oops */ 1348 if (decNumberIsNaN(rhs)) decNaNs(res, rhs, NULL, set, &status); 1349 else if (decNumberIsInfinite(rhs)) uprv_decNumberCopyAbs(res, rhs); 1350 else if (decNumberIsZero(rhs)) { 1351 uprv_decNumberZero(res); /* prepare for Infinity */ 1352 res->bits=DECNEG|DECINF; /* -Infinity */ 1353 status|=DEC_Division_by_zero; /* as per 754 */ 1354 } 1355 else { /* finite non-zero */ 1356 Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */ 1357 uprv_decNumberFromInt32(res, ae); /* lay it out */ 1358 } 1359 1360 if (status!=0) decStatus(res, status, set); 1361 return res; 1362 } /* decNumberLogB */ 1363 1364/* ------------------------------------------------------------------ */ 1365/* decNumberLog10 -- logarithm in base 10 */ 1366/* */ 1367/* This computes C = log10(A) */ 1368/* */ 1369/* res is C, the result. C may be A */ 1370/* rhs is A */ 1371/* set is the context; note that rounding mode has no effect */ 1372/* */ 1373/* C must have space for set->digits digits. */ 1374/* */ 1375/* Notable cases: */ 1376/* A<0 -> Invalid */ 1377/* A=0 -> -Infinity (Exact) */ 1378/* A=+Infinity -> +Infinity (Exact) */ 1379/* A=10**n (if n is an integer) -> n (Exact) */ 1380/* */ 1381/* Mathematical function restrictions apply (see above); a NaN is */ 1382/* returned with Invalid_operation if a restriction is violated. */ 1383/* */ 1384/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ 1385/* almost always be correctly rounded, but may be up to 1 ulp in */ 1386/* error in rare cases. */ 1387/* ------------------------------------------------------------------ */ 1388/* This calculates ln(A)/ln(10) using appropriate precision. For */ 1389/* ln(A) this is the max(p, rhs->digits + t) + 3, where p is the */ 1390/* requested digits and t is the number of digits in the exponent */ 1391/* (maximum 6). For ln(10) it is p + 3; this is often handled by the */ 1392/* fastpath in decLnOp. The final division is done to the requested */ 1393/* precision. */ 1394/* ------------------------------------------------------------------ */ 1395#if defined(__clang__) || (defined(__GNUC__) && ((__GNUC__ * 100 + __GNUC_MINOR__) >= 406)) 1396#pragma GCC diagnostic push 1397#pragma GCC diagnostic ignored "-Warray-bounds" 1398#endif 1399U_CAPI decNumber * U_EXPORT2 uprv_decNumberLog10(decNumber *res, const decNumber *rhs, 1400 decContext *set) { 1401 uInt status=0, ignore=0; /* status accumulators */ 1402 uInt needbytes; /* for space calculations */ 1403 Int p; /* working precision */ 1404 Int t; /* digits in exponent of A */ 1405 1406 /* buffers for a and b working decimals */ 1407 /* (adjustment calculator, same size) */ 1408 decNumber bufa[D2N(DECBUFFER+2)]; 1409 decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ 1410 decNumber *a=bufa; /* temporary a */ 1411 decNumber bufb[D2N(DECBUFFER+2)]; 1412 decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */ 1413 decNumber *b=bufb; /* temporary b */ 1414 decNumber bufw[D2N(10)]; /* working 2-10 digit number */ 1415 decNumber *w=bufw; /* .. */ 1416 #if DECSUBSET 1417 decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ 1418 #endif 1419 1420 decContext aset; /* working context */ 1421 1422 #if DECCHECK 1423 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 1424 #endif 1425 1426 /* Check restrictions; this is a math function; if not violated */ 1427 /* then carry out the operation. */ 1428 if (!decCheckMath(rhs, set, &status)) do { /* protect malloc */ 1429 #if DECSUBSET 1430 if (!set->extended) { 1431 /* reduce operand and set lostDigits status, as needed */ 1432 if (rhs->digits>set->digits) { 1433 allocrhs=decRoundOperand(rhs, set, &status); 1434 if (allocrhs==NULL) break; 1435 rhs=allocrhs; 1436 } 1437 /* special check in subset for rhs=0 */ 1438 if (ISZERO(rhs)) { /* +/- zeros -> error */ 1439 status|=DEC_Invalid_operation; 1440 break;} 1441 } /* extended=0 */ 1442 #endif 1443 1444 uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */ 1445 1446 /* handle exact powers of 10; only check if +ve finite */ 1447 if (!(rhs->bits&(DECNEG|DECSPECIAL)) && !ISZERO(rhs)) { 1448 Int residue=0; /* (no residue) */ 1449 uInt copystat=0; /* clean status */ 1450 1451 /* round to a single digit... */ 1452 aset.digits=1; 1453 decCopyFit(w, rhs, &aset, &residue, ©stat); /* copy & shorten */ 1454 /* if exact and the digit is 1, rhs is a power of 10 */ 1455 if (!(copystat&DEC_Inexact) && w->lsu[0]==1) { 1456 /* the exponent, conveniently, is the power of 10; making */ 1457 /* this the result needs a little care as it might not fit, */ 1458 /* so first convert it into the working number, and then move */ 1459 /* to res */ 1460 uprv_decNumberFromInt32(w, w->exponent); 1461 residue=0; 1462 decCopyFit(res, w, set, &residue, &status); /* copy & round */ 1463 decFinish(res, set, &residue, &status); /* cleanup/set flags */ 1464 break; 1465 } /* not a power of 10 */ 1466 } /* not a candidate for exact */ 1467 1468 /* simplify the information-content calculation to use 'total */ 1469 /* number of digits in a, including exponent' as compared to the */ 1470 /* requested digits, as increasing this will only rarely cost an */ 1471 /* iteration in ln(a) anyway */ 1472 t=6; /* it can never be >6 */ 1473 1474 /* allocate space when needed... */ 1475 p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3; 1476 needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit); 1477 if (needbytes>sizeof(bufa)) { /* need malloc space */ 1478 allocbufa=(decNumber *)malloc(needbytes); 1479 if (allocbufa==NULL) { /* hopeless -- abandon */ 1480 status|=DEC_Insufficient_storage; 1481 break;} 1482 a=allocbufa; /* use the allocated space */ 1483 } 1484 aset.digits=p; /* as calculated */ 1485 aset.emax=DEC_MAX_MATH; /* usual bounds */ 1486 aset.emin=-DEC_MAX_MATH; /* .. */ 1487 aset.clamp=0; /* and no concrete format */ 1488 decLnOp(a, rhs, &aset, &status); /* a=ln(rhs) */ 1489 1490 /* skip the division if the result so far is infinite, NaN, or */ 1491 /* zero, or there was an error; note NaN from sNaN needs copy */ 1492 if (status&DEC_NaNs && !(status&DEC_sNaN)) break; 1493 if (a->bits&DECSPECIAL || ISZERO(a)) { 1494 uprv_decNumberCopy(res, a); /* [will fit] */ 1495 break;} 1496 1497 /* for ln(10) an extra 3 digits of precision are needed */ 1498 p=set->digits+3; 1499 needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit); 1500 if (needbytes>sizeof(bufb)) { /* need malloc space */ 1501 allocbufb=(decNumber *)malloc(needbytes); 1502 if (allocbufb==NULL) { /* hopeless -- abandon */ 1503 status|=DEC_Insufficient_storage; 1504 break;} 1505 b=allocbufb; /* use the allocated space */ 1506 } 1507 uprv_decNumberZero(w); /* set up 10... */ 1508 #if DECDPUN==1 1509 w->lsu[1]=1; w->lsu[0]=0; /* .. */ 1510 #else 1511 w->lsu[0]=10; /* .. */ 1512 #endif 1513 w->digits=2; /* .. */ 1514 1515 aset.digits=p; 1516 decLnOp(b, w, &aset, &ignore); /* b=ln(10) */ 1517 1518 aset.digits=set->digits; /* for final divide */ 1519 decDivideOp(res, a, b, &aset, DIVIDE, &status); /* into result */ 1520 } while(0); /* [for break] */ 1521 1522 if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ 1523 if (allocbufb!=NULL) free(allocbufb); /* .. */ 1524 #if DECSUBSET 1525 if (allocrhs !=NULL) free(allocrhs); /* .. */ 1526 #endif 1527 /* apply significant status */ 1528 if (status!=0) decStatus(res, status, set); 1529 #if DECCHECK 1530 decCheckInexact(res, set); 1531 #endif 1532 return res; 1533 } /* decNumberLog10 */ 1534#if defined(__clang__) || (defined(__GNUC__) && ((__GNUC__ * 100 + __GNUC_MINOR__) >= 406)) 1535#pragma GCC diagnostic pop 1536#endif 1537 1538/* ------------------------------------------------------------------ */ 1539/* decNumberMax -- compare two Numbers and return the maximum */ 1540/* */ 1541/* This computes C = A ? B, returning the maximum by 754 rules */ 1542/* */ 1543/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ 1544/* lhs is A */ 1545/* rhs is B */ 1546/* set is the context */ 1547/* */ 1548/* C must have space for set->digits digits. */ 1549/* ------------------------------------------------------------------ */ 1550U_CAPI decNumber * U_EXPORT2 uprv_decNumberMax(decNumber *res, const decNumber *lhs, 1551 const decNumber *rhs, decContext *set) { 1552 uInt status=0; /* accumulator */ 1553 decCompareOp(res, lhs, rhs, set, COMPMAX, &status); 1554 if (status!=0) decStatus(res, status, set); 1555 #if DECCHECK 1556 decCheckInexact(res, set); 1557 #endif 1558 return res; 1559 } /* decNumberMax */ 1560 1561/* ------------------------------------------------------------------ */ 1562/* decNumberMaxMag -- compare and return the maximum by magnitude */ 1563/* */ 1564/* This computes C = A ? B, returning the maximum by 754 rules */ 1565/* */ 1566/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ 1567/* lhs is A */ 1568/* rhs is B */ 1569/* set is the context */ 1570/* */ 1571/* C must have space for set->digits digits. */ 1572/* ------------------------------------------------------------------ */ 1573U_CAPI decNumber * U_EXPORT2 uprv_decNumberMaxMag(decNumber *res, const decNumber *lhs, 1574 const decNumber *rhs, decContext *set) { 1575 uInt status=0; /* accumulator */ 1576 decCompareOp(res, lhs, rhs, set, COMPMAXMAG, &status); 1577 if (status!=0) decStatus(res, status, set); 1578 #if DECCHECK 1579 decCheckInexact(res, set); 1580 #endif 1581 return res; 1582 } /* decNumberMaxMag */ 1583 1584/* ------------------------------------------------------------------ */ 1585/* decNumberMin -- compare two Numbers and return the minimum */ 1586/* */ 1587/* This computes C = A ? B, returning the minimum by 754 rules */ 1588/* */ 1589/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ 1590/* lhs is A */ 1591/* rhs is B */ 1592/* set is the context */ 1593/* */ 1594/* C must have space for set->digits digits. */ 1595/* ------------------------------------------------------------------ */ 1596U_CAPI decNumber * U_EXPORT2 uprv_decNumberMin(decNumber *res, const decNumber *lhs, 1597 const decNumber *rhs, decContext *set) { 1598 uInt status=0; /* accumulator */ 1599 decCompareOp(res, lhs, rhs, set, COMPMIN, &status); 1600 if (status!=0) decStatus(res, status, set); 1601 #if DECCHECK 1602 decCheckInexact(res, set); 1603 #endif 1604 return res; 1605 } /* decNumberMin */ 1606 1607/* ------------------------------------------------------------------ */ 1608/* decNumberMinMag -- compare and return the minimum by magnitude */ 1609/* */ 1610/* This computes C = A ? B, returning the minimum by 754 rules */ 1611/* */ 1612/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ 1613/* lhs is A */ 1614/* rhs is B */ 1615/* set is the context */ 1616/* */ 1617/* C must have space for set->digits digits. */ 1618/* ------------------------------------------------------------------ */ 1619U_CAPI decNumber * U_EXPORT2 uprv_decNumberMinMag(decNumber *res, const decNumber *lhs, 1620 const decNumber *rhs, decContext *set) { 1621 uInt status=0; /* accumulator */ 1622 decCompareOp(res, lhs, rhs, set, COMPMINMAG, &status); 1623 if (status!=0) decStatus(res, status, set); 1624 #if DECCHECK 1625 decCheckInexact(res, set); 1626 #endif 1627 return res; 1628 } /* decNumberMinMag */ 1629 1630/* ------------------------------------------------------------------ */ 1631/* decNumberMinus -- prefix minus operator */ 1632/* */ 1633/* This computes C = 0 - A */ 1634/* */ 1635/* res is C, the result. C may be A */ 1636/* rhs is A */ 1637/* set is the context */ 1638/* */ 1639/* See also decNumberCopyNegate for a quiet bitwise version of this. */ 1640/* C must have space for set->digits digits. */ 1641/* ------------------------------------------------------------------ */ 1642/* Simply use AddOp for the subtract, which will do the necessary. */ 1643/* ------------------------------------------------------------------ */ 1644U_CAPI decNumber * U_EXPORT2 uprv_decNumberMinus(decNumber *res, const decNumber *rhs, 1645 decContext *set) { 1646 decNumber dzero; 1647 uInt status=0; /* accumulator */ 1648 1649 #if DECCHECK 1650 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 1651 #endif 1652 1653 uprv_decNumberZero(&dzero); /* make 0 */ 1654 dzero.exponent=rhs->exponent; /* [no coefficient expansion] */ 1655 decAddOp(res, &dzero, rhs, set, DECNEG, &status); 1656 if (status!=0) decStatus(res, status, set); 1657 #if DECCHECK 1658 decCheckInexact(res, set); 1659 #endif 1660 return res; 1661 } /* decNumberMinus */ 1662 1663/* ------------------------------------------------------------------ */ 1664/* decNumberNextMinus -- next towards -Infinity */ 1665/* */ 1666/* This computes C = A - infinitesimal, rounded towards -Infinity */ 1667/* */ 1668/* res is C, the result. C may be A */ 1669/* rhs is A */ 1670/* set is the context */ 1671/* */ 1672/* This is a generalization of 754 NextDown. */ 1673/* ------------------------------------------------------------------ */ 1674U_CAPI decNumber * U_EXPORT2 uprv_decNumberNextMinus(decNumber *res, const decNumber *rhs, 1675 decContext *set) { 1676 decNumber dtiny; /* constant */ 1677 decContext workset=*set; /* work */ 1678 uInt status=0; /* accumulator */ 1679 #if DECCHECK 1680 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 1681 #endif 1682 1683 /* +Infinity is the special case */ 1684 if ((rhs->bits&(DECINF|DECNEG))==DECINF) { 1685 decSetMaxValue(res, set); /* is +ve */ 1686 /* there is no status to set */ 1687 return res; 1688 } 1689 uprv_decNumberZero(&dtiny); /* start with 0 */ 1690 dtiny.lsu[0]=1; /* make number that is .. */ 1691 dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */ 1692 workset.round=DEC_ROUND_FLOOR; 1693 decAddOp(res, rhs, &dtiny, &workset, DECNEG, &status); 1694 status&=DEC_Invalid_operation|DEC_sNaN; /* only sNaN Invalid please */ 1695 if (status!=0) decStatus(res, status, set); 1696 return res; 1697 } /* decNumberNextMinus */ 1698 1699/* ------------------------------------------------------------------ */ 1700/* decNumberNextPlus -- next towards +Infinity */ 1701/* */ 1702/* This computes C = A + infinitesimal, rounded towards +Infinity */ 1703/* */ 1704/* res is C, the result. C may be A */ 1705/* rhs is A */ 1706/* set is the context */ 1707/* */ 1708/* This is a generalization of 754 NextUp. */ 1709/* ------------------------------------------------------------------ */ 1710U_CAPI decNumber * U_EXPORT2 uprv_decNumberNextPlus(decNumber *res, const decNumber *rhs, 1711 decContext *set) { 1712 decNumber dtiny; /* constant */ 1713 decContext workset=*set; /* work */ 1714 uInt status=0; /* accumulator */ 1715 #if DECCHECK 1716 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 1717 #endif 1718 1719 /* -Infinity is the special case */ 1720 if ((rhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) { 1721 decSetMaxValue(res, set); 1722 res->bits=DECNEG; /* negative */ 1723 /* there is no status to set */ 1724 return res; 1725 } 1726 uprv_decNumberZero(&dtiny); /* start with 0 */ 1727 dtiny.lsu[0]=1; /* make number that is .. */ 1728 dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */ 1729 workset.round=DEC_ROUND_CEILING; 1730 decAddOp(res, rhs, &dtiny, &workset, 0, &status); 1731 status&=DEC_Invalid_operation|DEC_sNaN; /* only sNaN Invalid please */ 1732 if (status!=0) decStatus(res, status, set); 1733 return res; 1734 } /* decNumberNextPlus */ 1735 1736/* ------------------------------------------------------------------ */ 1737/* decNumberNextToward -- next towards rhs */ 1738/* */ 1739/* This computes C = A +/- infinitesimal, rounded towards */ 1740/* +/-Infinity in the direction of B, as per 754-1985 nextafter */ 1741/* modified during revision but dropped from 754-2008. */ 1742/* */ 1743/* res is C, the result. C may be A or B. */ 1744/* lhs is A */ 1745/* rhs is B */ 1746/* set is the context */ 1747/* */ 1748/* This is a generalization of 754-1985 NextAfter. */ 1749/* ------------------------------------------------------------------ */ 1750U_CAPI decNumber * U_EXPORT2 uprv_decNumberNextToward(decNumber *res, const decNumber *lhs, 1751 const decNumber *rhs, decContext *set) { 1752 decNumber dtiny; /* constant */ 1753 decContext workset=*set; /* work */ 1754 Int result; /* .. */ 1755 uInt status=0; /* accumulator */ 1756 #if DECCHECK 1757 if (decCheckOperands(res, lhs, rhs, set)) return res; 1758 #endif 1759 1760 if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { 1761 decNaNs(res, lhs, rhs, set, &status); 1762 } 1763 else { /* Is numeric, so no chance of sNaN Invalid, etc. */ 1764 result=decCompare(lhs, rhs, 0); /* sign matters */ 1765 if (result==BADINT) status|=DEC_Insufficient_storage; /* rare */ 1766 else { /* valid compare */ 1767 if (result==0) uprv_decNumberCopySign(res, lhs, rhs); /* easy */ 1768 else { /* differ: need NextPlus or NextMinus */ 1769 uByte sub; /* add or subtract */ 1770 if (result<0) { /* lhs<rhs, do nextplus */ 1771 /* -Infinity is the special case */ 1772 if ((lhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) { 1773 decSetMaxValue(res, set); 1774 res->bits=DECNEG; /* negative */ 1775 return res; /* there is no status to set */ 1776 } 1777 workset.round=DEC_ROUND_CEILING; 1778 sub=0; /* add, please */ 1779 } /* plus */ 1780 else { /* lhs>rhs, do nextminus */ 1781 /* +Infinity is the special case */ 1782 if ((lhs->bits&(DECINF|DECNEG))==DECINF) { 1783 decSetMaxValue(res, set); 1784 return res; /* there is no status to set */ 1785 } 1786 workset.round=DEC_ROUND_FLOOR; 1787 sub=DECNEG; /* subtract, please */ 1788 } /* minus */ 1789 uprv_decNumberZero(&dtiny); /* start with 0 */ 1790 dtiny.lsu[0]=1; /* make number that is .. */ 1791 dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */ 1792 decAddOp(res, lhs, &dtiny, &workset, sub, &status); /* + or - */ 1793 /* turn off exceptions if the result is a normal number */ 1794 /* (including Nmin), otherwise let all status through */ 1795 if (uprv_decNumberIsNormal(res, set)) status=0; 1796 } /* unequal */ 1797 } /* compare OK */ 1798 } /* numeric */ 1799 if (status!=0) decStatus(res, status, set); 1800 return res; 1801 } /* decNumberNextToward */ 1802 1803/* ------------------------------------------------------------------ */ 1804/* decNumberOr -- OR two Numbers, digitwise */ 1805/* */ 1806/* This computes C = A | B */ 1807/* */ 1808/* res is C, the result. C may be A and/or B (e.g., X=X|X) */ 1809/* lhs is A */ 1810/* rhs is B */ 1811/* set is the context (used for result length and error report) */ 1812/* */ 1813/* C must have space for set->digits digits. */ 1814/* */ 1815/* Logical function restrictions apply (see above); a NaN is */ 1816/* returned with Invalid_operation if a restriction is violated. */ 1817/* ------------------------------------------------------------------ */ 1818U_CAPI decNumber * U_EXPORT2 uprv_decNumberOr(decNumber *res, const decNumber *lhs, 1819 const decNumber *rhs, decContext *set) { 1820 const Unit *ua, *ub; /* -> operands */ 1821 const Unit *msua, *msub; /* -> operand msus */ 1822 Unit *uc, *msuc; /* -> result and its msu */ 1823 Int msudigs; /* digits in res msu */ 1824 #if DECCHECK 1825 if (decCheckOperands(res, lhs, rhs, set)) return res; 1826 #endif 1827 1828 if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) 1829 || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { 1830 decStatus(res, DEC_Invalid_operation, set); 1831 return res; 1832 } 1833 /* operands are valid */ 1834 ua=lhs->lsu; /* bottom-up */ 1835 ub=rhs->lsu; /* .. */ 1836 uc=res->lsu; /* .. */ 1837 msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */ 1838 msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */ 1839 msuc=uc+D2U(set->digits)-1; /* -> msu of result */ 1840 msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ 1841 for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */ 1842 Unit a, b; /* extract units */ 1843 if (ua>msua) a=0; 1844 else a=*ua; 1845 if (ub>msub) b=0; 1846 else b=*ub; 1847 *uc=0; /* can now write back */ 1848 if (a|b) { /* maybe 1 bits to examine */ 1849 Int i, j; 1850 /* This loop could be unrolled and/or use BIN2BCD tables */ 1851 for (i=0; i<DECDPUN; i++) { 1852 if ((a|b)&1) *uc=*uc+(Unit)powers[i]; /* effect OR */ 1853 j=a%10; 1854 a=a/10; 1855 j|=b%10; 1856 b=b/10; 1857 if (j>1) { 1858 decStatus(res, DEC_Invalid_operation, set); 1859 return res; 1860 } 1861 if (uc==msuc && i==msudigs-1) break; /* just did final digit */ 1862 } /* each digit */ 1863 } /* non-zero */ 1864 } /* each unit */ 1865 /* [here uc-1 is the msu of the result] */ 1866 res->digits=decGetDigits(res->lsu, uc-res->lsu); 1867 res->exponent=0; /* integer */ 1868 res->bits=0; /* sign=0 */ 1869 return res; /* [no status to set] */ 1870 } /* decNumberOr */ 1871 1872/* ------------------------------------------------------------------ */ 1873/* decNumberPlus -- prefix plus operator */ 1874/* */ 1875/* This computes C = 0 + A */ 1876/* */ 1877/* res is C, the result. C may be A */ 1878/* rhs is A */ 1879/* set is the context */ 1880/* */ 1881/* See also decNumberCopy for a quiet bitwise version of this. */ 1882/* C must have space for set->digits digits. */ 1883/* ------------------------------------------------------------------ */ 1884/* This simply uses AddOp; Add will take fast path after preparing A. */ 1885/* Performance is a concern here, as this routine is often used to */ 1886/* check operands and apply rounding and overflow/underflow testing. */ 1887/* ------------------------------------------------------------------ */ 1888U_CAPI decNumber * U_EXPORT2 uprv_decNumberPlus(decNumber *res, const decNumber *rhs, 1889 decContext *set) { 1890 decNumber dzero; 1891 uInt status=0; /* accumulator */ 1892 #if DECCHECK 1893 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 1894 #endif 1895 1896 uprv_decNumberZero(&dzero); /* make 0 */ 1897 dzero.exponent=rhs->exponent; /* [no coefficient expansion] */ 1898 decAddOp(res, &dzero, rhs, set, 0, &status); 1899 if (status!=0) decStatus(res, status, set); 1900 #if DECCHECK 1901 decCheckInexact(res, set); 1902 #endif 1903 return res; 1904 } /* decNumberPlus */ 1905 1906/* ------------------------------------------------------------------ */ 1907/* decNumberMultiply -- multiply two Numbers */ 1908/* */ 1909/* This computes C = A x B */ 1910/* */ 1911/* res is C, the result. C may be A and/or B (e.g., X=X+X) */ 1912/* lhs is A */ 1913/* rhs is B */ 1914/* set is the context */ 1915/* */ 1916/* C must have space for set->digits digits. */ 1917/* ------------------------------------------------------------------ */ 1918U_CAPI decNumber * U_EXPORT2 uprv_decNumberMultiply(decNumber *res, const decNumber *lhs, 1919 const decNumber *rhs, decContext *set) { 1920 uInt status=0; /* accumulator */ 1921 decMultiplyOp(res, lhs, rhs, set, &status); 1922 if (status!=0) decStatus(res, status, set); 1923 #if DECCHECK 1924 decCheckInexact(res, set); 1925 #endif 1926 return res; 1927 } /* decNumberMultiply */ 1928 1929/* ------------------------------------------------------------------ */ 1930/* decNumberPower -- raise a number to a power */ 1931/* */ 1932/* This computes C = A ** B */ 1933/* */ 1934/* res is C, the result. C may be A and/or B (e.g., X=X**X) */ 1935/* lhs is A */ 1936/* rhs is B */ 1937/* set is the context */ 1938/* */ 1939/* C must have space for set->digits digits. */ 1940/* */ 1941/* Mathematical function restrictions apply (see above); a NaN is */ 1942/* returned with Invalid_operation if a restriction is violated. */ 1943/* */ 1944/* However, if 1999999997<=B<=999999999 and B is an integer then the */ 1945/* restrictions on A and the context are relaxed to the usual bounds, */ 1946/* for compatibility with the earlier (integer power only) version */ 1947/* of this function. */ 1948/* */ 1949/* When B is an integer, the result may be exact, even if rounded. */ 1950/* */ 1951/* The final result is rounded according to the context; it will */ 1952/* almost always be correctly rounded, but may be up to 1 ulp in */ 1953/* error in rare cases. */ 1954/* ------------------------------------------------------------------ */ 1955U_CAPI decNumber * U_EXPORT2 uprv_decNumberPower(decNumber *res, const decNumber *lhs, 1956 const decNumber *rhs, decContext *set) { 1957 #if DECSUBSET 1958 decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ 1959 decNumber *allocrhs=NULL; /* .., rhs */ 1960 #endif 1961 decNumber *allocdac=NULL; /* -> allocated acc buffer, iff used */ 1962 decNumber *allocinv=NULL; /* -> allocated 1/x buffer, iff used */ 1963 Int reqdigits=set->digits; /* requested DIGITS */ 1964 Int n; /* rhs in binary */ 1965 Flag rhsint=0; /* 1 if rhs is an integer */ 1966 Flag useint=0; /* 1 if can use integer calculation */ 1967 Flag isoddint=0; /* 1 if rhs is an integer and odd */ 1968 Int i; /* work */ 1969 #if DECSUBSET 1970 Int dropped; /* .. */ 1971 #endif 1972 uInt needbytes; /* buffer size needed */ 1973 Flag seenbit; /* seen a bit while powering */ 1974 Int residue=0; /* rounding residue */ 1975 uInt status=0; /* accumulators */ 1976 uByte bits=0; /* result sign if errors */ 1977 decContext aset; /* working context */ 1978 decNumber dnOne; /* work value 1... */ 1979 /* local accumulator buffer [a decNumber, with digits+elength+1 digits] */ 1980 decNumber dacbuff[D2N(DECBUFFER+9)]; 1981 decNumber *dac=dacbuff; /* -> result accumulator */ 1982 /* same again for possible 1/lhs calculation */ 1983 decNumber invbuff[D2N(DECBUFFER+9)]; 1984 1985 #if DECCHECK 1986 if (decCheckOperands(res, lhs, rhs, set)) return res; 1987 #endif 1988 1989 do { /* protect allocated storage */ 1990 #if DECSUBSET 1991 if (!set->extended) { /* reduce operands and set status, as needed */ 1992 if (lhs->digits>reqdigits) { 1993 alloclhs=decRoundOperand(lhs, set, &status); 1994 if (alloclhs==NULL) break; 1995 lhs=alloclhs; 1996 } 1997 if (rhs->digits>reqdigits) { 1998 allocrhs=decRoundOperand(rhs, set, &status); 1999 if (allocrhs==NULL) break; 2000 rhs=allocrhs; 2001 } 2002 } 2003 #endif 2004 /* [following code does not require input rounding] */ 2005 2006 /* handle NaNs and rhs Infinity (lhs infinity is harder) */ 2007 if (SPECIALARGS) { 2008 if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { /* NaNs */ 2009 decNaNs(res, lhs, rhs, set, &status); 2010 break;} 2011 if (decNumberIsInfinite(rhs)) { /* rhs Infinity */ 2012 Flag rhsneg=rhs->bits&DECNEG; /* save rhs sign */ 2013 if (decNumberIsNegative(lhs) /* lhs<0 */ 2014 && !decNumberIsZero(lhs)) /* .. */ 2015 status|=DEC_Invalid_operation; 2016 else { /* lhs >=0 */ 2017 uprv_decNumberZero(&dnOne); /* set up 1 */ 2018 dnOne.lsu[0]=1; 2019 uprv_decNumberCompare(dac, lhs, &dnOne, set); /* lhs ? 1 */ 2020 uprv_decNumberZero(res); /* prepare for 0/1/Infinity */ 2021 if (decNumberIsNegative(dac)) { /* lhs<1 */ 2022 if (rhsneg) res->bits|=DECINF; /* +Infinity [else is +0] */ 2023 } 2024 else if (dac->lsu[0]==0) { /* lhs=1 */ 2025 /* 1**Infinity is inexact, so return fully-padded 1.0000 */ 2026 Int shift=set->digits-1; 2027 *res->lsu=1; /* was 0, make int 1 */ 2028 res->digits=decShiftToMost(res->lsu, 1, shift); 2029 res->exponent=-shift; /* make 1.0000... */ 2030 status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */ 2031 } 2032 else { /* lhs>1 */ 2033 if (!rhsneg) res->bits|=DECINF; /* +Infinity [else is +0] */ 2034 } 2035 } /* lhs>=0 */ 2036 break;} 2037 /* [lhs infinity drops through] */ 2038 } /* specials */ 2039 2040 /* Original rhs may be an integer that fits and is in range */ 2041 n=decGetInt(rhs); 2042 if (n!=BADINT) { /* it is an integer */ 2043 rhsint=1; /* record the fact for 1**n */ 2044 isoddint=(Flag)n&1; /* [works even if big] */ 2045 if (n!=BIGEVEN && n!=BIGODD) /* can use integer path? */ 2046 useint=1; /* looks good */ 2047 } 2048 2049 if (decNumberIsNegative(lhs) /* -x .. */ 2050 && isoddint) bits=DECNEG; /* .. to an odd power */ 2051 2052 /* handle LHS infinity */ 2053 if (decNumberIsInfinite(lhs)) { /* [NaNs already handled] */ 2054 uByte rbits=rhs->bits; /* save */ 2055 uprv_decNumberZero(res); /* prepare */ 2056 if (n==0) *res->lsu=1; /* [-]Inf**0 => 1 */ 2057 else { 2058 /* -Inf**nonint -> error */ 2059 if (!rhsint && decNumberIsNegative(lhs)) { 2060 status|=DEC_Invalid_operation; /* -Inf**nonint is error */ 2061 break;} 2062 if (!(rbits & DECNEG)) bits|=DECINF; /* was not a **-n */ 2063 /* [otherwise will be 0 or -0] */ 2064 res->bits=bits; 2065 } 2066 break;} 2067 2068 /* similarly handle LHS zero */ 2069 if (decNumberIsZero(lhs)) { 2070 if (n==0) { /* 0**0 => Error */ 2071 #if DECSUBSET 2072 if (!set->extended) { /* [unless subset] */ 2073 uprv_decNumberZero(res); 2074 *res->lsu=1; /* return 1 */ 2075 break;} 2076 #endif 2077 status|=DEC_Invalid_operation; 2078 } 2079 else { /* 0**x */ 2080 uByte rbits=rhs->bits; /* save */ 2081 if (rbits & DECNEG) { /* was a 0**(-n) */ 2082 #if DECSUBSET 2083 if (!set->extended) { /* [bad if subset] */ 2084 status|=DEC_Invalid_operation; 2085 break;} 2086 #endif 2087 bits|=DECINF; 2088 } 2089 uprv_decNumberZero(res); /* prepare */ 2090 /* [otherwise will be 0 or -0] */ 2091 res->bits=bits; 2092 } 2093 break;} 2094 2095 /* here both lhs and rhs are finite; rhs==0 is handled in the */ 2096 /* integer path. Next handle the non-integer cases */ 2097 if (!useint) { /* non-integral rhs */ 2098 /* any -ve lhs is bad, as is either operand or context out of */ 2099 /* bounds */ 2100 if (decNumberIsNegative(lhs)) { 2101 status|=DEC_Invalid_operation; 2102 break;} 2103 if (decCheckMath(lhs, set, &status) 2104 || decCheckMath(rhs, set, &status)) break; /* variable status */ 2105 2106 uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */ 2107 aset.emax=DEC_MAX_MATH; /* usual bounds */ 2108 aset.emin=-DEC_MAX_MATH; /* .. */ 2109 aset.clamp=0; /* and no concrete format */ 2110 2111 /* calculate the result using exp(ln(lhs)*rhs), which can */ 2112 /* all be done into the accumulator, dac. The precision needed */ 2113 /* is enough to contain the full information in the lhs (which */ 2114 /* is the total digits, including exponent), or the requested */ 2115 /* precision, if larger, + 4; 6 is used for the exponent */ 2116 /* maximum length, and this is also used when it is shorter */ 2117 /* than the requested digits as it greatly reduces the >0.5 ulp */ 2118 /* cases at little cost (because Ln doubles digits each */ 2119 /* iteration so a few extra digits rarely causes an extra */ 2120 /* iteration) */ 2121 aset.digits=MAXI(lhs->digits, set->digits)+6+4; 2122 } /* non-integer rhs */ 2123 2124 else { /* rhs is in-range integer */ 2125 if (n==0) { /* x**0 = 1 */ 2126 /* (0**0 was handled above) */ 2127 uprv_decNumberZero(res); /* result=1 */ 2128 *res->lsu=1; /* .. */ 2129 break;} 2130 /* rhs is a non-zero integer */ 2131 if (n<0) n=-n; /* use abs(n) */ 2132 2133 aset=*set; /* clone the context */ 2134 aset.round=DEC_ROUND_HALF_EVEN; /* internally use balanced */ 2135 /* calculate the working DIGITS */ 2136 aset.digits=reqdigits+(rhs->digits+rhs->exponent)+2; 2137 #if DECSUBSET 2138 if (!set->extended) aset.digits--; /* use classic precision */ 2139 #endif 2140 /* it's an error if this is more than can be handled */ 2141 if (aset.digits>DECNUMMAXP) {status|=DEC_Invalid_operation; break;} 2142 } /* integer path */ 2143 2144 /* aset.digits is the count of digits for the accumulator needed */ 2145 /* if accumulator is too long for local storage, then allocate */ 2146 needbytes=sizeof(decNumber)+(D2U(aset.digits)-1)*sizeof(Unit); 2147 /* [needbytes also used below if 1/lhs needed] */ 2148 if (needbytes>sizeof(dacbuff)) { 2149 allocdac=(decNumber *)malloc(needbytes); 2150 if (allocdac==NULL) { /* hopeless -- abandon */ 2151 status|=DEC_Insufficient_storage; 2152 break;} 2153 dac=allocdac; /* use the allocated space */ 2154 } 2155 /* here, aset is set up and accumulator is ready for use */ 2156 2157 if (!useint) { /* non-integral rhs */ 2158 /* x ** y; special-case x=1 here as it will otherwise always */ 2159 /* reduce to integer 1; decLnOp has a fastpath which detects */ 2160 /* the case of x=1 */ 2161 decLnOp(dac, lhs, &aset, &status); /* dac=ln(lhs) */ 2162 /* [no error possible, as lhs 0 already handled] */ 2163 if (ISZERO(dac)) { /* x==1, 1.0, etc. */ 2164 /* need to return fully-padded 1.0000 etc., but rhsint->1 */ 2165 *dac->lsu=1; /* was 0, make int 1 */ 2166 if (!rhsint) { /* add padding */ 2167 Int shift=set->digits-1; 2168 dac->digits=decShiftToMost(dac->lsu, 1, shift); 2169 dac->exponent=-shift; /* make 1.0000... */ 2170 status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */ 2171 } 2172 } 2173 else { 2174 decMultiplyOp(dac, dac, rhs, &aset, &status); /* dac=dac*rhs */ 2175 decExpOp(dac, dac, &aset, &status); /* dac=exp(dac) */ 2176 } 2177 /* and drop through for final rounding */ 2178 } /* non-integer rhs */ 2179 2180 else { /* carry on with integer */ 2181 uprv_decNumberZero(dac); /* acc=1 */ 2182 *dac->lsu=1; /* .. */ 2183 2184 /* if a negative power the constant 1 is needed, and if not subset */ 2185 /* invert the lhs now rather than inverting the result later */ 2186 if (decNumberIsNegative(rhs)) { /* was a **-n [hence digits>0] */ 2187 decNumber *inv=invbuff; /* asssume use fixed buffer */ 2188 uprv_decNumberCopy(&dnOne, dac); /* dnOne=1; [needed now or later] */ 2189 #if DECSUBSET 2190 if (set->extended) { /* need to calculate 1/lhs */ 2191 #endif 2192 /* divide lhs into 1, putting result in dac [dac=1/dac] */ 2193 decDivideOp(dac, &dnOne, lhs, &aset, DIVIDE, &status); 2194 /* now locate or allocate space for the inverted lhs */ 2195 if (needbytes>sizeof(invbuff)) { 2196 allocinv=(decNumber *)malloc(needbytes); 2197 if (allocinv==NULL) { /* hopeless -- abandon */ 2198 status|=DEC_Insufficient_storage; 2199 break;} 2200 inv=allocinv; /* use the allocated space */ 2201 } 2202 /* [inv now points to big-enough buffer or allocated storage] */ 2203 uprv_decNumberCopy(inv, dac); /* copy the 1/lhs */ 2204 uprv_decNumberCopy(dac, &dnOne); /* restore acc=1 */ 2205 lhs=inv; /* .. and go forward with new lhs */ 2206 #if DECSUBSET 2207 } 2208 #endif 2209 } 2210 2211 /* Raise-to-the-power loop... */ 2212 seenbit=0; /* set once a 1-bit is encountered */ 2213 for (i=1;;i++){ /* for each bit [top bit ignored] */ 2214 /* abandon if had overflow or terminal underflow */ 2215 if (status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */ 2216 if (status&DEC_Overflow || ISZERO(dac)) break; 2217 } 2218 /* [the following two lines revealed an optimizer bug in a C++ */ 2219 /* compiler, with symptom: 5**3 -> 25, when n=n+n was used] */ 2220 n=n<<1; /* move next bit to testable position */ 2221 if (n<0) { /* top bit is set */ 2222 seenbit=1; /* OK, significant bit seen */ 2223 decMultiplyOp(dac, dac, lhs, &aset, &status); /* dac=dac*x */ 2224 } 2225 if (i==31) break; /* that was the last bit */ 2226 if (!seenbit) continue; /* no need to square 1 */ 2227 decMultiplyOp(dac, dac, dac, &aset, &status); /* dac=dac*dac [square] */ 2228 } /*i*/ /* 32 bits */ 2229 2230 /* complete internal overflow or underflow processing */ 2231 if (status & (DEC_Overflow|DEC_Underflow)) { 2232 #if DECSUBSET 2233 /* If subset, and power was negative, reverse the kind of -erflow */ 2234 /* [1/x not yet done] */ 2235 if (!set->extended && decNumberIsNegative(rhs)) { 2236 if (status & DEC_Overflow) 2237 status^=DEC_Overflow | DEC_Underflow | DEC_Subnormal; 2238 else { /* trickier -- Underflow may or may not be set */ 2239 status&=~(DEC_Underflow | DEC_Subnormal); /* [one or both] */ 2240 status|=DEC_Overflow; 2241 } 2242 } 2243 #endif 2244 dac->bits=(dac->bits & ~DECNEG) | bits; /* force correct sign */ 2245 /* round subnormals [to set.digits rather than aset.digits] */ 2246 /* or set overflow result similarly as required */ 2247 decFinalize(dac, set, &residue, &status); 2248 uprv_decNumberCopy(res, dac); /* copy to result (is now OK length) */ 2249 break; 2250 } 2251 2252 #if DECSUBSET 2253 if (!set->extended && /* subset math */ 2254 decNumberIsNegative(rhs)) { /* was a **-n [hence digits>0] */ 2255 /* so divide result into 1 [dac=1/dac] */ 2256 decDivideOp(dac, &dnOne, dac, &aset, DIVIDE, &status); 2257 } 2258 #endif 2259 } /* rhs integer path */ 2260 2261 /* reduce result to the requested length and copy to result */ 2262 decCopyFit(res, dac, set, &residue, &status); 2263 decFinish(res, set, &residue, &status); /* final cleanup */ 2264 #if DECSUBSET 2265 if (!set->extended) decTrim(res, set, 0, 1, &dropped); /* trailing zeros */ 2266 #endif 2267 } while(0); /* end protected */ 2268 2269 if (allocdac!