1/* ------------------------------------------------------------------ */ 2/* Decimal Number arithmetic module */ 3/* ------------------------------------------------------------------ */ 4/* Copyright (c) IBM Corporation, 2000-2014. 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#include "uassert.h" 185 186/* Constants */ 187/* Public lookup table used by the D2U macro */ 188static const uByte d2utable[DECMAXD2U+1]=D2UTABLE; 189 190#define DECVERB 1 /* set to 1 for verbose DECCHECK */ 191#define powers DECPOWERS /* old internal name */ 192 193/* Local constants */ 194#define DIVIDE 0x80 /* Divide operators */ 195#define REMAINDER 0x40 /* .. */ 196#define DIVIDEINT 0x20 /* .. */ 197#define REMNEAR 0x10 /* .. */ 198#define COMPARE 0x01 /* Compare operators */ 199#define COMPMAX 0x02 /* .. */ 200#define COMPMIN 0x03 /* .. */ 201#define COMPTOTAL 0x04 /* .. */ 202#define COMPNAN 0x05 /* .. [NaN processing] */ 203#define COMPSIG 0x06 /* .. [signaling COMPARE] */ 204#define COMPMAXMAG 0x07 /* .. */ 205#define COMPMINMAG 0x08 /* .. */ 206 207#define DEC_sNaN 0x40000000 /* local status: sNaN signal */ 208#define BADINT (Int)0x80000000 /* most-negative Int; error indicator */ 209/* Next two indicate an integer >= 10**6, and its parity (bottom bit) */ 210#define BIGEVEN (Int)0x80000002 211#define BIGODD (Int)0x80000003 212 213static const Unit uarrone[1]={1}; /* Unit array of 1, used for incrementing */ 214 215/* ------------------------------------------------------------------ */ 216/* round-for-reround digits */ 217/* ------------------------------------------------------------------ */ 218#if 0 219static const uByte DECSTICKYTAB[10]={1,1,2,3,4,6,6,7,8,9}; /* used if sticky */ 220#endif 221 222/* ------------------------------------------------------------------ */ 223/* Powers of ten (powers[n]==10**n, 0<=n<=9) */ 224/* ------------------------------------------------------------------ */ 225static const uInt DECPOWERS[10]={1, 10, 100, 1000, 10000, 100000, 1000000, 226 10000000, 100000000, 1000000000}; 227 228 229/* Granularity-dependent code */ 230#if DECDPUN<=4 231 #define eInt Int /* extended integer */ 232 #define ueInt uInt /* unsigned extended integer */ 233 /* Constant multipliers for divide-by-power-of five using reciprocal */ 234 /* multiply, after removing powers of 2 by shifting, and final shift */ 235 /* of 17 [we only need up to **4] */ 236 static const uInt multies[]={131073, 26215, 5243, 1049, 210}; 237 /* QUOT10 -- macro to return the quotient of unit u divided by 10**n */ 238 #define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17) 239#else 240 /* For DECDPUN>4 non-ANSI-89 64-bit types are needed. */ 241 #if !DECUSE64 242 #error decNumber.c: DECUSE64 must be 1 when DECDPUN>4 243 #endif 244 #define eInt Long /* extended integer */ 245 #define ueInt uLong /* unsigned extended integer */ 246#endif 247 248/* Local routines */ 249static decNumber * decAddOp(decNumber *, const decNumber *, const decNumber *, 250 decContext *, uByte, uInt *); 251static Flag decBiStr(const char *, const char *, const char *); 252static uInt decCheckMath(const decNumber *, decContext *, uInt *); 253static void decApplyRound(decNumber *, decContext *, Int, uInt *); 254static Int decCompare(const decNumber *lhs, const decNumber *rhs, Flag); 255static decNumber * decCompareOp(decNumber *, const decNumber *, 256 const decNumber *, decContext *, 257 Flag, uInt *); 258static void decCopyFit(decNumber *, const decNumber *, decContext *, 259 Int *, uInt *); 260static decNumber * decDecap(decNumber *, Int); 261static decNumber * decDivideOp(decNumber *, const decNumber *, 262 const decNumber *, decContext *, Flag, uInt *); 263static decNumber * decExpOp(decNumber *, const decNumber *, 264 decContext *, uInt *); 265static void decFinalize(decNumber *, decContext *, Int *, uInt *); 266static Int decGetDigits(Unit *, Int); 267static Int decGetInt(const decNumber *); 268static decNumber * decLnOp(decNumber *, const decNumber *, 269 decContext *, uInt *); 270static decNumber * decMultiplyOp(decNumber *, const decNumber *, 271 const decNumber *, decContext *, 272 uInt *); 273static decNumber * decNaNs(decNumber *, const decNumber *, 274 const decNumber *, decContext *, uInt *); 275static decNumber * decQuantizeOp(decNumber *, const decNumber *, 276 const decNumber *, decContext *, Flag, 277 uInt *); 278static void decReverse(Unit *, Unit *); 279static void decSetCoeff(decNumber *, decContext *, const Unit *, 280 Int, Int *, uInt *); 281static void decSetMaxValue(decNumber *, decContext *); 282static void decSetOverflow(decNumber *, decContext *, uInt *); 283static void decSetSubnormal(decNumber *, decContext *, Int *, uInt *); 284static Int decShiftToLeast(Unit *, Int, Int); 285static Int decShiftToMost(Unit *, Int, Int); 286static void decStatus(decNumber *, uInt, decContext *); 287static void decToString(const decNumber *, char[], Flag); 288static decNumber * decTrim(decNumber *, decContext *, Flag, Flag, Int *); 289static Int decUnitAddSub(const Unit *, Int, const Unit *, Int, Int, 290 Unit *, Int); 291static Int decUnitCompare(const Unit *, Int, const Unit *, Int, Int); 292 293#if !DECSUBSET 294/* decFinish == decFinalize when no subset arithmetic needed */ 295#define decFinish(a,b,c,d) decFinalize(a,b,c,d) 296#else 297static void decFinish(decNumber *, decContext *, Int *, uInt *); 298static decNumber * decRoundOperand(const decNumber *, decContext *, uInt *); 299#endif 300 301/* Local macros */ 302/* masked special-values bits */ 303#define SPECIALARG (rhs->bits & DECSPECIAL) 304#define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL) 305 306/* For use in ICU */ 307#define malloc(a) uprv_malloc(a) 308#define free(a) uprv_free(a) 309 310/* Diagnostic macros, etc. */ 311#if DECALLOC 312/* Handle malloc/free accounting. If enabled, our accountable routines */ 313/* are used; otherwise the code just goes straight to the system malloc */ 314/* and free routines. */ 315#define malloc(a) decMalloc(a) 316#define free(a) decFree(a) 317#define DECFENCE 0x5a /* corruption detector */ 318/* 'Our' malloc and free: */ 319static void *decMalloc(size_t); 320static void decFree(void *); 321uInt decAllocBytes=0; /* count of bytes allocated */ 322/* Note that DECALLOC code only checks for storage buffer overflow. */ 323/* To check for memory leaks, the decAllocBytes variable must be */ 324/* checked to be 0 at appropriate times (e.g., after the test */ 325/* harness completes a set of tests). This checking may be unreliable */ 326/* if the testing is done in a multi-thread environment. */ 327#endif 328 329#if DECCHECK 330/* Optional checking routines. Enabling these means that decNumber */ 331/* and decContext operands to operator routines are checked for */ 332/* correctness. This roughly doubles the execution time of the */ 333/* fastest routines (and adds 600+ bytes), so should not normally be */ 334/* used in 'production'. */ 335/* decCheckInexact is used to check that inexact results have a full */ 336/* complement of digits (where appropriate -- this is not the case */ 337/* for Quantize, for example) */ 338#define DECUNRESU ((decNumber *)(void *)0xffffffff) 339#define DECUNUSED ((const decNumber *)(void *)0xffffffff) 340#define DECUNCONT ((decContext *)(void *)(0xffffffff)) 341static Flag decCheckOperands(decNumber *, const decNumber *, 342 const decNumber *, decContext *); 343static Flag decCheckNumber(const decNumber *); 344static void decCheckInexact(const decNumber *, decContext *); 345#endif 346 347#if DECTRACE || DECCHECK 348/* Optional trace/debugging routines (may or may not be used) */ 349void decNumberShow(const decNumber *); /* displays the components of a number */ 350static void decDumpAr(char, const Unit *, Int); 351#endif 352 353/* ================================================================== */ 354/* Conversions */ 355/* ================================================================== */ 356 357/* ------------------------------------------------------------------ */ 358/* from-int32 -- conversion from Int or uInt */ 359/* */ 360/* dn is the decNumber to receive the integer */ 361/* in or uin is the integer to be converted */ 362/* returns dn */ 363/* */ 364/* No error is possible. */ 365/* ------------------------------------------------------------------ */ 366U_CAPI decNumber * U_EXPORT2 uprv_decNumberFromInt32(decNumber *dn, Int in) { 367 uInt unsig; 368 if (in>=0) unsig=in; 369 else { /* negative (possibly BADINT) */ 370 if (in==BADINT) unsig=(uInt)1073741824*2; /* special case */ 371 else unsig=-in; /* invert */ 372 } 373 /* in is now positive */ 374 uprv_decNumberFromUInt32(dn, unsig); 375 if (in<0) dn->bits=DECNEG; /* sign needed */ 376 return dn; 377 } /* decNumberFromInt32 */ 378 379U_CAPI decNumber * U_EXPORT2 uprv_decNumberFromUInt32(decNumber *dn, uInt uin) { 380 Unit *up; /* work pointer */ 381 uprv_decNumberZero(dn); /* clean */ 382 if (uin==0) return dn; /* [or decGetDigits bad call] */ 383 for (up=dn->lsu; uin>0; up++) { 384 *up=(Unit)(uin%(DECDPUNMAX+1)); 385 uin=uin/(DECDPUNMAX+1); 386 } 387 dn->digits=decGetDigits(dn->lsu, up-dn->lsu); 388 return dn; 389 } /* decNumberFromUInt32 */ 390 391/* ------------------------------------------------------------------ */ 392/* to-int32 -- conversion to Int or uInt */ 393/* */ 394/* dn is the decNumber to convert */ 395/* set is the context for reporting errors */ 396/* returns the converted decNumber, or 0 if Invalid is set */ 397/* */ 398/* Invalid is set if the decNumber does not have exponent==0 or if */ 399/* it is a NaN, Infinite, or out-of-range. */ 400/* ------------------------------------------------------------------ */ 401U_CAPI Int U_EXPORT2 uprv_decNumberToInt32(const decNumber *dn, decContext *set) { 402 #if DECCHECK 403 if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; 404 #endif 405 406 /* special or too many digits, or bad exponent */ 407 if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; /* bad */ 408 else { /* is a finite integer with 10 or fewer digits */ 409 Int d; /* work */ 410 const Unit *up; /* .. */ 411 uInt hi=0, lo; /* .. */ 412 up=dn->lsu; /* -> lsu */ 413 lo=*up; /* get 1 to 9 digits */ 414 #if DECDPUN>1 /* split to higher */ 415 hi=lo/10; 416 lo=lo%10; 417 #endif 418 up++; 419 /* collect remaining Units, if any, into hi */ 420 for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1]; 421 /* now low has the lsd, hi the remainder */ 422 if (hi>214748364 || (hi==214748364 && lo>7)) { /* out of range? */ 423 /* most-negative is a reprieve */ 424 if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000; 425 /* bad -- drop through */ 426 } 427 else { /* in-range always */ 428 Int i=X10(hi)+lo; 429 if (dn->bits&DECNEG) return -i; 430 return i; 431 } 432 } /* integer */ 433 uprv_decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */ 434 return 0; 435 } /* decNumberToInt32 */ 436 437U_CAPI uInt U_EXPORT2 uprv_decNumberToUInt32(const decNumber *dn, decContext *set) { 438 #if DECCHECK 439 if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; 440 #endif 441 /* special or too many digits, or bad exponent, or negative (<0) */ 442 if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0 443 || (dn->bits&DECNEG && !ISZERO(dn))); /* bad */ 444 else { /* is a finite integer with 10 or fewer digits */ 445 Int d; /* work */ 446 const Unit *up; /* .. */ 447 uInt hi=0, lo; /* .. */ 448 up=dn->lsu; /* -> lsu */ 449 lo=*up; /* get 1 to 9 digits */ 450 #if DECDPUN>1 /* split to higher */ 451 hi=lo/10; 452 lo=lo%10; 453 #endif 454 up++; 455 /* collect remaining Units, if any, into hi */ 456 for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1]; 457 458 /* now low has the lsd, hi the remainder */ 459 if (hi>429496729 || (hi==429496729 && lo>5)) ; /* no reprieve possible */ 460 else return X10(hi)+lo; 461 } /* integer */ 462 uprv_decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */ 463 return 0; 464 } /* decNumberToUInt32 */ 465 466/* ------------------------------------------------------------------ */ 467/* to-scientific-string -- conversion to numeric string */ 468/* to-engineering-string -- conversion to numeric string */ 469/* */ 470/* decNumberToString(dn, string); */ 471/* decNumberToEngString(dn, string); */ 472/* */ 473/* dn is the decNumber to convert */ 474/* string is the string where the result will be laid out */ 475/* */ 476/* string must be at least dn->digits+14 characters long */ 477/* */ 478/* No error is possible, and no status can be set. */ 479/* ------------------------------------------------------------------ */ 480U_CAPI char * U_EXPORT2 uprv_decNumberToString(const decNumber *dn, char *string){ 481 decToString(dn, string, 0); 482 return string; 483 } /* DecNumberToString */ 484 485U_CAPI char * U_EXPORT2 uprv_decNumberToEngString(const decNumber *dn, char *string){ 486 decToString(dn, string, 1); 487 return string; 488 } /* DecNumberToEngString */ 489 490/* ------------------------------------------------------------------ */ 491/* to-number -- conversion from numeric string */ 492/* */ 493/* decNumberFromString -- convert string to decNumber */ 494/* dn -- the number structure to fill */ 495/* chars[] -- the string to convert ('\0' terminated) */ 496/* set -- the context used for processing any error, */ 497/* determining the maximum precision available */ 498/* (set.digits), determining the maximum and minimum */ 499/* exponent (set.emax and set.emin), determining if */ 500/* extended values are allowed, and checking the */ 501/* rounding mode if overflow occurs or rounding is */ 502/* needed. */ 503/* */ 504/* The length of the coefficient and the size of the exponent are */ 505/* checked by this routine, so the correct error (Underflow or */ 506/* Overflow) can be reported or rounding applied, as necessary. */ 507/* */ 508/* If bad syntax is detected, the result will be a quiet NaN. */ 509/* ------------------------------------------------------------------ */ 510U_CAPI decNumber * U_EXPORT2 uprv_decNumberFromString(decNumber *dn, const char chars[], 511 decContext *set) { 512 Int exponent=0; /* working exponent [assume 0] */ 513 uByte bits=0; /* working flags [assume +ve] */ 514 Unit *res; /* where result will be built */ 515 Unit resbuff[SD2U(DECBUFFER+9)];/* local buffer in case need temporary */ 516 /* [+9 allows for ln() constants] */ 517 Unit *allocres=NULL; /* -> allocated result, iff allocated */ 518 Int d=0; /* count of digits found in decimal part */ 519 const char *dotchar=NULL; /* where dot was found */ 520 const char *cfirst=chars; /* -> first character of decimal part */ 521 const char *last=NULL; /* -> last digit of decimal part */ 522 const char *c; /* work */ 523 Unit *up; /* .. */ 524 #if DECDPUN>1 525 Int cut, out; /* .. */ 526 #endif 527 Int residue; /* rounding residue */ 528 uInt status=0; /* error code */ 529 530 #if DECCHECK 531 if (decCheckOperands(DECUNRESU, DECUNUSED, DECUNUSED, set)) 532 return uprv_decNumberZero(dn); 533 #endif 534 535 do { /* status & malloc protection */ 536 for (c=chars;; c++) { /* -> input character */ 537 if (*c>='0' && *c<='9') { /* test for Arabic digit */ 538 last=c; 539 d++; /* count of real digits */ 540 continue; /* still in decimal part */ 541 } 542 if (*c=='.' && dotchar==NULL) { /* first '.' */ 543 dotchar=c; /* record offset into decimal part */ 544 if (c==cfirst) cfirst++; /* first digit must follow */ 545 continue;} 546 if (c==chars) { /* first in string... */ 547 if (*c=='-') { /* valid - sign */ 548 cfirst++; 549 bits=DECNEG; 550 continue;} 551 if (*c=='+') { /* valid + sign */ 552 cfirst++; 553 continue;} 554 } 555 /* *c is not a digit, or a valid +, -, or '.' */ 556 break; 557 } /* c */ 558 559 if (last==NULL) { /* no digits yet */ 560 status=DEC_Conversion_syntax;/* assume the worst */ 561 if (*c=='\0') break; /* and no more to come... */ 562 #if DECSUBSET 563 /* if subset then infinities and NaNs are not allowed */ 564 if (!set->extended) break; /* hopeless */ 565 #endif 566 /* Infinities and NaNs are possible, here */ 567 if (dotchar!=NULL) break; /* .. unless had a dot */ 568 uprv_decNumberZero(dn); /* be optimistic */ 569 if (decBiStr(c, "infinity", "INFINITY") 570 || decBiStr(c, "inf", "INF")) { 571 dn->bits=bits | DECINF; 572 status=0; /* is OK */ 573 break; /* all done */ 574 } 575 /* a NaN expected */ 576 /* 2003.09.10 NaNs are now permitted to have a sign */ 577 dn->bits=bits | DECNAN; /* assume simple NaN */ 578 if (*c=='s' || *c=='S') { /* looks like an sNaN */ 579 c++; 580 dn->bits=bits | DECSNAN; 581 } 582 if (*c!='n' && *c!='N') break; /* check caseless "NaN" */ 583 c++; 584 if (*c!='a' && *c!='A') break; /* .. */ 585 c++; 586 if (*c!='n' && *c!='N') break; /* .. */ 587 c++; 588 /* now either nothing, or nnnn payload, expected */ 589 /* -> start of integer and skip leading 0s [including plain 0] */ 590 for (cfirst=c; *cfirst=='0';) cfirst++; 591 if (*cfirst=='\0') { /* "NaN" or "sNaN", maybe with all 0s */ 592 status=0; /* it's good */ 593 break; /* .. */ 594 } 595 /* something other than 0s; setup last and d as usual [no dots] */ 596 for (c=cfirst;; c++, d++) { 597 if (*c<'0' || *c>'9') break; /* test for Arabic digit */ 598 last=c; 599 } 600 if (*c!='\0') break; /* not all digits */ 601 if (d>set->digits-1) { 602 /* [NB: payload in a decNumber can be full length unless */ 603 /* clamped, in which case can only be digits-1] */ 604 if (set->clamp) break; 605 if (d>set->digits) break; 606 } /* too many digits? */ 607 /* good; drop through to convert the integer to coefficient */ 608 status=0; /* syntax is OK */ 609 bits=dn->bits; /* for copy-back */ 610 } /* last==NULL */ 611 612 else if (*c!='\0') { /* more to process... */ 613 /* had some digits; exponent is only valid sequence now */ 614 Flag nege; /* 1=negative exponent */ 615 const char *firstexp; /* -> first significant exponent digit */ 616 status=DEC_Conversion_syntax;/* assume the worst */ 617 if (*c!='e' && *c!='E') break; 618 /* Found 'e' or 'E' -- now process explicit exponent */ 619 /* 1998.07.11: sign no longer required */ 620 nege=0; 621 c++; /* to (possible) sign */ 622 if (*c=='-') {nege=1; c++;} 623 else if (*c=='+') c++; 624 if (*c=='\0') break; 625 626 for (; *c=='0' && *(c+1)!='\0';) c++; /* strip insignificant zeros */ 627 firstexp=c; /* save exponent digit place */ 628 for (; ;c++) { 629 if (*c<'0' || *c>'9') break; /* not a digit */ 630 exponent=X10(exponent)+(Int)*c-(Int)'0'; 631 } /* c */ 632 /* if not now on a '\0', *c must not be a digit */ 633 if (*c!='\0') break; 634 635 /* (this next test must be after the syntax checks) */ 636 /* if it was too long the exponent may have wrapped, so check */ 637 /* carefully and set it to a certain overflow if wrap possible */ 638 if (c>=firstexp+9+1) { 639 if (c>firstexp+9+1 || *firstexp>'1') exponent=DECNUMMAXE*2; 640 /* [up to 1999999999 is OK, for example 1E-1000000998] */ 641 } 642 if (nege) exponent=-exponent; /* was negative */ 643 status=0; /* is OK */ 644 } /* stuff after digits */ 645 646 /* Here when whole string has been inspected; syntax is good */ 647 /* cfirst->first digit (never dot), last->last digit (ditto) */ 648 649 /* strip leading zeros/dot [leave final 0 if all 0's] */ 650 if (*cfirst=='0') { /* [cfirst has stepped over .] */ 651 for (c=cfirst; c<last; c++, cfirst++) { 652 if (*c=='.') continue; /* ignore dots */ 653 if (*c!='0') break; /* non-zero found */ 654 d--; /* 0 stripped */ 655 } /* c */ 656 #if DECSUBSET 657 /* make a rapid exit for easy zeros if !extended */ 658 if (*cfirst=='0' && !set->extended) { 659 uprv_decNumberZero(dn); /* clean result */ 660 break; /* [could be return] */ 661 } 662 #endif 663 } /* at least one leading 0 */ 664 665 /* Handle decimal point... */ 666 if (dotchar!=NULL && dotchar<last) /* non-trailing '.' found? */ 667 exponent-=(last-dotchar); /* adjust exponent */ 668 /* [we can now ignore the .] */ 669 670 /* OK, the digits string is good. Assemble in the decNumber, or in */ 671 /* a temporary units array if rounding is needed */ 672 if (d<=set->digits) res=dn->lsu; /* fits into supplied decNumber */ 673 else { /* rounding needed */ 674 Int needbytes=D2U(d)*sizeof(Unit);/* bytes needed */ 675 res=resbuff; /* assume use local buffer */ 676 if (needbytes>(Int)sizeof(resbuff)) { /* too big for local */ 677 allocres=(Unit *)malloc(needbytes); 678 if (allocres==NULL) {status|=DEC_Insufficient_storage; break;} 679 res=allocres; 680 } 681 } 682 /* res now -> number lsu, buffer, or allocated storage for Unit array */ 683 684 /* Place the coefficient into the selected Unit array */ 685 /* [this is often 70% of the cost of this function when DECDPUN>1] */ 686 #if DECDPUN>1 687 out=0; /* accumulator */ 688 up=res+D2U(d)-1; /* -> msu */ 689 cut=d-(up-res)*DECDPUN; /* digits in top unit */ 690 for (c=cfirst;; c++) { /* along the digits */ 691 if (*c=='.') continue; /* ignore '.' [don't decrement cut] */ 692 out=X10(out)+(Int)*c-(Int)'0'; 693 if (c==last) break; /* done [never get to trailing '.'] */ 694 cut--; 695 if (cut>0) continue; /* more for this unit */ 696 *up=(Unit)out; /* write unit */ 697 up--; /* prepare for unit below.. */ 698 cut=DECDPUN; /* .. */ 699 out=0; /* .. */ 700 } /* c */ 701 *up=(Unit)out; /* write lsu */ 702 703 #else 704 /* DECDPUN==1 */ 705 up=res; /* -> lsu */ 706 for (c=last; c>=cfirst; c--) { /* over each character, from least */ 707 if (*c=='.') continue; /* ignore . [don't step up] */ 708 *up=(Unit)((Int)*c-(Int)'0'); 709 up++; 710 } /* c */ 711 #endif 712 713 dn->bits=bits; 714 dn->exponent=exponent; 715 dn->digits=d; 716 717 /* if not in number (too long) shorten into the number */ 718 if (d>set->digits) { 719 residue=0; 720 decSetCoeff(dn, set, res, d, &residue, &status); 721 /* always check for overflow or subnormal and round as needed */ 722 decFinalize(dn, set, &residue, &status); 723 } 724 else { /* no rounding, but may still have overflow or subnormal */ 725 /* [these tests are just for performance; finalize repeats them] */ 726 if ((dn->exponent-1<set->emin-dn->digits) 727 || (dn->exponent-1>set->emax-set->digits)) { 728 residue=0; 729 decFinalize(dn, set, &residue, &status); 730 } 731 } 732 /* decNumberShow(dn); */ 733 } while(0); /* [for break] */ 734 735 if (allocres!=NULL) free(allocres); /* drop any storage used */ 736 if (status!=0) decStatus(dn, status, set); 737 return dn; 738 } /* decNumberFromString */ 739 740/* ================================================================== */ 741/* Operators */ 742/* ================================================================== */ 743 744/* ------------------------------------------------------------------ */ 745/* decNumberAbs -- absolute value operator */ 746/* */ 747/* This computes C = abs(A) */ 748/* */ 749/* res is C, the result. C may be A */ 750/* rhs is A */ 751/* set is the context */ 752/* */ 753/* See also decNumberCopyAbs for a quiet bitwise version of this. */ 754/* C must have space for set->digits digits. */ 755/* ------------------------------------------------------------------ */ 756/* This has the same effect as decNumberPlus unless A is negative, */ 757/* in which case it has the same effect as decNumberMinus. */ 758/* ------------------------------------------------------------------ */ 759U_CAPI decNumber * U_EXPORT2 uprv_decNumberAbs(decNumber *res, const decNumber *rhs, 760 decContext *set) { 761 decNumber dzero; /* for 0 */ 762 uInt status=0; /* accumulator */ 763 764 #if DECCHECK 765 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 766 #endif 767 768 uprv_decNumberZero(&dzero); /* set 0 */ 769 dzero.exponent=rhs->exponent; /* [no coefficient expansion] */ 770 decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status); 771 if (status!=0) decStatus(res, status, set); 772 #if DECCHECK 773 decCheckInexact(res, set); 774 #endif 775 return res; 776 } /* decNumberAbs */ 777 778/* ------------------------------------------------------------------ */ 779/* decNumberAdd -- add two Numbers */ 780/* */ 781/* This computes C = A + B */ 782/* */ 783/* res is C, the result. C may be A and/or B (e.g., X=X+X) */ 784/* lhs is A */ 785/* rhs is B */ 786/* set is the context */ 787/* */ 788/* C must have space for set->digits digits. */ 789/* ------------------------------------------------------------------ */ 790/* This just calls the routine shared with Subtract */ 791U_CAPI decNumber * U_EXPORT2 uprv_decNumberAdd(decNumber *res, const decNumber *lhs, 792 const decNumber *rhs, decContext *set) { 793 uInt status=0; /* accumulator */ 794 decAddOp(res, lhs, rhs, set, 0, &status); 795 if (status!=0) decStatus(res, status, set); 796 #if DECCHECK 797 decCheckInexact(res, set); 798 #endif 799 return res; 800 } /* decNumberAdd */ 801 802/* ------------------------------------------------------------------ */ 803/* decNumberAnd -- AND two Numbers, digitwise */ 804/* */ 805/* This computes C = A & B */ 806/* */ 807/* res is C, the result. C may be A and/or B (e.g., X=X&X) */ 808/* lhs is A */ 809/* rhs is B */ 810/* set is the context (used for result length and error report) */ 811/* */ 812/* C must have space for set->digits digits. */ 813/* */ 814/* Logical function restrictions apply (see above); a NaN is */ 815/* returned with Invalid_operation if a restriction is violated. */ 816/* ------------------------------------------------------------------ */ 817U_CAPI decNumber * U_EXPORT2 uprv_decNumberAnd(decNumber *res, const decNumber *lhs, 818 const decNumber *rhs, decContext *set) { 819 const Unit *ua, *ub; /* -> operands */ 820 const Unit *msua, *msub; /* -> operand msus */ 821 Unit *uc, *msuc; /* -> result and its msu */ 822 Int msudigs; /* digits in res msu */ 823 #if DECCHECK 824 if (decCheckOperands(res, lhs, rhs, set)) return res; 825 #endif 826 827 if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) 828 || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { 829 decStatus(res, DEC_Invalid_operation, set); 830 return res; 831 } 832 833 /* operands are valid */ 834 ua=lhs->lsu; /* bottom-up */ 835 ub=rhs->lsu; /* .. */ 836 uc=res->lsu; /* .. */ 837 msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */ 838 msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */ 839 msuc=uc+D2U(set->digits)-1; /* -> msu of result */ 840 msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ 841 for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */ 842 Unit a, b; /* extract units */ 843 if (ua>msua) a=0; 844 else a=*ua; 845 if (ub>msub) b=0; 846 else b=*ub; 847 *uc=0; /* can now write back */ 848 if (a|b) { /* maybe 1 bits to examine */ 849 Int i, j; 850 *uc=0; /* can now write back */ 851 /* This loop could be unrolled and/or use BIN2BCD tables */ 852 for (i=0; i<DECDPUN; i++) { 853 if (a&b&1) *uc=*uc+(Unit)powers[i]; /* effect AND */ 854 j=a%10; 855 a=a/10; 856 j|=b%10; 857 b=b/10; 858 if (j>1) { 859 decStatus(res, DEC_Invalid_operation, set); 860 return res; 861 } 862 if (uc==msuc && i==msudigs-1) break; /* just did final digit */ 863 } /* each digit */ 864 } /* both OK */ 865 } /* each unit */ 866 /* [here uc-1 is the msu of the result] */ 867 res->digits=decGetDigits(res->lsu, uc-res->lsu); 868 res->exponent=0; /* integer */ 869 res->bits=0; /* sign=0 */ 870 return res; /* [no status to set] */ 871 } /* decNumberAnd */ 872 873/* ------------------------------------------------------------------ */ 874/* decNumberCompare -- compare two Numbers */ 875/* */ 876/* This computes C = A ? B */ 877/* */ 878/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ 879/* lhs is A */ 880/* rhs is B */ 881/* set is the context */ 882/* */ 883/* C must have space for one digit (or NaN). */ 884/* ------------------------------------------------------------------ */ 885U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompare(decNumber *res, const decNumber *lhs, 886 const decNumber *rhs, decContext *set) { 887 uInt status=0; /* accumulator */ 888 decCompareOp(res, lhs, rhs, set, COMPARE, &status); 889 if (status!=0) decStatus(res, status, set); 890 return res; 891 } /* decNumberCompare */ 892 893/* ------------------------------------------------------------------ */ 894/* decNumberCompareSignal -- compare, signalling on all NaNs */ 895/* */ 896/* This computes C = A ? B */ 897/* */ 898/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ 899/* lhs is A */ 900/* rhs is B */ 901/* set is the context */ 902/* */ 903/* C must have space for one digit (or NaN). */ 904/* ------------------------------------------------------------------ */ 905U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompareSignal(decNumber *res, const decNumber *lhs, 906 const decNumber *rhs, decContext *set) { 907 uInt status=0; /* accumulator */ 908 decCompareOp(res, lhs, rhs, set, COMPSIG, &status); 909 if (status!=0) decStatus(res, status, set); 910 return res; 911 } /* decNumberCompareSignal */ 912 913/* ------------------------------------------------------------------ */ 914/* decNumberCompareTotal -- compare two Numbers, using total ordering */ 915/* */ 916/* This computes C = A ? B, under total ordering */ 917/* */ 918/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ 919/* lhs is A */ 920/* rhs is B */ 921/* set is the context */ 922/* */ 923/* C must have space for one digit; the result will always be one of */ 924/* -1, 0, or 1. */ 925/* ------------------------------------------------------------------ */ 926U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompareTotal(decNumber *res, const decNumber *lhs, 927 const decNumber *rhs, decContext *set) { 928 uInt status=0; /* accumulator */ 929 decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status); 930 if (status!=0) decStatus(res, status, set); 931 return res; 932 } /* decNumberCompareTotal */ 933 934/* ------------------------------------------------------------------ */ 935/* decNumberCompareTotalMag -- compare, total ordering of magnitudes */ 936/* */ 937/* This computes C = |A| ? |B|, under total ordering */ 938/* */ 939/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ 940/* lhs is A */ 941/* rhs is B */ 942/* set is the context */ 943/* */ 944/* C must have space for one digit; the result will always be one of */ 945/* -1, 0, or 1. */ 946/* ------------------------------------------------------------------ */ 947U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompareTotalMag(decNumber *res, const decNumber *lhs, 948 const decNumber *rhs, decContext *set) { 949 uInt status=0; /* accumulator */ 950 uInt needbytes; /* for space calculations */ 951 decNumber bufa[D2N(DECBUFFER+1)];/* +1 in case DECBUFFER=0 */ 952 decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ 953 decNumber bufb[D2N(DECBUFFER+1)]; 954 decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */ 955 decNumber *a, *b; /* temporary pointers */ 956 957 #if DECCHECK 958 if (decCheckOperands(res, lhs, rhs, set)) return res; 959 #endif 960 961 do { /* protect allocated storage */ 962 /* if either is negative, take a copy and absolute */ 963 if (decNumberIsNegative(lhs)) { /* lhs<0 */ 964 a=bufa; 965 needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit); 966 if (needbytes>sizeof(bufa)) { /* need malloc space */ 967 allocbufa=(decNumber *)malloc(needbytes); 968 if (allocbufa==NULL) { /* hopeless -- abandon */ 969 status|=DEC_Insufficient_storage; 970 break;} 971 a=allocbufa; /* use the allocated space */ 972 } 973 uprv_decNumberCopy(a, lhs); /* copy content */ 974 a->bits&=~DECNEG; /* .. and clear the sign */ 975 lhs=a; /* use copy from here on */ 976 } 977 if (decNumberIsNegative(rhs)) { /* rhs<0 */ 978 b=bufb; 979 needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); 980 if (needbytes>sizeof(bufb)) { /* need malloc space */ 981 allocbufb=(decNumber *)malloc(needbytes); 982 if (allocbufb==NULL) { /* hopeless -- abandon */ 983 status|=DEC_Insufficient_storage; 984 break;} 985 b=allocbufb; /* use the allocated space */ 986 } 987 uprv_decNumberCopy(b, rhs); /* copy content */ 988 b->bits&=~DECNEG; /* .. and clear the sign */ 989 rhs=b; /* use copy from here on */ 990 } 991 decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status); 992 } while(0); /* end protected */ 993 994 if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ 995 if (allocbufb!=NULL) free(allocbufb); /* .. */ 996 if (status!=0) decStatus(res, status, set); 997 return res; 998 } /* decNumberCompareTotalMag */ 999 1000/* ------------------------------------------------------------------ */ 1001/* decNumberDivide -- divide one number by another */ 1002/* */ 1003/* This computes C = A / B */ 1004/* */ 1005/* res is C, the result. C may be A and/or B (e.g., X=X/X) */ 1006/* lhs is A */ 1007/* rhs is B */ 1008/* set is the context */ 1009/* */ 1010/* C must have space for set->digits digits. */ 1011/* ------------------------------------------------------------------ */ 1012U_CAPI decNumber * U_EXPORT2 uprv_decNumberDivide(decNumber *res, const decNumber *lhs, 1013 const decNumber *rhs, decContext *set) { 1014 uInt status=0; /* accumulator */ 1015 decDivideOp(res, lhs, rhs, set, DIVIDE, &status); 1016 if (status!=0) decStatus(res, status, set); 1017 #if DECCHECK 1018 decCheckInexact(res, set); 1019 #endif 1020 return res; 1021 } /* decNumberDivide */ 1022 1023/* ------------------------------------------------------------------ */ 1024/* decNumberDivideInteger -- divide and return integer quotient */ 1025/* */ 1026/* This computes C = A # B, where # is the integer divide operator */ 1027/* */ 1028/* res is C, the result. C may be A and/or B (e.g., X=X#X) */ 1029/* lhs is A */ 1030/* rhs is B */ 1031/* set is the context */ 1032/* */ 1033/* C must have space for set->digits digits. */ 1034/* ------------------------------------------------------------------ */ 1035U_CAPI decNumber * U_EXPORT2 uprv_decNumberDivideInteger(decNumber *res, const decNumber *lhs, 1036 const decNumber *rhs, decContext *set) { 1037 uInt status=0; /* accumulator */ 1038 decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status); 1039 if (status!=0) decStatus(res, status, set); 1040 return res; 1041 } /* decNumberDivideInteger */ 1042 1043/* ------------------------------------------------------------------ */ 1044/* decNumberExp -- exponentiation */ 1045/* */ 1046/* This computes C = exp(A) */ 1047/* */ 1048/* res is C, the result. C may be A */ 1049/* rhs is A */ 1050/* set is the context; note that rounding mode has no effect */ 1051/* */ 1052/* C must have space for set->digits digits. */ 1053/* */ 1054/* Mathematical function restrictions apply (see above); a NaN is */ 1055/* returned with Invalid_operation if a restriction is violated. */ 1056/* */ 1057/* Finite results will always be full precision and Inexact, except */ 1058/* when A is a zero or -Infinity (giving 1 or 0 respectively). */ 1059/* */ 1060/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ 1061/* almost always be correctly rounded, but may be up to 1 ulp in */ 1062/* error in rare cases. */ 1063/* ------------------------------------------------------------------ */ 1064/* This is a wrapper for decExpOp which can handle the slightly wider */ 1065/* (double) range needed by Ln (which has to be able to calculate */ 1066/* exp(-a) where a can be the tiniest number (Ntiny). */ 1067/* ------------------------------------------------------------------ */ 1068U_CAPI decNumber * U_EXPORT2 uprv_decNumberExp(decNumber *res, const decNumber *rhs, 1069 decContext *set) { 1070 uInt status=0; /* accumulator */ 1071 #if DECSUBSET 1072 decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ 1073 #endif 1074 1075 #if DECCHECK 1076 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 1077 #endif 1078 1079 /* Check restrictions; these restrictions ensure that if h=8 (see */ 1080 /* decExpOp) then the result will either overflow or underflow to 0. */ 1081 /* Other math functions restrict the input range, too, for inverses. */ 1082 /* If not violated then carry out the operation. */ 1083 if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */ 1084 #if DECSUBSET 1085 if (!set->extended) { 1086 /* reduce operand and set lostDigits status, as needed */ 1087 if (rhs->digits>set->digits) { 1088 allocrhs=decRoundOperand(rhs, set, &status); 1089 if (allocrhs==NULL) break; 1090 rhs=allocrhs; 1091 } 1092 } 1093 #endif 1094 decExpOp(res, rhs, set, &status); 1095 } while(0); /* end protected */ 1096 1097 #if DECSUBSET 1098 if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */ 1099 #endif 1100 /* apply significant status */ 1101 if (status!=0) decStatus(res, status, set); 1102 #if DECCHECK 1103 decCheckInexact(res, set); 1104 #endif 1105 return res; 1106 } /* decNumberExp */ 1107 1108/* ------------------------------------------------------------------ */ 1109/* decNumberFMA -- fused multiply add */ 1110/* */ 1111/* This computes D = (A * B) + C with only one rounding */ 1112/* */ 1113/* res is D, the result. D may be A or B or C (e.g., X=FMA(X,X,X)) */ 1114/* lhs is A */ 1115/* rhs is B */ 1116/* fhs is C [far hand side] */ 1117/* set is the context */ 1118/* */ 1119/* Mathematical function restrictions apply (see above); a NaN is */ 1120/* returned with Invalid_operation if a restriction is violated. */ 1121/* */ 1122/* C must have space for set->digits digits. */ 1123/* ------------------------------------------------------------------ */ 1124U_CAPI decNumber * U_EXPORT2 uprv_decNumberFMA(decNumber *res, const decNumber *lhs, 1125 const decNumber *rhs, const decNumber *fhs, 1126 decContext *set) { 1127 uInt status=0; /* accumulator */ 1128 decContext dcmul; /* context for the multiplication */ 1129 uInt needbytes; /* for space calculations */ 1130 decNumber bufa[D2N(DECBUFFER*2+1)]; 1131 decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ 1132 decNumber *acc; /* accumulator pointer */ 1133 decNumber dzero; /* work */ 1134 1135 #if DECCHECK 1136 if (decCheckOperands(res, lhs, rhs, set)) return res; 1137 if (decCheckOperands(res, fhs, DECUNUSED, set)) return res; 1138 #endif 1139 1140 do { /* protect allocated storage */ 1141 #if DECSUBSET 1142 if (!set->extended) { /* [undefined if subset] */ 1143 status|=DEC_Invalid_operation; 1144 break;} 1145 #endif 1146 /* Check math restrictions [these ensure no overflow or underflow] */ 1147 if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status)) 1148 || (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status)) 1149 || (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break; 1150 /* set up context for multiply */ 1151 dcmul=*set; 1152 dcmul.digits=lhs->digits+rhs->digits; /* just enough */ 1153 /* [The above may be an over-estimate for subset arithmetic, but that's OK] */ 1154 dcmul.emax=DEC_MAX_EMAX; /* effectively unbounded .. */ 1155 dcmul.emin=DEC_MIN_EMIN; /* [thanks to Math restrictions] */ 1156 /* set up decNumber space to receive the result of the multiply */ 1157 acc=bufa; /* may fit */ 1158 needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit); 1159 if (needbytes>sizeof(bufa)) { /* need malloc space */ 1160 allocbufa=(decNumber *)malloc(needbytes); 1161 if (allocbufa==NULL) { /* hopeless -- abandon */ 1162 status|=DEC_Insufficient_storage; 1163 break;} 1164 acc=allocbufa; /* use the allocated space */ 1165 } 1166 /* multiply with extended range and necessary precision */ 1167 /*printf("emin=%ld\n", dcmul.emin); */ 1168 decMultiplyOp(acc, lhs, rhs, &dcmul, &status); 1169 /* Only Invalid operation (from sNaN or Inf * 0) is possible in */ 1170 /* status; if either is seen than ignore fhs (in case it is */ 1171 /* another sNaN) and set acc to NaN unless we had an sNaN */ 1172 /* [decMultiplyOp leaves that to caller] */ 1173 /* Note sNaN has to go through addOp to shorten payload if */ 1174 /* necessary */ 1175 if ((status&DEC_Invalid_operation)!=0) { 1176 if (!(status&DEC_sNaN)) { /* but be true invalid */ 1177 uprv_decNumberZero(res); /* acc not yet set */ 1178 res->bits=DECNAN; 1179 break; 1180 } 1181 uprv_decNumberZero(&dzero); /* make 0 (any non-NaN would do) */ 1182 fhs=&dzero; /* use that */ 1183 } 1184 #if DECCHECK 1185 else { /* multiply was OK */ 1186 if (status!