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| 1 /* ------------------------------------------------------------------ */ |
| 2 /* Decimal Number arithmetic module */ |
| 3 /* ------------------------------------------------------------------ */ |
| 4 /* Copyright (c) IBM Corporation, 2000-2010. All rights reserved. */ |
| 5 /* */ |
| 6 /* This software is made available under the terms of the */ |
| 7 /* ICU License -- ICU 1.8.1 and later. */ |
| 8 /* */ |
| 9 /* The description and User's Guide ("The decNumber C Library") for */ |
| 10 /* this software is called decNumber.pdf. This document is */ |
| 11 /* available, together with arithmetic and format specifications, */ |
| 12 /* testcases, and Web links, on the General Decimal Arithmetic page. */ |
| 13 /* */ |
| 14 /* Please send comments, suggestions, and corrections to the author: */ |
| 15 /* mfc@uk.ibm.com */ |
| 16 /* Mike Cowlishaw, IBM Fellow */ |
| 17 /* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ |
| 18 /* ------------------------------------------------------------------ */ |
| 19 |
| 20 /* Modified version, for use from within ICU. |
| 21 * Renamed public functions, to avoid an unwanted export of the |
| 22 * standard names from the ICU library. |
| 23 * |
| 24 * Use ICU's uprv_malloc() and uprv_free() |
| 25 * |
| 26 * Revert comment syntax to plain C |
| 27 * |
| 28 * Remove a few compiler warnings. |
| 29 */ |
| 30 |
| 31 /* This module comprises the routines for arbitrary-precision General */ |
| 32 /* Decimal Arithmetic as defined in the specification which may be */ |
| 33 /* found on the General Decimal Arithmetic pages. It implements both */ |
| 34 /* the full ('extended') arithmetic and the simpler ('subset') */ |
| 35 /* arithmetic. */ |
| 36 /* */ |
| 37 /* Usage notes: */ |
| 38 /* */ |
| 39 /* 1. This code is ANSI C89 except: */ |
| 40 /* */ |
| 41 /* a) C99 line comments (double forward slash) are used. (Most C */ |
| 42 /* compilers accept these. If yours does not, a simple script */ |
| 43 /* can be used to convert them to ANSI C comments.) */ |
| 44 /* */ |
| 45 /* b) Types from C99 stdint.h are used. If you do not have this */ |
| 46 /* header file, see the User's Guide section of the decNumber */ |
| 47 /* documentation; this lists the necessary definitions. */ |
| 48 /* */ |
| 49 /* c) If DECDPUN>4 or DECUSE64=1, the C99 64-bit int64_t and */ |
| 50 /* uint64_t types may be used. To avoid these, set DECUSE64=0 */ |
| 51 /* and DECDPUN<=4 (see documentation). */ |
| 52 /* */ |
| 53 /* The code also conforms to C99 restrictions; in particular, */ |
| 54 /* strict aliasing rules are observed. */ |
| 55 /* */ |
| 56 /* 2. The decNumber format which this library uses is optimized for */ |
| 57 /* efficient processing of relatively short numbers; in particular */ |
| 58 /* it allows the use of fixed sized structures and minimizes copy */ |
| 59 /* and move operations. It does, however, support arbitrary */ |
| 60 /* precision (up to 999,999,999 digits) and arbitrary exponent */ |
| 61 /* range (Emax in the range 0 through 999,999,999 and Emin in the */ |
| 62 /* range -999,999,999 through 0). Mathematical functions (for */ |
| 63 /* example decNumberExp) as identified below are restricted more */ |
| 64 /* tightly: digits, emax, and -emin in the context must be <= */ |
| 65 /* DEC_MAX_MATH (999999), and their operand(s) must be within */ |
| 66 /* these bounds. */ |
| 67 /* */ |
| 68 /* 3. Logical functions are further restricted; their operands must */ |
| 69 /* be finite, positive, have an exponent of zero, and all digits */ |
| 70 /* must be either 0 or 1. The result will only contain digits */ |
| 71 /* which are 0 or 1 (and will have exponent=0 and a sign of 0). */ |
| 72 /* */ |
| 73 /* 4. Operands to operator functions are never modified unless they */ |
| 74 /* are also specified to be the result number (which is always */ |
| 75 /* permitted). Other than that case, operands must not overlap. */ |
| 76 /* */ |
| 77 /* 5. Error handling: the type of the error is ORed into the status */ |
| 78 /* flags in the current context (decContext structure). The */ |
| 79 /* SIGFPE signal is then raised if the corresponding trap-enabler */ |
| 80 /* flag in the decContext is set (is 1). */ |
| 81 /* */ |
| 82 /* It is the responsibility of the caller to clear the status */ |
| 83 /* flags as required. */ |
| 84 /* */ |
| 85 /* The result of any routine which returns a number will always */ |
| 86 /* be a valid number (which may be a special value, such as an */ |
| 87 /* Infinity or NaN). */ |
| 88 /* */ |
| 89 /* 6. The decNumber format is not an exchangeable concrete */ |
| 90 /* representation as it comprises fields which may be machine- */ |
| 91 /* dependent (packed or unpacked, or special length, for example). */ |
| 92 /* Canonical conversions to and from strings are provided; other */ |
| 93 /* conversions are available in separate modules. */ |
| 94 /* */ |
| 95 /* 7. Normally, input operands are assumed to be valid. Set DECCHECK */ |
| 96 /* to 1 for extended operand checking (including NULL operands). */ |
| 97 /* Results are undefined if a badly-formed structure (or a NULL */ |
| 98 /* pointer to a structure) is provided, though with DECCHECK */ |
| 99 /* enabled the operator routines are protected against exceptions. */ |
| 100 /* (Except if the result pointer is NULL, which is unrecoverable.) */ |
| 101 /* */ |
| 102 /* However, the routines will never cause exceptions if they are */ |
| 103 /* given well-formed operands, even if the value of the operands */ |
| 104 /* is inappropriate for the operation and DECCHECK is not set. */ |
| 105 /* (Except for SIGFPE, as and where documented.) */ |
| 106 /* */ |
| 107 /* 8. Subset arithmetic is available only if DECSUBSET is set to 1. */ |
| 108 /* ------------------------------------------------------------------ */ |
| 109 /* Implementation notes for maintenance of this module: */ |
| 110 /* */ |
| 111 /* 1. Storage leak protection: Routines which use malloc are not */ |
| 112 /* permitted to use return for fastpath or error exits (i.e., */ |
| 113 /* they follow strict structured programming conventions). */ |
| 114 /* Instead they have a do{}while(0); construct surrounding the */ |
| 115 /* code which is protected -- break may be used to exit this. */ |
| 116 /* Other routines can safely use the return statement inline. */ |
| 117 /* */ |
| 118 /* Storage leak accounting can be enabled using DECALLOC. */ |
| 119 /* */ |
| 120 /* 2. All loops use the for(;;) construct. Any do construct does */ |
| 121 /* not loop; it is for allocation protection as just described. */ |
| 122 /* */ |
| 123 /* 3. Setting status in the context must always be the very last */ |
| 124 /* action in a routine, as non-0 status may raise a trap and hence */ |
| 125 /* the call to set status may not return (if the handler uses long */ |
| 126 /* jump). Therefore all cleanup must be done first. In general, */ |
| 127 /* to achieve this status is accumulated and is only applied just */ |
| 128 /* before return by calling decContextSetStatus (via decStatus). */ |
| 129 /* */ |
| 130 /* Routines which allocate storage cannot, in general, use the */ |
| 131 /* 'top level' routines which could cause a non-returning */ |
| 132 /* transfer of control. The decXxxxOp routines are safe (do not */ |
| 133 /* call decStatus even if traps are set in the context) and should */ |
| 134 /* be used instead (they are also a little faster). */ |
| 135 /* */ |
| 136 /* 4. Exponent checking is minimized by allowing the exponent to */ |
| 137 /* grow outside its limits during calculations, provided that */ |