=NULL) free(allocdac); /* drop any storage used */ 2270 if (allocinv!=NULL) free(allocinv); /* .. */ 2271 #if DECSUBSET 2272 if (alloclhs!=NULL) free(alloclhs); /* .. */ 2273 if (allocrhs!=NULL) free(allocrhs); /* .. */ 2274 #endif 2275 if (status!=0) decStatus(res, status, set); 2276 #if DECCHECK 2277 decCheckInexact(res, set); 2278 #endif 2279 return res; 2280 } /* decNumberPower */ 2281 2282/* ------------------------------------------------------------------ */ 2283/* decNumberQuantize -- force exponent to requested value */ 2284/* */ 2285/* This computes C = op(A, B), where op adjusts the coefficient */ 2286/* of C (by rounding or shifting) such that the exponent (-scale) */ 2287/* of C has exponent of B. The numerical value of C will equal A, */ 2288/* except for the effects of any rounding that occurred. */ 2289/* */ 2290/* res is C, the result. C may be A or B */ 2291/* lhs is A, the number to adjust */ 2292/* rhs is B, the number with exponent to match */ 2293/* set is the context */ 2294/* */ 2295/* C must have space for set->digits digits. */ 2296/* */ 2297/* Unless there is an error or the result is infinite, the exponent */ 2298/* after the operation is guaranteed to be equal to that of B. */ 2299/* ------------------------------------------------------------------ */ 2300U_CAPI decNumber * U_EXPORT2 uprv_decNumberQuantize(decNumber *res, const decNumber *lhs, 2301 const decNumber *rhs, decContext *set) { 2302 uInt status=0; /* accumulator */ 2303 decQuantizeOp(res, lhs, rhs, set, 1, &status); 2304 if (status!=0) decStatus(res, status, set); 2305 return res; 2306 } /* decNumberQuantize */ 2307 2308/* ------------------------------------------------------------------ */ 2309/* decNumberReduce -- remove trailing zeros */ 2310/* */ 2311/* This computes C = 0 + A, and normalizes the result */ 2312/* */ 2313/* res is C, the result. C may be A */ 2314/* rhs is A */ 2315/* set is the context */ 2316/* */ 2317/* C must have space for set->digits digits. */ 2318/* ------------------------------------------------------------------ */ 2319/* Previously known as Normalize */ 2320U_CAPI decNumber * U_EXPORT2 uprv_decNumberNormalize(decNumber *res, const decNumber *rhs, 2321 decContext *set) { 2322 return uprv_decNumberReduce(res, rhs, set); 2323 } /* decNumberNormalize */ 2324 2325U_CAPI decNumber * U_EXPORT2 uprv_decNumberReduce(decNumber *res, const decNumber *rhs, 2326 decContext *set) { 2327 #if DECSUBSET 2328 decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ 2329 #endif 2330 uInt status=0; /* as usual */ 2331 Int residue=0; /* as usual */ 2332 Int dropped; /* work */ 2333 2334 #if DECCHECK 2335 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 2336 #endif 2337 2338 do { /* protect allocated storage */ 2339 #if DECSUBSET 2340 if (!set->extended) { 2341 /* reduce operand and set lostDigits status, as needed */ 2342 if (rhs->digits>set->digits) { 2343 allocrhs=decRoundOperand(rhs, set, &status); 2344 if (allocrhs==NULL) break; 2345 rhs=allocrhs; 2346 } 2347 } 2348 #endif 2349 /* [following code does not require input rounding] */ 2350 2351 /* Infinities copy through; NaNs need usual treatment */ 2352 if (decNumberIsNaN(rhs)) { 2353 decNaNs(res, rhs, NULL, set, &status); 2354 break; 2355 } 2356 2357 /* reduce result to the requested length and copy to result */ 2358 decCopyFit(res, rhs, set, &residue, &status); /* copy & round */ 2359 decFinish(res, set, &residue, &status); /* cleanup/set flags */ 2360 decTrim(res, set, 1, 0, &dropped); /* normalize in place */ 2361 /* [may clamp] */ 2362 } while(0); /* end protected */ 2363 2364 #if DECSUBSET 2365 if (allocrhs !=NULL) free(allocrhs); /* .. */ 2366 #endif 2367 if (status!=0) decStatus(res, status, set);/* then report status */ 2368 return res; 2369 } /* decNumberReduce */ 2370 2371/* ------------------------------------------------------------------ */ 2372/* decNumberRescale -- force exponent to requested value */ 2373/* */ 2374/* This computes C = op(A, B), where op adjusts the coefficient */ 2375/* of C (by rounding or shifting) such that the exponent (-scale) */ 2376/* of C has the value B. The numerical value of C will equal A, */ 2377/* except for the effects of any rounding that occurred. */ 2378/* */ 2379/* res is C, the result. C may be A or B */ 2380/* lhs is A, the number to adjust */ 2381/* rhs is B, the requested exponent */ 2382/* set is the context */ 2383/* */ 2384/* C must have space for set->digits digits. */ 2385/* */ 2386/* Unless there is an error or the result is infinite, the exponent */ 2387/* after the operation is guaranteed to be equal to B. */ 2388/* ------------------------------------------------------------------ */ 2389U_CAPI decNumber * U_EXPORT2 uprv_decNumberRescale(decNumber *res, const decNumber *lhs, 2390 const decNumber *rhs, decContext *set) { 2391 uInt status=0; /* accumulator */ 2392 decQuantizeOp(res, lhs, rhs, set, 0, &status); 2393 if (status!=0) decStatus(res, status, set); 2394 return res; 2395 } /* decNumberRescale */ 2396 2397/* ------------------------------------------------------------------ */ 2398/* decNumberRemainder -- divide and return remainder */ 2399/* */ 2400/* This computes C = A % B */ 2401/* */ 2402/* res is C, the result. C may be A and/or B (e.g., X=X%X) */ 2403/* lhs is A */ 2404/* rhs is B */ 2405/* set is the context */ 2406/* */ 2407/* C must have space for set->digits digits. */ 2408/* ------------------------------------------------------------------ */ 2409U_CAPI decNumber * U_EXPORT2 uprv_decNumberRemainder(decNumber *res, const decNumber *lhs, 2410 const decNumber *rhs, decContext *set) { 2411 uInt status=0; /* accumulator */ 2412 decDivideOp(res, lhs, rhs, set, REMAINDER, &status); 2413 if (status!=0) decStatus(res, status, set); 2414 #if DECCHECK 2415 decCheckInexact(res, set); 2416 #endif 2417 return res; 2418 } /* decNumberRemainder */ 2419 2420/* ------------------------------------------------------------------ */ 2421/* decNumberRemainderNear -- divide and return remainder from nearest */ 2422/* */ 2423/* This computes C = A % B, where % is the IEEE remainder operator */ 2424/* */ 2425/* res is C, the result. C may be A and/or B (e.g., X=X%X) */ 2426/* lhs is A */ 2427/* rhs is B */ 2428/* set is the context */ 2429/* */ 2430/* C must have space for set->digits digits. */ 2431/* ------------------------------------------------------------------ */ 2432U_CAPI decNumber * U_EXPORT2 uprv_decNumberRemainderNear(decNumber *res, const decNumber *lhs, 2433 const decNumber *rhs, decContext *set) { 2434 uInt status=0; /* accumulator */ 2435 decDivideOp(res, lhs, rhs, set, REMNEAR, &status); 2436 if (status!=0) decStatus(res, status, set); 2437 #if DECCHECK 2438 decCheckInexact(res, set); 2439 #endif 2440 return res; 2441 } /* decNumberRemainderNear */ 2442 2443/* ------------------------------------------------------------------ */ 2444/* decNumberRotate -- rotate the coefficient of a Number left/right */ 2445/* */ 2446/* This computes C = A rot B (in base ten and rotating set->digits */ 2447/* digits). */ 2448/* */ 2449/* res is C, the result. C may be A and/or B (e.g., X=XrotX) */ 2450/* lhs is A */ 2451/* rhs is B, the number of digits to rotate (-ve to right) */ 2452/* set is the context */ 2453/* */ 2454/* The digits of the coefficient of A are rotated to the left (if B */ 2455/* is positive) or to the right (if B is negative) without adjusting */ 2456/* the exponent or the sign of A. If lhs->digits is less than */ 2457/* set->digits the coefficient is padded with zeros on the left */ 2458/* before the rotate. Any leading zeros in the result are removed */ 2459/* as usual. */ 2460/* */ 2461/* B must be an integer (q=0) and in the range -set->digits through */ 2462/* +set->digits. */ 2463/* C must have space for set->digits digits. */ 2464/* NaNs are propagated as usual. Infinities are unaffected (but */ 2465/* B must be valid). No status is set unless B is invalid or an */ 2466/* operand is an sNaN. */ 2467/* ------------------------------------------------------------------ */ 2468U_CAPI decNumber * U_EXPORT2 uprv_decNumberRotate(decNumber *res, const decNumber *lhs, 2469 const decNumber *rhs, decContext *set) { 2470 uInt status=0; /* accumulator */ 2471 Int rotate; /* rhs as an Int */ 2472 2473 #if DECCHECK 2474 if (decCheckOperands(res, lhs, rhs, set)) return res; 2475 #endif 2476 2477 /* NaNs propagate as normal */ 2478 if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) 2479 decNaNs(res, lhs, rhs, set, &status); 2480 /* rhs must be an integer */ 2481 else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) 2482 status=DEC_Invalid_operation; 2483 else { /* both numeric, rhs is an integer */ 2484 rotate=decGetInt(rhs); /* [cannot fail] */ 2485 if (rotate==BADINT /* something bad .. */ 2486 || rotate==BIGODD || rotate==BIGEVEN /* .. very big .. */ 2487 || abs(rotate)>set->digits) /* .. or out of range */ 2488 status=DEC_Invalid_operation; 2489 else { /* rhs is OK */ 2490 uprv_decNumberCopy(res, lhs); 2491 /* convert -ve rotate to equivalent positive rotation */ 2492 if (rotate<0) rotate=set->digits+rotate; 2493 if (rotate!=0 && rotate!=set->digits /* zero or full rotation */ 2494 && !decNumberIsInfinite(res)) { /* lhs was infinite */ 2495 /* left-rotate to do; 0 < rotate < set->digits */ 2496 uInt units, shift; /* work */ 2497 uInt msudigits; /* digits in result msu */ 2498 Unit *msu=res->lsu+D2U(res->digits)-1; /* current msu */ 2499 Unit *msumax=res->lsu+D2U(set->digits)-1; /* rotation msu */ 2500 for (msu++; msu<=msumax; msu++) *msu=0; /* ensure high units=0 */ 2501 res->digits=set->digits; /* now full-length */ 2502 msudigits=MSUDIGITS(res->digits); /* actual digits in msu */ 2503 2504 /* rotation here is done in-place, in three steps */ 2505 /* 1. shift all to least up to one unit to unit-align final */ 2506 /* lsd [any digits shifted out are rotated to the left, */ 2507 /* abutted to the original msd (which may require split)] */ 2508 /* */ 2509 /* [if there are no whole units left to rotate, the */ 2510 /* rotation is now complete] */ 2511 /* */ 2512 /* 2. shift to least, from below the split point only, so that */ 2513 /* the final msd is in the right place in its Unit [any */ 2514 /* digits shifted out will fit exactly in the current msu, */ 2515 /* left aligned, no split required] */ 2516 /* */ 2517 /* 3. rotate all the units by reversing left part, right */ 2518 /* part, and then whole */ 2519 /* */ 2520 /* example: rotate right 8 digits (2 units + 2), DECDPUN=3. */ 2521 /* */ 2522 /* start: 00a bcd efg hij klm npq */ 2523 /* */ 2524 /* 1a 000 0ab cde fgh|ijk lmn [pq saved] */ 2525 /* 1b 00p qab cde fgh|ijk lmn */ 2526 /* */ 2527 /* 2a 00p qab cde fgh|00i jkl [mn saved] */ 2528 /* 2b mnp qab cde fgh|00i jkl */ 2529 /* */ 2530 /* 3a fgh cde qab mnp|00i jkl */ 2531 /* 3b fgh cde qab mnp|jkl 00i */ 2532 /* 3c 00i jkl mnp qab cde fgh */ 2533 2534 /* Step 1: amount to shift is the partial right-rotate count */ 2535 rotate=set->digits-rotate; /* make it right-rotate */ 2536 units=rotate/DECDPUN; /* whole units to rotate */ 2537 shift=rotate%DECDPUN; /* left-over digits count */ 2538 if (shift>0) { /* not an exact number of units */ 2539 uInt save=res->lsu[0]%powers[shift]; /* save low digit(s) */ 2540 decShiftToLeast(res->lsu, D2U(res->digits), shift); 2541 if (shift>msudigits) { /* msumax-1 needs >0 digits */ 2542 uInt rem=save%powers[shift-msudigits];/* split save */ 2543 *msumax=(Unit)(save/powers[shift-msudigits]); /* and insert */ 2544 *(msumax-1)=*(msumax-1) 2545 +(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); /* .. */ 2546 } 2547 else { /* all fits in msumax */ 2548 *msumax=*msumax+(Unit)(save*powers[msudigits-shift]); /* [maybe *1] */ 2549 } 2550 } /* digits shift needed */ 2551 2552 /* If whole units to rotate... */ 2553 if (units>0) { /* some to do */ 2554 /* Step 2: the units to touch are the whole ones in rotate, */ 2555 /* if any, and the shift is DECDPUN-msudigits (which may be */ 2556 /* 0, again) */ 2557 shift=DECDPUN-msudigits; 2558 if (shift>0) { /* not an exact number of units */ 2559 uInt save=res->lsu[0]%powers[shift]; /* save low digit(s) */ 2560 decShiftToLeast(res->lsu, units, shift); 2561 *msumax=*msumax+(Unit)(save*powers[msudigits]); 2562 } /* partial shift needed */ 2563 2564 /* Step 3: rotate the units array using triple reverse */ 2565 /* (reversing is easy and fast) */ 2566 decReverse(res->lsu+units, msumax); /* left part */ 2567 decReverse(res->lsu, res->lsu+units-1); /* right part */ 2568 decReverse(res->lsu, msumax); /* whole */ 2569 } /* whole units to rotate */ 2570 /* the rotation may have left an undetermined number of zeros */ 2571 /* on the left, so true length needs to be calculated */ 2572 res->digits=decGetDigits(res->lsu, msumax-res->lsu+1); 2573 } /* rotate needed */ 2574 } /* rhs OK */ 2575 } /* numerics */ 2576 if (status!=0) decStatus(res, status, set); 2577 return res; 2578 } /* decNumberRotate */ 2579 2580/* ------------------------------------------------------------------ */ 2581/* decNumberSameQuantum -- test for equal exponents */ 2582/* */ 2583/* res is the result number, which will contain either 0 or 1 */ 2584/* lhs is a number to test */ 2585/* rhs is the second (usually a pattern) */ 2586/* */ 2587/* No errors are possible and no context is needed. */ 2588/* ------------------------------------------------------------------ */ 2589U_CAPI decNumber * U_EXPORT2 uprv_decNumberSameQuantum(decNumber *res, const decNumber *lhs, 2590 const decNumber *rhs) { 2591 Unit ret=0; /* return value */ 2592 2593 #if DECCHECK 2594 if (decCheckOperands(res, lhs, rhs, DECUNCONT)) return res; 2595 #endif 2596 2597 if (SPECIALARGS) { 2598 if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1; 2599 else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1; 2600 /* [anything else with a special gives 0] */ 2601 } 2602 else if (lhs->exponent==rhs->exponent) ret=1; 2603 2604 uprv_decNumberZero(res); /* OK to overwrite an operand now */ 2605 *res->lsu=ret; 2606 return res; 2607 } /* decNumberSameQuantum */ 2608 2609/* ------------------------------------------------------------------ */ 2610/* decNumberScaleB -- multiply by a power of 10 */ 2611/* */ 2612/* This computes C = A x 10**B where B is an integer (q=0) with */ 2613/* maximum magnitude 2*(emax+digits) */ 2614/* */ 2615/* res is C, the result. C may be A or B */ 2616/* lhs is A, the number to adjust */ 2617/* rhs is B, the requested power of ten to use */ 2618/* set is the context */ 2619/* */ 2620/* C must have space for set->digits digits. */ 2621/* */ 2622/* The result may underflow or overflow. */ 2623/* ------------------------------------------------------------------ */ 2624U_CAPI decNumber * U_EXPORT2 uprv_decNumberScaleB(decNumber *res, const decNumber *lhs, 2625 const decNumber *rhs, decContext *set) { 2626 Int reqexp; /* requested exponent change [B] */ 2627 uInt status=0; /* accumulator */ 2628 Int residue; /* work */ 2629 2630 #if DECCHECK 2631 if (decCheckOperands(res, lhs, rhs, set)) return res; 2632 #endif 2633 2634 /* Handle special values except lhs infinite */ 2635 if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) 2636 decNaNs(res, lhs, rhs, set, &status); 2637 /* rhs must be an integer */ 2638 else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) 2639 status=DEC_Invalid_operation; 2640 else { 2641 /* lhs is a number; rhs is a finite with q==0 */ 2642 reqexp=decGetInt(rhs); /* [cannot fail] */ 2643 if (reqexp==BADINT /* something bad .. */ 2644 || reqexp==BIGODD || reqexp==BIGEVEN /* .. very big .. */ 2645 || abs(reqexp)>(2*(set->digits+set->emax))) /* .. or out of range */ 2646 status=DEC_Invalid_operation; 2647 else { /* rhs is OK */ 2648 uprv_decNumberCopy(res, lhs); /* all done if infinite lhs */ 2649 if (!decNumberIsInfinite(res)) { /* prepare to scale */ 2650 res->exponent+=reqexp; /* adjust the exponent */ 2651 residue=0; 2652 decFinalize(res, set, &residue, &status); /* .. and check */ 2653 } /* finite LHS */ 2654 } /* rhs OK */ 2655 } /* rhs finite */ 2656 if (status!=0) decStatus(res, status, set); 2657 return res; 2658 } /* decNumberScaleB */ 2659 2660/* ------------------------------------------------------------------ */ 2661/* decNumberShift -- shift the coefficient of a Number left or right */ 2662/* */ 2663/* This computes C = A << B or C = A >> -B (in base ten). */ 2664/* */ 2665/* res is C, the result. C may be A and/or B (e.g., X=X<<X) */ 2666/* lhs is A */ 2667/* rhs is B, the number of digits to shift (-ve to right) */ 2668/* set is the context */ 2669/* */ 2670/* The digits of the coefficient of A are shifted to the left (if B */ 2671/* is positive) or to the right (if B is negative) without adjusting */ 2672/* the exponent or the sign of A. */ 2673/* */ 2674/* B must be an integer (q=0) and in the range -set->digits through */ 2675/* +set->digits. */ 2676/* C must have space for set->digits digits. */ 2677/* NaNs are propagated as usual. Infinities are unaffected (but */ 2678/* B must be valid). No status is set unless B is invalid or an */ 2679/* operand is an sNaN. */ 2680/* ------------------------------------------------------------------ */ 2681U_CAPI decNumber * U_EXPORT2 uprv_decNumberShift(decNumber *res, const decNumber *lhs, 2682 const decNumber *rhs, decContext *set) { 2683 uInt status=0; /* accumulator */ 2684 Int shift; /* rhs as an Int */ 2685 2686 #if DECCHECK 2687 if (decCheckOperands(res, lhs, rhs, set)) return res; 2688 #endif 2689 2690 /* NaNs propagate as normal */ 2691 if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) 2692 decNaNs(res, lhs, rhs, set, &status); 2693 /* rhs must be an integer */ 2694 else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) 2695 status=DEC_Invalid_operation; 2696 else { /* both numeric, rhs is an integer */ 2697 shift=decGetInt(rhs); /* [cannot fail] */ 2698 if (shift==BADINT /* something bad .. */ 2699 || shift==BIGODD || shift==BIGEVEN /* .. very big .. */ 2700 || abs(shift)>set->digits) /* .. or out of range */ 2701 status=DEC_Invalid_operation; 2702 else { /* rhs is OK */ 2703 uprv_decNumberCopy(res, lhs); 2704 if (shift!=0 && !decNumberIsInfinite(res)) { /* something to do */ 2705 if (shift>0) { /* to left */ 2706 if (shift==set->digits) { /* removing all */ 2707 *res->lsu=0; /* so place 0 */ 2708 res->digits=1; /* .. */ 2709 } 2710 else { /* */ 2711 /* first remove leading digits if necessary */ 2712 if (res->digits+shift>set->digits) { 2713 decDecap(res, res->digits+shift-set->digits); 2714 /* that updated res->digits; may have gone to 1 (for a */ 2715 /* single digit or for zero */ 2716 } 2717 if (res->digits>1 || *res->lsu) /* if non-zero.. */ 2718 res->digits=decShiftToMost(res->lsu, res->digits, shift); 2719 } /* partial left */ 2720 } /* left */ 2721 else { /* to right */ 2722 if (-shift>=res->digits) { /* discarding all */ 2723 *res->lsu=0; /* so place 0 */ 2724 res->digits=1; /* .. */ 2725 } 2726 else { 2727 decShiftToLeast(res->lsu, D2U(res->digits), -shift); 2728 res->digits-=(-shift); 2729 } 2730 } /* to right */ 2731 } /* non-0 non-Inf shift */ 2732 } /* rhs OK */ 2733 } /* numerics */ 2734 if (status!=0) decStatus(res, status, set); 2735 return res; 2736 } /* decNumberShift */ 2737 2738/* ------------------------------------------------------------------ */ 2739/* decNumberSquareRoot -- square root operator */ 2740/* */ 2741/* This computes C = squareroot(A) */ 2742/* */ 2743/* res is C, the result. C may be A */ 2744/* rhs is A */ 2745/* set is the context; note that rounding mode has no effect */ 2746/* */ 2747/* C must have space for set->digits digits. */ 2748/* ------------------------------------------------------------------ */ 2749/* This uses the following varying-precision algorithm in: */ 2750/* */ 2751/* Properly Rounded Variable Precision Square Root, T. E. Hull and */ 2752/* A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */ 2753/* pp229-237, ACM, September 1985. */ 2754/* */ 2755/* The square-root is calculated using Newton's method, after which */ 2756/* a check is made to ensure the result is correctly rounded. */ 2757/* */ 2758/* % [Reformatted original Numerical Turing source code follows.] */ 2759/* function sqrt(x : real) : real */ 2760/* % sqrt(x) returns the properly rounded approximation to the square */ 2761/* % root of x, in the precision of the calling environment, or it */ 2762/* % fails if x < 0. */ 2763/* % t e hull and a abrham, august, 1984 */ 2764/* if x <= 0 then */ 2765/* if x < 0 then */ 2766/* assert false */ 2767/* else */ 2768/* result 0 */ 2769/* end if */ 2770/* end if */ 2771/* var f := setexp(x, 0) % fraction part of x [0.1 <= x < 1] */ 2772/* var e := getexp(x) % exponent part of x */ 2773/* var approx : real */ 2774/* if e mod 2 = 0 then */ 2775/* approx := .259 + .819 * f % approx to root of f */ 2776/* else */ 2777/* f := f/l0 % adjustments */ 2778/* e := e + 1 % for odd */ 2779/* approx := .0819 + 2.59 * f % exponent */ 2780/* end if */ 2781/* */ 2782/* var p:= 3 */ 2783/* const maxp := currentprecision + 2 */ 2784/* loop */ 2785/* p := min(2*p - 2, maxp) % p = 4,6,10, . . . , maxp */ 2786/* precision p */ 2787/* approx := .5 * (approx + f/approx) */ 2788/* exit when p = maxp */ 2789/* end loop */ 2790/* */ 2791/* % approx is now within 1 ulp of the properly rounded square root */ 2792/* % of f; to ensure proper rounding, compare squares of (approx - */ 2793/* % l/2 ulp) and (approx + l/2 ulp) with f. */ 2794/* p := currentprecision */ 2795/* begin */ 2796/* precision p + 2 */ 2797/* const approxsubhalf := approx - setexp(.5, -p) */ 2798/* if mulru(approxsubhalf, approxsubhalf) > f then */ 2799/* approx := approx - setexp(.l, -p + 1) */ 2800/* else */ 2801/* const approxaddhalf := approx + setexp(.5, -p) */ 2802/* if mulrd(approxaddhalf, approxaddhalf) < f then */ 2803/* approx := approx + setexp(.l, -p + 1) */ 2804/* end if */ 2805/* end if */ 2806/* end */ 2807/* result setexp(approx, e div 2) % fix exponent */ 2808/* end sqrt */ 2809/* ------------------------------------------------------------------ */ 2810#if defined(__clang__) || (defined(__GNUC__) && ((__GNUC__ * 100 + __GNUC_MINOR__) >= 406)) 2811#pragma GCC diagnostic push 2812#pragma GCC diagnostic ignored "-Warray-bounds" 2813#endif 2814U_CAPI decNumber * U_EXPORT2 uprv_decNumberSquareRoot(decNumber *res, const decNumber *rhs, 2815 decContext *set) { 2816 decContext workset, approxset; /* work contexts */ 2817 decNumber dzero; /* used for constant zero */ 2818 Int maxp; /* largest working precision */ 2819 Int workp; /* working precision */ 2820 Int residue=0; /* rounding residue */ 2821 uInt status=0, ignore=0; /* status accumulators */ 2822 uInt rstatus; /* .. */ 2823 Int exp; /* working exponent */ 2824 Int ideal; /* ideal (preferred) exponent */ 2825 Int needbytes; /* work */ 2826 Int dropped; /* .. */ 2827 2828 #if DECSUBSET 2829 decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ 2830 #endif 2831 /* buffer for f [needs +1 in case DECBUFFER 0] */ 2832 decNumber buff[D2N(DECBUFFER+1)]; 2833 /* buffer for a [needs +2 to match likely maxp] */ 2834 decNumber bufa[D2N(DECBUFFER+2)]; 2835 /* buffer for temporary, b [must be same size as a] */ 2836 decNumber bufb[D2N(DECBUFFER+2)]; 2837 decNumber *allocbuff=NULL; /* -> allocated buff, iff allocated */ 2838 decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ 2839 decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */ 2840 decNumber *f=buff; /* reduced fraction */ 2841 decNumber *a=bufa; /* approximation to result */ 2842 decNumber *b=bufb; /* intermediate result */ 2843 /* buffer for temporary variable, up to 3 digits */ 2844 decNumber buft[D2N(3)]; 2845 decNumber *t=buft; /* up-to-3-digit constant or work */ 2846 2847 #if DECCHECK 2848 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 2849 #endif 2850 2851 do { /* protect allocated storage */ 2852 #if DECSUBSET 2853 if (!set->extended) { 2854 /* reduce operand and set lostDigits status, as needed */ 2855 if (rhs->digits>set->digits) { 2856 allocrhs=decRoundOperand(rhs, set, &status); 2857 if (allocrhs==NULL) break; 2858 /* [Note: 'f' allocation below could reuse this buffer if */ 2859 /* used, but as this is rare they are kept separate for clarity.] */ 2860 rhs=allocrhs; 2861 } 2862 } 2863 #endif 2864 /* [following code does not require input rounding] */ 2865 2866 /* handle infinities and NaNs */ 2867 if (SPECIALARG) { 2868 if (decNumberIsInfinite(rhs)) { /* an infinity */ 2869 if (decNumberIsNegative(rhs)) status|=DEC_Invalid_operation; 2870 else uprv_decNumberCopy(res, rhs); /* +Infinity */ 2871 } 2872 else decNaNs(res, rhs, NULL, set, &status); /* a NaN */ 2873 break; 2874 } 2875 2876 /* calculate the ideal (preferred) exponent [floor(exp/2)] */ 2877 /* [It would be nicer to write: ideal=rhs->exponent>>1, but this */ 2878 /* generates a compiler warning. Generated code is the same.] */ 2879 ideal=(rhs->exponent&~1)/2; /* target */ 2880 2881 /* handle zeros */ 2882 if (ISZERO(rhs)) { 2883 uprv_decNumberCopy(res, rhs); /* could be 0 or -0 */ 2884 res->exponent=ideal; /* use the ideal [safe] */ 2885 /* use decFinish to clamp any out-of-range exponent, etc. */ 2886 decFinish(res, set, &residue, &status); 2887 break; 2888 } 2889 2890 /* any other -x is an oops */ 2891 if (decNumberIsNegative(rhs)) { 2892 status|=DEC_Invalid_operation; 2893 break; 2894 } 2895 2896 /* space is needed for three working variables */ 2897 /* f -- the same precision as the RHS, reduced to 0.01->0.99... */ 2898 /* a -- Hull's approximation -- precision, when assigned, is */ 2899 /* currentprecision+1 or the input argument precision, */ 2900 /* whichever is larger (+2 for use as temporary) */ 2901 /* b -- intermediate temporary result (same size as a) */ 2902 /* if any is too long for local storage, then allocate */ 2903 workp=MAXI(set->digits+1, rhs->digits); /* actual rounding precision */ 2904 workp=MAXI(workp, 7); /* at least 7 for low cases */ 2905 maxp=workp+2; /* largest working precision */ 2906 2907 needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); 2908 if (needbytes>(Int)sizeof(buff)) { 2909 allocbuff=(decNumber *)malloc(needbytes); 2910 if (allocbuff==NULL) { /* hopeless -- abandon */ 2911 status|=DEC_Insufficient_storage; 2912 break;} 2913 f=allocbuff; /* use the allocated space */ 2914 } 2915 /* a and b both need to be able to hold a maxp-length number */ 2916 needbytes=sizeof(decNumber)+(D2U(maxp)-1)*sizeof(Unit); 2917 if (needbytes>(Int)sizeof(bufa)) { /* [same applies to b] */ 2918 allocbufa=(decNumber *)malloc(needbytes); 2919 allocbufb=(decNumber *)malloc(needbytes); 2920 if (allocbufa==NULL || allocbufb==NULL) { /* hopeless */ 2921 status|=DEC_Insufficient_storage; 2922 break;} 2923 a=allocbufa; /* use the allocated spaces */ 2924 b=allocbufb; /* .. */ 2925 } 2926 2927 /* copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1 */ 2928 uprv_decNumberCopy(f, rhs); 2929 exp=f->exponent+f->digits; /* adjusted to Hull rules */ 2930 f->exponent=-(f->digits); /* to range */ 2931 2932 /* set up working context */ 2933 uprv_decContextDefault(&workset, DEC_INIT_DECIMAL64); 2934 workset.emax=DEC_MAX_EMAX; 2935 workset.emin=DEC_MIN_EMIN; 2936 2937 /* [Until further notice, no error is possible and status bits */ 2938 /* (Rounded, etc.) should be ignored, not accumulated.] */ 2939 2940 /* Calculate initial approximation, and allow for odd exponent */ 2941 workset.digits=workp; /* p for initial calculation */ 2942 t->bits=0; t->digits=3; 2943 a->bits=0; a->digits=3; 2944 if ((exp & 1)==0) { /* even exponent */ 2945 /* Set t=0.259, a=0.819 */ 2946 t->exponent=-3; 2947 a->exponent=-3; 2948 #if DECDPUN>=3 2949 t->lsu[0]=259; 2950 a->lsu[0]=819; 2951 #elif DECDPUN==2 2952 t->lsu[0]=59; t->lsu[1]=2; 2953 a->lsu[0]=19; a->lsu[1]=8; 2954 #else 2955 t->lsu[0]=9; t->lsu[1]=5; t->lsu[2]=2; 2956 a->lsu[0]=9; a->lsu[1]=1; a->lsu[2]=8; 2957 #endif 2958 } 2959 else { /* odd exponent */ 2960 /* Set t=0.0819, a=2.59 */ 2961 f->exponent--; /* f=f/10 */ 2962 exp++; /* e=e+1 */ 2963 t->exponent=-4; 2964 a->exponent=-2; 2965 #if DECDPUN>=3 2966 t->lsu[0]=819; 2967 a->lsu[0]=259; 2968 #elif DECDPUN==2 2969 t->lsu[0]=19; t->lsu[1]=8; 2970 a->lsu[0]=59; a->lsu[1]=2; 2971 #else 2972 t->lsu[0]=9; t->lsu[1]=1; t->lsu[2]=8; 2973 a->lsu[0]=9; a->lsu[1]=5; a->lsu[2]=2; 2974 #endif 2975 } 2976 2977 decMultiplyOp(a, a, f, &workset, &ignore); /* a=a*f */ 2978 decAddOp(a, a, t, &workset, 0, &ignore); /* ..+t */ 2979 /* [a is now the initial approximation for sqrt(f), calculated with */ 2980 /* currentprecision, which is also a's precision.] */ 2981 2982 /* the main calculation loop */ 2983 uprv_decNumberZero(&dzero); /* make 0 */ 2984 uprv_decNumberZero(t); /* set t = 0.5 */ 2985 t->lsu[0]=5; /* .. */ 2986 t->exponent=-1; /* .. */ 2987 workset.digits=3; /* initial p */ 2988 for (; workset.digits<maxp;) { 2989 /* set p to min(2*p - 2, maxp) [hence 3; or: 4, 6, 10, ... , maxp] */ 2990 workset.digits=MINI(workset.digits*2-2, maxp); 2991 /* a = 0.5 * (a + f/a) */ 2992 /* [calculated at p then rounded to currentprecision] */ 2993 decDivideOp(b, f, a, &workset, DIVIDE, &ignore); /* b=f/a */ 2994 decAddOp(b, b, a, &workset, 0, &ignore); /* b=b+a */ 2995 decMultiplyOp(a, b, t, &workset, &ignore); /* a=b*0.5 */ 2996 } /* loop */ 2997 2998 /* Here, 0.1 <= a < 1 [Hull], and a has maxp digits */ 2999 /* now reduce to length, etc.; this needs to be done with a */ 3000 /* having the correct exponent so as to handle subnormals */ 3001 /* correctly */ 3002 approxset=*set; /* get emin, emax, etc. */ 3003 approxset.round=DEC_ROUND_HALF_EVEN; 3004 a->exponent+=exp/2; /* set correct exponent */ 3005 rstatus=0; /* clear status */ 3006 residue=0; /* .. and accumulator */ 3007 decCopyFit(a, a, &approxset, &residue, &rstatus); /* reduce (if needed) */ 3008 decFinish(a, &approxset, &residue, &rstatus); /* clean and finalize */ 3009 3010 /* Overflow was possible if the input exponent was out-of-range, */ 3011 /* in which case quit */ 3012 if (rstatus&DEC_Overflow) { 3013 status=rstatus; /* use the status as-is */ 3014 uprv_decNumberCopy(res, a); /* copy to result */ 3015 break; 3016 } 3017 3018 /* Preserve status except Inexact/Rounded */ 3019 status|=(rstatus & ~(DEC_Rounded|DEC_Inexact)); 3020 3021 /* Carry out the Hull correction */ 3022 a->exponent-=exp/2; /* back to 0.1->1 */ 3023 3024 /* a is now at final precision and within 1 ulp of the properly */ 3025 /* rounded square root of f; to ensure proper rounding, compare */ 3026 /* squares of (a - l/2 ulp) and (a + l/2 ulp) with f. */ 3027 /* Here workset.digits=maxp and t=0.5, and a->digits determines */ 3028 /* the ulp */ 3029 workset.digits--; /* maxp-1 is OK now */ 3030 t->exponent=-a->digits-1; /* make 0.5 ulp */ 3031 decAddOp(b, a, t, &workset, DECNEG, &ignore); /* b = a - 0.5 ulp */ 3032 workset.round=DEC_ROUND_UP; 3033 decMultiplyOp(b, b, b, &workset, &ignore); /* b = mulru(b, b) */ 3034 decCompareOp(b, f, b, &workset, COMPARE, &ignore); /* b ? f, reversed */ 3035 if (decNumberIsNegative(b)) { /* f < b [i.e., b > f] */ 3036 /* this is the more common adjustment, though both are rare */ 3037 t->exponent++; /* make 1.0 ulp */ 3038 t->lsu[0]=1; /* .. */ 3039 decAddOp(a, a, t, &workset, DECNEG, &ignore); /* a = a - 1 ulp */ 3040 /* assign to approx [round to length] */ 3041 approxset.emin-=exp/2; /* adjust to match a */ 3042 approxset.emax-=exp/2; 3043 decAddOp(a, &dzero, a, &approxset, 0, &ignore); 3044 } 3045 else { 3046 decAddOp(b, a, t, &workset, 0, &ignore); /* b = a + 0.5 ulp */ 3047 workset.round=DEC_ROUND_DOWN; 3048 decMultiplyOp(b, b, b, &workset, &ignore); /* b = mulrd(b, b) */ 3049 decCompareOp(b, b, f, &workset, COMPARE, &ignore); /* b ? f */ 3050 if (decNumberIsNegative(b)) { /* b < f */ 3051 t->exponent++; /* make 1.0 ulp */ 3052 t->lsu[0]=1; /* .. */ 3053 decAddOp(a, a, t, &workset, 0, &ignore); /* a = a + 1 ulp */ 3054 /* assign to approx [round to length] */ 3055 approxset.emin-=exp/2; /* adjust to match a */ 3056 approxset.emax-=exp/2; 3057 decAddOp(a, &dzero, a, &approxset, 0, &ignore); 3058 } 3059 } 3060 /* [no errors are possible in the above, and rounding/inexact during */ 3061 /* estimation are irrelevant, so status was not accumulated] */ 3062 3063 /* Here, 0.1 <= a < 1 (still), so adjust back */ 3064 a->exponent+=exp/2; /* set correct exponent */ 3065 3066 /* count droppable zeros [after any subnormal rounding] by */ 3067 /* trimming a copy */ 3068 uprv_decNumberCopy(b, a); 3069 decTrim(b, set, 1, 1, &dropped); /* [drops trailing zeros] */ 3070 3071 /* Set Inexact and Rounded. The answer can only be exact if */ 3072 /* it is short enough so that squaring it could fit in workp */ 3073 /* digits, so this is the only (relatively rare) condition that */ 3074 /* a careful check is needed */ 3075 if (b->digits*2-1 > workp) { /* cannot fit */ 3076 status|=DEC_Inexact|DEC_Rounded; 3077 } 3078 else { /* could be exact/unrounded */ 3079 uInt mstatus=0; /* local status */ 3080 decMultiplyOp(b, b, b, &workset, &mstatus); /* try the multiply */ 3081 if (mstatus&DEC_Overflow) { /* result just won't fit */ 3082 status|=DEC_Inexact|DEC_Rounded; 3083 } 3084 else { /* plausible */ 3085 decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); /* b ? rhs */ 3086 if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; /* not equal */ 3087 else { /* is Exact */ 3088 /* here, dropped is the count of trailing zeros in 'a' */ 3089 /* use closest exponent to ideal... */ 3090 Int todrop=ideal-a->exponent; /* most that can be dropped */ 3091 if (todrop<0) status|=DEC_Rounded; /* ideally would add 0s */ 3092 else { /* unrounded */ 3093 /* there are some to drop, but emax may not allow all */ 3094 Int maxexp=set->emax-set->digits+1; 3095 Int maxdrop=maxexp-a->exponent; 3096 if (todrop>maxdrop && set->clamp) { /* apply clamping */ 3097 todrop=maxdrop; 3098 status|=DEC_Clamped; 3099 } 3100 if (dropped<todrop) { /* clamp to those available */ 3101 todrop=dropped; 3102 status|=DEC_Clamped; 3103 } 3104 if (todrop>0) { /* have some to drop */ 3105 decShiftToLeast(a->lsu, D2U(a->digits), todrop); 3106 a->exponent+=todrop; /* maintain numerical value */ 3107 a->digits-=todrop; /* new length */ 3108 } 3109 } 3110 } 3111 } 3112 } 3113 3114 /* double-check Underflow, as perhaps the result could not have */ 3115 /* been subnormal (initial argument too big), or it is now Exact */ 3116 if (status&DEC_Underflow) { 3117 Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */ 3118 /* check if truly subnormal */ 3119 #if DECEXTFLAG /* DEC_Subnormal too */ 3120 if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow); 3121 #else 3122 if (ae>=set->emin*2) status&=~DEC_Underflow; 3123 #endif 3124 /* check if truly inexact */ 3125 if (!