=0) printf("Status=%08lx after FMA multiply\n", (LI)status); 1187 } 1188 #endif 1189 /* add the third operand and result -> res, and all is done */ 1190 decAddOp(res, acc, fhs, set, 0, &status); 1191 } while(0); /* end protected */ 1192 1193 if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ 1194 if (status!=0) decStatus(res, status, set); 1195 #if DECCHECK 1196 decCheckInexact(res, set); 1197 #endif 1198 return res; 1199 } /* decNumberFMA */ 1200 1201/* ------------------------------------------------------------------ */ 1202/* decNumberInvert -- invert a Number, digitwise */ 1203/* */ 1204/* This computes C = ~A */ 1205/* */ 1206/* res is C, the result. C may be A (e.g., X=~X) */ 1207/* rhs is A */ 1208/* set is the context (used for result length and error report) */ 1209/* */ 1210/* C must have space for set->digits digits. */ 1211/* */ 1212/* Logical function restrictions apply (see above); a NaN is */ 1213/* returned with Invalid_operation if a restriction is violated. */ 1214/* ------------------------------------------------------------------ */ 1215U_CAPI decNumber * U_EXPORT2 uprv_decNumberInvert(decNumber *res, const decNumber *rhs, 1216 decContext *set) { 1217 const Unit *ua, *msua; /* -> operand and its msu */ 1218 Unit *uc, *msuc; /* -> result and its msu */ 1219 Int msudigs; /* digits in res msu */ 1220 #if DECCHECK 1221 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 1222 #endif 1223 1224 if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { 1225 decStatus(res, DEC_Invalid_operation, set); 1226 return res; 1227 } 1228 /* operand is valid */ 1229 ua=rhs->lsu; /* bottom-up */ 1230 uc=res->lsu; /* .. */ 1231 msua=ua+D2U(rhs->digits)-1; /* -> msu of rhs */ 1232 msuc=uc+D2U(set->digits)-1; /* -> msu of result */ 1233 msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ 1234 for (; uc<=msuc; ua++, uc++) { /* Unit loop */ 1235 Unit a; /* extract unit */ 1236 Int i, j; /* work */ 1237 if (ua>msua) a=0; 1238 else a=*ua; 1239 *uc=0; /* can now write back */ 1240 /* always need to examine all bits in rhs */ 1241 /* This loop could be unrolled and/or use BIN2BCD tables */ 1242 for (i=0; i<DECDPUN; i++) { 1243 if ((~a)&1) *uc=*uc+(Unit)powers[i]; /* effect INVERT */ 1244 j=a%10; 1245 a=a/10; 1246 if (j>1) { 1247 decStatus(res, DEC_Invalid_operation, set); 1248 return res; 1249 } 1250 if (uc==msuc && i==msudigs-1) break; /* just did final digit */ 1251 } /* each digit */ 1252 } /* each unit */ 1253 /* [here uc-1 is the msu of the result] */ 1254 res->digits=decGetDigits(res->lsu, uc-res->lsu); 1255 res->exponent=0; /* integer */ 1256 res->bits=0; /* sign=0 */ 1257 return res; /* [no status to set] */ 1258 } /* decNumberInvert */ 1259 1260/* ------------------------------------------------------------------ */ 1261/* decNumberLn -- natural logarithm */ 1262/* */ 1263/* This computes C = ln(A) */ 1264/* */ 1265/* res is C, the result. C may be A */ 1266/* rhs is A */ 1267/* set is the context; note that rounding mode has no effect */ 1268/* */ 1269/* C must have space for set->digits digits. */ 1270/* */ 1271/* Notable cases: */ 1272/* A<0 -> Invalid */ 1273/* A=0 -> -Infinity (Exact) */ 1274/* A=+Infinity -> +Infinity (Exact) */ 1275/* A=1 exactly -> 0 (Exact) */ 1276/* */ 1277/* Mathematical function restrictions apply (see above); a NaN is */ 1278/* returned with Invalid_operation if a restriction is violated. */ 1279/* */ 1280/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ 1281/* almost always be correctly rounded, but may be up to 1 ulp in */ 1282/* error in rare cases. */ 1283/* ------------------------------------------------------------------ */ 1284/* This is a wrapper for decLnOp which can handle the slightly wider */ 1285/* (+11) range needed by Ln, Log10, etc. (which may have to be able */ 1286/* to calculate at p+e+2). */ 1287/* ------------------------------------------------------------------ */ 1288U_CAPI decNumber * U_EXPORT2 uprv_decNumberLn(decNumber *res, const decNumber *rhs, 1289 decContext *set) { 1290 uInt status=0; /* accumulator */ 1291 #if DECSUBSET 1292 decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ 1293 #endif 1294 1295 #if DECCHECK 1296 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 1297 #endif 1298 1299 /* Check restrictions; this is a math function; if not violated */ 1300 /* then carry out the operation. */ 1301 if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */ 1302 #if DECSUBSET 1303 if (!set->extended) { 1304 /* reduce operand and set lostDigits status, as needed */ 1305 if (rhs->digits>set->digits) { 1306 allocrhs=decRoundOperand(rhs, set, &status); 1307 if (allocrhs==NULL) break; 1308 rhs=allocrhs; 1309 } 1310 /* special check in subset for rhs=0 */ 1311 if (ISZERO(rhs)) { /* +/- zeros -> error */ 1312 status|=DEC_Invalid_operation; 1313 break;} 1314 } /* extended=0 */ 1315 #endif 1316 decLnOp(res, rhs, set, &status); 1317 } while(0); /* end protected */ 1318 1319 #if DECSUBSET 1320 if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */ 1321 #endif 1322 /* apply significant status */ 1323 if (status!=0) decStatus(res, status, set); 1324 #if DECCHECK 1325 decCheckInexact(res, set); 1326 #endif 1327 return res; 1328 } /* decNumberLn */ 1329 1330/* ------------------------------------------------------------------ */ 1331/* decNumberLogB - get adjusted exponent, by 754 rules */ 1332/* */ 1333/* This computes C = adjustedexponent(A) */ 1334/* */ 1335/* res is C, the result. C may be A */ 1336/* rhs is A */ 1337/* set is the context, used only for digits and status */ 1338/* */ 1339/* C must have space for 10 digits (A might have 10**9 digits and */ 1340/* an exponent of +999999999, or one digit and an exponent of */ 1341/* -1999999999). */ 1342/* */ 1343/* This returns the adjusted exponent of A after (in theory) padding */ 1344/* with zeros on the right to set->digits digits while keeping the */ 1345/* same value. The exponent is not limited by emin/emax. */ 1346/* */ 1347/* Notable cases: */ 1348/* A<0 -> Use |A| */ 1349/* A=0 -> -Infinity (Division by zero) */ 1350/* A=Infinite -> +Infinity (Exact) */ 1351/* A=1 exactly -> 0 (Exact) */ 1352/* NaNs are propagated as usual */ 1353/* ------------------------------------------------------------------ */ 1354U_CAPI decNumber * U_EXPORT2 uprv_decNumberLogB(decNumber *res, const decNumber *rhs, 1355 decContext *set) { 1356 uInt status=0; /* accumulator */ 1357 1358 #if DECCHECK 1359 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 1360 #endif 1361 1362 /* NaNs as usual; Infinities return +Infinity; 0->oops */ 1363 if (decNumberIsNaN(rhs)) decNaNs(res, rhs, NULL, set, &status); 1364 else if (decNumberIsInfinite(rhs)) uprv_decNumberCopyAbs(res, rhs); 1365 else if (decNumberIsZero(rhs)) { 1366 uprv_decNumberZero(res); /* prepare for Infinity */ 1367 res->bits=DECNEG|DECINF; /* -Infinity */ 1368 status|=DEC_Division_by_zero; /* as per 754 */ 1369 } 1370 else { /* finite non-zero */ 1371 Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */ 1372 uprv_decNumberFromInt32(res, ae); /* lay it out */ 1373 } 1374 1375 if (status!=0) decStatus(res, status, set); 1376 return res; 1377 } /* decNumberLogB */ 1378 1379/* ------------------------------------------------------------------ */ 1380/* decNumberLog10 -- logarithm in base 10 */ 1381/* */ 1382/* This computes C = log10(A) */ 1383/* */ 1384/* res is C, the result. C may be A */ 1385/* rhs is A */ 1386/* set is the context; note that rounding mode has no effect */ 1387/* */ 1388/* C must have space for set->digits digits. */ 1389/* */ 1390/* Notable cases: */ 1391/* A<0 -> Invalid */ 1392/* A=0 -> -Infinity (Exact) */ 1393/* A=+Infinity -> +Infinity (Exact) */ 1394/* A=10**n (if n is an integer) -> n (Exact) */ 1395/* */ 1396/* Mathematical function restrictions apply (see above); a NaN is */ 1397/* returned with Invalid_operation if a restriction is violated. */ 1398/* */ 1399/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ 1400/* almost always be correctly rounded, but may be up to 1 ulp in */ 1401/* error in rare cases. */ 1402/* ------------------------------------------------------------------ */ 1403/* This calculates ln(A)/ln(10) using appropriate precision. For */ 1404/* ln(A) this is the max(p, rhs->digits + t) + 3, where p is the */ 1405/* requested digits and t is the number of digits in the exponent */ 1406/* (maximum 6). For ln(10) it is p + 3; this is often handled by the */ 1407/* fastpath in decLnOp. The final division is done to the requested */ 1408/* precision. */ 1409/* ------------------------------------------------------------------ */ 1410#if defined(__clang__) || U_GCC_MAJOR_MINOR >= 406 1411#pragma GCC diagnostic push 1412#pragma GCC diagnostic ignored "-Warray-bounds" 1413#endif 1414U_CAPI decNumber * U_EXPORT2 uprv_decNumberLog10(decNumber *res, const decNumber *rhs, 1415 decContext *set) { 1416 uInt status=0, ignore=0; /* status accumulators */ 1417 uInt needbytes; /* for space calculations */ 1418 Int p; /* working precision */ 1419 Int t; /* digits in exponent of A */ 1420 1421 /* buffers for a and b working decimals */ 1422 /* (adjustment calculator, same size) */ 1423 decNumber bufa[D2N(DECBUFFER+2)]; 1424 decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ 1425 decNumber *a=bufa; /* temporary a */ 1426 decNumber bufb[D2N(DECBUFFER+2)]; 1427 decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */ 1428 decNumber *b=bufb; /* temporary b */ 1429 decNumber bufw[D2N(10)]; /* working 2-10 digit number */ 1430 decNumber *w=bufw; /* .. */ 1431 #if DECSUBSET 1432 decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ 1433 #endif 1434 1435 decContext aset; /* working context */ 1436 1437 #if DECCHECK 1438 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 1439 #endif 1440 1441 /* Check restrictions; this is a math function; if not violated */ 1442 /* then carry out the operation. */ 1443 if (!decCheckMath(rhs, set, &status)) do { /* protect malloc */ 1444 #if DECSUBSET 1445 if (!set->extended) { 1446 /* reduce operand and set lostDigits status, as needed */ 1447 if (rhs->digits>set->digits) { 1448 allocrhs=decRoundOperand(rhs, set, &status); 1449 if (allocrhs==NULL) break; 1450 rhs=allocrhs; 1451 } 1452 /* special check in subset for rhs=0 */ 1453 if (ISZERO(rhs)) { /* +/- zeros -> error */ 1454 status|=DEC_Invalid_operation; 1455 break;} 1456 } /* extended=0 */ 1457 #endif 1458 1459 uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */ 1460 1461 /* handle exact powers of 10; only check if +ve finite */ 1462 if (!(rhs->bits&(DECNEG|DECSPECIAL)) && !ISZERO(rhs)) { 1463 Int residue=0; /* (no residue) */ 1464 uInt copystat=0; /* clean status */ 1465 1466 /* round to a single digit... */ 1467 aset.digits=1; 1468 decCopyFit(w, rhs, &aset, &residue, ©stat); /* copy & shorten */ 1469 /* if exact and the digit is 1, rhs is a power of 10 */ 1470 if (!(copystat&DEC_Inexact) && w->lsu[0]==1) { 1471 /* the exponent, conveniently, is the power of 10; making */ 1472 /* this the result needs a little care as it might not fit, */ 1473 /* so first convert it into the working number, and then move */ 1474 /* to res */ 1475 uprv_decNumberFromInt32(w, w->exponent); 1476 residue=0; 1477 decCopyFit(res, w, set, &residue, &status); /* copy & round */ 1478 decFinish(res, set, &residue, &status); /* cleanup/set flags */ 1479 break; 1480 } /* not a power of 10 */ 1481 } /* not a candidate for exact */ 1482 1483 /* simplify the information-content calculation to use 'total */ 1484 /* number of digits in a, including exponent' as compared to the */ 1485 /* requested digits, as increasing this will only rarely cost an */ 1486 /* iteration in ln(a) anyway */ 1487 t=6; /* it can never be >6 */ 1488 1489 /* allocate space when needed... */ 1490 p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3; 1491 needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit); 1492 if (needbytes>sizeof(bufa)) { /* need malloc space */ 1493 allocbufa=(decNumber *)malloc(needbytes); 1494 if (allocbufa==NULL) { /* hopeless -- abandon */ 1495 status|=DEC_Insufficient_storage; 1496 break;} 1497 a=allocbufa; /* use the allocated space */ 1498 } 1499 aset.digits=p; /* as calculated */ 1500 aset.emax=DEC_MAX_MATH; /* usual bounds */ 1501 aset.emin=-DEC_MAX_MATH; /* .. */ 1502 aset.clamp=0; /* and no concrete format */ 1503 decLnOp(a, rhs, &aset, &status); /* a=ln(rhs) */ 1504 1505 /* skip the division if the result so far is infinite, NaN, or */ 1506 /* zero, or there was an error; note NaN from sNaN needs copy */ 1507 if (status&DEC_NaNs && !(status&DEC_sNaN)) break; 1508 if (a->bits&DECSPECIAL || ISZERO(a)) { 1509 uprv_decNumberCopy(res, a); /* [will fit] */ 1510 break;} 1511 1512 /* for ln(10) an extra 3 digits of precision are needed */ 1513 p=set->digits+3; 1514 needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit); 1515 if (needbytes>sizeof(bufb)) { /* need malloc space */ 1516 allocbufb=(decNumber *)malloc(needbytes); 1517 if (allocbufb==NULL) { /* hopeless -- abandon */ 1518 status|=DEC_Insufficient_storage; 1519 break;} 1520 b=allocbufb; /* use the allocated space */ 1521 } 1522 uprv_decNumberZero(w); /* set up 10... */ 1523 #if DECDPUN==1 1524 w->lsu[1]=1; w->lsu[0]=0; /* .. */ 1525 #else 1526 w->lsu[0]=10; /* .. */ 1527 #endif 1528 w->digits=2; /* .. */ 1529 1530 aset.digits=p; 1531 decLnOp(b, w, &aset, &ignore); /* b=ln(10) */ 1532 1533 aset.digits=set->digits; /* for final divide */ 1534 decDivideOp(res, a, b, &aset, DIVIDE, &status); /* into result */ 1535 } while(0); /* [for break] */ 1536 1537 if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ 1538 if (allocbufb!=NULL) free(allocbufb); /* .. */ 1539 #if DECSUBSET 1540 if (allocrhs !=NULL) free(allocrhs); /* .. */ 1541 #endif 1542 /* apply significant status */ 1543 if (status!=0) decStatus(res, status, set); 1544 #if DECCHECK 1545 decCheckInexact(res, set); 1546 #endif 1547 return res; 1548 } /* decNumberLog10 */ 1549#if defined(__clang__) || U_GCC_MAJOR_MINOR >= 406 1550#pragma GCC diagnostic pop 1551#endif 1552 1553/* ------------------------------------------------------------------ */ 1554/* decNumberMax -- compare two Numbers and return the maximum */ 1555/* */ 1556/* This computes C = A ? B, returning the maximum by 754 rules */ 1557/* */ 1558/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ 1559/* lhs is A */ 1560/* rhs is B */ 1561/* set is the context */ 1562/* */ 1563/* C must have space for set->digits digits. */ 1564/* ------------------------------------------------------------------ */ 1565U_CAPI decNumber * U_EXPORT2 uprv_decNumberMax(decNumber *res, const decNumber *lhs, 1566 const decNumber *rhs, decContext *set) { 1567 uInt status=0; /* accumulator */ 1568 decCompareOp(res, lhs, rhs, set, COMPMAX, &status); 1569 if (status!=0) decStatus(res, status, set); 1570 #if DECCHECK 1571 decCheckInexact(res, set); 1572 #endif 1573 return res; 1574 } /* decNumberMax */ 1575 1576/* ------------------------------------------------------------------ */ 1577/* decNumberMaxMag -- compare and return the maximum by magnitude */ 1578/* */ 1579/* This computes C = A ? B, returning the maximum by 754 rules */ 1580/* */ 1581/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ 1582/* lhs is A */ 1583/* rhs is B */ 1584/* set is the context */ 1585/* */ 1586/* C must have space for set->digits digits. */ 1587/* ------------------------------------------------------------------ */ 1588U_CAPI decNumber * U_EXPORT2 uprv_decNumberMaxMag(decNumber *res, const decNumber *lhs, 1589 const decNumber *rhs, decContext *set) { 1590 uInt status=0; /* accumulator */ 1591 decCompareOp(res, lhs, rhs, set, COMPMAXMAG, &status); 1592 if (status!=0) decStatus(res, status, set); 1593 #if DECCHECK 1594 decCheckInexact(res, set); 1595 #endif 1596 return res; 1597 } /* decNumberMaxMag */ 1598 1599/* ------------------------------------------------------------------ */ 1600/* decNumberMin -- compare two Numbers and return the minimum */ 1601/* */ 1602/* This computes C = A ? B, returning the minimum by 754 rules */ 1603/* */ 1604/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ 1605/* lhs is A */ 1606/* rhs is B */ 1607/* set is the context */ 1608/* */ 1609/* C must have space for set->digits digits. */ 1610/* ------------------------------------------------------------------ */ 1611U_CAPI decNumber * U_EXPORT2 uprv_decNumberMin(decNumber *res, const decNumber *lhs, 1612 const decNumber *rhs, decContext *set) { 1613 uInt status=0; /* accumulator */ 1614 decCompareOp(res, lhs, rhs, set, COMPMIN, &status); 1615 if (status!=0) decStatus(res, status, set); 1616 #if DECCHECK 1617 decCheckInexact(res, set); 1618 #endif 1619 return res; 1620 } /* decNumberMin */ 1621 1622/* ------------------------------------------------------------------ */ 1623/* decNumberMinMag -- compare and return the minimum by magnitude */ 1624/* */ 1625/* This computes C = A ? B, returning the minimum by 754 rules */ 1626/* */ 1627/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ 1628/* lhs is A */ 1629/* rhs is B */ 1630/* set is the context */ 1631/* */ 1632/* C must have space for set->digits digits. */ 1633/* ------------------------------------------------------------------ */ 1634U_CAPI decNumber * U_EXPORT2 uprv_decNumberMinMag(decNumber *res, const decNumber *lhs, 1635 const decNumber *rhs, decContext *set) { 1636 uInt status=0; /* accumulator */ 1637 decCompareOp(res, lhs, rhs, set, COMPMINMAG, &status); 1638 if (status!=0) decStatus(res, status, set); 1639 #if DECCHECK 1640 decCheckInexact(res, set); 1641 #endif 1642 return res; 1643 } /* decNumberMinMag */ 1644 1645/* ------------------------------------------------------------------ */ 1646/* decNumberMinus -- prefix minus operator */ 1647/* */ 1648/* This computes C = 0 - A */ 1649/* */ 1650/* res is C, the result. C may be A */ 1651/* rhs is A */ 1652/* set is the context */ 1653/* */ 1654/* See also decNumberCopyNegate for a quiet bitwise version of this. */ 1655/* C must have space for set->digits digits. */ 1656/* ------------------------------------------------------------------ */ 1657/* Simply use AddOp for the subtract, which will do the necessary. */ 1658/* ------------------------------------------------------------------ */ 1659U_CAPI decNumber * U_EXPORT2 uprv_decNumberMinus(decNumber *res, const decNumber *rhs, 1660 decContext *set) { 1661 decNumber dzero; 1662 uInt status=0; /* accumulator */ 1663 1664 #if DECCHECK 1665 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 1666 #endif 1667 1668 uprv_decNumberZero(&dzero); /* make 0 */ 1669 dzero.exponent=rhs->exponent; /* [no coefficient expansion] */ 1670 decAddOp(res, &dzero, rhs, set, DECNEG, &status); 1671 if (status!=0) decStatus(res, status, set); 1672 #if DECCHECK 1673 decCheckInexact(res, set); 1674 #endif 1675 return res; 1676 } /* decNumberMinus */ 1677 1678/* ------------------------------------------------------------------ */ 1679/* decNumberNextMinus -- next towards -Infinity */ 1680/* */ 1681/* This computes C = A - infinitesimal, rounded towards -Infinity */ 1682/* */ 1683/* res is C, the result. C may be A */ 1684/* rhs is A */ 1685/* set is the context */ 1686/* */ 1687/* This is a generalization of 754 NextDown. */ 1688/* ------------------------------------------------------------------ */ 1689U_CAPI decNumber * U_EXPORT2 uprv_decNumberNextMinus(decNumber *res, const decNumber *rhs, 1690 decContext *set) { 1691 decNumber dtiny; /* constant */ 1692 decContext workset=*set; /* work */ 1693 uInt status=0; /* accumulator */ 1694 #if DECCHECK 1695 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 1696 #endif 1697 1698 /* +Infinity is the special case */ 1699 if ((rhs->bits&(DECINF|DECNEG))==DECINF) { 1700 decSetMaxValue(res, set); /* is +ve */ 1701 /* there is no status to set */ 1702 return res; 1703 } 1704 uprv_decNumberZero(&dtiny); /* start with 0 */ 1705 dtiny.lsu[0]=1; /* make number that is .. */ 1706 dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */ 1707 workset.round=DEC_ROUND_FLOOR; 1708 decAddOp(res, rhs, &dtiny, &workset, DECNEG, &status); 1709 status&=DEC_Invalid_operation|DEC_sNaN; /* only sNaN Invalid please */ 1710 if (status!=0) decStatus(res, status, set); 1711 return res; 1712 } /* decNumberNextMinus */ 1713 1714/* ------------------------------------------------------------------ */ 1715/* decNumberNextPlus -- next towards +Infinity */ 1716/* */ 1717/* This computes C = A + infinitesimal, rounded towards +Infinity */ 1718/* */ 1719/* res is C, the result. C may be A */ 1720/* rhs is A */ 1721/* set is the context */ 1722/* */ 1723/* This is a generalization of 754 NextUp. */ 1724/* ------------------------------------------------------------------ */ 1725U_CAPI decNumber * U_EXPORT2 uprv_decNumberNextPlus(decNumber *res, const decNumber *rhs, 1726 decContext *set) { 1727 decNumber dtiny; /* constant */ 1728 decContext workset=*set; /* work */ 1729 uInt status=0; /* accumulator */ 1730 #if DECCHECK 1731 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 1732 #endif 1733 1734 /* -Infinity is the special case */ 1735 if ((rhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) { 1736 decSetMaxValue(res, set); 1737 res->bits=DECNEG; /* negative */ 1738 /* there is no status to set */ 1739 return res; 1740 } 1741 uprv_decNumberZero(&dtiny); /* start with 0 */ 1742 dtiny.lsu[0]=1; /* make number that is .. */ 1743 dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */ 1744 workset.round=DEC_ROUND_CEILING; 1745 decAddOp(res, rhs, &dtiny, &workset, 0, &status); 1746 status&=DEC_Invalid_operation|DEC_sNaN; /* only sNaN Invalid please */ 1747 if (status!=0) decStatus(res, status, set); 1748 return res; 1749 } /* decNumberNextPlus */ 1750 1751/* ------------------------------------------------------------------ */ 1752/* decNumberNextToward -- next towards rhs */ 1753/* */ 1754/* This computes C = A +/- infinitesimal, rounded towards */ 1755/* +/-Infinity in the direction of B, as per 754-1985 nextafter */ 1756/* modified during revision but dropped from 754-2008. */ 1757/* */ 1758/* res is C, the result. C may be A or B. */ 1759/* lhs is A */ 1760/* rhs is B */ 1761/* set is the context */ 1762/* */ 1763/* This is a generalization of 754-1985 NextAfter. */ 1764/* ------------------------------------------------------------------ */ 1765U_CAPI decNumber * U_EXPORT2 uprv_decNumberNextToward(decNumber *res, const decNumber *lhs, 1766 const decNumber *rhs, decContext *set) { 1767 decNumber dtiny; /* constant */ 1768 decContext workset=*set; /* work */ 1769 Int result; /* .. */ 1770 uInt status=0; /* accumulator */ 1771 #if DECCHECK 1772 if (decCheckOperands(res, lhs, rhs, set)) return res; 1773 #endif 1774 1775 if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { 1776 decNaNs(res, lhs, rhs, set, &status); 1777 } 1778 else { /* Is numeric, so no chance of sNaN Invalid, etc. */ 1779 result=decCompare(lhs, rhs, 0); /* sign matters */ 1780 if (result==BADINT) status|=DEC_Insufficient_storage; /* rare */ 1781 else { /* valid compare */ 1782 if (result==0) uprv_decNumberCopySign(res, lhs, rhs); /* easy */ 1783 else { /* differ: need NextPlus or NextMinus */ 1784 uByte sub; /* add or subtract */ 1785 if (result<0) { /* lhs<rhs, do nextplus */ 1786 /* -Infinity is the special case */ 1787 if ((lhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) { 1788 decSetMaxValue(res, set); 1789 res->bits=DECNEG; /* negative */ 1790 return res; /* there is no status to set */ 1791 } 1792 workset.round=DEC_ROUND_CEILING; 1793 sub=0; /* add, please */ 1794 } /* plus */ 1795 else { /* lhs>rhs, do nextminus */ 1796 /* +Infinity is the special case */ 1797 if ((lhs->bits&(DECINF|DECNEG))==DECINF) { 1798 decSetMaxValue(res, set); 1799 return res; /* there is no status to set */ 1800 } 1801 workset.round=DEC_ROUND_FLOOR; 1802 sub=DECNEG; /* subtract, please */ 1803 } /* minus */ 1804 uprv_decNumberZero(&dtiny); /* start with 0 */ 1805 dtiny.lsu[0]=1; /* make number that is .. */ 1806 dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */ 1807 decAddOp(res, lhs, &dtiny, &workset, sub, &status); /* + or - */ 1808 /* turn off exceptions if the result is a normal number */ 1809 /* (including Nmin), otherwise let all status through */ 1810 if (uprv_decNumberIsNormal(res, set)) status=0; 1811 } /* unequal */ 1812 } /* compare OK */ 1813 } /* numeric */ 1814 if (status!=0) decStatus(res, status, set); 1815 return res; 1816 } /* decNumberNextToward */ 1817 1818/* ------------------------------------------------------------------ */ 1819/* decNumberOr -- OR two Numbers, digitwise */ 1820/* */ 1821/* This computes C = A | B */ 1822/* */ 1823/* res is C, the result. C may be A and/or B (e.g., X=X|X) */ 1824/* lhs is A */ 1825/* rhs is B */ 1826/* set is the context (used for result length and error report) */ 1827/* */ 1828/* C must have space for set->digits digits. */ 1829/* */ 1830/* Logical function restrictions apply (see above); a NaN is */ 1831/* returned with Invalid_operation if a restriction is violated. */ 1832/* ------------------------------------------------------------------ */ 1833U_CAPI decNumber * U_EXPORT2 uprv_decNumberOr(decNumber *res, const decNumber *lhs, 1834 const decNumber *rhs, decContext *set) { 1835 const Unit *ua, *ub; /* -> operands */ 1836 const Unit *msua, *msub; /* -> operand msus */ 1837 Unit *uc, *msuc; /* -> result and its msu */ 1838 Int msudigs; /* digits in res msu */ 1839 #if DECCHECK 1840 if (decCheckOperands(res, lhs, rhs, set)) return res; 1841 #endif 1842 1843 if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) 1844 || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { 1845 decStatus(res, DEC_Invalid_operation, set); 1846 return res; 1847 } 1848 /* operands are valid */ 1849 ua=lhs->lsu; /* bottom-up */ 1850 ub=rhs->lsu; /* .. */ 1851 uc=res->lsu; /* .. */ 1852 msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */ 1853 msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */ 1854 msuc=uc+D2U(set->digits)-1; /* -> msu of result */ 1855 msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ 1856 for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */ 1857 Unit a, b; /* extract units */ 1858 if (ua>msua) a=0; 1859 else a=*ua; 1860 if (ub>msub) b=0; 1861 else b=*ub; 1862 *uc=0; /* can now write back */ 1863 if (a|b) { /* maybe 1 bits to examine */ 1864 Int i, j; 1865 /* This loop could be unrolled and/or use BIN2BCD tables */ 1866 for (i=0; i<DECDPUN; i++) { 1867 if ((a|b)&1) *uc=*uc+(Unit)powers[i]; /* effect OR */ 1868 j=a%10; 1869 a=a/10; 1870 j|=b%10; 1871 b=b/10; 1872 if (j>1) { 1873 decStatus(res, DEC_Invalid_operation, set); 1874 return res; 1875 } 1876 if (uc==msuc && i==msudigs-1) break; /* just did final digit */ 1877 } /* each digit */ 1878 } /* non-zero */ 1879 } /* each unit */ 1880 /* [here uc-1 is the msu of the result] */ 1881 res->digits=decGetDigits(res->lsu, uc-res->lsu); 1882 res->exponent=0; /* integer */ 1883 res->bits=0; /* sign=0 */ 1884 return res; /* [no status to set] */ 1885 } /* decNumberOr */ 1886 1887/* ------------------------------------------------------------------ */ 1888/* decNumberPlus -- prefix plus operator */ 1889/* */ 1890/* This computes C = 0 + A */ 1891/* */ 1892/* res is C, the result. C may be A */ 1893/* rhs is A */ 1894/* set is the context */ 1895/* */ 1896/* See also decNumberCopy for a quiet bitwise version of this. */ 1897/* C must have space for set->digits digits. */ 1898/* ------------------------------------------------------------------ */ 1899/* This simply uses AddOp; Add will take fast path after preparing A. */ 1900/* Performance is a concern here, as this routine is often used to */ 1901/* check operands and apply rounding and overflow/underflow testing. */ 1902/* ------------------------------------------------------------------ */ 1903U_CAPI decNumber * U_EXPORT2 uprv_decNumberPlus(decNumber *res, const decNumber *rhs, 1904 decContext *set) { 1905 decNumber dzero; 1906 uInt status=0; /* accumulator */ 1907 #if DECCHECK 1908 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 1909 #endif 1910 1911 uprv_decNumberZero(&dzero); /* make 0 */ 1912 dzero.exponent=rhs->exponent; /* [no coefficient expansion] */ 1913 decAddOp(res, &dzero, rhs, set, 0, &status); 1914 if (status!=0) decStatus(res, status, set); 1915 #if DECCHECK 1916 decCheckInexact(res, set); 1917 #endif 1918 return res; 1919 } /* decNumberPlus */ 1920 1921/* ------------------------------------------------------------------ */ 1922/* decNumberMultiply -- multiply two Numbers */ 1923/* */ 1924/* This computes C = A x B */ 1925/* */ 1926/* res is C, the result. C may be A and/or B (e.g., X=X+X) */ 1927/* lhs is A */ 1928/* rhs is B */ 1929/* set is the context */ 1930/* */ 1931/* C must have space for set->digits digits. */ 1932/* ------------------------------------------------------------------ */ 1933U_CAPI decNumber * U_EXPORT2 uprv_decNumberMultiply(decNumber *res, const decNumber *lhs, 1934 const decNumber *rhs, decContext *set) { 1935 uInt status=0; /* accumulator */ 1936 decMultiplyOp(res, lhs, rhs, set, &status); 1937 if (status!=0) decStatus(res, status, set); 1938 #if DECCHECK 1939 decCheckInexact(res, set); 1940 #endif 1941 return res; 1942 } /* decNumberMultiply */ 1943 1944/* ------------------------------------------------------------------ */ 1945/* decNumberPower -- raise a number to a power */ 1946/* */ 1947/* This computes C = A ** B */ 1948/* */ 1949/* res is C, the result. C may be A and/or B (e.g., X=X**X) */ 1950/* lhs is A */ 1951/* rhs is B */ 1952/* set is the context */ 1953/* */ 1954/* C must have space for set->digits digits. */ 1955/* */ 1956/* Mathematical function restrictions apply (see above); a NaN is */ 1957/* returned with Invalid_operation if a restriction is violated. */ 1958/* */ 1959/* However, if 1999999997<=B<=999999999 and B is an integer then the */ 1960/* restrictions on A and the context are relaxed to the usual bounds, */ 1961/* for compatibility with the earlier (integer power only) version */ 1962/* of this function. */ 1963/* */ 1964/* When B is an integer, the result may be exact, even if rounded. */ 1965/* */ 1966/* The final result is rounded according to the context; it will */ 1967/* almost always be correctly rounded, but may be up to 1 ulp in */ 1968/* error in rare cases. */ 1969/* ------------------------------------------------------------------ */ 1970U_CAPI decNumber * U_EXPORT2 uprv_decNumberPower(decNumber *res, const decNumber *lhs, 1971 const decNumber *rhs, decContext *set) { 1972 #if DECSUBSET 1973 decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ 1974 decNumber *allocrhs=NULL; /* .., rhs */ 1975 #endif 1976 decNumber *allocdac=NULL; /* -> allocated acc buffer, iff used */ 1977 decNumber *allocinv=NULL; /* -> allocated 1/x buffer, iff used */ 1978 Int reqdigits=set->digits; /* requested DIGITS */ 1979 Int n; /* rhs in binary */ 1980 Flag rhsint=0; /* 1 if rhs is an integer */ 1981 Flag useint=0; /* 1 if can use integer calculation */ 1982 Flag isoddint=0; /* 1 if rhs is an integer and odd */ 1983 Int i; /* work */ 1984 #if DECSUBSET 1985 Int dropped; /* .. */ 1986 #endif 1987 uInt needbytes; /* buffer size needed */ 1988 Flag seenbit; /* seen a bit while powering */ 1989 Int residue=0; /* rounding residue */ 1990 uInt status=0; /* accumulators */ 1991 uByte bits=0; /* result sign if errors */ 1992 decContext aset; /* working context */ 1993 decNumber dnOne; /* work value 1... */ 1994 /* local accumulator buffer [a decNumber, with digits+elength+1 digits] */ 1995 decNumber dacbuff[D2N(DECBUFFER+9)]; 1996 decNumber *dac=dacbuff; /* -> result accumulator */ 1997 /* same again for possible 1/lhs calculation */ 1998 decNumber invbuff[D2N(DECBUFFER+9)]; 1999 2000 #if DECCHECK 2001 if (decCheckOperands(res, lhs, rhs, set)) return res; 2002 #endif 2003 2004 do { /* protect allocated storage */ 2005 #if DECSUBSET 2006 if (!set->extended) { /* reduce operands and set status, as needed */ 2007 if (lhs->digits>reqdigits) { 2008 alloclhs=decRoundOperand(lhs, set, &status); 2009 if (alloclhs==NULL) break; 2010 lhs=alloclhs; 2011 } 2012 if (rhs->digits>reqdigits) { 2013 allocrhs=decRoundOperand(rhs, set, &status); 2014 if (allocrhs==NULL) break; 2015 rhs=allocrhs; 2016 } 2017 } 2018 #endif 2019 /* [following code does not require input rounding] */ 2020 2021 /* handle NaNs and rhs Infinity (lhs infinity is harder) */ 2022 if (SPECIALARGS) { 2023 if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { /* NaNs */ 2024 decNaNs(res, lhs, rhs, set, &status); 2025 break;} 2026 if (decNumberIsInfinite(rhs)) { /* rhs Infinity */ 2027 Flag rhsneg=rhs->bits&DECNEG; /* save rhs sign */ 2028 if (decNumberIsNegative(lhs) /* lhs<0 */ 2029 && !decNumberIsZero(lhs)) /* .. */ 2030 status|=DEC_Invalid_operation; 2031 else { /* lhs >=0 */ 2032 uprv_decNumberZero(&dnOne); /* set up 1 */ 2033 dnOne.lsu[0]=1; 2034 uprv_decNumberCompare(dac, lhs, &dnOne, set); /* lhs ? 1 */ 2035 uprv_decNumberZero(res); /* prepare for 0/1/Infinity */ 2036 if (decNumberIsNegative(dac)) { /* lhs<1 */ 2037 if (rhsneg) res->bits|=DECINF; /* +Infinity [else is +0] */ 2038 } 2039 else if (dac->lsu[0]==0) { /* lhs=1 */ 2040 /* 1**Infinity is inexact, so return fully-padded 1.0000 */ 2041 Int shift=set->digits-1; 2042 *res->lsu=1; /* was 0, make int 1 */ 2043 res->digits=decShiftToMost(res->lsu, 1, shift); 2044 res->exponent=-shift; /* make 1.0000... */ 2045 status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */ 2046 } 2047 else { /* lhs>1 */ 2048 if (!rhsneg) res->bits|=DECINF; /* +Infinity [else is +0] */ 2049 } 2050 } /* lhs>=0 */ 2051 break;} 2052 /* [lhs infinity drops through] */ 2053 } /* specials */ 2054 2055 /* Original rhs may be an integer that fits and is in range */ 2056 n=decGetInt(rhs); 2057 if (n!=BADINT) { /* it is an integer */ 2058 rhsint=1; /* record the fact for 1**n */ 2059 isoddint=(Flag)n&1; /* [works even if big] */ 2060 if (n!=BIGEVEN && n!=BIGODD) /* can use integer path? */ 2061 useint=1; /* looks good */ 2062 } 2063 2064 if (decNumberIsNegative(lhs) /* -x .. */ 2065 && isoddint) bits=DECNEG; /* .. to an odd power */ 2066 2067 /* handle LHS infinity */ 2068 if (decNumberIsInfinite(lhs)) { /* [NaNs already handled] */ 2069 uByte rbits=rhs->bits; /* save */ 2070 uprv_decNumberZero(res); /* prepare */ 2071 if (n==0) *res->lsu=1; /* [-]Inf**0 => 1 */ 2072 else { 2073 /* -Inf**nonint -> error */ 2074 if (!rhsint && decNumberIsNegative(lhs)) { 2075 status|=DEC_Invalid_operation; /* -Inf**nonint is error */ 2076 break;} 2077 if (!(rbits & DECNEG)) bits|=DECINF; /* was not a **-n */ 2078 /* [otherwise will be 0 or -0] */ 2079 res->bits=bits; 2080 } 2081 break;} 2082 2083 /* similarly handle LHS zero */ 2084 if (decNumberIsZero(lhs)) { 2085 if (n==0) { /* 0**0 => Error */ 2086 #if DECSUBSET 2087 if (!set->extended) { /* [unless subset] */ 2088 uprv_decNumberZero(res); 2089 *res->lsu=1; /* return 1 */ 2090 break;} 2091 #endif 2092 status|=DEC_Invalid_operation; 2093 } 2094 else { /* 0**x */ 2095 uByte rbits=rhs->bits; /* save */ 2096 if (rbits & DECNEG) { /* was a 0**(-n) */ 2097 #if DECSUBSET 2098 if (!set->extended) { /* [bad if subset] */ 2099 status|=DEC_Invalid_operation; 2100 break;} 2101 #endif 2102 bits|=DECINF; 2103 } 2104 uprv_decNumberZero(res); /* prepare */ 2105 /* [otherwise will be 0 or -0] */ 2106 res->bits=bits; 2107 } 2108 break;} 2109 2110 /* here both lhs and rhs are finite; rhs==0 is handled in the */ 2111 /* integer path. Next handle the non-integer cases */ 2112 if (!useint) { /* non-integral rhs */ 2113 /* any -ve lhs is bad, as is either operand or context out of */ 2114 /* bounds */ 2115 if (decNumberIsNegative(lhs)) { 2116 status|=DEC_Invalid_operation; 2117 break;} 2118 if (decCheckMath(lhs, set, &status) 2119 || decCheckMath(rhs, set, &status)) break; /* variable status */ 2120 2121 uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */ 2122 aset.emax=DEC_MAX_MATH; /* usual bounds */ 2123 aset.emin=-DEC_MAX_MATH; /* .. */ 2124 aset.clamp=0; /* and no concrete format */ 2125 2126 /* calculate the result using exp(ln(lhs)*rhs), which can */ 2127 /* all be done into the accumulator, dac. The precision needed */ 2128 /* is enough to contain the full information in the lhs (which */ 2129 /* is the total digits, including exponent), or the requested */ 2130 /* precision, if larger, + 4; 6 is used for the exponent */ 2131 /* maximum length, and this is also used when it is shorter */ 2132 /* than the requested digits as it greatly reduces the >0.5 ulp */ 2133 /* cases at little cost (because Ln doubles digits each */ 2134 /* iteration so a few extra digits rarely causes an extra */ 2135 /* iteration) */ 2136 aset.digits=MAXI(lhs->digits, set->digits)+6+4; 2137 } /* non-integer rhs */ 2138 2139 else { /* rhs is in-range integer */ 2140 if (n==0) { /* x**0 = 1 */ 2141 /* (0**0 was handled above) */ 2142 uprv_decNumberZero(res); /* result=1 */ 2143 *res->lsu=1; /* .. */ 2144 break;} 2145 /* rhs is a non-zero integer */ 2146 if (n<0) n=-n; /* use abs(n) */ 2147 2148 aset=*set; /* clone the context */ 2149 aset.round=DEC_ROUND_HALF_EVEN; /* internally use balanced */ 2150 /* calculate the working DIGITS */ 2151 aset.digits=reqdigits+(rhs->digits+rhs->exponent)+2; 2152 #if DECSUBSET 2153 if (!set->extended) aset.digits--; /* use classic precision */ 2154 #endif 2155 /* it's an error if this is more than can be handled */ 2156 if (aset.digits>DECNUMMAXP) {status|=DEC_Invalid_operation; break;} 2157 } /* integer path */ 2158 2159 /* aset.digits is the count of digits for the accumulator needed */ 2160 /* if accumulator is too long for local storage, then allocate */ 2161 needbytes=sizeof(decNumber)+(D2U(aset.digits)-1)*sizeof(Unit); 2162 /* [needbytes also used below if 1/lhs needed] */ 2163 if (needbytes>sizeof(dacbuff)) { 2164 allocdac=(decNumber *)malloc(needbytes); 2165 if (allocdac==NULL) { /* hopeless -- abandon */ 2166 status|=DEC_Insufficient_storage; 2167 break;} 2168 dac=allocdac; /* use the allocated space */ 2169 } 2170 /* here, aset is set up and accumulator is ready for use */ 2171 2172 if (!useint) { /* non-integral rhs */ 2173 /* x ** y; special-case x=1 here as it will otherwise always */ 2174 /* reduce to integer 1; decLnOp has a fastpath which detects */ 2175 /* the case of x=1 */ 2176 decLnOp(dac, lhs, &aset, &status); /* dac=ln(lhs) */ 2177 /* [no error possible, as lhs 0 already handled] */ 2178 if (ISZERO(dac)) { /* x==1, 1.0, etc. */ 2179 /* need to return fully-padded 1.0000 etc., but rhsint->1 */ 2180 *dac->lsu=1; /* was 0, make int 1 */ 2181 if (!rhsint) { /* add padding */ 2182 Int shift=set->digits-1; 2183 dac->digits=decShiftToMost(dac->lsu, 1, shift); 2184 dac->exponent=-shift; /* make 1.0000... */ 2185 status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */ 2186 } 2187 } 2188 else { 2189 decMultiplyOp(dac, dac, rhs, &aset, &status); /* dac=dac*rhs */ 2190 decExpOp(dac, dac, &aset, &status); /* dac=exp(dac) */ 2191 } 2192 /* and drop through for final rounding */ 2193 } /* non-integer rhs */ 2194 2195 else { /* carry on with integer */ 2196 uprv_decNumberZero(dac); /* acc=1 */ 2197 *dac->lsu=1; /* .. */ 2198 2199 /* if a negative power the constant 1 is needed, and if not subset */ 2200 /* invert the lhs now rather than inverting the result later */ 2201 if (decNumberIsNegative(rhs)) { /* was a **-n [hence digits>0] */ 2202 decNumber *inv=invbuff; /* asssume use fixed buffer */ 2203 uprv_decNumberCopy(&dnOne, dac); /* dnOne=1; [needed now or later] */ 2204 #if DECSUBSET 2205 if (set->extended) { /* need to calculate 1/lhs */ 2206 #endif 2207 /* divide lhs into 1, putting result in dac [dac=1/dac] */ 2208 decDivideOp(dac, &dnOne, lhs, &aset, DIVIDE, &status); 2209 /* now locate or allocate space for the inverted lhs */ 2210 if (needbytes>sizeof(invbuff)) { 2211 allocinv=(decNumber *)malloc(needbytes); 2212 if (allocinv==NULL) { /* hopeless -- abandon */ 2213 status|=DEC_Insufficient_storage; 2214 break;} 2215 inv=allocinv; /* use the allocated space */ 2216 } 2217 /* [inv now points to big-enough buffer or allocated storage] */ 2218 uprv_decNumberCopy(inv, dac); /* copy the 1/lhs */ 2219 uprv_decNumberCopy(dac, &dnOne); /* restore acc=1 */ 2220 lhs=inv; /* .. and go forward with new lhs */ 2221 #if DECSUBSET 2222 } 2223 #endif 2224 } 2225 2226 /* Raise-to-the-power loop... */ 2227 seenbit=0; /* set once a 1-bit is encountered */ 2228 for (i=1;;i++){ /* for each bit [top bit ignored] */ 2229 /* abandon if had overflow or terminal underflow */ 2230 if (status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */ 2231 if (status&DEC_Overflow || ISZERO(dac)) break; 2232 } 2233 /* [the following two lines revealed an optimizer bug in a C++ */ 2234 /* compiler, with symptom: 5**3 -> 25, when n=n+n was used] */ 2235 n=n<<1; /* move next bit to testable position */ 2236 if (n<0) { /* top bit is set */ 2237 seenbit=1; /* OK, significant bit seen */ 2238 decMultiplyOp(dac, dac, lhs, &aset, &status); /* dac=dac*x */ 2239 } 2240 if (i==31) break; /* that was the last bit */ 2241 if (!seenbit) continue; /* no need to square 1 */ 2242 decMultiplyOp(dac, dac, dac, &aset, &status); /* dac=dac*dac [square] */ 2243 } /*i*/ /* 32 bits */ 2244 2245 /* complete internal overflow or underflow processing */ 2246 if (status & (DEC_Overflow|DEC_Underflow)) { 2247 #if DECSUBSET 2248 /* If subset, and power was negative, reverse the kind of -erflow */ 2249 /* [1/x not yet done] */ 2250 if (!set->extended && decNumberIsNegative(rhs)) { 2251 if (status & DEC_Overflow) 2252 status^=DEC_Overflow | DEC_Underflow | DEC_Subnormal; 2253 else { /* trickier -- Underflow may or may not be set */ 2254 status&=~(DEC_Underflow | DEC_Subnormal); /* [one or both] */ 2255 status|=DEC_Overflow; 2256 } 2257 } 2258 #endif 2259 dac->bits=(dac->bits & ~DECNEG) | bits; /* force correct sign */ 2260 /* round subnormals [to set.digits rather than aset.digits] */ 2261 /* or set overflow result similarly as required */ 2262 decFinalize(dac, set, &residue, &status); 2263 uprv_decNumberCopy(res, dac); /* copy to result (is now OK length) */ 2264 break; 2265 } 2266 2267 #if DECSUBSET 2268 if (!set->extended && /* subset math */ 2269 decNumberIsNegative(rhs)) { /* was a **-n [hence digits>0] */ 2270 /* so divide result into 1 [dac=1/dac] */ 2271 decDivideOp(dac, &dnOne, dac, &aset, DIVIDE, &status); 2272 } 2273 #endif 2274 } /* rhs integer path */ 2275 2276 /* reduce result to the requested length and copy to result */ 2277 decCopyFit(res, dac, set, &residue, &status); 2278 decFinish(res, set, &residue, &status); /* final cleanup */ 2279 #if DECSUBSET 2280 if (!set->extended) decTrim(res, set, 0, 1, &dropped); /* trailing zeros */ 2281 #endif 2282 } while(0); /* end protected */ 2283 2284 if (allocdac!