| 138 /* the decFinalize function is called later. Multiplication and */ |
| 139 /* division, and intermediate calculations in exponentiation, */ |
| 140 /* require more careful checks because of the risk of 31-bit */ |
| 141 /* overflow (the most negative valid exponent is -1999999997, for */ |
| 142 /* a 999999999-digit number with adjusted exponent of -999999999). */ |
| 143 /* */ |
| 144 /* 5. Rounding is deferred until finalization of results, with any */ |
| 145 /* 'off to the right' data being represented as a single digit */ |
| 146 /* residue (in the range -1 through 9). This avoids any double- */ |
| 147 /* rounding when more than one shortening takes place (for */ |
| 148 /* example, when a result is subnormal). */ |
| 149 /* */ |
| 150 /* 6. The digits count is allowed to rise to a multiple of DECDPUN */ |
| 151 /* during many operations, so whole Units are handled and exact */ |
| 152 /* accounting of digits is not needed. The correct digits value */ |
| 153 /* is found by decGetDigits, which accounts for leading zeros. */ |
| 154 /* This must be called before any rounding if the number of digits */ |
| 155 /* is not known exactly. */ |
| 156 /* */ |
| 157 /* 7. The multiply-by-reciprocal 'trick' is used for partitioning */ |
| 158 /* numbers up to four digits, using appropriate constants. This */ |
| 159 /* is not useful for longer numbers because overflow of 32 bits */ |
| 160 /* would lead to 4 multiplies, which is almost as expensive as */ |
| 161 /* a divide (unless a floating-point or 64-bit multiply is */ |
| 162 /* assumed to be available). */ |
| 163 /* */ |
| 164 /* 8. Unusual abbreviations that may be used in the commentary: */ |
| 165 /* lhs -- left hand side (operand, of an operation) */ |
| 166 /* lsd -- least significant digit (of coefficient) */ |
| 167 /* lsu -- least significant Unit (of coefficient) */ |
| 168 /* msd -- most significant digit (of coefficient) */ |
| 169 /* msi -- most significant item (in an array) */ |
| 170 /* msu -- most significant Unit (of coefficient) */ |
| 171 /* rhs -- right hand side (operand, of an operation) */ |
| 172 /* +ve -- positive */ |
| 173 /* -ve -- negative */ |
| 174 /* ** -- raise to the power */ |
| 175 /* ------------------------------------------------------------------ */ |
| 176 |
| 177 #include <stdlib.h> /* for malloc, free, etc. */ |
| 178 /* #include <stdio.h> */ /* for printf [if needed] */ |
| 179 #include <string.h> /* for strcpy */ |
| 180 #include <ctype.h> /* for lower */ |
| 181 #include "cmemory.h" /* for uprv_malloc, etc., in ICU */ |
| 182 #include "decNumber.h" /* base number library */ |
| 183 #include "decNumberLocal.h" /* decNumber local types, etc. */ |
| 184 |
| 185 /* Constants */ |
| 186 /* Public lookup table used by the D2U macro */ |
| 187 const uByte d2utable[DECMAXD2U+1]=D2UTABLE; |
| 188 |
| 189 #define DECVERB 1 /* set to 1 for verbose DECCHECK */ |
| 190 #define powers DECPOWERS /* old internal name */ |
| 191 |
| 192 /* Local constants */ |
| 193 #define DIVIDE 0x80 /* Divide operators */ |
| 194 #define REMAINDER 0x40 /* .. */ |
| 195 #define DIVIDEINT 0x20 /* .. */ |
| 196 #define REMNEAR 0x10 /* .. */ |
| 197 #define COMPARE 0x01 /* Compare operators */ |
| 198 #define COMPMAX 0x02 /* .. */ |
| 199 #define COMPMIN 0x03 /* .. */ |
| 200 #define COMPTOTAL 0x04 /* .. */ |
| 201 #define COMPNAN 0x05 /* .. [NaN processing] */ |
| 202 #define COMPSIG 0x06 /* .. [signaling COMPARE] */ |
| 203 #define COMPMAXMAG 0x07 /* .. */ |
| 204 #define COMPMINMAG 0x08 /* .. */ |
| 205 |
| 206 #define DEC_sNaN 0x40000000 /* local status: sNaN signal */ |
| 207 #define BADINT (Int)0x80000000 /* most-negative Int; error indicator */ |
| 208 /* Next two indicate an integer >= 10**6, and its parity (bottom bit) */ |
| 209 #define BIGEVEN (Int)0x80000002 |
| 210 #define BIGODD (Int)0x80000003 |
| 211 |
| 212 static Unit uarrone[1]={1}; /* Unit array of 1, used for incrementing */ |
| 213 |
| 214 /* Granularity-dependent code */ |
| 215 #if DECDPUN<=4 |
| 216 #define eInt Int /* extended integer */ |
| 217 #define ueInt uInt /* unsigned extended integer */ |
| 218 /* Constant multipliers for divide-by-power-of five using reciprocal */ |
| 219 /* multiply, after removing powers of 2 by shifting, and final shift */ |
| 220 /* of 17 [we only need up to **4] */ |
| 221 static const uInt multies[]={131073, 26215, 5243, 1049, 210}; |
| 222 /* QUOT10 -- macro to return the quotient of unit u divided by 10**n */ |
| 223 #define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17) |
| 224 #else |
| 225 /* For DECDPUN>4 non-ANSI-89 64-bit types are needed. */ |
| 226 #if !DECUSE64 |
| 227 #error decNumber.c: DECUSE64 must be 1 when DECDPUN>4 |
| 228 #endif |
| 229 #define eInt Long /* extended integer */ |
| 230 #define ueInt uLong /* unsigned extended integer */ |
| 231 #endif |
| 232 |
| 233 /* Local routines */ |
| 234 static decNumber * decAddOp(decNumber *, const decNumber *, const decNumber *, |
| 235 decContext *, uByte, uInt *); |
| 236 static Flag decBiStr(const char *, const char *, const char *); |
| 237 static uInt decCheckMath(const decNumber *, decContext *, uInt *); |
| 238 static void decApplyRound(decNumber *, decContext *, Int, uInt *); |
| 239 static Int decCompare(const decNumber *lhs, const decNumber *rhs, Flag); |
| 240 static decNumber * decCompareOp(decNumber *, const decNumber *, |
| 241 const decNumber *, decContext *, |
| 242 Flag, uInt *); |
| 243 static void decCopyFit(decNumber *, const decNumber *, decContext *, |
| 244 Int *, uInt *); |
| 245 static decNumber * decDecap(decNumber *, Int); |
| 246 static decNumber * decDivideOp(decNumber *, const decNumber *, |
| 247 const decNumber *, decContext *, Flag, uInt *); |
| 248 static decNumber * decExpOp(decNumber *, const decNumber *, |
| 249 decContext *, uInt *); |
| 250 static void decFinalize(decNumber *, decContext *, Int *, uInt *); |
| 251 static Int decGetDigits(Unit *, Int); |
| 252 static Int decGetInt(const decNumber *); |
| 253 static decNumber * decLnOp(decNumber *, const decNumber *, |
| 254 decContext *, uInt *); |
| 255 static decNumber * decMultiplyOp(decNumber *, const decNumber *, |
| 256 const decNumber *, decContext *, |
| 257 uInt *); |
| 258 static decNumber * decNaNs(decNumber *, const decNumber *, |
| 259 const decNumber *, decContext *, uInt *); |
| 260 static decNumber * decQuantizeOp(decNumber *, const decNumber *, |
| 261 const decNumber *, decContext *, Flag, |
| 262 uInt *); |
| 263 static void decReverse(Unit *, Unit *); |
| 264 static void decSetCoeff(decNumber *, decContext *, const Unit *, |
| 265 Int, Int *, uInt *); |
| 266 static void decSetMaxValue(decNumber *, decContext *); |
| 267 static void decSetOverflow(decNumber *, decContext *, uInt *); |
| 268 static void decSetSubnormal(decNumber *, decContext *, Int *, uInt *); |
| 269 static Int decShiftToLeast(Unit *, Int, Int); |
| 270 static Int decShiftToMost(Unit *, Int, Int); |
| 271 static void decStatus(decNumber *, uInt, decContext *); |
| 272 static void decToString(const decNumber *, char[], Flag); |
| 273 static decNumber * decTrim(decNumber *, decContext *, Flag, Flag, Int *); |
| 274 static Int decUnitAddSub(const Unit *, Int, const Unit *, Int, Int, |
| 275 Unit *, Int); |
| 276 static Int decUnitCompare(const Unit *, Int, const Unit *, Int, Int); |
| 277 |
| 278 #if !DECSUBSET |
| 279 /* decFinish == decFinalize when no subset arithmetic needed */ |
| 280 #define decFinish(a,b,c,d) decFinalize(a,b,c,d) |
| 281 #else |
| 282 static void decFinish(decNumber *, decContext *, Int *, uInt *); |
| 283 static decNumber * decRoundOperand(const decNumber *, decContext *, uInt *); |
| 284 #endif |