(status&DEC_Inexact)) status&=~DEC_Underflow; 3126 } 3127 3128 uprv_decNumberCopy(res, a); /* a is now the result */ 3129 } while(0); /* end protected */ 3130 3131 if (allocbuff!=NULL) free(allocbuff); /* drop any storage used */ 3132 if (allocbufa!=NULL) free(allocbufa); /* .. */ 3133 if (allocbufb!=NULL) free(allocbufb); /* .. */ 3134 #if DECSUBSET 3135 if (allocrhs !=NULL) free(allocrhs); /* .. */ 3136 #endif 3137 if (status!=0) decStatus(res, status, set);/* then report status */ 3138 #if DECCHECK 3139 decCheckInexact(res, set); 3140 #endif 3141 return res; 3142 } /* decNumberSquareRoot */ 3143#if defined(__clang__) || (defined(__GNUC__) && ((__GNUC__ * 100 + __GNUC_MINOR__) >= 406)) 3144#pragma GCC diagnostic pop 3145#endif 3146 3147/* ------------------------------------------------------------------ */ 3148/* decNumberSubtract -- subtract two Numbers */ 3149/* */ 3150/* This computes C = A - B */ 3151/* */ 3152/* res is C, the result. C may be A and/or B (e.g., X=X-X) */ 3153/* lhs is A */ 3154/* rhs is B */ 3155/* set is the context */ 3156/* */ 3157/* C must have space for set->digits digits. */ 3158/* ------------------------------------------------------------------ */ 3159U_CAPI decNumber * U_EXPORT2 uprv_decNumberSubtract(decNumber *res, const decNumber *lhs, 3160 const decNumber *rhs, decContext *set) { 3161 uInt status=0; /* accumulator */ 3162 3163 decAddOp(res, lhs, rhs, set, DECNEG, &status); 3164 if (status!=0) decStatus(res, status, set); 3165 #if DECCHECK 3166 decCheckInexact(res, set); 3167 #endif 3168 return res; 3169 } /* decNumberSubtract */ 3170 3171/* ------------------------------------------------------------------ */ 3172/* decNumberToIntegralExact -- round-to-integral-value with InExact */ 3173/* decNumberToIntegralValue -- round-to-integral-value */ 3174/* */ 3175/* res is the result */ 3176/* rhs is input number */ 3177/* set is the context */ 3178/* */ 3179/* res must have space for any value of rhs. */ 3180/* */ 3181/* This implements the IEEE special operators and therefore treats */ 3182/* special values as valid. For finite numbers it returns */ 3183/* rescale(rhs, 0) if rhs->exponent is <0. */ 3184/* Otherwise the result is rhs (so no error is possible, except for */ 3185/* sNaN). */ 3186/* */ 3187/* The context is used for rounding mode and status after sNaN, but */ 3188/* the digits setting is ignored. The Exact version will signal */ 3189/* Inexact if the result differs numerically from rhs; the other */ 3190/* never signals Inexact. */ 3191/* ------------------------------------------------------------------ */ 3192U_CAPI decNumber * U_EXPORT2 uprv_decNumberToIntegralExact(decNumber *res, const decNumber *rhs, 3193 decContext *set) { 3194 decNumber dn; 3195 decContext workset; /* working context */ 3196 uInt status=0; /* accumulator */ 3197 3198 #if DECCHECK 3199 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 3200 #endif 3201 3202 /* handle infinities and NaNs */ 3203 if (SPECIALARG) { 3204 if (decNumberIsInfinite(rhs)) uprv_decNumberCopy(res, rhs); /* an Infinity */ 3205 else decNaNs(res, rhs, NULL, set, &status); /* a NaN */ 3206 } 3207 else { /* finite */ 3208 /* have a finite number; no error possible (res must be big enough) */ 3209 if (rhs->exponent>=0) return uprv_decNumberCopy(res, rhs); 3210 /* that was easy, but if negative exponent there is work to do... */ 3211 workset=*set; /* clone rounding, etc. */ 3212 workset.digits=rhs->digits; /* no length rounding */ 3213 workset.traps=0; /* no traps */ 3214 uprv_decNumberZero(&dn); /* make a number with exponent 0 */ 3215 uprv_decNumberQuantize(res, rhs, &dn, &workset); 3216 status|=workset.status; 3217 } 3218 if (status!=0) decStatus(res, status, set); 3219 return res; 3220 } /* decNumberToIntegralExact */ 3221 3222U_CAPI decNumber * U_EXPORT2 uprv_decNumberToIntegralValue(decNumber *res, const decNumber *rhs, 3223 decContext *set) { 3224 decContext workset=*set; /* working context */ 3225 workset.traps=0; /* no traps */ 3226 uprv_decNumberToIntegralExact(res, rhs, &workset); 3227 /* this never affects set, except for sNaNs; NaN will have been set */ 3228 /* or propagated already, so no need to call decStatus */ 3229 set->status|=workset.status&DEC_Invalid_operation; 3230 return res; 3231 } /* decNumberToIntegralValue */ 3232 3233/* ------------------------------------------------------------------ */ 3234/* decNumberXor -- XOR two Numbers, digitwise */ 3235/* */ 3236/* This computes C = A ^ B */ 3237/* */ 3238/* res is C, the result. C may be A and/or B (e.g., X=X^X) */ 3239/* lhs is A */ 3240/* rhs is B */ 3241/* set is the context (used for result length and error report) */ 3242/* */ 3243/* C must have space for set->digits digits. */ 3244/* */ 3245/* Logical function restrictions apply (see above); a NaN is */ 3246/* returned with Invalid_operation if a restriction is violated. */ 3247/* ------------------------------------------------------------------ */ 3248U_CAPI decNumber * U_EXPORT2 uprv_decNumberXor(decNumber *res, const decNumber *lhs, 3249 const decNumber *rhs, decContext *set) { 3250 const Unit *ua, *ub; /* -> operands */ 3251 const Unit *msua, *msub; /* -> operand msus */ 3252 Unit *uc, *msuc; /* -> result and its msu */ 3253 Int msudigs; /* digits in res msu */ 3254 #if DECCHECK 3255 if (decCheckOperands(res, lhs, rhs, set)) return res; 3256 #endif 3257 3258 if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) 3259 || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { 3260 decStatus(res, DEC_Invalid_operation, set); 3261 return res; 3262 } 3263 /* operands are valid */ 3264 ua=lhs->lsu; /* bottom-up */ 3265 ub=rhs->lsu; /* .. */ 3266 uc=res->lsu; /* .. */ 3267 msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */ 3268 msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */ 3269 msuc=uc+D2U(set->digits)-1; /* -> msu of result */ 3270 msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ 3271 for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */ 3272 Unit a, b; /* extract units */ 3273 if (ua>msua) a=0; 3274 else a=*ua; 3275 if (ub>msub) b=0; 3276 else b=*ub; 3277 *uc=0; /* can now write back */ 3278 if (a|b) { /* maybe 1 bits to examine */ 3279 Int i, j; 3280 /* This loop could be unrolled and/or use BIN2BCD tables */ 3281 for (i=0; i<DECDPUN; i++) { 3282 if ((a^b)&1) *uc=*uc+(Unit)powers[i]; /* effect XOR */ 3283 j=a%10; 3284 a=a/10; 3285 j|=b%10; 3286 b=b/10; 3287 if (j>1) { 3288 decStatus(res, DEC_Invalid_operation, set); 3289 return res; 3290 } 3291 if (uc==msuc && i==msudigs-1) break; /* just did final digit */ 3292 } /* each digit */ 3293 } /* non-zero */ 3294 } /* each unit */ 3295 /* [here uc-1 is the msu of the result] */ 3296 res->digits=decGetDigits(res->lsu, uc-res->lsu); 3297 res->exponent=0; /* integer */ 3298 res->bits=0; /* sign=0 */ 3299 return res; /* [no status to set] */ 3300 } /* decNumberXor */ 3301 3302 3303/* ================================================================== */ 3304/* Utility routines */ 3305/* ================================================================== */ 3306 3307/* ------------------------------------------------------------------ */ 3308/* decNumberClass -- return the decClass of a decNumber */ 3309/* dn -- the decNumber to test */ 3310/* set -- the context to use for Emin */ 3311/* returns the decClass enum */ 3312/* ------------------------------------------------------------------ */ 3313enum decClass uprv_decNumberClass(const decNumber *dn, decContext *set) { 3314 if (decNumberIsSpecial(dn)) { 3315 if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN; 3316 if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN; 3317 /* must be an infinity */ 3318 if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF; 3319 return DEC_CLASS_POS_INF; 3320 } 3321 /* is finite */ 3322 if (uprv_decNumberIsNormal(dn, set)) { /* most common */ 3323 if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL; 3324 return DEC_CLASS_POS_NORMAL; 3325 } 3326 /* is subnormal or zero */ 3327 if (decNumberIsZero(dn)) { /* most common */ 3328 if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO; 3329 return DEC_CLASS_POS_ZERO; 3330 } 3331 if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL; 3332 return DEC_CLASS_POS_SUBNORMAL; 3333 } /* decNumberClass */ 3334 3335/* ------------------------------------------------------------------ */ 3336/* decNumberClassToString -- convert decClass to a string */ 3337/* */ 3338/* eclass is a valid decClass */ 3339/* returns a constant string describing the class (max 13+1 chars) */ 3340/* ------------------------------------------------------------------ */ 3341const char *uprv_decNumberClassToString(enum decClass eclass) { 3342 if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN; 3343 if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN; 3344 if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ; 3345 if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ; 3346 if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS; 3347 if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS; 3348 if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI; 3349 if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI; 3350 if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN; 3351 if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN; 3352 return DEC_ClassString_UN; /* Unknown */ 3353 } /* decNumberClassToString */ 3354 3355/* ------------------------------------------------------------------ */ 3356/* decNumberCopy -- copy a number */ 3357/* */ 3358/* dest is the target decNumber */ 3359/* src is the source decNumber */ 3360/* returns dest */ 3361/* */ 3362/* (dest==src is allowed and is a no-op) */ 3363/* All fields are updated as required. This is a utility operation, */ 3364/* so special values are unchanged and no error is possible. */ 3365/* ------------------------------------------------------------------ */ 3366U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopy(decNumber *dest, const decNumber *src) { 3367 3368 #if DECCHECK 3369 if (src==NULL) return uprv_decNumberZero(dest); 3370 #endif 3371 3372 if (dest==src) return dest; /* no copy required */ 3373 3374 /* Use explicit assignments here as structure assignment could copy */ 3375 /* more than just the lsu (for small DECDPUN). This would not affect */ 3376 /* the value of the results, but could disturb test harness spill */ 3377 /* checking. */ 3378 dest->bits=src->bits; 3379 dest->exponent=src->exponent; 3380 dest->digits=src->digits; 3381 dest->lsu[0]=src->lsu[0]; 3382 if (src->digits>DECDPUN) { /* more Units to come */ 3383 const Unit *smsup, *s; /* work */ 3384 Unit *d; /* .. */ 3385 /* memcpy for the remaining Units would be safe as they cannot */ 3386 /* overlap. However, this explicit loop is faster in short cases. */ 3387 d=dest->lsu+1; /* -> first destination */ 3388 smsup=src->lsu+D2U(src->digits); /* -> source msu+1 */ 3389 for (s=src->lsu+1; s<smsup; s++, d++) *d=*s; 3390 } 3391 return dest; 3392 } /* decNumberCopy */ 3393 3394/* ------------------------------------------------------------------ */ 3395/* decNumberCopyAbs -- quiet absolute value operator */ 3396/* */ 3397/* This sets C = abs(A) */ 3398/* */ 3399/* res is C, the result. C may be A */ 3400/* rhs is A */ 3401/* */ 3402/* C must have space for set->digits digits. */ 3403/* No exception or error can occur; this is a quiet bitwise operation.*/ 3404/* See also decNumberAbs for a checking version of this. */ 3405/* ------------------------------------------------------------------ */ 3406U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopyAbs(decNumber *res, const decNumber *rhs) { 3407 #if DECCHECK 3408 if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; 3409 #endif 3410 uprv_decNumberCopy(res, rhs); 3411 res->bits&=~DECNEG; /* turn off sign */ 3412 return res; 3413 } /* decNumberCopyAbs */ 3414 3415/* ------------------------------------------------------------------ */ 3416/* decNumberCopyNegate -- quiet negate value operator */ 3417/* */ 3418/* This sets C = negate(A) */ 3419/* */ 3420/* res is C, the result. C may be A */ 3421/* rhs is A */ 3422/* */ 3423/* C must have space for set->digits digits. */ 3424/* No exception or error can occur; this is a quiet bitwise operation.*/ 3425/* See also decNumberMinus for a checking version of this. */ 3426/* ------------------------------------------------------------------ */ 3427U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopyNegate(decNumber *res, const decNumber *rhs) { 3428 #if DECCHECK 3429 if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; 3430 #endif 3431 uprv_decNumberCopy(res, rhs); 3432 res->bits^=DECNEG; /* invert the sign */ 3433 return res; 3434 } /* decNumberCopyNegate */ 3435 3436/* ------------------------------------------------------------------ */ 3437/* decNumberCopySign -- quiet copy and set sign operator */ 3438/* */ 3439/* This sets C = A with the sign of B */ 3440/* */ 3441/* res is C, the result. C may be A */ 3442/* lhs is A */ 3443/* rhs is B */ 3444/* */ 3445/* C must have space for set->digits digits. */ 3446/* No exception or error can occur; this is a quiet bitwise operation.*/ 3447/* ------------------------------------------------------------------ */ 3448U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopySign(decNumber *res, const decNumber *lhs, 3449 const decNumber *rhs) { 3450 uByte sign; /* rhs sign */ 3451 #if DECCHECK 3452 if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; 3453 #endif 3454 sign=rhs->bits & DECNEG; /* save sign bit */ 3455 uprv_decNumberCopy(res, lhs); 3456 res->bits&=~DECNEG; /* clear the sign */ 3457 res->bits|=sign; /* set from rhs */ 3458 return res; 3459 } /* decNumberCopySign */ 3460 3461/* ------------------------------------------------------------------ */ 3462/* decNumberGetBCD -- get the coefficient in BCD8 */ 3463/* dn is the source decNumber */ 3464/* bcd is the uInt array that will receive dn->digits BCD bytes, */ 3465/* most-significant at offset 0 */ 3466/* returns bcd */ 3467/* */ 3468/* bcd must have at least dn->digits bytes. No error is possible; if */ 3469/* dn is a NaN or Infinite, digits must be 1 and the coefficient 0. */ 3470/* ------------------------------------------------------------------ */ 3471U_CAPI uByte * U_EXPORT2 uprv_decNumberGetBCD(const decNumber *dn, uByte *bcd) { 3472 uByte *ub=bcd+dn->digits-1; /* -> lsd */ 3473 const Unit *up=dn->lsu; /* Unit pointer, -> lsu */ 3474 3475 #if DECDPUN==1 /* trivial simple copy */ 3476 for (; ub>=bcd; ub--, up++) *ub=*up; 3477 #else /* chopping needed */ 3478 uInt u=*up; /* work */ 3479 uInt cut=DECDPUN; /* downcounter through unit */ 3480 for (; ub>=bcd; ub--) { 3481 *ub=(uByte)(u%10); /* [*6554 trick inhibits, here] */ 3482 u=u/10; 3483 cut--; 3484 if (cut>0) continue; /* more in this unit */ 3485 up++; 3486 u=*up; 3487 cut=DECDPUN; 3488 } 3489 #endif 3490 return bcd; 3491 } /* decNumberGetBCD */ 3492 3493/* ------------------------------------------------------------------ */ 3494/* decNumberSetBCD -- set (replace) the coefficient from BCD8 */ 3495/* dn is the target decNumber */ 3496/* bcd is the uInt array that will source n BCD bytes, most- */ 3497/* significant at offset 0 */ 3498/* n is the number of digits in the source BCD array (bcd) */ 3499/* returns dn */ 3500/* */ 3501/* dn must have space for at least n digits. No error is possible; */ 3502/* if dn is a NaN, or Infinite, or is to become a zero, n must be 1 */ 3503/* and bcd[0] zero. */ 3504/* ------------------------------------------------------------------ */ 3505U_CAPI decNumber * U_EXPORT2 uprv_decNumberSetBCD(decNumber *dn, const uByte *bcd, uInt n) { 3506 Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [target pointer] */ 3507 const uByte *ub=bcd; /* -> source msd */ 3508 3509 #if DECDPUN==1 /* trivial simple copy */ 3510 for (; ub<bcd+n; ub++, up--) *up=*ub; 3511 #else /* some assembly needed */ 3512 /* calculate how many digits in msu, and hence first cut */ 3513 Int cut=MSUDIGITS(n); /* [faster than remainder] */ 3514 for (;up>=dn->lsu; up--) { /* each Unit from msu */ 3515 *up=0; /* will take <=DECDPUN digits */ 3516 for (; cut>0; ub++, cut--) *up=X10(*up)+*ub; 3517 cut=DECDPUN; /* next Unit has all digits */ 3518 } 3519 #endif 3520 dn->digits=n; /* set digit count */ 3521 return dn; 3522 } /* decNumberSetBCD */ 3523 3524/* ------------------------------------------------------------------ */ 3525/* decNumberIsNormal -- test normality of a decNumber */ 3526/* dn is the decNumber to test */ 3527/* set is the context to use for Emin */ 3528/* returns 1 if |dn| is finite and >=Nmin, 0 otherwise */ 3529/* ------------------------------------------------------------------ */ 3530Int uprv_decNumberIsNormal(const decNumber *dn, decContext *set) { 3531 Int ae; /* adjusted exponent */ 3532 #if DECCHECK 3533 if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; 3534 #endif 3535 3536 if (decNumberIsSpecial(dn)) return 0; /* not finite */ 3537 if (decNumberIsZero(dn)) return 0; /* not non-zero */ 3538 3539 ae=dn->exponent+dn->digits-1; /* adjusted exponent */ 3540 if (ae<set->emin) return 0; /* is subnormal */ 3541 return 1; 3542 } /* decNumberIsNormal */ 3543 3544/* ------------------------------------------------------------------ */ 3545/* decNumberIsSubnormal -- test subnormality of a decNumber */ 3546/* dn is the decNumber to test */ 3547/* set is the context to use for Emin */ 3548/* returns 1 if |dn| is finite, non-zero, and <Nmin, 0 otherwise */ 3549/* ------------------------------------------------------------------ */ 3550Int uprv_decNumberIsSubnormal(const decNumber *dn, decContext *set) { 3551 Int ae; /* adjusted exponent */ 3552 #if DECCHECK 3553 if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; 3554 #endif 3555 3556 if (decNumberIsSpecial(dn)) return 0; /* not finite */ 3557 if (decNumberIsZero(dn)) return 0; /* not non-zero */ 3558 3559 ae=dn->exponent+dn->digits-1; /* adjusted exponent */ 3560 if (ae<set->emin) return 1; /* is subnormal */ 3561 return 0; 3562 } /* decNumberIsSubnormal */ 3563 3564/* ------------------------------------------------------------------ */ 3565/* decNumberTrim -- remove insignificant zeros */ 3566/* */ 3567/* dn is the number to trim */ 3568/* returns dn */ 3569/* */ 3570/* All fields are updated as required. This is a utility operation, */ 3571/* so special values are unchanged and no error is possible. The */ 3572/* zeros are removed unconditionally. */ 3573/* ------------------------------------------------------------------ */ 3574U_CAPI decNumber * U_EXPORT2 uprv_decNumberTrim(decNumber *dn) { 3575 Int dropped; /* work */ 3576 decContext set; /* .. */ 3577 #if DECCHECK 3578 if (decCheckOperands(DECUNRESU, DECUNUSED, dn, DECUNCONT)) return dn; 3579 #endif 3580 uprv_decContextDefault(&set, DEC_INIT_BASE); /* clamp=0 */ 3581 return decTrim(dn, &set, 0, 1, &dropped); 3582 } /* decNumberTrim */ 3583 3584/* ------------------------------------------------------------------ */ 3585/* decNumberVersion -- return the name and version of this module */ 3586/* */ 3587/* No error is possible. */ 3588/* ------------------------------------------------------------------ */ 3589const char * uprv_decNumberVersion(void) { 3590 return DECVERSION; 3591 } /* decNumberVersion */ 3592 3593/* ------------------------------------------------------------------ */ 3594/* decNumberZero -- set a number to 0 */ 3595/* */ 3596/* dn is the number to set, with space for one digit */ 3597/* returns dn */ 3598/* */ 3599/* No error is possible. */ 3600/* ------------------------------------------------------------------ */ 3601/* Memset is not used as it is much slower in some environments. */ 3602U_CAPI decNumber * U_EXPORT2 uprv_decNumberZero(decNumber *dn) { 3603 3604 #if DECCHECK 3605 if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn; 3606 #endif 3607 3608 dn->bits=0; 3609 dn->exponent=0; 3610 dn->digits=1; 3611 dn->lsu[0]=0; 3612 return dn; 3613 } /* decNumberZero */ 3614 3615/* ================================================================== */ 3616/* Local routines */ 3617/* ================================================================== */ 3618 3619/* ------------------------------------------------------------------ */ 3620/* decToString -- lay out a number into a string */ 3621/* */ 3622/* dn is the number to lay out */ 3623/* string is where to lay out the number */ 3624/* eng is 1 if Engineering, 0 if Scientific */ 3625/* */ 3626/* string must be at least dn->digits+14 characters long */ 3627/* No error is possible. */ 3628/* */ 3629/* Note that this routine can generate a -0 or 0.000. These are */ 3630/* never generated in subset to-number or arithmetic, but can occur */ 3631/* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234). */ 3632/* ------------------------------------------------------------------ */ 3633/* If DECCHECK is enabled the string "?" is returned if a number is */ 3634/* invalid. */ 3635static void decToString(const decNumber *dn, char *string, Flag eng) { 3636 Int exp=dn->exponent; /* local copy */ 3637 Int e; /* E-part value */ 3638 Int pre; /* digits before the '.' */ 3639 Int cut; /* for counting digits in a Unit */ 3640 char *c=string; /* work [output pointer] */ 3641 const Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [input pointer] */ 3642 uInt u, pow; /* work */ 3643 3644 #if DECCHECK 3645 if (decCheckOperands(DECUNRESU, dn, DECUNUSED, DECUNCONT)) { 3646 strcpy(string, "?"); 3647 return;} 3648 #endif 3649 3650 if (decNumberIsNegative(dn)) { /* Negatives get a minus */ 3651 *c='-'; 3652 c++; 3653 } 3654 if (dn->bits&DECSPECIAL) { /* Is a special value */ 3655 if (decNumberIsInfinite(dn)) { 3656 strcpy(c, "Inf"); 3657 strcpy(c+3, "inity"); 3658 return;} 3659 /* a NaN */ 3660 if (dn->bits&DECSNAN) { /* signalling NaN */ 3661 *c='s'; 3662 c++; 3663 } 3664 strcpy(c, "NaN"); 3665 c+=3; /* step past */ 3666 /* if not a clean non-zero coefficient, that's all there is in a */ 3667 /* NaN string */ 3668 if (exp!=0 || (*dn->lsu==0 && dn->digits==1)) return; 3669 /* [drop through to add integer] */ 3670 } 3671 3672 /* calculate how many digits in msu, and hence first cut */ 3673 cut=MSUDIGITS(dn->digits); /* [faster than remainder] */ 3674 cut--; /* power of ten for digit */ 3675 3676 if (exp==0) { /* simple integer [common fastpath] */ 3677 for (;up>=dn->lsu; up--) { /* each Unit from msu */ 3678 u=*up; /* contains DECDPUN digits to lay out */ 3679 for (; cut>=0; c++, cut--) TODIGIT(u, cut, c, pow); 3680 cut=DECDPUN-1; /* next Unit has all digits */ 3681 } 3682 *c='\0'; /* terminate the string */ 3683 return;} 3684 3685 /* non-0 exponent -- assume plain form */ 3686 pre=dn->digits+exp; /* digits before '.' */ 3687 e=0; /* no E */ 3688 if ((exp>0) || (pre<-5)) { /* need exponential form */ 3689 e=exp+dn->digits-1; /* calculate E value */ 3690 pre=1; /* assume one digit before '.' */ 3691 if (eng && (e!=0)) { /* engineering: may need to adjust */ 3692 Int adj; /* adjustment */ 3693 /* The C remainder operator is undefined for negative numbers, so */ 3694 /* a positive remainder calculation must be used here */ 3695 if (e<0) { 3696 adj=(-e)%3; 3697 if (adj!=0) adj=3-adj; 3698 } 3699 else { /* e>0 */ 3700 adj=e%3; 3701 } 3702 e=e-adj; 3703 /* if dealing with zero still produce an exponent which is a */ 3704 /* multiple of three, as expected, but there will only be the */ 3705 /* one zero before the E, still. Otherwise note the padding. */ 3706 if (!ISZERO(dn)) pre+=adj; 3707 else { /* is zero */ 3708 if (adj!=0) { /* 0.00Esnn needed */ 3709 e=e+3; 3710 pre=-(2-adj); 3711 } 3712 } /* zero */ 3713 } /* eng */ 3714 } /* need exponent */ 3715 3716 /* lay out the digits of the coefficient, adding 0s and . as needed */ 3717 u=*up; 3718 if (pre>0) { /* xxx.xxx or xx00 (engineering) form */ 3719 Int n=pre; 3720 for (; pre>0; pre--, c++, cut--) { 3721 if (cut<0) { /* need new Unit */ 3722 if (up==dn->lsu) break; /* out of input digits (pre>digits) */ 3723 up--; 3724 cut=DECDPUN-1; 3725 u=*up; 3726 } 3727 TODIGIT(u, cut, c, pow); 3728 } 3729 if (n<dn->digits) { /* more to come, after '.' */ 3730 *c='.'; c++; 3731 for (;; c++, cut--) { 3732 if (cut<0) { /* need new Unit */ 3733 if (up==dn->lsu) break; /* out of input digits */ 3734 up--; 3735 cut=DECDPUN-1; 3736 u=*up; 3737 } 3738 TODIGIT(u, cut, c, pow); 3739 } 3740 } 3741 else for (; pre>0; pre--, c++) *c='0'; /* 0 padding (for engineering) needed */ 3742 } 3743 else { /* 0.xxx or 0.000xxx form */ 3744 *c='0'; c++; 3745 *c='.'; c++; 3746 for (; pre<0; pre++, c++) *c='0'; /* add any 0's after '.' */ 3747 for (; ; c++, cut--) { 3748 if (cut<0) { /* need new Unit */ 3749 if (up==dn->lsu) break; /* out of input digits */ 3750 up--; 3751 cut=DECDPUN-1; 3752 u=*up; 3753 } 3754 TODIGIT(u, cut, c, pow); 3755 } 3756 } 3757 3758 /* Finally add the E-part, if needed. It will never be 0, has a 3759 base maximum and minimum of +999999999 through -999999999, but 3760 could range down to -1999999998 for anormal numbers */ 3761 if (e!=0) { 3762 Flag had=0; /* 1=had non-zero */ 3763 *c='E'; c++; 3764 *c='+'; c++; /* assume positive */ 3765 u=e; /* .. */ 3766 if (e<0) { 3767 *(c-1)='-'; /* oops, need - */ 3768 u=-e; /* uInt, please */ 3769 } 3770 /* lay out the exponent [_itoa or equivalent is not ANSI C] */ 3771 for (cut=9; cut>=0; cut--) { 3772 TODIGIT(u, cut, c, pow); 3773 if (*c=='0' && !had) continue; /* skip leading zeros */ 3774 had=1; /* had non-0 */ 3775 c++; /* step for next */ 3776 } /* cut */ 3777 } 3778 *c='\0'; /* terminate the string (all paths) */ 3779 return; 3780 } /* decToString */ 3781 3782/* ------------------------------------------------------------------ */ 3783/* decAddOp -- add/subtract operation */ 3784/* */ 3785/* This computes C = A + B */ 3786/* */ 3787/* res is C, the result. C may be A and/or B (e.g., X=X+X) */ 3788/* lhs is A */ 3789/* rhs is B */ 3790/* set is the context */ 3791/* negate is DECNEG if rhs should be negated, or 0 otherwise */ 3792/* status accumulates status for the caller */ 3793/* */ 3794/* C must have space for set->digits digits. */ 3795/* Inexact in status must be 0 for correct Exact zero sign in result */ 3796/* ------------------------------------------------------------------ */ 3797/* If possible, the coefficient is calculated directly into C. */ 3798/* However, if: */ 3799/* -- a digits+1 calculation is needed because the numbers are */ 3800/* unaligned and span more than set->digits digits */ 3801/* -- a carry to digits+1 digits looks possible */ 3802/* -- C is the same as A or B, and the result would destructively */ 3803/* overlap the A or B coefficient */ 3804/* then the result must be calculated into a temporary buffer. In */ 3805/* this case a local (stack) buffer is used if possible, and only if */ 3806/* too long for that does malloc become the final resort. */ 3807/* */ 3808/* Misalignment is handled as follows: */ 3809/* Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp. */ 3810/* BPad: Apply the padding by a combination of shifting (whole */ 3811/* units) and multiplication (part units). */ 3812/* */ 3813/* Addition, especially x=x+1, is speed-critical. */ 3814/* The static buffer is larger than might be expected to allow for */ 3815/* calls from higher-level funtions (notable exp). */ 3816/* ------------------------------------------------------------------ */ 3817static decNumber * decAddOp(decNumber *res, const decNumber *lhs, 3818 const decNumber *rhs, decContext *set, 3819 uByte negate, uInt *status) { 3820 #if DECSUBSET 3821 decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ 3822 decNumber *allocrhs=NULL; /* .., rhs */ 3823 #endif 3824 Int rhsshift; /* working shift (in Units) */ 3825 Int maxdigits; /* longest logical length */ 3826 Int mult; /* multiplier */ 3827 Int residue; /* rounding accumulator */ 3828 uByte bits; /* result bits */ 3829 Flag diffsign; /* non-0 if arguments have different sign */ 3830 Unit *acc; /* accumulator for result */ 3831 Unit accbuff[SD2U(DECBUFFER*2+20)]; /* local buffer [*2+20 reduces many */ 3832 /* allocations when called from */ 3833 /* other operations, notable exp] */ 3834 Unit *allocacc=NULL; /* -> allocated acc buffer, iff allocated */ 3835 Int reqdigits=set->digits; /* local copy; requested DIGITS */ 3836 Int padding; /* work */ 3837 3838 #if DECCHECK 3839 if (decCheckOperands(res, lhs, rhs, set)) return res; 3840 #endif 3841 3842 do { /* protect allocated storage */ 3843 #if DECSUBSET 3844 if (!set->extended) { 3845 /* reduce operands and set lostDigits status, as needed */ 3846 if (lhs->digits>reqdigits) { 3847 alloclhs=decRoundOperand(lhs, set, status); 3848 if (alloclhs==NULL) break; 3849 lhs=alloclhs; 3850 } 3851 if (rhs->digits>reqdigits) { 3852 allocrhs=decRoundOperand(rhs, set, status); 3853 if (allocrhs==NULL) break; 3854 rhs=allocrhs; 3855 } 3856 } 3857 #endif 3858 /* [following code does not require input rounding] */ 3859 3860 /* note whether signs differ [used all paths] */ 3861 diffsign=(Flag)((lhs->bits^rhs->bits^negate)&DECNEG); 3862 3863 /* handle infinities and NaNs */ 3864 if (SPECIALARGS) { /* a special bit set */ 3865 if (SPECIALARGS & (DECSNAN | DECNAN)) /* a NaN */ 3866 decNaNs(res, lhs, rhs, set, status); 3867 else { /* one or two infinities */ 3868 if (decNumberIsInfinite(lhs)) { /* LHS is infinity */ 3869 /* two infinities with different signs is invalid */ 3870 if (decNumberIsInfinite(rhs) && diffsign) { 3871 *status|=DEC_Invalid_operation; 3872 break; 3873 } 3874 bits=lhs->bits & DECNEG; /* get sign from LHS */ 3875 } 3876 else bits=(rhs->bits^negate) & DECNEG;/* RHS must be Infinity */ 3877 bits|=DECINF; 3878 uprv_decNumberZero(res); 3879 res->bits=bits; /* set +/- infinity */ 3880 } /* an infinity */ 3881 break; 3882 } 3883 3884 /* Quick exit for add 0s; return the non-0, modified as need be */ 3885 if (ISZERO(lhs)) { 3886 Int adjust; /* work */ 3887 Int lexp=lhs->exponent; /* save in case LHS==RES */ 3888 bits=lhs->bits; /* .. */ 3889 residue=0; /* clear accumulator */ 3890 decCopyFit(res, rhs, set, &residue, status); /* copy (as needed) */ 3891 res->bits^=negate; /* flip if rhs was negated */ 3892 #if DECSUBSET 3893 if (set->extended) { /* exponents on zeros count */ 3894 #endif 3895 /* exponent will be the lower of the two */ 3896 adjust=lexp-res->exponent; /* adjustment needed [if -ve] */ 3897 if (ISZERO(res)) { /* both 0: special IEEE 754 rules */ 3898 if (adjust<0) res->exponent=lexp; /* set exponent */ 3899 /* 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0 */ 3900 if (diffsign) { 3901 if (set->round!