=NULL) free(allocdac); /* drop any storage used */ 2285 if (allocinv!=NULL) free(allocinv); /* .. */ 2286 #if DECSUBSET 2287 if (alloclhs!=NULL) free(alloclhs); /* .. */ 2288 if (allocrhs!=NULL) free(allocrhs); /* .. */ 2289 #endif 2290 if (status!=0) decStatus(res, status, set); 2291 #if DECCHECK 2292 decCheckInexact(res, set); 2293 #endif 2294 return res; 2295 } /* decNumberPower */ 2296 2297/* ------------------------------------------------------------------ */ 2298/* decNumberQuantize -- force exponent to requested value */ 2299/* */ 2300/* This computes C = op(A, B), where op adjusts the coefficient */ 2301/* of C (by rounding or shifting) such that the exponent (-scale) */ 2302/* of C has exponent of B. The numerical value of C will equal A, */ 2303/* except for the effects of any rounding that occurred. */ 2304/* */ 2305/* res is C, the result. C may be A or B */ 2306/* lhs is A, the number to adjust */ 2307/* rhs is B, the number with exponent to match */ 2308/* set is the context */ 2309/* */ 2310/* C must have space for set->digits digits. */ 2311/* */ 2312/* Unless there is an error or the result is infinite, the exponent */ 2313/* after the operation is guaranteed to be equal to that of B. */ 2314/* ------------------------------------------------------------------ */ 2315U_CAPI decNumber * U_EXPORT2 uprv_decNumberQuantize(decNumber *res, const decNumber *lhs, 2316 const decNumber *rhs, decContext *set) { 2317 uInt status=0; /* accumulator */ 2318 decQuantizeOp(res, lhs, rhs, set, 1, &status); 2319 if (status!=0) decStatus(res, status, set); 2320 return res; 2321 } /* decNumberQuantize */ 2322 2323/* ------------------------------------------------------------------ */ 2324/* decNumberReduce -- remove trailing zeros */ 2325/* */ 2326/* This computes C = 0 + A, and normalizes the result */ 2327/* */ 2328/* res is C, the result. C may be A */ 2329/* rhs is A */ 2330/* set is the context */ 2331/* */ 2332/* C must have space for set->digits digits. */ 2333/* ------------------------------------------------------------------ */ 2334/* Previously known as Normalize */ 2335U_CAPI decNumber * U_EXPORT2 uprv_decNumberNormalize(decNumber *res, const decNumber *rhs, 2336 decContext *set) { 2337 return uprv_decNumberReduce(res, rhs, set); 2338 } /* decNumberNormalize */ 2339 2340U_CAPI decNumber * U_EXPORT2 uprv_decNumberReduce(decNumber *res, const decNumber *rhs, 2341 decContext *set) { 2342 #if DECSUBSET 2343 decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ 2344 #endif 2345 uInt status=0; /* as usual */ 2346 Int residue=0; /* as usual */ 2347 Int dropped; /* work */ 2348 2349 #if DECCHECK 2350 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 2351 #endif 2352 2353 do { /* protect allocated storage */ 2354 #if DECSUBSET 2355 if (!set->extended) { 2356 /* reduce operand and set lostDigits status, as needed */ 2357 if (rhs->digits>set->digits) { 2358 allocrhs=decRoundOperand(rhs, set, &status); 2359 if (allocrhs==NULL) break; 2360 rhs=allocrhs; 2361 } 2362 } 2363 #endif 2364 /* [following code does not require input rounding] */ 2365 2366 /* Infinities copy through; NaNs need usual treatment */ 2367 if (decNumberIsNaN(rhs)) { 2368 decNaNs(res, rhs, NULL, set, &status); 2369 break; 2370 } 2371 2372 /* reduce result to the requested length and copy to result */ 2373 decCopyFit(res, rhs, set, &residue, &status); /* copy & round */ 2374 decFinish(res, set, &residue, &status); /* cleanup/set flags */ 2375 decTrim(res, set, 1, 0, &dropped); /* normalize in place */ 2376 /* [may clamp] */ 2377 } while(0); /* end protected */ 2378 2379 #if DECSUBSET 2380 if (allocrhs !=NULL) free(allocrhs); /* .. */ 2381 #endif 2382 if (status!=0) decStatus(res, status, set);/* then report status */ 2383 return res; 2384 } /* decNumberReduce */ 2385 2386/* ------------------------------------------------------------------ */ 2387/* decNumberRescale -- force exponent to requested value */ 2388/* */ 2389/* This computes C = op(A, B), where op adjusts the coefficient */ 2390/* of C (by rounding or shifting) such that the exponent (-scale) */ 2391/* of C has the value B. The numerical value of C will equal A, */ 2392/* except for the effects of any rounding that occurred. */ 2393/* */ 2394/* res is C, the result. C may be A or B */ 2395/* lhs is A, the number to adjust */ 2396/* rhs is B, the requested exponent */ 2397/* set is the context */ 2398/* */ 2399/* C must have space for set->digits digits. */ 2400/* */ 2401/* Unless there is an error or the result is infinite, the exponent */ 2402/* after the operation is guaranteed to be equal to B. */ 2403/* ------------------------------------------------------------------ */ 2404U_CAPI decNumber * U_EXPORT2 uprv_decNumberRescale(decNumber *res, const decNumber *lhs, 2405 const decNumber *rhs, decContext *set) { 2406 uInt status=0; /* accumulator */ 2407 decQuantizeOp(res, lhs, rhs, set, 0, &status); 2408 if (status!=0) decStatus(res, status, set); 2409 return res; 2410 } /* decNumberRescale */ 2411 2412/* ------------------------------------------------------------------ */ 2413/* decNumberRemainder -- divide and return remainder */ 2414/* */ 2415/* This computes C = A % B */ 2416/* */ 2417/* res is C, the result. C may be A and/or B (e.g., X=X%X) */ 2418/* lhs is A */ 2419/* rhs is B */ 2420/* set is the context */ 2421/* */ 2422/* C must have space for set->digits digits. */ 2423/* ------------------------------------------------------------------ */ 2424U_CAPI decNumber * U_EXPORT2 uprv_decNumberRemainder(decNumber *res, const decNumber *lhs, 2425 const decNumber *rhs, decContext *set) { 2426 uInt status=0; /* accumulator */ 2427 decDivideOp(res, lhs, rhs, set, REMAINDER, &status); 2428 if (status!=0) decStatus(res, status, set); 2429 #if DECCHECK 2430 decCheckInexact(res, set); 2431 #endif 2432 return res; 2433 } /* decNumberRemainder */ 2434 2435/* ------------------------------------------------------------------ */ 2436/* decNumberRemainderNear -- divide and return remainder from nearest */ 2437/* */ 2438/* This computes C = A % B, where % is the IEEE remainder operator */ 2439/* */ 2440/* res is C, the result. C may be A and/or B (e.g., X=X%X) */ 2441/* lhs is A */ 2442/* rhs is B */ 2443/* set is the context */ 2444/* */ 2445/* C must have space for set->digits digits. */ 2446/* ------------------------------------------------------------------ */ 2447U_CAPI decNumber * U_EXPORT2 uprv_decNumberRemainderNear(decNumber *res, const decNumber *lhs, 2448 const decNumber *rhs, decContext *set) { 2449 uInt status=0; /* accumulator */ 2450 decDivideOp(res, lhs, rhs, set, REMNEAR, &status); 2451 if (status!=0) decStatus(res, status, set); 2452 #if DECCHECK 2453 decCheckInexact(res, set); 2454 #endif 2455 return res; 2456 } /* decNumberRemainderNear */ 2457 2458/* ------------------------------------------------------------------ */ 2459/* decNumberRotate -- rotate the coefficient of a Number left/right */ 2460/* */ 2461/* This computes C = A rot B (in base ten and rotating set->digits */ 2462/* digits). */ 2463/* */ 2464/* res is C, the result. C may be A and/or B (e.g., X=XrotX) */ 2465/* lhs is A */ 2466/* rhs is B, the number of digits to rotate (-ve to right) */ 2467/* set is the context */ 2468/* */ 2469/* The digits of the coefficient of A are rotated to the left (if B */ 2470/* is positive) or to the right (if B is negative) without adjusting */ 2471/* the exponent or the sign of A. If lhs->digits is less than */ 2472/* set->digits the coefficient is padded with zeros on the left */ 2473/* before the rotate. Any leading zeros in the result are removed */ 2474/* as usual. */ 2475/* */ 2476/* B must be an integer (q=0) and in the range -set->digits through */ 2477/* +set->digits. */ 2478/* C must have space for set->digits digits. */ 2479/* NaNs are propagated as usual. Infinities are unaffected (but */ 2480/* B must be valid). No status is set unless B is invalid or an */ 2481/* operand is an sNaN. */ 2482/* ------------------------------------------------------------------ */ 2483U_CAPI decNumber * U_EXPORT2 uprv_decNumberRotate(decNumber *res, const decNumber *lhs, 2484 const decNumber *rhs, decContext *set) { 2485 uInt status=0; /* accumulator */ 2486 Int rotate; /* rhs as an Int */ 2487 2488 #if DECCHECK 2489 if (decCheckOperands(res, lhs, rhs, set)) return res; 2490 #endif 2491 2492 /* NaNs propagate as normal */ 2493 if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) 2494 decNaNs(res, lhs, rhs, set, &status); 2495 /* rhs must be an integer */ 2496 else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) 2497 status=DEC_Invalid_operation; 2498 else { /* both numeric, rhs is an integer */ 2499 rotate=decGetInt(rhs); /* [cannot fail] */ 2500 if (rotate==BADINT /* something bad .. */ 2501 || rotate==BIGODD || rotate==BIGEVEN /* .. very big .. */ 2502 || abs(rotate)>set->digits) /* .. or out of range */ 2503 status=DEC_Invalid_operation; 2504 else { /* rhs is OK */ 2505 uprv_decNumberCopy(res, lhs); 2506 /* convert -ve rotate to equivalent positive rotation */ 2507 if (rotate<0) rotate=set->digits+rotate; 2508 if (rotate!=0 && rotate!=set->digits /* zero or full rotation */ 2509 && !decNumberIsInfinite(res)) { /* lhs was infinite */ 2510 /* left-rotate to do; 0 < rotate < set->digits */ 2511 uInt units, shift; /* work */ 2512 uInt msudigits; /* digits in result msu */ 2513 Unit *msu=res->lsu+D2U(res->digits)-1; /* current msu */ 2514 Unit *msumax=res->lsu+D2U(set->digits)-1; /* rotation msu */ 2515 for (msu++; msu<=msumax; msu++) *msu=0; /* ensure high units=0 */ 2516 res->digits=set->digits; /* now full-length */ 2517 msudigits=MSUDIGITS(res->digits); /* actual digits in msu */ 2518 2519 /* rotation here is done in-place, in three steps */ 2520 /* 1. shift all to least up to one unit to unit-align final */ 2521 /* lsd [any digits shifted out are rotated to the left, */ 2522 /* abutted to the original msd (which may require split)] */ 2523 /* */ 2524 /* [if there are no whole units left to rotate, the */ 2525 /* rotation is now complete] */ 2526 /* */ 2527 /* 2. shift to least, from below the split point only, so that */ 2528 /* the final msd is in the right place in its Unit [any */ 2529 /* digits shifted out will fit exactly in the current msu, */ 2530 /* left aligned, no split required] */ 2531 /* */ 2532 /* 3. rotate all the units by reversing left part, right */ 2533 /* part, and then whole */ 2534 /* */ 2535 /* example: rotate right 8 digits (2 units + 2), DECDPUN=3. */ 2536 /* */ 2537 /* start: 00a bcd efg hij klm npq */ 2538 /* */ 2539 /* 1a 000 0ab cde fgh|ijk lmn [pq saved] */ 2540 /* 1b 00p qab cde fgh|ijk lmn */ 2541 /* */ 2542 /* 2a 00p qab cde fgh|00i jkl [mn saved] */ 2543 /* 2b mnp qab cde fgh|00i jkl */ 2544 /* */ 2545 /* 3a fgh cde qab mnp|00i jkl */ 2546 /* 3b fgh cde qab mnp|jkl 00i */ 2547 /* 3c 00i jkl mnp qab cde fgh */ 2548 2549 /* Step 1: amount to shift is the partial right-rotate count */ 2550 rotate=set->digits-rotate; /* make it right-rotate */ 2551 units=rotate/DECDPUN; /* whole units to rotate */ 2552 shift=rotate%DECDPUN; /* left-over digits count */ 2553 if (shift>0) { /* not an exact number of units */ 2554 uInt save=res->lsu[0]%powers[shift]; /* save low digit(s) */ 2555 decShiftToLeast(res->lsu, D2U(res->digits), shift); 2556 if (shift>msudigits) { /* msumax-1 needs >0 digits */ 2557 uInt rem=save%powers[shift-msudigits];/* split save */ 2558 *msumax=(Unit)(save/powers[shift-msudigits]); /* and insert */ 2559 *(msumax-1)=*(msumax-1) 2560 +(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); /* .. */ 2561 } 2562 else { /* all fits in msumax */ 2563 *msumax=*msumax+(Unit)(save*powers[msudigits-shift]); /* [maybe *1] */ 2564 } 2565 } /* digits shift needed */ 2566 2567 /* If whole units to rotate... */ 2568 if (units>0) { /* some to do */ 2569 /* Step 2: the units to touch are the whole ones in rotate, */ 2570 /* if any, and the shift is DECDPUN-msudigits (which may be */ 2571 /* 0, again) */ 2572 shift=DECDPUN-msudigits; 2573 if (shift>0) { /* not an exact number of units */ 2574 uInt save=res->lsu[0]%powers[shift]; /* save low digit(s) */ 2575 decShiftToLeast(res->lsu, units, shift); 2576 *msumax=*msumax+(Unit)(save*powers[msudigits]); 2577 } /* partial shift needed */ 2578 2579 /* Step 3: rotate the units array using triple reverse */ 2580 /* (reversing is easy and fast) */ 2581 decReverse(res->lsu+units, msumax); /* left part */ 2582 decReverse(res->lsu, res->lsu+units-1); /* right part */ 2583 decReverse(res->lsu, msumax); /* whole */ 2584 } /* whole units to rotate */ 2585 /* the rotation may have left an undetermined number of zeros */ 2586 /* on the left, so true length needs to be calculated */ 2587 res->digits=decGetDigits(res->lsu, msumax-res->lsu+1); 2588 } /* rotate needed */ 2589 } /* rhs OK */ 2590 } /* numerics */ 2591 if (status!=0) decStatus(res, status, set); 2592 return res; 2593 } /* decNumberRotate */ 2594 2595/* ------------------------------------------------------------------ */ 2596/* decNumberSameQuantum -- test for equal exponents */ 2597/* */ 2598/* res is the result number, which will contain either 0 or 1 */ 2599/* lhs is a number to test */ 2600/* rhs is the second (usually a pattern) */ 2601/* */ 2602/* No errors are possible and no context is needed. */ 2603/* ------------------------------------------------------------------ */ 2604U_CAPI decNumber * U_EXPORT2 uprv_decNumberSameQuantum(decNumber *res, const decNumber *lhs, 2605 const decNumber *rhs) { 2606 Unit ret=0; /* return value */ 2607 2608 #if DECCHECK 2609 if (decCheckOperands(res, lhs, rhs, DECUNCONT)) return res; 2610 #endif 2611 2612 if (SPECIALARGS) { 2613 if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1; 2614 else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1; 2615 /* [anything else with a special gives 0] */ 2616 } 2617 else if (lhs->exponent==rhs->exponent) ret=1; 2618 2619 uprv_decNumberZero(res); /* OK to overwrite an operand now */ 2620 *res->lsu=ret; 2621 return res; 2622 } /* decNumberSameQuantum */ 2623 2624/* ------------------------------------------------------------------ */ 2625/* decNumberScaleB -- multiply by a power of 10 */ 2626/* */ 2627/* This computes C = A x 10**B where B is an integer (q=0) with */ 2628/* maximum magnitude 2*(emax+digits) */ 2629/* */ 2630/* res is C, the result. C may be A or B */ 2631/* lhs is A, the number to adjust */ 2632/* rhs is B, the requested power of ten to use */ 2633/* set is the context */ 2634/* */ 2635/* C must have space for set->digits digits. */ 2636/* */ 2637/* The result may underflow or overflow. */ 2638/* ------------------------------------------------------------------ */ 2639U_CAPI decNumber * U_EXPORT2 uprv_decNumberScaleB(decNumber *res, const decNumber *lhs, 2640 const decNumber *rhs, decContext *set) { 2641 Int reqexp; /* requested exponent change [B] */ 2642 uInt status=0; /* accumulator */ 2643 Int residue; /* work */ 2644 2645 #if DECCHECK 2646 if (decCheckOperands(res, lhs, rhs, set)) return res; 2647 #endif 2648 2649 /* Handle special values except lhs infinite */ 2650 if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) 2651 decNaNs(res, lhs, rhs, set, &status); 2652 /* rhs must be an integer */ 2653 else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) 2654 status=DEC_Invalid_operation; 2655 else { 2656 /* lhs is a number; rhs is a finite with q==0 */ 2657 reqexp=decGetInt(rhs); /* [cannot fail] */ 2658 if (reqexp==BADINT /* something bad .. */ 2659 || reqexp==BIGODD || reqexp==BIGEVEN /* .. very big .. */ 2660 || abs(reqexp)>(2*(set->digits+set->emax))) /* .. or out of range */ 2661 status=DEC_Invalid_operation; 2662 else { /* rhs is OK */ 2663 uprv_decNumberCopy(res, lhs); /* all done if infinite lhs */ 2664 if (!decNumberIsInfinite(res)) { /* prepare to scale */ 2665 res->exponent+=reqexp; /* adjust the exponent */ 2666 residue=0; 2667 decFinalize(res, set, &residue, &status); /* .. and check */ 2668 } /* finite LHS */ 2669 } /* rhs OK */ 2670 } /* rhs finite */ 2671 if (status!=0) decStatus(res, status, set); 2672 return res; 2673 } /* decNumberScaleB */ 2674 2675/* ------------------------------------------------------------------ */ 2676/* decNumberShift -- shift the coefficient of a Number left or right */ 2677/* */ 2678/* This computes C = A << B or C = A >> -B (in base ten). */ 2679/* */ 2680/* res is C, the result. C may be A and/or B (e.g., X=X<<X) */ 2681/* lhs is A */ 2682/* rhs is B, the number of digits to shift (-ve to right) */ 2683/* set is the context */ 2684/* */ 2685/* The digits of the coefficient of A are shifted to the left (if B */ 2686/* is positive) or to the right (if B is negative) without adjusting */ 2687/* the exponent or the sign of A. */ 2688/* */ 2689/* B must be an integer (q=0) and in the range -set->digits through */ 2690/* +set->digits. */ 2691/* C must have space for set->digits digits. */ 2692/* NaNs are propagated as usual. Infinities are unaffected (but */ 2693/* B must be valid). No status is set unless B is invalid or an */ 2694/* operand is an sNaN. */ 2695/* ------------------------------------------------------------------ */ 2696U_CAPI decNumber * U_EXPORT2 uprv_decNumberShift(decNumber *res, const decNumber *lhs, 2697 const decNumber *rhs, decContext *set) { 2698 uInt status=0; /* accumulator */ 2699 Int shift; /* rhs as an Int */ 2700 2701 #if DECCHECK 2702 if (decCheckOperands(res, lhs, rhs, set)) return res; 2703 #endif 2704 2705 /* NaNs propagate as normal */ 2706 if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) 2707 decNaNs(res, lhs, rhs, set, &status); 2708 /* rhs must be an integer */ 2709 else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) 2710 status=DEC_Invalid_operation; 2711 else { /* both numeric, rhs is an integer */ 2712 shift=decGetInt(rhs); /* [cannot fail] */ 2713 if (shift==BADINT /* something bad .. */ 2714 || shift==BIGODD || shift==BIGEVEN /* .. very big .. */ 2715 || abs(shift)>set->digits) /* .. or out of range */ 2716 status=DEC_Invalid_operation; 2717 else { /* rhs is OK */ 2718 uprv_decNumberCopy(res, lhs); 2719 if (shift!=0 && !decNumberIsInfinite(res)) { /* something to do */ 2720 if (shift>0) { /* to left */ 2721 if (shift==set->digits) { /* removing all */ 2722 *res->lsu=0; /* so place 0 */ 2723 res->digits=1; /* .. */ 2724 } 2725 else { /* */ 2726 /* first remove leading digits if necessary */ 2727 if (res->digits+shift>set->digits) { 2728 decDecap(res, res->digits+shift-set->digits); 2729 /* that updated res->digits; may have gone to 1 (for a */ 2730 /* single digit or for zero */ 2731 } 2732 if (res->digits>1 || *res->lsu) /* if non-zero.. */ 2733 res->digits=decShiftToMost(res->lsu, res->digits, shift); 2734 } /* partial left */ 2735 } /* left */ 2736 else { /* to right */ 2737 if (-shift>=res->digits) { /* discarding all */ 2738 *res->lsu=0; /* so place 0 */ 2739 res->digits=1; /* .. */ 2740 } 2741 else { 2742 decShiftToLeast(res->lsu, D2U(res->digits), -shift); 2743 res->digits-=(-shift); 2744 } 2745 } /* to right */ 2746 } /* non-0 non-Inf shift */ 2747 } /* rhs OK */ 2748 } /* numerics */ 2749 if (status!=0) decStatus(res, status, set); 2750 return res; 2751 } /* decNumberShift */ 2752 2753/* ------------------------------------------------------------------ */ 2754/* decNumberSquareRoot -- square root operator */ 2755/* */ 2756/* This computes C = squareroot(A) */ 2757/* */ 2758/* res is C, the result. C may be A */ 2759/* rhs is A */ 2760/* set is the context; note that rounding mode has no effect */ 2761/* */ 2762/* C must have space for set->digits digits. */ 2763/* ------------------------------------------------------------------ */ 2764/* This uses the following varying-precision algorithm in: */ 2765/* */ 2766/* Properly Rounded Variable Precision Square Root, T. E. Hull and */ 2767/* A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */ 2768/* pp229-237, ACM, September 1985. */ 2769/* */ 2770/* The square-root is calculated using Newton's method, after which */ 2771/* a check is made to ensure the result is correctly rounded. */ 2772/* */ 2773/* % [Reformatted original Numerical Turing source code follows.] */ 2774/* function sqrt(x : real) : real */ 2775/* % sqrt(x) returns the properly rounded approximation to the square */ 2776/* % root of x, in the precision of the calling environment, or it */ 2777/* % fails if x < 0. */ 2778/* % t e hull and a abrham, august, 1984 */ 2779/* if x <= 0 then */ 2780/* if x < 0 then */ 2781/* assert false */ 2782/* else */ 2783/* result 0 */ 2784/* end if */ 2785/* end if */ 2786/* var f := setexp(x, 0) % fraction part of x [0.1 <= x < 1] */ 2787/* var e := getexp(x) % exponent part of x */ 2788/* var approx : real */ 2789/* if e mod 2 = 0 then */ 2790/* approx := .259 + .819 * f % approx to root of f */ 2791/* else */ 2792/* f := f/l0 % adjustments */ 2793/* e := e + 1 % for odd */ 2794/* approx := .0819 + 2.59 * f % exponent */ 2795/* end if */ 2796/* */ 2797/* var p:= 3 */ 2798/* const maxp := currentprecision + 2 */ 2799/* loop */ 2800/* p := min(2*p - 2, maxp) % p = 4,6,10, . . . , maxp */ 2801/* precision p */ 2802/* approx := .5 * (approx + f/approx) */ 2803/* exit when p = maxp */ 2804/* end loop */ 2805/* */ 2806/* % approx is now within 1 ulp of the properly rounded square root */ 2807/* % of f; to ensure proper rounding, compare squares of (approx - */ 2808/* % l/2 ulp) and (approx + l/2 ulp) with f. */ 2809/* p := currentprecision */ 2810/* begin */ 2811/* precision p + 2 */ 2812/* const approxsubhalf := approx - setexp(.5, -p) */ 2813/* if mulru(approxsubhalf, approxsubhalf) > f then */ 2814/* approx := approx - setexp(.l, -p + 1) */ 2815/* else */ 2816/* const approxaddhalf := approx + setexp(.5, -p) */ 2817/* if mulrd(approxaddhalf, approxaddhalf) < f then */ 2818/* approx := approx + setexp(.l, -p + 1) */ 2819/* end if */ 2820/* end if */ 2821/* end */ 2822/* result setexp(approx, e div 2) % fix exponent */ 2823/* end sqrt */ 2824/* ------------------------------------------------------------------ */ 2825#if defined(__clang__) || U_GCC_MAJOR_MINOR >= 406 2826#pragma GCC diagnostic push 2827#pragma GCC diagnostic ignored "-Warray-bounds" 2828#endif 2829U_CAPI decNumber * U_EXPORT2 uprv_decNumberSquareRoot(decNumber *res, const decNumber *rhs, 2830 decContext *set) { 2831 decContext workset, approxset; /* work contexts */ 2832 decNumber dzero; /* used for constant zero */ 2833 Int maxp; /* largest working precision */ 2834 Int workp; /* working precision */ 2835 Int residue=0; /* rounding residue */ 2836 uInt status=0, ignore=0; /* status accumulators */ 2837 uInt rstatus; /* .. */ 2838 Int exp; /* working exponent */ 2839 Int ideal; /* ideal (preferred) exponent */ 2840 Int needbytes; /* work */ 2841 Int dropped; /* .. */ 2842 2843 #if DECSUBSET 2844 decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ 2845 #endif 2846 /* buffer for f [needs +1 in case DECBUFFER 0] */ 2847 decNumber buff[D2N(DECBUFFER+1)]; 2848 /* buffer for a [needs +2 to match likely maxp] */ 2849 decNumber bufa[D2N(DECBUFFER+2)]; 2850 /* buffer for temporary, b [must be same size as a] */ 2851 decNumber bufb[D2N(DECBUFFER+2)]; 2852 decNumber *allocbuff=NULL; /* -> allocated buff, iff allocated */ 2853 decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ 2854 decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */ 2855 decNumber *f=buff; /* reduced fraction */ 2856 decNumber *a=bufa; /* approximation to result */ 2857 decNumber *b=bufb; /* intermediate result */ 2858 /* buffer for temporary variable, up to 3 digits */ 2859 decNumber buft[D2N(3)]; 2860 decNumber *t=buft; /* up-to-3-digit constant or work */ 2861 2862 #if DECCHECK 2863 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 2864 #endif 2865 2866 do { /* protect allocated storage */ 2867 #if DECSUBSET 2868 if (!set->extended) { 2869 /* reduce operand and set lostDigits status, as needed */ 2870 if (rhs->digits>set->digits) { 2871 allocrhs=decRoundOperand(rhs, set, &status); 2872 if (allocrhs==NULL) break; 2873 /* [Note: 'f' allocation below could reuse this buffer if */ 2874 /* used, but as this is rare they are kept separate for clarity.] */ 2875 rhs=allocrhs; 2876 } 2877 } 2878 #endif 2879 /* [following code does not require input rounding] */ 2880 2881 /* handle infinities and NaNs */ 2882 if (SPECIALARG) { 2883 if (decNumberIsInfinite(rhs)) { /* an infinity */ 2884 if (decNumberIsNegative(rhs)) status|=DEC_Invalid_operation; 2885 else uprv_decNumberCopy(res, rhs); /* +Infinity */ 2886 } 2887 else decNaNs(res, rhs, NULL, set, &status); /* a NaN */ 2888 break; 2889 } 2890 2891 /* calculate the ideal (preferred) exponent [floor(exp/2)] */ 2892 /* [It would be nicer to write: ideal=rhs->exponent>>1, but this */ 2893 /* generates a compiler warning. Generated code is the same.] */ 2894 ideal=(rhs->exponent&~1)/2; /* target */ 2895 2896 /* handle zeros */ 2897 if (ISZERO(rhs)) { 2898 uprv_decNumberCopy(res, rhs); /* could be 0 or -0 */ 2899 res->exponent=ideal; /* use the ideal [safe] */ 2900 /* use decFinish to clamp any out-of-range exponent, etc. */ 2901 decFinish(res, set, &residue, &status); 2902 break; 2903 } 2904 2905 /* any other -x is an oops */ 2906 if (decNumberIsNegative(rhs)) { 2907 status|=DEC_Invalid_operation; 2908 break; 2909 } 2910 2911 /* space is needed for three working variables */ 2912 /* f -- the same precision as the RHS, reduced to 0.01->0.99... */ 2913 /* a -- Hull's approximation -- precision, when assigned, is */ 2914 /* currentprecision+1 or the input argument precision, */ 2915 /* whichever is larger (+2 for use as temporary) */ 2916 /* b -- intermediate temporary result (same size as a) */ 2917 /* if any is too long for local storage, then allocate */ 2918 workp=MAXI(set->digits+1, rhs->digits); /* actual rounding precision */ 2919 workp=MAXI(workp, 7); /* at least 7 for low cases */ 2920 maxp=workp+2; /* largest working precision */ 2921 2922 needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); 2923 if (needbytes>(Int)sizeof(buff)) { 2924 allocbuff=(decNumber *)malloc(needbytes); 2925 if (allocbuff==NULL) { /* hopeless -- abandon */ 2926 status|=DEC_Insufficient_storage; 2927 break;} 2928 f=allocbuff; /* use the allocated space */ 2929 } 2930 /* a and b both need to be able to hold a maxp-length number */ 2931 needbytes=sizeof(decNumber)+(D2U(maxp)-1)*sizeof(Unit); 2932 if (needbytes>(Int)sizeof(bufa)) { /* [same applies to b] */ 2933 allocbufa=(decNumber *)malloc(needbytes); 2934 allocbufb=(decNumber *)malloc(needbytes); 2935 if (allocbufa==NULL || allocbufb==NULL) { /* hopeless */ 2936 status|=DEC_Insufficient_storage; 2937 break;} 2938 a=allocbufa; /* use the allocated spaces */ 2939 b=allocbufb; /* .. */ 2940 } 2941 2942 /* copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1 */ 2943 uprv_decNumberCopy(f, rhs); 2944 exp=f->exponent+f->digits; /* adjusted to Hull rules */ 2945 f->exponent=-(f->digits); /* to range */ 2946 2947 /* set up working context */ 2948 uprv_decContextDefault(&workset, DEC_INIT_DECIMAL64); 2949 workset.emax=DEC_MAX_EMAX; 2950 workset.emin=DEC_MIN_EMIN; 2951 2952 /* [Until further notice, no error is possible and status bits */ 2953 /* (Rounded, etc.) should be ignored, not accumulated.] */ 2954 2955 /* Calculate initial approximation, and allow for odd exponent */ 2956 workset.digits=workp; /* p for initial calculation */ 2957 t->bits=0; t->digits=3; 2958 a->bits=0; a->digits=3; 2959 if ((exp & 1)==0) { /* even exponent */ 2960 /* Set t=0.259, a=0.819 */ 2961 t->exponent=-3; 2962 a->exponent=-3; 2963 #if DECDPUN>=3 2964 t->lsu[0]=259; 2965 a->lsu[0]=819; 2966 #elif DECDPUN==2 2967 t->lsu[0]=59; t->lsu[1]=2; 2968 a->lsu[0]=19; a->lsu[1]=8; 2969 #else 2970 t->lsu[0]=9; t->lsu[1]=5; t->lsu[2]=2; 2971 a->lsu[0]=9; a->lsu[1]=1; a->lsu[2]=8; 2972 #endif 2973 } 2974 else { /* odd exponent */ 2975 /* Set t=0.0819, a=2.59 */ 2976 f->exponent--; /* f=f/10 */ 2977 exp++; /* e=e+1 */ 2978 t->exponent=-4; 2979 a->exponent=-2; 2980 #if DECDPUN>=3 2981 t->lsu[0]=819; 2982 a->lsu[0]=259; 2983 #elif DECDPUN==2 2984 t->lsu[0]=19; t->lsu[1]=8; 2985 a->lsu[0]=59; a->lsu[1]=2; 2986 #else 2987 t->lsu[0]=9; t->lsu[1]=1; t->lsu[2]=8; 2988 a->lsu[0]=9; a->lsu[1]=5; a->lsu[2]=2; 2989 #endif 2990 } 2991 2992 decMultiplyOp(a, a, f, &workset, &ignore); /* a=a*f */ 2993 decAddOp(a, a, t, &workset, 0, &ignore); /* ..+t */ 2994 /* [a is now the initial approximation for sqrt(f), calculated with */ 2995 /* currentprecision, which is also a's precision.] */ 2996 2997 /* the main calculation loop */ 2998 uprv_decNumberZero(&dzero); /* make 0 */ 2999 uprv_decNumberZero(t); /* set t = 0.5 */ 3000 t->lsu[0]=5; /* .. */ 3001 t->exponent=-1; /* .. */ 3002 workset.digits=3; /* initial p */ 3003 for (; workset.digits<maxp;) { 3004 /* set p to min(2*p - 2, maxp) [hence 3; or: 4, 6, 10, ... , maxp] */ 3005 workset.digits=MINI(workset.digits*2-2, maxp); 3006 /* a = 0.5 * (a + f/a) */ 3007 /* [calculated at p then rounded to currentprecision] */ 3008 decDivideOp(b, f, a, &workset, DIVIDE, &ignore); /* b=f/a */ 3009 decAddOp(b, b, a, &workset, 0, &ignore); /* b=b+a */ 3010 decMultiplyOp(a, b, t, &workset, &ignore); /* a=b*0.5 */ 3011 } /* loop */ 3012 3013 /* Here, 0.1 <= a < 1 [Hull], and a has maxp digits */ 3014 /* now reduce to length, etc.; this needs to be done with a */ 3015 /* having the correct exponent so as to handle subnormals */ 3016 /* correctly */ 3017 approxset=*set; /* get emin, emax, etc. */ 3018 approxset.round=DEC_ROUND_HALF_EVEN; 3019 a->exponent+=exp/2; /* set correct exponent */ 3020 rstatus=0; /* clear status */ 3021 residue=0; /* .. and accumulator */ 3022 decCopyFit(a, a, &approxset, &residue, &rstatus); /* reduce (if needed) */ 3023 decFinish(a, &approxset, &residue, &rstatus); /* clean and finalize */ 3024 3025 /* Overflow was possible if the input exponent was out-of-range, */ 3026 /* in which case quit */ 3027 if (rstatus&DEC_Overflow) { 3028 status=rstatus; /* use the status as-is */ 3029 uprv_decNumberCopy(res, a); /* copy to result */ 3030 break; 3031 } 3032 3033 /* Preserve status except Inexact/Rounded */ 3034 status|=(rstatus & ~(DEC_Rounded|DEC_Inexact)); 3035 3036 /* Carry out the Hull correction */ 3037 a->exponent-=exp/2; /* back to 0.1->1 */ 3038 3039 /* a is now at final precision and within 1 ulp of the properly */ 3040 /* rounded square root of f; to ensure proper rounding, compare */ 3041 /* squares of (a - l/2 ulp) and (a + l/2 ulp) with f. */ 3042 /* Here workset.digits=maxp and t=0.5, and a->digits determines */ 3043 /* the ulp */ 3044 workset.digits--; /* maxp-1 is OK now */ 3045 t->exponent=-a->digits-1; /* make 0.5 ulp */ 3046 decAddOp(b, a, t, &workset, DECNEG, &ignore); /* b = a - 0.5 ulp */ 3047 workset.round=DEC_ROUND_UP; 3048 decMultiplyOp(b, b, b, &workset, &ignore); /* b = mulru(b, b) */ 3049 decCompareOp(b, f, b, &workset, COMPARE, &ignore); /* b ? f, reversed */ 3050 if (decNumberIsNegative(b)) { /* f < b [i.e., b > f] */ 3051 /* this is the more common adjustment, though both are rare */ 3052 t->exponent++; /* make 1.0 ulp */ 3053 t->lsu[0]=1; /* .. */ 3054 decAddOp(a, a, t, &workset, DECNEG, &ignore); /* a = a - 1 ulp */ 3055 /* assign to approx [round to length] */ 3056 approxset.emin-=exp/2; /* adjust to match a */ 3057 approxset.emax-=exp/2; 3058 decAddOp(a, &dzero, a, &approxset, 0, &ignore); 3059 } 3060 else { 3061 decAddOp(b, a, t, &workset, 0, &ignore); /* b = a + 0.5 ulp */ 3062 workset.round=DEC_ROUND_DOWN; 3063 decMultiplyOp(b, b, b, &workset, &ignore); /* b = mulrd(b, b) */ 3064 decCompareOp(b, b, f, &workset, COMPARE, &ignore); /* b ? f */ 3065 if (decNumberIsNegative(b)) { /* b < f */ 3066 t->exponent++; /* make 1.0 ulp */ 3067 t->lsu[0]=1; /* .. */ 3068 decAddOp(a, a, t, &workset, 0, &ignore); /* a = a + 1 ulp */ 3069 /* assign to approx [round to length] */ 3070 approxset.emin-=exp/2; /* adjust to match a */ 3071 approxset.emax-=exp/2; 3072 decAddOp(a, &dzero, a, &approxset, 0, &ignore); 3073 } 3074 } 3075 /* [no errors are possible in the above, and rounding/inexact during */ 3076 /* estimation are irrelevant, so status was not accumulated] */ 3077 3078 /* Here, 0.1 <= a < 1 (still), so adjust back */ 3079 a->exponent+=exp/2; /* set correct exponent */ 3080 3081 /* count droppable zeros [after any subnormal rounding] by */ 3082 /* trimming a copy */ 3083 uprv_decNumberCopy(b, a); 3084 decTrim(b, set, 1, 1, &dropped); /* [drops trailing zeros] */ 3085 3086 /* Set Inexact and Rounded. The answer can only be exact if */ 3087 /* it is short enough so that squaring it could fit in workp */ 3088 /* digits, so this is the only (relatively rare) condition that */ 3089 /* a careful check is needed */ 3090 if (b->digits*2-1 > workp) { /* cannot fit */ 3091 status|=DEC_Inexact|DEC_Rounded; 3092 } 3093 else { /* could be exact/unrounded */ 3094 uInt mstatus=0; /* local status */ 3095 decMultiplyOp(b, b, b, &workset, &mstatus); /* try the multiply */ 3096 if (mstatus&DEC_Overflow) { /* result just won't fit */ 3097 status|=DEC_Inexact|DEC_Rounded; 3098 } 3099 else { /* plausible */ 3100 decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); /* b ? rhs */ 3101 if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; /* not equal */ 3102 else { /* is Exact */ 3103 /* here, dropped is the count of trailing zeros in 'a' */ 3104 /* use closest exponent to ideal... */ 3105 Int todrop=ideal-a->exponent; /* most that can be dropped */ 3106 if (todrop<0) status|=DEC_Rounded; /* ideally would add 0s */ 3107 else { /* unrounded */ 3108 /* there are some to drop, but emax may not allow all */ 3109 Int maxexp=set->emax-set->digits+1; 3110 Int maxdrop=maxexp-a->exponent; 3111 if (todrop>maxdrop && set->clamp) { /* apply clamping */ 3112 todrop=maxdrop; 3113 status|=DEC_Clamped; 3114 } 3115 if (dropped<todrop) { /* clamp to those available */ 3116 todrop=dropped; 3117 status|=DEC_Clamped; 3118 } 3119 if (todrop>0) { /* have some to drop */ 3120 decShiftToLeast(a->lsu, D2U(a->digits), todrop); 3121 a->exponent+=todrop; /* maintain numerical value */ 3122 a->digits-=todrop; /* new length */ 3123 } 3124 } 3125 } 3126 } 3127 } 3128 3129 /* double-check Underflow, as perhaps the result could not have */ 3130 /* been subnormal (initial argument too big), or it is now Exact */ 3131 if (status&DEC_Underflow) { 3132 Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */ 3133 /* check if truly subnormal */ 3134 #if DECEXTFLAG /* DEC_Subnormal too */ 3135 if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow); 3136 #else 3137 if (ae>=set->emin*2) status&=~DEC_Underflow; 3138 #endif 3139 /* check if truly inexact */ 3140 if (!(status&DEC_Inexact)) status&=~DEC_Underflow; 3141 } 3142 3143 uprv_decNumberCopy(res, a); /* a is now the result */ 3144 } while(0); /* end protected */ 3145 3146 if (allocbuff!=NULL) free(allocbuff); /* drop any storage used */ 3147 if (allocbufa!=NULL) free(allocbufa); /* .. */ 3148 if (allocbufb!=NULL) free(allocbufb); /* .. */ 3149 #if DECSUBSET 3150 if (allocrhs !=NULL) free(allocrhs); /* .. */ 3151 #endif 3152 if (status!=0) decStatus(res, status, set);/* then report status */ 3153 #if DECCHECK 3154 decCheckInexact(res, set); 3155 #endif 3156 return res; 3157 } /* decNumberSquareRoot */ 3158#if defined(__clang__) || U_GCC_MAJOR_MINOR >= 406 3159#pragma GCC diagnostic pop 3160#endif 3161 3162/* ------------------------------------------------------------------ */ 3163/* decNumberSubtract -- subtract two Numbers */ 3164/* */ 3165/* This computes C = A - B */ 3166/* */ 3167/* res is C, the result. C may be A and/or B (e.g., X=X-X) */ 3168/* lhs is A */ 3169/* rhs is B */ 3170/* set is the context */ 3171/* */ 3172/* C must have space for set->digits digits. */ 3173/* ------------------------------------------------------------------ */ 3174U_CAPI decNumber * U_EXPORT2 uprv_decNumberSubtract(decNumber *res, const decNumber *lhs, 3175 const decNumber *rhs, decContext *set) { 3176 uInt status=0; /* accumulator */ 3177 3178 decAddOp(res, lhs, rhs, set, DECNEG, &status); 3179 if (status!=0) decStatus(res, status, set); 3180 #if DECCHECK 3181 decCheckInexact(res, set); 3182 #endif 3183 return res; 3184 } /* decNumberSubtract */ 3185 3186/* ------------------------------------------------------------------ */ 3187/* decNumberToIntegralExact -- round-to-integral-value with InExact */ 3188/* decNumberToIntegralValue -- round-to-integral-value */ 3189/* */ 3190/* res is the result */ 3191/* rhs is input number */ 3192/* set is the context */ 3193/* */ 3194/* res must have space for any value of rhs. */ 3195/* */ 3196/* This implements the IEEE special operators and therefore treats */ 3197/* special values as valid. For finite numbers it returns */ 3198/* rescale(rhs, 0) if rhs->exponent is <0. */ 3199/* Otherwise the result is rhs (so no error is possible, except for */ 3200/* sNaN). */ 3201/* */ 3202/* The context is used for rounding mode and status after sNaN, but */ 3203/* the digits setting is ignored. The Exact version will signal */ 3204/* Inexact if the result differs numerically from rhs; the other */ 3205/* never signals Inexact. */ 3206/* ------------------------------------------------------------------ */ 3207U_CAPI decNumber * U_EXPORT2 uprv_decNumberToIntegralExact(decNumber *res, const decNumber *rhs, 3208 decContext *set) { 3209 decNumber dn; 3210 decContext workset; /* working context */ 3211 uInt status=0; /* accumulator */ 3212 3213 #if DECCHECK 3214 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 3215 #endif 3216 3217 /* handle infinities and NaNs */ 3218 if (SPECIALARG) { 3219 if (decNumberIsInfinite(rhs)) uprv_decNumberCopy(res, rhs); /* an Infinity */ 3220 else decNaNs(res, rhs, NULL, set, &status); /* a NaN */ 3221 } 3222 else { /* finite */ 3223 /* have a finite number; no error possible (res must be big enough) */ 3224 if (rhs->exponent>=0) return uprv_decNumberCopy(res, rhs); 3225 /* that was easy, but if negative exponent there is work to do... */ 3226 workset=*set; /* clone rounding, etc. */ 3227 workset.digits=rhs->digits; /* no length rounding */ 3228 workset.traps=0; /* no traps */ 3229 uprv_decNumberZero(&dn); /* make a number with exponent 0 */ 3230 uprv_decNumberQuantize(res, rhs, &dn, &workset); 3231 status|=workset.status; 3232 } 3233 if (status!