| 285 |
| 286 /* Local macros */ |
| 287 /* masked special-values bits */ |
| 288 #define SPECIALARG (rhs->bits & DECSPECIAL) |
| 289 #define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL) |
| 290 |
| 291 /* For use in ICU */ |
| 292 #define malloc(a) uprv_malloc(a) |
| 293 #define free(a) uprv_free(a) |
| 294 |
| 295 /* Diagnostic macros, etc. */ |
| 296 #if DECALLOC |
| 297 /* Handle malloc/free accounting. If enabled, our accountable routines */ |
| 298 /* are used; otherwise the code just goes straight to the system malloc */ |
| 299 /* and free routines. */ |
| 300 #define malloc(a) decMalloc(a) |
| 301 #define free(a) decFree(a) |
| 302 #define DECFENCE 0x5a /* corruption detector */ |
| 303 /* 'Our' malloc and free: */ |
| 304 static void *decMalloc(size_t); |
| 305 static void decFree(void *); |
| 306 uInt decAllocBytes=0; /* count of bytes allocated */ |
| 307 /* Note that DECALLOC code only checks for storage buffer overflow. */ |
| 308 /* To check for memory leaks, the decAllocBytes variable must be */ |
| 309 /* checked to be 0 at appropriate times (e.g., after the test */ |
| 310 /* harness completes a set of tests). This checking may be unreliable */ |
| 311 /* if the testing is done in a multi-thread environment. */ |
| 312 #endif |
| 313 |
| 314 #if DECCHECK |
| 315 /* Optional checking routines. Enabling these means that decNumber */ |
| 316 /* and decContext operands to operator routines are checked for */ |
| 317 /* correctness. This roughly doubles the execution time of the */ |
| 318 /* fastest routines (and adds 600+ bytes), so should not normally be */ |
| 319 /* used in 'production'. */ |
| 320 /* decCheckInexact is used to check that inexact results have a full */ |
| 321 /* complement of digits (where appropriate -- this is not the case */ |
| 322 /* for Quantize, for example) */ |
| 323 #define DECUNRESU ((decNumber *)(void *)0xffffffff) |
| 324 #define DECUNUSED ((const decNumber *)(void *)0xffffffff) |
| 325 #define DECUNCONT ((decContext *)(void *)(0xffffffff)) |
| 326 static Flag decCheckOperands(decNumber *, const decNumber *, |
| 327 const decNumber *, decContext *); |
| 328 static Flag decCheckNumber(const decNumber *); |
| 329 static void decCheckInexact(const decNumber *, decContext *); |
| 330 #endif |
| 331 |
| 332 #if DECTRACE || DECCHECK |
| 333 /* Optional trace/debugging routines (may or may not be used) */ |
| 334 void decNumberShow(const decNumber *); /* displays the components of a number
*/ |
| 335 static void decDumpAr(char, const Unit *, Int); |
| 336 #endif |
| 337 |
| 338 /* ================================================================== */ |
| 339 /* Conversions */ |
| 340 /* ================================================================== */ |
| 341 |
| 342 /* ------------------------------------------------------------------ */ |
| 343 /* from-int32 -- conversion from Int or uInt */ |
| 344 /* */ |
| 345 /* dn is the decNumber to receive the integer */ |
| 346 /* in or uin is the integer to be converted */ |
| 347 /* returns dn */ |
| 348 /* */ |
| 349 /* No error is possible. */ |
| 350 /* ------------------------------------------------------------------ */ |
| 351 U_CAPI decNumber * U_EXPORT2 uprv_decNumberFromInt32(decNumber *dn, Int in) { |
| 352 uInt unsig; |
| 353 if (in>=0) unsig=in; |
| 354 else { /* negative (possibly BADINT) */ |
| 355 if (in==BADINT) unsig=(uInt)1073741824*2; /* special case */ |
| 356 else unsig=-in; /* invert */ |
| 357 } |
| 358 /* in is now positive */ |
| 359 uprv_decNumberFromUInt32(dn, unsig); |
| 360 if (in<0) dn->bits=DECNEG; /* sign needed */ |
| 361 return dn; |
| 362 } /* decNumberFromInt32 */ |
| 363 |
| 364 U_CAPI decNumber * U_EXPORT2 uprv_decNumberFromUInt32(decNumber *dn, uInt uin) { |
| 365 Unit *up; /* work pointer */ |
| 366 uprv_decNumberZero(dn); /* clean */ |
| 367 if (uin==0) return dn; /* [or decGetDigits bad call] */ |
| 368 for (up=dn->lsu; uin>0; up++) { |
| 369 *up=(Unit)(uin%(DECDPUNMAX+1)); |
| 370 uin=uin/(DECDPUNMAX+1); |
| 371 } |
| 372 dn->digits=decGetDigits(dn->lsu, up-dn->lsu); |
| 373 return dn; |
| 374 } /* decNumberFromUInt32 */ |
| 375 |
| 376 /* ------------------------------------------------------------------ */ |
| 377 /* to-int32 -- conversion to Int or uInt */ |
| 378 /* */ |
| 379 /* dn is the decNumber to convert */ |
| 380 /* set is the context for reporting errors */ |
| 381 /* returns the converted decNumber, or 0 if Invalid is set */ |
| 382 /* */ |
| 383 /* Invalid is set if the decNumber does not have exponent==0 or if */ |
| 384 /* it is a NaN, Infinite, or out-of-range. */ |
| 385 /* ------------------------------------------------------------------ */ |
| 386 U_CAPI Int U_EXPORT2 uprv_decNumberToInt32(const decNumber *dn, decContext *set)
{ |
| 387 #if DECCHECK |
| 388 if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; |
| 389 #endif |
| 390 |
| 391 /* special or too many digits, or bad exponent */ |
| 392 if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; /* bad */ |
| 393 else { /* is a finite integer with 10 or fewer digits */ |
| 394 Int d; /* work */ |
| 395 const Unit *up; /* .. */ |
| 396 uInt hi=0, lo; /* .. */ |
| 397 up=dn->lsu; /* -> lsu */ |
| 398 lo=*up; /* get 1 to 9 digits */ |
| 399 #if DECDPUN>1 /* split to higher */ |
| 400 hi=lo/10; |
| 401 lo=lo%10; |
| 402 #endif |
| 403 up++; |
| 404 /* collect remaining Units, if any, into hi */ |
| 405 for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1]; |
| 406 /* now low has the lsd, hi the remainder */ |
| 407 if (hi>214748364 || (hi==214748364 && lo>7)) { /* out of range? */ |
| 408 /* most-negative is a reprieve */ |
| 409 if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000; |
| 410 /* bad -- drop through */ |
| 411 } |
| 412 else { /* in-range always */ |
| 413 Int i=X10(hi)+lo; |
| 414 if (dn->bits&DECNEG) return -i; |
| 415 return i; |
| 416 } |
| 417 } /* integer */ |
| 418 uprv_decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */ |
| 419 return 0; |
| 420 } /* decNumberToInt32 */ |
| 421 |
| 422 U_CAPI uInt U_EXPORT2 uprv_decNumberToUInt32(const decNumber *dn, decContext *se
t) { |
| 423 #if DECCHECK |
| 424 if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; |
| 425 #endif |
| 426 /* special or too many digits, or bad exponent, or negative (<0) */ |
| 427 if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0 |
| 428 || (dn->bits&DECNEG && !ISZERO(dn))); /* bad */ |
| 429 else { /* is a finite integer with 10 or fewer digits */ |
| 430 Int d; /* work */ |
| 431 const Unit *up; /* .. */ |
| 432 uInt hi=0, lo; /* .. */ |
| 433 up=dn->lsu; /* -> lsu */ |
| 434 lo=*up; /* get 1 to 9 digits */ |
| 435 #if DECDPUN>1 /* split to higher */ |
| 436 hi=lo/10; |
| 437 lo=lo%10; |
| 438 #endif |
| 439 up++; |
| 440 /* collect remaining Units, if any, into hi */ |
| 441 for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1]; |
| 442 |
| 443 /* now low has the lsd, hi the remainder */ |
| 444 if (hi>429496729 || (hi==429496729 && lo>5)) ; /* no reprieve possible */ |
| 445 else return X10(hi)+lo; |
| 446 } /* integer */ |
| 447 uprv_decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */ |
| 448 return 0; |
| 449 } /* decNumberToUInt32 */ |
| 450 |
| 451 /* ------------------------------------------------------------------ */ |
| 452 /* to-scientific-string -- conversion to numeric string */ |
| 453 /* to-engineering-string -- conversion to numeric string */ |
| 454 /* */ |
| 455 /* decNumberToString(dn, string); */ |
| 456 /* decNumberToEngString(dn, string); */ |
| 457 /* */ |
| 458 /* dn is the decNumber to convert */ |
| 459 /* string is the string where the result will be laid out */ |