=DEC_ROUND_FLOOR) res->bits=0; 3902 else res->bits=DECNEG; /* preserve 0 sign */ 3903 } 3904 } 3905 else { /* non-0 res */ 3906 if (adjust<0) { /* 0-padding needed */ 3907 if ((res->digits-adjust)>set->digits) { 3908 adjust=res->digits-set->digits; /* to fit exactly */ 3909 *status|=DEC_Rounded; /* [but exact] */ 3910 } 3911 res->digits=decShiftToMost(res->lsu, res->digits, -adjust); 3912 res->exponent+=adjust; /* set the exponent. */ 3913 } 3914 } /* non-0 res */ 3915 #if DECSUBSET 3916 } /* extended */ 3917 #endif 3918 decFinish(res, set, &residue, status); /* clean and finalize */ 3919 break;} 3920 3921 if (ISZERO(rhs)) { /* [lhs is non-zero] */ 3922 Int adjust; /* work */ 3923 Int rexp=rhs->exponent; /* save in case RHS==RES */ 3924 bits=rhs->bits; /* be clean */ 3925 residue=0; /* clear accumulator */ 3926 decCopyFit(res, lhs, set, &residue, status); /* copy (as needed) */ 3927 #if DECSUBSET 3928 if (set->extended) { /* exponents on zeros count */ 3929 #endif 3930 /* exponent will be the lower of the two */ 3931 /* [0-0 case handled above] */ 3932 adjust=rexp-res->exponent; /* adjustment needed [if -ve] */ 3933 if (adjust<0) { /* 0-padding needed */ 3934 if ((res->digits-adjust)>set->digits) { 3935 adjust=res->digits-set->digits; /* to fit exactly */ 3936 *status|=DEC_Rounded; /* [but exact] */ 3937 } 3938 res->digits=decShiftToMost(res->lsu, res->digits, -adjust); 3939 res->exponent+=adjust; /* set the exponent. */ 3940 } 3941 #if DECSUBSET 3942 } /* extended */ 3943 #endif 3944 decFinish(res, set, &residue, status); /* clean and finalize */ 3945 break;} 3946 3947 /* [NB: both fastpath and mainpath code below assume these cases */ 3948 /* (notably 0-0) have already been handled] */ 3949 3950 /* calculate the padding needed to align the operands */ 3951 padding=rhs->exponent-lhs->exponent; 3952 3953 /* Fastpath cases where the numbers are aligned and normal, the RHS */ 3954 /* is all in one unit, no operand rounding is needed, and no carry, */ 3955 /* lengthening, or borrow is needed */ 3956 if (padding==0 3957 && rhs->digits<=DECDPUN 3958 && rhs->exponent>=set->emin /* [some normals drop through] */ 3959 && rhs->exponent<=set->emax-set->digits+1 /* [could clamp] */ 3960 && rhs->digits<=reqdigits 3961 && lhs->digits<=reqdigits) { 3962 Int partial=*lhs->lsu; 3963 if (!diffsign) { /* adding */ 3964 partial+=*rhs->lsu; 3965 if ((partial<=DECDPUNMAX) /* result fits in unit */ 3966 && (lhs->digits>=DECDPUN || /* .. and no digits-count change */ 3967 partial<(Int)powers[lhs->digits])) { /* .. */ 3968 if (res!=lhs) uprv_decNumberCopy(res, lhs); /* not in place */ 3969 *res->lsu=(Unit)partial; /* [copy could have overwritten RHS] */ 3970 break; 3971 } 3972 /* else drop out for careful add */ 3973 } 3974 else { /* signs differ */ 3975 partial-=*rhs->lsu; 3976 if (partial>0) { /* no borrow needed, and non-0 result */ 3977 if (res!=lhs) uprv_decNumberCopy(res, lhs); /* not in place */ 3978 *res->lsu=(Unit)partial; 3979 /* this could have reduced digits [but result>0] */ 3980 res->digits=decGetDigits(res->lsu, D2U(res->digits)); 3981 break; 3982 } 3983 /* else drop out for careful subtract */ 3984 } 3985 } 3986 3987 /* Now align (pad) the lhs or rhs so they can be added or */ 3988 /* subtracted, as necessary. If one number is much larger than */ 3989 /* the other (that is, if in plain form there is a least one */ 3990 /* digit between the lowest digit of one and the highest of the */ 3991 /* other) padding with up to DIGITS-1 trailing zeros may be */ 3992 /* needed; then apply rounding (as exotic rounding modes may be */ 3993 /* affected by the residue). */ 3994 rhsshift=0; /* rhs shift to left (padding) in Units */ 3995 bits=lhs->bits; /* assume sign is that of LHS */ 3996 mult=1; /* likely multiplier */ 3997 3998 /* [if padding==0 the operands are aligned; no padding is needed] */ 3999 if (padding!=0) { 4000 /* some padding needed; always pad the RHS, as any required */ 4001 /* padding can then be effected by a simple combination of */ 4002 /* shifts and a multiply */ 4003 Flag swapped=0; 4004 if (padding<0) { /* LHS needs the padding */ 4005 const decNumber *t; 4006 padding=-padding; /* will be +ve */ 4007 bits=(uByte)(rhs->bits^negate); /* assumed sign is now that of RHS */ 4008 t=lhs; lhs=rhs; rhs=t; 4009 swapped=1; 4010 } 4011 4012 /* If, after pad, rhs would be longer than lhs by digits+1 or */ 4013 /* more then lhs cannot affect the answer, except as a residue, */ 4014 /* so only need to pad up to a length of DIGITS+1. */ 4015 if (rhs->digits+padding > lhs->digits+reqdigits+1) { 4016 /* The RHS is sufficient */ 4017 /* for residue use the relative sign indication... */ 4018 Int shift=reqdigits-rhs->digits; /* left shift needed */ 4019 residue=1; /* residue for rounding */ 4020 if (diffsign) residue=-residue; /* signs differ */ 4021 /* copy, shortening if necessary */ 4022 decCopyFit(res, rhs, set, &residue, status); 4023 /* if it was already shorter, then need to pad with zeros */ 4024 if (shift>0) { 4025 res->digits=decShiftToMost(res->lsu, res->digits, shift); 4026 res->exponent-=shift; /* adjust the exponent. */ 4027 } 4028 /* flip the result sign if unswapped and rhs was negated */ 4029 if (!swapped) res->bits^=negate; 4030 decFinish(res, set, &residue, status); /* done */ 4031 break;} 4032 4033 /* LHS digits may affect result */ 4034 rhsshift=D2U(padding+1)-1; /* this much by Unit shift .. */ 4035 mult=powers[padding-(rhsshift*DECDPUN)]; /* .. this by multiplication */ 4036 } /* padding needed */ 4037 4038 if (diffsign) mult=-mult; /* signs differ */ 4039 4040 /* determine the longer operand */ 4041 maxdigits=rhs->digits+padding; /* virtual length of RHS */ 4042 if (lhs->digits>maxdigits) maxdigits=lhs->digits; 4043 4044 /* Decide on the result buffer to use; if possible place directly */ 4045 /* into result. */ 4046 acc=res->lsu; /* assume add direct to result */ 4047 /* If destructive overlap, or the number is too long, or a carry or */ 4048 /* borrow to DIGITS+1 might be possible, a buffer must be used. */ 4049 /* [Might be worth more sophisticated tests when maxdigits==reqdigits] */ 4050 if ((maxdigits>=reqdigits) /* is, or could be, too large */ 4051 || (res==rhs && rhsshift>0)) { /* destructive overlap */ 4052 /* buffer needed, choose it; units for maxdigits digits will be */ 4053 /* needed, +1 Unit for carry or borrow */ 4054 Int need=D2U(maxdigits)+1; 4055 acc=accbuff; /* assume use local buffer */ 4056 if (need*sizeof(Unit)>sizeof(accbuff)) { 4057 /* printf("malloc add %ld %ld\n", need, sizeof(accbuff)); */ 4058 allocacc=(Unit *)malloc(need*sizeof(Unit)); 4059 if (allocacc==NULL) { /* hopeless -- abandon */ 4060 *status|=DEC_Insufficient_storage; 4061 break;} 4062 acc=allocacc; 4063 } 4064 } 4065 4066 res->bits=(uByte)(bits&DECNEG); /* it's now safe to overwrite.. */ 4067 res->exponent=lhs->exponent; /* .. operands (even if aliased) */ 4068 4069 #if DECTRACE 4070 decDumpAr('A', lhs->lsu, D2U(lhs->digits)); 4071 decDumpAr('B', rhs->lsu, D2U(rhs->digits)); 4072 printf(" :h: %ld %ld\n", rhsshift, mult); 4073 #endif 4074 4075 /* add [A+B*m] or subtract [A+B*(-m)] */ 4076 res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits), 4077 rhs->lsu, D2U(rhs->digits), 4078 rhsshift, acc, mult) 4079 *DECDPUN; /* [units -> digits] */ 4080 if (res->digits<0) { /* borrowed... */ 4081 res->digits=-res->digits; 4082 res->bits^=DECNEG; /* flip the sign */ 4083 } 4084 #if DECTRACE 4085 decDumpAr('+', acc, D2U(res->digits)); 4086 #endif 4087 4088 /* If a buffer was used the result must be copied back, possibly */ 4089 /* shortening. (If no buffer was used then the result must have */ 4090 /* fit, so can't need rounding and residue must be 0.) */ 4091 residue=0; /* clear accumulator */ 4092 if (acc!=res->lsu) { 4093 #if DECSUBSET 4094 if (set->extended) { /* round from first significant digit */ 4095 #endif 4096 /* remove leading zeros that were added due to rounding up to */ 4097 /* integral Units -- before the test for rounding. */ 4098 if (res->digits>reqdigits) 4099 res->digits=decGetDigits(acc, D2U(res->digits)); 4100 decSetCoeff(res, set, acc, res->digits, &residue, status); 4101 #if DECSUBSET 4102 } 4103 else { /* subset arithmetic rounds from original significant digit */ 4104 /* May have an underestimate. This only occurs when both */ 4105 /* numbers fit in DECDPUN digits and are padding with a */ 4106 /* negative multiple (-10, -100...) and the top digit(s) become */ 4107 /* 0. (This only matters when using X3.274 rules where the */ 4108 /* leading zero could be included in the rounding.) */ 4109 if (res->digits<maxdigits) { 4110 *(acc+D2U(res->digits))=0; /* ensure leading 0 is there */ 4111 res->digits=maxdigits; 4112 } 4113 else { 4114 /* remove leading zeros that added due to rounding up to */ 4115 /* integral Units (but only those in excess of the original */ 4116 /* maxdigits length, unless extended) before test for rounding. */ 4117 if (res->digits>reqdigits) { 4118 res->digits=decGetDigits(acc, D2U(res->digits)); 4119 if (res->digits<maxdigits) res->digits=maxdigits; 4120 } 4121 } 4122 decSetCoeff(res, set, acc, res->digits, &residue, status); 4123 /* Now apply rounding if needed before removing leading zeros. */ 4124 /* This is safe because subnormals are not a possibility */ 4125 if (residue!=0) { 4126 decApplyRound(res, set, residue, status); 4127 residue=0; /* did what needed to be done */ 4128 } 4129 } /* subset */ 4130 #endif 4131 } /* used buffer */ 4132 4133 /* strip leading zeros [these were left on in case of subset subtract] */ 4134 res->digits=decGetDigits(res->lsu, D2U(res->digits)); 4135 4136 /* apply checks and rounding */ 4137 decFinish(res, set, &residue, status); 4138 4139 /* "When the sum of two operands with opposite signs is exactly */ 4140 /* zero, the sign of that sum shall be '+' in all rounding modes */ 4141 /* except round toward -Infinity, in which mode that sign shall be */ 4142 /* '-'." [Subset zeros also never have '-', set by decFinish.] */ 4143 if (ISZERO(res) && diffsign 4144 #if DECSUBSET 4145 && set->extended 4146 #endif 4147 && (*status&DEC_Inexact)==0) { 4148 if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG; /* sign - */ 4149 else res->bits&=~DECNEG; /* sign + */ 4150 } 4151 } while(0); /* end protected */ 4152 4153 if (allocacc!=NULL) free(allocacc); /* drop any storage used */ 4154 #if DECSUBSET 4155 if (allocrhs!=NULL) free(allocrhs); /* .. */ 4156 if (alloclhs!=NULL) free(alloclhs); /* .. */ 4157 #endif 4158 return res; 4159 } /* decAddOp */ 4160 4161/* ------------------------------------------------------------------ */ 4162/* decDivideOp -- division operation */ 4163/* */ 4164/* This routine performs the calculations for all four division */ 4165/* operators (divide, divideInteger, remainder, remainderNear). */ 4166/* */ 4167/* C=A op B */ 4168/* */ 4169/* res is C, the result. C may be A and/or B (e.g., X=X/X) */ 4170/* lhs is A */ 4171/* rhs is B */ 4172/* set is the context */ 4173/* op is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively. */ 4174/* status is the usual accumulator */ 4175/* */ 4176/* C must have space for set->digits digits. */ 4177/* */ 4178/* ------------------------------------------------------------------ */ 4179/* The underlying algorithm of this routine is the same as in the */ 4180/* 1981 S/370 implementation, that is, non-restoring long division */ 4181/* with bi-unit (rather than bi-digit) estimation for each unit */ 4182/* multiplier. In this pseudocode overview, complications for the */ 4183/* Remainder operators and division residues for exact rounding are */ 4184/* omitted for clarity. */ 4185/* */ 4186/* Prepare operands and handle special values */ 4187/* Test for x/0 and then 0/x */ 4188/* Exp =Exp1 - Exp2 */ 4189/* Exp =Exp +len(var1) -len(var2) */ 4190/* Sign=Sign1 * Sign2 */ 4191/* Pad accumulator (Var1) to double-length with 0's (pad1) */ 4192/* Pad Var2 to same length as Var1 */ 4193/* msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round */ 4194/* have=0 */ 4195/* Do until (have=digits+1 OR residue=0) */ 4196/* if exp<0 then if integer divide/residue then leave */ 4197/* this_unit=0 */ 4198/* Do forever */ 4199/* compare numbers */ 4200/* if <0 then leave inner_loop */ 4201/* if =0 then (* quick exit without subtract *) do */ 4202/* this_unit=this_unit+1; output this_unit */ 4203/* leave outer_loop; end */ 4204/* Compare lengths of numbers (mantissae): */ 4205/* If same then tops2=msu2pair -- {units 1&2 of var2} */ 4206/* else tops2=msu2plus -- {0, unit 1 of var2} */ 4207/* tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */ 4208/* mult=tops1/tops2 -- Good and safe guess at divisor */ 4209/* if mult=0 then mult=1 */ 4210/* this_unit=this_unit+mult */ 4211/* subtract */ 4212/* end inner_loop */ 4213/* if have\=0 | this_unit\=0 then do */ 4214/* output this_unit */ 4215/* have=have+1; end */ 4216/* var2=var2/10 */ 4217/* exp=exp-1 */ 4218/* end outer_loop */ 4219/* exp=exp+1 -- set the proper exponent */ 4220/* if have=0 then generate answer=0 */ 4221/* Return (Result is defined by Var1) */ 4222/* */ 4223/* ------------------------------------------------------------------ */ 4224/* Two working buffers are needed during the division; one (digits+ */ 4225/* 1) to accumulate the result, and the other (up to 2*digits+1) for */ 4226/* long subtractions. These are acc and var1 respectively. */ 4227/* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/ 4228/* The static buffers may be larger than might be expected to allow */ 4229/* for calls from higher-level funtions (notable exp). */ 4230/* ------------------------------------------------------------------ */ 4231static decNumber * decDivideOp(decNumber *res, 4232 const decNumber *lhs, const decNumber *rhs, 4233 decContext *set, Flag op, uInt *status) { 4234 #if DECSUBSET 4235 decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ 4236 decNumber *allocrhs=NULL; /* .., rhs */ 4237 #endif 4238 Unit accbuff[SD2U(DECBUFFER+DECDPUN+10)]; /* local buffer */ 4239 Unit *acc=accbuff; /* -> accumulator array for result */ 4240 Unit *allocacc=NULL; /* -> allocated buffer, iff allocated */ 4241 Unit *accnext; /* -> where next digit will go */ 4242 Int acclength; /* length of acc needed [Units] */ 4243 Int accunits; /* count of units accumulated */ 4244 Int accdigits; /* count of digits accumulated */ 4245 4246 Unit varbuff[SD2U(DECBUFFER*2+DECDPUN)]; /* buffer for var1 */ 4247 Unit *var1=varbuff; /* -> var1 array for long subtraction */ 4248 Unit *varalloc=NULL; /* -> allocated buffer, iff used */ 4249 Unit *msu1; /* -> msu of var1 */ 4250 4251 const Unit *var2; /* -> var2 array */ 4252 const Unit *msu2; /* -> msu of var2 */ 4253 Int msu2plus; /* msu2 plus one [does not vary] */ 4254 eInt msu2pair; /* msu2 pair plus one [does not vary] */ 4255 4256 Int var1units, var2units; /* actual lengths */ 4257 Int var2ulen; /* logical length (units) */ 4258 Int var1initpad=0; /* var1 initial padding (digits) */ 4259 Int maxdigits; /* longest LHS or required acc length */ 4260 Int mult; /* multiplier for subtraction */ 4261 Unit thisunit; /* current unit being accumulated */ 4262 Int residue; /* for rounding */ 4263 Int reqdigits=set->digits; /* requested DIGITS */ 4264 Int exponent; /* working exponent */ 4265 Int maxexponent=0; /* DIVIDE maximum exponent if unrounded */ 4266 uByte bits; /* working sign */ 4267 Unit *target; /* work */ 4268 const Unit *source; /* .. */ 4269 uInt const *pow; /* .. */ 4270 Int shift, cut; /* .. */ 4271 #if DECSUBSET 4272 Int dropped; /* work */ 4273 #endif 4274 4275 #if DECCHECK 4276 if (decCheckOperands(res, lhs, rhs, set)) return res; 4277 #endif 4278 4279 do { /* protect allocated storage */ 4280 #if DECSUBSET 4281 if (!set->extended) { 4282 /* reduce operands and set lostDigits status, as needed */ 4283 if (lhs->digits>reqdigits) { 4284 alloclhs=decRoundOperand(lhs, set, status); 4285 if (alloclhs==NULL) break; 4286 lhs=alloclhs; 4287 } 4288 if (rhs->digits>reqdigits) { 4289 allocrhs=decRoundOperand(rhs, set, status); 4290 if (allocrhs==NULL) break; 4291 rhs=allocrhs; 4292 } 4293 } 4294 #endif 4295 /* [following code does not require input rounding] */ 4296 4297 bits=(lhs->bits^rhs->bits)&DECNEG; /* assumed sign for divisions */ 4298 4299 /* handle infinities and NaNs */ 4300 if (SPECIALARGS) { /* a special bit set */ 4301 if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */ 4302 decNaNs(res, lhs, rhs, set, status); 4303 break; 4304 } 4305 /* one or two infinities */ 4306 if (decNumberIsInfinite(lhs)) { /* LHS (dividend) is infinite */ 4307 if (decNumberIsInfinite(rhs) || /* two infinities are invalid .. */ 4308 op & (REMAINDER | REMNEAR)) { /* as is remainder of infinity */ 4309 *status|=DEC_Invalid_operation; 4310 break; 4311 } 4312 /* [Note that infinity/0 raises no exceptions] */ 4313 uprv_decNumberZero(res); 4314 res->bits=bits|DECINF; /* set +/- infinity */ 4315 break; 4316 } 4317 else { /* RHS (divisor) is infinite */ 4318 residue=0; 4319 if (op&(REMAINDER|REMNEAR)) { 4320 /* result is [finished clone of] lhs */ 4321 decCopyFit(res, lhs, set, &residue, status); 4322 } 4323 else { /* a division */ 4324 uprv_decNumberZero(res); 4325 res->bits=bits; /* set +/- zero */ 4326 /* for DIVIDEINT the exponent is always 0. For DIVIDE, result */ 4327 /* is a 0 with infinitely negative exponent, clamped to minimum */ 4328 if (op&DIVIDE) { 4329 res->exponent=set->emin-set->digits+1; 4330 *status|=DEC_Clamped; 4331 } 4332 } 4333 decFinish(res, set, &residue, status); 4334 break; 4335 } 4336 } 4337 4338 /* handle 0 rhs (x/0) */ 4339 if (ISZERO(rhs)) { /* x/0 is always exceptional */ 4340 if (ISZERO(lhs)) { 4341 uprv_decNumberZero(res); /* [after lhs test] */ 4342 *status|=DEC_Division_undefined;/* 0/0 will become NaN */ 4343 } 4344 else { 4345 uprv_decNumberZero(res); 4346 if (op&(REMAINDER|REMNEAR)) *status|=DEC_Invalid_operation; 4347 else { 4348 *status|=DEC_Division_by_zero; /* x/0 */ 4349 res->bits=bits|DECINF; /* .. is +/- Infinity */ 4350 } 4351 } 4352 break;} 4353 4354 /* handle 0 lhs (0/x) */ 4355 if (ISZERO(lhs)) { /* 0/x [x!=0] */ 4356 #if DECSUBSET 4357 if (!set->extended) uprv_decNumberZero(res); 4358 else { 4359 #endif 4360 if (op&DIVIDE) { 4361 residue=0; 4362 exponent=lhs->exponent-rhs->exponent; /* ideal exponent */ 4363 uprv_decNumberCopy(res, lhs); /* [zeros always fit] */ 4364 res->bits=bits; /* sign as computed */ 4365 res->exponent=exponent; /* exponent, too */ 4366 decFinalize(res, set, &residue, status); /* check exponent */ 4367 } 4368 else if (op&DIVIDEINT) { 4369 uprv_decNumberZero(res); /* integer 0 */ 4370 res->bits=bits; /* sign as computed */ 4371 } 4372 else { /* a remainder */ 4373 exponent=rhs->exponent; /* [save in case overwrite] */ 4374 uprv_decNumberCopy(res, lhs); /* [zeros always fit] */ 4375 if (exponent<res->exponent) res->exponent=exponent; /* use lower */ 4376 } 4377 #if DECSUBSET 4378 } 4379 #endif 4380 break;} 4381 4382 /* Precalculate exponent. This starts off adjusted (and hence fits */ 4383 /* in 31 bits) and becomes the usual unadjusted exponent as the */ 4384 /* division proceeds. The order of evaluation is important, here, */ 4385 /* to avoid wrap. */ 4386 exponent=(lhs->exponent+lhs->digits)-(rhs->exponent+rhs->digits); 4387 4388 /* If the working exponent is -ve, then some quick exits are */ 4389 /* possible because the quotient is known to be <1 */ 4390 /* [for REMNEAR, it needs to be < -1, as -0.5 could need work] */ 4391 if (exponent<0 && !(op==DIVIDE)) { 4392 if (op&DIVIDEINT) { 4393 uprv_decNumberZero(res); /* integer part is 0 */ 4394 #if DECSUBSET 4395 if (set->extended) 4396 #endif 4397 res->bits=bits; /* set +/- zero */ 4398 break;} 4399 /* fastpath remainders so long as the lhs has the smaller */ 4400 /* (or equal) exponent */ 4401 if (lhs->exponent<=rhs->exponent) { 4402 if (op&REMAINDER || exponent<-1) { 4403 /* It is REMAINDER or safe REMNEAR; result is [finished */ 4404 /* clone of] lhs (r = x - 0*y) */ 4405 residue=0; 4406 decCopyFit(res, lhs, set, &residue, status); 4407 decFinish(res, set, &residue, status); 4408 break; 4409 } 4410 /* [unsafe REMNEAR drops through] */ 4411 } 4412 } /* fastpaths */ 4413 4414 /* Long (slow) division is needed; roll up the sleeves... */ 4415 4416 /* The accumulator will hold the quotient of the division. */ 4417 /* If it needs to be too long for stack storage, then allocate. */ 4418 acclength=D2U(reqdigits+DECDPUN); /* in Units */ 4419 if (acclength*sizeof(Unit)>sizeof(accbuff)) { 4420 /* printf("malloc dvacc %ld units\n", acclength); */ 4421 allocacc=(Unit *)malloc(acclength*sizeof(Unit)); 4422 if (allocacc==NULL) { /* hopeless -- abandon */ 4423 *status|=DEC_Insufficient_storage; 4424 break;} 4425 acc=allocacc; /* use the allocated space */ 4426 } 4427 4428 /* var1 is the padded LHS ready for subtractions. */ 4429 /* If it needs to be too long for stack storage, then allocate. */ 4430 /* The maximum units needed for var1 (long subtraction) is: */ 4431 /* Enough for */ 4432 /* (rhs->digits+reqdigits-1) -- to allow full slide to right */ 4433 /* or (lhs->digits) -- to allow for long lhs */ 4434 /* whichever is larger */ 4435 /* +1 -- for rounding of slide to right */ 4436 /* +1 -- for leading 0s */ 4437 /* +1 -- for pre-adjust if a remainder or DIVIDEINT */ 4438 /* [Note: unused units do not participate in decUnitAddSub data] */ 4439 maxdigits=rhs->digits+reqdigits-1; 4440 if (lhs->digits>maxdigits) maxdigits=lhs->digits; 4441 var1units=D2U(maxdigits)+2; 4442 /* allocate a guard unit above msu1 for REMAINDERNEAR */ 4443 if (!(op&DIVIDE)) var1units++; 4444 if ((var1units+1)*sizeof(Unit)>sizeof(varbuff)) { 4445 /* printf("malloc dvvar %ld units\n", var1units+1); */ 4446 varalloc=(Unit *)malloc((var1units+1)*sizeof(Unit)); 4447 if (varalloc==NULL) { /* hopeless -- abandon */ 4448 *status|=DEC_Insufficient_storage; 4449 break;} 4450 var1=varalloc; /* use the allocated space */ 4451 } 4452 4453 /* Extend the lhs and rhs to full long subtraction length. The lhs */ 4454 /* is truly extended into the var1 buffer, with 0 padding, so a */ 4455 /* subtract in place is always possible. The rhs (var2) has */ 4456 /* virtual padding (implemented by decUnitAddSub). */ 4457 /* One guard unit was allocated above msu1 for rem=rem+rem in */ 4458 /* REMAINDERNEAR. */ 4459 msu1=var1+var1units-1; /* msu of var1 */ 4460 source=lhs->lsu+D2U(lhs->digits)-1; /* msu of input array */ 4461 for (target=msu1; source>=lhs->lsu; source--, target--) *target=*source; 4462 for (; target>=var1; target--) *target=0; 4463 4464 /* rhs (var2) is left-aligned with var1 at the start */ 4465 var2ulen=var1units; /* rhs logical length (units) */ 4466 var2units=D2U(rhs->digits); /* rhs actual length (units) */ 4467 var2=rhs->lsu; /* -> rhs array */ 4468 msu2=var2+var2units-1; /* -> msu of var2 [never changes] */ 4469 /* now set up the variables which will be used for estimating the */ 4470 /* multiplication factor. If these variables are not exact, add */ 4471 /* 1 to make sure that the multiplier is never overestimated. */ 4472 msu2plus=*msu2; /* it's value .. */ 4473 if (var2units>1) msu2plus++; /* .. +1 if any more */ 4474 msu2pair=(eInt)*msu2*(DECDPUNMAX+1);/* top two pair .. */ 4475 if (var2units>1) { /* .. [else treat 2nd as 0] */ 4476 msu2pair+=*(msu2-1); /* .. */ 4477 if (var2units>2) msu2pair++; /* .. +1 if any more */ 4478 } 4479 4480 /* The calculation is working in units, which may have leading zeros, */ 4481 /* but the exponent was calculated on the assumption that they are */ 4482 /* both left-aligned. Adjust the exponent to compensate: add the */ 4483 /* number of leading zeros in var1 msu and subtract those in var2 msu. */ 4484 /* [This is actually done by counting the digits and negating, as */ 4485 /* lead1=DECDPUN-digits1, and similarly for lead2.] */ 4486 for (pow=&powers[1]; *msu1>=*pow; pow++) exponent--; 4487 for (pow=&powers[1]; *msu2>=*pow; pow++) exponent++; 4488 4489 /* Now, if doing an integer divide or remainder, ensure that */ 4490 /* the result will be Unit-aligned. To do this, shift the var1 */ 4491 /* accumulator towards least if need be. (It's much easier to */ 4492 /* do this now than to reassemble the residue afterwards, if */ 4493 /* doing a remainder.) Also ensure the exponent is not negative. */ 4494 if (!(op&DIVIDE)) { 4495 Unit *u; /* work */ 4496 /* save the initial 'false' padding of var1, in digits */ 4497 var1initpad=(var1units-D2U(lhs->digits))*DECDPUN; 4498 /* Determine the shift to do. */ 4499 if (exponent<0) cut=-exponent; 4500 else cut=DECDPUN-exponent%DECDPUN; 4501 decShiftToLeast(var1, var1units, cut); 4502 exponent+=cut; /* maintain numerical value */ 4503 var1initpad-=cut; /* .. and reduce padding */ 4504 /* clean any most-significant units which were just emptied */ 4505 for (u=msu1; cut>=DECDPUN; cut-=DECDPUN, u--) *u=0; 4506 } /* align */ 4507 else { /* is DIVIDE */ 4508 maxexponent=lhs->exponent-rhs->exponent; /* save */ 4509 /* optimization: if the first iteration will just produce 0, */ 4510 /* preadjust to skip it [valid for DIVIDE only] */ 4511 if (*msu1<*msu2) { 4512 var2ulen--; /* shift down */ 4513 exponent-=DECDPUN; /* update the exponent */ 4514 } 4515 } 4516 4517 /* ---- start the long-division loops ------------------------------ */ 4518 accunits=0; /* no units accumulated yet */ 4519 accdigits=0; /* .. or digits */ 4520 accnext=acc+acclength-1; /* -> msu of acc [NB: allows digits+1] */ 4521 for (;;) { /* outer forever loop */ 4522 thisunit=0; /* current unit assumed 0 */ 4523 /* find the next unit */ 4524 for (;;) { /* inner forever loop */ 4525 /* strip leading zero units [from either pre-adjust or from */ 4526 /* subtract last time around]. Leave at least one unit. */ 4527 for (; *msu1==0 && msu1>var1; msu1--) var1units--; 4528 4529 if (var1units<var2ulen) break; /* var1 too low for subtract */ 4530 if (var1units==var2ulen) { /* unit-by-unit compare needed */ 4531 /* compare the two numbers, from msu */ 4532 const Unit *pv1, *pv2; 4533 Unit v2; /* units to compare */ 4534 pv2=msu2; /* -> msu */ 4535 for (pv1=msu1; ; pv1--, pv2--) { 4536 /* v1=*pv1 -- always OK */ 4537 v2=0; /* assume in padding */ 4538 if (pv2>=var2) v2=*pv2; /* in range */ 4539 if (*pv1!=v2) break; /* no longer the same */ 4540 if (pv1==var1) break; /* done; leave pv1 as is */ 4541 } 4542 /* here when all inspected or a difference seen */ 4543 if (*pv1<v2) break; /* var1 too low to subtract */ 4544 if (*pv1==v2) { /* var1 == var2 */ 4545 /* reach here if var1 and var2 are identical; subtraction */ 4546 /* would increase digit by one, and the residue will be 0 so */ 4547 /* the calculation is done; leave the loop with residue=0. */ 4548 thisunit++; /* as though subtracted */ 4549 *var1=0; /* set var1 to 0 */ 4550 var1units=1; /* .. */ 4551 break; /* from inner */ 4552 } /* var1 == var2 */ 4553 /* *pv1>v2. Prepare for real subtraction; the lengths are equal */ 4554 /* Estimate the multiplier (there's always a msu1-1)... */ 4555 /* Bring in two units of var2 to provide a good estimate. */ 4556 mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2pair); 4557 } /* lengths the same */ 4558 else { /* var1units > var2ulen, so subtraction is safe */ 4559 /* The var2 msu is one unit towards the lsu of the var1 msu, */ 4560 /* so only one unit for var2 can be used. */ 4561 mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2plus); 4562 } 4563 if (mult==0) mult=1; /* must always be at least 1 */ 4564 /* subtraction needed; var1 is > var2 */ 4565 thisunit=(Unit)(thisunit+mult); /* accumulate */ 4566 /* subtract var1-var2, into var1; only the overlap needs */ 4567 /* processing, as this is an in-place calculation */ 4568 shift=var2ulen-var2units; 4569 #if DECTRACE 4570 decDumpAr('1', &var1[shift], var1units-shift); 4571 decDumpAr('2', var2, var2units); 4572 printf("m=%ld\n", -mult); 4573 #endif 4574 decUnitAddSub(&var1[shift], var1units-shift, 4575 var2, var2units, 0, 4576 &var1[shift], -mult); 4577 #if DECTRACE 4578 decDumpAr('#', &var1[shift], var1units-shift); 4579 #endif 4580 /* var1 now probably has leading zeros; these are removed at the */ 4581 /* top of the inner loop. */ 4582 } /* inner loop */ 4583 4584 /* The next unit has been calculated in full; unless it's a */ 4585 /* leading zero, add to acc */ 4586 if (accunits!=0 || thisunit!=0) { /* is first or non-zero */ 4587 *accnext=thisunit; /* store in accumulator */ 4588 /* account exactly for the new digits */ 4589 if (accunits==0) { 4590 accdigits++; /* at least one */ 4591 for (pow=&powers[1]; thisunit>=*pow; pow++) accdigits++; 4592 } 4593 else accdigits+=DECDPUN; 4594 accunits++; /* update count */ 4595 accnext--; /* ready for next */ 4596 if (accdigits>reqdigits) break; /* have enough digits */ 4597 } 4598 4599 /* if the residue is zero, the operation is done (unless divide */ 4600 /* or divideInteger and still not enough digits yet) */ 4601 if (*var1==0 && var1units==1) { /* residue is 0 */ 4602 if (op&(REMAINDER|REMNEAR)) break; 4603 if ((op&DIVIDE) && (exponent<=maxexponent)) break; 4604 /* [drop through if divideInteger] */ 4605 } 4606 /* also done enough if calculating remainder or integer */ 4607 /* divide and just did the last ('units') unit */ 4608 if (exponent==0 && !(op&DIVIDE)) break; 4609 4610 /* to get here, var1 is less than var2, so divide var2 by the per- */ 4611 /* Unit power of ten and go for the next digit */ 4612 var2ulen--; /* shift down */ 4613 exponent-=DECDPUN; /* update the exponent */ 4614 } /* outer loop */ 4615 4616 /* ---- division is complete --------------------------------------- */ 4617 /* here: acc has at least reqdigits+1 of good results (or fewer */ 4618 /* if early stop), starting at accnext+1 (its lsu) */ 4619 /* var1 has any residue at the stopping point */ 4620 /* accunits is the number of digits collected in acc */ 4621 if (accunits==0) { /* acc is 0 */ 4622 accunits=1; /* show have a unit .. */ 4623 accdigits=1; /* .. */ 4624 *accnext=0; /* .. whose value is 0 */ 4625 } 4626 else accnext++; /* back to last placed */ 4627 /* accnext now -> lowest unit of result */ 4628 4629 residue=0; /* assume no residue */ 4630 if (op&DIVIDE) { 4631 /* record the presence of any residue, for rounding */ 4632 if (*var1!=0 || var1units>1) residue=1; 4633 else { /* no residue */ 4634 /* Had an exact division; clean up spurious trailing 0s. */ 4635 /* There will be at most DECDPUN-1, from the final multiply, */ 4636 /* and then only if the result is non-0 (and even) and the */ 4637 /* exponent is 'loose'. */ 4638 #if DECDPUN>1 4639 Unit lsu=*accnext; 4640 if (!(lsu&0x01) && (lsu!=0)) { 4641 /* count the trailing zeros */ 4642 Int drop=0; 4643 for (;; drop++) { /* [will terminate because lsu!=0] */ 4644 if (exponent>=maxexponent) break; /* don't chop real 0s */ 4645 #if DECDPUN<=4 4646 if ((lsu-QUOT10(lsu, drop+1) 4647 *powers[drop+1])!=0) break; /* found non-0 digit */ 4648 #else 4649 if (lsu%powers[drop+1]!=0) break; /* found non-0 digit */ 4650 #endif 4651 exponent++; 4652 } 4653 if (drop>0) { 4654 accunits=decShiftToLeast(accnext, accunits, drop); 4655 accdigits=decGetDigits(accnext, accunits); 4656 accunits=D2U(accdigits); 4657 /* [exponent was adjusted in the loop] */ 4658 } 4659 } /* neither odd nor 0 */ 4660 #endif 4661 } /* exact divide */ 4662 } /* divide */ 4663 else /* op!=DIVIDE */ { 4664 /* check for coefficient overflow */ 4665 if (accdigits+exponent>reqdigits) { 4666 *status|=DEC_Division_impossible; 4667 break; 4668 } 4669 if (op & (REMAINDER|REMNEAR)) { 4670 /* [Here, the exponent will be 0, because var1 was adjusted */ 4671 /* appropriately.] */ 4672 Int postshift; /* work */ 4673 Flag wasodd=0; /* integer was odd */ 4674 Unit *quotlsu; /* for save */ 4675 Int quotdigits; /* .. */ 4676 4677 bits=lhs->bits; /* remainder sign is always as lhs */ 4678 4679 /* Fastpath when residue is truly 0 is worthwhile [and */ 4680 /* simplifies the code below] */ 4681 if (*var1==0 && var1units==1) { /* residue is 0 */ 4682 Int exp=lhs->exponent; /* save min(exponents) */ 4683 if (rhs->exponent<exp) exp=rhs->exponent; 4684 uprv_decNumberZero(res); /* 0 coefficient */ 4685 #if DECSUBSET 4686 if (set->extended) 4687 #endif 4688 res->exponent=exp; /* .. with proper exponent */ 4689 res->bits=(uByte)(bits&DECNEG); /* [cleaned] */ 4690 decFinish(res, set, &residue, status); /* might clamp */ 4691 break; 4692 } 4693 /* note if the quotient was odd */ 4694 if (*accnext & 0x01) wasodd=1; /* acc is odd */ 4695 quotlsu=accnext; /* save in case need to reinspect */ 4696 quotdigits=accdigits; /* .. */ 4697 4698 /* treat the residue, in var1, as the value to return, via acc */ 4699 /* calculate the unused zero digits. This is the smaller of: */ 4700 /* var1 initial padding (saved above) */ 4701 /* var2 residual padding, which happens to be given by: */ 4702 postshift=var1initpad+exponent-lhs->exponent+rhs->exponent; 4703 /* [the 'exponent' term accounts for the shifts during divide] */ 4704 if (var1initpad<postshift) postshift=var1initpad; 4705 4706 /* shift var1 the requested amount, and adjust its digits */ 4707 var1units=decShiftToLeast(var1, var1units, postshift); 4708 accnext=var1; 4709 accdigits=decGetDigits(var1, var1units); 4710 accunits=D2U(accdigits); 4711 4712 exponent=lhs->exponent; /* exponent is smaller of lhs & rhs */ 4713 if (rhs->exponent<exponent) exponent=rhs->exponent; 4714 4715 /* Now correct the result if doing remainderNear; if it */ 4716 /* (looking just at coefficients) is > rhs/2, or == rhs/2 and */ 4717 /* the integer was odd then the result should be rem-rhs. */ 4718 if (op&REMNEAR) { 4719 Int compare, tarunits; /* work */ 4720 Unit *up; /* .. */ 4721 /* calculate remainder*2 into the var1 buffer (which has */ 4722 /* 'headroom' of an extra unit and hence enough space) */ 4723 /* [a dedicated 'double' loop would be faster, here] */ 4724 tarunits=decUnitAddSub(accnext, accunits, accnext, accunits, 4725 0, accnext, 1); 4726 /* decDumpAr('r', accnext, tarunits); */ 4727 4728 /* Here, accnext (var1) holds tarunits Units with twice the */ 4729 /* remainder's coefficient, which must now be compared to the */ 4730 /* RHS. The remainder's exponent may be smaller than the RHS's. */ 4731 compare=decUnitCompare(accnext, tarunits, rhs->lsu, D2U(rhs->digits), 4732 rhs->exponent-exponent); 4733 if (compare==BADINT) { /* deep trouble */ 4734 *status|=DEC_Insufficient_storage; 4735 break;} 4736 4737 /* now restore the remainder by dividing by two; the lsu */ 4738 /* is known to be even. */ 4739 for (up=accnext; up<accnext+tarunits; up++) { 4740 Int half; /* half to add to lower unit */ 4741 half=*up & 0x01; 4742 *up/=2; /* [shift] */ 4743 if (!half) continue; 4744 *(up-1)+=(DECDPUNMAX+1)/2; 4745 } 4746 /* [accunits still describes the original remainder length] */ 4747 4748 if (compare>0 || (compare==0 && wasodd)) { /* adjustment needed */ 4749 Int exp, expunits, exprem; /* work */ 4750 /* This is effectively causing round-up of the quotient, */ 4751 /* so if it was the rare case where it was full and all */ 4752 /* nines, it would overflow and hence division-impossible */ 4753 /* should be raised */ 4754 Flag allnines=0; /* 1 if quotient all nines */ 4755 if (quotdigits==reqdigits) { /* could be borderline */ 4756 for (up=quotlsu; ; up++) { 4757 if (quotdigits>DECDPUN) { 4758 if (*up!