=0) decStatus(res, status, set); 3234 return res; 3235 } /* decNumberToIntegralExact */ 3236 3237U_CAPI decNumber * U_EXPORT2 uprv_decNumberToIntegralValue(decNumber *res, const decNumber *rhs, 3238 decContext *set) { 3239 decContext workset=*set; /* working context */ 3240 workset.traps=0; /* no traps */ 3241 uprv_decNumberToIntegralExact(res, rhs, &workset); 3242 /* this never affects set, except for sNaNs; NaN will have been set */ 3243 /* or propagated already, so no need to call decStatus */ 3244 set->status|=workset.status&DEC_Invalid_operation; 3245 return res; 3246 } /* decNumberToIntegralValue */ 3247 3248/* ------------------------------------------------------------------ */ 3249/* decNumberXor -- XOR two Numbers, digitwise */ 3250/* */ 3251/* This computes C = A ^ B */ 3252/* */ 3253/* res is C, the result. C may be A and/or B (e.g., X=X^X) */ 3254/* lhs is A */ 3255/* rhs is B */ 3256/* set is the context (used for result length and error report) */ 3257/* */ 3258/* C must have space for set->digits digits. */ 3259/* */ 3260/* Logical function restrictions apply (see above); a NaN is */ 3261/* returned with Invalid_operation if a restriction is violated. */ 3262/* ------------------------------------------------------------------ */ 3263U_CAPI decNumber * U_EXPORT2 uprv_decNumberXor(decNumber *res, const decNumber *lhs, 3264 const decNumber *rhs, decContext *set) { 3265 const Unit *ua, *ub; /* -> operands */ 3266 const Unit *msua, *msub; /* -> operand msus */ 3267 Unit *uc, *msuc; /* -> result and its msu */ 3268 Int msudigs; /* digits in res msu */ 3269 #if DECCHECK 3270 if (decCheckOperands(res, lhs, rhs, set)) return res; 3271 #endif 3272 3273 if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) 3274 || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { 3275 decStatus(res, DEC_Invalid_operation, set); 3276 return res; 3277 } 3278 /* operands are valid */ 3279 ua=lhs->lsu; /* bottom-up */ 3280 ub=rhs->lsu; /* .. */ 3281 uc=res->lsu; /* .. */ 3282 msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */ 3283 msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */ 3284 msuc=uc+D2U(set->digits)-1; /* -> msu of result */ 3285 msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ 3286 for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */ 3287 Unit a, b; /* extract units */ 3288 if (ua>msua) a=0; 3289 else a=*ua; 3290 if (ub>msub) b=0; 3291 else b=*ub; 3292 *uc=0; /* can now write back */ 3293 if (a|b) { /* maybe 1 bits to examine */ 3294 Int i, j; 3295 /* This loop could be unrolled and/or use BIN2BCD tables */ 3296 for (i=0; i<DECDPUN; i++) { 3297 if ((a^b)&1) *uc=*uc+(Unit)powers[i]; /* effect XOR */ 3298 j=a%10; 3299 a=a/10; 3300 j|=b%10; 3301 b=b/10; 3302 if (j>1) { 3303 decStatus(res, DEC_Invalid_operation, set); 3304 return res; 3305 } 3306 if (uc==msuc && i==msudigs-1) break; /* just did final digit */ 3307 } /* each digit */ 3308 } /* non-zero */ 3309 } /* each unit */ 3310 /* [here uc-1 is the msu of the result] */ 3311 res->digits=decGetDigits(res->lsu, uc-res->lsu); 3312 res->exponent=0; /* integer */ 3313 res->bits=0; /* sign=0 */ 3314 return res; /* [no status to set] */ 3315 } /* decNumberXor */ 3316 3317 3318/* ================================================================== */ 3319/* Utility routines */ 3320/* ================================================================== */ 3321 3322/* ------------------------------------------------------------------ */ 3323/* decNumberClass -- return the decClass of a decNumber */ 3324/* dn -- the decNumber to test */ 3325/* set -- the context to use for Emin */ 3326/* returns the decClass enum */ 3327/* ------------------------------------------------------------------ */ 3328enum decClass uprv_decNumberClass(const decNumber *dn, decContext *set) { 3329 if (decNumberIsSpecial(dn)) { 3330 if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN; 3331 if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN; 3332 /* must be an infinity */ 3333 if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF; 3334 return DEC_CLASS_POS_INF; 3335 } 3336 /* is finite */ 3337 if (uprv_decNumberIsNormal(dn, set)) { /* most common */ 3338 if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL; 3339 return DEC_CLASS_POS_NORMAL; 3340 } 3341 /* is subnormal or zero */ 3342 if (decNumberIsZero(dn)) { /* most common */ 3343 if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO; 3344 return DEC_CLASS_POS_ZERO; 3345 } 3346 if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL; 3347 return DEC_CLASS_POS_SUBNORMAL; 3348 } /* decNumberClass */ 3349 3350/* ------------------------------------------------------------------ */ 3351/* decNumberClassToString -- convert decClass to a string */ 3352/* */ 3353/* eclass is a valid decClass */ 3354/* returns a constant string describing the class (max 13+1 chars) */ 3355/* ------------------------------------------------------------------ */ 3356const char *uprv_decNumberClassToString(enum decClass eclass) { 3357 if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN; 3358 if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN; 3359 if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ; 3360 if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ; 3361 if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS; 3362 if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS; 3363 if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI; 3364 if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI; 3365 if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN; 3366 if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN; 3367 return DEC_ClassString_UN; /* Unknown */ 3368 } /* decNumberClassToString */ 3369 3370/* ------------------------------------------------------------------ */ 3371/* decNumberCopy -- copy a number */ 3372/* */ 3373/* dest is the target decNumber */ 3374/* src is the source decNumber */ 3375/* returns dest */ 3376/* */ 3377/* (dest==src is allowed and is a no-op) */ 3378/* All fields are updated as required. This is a utility operation, */ 3379/* so special values are unchanged and no error is possible. */ 3380/* ------------------------------------------------------------------ */ 3381U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopy(decNumber *dest, const decNumber *src) { 3382 3383 #if DECCHECK 3384 if (src==NULL) return uprv_decNumberZero(dest); 3385 #endif 3386 3387 if (dest==src) return dest; /* no copy required */ 3388 3389 /* Use explicit assignments here as structure assignment could copy */ 3390 /* more than just the lsu (for small DECDPUN). This would not affect */ 3391 /* the value of the results, but could disturb test harness spill */ 3392 /* checking. */ 3393 dest->bits=src->bits; 3394 dest->exponent=src->exponent; 3395 dest->digits=src->digits; 3396 dest->lsu[0]=src->lsu[0]; 3397 if (src->digits>DECDPUN) { /* more Units to come */ 3398 const Unit *smsup, *s; /* work */ 3399 Unit *d; /* .. */ 3400 /* memcpy for the remaining Units would be safe as they cannot */ 3401 /* overlap. However, this explicit loop is faster in short cases. */ 3402 d=dest->lsu+1; /* -> first destination */ 3403 smsup=src->lsu+D2U(src->digits); /* -> source msu+1 */ 3404 for (s=src->lsu+1; s<smsup; s++, d++) *d=*s; 3405 } 3406 return dest; 3407 } /* decNumberCopy */ 3408 3409/* ------------------------------------------------------------------ */ 3410/* decNumberCopyAbs -- quiet absolute value operator */ 3411/* */ 3412/* This sets C = abs(A) */ 3413/* */ 3414/* res is C, the result. C may be A */ 3415/* rhs is A */ 3416/* */ 3417/* C must have space for set->digits digits. */ 3418/* No exception or error can occur; this is a quiet bitwise operation.*/ 3419/* See also decNumberAbs for a checking version of this. */ 3420/* ------------------------------------------------------------------ */ 3421U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopyAbs(decNumber *res, const decNumber *rhs) { 3422 #if DECCHECK 3423 if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; 3424 #endif 3425 uprv_decNumberCopy(res, rhs); 3426 res->bits&=~DECNEG; /* turn off sign */ 3427 return res; 3428 } /* decNumberCopyAbs */ 3429 3430/* ------------------------------------------------------------------ */ 3431/* decNumberCopyNegate -- quiet negate value operator */ 3432/* */ 3433/* This sets C = negate(A) */ 3434/* */ 3435/* res is C, the result. C may be A */ 3436/* rhs is A */ 3437/* */ 3438/* C must have space for set->digits digits. */ 3439/* No exception or error can occur; this is a quiet bitwise operation.*/ 3440/* See also decNumberMinus for a checking version of this. */ 3441/* ------------------------------------------------------------------ */ 3442U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopyNegate(decNumber *res, const decNumber *rhs) { 3443 #if DECCHECK 3444 if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; 3445 #endif 3446 uprv_decNumberCopy(res, rhs); 3447 res->bits^=DECNEG; /* invert the sign */ 3448 return res; 3449 } /* decNumberCopyNegate */ 3450 3451/* ------------------------------------------------------------------ */ 3452/* decNumberCopySign -- quiet copy and set sign operator */ 3453/* */ 3454/* This sets C = A with the sign of B */ 3455/* */ 3456/* res is C, the result. C may be A */ 3457/* lhs is A */ 3458/* rhs is B */ 3459/* */ 3460/* C must have space for set->digits digits. */ 3461/* No exception or error can occur; this is a quiet bitwise operation.*/ 3462/* ------------------------------------------------------------------ */ 3463U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopySign(decNumber *res, const decNumber *lhs, 3464 const decNumber *rhs) { 3465 uByte sign; /* rhs sign */ 3466 #if DECCHECK 3467 if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; 3468 #endif 3469 sign=rhs->bits & DECNEG; /* save sign bit */ 3470 uprv_decNumberCopy(res, lhs); 3471 res->bits&=~DECNEG; /* clear the sign */ 3472 res->bits|=sign; /* set from rhs */ 3473 return res; 3474 } /* decNumberCopySign */ 3475 3476/* ------------------------------------------------------------------ */ 3477/* decNumberGetBCD -- get the coefficient in BCD8 */ 3478/* dn is the source decNumber */ 3479/* bcd is the uInt array that will receive dn->digits BCD bytes, */ 3480/* most-significant at offset 0 */ 3481/* returns bcd */ 3482/* */ 3483/* bcd must have at least dn->digits bytes. No error is possible; if */ 3484/* dn is a NaN or Infinite, digits must be 1 and the coefficient 0. */ 3485/* ------------------------------------------------------------------ */ 3486U_CAPI uByte * U_EXPORT2 uprv_decNumberGetBCD(const decNumber *dn, uByte *bcd) { 3487 uByte *ub=bcd+dn->digits-1; /* -> lsd */ 3488 const Unit *up=dn->lsu; /* Unit pointer, -> lsu */ 3489 3490 #if DECDPUN==1 /* trivial simple copy */ 3491 for (; ub>=bcd; ub--, up++) *ub=*up; 3492 #else /* chopping needed */ 3493 uInt u=*up; /* work */ 3494 uInt cut=DECDPUN; /* downcounter through unit */ 3495 for (; ub>=bcd; ub--) { 3496 *ub=(uByte)(u%10); /* [*6554 trick inhibits, here] */ 3497 u=u/10; 3498 cut--; 3499 if (cut>0) continue; /* more in this unit */ 3500 up++; 3501 u=*up; 3502 cut=DECDPUN; 3503 } 3504 #endif 3505 return bcd; 3506 } /* decNumberGetBCD */ 3507 3508/* ------------------------------------------------------------------ */ 3509/* decNumberSetBCD -- set (replace) the coefficient from BCD8 */ 3510/* dn is the target decNumber */ 3511/* bcd is the uInt array that will source n BCD bytes, most- */ 3512/* significant at offset 0 */ 3513/* n is the number of digits in the source BCD array (bcd) */ 3514/* returns dn */ 3515/* */ 3516/* dn must have space for at least n digits. No error is possible; */ 3517/* if dn is a NaN, or Infinite, or is to become a zero, n must be 1 */ 3518/* and bcd[0] zero. */ 3519/* ------------------------------------------------------------------ */ 3520U_CAPI decNumber * U_EXPORT2 uprv_decNumberSetBCD(decNumber *dn, const uByte *bcd, uInt n) { 3521 Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [target pointer] */ 3522 const uByte *ub=bcd; /* -> source msd */ 3523 3524 #if DECDPUN==1 /* trivial simple copy */ 3525 for (; ub<bcd+n; ub++, up--) *up=*ub; 3526 #else /* some assembly needed */ 3527 /* calculate how many digits in msu, and hence first cut */ 3528 Int cut=MSUDIGITS(n); /* [faster than remainder] */ 3529 for (;up>=dn->lsu; up--) { /* each Unit from msu */ 3530 *up=0; /* will take <=DECDPUN digits */ 3531 for (; cut>0; ub++, cut--) *up=X10(*up)+*ub; 3532 cut=DECDPUN; /* next Unit has all digits */ 3533 } 3534 #endif 3535 dn->digits=n; /* set digit count */ 3536 return dn; 3537 } /* decNumberSetBCD */ 3538 3539/* ------------------------------------------------------------------ */ 3540/* decNumberIsNormal -- test normality of a decNumber */ 3541/* dn is the decNumber to test */ 3542/* set is the context to use for Emin */ 3543/* returns 1 if |dn| is finite and >=Nmin, 0 otherwise */ 3544/* ------------------------------------------------------------------ */ 3545Int uprv_decNumberIsNormal(const decNumber *dn, decContext *set) { 3546 Int ae; /* adjusted exponent */ 3547 #if DECCHECK 3548 if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; 3549 #endif 3550 3551 if (decNumberIsSpecial(dn)) return 0; /* not finite */ 3552 if (decNumberIsZero(dn)) return 0; /* not non-zero */ 3553 3554 ae=dn->exponent+dn->digits-1; /* adjusted exponent */ 3555 if (ae<set->emin) return 0; /* is subnormal */ 3556 return 1; 3557 } /* decNumberIsNormal */ 3558 3559/* ------------------------------------------------------------------ */ 3560/* decNumberIsSubnormal -- test subnormality of a decNumber */ 3561/* dn is the decNumber to test */ 3562/* set is the context to use for Emin */ 3563/* returns 1 if |dn| is finite, non-zero, and <Nmin, 0 otherwise */ 3564/* ------------------------------------------------------------------ */ 3565Int uprv_decNumberIsSubnormal(const decNumber *dn, decContext *set) { 3566 Int ae; /* adjusted exponent */ 3567 #if DECCHECK 3568 if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; 3569 #endif 3570 3571 if (decNumberIsSpecial(dn)) return 0; /* not finite */ 3572 if (decNumberIsZero(dn)) return 0; /* not non-zero */ 3573 3574 ae=dn->exponent+dn->digits-1; /* adjusted exponent */ 3575 if (ae<set->emin) return 1; /* is subnormal */ 3576 return 0; 3577 } /* decNumberIsSubnormal */ 3578 3579/* ------------------------------------------------------------------ */ 3580/* decNumberTrim -- remove insignificant zeros */ 3581/* */ 3582/* dn is the number to trim */ 3583/* returns dn */ 3584/* */ 3585/* All fields are updated as required. This is a utility operation, */ 3586/* so special values are unchanged and no error is possible. The */ 3587/* zeros are removed unconditionally. */ 3588/* ------------------------------------------------------------------ */ 3589U_CAPI decNumber * U_EXPORT2 uprv_decNumberTrim(decNumber *dn) { 3590 Int dropped; /* work */ 3591 decContext set; /* .. */ 3592 #if DECCHECK 3593 if (decCheckOperands(DECUNRESU, DECUNUSED, dn, DECUNCONT)) return dn; 3594 #endif 3595 uprv_decContextDefault(&set, DEC_INIT_BASE); /* clamp=0 */ 3596 return decTrim(dn, &set, 0, 1, &dropped); 3597 } /* decNumberTrim */ 3598 3599/* ------------------------------------------------------------------ */ 3600/* decNumberVersion -- return the name and version of this module */ 3601/* */ 3602/* No error is possible. */ 3603/* ------------------------------------------------------------------ */ 3604const char * uprv_decNumberVersion(void) { 3605 return DECVERSION; 3606 } /* decNumberVersion */ 3607 3608/* ------------------------------------------------------------------ */ 3609/* decNumberZero -- set a number to 0 */ 3610/* */ 3611/* dn is the number to set, with space for one digit */ 3612/* returns dn */ 3613/* */ 3614/* No error is possible. */ 3615/* ------------------------------------------------------------------ */ 3616/* Memset is not used as it is much slower in some environments. */ 3617U_CAPI decNumber * U_EXPORT2 uprv_decNumberZero(decNumber *dn) { 3618 3619 #if DECCHECK 3620 if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn; 3621 #endif 3622 3623 dn->bits=0; 3624 dn->exponent=0; 3625 dn->digits=1; 3626 dn->lsu[0]=0; 3627 return dn; 3628 } /* decNumberZero */ 3629 3630/* ================================================================== */ 3631/* Local routines */ 3632/* ================================================================== */ 3633 3634/* ------------------------------------------------------------------ */ 3635/* decToString -- lay out a number into a string */ 3636/* */ 3637/* dn is the number to lay out */ 3638/* string is where to lay out the number */ 3639/* eng is 1 if Engineering, 0 if Scientific */ 3640/* */ 3641/* string must be at least dn->digits+14 characters long */ 3642/* No error is possible. */ 3643/* */ 3644/* Note that this routine can generate a -0 or 0.000. These are */ 3645/* never generated in subset to-number or arithmetic, but can occur */ 3646/* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234). */ 3647/* ------------------------------------------------------------------ */ 3648/* If DECCHECK is enabled the string "?" is returned if a number is */ 3649/* invalid. */ 3650static void decToString(const decNumber *dn, char *string, Flag eng) { 3651 Int exp=dn->exponent; /* local copy */ 3652 Int e; /* E-part value */ 3653 Int pre; /* digits before the '.' */ 3654 Int cut; /* for counting digits in a Unit */ 3655 char *c=string; /* work [output pointer] */ 3656 const Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [input pointer] */ 3657 uInt u, pow; /* work */ 3658 3659 #if DECCHECK 3660 if (decCheckOperands(DECUNRESU, dn, DECUNUSED, DECUNCONT)) { 3661 strcpy(string, "?"); 3662 return;} 3663 #endif 3664 3665 if (decNumberIsNegative(dn)) { /* Negatives get a minus */ 3666 *c='-'; 3667 c++; 3668 } 3669 if (dn->bits&DECSPECIAL) { /* Is a special value */ 3670 if (decNumberIsInfinite(dn)) { 3671 strcpy(c, "Inf"); 3672 strcpy(c+3, "inity"); 3673 return;} 3674 /* a NaN */ 3675 if (dn->bits&DECSNAN) { /* signalling NaN */ 3676 *c='s'; 3677 c++; 3678 } 3679 strcpy(c, "NaN"); 3680 c+=3; /* step past */ 3681 /* if not a clean non-zero coefficient, that's all there is in a */ 3682 /* NaN string */ 3683 if (exp!=0 || (*dn->lsu==0 && dn->digits==1)) return; 3684 /* [drop through to add integer] */ 3685 } 3686 3687 /* calculate how many digits in msu, and hence first cut */ 3688 cut=MSUDIGITS(dn->digits); /* [faster than remainder] */ 3689 cut--; /* power of ten for digit */ 3690 3691 if (exp==0) { /* simple integer [common fastpath] */ 3692 for (;up>=dn->lsu; up--) { /* each Unit from msu */ 3693 u=*up; /* contains DECDPUN digits to lay out */ 3694 for (; cut>=0; c++, cut--) TODIGIT(u, cut, c, pow); 3695 cut=DECDPUN-1; /* next Unit has all digits */ 3696 } 3697 *c='\0'; /* terminate the string */ 3698 return;} 3699 3700 /* non-0 exponent -- assume plain form */ 3701 pre=dn->digits+exp; /* digits before '.' */ 3702 e=0; /* no E */ 3703 if ((exp>0) || (pre<-5)) { /* need exponential form */ 3704 e=exp+dn->digits-1; /* calculate E value */ 3705 pre=1; /* assume one digit before '.' */ 3706 if (eng && (e!=0)) { /* engineering: may need to adjust */ 3707 Int adj; /* adjustment */ 3708 /* The C remainder operator is undefined for negative numbers, so */ 3709 /* a positive remainder calculation must be used here */ 3710 if (e<0) { 3711 adj=(-e)%3; 3712 if (adj!=0) adj=3-adj; 3713 } 3714 else { /* e>0 */ 3715 adj=e%3; 3716 } 3717 e=e-adj; 3718 /* if dealing with zero still produce an exponent which is a */ 3719 /* multiple of three, as expected, but there will only be the */ 3720 /* one zero before the E, still. Otherwise note the padding. */ 3721 if (!ISZERO(dn)) pre+=adj; 3722 else { /* is zero */ 3723 if (adj!=0) { /* 0.00Esnn needed */ 3724 e=e+3; 3725 pre=-(2-adj); 3726 } 3727 } /* zero */ 3728 } /* eng */ 3729 } /* need exponent */ 3730 3731 /* lay out the digits of the coefficient, adding 0s and . as needed */ 3732 u=*up; 3733 if (pre>0) { /* xxx.xxx or xx00 (engineering) form */ 3734 Int n=pre; 3735 for (; pre>0; pre--, c++, cut--) { 3736 if (cut<0) { /* need new Unit */ 3737 if (up==dn->lsu) break; /* out of input digits (pre>digits) */ 3738 up--; 3739 cut=DECDPUN-1; 3740 u=*up; 3741 } 3742 TODIGIT(u, cut, c, pow); 3743 } 3744 if (n<dn->digits) { /* more to come, after '.' */ 3745 *c='.'; c++; 3746 for (;; c++, cut--) { 3747 if (cut<0) { /* need new Unit */ 3748 if (up==dn->lsu) break; /* out of input digits */ 3749 up--; 3750 cut=DECDPUN-1; 3751 u=*up; 3752 } 3753 TODIGIT(u, cut, c, pow); 3754 } 3755 } 3756 else for (; pre>0; pre--, c++) *c='0'; /* 0 padding (for engineering) needed */ 3757 } 3758 else { /* 0.xxx or 0.000xxx form */ 3759 *c='0'; c++; 3760 *c='.'; c++; 3761 for (; pre<0; pre++, c++) *c='0'; /* add any 0's after '.' */ 3762 for (; ; c++, cut--) { 3763 if (cut<0) { /* need new Unit */ 3764 if (up==dn->lsu) break; /* out of input digits */ 3765 up--; 3766 cut=DECDPUN-1; 3767 u=*up; 3768 } 3769 TODIGIT(u, cut, c, pow); 3770 } 3771 } 3772 3773 /* Finally add the E-part, if needed. It will never be 0, has a 3774 base maximum and minimum of +999999999 through -999999999, but 3775 could range down to -1999999998 for anormal numbers */ 3776 if (e!=0) { 3777 Flag had=0; /* 1=had non-zero */ 3778 *c='E'; c++; 3779 *c='+'; c++; /* assume positive */ 3780 u=e; /* .. */ 3781 if (e<0) { 3782 *(c-1)='-'; /* oops, need - */ 3783 u=-e; /* uInt, please */ 3784 } 3785 /* lay out the exponent [_itoa or equivalent is not ANSI C] */ 3786 for (cut=9; cut>=0; cut--) { 3787 TODIGIT(u, cut, c, pow); 3788 if (*c=='0' && !had) continue; /* skip leading zeros */ 3789 had=1; /* had non-0 */ 3790 c++; /* step for next */ 3791 } /* cut */ 3792 } 3793 *c='\0'; /* terminate the string (all paths) */ 3794 return; 3795 } /* decToString */ 3796 3797/* ------------------------------------------------------------------ */ 3798/* decAddOp -- add/subtract operation */ 3799/* */ 3800/* This computes C = A + B */ 3801/* */ 3802/* res is C, the result. C may be A and/or B (e.g., X=X+X) */ 3803/* lhs is A */ 3804/* rhs is B */ 3805/* set is the context */ 3806/* negate is DECNEG if rhs should be negated, or 0 otherwise */ 3807/* status accumulates status for the caller */ 3808/* */ 3809/* C must have space for set->digits digits. */ 3810/* Inexact in status must be 0 for correct Exact zero sign in result */ 3811/* ------------------------------------------------------------------ */ 3812/* If possible, the coefficient is calculated directly into C. */ 3813/* However, if: */ 3814/* -- a digits+1 calculation is needed because the numbers are */ 3815/* unaligned and span more than set->digits digits */ 3816/* -- a carry to digits+1 digits looks possible */ 3817/* -- C is the same as A or B, and the result would destructively */ 3818/* overlap the A or B coefficient */ 3819/* then the result must be calculated into a temporary buffer. In */ 3820/* this case a local (stack) buffer is used if possible, and only if */ 3821/* too long for that does malloc become the final resort. */ 3822/* */ 3823/* Misalignment is handled as follows: */ 3824/* Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp. */ 3825/* BPad: Apply the padding by a combination of shifting (whole */ 3826/* units) and multiplication (part units). */ 3827/* */ 3828/* Addition, especially x=x+1, is speed-critical. */ 3829/* The static buffer is larger than might be expected to allow for */ 3830/* calls from higher-level funtions (notable exp). */ 3831/* ------------------------------------------------------------------ */ 3832static decNumber * decAddOp(decNumber *res, const decNumber *lhs, 3833 const decNumber *rhs, decContext *set, 3834 uByte negate, uInt *status) { 3835 #if DECSUBSET 3836 decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ 3837 decNumber *allocrhs=NULL; /* .., rhs */ 3838 #endif 3839 Int rhsshift; /* working shift (in Units) */ 3840 Int maxdigits; /* longest logical length */ 3841 Int mult; /* multiplier */ 3842 Int residue; /* rounding accumulator */ 3843 uByte bits; /* result bits */ 3844 Flag diffsign; /* non-0 if arguments have different sign */ 3845 Unit *acc; /* accumulator for result */ 3846 Unit accbuff[SD2U(DECBUFFER*2+20)]; /* local buffer [*2+20 reduces many */ 3847 /* allocations when called from */ 3848 /* other operations, notable exp] */ 3849 Unit *allocacc=NULL; /* -> allocated acc buffer, iff allocated */ 3850 Int reqdigits=set->digits; /* local copy; requested DIGITS */ 3851 Int padding; /* work */ 3852 3853 #if DECCHECK 3854 if (decCheckOperands(res, lhs, rhs, set)) return res; 3855 #endif 3856 3857 do { /* protect allocated storage */ 3858 #if DECSUBSET 3859 if (!set->extended) { 3860 /* reduce operands and set lostDigits status, as needed */ 3861 if (lhs->digits>reqdigits) { 3862 alloclhs=decRoundOperand(lhs, set, status); 3863 if (alloclhs==NULL) break; 3864 lhs=alloclhs; 3865 } 3866 if (rhs->digits>reqdigits) { 3867 allocrhs=decRoundOperand(rhs, set, status); 3868 if (allocrhs==NULL) break; 3869 rhs=allocrhs; 3870 } 3871 } 3872 #endif 3873 /* [following code does not require input rounding] */ 3874 3875 /* note whether signs differ [used all paths] */ 3876 diffsign=(Flag)((lhs->bits^rhs->bits^negate)&DECNEG); 3877 3878 /* handle infinities and NaNs */ 3879 if (SPECIALARGS) { /* a special bit set */ 3880 if (SPECIALARGS & (DECSNAN | DECNAN)) /* a NaN */ 3881 decNaNs(res, lhs, rhs, set, status); 3882 else { /* one or two infinities */ 3883 if (decNumberIsInfinite(lhs)) { /* LHS is infinity */ 3884 /* two infinities with different signs is invalid */ 3885 if (decNumberIsInfinite(rhs) && diffsign) { 3886 *status|=DEC_Invalid_operation; 3887 break; 3888 } 3889 bits=lhs->bits & DECNEG; /* get sign from LHS */ 3890 } 3891 else bits=(rhs->bits^negate) & DECNEG;/* RHS must be Infinity */ 3892 bits|=DECINF; 3893 uprv_decNumberZero(res); 3894 res->bits=bits; /* set +/- infinity */ 3895 } /* an infinity */ 3896 break; 3897 } 3898 3899 /* Quick exit for add 0s; return the non-0, modified as need be */ 3900 if (ISZERO(lhs)) { 3901 Int adjust; /* work */ 3902 Int lexp=lhs->exponent; /* save in case LHS==RES */ 3903 bits=lhs->bits; /* .. */ 3904 residue=0; /* clear accumulator */ 3905 decCopyFit(res, rhs, set, &residue, status); /* copy (as needed) */ 3906 res->bits^=negate; /* flip if rhs was negated */ 3907 #if DECSUBSET 3908 if (set->extended) { /* exponents on zeros count */ 3909 #endif 3910 /* exponent will be the lower of the two */ 3911 adjust=lexp-res->exponent; /* adjustment needed [if -ve] */ 3912 if (ISZERO(res)) { /* both 0: special IEEE 754 rules */ 3913 if (adjust<0) res->exponent=lexp; /* set exponent */ 3914 /* 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0 */ 3915 if (diffsign) { 3916 if (set->round!=DEC_ROUND_FLOOR) res->bits=0; 3917 else res->bits=DECNEG; /* preserve 0 sign */ 3918 } 3919 } 3920 else { /* non-0 res */ 3921 if (adjust<0) { /* 0-padding needed */ 3922 if ((res->digits-adjust)>set->digits) { 3923 adjust=res->digits-set->digits; /* to fit exactly */ 3924 *status|=DEC_Rounded; /* [but exact] */ 3925 } 3926 res->digits=decShiftToMost(res->lsu, res->digits, -adjust); 3927 res->exponent+=adjust; /* set the exponent. */ 3928 } 3929 } /* non-0 res */ 3930 #if DECSUBSET 3931 } /* extended */ 3932 #endif 3933 decFinish(res, set, &residue, status); /* clean and finalize */ 3934 break;} 3935 3936 if (ISZERO(rhs)) { /* [lhs is non-zero] */ 3937 Int adjust; /* work */ 3938 Int rexp=rhs->exponent; /* save in case RHS==RES */ 3939 bits=rhs->bits; /* be clean */ 3940 residue=0; /* clear accumulator */ 3941 decCopyFit(res, lhs, set, &residue, status); /* copy (as needed) */ 3942 #if DECSUBSET 3943 if (set->extended) { /* exponents on zeros count */ 3944 #endif 3945 /* exponent will be the lower of the two */ 3946 /* [0-0 case handled above] */ 3947 adjust=rexp-res->exponent; /* adjustment needed [if -ve] */ 3948 if (adjust<0) { /* 0-padding needed */ 3949 if ((res->digits-adjust)>set->digits) { 3950 adjust=res->digits-set->digits; /* to fit exactly */ 3951 *status|=DEC_Rounded; /* [but exact] */ 3952 } 3953 res->digits=decShiftToMost(res->lsu, res->digits, -adjust); 3954 res->exponent+=adjust; /* set the exponent. */ 3955 } 3956 #if DECSUBSET 3957 } /* extended */ 3958 #endif 3959 decFinish(res, set, &residue, status); /* clean and finalize */ 3960 break;} 3961 3962 /* [NB: both fastpath and mainpath code below assume these cases */ 3963 /* (notably 0-0) have already been handled] */ 3964 3965 /* calculate the padding needed to align the operands */ 3966 padding=rhs->exponent-lhs->exponent; 3967 3968 /* Fastpath cases where the numbers are aligned and normal, the RHS */ 3969 /* is all in one unit, no operand rounding is needed, and no carry, */ 3970 /* lengthening, or borrow is needed */ 3971 if (padding==0 3972 && rhs->digits<=DECDPUN 3973 && rhs->exponent>=set->emin /* [some normals drop through] */ 3974 && rhs->exponent<=set->emax-set->digits+1 /* [could clamp] */ 3975 && rhs->digits<=reqdigits 3976 && lhs->digits<=reqdigits) { 3977 Int partial=*lhs->lsu; 3978 if (!diffsign) { /* adding */ 3979 partial+=*rhs->lsu; 3980 if ((partial<=DECDPUNMAX) /* result fits in unit */ 3981 && (lhs->digits>=DECDPUN || /* .. and no digits-count change */ 3982 partial<(Int)powers[lhs->digits])) { /* .. */ 3983 if (res!=lhs) uprv_decNumberCopy(res, lhs); /* not in place */ 3984 *res->lsu=(Unit)partial; /* [copy could have overwritten RHS] */ 3985 break; 3986 } 3987 /* else drop out for careful add */ 3988 } 3989 else { /* signs differ */ 3990 partial-=*rhs->lsu; 3991 if (partial>0) { /* no borrow needed, and non-0 result */ 3992 if (res!=lhs) uprv_decNumberCopy(res, lhs); /* not in place */ 3993 *res->lsu=(Unit)partial; 3994 /* this could have reduced digits [but result>0] */ 3995 res->digits=decGetDigits(res->lsu, D2U(res->digits)); 3996 break; 3997 } 3998 /* else drop out for careful subtract */ 3999 } 4000 } 4001 4002 /* Now align (pad) the lhs or rhs so they can be added or */ 4003 /* subtracted, as necessary. If one number is much larger than */ 4004 /* the other (that is, if in plain form there is a least one */ 4005 /* digit between the lowest digit of one and the highest of the */ 4006 /* other) padding with up to DIGITS-1 trailing zeros may be */ 4007 /* needed; then apply rounding (as exotic rounding modes may be */ 4008 /* affected by the residue). */ 4009 rhsshift=0; /* rhs shift to left (padding) in Units */ 4010 bits=lhs->bits; /* assume sign is that of LHS */ 4011 mult=1; /* likely multiplier */ 4012 4013 /* [if padding==0 the operands are aligned; no padding is needed] */ 4014 if (padding!=0) { 4015 /* some padding needed; always pad the RHS, as any required */ 4016 /* padding can then be effected by a simple combination of */ 4017 /* shifts and a multiply */ 4018 Flag swapped=0; 4019 if (padding<0) { /* LHS needs the padding */ 4020 const decNumber *t; 4021 padding=-padding; /* will be +ve */ 4022 bits=(uByte)(rhs->bits^negate); /* assumed sign is now that of RHS */ 4023 t=lhs; lhs=rhs; rhs=t; 4024 swapped=1; 4025 } 4026 4027 /* If, after pad, rhs would be longer than lhs by digits+1 or */ 4028 /* more then lhs cannot affect the answer, except as a residue, */ 4029 /* so only need to pad up to a length of DIGITS+1. */ 4030 if (rhs->digits+padding > lhs->digits+reqdigits+1) { 4031 /* The RHS is sufficient */ 4032 /* for residue use the relative sign indication... */ 4033 Int shift=reqdigits-rhs->digits; /* left shift needed */ 4034 residue=1; /* residue for rounding */ 4035 if (diffsign) residue=-residue; /* signs differ */ 4036 /* copy, shortening if necessary */ 4037 decCopyFit(res, rhs, set, &residue, status); 4038 /* if it was already shorter, then need to pad with zeros */ 4039 if (shift>0) { 4040 res->digits=decShiftToMost(res->lsu, res->digits, shift); 4041 res->exponent-=shift; /* adjust the exponent. */ 4042 } 4043 /* flip the result sign if unswapped and rhs was negated */ 4044 if (!swapped) res->bits^=negate; 4045 decFinish(res, set, &residue, status); /* done */ 4046 break;} 4047 4048 /* LHS digits may affect result */ 4049 rhsshift=D2U(padding+1)-1; /* this much by Unit shift .. */ 4050 mult=powers[padding-(rhsshift*DECDPUN)]; /* .. this by multiplication */ 4051 } /* padding needed */ 4052 4053 if (diffsign) mult=-mult; /* signs differ */ 4054 4055 /* determine the longer operand */ 4056 maxdigits=rhs->digits+padding; /* virtual length of RHS */ 4057 if (lhs->digits>maxdigits) maxdigits=lhs->digits; 4058 4059 /* Decide on the result buffer to use; if possible place directly */ 4060 /* into result. */ 4061 acc=res->lsu; /* assume add direct to result */ 4062 /* If destructive overlap, or the number is too long, or a carry or */ 4063 /* borrow to DIGITS+1 might be possible, a buffer must be used. */ 4064 /* [Might be worth more sophisticated tests when maxdigits==reqdigits] */ 4065 if ((maxdigits>=reqdigits) /* is, or could be, too large */ 4066 || (res==rhs && rhsshift>0)) { /* destructive overlap */ 4067 /* buffer needed, choose it; units for maxdigits digits will be */ 4068 /* needed, +1 Unit for carry or borrow */ 4069 Int need=D2U(maxdigits)+1; 4070 acc=accbuff; /* assume use local buffer */ 4071 if (need*sizeof(Unit)>sizeof(accbuff)) { 4072 /* printf("malloc add %ld %ld\n", need, sizeof(accbuff)); */ 4073 allocacc=(Unit *)malloc(need*sizeof(Unit)); 4074 if (allocacc==NULL) { /* hopeless -- abandon */ 4075 *status|=DEC_Insufficient_storage; 4076 break;} 4077 acc=allocacc; 4078 } 4079 } 4080 4081 res->bits=(uByte)(bits&DECNEG); /* it's now safe to overwrite.. */ 4082 res->exponent=lhs->exponent; /* .. operands (even if aliased) */ 4083 4084 #if DECTRACE 4085 decDumpAr('A', lhs->lsu, D2U(lhs->digits)); 4086 decDumpAr('B', rhs->lsu, D2U(rhs->digits)); 4087 printf(" :h: %ld %ld\n", rhsshift, mult); 4088 #endif 4089 4090 /* add [A+B*m] or subtract [A+B*(-m)] */ 4091 U_ASSERT(rhs->digits > 0); 4092 U_ASSERT(lhs->digits > 0); 4093 res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits), 4094 rhs->lsu, D2U(rhs->digits), 4095 rhsshift, acc, mult) 4096 *DECDPUN; /* [units -> digits] */ 4097 if (res->digits<0) { /* borrowed... */ 4098 res->digits=-res->digits; 4099 res->bits^=DECNEG; /* flip the sign */ 4100 } 4101 #if DECTRACE 4102 decDumpAr('+', acc, D2U(res->digits)); 4103 #endif 4104 4105 /* If a buffer was used the result must be copied back, possibly */ 4106 /* shortening. (If no buffer was used then the result must have */ 4107 /* fit, so can't need rounding and residue must be 0.) */ 4108 residue=0; /* clear accumulator */ 4109 if (acc!=res->lsu) { 4110 #if DECSUBSET 4111 if (set->extended) { /* round from first significant digit */ 4112 #endif 4113 /* remove leading zeros that were added due to rounding up to */ 4114 /* integral Units -- before the test for rounding. */ 4115 if (res->digits>reqdigits) 4116 res->digits=decGetDigits(acc, D2U(res->digits)); 4117 decSetCoeff(res, set, acc, res->digits, &residue, status); 4118 #if DECSUBSET 4119 } 4120 else { /* subset arithmetic rounds from original significant digit */ 4121 /* May have an underestimate. This only occurs when both */ 4122 /* numbers fit in DECDPUN digits and are padding with a */ 4123 /* negative multiple (-10, -100...) and the top digit(s) become */ 4124 /* 0. (This only matters when using X3.274 rules where the */ 4125 /* leading zero could be included in the rounding.) */ 4126 if (res->digits<maxdigits) { 4127 *(acc+D2U(res->digits))=0; /* ensure leading 0 is there */ 4128 res->digits=maxdigits; 4129 } 4130 else { 4131 /* remove leading zeros that added due to rounding up to */ 4132 /* integral Units (but only those in excess of the original */ 4133 /* maxdigits length, unless extended) before test for rounding. */ 4134 if (res->digits>reqdigits) { 4135 res->digits=decGetDigits(acc, D2U(res->digits)); 4136 if (res->digits<maxdigits) res->digits=maxdigits; 4137 } 4138 } 4139 decSetCoeff(res, set, acc, res->digits, &residue, status); 4140 /* Now apply rounding if needed before removing leading zeros. */ 4141 /* This is safe because subnormals are not a possibility */ 4142 if (residue!=0) { 4143 decApplyRound(res, set, residue, status); 4144 residue=0; /* did what needed to be done */ 4145 } 4146 } /* subset */ 4147 #endif 4148 } /* used buffer */ 4149 4150 /* strip leading zeros [these were left on in case of subset subtract] */ 4151 res->digits=decGetDigits(res->lsu, D2U(res->digits)); 4152 4153 /* apply checks and rounding */ 4154 decFinish(res, set, &residue, status); 4155 4156 /* "When the sum of two operands with opposite signs is exactly */ 4157 /* zero, the sign of that sum shall be '+' in all rounding modes */ 4158 /* except round toward -Infinity, in which mode that sign shall be */ 4159 /* '-'." [Subset zeros also never have '-', set by decFinish.] */ 4160 if (ISZERO(res) && diffsign 4161 #if DECSUBSET 4162 && set->extended 4163 #endif 4164 && (*status&DEC_Inexact)==0) { 4165 if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG; /* sign - */ 4166 else res->bits&=~DECNEG; /* sign + */ 4167 } 4168 } while(0); /* end protected */ 4169 4170 if (allocacc!=NULL) free(allocacc); /* drop any storage used */ 4171 #if DECSUBSET 4172 if (allocrhs!=NULL) free(allocrhs); /* .. */ 4173 if (alloclhs!