| 460 /* */ |
| 461 /* string must be at least dn->digits+14 characters long */ |
| 462 /* */ |
| 463 /* No error is possible, and no status can be set. */ |
| 464 /* ------------------------------------------------------------------ */ |
| 465 U_CAPI char * U_EXPORT2 uprv_decNumberToString(const decNumber *dn, char *string
){ |
| 466 decToString(dn, string, 0); |
| 467 return string; |
| 468 } /* DecNumberToString */ |
| 469 |
| 470 U_CAPI char * U_EXPORT2 uprv_decNumberToEngString(const decNumber *dn, char *str
ing){ |
| 471 decToString(dn, string, 1); |
| 472 return string; |
| 473 } /* DecNumberToEngString */ |
| 474 |
| 475 /* ------------------------------------------------------------------ */ |
| 476 /* to-number -- conversion from numeric string */ |
| 477 /* */ |
| 478 /* decNumberFromString -- convert string to decNumber */ |
| 479 /* dn -- the number structure to fill */ |
| 480 /* chars[] -- the string to convert ('\0' terminated) */ |
| 481 /* set -- the context used for processing any error, */ |
| 482 /* determining the maximum precision available */ |
| 483 /* (set.digits), determining the maximum and minimum */ |
| 484 /* exponent (set.emax and set.emin), determining if */ |
| 485 /* extended values are allowed, and checking the */ |
| 486 /* rounding mode if overflow occurs or rounding is */ |
| 487 /* needed. */ |
| 488 /* */ |
| 489 /* The length of the coefficient and the size of the exponent are */ |
| 490 /* checked by this routine, so the correct error (Underflow or */ |
| 491 /* Overflow) can be reported or rounding applied, as necessary. */ |
| 492 /* */ |
| 493 /* If bad syntax is detected, the result will be a quiet NaN. */ |
| 494 /* ------------------------------------------------------------------ */ |
| 495 U_CAPI decNumber * U_EXPORT2 uprv_decNumberFromString(decNumber *dn, const char
chars[], |
| 496 decContext *set) { |
| 497 Int exponent=0; /* working exponent [assume 0] */ |
| 498 uByte bits=0; /* working flags [assume +ve] */ |
| 499 Unit *res; /* where result will be built */ |
| 500 Unit resbuff[SD2U(DECBUFFER+9)];/* local buffer in case need temporary */ |
| 501 /* [+9 allows for ln() constants] */ |
| 502 Unit *allocres=NULL; /* -> allocated result, iff allocated */ |
| 503 Int d=0; /* count of digits found in decimal part */ |
| 504 const char *dotchar=NULL; /* where dot was found */ |
| 505 const char *cfirst=chars; /* -> first character of decimal part */ |
| 506 const char *last=NULL; /* -> last digit of decimal part */ |
| 507 const char *c; /* work */ |
| 508 Unit *up; /* .. */ |
| 509 #if DECDPUN>1 |
| 510 Int cut, out; /* .. */ |
| 511 #endif |
| 512 Int residue; /* rounding residue */ |
| 513 uInt status=0; /* error code */ |
| 514 |
| 515 #if DECCHECK |
| 516 if (decCheckOperands(DECUNRESU, DECUNUSED, DECUNUSED, set)) |
| 517 return uprv_decNumberZero(dn); |
| 518 #endif |
| 519 |
| 520 do { /* status & malloc protection */ |
| 521 for (c=chars;; c++) { /* -> input character */ |
| 522 if (*c>='0' && *c<='9') { /* test for Arabic digit */ |
| 523 last=c; |
| 524 d++; /* count of real digits */ |
| 525 continue; /* still in decimal part */ |
| 526 } |
| 527 if (*c=='.' && dotchar==NULL) { /* first '.' */ |
| 528 dotchar=c; /* record offset into decimal part */ |
| 529 if (c==cfirst) cfirst++; /* first digit must follow */ |
| 530 continue;} |
| 531 if (c==chars) { /* first in string... */ |
| 532 if (*c=='-') { /* valid - sign */ |
| 533 cfirst++; |
| 534 bits=DECNEG; |
| 535 continue;} |
| 536 if (*c=='+') { /* valid + sign */ |
| 537 cfirst++; |
| 538 continue;} |
| 539 } |
| 540 /* *c is not a digit, or a valid +, -, or '.' */ |
| 541 break; |
| 542 } /* c */ |
| 543 |
| 544 if (last==NULL) { /* no digits yet */ |
| 545 status=DEC_Conversion_syntax;/* assume the worst */ |
| 546 if (*c=='\0') break; /* and no more to come... */ |
| 547 #if DECSUBSET |
| 548 /* if subset then infinities and NaNs are not allowed */ |
| 549 if (!set->extended) break; /* hopeless */ |
| 550 #endif |
| 551 /* Infinities and NaNs are possible, here */ |
| 552 if (dotchar!=NULL) break; /* .. unless had a dot */ |
| 553 uprv_decNumberZero(dn); /* be optimistic */ |
| 554 if (decBiStr(c, "infinity", "INFINITY") |
| 555 || decBiStr(c, "inf", "INF")) { |
| 556 dn->bits=bits | DECINF; |
| 557 status=0; /* is OK */ |
| 558 break; /* all done */ |
| 559 } |
| 560 /* a NaN expected */ |
| 561 /* 2003.09.10 NaNs are now permitted to have a sign */ |
| 562 dn->bits=bits | DECNAN; /* assume simple NaN */ |
| 563 if (*c=='s' || *c=='S') { /* looks like an sNaN */ |
| 564 c++; |
| 565 dn->bits=bits | DECSNAN; |
| 566 } |
| 567 if (*c!='n' && *c!='N') break; /* check caseless "NaN" */ |
| 568 c++; |
| 569 if (*c!='a' && *c!='A') break; /* .. */ |
| 570 c++; |
| 571 if (*c!='n' && *c!='N') break; /* .. */ |
| 572 c++; |
| 573 /* now either nothing, or nnnn payload, expected */ |
| 574 /* -> start of integer and skip leading 0s [including plain 0] */ |
| 575 for (cfirst=c; *cfirst=='0';) cfirst++; |
| 576 if (*cfirst=='\0') { /* "NaN" or "sNaN", maybe with all 0s */ |
| 577 status=0; /* it's good */ |
| 578 break; /* .. */ |
| 579 } |
| 580 /* something other than 0s; setup last and d as usual [no dots] */ |
| 581 for (c=cfirst;; c++, d++) { |
| 582 if (*c<'0' || *c>'9') break; /* test for Arabic digit */ |
| 583 last=c; |
| 584 } |
| 585 if (*c!='\0') break; /* not all digits */ |
| 586 if (d>set->digits-1) { |
| 587 /* [NB: payload in a decNumber can be full length unless */ |
| 588 /* clamped, in which case can only be digits-1] */ |
| 589 if (set->clamp) break; |
| 590 if (d>set->digits) break; |
| 591 } /* too many digits? */ |
| 592 /* good; drop through to convert the integer to coefficient */ |
| 593 status=0; /* syntax is OK */ |
| 594 bits=dn->bits; /* for copy-back */ |
| 595 } /* last==NULL */ |
| 596 |
| 597 else if (*c!='\0') { /* more to process... */ |
| 598 /* had some digits; exponent is only valid sequence now */ |
| 599 Flag nege; /* 1=negative exponent */ |
| 600 const char *firstexp; /* -> first significant exponent digit */ |
| 601 status=DEC_Conversion_syntax;/* assume the worst */ |
| 602 if (*c!='e' && *c!='E') break; |
| 603 /* Found 'e' or 'E' -- now process explicit exponent */ |
| 604 /* 1998.07.11: sign no longer required */ |
| 605 nege=0; |
| 606 c++; /* to (possible) sign */ |
| 607 if (*c=='-') {nege=1; c++;} |
| 608 else if (*c=='+') c++; |
| 609 if (*c=='\0') break; |
| 610 |
| 611 for (; *c=='0' && *(c+1)!='\0';) c++; /* strip insignificant zeros */ |
| 612 firstexp=c; /* save exponent digit place */ |
| 613 for (; ;c++) { |
| 614 if (*c<'0' || *c>'9') break; /* not a digit */ |
| 615 exponent=X10(exponent)+(Int)*c-(Int)'0'; |
| 616 } /* c */ |
| 617 /* if not now on a '\0', *c must not be a digit */ |
| 618 if (*c!='\0') break; |
| 619 |
| 620 /* (this next test must be after the syntax checks) */ |
| 621 /* if it was too long the exponent may have wrapped, so check */ |
| 622 /* carefully and set it to a certain overflow if wrap possible */ |
| 623 if (c>=firstexp+9+1) { |
| 624 if (c>firstexp+9+1 || *firstexp>'1') exponent=DECNUMMAXE*2; |
| 625 /* [up to 1999999999 is OK, for example 1E-1000000998] */ |
| 626 } |
| 627 if (nege) exponent=-exponent; /* was negative */ |
| 628 status=0; /* is OK */ |
| 629 } /* stuff after digits */ |
| 630 |
| 631 /* Here when whole string has been inspected; syntax is good */ |
| 632 /* cfirst->first digit (never dot), last->last digit (ditto) */ |
| 633 |
| 634 /* strip leading zeros/dot [leave final 0 if all 0's] */ |
| 635 if (*cfirst=='0') { /* [cfirst has stepped over .] */ |
| 636 for (c=cfirst; c<last; c++, cfirst++) { |