=DECDPUNMAX) break;/* non-nines */ 4759 } 4760 else { /* this is the last Unit */ 4761 if (*up==powers[quotdigits]-1) allnines=1; 4762 break; 4763 } 4764 quotdigits-=DECDPUN; /* checked those digits */ 4765 } /* up */ 4766 } /* borderline check */ 4767 if (allnines) { 4768 *status|=DEC_Division_impossible; 4769 break;} 4770 4771 /* rem-rhs is needed; the sign will invert. Again, var1 */ 4772 /* can safely be used for the working Units array. */ 4773 exp=rhs->exponent-exponent; /* RHS padding needed */ 4774 /* Calculate units and remainder from exponent. */ 4775 expunits=exp/DECDPUN; 4776 exprem=exp%DECDPUN; 4777 /* subtract [A+B*(-m)]; the result will always be negative */ 4778 accunits=-decUnitAddSub(accnext, accunits, 4779 rhs->lsu, D2U(rhs->digits), 4780 expunits, accnext, -(Int)powers[exprem]); 4781 accdigits=decGetDigits(accnext, accunits); /* count digits exactly */ 4782 accunits=D2U(accdigits); /* and recalculate the units for copy */ 4783 /* [exponent is as for original remainder] */ 4784 bits^=DECNEG; /* flip the sign */ 4785 } 4786 } /* REMNEAR */ 4787 } /* REMAINDER or REMNEAR */ 4788 } /* not DIVIDE */ 4789 4790 /* Set exponent and bits */ 4791 res->exponent=exponent; 4792 res->bits=(uByte)(bits&DECNEG); /* [cleaned] */ 4793 4794 /* Now the coefficient. */ 4795 decSetCoeff(res, set, accnext, accdigits, &residue, status); 4796 4797 decFinish(res, set, &residue, status); /* final cleanup */ 4798 4799 #if DECSUBSET 4800 /* If a divide then strip trailing zeros if subset [after round] */ 4801 if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, 1, &dropped); 4802 #endif 4803 } while(0); /* end protected */ 4804 4805 if (varalloc!=NULL) free(varalloc); /* drop any storage used */ 4806 if (allocacc!=NULL) free(allocacc); /* .. */ 4807 #if DECSUBSET 4808 if (allocrhs!=NULL) free(allocrhs); /* .. */ 4809 if (alloclhs!=NULL) free(alloclhs); /* .. */ 4810 #endif 4811 return res; 4812 } /* decDivideOp */ 4813 4814/* ------------------------------------------------------------------ */ 4815/* decMultiplyOp -- multiplication operation */ 4816/* */ 4817/* This routine performs the multiplication C=A x B. */ 4818/* */ 4819/* res is C, the result. C may be A and/or B (e.g., X=X*X) */ 4820/* lhs is A */ 4821/* rhs is B */ 4822/* set is the context */ 4823/* status is the usual accumulator */ 4824/* */ 4825/* C must have space for set->digits digits. */ 4826/* */ 4827/* ------------------------------------------------------------------ */ 4828/* 'Classic' multiplication is used rather than Karatsuba, as the */ 4829/* latter would give only a minor improvement for the short numbers */ 4830/* expected to be handled most (and uses much more memory). */ 4831/* */ 4832/* There are two major paths here: the general-purpose ('old code') */ 4833/* path which handles all DECDPUN values, and a fastpath version */ 4834/* which is used if 64-bit ints are available, DECDPUN<=4, and more */ 4835/* than two calls to decUnitAddSub would be made. */ 4836/* */ 4837/* The fastpath version lumps units together into 8-digit or 9-digit */ 4838/* chunks, and also uses a lazy carry strategy to minimise expensive */ 4839/* 64-bit divisions. The chunks are then broken apart again into */ 4840/* units for continuing processing. Despite this overhead, the */ 4841/* fastpath can speed up some 16-digit operations by 10x (and much */ 4842/* more for higher-precision calculations). */ 4843/* */ 4844/* A buffer always has to be used for the accumulator; in the */ 4845/* fastpath, buffers are also always needed for the chunked copies of */ 4846/* of the operand coefficients. */ 4847/* Static buffers are larger than needed just for multiply, to allow */ 4848/* for calls from other operations (notably exp). */ 4849/* ------------------------------------------------------------------ */ 4850#define FASTMUL (DECUSE64 && DECDPUN<5) 4851static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs, 4852 const decNumber *rhs, decContext *set, 4853 uInt *status) { 4854 Int accunits; /* Units of accumulator in use */ 4855 Int exponent; /* work */ 4856 Int residue=0; /* rounding residue */ 4857 uByte bits; /* result sign */ 4858 Unit *acc; /* -> accumulator Unit array */ 4859 Int needbytes; /* size calculator */ 4860 void *allocacc=NULL; /* -> allocated accumulator, iff allocated */ 4861 Unit accbuff[SD2U(DECBUFFER*4+1)]; /* buffer (+1 for DECBUFFER==0, */ 4862 /* *4 for calls from other operations) */ 4863 const Unit *mer, *mermsup; /* work */ 4864 Int madlength; /* Units in multiplicand */ 4865 Int shift; /* Units to shift multiplicand by */ 4866 4867 #if FASTMUL 4868 /* if DECDPUN is 1 or 3 work in base 10**9, otherwise */ 4869 /* (DECDPUN is 2 or 4) then work in base 10**8 */ 4870 #if DECDPUN & 1 /* odd */ 4871 #define FASTBASE 1000000000 /* base */ 4872 #define FASTDIGS 9 /* digits in base */ 4873 #define FASTLAZY 18 /* carry resolution point [1->18] */ 4874 #else 4875 #define FASTBASE 100000000 4876 #define FASTDIGS 8 4877 #define FASTLAZY 1844 /* carry resolution point [1->1844] */ 4878 #endif 4879 /* three buffers are used, two for chunked copies of the operands */ 4880 /* (base 10**8 or base 10**9) and one base 2**64 accumulator with */ 4881 /* lazy carry evaluation */ 4882 uInt zlhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */ 4883 uInt *zlhi=zlhibuff; /* -> lhs array */ 4884 uInt *alloclhi=NULL; /* -> allocated buffer, iff allocated */ 4885 uInt zrhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */ 4886 uInt *zrhi=zrhibuff; /* -> rhs array */ 4887 uInt *allocrhi=NULL; /* -> allocated buffer, iff allocated */ 4888 uLong zaccbuff[(DECBUFFER*2+1)/4+2]; /* buffer (+1 for DECBUFFER==0) */ 4889 /* [allocacc is shared for both paths, as only one will run] */ 4890 uLong *zacc=zaccbuff; /* -> accumulator array for exact result */ 4891 #if DECDPUN==1 4892 Int zoff; /* accumulator offset */ 4893 #endif 4894 uInt *lip, *rip; /* item pointers */ 4895 uInt *lmsi, *rmsi; /* most significant items */ 4896 Int ilhs, irhs, iacc; /* item counts in the arrays */ 4897 Int lazy; /* lazy carry counter */ 4898 uLong lcarry; /* uLong carry */ 4899 uInt carry; /* carry (NB not uLong) */ 4900 Int count; /* work */ 4901 const Unit *cup; /* .. */ 4902 Unit *up; /* .. */ 4903 uLong *lp; /* .. */ 4904 Int p; /* .. */ 4905 #endif 4906 4907 #if DECSUBSET 4908 decNumber *alloclhs=NULL; /* -> allocated buffer, iff allocated */ 4909 decNumber *allocrhs=NULL; /* -> allocated buffer, iff allocated */ 4910 #endif 4911 4912 #if DECCHECK 4913 if (decCheckOperands(res, lhs, rhs, set)) return res; 4914 #endif 4915 4916 /* precalculate result sign */ 4917 bits=(uByte)((lhs->bits^rhs->bits)&DECNEG); 4918 4919 /* handle infinities and NaNs */ 4920 if (SPECIALARGS) { /* a special bit set */ 4921 if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */ 4922 decNaNs(res, lhs, rhs, set, status); 4923 return res;} 4924 /* one or two infinities; Infinity * 0 is invalid */ 4925 if (((lhs->bits & DECINF)==0 && ISZERO(lhs)) 4926 ||((rhs->bits & DECINF)==0 && ISZERO(rhs))) { 4927 *status|=DEC_Invalid_operation; 4928 return res;} 4929 uprv_decNumberZero(res); 4930 res->bits=bits|DECINF; /* infinity */ 4931 return res;} 4932 4933 /* For best speed, as in DMSRCN [the original Rexx numerics */ 4934 /* module], use the shorter number as the multiplier (rhs) and */ 4935 /* the longer as the multiplicand (lhs) to minimise the number of */ 4936 /* adds (partial products) */ 4937 if (lhs->digits<rhs->digits) { /* swap... */ 4938 const decNumber *hold=lhs; 4939 lhs=rhs; 4940 rhs=hold; 4941 } 4942 4943 do { /* protect allocated storage */ 4944 #if DECSUBSET 4945 if (!set->extended) { 4946 /* reduce operands and set lostDigits status, as needed */ 4947 if (lhs->digits>set->digits) { 4948 alloclhs=decRoundOperand(lhs, set, status); 4949 if (alloclhs==NULL) break; 4950 lhs=alloclhs; 4951 } 4952 if (rhs->digits>set->digits) { 4953 allocrhs=decRoundOperand(rhs, set, status); 4954 if (allocrhs==NULL) break; 4955 rhs=allocrhs; 4956 } 4957 } 4958 #endif 4959 /* [following code does not require input rounding] */ 4960 4961 #if FASTMUL /* fastpath can be used */ 4962 /* use the fast path if there are enough digits in the shorter */ 4963 /* operand to make the setup and takedown worthwhile */ 4964 #define NEEDTWO (DECDPUN*2) /* within two decUnitAddSub calls */ 4965 if (rhs->digits>NEEDTWO) { /* use fastpath... */ 4966 /* calculate the number of elements in each array */ 4967 ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; /* [ceiling] */ 4968 irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; /* .. */ 4969 iacc=ilhs+irhs; 4970 4971 /* allocate buffers if required, as usual */ 4972 needbytes=ilhs*sizeof(uInt); 4973 if (needbytes>(Int)sizeof(zlhibuff)) { 4974 alloclhi=(uInt *)malloc(needbytes); 4975 zlhi=alloclhi;} 4976 needbytes=irhs*sizeof(uInt); 4977 if (needbytes>(Int)sizeof(zrhibuff)) { 4978 allocrhi=(uInt *)malloc(needbytes); 4979 zrhi=allocrhi;} 4980 4981 /* Allocating the accumulator space needs a special case when */ 4982 /* DECDPUN=1 because when converting the accumulator to Units */ 4983 /* after the multiplication each 8-byte item becomes 9 1-byte */ 4984 /* units. Therefore iacc extra bytes are needed at the front */ 4985 /* (rounded up to a multiple of 8 bytes), and the uLong */ 4986 /* accumulator starts offset the appropriate number of units */ 4987 /* to the right to avoid overwrite during the unchunking. */ 4988 needbytes=iacc*sizeof(uLong); 4989 #if DECDPUN==1 4990 zoff=(iacc+7)/8; /* items to offset by */ 4991 needbytes+=zoff*8; 4992 #endif 4993 if (needbytes>(Int)sizeof(zaccbuff)) { 4994 allocacc=(uLong *)malloc(needbytes); 4995 zacc=(uLong *)allocacc;} 4996 if (zlhi==NULL||zrhi==NULL||zacc==NULL) { 4997 *status|=DEC_Insufficient_storage; 4998 break;} 4999 5000 acc=(Unit *)zacc; /* -> target Unit array */ 5001 #if DECDPUN==1 5002 zacc+=zoff; /* start uLong accumulator to right */ 5003 #endif 5004 5005 /* assemble the chunked copies of the left and right sides */ 5006 for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++) 5007 for (p=0, *lip=0; p<FASTDIGS && count>0; 5008 p+=DECDPUN, cup++, count-=DECDPUN) 5009 *lip+=*cup*powers[p]; 5010 lmsi=lip-1; /* save -> msi */ 5011 for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++) 5012 for (p=0, *rip=0; p<FASTDIGS && count>0; 5013 p+=DECDPUN, cup++, count-=DECDPUN) 5014 *rip+=*cup*powers[p]; 5015 rmsi=rip-1; /* save -> msi */ 5016 5017 /* zero the accumulator */ 5018 for (lp=zacc; lp<zacc+iacc; lp++) *lp=0; 5019 5020 /* Start the multiplication */ 5021 /* Resolving carries can dominate the cost of accumulating the */ 5022 /* partial products, so this is only done when necessary. */ 5023 /* Each uLong item in the accumulator can hold values up to */ 5024 /* 2**64-1, and each partial product can be as large as */ 5025 /* (10**FASTDIGS-1)**2. When FASTDIGS=9, this can be added to */ 5026 /* itself 18.4 times in a uLong without overflowing, so during */ 5027 /* the main calculation resolution is carried out every 18th */ 5028 /* add -- every 162 digits. Similarly, when FASTDIGS=8, the */ 5029 /* partial products can be added to themselves 1844.6 times in */ 5030 /* a uLong without overflowing, so intermediate carry */ 5031 /* resolution occurs only every 14752 digits. Hence for common */ 5032 /* short numbers usually only the one final carry resolution */ 5033 /* occurs. */ 5034 /* (The count is set via FASTLAZY to simplify experiments to */ 5035 /* measure the value of this approach: a 35% improvement on a */ 5036 /* [34x34] multiply.) */ 5037 lazy=FASTLAZY; /* carry delay count */ 5038 for (rip=zrhi; rip<=rmsi; rip++) { /* over each item in rhs */ 5039 lp=zacc+(rip-zrhi); /* where to add the lhs */ 5040 for (lip=zlhi; lip<=lmsi; lip++, lp++) { /* over each item in lhs */ 5041 *lp+=(uLong)(*lip)*(*rip); /* [this should in-line] */ 5042 } /* lip loop */ 5043 lazy--; 5044 if (lazy>0 && rip!=rmsi) continue; 5045 lazy=FASTLAZY; /* reset delay count */ 5046 /* spin up the accumulator resolving overflows */ 5047 for (lp=zacc; lp<zacc+iacc; lp++) { 5048 if (*lp<FASTBASE) continue; /* it fits */ 5049 lcarry=*lp/FASTBASE; /* top part [slow divide] */ 5050 /* lcarry can exceed 2**32-1, so check again; this check */ 5051 /* and occasional extra divide (slow) is well worth it, as */ 5052 /* it allows FASTLAZY to be increased to 18 rather than 4 */ 5053 /* in the FASTDIGS=9 case */ 5054 if (lcarry<FASTBASE) carry=(uInt)lcarry; /* [usual] */ 5055 else { /* two-place carry [fairly rare] */ 5056 uInt carry2=(uInt)(lcarry/FASTBASE); /* top top part */ 5057 *(lp+2)+=carry2; /* add to item+2 */ 5058 *lp-=((uLong)FASTBASE*FASTBASE*carry2); /* [slow] */ 5059 carry=(uInt)(lcarry-((uLong)FASTBASE*carry2)); /* [inline] */ 5060 } 5061 *(lp+1)+=carry; /* add to item above [inline] */ 5062 *lp-=((uLong)FASTBASE*carry); /* [inline] */ 5063 } /* carry resolution */ 5064 } /* rip loop */ 5065 5066 /* The multiplication is complete; time to convert back into */ 5067 /* units. This can be done in-place in the accumulator and in */ 5068 /* 32-bit operations, because carries were resolved after the */ 5069 /* final add. This needs N-1 divides and multiplies for */ 5070 /* each item in the accumulator (which will become up to N */ 5071 /* units, where 2<=N<=9). */ 5072 for (lp=zacc, up=acc; lp<zacc+iacc; lp++) { 5073 uInt item=(uInt)*lp; /* decapitate to uInt */ 5074 for (p=0; p<FASTDIGS-DECDPUN; p+=DECDPUN, up++) { 5075 uInt part=item/(DECDPUNMAX+1); 5076 *up=(Unit)(item-(part*(DECDPUNMAX+1))); 5077 item=part; 5078 } /* p */ 5079 *up=(Unit)item; up++; /* [final needs no division] */ 5080 } /* lp */ 5081 accunits=up-acc; /* count of units */ 5082 } 5083 else { /* here to use units directly, without chunking ['old code'] */ 5084 #endif 5085 5086 /* if accumulator will be too long for local storage, then allocate */ 5087 acc=accbuff; /* -> assume buffer for accumulator */ 5088 needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit); 5089 if (needbytes>(Int)sizeof(accbuff)) { 5090 allocacc=(Unit *)malloc(needbytes); 5091 if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;} 5092 acc=(Unit *)allocacc; /* use the allocated space */ 5093 } 5094 5095 /* Now the main long multiplication loop */ 5096 /* Unlike the equivalent in the IBM Java implementation, there */ 5097 /* is no advantage in calculating from msu to lsu. So, do it */ 5098 /* by the book, as it were. */ 5099 /* Each iteration calculates ACC=ACC+MULTAND*MULT */ 5100 accunits=1; /* accumulator starts at '0' */ 5101 *acc=0; /* .. (lsu=0) */ 5102 shift=0; /* no multiplicand shift at first */ 5103 madlength=D2U(lhs->digits); /* this won't change */ 5104 mermsup=rhs->lsu+D2U(rhs->digits); /* -> msu+1 of multiplier */ 5105 5106 for (mer=rhs->lsu; mer<mermsup; mer++) { 5107 /* Here, *mer is the next Unit in the multiplier to use */ 5108 /* If non-zero [optimization] add it... */ 5109 if (*mer!=0) accunits=decUnitAddSub(&acc[shift], accunits-shift, 5110 lhs->lsu, madlength, 0, 5111 &acc[shift], *mer) 5112 + shift; 5113 else { /* extend acc with a 0; it will be used shortly */ 5114 *(acc+accunits)=0; /* [this avoids length of <=0 later] */ 5115 accunits++; 5116 } 5117 /* multiply multiplicand by 10**DECDPUN for next Unit to left */ 5118 shift++; /* add this for 'logical length' */ 5119 } /* n */ 5120 #if FASTMUL 5121 } /* unchunked units */ 5122 #endif 5123 /* common end-path */ 5124 #if DECTRACE 5125 decDumpAr('*', acc, accunits); /* Show exact result */ 5126 #endif 5127 5128 /* acc now contains the exact result of the multiplication, */ 5129 /* possibly with a leading zero unit; build the decNumber from */ 5130 /* it, noting if any residue */ 5131 res->bits=bits; /* set sign */ 5132 res->digits=decGetDigits(acc, accunits); /* count digits exactly */ 5133 5134 /* There can be a 31-bit wrap in calculating the exponent. */ 5135 /* This can only happen if both input exponents are negative and */ 5136 /* both their magnitudes are large. If there was a wrap, set a */ 5137 /* safe very negative exponent, from which decFinalize() will */ 5138 /* raise a hard underflow shortly. */ 5139 exponent=lhs->exponent+rhs->exponent; /* calculate exponent */ 5140 if (lhs->exponent<0 && rhs->exponent<0 && exponent>0) 5141 exponent=-2*DECNUMMAXE; /* force underflow */ 5142 res->exponent=exponent; /* OK to overwrite now */ 5143 5144 5145 /* Set the coefficient. If any rounding, residue records */ 5146 decSetCoeff(res, set, acc, res->digits, &residue, status); 5147 decFinish(res, set, &residue, status); /* final cleanup */ 5148 } while(0); /* end protected */ 5149 5150 if (allocacc!=NULL) free(allocacc); /* drop any storage used */ 5151 #if DECSUBSET 5152 if (allocrhs!=NULL) free(allocrhs); /* .. */ 5153 if (alloclhs!=NULL) free(alloclhs); /* .. */ 5154 #endif 5155 #if FASTMUL 5156 if (allocrhi!=NULL) free(allocrhi); /* .. */ 5157 if (alloclhi!=NULL) free(alloclhi); /* .. */ 5158 #endif 5159 return res; 5160 } /* decMultiplyOp */ 5161 5162/* ------------------------------------------------------------------ */ 5163/* decExpOp -- effect exponentiation */ 5164/* */ 5165/* This computes C = exp(A) */ 5166/* */ 5167/* res is C, the result. C may be A */ 5168/* rhs is A */ 5169/* set is the context; note that rounding mode has no effect */ 5170/* */ 5171/* C must have space for set->digits digits. status is updated but */ 5172/* not set. */ 5173/* */ 5174/* Restrictions: */ 5175/* */ 5176/* digits, emax, and -emin in the context must be less than */ 5177/* 2*DEC_MAX_MATH (1999998), and the rhs must be within these */ 5178/* bounds or a zero. This is an internal routine, so these */ 5179/* restrictions are contractual and not enforced. */ 5180/* */ 5181/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */ 5182/* almost always be correctly rounded, but may be up to 1 ulp in */ 5183/* error in rare cases. */ 5184/* */ 5185/* Finite results will always be full precision and Inexact, except */ 5186/* when A is a zero or -Infinity (giving 1 or 0 respectively). */ 5187/* ------------------------------------------------------------------ */ 5188/* This approach used here is similar to the algorithm described in */ 5189/* */ 5190/* Variable Precision Exponential Function, T. E. Hull and */ 5191/* A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */ 5192/* pp79-91, ACM, June 1986. */ 5193/* */ 5194/* with the main difference being that the iterations in the series */ 5195/* evaluation are terminated dynamically (which does not require the */ 5196/* extra variable-precision variables which are expensive in this */ 5197/* context). */ 5198/* */ 5199/* The error analysis in Hull & Abrham's paper applies except for the */ 5200/* round-off error accumulation during the series evaluation. This */ 5201/* code does not precalculate the number of iterations and so cannot */ 5202/* use Horner's scheme. Instead, the accumulation is done at double- */ 5203/* precision, which ensures that the additions of the terms are exact */ 5204/* and do not accumulate round-off (and any round-off errors in the */ 5205/* terms themselves move 'to the right' faster than they can */ 5206/* accumulate). This code also extends the calculation by allowing, */ 5207/* in the spirit of other decNumber operators, the input to be more */ 5208/* precise than the result (the precision used is based on the more */ 5209/* precise of the input or requested result). */ 5210/* */ 5211/* Implementation notes: */ 5212/* */ 5213/* 1. This is separated out as decExpOp so it can be called from */ 5214/* other Mathematical functions (notably Ln) with a wider range */ 5215/* than normal. In particular, it can handle the slightly wider */ 5216/* (double) range needed by Ln (which has to be able to calculate */ 5217/* exp(-x) where x can be the tiniest number (Ntiny). */ 5218/* */ 5219/* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop */ 5220/* iterations by appoximately a third with additional (although */ 5221/* diminishing) returns as the range is reduced to even smaller */ 5222/* fractions. However, h (the power of 10 used to correct the */ 5223/* result at the end, see below) must be kept <=8 as otherwise */ 5224/* the final result cannot be computed. Hence the leverage is a */ 5225/* sliding value (8-h), where potentially the range is reduced */ 5226/* more for smaller values. */ 5227/* */ 5228/* The leverage that can be applied in this way is severely */ 5229/* limited by the cost of the raise-to-the power at the end, */ 5230/* which dominates when the number of iterations is small (less */ 5231/* than ten) or when rhs is short. As an example, the adjustment */ 5232/* x**10,000,000 needs 31 multiplications, all but one full-width. */ 5233/* */ 5234/* 3. The restrictions (especially precision) could be raised with */ 5235/* care, but the full decNumber range seems very hard within the */ 5236/* 32-bit limits. */ 5237/* */ 5238/* 4. The working precisions for the static buffers are twice the */ 5239/* obvious size to allow for calls from decNumberPower. */ 5240/* ------------------------------------------------------------------ */ 5241decNumber * decExpOp(decNumber *res, const decNumber *rhs, 5242 decContext *set, uInt *status) { 5243 uInt ignore=0; /* working status */ 5244 Int h; /* adjusted exponent for 0.xxxx */ 5245 Int p; /* working precision */ 5246 Int residue; /* rounding residue */ 5247 uInt needbytes; /* for space calculations */ 5248 const decNumber *x=rhs; /* (may point to safe copy later) */ 5249 decContext aset, tset, dset; /* working contexts */ 5250 Int comp; /* work */ 5251 5252 /* the argument is often copied to normalize it, so (unusually) it */ 5253 /* is treated like other buffers, using DECBUFFER, +1 in case */ 5254 /* DECBUFFER is 0 */ 5255 decNumber bufr[D2N(DECBUFFER*2+1)]; 5256 decNumber *allocrhs=NULL; /* non-NULL if rhs buffer allocated */ 5257 5258 /* the working precision will be no more than set->digits+8+1 */ 5259 /* so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER */ 5260 /* is 0 (and twice that for the accumulator) */ 5261 5262 /* buffer for t, term (working precision plus) */ 5263 decNumber buft[D2N(DECBUFFER*2+9+1)]; 5264 decNumber *allocbuft=NULL; /* -> allocated buft, iff allocated */ 5265 decNumber *t=buft; /* term */ 5266 /* buffer for a, accumulator (working precision * 2), at least 9 */ 5267 decNumber bufa[D2N(DECBUFFER*4+18+1)]; 5268 decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ 5269 decNumber *a=bufa; /* accumulator */ 5270 /* decNumber for the divisor term; this needs at most 9 digits */ 5271 /* and so can be fixed size [16 so can use standard context] */ 5272 decNumber bufd[D2N(16)]; 5273 decNumber *d=bufd; /* divisor */ 5274 decNumber numone; /* constant 1 */ 5275 5276 #if DECCHECK 5277 Int iterations=0; /* for later sanity check */ 5278 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 5279 #endif 5280 5281 do { /* protect allocated storage */ 5282 if (SPECIALARG) { /* handle infinities and NaNs */ 5283 if (decNumberIsInfinite(rhs)) { /* an infinity */ 5284 if (decNumberIsNegative(rhs)) /* -Infinity -> +0 */ 5285 uprv_decNumberZero(res); 5286 else uprv_decNumberCopy(res, rhs); /* +Infinity -> self */ 5287 } 5288 else decNaNs(res, rhs, NULL, set, status); /* a NaN */ 5289 break;} 5290 5291 if (ISZERO(rhs)) { /* zeros -> exact 1 */ 5292 uprv_decNumberZero(res); /* make clean 1 */ 5293 *res->lsu=1; /* .. */ 5294 break;} /* [no status to set] */ 5295 5296 /* e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path */ 5297 /* positive and negative tiny cases which will result in inexact */ 5298 /* 1. This also allows the later add-accumulate to always be */ 5299 /* exact (because its length will never be more than twice the */ 5300 /* working precision). */ 5301 /* The comparator (tiny) needs just one digit, so use the */ 5302 /* decNumber d for it (reused as the divisor, etc., below); its */ 5303 /* exponent is such that if x is positive it will have */ 5304 /* set->digits-1 zeros between the decimal point and the digit, */ 5305 /* which is 4, and if x is negative one more zero there as the */ 5306 /* more precise result will be of the form 0.9999999 rather than */ 5307 /* 1.0000001. Hence, tiny will be 0.0000004 if digits=7 and x>0 */ 5308 /* or 0.00000004 if digits=7 and x<0. If RHS not larger than */ 5309 /* this then the result will be 1.000000 */ 5310 uprv_decNumberZero(d); /* clean */ 5311 *d->lsu=4; /* set 4 .. */ 5312 d->exponent=-set->digits; /* * 10**(-d) */ 5313 if (decNumberIsNegative(rhs)) d->exponent--; /* negative case */ 5314 comp=decCompare(d, rhs, 1); /* signless compare */ 5315 if (comp==BADINT) { 5316 *status|=DEC_Insufficient_storage; 5317 break;} 5318 if (comp>=0) { /* rhs < d */ 5319 Int shift=set->digits-1; 5320 uprv_decNumberZero(res); /* set 1 */ 5321 *res->lsu=1; /* .. */ 5322 res->digits=decShiftToMost(res->lsu, 1, shift); 5323 res->exponent=-shift; /* make 1.0000... */ 5324 *status|=DEC_Inexact | DEC_Rounded; /* .. inexactly */ 5325 break;} /* tiny */ 5326 5327 /* set up the context to be used for calculating a, as this is */ 5328 /* used on both paths below */ 5329 uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); 5330 /* accumulator bounds are as requested (could underflow) */ 5331 aset.emax=set->emax; /* usual bounds */ 5332 aset.emin=set->emin; /* .. */ 5333 aset.clamp=0; /* and no concrete format */ 5334 5335 /* calculate the adjusted (Hull & Abrham) exponent (where the */ 5336 /* decimal point is just to the left of the coefficient msd) */ 5337 h=rhs->exponent+rhs->digits; 5338 /* if h>8 then 10**h cannot be calculated safely; however, when */ 5339 /* h=8 then exp(|rhs|) will be at least exp(1E+7) which is at */ 5340 /* least 6.59E+4342944, so (due to the restriction on Emax/Emin) */ 5341 /* overflow (or underflow to 0) is guaranteed -- so this case can */ 5342 /* be handled by simply forcing the appropriate excess */ 5343 if (h>8) { /* overflow/underflow */ 5344 /* set up here so Power call below will over or underflow to */ 5345 /* zero; set accumulator to either 2 or 0.02 */ 5346 /* [stack buffer for a is always big enough for this] */ 5347 uprv_decNumberZero(a); 5348 *a->lsu=2; /* not 1 but < exp(1) */ 5349 if (decNumberIsNegative(rhs)) a->exponent=-2; /* make 0.02 */ 5350 h=8; /* clamp so 10**h computable */ 5351 p=9; /* set a working precision */ 5352 } 5353 else { /* h<=8 */ 5354 Int maxlever=(rhs->digits>8?1:0); 5355 /* [could/should increase this for precisions >40 or so, too] */ 5356 5357 /* if h is 8, cannot normalize to a lower upper limit because */ 5358 /* the final result will not be computable (see notes above), */ 5359 /* but leverage can be applied whenever h is less than 8. */ 5360 /* Apply as much as possible, up to a MAXLEVER digits, which */ 5361 /* sets the tradeoff against the cost of the later a**(10**h). */ 5362 /* As h is increased, the working precision below also */ 5363 /* increases to compensate for the "constant digits at the */ 5364 /* front" effect. */ 5365 Int lever=MINI(8-h, maxlever); /* leverage attainable */ 5366 Int use=-rhs->digits-lever; /* exponent to use for RHS */ 5367 h+=lever; /* apply leverage selected */ 5368 if (h<0) { /* clamp */ 5369 use+=h; /* [may end up subnormal] */ 5370 h=0; 5371 } 5372 /* Take a copy of RHS if it needs normalization (true whenever x>=1) */ 5373 if (rhs->exponent!=use) { 5374 decNumber *newrhs=bufr; /* assume will fit on stack */ 5375 needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); 5376 if (needbytes>sizeof(bufr)) { /* need malloc space */ 5377 allocrhs=(decNumber *)malloc(needbytes); 5378 if (allocrhs==NULL) { /* hopeless -- abandon */ 5379 *status|=DEC_Insufficient_storage; 5380 break;} 5381 newrhs=allocrhs; /* use the allocated space */ 5382 } 5383 uprv_decNumberCopy(newrhs, rhs); /* copy to safe space */ 5384 newrhs->exponent=use; /* normalize; now <1 */ 5385 x=newrhs; /* ready for use */ 5386 /* decNumberShow(x); */ 5387 } 5388 5389 /* Now use the usual power series to evaluate exp(x). The */ 5390 /* series starts as 1 + x + x^2/2 ... so prime ready for the */ 5391 /* third term by setting the term variable t=x, the accumulator */ 5392 /* a=1, and the divisor d=2. */ 5393 5394 /* First determine the working precision. From Hull & Abrham */ 5395 /* this is set->digits+h+2. However, if x is 'over-precise' we */ 5396 /* need to allow for all its digits to potentially participate */ 5397 /* (consider an x where all the excess digits are 9s) so in */ 5398 /* this case use x->digits+h+2 */ 5399 p=MAXI(x->digits, set->digits)+h+2; /* [h<=8] */ 5400 5401 /* a and t are variable precision, and depend on p, so space */ 5402 /* must be allocated for them if necessary */ 5403 5404 /* the accumulator needs to be able to hold 2p digits so that */ 5405 /* the additions on the second and subsequent iterations are */ 5406 /* sufficiently exact. */ 5407 needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit); 5408 if (needbytes>sizeof(bufa)) { /* need malloc space */ 5409 allocbufa=(decNumber *)malloc(needbytes); 5410 if (allocbufa==NULL) { /* hopeless -- abandon */ 5411 *status|=DEC_Insufficient_storage; 5412 break;} 5413 a=allocbufa; /* use the allocated space */ 5414 } 5415 /* the term needs to be able to hold p digits (which is */ 5416 /* guaranteed to be larger than x->digits, so the initial copy */ 5417 /* is safe); it may also be used for the raise-to-power */ 5418 /* calculation below, which needs an extra two digits */ 5419 needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit); 5420 if (needbytes>sizeof(buft)) { /* need malloc space */ 5421 allocbuft=(decNumber *)malloc(needbytes); 5422 if (allocbuft==NULL) { /* hopeless -- abandon */ 5423 *status|=DEC_Insufficient_storage; 5424 break;} 5425 t=allocbuft; /* use the allocated space */ 5426 } 5427 5428 uprv_decNumberCopy(t, x); /* term=x */ 5429 uprv_decNumberZero(a); *a->lsu=1; /* accumulator=1 */ 5430 uprv_decNumberZero(d); *d->lsu=2; /* divisor=2 */ 5431 uprv_decNumberZero(&numone); *numone.lsu=1; /* constant 1 for increment */ 5432 5433 /* set up the contexts for calculating a, t, and d */ 5434 uprv_decContextDefault(&tset, DEC_INIT_DECIMAL64); 5435 dset=tset; 5436 /* accumulator bounds are set above, set precision now */ 5437 aset.digits=p*2; /* double */ 5438 /* term bounds avoid any underflow or overflow */ 5439 tset.digits=p; 5440 tset.emin=DEC_MIN_EMIN; /* [emax is plenty] */ 5441 /* [dset.digits=16, etc., are sufficient] */ 5442 5443 /* finally ready to roll */ 5444 for (;;) { 5445 #if DECCHECK 5446 iterations++; 5447 #endif 5448 /* only the status from the accumulation is interesting */ 5449 /* [but it should remain unchanged after first add] */ 5450 decAddOp(a, a, t, &aset, 0, status); /* a=a+t */ 5451 decMultiplyOp(t, t, x, &tset, &ignore); /* t=t*x */ 5452 decDivideOp(t, t, d, &tset, DIVIDE, &ignore); /* t=t/d */ 5453 /* the iteration ends when the term cannot affect the result, */ 5454 /* if rounded to p digits, which is when its value is smaller */ 5455 /* than the accumulator by p+1 digits. There must also be */ 5456 /* full precision in a. */ 5457 if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1)) 5458 && (a->digits>=p)) break; 5459 decAddOp(d, d, &numone, &dset, 0, &ignore); /* d=d+1 */ 5460 } /* iterate */ 5461 5462 #if DECCHECK 5463 /* just a sanity check; comment out test to show always */ 5464 if (iterations>p+3) 5465 printf("Exp iterations=%ld, status=%08lx, p=%ld, d=%ld\n", 5466 (LI)iterations, (LI)*status, (LI)p, (LI)x->digits); 5467 #endif 5468 } /* h<=8 */ 5469 5470 /* apply postconditioning: a=a**(10**h) -- this is calculated */ 5471 /* at a slightly higher precision than Hull & Abrham suggest */ 5472 if (h>0) { 5473 Int seenbit=0; /* set once a 1-bit is seen */ 5474 Int i; /* counter */ 5475 Int n=powers[h]; /* always positive */ 5476 aset.digits=p+2; /* sufficient precision */ 5477 /* avoid the overhead and many extra digits of decNumberPower */ 5478 /* as all that is needed is the short 'multipliers' loop; here */ 5479 /* accumulate the answer into t */ 5480 uprv_decNumberZero(t); *t->lsu=1; /* acc=1 */ 5481 for (i=1;;i++){ /* for each bit [top bit ignored] */ 5482 /* abandon if have had overflow or terminal underflow */ 5483 if (*status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */ 5484 if (*status&DEC_Overflow || ISZERO(t)) break;} 5485 n=n<<1; /* move next bit to testable position */ 5486 if (n<0) { /* top bit is set */ 5487 seenbit=1; /* OK, have a significant bit */ 5488 decMultiplyOp(t, t, a, &aset, status); /* acc=acc*x */ 5489 } 5490 if (i==31) break; /* that was the last bit */ 5491 if (!seenbit) continue; /* no need to square 1 */ 5492 decMultiplyOp(t, t, t, &aset, status); /* acc=acc*acc [square] */ 5493 } /*i*/ /* 32 bits */ 5494 /* decNumberShow(t); */ 5495 a=t; /* and carry on using t instead of a */ 5496 } 5497 5498 /* Copy and round the result to res */ 5499 residue=1; /* indicate dirt to right .. */ 5500 if (ISZERO(a)) residue=0; /* .. unless underflowed to 0 */ 5501 aset.digits=set->digits; /* [use default rounding] */ 5502 decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */ 5503 decFinish(res, set, &residue, status); /* cleanup/set flags */ 5504 } while(0); /* end protected */ 5505 5506 if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */ 5507 if (allocbufa!=NULL) free(allocbufa); /* .. */ 5508 if (allocbuft!