=NULL) free(alloclhs); /* .. */ 4174 #endif 4175 return res; 4176 } /* decAddOp */ 4177 4178/* ------------------------------------------------------------------ */ 4179/* decDivideOp -- division operation */ 4180/* */ 4181/* This routine performs the calculations for all four division */ 4182/* operators (divide, divideInteger, remainder, remainderNear). */ 4183/* */ 4184/* C=A op B */ 4185/* */ 4186/* res is C, the result. C may be A and/or B (e.g., X=X/X) */ 4187/* lhs is A */ 4188/* rhs is B */ 4189/* set is the context */ 4190/* op is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively. */ 4191/* status is the usual accumulator */ 4192/* */ 4193/* C must have space for set->digits digits. */ 4194/* */ 4195/* ------------------------------------------------------------------ */ 4196/* The underlying algorithm of this routine is the same as in the */ 4197/* 1981 S/370 implementation, that is, non-restoring long division */ 4198/* with bi-unit (rather than bi-digit) estimation for each unit */ 4199/* multiplier. In this pseudocode overview, complications for the */ 4200/* Remainder operators and division residues for exact rounding are */ 4201/* omitted for clarity. */ 4202/* */ 4203/* Prepare operands and handle special values */ 4204/* Test for x/0 and then 0/x */ 4205/* Exp =Exp1 - Exp2 */ 4206/* Exp =Exp +len(var1) -len(var2) */ 4207/* Sign=Sign1 * Sign2 */ 4208/* Pad accumulator (Var1) to double-length with 0's (pad1) */ 4209/* Pad Var2 to same length as Var1 */ 4210/* msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round */ 4211/* have=0 */ 4212/* Do until (have=digits+1 OR residue=0) */ 4213/* if exp<0 then if integer divide/residue then leave */ 4214/* this_unit=0 */ 4215/* Do forever */ 4216/* compare numbers */ 4217/* if <0 then leave inner_loop */ 4218/* if =0 then (* quick exit without subtract *) do */ 4219/* this_unit=this_unit+1; output this_unit */ 4220/* leave outer_loop; end */ 4221/* Compare lengths of numbers (mantissae): */ 4222/* If same then tops2=msu2pair -- {units 1&2 of var2} */ 4223/* else tops2=msu2plus -- {0, unit 1 of var2} */ 4224/* tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */ 4225/* mult=tops1/tops2 -- Good and safe guess at divisor */ 4226/* if mult=0 then mult=1 */ 4227/* this_unit=this_unit+mult */ 4228/* subtract */ 4229/* end inner_loop */ 4230/* if have\=0 | this_unit\=0 then do */ 4231/* output this_unit */ 4232/* have=have+1; end */ 4233/* var2=var2/10 */ 4234/* exp=exp-1 */ 4235/* end outer_loop */ 4236/* exp=exp+1 -- set the proper exponent */ 4237/* if have=0 then generate answer=0 */ 4238/* Return (Result is defined by Var1) */ 4239/* */ 4240/* ------------------------------------------------------------------ */ 4241/* Two working buffers are needed during the division; one (digits+ */ 4242/* 1) to accumulate the result, and the other (up to 2*digits+1) for */ 4243/* long subtractions. These are acc and var1 respectively. */ 4244/* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/ 4245/* The static buffers may be larger than might be expected to allow */ 4246/* for calls from higher-level funtions (notable exp). */ 4247/* ------------------------------------------------------------------ */ 4248static decNumber * decDivideOp(decNumber *res, 4249 const decNumber *lhs, const decNumber *rhs, 4250 decContext *set, Flag op, uInt *status) { 4251 #if DECSUBSET 4252 decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ 4253 decNumber *allocrhs=NULL; /* .., rhs */ 4254 #endif 4255 Unit accbuff[SD2U(DECBUFFER+DECDPUN+10)]; /* local buffer */ 4256 Unit *acc=accbuff; /* -> accumulator array for result */ 4257 Unit *allocacc=NULL; /* -> allocated buffer, iff allocated */ 4258 Unit *accnext; /* -> where next digit will go */ 4259 Int acclength; /* length of acc needed [Units] */ 4260 Int accunits; /* count of units accumulated */ 4261 Int accdigits; /* count of digits accumulated */ 4262 4263 Unit varbuff[SD2U(DECBUFFER*2+DECDPUN)]; /* buffer for var1 */ 4264 Unit *var1=varbuff; /* -> var1 array for long subtraction */ 4265 Unit *varalloc=NULL; /* -> allocated buffer, iff used */ 4266 Unit *msu1; /* -> msu of var1 */ 4267 4268 const Unit *var2; /* -> var2 array */ 4269 const Unit *msu2; /* -> msu of var2 */ 4270 Int msu2plus; /* msu2 plus one [does not vary] */ 4271 eInt msu2pair; /* msu2 pair plus one [does not vary] */ 4272 4273 Int var1units, var2units; /* actual lengths */ 4274 Int var2ulen; /* logical length (units) */ 4275 Int var1initpad=0; /* var1 initial padding (digits) */ 4276 Int maxdigits; /* longest LHS or required acc length */ 4277 Int mult; /* multiplier for subtraction */ 4278 Unit thisunit; /* current unit being accumulated */ 4279 Int residue; /* for rounding */ 4280 Int reqdigits=set->digits; /* requested DIGITS */ 4281 Int exponent; /* working exponent */ 4282 Int maxexponent=0; /* DIVIDE maximum exponent if unrounded */ 4283 uByte bits; /* working sign */ 4284 Unit *target; /* work */ 4285 const Unit *source; /* .. */ 4286 uInt const *pow; /* .. */ 4287 Int shift, cut; /* .. */ 4288 #if DECSUBSET 4289 Int dropped; /* work */ 4290 #endif 4291 4292 #if DECCHECK 4293 if (decCheckOperands(res, lhs, rhs, set)) return res; 4294 #endif 4295 4296 do { /* protect allocated storage */ 4297 #if DECSUBSET 4298 if (!set->extended) { 4299 /* reduce operands and set lostDigits status, as needed */ 4300 if (lhs->digits>reqdigits) { 4301 alloclhs=decRoundOperand(lhs, set, status); 4302 if (alloclhs==NULL) break; 4303 lhs=alloclhs; 4304 } 4305 if (rhs->digits>reqdigits) { 4306 allocrhs=decRoundOperand(rhs, set, status); 4307 if (allocrhs==NULL) break; 4308 rhs=allocrhs; 4309 } 4310 } 4311 #endif 4312 /* [following code does not require input rounding] */ 4313 4314 bits=(lhs->bits^rhs->bits)&DECNEG; /* assumed sign for divisions */ 4315 4316 /* handle infinities and NaNs */ 4317 if (SPECIALARGS) { /* a special bit set */ 4318 if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */ 4319 decNaNs(res, lhs, rhs, set, status); 4320 break; 4321 } 4322 /* one or two infinities */ 4323 if (decNumberIsInfinite(lhs)) { /* LHS (dividend) is infinite */ 4324 if (decNumberIsInfinite(rhs) || /* two infinities are invalid .. */ 4325 op & (REMAINDER | REMNEAR)) { /* as is remainder of infinity */ 4326 *status|=DEC_Invalid_operation; 4327 break; 4328 } 4329 /* [Note that infinity/0 raises no exceptions] */ 4330 uprv_decNumberZero(res); 4331 res->bits=bits|DECINF; /* set +/- infinity */ 4332 break; 4333 } 4334 else { /* RHS (divisor) is infinite */ 4335 residue=0; 4336 if (op&(REMAINDER|REMNEAR)) { 4337 /* result is [finished clone of] lhs */ 4338 decCopyFit(res, lhs, set, &residue, status); 4339 } 4340 else { /* a division */ 4341 uprv_decNumberZero(res); 4342 res->bits=bits; /* set +/- zero */ 4343 /* for DIVIDEINT the exponent is always 0. For DIVIDE, result */ 4344 /* is a 0 with infinitely negative exponent, clamped to minimum */ 4345 if (op&DIVIDE) { 4346 res->exponent=set->emin-set->digits+1; 4347 *status|=DEC_Clamped; 4348 } 4349 } 4350 decFinish(res, set, &residue, status); 4351 break; 4352 } 4353 } 4354 4355 /* handle 0 rhs (x/0) */ 4356 if (ISZERO(rhs)) { /* x/0 is always exceptional */ 4357 if (ISZERO(lhs)) { 4358 uprv_decNumberZero(res); /* [after lhs test] */ 4359 *status|=DEC_Division_undefined;/* 0/0 will become NaN */ 4360 } 4361 else { 4362 uprv_decNumberZero(res); 4363 if (op&(REMAINDER|REMNEAR)) *status|=DEC_Invalid_operation; 4364 else { 4365 *status|=DEC_Division_by_zero; /* x/0 */ 4366 res->bits=bits|DECINF; /* .. is +/- Infinity */ 4367 } 4368 } 4369 break;} 4370 4371 /* handle 0 lhs (0/x) */ 4372 if (ISZERO(lhs)) { /* 0/x [x!=0] */ 4373 #if DECSUBSET 4374 if (!set->extended) uprv_decNumberZero(res); 4375 else { 4376 #endif 4377 if (op&DIVIDE) { 4378 residue=0; 4379 exponent=lhs->exponent-rhs->exponent; /* ideal exponent */ 4380 uprv_decNumberCopy(res, lhs); /* [zeros always fit] */ 4381 res->bits=bits; /* sign as computed */ 4382 res->exponent=exponent; /* exponent, too */ 4383 decFinalize(res, set, &residue, status); /* check exponent */ 4384 } 4385 else if (op&DIVIDEINT) { 4386 uprv_decNumberZero(res); /* integer 0 */ 4387 res->bits=bits; /* sign as computed */ 4388 } 4389 else { /* a remainder */ 4390 exponent=rhs->exponent; /* [save in case overwrite] */ 4391 uprv_decNumberCopy(res, lhs); /* [zeros always fit] */ 4392 if (exponent<res->exponent) res->exponent=exponent; /* use lower */ 4393 } 4394 #if DECSUBSET 4395 } 4396 #endif 4397 break;} 4398 4399 /* Precalculate exponent. This starts off adjusted (and hence fits */ 4400 /* in 31 bits) and becomes the usual unadjusted exponent as the */ 4401 /* division proceeds. The order of evaluation is important, here, */ 4402 /* to avoid wrap. */ 4403 exponent=(lhs->exponent+lhs->digits)-(rhs->exponent+rhs->digits); 4404 4405 /* If the working exponent is -ve, then some quick exits are */ 4406 /* possible because the quotient is known to be <1 */ 4407 /* [for REMNEAR, it needs to be < -1, as -0.5 could need work] */ 4408 if (exponent<0 && !(op==DIVIDE)) { 4409 if (op&DIVIDEINT) { 4410 uprv_decNumberZero(res); /* integer part is 0 */ 4411 #if DECSUBSET 4412 if (set->extended) 4413 #endif 4414 res->bits=bits; /* set +/- zero */ 4415 break;} 4416 /* fastpath remainders so long as the lhs has the smaller */ 4417 /* (or equal) exponent */ 4418 if (lhs->exponent<=rhs->exponent) { 4419 if (op&REMAINDER || exponent<-1) { 4420 /* It is REMAINDER or safe REMNEAR; result is [finished */ 4421 /* clone of] lhs (r = x - 0*y) */ 4422 residue=0; 4423 decCopyFit(res, lhs, set, &residue, status); 4424 decFinish(res, set, &residue, status); 4425 break; 4426 } 4427 /* [unsafe REMNEAR drops through] */ 4428 } 4429 } /* fastpaths */ 4430 4431 /* Long (slow) division is needed; roll up the sleeves... */ 4432 4433 /* The accumulator will hold the quotient of the division. */ 4434 /* If it needs to be too long for stack storage, then allocate. */ 4435 acclength=D2U(reqdigits+DECDPUN); /* in Units */ 4436 if (acclength*sizeof(Unit)>sizeof(accbuff)) { 4437 /* printf("malloc dvacc %ld units\n", acclength); */ 4438 allocacc=(Unit *)malloc(acclength*sizeof(Unit)); 4439 if (allocacc==NULL) { /* hopeless -- abandon */ 4440 *status|=DEC_Insufficient_storage; 4441 break;} 4442 acc=allocacc; /* use the allocated space */ 4443 } 4444 4445 /* var1 is the padded LHS ready for subtractions. */ 4446 /* If it needs to be too long for stack storage, then allocate. */ 4447 /* The maximum units needed for var1 (long subtraction) is: */ 4448 /* Enough for */ 4449 /* (rhs->digits+reqdigits-1) -- to allow full slide to right */ 4450 /* or (lhs->digits) -- to allow for long lhs */ 4451 /* whichever is larger */ 4452 /* +1 -- for rounding of slide to right */ 4453 /* +1 -- for leading 0s */ 4454 /* +1 -- for pre-adjust if a remainder or DIVIDEINT */ 4455 /* [Note: unused units do not participate in decUnitAddSub data] */ 4456 maxdigits=rhs->digits+reqdigits-1; 4457 if (lhs->digits>maxdigits) maxdigits=lhs->digits; 4458 var1units=D2U(maxdigits)+2; 4459 /* allocate a guard unit above msu1 for REMAINDERNEAR */ 4460 if (!(op&DIVIDE)) var1units++; 4461 if ((var1units+1)*sizeof(Unit)>sizeof(varbuff)) { 4462 /* printf("malloc dvvar %ld units\n", var1units+1); */ 4463 varalloc=(Unit *)malloc((var1units+1)*sizeof(Unit)); 4464 if (varalloc==NULL) { /* hopeless -- abandon */ 4465 *status|=DEC_Insufficient_storage; 4466 break;} 4467 var1=varalloc; /* use the allocated space */ 4468 } 4469 4470 /* Extend the lhs and rhs to full long subtraction length. The lhs */ 4471 /* is truly extended into the var1 buffer, with 0 padding, so a */ 4472 /* subtract in place is always possible. The rhs (var2) has */ 4473 /* virtual padding (implemented by decUnitAddSub). */ 4474 /* One guard unit was allocated above msu1 for rem=rem+rem in */ 4475 /* REMAINDERNEAR. */ 4476 msu1=var1+var1units-1; /* msu of var1 */ 4477 source=lhs->lsu+D2U(lhs->digits)-1; /* msu of input array */ 4478 for (target=msu1; source>=lhs->lsu; source--, target--) *target=*source; 4479 for (; target>=var1; target--) *target=0; 4480 4481 /* rhs (var2) is left-aligned with var1 at the start */ 4482 var2ulen=var1units; /* rhs logical length (units) */ 4483 var2units=D2U(rhs->digits); /* rhs actual length (units) */ 4484 var2=rhs->lsu; /* -> rhs array */ 4485 msu2=var2+var2units-1; /* -> msu of var2 [never changes] */ 4486 /* now set up the variables which will be used for estimating the */ 4487 /* multiplication factor. If these variables are not exact, add */ 4488 /* 1 to make sure that the multiplier is never overestimated. */ 4489 msu2plus=*msu2; /* it's value .. */ 4490 if (var2units>1) msu2plus++; /* .. +1 if any more */ 4491 msu2pair=(eInt)*msu2*(DECDPUNMAX+1);/* top two pair .. */ 4492 if (var2units>1) { /* .. [else treat 2nd as 0] */ 4493 msu2pair+=*(msu2-1); /* .. */ 4494 if (var2units>2) msu2pair++; /* .. +1 if any more */ 4495 } 4496 4497 /* The calculation is working in units, which may have leading zeros, */ 4498 /* but the exponent was calculated on the assumption that they are */ 4499 /* both left-aligned. Adjust the exponent to compensate: add the */ 4500 /* number of leading zeros in var1 msu and subtract those in var2 msu. */ 4501 /* [This is actually done by counting the digits and negating, as */ 4502 /* lead1=DECDPUN-digits1, and similarly for lead2.] */ 4503 for (pow=&powers[1]; *msu1>=*pow; pow++) exponent--; 4504 for (pow=&powers[1]; *msu2>=*pow; pow++) exponent++; 4505 4506 /* Now, if doing an integer divide or remainder, ensure that */ 4507 /* the result will be Unit-aligned. To do this, shift the var1 */ 4508 /* accumulator towards least if need be. (It's much easier to */ 4509 /* do this now than to reassemble the residue afterwards, if */ 4510 /* doing a remainder.) Also ensure the exponent is not negative. */ 4511 if (!(op&DIVIDE)) { 4512 Unit *u; /* work */ 4513 /* save the initial 'false' padding of var1, in digits */ 4514 var1initpad=(var1units-D2U(lhs->digits))*DECDPUN; 4515 /* Determine the shift to do. */ 4516 if (exponent<0) cut=-exponent; 4517 else cut=DECDPUN-exponent%DECDPUN; 4518 decShiftToLeast(var1, var1units, cut); 4519 exponent+=cut; /* maintain numerical value */ 4520 var1initpad-=cut; /* .. and reduce padding */ 4521 /* clean any most-significant units which were just emptied */ 4522 for (u=msu1; cut>=DECDPUN; cut-=DECDPUN, u--) *u=0; 4523 } /* align */ 4524 else { /* is DIVIDE */ 4525 maxexponent=lhs->exponent-rhs->exponent; /* save */ 4526 /* optimization: if the first iteration will just produce 0, */ 4527 /* preadjust to skip it [valid for DIVIDE only] */ 4528 if (*msu1<*msu2) { 4529 var2ulen--; /* shift down */ 4530 exponent-=DECDPUN; /* update the exponent */ 4531 } 4532 } 4533 4534 /* ---- start the long-division loops ------------------------------ */ 4535 accunits=0; /* no units accumulated yet */ 4536 accdigits=0; /* .. or digits */ 4537 accnext=acc+acclength-1; /* -> msu of acc [NB: allows digits+1] */ 4538 for (;;) { /* outer forever loop */ 4539 thisunit=0; /* current unit assumed 0 */ 4540 /* find the next unit */ 4541 for (;;) { /* inner forever loop */ 4542 /* strip leading zero units [from either pre-adjust or from */ 4543 /* subtract last time around]. Leave at least one unit. */ 4544 for (; *msu1==0 && msu1>var1; msu1--) var1units--; 4545 4546 if (var1units<var2ulen) break; /* var1 too low for subtract */ 4547 if (var1units==var2ulen) { /* unit-by-unit compare needed */ 4548 /* compare the two numbers, from msu */ 4549 const Unit *pv1, *pv2; 4550 Unit v2; /* units to compare */ 4551 pv2=msu2; /* -> msu */ 4552 for (pv1=msu1; ; pv1--, pv2--) { 4553 /* v1=*pv1 -- always OK */ 4554 v2=0; /* assume in padding */ 4555 if (pv2>=var2) v2=*pv2; /* in range */ 4556 if (*pv1!=v2) break; /* no longer the same */ 4557 if (pv1==var1) break; /* done; leave pv1 as is */ 4558 } 4559 /* here when all inspected or a difference seen */ 4560 if (*pv1<v2) break; /* var1 too low to subtract */ 4561 if (*pv1==v2) { /* var1 == var2 */ 4562 /* reach here if var1 and var2 are identical; subtraction */ 4563 /* would increase digit by one, and the residue will be 0 so */ 4564 /* the calculation is done; leave the loop with residue=0. */ 4565 thisunit++; /* as though subtracted */ 4566 *var1=0; /* set var1 to 0 */ 4567 var1units=1; /* .. */ 4568 break; /* from inner */ 4569 } /* var1 == var2 */ 4570 /* *pv1>v2. Prepare for real subtraction; the lengths are equal */ 4571 /* Estimate the multiplier (there's always a msu1-1)... */ 4572 /* Bring in two units of var2 to provide a good estimate. */ 4573 mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2pair); 4574 } /* lengths the same */ 4575 else { /* var1units > var2ulen, so subtraction is safe */ 4576 /* The var2 msu is one unit towards the lsu of the var1 msu, */ 4577 /* so only one unit for var2 can be used. */ 4578 mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2plus); 4579 } 4580 if (mult==0) mult=1; /* must always be at least 1 */ 4581 /* subtraction needed; var1 is > var2 */ 4582 thisunit=(Unit)(thisunit+mult); /* accumulate */ 4583 /* subtract var1-var2, into var1; only the overlap needs */ 4584 /* processing, as this is an in-place calculation */ 4585 shift=var2ulen-var2units; 4586 #if DECTRACE 4587 decDumpAr('1', &var1[shift], var1units-shift); 4588 decDumpAr('2', var2, var2units); 4589 printf("m=%ld\n", -mult); 4590 #endif 4591 decUnitAddSub(&var1[shift], var1units-shift, 4592 var2, var2units, 0, 4593 &var1[shift], -mult); 4594 #if DECTRACE 4595 decDumpAr('#', &var1[shift], var1units-shift); 4596 #endif 4597 /* var1 now probably has leading zeros; these are removed at the */ 4598 /* top of the inner loop. */ 4599 } /* inner loop */ 4600 4601 /* The next unit has been calculated in full; unless it's a */ 4602 /* leading zero, add to acc */ 4603 if (accunits!=0 || thisunit!=0) { /* is first or non-zero */ 4604 *accnext=thisunit; /* store in accumulator */ 4605 /* account exactly for the new digits */ 4606 if (accunits==0) { 4607 accdigits++; /* at least one */ 4608 for (pow=&powers[1]; thisunit>=*pow; pow++) accdigits++; 4609 } 4610 else accdigits+=DECDPUN; 4611 accunits++; /* update count */ 4612 accnext--; /* ready for next */ 4613 if (accdigits>reqdigits) break; /* have enough digits */ 4614 } 4615 4616 /* if the residue is zero, the operation is done (unless divide */ 4617 /* or divideInteger and still not enough digits yet) */ 4618 if (*var1==0 && var1units==1) { /* residue is 0 */ 4619 if (op&(REMAINDER|REMNEAR)) break; 4620 if ((op&DIVIDE) && (exponent<=maxexponent)) break; 4621 /* [drop through if divideInteger] */ 4622 } 4623 /* also done enough if calculating remainder or integer */ 4624 /* divide and just did the last ('units') unit */ 4625 if (exponent==0 && !(op&DIVIDE)) break; 4626 4627 /* to get here, var1 is less than var2, so divide var2 by the per- */ 4628 /* Unit power of ten and go for the next digit */ 4629 var2ulen--; /* shift down */ 4630 exponent-=DECDPUN; /* update the exponent */ 4631 } /* outer loop */ 4632 4633 /* ---- division is complete --------------------------------------- */ 4634 /* here: acc has at least reqdigits+1 of good results (or fewer */ 4635 /* if early stop), starting at accnext+1 (its lsu) */ 4636 /* var1 has any residue at the stopping point */ 4637 /* accunits is the number of digits collected in acc */ 4638 if (accunits==0) { /* acc is 0 */ 4639 accunits=1; /* show have a unit .. */ 4640 accdigits=1; /* .. */ 4641 *accnext=0; /* .. whose value is 0 */ 4642 } 4643 else accnext++; /* back to last placed */ 4644 /* accnext now -> lowest unit of result */ 4645 4646 residue=0; /* assume no residue */ 4647 if (op&DIVIDE) { 4648 /* record the presence of any residue, for rounding */ 4649 if (*var1!=0 || var1units>1) residue=1; 4650 else { /* no residue */ 4651 /* Had an exact division; clean up spurious trailing 0s. */ 4652 /* There will be at most DECDPUN-1, from the final multiply, */ 4653 /* and then only if the result is non-0 (and even) and the */ 4654 /* exponent is 'loose'. */ 4655 #if DECDPUN>1 4656 Unit lsu=*accnext; 4657 if (!(lsu&0x01) && (lsu!=0)) { 4658 /* count the trailing zeros */ 4659 Int drop=0; 4660 for (;; drop++) { /* [will terminate because lsu!=0] */ 4661 if (exponent>=maxexponent) break; /* don't chop real 0s */ 4662 #if DECDPUN<=4 4663 if ((lsu-QUOT10(lsu, drop+1) 4664 *powers[drop+1])!=0) break; /* found non-0 digit */ 4665 #else 4666 if (lsu%powers[drop+1]!=0) break; /* found non-0 digit */ 4667 #endif 4668 exponent++; 4669 } 4670 if (drop>0) { 4671 accunits=decShiftToLeast(accnext, accunits, drop); 4672 accdigits=decGetDigits(accnext, accunits); 4673 accunits=D2U(accdigits); 4674 /* [exponent was adjusted in the loop] */ 4675 } 4676 } /* neither odd nor 0 */ 4677 #endif 4678 } /* exact divide */ 4679 } /* divide */ 4680 else /* op!=DIVIDE */ { 4681 /* check for coefficient overflow */ 4682 if (accdigits+exponent>reqdigits) { 4683 *status|=DEC_Division_impossible; 4684 break; 4685 } 4686 if (op & (REMAINDER|REMNEAR)) { 4687 /* [Here, the exponent will be 0, because var1 was adjusted */ 4688 /* appropriately.] */ 4689 Int postshift; /* work */ 4690 Flag wasodd=0; /* integer was odd */ 4691 Unit *quotlsu; /* for save */ 4692 Int quotdigits; /* .. */ 4693 4694 bits=lhs->bits; /* remainder sign is always as lhs */ 4695 4696 /* Fastpath when residue is truly 0 is worthwhile [and */ 4697 /* simplifies the code below] */ 4698 if (*var1==0 && var1units==1) { /* residue is 0 */ 4699 Int exp=lhs->exponent; /* save min(exponents) */ 4700 if (rhs->exponent<exp) exp=rhs->exponent; 4701 uprv_decNumberZero(res); /* 0 coefficient */ 4702 #if DECSUBSET 4703 if (set->extended) 4704 #endif 4705 res->exponent=exp; /* .. with proper exponent */ 4706 res->bits=(uByte)(bits&DECNEG); /* [cleaned] */ 4707 decFinish(res, set, &residue, status); /* might clamp */ 4708 break; 4709 } 4710 /* note if the quotient was odd */ 4711 if (*accnext & 0x01) wasodd=1; /* acc is odd */ 4712 quotlsu=accnext; /* save in case need to reinspect */ 4713 quotdigits=accdigits; /* .. */ 4714 4715 /* treat the residue, in var1, as the value to return, via acc */ 4716 /* calculate the unused zero digits. This is the smaller of: */ 4717 /* var1 initial padding (saved above) */ 4718 /* var2 residual padding, which happens to be given by: */ 4719 postshift=var1initpad+exponent-lhs->exponent+rhs->exponent; 4720 /* [the 'exponent' term accounts for the shifts during divide] */ 4721 if (var1initpad<postshift) postshift=var1initpad; 4722 4723 /* shift var1 the requested amount, and adjust its digits */ 4724 var1units=decShiftToLeast(var1, var1units, postshift); 4725 accnext=var1; 4726 accdigits=decGetDigits(var1, var1units); 4727 accunits=D2U(accdigits); 4728 4729 exponent=lhs->exponent; /* exponent is smaller of lhs & rhs */ 4730 if (rhs->exponent<exponent) exponent=rhs->exponent; 4731 4732 /* Now correct the result if doing remainderNear; if it */ 4733 /* (looking just at coefficients) is > rhs/2, or == rhs/2 and */ 4734 /* the integer was odd then the result should be rem-rhs. */ 4735 if (op&REMNEAR) { 4736 Int compare, tarunits; /* work */ 4737 Unit *up; /* .. */ 4738 /* calculate remainder*2 into the var1 buffer (which has */ 4739 /* 'headroom' of an extra unit and hence enough space) */ 4740 /* [a dedicated 'double' loop would be faster, here] */ 4741 tarunits=decUnitAddSub(accnext, accunits, accnext, accunits, 4742 0, accnext, 1); 4743 /* decDumpAr('r', accnext, tarunits); */ 4744 4745 /* Here, accnext (var1) holds tarunits Units with twice the */ 4746 /* remainder's coefficient, which must now be compared to the */ 4747 /* RHS. The remainder's exponent may be smaller than the RHS's. */ 4748 compare=decUnitCompare(accnext, tarunits, rhs->lsu, D2U(rhs->digits), 4749 rhs->exponent-exponent); 4750 if (compare==BADINT) { /* deep trouble */ 4751 *status|=DEC_Insufficient_storage; 4752 break;} 4753 4754 /* now restore the remainder by dividing by two; the lsu */ 4755 /* is known to be even. */ 4756 for (up=accnext; up<accnext+tarunits; up++) { 4757 Int half; /* half to add to lower unit */ 4758 half=*up & 0x01; 4759 *up/=2; /* [shift] */ 4760 if (!half) continue; 4761 *(up-1)+=(DECDPUNMAX+1)/2; 4762 } 4763 /* [accunits still describes the original remainder length] */ 4764 4765 if (compare>0 || (compare==0 && wasodd)) { /* adjustment needed */ 4766 Int exp, expunits, exprem; /* work */ 4767 /* This is effectively causing round-up of the quotient, */ 4768 /* so if it was the rare case where it was full and all */ 4769 /* nines, it would overflow and hence division-impossible */ 4770 /* should be raised */ 4771 Flag allnines=0; /* 1 if quotient all nines */ 4772 if (quotdigits==reqdigits) { /* could be borderline */ 4773 for (up=quotlsu; ; up++) { 4774 if (quotdigits>DECDPUN) { 4775 if (*up!=DECDPUNMAX) break;/* non-nines */ 4776 } 4777 else { /* this is the last Unit */ 4778 if (*up==powers[quotdigits]-1) allnines=1; 4779 break; 4780 } 4781 quotdigits-=DECDPUN; /* checked those digits */ 4782 } /* up */ 4783 } /* borderline check */ 4784 if (allnines) { 4785 *status|=DEC_Division_impossible; 4786 break;} 4787 4788 /* rem-rhs is needed; the sign will invert. Again, var1 */ 4789 /* can safely be used for the working Units array. */ 4790 exp=rhs->exponent-exponent; /* RHS padding needed */ 4791 /* Calculate units and remainder from exponent. */ 4792 expunits=exp/DECDPUN; 4793 exprem=exp%DECDPUN; 4794 /* subtract [A+B*(-m)]; the result will always be negative */ 4795 accunits=-decUnitAddSub(accnext, accunits, 4796 rhs->lsu, D2U(rhs->digits), 4797 expunits, accnext, -(Int)powers[exprem]); 4798 accdigits=decGetDigits(accnext, accunits); /* count digits exactly */ 4799 accunits=D2U(accdigits); /* and recalculate the units for copy */ 4800 /* [exponent is as for original remainder] */ 4801 bits^=DECNEG; /* flip the sign */ 4802 } 4803 } /* REMNEAR */ 4804 } /* REMAINDER or REMNEAR */ 4805 } /* not DIVIDE */ 4806 4807 /* Set exponent and bits */ 4808 res->exponent=exponent; 4809 res->bits=(uByte)(bits&DECNEG); /* [cleaned] */ 4810 4811 /* Now the coefficient. */ 4812 decSetCoeff(res, set, accnext, accdigits, &residue, status); 4813 4814 decFinish(res, set, &residue, status); /* final cleanup */ 4815 4816 #if DECSUBSET 4817 /* If a divide then strip trailing zeros if subset [after round] */ 4818 if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, 1, &dropped); 4819 #endif 4820 } while(0); /* end protected */ 4821 4822 if (varalloc!=NULL) free(varalloc); /* drop any storage used */ 4823 if (allocacc!=NULL) free(allocacc); /* .. */ 4824 #if DECSUBSET 4825 if (allocrhs!=NULL) free(allocrhs); /* .. */ 4826 if (alloclhs!=NULL) free(alloclhs); /* .. */ 4827 #endif 4828 return res; 4829 } /* decDivideOp */ 4830 4831/* ------------------------------------------------------------------ */ 4832/* decMultiplyOp -- multiplication operation */ 4833/* */ 4834/* This routine performs the multiplication C=A x B. */ 4835/* */ 4836/* res is C, the result. C may be A and/or B (e.g., X=X*X) */ 4837/* lhs is A */ 4838/* rhs is B */ 4839/* set is the context */ 4840/* status is the usual accumulator */ 4841/* */ 4842/* C must have space for set->digits digits. */ 4843/* */ 4844/* ------------------------------------------------------------------ */ 4845/* 'Classic' multiplication is used rather than Karatsuba, as the */ 4846/* latter would give only a minor improvement for the short numbers */ 4847/* expected to be handled most (and uses much more memory). */ 4848/* */ 4849/* There are two major paths here: the general-purpose ('old code') */ 4850/* path which handles all DECDPUN values, and a fastpath version */ 4851/* which is used if 64-bit ints are available, DECDPUN<=4, and more */ 4852/* than two calls to decUnitAddSub would be made. */ 4853/* */ 4854/* The fastpath version lumps units together into 8-digit or 9-digit */ 4855/* chunks, and also uses a lazy carry strategy to minimise expensive */ 4856/* 64-bit divisions. The chunks are then broken apart again into */ 4857/* units for continuing processing. Despite this overhead, the */ 4858/* fastpath can speed up some 16-digit operations by 10x (and much */ 4859/* more for higher-precision calculations). */ 4860/* */ 4861/* A buffer always has to be used for the accumulator; in the */ 4862/* fastpath, buffers are also always needed for the chunked copies of */ 4863/* of the operand coefficients. */ 4864/* Static buffers are larger than needed just for multiply, to allow */ 4865/* for calls from other operations (notably exp). */ 4866/* ------------------------------------------------------------------ */ 4867#define FASTMUL (DECUSE64 && DECDPUN<5) 4868static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs, 4869 const decNumber *rhs, decContext *set, 4870 uInt *status) { 4871 Int accunits; /* Units of accumulator in use */ 4872 Int exponent; /* work */ 4873 Int residue=0; /* rounding residue */ 4874 uByte bits; /* result sign */ 4875 Unit *acc; /* -> accumulator Unit array */ 4876 Int needbytes; /* size calculator */ 4877 void *allocacc=NULL; /* -> allocated accumulator, iff allocated */ 4878 Unit accbuff[SD2U(DECBUFFER*4+1)]; /* buffer (+1 for DECBUFFER==0, */ 4879 /* *4 for calls from other operations) */ 4880 const Unit *mer, *mermsup; /* work */ 4881 Int madlength; /* Units in multiplicand */ 4882 Int shift; /* Units to shift multiplicand by */ 4883 4884 #if FASTMUL 4885 /* if DECDPUN is 1 or 3 work in base 10**9, otherwise */ 4886 /* (DECDPUN is 2 or 4) then work in base 10**8 */ 4887 #if DECDPUN & 1 /* odd */ 4888 #define FASTBASE 1000000000 /* base */ 4889 #define FASTDIGS 9 /* digits in base */ 4890 #define FASTLAZY 18 /* carry resolution point [1->18] */ 4891 #else 4892 #define FASTBASE 100000000 4893 #define FASTDIGS 8 4894 #define FASTLAZY 1844 /* carry resolution point [1->1844] */ 4895 #endif 4896 /* three buffers are used, two for chunked copies of the operands */ 4897 /* (base 10**8 or base 10**9) and one base 2**64 accumulator with */ 4898 /* lazy carry evaluation */ 4899 uInt zlhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */ 4900 uInt *zlhi=zlhibuff; /* -> lhs array */ 4901 uInt *alloclhi=NULL; /* -> allocated buffer, iff allocated */ 4902 uInt zrhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */ 4903 uInt *zrhi=zrhibuff; /* -> rhs array */ 4904 uInt *allocrhi=NULL; /* -> allocated buffer, iff allocated */ 4905 uLong zaccbuff[(DECBUFFER*2+1)/4+2]; /* buffer (+1 for DECBUFFER==0) */ 4906 /* [allocacc is shared for both paths, as only one will run] */ 4907 uLong *zacc=zaccbuff; /* -> accumulator array for exact result */ 4908 #if DECDPUN==1 4909 Int zoff; /* accumulator offset */ 4910 #endif 4911 uInt *lip, *rip; /* item pointers */ 4912 uInt *lmsi, *rmsi; /* most significant items */ 4913 Int ilhs, irhs, iacc; /* item counts in the arrays */ 4914 Int lazy; /* lazy carry counter */ 4915 uLong lcarry; /* uLong carry */ 4916 uInt carry; /* carry (NB not uLong) */ 4917 Int count; /* work */ 4918 const Unit *cup; /* .. */ 4919 Unit *up; /* .. */ 4920 uLong *lp; /* .. */ 4921 Int p; /* .. */ 4922 #endif 4923 4924 #if DECSUBSET 4925 decNumber *alloclhs=NULL; /* -> allocated buffer, iff allocated */ 4926 decNumber *allocrhs=NULL; /* -> allocated buffer, iff allocated */ 4927 #endif 4928 4929 #if DECCHECK 4930 if (decCheckOperands(res, lhs, rhs, set)) return res; 4931 #endif 4932 4933 /* precalculate result sign */ 4934 bits=(uByte)((lhs->bits^rhs->bits)&DECNEG); 4935 4936 /* handle infinities and NaNs */ 4937 if (SPECIALARGS) { /* a special bit set */ 4938 if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */ 4939 decNaNs(res, lhs, rhs, set, status); 4940 return res;} 4941 /* one or two infinities; Infinity * 0 is invalid */ 4942 if (((lhs->bits & DECINF)==0 && ISZERO(lhs)) 4943 ||((rhs->bits & DECINF)==0 && ISZERO(rhs))) { 4944 *status|=DEC_Invalid_operation; 4945 return res;} 4946 uprv_decNumberZero(res); 4947 res->bits=bits|DECINF; /* infinity */ 4948 return res;} 4949 4950 /* For best speed, as in DMSRCN [the original Rexx numerics */ 4951 /* module], use the shorter number as the multiplier (rhs) and */ 4952 /* the longer as the multiplicand (lhs) to minimise the number of */ 4953 /* adds (partial products) */ 4954 if (lhs->digits<rhs->digits) { /* swap... */ 4955 const decNumber *hold=lhs; 4956 lhs=rhs; 4957 rhs=hold; 4958 } 4959 4960 do { /* protect allocated storage */ 4961 #if DECSUBSET 4962 if (!set->extended) { 4963 /* reduce operands and set lostDigits status, as needed */ 4964 if (lhs->digits>set->digits) { 4965 alloclhs=decRoundOperand(lhs, set, status); 4966 if (alloclhs==NULL) break; 4967 lhs=alloclhs; 4968 } 4969 if (rhs->digits>set->digits) { 4970 allocrhs=decRoundOperand(rhs, set, status); 4971 if (allocrhs==NULL) break; 4972 rhs=allocrhs; 4973 } 4974 } 4975 #endif 4976 /* [following code does not require input rounding] */ 4977 4978 #if FASTMUL /* fastpath can be used */ 4979 /* use the fast path if there are enough digits in the shorter */ 4980 /* operand to make the setup and takedown worthwhile */ 4981 #define NEEDTWO (DECDPUN*2) /* within two decUnitAddSub calls */ 4982 if (rhs->digits>NEEDTWO) { /* use fastpath... */ 4983 /* calculate the number of elements in each array */ 4984 ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; /* [ceiling] */ 4985 irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; /* .. */ 4986 iacc=ilhs+irhs; 4987 4988 /* allocate buffers if required, as usual */ 4989 needbytes=ilhs*sizeof(uInt); 4990 if (needbytes>(Int)sizeof(zlhibuff)) { 4991 alloclhi=(uInt *)malloc(needbytes); 4992 zlhi=alloclhi;} 4993 needbytes=irhs*sizeof(uInt); 4994 if (needbytes>(Int)sizeof(zrhibuff)) { 4995 allocrhi=(uInt *)malloc(needbytes); 4996 zrhi=allocrhi;} 4997 4998 /* Allocating the accumulator space needs a special case when */ 4999 /* DECDPUN=1 because when converting the accumulator to Units */ 5000 /* after the multiplication each 8-byte item becomes 9 1-byte */ 5001 /* units. Therefore iacc extra bytes are needed at the front */ 5002 /* (rounded up to a multiple of 8 bytes), and the uLong */ 5003 /* accumulator starts offset the appropriate number of units */ 5004 /* to the right to avoid overwrite during the unchunking. */ 5005 5006 /* Make sure no signed int overflow below. This is always true */ 5007 /* if the given numbers have less digits than DEC_MAX_DIGITS. */ 5008 U_ASSERT(iacc <= INT32_MAX/sizeof(uLong)); 5009 needbytes=iacc*sizeof(uLong); 5010 #if DECDPUN==1 5011 zoff=(iacc+7)/8; /* items to offset by */ 5012 needbytes+=zoff*8; 5013 #endif 5014 if (needbytes>(Int)sizeof(zaccbuff)) { 5015 allocacc=(uLong *)malloc(needbytes); 5016 zacc=(uLong *)allocacc;} 5017 if (zlhi==NULL||zrhi==NULL||zacc==NULL) { 5018 *status|=DEC_Insufficient_storage; 5019 break;} 5020 5021 acc=(Unit *)zacc; /* -> target Unit array */ 5022 #if DECDPUN==1 5023 zacc+=zoff; /* start uLong accumulator to right */ 5024 #endif 5025 5026 /* assemble the chunked copies of the left and right sides */ 5027 for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++) 5028 for (p=0, *lip=0; p<FASTDIGS && count>0; 5029 p+=DECDPUN, cup++, count-=DECDPUN) 5030 *lip+=*cup*powers[p]; 5031 lmsi=lip-1; /* save -> msi */ 5032 for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++) 5033 for (p=0, *rip=0; p<FASTDIGS && count>0; 5034 p+=DECDPUN, cup++, count-=DECDPUN) 5035 *rip+=*cup*powers[p]; 5036 rmsi=rip-1; /* save -> msi */ 5037 5038 /* zero the accumulator */ 5039 for (lp=zacc; lp<zacc+iacc; lp++) *lp=0; 5040 5041 /* Start the multiplication */ 5042 /* Resolving carries can dominate the cost of accumulating the */ 5043 /* partial products, so this is only done when necessary. */ 5044 /* Each uLong item in the accumulator can hold values up to */ 5045 /* 2**64-1, and each partial product can be as large as */ 5046 /* (10**FASTDIGS-1)**2. When FASTDIGS=9, this can be added to */ 5047 /* itself 18.4 times in a uLong without overflowing, so during */ 5048 /* the main calculation resolution is carried out every 18th */ 5049 /* add -- every 162 digits. Similarly, when FASTDIGS=8, the */ 5050 /* partial products can be added to themselves 1844.6 times in */ 5051 /* a uLong without overflowing, so intermediate carry */ 5052 /* resolution occurs only every 14752 digits. Hence for common */ 5053 /* short numbers usually only the one final carry resolution */ 5054 /* occurs. */ 5055 /* (The count is set via FASTLAZY to simplify experiments to */ 5056 /* measure the value of this approach: a 35% improvement on a */ 5057 /* [34x34] multiply.) */ 5058 lazy=FASTLAZY; /* carry delay count */ 5059 for (rip=zrhi; rip<=rmsi; rip++) { /* over each item in rhs */ 5060 lp=zacc+(rip-zrhi); /* where to add the lhs */ 5061 for (lip=zlhi; lip<=lmsi; lip++, lp++) { /* over each item in lhs */ 5062 *lp+=(uLong)(*lip)*(*rip); /* [this should in-line] */ 5063 } /* lip loop */ 5064 lazy--; 5065 if (lazy>0 && rip!=rmsi) continue; 5066 lazy=FASTLAZY; /* reset delay count */ 5067 /* spin up the accumulator resolving overflows */ 5068 for (lp=zacc; lp<zacc+iacc; lp++) { 5069 if (*lp<FASTBASE) continue; /* it fits */ 5070 lcarry=*lp/FASTBASE; /* top part [slow divide] */ 5071 /* lcarry can exceed 2**32-1, so check again; this check */ 5072 /* and occasional extra divide (slow) is well worth it, as */ 5073 /* it allows FASTLAZY to be increased to 18 rather than 4 */ 5074 /* in the FASTDIGS=9 case */ 5075 if (lcarry<FASTBASE) carry=(uInt)lcarry; /* [usual] */ 5076 else { /* two-place carry [fairly rare] */ 5077 uInt carry2=(uInt)(lcarry/FASTBASE); /* top top part */ 5078 *(lp+2)+=carry2; /* add to item+2 */ 5079 *lp-=((uLong)FASTBASE*FASTBASE*carry2); /* [slow] */ 5080 carry=(uInt)(lcarry-((uLong)FASTBASE*carry2)); /* [inline] */ 5081 } 5082 *(lp+1)+=carry; /* add to item above [inline] */ 5083 *lp-=((uLong)FASTBASE*carry); /* [inline] */ 5084 } /* carry resolution */ 5085 } /* rip loop */ 5086 5087 /* The multiplication is complete; time to convert back into */ 5088 /* units. This can be done in-place in the accumulator and in */ 5089 /* 32-bit operations, because carries were resolved after the */ 5090 /* final add. This needs N-1 divides and multiplies for */ 5091 /* each item in the accumulator (which will become up to N */ 5092 /* units, where 2<=N<=9). */ 5093 for (lp=zacc, up=acc; lp<zacc+iacc; lp++) { 5094 uInt item=(uInt)*lp; /* decapitate to uInt */ 5095 for (p=0; p<FASTDIGS-DECDPUN; p+=DECDPUN, up++) { 5096 uInt part=item/(DECDPUNMAX+1); 5097 *up=(Unit)(item-(part*(DECDPUNMAX+1))); 5098 item=part; 5099 } /* p */ 5100 *up=(Unit)item; up++; /* [final needs no division] */ 5101 } /* lp */ 5102 accunits=up-acc; /* count of units */ 5103 } 5104 else { /* here to use units directly, without chunking ['old code'] */ 5105 #endif 5106 5107 /* if accumulator will be too long for local storage, then allocate */ 5108 acc=accbuff; /* -> assume buffer for accumulator */ 5109 needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit); 5110 if (needbytes>(Int)sizeof(accbuff)) { 5111 allocacc=(Unit *)malloc(needbytes); 5112 if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;} 5113 acc=(Unit *)allocacc; /* use the allocated space */ 5114 } 5115 5116 /* Now the main long multiplication loop */ 5117 /* Unlike the equivalent in the IBM Java implementation, there */ 5118 /* is no advantage in calculating from msu to lsu. So, do it */ 5119 /* by the book, as it were. */ 5120 /* Each iteration calculates ACC=ACC+MULTAND*MULT */ 5121 accunits=1; /* accumulator starts at '0' */ 5122 *acc=0; /* .. (lsu=0) */ 5123 shift=0; /* no multiplicand shift at first */ 5124 madlength=D2U(lhs->digits); /* this won't change */ 5125 mermsup=rhs->lsu+D2U(rhs->digits); /* -> msu+1 of multiplier */ 5126 5127 for (mer=rhs->lsu; mer<mermsup; mer++) { 5128 /* Here, *mer is the next Unit in the multiplier to use */ 5129 /* If non-zero [optimization] add it... */ 5130 if (*mer!=0) accunits=decUnitAddSub(&acc[shift], accunits-shift, 5131 lhs->lsu, madlength, 0, 5132 &acc[shift], *mer) 5133 + shift; 5134 else { /* extend acc with a 0; it will be used shortly */ 5135 *(acc+accunits)=0; /* [this avoids length of <=0 later] */ 5136 accunits++; 5137 } 5138 /* multiply multiplicand by 10**DECDPUN for next Unit to left */ 5139 shift++; /* add this for 'logical length' */ 5140 } /* n */ 5141 #if FASTMUL 5142 } /* unchunked units */ 5143 #endif 5144 /* common end-path */ 5145 #if DECTRACE 5146 decDumpAr('*', acc, accunits); /* Show exact result */ 5147 #endif 5148 5149 /* acc now contains the exact result of the multiplication, */ 5150 /* possibly with a leading zero unit; build the decNumber from */ 5151 /* it, noting if any residue */ 5152 res->bits=bits; /* set sign */ 5153 res->digits=decGetDigits(acc, accunits); /* count digits exactly */ 5154 5155 /* There can be a 31-bit wrap in calculating the exponent. */ 5156 /* This can only happen if both input exponents are negative and */ 5157 /* both their magnitudes are large. If there was a wrap, set a */ 5158 /* safe very negative exponent, from which decFinalize() will */ 5159 /* raise a hard underflow shortly. */ 5160 exponent=lhs->exponent+rhs->exponent; /* calculate exponent */ 5161 if (lhs->exponent<0 && rhs->exponent<0 && exponent>0) 5162 exponent=-2*DECNUMMAXE; /* force underflow */ 5163 res->exponent=exponent; /* OK to overwrite now */ 5164 5165 5166 /* Set the coefficient. If any rounding, residue records */ 5167 decSetCoeff(res, set, acc, res->digits, &residue, status); 5168 decFinish(res, set, &residue, status); /* final cleanup */ 5169 } while(0); /* end protected */ 5170 5171 if (allocacc!=NULL) free(allocacc); /* drop any storage used */ 5172 #if DECSUBSET 5173 if (allocrhs!=NULL) free(allocrhs); /* .. */ 5174 if (alloclhs!