| 637 if (*c=='.') continue; /* ignore dots */ |
| 638 if (*c!='0') break; /* non-zero found */ |
| 639 d--; /* 0 stripped */ |
| 640 } /* c */ |
| 641 #if DECSUBSET |
| 642 /* make a rapid exit for easy zeros if !extended */ |
| 643 if (*cfirst=='0' && !set->extended) { |
| 644 uprv_decNumberZero(dn); /* clean result */ |
| 645 break; /* [could be return] */ |
| 646 } |
| 647 #endif |
| 648 } /* at least one leading 0 */ |
| 649 |
| 650 /* Handle decimal point... */ |
| 651 if (dotchar!=NULL && dotchar<last) /* non-trailing '.' found? */ |
| 652 exponent-=(last-dotchar); /* adjust exponent */ |
| 653 /* [we can now ignore the .] */ |
| 654 |
| 655 /* OK, the digits string is good. Assemble in the decNumber, or in */ |
| 656 /* a temporary units array if rounding is needed */ |
| 657 if (d<=set->digits) res=dn->lsu; /* fits into supplied decNumber */ |
| 658 else { /* rounding needed */ |
| 659 Int needbytes=D2U(d)*sizeof(Unit);/* bytes needed */ |
| 660 res=resbuff; /* assume use local buffer */ |
| 661 if (needbytes>(Int)sizeof(resbuff)) { /* too big for local */ |
| 662 allocres=(Unit *)malloc(needbytes); |
| 663 if (allocres==NULL) {status|=DEC_Insufficient_storage; break;} |
| 664 res=allocres; |
| 665 } |
| 666 } |
| 667 /* res now -> number lsu, buffer, or allocated storage for Unit array */ |
| 668 |
| 669 /* Place the coefficient into the selected Unit array */ |
| 670 /* [this is often 70% of the cost of this function when DECDPUN>1] */ |
| 671 #if DECDPUN>1 |
| 672 out=0; /* accumulator */ |
| 673 up=res+D2U(d)-1; /* -> msu */ |
| 674 cut=d-(up-res)*DECDPUN; /* digits in top unit */ |
| 675 for (c=cfirst;; c++) { /* along the digits */ |
| 676 if (*c=='.') continue; /* ignore '.' [don't decrement cut] */ |
| 677 out=X10(out)+(Int)*c-(Int)'0'; |
| 678 if (c==last) break; /* done [never get to trailing '.'] */ |
| 679 cut--; |
| 680 if (cut>0) continue; /* more for this unit */ |
| 681 *up=(Unit)out; /* write unit */ |
| 682 up--; /* prepare for unit below.. */ |
| 683 cut=DECDPUN; /* .. */ |
| 684 out=0; /* .. */ |
| 685 } /* c */ |
| 686 *up=(Unit)out; /* write lsu */ |
| 687 |
| 688 #else |
| 689 /* DECDPUN==1 */ |
| 690 up=res; /* -> lsu */ |
| 691 for (c=last; c>=cfirst; c--) { /* over each character, from least */ |
| 692 if (*c=='.') continue; /* ignore . [don't step up] */ |
| 693 *up=(Unit)((Int)*c-(Int)'0'); |
| 694 up++; |
| 695 } /* c */ |
| 696 #endif |
| 697 |
| 698 dn->bits=bits; |
| 699 dn->exponent=exponent; |
| 700 dn->digits=d; |
| 701 |
| 702 /* if not in number (too long) shorten into the number */ |
| 703 if (d>set->digits) { |
| 704 residue=0; |
| 705 decSetCoeff(dn, set, res, d, &residue, &status); |
| 706 /* always check for overflow or subnormal and round as needed */ |
| 707 decFinalize(dn, set, &residue, &status); |
| 708 } |
| 709 else { /* no rounding, but may still have overflow or subnormal */ |
| 710 /* [these tests are just for performance; finalize repeats them] */ |
| 711 if ((dn->exponent-1<set->emin-dn->digits) |
| 712 || (dn->exponent-1>set->emax-set->digits)) { |
| 713 residue=0; |
| 714 decFinalize(dn, set, &residue, &status); |
| 715 } |
| 716 } |
| 717 /* decNumberShow(dn); */ |
| 718 } while(0); /* [for break] */ |
| 719 |
| 720 if (allocres!=NULL) free(allocres); /* drop any storage used */ |
| 721 if (status!=0) decStatus(dn, status, set); |
| 722 return dn; |
| 723 } /* decNumberFromString */ |
| 724 |
| 725 /* ================================================================== */ |
| 726 /* Operators */ |
| 727 /* ================================================================== */ |
| 728 |
| 729 /* ------------------------------------------------------------------ */ |
| 730 /* decNumberAbs -- absolute value operator */ |
| 731 /* */ |
| 732 /* This computes C = abs(A) */ |
| 733 /* */ |
| 734 /* res is C, the result. C may be A */ |
| 735 /* rhs is A */ |
| 736 /* set is the context */ |
| 737 /* */ |
| 738 /* See also decNumberCopyAbs for a quiet bitwise version of this. */ |
| 739 /* C must have space for set->digits digits. */ |
| 740 /* ------------------------------------------------------------------ */ |
| 741 /* This has the same effect as decNumberPlus unless A is negative, */ |
| 742 /* in which case it has the same effect as decNumberMinus. */ |
| 743 /* ------------------------------------------------------------------ */ |
| 744 U_CAPI decNumber * U_EXPORT2 uprv_decNumberAbs(decNumber *res, const decNumber *
rhs, |
| 745 decContext *set) { |
| 746 decNumber dzero; /* for 0 */ |
| 747 uInt status=0; /* accumulator */ |
| 748 |
| 749 #if DECCHECK |
| 750 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
| 751 #endif |
| 752 |
| 753 uprv_decNumberZero(&dzero); /* set 0 */ |
| 754 dzero.exponent=rhs->exponent; /* [no coefficient expansion] */ |
| 755 decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status); |
| 756 if (status!=0) decStatus(res, status, set); |
| 757 #if DECCHECK |
| 758 decCheckInexact(res, set); |
| 759 #endif |
| 760 return res; |
| 761 } /* decNumberAbs */ |
| 762 |
| 763 /* ------------------------------------------------------------------ */ |
| 764 /* decNumberAdd -- add two Numbers */ |
| 765 /* */ |
| 766 /* This computes C = A + B */ |
| 767 /* */ |
| 768 /* res is C, the result. C may be A and/or B (e.g., X=X+X) */ |
| 769 /* lhs is A */ |
| 770 /* rhs is B */ |
| 771 /* set is the context */ |
| 772 /* */ |
| 773 /* C must have space for set->digits digits. */ |
| 774 /* ------------------------------------------------------------------ */ |
| 775 /* This just calls the routine shared with Subtract */ |
| 776 U_CAPI decNumber * U_EXPORT2 uprv_decNumberAdd(decNumber *res, const decNumber *
lhs, |
| 777 const decNumber *rhs, decContext *set) { |
| 778 uInt status=0; /* accumulator */ |
| 779 decAddOp(res, lhs, rhs, set, 0, &status); |
| 780 if (status!=0) decStatus(res, status, set); |
| 781 #if DECCHECK |
| 782 decCheckInexact(res, set); |
| 783 #endif |
| 784 return res; |
| 785 } /* decNumberAdd */ |
| 786 |
| 787 /* ------------------------------------------------------------------ */ |
| 788 /* decNumberAnd -- AND two Numbers, digitwise */ |
| 789 /* */ |
| 790 /* This computes C = A & B */ |
| 791 /* */ |
| 792 /* res is C, the result. C may be A and/or B (e.g., X=X&X) */ |
| 793 /* lhs is A */ |
| 794 /* rhs is B */ |
| 795 /* set is the context (used for result length and error report) */ |
| 796 /* */ |
| 797 /* C must have space for set->digits digits. */ |
| 798 /* */ |
| 799 /* Logical function restrictions apply (see above); a NaN is */ |
| 800 /* returned with Invalid_operation if a restriction is violated. */ |
| 801 /* ------------------------------------------------------------------ */ |
| 802 U_CAPI decNumber * U_EXPORT2 uprv_decNumberAnd(decNumber *res, const decNumber *
lhs, |
| 803 const decNumber *rhs, decContext *set) { |
| 804 const Unit *ua, *ub; /* -> operands */ |
| 805 const Unit *msua, *msub; /* -> operand msus */ |
| 806 Unit *uc, *msuc; /* -> result and its msu */ |
| 807 Int msudigs; /* digits in res msu */ |
| 808 #if DECCHECK |
| 809 if (decCheckOperands(res, lhs, rhs, set)) return res; |
| 810 #endif |
| 811 |
| 812 if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) |
| 813 || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { |
| 814 decStatus(res, DEC_Invalid_operation, set); |
| 815 return res; |
| 816 } |
| 817 |
| 818 /* operands are valid */ |
| 819 ua=lhs->lsu; /* bottom-up */ |
| 820 ub=rhs->lsu; /* .. */ |
| 821 uc=res->lsu; /* .. */ |
| 822 msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */ |
| 823 msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */ |
| 824 msuc=uc+D2U(set->digits)-1; /* -> msu of result */ |
| 825 msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ |
| 826 for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */ |
| 827 Unit a, b; /* extract units */ |
| 828 if (ua>msua) a=0; |
| 829 else a=*ua; |
| 830 if (ub>msub) b=0; |
| 831 else b=*ub; |
| 832 *uc=0; /* can now write back */ |
| 833 if (a|b) { /* maybe 1 bits to examine */ |
| 834 Int i, j; |
| 835 *uc=0; /* can now write back */ |
| 836 /* This loop could be unrolled and/or use BIN2BCD tables */ |
| 837 for (i=0; i<DECDPUN; i++) { |
| 838 if (a&b&1) *uc=*uc+(Unit)powers[i]; /* effect AND */ |
| 839 j=a%10; |
| 840 a=a/10; |
| 841 j|=b%10; |
| 842 b=b/10; |
| 843 if (j>1) { |
| 844 decStatus(res, DEC_Invalid_operation, set); |
| 845 return res; |
| 846 } |
| 847 if (uc==msuc && i==msudigs-1) break; /* just did final digit */ |
| 848 } /* each digit */ |
| 849 } /* both OK */ |
| 850 } /* each unit */ |
| 851 /* [here uc-1 is the msu of the result] */ |
| 852 res->digits=decGetDigits(res->lsu, uc-res->lsu); |
| 853 res->exponent=0; /* integer */ |
| 854 res->bits=0; /* sign=0 */ |
| 855 return res; /* [no status to set] */ |
| 856 } /* decNumberAnd */ |
| 857 |
| 858 /* ------------------------------------------------------------------ */ |
| 859 /* decNumberCompare -- compare two Numbers */ |
| 860 /* */ |
| 861 /* This computes C = A ? B */ |
| 862 /* */ |
| 863 /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ |
| 864 /* lhs is A */ |
| 865 /* rhs is B */ |
| 866 /* set is the context */ |
| 867 /* */ |
| 868 /* C must have space for one digit (or NaN). */ |
| 869 /* ------------------------------------------------------------------ */ |
| 870 U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompare(decNumber *res, const decNumb
er *lhs, |
| 871 const decNumber *rhs, decContext *set) { |
| 872 uInt status=0; /* accumulator */ |
| 873 decCompareOp(res, lhs, rhs, set, COMPARE, &status); |
| 874 if (status!=0) decStatus(res, status, set); |
| 875 return res; |
| 876 } /* decNumberCompare */ |
| 877 |
| 878 /* ------------------------------------------------------------------ */ |
| 879 /* decNumberCompareSignal -- compare, signalling on all NaNs */ |
| 880 /* */ |
| 881 /* This computes C = A ? B */ |
| 882 /* */ |
| 883 /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ |
| 884 /* lhs is A */ |
| 885 /* rhs is B */ |
| 886 /* set is the context */ |
| 887 /* */ |
| 888 /* C must have space for one digit (or NaN). */ |
| 889 /* ------------------------------------------------------------------ */ |
| 890 U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompareSignal(decNumber *res, const d
ecNumber *lhs, |
| 891 const decNumber *rhs, decContext *set) { |
| 892 uInt status=0; /* accumulator */ |
| 893 decCompareOp(res, lhs, rhs, set, COMPSIG, &status); |
| 894 if (status!=0) decStatus(res, status, set); |
| 895 return res; |
| 896 } /* decNumberCompareSignal */ |
| 897 |
| 898 /* ------------------------------------------------------------------ */ |
| 899 /* decNumberCompareTotal -- compare two Numbers, using total ordering */ |
| 900 /* */ |
| 901 /* This computes C = A ? B, under total ordering */ |
| 902 /* */ |
| 903 /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ |
| 904 /* lhs is A */ |
| 905 /* rhs is B */ |
| 906 /* set is the context */ |
| 907 /* */ |
| 908 /* C must have space for one digit; the result will always be one of */ |
| 909 /* -1, 0, or 1. */ |
| 910 /* ------------------------------------------------------------------ */ |
| 911 U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompareTotal(decNumber *res, const de
cNumber *lhs, |
| 912 const decNumber *rhs, decContext *set) { |
| 913 uInt status=0; /* accumulator */ |
| 914 decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status); |
| 915 if (status!=0) decStatus(res, status, set); |
| 916 return res; |
| 917 } /* decNumberCompareTotal */ |
| 918 |
| 919 /* ------------------------------------------------------------------ */ |
| 920 /* decNumberCompareTotalMag -- compare, total ordering of magnitudes */ |
| 921 /* */ |
| 922 /* This computes C = |A| ? |B|, under total ordering */ |
| 923 /* */ |
| 924 /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ |
| 925 /* lhs is A */ |
| 926 /* rhs is B */ |
| 927 /* set is the context */ |
| 928 /* */ |
| 929 /* C must have space for one digit; the result will always be one of */ |
| 930 /* -1, 0, or 1. */ |
| 931 /* ------------------------------------------------------------------ */ |
| 932 U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompareTotalMag(decNumber *res, const
decNumber *lhs, |
| 933 const decNumber *rhs, decContext *set) { |
| 934 uInt status=0; /* accumulator */ |
| 935 uInt needbytes; /* for space calculations */ |
| 936 decNumber bufa[D2N(DECBUFFER+1)];/* +1 in case DECBUFFER=0 */ |
| 937 decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ |
| 938 decNumber bufb[D2N(DECBUFFER+1)]; |
| 939 decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */ |
| 940 decNumber *a, *b; /* temporary pointers */ |
| 941 |
| 942 #if DECCHECK |
| 943 if (decCheckOperands(res, lhs, rhs, set)) return res; |
| 944 #endif |
| 945 |
| 946 do { /* protect allocated storage */ |
| 947 /* if either is negative, take a copy and absolute */ |
| 948 if (decNumberIsNegative(lhs)) { /* lhs<0 */ |
| 949 a=bufa; |
| 950 needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit); |
| 951 if (needbytes>sizeof(bufa)) { /* need malloc space */ |
| 952 allocbufa=(decNumber *)malloc(needbytes); |
| 953 if (allocbufa==NULL) { /* hopeless -- abandon */ |
| 954 status|=DEC_Insufficient_storage; |
| 955 break;} |
| 956 a=allocbufa; /* use the allocated space */ |
| 957 } |
| 958 uprv_decNumberCopy(a, lhs); /* copy content */ |
| 959 a->bits&=~DECNEG; /* .. and clear the sign */ |
| 960 lhs=a; /* use copy from here on */ |
| 961 } |
| 962 if (decNumberIsNegative(rhs)) { /* rhs<0 */ |
| 963 b=bufb; |
| 964 needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); |
| 965 if (needbytes>sizeof(bufb)) { /* need malloc space */ |
| 966 allocbufb=(decNumber *)malloc(needbytes); |
| 967 if (allocbufb==NULL) { /* hopeless -- abandon */ |
| 968 status|=DEC_Insufficient_storage; |
| 969 break;} |
| 970 b=allocbufb; /* use the allocated space */ |
| 971 } |
| 972 uprv_decNumberCopy(b, rhs); /* copy content */ |
| 973 b->bits&=~DECNEG; /* .. and clear the sign */ |
| 974 rhs=b; /* use copy from here on */ |
| 975 } |
| 976 decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status); |
| 977 } while(0); /* end protected */ |
| 978 |
| 979 if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ |
| 980 if (allocbufb!=NULL) free(allocbufb); /* .. */ |
| 981 if (status!=0) decStatus(res, status, set); |
| 982 return res; |
| 983 } /* decNumberCompareTotalMag */ |
| 984 |
| 985 /* ------------------------------------------------------------------ */ |
| 986 /* decNumberDivide -- divide one number by another */ |
| 987 /* */ |
| 988 /* This computes C = A / B */ |
| 989 /* */ |
| 990 /* res is C, the result. C may be A and/or B (e.g., X=X/X) */ |
| 991 /* lhs is A */ |
| 992 /* rhs is B */ |
| 993 /* set is the context */ |
| 994 /* */ |
| 995 /* C must have space for set->digits digits. */ |
| 996 /* ------------------------------------------------------------------ */ |
| 997 U_CAPI decNumber * U_EXPORT2 uprv_decNumberDivide(decNumber *res, const decNumbe
r *lhs, |
| 998 const decNumber *rhs, decContext *set) { |
| 999 uInt status=0; /* accumulator */ |
| 1000 decDivideOp(res, lhs, rhs, set, DIVIDE, &status); |
| 1001 if (status!=0) decStatus(res, status, set); |