=NULL) free(allocbuft); /* .. */ 5509 /* [status is handled by caller] */ 5510 return res; 5511 } /* decExpOp */ 5512 5513/* ------------------------------------------------------------------ */ 5514/* Initial-estimate natural logarithm table */ 5515/* */ 5516/* LNnn -- 90-entry 16-bit table for values from .10 through .99. */ 5517/* The result is a 4-digit encode of the coefficient (c=the */ 5518/* top 14 bits encoding 0-9999) and a 2-digit encode of the */ 5519/* exponent (e=the bottom 2 bits encoding 0-3) */ 5520/* */ 5521/* The resulting value is given by: */ 5522/* */ 5523/* v = -c * 10**(-e-3) */ 5524/* */ 5525/* where e and c are extracted from entry k = LNnn[x-10] */ 5526/* where x is truncated (NB) into the range 10 through 99, */ 5527/* and then c = k>>2 and e = k&3. */ 5528/* ------------------------------------------------------------------ */ 5529const uShort LNnn[90]={9016, 8652, 8316, 8008, 7724, 7456, 7208, 5530 6972, 6748, 6540, 6340, 6148, 5968, 5792, 5628, 5464, 5312, 5531 5164, 5020, 4884, 4748, 4620, 4496, 4376, 4256, 4144, 4032, 5532 39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629, 5533 29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837, 5534 22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321, 5535 15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717, 5536 10197, 9685, 9177, 8677, 8185, 7697, 7213, 6737, 6269, 5801, 5537 5341, 4889, 4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254, 5538 10130, 6046, 20055}; 5539 5540/* ------------------------------------------------------------------ */ 5541/* decLnOp -- effect natural logarithm */ 5542/* */ 5543/* This computes C = ln(A) */ 5544/* */ 5545/* res is C, the result. C may be A */ 5546/* rhs is A */ 5547/* set is the context; note that rounding mode has no effect */ 5548/* */ 5549/* C must have space for set->digits digits. */ 5550/* */ 5551/* Notable cases: */ 5552/* A<0 -> Invalid */ 5553/* A=0 -> -Infinity (Exact) */ 5554/* A=+Infinity -> +Infinity (Exact) */ 5555/* A=1 exactly -> 0 (Exact) */ 5556/* */ 5557/* Restrictions (as for Exp): */ 5558/* */ 5559/* digits, emax, and -emin in the context must be less than */ 5560/* DEC_MAX_MATH+11 (1000010), and the rhs must be within these */ 5561/* bounds or a zero. This is an internal routine, so these */ 5562/* restrictions are contractual and not enforced. */ 5563/* */ 5564/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */ 5565/* almost always be correctly rounded, but may be up to 1 ulp in */ 5566/* error in rare cases. */ 5567/* ------------------------------------------------------------------ */ 5568/* The result is calculated using Newton's method, with each */ 5569/* iteration calculating a' = a + x * exp(-a) - 1. See, for example, */ 5570/* Epperson 1989. */ 5571/* */ 5572/* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */ 5573/* This has to be calculated at the sum of the precision of x and the */ 5574/* working precision. */ 5575/* */ 5576/* Implementation notes: */ 5577/* */ 5578/* 1. This is separated out as decLnOp so it can be called from */ 5579/* other Mathematical functions (e.g., Log 10) with a wider range */ 5580/* than normal. In particular, it can handle the slightly wider */ 5581/* (+9+2) range needed by a power function. */ 5582/* */ 5583/* 2. The speed of this function is about 10x slower than exp, as */ 5584/* it typically needs 4-6 iterations for short numbers, and the */ 5585/* extra precision needed adds a squaring effect, twice. */ 5586/* */ 5587/* 3. Fastpaths are included for ln(10) and ln(2), up to length 40, */ 5588/* as these are common requests. ln(10) is used by log10(x). */ 5589/* */ 5590/* 4. An iteration might be saved by widening the LNnn table, and */ 5591/* would certainly save at least one if it were made ten times */ 5592/* bigger, too (for truncated fractions 0.100 through 0.999). */ 5593/* However, for most practical evaluations, at least four or five */ 5594/* iterations will be neede -- so this would only speed up by */ 5595/* 20-25% and that probably does not justify increasing the table */ 5596/* size. */ 5597/* */ 5598/* 5. The static buffers are larger than might be expected to allow */ 5599/* for calls from decNumberPower. */ 5600/* ------------------------------------------------------------------ */ 5601#if defined(__clang__) || (defined(__GNUC__) && ((__GNUC__ * 100 + __GNUC_MINOR__) >= 406)) 5602#pragma GCC diagnostic push 5603#pragma GCC diagnostic ignored "-Warray-bounds" 5604#endif 5605decNumber * decLnOp(decNumber *res, const decNumber *rhs, 5606 decContext *set, uInt *status) { 5607 uInt ignore=0; /* working status accumulator */ 5608 uInt needbytes; /* for space calculations */ 5609 Int residue; /* rounding residue */ 5610 Int r; /* rhs=f*10**r [see below] */ 5611 Int p; /* working precision */ 5612 Int pp; /* precision for iteration */ 5613 Int t; /* work */ 5614 5615 /* buffers for a (accumulator, typically precision+2) and b */ 5616 /* (adjustment calculator, same size) */ 5617 decNumber bufa[D2N(DECBUFFER+12)]; 5618 decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ 5619 decNumber *a=bufa; /* accumulator/work */ 5620 decNumber bufb[D2N(DECBUFFER*2+2)]; 5621 decNumber *allocbufb=NULL; /* -> allocated bufa, iff allocated */ 5622 decNumber *b=bufb; /* adjustment/work */ 5623 5624 decNumber numone; /* constant 1 */ 5625 decNumber cmp; /* work */ 5626 decContext aset, bset; /* working contexts */ 5627 5628 #if DECCHECK 5629 Int iterations=0; /* for later sanity check */ 5630 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 5631 #endif 5632 5633 do { /* protect allocated storage */ 5634 if (SPECIALARG) { /* handle infinities and NaNs */ 5635 if (decNumberIsInfinite(rhs)) { /* an infinity */ 5636 if (decNumberIsNegative(rhs)) /* -Infinity -> error */ 5637 *status|=DEC_Invalid_operation; 5638 else uprv_decNumberCopy(res, rhs); /* +Infinity -> self */ 5639 } 5640 else decNaNs(res, rhs, NULL, set, status); /* a NaN */ 5641 break;} 5642 5643 if (ISZERO(rhs)) { /* +/- zeros -> -Infinity */ 5644 uprv_decNumberZero(res); /* make clean */ 5645 res->bits=DECINF|DECNEG; /* set - infinity */ 5646 break;} /* [no status to set] */ 5647 5648 /* Non-zero negatives are bad... */ 5649 if (decNumberIsNegative(rhs)) { /* -x -> error */ 5650 *status|=DEC_Invalid_operation; 5651 break;} 5652 5653 /* Here, rhs is positive, finite, and in range */ 5654 5655 /* lookaside fastpath code for ln(2) and ln(10) at common lengths */ 5656 if (rhs->exponent==0 && set->digits<=40) { 5657 #if DECDPUN==1 5658 if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { /* ln(10) */ 5659 #else 5660 if (rhs->lsu[0]==10 && rhs->digits==2) { /* ln(10) */ 5661 #endif 5662 aset=*set; aset.round=DEC_ROUND_HALF_EVEN; 5663 #define LN10 "2.302585092994045684017991454684364207601" 5664 uprv_decNumberFromString(res, LN10, &aset); 5665 *status|=(DEC_Inexact | DEC_Rounded); /* is inexact */ 5666 break;} 5667 if (rhs->lsu[0]==2 && rhs->digits==1) { /* ln(2) */ 5668 aset=*set; aset.round=DEC_ROUND_HALF_EVEN; 5669 #define LN2 "0.6931471805599453094172321214581765680755" 5670 uprv_decNumberFromString(res, LN2, &aset); 5671 *status|=(DEC_Inexact | DEC_Rounded); 5672 break;} 5673 } /* integer and short */ 5674 5675 /* Determine the working precision. This is normally the */ 5676 /* requested precision + 2, with a minimum of 9. However, if */ 5677 /* the rhs is 'over-precise' then allow for all its digits to */ 5678 /* potentially participate (consider an rhs where all the excess */ 5679 /* digits are 9s) so in this case use rhs->digits+2. */ 5680 p=MAXI(rhs->digits, MAXI(set->digits, 7))+2; 5681 5682 /* Allocate space for the accumulator and the high-precision */ 5683 /* adjustment calculator, if necessary. The accumulator must */ 5684 /* be able to hold p digits, and the adjustment up to */ 5685 /* rhs->digits+p digits. They are also made big enough for 16 */ 5686 /* digits so that they can be used for calculating the initial */ 5687 /* estimate. */ 5688 needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit); 5689 if (needbytes>sizeof(bufa)) { /* need malloc space */ 5690 allocbufa=(decNumber *)malloc(needbytes); 5691 if (allocbufa==NULL) { /* hopeless -- abandon */ 5692 *status|=DEC_Insufficient_storage; 5693 break;} 5694 a=allocbufa; /* use the allocated space */ 5695 } 5696 pp=p+rhs->digits; 5697 needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit); 5698 if (needbytes>sizeof(bufb)) { /* need malloc space */ 5699 allocbufb=(decNumber *)malloc(needbytes); 5700 if (allocbufb==NULL) { /* hopeless -- abandon */ 5701 *status|=DEC_Insufficient_storage; 5702 break;} 5703 b=allocbufb; /* use the allocated space */ 5704 } 5705 5706 /* Prepare an initial estimate in acc. Calculate this by */ 5707 /* considering the coefficient of x to be a normalized fraction, */ 5708 /* f, with the decimal point at far left and multiplied by */ 5709 /* 10**r. Then, rhs=f*10**r and 0.1<=f<1, and */ 5710 /* ln(x) = ln(f) + ln(10)*r */ 5711 /* Get the initial estimate for ln(f) from a small lookup */ 5712 /* table (see above) indexed by the first two digits of f, */ 5713 /* truncated. */ 5714 5715 uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); /* 16-digit extended */ 5716 r=rhs->exponent+rhs->digits; /* 'normalised' exponent */ 5717 uprv_decNumberFromInt32(a, r); /* a=r */ 5718 uprv_decNumberFromInt32(b, 2302585); /* b=ln(10) (2.302585) */ 5719 b->exponent=-6; /* .. */ 5720 decMultiplyOp(a, a, b, &aset, &ignore); /* a=a*b */ 5721 /* now get top two digits of rhs into b by simple truncate and */ 5722 /* force to integer */ 5723 residue=0; /* (no residue) */ 5724 aset.digits=2; aset.round=DEC_ROUND_DOWN; 5725 decCopyFit(b, rhs, &aset, &residue, &ignore); /* copy & shorten */ 5726 b->exponent=0; /* make integer */ 5727 t=decGetInt(b); /* [cannot fail] */ 5728 if (t<10) t=X10(t); /* adjust single-digit b */ 5729 t=LNnn[t-10]; /* look up ln(b) */ 5730 uprv_decNumberFromInt32(b, t>>2); /* b=ln(b) coefficient */ 5731 b->exponent=-(t&3)-3; /* set exponent */ 5732 b->bits=DECNEG; /* ln(0.10)->ln(0.99) always -ve */ 5733 aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; /* restore */ 5734 decAddOp(a, a, b, &aset, 0, &ignore); /* acc=a+b */ 5735 /* the initial estimate is now in a, with up to 4 digits correct. */ 5736 /* When rhs is at or near Nmax the estimate will be low, so we */ 5737 /* will approach it from below, avoiding overflow when calling exp. */ 5738 5739 uprv_decNumberZero(&numone); *numone.lsu=1; /* constant 1 for adjustment */ 5740 5741 /* accumulator bounds are as requested (could underflow, but */ 5742 /* cannot overflow) */ 5743 aset.emax=set->emax; 5744 aset.emin=set->emin; 5745 aset.clamp=0; /* no concrete format */ 5746 /* set up a context to be used for the multiply and subtract */ 5747 bset=aset; 5748 bset.emax=DEC_MAX_MATH*2; /* use double bounds for the */ 5749 bset.emin=-DEC_MAX_MATH*2; /* adjustment calculation */ 5750 /* [see decExpOp call below] */ 5751 /* for each iteration double the number of digits to calculate, */ 5752 /* up to a maximum of p */ 5753 pp=9; /* initial precision */ 5754 /* [initially 9 as then the sequence starts 7+2, 16+2, and */ 5755 /* 34+2, which is ideal for standard-sized numbers] */ 5756 aset.digits=pp; /* working context */ 5757 bset.digits=pp+rhs->digits; /* wider context */ 5758 for (;;) { /* iterate */ 5759 #if DECCHECK 5760 iterations++; 5761 if (iterations>24) break; /* consider 9 * 2**24 */ 5762 #endif 5763 /* calculate the adjustment (exp(-a)*x-1) into b. This is a */ 5764 /* catastrophic subtraction but it really is the difference */ 5765 /* from 1 that is of interest. */ 5766 /* Use the internal entry point to Exp as it allows the double */ 5767 /* range for calculating exp(-a) when a is the tiniest subnormal. */ 5768 a->bits^=DECNEG; /* make -a */ 5769 decExpOp(b, a, &bset, &ignore); /* b=exp(-a) */ 5770 a->bits^=DECNEG; /* restore sign of a */ 5771 /* now multiply by rhs and subtract 1, at the wider precision */ 5772 decMultiplyOp(b, b, rhs, &bset, &ignore); /* b=b*rhs */ 5773 decAddOp(b, b, &numone, &bset, DECNEG, &ignore); /* b=b-1 */ 5774 5775 /* the iteration ends when the adjustment cannot affect the */ 5776 /* result by >=0.5 ulp (at the requested digits), which */ 5777 /* is when its value is smaller than the accumulator by */ 5778 /* set->digits+1 digits (or it is zero) -- this is a looser */ 5779 /* requirement than for Exp because all that happens to the */ 5780 /* accumulator after this is the final rounding (but note that */ 5781 /* there must also be full precision in a, or a=0). */ 5782 5783 if (decNumberIsZero(b) || 5784 (a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) { 5785 if (a->digits==p) break; 5786 if (decNumberIsZero(a)) { 5787 decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); /* rhs=1 ? */ 5788 if (cmp.lsu[0]==0) a->exponent=0; /* yes, exact 0 */ 5789 else *status|=(DEC_Inexact | DEC_Rounded); /* no, inexact */ 5790 break; 5791 } 5792 /* force padding if adjustment has gone to 0 before full length */ 5793 if (decNumberIsZero(b)) b->exponent=a->exponent-p; 5794 } 5795 5796 /* not done yet ... */ 5797 decAddOp(a, a, b, &aset, 0, &ignore); /* a=a+b for next estimate */ 5798 if (pp==p) continue; /* precision is at maximum */ 5799 /* lengthen the next calculation */ 5800 pp=pp*2; /* double precision */ 5801 if (pp>p) pp=p; /* clamp to maximum */ 5802 aset.digits=pp; /* working context */ 5803 bset.digits=pp+rhs->digits; /* wider context */ 5804 } /* Newton's iteration */ 5805 5806 #if DECCHECK 5807 /* just a sanity check; remove the test to show always */ 5808 if (iterations>24) 5809 printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n", 5810 (LI)iterations, (LI)*status, (LI)p, (LI)rhs->digits); 5811 #endif 5812 5813 /* Copy and round the result to res */ 5814 residue=1; /* indicate dirt to right */ 5815 if (ISZERO(a)) residue=0; /* .. unless underflowed to 0 */ 5816 aset.digits=set->digits; /* [use default rounding] */ 5817 decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */ 5818 decFinish(res, set, &residue, status); /* cleanup/set flags */ 5819 } while(0); /* end protected */ 5820 5821 if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ 5822 if (allocbufb!=NULL) free(allocbufb); /* .. */ 5823 /* [status is handled by caller] */ 5824 return res; 5825 } /* decLnOp */ 5826#if defined(__clang__) || (defined(__GNUC__) && ((__GNUC__ * 100 + __GNUC_MINOR__) >= 406)) 5827#pragma GCC diagnostic pop 5828#endif 5829 5830/* ------------------------------------------------------------------ */ 5831/* decQuantizeOp -- force exponent to requested value */ 5832/* */ 5833/* This computes C = op(A, B), where op adjusts the coefficient */ 5834/* of C (by rounding or shifting) such that the exponent (-scale) */ 5835/* of C has the value B or matches the exponent of B. */ 5836/* The numerical value of C will equal A, except for the effects of */ 5837/* any rounding that occurred. */ 5838/* */ 5839/* res is C, the result. C may be A or B */ 5840/* lhs is A, the number to adjust */ 5841/* rhs is B, the requested exponent */ 5842/* set is the context */ 5843/* quant is 1 for quantize or 0 for rescale */ 5844/* status is the status accumulator (this can be called without */ 5845/* risk of control loss) */ 5846/* */ 5847/* C must have space for set->digits digits. */ 5848/* */ 5849/* Unless there is an error or the result is infinite, the exponent */ 5850/* after the operation is guaranteed to be that requested. */ 5851/* ------------------------------------------------------------------ */ 5852static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs, 5853 const decNumber *rhs, decContext *set, 5854 Flag quant, uInt *status) { 5855 #if DECSUBSET 5856 decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ 5857 decNumber *allocrhs=NULL; /* .., rhs */ 5858 #endif 5859 const decNumber *inrhs=rhs; /* save original rhs */ 5860 Int reqdigits=set->digits; /* requested DIGITS */ 5861 Int reqexp; /* requested exponent [-scale] */ 5862 Int residue=0; /* rounding residue */ 5863 Int etiny=set->emin-(reqdigits-1); 5864 5865 #if DECCHECK 5866 if (decCheckOperands(res, lhs, rhs, set)) return res; 5867 #endif 5868 5869 do { /* protect allocated storage */ 5870 #if DECSUBSET 5871 if (!set->extended) { 5872 /* reduce operands and set lostDigits status, as needed */ 5873 if (lhs->digits>reqdigits) { 5874 alloclhs=decRoundOperand(lhs, set, status); 5875 if (alloclhs==NULL) break; 5876 lhs=alloclhs; 5877 } 5878 if (rhs->digits>reqdigits) { /* [this only checks lostDigits] */ 5879 allocrhs=decRoundOperand(rhs, set, status); 5880 if (allocrhs==NULL) break; 5881 rhs=allocrhs; 5882 } 5883 } 5884 #endif 5885 /* [following code does not require input rounding] */ 5886 5887 /* Handle special values */ 5888 if (SPECIALARGS) { 5889 /* NaNs get usual processing */ 5890 if (SPECIALARGS & (DECSNAN | DECNAN)) 5891 decNaNs(res, lhs, rhs, set, status); 5892 /* one infinity but not both is bad */ 5893 else if ((lhs->bits ^ rhs->bits) & DECINF) 5894 *status|=DEC_Invalid_operation; 5895 /* both infinity: return lhs */ 5896 else uprv_decNumberCopy(res, lhs); /* [nop if in place] */ 5897 break; 5898 } 5899 5900 /* set requested exponent */ 5901 if (quant) reqexp=inrhs->exponent; /* quantize -- match exponents */ 5902 else { /* rescale -- use value of rhs */ 5903 /* Original rhs must be an integer that fits and is in range, */ 5904 /* which could be from -1999999997 to +999999999, thanks to */ 5905 /* subnormals */ 5906 reqexp=decGetInt(inrhs); /* [cannot fail] */ 5907 } 5908 5909 #if DECSUBSET 5910 if (!set->extended) etiny=set->emin; /* no subnormals */ 5911 #endif 5912 5913 if (reqexp==BADINT /* bad (rescale only) or .. */ 5914 || reqexp==BIGODD || reqexp==BIGEVEN /* very big (ditto) or .. */ 5915 || (reqexp<etiny) /* < lowest */ 5916 || (reqexp>set->emax)) { /* > emax */ 5917 *status|=DEC_Invalid_operation; 5918 break;} 5919 5920 /* the RHS has been processed, so it can be overwritten now if necessary */ 5921 if (ISZERO(lhs)) { /* zero coefficient unchanged */ 5922 uprv_decNumberCopy(res, lhs); /* [nop if in place] */ 5923 res->exponent=reqexp; /* .. just set exponent */ 5924 #if DECSUBSET 5925 if (!set->extended) res->bits=0; /* subset specification; no -0 */ 5926 #endif 5927 } 5928 else { /* non-zero lhs */ 5929 Int adjust=reqexp-lhs->exponent; /* digit adjustment needed */ 5930 /* if adjusted coefficient will definitely not fit, give up now */ 5931 if ((lhs->digits-adjust)>reqdigits) { 5932 *status|=DEC_Invalid_operation; 5933 break; 5934 } 5935 5936 if (adjust>0) { /* increasing exponent */ 5937 /* this will decrease the length of the coefficient by adjust */ 5938 /* digits, and must round as it does so */ 5939 decContext workset; /* work */ 5940 workset=*set; /* clone rounding, etc. */ 5941 workset.digits=lhs->digits-adjust; /* set requested length */ 5942 /* [note that the latter can be <1, here] */ 5943 decCopyFit(res, lhs, &workset, &residue, status); /* fit to result */ 5944 decApplyRound(res, &workset, residue, status); /* .. and round */ 5945 residue=0; /* [used] */ 5946 /* If just rounded a 999s case, exponent will be off by one; */ 5947 /* adjust back (after checking space), if so. */ 5948 if (res->exponent>reqexp) { 5949 /* re-check needed, e.g., for quantize(0.9999, 0.001) under */ 5950 /* set->digits==3 */ 5951 if (res->digits==reqdigits) { /* cannot shift by 1 */ 5952 *status&=~(DEC_Inexact | DEC_Rounded); /* [clean these] */ 5953 *status|=DEC_Invalid_operation; 5954 break; 5955 } 5956 res->digits=decShiftToMost(res->lsu, res->digits, 1); /* shift */ 5957 res->exponent--; /* (re)adjust the exponent. */ 5958 } 5959 #if DECSUBSET 5960 if (ISZERO(res) && !set->extended) res->bits=0; /* subset; no -0 */ 5961 #endif 5962 } /* increase */ 5963 else /* adjust<=0 */ { /* decreasing or = exponent */ 5964 /* this will increase the length of the coefficient by -adjust */ 5965 /* digits, by adding zero or more trailing zeros; this is */ 5966 /* already checked for fit, above */ 5967 uprv_decNumberCopy(res, lhs); /* [it will fit] */ 5968 /* if padding needed (adjust<0), add it now... */ 5969 if (adjust<0) { 5970 res->digits=decShiftToMost(res->lsu, res->digits, -adjust); 5971 res->exponent+=adjust; /* adjust the exponent */ 5972 } 5973 } /* decrease */ 5974 } /* non-zero */ 5975 5976 /* Check for overflow [do not use Finalize in this case, as an */ 5977 /* overflow here is a "don't fit" situation] */ 5978 if (res->exponent>set->emax-res->digits+1) { /* too big */ 5979 *status|=DEC_Invalid_operation; 5980 break; 5981 } 5982 else { 5983 decFinalize(res, set, &residue, status); /* set subnormal flags */ 5984 *status&=~DEC_Underflow; /* suppress Underflow [as per 754] */ 5985 } 5986 } while(0); /* end protected */ 5987 5988 #if DECSUBSET 5989 if (allocrhs!=NULL) free(allocrhs); /* drop any storage used */ 5990 if (alloclhs!=NULL) free(alloclhs); /* .. */ 5991 #endif 5992 return res; 5993 } /* decQuantizeOp */ 5994 5995/* ------------------------------------------------------------------ */ 5996/* decCompareOp -- compare, min, or max two Numbers */ 5997/* */ 5998/* This computes C = A ? B and carries out one of four operations: */ 5999/* COMPARE -- returns the signum (as a number) giving the */ 6000/* result of a comparison unless one or both */ 6001/* operands is a NaN (in which case a NaN results) */ 6002/* COMPSIG -- as COMPARE except that a quiet NaN raises */ 6003/* Invalid operation. */ 6004/* COMPMAX -- returns the larger of the operands, using the */ 6005/* 754 maxnum operation */ 6006/* COMPMAXMAG -- ditto, comparing absolute values */ 6007/* COMPMIN -- the 754 minnum operation */ 6008/* COMPMINMAG -- ditto, comparing absolute values */ 6009/* COMTOTAL -- returns the signum (as a number) giving the */ 6010/* result of a comparison using 754 total ordering */ 6011/* */ 6012/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ 6013/* lhs is A */ 6014/* rhs is B */ 6015/* set is the context */ 6016/* op is the operation flag */ 6017/* status is the usual accumulator */ 6018/* */ 6019/* C must have space for one digit for COMPARE or set->digits for */ 6020/* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG. */ 6021/* ------------------------------------------------------------------ */ 6022/* The emphasis here is on speed for common cases, and avoiding */ 6023/* coefficient comparison if possible. */ 6024/* ------------------------------------------------------------------ */ 6025static decNumber * decCompareOp(decNumber *res, const decNumber *lhs, 6026 const decNumber *rhs, decContext *set, 6027 Flag op, uInt *status) { 6028 #if DECSUBSET 6029 decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ 6030 decNumber *allocrhs=NULL; /* .., rhs */ 6031 #endif 6032 Int result=0; /* default result value */ 6033 uByte merged; /* work */ 6034 6035 #if DECCHECK 6036 if (decCheckOperands(res, lhs, rhs, set)) return res; 6037 #endif 6038 6039 do { /* protect allocated storage */ 6040 #if DECSUBSET 6041 if (!set->extended) { 6042 /* reduce operands and set lostDigits status, as needed */ 6043 if (lhs->digits>set->digits) { 6044 alloclhs=decRoundOperand(lhs, set, status); 6045 if (alloclhs==NULL) {result=BADINT; break;} 6046 lhs=alloclhs; 6047 } 6048 if (rhs->digits>set->digits) { 6049 allocrhs=decRoundOperand(rhs, set, status); 6050 if (allocrhs==NULL) {result=BADINT; break;} 6051 rhs=allocrhs; 6052 } 6053 } 6054 #endif 6055 /* [following code does not require input rounding] */ 6056 6057 /* If total ordering then handle differing signs 'up front' */ 6058 if (op==COMPTOTAL) { /* total ordering */ 6059 if (decNumberIsNegative(lhs) & !decNumberIsNegative(rhs)) { 6060 result=-1; 6061 break; 6062 } 6063 if (!decNumberIsNegative(lhs) & decNumberIsNegative(rhs)) { 6064 result=+1; 6065 break; 6066 } 6067 } 6068 6069 /* handle NaNs specially; let infinities drop through */ 6070 /* This assumes sNaN (even just one) leads to NaN. */ 6071 merged=(lhs->bits | rhs->bits) & (DECSNAN | DECNAN); 6072 if (merged) { /* a NaN bit set */ 6073 if (op==COMPARE); /* result will be NaN */ 6074 else if (op==COMPSIG) /* treat qNaN as sNaN */ 6075 *status|=DEC_Invalid_operation | DEC_sNaN; 6076 else if (op==COMPTOTAL) { /* total ordering, always finite */ 6077 /* signs are known to be the same; compute the ordering here */ 6078 /* as if the signs are both positive, then invert for negatives */ 6079 if (!decNumberIsNaN(lhs)) result=-1; 6080 else if (!decNumberIsNaN(rhs)) result=+1; 6081 /* here if both NaNs */ 6082 else if (decNumberIsSNaN(lhs) && decNumberIsQNaN(rhs)) result=-1; 6083 else if (decNumberIsQNaN(lhs) && decNumberIsSNaN(rhs)) result=+1; 6084 else { /* both NaN or both sNaN */ 6085 /* now it just depends on the payload */ 6086 result=decUnitCompare(lhs->lsu, D2U(lhs->digits), 6087 rhs->lsu, D2U(rhs->digits), 0); 6088 /* [Error not possible, as these are 'aligned'] */ 6089 } /* both same NaNs */ 6090 if (decNumberIsNegative(lhs)) result=-result; 6091 break; 6092 } /* total order */ 6093 6094 else if (merged & DECSNAN); /* sNaN -> qNaN */ 6095 else { /* here if MIN or MAX and one or two quiet NaNs */ 6096 /* min or max -- 754 rules ignore single NaN */ 6097 if (!decNumberIsNaN(lhs) || !decNumberIsNaN(rhs)) { 6098 /* just one NaN; force choice to be the non-NaN operand */ 6099 op=COMPMAX; 6100 if (lhs->bits & DECNAN) result=-1; /* pick rhs */ 6101 else result=+1; /* pick lhs */ 6102 break; 6103 } 6104 } /* max or min */ 6105 op=COMPNAN; /* use special path */ 6106 decNaNs(res, lhs, rhs, set, status); /* propagate NaN */ 6107 break; 6108 } 6109 /* have numbers */ 6110 if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1); 6111 else result=decCompare(lhs, rhs, 0); /* sign matters */ 6112 } while(0); /* end protected */ 6113 6114 if (result==BADINT) *status|=DEC_Insufficient_storage; /* rare */ 6115 else { 6116 if (op==COMPARE || op==COMPSIG ||op==COMPTOTAL) { /* returning signum */ 6117 if (op==COMPTOTAL && result==0) { 6118 /* operands are numerically equal or same NaN (and same sign, */ 6119 /* tested first); if identical, leave result 0 */ 6120 if (lhs->exponent!=rhs->exponent) { 6121 if (lhs->exponent<rhs->exponent) result=-1; 6122 else result=+1; 6123 if (decNumberIsNegative(lhs)) result=-result; 6124 } /* lexp!=rexp */ 6125 } /* total-order by exponent */ 6126 uprv_decNumberZero(res); /* [always a valid result] */ 6127 if (result!=0) { /* must be -1 or +1 */ 6128 *res->lsu=1; 6129 if (result<0) res->bits=DECNEG; 6130 } 6131 } 6132 else if (op==COMPNAN); /* special, drop through */ 6133 else { /* MAX or MIN, non-NaN result */ 6134 Int residue=0; /* rounding accumulator */ 6135 /* choose the operand for the result */ 6136 const decNumber *choice; 6137 if (result==0) { /* operands are numerically equal */ 6138 /* choose according to sign then exponent (see 754) */ 6139 uByte slhs=(lhs->bits & DECNEG); 6140 uByte srhs=(rhs->bits & DECNEG); 6141 #if DECSUBSET 6142 if (!set->extended) { /* subset: force left-hand */ 6143 op=COMPMAX; 6144 result=+1; 6145 } 6146 else 6147 #endif 6148 if (slhs!=srhs) { /* signs differ */ 6149 if (slhs) result=-1; /* rhs is max */ 6150 else result=+1; /* lhs is max */ 6151 } 6152 else if (slhs && srhs) { /* both negative */ 6153 if (lhs->exponent<rhs->exponent) result=+1; 6154 else result=-1; 6155 /* [if equal, use lhs, technically identical] */ 6156 } 6157 else { /* both positive */ 6158 if (lhs->exponent>rhs->exponent) result=+1; 6159 else result=-1; 6160 /* [ditto] */ 6161 } 6162 } /* numerically equal */ 6163 /* here result will be non-0; reverse if looking for MIN */ 6164 if (op==COMPMIN || op==COMPMINMAG) result=-result; 6165 choice=(result>0 ? lhs : rhs); /* choose */ 6166 /* copy chosen to result, rounding if need be */ 6167 decCopyFit(res, choice, set, &residue, status); 6168 decFinish(res, set, &residue, status); 6169 } 6170 } 6171 #if DECSUBSET 6172 if (allocrhs!=NULL) free(allocrhs); /* free any storage used */ 6173 if (alloclhs!=NULL) free(alloclhs); /* .. */ 6174 #endif 6175 return res; 6176 } /* decCompareOp */ 6177 6178/* ------------------------------------------------------------------ */ 6179/* decCompare -- compare two decNumbers by numerical value */ 6180/* */ 6181/* This routine compares A ? B without altering them. */ 6182/* */ 6183/* Arg1 is A, a decNumber which is not a NaN */ 6184/* Arg2 is B, a decNumber which is not a NaN */ 6185/* Arg3 is 1 for a sign-independent compare, 0 otherwise */ 6186/* */ 6187/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */ 6188/* (the only possible failure is an allocation error) */ 6189/* ------------------------------------------------------------------ */ 6190static Int decCompare(const decNumber *lhs, const decNumber *rhs, 6191 Flag abs_c) { 6192 Int result; /* result value */ 6193 Int sigr; /* rhs signum */ 6194 Int compare; /* work */ 6195 6196 result=1; /* assume signum(lhs) */ 6197 if (ISZERO(lhs)) result=0; 6198 if (abs_c) { 6199 if (ISZERO(rhs)) return result; /* LHS wins or both 0 */ 6200 /* RHS is non-zero */ 6201 if (result==0) return -1; /* LHS is 0; RHS wins */ 6202 /* [here, both non-zero, result=1] */ 6203 } 6204 else { /* signs matter */ 6205 if (result && decNumberIsNegative(lhs)) result=-1; 6206 sigr=1; /* compute signum(rhs) */ 6207 if (ISZERO(rhs)) sigr=0; 6208 else if (decNumberIsNegative(rhs)) sigr=-1; 6209 if (result > sigr) return +1; /* L > R, return 1 */ 6210 if (result < sigr) return -1; /* L < R, return -1 */ 6211 if (result==0) return 0; /* both 0 */ 6212 } 6213 6214 /* signums are the same; both are non-zero */ 6215 if ((lhs->bits | rhs->bits) & DECINF) { /* one or more infinities */ 6216 if (decNumberIsInfinite(rhs)) { 6217 if (decNumberIsInfinite(lhs)) result=0;/* both infinite */ 6218 else result=-result; /* only rhs infinite */ 6219 } 6220 return result; 6221 } 6222 /* must compare the coefficients, allowing for exponents */ 6223 if (lhs->exponent>rhs->exponent) { /* LHS exponent larger */ 6224 /* swap sides, and sign */ 6225 const decNumber *temp=lhs; 6226 lhs=rhs; 6227 rhs=temp; 6228 result=-result; 6229 } 6230 compare=decUnitCompare(lhs->lsu, D2U(lhs->digits), 6231 rhs->lsu, D2U(rhs->digits), 6232 rhs->exponent-lhs->exponent); 6233 if (compare!=BADINT) compare*=result; /* comparison succeeded */ 6234 return compare; 6235 } /* decCompare */ 6236 6237/* ------------------------------------------------------------------ */ 6238/* decUnitCompare -- compare two >=0 integers in Unit arrays */ 6239/* */ 6240/* This routine compares A ? B*10**E where A and B are unit arrays */ 6241/* A is a plain integer */ 6242/* B has an exponent of E (which must be non-negative) */ 6243/* */ 6244/* Arg1 is A first Unit (lsu) */ 6245/* Arg2 is A length in Units */ 6246/* Arg3 is B first Unit (lsu) */ 6247/* Arg4 is B length in Units */ 6248/* Arg5 is E (0 if the units are aligned) */ 6249/* */ 6250/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */ 6251/* (the only possible failure is an allocation error, which can */ 6252/* only occur if E!=0) */ 6253/* ------------------------------------------------------------------ */ 6254static Int decUnitCompare(const Unit *a, Int alength, 6255 const Unit *b, Int blength, Int exp) { 6256 Unit *acc; /* accumulator for result */ 6257 Unit accbuff[SD2U(DECBUFFER*2+1)]; /* local buffer */ 6258 Unit *allocacc=NULL; /* -> allocated acc buffer, iff allocated */ 6259 Int accunits, need; /* units in use or needed for acc */ 6260 const Unit *l, *r, *u; /* work */ 6261 Int expunits, exprem, result; /* .. */ 6262 6263 if (exp==0) { /* aligned; fastpath */ 6264 if (alength>blength) return 1; 6265 if (alength<blength) return -1; 6266 /* same number of units in both -- need unit-by-unit compare */ 6267 l=a+alength-1; 6268 r=b+alength-1; 6269 for (;l>=a; l--, r--) { 6270 if (*l>*r) return 1; 6271 if (*l<*r) return -1; 6272 } 6273 return 0; /* all units match */ 6274 } /* aligned */ 6275 6276 /* Unaligned. If one is >1 unit longer than the other, padded */ 6277 /* approximately, then can return easily */ 6278 if (alength>blength+(Int)D2U(exp)) return 1; 6279 if (alength+1<blength+(Int)D2U(exp)) return -1; 6280 6281 /* Need to do a real subtract. For this, a result buffer is needed */ 6282 /* even though only the sign is of interest. Its length needs */ 6283 /* to be the larger of alength and padded blength, +2 */ 6284 need=blength+D2U(exp); /* maximum real length of B */ 6285 if (need<alength) need=alength; 6286 need+=2; 6287 acc=accbuff; /* assume use local buffer */ 6288 if (need*sizeof(Unit)>sizeof(accbuff)) { 6289 allocacc=(Unit *)malloc(need*sizeof(Unit)); 6290 if (allocacc==NULL) return BADINT; /* hopeless -- abandon */ 6291 acc=allocacc; 6292 } 6293 /* Calculate units and remainder from exponent. */ 6294 expunits=exp/DECDPUN; 6295 exprem=exp%DECDPUN; 6296 /* subtract [A+B*(-m)] */ 6297 accunits=decUnitAddSub(a, alength, b, blength, expunits, acc, 6298 -(Int)powers[exprem]); 6299 /* [UnitAddSub result may have leading zeros, even on zero] */ 6300 if (accunits<0) result=-1; /* negative result */ 6301 else { /* non-negative result */ 6302 /* check units of the result before freeing any storage */ 6303 for (u=acc; u<acc+accunits-1 && *u==0;) u++; 6304 result=(*u==0 ? 0 : +1); 6305 } 6306 /* clean up and return the result */ 6307 if (allocacc!=NULL) free(allocacc); /* drop any storage used */ 6308 return result; 6309 } /* decUnitCompare */ 6310 6311/* ------------------------------------------------------------------ */ 6312/* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays */ 6313/* */ 6314/* This routine performs the calculation: */ 6315/* */ 6316/* C=A+(B*M) */ 6317/* */ 6318/* Where M is in the range -DECDPUNMAX through +DECDPUNMAX. */ 6319/* */ 6320/* A may be shorter or longer than B. */ 6321/* */ 6322/* Leading zeros are not removed after a calculation. The result is */ 6323/* either the same length as the longer of A and B (adding any */ 6324/* shift), or one Unit longer than that (if a Unit carry occurred). */ 6325/* */ 6326/* A and B content are not altered unless C is also A or B. */ 6327/* C may be the same array as A or B, but only if no zero padding is */ 6328/* requested (that is, C may be B only if bshift==0). */ 6329/* C is filled from the lsu; only those units necessary to complete */ 6330/* the calculation are referenced. */ 6331/* */ 6332/* Arg1 is A first Unit (lsu) */ 6333/* Arg2 is A length in Units */ 6334/* Arg3 is B first Unit (lsu) */ 6335/* Arg4 is B length in Units */ 6336/* Arg5 is B shift in Units (>=0; pads with 0 units if positive) */ 6337/* Arg6 is C first Unit (lsu) */ 6338/* Arg7 is M, the multiplier */ 6339/* */ 6340/* returns the count of Units written to C, which will be non-zero */ 6341/* and negated if the result is negative. That is, the sign of the */ 6342/* returned Int is the sign of the result (positive for zero) and */ 6343/* the absolute value of the Int is the count of Units. */ 6344/* */ 6345/* It is the caller's responsibility to make sure that C size is */ 6346/* safe, allowing space if necessary for a one-Unit carry. */ 6347/* */ 6348/* This routine is severely performance-critical; *any* change here */ 6349/* must be measured (timed) to assure no performance degradation. */ 6350/* In particular, trickery here tends to be counter-productive, as */ 6351/* increased complexity of code hurts register optimizations on */ 6352/* register-poor architectures. Avoiding divisions is nearly */ 6353/* always a Good Idea, however. */ 6354/* */ 6355/* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark */ 6356/* (IBM Warwick, UK) for some of the ideas used in this routine. */ 6357/* ------------------------------------------------------------------ */ 6358static Int decUnitAddSub(const Unit *a, Int alength, 6359 const Unit *b, Int blength, Int bshift, 6360 Unit *c, Int m) { 6361 const Unit *alsu=a; /* A lsu [need to remember it] */ 6362 Unit *clsu=c; /* C ditto */ 6363 Unit *minC; /* low water mark for C */ 6364 Unit *maxC; /* high water mark for C */ 6365 eInt carry=0; /* carry integer (could be Long) */ 6366 Int add; /* work */ 6367 #if DECDPUN<=4 /* myriadal, millenary, etc. */ 6368 Int est; /* estimated quotient */ 6369 #endif 6370 6371 #if DECTRACE 6372 if (alength<1 || blength<1) 6373 printf("decUnitAddSub: alen blen m %ld %ld [%ld]\n", alength, blength, m); 6374 #endif 6375 6376 maxC=c+alength; /* A is usually the longer */ 6377 minC=c+blength; /* .. and B the shorter */ 6378 if (bshift!