=NULL) free(alloclhs); /* .. */ 5175 #endif 5176 #if FASTMUL 5177 if (allocrhi!=NULL) free(allocrhi); /* .. */ 5178 if (alloclhi!=NULL) free(alloclhi); /* .. */ 5179 #endif 5180 return res; 5181 } /* decMultiplyOp */ 5182 5183/* ------------------------------------------------------------------ */ 5184/* decExpOp -- effect exponentiation */ 5185/* */ 5186/* This computes C = exp(A) */ 5187/* */ 5188/* res is C, the result. C may be A */ 5189/* rhs is A */ 5190/* set is the context; note that rounding mode has no effect */ 5191/* */ 5192/* C must have space for set->digits digits. status is updated but */ 5193/* not set. */ 5194/* */ 5195/* Restrictions: */ 5196/* */ 5197/* digits, emax, and -emin in the context must be less than */ 5198/* 2*DEC_MAX_MATH (1999998), and the rhs must be within these */ 5199/* bounds or a zero. This is an internal routine, so these */ 5200/* restrictions are contractual and not enforced. */ 5201/* */ 5202/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */ 5203/* almost always be correctly rounded, but may be up to 1 ulp in */ 5204/* error in rare cases. */ 5205/* */ 5206/* Finite results will always be full precision and Inexact, except */ 5207/* when A is a zero or -Infinity (giving 1 or 0 respectively). */ 5208/* ------------------------------------------------------------------ */ 5209/* This approach used here is similar to the algorithm described in */ 5210/* */ 5211/* Variable Precision Exponential Function, T. E. Hull and */ 5212/* A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */ 5213/* pp79-91, ACM, June 1986. */ 5214/* */ 5215/* with the main difference being that the iterations in the series */ 5216/* evaluation are terminated dynamically (which does not require the */ 5217/* extra variable-precision variables which are expensive in this */ 5218/* context). */ 5219/* */ 5220/* The error analysis in Hull & Abrham's paper applies except for the */ 5221/* round-off error accumulation during the series evaluation. This */ 5222/* code does not precalculate the number of iterations and so cannot */ 5223/* use Horner's scheme. Instead, the accumulation is done at double- */ 5224/* precision, which ensures that the additions of the terms are exact */ 5225/* and do not accumulate round-off (and any round-off errors in the */ 5226/* terms themselves move 'to the right' faster than they can */ 5227/* accumulate). This code also extends the calculation by allowing, */ 5228/* in the spirit of other decNumber operators, the input to be more */ 5229/* precise than the result (the precision used is based on the more */ 5230/* precise of the input or requested result). */ 5231/* */ 5232/* Implementation notes: */ 5233/* */ 5234/* 1. This is separated out as decExpOp so it can be called from */ 5235/* other Mathematical functions (notably Ln) with a wider range */ 5236/* than normal. In particular, it can handle the slightly wider */ 5237/* (double) range needed by Ln (which has to be able to calculate */ 5238/* exp(-x) where x can be the tiniest number (Ntiny). */ 5239/* */ 5240/* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop */ 5241/* iterations by appoximately a third with additional (although */ 5242/* diminishing) returns as the range is reduced to even smaller */ 5243/* fractions. However, h (the power of 10 used to correct the */ 5244/* result at the end, see below) must be kept <=8 as otherwise */ 5245/* the final result cannot be computed. Hence the leverage is a */ 5246/* sliding value (8-h), where potentially the range is reduced */ 5247/* more for smaller values. */ 5248/* */ 5249/* The leverage that can be applied in this way is severely */ 5250/* limited by the cost of the raise-to-the power at the end, */ 5251/* which dominates when the number of iterations is small (less */ 5252/* than ten) or when rhs is short. As an example, the adjustment */ 5253/* x**10,000,000 needs 31 multiplications, all but one full-width. */ 5254/* */ 5255/* 3. The restrictions (especially precision) could be raised with */ 5256/* care, but the full decNumber range seems very hard within the */ 5257/* 32-bit limits. */ 5258/* */ 5259/* 4. The working precisions for the static buffers are twice the */ 5260/* obvious size to allow for calls from decNumberPower. */ 5261/* ------------------------------------------------------------------ */ 5262decNumber * decExpOp(decNumber *res, const decNumber *rhs, 5263 decContext *set, uInt *status) { 5264 uInt ignore=0; /* working status */ 5265 Int h; /* adjusted exponent for 0.xxxx */ 5266 Int p; /* working precision */ 5267 Int residue; /* rounding residue */ 5268 uInt needbytes; /* for space calculations */ 5269 const decNumber *x=rhs; /* (may point to safe copy later) */ 5270 decContext aset, tset, dset; /* working contexts */ 5271 Int comp; /* work */ 5272 5273 /* the argument is often copied to normalize it, so (unusually) it */ 5274 /* is treated like other buffers, using DECBUFFER, +1 in case */ 5275 /* DECBUFFER is 0 */ 5276 decNumber bufr[D2N(DECBUFFER*2+1)]; 5277 decNumber *allocrhs=NULL; /* non-NULL if rhs buffer allocated */ 5278 5279 /* the working precision will be no more than set->digits+8+1 */ 5280 /* so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER */ 5281 /* is 0 (and twice that for the accumulator) */ 5282 5283 /* buffer for t, term (working precision plus) */ 5284 decNumber buft[D2N(DECBUFFER*2+9+1)]; 5285 decNumber *allocbuft=NULL; /* -> allocated buft, iff allocated */ 5286 decNumber *t=buft; /* term */ 5287 /* buffer for a, accumulator (working precision * 2), at least 9 */ 5288 decNumber bufa[D2N(DECBUFFER*4+18+1)]; 5289 decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ 5290 decNumber *a=bufa; /* accumulator */ 5291 /* decNumber for the divisor term; this needs at most 9 digits */ 5292 /* and so can be fixed size [16 so can use standard context] */ 5293 decNumber bufd[D2N(16)]; 5294 decNumber *d=bufd; /* divisor */ 5295 decNumber numone; /* constant 1 */ 5296 5297 #if DECCHECK 5298 Int iterations=0; /* for later sanity check */ 5299 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 5300 #endif 5301 5302 do { /* protect allocated storage */ 5303 if (SPECIALARG) { /* handle infinities and NaNs */ 5304 if (decNumberIsInfinite(rhs)) { /* an infinity */ 5305 if (decNumberIsNegative(rhs)) /* -Infinity -> +0 */ 5306 uprv_decNumberZero(res); 5307 else uprv_decNumberCopy(res, rhs); /* +Infinity -> self */ 5308 } 5309 else decNaNs(res, rhs, NULL, set, status); /* a NaN */ 5310 break;} 5311 5312 if (ISZERO(rhs)) { /* zeros -> exact 1 */ 5313 uprv_decNumberZero(res); /* make clean 1 */ 5314 *res->lsu=1; /* .. */ 5315 break;} /* [no status to set] */ 5316 5317 /* e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path */ 5318 /* positive and negative tiny cases which will result in inexact */ 5319 /* 1. This also allows the later add-accumulate to always be */ 5320 /* exact (because its length will never be more than twice the */ 5321 /* working precision). */ 5322 /* The comparator (tiny) needs just one digit, so use the */ 5323 /* decNumber d for it (reused as the divisor, etc., below); its */ 5324 /* exponent is such that if x is positive it will have */ 5325 /* set->digits-1 zeros between the decimal point and the digit, */ 5326 /* which is 4, and if x is negative one more zero there as the */ 5327 /* more precise result will be of the form 0.9999999 rather than */ 5328 /* 1.0000001. Hence, tiny will be 0.0000004 if digits=7 and x>0 */ 5329 /* or 0.00000004 if digits=7 and x<0. If RHS not larger than */ 5330 /* this then the result will be 1.000000 */ 5331 uprv_decNumberZero(d); /* clean */ 5332 *d->lsu=4; /* set 4 .. */ 5333 d->exponent=-set->digits; /* * 10**(-d) */ 5334 if (decNumberIsNegative(rhs)) d->exponent--; /* negative case */ 5335 comp=decCompare(d, rhs, 1); /* signless compare */ 5336 if (comp==BADINT) { 5337 *status|=DEC_Insufficient_storage; 5338 break;} 5339 if (comp>=0) { /* rhs < d */ 5340 Int shift=set->digits-1; 5341 uprv_decNumberZero(res); /* set 1 */ 5342 *res->lsu=1; /* .. */ 5343 res->digits=decShiftToMost(res->lsu, 1, shift); 5344 res->exponent=-shift; /* make 1.0000... */ 5345 *status|=DEC_Inexact | DEC_Rounded; /* .. inexactly */ 5346 break;} /* tiny */ 5347 5348 /* set up the context to be used for calculating a, as this is */ 5349 /* used on both paths below */ 5350 uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); 5351 /* accumulator bounds are as requested (could underflow) */ 5352 aset.emax=set->emax; /* usual bounds */ 5353 aset.emin=set->emin; /* .. */ 5354 aset.clamp=0; /* and no concrete format */ 5355 5356 /* calculate the adjusted (Hull & Abrham) exponent (where the */ 5357 /* decimal point is just to the left of the coefficient msd) */ 5358 h=rhs->exponent+rhs->digits; 5359 /* if h>8 then 10**h cannot be calculated safely; however, when */ 5360 /* h=8 then exp(|rhs|) will be at least exp(1E+7) which is at */ 5361 /* least 6.59E+4342944, so (due to the restriction on Emax/Emin) */ 5362 /* overflow (or underflow to 0) is guaranteed -- so this case can */ 5363 /* be handled by simply forcing the appropriate excess */ 5364 if (h>8) { /* overflow/underflow */ 5365 /* set up here so Power call below will over or underflow to */ 5366 /* zero; set accumulator to either 2 or 0.02 */ 5367 /* [stack buffer for a is always big enough for this] */ 5368 uprv_decNumberZero(a); 5369 *a->lsu=2; /* not 1 but < exp(1) */ 5370 if (decNumberIsNegative(rhs)) a->exponent=-2; /* make 0.02 */ 5371 h=8; /* clamp so 10**h computable */ 5372 p=9; /* set a working precision */ 5373 } 5374 else { /* h<=8 */ 5375 Int maxlever=(rhs->digits>8?1:0); 5376 /* [could/should increase this for precisions >40 or so, too] */ 5377 5378 /* if h is 8, cannot normalize to a lower upper limit because */ 5379 /* the final result will not be computable (see notes above), */ 5380 /* but leverage can be applied whenever h is less than 8. */ 5381 /* Apply as much as possible, up to a MAXLEVER digits, which */ 5382 /* sets the tradeoff against the cost of the later a**(10**h). */ 5383 /* As h is increased, the working precision below also */ 5384 /* increases to compensate for the "constant digits at the */ 5385 /* front" effect. */ 5386 Int lever=MINI(8-h, maxlever); /* leverage attainable */ 5387 Int use=-rhs->digits-lever; /* exponent to use for RHS */ 5388 h+=lever; /* apply leverage selected */ 5389 if (h<0) { /* clamp */ 5390 use+=h; /* [may end up subnormal] */ 5391 h=0; 5392 } 5393 /* Take a copy of RHS if it needs normalization (true whenever x>=1) */ 5394 if (rhs->exponent!=use) { 5395 decNumber *newrhs=bufr; /* assume will fit on stack */ 5396 needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); 5397 if (needbytes>sizeof(bufr)) { /* need malloc space */ 5398 allocrhs=(decNumber *)malloc(needbytes); 5399 if (allocrhs==NULL) { /* hopeless -- abandon */ 5400 *status|=DEC_Insufficient_storage; 5401 break;} 5402 newrhs=allocrhs; /* use the allocated space */ 5403 } 5404 uprv_decNumberCopy(newrhs, rhs); /* copy to safe space */ 5405 newrhs->exponent=use; /* normalize; now <1 */ 5406 x=newrhs; /* ready for use */ 5407 /* decNumberShow(x); */ 5408 } 5409 5410 /* Now use the usual power series to evaluate exp(x). The */ 5411 /* series starts as 1 + x + x^2/2 ... so prime ready for the */ 5412 /* third term by setting the term variable t=x, the accumulator */ 5413 /* a=1, and the divisor d=2. */ 5414 5415 /* First determine the working precision. From Hull & Abrham */ 5416 /* this is set->digits+h+2. However, if x is 'over-precise' we */ 5417 /* need to allow for all its digits to potentially participate */ 5418 /* (consider an x where all the excess digits are 9s) so in */ 5419 /* this case use x->digits+h+2 */ 5420 p=MAXI(x->digits, set->digits)+h+2; /* [h<=8] */ 5421 5422 /* a and t are variable precision, and depend on p, so space */ 5423 /* must be allocated for them if necessary */ 5424 5425 /* the accumulator needs to be able to hold 2p digits so that */ 5426 /* the additions on the second and subsequent iterations are */ 5427 /* sufficiently exact. */ 5428 needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit); 5429 if (needbytes>sizeof(bufa)) { /* need malloc space */ 5430 allocbufa=(decNumber *)malloc(needbytes); 5431 if (allocbufa==NULL) { /* hopeless -- abandon */ 5432 *status|=DEC_Insufficient_storage; 5433 break;} 5434 a=allocbufa; /* use the allocated space */ 5435 } 5436 /* the term needs to be able to hold p digits (which is */ 5437 /* guaranteed to be larger than x->digits, so the initial copy */ 5438 /* is safe); it may also be used for the raise-to-power */ 5439 /* calculation below, which needs an extra two digits */ 5440 needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit); 5441 if (needbytes>sizeof(buft)) { /* need malloc space */ 5442 allocbuft=(decNumber *)malloc(needbytes); 5443 if (allocbuft==NULL) { /* hopeless -- abandon */ 5444 *status|=DEC_Insufficient_storage; 5445 break;} 5446 t=allocbuft; /* use the allocated space */ 5447 } 5448 5449 uprv_decNumberCopy(t, x); /* term=x */ 5450 uprv_decNumberZero(a); *a->lsu=1; /* accumulator=1 */ 5451 uprv_decNumberZero(d); *d->lsu=2; /* divisor=2 */ 5452 uprv_decNumberZero(&numone); *numone.lsu=1; /* constant 1 for increment */ 5453 5454 /* set up the contexts for calculating a, t, and d */ 5455 uprv_decContextDefault(&tset, DEC_INIT_DECIMAL64); 5456 dset=tset; 5457 /* accumulator bounds are set above, set precision now */ 5458 aset.digits=p*2; /* double */ 5459 /* term bounds avoid any underflow or overflow */ 5460 tset.digits=p; 5461 tset.emin=DEC_MIN_EMIN; /* [emax is plenty] */ 5462 /* [dset.digits=16, etc., are sufficient] */ 5463 5464 /* finally ready to roll */ 5465 for (;;) { 5466 #if DECCHECK 5467 iterations++; 5468 #endif 5469 /* only the status from the accumulation is interesting */ 5470 /* [but it should remain unchanged after first add] */ 5471 decAddOp(a, a, t, &aset, 0, status); /* a=a+t */ 5472 decMultiplyOp(t, t, x, &tset, &ignore); /* t=t*x */ 5473 decDivideOp(t, t, d, &tset, DIVIDE, &ignore); /* t=t/d */ 5474 /* the iteration ends when the term cannot affect the result, */ 5475 /* if rounded to p digits, which is when its value is smaller */ 5476 /* than the accumulator by p+1 digits. There must also be */ 5477 /* full precision in a. */ 5478 if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1)) 5479 && (a->digits>=p)) break; 5480 decAddOp(d, d, &numone, &dset, 0, &ignore); /* d=d+1 */ 5481 } /* iterate */ 5482 5483 #if DECCHECK 5484 /* just a sanity check; comment out test to show always */ 5485 if (iterations>p+3) 5486 printf("Exp iterations=%ld, status=%08lx, p=%ld, d=%ld\n", 5487 (LI)iterations, (LI)*status, (LI)p, (LI)x->digits); 5488 #endif 5489 } /* h<=8 */ 5490 5491 /* apply postconditioning: a=a**(10**h) -- this is calculated */ 5492 /* at a slightly higher precision than Hull & Abrham suggest */ 5493 if (h>0) { 5494 Int seenbit=0; /* set once a 1-bit is seen */ 5495 Int i; /* counter */ 5496 Int n=powers[h]; /* always positive */ 5497 aset.digits=p+2; /* sufficient precision */ 5498 /* avoid the overhead and many extra digits of decNumberPower */ 5499 /* as all that is needed is the short 'multipliers' loop; here */ 5500 /* accumulate the answer into t */ 5501 uprv_decNumberZero(t); *t->lsu=1; /* acc=1 */ 5502 for (i=1;;i++){ /* for each bit [top bit ignored] */ 5503 /* abandon if have had overflow or terminal underflow */ 5504 if (*status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */ 5505 if (*status&DEC_Overflow || ISZERO(t)) break;} 5506 n=n<<1; /* move next bit to testable position */ 5507 if (n<0) { /* top bit is set */ 5508 seenbit=1; /* OK, have a significant bit */ 5509 decMultiplyOp(t, t, a, &aset, status); /* acc=acc*x */ 5510 } 5511 if (i==31) break; /* that was the last bit */ 5512 if (!seenbit) continue; /* no need to square 1 */ 5513 decMultiplyOp(t, t, t, &aset, status); /* acc=acc*acc [square] */ 5514 } /*i*/ /* 32 bits */ 5515 /* decNumberShow(t); */ 5516 a=t; /* and carry on using t instead of a */ 5517 } 5518 5519 /* Copy and round the result to res */ 5520 residue=1; /* indicate dirt to right .. */ 5521 if (ISZERO(a)) residue=0; /* .. unless underflowed to 0 */ 5522 aset.digits=set->digits; /* [use default rounding] */ 5523 decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */ 5524 decFinish(res, set, &residue, status); /* cleanup/set flags */ 5525 } while(0); /* end protected */ 5526 5527 if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */ 5528 if (allocbufa!=NULL) free(allocbufa); /* .. */ 5529 if (allocbuft!=NULL) free(allocbuft); /* .. */ 5530 /* [status is handled by caller] */ 5531 return res; 5532 } /* decExpOp */ 5533 5534/* ------------------------------------------------------------------ */ 5535/* Initial-estimate natural logarithm table */ 5536/* */ 5537/* LNnn -- 90-entry 16-bit table for values from .10 through .99. */ 5538/* The result is a 4-digit encode of the coefficient (c=the */ 5539/* top 14 bits encoding 0-9999) and a 2-digit encode of the */ 5540/* exponent (e=the bottom 2 bits encoding 0-3) */ 5541/* */ 5542/* The resulting value is given by: */ 5543/* */ 5544/* v = -c * 10**(-e-3) */ 5545/* */ 5546/* where e and c are extracted from entry k = LNnn[x-10] */ 5547/* where x is truncated (NB) into the range 10 through 99, */ 5548/* and then c = k>>2 and e = k&3. */ 5549/* ------------------------------------------------------------------ */ 5550static const uShort LNnn[90]={9016, 8652, 8316, 8008, 7724, 7456, 7208, 5551 6972, 6748, 6540, 6340, 6148, 5968, 5792, 5628, 5464, 5312, 5552 5164, 5020, 4884, 4748, 4620, 4496, 4376, 4256, 4144, 4032, 5553 39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629, 5554 29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837, 5555 22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321, 5556 15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717, 5557 10197, 9685, 9177, 8677, 8185, 7697, 7213, 6737, 6269, 5801, 5558 5341, 4889, 4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254, 5559 10130, 6046, 20055}; 5560 5561/* ------------------------------------------------------------------ */ 5562/* decLnOp -- effect natural logarithm */ 5563/* */ 5564/* This computes C = ln(A) */ 5565/* */ 5566/* res is C, the result. C may be A */ 5567/* rhs is A */ 5568/* set is the context; note that rounding mode has no effect */ 5569/* */ 5570/* C must have space for set->digits digits. */ 5571/* */ 5572/* Notable cases: */ 5573/* A<0 -> Invalid */ 5574/* A=0 -> -Infinity (Exact) */ 5575/* A=+Infinity -> +Infinity (Exact) */ 5576/* A=1 exactly -> 0 (Exact) */ 5577/* */ 5578/* Restrictions (as for Exp): */ 5579/* */ 5580/* digits, emax, and -emin in the context must be less than */ 5581/* DEC_MAX_MATH+11 (1000010), and the rhs must be within these */ 5582/* bounds or a zero. This is an internal routine, so these */ 5583/* restrictions are contractual and not enforced. */ 5584/* */ 5585/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */ 5586/* almost always be correctly rounded, but may be up to 1 ulp in */ 5587/* error in rare cases. */ 5588/* ------------------------------------------------------------------ */ 5589/* The result is calculated using Newton's method, with each */ 5590/* iteration calculating a' = a + x * exp(-a) - 1. See, for example, */ 5591/* Epperson 1989. */ 5592/* */ 5593/* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */ 5594/* This has to be calculated at the sum of the precision of x and the */ 5595/* working precision. */ 5596/* */ 5597/* Implementation notes: */ 5598/* */ 5599/* 1. This is separated out as decLnOp so it can be called from */ 5600/* other Mathematical functions (e.g., Log 10) with a wider range */ 5601/* than normal. In particular, it can handle the slightly wider */ 5602/* (+9+2) range needed by a power function. */ 5603/* */ 5604/* 2. The speed of this function is about 10x slower than exp, as */ 5605/* it typically needs 4-6 iterations for short numbers, and the */ 5606/* extra precision needed adds a squaring effect, twice. */ 5607/* */ 5608/* 3. Fastpaths are included for ln(10) and ln(2), up to length 40, */ 5609/* as these are common requests. ln(10) is used by log10(x). */ 5610/* */ 5611/* 4. An iteration might be saved by widening the LNnn table, and */ 5612/* would certainly save at least one if it were made ten times */ 5613/* bigger, too (for truncated fractions 0.100 through 0.999). */ 5614/* However, for most practical evaluations, at least four or five */ 5615/* iterations will be neede -- so this would only speed up by */ 5616/* 20-25% and that probably does not justify increasing the table */ 5617/* size. */ 5618/* */ 5619/* 5. The static buffers are larger than might be expected to allow */ 5620/* for calls from decNumberPower. */ 5621/* ------------------------------------------------------------------ */ 5622#if defined(__clang__) || U_GCC_MAJOR_MINOR >= 406 5623#pragma GCC diagnostic push 5624#pragma GCC diagnostic ignored "-Warray-bounds" 5625#endif 5626decNumber * decLnOp(decNumber *res, const decNumber *rhs, 5627 decContext *set, uInt *status) { 5628 uInt ignore=0; /* working status accumulator */ 5629 uInt needbytes; /* for space calculations */ 5630 Int residue; /* rounding residue */ 5631 Int r; /* rhs=f*10**r [see below] */ 5632 Int p; /* working precision */ 5633 Int pp; /* precision for iteration */ 5634 Int t; /* work */ 5635 5636 /* buffers for a (accumulator, typically precision+2) and b */ 5637 /* (adjustment calculator, same size) */ 5638 decNumber bufa[D2N(DECBUFFER+12)]; 5639 decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ 5640 decNumber *a=bufa; /* accumulator/work */ 5641 decNumber bufb[D2N(DECBUFFER*2+2)]; 5642 decNumber *allocbufb=NULL; /* -> allocated bufa, iff allocated */ 5643 decNumber *b=bufb; /* adjustment/work */ 5644 5645 decNumber numone; /* constant 1 */ 5646 decNumber cmp; /* work */ 5647 decContext aset, bset; /* working contexts */ 5648 5649 #if DECCHECK 5650 Int iterations=0; /* for later sanity check */ 5651 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; 5652 #endif 5653 5654 do { /* protect allocated storage */ 5655 if (SPECIALARG) { /* handle infinities and NaNs */ 5656 if (decNumberIsInfinite(rhs)) { /* an infinity */ 5657 if (decNumberIsNegative(rhs)) /* -Infinity -> error */ 5658 *status|=DEC_Invalid_operation; 5659 else uprv_decNumberCopy(res, rhs); /* +Infinity -> self */ 5660 } 5661 else decNaNs(res, rhs, NULL, set, status); /* a NaN */ 5662 break;} 5663 5664 if (ISZERO(rhs)) { /* +/- zeros -> -Infinity */ 5665 uprv_decNumberZero(res); /* make clean */ 5666 res->bits=DECINF|DECNEG; /* set - infinity */ 5667 break;} /* [no status to set] */ 5668 5669 /* Non-zero negatives are bad... */ 5670 if (decNumberIsNegative(rhs)) { /* -x -> error */ 5671 *status|=DEC_Invalid_operation; 5672 break;} 5673 5674 /* Here, rhs is positive, finite, and in range */ 5675 5676 /* lookaside fastpath code for ln(2) and ln(10) at common lengths */ 5677 if (rhs->exponent==0 && set->digits<=40) { 5678 #if DECDPUN==1 5679 if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { /* ln(10) */ 5680 #else 5681 if (rhs->lsu[0]==10 && rhs->digits==2) { /* ln(10) */ 5682 #endif 5683 aset=*set; aset.round=DEC_ROUND_HALF_EVEN; 5684 #define LN10 "2.302585092994045684017991454684364207601" 5685 uprv_decNumberFromString(res, LN10, &aset); 5686 *status|=(DEC_Inexact | DEC_Rounded); /* is inexact */ 5687 break;} 5688 if (rhs->lsu[0]==2 && rhs->digits==1) { /* ln(2) */ 5689 aset=*set; aset.round=DEC_ROUND_HALF_EVEN; 5690 #define LN2 "0.6931471805599453094172321214581765680755" 5691 uprv_decNumberFromString(res, LN2, &aset); 5692 *status|=(DEC_Inexact | DEC_Rounded); 5693 break;} 5694 } /* integer and short */ 5695 5696 /* Determine the working precision. This is normally the */ 5697 /* requested precision + 2, with a minimum of 9. However, if */ 5698 /* the rhs is 'over-precise' then allow for all its digits to */ 5699 /* potentially participate (consider an rhs where all the excess */ 5700 /* digits are 9s) so in this case use rhs->digits+2. */ 5701 p=MAXI(rhs->digits, MAXI(set->digits, 7))+2; 5702 5703 /* Allocate space for the accumulator and the high-precision */ 5704 /* adjustment calculator, if necessary. The accumulator must */ 5705 /* be able to hold p digits, and the adjustment up to */ 5706 /* rhs->digits+p digits. They are also made big enough for 16 */ 5707 /* digits so that they can be used for calculating the initial */ 5708 /* estimate. */ 5709 needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit); 5710 if (needbytes>sizeof(bufa)) { /* need malloc space */ 5711 allocbufa=(decNumber *)malloc(needbytes); 5712 if (allocbufa==NULL) { /* hopeless -- abandon */ 5713 *status|=DEC_Insufficient_storage; 5714 break;} 5715 a=allocbufa; /* use the allocated space */ 5716 } 5717 pp=p+rhs->digits; 5718 needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit); 5719 if (needbytes>sizeof(bufb)) { /* need malloc space */ 5720 allocbufb=(decNumber *)malloc(needbytes); 5721 if (allocbufb==NULL) { /* hopeless -- abandon */ 5722 *status|=DEC_Insufficient_storage; 5723 break;} 5724 b=allocbufb; /* use the allocated space */ 5725 } 5726 5727 /* Prepare an initial estimate in acc. Calculate this by */ 5728 /* considering the coefficient of x to be a normalized fraction, */ 5729 /* f, with the decimal point at far left and multiplied by */ 5730 /* 10**r. Then, rhs=f*10**r and 0.1<=f<1, and */ 5731 /* ln(x) = ln(f) + ln(10)*r */ 5732 /* Get the initial estimate for ln(f) from a small lookup */ 5733 /* table (see above) indexed by the first two digits of f, */ 5734 /* truncated. */ 5735 5736 uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); /* 16-digit extended */ 5737 r=rhs->exponent+rhs->digits; /* 'normalised' exponent */ 5738 uprv_decNumberFromInt32(a, r); /* a=r */ 5739 uprv_decNumberFromInt32(b, 2302585); /* b=ln(10) (2.302585) */ 5740 b->exponent=-6; /* .. */ 5741 decMultiplyOp(a, a, b, &aset, &ignore); /* a=a*b */ 5742 /* now get top two digits of rhs into b by simple truncate and */ 5743 /* force to integer */ 5744 residue=0; /* (no residue) */ 5745 aset.digits=2; aset.round=DEC_ROUND_DOWN; 5746 decCopyFit(b, rhs, &aset, &residue, &ignore); /* copy & shorten */ 5747 b->exponent=0; /* make integer */ 5748 t=decGetInt(b); /* [cannot fail] */ 5749 if (t<10) t=X10(t); /* adjust single-digit b */ 5750 t=LNnn[t-10]; /* look up ln(b) */ 5751 uprv_decNumberFromInt32(b, t>>2); /* b=ln(b) coefficient */ 5752 b->exponent=-(t&3)-3; /* set exponent */ 5753 b->bits=DECNEG; /* ln(0.10)->ln(0.99) always -ve */ 5754 aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; /* restore */ 5755 decAddOp(a, a, b, &aset, 0, &ignore); /* acc=a+b */ 5756 /* the initial estimate is now in a, with up to 4 digits correct. */ 5757 /* When rhs is at or near Nmax the estimate will be low, so we */ 5758 /* will approach it from below, avoiding overflow when calling exp. */ 5759 5760 uprv_decNumberZero(&numone); *numone.lsu=1; /* constant 1 for adjustment */ 5761 5762 /* accumulator bounds are as requested (could underflow, but */ 5763 /* cannot overflow) */ 5764 aset.emax=set->emax; 5765 aset.emin=set->emin; 5766 aset.clamp=0; /* no concrete format */ 5767 /* set up a context to be used for the multiply and subtract */ 5768 bset=aset; 5769 bset.emax=DEC_MAX_MATH*2; /* use double bounds for the */ 5770 bset.emin=-DEC_MAX_MATH*2; /* adjustment calculation */ 5771 /* [see decExpOp call below] */ 5772 /* for each iteration double the number of digits to calculate, */ 5773 /* up to a maximum of p */ 5774 pp=9; /* initial precision */ 5775 /* [initially 9 as then the sequence starts 7+2, 16+2, and */ 5776 /* 34+2, which is ideal for standard-sized numbers] */ 5777 aset.digits=pp; /* working context */ 5778 bset.digits=pp+rhs->digits; /* wider context */ 5779 for (;;) { /* iterate */ 5780 #if DECCHECK 5781 iterations++; 5782 if (iterations>24) break; /* consider 9 * 2**24 */ 5783 #endif 5784 /* calculate the adjustment (exp(-a)*x-1) into b. This is a */ 5785 /* catastrophic subtraction but it really is the difference */ 5786 /* from 1 that is of interest. */ 5787 /* Use the internal entry point to Exp as it allows the double */ 5788 /* range for calculating exp(-a) when a is the tiniest subnormal. */ 5789 a->bits^=DECNEG; /* make -a */ 5790 decExpOp(b, a, &bset, &ignore); /* b=exp(-a) */ 5791 a->bits^=DECNEG; /* restore sign of a */ 5792 /* now multiply by rhs and subtract 1, at the wider precision */ 5793 decMultiplyOp(b, b, rhs, &bset, &ignore); /* b=b*rhs */ 5794 decAddOp(b, b, &numone, &bset, DECNEG, &ignore); /* b=b-1 */ 5795 5796 /* the iteration ends when the adjustment cannot affect the */ 5797 /* result by >=0.5 ulp (at the requested digits), which */ 5798 /* is when its value is smaller than the accumulator by */ 5799 /* set->digits+1 digits (or it is zero) -- this is a looser */ 5800 /* requirement than for Exp because all that happens to the */ 5801 /* accumulator after this is the final rounding (but note that */ 5802 /* there must also be full precision in a, or a=0). */ 5803 5804 if (decNumberIsZero(b) || 5805 (a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) { 5806 if (a->digits==p) break; 5807 if (decNumberIsZero(a)) { 5808 decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); /* rhs=1 ? */ 5809 if (cmp.lsu[0]==0) a->exponent=0; /* yes, exact 0 */ 5810 else *status|=(DEC_Inexact | DEC_Rounded); /* no, inexact */ 5811 break; 5812 } 5813 /* force padding if adjustment has gone to 0 before full length */ 5814 if (decNumberIsZero(b)) b->exponent=a->exponent-p; 5815 } 5816 5817 /* not done yet ... */ 5818 decAddOp(a, a, b, &aset, 0, &ignore); /* a=a+b for next estimate */ 5819 if (pp==p) continue; /* precision is at maximum */ 5820 /* lengthen the next calculation */ 5821 pp=pp*2; /* double precision */ 5822 if (pp>p) pp=p; /* clamp to maximum */ 5823 aset.digits=pp; /* working context */ 5824 bset.digits=pp+rhs->digits; /* wider context */ 5825 } /* Newton's iteration */ 5826 5827 #if DECCHECK 5828 /* just a sanity check; remove the test to show always */ 5829 if (iterations>24) 5830 printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n", 5831 (LI)iterations, (LI)*status, (LI)p, (LI)rhs->digits); 5832 #endif 5833 5834 /* Copy and round the result to res */ 5835 residue=1; /* indicate dirt to right */ 5836 if (ISZERO(a)) residue=0; /* .. unless underflowed to 0 */ 5837 aset.digits=set->digits; /* [use default rounding] */ 5838 decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */ 5839 decFinish(res, set, &residue, status); /* cleanup/set flags */ 5840 } while(0); /* end protected */ 5841 5842 if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ 5843 if (allocbufb!=NULL) free(allocbufb); /* .. */ 5844 /* [status is handled by caller] */ 5845 return res; 5846 } /* decLnOp */ 5847#if defined(__clang__) || U_GCC_MAJOR_MINOR >= 406 5848#pragma GCC diagnostic pop 5849#endif 5850 5851/* ------------------------------------------------------------------ */ 5852/* decQuantizeOp -- force exponent to requested value */ 5853/* */ 5854/* This computes C = op(A, B), where op adjusts the coefficient */ 5855/* of C (by rounding or shifting) such that the exponent (-scale) */ 5856/* of C has the value B or matches the exponent of B. */ 5857/* The numerical value of C will equal A, except for the effects of */ 5858/* any rounding that occurred. */ 5859/* */ 5860/* res is C, the result. C may be A or B */ 5861/* lhs is A, the number to adjust */ 5862/* rhs is B, the requested exponent */ 5863/* set is the context */ 5864/* quant is 1 for quantize or 0 for rescale */ 5865/* status is the status accumulator (this can be called without */ 5866/* risk of control loss) */ 5867/* */ 5868/* C must have space for set->digits digits. */ 5869/* */ 5870/* Unless there is an error or the result is infinite, the exponent */ 5871/* after the operation is guaranteed to be that requested. */ 5872/* ------------------------------------------------------------------ */ 5873static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs, 5874 const decNumber *rhs, decContext *set, 5875 Flag quant, uInt *status) { 5876 #if DECSUBSET 5877 decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ 5878 decNumber *allocrhs=NULL; /* .., rhs */ 5879 #endif 5880 const decNumber *inrhs=rhs; /* save original rhs */ 5881 Int reqdigits=set->digits; /* requested DIGITS */ 5882 Int reqexp; /* requested exponent [-scale] */ 5883 Int residue=0; /* rounding residue */ 5884 Int etiny=set->emin-(reqdigits-1); 5885 5886 #if DECCHECK 5887 if (decCheckOperands(res, lhs, rhs, set)) return res; 5888 #endif 5889 5890 do { /* protect allocated storage */ 5891 #if DECSUBSET 5892 if (!set->extended) { 5893 /* reduce operands and set lostDigits status, as needed */ 5894 if (lhs->digits>reqdigits) { 5895 alloclhs=decRoundOperand(lhs, set, status); 5896 if (alloclhs==NULL) break; 5897 lhs=alloclhs; 5898 } 5899 if (rhs->digits>reqdigits) { /* [this only checks lostDigits] */ 5900 allocrhs=decRoundOperand(rhs, set, status); 5901 if (allocrhs==NULL) break; 5902 rhs=allocrhs; 5903 } 5904 } 5905 #endif 5906 /* [following code does not require input rounding] */ 5907 5908 /* Handle special values */ 5909 if (SPECIALARGS) { 5910 /* NaNs get usual processing */ 5911 if (SPECIALARGS & (DECSNAN | DECNAN)) 5912 decNaNs(res, lhs, rhs, set, status); 5913 /* one infinity but not both is bad */ 5914 else if ((lhs->bits ^ rhs->bits) & DECINF) 5915 *status|=DEC_Invalid_operation; 5916 /* both infinity: return lhs */ 5917 else uprv_decNumberCopy(res, lhs); /* [nop if in place] */ 5918 break; 5919 } 5920 5921 /* set requested exponent */ 5922 if (quant) reqexp=inrhs->exponent; /* quantize -- match exponents */ 5923 else { /* rescale -- use value of rhs */ 5924 /* Original rhs must be an integer that fits and is in range, */ 5925 /* which could be from -1999999997 to +999999999, thanks to */ 5926 /* subnormals */ 5927 reqexp=decGetInt(inrhs); /* [cannot fail] */ 5928 } 5929 5930 #if DECSUBSET 5931 if (!set->extended) etiny=set->emin; /* no subnormals */ 5932 #endif 5933 5934 if (reqexp==BADINT /* bad (rescale only) or .. */ 5935 || reqexp==BIGODD || reqexp==BIGEVEN /* very big (ditto) or .. */ 5936 || (reqexp<etiny) /* < lowest */ 5937 || (reqexp>set->emax)) { /* > emax */ 5938 *status|=DEC_Invalid_operation; 5939 break;} 5940 5941 /* the RHS has been processed, so it can be overwritten now if necessary */ 5942 if (ISZERO(lhs)) { /* zero coefficient unchanged */ 5943 uprv_decNumberCopy(res, lhs); /* [nop if in place] */ 5944 res->exponent=reqexp; /* .. just set exponent */ 5945 #if DECSUBSET 5946 if (!set->extended) res->bits=0; /* subset specification; no -0 */ 5947 #endif 5948 } 5949 else { /* non-zero lhs */ 5950 Int adjust=reqexp-lhs->exponent; /* digit adjustment needed */ 5951 /* if adjusted coefficient will definitely not fit, give up now */ 5952 if ((lhs->digits-adjust)>reqdigits) { 5953 *status|=DEC_Invalid_operation; 5954 break; 5955 } 5956 5957 if (adjust>0) { /* increasing exponent */ 5958 /* this will decrease the length of the coefficient by adjust */ 5959 /* digits, and must round as it does so */ 5960 decContext workset; /* work */ 5961 workset=*set; /* clone rounding, etc. */ 5962 workset.digits=lhs->digits-adjust; /* set requested length */ 5963 /* [note that the latter can be <1, here] */ 5964 decCopyFit(res, lhs, &workset, &residue, status); /* fit to result */ 5965 decApplyRound(res, &workset, residue, status); /* .. and round */ 5966 residue=0; /* [used] */ 5967 /* If just rounded a 999s case, exponent will be off by one; */ 5968 /* adjust back (after checking space), if so. */ 5969 if (res->exponent>reqexp) { 5970 /* re-check needed, e.g., for quantize(0.9999, 0.001) under */ 5971 /* set->digits==3 */ 5972 if (res->digits==reqdigits) { /* cannot shift by 1 */ 5973 *status&=~(DEC_Inexact | DEC_Rounded); /* [clean these] */ 5974 *status|=DEC_Invalid_operation; 5975 break; 5976 } 5977 res->digits=decShiftToMost(res->lsu, res->digits, 1); /* shift */ 5978 res->exponent--; /* (re)adjust the exponent. */ 5979 } 5980 #if DECSUBSET 5981 if (ISZERO(res) && !set->extended) res->bits=0; /* subset; no -0 */ 5982 #endif 5983 } /* increase */ 5984 else /* adjust<=0 */ { /* decreasing or = exponent */ 5985 /* this will increase the length of the coefficient by -adjust */ 5986 /* digits, by adding zero or more trailing zeros; this is */ 5987 /* already checked for fit, above */ 5988 uprv_decNumberCopy(res, lhs); /* [it will fit] */ 5989 /* if padding needed (adjust<0), add it now... */ 5990 if (adjust<0) { 5991 res->digits=decShiftToMost(res->lsu, res->digits, -adjust); 5992 res->exponent+=adjust; /* adjust the exponent */ 5993 } 5994 } /* decrease */ 5995 } /* non-zero */ 5996 5997 /* Check for overflow [do not use Finalize in this case, as an */ 5998 /* overflow here is a "don't fit" situation] */ 5999 if (res->exponent>set->emax-res->digits+1) { /* too big */ 6000 *status|=DEC_Invalid_operation; 6001 break; 6002 } 6003 else { 6004 decFinalize(res, set, &residue, status); /* set subnormal flags */ 6005 *status&=~DEC_Underflow; /* suppress Underflow [as per 754] */ 6006 } 6007 } while(0); /* end protected */ 6008 6009 #if DECSUBSET 6010 if (allocrhs!=NULL) free(allocrhs); /* drop any storage used */ 6011 if (alloclhs!=NULL) free(alloclhs); /* .. */ 6012 #endif 6013 return res; 6014 } /* decQuantizeOp */ 6015 6016/* ------------------------------------------------------------------ */ 6017/* decCompareOp -- compare, min, or max two Numbers */ 6018/* */ 6019/* This computes C = A ? B and carries out one of four operations: */ 6020/* COMPARE -- returns the signum (as a number) giving the */ 6021/* result of a comparison unless one or both */ 6022/* operands is a NaN (in which case a NaN results) */ 6023/* COMPSIG -- as COMPARE except that a quiet NaN raises */ 6024/* Invalid operation. */ 6025/* COMPMAX -- returns the larger of the operands, using the */ 6026/* 754 maxnum operation */ 6027/* COMPMAXMAG -- ditto, comparing absolute values */ 6028/* COMPMIN -- the 754 minnum operation */ 6029/* COMPMINMAG -- ditto, comparing absolute values */ 6030/* COMTOTAL -- returns the signum (as a number) giving the */ 6031/* result of a comparison using 754 total ordering */ 6032/* */ 6033/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ 6034/* lhs is A */ 6035/* rhs is B */ 6036/* set is the context */ 6037/* op is the operation flag */ 6038/* status is the usual accumulator */ 6039/* */ 6040/* C must have space for one digit for COMPARE or set->digits for */ 6041/* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG. */ 6042/* ------------------------------------------------------------------ */ 6043/* The emphasis here is on speed for common cases, and avoiding */ 6044/* coefficient comparison if possible. */ 6045/* ------------------------------------------------------------------ */ 6046static decNumber * decCompareOp(decNumber *res, const decNumber *lhs, 6047 const decNumber *rhs, decContext *set, 6048 Flag op, uInt *status) { 6049 #if DECSUBSET 6050 decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ 6051 decNumber *allocrhs=NULL; /* .., rhs */ 6052 #endif 6053 Int result=0; /* default result value */ 6054 uByte merged; /* work */ 6055 6056 #if DECCHECK 6057 if (decCheckOperands(res, lhs, rhs, set)) return res; 6058 #endif 6059 6060 do { /* protect allocated storage */ 6061 #if DECSUBSET 6062 if (!set->extended) { 6063 /* reduce operands and set lostDigits status, as needed */ 6064 if (lhs->digits>set->digits) { 6065 alloclhs=decRoundOperand(lhs, set, status); 6066 if (alloclhs==NULL) {result=BADINT; break;} 6067 lhs=alloclhs; 6068 } 6069 if (rhs->digits>set->digits) { 6070 allocrhs=decRoundOperand(rhs, set, status); 6071 if (allocrhs==NULL) {result=BADINT; break;} 6072 rhs=allocrhs; 6073 } 6074 } 6075 #endif 6076 /* [following code does not require input rounding] */ 6077 6078 /* If total ordering then handle differing signs 'up front' */ 6079 if (op==COMPTOTAL) { /* total ordering */ 6080 if (decNumberIsNegative(lhs) && !decNumberIsNegative(rhs)) { 6081 result=-1; 6082 break; 6083 } 6084 if (!decNumberIsNegative(lhs) && decNumberIsNegative(rhs)) { 6085 result=+1; 6086 break; 6087 } 6088 } 6089 6090 /* handle NaNs specially; let infinities drop through */ 6091 /* This assumes sNaN (even just one) leads to NaN. */ 6092 merged=(lhs->bits | rhs->bits) & (DECSNAN | DECNAN); 6093 if (merged) { /* a NaN bit set */ 6094 if (op==COMPARE); /* result will be NaN */ 6095 else if (op==COMPSIG) /* treat qNaN as sNaN */ 6096 *status|=DEC_Invalid_operation | DEC_sNaN; 6097 else if (op==COMPTOTAL) { /* total ordering, always finite */ 6098 /* signs are known to be the same; compute the ordering here */ 6099 /* as if the signs are both positive, then invert for negatives */ 6100 if (!decNumberIsNaN(lhs)) result=-1; 6101 else if (!decNumberIsNaN(rhs)) result=+1; 6102 /* here if both NaNs */ 6103 else if (decNumberIsSNaN(lhs) && decNumberIsQNaN(rhs)) result=-1; 6104 else if (decNumberIsQNaN(lhs) && decNumberIsSNaN(rhs)) result=+1; 6105 else { /* both NaN or both sNaN */ 6106 /* now it just depends on the payload */ 6107 result=decUnitCompare(lhs->lsu, D2U(lhs->digits), 6108 rhs->lsu, D2U(rhs->digits), 0); 6109 /* [Error not possible, as these are 'aligned'] */ 6110 } /* both same NaNs */ 6111 if (decNumberIsNegative(lhs)) result=-result; 6112 break; 6113 } /* total order */ 6114 6115 else if (merged & DECSNAN); /* sNaN -> qNaN */ 6116 else { /* here if MIN or MAX and one or two quiet NaNs */ 6117 /* min or max -- 754 rules ignore single NaN */ 6118 if (!decNumberIsNaN(lhs) || !decNumberIsNaN(rhs)) { 6119 /* just one NaN; force choice to be the non-NaN operand */ 6120 op=COMPMAX; 6121 if (lhs->bits & DECNAN) result=-1; /* pick rhs */ 6122 else result=+1; /* pick lhs */ 6123 break; 6124 } 6125 } /* max or min */ 6126 op=COMPNAN; /* use special path */ 6127 decNaNs(res, lhs, rhs, set, status); /* propagate NaN */ 6128 break; 6129 } 6130 /* have numbers */ 6131 if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1); 6132 else result=decCompare(lhs, rhs, 0); /* sign matters */ 6133 } while(0); /* end protected */ 6134 6135 if (result==BADINT) *status|=DEC_Insufficient_storage; /* rare */ 6136 else { 6137 if (op==COMPARE || op==COMPSIG ||op==COMPTOTAL) { /* returning signum */ 6138 if (op==COMPTOTAL && result==0) { 6139 /* operands are numerically equal or same NaN (and same sign, */ 6140 /* tested first); if identical, leave result 0 */ 6141 if (lhs->exponent!