| 1002 #if DECCHECK |
| 1003 decCheckInexact(res, set); |
| 1004 #endif |
| 1005 return res; |
| 1006 } /* decNumberDivide */ |
| 1007 |
| 1008 /* ------------------------------------------------------------------ */ |
| 1009 /* decNumberDivideInteger -- divide and return integer quotient */ |
| 1010 /* */ |
| 1011 /* This computes C = A # B, where # is the integer divide operator */ |
| 1012 /* */ |
| 1013 /* res is C, the result. C may be A and/or B (e.g., X=X#X) */ |
| 1014 /* lhs is A */ |
| 1015 /* rhs is B */ |
| 1016 /* set is the context */ |
| 1017 /* */ |
| 1018 /* C must have space for set->digits digits. */ |
| 1019 /* ------------------------------------------------------------------ */ |
| 1020 U_CAPI decNumber * U_EXPORT2 uprv_decNumberDivideInteger(decNumber *res, const d
ecNumber *lhs, |
| 1021 const decNumber *rhs, decContext *set) { |
| 1022 uInt status=0; /* accumulator */ |
| 1023 decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status); |
| 1024 if (status!=0) decStatus(res, status, set); |
| 1025 return res; |
| 1026 } /* decNumberDivideInteger */ |
| 1027 |
| 1028 /* ------------------------------------------------------------------ */ |
| 1029 /* decNumberExp -- exponentiation */ |
| 1030 /* */ |
| 1031 /* This computes C = exp(A) */ |
| 1032 /* */ |
| 1033 /* res is C, the result. C may be A */ |
| 1034 /* rhs is A */ |
| 1035 /* set is the context; note that rounding mode has no effect */ |
| 1036 /* */ |
| 1037 /* C must have space for set->digits digits. */ |
| 1038 /* */ |
| 1039 /* Mathematical function restrictions apply (see above); a NaN is */ |
| 1040 /* returned with Invalid_operation if a restriction is violated. */ |
| 1041 /* */ |
| 1042 /* Finite results will always be full precision and Inexact, except */ |
| 1043 /* when A is a zero or -Infinity (giving 1 or 0 respectively). */ |
| 1044 /* */ |
| 1045 /* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ |
| 1046 /* almost always be correctly rounded, but may be up to 1 ulp in */ |
| 1047 /* error in rare cases. */ |
| 1048 /* ------------------------------------------------------------------ */ |
| 1049 /* This is a wrapper for decExpOp which can handle the slightly wider */ |
| 1050 /* (double) range needed by Ln (which has to be able to calculate */ |
| 1051 /* exp(-a) where a can be the tiniest number (Ntiny). */ |
| 1052 /* ------------------------------------------------------------------ */ |
| 1053 U_CAPI decNumber * U_EXPORT2 uprv_decNumberExp(decNumber *res, const decNumber *
rhs, |
| 1054 decContext *set) { |
| 1055 uInt status=0; /* accumulator */ |
| 1056 #if DECSUBSET |
| 1057 decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ |
| 1058 #endif |
| 1059 |
| 1060 #if DECCHECK |
| 1061 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
| 1062 #endif |
| 1063 |
| 1064 /* Check restrictions; these restrictions ensure that if h=8 (see */ |
| 1065 /* decExpOp) then the result will either overflow or underflow to 0. */ |
| 1066 /* Other math functions restrict the input range, too, for inverses. */ |
| 1067 /* If not violated then carry out the operation. */ |
| 1068 if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */ |
| 1069 #if DECSUBSET |
| 1070 if (!set->extended) { |
| 1071 /* reduce operand and set lostDigits status, as needed */ |
| 1072 if (rhs->digits>set->digits) { |
| 1073 allocrhs=decRoundOperand(rhs, set, &status); |
| 1074 if (allocrhs==NULL) break; |
| 1075 rhs=allocrhs; |
| 1076 } |
| 1077 } |
| 1078 #endif |
| 1079 decExpOp(res, rhs, set, &status); |
| 1080 } while(0); /* end protected */ |
| 1081 |
| 1082 #if DECSUBSET |
| 1083 if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */ |
| 1084 #endif |
| 1085 /* apply significant status */ |
| 1086 if (status!=0) decStatus(res, status, set); |
| 1087 #if DECCHECK |
| 1088 decCheckInexact(res, set); |
| 1089 #endif |
| 1090 return res; |
| 1091 } /* decNumberExp */ |
| 1092 |
| 1093 /* ------------------------------------------------------------------ */ |
| 1094 /* decNumberFMA -- fused multiply add */ |
| 1095 /* */ |
| 1096 /* This computes D = (A * B) + C with only one rounding */ |
| 1097 /* */ |
| 1098 /* res is D, the result. D may be A or B or C (e.g., X=FMA(X,X,X)) */ |
| 1099 /* lhs is A */ |
| 1100 /* rhs is B */ |
| 1101 /* fhs is C [far hand side] */ |
| 1102 /* set is the context */ |
| 1103 /* */ |
| 1104 /* Mathematical function restrictions apply (see above); a NaN is */ |
| 1105 /* returned with Invalid_operation if a restriction is violated. */ |
| 1106 /* */ |
| 1107 /* C must have space for set->digits digits. */ |
| 1108 /* ------------------------------------------------------------------ */ |
| 1109 U_CAPI decNumber * U_EXPORT2 uprv_decNumberFMA(decNumber *res, const decNumber *
lhs, |
| 1110 const decNumber *rhs, const decNumber *fhs, |
| 1111 decContext *set) { |
| 1112 uInt status=0; /* accumulator */ |
| 1113 decContext dcmul; /* context for the multiplication */ |
| 1114 uInt needbytes; /* for space calculations */ |
| 1115 decNumber bufa[D2N(DECBUFFER*2+1)]; |
| 1116 decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ |
| 1117 decNumber *acc; /* accumulator pointer */ |
| 1118 decNumber dzero; /* work */ |
| 1119 |
| 1120 #if DECCHECK |
| 1121 if (decCheckOperands(res, lhs, rhs, set)) return res; |
| 1122 if (decCheckOperands(res, fhs, DECUNUSED, set)) return res; |
| 1123 #endif |
| 1124 |
| 1125 do { /* protect allocated storage */ |
| 1126 #if DECSUBSET |
| 1127 if (!set->extended) { /* [undefined if subset] */ |
| 1128 status|=DEC_Invalid_operation; |
| 1129 break;} |
| 1130 #endif |
| 1131 /* Check math restrictions [these ensure no overflow or underflow] */ |
| 1132 if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status)) |
| 1133 || (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status)) |
| 1134 || (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break; |
| 1135 /* set up context for multiply */ |
| 1136 dcmul=*set; |
| 1137 dcmul.digits=lhs->digits+rhs->digits; /* just enough */ |
| 1138 /* [The above may be an over-estimate for subset arithmetic, but that's OK]
*/ |
| 1139 dcmul.emax=DEC_MAX_EMAX; /* effectively unbounded .. */ |
| 1140 dcmul.emin=DEC_MIN_EMIN; /* [thanks to Math restrictions] */ |
| 1141 /* set up decNumber space to receive the result of the multiply */ |
| 1142 acc=bufa; /* may fit */ |
| 1143 needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit); |
| 1144 if (needbytes>sizeof(bufa)) { /* need malloc space */ |
| 1145 allocbufa=(decNumber *)malloc(needbytes); |
| 1146 if (allocbufa==NULL) { /* hopeless -- abandon */ |
| 1147 status|=DEC_Insufficient_storage; |
| 1148 break;} |
| 1149 acc=allocbufa; /* use the allocated space */ |
| 1150 } |
| 1151 /* multiply with extended range and necessary precision */ |
| 1152 /*printf("emin=%ld\n", dcmul.emin); */ |
| 1153 decMultiplyOp(acc, lhs, rhs, &dcmul, &status); |
| 1154 /* Only Invalid operation (from sNaN or Inf * 0) is possible in */ |
| 1155 /* status; if either is seen than ignore fhs (in case it is */ |
| 1156 /* another sNaN) and set acc to NaN unless we had an sNaN */ |
| 1157 /* [decMultiplyOp leaves that to caller] */ |
| 1158 /* Note sNaN has to go through addOp to shorten payload if */ |
| 1159 /* necessary */ |
| 1160 if ((status&DEC_Invalid_operation)!=0) { |
| 1161 if (!(status&DEC_sNaN)) { /* but be true invalid */ |
| 1162 uprv_decNumberZero(res); /* acc not yet set */ |
| 1163 res->bits=DECNAN; |
| 1164 break; |
| 1165 } |
| 1166 uprv_decNumberZero(&dzero); /* make 0 (any non-NaN would do) *
/ |
| 1167 fhs=&dzero; /* use that */ |
| 1168 } |
| 1169 #if DECCHECK |