=0) { /* B is shifted; low As copy across */ 6379 minC+=bshift; 6380 /* if in place [common], skip copy unless there's a gap [rare] */ 6381 if (a==c && bshift<=alength) { 6382 c+=bshift; 6383 a+=bshift; 6384 } 6385 else for (; c<clsu+bshift; a++, c++) { /* copy needed */ 6386 if (a<alsu+alength) *c=*a; 6387 else *c=0; 6388 } 6389 } 6390 if (minC>maxC) { /* swap */ 6391 Unit *hold=minC; 6392 minC=maxC; 6393 maxC=hold; 6394 } 6395 6396 /* For speed, do the addition as two loops; the first where both A */ 6397 /* and B contribute, and the second (if necessary) where only one or */ 6398 /* other of the numbers contribute. */ 6399 /* Carry handling is the same (i.e., duplicated) in each case. */ 6400 for (; c<minC; c++) { 6401 carry+=*a; 6402 a++; 6403 carry+=((eInt)*b)*m; /* [special-casing m=1/-1 */ 6404 b++; /* here is not a win] */ 6405 /* here carry is new Unit of digits; it could be +ve or -ve */ 6406 if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */ 6407 *c=(Unit)carry; 6408 carry=0; 6409 continue; 6410 } 6411 #if DECDPUN==4 /* use divide-by-multiply */ 6412 if (carry>=0) { 6413 est=(((ueInt)carry>>11)*53687)>>18; 6414 *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ 6415 carry=est; /* likely quotient [89%] */ 6416 if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ 6417 carry++; 6418 *c-=DECDPUNMAX+1; 6419 continue; 6420 } 6421 /* negative case */ 6422 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ 6423 est=(((ueInt)carry>>11)*53687)>>18; 6424 *c=(Unit)(carry-est*(DECDPUNMAX+1)); 6425 carry=est-(DECDPUNMAX+1); /* correctly negative */ 6426 if (*c<DECDPUNMAX+1) continue; /* was OK */ 6427 carry++; 6428 *c-=DECDPUNMAX+1; 6429 #elif DECDPUN==3 6430 if (carry>=0) { 6431 est=(((ueInt)carry>>3)*16777)>>21; 6432 *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ 6433 carry=est; /* likely quotient [99%] */ 6434 if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ 6435 carry++; 6436 *c-=DECDPUNMAX+1; 6437 continue; 6438 } 6439 /* negative case */ 6440 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ 6441 est=(((ueInt)carry>>3)*16777)>>21; 6442 *c=(Unit)(carry-est*(DECDPUNMAX+1)); 6443 carry=est-(DECDPUNMAX+1); /* correctly negative */ 6444 if (*c<DECDPUNMAX+1) continue; /* was OK */ 6445 carry++; 6446 *c-=DECDPUNMAX+1; 6447 #elif DECDPUN<=2 6448 /* Can use QUOT10 as carry <= 4 digits */ 6449 if (carry>=0) { 6450 est=QUOT10(carry, DECDPUN); 6451 *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ 6452 carry=est; /* quotient */ 6453 continue; 6454 } 6455 /* negative case */ 6456 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ 6457 est=QUOT10(carry, DECDPUN); 6458 *c=(Unit)(carry-est*(DECDPUNMAX+1)); 6459 carry=est-(DECDPUNMAX+1); /* correctly negative */ 6460 #else 6461 /* remainder operator is undefined if negative, so must test */ 6462 if ((ueInt)carry<(DECDPUNMAX+1)*2) { /* fastpath carry +1 */ 6463 *c=(Unit)(carry-(DECDPUNMAX+1)); /* [helps additions] */ 6464 carry=1; 6465 continue; 6466 } 6467 if (carry>=0) { 6468 *c=(Unit)(carry%(DECDPUNMAX+1)); 6469 carry=carry/(DECDPUNMAX+1); 6470 continue; 6471 } 6472 /* negative case */ 6473 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ 6474 *c=(Unit)(carry%(DECDPUNMAX+1)); 6475 carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1); 6476 #endif 6477 } /* c */ 6478 6479 /* now may have one or other to complete */ 6480 /* [pretest to avoid loop setup/shutdown] */ 6481 if (c<maxC) for (; c<maxC; c++) { 6482 if (a<alsu+alength) { /* still in A */ 6483 carry+=*a; 6484 a++; 6485 } 6486 else { /* inside B */ 6487 carry+=((eInt)*b)*m; 6488 b++; 6489 } 6490 /* here carry is new Unit of digits; it could be +ve or -ve and */ 6491 /* magnitude up to DECDPUNMAX squared */ 6492 if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */ 6493 *c=(Unit)carry; 6494 carry=0; 6495 continue; 6496 } 6497 /* result for this unit is negative or >DECDPUNMAX */ 6498 #if DECDPUN==4 /* use divide-by-multiply */ 6499 if (carry>=0) { 6500 est=(((ueInt)carry>>11)*53687)>>18; 6501 *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ 6502 carry=est; /* likely quotient [79.7%] */ 6503 if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ 6504 carry++; 6505 *c-=DECDPUNMAX+1; 6506 continue; 6507 } 6508 /* negative case */ 6509 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ 6510 est=(((ueInt)carry>>11)*53687)>>18; 6511 *c=(Unit)(carry-est*(DECDPUNMAX+1)); 6512 carry=est-(DECDPUNMAX+1); /* correctly negative */ 6513 if (*c<DECDPUNMAX+1) continue; /* was OK */ 6514 carry++; 6515 *c-=DECDPUNMAX+1; 6516 #elif DECDPUN==3 6517 if (carry>=0) { 6518 est=(((ueInt)carry>>3)*16777)>>21; 6519 *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ 6520 carry=est; /* likely quotient [99%] */ 6521 if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ 6522 carry++; 6523 *c-=DECDPUNMAX+1; 6524 continue; 6525 } 6526 /* negative case */ 6527 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ 6528 est=(((ueInt)carry>>3)*16777)>>21; 6529 *c=(Unit)(carry-est*(DECDPUNMAX+1)); 6530 carry=est-(DECDPUNMAX+1); /* correctly negative */ 6531 if (*c<DECDPUNMAX+1) continue; /* was OK */ 6532 carry++; 6533 *c-=DECDPUNMAX+1; 6534 #elif DECDPUN<=2 6535 if (carry>=0) { 6536 est=QUOT10(carry, DECDPUN); 6537 *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ 6538 carry=est; /* quotient */ 6539 continue; 6540 } 6541 /* negative case */ 6542 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ 6543 est=QUOT10(carry, DECDPUN); 6544 *c=(Unit)(carry-est*(DECDPUNMAX+1)); 6545 carry=est-(DECDPUNMAX+1); /* correctly negative */ 6546 #else 6547 if ((ueInt)carry<(DECDPUNMAX+1)*2){ /* fastpath carry 1 */ 6548 *c=(Unit)(carry-(DECDPUNMAX+1)); 6549 carry=1; 6550 continue; 6551 } 6552 /* remainder operator is undefined if negative, so must test */ 6553 if (carry>=0) { 6554 *c=(Unit)(carry%(DECDPUNMAX+1)); 6555 carry=carry/(DECDPUNMAX+1); 6556 continue; 6557 } 6558 /* negative case */ 6559 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ 6560 *c=(Unit)(carry%(DECDPUNMAX+1)); 6561 carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1); 6562 #endif 6563 } /* c */ 6564 6565 /* OK, all A and B processed; might still have carry or borrow */ 6566 /* return number of Units in the result, negated if a borrow */ 6567 if (carry==0) return c-clsu; /* no carry, so no more to do */ 6568 if (carry>0) { /* positive carry */ 6569 *c=(Unit)carry; /* place as new unit */ 6570 c++; /* .. */ 6571 return c-clsu; 6572 } 6573 /* -ve carry: it's a borrow; complement needed */ 6574 add=1; /* temporary carry... */ 6575 for (c=clsu; c<maxC; c++) { 6576 add=DECDPUNMAX+add-*c; 6577 if (add<=DECDPUNMAX) { 6578 *c=(Unit)add; 6579 add=0; 6580 } 6581 else { 6582 *c=0; 6583 add=1; 6584 } 6585 } 6586 /* add an extra unit iff it would be non-zero */ 6587 #if DECTRACE 6588 printf("UAS borrow: add %ld, carry %ld\n", add, carry); 6589 #endif 6590 if ((add-carry-1)!=0) { 6591 *c=(Unit)(add-carry-1); 6592 c++; /* interesting, include it */ 6593 } 6594 return clsu-c; /* -ve result indicates borrowed */ 6595 } /* decUnitAddSub */ 6596 6597/* ------------------------------------------------------------------ */ 6598/* decTrim -- trim trailing zeros or normalize */ 6599/* */ 6600/* dn is the number to trim or normalize */ 6601/* set is the context to use to check for clamp */ 6602/* all is 1 to remove all trailing zeros, 0 for just fraction ones */ 6603/* noclamp is 1 to unconditional (unclamped) trim */ 6604/* dropped returns the number of discarded trailing zeros */ 6605/* returns dn */ 6606/* */ 6607/* If clamp is set in the context then the number of zeros trimmed */ 6608/* may be limited if the exponent is high. */ 6609/* All fields are updated as required. This is a utility operation, */ 6610/* so special values are unchanged and no error is possible. */ 6611/* ------------------------------------------------------------------ */ 6612static decNumber * decTrim(decNumber *dn, decContext *set, Flag all, 6613 Flag noclamp, Int *dropped) { 6614 Int d, exp; /* work */ 6615 uInt cut; /* .. */ 6616 Unit *up; /* -> current Unit */ 6617 6618 #if DECCHECK 6619 if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn; 6620 #endif 6621 6622 *dropped=0; /* assume no zeros dropped */ 6623 if ((dn->bits & DECSPECIAL) /* fast exit if special .. */ 6624 || (*dn->lsu & 0x01)) return dn; /* .. or odd */ 6625 if (ISZERO(dn)) { /* .. or 0 */ 6626 dn->exponent=0; /* (sign is preserved) */ 6627 return dn; 6628 } 6629 6630 /* have a finite number which is even */ 6631 exp=dn->exponent; 6632 cut=1; /* digit (1-DECDPUN) in Unit */ 6633 up=dn->lsu; /* -> current Unit */ 6634 for (d=0; d<dn->digits-1; d++) { /* [don't strip the final digit] */ 6635 /* slice by powers */ 6636 #if DECDPUN<=4 6637 uInt quot=QUOT10(*up, cut); 6638 if ((*up-quot*powers[cut])!=0) break; /* found non-0 digit */ 6639 #else 6640 if (*up%powers[cut]!=0) break; /* found non-0 digit */ 6641 #endif 6642 /* have a trailing 0 */ 6643 if (!all) { /* trimming */ 6644 /* [if exp>0 then all trailing 0s are significant for trim] */ 6645 if (exp<=0) { /* if digit might be significant */ 6646 if (exp==0) break; /* then quit */ 6647 exp++; /* next digit might be significant */ 6648 } 6649 } 6650 cut++; /* next power */ 6651 if (cut>DECDPUN) { /* need new Unit */ 6652 up++; 6653 cut=1; 6654 } 6655 } /* d */ 6656 if (d==0) return dn; /* none to drop */ 6657 6658 /* may need to limit drop if clamping */ 6659 if (set->clamp && !noclamp) { 6660 Int maxd=set->emax-set->digits+1-dn->exponent; 6661 if (maxd<=0) return dn; /* nothing possible */ 6662 if (d>maxd) d=maxd; 6663 } 6664 6665 /* effect the drop */ 6666 decShiftToLeast(dn->lsu, D2U(dn->digits), d); 6667 dn->exponent+=d; /* maintain numerical value */ 6668 dn->digits-=d; /* new length */ 6669 *dropped=d; /* report the count */ 6670 return dn; 6671 } /* decTrim */ 6672 6673/* ------------------------------------------------------------------ */ 6674/* decReverse -- reverse a Unit array in place */ 6675/* */ 6676/* ulo is the start of the array */ 6677/* uhi is the end of the array (highest Unit to include) */ 6678/* */ 6679/* The units ulo through uhi are reversed in place (if the number */ 6680/* of units is odd, the middle one is untouched). Note that the */ 6681/* digit(s) in each unit are unaffected. */ 6682/* ------------------------------------------------------------------ */ 6683static void decReverse(Unit *ulo, Unit *uhi) { 6684 Unit temp; 6685 for (; ulo<uhi; ulo++, uhi--) { 6686 temp=*ulo; 6687 *ulo=*uhi; 6688 *uhi=temp; 6689 } 6690 return; 6691 } /* decReverse */ 6692 6693/* ------------------------------------------------------------------ */ 6694/* decShiftToMost -- shift digits in array towards most significant */ 6695/* */ 6696/* uar is the array */ 6697/* digits is the count of digits in use in the array */ 6698/* shift is the number of zeros to pad with (least significant); */ 6699/* it must be zero or positive */ 6700/* */ 6701/* returns the new length of the integer in the array, in digits */ 6702/* */ 6703/* No overflow is permitted (that is, the uar array must be known to */ 6704/* be large enough to hold the result, after shifting). */ 6705/* ------------------------------------------------------------------ */ 6706static Int decShiftToMost(Unit *uar, Int digits, Int shift) { 6707 Unit *target, *source, *first; /* work */ 6708 Int cut; /* odd 0's to add */ 6709 uInt next; /* work */ 6710 6711 if (shift==0) return digits; /* [fastpath] nothing to do */ 6712 if ((digits+shift)<=DECDPUN) { /* [fastpath] single-unit case */ 6713 *uar=(Unit)(*uar*powers[shift]); 6714 return digits+shift; 6715 } 6716 6717 next=0; /* all paths */ 6718 source=uar+D2U(digits)-1; /* where msu comes from */ 6719 target=source+D2U(shift); /* where upper part of first cut goes */ 6720 cut=DECDPUN-MSUDIGITS(shift); /* where to slice */ 6721 if (cut==0) { /* unit-boundary case */ 6722 for (; source>=uar; source--, target--) *target=*source; 6723 } 6724 else { 6725 first=uar+D2U(digits+shift)-1; /* where msu of source will end up */ 6726 for (; source>=uar; source--, target--) { 6727 /* split the source Unit and accumulate remainder for next */ 6728 #if DECDPUN<=4 6729 uInt quot=QUOT10(*source, cut); 6730 uInt rem=*source-quot*powers[cut]; 6731 next+=quot; 6732 #else 6733 uInt rem=*source%powers[cut]; 6734 next+=*source/powers[cut]; 6735 #endif 6736 if (target<=first) *target=(Unit)next; /* write to target iff valid */ 6737 next=rem*powers[DECDPUN-cut]; /* save remainder for next Unit */ 6738 } 6739 } /* shift-move */ 6740 6741 /* propagate any partial unit to one below and clear the rest */ 6742 for (; target>=uar; target--) { 6743 *target=(Unit)next; 6744 next=0; 6745 } 6746 return digits+shift; 6747 } /* decShiftToMost */ 6748 6749/* ------------------------------------------------------------------ */ 6750/* decShiftToLeast -- shift digits in array towards least significant */ 6751/* */ 6752/* uar is the array */ 6753/* units is length of the array, in units */ 6754/* shift is the number of digits to remove from the lsu end; it */ 6755/* must be zero or positive and <= than units*DECDPUN. */ 6756/* */ 6757/* returns the new length of the integer in the array, in units */ 6758/* */ 6759/* Removed digits are discarded (lost). Units not required to hold */ 6760/* the final result are unchanged. */ 6761/* ------------------------------------------------------------------ */ 6762static Int decShiftToLeast(Unit *uar, Int units, Int shift) { 6763 Unit *target, *up; /* work */ 6764 Int cut, count; /* work */ 6765 Int quot, rem; /* for division */ 6766 6767 if (shift==0) return units; /* [fastpath] nothing to do */ 6768 if (shift==units*DECDPUN) { /* [fastpath] little to do */ 6769 *uar=0; /* all digits cleared gives zero */ 6770 return 1; /* leaves just the one */ 6771 } 6772 6773 target=uar; /* both paths */ 6774 cut=MSUDIGITS(shift); 6775 if (cut==DECDPUN) { /* unit-boundary case; easy */ 6776 up=uar+D2U(shift); 6777 for (; up<uar+units; target++, up++) *target=*up; 6778 return target-uar; 6779 } 6780 6781 /* messier */ 6782 up=uar+D2U(shift-cut); /* source; correct to whole Units */ 6783 count=units*DECDPUN-shift; /* the maximum new length */ 6784 #if DECDPUN<=4 6785 quot=QUOT10(*up, cut); 6786 #else 6787 quot=*up/powers[cut]; 6788 #endif 6789 for (; ; target++) { 6790 *target=(Unit)quot; 6791 count-=(DECDPUN-cut); 6792 if (count<=0) break; 6793 up++; 6794 quot=*up; 6795 #if DECDPUN<=4 6796 quot=QUOT10(quot, cut); 6797 rem=*up-quot*powers[cut]; 6798 #else 6799 rem=quot%powers[cut]; 6800 quot=quot/powers[cut]; 6801 #endif 6802 *target=(Unit)(*target+rem*powers[DECDPUN-cut]); 6803 count-=cut; 6804 if (count<=0) break; 6805 } 6806 return target-uar+1; 6807 } /* decShiftToLeast */ 6808 6809#if DECSUBSET 6810/* ------------------------------------------------------------------ */ 6811/* decRoundOperand -- round an operand [used for subset only] */ 6812/* */ 6813/* dn is the number to round (dn->digits is > set->digits) */ 6814/* set is the relevant context */ 6815/* status is the status accumulator */ 6816/* */ 6817/* returns an allocated decNumber with the rounded result. */ 6818/* */ 6819/* lostDigits and other status may be set by this. */ 6820/* */ 6821/* Since the input is an operand, it must not be modified. */ 6822/* Instead, return an allocated decNumber, rounded as required. */ 6823/* It is the caller's responsibility to free the allocated storage. */ 6824/* */ 6825/* If no storage is available then the result cannot be used, so NULL */ 6826/* is returned. */ 6827/* ------------------------------------------------------------------ */ 6828static decNumber *decRoundOperand(const decNumber *dn, decContext *set, 6829 uInt *status) { 6830 decNumber *res; /* result structure */ 6831 uInt newstatus=0; /* status from round */ 6832 Int residue=0; /* rounding accumulator */ 6833 6834 /* Allocate storage for the returned decNumber, big enough for the */ 6835 /* length specified by the context */ 6836 res=(decNumber *)malloc(sizeof(decNumber) 6837 +(D2U(set->digits)-1)*sizeof(Unit)); 6838 if (res==NULL) { 6839 *status|=DEC_Insufficient_storage; 6840 return NULL; 6841 } 6842 decCopyFit(res, dn, set, &residue, &newstatus); 6843 decApplyRound(res, set, residue, &newstatus); 6844 6845 /* If that set Inexact then "lost digits" is raised... */ 6846 if (newstatus & DEC_Inexact) newstatus|=DEC_Lost_digits; 6847 *status|=newstatus; 6848 return res; 6849 } /* decRoundOperand */ 6850#endif 6851 6852/* ------------------------------------------------------------------ */ 6853/* decCopyFit -- copy a number, truncating the coefficient if needed */ 6854/* */ 6855/* dest is the target decNumber */ 6856/* src is the source decNumber */ 6857/* set is the context [used for length (digits) and rounding mode] */ 6858/* residue is the residue accumulator */ 6859/* status contains the current status to be updated */ 6860/* */ 6861/* (dest==src is allowed and will be a no-op if fits) */ 6862/* All fields are updated as required. */ 6863/* ------------------------------------------------------------------ */ 6864static void decCopyFit(decNumber *dest, const decNumber *src, 6865 decContext *set, Int *residue, uInt *status) { 6866 dest->bits=src->bits; 6867 dest->exponent=src->exponent; 6868 decSetCoeff(dest, set, src->lsu, src->digits, residue, status); 6869 } /* decCopyFit */ 6870 6871/* ------------------------------------------------------------------ */ 6872/* decSetCoeff -- set the coefficient of a number */ 6873/* */ 6874/* dn is the number whose coefficient array is to be set. */ 6875/* It must have space for set->digits digits */ 6876/* set is the context [for size] */ 6877/* lsu -> lsu of the source coefficient [may be dn->lsu] */ 6878/* len is digits in the source coefficient [may be dn->digits] */ 6879/* residue is the residue accumulator. This has values as in */ 6880/* decApplyRound, and will be unchanged unless the */ 6881/* target size is less than len. In this case, the */ 6882/* coefficient is truncated and the residue is updated to */ 6883/* reflect the previous residue and the dropped digits. */ 6884/* status is the status accumulator, as usual */ 6885/* */ 6886/* The coefficient may already be in the number, or it can be an */ 6887/* external intermediate array. If it is in the number, lsu must == */ 6888/* dn->lsu and len must == dn->digits. */ 6889/* */ 6890/* Note that the coefficient length (len) may be < set->digits, and */ 6891/* in this case this merely copies the coefficient (or is a no-op */ 6892/* if dn->lsu==lsu). */ 6893/* */ 6894/* Note also that (only internally, from decQuantizeOp and */ 6895/* decSetSubnormal) the value of set->digits may be less than one, */ 6896/* indicating a round to left. This routine handles that case */ 6897/* correctly; caller ensures space. */ 6898/* */ 6899/* dn->digits, dn->lsu (and as required), and dn->exponent are */ 6900/* updated as necessary. dn->bits (sign) is unchanged. */ 6901/* */ 6902/* DEC_Rounded status is set if any digits are discarded. */ 6903/* DEC_Inexact status is set if any non-zero digits are discarded, or */ 6904/* incoming residue was non-0 (implies rounded) */ 6905/* ------------------------------------------------------------------ */ 6906/* mapping array: maps 0-9 to canonical residues, so that a residue */ 6907/* can be adjusted in the range [-1, +1] and achieve correct rounding */ 6908/* 0 1 2 3 4 5 6 7 8 9 */ 6909static const uByte resmap[10]={0, 3, 3, 3, 3, 5, 7, 7, 7, 7}; 6910static void decSetCoeff(decNumber *dn, decContext *set, const Unit *lsu, 6911 Int len, Int *residue, uInt *status) { 6912 Int discard; /* number of digits to discard */ 6913 uInt cut; /* cut point in Unit */ 6914 const Unit *up; /* work */ 6915 Unit *target; /* .. */ 6916 Int count; /* .. */ 6917 #if DECDPUN<=4 6918 uInt temp; /* .. */ 6919 #endif 6920 6921 discard=len-set->digits; /* digits to discard */ 6922 if (discard<=0) { /* no digits are being discarded */ 6923 if (dn->lsu!=lsu) { /* copy needed */ 6924 /* copy the coefficient array to the result number; no shift needed */ 6925 count=len; /* avoids D2U */ 6926 up=lsu; 6927 for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN) 6928 *target=*up; 6929 dn->digits=len; /* set the new length */ 6930 } 6931 /* dn->exponent and residue are unchanged, record any inexactitude */ 6932 if (*residue!=0) *status|=(DEC_Inexact | DEC_Rounded); 6933 return; 6934 } 6935 6936 /* some digits must be discarded ... */ 6937 dn->exponent+=discard; /* maintain numerical value */ 6938 *status|=DEC_Rounded; /* accumulate Rounded status */ 6939 if (*residue>1) *residue=1; /* previous residue now to right, so reduce */ 6940 6941 if (discard>len) { /* everything, +1, is being discarded */ 6942 /* guard digit is 0 */ 6943 /* residue is all the number [NB could be all 0s] */ 6944 if (*residue<=0) { /* not already positive */ 6945 count=len; /* avoids D2U */ 6946 for (up=lsu; count>0; up++, count-=DECDPUN) if (*up!=0) { /* found non-0 */ 6947 *residue=1; 6948 break; /* no need to check any others */ 6949 } 6950 } 6951 if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */ 6952 *dn->lsu=0; /* coefficient will now be 0 */ 6953 dn->digits=1; /* .. */ 6954 return; 6955 } /* total discard */ 6956 6957 /* partial discard [most common case] */ 6958 /* here, at least the first (most significant) discarded digit exists */ 6959 6960 /* spin up the number, noting residue during the spin, until get to */ 6961 /* the Unit with the first discarded digit. When reach it, extract */ 6962 /* it and remember its position */ 6963 count=0; 6964 for (up=lsu;; up++) { 6965 count+=DECDPUN; 6966 if (count>=discard) break; /* full ones all checked */ 6967 if (*up!=0) *residue=1; 6968 } /* up */ 6969 6970 /* here up -> Unit with first discarded digit */ 6971 cut=discard-(count-DECDPUN)-1; 6972 if (cut==DECDPUN-1) { /* unit-boundary case (fast) */ 6973 Unit half=(Unit)powers[DECDPUN]>>1; 6974 /* set residue directly */ 6975 if (*up>=half) { 6976 if (*up>half) *residue=7; 6977 else *residue+=5; /* add sticky bit */ 6978 } 6979 else { /* <half */ 6980 if (*up!=0) *residue=3; /* [else is 0, leave as sticky bit] */ 6981 } 6982 if (set->digits<=0) { /* special for Quantize/Subnormal :-( */ 6983 *dn->lsu=0; /* .. result is 0 */ 6984 dn->digits=1; /* .. */ 6985 } 6986 else { /* shift to least */ 6987 count=set->digits; /* now digits to end up with */ 6988 dn->digits=count; /* set the new length */ 6989 up++; /* move to next */ 6990 /* on unit boundary, so shift-down copy loop is simple */ 6991 for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN) 6992 *target=*up; 6993 } 6994 } /* unit-boundary case */ 6995 6996 else { /* discard digit is in low digit(s), and not top digit */ 6997 uInt discard1; /* first discarded digit */ 6998 uInt quot, rem; /* for divisions */ 6999 if (cut==0) quot=*up; /* is at bottom of unit */ 7000 else /* cut>0 */ { /* it's not at bottom of unit */ 7001 #if DECDPUN<=4 7002 quot=QUOT10(*up, cut); 7003 rem=*up-quot*powers[cut]; 7004 #else 7005 rem=*up%powers[cut]; 7006 quot=*up/powers[cut]; 7007 #endif 7008 if (rem!=0) *residue=1; 7009 } 7010 /* discard digit is now at bottom of quot */ 7011 #if DECDPUN<=4 7012 temp=(quot*6554)>>16; /* fast /10 */ 7013 /* Vowels algorithm here not a win (9 instructions) */ 7014 discard1=quot-X10(temp); 7015 quot=temp; 7016 #else 7017 discard1=quot%10; 7018 quot=quot/10; 7019 #endif 7020 /* here, discard1 is the guard digit, and residue is everything */ 7021 /* else [use mapping array to accumulate residue safely] */ 7022 *residue+=resmap[discard1]; 7023 cut++; /* update cut */ 7024 /* here: up -> Unit of the array with bottom digit */ 7025 /* cut is the division point for each Unit */ 7026 /* quot holds the uncut high-order digits for the current unit */ 7027 if (set->digits<=0) { /* special for Quantize/Subnormal :-( */ 7028 *dn->lsu=0; /* .. result is 0 */ 7029 dn->digits=1; /* .. */ 7030 } 7031 else { /* shift to least needed */ 7032 count=set->digits; /* now digits to end up with */ 7033 dn->digits=count; /* set the new length */ 7034 /* shift-copy the coefficient array to the result number */ 7035 for (target=dn->lsu; ; target++) { 7036 *target=(Unit)quot; 7037 count-=(DECDPUN-cut); 7038 if (count<=0) break; 7039 up++; 7040 quot=*up; 7041 #if DECDPUN<=4 7042 quot=QUOT10(quot, cut); 7043 rem=*up-quot*powers[cut]; 7044 #else 7045 rem=quot%powers[cut]; 7046 quot=quot/powers[cut]; 7047 #endif 7048 *target=(Unit)(*target+rem*powers[DECDPUN-cut]); 7049 count-=cut; 7050 if (count<=0) break; 7051 } /* shift-copy loop */ 7052 } /* shift to least */ 7053 } /* not unit boundary */ 7054 7055 if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */ 7056 return; 7057 } /* decSetCoeff */ 7058 7059/* ------------------------------------------------------------------ */ 7060/* decApplyRound -- apply pending rounding to a number */ 7061/* */ 7062/* dn is the number, with space for set->digits digits */ 7063/* set is the context [for size and rounding mode] */ 7064/* residue indicates pending rounding, being any accumulated */ 7065/* guard and sticky information. It may be: */ 7066/* 6-9: rounding digit is >5 */ 7067/* 5: rounding digit is exactly half-way */ 7068/* 1-4: rounding digit is <5 and >0 */ 7069/* 0: the coefficient is exact */ 7070/* -1: as 1, but the hidden digits are subtractive, that */ 7071/* is, of the opposite sign to dn. In this case the */ 7072/* coefficient must be non-0. This case occurs when */ 7073/* subtracting a small number (which can be reduced to */ 7074/* a sticky bit); see decAddOp. */ 7075/* status is the status accumulator, as usual */ 7076/* */ 7077/* This routine applies rounding while keeping the length of the */ 7078/* coefficient constant. The exponent and status are unchanged */ 7079/* except if: */ 7080/* */ 7081/* -- the coefficient was increased and is all nines (in which */ 7082/* case Overflow could occur, and is handled directly here so */ 7083/* the caller does not need to re-test for overflow) */ 7084/* */ 7085/* -- the coefficient was decreased and becomes all nines (in which */ 7086/* case Underflow could occur, and is also handled directly). */ 7087/* */ 7088/* All fields in dn are updated as required. */ 7089/* */ 7090/* ------------------------------------------------------------------ */ 7091static void decApplyRound(decNumber *dn, decContext *set, Int residue, 7092 uInt *status) { 7093 Int bump; /* 1 if coefficient needs to be incremented */ 7094 /* -1 if coefficient needs to be decremented */ 7095 7096 if (residue==0) return; /* nothing to apply */ 7097 7098 bump=0; /* assume a smooth ride */ 7099 7100 /* now decide whether, and how, to round, depending on mode */ 7101 switch (set->round) { 7102 case DEC_ROUND_05UP: { /* round zero or five up (for reround) */ 7103 /* This is the same as DEC_ROUND_DOWN unless there is a */ 7104 /* positive residue and the lsd of dn is 0 or 5, in which case */ 7105 /* it is bumped; when residue is <0, the number is therefore */ 7106 /* bumped down unless the final digit was 1 or 6 (in which */ 7107 /* case it is bumped down and then up -- a no-op) */ 7108 Int lsd5=*dn->lsu%5; /* get lsd and quintate */ 7109 if (residue<0 && lsd5!=1) bump=-1; 7110 else if (residue>0 && lsd5==0) bump=1; 7111 /* [bump==1 could be applied directly; use common path for clarity] */ 7112 break;} /* r-05 */ 7113 7114 case DEC_ROUND_DOWN: { 7115 /* no change, except if negative residue */ 7116 if (residue<0) bump=-1; 7117 break;} /* r-d */ 7118 7119 case DEC_ROUND_HALF_DOWN: { 7120 if (residue>5) bump=1; 7121 break;} /* r-h-d */ 7122 7123 case DEC_ROUND_HALF_EVEN: { 7124 if (residue>5) bump=1; /* >0.5 goes up */ 7125 else if (residue==5) { /* exactly 0.5000... */ 7126 /* 0.5 goes up iff [new] lsd is odd */ 7127 if (*dn->lsu & 0x01) bump=1; 7128 } 7129 break;} /* r-h-e */ 7130 7131 case DEC_ROUND_HALF_UP: { 7132 if (residue>=5) bump=1; 7133 break;} /* r-h-u */ 7134 7135 case DEC_ROUND_UP: { 7136 if (residue>0) bump=1; 7137 break;} /* r-u */ 7138 7139 case DEC_ROUND_CEILING: { 7140 /* same as _UP for positive numbers, and as _DOWN for negatives */ 7141 /* [negative residue cannot occur on 0] */ 7142 if (decNumberIsNegative(dn)) { 7143 if (residue<0) bump=-1; 7144 } 7145 else { 7146 if (residue>0) bump=1; 7147 } 7148 break;} /* r-c */ 7149 7150 case DEC_ROUND_FLOOR: { 7151 /* same as _UP for negative numbers, and as _DOWN for positive */ 7152 /* [negative residue cannot occur on 0] */ 7153 if (!decNumberIsNegative(dn)) { 7154 if (residue<0) bump=-1; 7155 } 7156 else { 7157 if (residue>0) bump=1; 7158 } 7159 break;} /* r-f */ 7160 7161 default: { /* e.g., DEC_ROUND_MAX */ 7162 *status|=DEC_Invalid_context; 7163 #if DECTRACE || (DECCHECK && DECVERB) 7164 printf("Unknown rounding mode: %d\n", set->round); 7165 #endif 7166 break;} 7167 } /* switch */ 7168 7169 /* now bump the number, up or down, if need be */ 7170 if (bump==0) return; /* no action required */ 7171 7172 /* Simply use decUnitAddSub unless bumping up and the number is */ 7173 /* all nines. In this special case set to 100... explicitly */ 7174 /* and adjust the exponent by one (as otherwise could overflow */ 7175 /* the array) */ 7176 /* Similarly handle all-nines result if bumping down. */ 7177 if (bump>0) { 7178 Unit *up; /* work */ 7179 uInt count=dn->digits; /* digits to be checked */ 7180 for (up=dn->lsu; ; up++) { 7181 if (count<=DECDPUN) { 7182 /* this is the last Unit (the msu) */ 7183 if (*up!=powers[count]-1) break; /* not still 9s */ 7184 /* here if it, too, is all nines */ 7185 *up=(Unit)powers[count-1]; /* here 999 -> 100 etc. */ 7186 for (up=up-1; up>=dn->lsu; up--) *up=0; /* others all to 0 */ 7187 dn->exponent++; /* and bump exponent */ 7188 /* [which, very rarely, could cause Overflow...] */ 7189 if ((dn->exponent+dn->digits)>set->emax+1) { 7190 decSetOverflow(dn, set, status); 7191 } 7192 return; /* done */ 7193 } 7194 /* a full unit to check, with more to come */ 7195 if (*up!=DECDPUNMAX) break; /* not still 9s */ 7196 count-=DECDPUN; 7197 } /* up */ 7198 } /* bump>0 */ 7199 else { /* -1 */ 7200 /* here checking for a pre-bump of 1000... (leading 1, all */ 7201 /* other digits zero) */ 7202 Unit *up, *sup; /* work */ 7203 uInt count=dn->digits; /* digits to be checked */ 7204 for (up=dn->lsu; ; up++) { 7205 if (count<=DECDPUN) { 7206 /* this is the last Unit (the msu) */ 7207 if (*up!=powers[count-1]) break; /* not 100.. */ 7208 /* here if have the 1000... case */ 7209 sup=up; /* save msu pointer */ 7210 *up=(Unit)powers[count]-1; /* here 100 in msu -> 999 */ 7211 /* others all to all-nines, too */ 7212 for (up=up-1; up>=dn->lsu; up--) *up=(Unit)powers[DECDPUN]-1; 7213 dn->exponent--; /* and bump exponent */ 7214 7215 /* iff the number was at the subnormal boundary (exponent=etiny) */ 7216 /* then the exponent is now out of range, so it will in fact get */ 7217 /* clamped to etiny and the final 9 dropped. */ 7218 /* printf(">> emin=%d exp=%d sdig=%d\n", set->emin, */ 7219 /* dn->exponent, set->digits); */ 7220 if (dn->exponent+1==set->emin-set->digits+1) { 7221 if (count==1 && dn->digits==1) *sup=0; /* here 9 -> 0[.9] */ 7222 else { 7223 *sup=(Unit)powers[count-1]-1; /* here 999.. in msu -> 99.. */ 7224 dn->digits--; 7225 } 7226 dn->exponent++; 7227 *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded; 7228 } 7229 return; /* done */ 7230 } 7231 7232 /* a full unit to check, with more to come */ 7233 if (*up!