=rhs->exponent) { 6142 if (lhs->exponent<rhs->exponent) result=-1; 6143 else result=+1; 6144 if (decNumberIsNegative(lhs)) result=-result; 6145 } /* lexp!=rexp */ 6146 } /* total-order by exponent */ 6147 uprv_decNumberZero(res); /* [always a valid result] */ 6148 if (result!=0) { /* must be -1 or +1 */ 6149 *res->lsu=1; 6150 if (result<0) res->bits=DECNEG; 6151 } 6152 } 6153 else if (op==COMPNAN); /* special, drop through */ 6154 else { /* MAX or MIN, non-NaN result */ 6155 Int residue=0; /* rounding accumulator */ 6156 /* choose the operand for the result */ 6157 const decNumber *choice; 6158 if (result==0) { /* operands are numerically equal */ 6159 /* choose according to sign then exponent (see 754) */ 6160 uByte slhs=(lhs->bits & DECNEG); 6161 uByte srhs=(rhs->bits & DECNEG); 6162 #if DECSUBSET 6163 if (!set->extended) { /* subset: force left-hand */ 6164 op=COMPMAX; 6165 result=+1; 6166 } 6167 else 6168 #endif 6169 if (slhs!=srhs) { /* signs differ */ 6170 if (slhs) result=-1; /* rhs is max */ 6171 else result=+1; /* lhs is max */ 6172 } 6173 else if (slhs && srhs) { /* both negative */ 6174 if (lhs->exponent<rhs->exponent) result=+1; 6175 else result=-1; 6176 /* [if equal, use lhs, technically identical] */ 6177 } 6178 else { /* both positive */ 6179 if (lhs->exponent>rhs->exponent) result=+1; 6180 else result=-1; 6181 /* [ditto] */ 6182 } 6183 } /* numerically equal */ 6184 /* here result will be non-0; reverse if looking for MIN */ 6185 if (op==COMPMIN || op==COMPMINMAG) result=-result; 6186 choice=(result>0 ? lhs : rhs); /* choose */ 6187 /* copy chosen to result, rounding if need be */ 6188 decCopyFit(res, choice, set, &residue, status); 6189 decFinish(res, set, &residue, status); 6190 } 6191 } 6192 #if DECSUBSET 6193 if (allocrhs!=NULL) free(allocrhs); /* free any storage used */ 6194 if (alloclhs!=NULL) free(alloclhs); /* .. */ 6195 #endif 6196 return res; 6197 } /* decCompareOp */ 6198 6199/* ------------------------------------------------------------------ */ 6200/* decCompare -- compare two decNumbers by numerical value */ 6201/* */ 6202/* This routine compares A ? B without altering them. */ 6203/* */ 6204/* Arg1 is A, a decNumber which is not a NaN */ 6205/* Arg2 is B, a decNumber which is not a NaN */ 6206/* Arg3 is 1 for a sign-independent compare, 0 otherwise */ 6207/* */ 6208/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */ 6209/* (the only possible failure is an allocation error) */ 6210/* ------------------------------------------------------------------ */ 6211static Int decCompare(const decNumber *lhs, const decNumber *rhs, 6212 Flag abs_c) { 6213 Int result; /* result value */ 6214 Int sigr; /* rhs signum */ 6215 Int compare; /* work */ 6216 6217 result=1; /* assume signum(lhs) */ 6218 if (ISZERO(lhs)) result=0; 6219 if (abs_c) { 6220 if (ISZERO(rhs)) return result; /* LHS wins or both 0 */ 6221 /* RHS is non-zero */ 6222 if (result==0) return -1; /* LHS is 0; RHS wins */ 6223 /* [here, both non-zero, result=1] */ 6224 } 6225 else { /* signs matter */ 6226 if (result && decNumberIsNegative(lhs)) result=-1; 6227 sigr=1; /* compute signum(rhs) */ 6228 if (ISZERO(rhs)) sigr=0; 6229 else if (decNumberIsNegative(rhs)) sigr=-1; 6230 if (result > sigr) return +1; /* L > R, return 1 */ 6231 if (result < sigr) return -1; /* L < R, return -1 */ 6232 if (result==0) return 0; /* both 0 */ 6233 } 6234 6235 /* signums are the same; both are non-zero */ 6236 if ((lhs->bits | rhs->bits) & DECINF) { /* one or more infinities */ 6237 if (decNumberIsInfinite(rhs)) { 6238 if (decNumberIsInfinite(lhs)) result=0;/* both infinite */ 6239 else result=-result; /* only rhs infinite */ 6240 } 6241 return result; 6242 } 6243 /* must compare the coefficients, allowing for exponents */ 6244 if (lhs->exponent>rhs->exponent) { /* LHS exponent larger */ 6245 /* swap sides, and sign */ 6246 const decNumber *temp=lhs; 6247 lhs=rhs; 6248 rhs=temp; 6249 result=-result; 6250 } 6251 compare=decUnitCompare(lhs->lsu, D2U(lhs->digits), 6252 rhs->lsu, D2U(rhs->digits), 6253 rhs->exponent-lhs->exponent); 6254 if (compare!=BADINT) compare*=result; /* comparison succeeded */ 6255 return compare; 6256 } /* decCompare */ 6257 6258/* ------------------------------------------------------------------ */ 6259/* decUnitCompare -- compare two >=0 integers in Unit arrays */ 6260/* */ 6261/* This routine compares A ? B*10**E where A and B are unit arrays */ 6262/* A is a plain integer */ 6263/* B has an exponent of E (which must be non-negative) */ 6264/* */ 6265/* Arg1 is A first Unit (lsu) */ 6266/* Arg2 is A length in Units */ 6267/* Arg3 is B first Unit (lsu) */ 6268/* Arg4 is B length in Units */ 6269/* Arg5 is E (0 if the units are aligned) */ 6270/* */ 6271/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */ 6272/* (the only possible failure is an allocation error, which can */ 6273/* only occur if E!=0) */ 6274/* ------------------------------------------------------------------ */ 6275static Int decUnitCompare(const Unit *a, Int alength, 6276 const Unit *b, Int blength, Int exp) { 6277 Unit *acc; /* accumulator for result */ 6278 Unit accbuff[SD2U(DECBUFFER*2+1)]; /* local buffer */ 6279 Unit *allocacc=NULL; /* -> allocated acc buffer, iff allocated */ 6280 Int accunits, need; /* units in use or needed for acc */ 6281 const Unit *l, *r, *u; /* work */ 6282 Int expunits, exprem, result; /* .. */ 6283 6284 if (exp==0) { /* aligned; fastpath */ 6285 if (alength>blength) return 1; 6286 if (alength<blength) return -1; 6287 /* same number of units in both -- need unit-by-unit compare */ 6288 l=a+alength-1; 6289 r=b+alength-1; 6290 for (;l>=a; l--, r--) { 6291 if (*l>*r) return 1; 6292 if (*l<*r) return -1; 6293 } 6294 return 0; /* all units match */ 6295 } /* aligned */ 6296 6297 /* Unaligned. If one is >1 unit longer than the other, padded */ 6298 /* approximately, then can return easily */ 6299 if (alength>blength+(Int)D2U(exp)) return 1; 6300 if (alength+1<blength+(Int)D2U(exp)) return -1; 6301 6302 /* Need to do a real subtract. For this, a result buffer is needed */ 6303 /* even though only the sign is of interest. Its length needs */ 6304 /* to be the larger of alength and padded blength, +2 */ 6305 need=blength+D2U(exp); /* maximum real length of B */ 6306 if (need<alength) need=alength; 6307 need+=2; 6308 acc=accbuff; /* assume use local buffer */ 6309 if (need*sizeof(Unit)>sizeof(accbuff)) { 6310 allocacc=(Unit *)malloc(need*sizeof(Unit)); 6311 if (allocacc==NULL) return BADINT; /* hopeless -- abandon */ 6312 acc=allocacc; 6313 } 6314 /* Calculate units and remainder from exponent. */ 6315 expunits=exp/DECDPUN; 6316 exprem=exp%DECDPUN; 6317 /* subtract [A+B*(-m)] */ 6318 accunits=decUnitAddSub(a, alength, b, blength, expunits, acc, 6319 -(Int)powers[exprem]); 6320 /* [UnitAddSub result may have leading zeros, even on zero] */ 6321 if (accunits<0) result=-1; /* negative result */ 6322 else { /* non-negative result */ 6323 /* check units of the result before freeing any storage */ 6324 for (u=acc; u<acc+accunits-1 && *u==0;) u++; 6325 result=(*u==0 ? 0 : +1); 6326 } 6327 /* clean up and return the result */ 6328 if (allocacc!=NULL) free(allocacc); /* drop any storage used */ 6329 return result; 6330 } /* decUnitCompare */ 6331 6332/* ------------------------------------------------------------------ */ 6333/* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays */ 6334/* */ 6335/* This routine performs the calculation: */ 6336/* */ 6337/* C=A+(B*M) */ 6338/* */ 6339/* Where M is in the range -DECDPUNMAX through +DECDPUNMAX. */ 6340/* */ 6341/* A may be shorter or longer than B. */ 6342/* */ 6343/* Leading zeros are not removed after a calculation. The result is */ 6344/* either the same length as the longer of A and B (adding any */ 6345/* shift), or one Unit longer than that (if a Unit carry occurred). */ 6346/* */ 6347/* A and B content are not altered unless C is also A or B. */ 6348/* C may be the same array as A or B, but only if no zero padding is */ 6349/* requested (that is, C may be B only if bshift==0). */ 6350/* C is filled from the lsu; only those units necessary to complete */ 6351/* the calculation are referenced. */ 6352/* */ 6353/* Arg1 is A first Unit (lsu) */ 6354/* Arg2 is A length in Units */ 6355/* Arg3 is B first Unit (lsu) */ 6356/* Arg4 is B length in Units */ 6357/* Arg5 is B shift in Units (>=0; pads with 0 units if positive) */ 6358/* Arg6 is C first Unit (lsu) */ 6359/* Arg7 is M, the multiplier */ 6360/* */ 6361/* returns the count of Units written to C, which will be non-zero */ 6362/* and negated if the result is negative. That is, the sign of the */ 6363/* returned Int is the sign of the result (positive for zero) and */ 6364/* the absolute value of the Int is the count of Units. */ 6365/* */ 6366/* It is the caller's responsibility to make sure that C size is */ 6367/* safe, allowing space if necessary for a one-Unit carry. */ 6368/* */ 6369/* This routine is severely performance-critical; *any* change here */ 6370/* must be measured (timed) to assure no performance degradation. */ 6371/* In particular, trickery here tends to be counter-productive, as */ 6372/* increased complexity of code hurts register optimizations on */ 6373/* register-poor architectures. Avoiding divisions is nearly */ 6374/* always a Good Idea, however. */ 6375/* */ 6376/* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark */ 6377/* (IBM Warwick, UK) for some of the ideas used in this routine. */ 6378/* ------------------------------------------------------------------ */ 6379static Int decUnitAddSub(const Unit *a, Int alength, 6380 const Unit *b, Int blength, Int bshift, 6381 Unit *c, Int m) { 6382 const Unit *alsu=a; /* A lsu [need to remember it] */ 6383 Unit *clsu=c; /* C ditto */ 6384 Unit *minC; /* low water mark for C */ 6385 Unit *maxC; /* high water mark for C */ 6386 eInt carry=0; /* carry integer (could be Long) */ 6387 Int add; /* work */ 6388 #if DECDPUN<=4 /* myriadal, millenary, etc. */ 6389 Int est; /* estimated quotient */ 6390 #endif 6391 6392 #if DECTRACE 6393 if (alength<1 || blength<1) 6394 printf("decUnitAddSub: alen blen m %ld %ld [%ld]\n", alength, blength, m); 6395 #endif 6396 6397 maxC=c+alength; /* A is usually the longer */ 6398 minC=c+blength; /* .. and B the shorter */ 6399 if (bshift!=0) { /* B is shifted; low As copy across */ 6400 minC+=bshift; 6401 /* if in place [common], skip copy unless there's a gap [rare] */ 6402 if (a==c && bshift<=alength) { 6403 c+=bshift; 6404 a+=bshift; 6405 } 6406 else for (; c<clsu+bshift; a++, c++) { /* copy needed */ 6407 if (a<alsu+alength) *c=*a; 6408 else *c=0; 6409 } 6410 } 6411 if (minC>maxC) { /* swap */ 6412 Unit *hold=minC; 6413 minC=maxC; 6414 maxC=hold; 6415 } 6416 6417 /* For speed, do the addition as two loops; the first where both A */ 6418 /* and B contribute, and the second (if necessary) where only one or */ 6419 /* other of the numbers contribute. */ 6420 /* Carry handling is the same (i.e., duplicated) in each case. */ 6421 for (; c<minC; c++) { 6422 carry+=*a; 6423 a++; 6424 carry+=((eInt)*b)*m; /* [special-casing m=1/-1 */ 6425 b++; /* here is not a win] */ 6426 /* here carry is new Unit of digits; it could be +ve or -ve */ 6427 if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */ 6428 *c=(Unit)carry; 6429 carry=0; 6430 continue; 6431 } 6432 #if DECDPUN==4 /* use divide-by-multiply */ 6433 if (carry>=0) { 6434 est=(((ueInt)carry>>11)*53687)>>18; 6435 *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ 6436 carry=est; /* likely quotient [89%] */ 6437 if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ 6438 carry++; 6439 *c-=DECDPUNMAX+1; 6440 continue; 6441 } 6442 /* negative case */ 6443 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ 6444 est=(((ueInt)carry>>11)*53687)>>18; 6445 *c=(Unit)(carry-est*(DECDPUNMAX+1)); 6446 carry=est-(DECDPUNMAX+1); /* correctly negative */ 6447 if (*c<DECDPUNMAX+1) continue; /* was OK */ 6448 carry++; 6449 *c-=DECDPUNMAX+1; 6450 #elif DECDPUN==3 6451 if (carry>=0) { 6452 est=(((ueInt)carry>>3)*16777)>>21; 6453 *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ 6454 carry=est; /* likely quotient [99%] */ 6455 if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ 6456 carry++; 6457 *c-=DECDPUNMAX+1; 6458 continue; 6459 } 6460 /* negative case */ 6461 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ 6462 est=(((ueInt)carry>>3)*16777)>>21; 6463 *c=(Unit)(carry-est*(DECDPUNMAX+1)); 6464 carry=est-(DECDPUNMAX+1); /* correctly negative */ 6465 if (*c<DECDPUNMAX+1) continue; /* was OK */ 6466 carry++; 6467 *c-=DECDPUNMAX+1; 6468 #elif DECDPUN<=2 6469 /* Can use QUOT10 as carry <= 4 digits */ 6470 if (carry>=0) { 6471 est=QUOT10(carry, DECDPUN); 6472 *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ 6473 carry=est; /* quotient */ 6474 continue; 6475 } 6476 /* negative case */ 6477 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ 6478 est=QUOT10(carry, DECDPUN); 6479 *c=(Unit)(carry-est*(DECDPUNMAX+1)); 6480 carry=est-(DECDPUNMAX+1); /* correctly negative */ 6481 #else 6482 /* remainder operator is undefined if negative, so must test */ 6483 if ((ueInt)carry<(DECDPUNMAX+1)*2) { /* fastpath carry +1 */ 6484 *c=(Unit)(carry-(DECDPUNMAX+1)); /* [helps additions] */ 6485 carry=1; 6486 continue; 6487 } 6488 if (carry>=0) { 6489 *c=(Unit)(carry%(DECDPUNMAX+1)); 6490 carry=carry/(DECDPUNMAX+1); 6491 continue; 6492 } 6493 /* negative case */ 6494 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ 6495 *c=(Unit)(carry%(DECDPUNMAX+1)); 6496 carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1); 6497 #endif 6498 } /* c */ 6499 6500 /* now may have one or other to complete */ 6501 /* [pretest to avoid loop setup/shutdown] */ 6502 if (c<maxC) for (; c<maxC; c++) { 6503 if (a<alsu+alength) { /* still in A */ 6504 carry+=*a; 6505 a++; 6506 } 6507 else { /* inside B */ 6508 carry+=((eInt)*b)*m; 6509 b++; 6510 } 6511 /* here carry is new Unit of digits; it could be +ve or -ve and */ 6512 /* magnitude up to DECDPUNMAX squared */ 6513 if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */ 6514 *c=(Unit)carry; 6515 carry=0; 6516 continue; 6517 } 6518 /* result for this unit is negative or >DECDPUNMAX */ 6519 #if DECDPUN==4 /* use divide-by-multiply */ 6520 if (carry>=0) { 6521 est=(((ueInt)carry>>11)*53687)>>18; 6522 *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ 6523 carry=est; /* likely quotient [79.7%] */ 6524 if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ 6525 carry++; 6526 *c-=DECDPUNMAX+1; 6527 continue; 6528 } 6529 /* negative case */ 6530 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ 6531 est=(((ueInt)carry>>11)*53687)>>18; 6532 *c=(Unit)(carry-est*(DECDPUNMAX+1)); 6533 carry=est-(DECDPUNMAX+1); /* correctly negative */ 6534 if (*c<DECDPUNMAX+1) continue; /* was OK */ 6535 carry++; 6536 *c-=DECDPUNMAX+1; 6537 #elif DECDPUN==3 6538 if (carry>=0) { 6539 est=(((ueInt)carry>>3)*16777)>>21; 6540 *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ 6541 carry=est; /* likely quotient [99%] */ 6542 if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ 6543 carry++; 6544 *c-=DECDPUNMAX+1; 6545 continue; 6546 } 6547 /* negative case */ 6548 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ 6549 est=(((ueInt)carry>>3)*16777)>>21; 6550 *c=(Unit)(carry-est*(DECDPUNMAX+1)); 6551 carry=est-(DECDPUNMAX+1); /* correctly negative */ 6552 if (*c<DECDPUNMAX+1) continue; /* was OK */ 6553 carry++; 6554 *c-=DECDPUNMAX+1; 6555 #elif DECDPUN<=2 6556 if (carry>=0) { 6557 est=QUOT10(carry, DECDPUN); 6558 *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ 6559 carry=est; /* quotient */ 6560 continue; 6561 } 6562 /* negative case */ 6563 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ 6564 est=QUOT10(carry, DECDPUN); 6565 *c=(Unit)(carry-est*(DECDPUNMAX+1)); 6566 carry=est-(DECDPUNMAX+1); /* correctly negative */ 6567 #else 6568 if ((ueInt)carry<(DECDPUNMAX+1)*2){ /* fastpath carry 1 */ 6569 *c=(Unit)(carry-(DECDPUNMAX+1)); 6570 carry=1; 6571 continue; 6572 } 6573 /* remainder operator is undefined if negative, so must test */ 6574 if (carry>=0) { 6575 *c=(Unit)(carry%(DECDPUNMAX+1)); 6576 carry=carry/(DECDPUNMAX+1); 6577 continue; 6578 } 6579 /* negative case */ 6580 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ 6581 *c=(Unit)(carry%(DECDPUNMAX+1)); 6582 carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1); 6583 #endif 6584 } /* c */ 6585 6586 /* OK, all A and B processed; might still have carry or borrow */ 6587 /* return number of Units in the result, negated if a borrow */ 6588 if (carry==0) return c-clsu; /* no carry, so no more to do */ 6589 if (carry>0) { /* positive carry */ 6590 *c=(Unit)carry; /* place as new unit */ 6591 c++; /* .. */ 6592 return c-clsu; 6593 } 6594 /* -ve carry: it's a borrow; complement needed */ 6595 add=1; /* temporary carry... */ 6596 for (c=clsu; c<maxC; c++) { 6597 add=DECDPUNMAX+add-*c; 6598 if (add<=DECDPUNMAX) { 6599 *c=(Unit)add; 6600 add=0; 6601 } 6602 else { 6603 *c=0; 6604 add=1; 6605 } 6606 } 6607 /* add an extra unit iff it would be non-zero */ 6608 #if DECTRACE 6609 printf("UAS borrow: add %ld, carry %ld\n", add, carry); 6610 #endif 6611 if ((add-carry-1)!=0) { 6612 *c=(Unit)(add-carry-1); 6613 c++; /* interesting, include it */ 6614 } 6615 return clsu-c; /* -ve result indicates borrowed */ 6616 } /* decUnitAddSub */ 6617 6618/* ------------------------------------------------------------------ */ 6619/* decTrim -- trim trailing zeros or normalize */ 6620/* */ 6621/* dn is the number to trim or normalize */ 6622/* set is the context to use to check for clamp */ 6623/* all is 1 to remove all trailing zeros, 0 for just fraction ones */ 6624/* noclamp is 1 to unconditional (unclamped) trim */ 6625/* dropped returns the number of discarded trailing zeros */ 6626/* returns dn */ 6627/* */ 6628/* If clamp is set in the context then the number of zeros trimmed */ 6629/* may be limited if the exponent is high. */ 6630/* All fields are updated as required. This is a utility operation, */ 6631/* so special values are unchanged and no error is possible. */ 6632/* ------------------------------------------------------------------ */ 6633static decNumber * decTrim(decNumber *dn, decContext *set, Flag all, 6634 Flag noclamp, Int *dropped) { 6635 Int d, exp; /* work */ 6636 uInt cut; /* .. */ 6637 Unit *up; /* -> current Unit */ 6638 6639 #if DECCHECK 6640 if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn; 6641 #endif 6642 6643 *dropped=0; /* assume no zeros dropped */ 6644 if ((dn->bits & DECSPECIAL) /* fast exit if special .. */ 6645 || (*dn->lsu & 0x01)) return dn; /* .. or odd */ 6646 if (ISZERO(dn)) { /* .. or 0 */ 6647 dn->exponent=0; /* (sign is preserved) */ 6648 return dn; 6649 } 6650 6651 /* have a finite number which is even */ 6652 exp=dn->exponent; 6653 cut=1; /* digit (1-DECDPUN) in Unit */ 6654 up=dn->lsu; /* -> current Unit */ 6655 for (d=0; d<dn->digits-1; d++) { /* [don't strip the final digit] */ 6656 /* slice by powers */ 6657 #if DECDPUN<=4 6658 uInt quot=QUOT10(*up, cut); 6659 if ((*up-quot*powers[cut])!=0) break; /* found non-0 digit */ 6660 #else 6661 if (*up%powers[cut]!=0) break; /* found non-0 digit */ 6662 #endif 6663 /* have a trailing 0 */ 6664 if (!all) { /* trimming */ 6665 /* [if exp>0 then all trailing 0s are significant for trim] */ 6666 if (exp<=0) { /* if digit might be significant */ 6667 if (exp==0) break; /* then quit */ 6668 exp++; /* next digit might be significant */ 6669 } 6670 } 6671 cut++; /* next power */ 6672 if (cut>DECDPUN) { /* need new Unit */ 6673 up++; 6674 cut=1; 6675 } 6676 } /* d */ 6677 if (d==0) return dn; /* none to drop */ 6678 6679 /* may need to limit drop if clamping */ 6680 if (set->clamp && !noclamp) { 6681 Int maxd=set->emax-set->digits+1-dn->exponent; 6682 if (maxd<=0) return dn; /* nothing possible */ 6683 if (d>maxd) d=maxd; 6684 } 6685 6686 /* effect the drop */ 6687 decShiftToLeast(dn->lsu, D2U(dn->digits), d); 6688 dn->exponent+=d; /* maintain numerical value */ 6689 dn->digits-=d; /* new length */ 6690 *dropped=d; /* report the count */ 6691 return dn; 6692 } /* decTrim */ 6693 6694/* ------------------------------------------------------------------ */ 6695/* decReverse -- reverse a Unit array in place */ 6696/* */ 6697/* ulo is the start of the array */ 6698/* uhi is the end of the array (highest Unit to include) */ 6699/* */ 6700/* The units ulo through uhi are reversed in place (if the number */ 6701/* of units is odd, the middle one is untouched). Note that the */ 6702/* digit(s) in each unit are unaffected. */ 6703/* ------------------------------------------------------------------ */ 6704static void decReverse(Unit *ulo, Unit *uhi) { 6705 Unit temp; 6706 for (; ulo<uhi; ulo++, uhi--) { 6707 temp=*ulo; 6708 *ulo=*uhi; 6709 *uhi=temp; 6710 } 6711 return; 6712 } /* decReverse */ 6713 6714/* ------------------------------------------------------------------ */ 6715/* decShiftToMost -- shift digits in array towards most significant */ 6716/* */ 6717/* uar is the array */ 6718/* digits is the count of digits in use in the array */ 6719/* shift is the number of zeros to pad with (least significant); */ 6720/* it must be zero or positive */ 6721/* */ 6722/* returns the new length of the integer in the array, in digits */ 6723/* */ 6724/* No overflow is permitted (that is, the uar array must be known to */ 6725/* be large enough to hold the result, after shifting). */ 6726/* ------------------------------------------------------------------ */ 6727static Int decShiftToMost(Unit *uar, Int digits, Int shift) { 6728 Unit *target, *source, *first; /* work */ 6729 Int cut; /* odd 0's to add */ 6730 uInt next; /* work */ 6731 6732 if (shift==0) return digits; /* [fastpath] nothing to do */ 6733 if ((digits+shift)<=DECDPUN) { /* [fastpath] single-unit case */ 6734 *uar=(Unit)(*uar*powers[shift]); 6735 return digits+shift; 6736 } 6737 6738 next=0; /* all paths */ 6739 source=uar+D2U(digits)-1; /* where msu comes from */ 6740 target=source+D2U(shift); /* where upper part of first cut goes */ 6741 cut=DECDPUN-MSUDIGITS(shift); /* where to slice */ 6742 if (cut==0) { /* unit-boundary case */ 6743 for (; source>=uar; source--, target--) *target=*source; 6744 } 6745 else { 6746 first=uar+D2U(digits+shift)-1; /* where msu of source will end up */ 6747 for (; source>=uar; source--, target--) { 6748 /* split the source Unit and accumulate remainder for next */ 6749 #if DECDPUN<=4 6750 uInt quot=QUOT10(*source, cut); 6751 uInt rem=*source-quot*powers[cut]; 6752 next+=quot; 6753 #else 6754 uInt rem=*source%powers[cut]; 6755 next+=*source/powers[cut]; 6756 #endif 6757 if (target<=first) *target=(Unit)next; /* write to target iff valid */ 6758 next=rem*powers[DECDPUN-cut]; /* save remainder for next Unit */ 6759 } 6760 } /* shift-move */ 6761 6762 /* propagate any partial unit to one below and clear the rest */ 6763 for (; target>=uar; target--) { 6764 *target=(Unit)next; 6765 next=0; 6766 } 6767 return digits+shift; 6768 } /* decShiftToMost */ 6769 6770/* ------------------------------------------------------------------ */ 6771/* decShiftToLeast -- shift digits in array towards least significant */ 6772/* */ 6773/* uar is the array */ 6774/* units is length of the array, in units */ 6775/* shift is the number of digits to remove from the lsu end; it */ 6776/* must be zero or positive and <= than units*DECDPUN. */ 6777/* */ 6778/* returns the new length of the integer in the array, in units */ 6779/* */ 6780/* Removed digits are discarded (lost). Units not required to hold */ 6781/* the final result are unchanged. */ 6782/* ------------------------------------------------------------------ */ 6783static Int decShiftToLeast(Unit *uar, Int units, Int shift) { 6784 Unit *target, *up; /* work */ 6785 Int cut, count; /* work */ 6786 Int quot, rem; /* for division */ 6787 6788 if (shift==0) return units; /* [fastpath] nothing to do */ 6789 if (shift==units*DECDPUN) { /* [fastpath] little to do */ 6790 *uar=0; /* all digits cleared gives zero */ 6791 return 1; /* leaves just the one */ 6792 } 6793 6794 target=uar; /* both paths */ 6795 cut=MSUDIGITS(shift); 6796 if (cut==DECDPUN) { /* unit-boundary case; easy */ 6797 up=uar+D2U(shift); 6798 for (; up<uar+units; target++, up++) *target=*up; 6799 return target-uar; 6800 } 6801 6802 /* messier */ 6803 up=uar+D2U(shift-cut); /* source; correct to whole Units */ 6804 count=units*DECDPUN-shift; /* the maximum new length */ 6805 #if DECDPUN<=4 6806 quot=QUOT10(*up, cut); 6807 #else 6808 quot=*up/powers[cut]; 6809 #endif 6810 for (; ; target++) { 6811 *target=(Unit)quot; 6812 count-=(DECDPUN-cut); 6813 if (count<=0) break; 6814 up++; 6815 quot=*up; 6816 #if DECDPUN<=4 6817 quot=QUOT10(quot, cut); 6818 rem=*up-quot*powers[cut]; 6819 #else 6820 rem=quot%powers[cut]; 6821 quot=quot/powers[cut]; 6822 #endif 6823 *target=(Unit)(*target+rem*powers[DECDPUN-cut]); 6824 count-=cut; 6825 if (count<=0) break; 6826 } 6827 return target-uar+1; 6828 } /* decShiftToLeast */ 6829 6830#if DECSUBSET 6831/* ------------------------------------------------------------------ */ 6832/* decRoundOperand -- round an operand [used for subset only] */ 6833/* */ 6834/* dn is the number to round (dn->digits is > set->digits) */ 6835/* set is the relevant context */ 6836/* status is the status accumulator */ 6837/* */ 6838/* returns an allocated decNumber with the rounded result. */ 6839/* */ 6840/* lostDigits and other status may be set by this. */ 6841/* */ 6842/* Since the input is an operand, it must not be modified. */ 6843/* Instead, return an allocated decNumber, rounded as required. */ 6844/* It is the caller's responsibility to free the allocated storage. */ 6845/* */ 6846/* If no storage is available then the result cannot be used, so NULL */ 6847/* is returned. */ 6848/* ------------------------------------------------------------------ */ 6849static decNumber *decRoundOperand(const decNumber *dn, decContext *set, 6850 uInt *status) { 6851 decNumber *res; /* result structure */ 6852 uInt newstatus=0; /* status from round */ 6853 Int residue=0; /* rounding accumulator */ 6854 6855 /* Allocate storage for the returned decNumber, big enough for the */ 6856 /* length specified by the context */ 6857 res=(decNumber *)malloc(sizeof(decNumber) 6858 +(D2U(set->digits)-1)*sizeof(Unit)); 6859 if (res==NULL) { 6860 *status|=DEC_Insufficient_storage; 6861 return NULL; 6862 } 6863 decCopyFit(res, dn, set, &residue, &newstatus); 6864 decApplyRound(res, set, residue, &newstatus); 6865 6866 /* If that set Inexact then "lost digits" is raised... */ 6867 if (newstatus & DEC_Inexact) newstatus|=DEC_Lost_digits; 6868 *status|=newstatus; 6869 return res; 6870 } /* decRoundOperand */ 6871#endif 6872 6873/* ------------------------------------------------------------------ */ 6874/* decCopyFit -- copy a number, truncating the coefficient if needed */ 6875/* */ 6876/* dest is the target decNumber */ 6877/* src is the source decNumber */ 6878/* set is the context [used for length (digits) and rounding mode] */ 6879/* residue is the residue accumulator */ 6880/* status contains the current status to be updated */ 6881/* */ 6882/* (dest==src is allowed and will be a no-op if fits) */ 6883/* All fields are updated as required. */ 6884/* ------------------------------------------------------------------ */ 6885static void decCopyFit(decNumber *dest, const decNumber *src, 6886 decContext *set, Int *residue, uInt *status) { 6887 dest->bits=src->bits; 6888 dest->exponent=src->exponent; 6889 decSetCoeff(dest, set, src->lsu, src->digits, residue, status); 6890 } /* decCopyFit */ 6891 6892/* ------------------------------------------------------------------ */ 6893/* decSetCoeff -- set the coefficient of a number */ 6894/* */ 6895/* dn is the number whose coefficient array is to be set. */ 6896/* It must have space for set->digits digits */ 6897/* set is the context [for size] */ 6898/* lsu -> lsu of the source coefficient [may be dn->lsu] */ 6899/* len is digits in the source coefficient [may be dn->digits] */ 6900/* residue is the residue accumulator. This has values as in */ 6901/* decApplyRound, and will be unchanged unless the */ 6902/* target size is less than len. In this case, the */ 6903/* coefficient is truncated and the residue is updated to */ 6904/* reflect the previous residue and the dropped digits. */ 6905/* status is the status accumulator, as usual */ 6906/* */ 6907/* The coefficient may already be in the number, or it can be an */ 6908/* external intermediate array. If it is in the number, lsu must == */ 6909/* dn->lsu and len must == dn->digits. */ 6910/* */ 6911/* Note that the coefficient length (len) may be < set->digits, and */ 6912/* in this case this merely copies the coefficient (or is a no-op */ 6913/* if dn->lsu==lsu). */ 6914/* */ 6915/* Note also that (only internally, from decQuantizeOp and */ 6916/* decSetSubnormal) the value of set->digits may be less than one, */ 6917/* indicating a round to left. This routine handles that case */ 6918/* correctly; caller ensures space. */ 6919/* */ 6920/* dn->digits, dn->lsu (and as required), and dn->exponent are */ 6921/* updated as necessary. dn->bits (sign) is unchanged. */ 6922/* */ 6923/* DEC_Rounded status is set if any digits are discarded. */ 6924/* DEC_Inexact status is set if any non-zero digits are discarded, or */ 6925/* incoming residue was non-0 (implies rounded) */ 6926/* ------------------------------------------------------------------ */ 6927/* mapping array: maps 0-9 to canonical residues, so that a residue */ 6928/* can be adjusted in the range [-1, +1] and achieve correct rounding */ 6929/* 0 1 2 3 4 5 6 7 8 9 */ 6930static const uByte resmap[10]={0, 3, 3, 3, 3, 5, 7, 7, 7, 7}; 6931static void decSetCoeff(decNumber *dn, decContext *set, const Unit *lsu, 6932 Int len, Int *residue, uInt *status) { 6933 Int discard; /* number of digits to discard */ 6934 uInt cut; /* cut point in Unit */ 6935 const Unit *up; /* work */ 6936 Unit *target; /* .. */ 6937 Int count; /* .. */ 6938 #if DECDPUN<=4 6939 uInt temp; /* .. */ 6940 #endif 6941 6942 discard=len-set->digits; /* digits to discard */ 6943 if (discard<=0) { /* no digits are being discarded */ 6944 if (dn->lsu!=lsu) { /* copy needed */ 6945 /* copy the coefficient array to the result number; no shift needed */ 6946 count=len; /* avoids D2U */ 6947 up=lsu; 6948 for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN) 6949 *target=*up; 6950 dn->digits=len; /* set the new length */ 6951 } 6952 /* dn->exponent and residue are unchanged, record any inexactitude */ 6953 if (*residue!=0) *status|=(DEC_Inexact | DEC_Rounded); 6954 return; 6955 } 6956 6957 /* some digits must be discarded ... */ 6958 dn->exponent+=discard; /* maintain numerical value */ 6959 *status|=DEC_Rounded; /* accumulate Rounded status */ 6960 if (*residue>1) *residue=1; /* previous residue now to right, so reduce */ 6961 6962 if (discard>len) { /* everything, +1, is being discarded */ 6963 /* guard digit is 0 */ 6964 /* residue is all the number [NB could be all 0s] */ 6965 if (*residue<=0) { /* not already positive */ 6966 count=len; /* avoids D2U */ 6967 for (up=lsu; count>0; up++, count-=DECDPUN) if (*up!=0) { /* found non-0 */ 6968 *residue=1; 6969 break; /* no need to check any others */ 6970 } 6971 } 6972 if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */ 6973 *dn->lsu=0; /* coefficient will now be 0 */ 6974 dn->digits=1; /* .. */ 6975 return; 6976 } /* total discard */ 6977 6978 /* partial discard [most common case] */ 6979 /* here, at least the first (most significant) discarded digit exists */ 6980 6981 /* spin up the number, noting residue during the spin, until get to */ 6982 /* the Unit with the first discarded digit. When reach it, extract */ 6983 /* it and remember its position */ 6984 count=0; 6985 for (up=lsu;; up++) { 6986 count+=DECDPUN; 6987 if (count>=discard) break; /* full ones all checked */ 6988 if (*up!=0) *residue=1; 6989 } /* up */ 6990 6991 /* here up -> Unit with first discarded digit */ 6992 cut=discard-(count-DECDPUN)-1; 6993 if (cut==DECDPUN-1) { /* unit-boundary case (fast) */ 6994 Unit half=(Unit)powers[DECDPUN]>>1; 6995 /* set residue directly */ 6996 if (*up>=half) { 6997 if (*up>half) *residue=7; 6998 else *residue+=5; /* add sticky bit */ 6999 } 7000 else { /* <half */ 7001 if (*up!=0) *residue=3; /* [else is 0, leave as sticky bit] */ 7002 } 7003 if (set->digits<=0) { /* special for Quantize/Subnormal :-( */ 7004 *dn->lsu=0; /* .. result is 0 */ 7005 dn->digits=1; /* .. */ 7006 } 7007 else { /* shift to least */ 7008 count=set->digits; /* now digits to end up with */ 7009 dn->digits=count; /* set the new length */ 7010 up++; /* move to next */ 7011 /* on unit boundary, so shift-down copy loop is simple */ 7012 for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN) 7013 *target=*up; 7014 } 7015 } /* unit-boundary case */ 7016 7017 else { /* discard digit is in low digit(s), and not top digit */ 7018 uInt discard1; /* first discarded digit */ 7019 uInt quot, rem; /* for divisions */ 7020 if (cut==0) quot=*up; /* is at bottom of unit */ 7021 else /* cut>0 */ { /* it's not at bottom of unit */ 7022 #if DECDPUN<=4 7023 U_ASSERT(/* cut >= 0 &&*/ cut <= 4); 7024 quot=QUOT10(*up, cut); 7025 rem=*up-quot*powers[cut]; 7026 #else 7027 rem=*up%powers[cut]; 7028 quot=*up/powers[cut]; 7029 #endif 7030 if (rem!=0) *residue=1; 7031 } 7032 /* discard digit is now at bottom of quot */ 7033 #if DECDPUN<=4 7034 temp=(quot*6554)>>16; /* fast /10 */ 7035 /* Vowels algorithm here not a win (9 instructions) */ 7036 discard1=quot-X10(temp); 7037 quot=temp; 7038 #else 7039 discard1=quot%10; 7040 quot=quot/10; 7041 #endif 7042 /* here, discard1 is the guard digit, and residue is everything */ 7043 /* else [use mapping array to accumulate residue safely] */ 7044 *residue+=resmap[discard1]; 7045 cut++; /* update cut */ 7046 /* here: up -> Unit of the array with bottom digit */ 7047 /* cut is the division point for each Unit */ 7048 /* quot holds the uncut high-order digits for the current unit */ 7049 if (set->digits<=0) { /* special for Quantize/Subnormal :-( */ 7050 *dn->lsu=0; /* .. result is 0 */ 7051 dn->digits=1; /* .. */ 7052 } 7053 else { /* shift to least needed */ 7054 count=set->digits; /* now digits to end up with */ 7055 dn->digits=count; /* set the new length */ 7056 /* shift-copy the coefficient array to the result number */ 7057 for (target=dn->lsu; ; target++) { 7058 *target=(Unit)quot; 7059 count-=(DECDPUN-cut); 7060 if (count<=0) break; 7061 up++; 7062 quot=*up; 7063 #if DECDPUN<=4 7064 quot=QUOT10(quot, cut); 7065 rem=*up-quot*powers[cut]; 7066 #else 7067 rem=quot%powers[cut]; 7068 quot=quot/powers[cut]; 7069 #endif 7070 *target=(Unit)(*target+rem*powers[DECDPUN-cut]); 7071 count-=cut; 7072 if (count<=0) break; 7073 } /* shift-copy loop */ 7074 } /* shift to least */ 7075 } /* not unit boundary */ 7076 7077 if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */ 7078 return; 7079 } /* decSetCoeff */ 7080 7081/* ------------------------------------------------------------------ */ 7082/* decApplyRound -- apply pending rounding to a number */ 7083/* */ 7084/* dn is the number, with space for set->digits digits */ 7085/* set is the context [for size and rounding mode] */ 7086/* residue indicates pending rounding, being any accumulated */ 7087/* guard and sticky information. It may be: */ 7088/* 6-9: rounding digit is >5 */ 7089/* 5: rounding digit is exactly half-way */ 7090/* 1-4: rounding digit is <5 and >0 */ 7091/* 0: the coefficient is exact */ 7092/* -1: as 1, but the hidden digits are subtractive, that */ 7093/* is, of the opposite sign to dn. In this case the */ 7094/* coefficient must be non-0. This case occurs when */ 7095/* subtracting a small number (which can be reduced to */ 7096/* a sticky bit); see decAddOp. */ 7097/* status is the status accumulator, as usual */ 7098/* */ 7099/* This routine applies rounding while keeping the length of the */ 7100/* coefficient constant. The exponent and status are unchanged */ 7101/* except if: */ 7102/* */ 7103/* -- the coefficient was increased and is all nines (in which */ 7104/* case Overflow could occur, and is handled directly here so */ 7105/* the caller does not need to re-test for overflow) */ 7106/* */ 7107/* -- the coefficient was decreased and becomes all nines (in which */ 7108/* case Underflow could occur, and is also handled directly). */ 7109/* */ 7110/* All fields in dn are updated as required. */ 7111/* */ 7112/* ------------------------------------------------------------------ */ 7113static void decApplyRound(decNumber *dn, decContext *set, Int residue, 7114 uInt *status) { 7115 Int bump; /* 1 if coefficient needs to be incremented */ 7116 /* -1 if coefficient needs to be decremented */ 7117 7118 if (residue==0) return; /* nothing to apply */ 7119 7120 bump=0; /* assume a smooth ride */ 7121 7122 /* now decide whether, and how, to round, depending on mode */ 7123 switch (set->round) { 7124 case DEC_ROUND_05UP: { /* round zero or five up (for reround) */ 7125 /* This is the same as DEC_ROUND_DOWN unless there is a */ 7126 /* positive residue and the lsd of dn is 0 or 5, in which case */ 7127 /* it is bumped; when residue is <0, the number is therefore */ 7128 /* bumped down unless the final digit was 1 or 6 (in which */ 7129 /* case it is bumped down and then up -- a no-op) */ 7130 Int lsd5=*dn->lsu%5; /* get lsd and quintate */ 7131 if (residue<0 && lsd5!=1) bump=-1; 7132 else if (residue>0 && lsd5==0) bump=1; 7133 /* [bump==1 could be applied directly; use common path for clarity] */ 7134 break;} /* r-05 */ 7135 7136 case DEC_ROUND_DOWN: { 7137 /* no change, except if negative residue */ 7138 if (residue<0) bump=-1; 7139 break;} /* r-d */ 7140 7141 case DEC_ROUND_HALF_DOWN: { 7142 if (residue>5) bump=1; 7143 break;} /* r-h-d */ 7144 7145 case DEC_ROUND_HALF_EVEN: { 7146 if (residue>5) bump=1; /* >0.5 goes up */ 7147 else if (residue==5) { /* exactly 0.5000... */ 7148 /* 0.5 goes up iff [new] lsd is odd */ 7149 if (*dn->lsu & 0x01) bump=1; 7150 } 7151 break;} /* r-h-e */ 7152 7153 case DEC_ROUND_HALF_UP: { 7154 if (residue>=5) bump=1; 7155 break;} /* r-h-u */ 7156 7157 case DEC_ROUND_UP: { 7158 if (residue>0) bump=1; 7159 break;} /* r-u */ 7160 7161 case DEC_ROUND_CEILING: { 7162 /* same as _UP for positive numbers, and as _DOWN for negatives */ 7163 /* [negative residue cannot occur on 0] */ 7164 if (decNumberIsNegative(dn)) { 7165 if (residue<0) bump=-1; 7166 } 7167 else { 7168 if (residue>0) bump=1; 7169 } 7170 break;} /* r-c */ 7171 7172 case DEC_ROUND_FLOOR: { 7173 /* same as _UP for negative numbers, and as _DOWN for positive */ 7174 /* [negative residue cannot occur on 0] */ 7175 if (!decNumberIsNegative(dn)) { 7176 if (residue<0) bump=-1; 7177 } 7178 else { 7179 if (residue>0) bump=1; 7180 } 7181 break;} /* r-f */ 7182 7183 default: { /* e.g., DEC_ROUND_MAX */ 7184 *status|=DEC_Invalid_context; 7185 #if DECTRACE || (DECCHECK && DECVERB) 7186 printf("Unknown rounding mode: %d\n", set->round); 7187 #endif 7188 break;} 7189 } /* switch */ 7190 7191 /* now bump the number, up or down, if need be */ 7192 if (bump==0) return; /* no action required */ 7193 7194 /* Simply use decUnitAddSub unless bumping up and the number is */ 7195 /* all nines. In this special case set to 100... explicitly */ 7196 /* and adjust the exponent by one (as otherwise could overflow */ 7197 /* the array) */ 7198 /* Similarly handle all-nines result if bumping down. */ 7199 if (bump>0) { 7200 Unit *up; /* work */ 7201 uInt count=dn->digits; /* digits to be checked */ 7202 for (up=dn->lsu; ; up++) { 7203 if (count<=DECDPUN) { 7204 /* this is the last Unit (the msu) */ 7205 if (*up!=powers[count]-1) break; /* not still 9s */ 7206 /* here if it, too, is all nines */ 7207 *up=(Unit)powers[count-1]; /* here 999 -> 100 etc. */ 7208 for (up=up-1; up>=dn->lsu; up--) *up=0; /* others all to 0 */ 7209 dn->exponent++; /* and bump exponent */ 7210 /* [which, very rarely, could cause Overflow...] */ 7211 if ((dn->exponent+dn->digits)>set->emax+1) { 7212 decSetOverflow(dn, set, status); 7213 } 7214 return; /* done */ 7215 } 7216 /* a full unit to check, with more to come */ 7217 if (*up!=DECDPUNMAX) break; /* not still 9s */ 7218 count-=DECDPUN; 7219 } /* up */ 7220 } /* bump>0 */ 7221 else { /* -1 */ 7222 /* here checking for a pre-bump of 1000... (leading 1, all */ 7223 /* other digits zero) */ 7224 Unit *up, *sup; /* work */ 7225 uInt count=dn->digits; /* digits to be checked */ 7226 for (up=dn->lsu; ; up++) { 7227 if (count<=DECDPUN) { 7228 /* this is the last Unit (the msu) */ 7229 if (*up!=powers[count-1]) break; /* not 100.. */ 7230 /* here if have the 1000... case */ 7231 sup=up; /* save msu pointer */ 7232 *up=(Unit)powers[count]-1; /* here 100 in msu -> 999 */ 7233 /* others all to all-nines, too */ 7234 for (up=up-1; up>=dn->lsu; up--) *up=(Unit)powers[DECDPUN]-1; 7235 dn->exponent--; /* and bump exponent */ 7236 7237 /* iff the number was at the subnormal boundary (exponent=etiny) */ 7238 /* then the exponent is now out of range, so it will in fact get */ 7239 /* clamped to etiny and the final 9 dropped. */ 7240 /* printf(">> emin=%d exp=%d sdig=%d\n", set->emin, */ 7241 /* dn->exponent, set->digits); */ 7242 if (dn->exponent+1==set->emin-set->digits+1) { 7243 if (count==1 && dn->digits==1) *sup=0; /* here 9 -> 0[.9] */ 7244 else { 7245 *sup=(Unit)powers[count-1]-1; /* here 999.. in msu -> 99.. */ 7246 dn->digits--; 7247 } 7248 dn->exponent++; 7249 *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded; 7250 } 7251 return; /* done */ 7252 } 7253 7254 /* a full unit to check, with more to come */ 7255 if (*up!=0) break; /* not still 0s */ 7256 count-=DECDPUN; 7257 } /* up */ 7258 7259 } /* bump<0 */ 7260 7261 /* Actual bump needed. Do it. */ 7262 decUnitAddSub(dn->lsu, D2U(dn->digits), uarrone, 1, 0, dn->lsu, bump); 7263 } /* decApplyRound */ 7264 7265#if DECSUBSET 7266/* ------------------------------------------------------------------ */ 7267/* decFinish -- finish processing a number */ 7268/* */ 7269/* dn is the number */ 7270/* set is the context */ 7271/* residue is the rounding accumulator (as in decApplyRound) */ 7272/* status is the accumulator */ 7273/* */ 7274/* This finishes off the current number by: */ 7275/* 1. If not extended: */ 7276/* a. Converting a zero result to clean '0' */ 7277/* b. Reducing positive exponents to 0, if would fit in digits */ 7278/* 2. Checking for overflow and subnormals (always) */ 7279/* Note this is just Finalize when no subset arithmetic. */ 7280/* All fields are updated as required. */ 7281/* ------------------------------------------------------------------ */ 7282static void decFinish(decNumber *dn, decContext *set, Int *residue, 7283 uInt *status) { 7284 if (!set->extended) { 7285 if ISZERO(dn) { /* value is zero */ 7286 dn->exponent=0; /* clean exponent .. */ 7287 dn->bits=0; /* .. and sign */ 7288 return; /* no error possible */ 7289 } 7290 if (dn->exponent>=0) { /* non-negative exponent */ 7291 /* >0; reduce to integer if possible */ 7292 if (set->digits >= (dn->exponent+dn->digits)) { 7293 dn->digits=decShiftToMost(dn->lsu, dn->digits, dn->exponent); 7294 dn->exponent=0; 7295 } 7296 } 7297 } /* !extended */ 7298 7299 decFinalize(dn, set, residue, status); 7300 } /* decFinish */ 7301#endif 7302 7303/* ------------------------------------------------------------------ */ 7304/* decFinalize -- final check, clamp, and round of a number */ 7305/* */ 7306/* dn is the number */ 7307/* set is the context */ 7308/* residue is the rounding accumulator (as in decApplyRound) */ 7309/* status is the status accumulator */ 7310/* */ 7311/* This finishes off the current number by checking for subnormal */ 7312/* results, applying any pending rounding, checking for overflow, */ 7313/* and applying any clamping. */ 7314/* Underflow and overflow conditions are raised as appropriate. */ 7315/* All fields are updated as required. */ 7316/* ------------------------------------------------------------------ */ 7317static void decFinalize(decNumber *dn, decContext *set, Int *residue, 7318 uInt *status) { 7319 Int shift; /* shift needed if clamping */ 7320 Int tinyexp=set->emin-dn->digits+1; /* precalculate subnormal boundary */ 7321 7322 /* Must be careful, here, when checking the exponent as the */ 7323 /* adjusted exponent could overflow 31 bits [because it may already */ 7324 /* be up to twice the expected]. */ 7325 7326 /* First test for subnormal. This must be done before any final */ 7327 /* round as the result could be rounded to Nmin or 0. */ 7328 if (dn->exponent<=tinyexp) { /* prefilter */ 7329 Int comp; 7330 decNumber nmin; 7331 /* A very nasty case here is dn == Nmin and residue<0 */ 7332 if (dn->exponent<tinyexp) { 7333 /* Go handle subnormals; this will apply round if needed. */ 7334 decSetSubnormal(dn, set, residue, status); 7335 return; 7336 } 7337 /* Equals case: only subnormal if dn=Nmin and negative residue */ 7338 uprv_decNumberZero(&nmin); 7339 nmin.lsu[0]=1; 7340 nmin.exponent=set->emin; 7341 comp=decCompare(dn, &nmin, 1); /* (signless compare) */ 7342 if (comp==BADINT) { /* oops */ 7343 *status|=DEC_Insufficient_storage; /* abandon... */ 7344 return; 7345 } 7346 if (*residue<0 && comp==0) { /* neg residue and dn==Nmin */ 7347 decApplyRound(dn, set, *residue, status); /* might force down */ 7348 decSetSubnormal(dn, set, residue, status); 7349 return; 7350 } 7351 } 7352 7353 /* now apply any pending round (this could raise overflow). */ 7354 if (*residue!=0) decApplyRound(dn, set, *residue, status); 7355 7356 /* Check for overflow [redundant in the 'rare' case] or clamp */ 7357 if (dn->exponent<=set->emax-set->digits+1) return; /* neither needed */ 7358 7359 7360 /* here when might have an overflow or clamp to do */ 7361 if (dn->exponent>set->emax-dn->digits+1) { /* too big */ 7362 decSetOverflow(dn, set, status); 7363 return; 7364 } 7365 /* here when the result is normal but in clamp range */ 7366 if (!set->clamp) return; 7367 7368 /* here when need to apply the IEEE exponent clamp (fold-down) */ 7369 shift=dn->exponent-(set->emax-set->digits+1); 7370 7371 /* shift coefficient (if non-zero) */ 7372 if (!ISZERO(dn)) { 7373 dn->digits=decShiftToMost(dn->lsu, dn->digits, shift); 7374 } 7375 dn->exponent-=shift; /* adjust the exponent to match */ 7376 *status|=DEC_Clamped; /* and record the dirty deed */ 7377 return; 7378 } /* decFinalize */ 7379 7380/* ------------------------------------------------------------------ */ 7381/* decSetOverflow -- set number to proper overflow value */ 7382/* */ 7383/* dn is the number (used for sign [only] and result) */ 7384/* set is the context [used for the rounding mode, etc.] */ 7385/* status contains the current status to be updated */ 7386/* */ 7387/* This sets the sign of a number and sets its value to either */ 7388/* Infinity or the maximum finite value, depending on the sign of */ 7389/* dn and the rounding mode, following IEEE 754 rules. */ 7390/* ------------------------------------------------------------------ */ 7391static void decSetOverflow(decNumber *dn, decContext *set, uInt *status) { 7392 Flag needmax=0; /* result is maximum finite value */ 7393 uByte sign=dn->bits&DECNEG; /* clean and save sign bit */ 7394 7395 if (ISZERO(dn)) { /* zero does not overflow magnitude */ 7396 Int emax=set->emax; /* limit value */ 7397 if (set->clamp) emax-=set->digits-1; /* lower if clamping */ 7398 if (dn->exponent>emax) { /* clamp required */ 7399 dn->exponent=emax; 7400 *status|=DEC_Clamped; 7401 } 7402 return; 7403 } 7404 7405 uprv_decNumberZero(dn); 7406 switch (set->round) { 7407 case DEC_ROUND_DOWN: { 7408 needmax=1; /* never Infinity */ 7409 break;} /* r-d */ 7410 case DEC_ROUND_05UP: { 7411 needmax=1; /* never Infinity */ 7412 break;} /* r-05 */ 7413 case DEC_ROUND_CEILING: { 7414 if (sign) needmax=1; /* Infinity if non-negative */ 7415 break;} /* r-c */ 7416 case DEC_ROUND_FLOOR: { 7417 if (!sign) needmax=1; /* Infinity if negative */ 7418 break;} /* r-f */ 7419 default: break; /* Infinity in all other cases */ 7420 } 7421 if (needmax) { 7422 decSetMaxValue(dn, set); 7423 dn->bits=sign; /* set sign */ 7424 } 7425 else dn->bits=sign|DECINF; /* Value is +/-Infinity */ 7426 *status|=DEC_Overflow | DEC_Inexact | DEC_Rounded; 7427 } /* decSetOverflow */ 7428 7429/* ------------------------------------------------------------------ */ 7430/* decSetMaxValue -- set number to +Nmax (maximum normal value) */ 7431/* */ 7432/* dn is the number to set */ 7433/* set is the context [used for digits and emax] */ 7434/* */ 7435/* This sets the number to the maximum positive value. */ 7436/* ------------------------------------------------------------------ */ 7437static void decSetMaxValue(decNumber *dn, decContext *set) { 7438 Unit *up; /* work */ 7439 Int count=set->digits; /* nines to add */ 7440 dn->digits=count; 7441 /* fill in all nines to set maximum value */ 7442 for (up=dn->lsu; ; up++) { 7443 if (count>DECDPUN) *up=DECDPUNMAX; /* unit full o'nines */ 7444 else { /* this is the msu */ 7445 *up=(Unit)(powers[count]-1); 7446 break; 7447 } 7448 count-=DECDPUN; /* filled those digits */ 7449 } /* up */ 7450 dn->bits=0; /* + sign */ 7451 dn->exponent=set->emax-set->digits+1; 7452 } /* decSetMaxValue */ 7453 7454/* ------------------------------------------------------------------ */ 7455/* decSetSubnormal -- process value whose exponent is <Emin */ 7456/* */ 7457/* dn is the number (used as input as well as output; it may have */ 7458/* an allowed subnormal value, which may need to be rounded) */ 7459/* set is the context [used for the rounding mode] */ 7460/* residue is any pending residue */ 7461/* status contains the current status to be updated */ 7462/* */ 7463/* If subset mode, set result to zero and set Underflow flags. */ 7464/* */ 7465/* Value may be zero with a low exponent; this does not set Subnormal */ 7466/* but the exponent will be clamped to Etiny. */ 7467/* */ 7468/* Otherwise ensure exponent is not out of range, and round as */ 7469/* necessary. Underflow is set if the result is Inexact. */ 7470/* ------------------------------------------------------------------ */ 7471static void decSetSubnormal(decNumber *dn, decContext *set, Int *residue, 7472 uInt *status) { 7473 decContext workset; /* work */ 7474 Int etiny, adjust; /* .. */ 7475 7476 #if DECSUBSET 7477 /* simple set to zero and 'hard underflow' for subset */ 7478 if (!set->extended) { 7479 uprv_decNumberZero(dn); 7480 /* always full overflow */ 7481 *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded; 7482 return; 7483 } 7484 #endif 7485 7486 /* Full arithmetic -- allow subnormals, rounded to minimum exponent */ 7487 /* (Etiny) if needed */ 7488 etiny=set->emin-(set->digits-1); /* smallest allowed exponent */ 7489 7490 if ISZERO(dn) { /* value is zero */ 7491 /* residue can never be non-zero here */ 7492 #if DECCHECK 7493 if (*residue!=0) { 7494 printf("++ Subnormal 0 residue %ld\n", (LI)*residue); 7495 *status|=DEC_Invalid_operation; 7496 } 7497 #endif 7498 if (dn->exponent<etiny) { /* clamp required */ 7499 dn->exponent=etiny; 7500 *status|=DEC_Clamped; 7501 } 7502 return; 7503 } 7504 7505 *status|=DEC_Subnormal; /* have a non-zero subnormal */ 7506 adjust=etiny-dn->exponent; /* calculate digits to remove */ 7507 if (adjust<=0) { /* not out of range; unrounded */ 7508 /* residue can never be non-zero here, except in the Nmin-residue */ 7509 /* case (which is a subnormal result), so can take fast-path here */ 7510 /* it may already be inexact (from setting the coefficient) */ 7511 if (*status&DEC_Inexact) *status|=DEC_Underflow; 7512 return; 7513 } 7514 7515 /* adjust>0, so need to rescale the result so exponent becomes Etiny */ 7516 /* [this code is similar to that in rescale] */ 7517 workset=*set; /* clone rounding, etc. */ 7518 workset.digits=dn->digits-adjust; /* set requested length */ 7519 workset.emin-=adjust; /* and adjust emin to match */ 7520 /* [note that the latter can be <1, here, similar to Rescale case] */ 7521 decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status); 7522 decApplyRound(dn, &workset, *residue, status); 7523 7524 /* Use 754 default rule: Underflow is set iff Inexact */ 7525 /* [independent of whether trapped] */ 7526 if (*status&DEC_Inexact) *status|=DEC_Underflow; 7527 7528 /* if rounded up a 999s case, exponent will be off by one; adjust */ 7529 /* back if so [it will fit, because it was shortened earlier] */ 7530 if (dn->exponent>etiny) { 7531 dn->digits=decShiftToMost(dn->lsu, dn->digits, 1); 7532 dn->exponent--; /* (re)adjust the exponent. */ 7533 } 7534 7535 /* if rounded to zero, it is by definition clamped... */ 7536 if (ISZERO(dn)) *status|=DEC_Clamped; 7537 } /* decSetSubnormal */ 7538 7539/* ------------------------------------------------------------------ */ 7540/* decCheckMath - check entry conditions for a math function */ 7541/* */ 7542/* This checks the context and the operand */ 7543/* */ 7544/* rhs is the operand to check */ 7545/* set is the context to check */ 7546/* status is unchanged if both are good */ 7547/* */ 7548/* returns non-zero if status is changed, 0 otherwise */ 7549/* */ 7550/* Restrictions enforced: */ 7551/* */ 7552/* digits, emax, and -emin in the context must be less than */ 7553/* DEC_MAX_MATH (999999), and A must be within these bounds if */ 7554/* non-zero. Invalid_operation is set in the status if a */ 7555/* restriction is violated. */ 7556/* ------------------------------------------------------------------ */ 7557static uInt decCheckMath(const decNumber *rhs, decContext *set, 7558 uInt *status) { 7559 uInt save=*status; /* record */ 7560 if (set->digits>DEC_MAX_MATH 7561 || set->emax>DEC_MAX_MATH 7562 || -set->emin>DEC_MAX_MATH) *status|=DEC_Invalid_context; 7563 else if ((rhs->digits>DEC_MAX_MATH 7564 || rhs->exponent+rhs->digits>DEC_MAX_MATH+1 7565 || rhs->exponent+rhs->digits<2*(1-DEC_MAX_MATH)) 7566 && !ISZERO(rhs)) *status|=DEC_Invalid_operation; 7567 return (*status!=save); 7568 } /* decCheckMath */ 7569 7570/* ------------------------------------------------------------------ */ 7571/* decGetInt -- get integer from a number */ 7572/* */ 7573/* dn is the number [which will not be altered] */ 7574/* */ 7575/* returns one of: */ 7576/* BADINT if there is a non-zero fraction */ 7577/* the converted integer */ 7578/* BIGEVEN if the integer is even and magnitude > 2*10**9 */ 7579/* BIGODD if the integer is odd and magnitude > 2*10**9 */ 7580/* */ 7581/* This checks and gets a whole number from the input decNumber. */ 7582/* The sign can be determined from dn by the caller when BIGEVEN or */ 7583/* BIGODD is returned. */ 7584/* ------------------------------------------------------------------ */ 7585static Int decGetInt(const decNumber *dn) { 7586 Int theInt; /* result accumulator */ 7587 const Unit *up; /* work */ 7588 Int got; /* digits (real or not) processed */ 7589 Int ilength=dn->digits+dn->exponent; /* integral length */ 7590 Flag neg=decNumberIsNegative(dn); /* 1 if -ve */ 7591 7592 /* The number must be an integer that fits in 10 digits */ 7593 /* Assert, here, that 10 is enough for any rescale Etiny */ 7594 #if DEC_MAX_EMAX > 999999999 7595 #error GetInt may need updating [for Emax] 7596 #endif 7597 #if DEC_MIN_EMIN < -999999999 7598 #error GetInt may need updating [for Emin] 7599 #endif 7600 if (ISZERO(dn)) return 0; /* zeros are OK, with any exponent */ 7601 7602 up=dn->lsu; /* ready for lsu */ 7603 theInt=0; /* ready to accumulate */ 7604 if (dn->exponent>=0) { /* relatively easy */ 7605 /* no fractional part [usual]; allow for positive exponent */ 7606 got=dn->exponent; 7607 } 7608 else { /* -ve exponent; some fractional part to check and discard */ 7609 Int count=-dn->exponent; /* digits to discard */ 7610 /* spin up whole units until reach the Unit with the unit digit */ 7611 for (; count>=DECDPUN; up++) { 7612 if (*up!=0) return BADINT; /* non-zero Unit to discard */ 7613 count-=DECDPUN; 7614 } 7615 if (count==0) got=0; /* [a multiple of DECDPUN] */ 7616 else { /* [not multiple of DECDPUN] */ 7617 Int rem; /* work */ 7618 /* slice off fraction digits and check for non-zero */ 7619 #if DECDPUN<=4 7620 theInt=QUOT10(*up, count); 7621 rem=*up-theInt*powers[count]; 7622 #else 7623 rem=*up%powers[count]; /* slice off discards */ 7624 theInt=*up/powers[count]; 7625 #endif 7626 if (rem!=0) return BADINT; /* non-zero fraction */ 7627 /* it looks good */ 7628 got=DECDPUN-count; /* number of digits so far */ 7629 up++; /* ready for next */ 7630 } 7631 } 7632 /* now it's known there's no fractional part */ 7633 7634 /* tricky code now, to accumulate up to 9.3 digits */ 7635 if (got==0) {theInt=*up; got+=DECDPUN; up++;} /* ensure lsu is there */ 7636 7637 if (ilength<11) { 7638 Int save=theInt; 7639 /* collect any remaining unit(s) */ 7640 for (; got<ilength; up++) { 7641 theInt+=*up*powers[got]; 7642 got+=DECDPUN; 7643 } 7644 if (ilength==10) { /* need to check for wrap */ 7645 if (theInt/(Int)powers[got-DECDPUN]!=(Int)*(up-1)) ilength=11; 7646 /* [that test also disallows the BADINT result case] */ 7647 else if (neg && theInt>1999999997) ilength=11; 7648 else if (!neg && theInt>999999999) ilength=11; 7649 if (ilength==11) theInt=save; /* restore correct low bit */ 7650 } 7651 } 7652 7653 if (ilength>10) { /* too big */ 7654 if (theInt&1) return BIGODD; /* bottom bit 1 */ 7655 return BIGEVEN; /* bottom bit 0 */ 7656 } 7657 7658 if (neg) theInt=-theInt; /* apply sign */ 7659 return theInt; 7660 } /* decGetInt */ 7661 7662/* ------------------------------------------------------------------ */ 7663/* decDecap -- decapitate the coefficient of a number */ 7664/* */ 7665/* dn is the number to be decapitated */ 7666/* drop is the number of digits to be removed from the left of dn; */ 7667/* this must be <= dn->digits (if equal, the coefficient is */ 7668/* set to 0) */ 7669/* */ 7670/* Returns dn; dn->digits will be <= the initial digits less drop */ 7671/* (after removing drop digits there may be leading zero digits */ 7672/* which will also be removed). Only dn->lsu and dn->digits change. */ 7673/* ------------------------------------------------------------------ */ 7674static decNumber *decDecap(decNumber *dn, Int drop) { 7675 Unit *msu; /* -> target cut point */ 7676 Int cut; /* work */ 7677 if (drop>=dn->digits) { /* losing the whole thing */ 7678 #if DECCHECK 7679 if (drop>dn->digits) 7680 printf("decDecap called with drop>digits [%ld>%ld]\n", 7681 (LI)drop, (LI)dn->digits); 7682 #endif 7683 dn->lsu[0]=0; 7684 dn->digits=1; 7685 return dn; 7686 } 7687 msu=dn->lsu+D2U(dn->digits-drop)-1; /* -> likely msu */ 7688 cut=MSUDIGITS(dn->digits-drop); /* digits to be in use in msu */ 7689 if (cut!=DECDPUN) *msu%=powers[cut]; /* clear left digits */ 7690 /* that may have left leading zero digits, so do a proper count... */ 7691 dn->digits=decGetDigits(dn->lsu, msu-dn->lsu+1); 7692 return dn; 7693 } /* decDecap */ 7694 7695/* ------------------------------------------------------------------ */ 7696/* decBiStr -- compare string with pairwise options */ 7697/* */ 7698/* targ is the string to compare */ 7699/* str1 is one of the strings to compare against (length may be 0) */ 7700/* str2 is the other; it must be the same length as str1 */ 7701/* */ 7702/* returns 1 if strings compare equal, (that is, it is the same */ 7703/* length as str1 and str2, and each character of targ is in either */ 7704/* str1 or str2 in the corresponding position), or 0 otherwise */ 7705/* */ 7706/* This is used for generic caseless compare, including the awkward */ 7707/* case of the Turkish dotted and dotless Is. Use as (for example): */ 7708/* if (decBiStr(test, "mike", "MIKE")) ... */ 7709/* ------------------------------------------------------------------ */ 7710static Flag decBiStr(const char *targ, const char *str1, const char *str2) { 7711 for (;;targ++, str1++, str2++) { 7712 if (*targ!=*str1 && *targ!=*str2) return 0; 7713 /* *targ has a match in one (or both, if terminator) */ 7714 if (*targ=='\0') break; 7715 } /* forever */ 7716 return 1; 7717 } /* decBiStr */ 7718 7719/* ------------------------------------------------------------------ */ 7720/* decNaNs -- handle NaN operand or operands */ 7721/* */ 7722/* res is the result number */ 7723/* lhs is the first operand */ 7724/* rhs is the second operand, or NULL if none */ 7725/* context is used to limit payload length */ 7726/* status contains the current status */ 7727/* returns res in case convenient */ 7728/* */ 7729/* Called when one or both operands is a NaN, and propagates the */ 7730/* appropriate result to res. When an sNaN is found, it is changed */ 7731/* to a qNaN and Invalid operation is set. */ 7732/* ------------------------------------------------------------------ */ 7733static decNumber * decNaNs(decNumber *res, const decNumber *lhs, 7734 const decNumber *rhs, decContext *set, 7735 uInt *status) { 7736 /* This decision tree ends up with LHS being the source pointer, */ 7737 /* and status updated if need be */ 7738 if (lhs->bits & DECSNAN) 7739 *status|=DEC_Invalid_operation | DEC_sNaN; 7740 else if (rhs==NULL); 7741 else if (rhs->bits & DECSNAN) { 7742 lhs=rhs; 7743 *status|=DEC_Invalid_operation | DEC_sNaN; 7744 } 7745 else if (lhs->bits & DECNAN); 7746 else lhs=rhs; 7747 7748 /* propagate the payload */ 7749 if (lhs->digits<=set->digits) uprv_decNumberCopy(res, lhs); /* easy */ 7750 else { /* too long */ 7751 const Unit *ul; 7752 Unit *ur, *uresp1; 7753 /* copy safe number of units, then decapitate */ 7754 res->bits=lhs->bits; /* need sign etc. */ 7755 uresp1=res->lsu+D2U(set->digits); 7756 for (ur=res->lsu, ul=lhs->lsu; ur<uresp1; ur++, ul++) *ur=*ul; 7757 res->digits=D2U(set->digits)*DECDPUN; 7758 /* maybe still too long */ 7759 if (res->digits>set->digits) decDecap(res, res->digits-set->digits); 7760 } 7761 7762 res->bits&=~DECSNAN; /* convert any sNaN to NaN, while */ 7763 res->bits|=DECNAN; /* .. preserving sign */ 7764 res->exponent=0; /* clean exponent */ 7765 /* [coefficient was copied/decapitated] */ 7766 return res; 7767 } /* decNaNs */ 7768 7769/* ------------------------------------------------------------------ */ 7770/* decStatus -- apply non-zero status */ 7771/* */ 7772/* dn is the number to set if error */ 7773/* status contains the current status (not yet in context) */ 7774/* set is the context */ 7775/* */ 7776/* If the status is an error status, the number is set to a NaN, */ 7777/* unless the error was an overflow, divide-by-zero, or underflow, */ 7778/* in which case the number will have already been set. */ 7779/* */ 7780/* The context status is then updated with the new status. Note that */ 7781/* this may raise a signal, so control may never return from this */ 7782/* routine (hence resources must be recovered before it is called). */ 7783/* ------------------------------------------------------------------ */ 7784static void decStatus(decNumber *dn, uInt status, decContext *set) { 7785 if (status & DEC_NaNs) { /* error status -> NaN */ 7786 /* if cause was an sNaN, clear and propagate [NaN is already set up] */ 7787 if (status & DEC_sNaN) status&=~DEC_sNaN; 7788 else { 7789 uprv_decNumberZero(dn); /* other error: clean throughout */ 7790 dn->bits=DECNAN; /* and make a quiet NaN */ 7791 } 7792 } 7793 uprv_decContextSetStatus(set, status); /* [may not return] */ 7794 return; 7795 } /* decStatus */ 7796 7797/* ------------------------------------------------------------------ */ 7798/* decGetDigits -- count digits in a Units array */ 7799/* */ 7800/* uar is the Unit array holding the number (this is often an */ 7801/* accumulator of some sort) */ 7802/* len is the length of the array in units [>=1] */ 7803/* */ 7804/* returns the number of (significant) digits in the array */ 7805/* */ 7806/* All leading zeros are excluded, except the last if the array has */ 7807/* only zero Units. */ 7808/* ------------------------------------------------------------------ */ 7809/* This may be called twice during some operations. */ 7810static Int decGetDigits(Unit *uar, Int len) { 7811 Unit *up=uar+(len-1); /* -> msu */ 7812 Int digits=(len-1)*DECDPUN+1; /* possible digits excluding msu */ 7813 #if DECDPUN>4 7814 uInt const *pow; /* work */ 7815 #endif 7816 /* (at least 1 in final msu) */ 7817 #if DECCHECK 7818 if (len<1) printf("decGetDigits called with len<1 [%ld]\n", (LI)len); 7819 #endif 7820 7821 for (; up>=uar; up--) { 7822 if (*up==0) { /* unit is all 0s */ 7823 if (digits==1) break; /* a zero has one digit */ 7824 digits-=DECDPUN; /* adjust for 0 unit */ 7825 continue;} 7826 /* found the first (most significant) non-zero Unit */ 7827 #if DECDPUN>1 /* not done yet */ 7828 if (*up<10) break; /* is 1-9 */ 7829 digits++; 7830 #if DECDPUN>2 /* not done yet */ 7831 if (*up<100) break; /* is 10-99 */ 7832 digits++; 7833 #if DECDPUN>3 /* not done yet */ 7834 if (*up<1000) break; /* is 100-999 */ 7835 digits++; 7836 #if DECDPUN>4 /* count the rest ... */ 7837 for (pow=&powers[4]; *up>=*pow; pow++) digits++; 7838 #endif 7839 #endif 7840 #endif 7841 #endif 7842 break; 7843 } /* up */ 7844 return digits; 7845 } /* decGetDigits */ 7846 7847#if DECTRACE | DECCHECK 7848/* ------------------------------------------------------------------ */ 7849/* decNumberShow -- display a number [debug aid] */ 7850/* dn is the number to show */ 7851/* */ 7852/* Shows: sign, exponent, coefficient (msu first), digits */ 7853/* or: sign, special-value */ 7854/* ------------------------------------------------------------------ */ 7855/* this is public so other modules can use it */ 7856void uprv_decNumberShow(const decNumber *dn) { 7857 const Unit *up; /* work */ 7858 uInt u, d; /* .. */ 7859 Int cut; /* .. */ 7860 char isign='+'; /* main sign */ 7861 if (dn==NULL) { 7862 printf("NULL\n"); 7863 return;} 7864 if (decNumberIsNegative(dn)) isign='-'; 7865 printf(" >> %c ", isign); 7866 if (dn->bits&DECSPECIAL) { /* Is a special value */ 7867 if (decNumberIsInfinite(dn)) printf("Infinity"); 7868 else { /* a NaN */ 7869 if (dn->bits&DECSNAN) printf("sNaN"); /* signalling NaN */ 7870 else printf("NaN"); 7871 } 7872 /* if coefficient and exponent are 0, no more to do */ 7873 if (dn->exponent==0 && dn->digits==1 && *dn->lsu==0) { 7874 printf("\n"); 7875 return;} 7876 /* drop through to report other information */ 7877 printf(" "); 7878 } 7879 7880 /* now carefully display the coefficient */ 7881 up=dn->lsu+D2U(dn->digits)-1; /* msu */ 7882 printf("%ld", (LI)*up); 7883 for (up=up-1; up>=dn->lsu; up--) { 7884 u=*up; 7885 printf(":"); 7886 for (cut=DECDPUN-1; cut>=0; cut--) { 7887 d=u/powers[cut]; 7888 u-=d*powers[cut]; 7889 printf("%ld", (LI)d); 7890 } /* cut */ 7891 } /* up */ 7892 if (dn->exponent!=0) { 7893 char esign='+'; 7894 if (dn->exponent<0) esign='-'; 7895 printf(" E%c%ld", esign, (LI)abs(dn->exponent)); 7896 } 7897 printf(" [%ld]\n", (LI)dn->digits); 7898 } /* decNumberShow */ 7899#endif 7900 7901#if DECTRACE || DECCHECK 7902/* ------------------------------------------------------------------ */ 7903/* decDumpAr -- display a unit array [debug/check aid] */ 7904/* name is a single-character tag name */ 7905/* ar is the array to display */ 7906/* len is the length of the array in Units */ 7907/* ------------------------------------------------------------------ */ 7908static void decDumpAr(char name, const Unit *ar, Int len) { 7909 Int i; 7910 const char *spec; 7911 #if DECDPUN==9 7912 spec="%09d "; 7913 #elif DECDPUN==8 7914 spec="%08d "; 7915 #elif DECDPUN==7 7916 spec="%07d "; 7917 #elif DECDPUN==6 7918 spec="%06d "; 7919 #elif DECDPUN==5 7920 spec="%05d "; 7921 #elif DECDPUN==4 7922 spec="%04d "; 7923 #elif DECDPUN==3 7924 spec="%03d "; 7925 #elif DECDPUN==2 7926 spec="%02d "; 7927 #else 7928 spec="%d "; 7929 #endif 7930 printf(" :%c: ", name); 7931 for (i=len-1; i>=0; i--) { 7932 if (i==len-1) printf("%ld ", (LI)ar[i]); 7933 else printf(spec, ar[i]); 7934 } 7935 printf("\n"); 7936 return;} 7937#endif 7938 7939#if DECCHECK 7940/* ------------------------------------------------------------------ */ 7941/* decCheckOperands -- check operand(s) to a routine */ 7942/* res is the result structure (not checked; it will be set to */ 7943/* quiet NaN if error found (and it is not NULL)) */ 7944/* lhs is the first operand (may be DECUNRESU) */ 7945/* rhs is the second (may be DECUNUSED) */ 7946/* set is the context (may be DECUNCONT) */ 7947/* returns 0 if both operands, and the context are clean, or 1 */ 7948/* otherwise (in which case the context will show an error, */ 7949/* unless NULL). Note that res is not cleaned; caller should */ 7950/* handle this so res=NULL case is safe. */ 7951/* The caller is expected to abandon immediately if 1 is returned. */ 7952/* ------------------------------------------------------------------ */ 7953static Flag decCheckOperands(decNumber *res, const decNumber *lhs, 7954 const decNumber *rhs, decContext *set) { 7955 Flag bad=0; 7956 if (set==NULL) { /* oops; hopeless */ 7957 #if DECTRACE || DECVERB 7958 printf("Reference to context is NULL.\n"); 7959 #endif 7960 bad=1; 7961 return 1;} 7962 else if (set!=DECUNCONT 7963 && (set->digits<1 || set->round>=DEC_ROUND_MAX)) { 7964 bad=1; 7965 #if DECTRACE || DECVERB 7966 printf("Bad context [digits=%ld round=%ld].\n", 7967 (LI)set->digits, (LI)set->round); 7968 #endif 7969 } 7970 else { 7971 if (res==NULL) { 7972 bad=1; 7973 #if DECTRACE 7974 /* this one not DECVERB as standard tests include NULL */ 7975 printf("Reference to result is NULL.\n"); 7976 #endif 7977 } 7978 if (!bad && lhs!=DECUNUSED) bad=(decCheckNumber(lhs)); 7979 if (!bad && rhs!=DECUNUSED) bad=(decCheckNumber(rhs)); 7980 } 7981 if (bad) { 7982 if (set!=DECUNCONT) uprv_decContextSetStatus(set, DEC_Invalid_operation); 7983 if (res!=DECUNRESU && res!=NULL) { 7984 uprv_decNumberZero(res); 7985 res->bits=DECNAN; /* qNaN */ 7986 } 7987 } 7988 return bad; 7989 } /* decCheckOperands */ 7990 7991/* ------------------------------------------------------------------ */ 7992/* decCheckNumber -- check a number */ 7993/* dn is the number to check */ 7994/* returns 0 if the number is clean, or 1 otherwise */ 7995/* */ 7996/* The number is considered valid if it could be a result from some */ 7997/* operation in some valid context. */ 7998/* ------------------------------------------------------------------ */ 7999static Flag decCheckNumber(const decNumber *dn) { 8000 const Unit *up; /* work */ 8001 uInt maxuint; /* .. */ 8002 Int ae, d, digits; /* .. */ 8003 Int emin, emax; /* .. */ 8004 8005 if (dn==NULL) { /* hopeless */ 8006 #if DECTRACE 8007 /* this one not DECVERB as standard tests include NULL */ 8008 printf("Reference to decNumber is NULL.\n"); 8009 #endif 8010 return 1;} 8011 8012 /* check special values */ 8013 if (dn->bits & DECSPECIAL) { 8014 if (dn->exponent!=0) { 8015 #if DECTRACE || DECVERB 8016 printf("Exponent %ld (not 0) for a special value [%02x].\n", 8017 (LI)dn->exponent, dn->bits); 8018 #endif 8019 return 1;} 8020 8021 /* 2003.09.08: NaNs may now have coefficients, so next tests Inf only */ 8022 if (decNumberIsInfinite(dn)) { 8023 if (dn->digits!=1) { 8024 #if DECTRACE || DECVERB 8025 printf("Digits %ld (not 1) for an infinity.\n", (LI)dn->digits); 8026 #endif 8027 return 1;} 8028 if (*dn->lsu!=0) { 8029 #if DECTRACE || DECVERB 8030 printf("LSU %ld (not 0) for an infinity.\n", (LI)*dn->lsu); 8031 #endif 8032 decDumpAr('I', dn->lsu, D2U(dn->digits)); 8033 return 1;} 8034 } /* Inf */ 8035 /* 2002.12.26: negative NaNs can now appear through proposed IEEE */ 8036 /* concrete formats (decimal64, etc.). */ 8037 return 0; 8038 } 8039 8040 /* check the coefficient */ 8041 if (dn->digits<1 || dn->digits>DECNUMMAXP) { 8042 #if DECTRACE || DECVERB 8043 printf("Digits %ld in number.\n", (LI)dn->digits); 8044 #endif 8045 return 1;} 8046 8047 d=dn->digits; 8048 8049 for (up=dn->lsu; d>0; up++) { 8050 if (d>DECDPUN) maxuint=DECDPUNMAX; 8051 else { /* reached the msu */ 8052 maxuint=powers[d]-1; 8053 if (dn->digits>1 && *up<powers[d-1]) { 8054 #if DECTRACE || DECVERB 8055 printf("Leading 0 in number.\n"); 8056 uprv_decNumberShow(dn); 8057 #endif 8058 return 1;} 8059 } 8060 if (*up>maxuint) { 8061 #if DECTRACE || DECVERB 8062 printf("Bad Unit [%08lx] in %ld-digit number at offset %ld [maxuint %ld].\n", 8063 (LI)*up, (LI)dn->digits, (LI)(up-dn->lsu), (LI)maxuint); 8064 #endif 8065 return 1;} 8066 d-=DECDPUN; 8067 } 8068 8069 /* check the exponent. Note that input operands can have exponents */ 8070 /* which are out of the set->emin/set->emax and set->digits range */ 8071 /* (just as they can have more digits than set->digits). */ 8072 ae=dn->exponent+dn->digits-1; /* adjusted exponent */ 8073 emax=DECNUMMAXE; 8074 emin=DECNUMMINE; 8075 digits=DECNUMMAXP; 8076 if (ae<emin-(digits-1)) { 8077 #if DECTRACE || DECVERB 8078 printf("Adjusted exponent underflow [%ld].\n", (LI)ae); 8079 uprv_decNumberShow(dn); 8080 #endif 8081 return 1;} 8082 if (ae>+emax) { 8083 #if DECTRACE || DECVERB 8084 printf("Adjusted exponent overflow [%ld].\n", (LI)ae); 8085 uprv_decNumberShow(dn); 8086 #endif 8087 return 1;} 8088 8089 return 0; /* it's OK */ 8090 } /* decCheckNumber */ 8091 8092/* ------------------------------------------------------------------ */ 8093/* decCheckInexact -- check a normal finite inexact result has digits */ 8094/* dn is the number to check */ 8095/* set is the context (for status and precision) */ 8096/* sets Invalid operation, etc., if some digits are missing */ 8097/* [this check is not made for DECSUBSET compilation or when */ 8098/* subnormal is not set] */ 8099/* ------------------------------------------------------------------ */ 8100static void decCheckInexact(const decNumber *dn, decContext *set) { 8101 #if !DECSUBSET && DECEXTFLAG 8102 if ((set->status & (DEC_Inexact|DEC_Subnormal))==DEC_Inexact 8103 && (set->digits!=dn->digits) && !(dn->bits & DECSPECIAL)) { 8104 #if DECTRACE || DECVERB 8105 printf("Insufficient digits [%ld] on normal Inexact result.\n", 8106 (LI)dn->digits); 8107 uprv_decNumberShow(dn); 8108 #endif 8109 uprv_decContextSetStatus(set, DEC_Invalid_operation); 8110 } 8111 #else 8112 /* next is a noop for quiet compiler */ 8113 if (dn!=NULL && dn->digits==0) set->status|=DEC_Invalid_operation; 8114 #endif 8115 return; 8116 } /* decCheckInexact */ 8117#endif 8118 8119#if DECALLOC 8120#undef malloc 8121#undef free 8122/* ------------------------------------------------------------------ */ 8123/* decMalloc -- accountable allocation routine */ 8124/* n is the number of bytes to allocate */ 8125/* */ 8126/* Semantics is the same as the stdlib malloc routine, but bytes */ 8127/* allocated are accounted for globally, and corruption fences are */ 8128/* added before and after the 'actual' storage. */ 8129/* ------------------------------------------------------------------ */ 8130/* This routine allocates storage with an extra twelve bytes; 8 are */ 8131/* at the start and hold: */ 8132/* 0-3 the original length requested */ 8133/* 4-7 buffer corruption detection fence (DECFENCE, x4) */ 8134/* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */ 8135/* ------------------------------------------------------------------ */ 8136static void *decMalloc(size_t n) { 8137 uInt size=n+12; /* true size */ 8138 void *alloc; /* -> allocated storage */ 8139 uByte *b, *b0; /* work */ 8140 uInt uiwork; /* for macros */ 8141 8142 alloc=malloc(size); /* -> allocated storage */ 8143 if (alloc==NULL) return NULL; /* out of strorage */ 8144 b0=(uByte *)alloc; /* as bytes */ 8145 decAllocBytes+=n; /* account for storage */ 8146 UBFROMUI(alloc, n); /* save n */ 8147 /* printf(" alloc ++ dAB: %ld (%ld)\n", (LI)decAllocBytes, (LI)n); */ 8148 for (b=b0+4; b<b0+8; b++) *b=DECFENCE; 8149 for (b=b0+n+8; b<b0+n+12; b++) *b=DECFENCE; 8150 return b0+8; /* -> play area */ 8151 } /* decMalloc */ 8152 8153/* ------------------------------------------------------------------ */ 8154/* decFree -- accountable free routine */ 8155/* alloc is the storage to free */ 8156/* */ 8157/* Semantics is the same as the stdlib malloc routine, except that */ 8158/* the global storage accounting is updated and the fences are */ 8159/* checked to ensure that no routine has written 'out of bounds'. */ 8160/* ------------------------------------------------------------------ */ 8161/* This routine first checks that the fences have not been corrupted. */ 8162/* It then frees the storage using the 'truw' storage address (that */ 8163/* is, offset by 8). */ 8164/* ------------------------------------------------------------------ */ 8165static void decFree(void *alloc) { 8166 uInt n; /* original length */ 8167 uByte *b, *b0; /* work */ 8168 uInt uiwork; /* for macros */ 8169 8170 if (alloc==NULL) return; /* allowed; it's a nop */ 8171 b0=(uByte *)alloc; /* as bytes */ 8172 b0-=8; /* -> true start of storage */ 8173 n=UBTOUI(b0); /* lift length */ 8174 for (b=b0+4; b<b0+8; b++) if (*b!=DECFENCE) 8175 printf("=== Corrupt byte [%02x] at offset %d from %ld ===\n", *b, 8176 b-b0-8, (LI)b0); 8177 for (b=b0+n+8; b<b0+n+12; b++) if (*b!=DECFENCE) 8178 printf("=== Corrupt byte [%02x] at offset +%d from %ld, n=%ld ===\n", *b, 8179 b-b0-8, (LI)b0, (LI)n); 8180 free(b0); /* drop the storage */ 8181 decAllocBytes-=n; /* account for storage */ 8182 /* printf(" free -- dAB: %d (%d)\n", decAllocBytes, -n); */ 8183 } /* decFree */ 8184#define malloc(a) decMalloc(a) 8185#define free(a) decFree(a) 8186#endif 8187