=0) break; /* not still 0s */ 7234 count-=DECDPUN; 7235 } /* up */ 7236 7237 } /* bump<0 */ 7238 7239 /* Actual bump needed. Do it. */ 7240 decUnitAddSub(dn->lsu, D2U(dn->digits), uarrone, 1, 0, dn->lsu, bump); 7241 } /* decApplyRound */ 7242 7243#if DECSUBSET 7244/* ------------------------------------------------------------------ */ 7245/* decFinish -- finish processing a number */ 7246/* */ 7247/* dn is the number */ 7248/* set is the context */ 7249/* residue is the rounding accumulator (as in decApplyRound) */ 7250/* status is the accumulator */ 7251/* */ 7252/* This finishes off the current number by: */ 7253/* 1. If not extended: */ 7254/* a. Converting a zero result to clean '0' */ 7255/* b. Reducing positive exponents to 0, if would fit in digits */ 7256/* 2. Checking for overflow and subnormals (always) */ 7257/* Note this is just Finalize when no subset arithmetic. */ 7258/* All fields are updated as required. */ 7259/* ------------------------------------------------------------------ */ 7260static void decFinish(decNumber *dn, decContext *set, Int *residue, 7261 uInt *status) { 7262 if (!set->extended) { 7263 if ISZERO(dn) { /* value is zero */ 7264 dn->exponent=0; /* clean exponent .. */ 7265 dn->bits=0; /* .. and sign */ 7266 return; /* no error possible */ 7267 } 7268 if (dn->exponent>=0) { /* non-negative exponent */ 7269 /* >0; reduce to integer if possible */ 7270 if (set->digits >= (dn->exponent+dn->digits)) { 7271 dn->digits=decShiftToMost(dn->lsu, dn->digits, dn->exponent); 7272 dn->exponent=0; 7273 } 7274 } 7275 } /* !extended */ 7276 7277 decFinalize(dn, set, residue, status); 7278 } /* decFinish */ 7279#endif 7280 7281/* ------------------------------------------------------------------ */ 7282/* decFinalize -- final check, clamp, and round of a number */ 7283/* */ 7284/* dn is the number */ 7285/* set is the context */ 7286/* residue is the rounding accumulator (as in decApplyRound) */ 7287/* status is the status accumulator */ 7288/* */ 7289/* This finishes off the current number by checking for subnormal */ 7290/* results, applying any pending rounding, checking for overflow, */ 7291/* and applying any clamping. */ 7292/* Underflow and overflow conditions are raised as appropriate. */ 7293/* All fields are updated as required. */ 7294/* ------------------------------------------------------------------ */ 7295static void decFinalize(decNumber *dn, decContext *set, Int *residue, 7296 uInt *status) { 7297 Int shift; /* shift needed if clamping */ 7298 Int tinyexp=set->emin-dn->digits+1; /* precalculate subnormal boundary */ 7299 7300 /* Must be careful, here, when checking the exponent as the */ 7301 /* adjusted exponent could overflow 31 bits [because it may already */ 7302 /* be up to twice the expected]. */ 7303 7304 /* First test for subnormal. This must be done before any final */ 7305 /* round as the result could be rounded to Nmin or 0. */ 7306 if (dn->exponent<=tinyexp) { /* prefilter */ 7307 Int comp; 7308 decNumber nmin; 7309 /* A very nasty case here is dn == Nmin and residue<0 */ 7310 if (dn->exponent<tinyexp) { 7311 /* Go handle subnormals; this will apply round if needed. */ 7312 decSetSubnormal(dn, set, residue, status); 7313 return; 7314 } 7315 /* Equals case: only subnormal if dn=Nmin and negative residue */ 7316 uprv_decNumberZero(&nmin); 7317 nmin.lsu[0]=1; 7318 nmin.exponent=set->emin; 7319 comp=decCompare(dn, &nmin, 1); /* (signless compare) */ 7320 if (comp==BADINT) { /* oops */ 7321 *status|=DEC_Insufficient_storage; /* abandon... */ 7322 return; 7323 } 7324 if (*residue<0 && comp==0) { /* neg residue and dn==Nmin */ 7325 decApplyRound(dn, set, *residue, status); /* might force down */ 7326 decSetSubnormal(dn, set, residue, status); 7327 return; 7328 } 7329 } 7330 7331 /* now apply any pending round (this could raise overflow). */ 7332 if (*residue!=0) decApplyRound(dn, set, *residue, status); 7333 7334 /* Check for overflow [redundant in the 'rare' case] or clamp */ 7335 if (dn->exponent<=set->emax-set->digits+1) return; /* neither needed */ 7336 7337 7338 /* here when might have an overflow or clamp to do */ 7339 if (dn->exponent>set->emax-dn->digits+1) { /* too big */ 7340 decSetOverflow(dn, set, status); 7341 return; 7342 } 7343 /* here when the result is normal but in clamp range */ 7344 if (!set->clamp) return; 7345 7346 /* here when need to apply the IEEE exponent clamp (fold-down) */ 7347 shift=dn->exponent-(set->emax-set->digits+1); 7348 7349 /* shift coefficient (if non-zero) */ 7350 if (!ISZERO(dn)) { 7351 dn->digits=decShiftToMost(dn->lsu, dn->digits, shift); 7352 } 7353 dn->exponent-=shift; /* adjust the exponent to match */ 7354 *status|=DEC_Clamped; /* and record the dirty deed */ 7355 return; 7356 } /* decFinalize */ 7357 7358/* ------------------------------------------------------------------ */ 7359/* decSetOverflow -- set number to proper overflow value */ 7360/* */ 7361/* dn is the number (used for sign [only] and result) */ 7362/* set is the context [used for the rounding mode, etc.] */ 7363/* status contains the current status to be updated */ 7364/* */ 7365/* This sets the sign of a number and sets its value to either */ 7366/* Infinity or the maximum finite value, depending on the sign of */ 7367/* dn and the rounding mode, following IEEE 754 rules. */ 7368/* ------------------------------------------------------------------ */ 7369static void decSetOverflow(decNumber *dn, decContext *set, uInt *status) { 7370 Flag needmax=0; /* result is maximum finite value */ 7371 uByte sign=dn->bits&DECNEG; /* clean and save sign bit */ 7372 7373 if (ISZERO(dn)) { /* zero does not overflow magnitude */ 7374 Int emax=set->emax; /* limit value */ 7375 if (set->clamp) emax-=set->digits-1; /* lower if clamping */ 7376 if (dn->exponent>emax) { /* clamp required */ 7377 dn->exponent=emax; 7378 *status|=DEC_Clamped; 7379 } 7380 return; 7381 } 7382 7383 uprv_decNumberZero(dn); 7384 switch (set->round) { 7385 case DEC_ROUND_DOWN: { 7386 needmax=1; /* never Infinity */ 7387 break;} /* r-d */ 7388 case DEC_ROUND_05UP: { 7389 needmax=1; /* never Infinity */ 7390 break;} /* r-05 */ 7391 case DEC_ROUND_CEILING: { 7392 if (sign) needmax=1; /* Infinity if non-negative */ 7393 break;} /* r-c */ 7394 case DEC_ROUND_FLOOR: { 7395 if (!sign) needmax=1; /* Infinity if negative */ 7396 break;} /* r-f */ 7397 default: break; /* Infinity in all other cases */ 7398 } 7399 if (needmax) { 7400 decSetMaxValue(dn, set); 7401 dn->bits=sign; /* set sign */ 7402 } 7403 else dn->bits=sign|DECINF; /* Value is +/-Infinity */ 7404 *status|=DEC_Overflow | DEC_Inexact | DEC_Rounded; 7405 } /* decSetOverflow */ 7406 7407/* ------------------------------------------------------------------ */ 7408/* decSetMaxValue -- set number to +Nmax (maximum normal value) */ 7409/* */ 7410/* dn is the number to set */ 7411/* set is the context [used for digits and emax] */ 7412/* */ 7413/* This sets the number to the maximum positive value. */ 7414/* ------------------------------------------------------------------ */ 7415static void decSetMaxValue(decNumber *dn, decContext *set) { 7416 Unit *up; /* work */ 7417 Int count=set->digits; /* nines to add */ 7418 dn->digits=count; 7419 /* fill in all nines to set maximum value */ 7420 for (up=dn->lsu; ; up++) { 7421 if (count>DECDPUN) *up=DECDPUNMAX; /* unit full o'nines */ 7422 else { /* this is the msu */ 7423 *up=(Unit)(powers[count]-1); 7424 break; 7425 } 7426 count-=DECDPUN; /* filled those digits */ 7427 } /* up */ 7428 dn->bits=0; /* + sign */ 7429 dn->exponent=set->emax-set->digits+1; 7430 } /* decSetMaxValue */ 7431 7432/* ------------------------------------------------------------------ */ 7433/* decSetSubnormal -- process value whose exponent is <Emin */ 7434/* */ 7435/* dn is the number (used as input as well as output; it may have */ 7436/* an allowed subnormal value, which may need to be rounded) */ 7437/* set is the context [used for the rounding mode] */ 7438/* residue is any pending residue */ 7439/* status contains the current status to be updated */ 7440/* */ 7441/* If subset mode, set result to zero and set Underflow flags. */ 7442/* */ 7443/* Value may be zero with a low exponent; this does not set Subnormal */ 7444/* but the exponent will be clamped to Etiny. */ 7445/* */ 7446/* Otherwise ensure exponent is not out of range, and round as */ 7447/* necessary. Underflow is set if the result is Inexact. */ 7448/* ------------------------------------------------------------------ */ 7449static void decSetSubnormal(decNumber *dn, decContext *set, Int *residue, 7450 uInt *status) { 7451 decContext workset; /* work */ 7452 Int etiny, adjust; /* .. */ 7453 7454 #if DECSUBSET 7455 /* simple set to zero and 'hard underflow' for subset */ 7456 if (!set->extended) { 7457 uprv_decNumberZero(dn); 7458 /* always full overflow */ 7459 *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded; 7460 return; 7461 } 7462 #endif 7463 7464 /* Full arithmetic -- allow subnormals, rounded to minimum exponent */ 7465 /* (Etiny) if needed */ 7466 etiny=set->emin-(set->digits-1); /* smallest allowed exponent */ 7467 7468 if ISZERO(dn) { /* value is zero */ 7469 /* residue can never be non-zero here */ 7470 #if DECCHECK 7471 if (*residue!=0) { 7472 printf("++ Subnormal 0 residue %ld\n", (LI)*residue); 7473 *status|=DEC_Invalid_operation; 7474 } 7475 #endif 7476 if (dn->exponent<etiny) { /* clamp required */ 7477 dn->exponent=etiny; 7478 *status|=DEC_Clamped; 7479 } 7480 return; 7481 } 7482 7483 *status|=DEC_Subnormal; /* have a non-zero subnormal */ 7484 adjust=etiny-dn->exponent; /* calculate digits to remove */ 7485 if (adjust<=0) { /* not out of range; unrounded */ 7486 /* residue can never be non-zero here, except in the Nmin-residue */ 7487 /* case (which is a subnormal result), so can take fast-path here */ 7488 /* it may already be inexact (from setting the coefficient) */ 7489 if (*status&DEC_Inexact) *status|=DEC_Underflow; 7490 return; 7491 } 7492 7493 /* adjust>0, so need to rescale the result so exponent becomes Etiny */ 7494 /* [this code is similar to that in rescale] */ 7495 workset=*set; /* clone rounding, etc. */ 7496 workset.digits=dn->digits-adjust; /* set requested length */ 7497 workset.emin-=adjust; /* and adjust emin to match */ 7498 /* [note that the latter can be <1, here, similar to Rescale case] */ 7499 decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status); 7500 decApplyRound(dn, &workset, *residue, status); 7501 7502 /* Use 754 default rule: Underflow is set iff Inexact */ 7503 /* [independent of whether trapped] */ 7504 if (*status&DEC_Inexact) *status|=DEC_Underflow; 7505 7506 /* if rounded up a 999s case, exponent will be off by one; adjust */ 7507 /* back if so [it will fit, because it was shortened earlier] */ 7508 if (dn->exponent>etiny) { 7509 dn->digits=decShiftToMost(dn->lsu, dn->digits, 1); 7510 dn->exponent--; /* (re)adjust the exponent. */ 7511 } 7512 7513 /* if rounded to zero, it is by definition clamped... */ 7514 if (ISZERO(dn)) *status|=DEC_Clamped; 7515 } /* decSetSubnormal */ 7516 7517/* ------------------------------------------------------------------ */ 7518/* decCheckMath - check entry conditions for a math function */ 7519/* */ 7520/* This checks the context and the operand */ 7521/* */ 7522/* rhs is the operand to check */ 7523/* set is the context to check */ 7524/* status is unchanged if both are good */ 7525/* */ 7526/* returns non-zero if status is changed, 0 otherwise */ 7527/* */ 7528/* Restrictions enforced: */ 7529/* */ 7530/* digits, emax, and -emin in the context must be less than */ 7531/* DEC_MAX_MATH (999999), and A must be within these bounds if */ 7532/* non-zero. Invalid_operation is set in the status if a */ 7533/* restriction is violated. */ 7534/* ------------------------------------------------------------------ */ 7535static uInt decCheckMath(const decNumber *rhs, decContext *set, 7536 uInt *status) { 7537 uInt save=*status; /* record */ 7538 if (set->digits>DEC_MAX_MATH 7539 || set->emax>DEC_MAX_MATH 7540 || -set->emin>DEC_MAX_MATH) *status|=DEC_Invalid_context; 7541 else if ((rhs->digits>DEC_MAX_MATH 7542 || rhs->exponent+rhs->digits>DEC_MAX_MATH+1 7543 || rhs->exponent+rhs->digits<2*(1-DEC_MAX_MATH)) 7544 && !ISZERO(rhs)) *status|=DEC_Invalid_operation; 7545 return (*status!=save); 7546 } /* decCheckMath */ 7547 7548/* ------------------------------------------------------------------ */ 7549/* decGetInt -- get integer from a number */ 7550/* */ 7551/* dn is the number [which will not be altered] */ 7552/* */ 7553/* returns one of: */ 7554/* BADINT if there is a non-zero fraction */ 7555/* the converted integer */ 7556/* BIGEVEN if the integer is even and magnitude > 2*10**9 */ 7557/* BIGODD if the integer is odd and magnitude > 2*10**9 */ 7558/* */ 7559/* This checks and gets a whole number from the input decNumber. */ 7560/* The sign can be determined from dn by the caller when BIGEVEN or */ 7561/* BIGODD is returned. */ 7562/* ------------------------------------------------------------------ */ 7563static Int decGetInt(const decNumber *dn) { 7564 Int theInt; /* result accumulator */ 7565 const Unit *up; /* work */ 7566 Int got; /* digits (real or not) processed */ 7567 Int ilength=dn->digits+dn->exponent; /* integral length */ 7568 Flag neg=decNumberIsNegative(dn); /* 1 if -ve */ 7569 7570 /* The number must be an integer that fits in 10 digits */ 7571 /* Assert, here, that 10 is enough for any rescale Etiny */ 7572 #if DEC_MAX_EMAX > 999999999 7573 #error GetInt may need updating [for Emax] 7574 #endif 7575 #if DEC_MIN_EMIN < -999999999 7576 #error GetInt may need updating [for Emin] 7577 #endif 7578 if (ISZERO(dn)) return 0; /* zeros are OK, with any exponent */ 7579 7580 up=dn->lsu; /* ready for lsu */ 7581 theInt=0; /* ready to accumulate */ 7582 if (dn->exponent>=0) { /* relatively easy */ 7583 /* no fractional part [usual]; allow for positive exponent */ 7584 got=dn->exponent; 7585 } 7586 else { /* -ve exponent; some fractional part to check and discard */ 7587 Int count=-dn->exponent; /* digits to discard */ 7588 /* spin up whole units until reach the Unit with the unit digit */ 7589 for (; count>=DECDPUN; up++) { 7590 if (*up!=0) return BADINT; /* non-zero Unit to discard */ 7591 count-=DECDPUN; 7592 } 7593 if (count==0) got=0; /* [a multiple of DECDPUN] */ 7594 else { /* [not multiple of DECDPUN] */ 7595 Int rem; /* work */ 7596 /* slice off fraction digits and check for non-zero */ 7597 #if DECDPUN<=4 7598 theInt=QUOT10(*up, count); 7599 rem=*up-theInt*powers[count]; 7600 #else 7601 rem=*up%powers[count]; /* slice off discards */ 7602 theInt=*up/powers[count]; 7603 #endif 7604 if (rem!=0) return BADINT; /* non-zero fraction */ 7605 /* it looks good */ 7606 got=DECDPUN-count; /* number of digits so far */ 7607 up++; /* ready for next */ 7608 } 7609 } 7610 /* now it's known there's no fractional part */ 7611 7612 /* tricky code now, to accumulate up to 9.3 digits */ 7613 if (got==0) {theInt=*up; got+=DECDPUN; up++;} /* ensure lsu is there */ 7614 7615 if (ilength<11) { 7616 Int save=theInt; 7617 /* collect any remaining unit(s) */ 7618 for (; got<ilength; up++) { 7619 theInt+=*up*powers[got]; 7620 got+=DECDPUN; 7621 } 7622 if (ilength==10) { /* need to check for wrap */ 7623 if (theInt/(Int)powers[got-DECDPUN]!=(Int)*(up-1)) ilength=11; 7624 /* [that test also disallows the BADINT result case] */ 7625 else if (neg && theInt>1999999997) ilength=11; 7626 else if (!neg && theInt>999999999) ilength=11; 7627 if (ilength==11) theInt=save; /* restore correct low bit */ 7628 } 7629 } 7630 7631 if (ilength>10) { /* too big */ 7632 if (theInt&1) return BIGODD; /* bottom bit 1 */ 7633 return BIGEVEN; /* bottom bit 0 */ 7634 } 7635 7636 if (neg) theInt=-theInt; /* apply sign */ 7637 return theInt; 7638 } /* decGetInt */ 7639 7640/* ------------------------------------------------------------------ */ 7641/* decDecap -- decapitate the coefficient of a number */ 7642/* */ 7643/* dn is the number to be decapitated */ 7644/* drop is the number of digits to be removed from the left of dn; */ 7645/* this must be <= dn->digits (if equal, the coefficient is */ 7646/* set to 0) */ 7647/* */ 7648/* Returns dn; dn->digits will be <= the initial digits less drop */ 7649/* (after removing drop digits there may be leading zero digits */ 7650/* which will also be removed). Only dn->lsu and dn->digits change. */ 7651/* ------------------------------------------------------------------ */ 7652static decNumber *decDecap(decNumber *dn, Int drop) { 7653 Unit *msu; /* -> target cut point */ 7654 Int cut; /* work */ 7655 if (drop>=dn->digits) { /* losing the whole thing */ 7656 #if DECCHECK 7657 if (drop>dn->digits) 7658 printf("decDecap called with drop>digits [%ld>%ld]\n", 7659 (LI)drop, (LI)dn->digits); 7660 #endif 7661 dn->lsu[0]=0; 7662 dn->digits=1; 7663 return dn; 7664 } 7665 msu=dn->lsu+D2U(dn->digits-drop)-1; /* -> likely msu */ 7666 cut=MSUDIGITS(dn->digits-drop); /* digits to be in use in msu */ 7667 if (cut!=DECDPUN) *msu%=powers[cut]; /* clear left digits */ 7668 /* that may have left leading zero digits, so do a proper count... */ 7669 dn->digits=decGetDigits(dn->lsu, msu-dn->lsu+1); 7670 return dn; 7671 } /* decDecap */ 7672 7673/* ------------------------------------------------------------------ */ 7674/* decBiStr -- compare string with pairwise options */ 7675/* */ 7676/* targ is the string to compare */ 7677/* str1 is one of the strings to compare against (length may be 0) */ 7678/* str2 is the other; it must be the same length as str1 */ 7679/* */ 7680/* returns 1 if strings compare equal, (that is, it is the same */ 7681/* length as str1 and str2, and each character of targ is in either */ 7682/* str1 or str2 in the corresponding position), or 0 otherwise */ 7683/* */ 7684/* This is used for generic caseless compare, including the awkward */ 7685/* case of the Turkish dotted and dotless Is. Use as (for example): */ 7686/* if (decBiStr(test, "mike", "MIKE")) ... */ 7687/* ------------------------------------------------------------------ */ 7688static Flag decBiStr(const char *targ, const char *str1, const char *str2) { 7689 for (;;targ++, str1++, str2++) { 7690 if (*targ!=*str1 && *targ!=*str2) return 0; 7691 /* *targ has a match in one (or both, if terminator) */ 7692 if (*targ=='\0') break; 7693 } /* forever */ 7694 return 1; 7695 } /* decBiStr */ 7696 7697/* ------------------------------------------------------------------ */ 7698/* decNaNs -- handle NaN operand or operands */ 7699/* */ 7700/* res is the result number */ 7701/* lhs is the first operand */ 7702/* rhs is the second operand, or NULL if none */ 7703/* context is used to limit payload length */ 7704/* status contains the current status */ 7705/* returns res in case convenient */ 7706/* */ 7707/* Called when one or both operands is a NaN, and propagates the */ 7708/* appropriate result to res. When an sNaN is found, it is changed */ 7709/* to a qNaN and Invalid operation is set. */ 7710/* ------------------------------------------------------------------ */ 7711static decNumber * decNaNs(decNumber *res, const decNumber *lhs, 7712 const decNumber *rhs, decContext *set, 7713 uInt *status) { 7714 /* This decision tree ends up with LHS being the source pointer, */ 7715 /* and status updated if need be */ 7716 if (lhs->bits & DECSNAN) 7717 *status|=DEC_Invalid_operation | DEC_sNaN; 7718 else if (rhs==NULL); 7719 else if (rhs->bits & DECSNAN) { 7720 lhs=rhs; 7721 *status|=DEC_Invalid_operation | DEC_sNaN; 7722 } 7723 else if (lhs->bits & DECNAN); 7724 else lhs=rhs; 7725 7726 /* propagate the payload */ 7727 if (lhs->digits<=set->digits) uprv_decNumberCopy(res, lhs); /* easy */ 7728 else { /* too long */ 7729 const Unit *ul; 7730 Unit *ur, *uresp1; 7731 /* copy safe number of units, then decapitate */ 7732 res->bits=lhs->bits; /* need sign etc. */ 7733 uresp1=res->lsu+D2U(set->digits); 7734 for (ur=res->lsu, ul=lhs->lsu; ur<uresp1; ur++, ul++) *ur=*ul; 7735 res->digits=D2U(set->digits)*DECDPUN; 7736 /* maybe still too long */ 7737 if (res->digits>set->digits) decDecap(res, res->digits-set->digits); 7738 } 7739 7740 res->bits&=~DECSNAN; /* convert any sNaN to NaN, while */ 7741 res->bits|=DECNAN; /* .. preserving sign */ 7742 res->exponent=0; /* clean exponent */ 7743 /* [coefficient was copied/decapitated] */ 7744 return res; 7745 } /* decNaNs */ 7746 7747/* ------------------------------------------------------------------ */ 7748/* decStatus -- apply non-zero status */ 7749/* */ 7750/* dn is the number to set if error */ 7751/* status contains the current status (not yet in context) */ 7752/* set is the context */ 7753/* */ 7754/* If the status is an error status, the number is set to a NaN, */ 7755/* unless the error was an overflow, divide-by-zero, or underflow, */ 7756/* in which case the number will have already been set. */ 7757/* */ 7758/* The context status is then updated with the new status. Note that */ 7759/* this may raise a signal, so control may never return from this */ 7760/* routine (hence resources must be recovered before it is called). */ 7761/* ------------------------------------------------------------------ */ 7762static void decStatus(decNumber *dn, uInt status, decContext *set) { 7763 if (status & DEC_NaNs) { /* error status -> NaN */ 7764 /* if cause was an sNaN, clear and propagate [NaN is already set up] */ 7765 if (status & DEC_sNaN) status&=~DEC_sNaN; 7766 else { 7767 uprv_decNumberZero(dn); /* other error: clean throughout */ 7768 dn->bits=DECNAN; /* and make a quiet NaN */ 7769 } 7770 } 7771 uprv_decContextSetStatus(set, status); /* [may not return] */ 7772 return; 7773 } /* decStatus */ 7774 7775/* ------------------------------------------------------------------ */ 7776/* decGetDigits -- count digits in a Units array */ 7777/* */ 7778/* uar is the Unit array holding the number (this is often an */ 7779/* accumulator of some sort) */ 7780/* len is the length of the array in units [>=1] */ 7781/* */ 7782/* returns the number of (significant) digits in the array */ 7783/* */ 7784/* All leading zeros are excluded, except the last if the array has */ 7785/* only zero Units. */ 7786/* ------------------------------------------------------------------ */ 7787/* This may be called twice during some operations. */ 7788static Int decGetDigits(Unit *uar, Int len) { 7789 Unit *up=uar+(len-1); /* -> msu */ 7790 Int digits=(len-1)*DECDPUN+1; /* possible digits excluding msu */ 7791 #if DECDPUN>4 7792 uInt const *pow; /* work */ 7793 #endif 7794 /* (at least 1 in final msu) */ 7795 #if DECCHECK 7796 if (len<1) printf("decGetDigits called with len<1 [%ld]\n", (LI)len); 7797 #endif 7798 7799 for (; up>=uar; up--) { 7800 if (*up==0) { /* unit is all 0s */ 7801 if (digits==1) break; /* a zero has one digit */ 7802 digits-=DECDPUN; /* adjust for 0 unit */ 7803 continue;} 7804 /* found the first (most significant) non-zero Unit */ 7805 #if DECDPUN>1 /* not done yet */ 7806 if (*up<10) break; /* is 1-9 */ 7807 digits++; 7808 #if DECDPUN>2 /* not done yet */ 7809 if (*up<100) break; /* is 10-99 */ 7810 digits++; 7811 #if DECDPUN>3 /* not done yet */ 7812 if (*up<1000) break; /* is 100-999 */ 7813 digits++; 7814 #if DECDPUN>4 /* count the rest ... */ 7815 for (pow=&powers[4]; *up>=*pow; pow++) digits++; 7816 #endif 7817 #endif 7818 #endif 7819 #endif 7820 break; 7821 } /* up */ 7822 return digits; 7823 } /* decGetDigits */ 7824 7825#if DECTRACE | DECCHECK 7826/* ------------------------------------------------------------------ */ 7827/* decNumberShow -- display a number [debug aid] */ 7828/* dn is the number to show */ 7829/* */ 7830/* Shows: sign, exponent, coefficient (msu first), digits */ 7831/* or: sign, special-value */ 7832/* ------------------------------------------------------------------ */ 7833/* this is public so other modules can use it */ 7834void uprv_decNumberShow(const decNumber *dn) { 7835 const Unit *up; /* work */ 7836 uInt u, d; /* .. */ 7837 Int cut; /* .. */ 7838 char isign='+'; /* main sign */ 7839 if (dn==NULL) { 7840 printf("NULL\n"); 7841 return;} 7842 if (decNumberIsNegative(dn)) isign='-'; 7843 printf(" >> %c ", isign); 7844 if (dn->bits&DECSPECIAL) { /* Is a special value */ 7845 if (decNumberIsInfinite(dn)) printf("Infinity"); 7846 else { /* a NaN */ 7847 if (dn->bits&DECSNAN) printf("sNaN"); /* signalling NaN */ 7848 else printf("NaN"); 7849 } 7850 /* if coefficient and exponent are 0, no more to do */ 7851 if (dn->exponent==0 && dn->digits==1 && *dn->lsu==0) { 7852 printf("\n"); 7853 return;} 7854 /* drop through to report other information */ 7855 printf(" "); 7856 } 7857 7858 /* now carefully display the coefficient */ 7859 up=dn->lsu+D2U(dn->digits)-1; /* msu */ 7860 printf("%ld", (LI)*up); 7861 for (up=up-1; up>=dn->lsu; up--) { 7862 u=*up; 7863 printf(":"); 7864 for (cut=DECDPUN-1; cut>=0; cut--) { 7865 d=u/powers[cut]; 7866 u-=d*powers[cut]; 7867 printf("%ld", (LI)d); 7868 } /* cut */ 7869 } /* up */ 7870 if (dn->exponent!=0) { 7871 char esign='+'; 7872 if (dn->exponent<0) esign='-'; 7873 printf(" E%c%ld", esign, (LI)abs(dn->exponent)); 7874 } 7875 printf(" [%ld]\n", (LI)dn->digits); 7876 } /* decNumberShow */ 7877#endif 7878 7879#if DECTRACE || DECCHECK 7880/* ------------------------------------------------------------------ */ 7881/* decDumpAr -- display a unit array [debug/check aid] */ 7882/* name is a single-character tag name */ 7883/* ar is the array to display */ 7884/* len is the length of the array in Units */ 7885/* ------------------------------------------------------------------ */ 7886static void decDumpAr(char name, const Unit *ar, Int len) { 7887 Int i; 7888 const char *spec; 7889 #if DECDPUN==9 7890 spec="%09d "; 7891 #elif DECDPUN==8 7892 spec="%08d "; 7893 #elif DECDPUN==7 7894 spec="%07d "; 7895 #elif DECDPUN==6 7896 spec="%06d "; 7897 #elif DECDPUN==5 7898 spec="%05d "; 7899 #elif DECDPUN==4 7900 spec="%04d "; 7901 #elif DECDPUN==3 7902 spec="%03d "; 7903 #elif DECDPUN==2 7904 spec="%02d "; 7905 #else 7906 spec="%d "; 7907 #endif 7908 printf(" :%c: ", name); 7909 for (i=len-1; i>=0; i--) { 7910 if (i==len-1) printf("%ld ", (LI)ar[i]); 7911 else printf(spec, ar[i]); 7912 } 7913 printf("\n"); 7914 return;} 7915#endif 7916 7917#if DECCHECK 7918/* ------------------------------------------------------------------ */ 7919/* decCheckOperands -- check operand(s) to a routine */ 7920/* res is the result structure (not checked; it will be set to */ 7921/* quiet NaN if error found (and it is not NULL)) */ 7922/* lhs is the first operand (may be DECUNRESU) */ 7923/* rhs is the second (may be DECUNUSED) */ 7924/* set is the context (may be DECUNCONT) */ 7925/* returns 0 if both operands, and the context are clean, or 1 */ 7926/* otherwise (in which case the context will show an error, */ 7927/* unless NULL). Note that res is not cleaned; caller should */ 7928/* handle this so res=NULL case is safe. */ 7929/* The caller is expected to abandon immediately if 1 is returned. */ 7930/* ------------------------------------------------------------------ */ 7931static Flag decCheckOperands(decNumber *res, const decNumber *lhs, 7932 const decNumber *rhs, decContext *set) { 7933 Flag bad=0; 7934 if (set==NULL) { /* oops; hopeless */ 7935 #if DECTRACE || DECVERB 7936 printf("Reference to context is NULL.\n"); 7937 #endif 7938 bad=1; 7939 return 1;} 7940 else if (set!=DECUNCONT 7941 && (set->digits<1 || set->round>=DEC_ROUND_MAX)) { 7942 bad=1; 7943 #if DECTRACE || DECVERB 7944 printf("Bad context [digits=%ld round=%ld].\n", 7945 (LI)set->digits, (LI)set->round); 7946 #endif 7947 } 7948 else { 7949 if (res==NULL) { 7950 bad=1; 7951 #if DECTRACE 7952 /* this one not DECVERB as standard tests include NULL */ 7953 printf("Reference to result is NULL.\n"); 7954 #endif 7955 } 7956 if (!bad && lhs!=DECUNUSED) bad=(decCheckNumber(lhs)); 7957 if (!bad && rhs!=DECUNUSED) bad=(decCheckNumber(rhs)); 7958 } 7959 if (bad) { 7960 if (set!=DECUNCONT) uprv_decContextSetStatus(set, DEC_Invalid_operation); 7961 if (res!=DECUNRESU && res!=NULL) { 7962 uprv_decNumberZero(res); 7963 res->bits=DECNAN; /* qNaN */ 7964 } 7965 } 7966 return bad; 7967 } /* decCheckOperands */ 7968 7969/* ------------------------------------------------------------------ */ 7970/* decCheckNumber -- check a number */ 7971/* dn is the number to check */ 7972/* returns 0 if the number is clean, or 1 otherwise */ 7973/* */ 7974/* The number is considered valid if it could be a result from some */ 7975/* operation in some valid context. */ 7976/* ------------------------------------------------------------------ */ 7977static Flag decCheckNumber(const decNumber *dn) { 7978 const Unit *up; /* work */ 7979 uInt maxuint; /* .. */ 7980 Int ae, d, digits; /* .. */ 7981 Int emin, emax; /* .. */ 7982 7983 if (dn==NULL) { /* hopeless */ 7984 #if DECTRACE 7985 /* this one not DECVERB as standard tests include NULL */ 7986 printf("Reference to decNumber is NULL.\n"); 7987 #endif 7988 return 1;} 7989 7990 /* check special values */ 7991 if (dn->bits & DECSPECIAL) { 7992 if (dn->exponent!=0) { 7993 #if DECTRACE || DECVERB 7994 printf("Exponent %ld (not 0) for a special value [%02x].\n", 7995 (LI)dn->exponent, dn->bits); 7996 #endif 7997 return 1;} 7998 7999 /* 2003.09.08: NaNs may now have coefficients, so next tests Inf only */ 8000 if (decNumberIsInfinite(dn)) { 8001 if (dn->digits!=1) { 8002 #if DECTRACE || DECVERB 8003 printf("Digits %ld (not 1) for an infinity.\n", (LI)dn->digits); 8004 #endif 8005 return 1;} 8006 if (*dn->lsu!=0) { 8007 #if DECTRACE || DECVERB 8008 printf("LSU %ld (not 0) for an infinity.\n", (LI)*dn->lsu); 8009 #endif 8010 decDumpAr('I', dn->lsu, D2U(dn->digits)); 8011 return 1;} 8012 } /* Inf */ 8013 /* 2002.12.26: negative NaNs can now appear through proposed IEEE */ 8014 /* concrete formats (decimal64, etc.). */ 8015 return 0; 8016 } 8017 8018 /* check the coefficient */ 8019 if (dn->digits<1 || dn->digits>DECNUMMAXP) { 8020 #if DECTRACE || DECVERB 8021 printf("Digits %ld in number.\n", (LI)dn->digits); 8022 #endif 8023 return 1;} 8024 8025 d=dn->digits; 8026 8027 for (up=dn->lsu; d>0; up++) { 8028 if (d>DECDPUN) maxuint=DECDPUNMAX; 8029 else { /* reached the msu */ 8030 maxuint=powers[d]-1; 8031 if (dn->digits>1 && *up<powers[d-1]) { 8032 #if DECTRACE || DECVERB 8033 printf("Leading 0 in number.\n"); 8034 uprv_decNumberShow(dn); 8035 #endif 8036 return 1;} 8037 } 8038 if (*up>maxuint) { 8039 #if DECTRACE || DECVERB 8040 printf("Bad Unit [%08lx] in %ld-digit number at offset %ld [maxuint %ld].\n", 8041 (LI)*up, (LI)dn->digits, (LI)(up-dn->lsu), (LI)maxuint); 8042 #endif 8043 return 1;} 8044 d-=DECDPUN; 8045 } 8046 8047 /* check the exponent. Note that input operands can have exponents */ 8048 /* which are out of the set->emin/set->emax and set->digits range */ 8049 /* (just as they can have more digits than set->digits). */ 8050 ae=dn->exponent+dn->digits-1; /* adjusted exponent */ 8051 emax=DECNUMMAXE; 8052 emin=DECNUMMINE; 8053 digits=DECNUMMAXP; 8054 if (ae<emin-(digits-1)) { 8055 #if DECTRACE || DECVERB 8056 printf("Adjusted exponent underflow [%ld].\n", (LI)ae); 8057 uprv_decNumberShow(dn); 8058 #endif 8059 return 1;} 8060 if (ae>+emax) { 8061 #if DECTRACE || DECVERB 8062 printf("Adjusted exponent overflow [%ld].\n", (LI)ae); 8063 uprv_decNumberShow(dn); 8064 #endif 8065 return 1;} 8066 8067 return 0; /* it's OK */ 8068 } /* decCheckNumber */ 8069 8070/* ------------------------------------------------------------------ */ 8071/* decCheckInexact -- check a normal finite inexact result has digits */ 8072/* dn is the number to check */ 8073/* set is the context (for status and precision) */ 8074/* sets Invalid operation, etc., if some digits are missing */ 8075/* [this check is not made for DECSUBSET compilation or when */ 8076/* subnormal is not set] */ 8077/* ------------------------------------------------------------------ */ 8078static void decCheckInexact(const decNumber *dn, decContext *set) { 8079 #if !DECSUBSET && DECEXTFLAG 8080 if ((set->status & (DEC_Inexact|DEC_Subnormal))==DEC_Inexact 8081 && (set->digits!=dn->digits) && !(dn->bits & DECSPECIAL)) { 8082 #if DECTRACE || DECVERB 8083 printf("Insufficient digits [%ld] on normal Inexact result.\n", 8084 (LI)dn->digits); 8085 uprv_decNumberShow(dn); 8086 #endif 8087 uprv_decContextSetStatus(set, DEC_Invalid_operation); 8088 } 8089 #else 8090 /* next is a noop for quiet compiler */ 8091 if (dn!=NULL && dn->digits==0) set->status|=DEC_Invalid_operation; 8092 #endif 8093 return; 8094 } /* decCheckInexact */ 8095#endif 8096 8097#if DECALLOC 8098#undef malloc 8099#undef free 8100/* ------------------------------------------------------------------ */ 8101/* decMalloc -- accountable allocation routine */ 8102/* n is the number of bytes to allocate */ 8103/* */ 8104/* Semantics is the same as the stdlib malloc routine, but bytes */ 8105/* allocated are accounted for globally, and corruption fences are */ 8106/* added before and after the 'actual' storage. */ 8107/* ------------------------------------------------------------------ */ 8108/* This routine allocates storage with an extra twelve bytes; 8 are */ 8109/* at the start and hold: */ 8110/* 0-3 the original length requested */ 8111/* 4-7 buffer corruption detection fence (DECFENCE, x4) */ 8112/* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */ 8113/* ------------------------------------------------------------------ */ 8114static void *decMalloc(size_t n) { 8115 uInt size=n+12; /* true size */ 8116 void *alloc; /* -> allocated storage */ 8117 uByte *b, *b0; /* work */ 8118 uInt uiwork; /* for macros */ 8119 8120 alloc=malloc(size); /* -> allocated storage */ 8121 if (alloc==NULL) return NULL; /* out of strorage */ 8122 b0=(uByte *)alloc; /* as bytes */ 8123 decAllocBytes+=n; /* account for storage */ 8124 UBFROMUI(alloc, n); /* save n */ 8125 /* printf(" alloc ++ dAB: %ld (%ld)\n", (LI)decAllocBytes, (LI)n); */ 8126 for (b=b0+4; b<b0+8; b++) *b=DECFENCE; 8127 for (b=b0+n+8; b<b0+n+12; b++) *b=DECFENCE; 8128 return b0+8; /* -> play area */ 8129 } /* decMalloc */ 8130 8131/* ------------------------------------------------------------------ */ 8132/* decFree -- accountable free routine */ 8133/* alloc is the storage to free */ 8134/* */ 8135/* Semantics is the same as the stdlib malloc routine, except that */ 8136/* the global storage accounting is updated and the fences are */ 8137/* checked to ensure that no routine has written 'out of bounds'. */ 8138/* ------------------------------------------------------------------ */ 8139/* This routine first checks that the fences have not been corrupted. */ 8140/* It then frees the storage using the 'truw' storage address (that */ 8141/* is, offset by 8). */ 8142/* ------------------------------------------------------------------ */ 8143static void decFree(void *alloc) { 8144 uInt n; /* original length */ 8145 uByte *b, *b0; /* work */ 8146 uInt uiwork; /* for macros */ 8147 8148 if (alloc==NULL) return; /* allowed; it's a nop */ 8149 b0=(uByte *)alloc; /* as bytes */ 8150 b0-=8; /* -> true start of storage */ 8151 n=UBTOUI(b0); /* lift length */ 8152 for (b=b0+4; b<b0+8; b++) if (*b!=DECFENCE) 8153 printf("=== Corrupt byte [%02x] at offset %d from %ld ===\n", *b, 8154 b-b0-8, (LI)b0); 8155 for (b=b0+n+8; b<b0+n+12; b++) if (*b!=DECFENCE) 8156 printf("=== Corrupt byte [%02x] at offset +%d from %ld, n=%ld ===\n", *b, 8157 b-b0-8, (LI)b0, (LI)n); 8158 free(b0); /* drop the storage */ 8159 decAllocBytes-=n; /* account for storage */ 8160 /* printf(" free -- dAB: %d (%d)\n", decAllocBytes, -n); */ 8161 } /* decFree */ 8162#define malloc(a) decMalloc(a) 8163#define free(a) decFree(a) 8164#endif 8165