| 1170 else { /* multiply was OK */ |
| 1171 if (status!=0) printf("Status=%08lx after FMA multiply\n", (LI)status); |
| 1172 } |
| 1173 #endif |
| 1174 /* add the third operand and result -> res, and all is done */ |
| 1175 decAddOp(res, acc, fhs, set, 0, &status); |
| 1176 } while(0); /* end protected */ |
| 1177 |
| 1178 if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ |
| 1179 if (status!=0) decStatus(res, status, set); |
| 1180 #if DECCHECK |
| 1181 decCheckInexact(res, set); |
| 1182 #endif |
| 1183 return res; |
| 1184 } /* decNumberFMA */ |
| 1185 |
| 1186 /* ------------------------------------------------------------------ */ |
| 1187 /* decNumberInvert -- invert a Number, digitwise */ |
| 1188 /* */ |
| 1189 /* This computes C = ~A */ |
| 1190 /* */ |
| 1191 /* res is C, the result. C may be A (e.g., X=~X) */ |
| 1192 /* rhs is A */ |
| 1193 /* set is the context (used for result length and error report) */ |
| 1194 /* */ |
| 1195 /* C must have space for set->digits digits. */ |
| 1196 /* */ |
| 1197 /* Logical function restrictions apply (see above); a NaN is */ |
| 1198 /* returned with Invalid_operation if a restriction is violated. */ |
| 1199 /* ------------------------------------------------------------------ */ |
| 1200 U_CAPI decNumber * U_EXPORT2 uprv_decNumberInvert(decNumber *res, const decNumbe
r *rhs, |
| 1201 decContext *set) { |
| 1202 const Unit *ua, *msua; /* -> operand and its msu */ |
| 1203 Unit *uc, *msuc; /* -> result and its msu */ |
| 1204 Int msudigs; /* digits in res msu */ |
| 1205 #if DECCHECK |
| 1206 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
| 1207 #endif |
| 1208 |
| 1209 if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { |
| 1210 decStatus(res, DEC_Invalid_operation, set); |
| 1211 return res; |
| 1212 } |
| 1213 /* operand is valid */ |
| 1214 ua=rhs->lsu; /* bottom-up */ |
| 1215 uc=res->lsu; /* .. */ |
| 1216 msua=ua+D2U(rhs->digits)-1; /* -> msu of rhs */ |
| 1217 msuc=uc+D2U(set->digits)-1; /* -> msu of result */ |
| 1218 msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ |
| 1219 for (; uc<=msuc; ua++, uc++) { /* Unit loop */ |
| 1220 Unit a; /* extract unit */ |
| 1221 Int i, j; /* work */ |
| 1222 if (ua>msua) a=0; |
| 1223 else a=*ua; |
| 1224 *uc=0; /* can now write back */ |
| 1225 /* always need to examine all bits in rhs */ |
| 1226 /* This loop could be unrolled and/or use BIN2BCD tables */ |
| 1227 for (i=0; i<DECDPUN; i++) { |
| 1228 if ((~a)&1) *uc=*uc+(Unit)powers[i]; /* effect INVERT */ |
| 1229 j=a%10; |
| 1230 a=a/10; |
| 1231 if (j>1) { |
| 1232 decStatus(res, DEC_Invalid_operation, set); |
| 1233 return res; |
| 1234 } |
| 1235 if (uc==msuc && i==msudigs-1) break; /* just did final digit */ |
| 1236 } /* each digit */ |
| 1237 } /* each unit */ |
| 1238 /* [here uc-1 is the msu of the result] */ |
| 1239 res->digits=decGetDigits(res->lsu, uc-res->lsu); |
| 1240 res->exponent=0; /* integer */ |
| 1241 res->bits=0; /* sign=0 */ |
| 1242 return res; /* [no status to set] */ |
| 1243 } /* decNumberInvert */ |
| 1244 |
| 1245 /* ------------------------------------------------------------------ */ |
| 1246 /* decNumberLn -- natural logarithm */ |
| 1247 /* */ |
| 1248 /* This computes C = ln(A) */ |
| 1249 /* */ |
| 1250 /* res is C, the result. C may be A */ |
| 1251 /* rhs is A */ |
| 1252 /* set is the context; note that rounding mode has no effect */ |
| 1253 /* */ |
| 1254 /* C must have space for set->digits digits. */ |
| 1255 /* */ |
| 1256 /* Notable cases: */ |
| 1257 /* A<0 -> Invalid */ |
| 1258 /* A=0 -> -Infinity (Exact) */ |
| 1259 /* A=+Infinity -> +Infinity (Exact) */ |
| 1260 /* A=1 exactly -> 0 (Exact) */ |
| 1261 /* */ |
| 1262 /* Mathematical function restrictions apply (see above); a NaN is */ |
| 1263 /* returned with Invalid_operation if a restriction is violated. */ |
| 1264 /* */ |
| 1265 /* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ |
| 1266 /* almost always be correctly rounded, but may be up to 1 ulp in */ |
| 1267 /* error in rare cases. */ |
| 1268 /* ------------------------------------------------------------------ */ |
| 1269 /* This is a wrapper for decLnOp which can handle the slightly wider */ |
| 1270 /* (+11) range needed by Ln, Log10, etc. (which may have to be able */ |
| 1271 /* to calculate at p+e+2). */ |
| 1272 /* ------------------------------------------------------------------ */ |
| 1273 U_CAPI decNumber * U_EXPORT2 uprv_decNumberLn(decNumber *res, const decNumber *r
hs, |
| 1274 decContext *set) { |
| 1275 uInt status=0; /* accumulator */ |
| 1276 #if DECSUBSET |
| 1277 decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ |
| 1278 #endif |
| 1279 |
| 1280 #if DECCHECK |
| 1281 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
| 1282 #endif |
| 1283 |
| 1284 /* Check restrictions; this is a math function; if not violated */ |
| 1285 /* then carry out the operation. */ |
| 1286 if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */ |
| 1287 #if DECSUBSET |
| 1288 if (!set->extended) { |
| 1289 /* reduce operand and set lostDigits status, as needed */ |
| 1290 if (rhs->digits>set->digits) { |
| 1291 allocrhs=decRoundOperand(rhs, set, &status); |
| 1292 if (allocrhs==NULL) break; |
| 1293 rhs=allocrhs; |
| 1294 } |
| 1295 /* special check in subset for rhs=0 */ |
| 1296 if (ISZERO(rhs)) { /* +/- zeros -> error */ |
| 1297 status|=DEC_Invalid_operation; |
| 1298 break;} |
| 1299 } /* extended=0 */ |
| 1300 #endif |
| 1301 decLnOp(res, rhs, set, &status); |
| 1302 } while(0); /* end protected */ |
| 1303 |
| 1304 #if DECSUBSET |
| 1305 if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */ |
| 1306 #endif |
| 1307 /* apply significant status */ |
| 1308 if (status!=0) decStatus(res, status, set); |
| 1309 #if DECCHECK |
| 1310 decCheckInexact(res, set); |
| 1311 #endif |
| 1312 return res; |
| 1313 } /* decNumberLn */ |
| 1314 |
| 1315 /* ------------------------------------------------------------------ */ |
| 1316 /* decNumberLogB - get adjusted exponent, by 754 rules */ |
| 1317 /* */ |
| 1318 /* This computes C = adjustedexponent(A) */ |
| 1319 /* */ |
| 1320 /* res is C, the result. C may be A */ |
| 1321 /* rhs is A */ |
| 1322 /* set is the context, used only for digits and status */ |
| 1323 /* */ |
| 1324 /* C must have space for 10 digits (A might have 10**9 digits and */ |
| 1325 /* an exponent of +999999999, or one digit and an exponent of */ |
| 1326 /* -1999999999). */ |
| 1327 /* */ |
| 1328 /* This returns the adjusted exponent of A after (in theory) padding */ |
| 1329 /* with zeros on the right to set->digits digits while keeping the */ |
| 1330 /* same value. The exponent is not limited by emin/emax. */ |
| 1331 /* */ |
| 1332 /* Notable cases: */ |
| 1333 /* A<0 -> Use |A| */ |
| 1334 /* A=0 -> -Infinity (Division by zero) */ |
| 1335 /* A=Infinite -> +Infinity (Exact) */ |
| 1336 /* A=1 exactly -> 0 (Exact) */ |
| 1337 /* NaNs are propagated as usual */ |
| 1338 /* ------------------------------------------------------------------ */ |
| 1339 U_CAPI decNumber * U_EXPORT2 uprv_decNumberLogB(decNumber *res, const decNumber
*rhs, |
| 1340 decContext *set) { |
| 1341 uInt status=0; /* accumulator */ |
| 1342 |
| 1343 #if DECCHECK |
| 1344 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
| 1345 #endif |
| 1346 |
| 1347 /* NaNs as usual; Infinities return +Infinity; 0->oops */ |
| 1348 if (decNumberIsNaN(rhs)) decNaNs(res, rhs, NULL, set, &status); |
| 1349 else if (decNumberIsInfinite(rhs)) uprv_decNumberCopyAbs(res, rhs); |
| 1350 else if (decNumberIsZero(rhs)) { |
| 1351 uprv_decNumberZero(res); /* prepare for Infinity */ |
| 1352 res->bits=DECNEG|DECINF; /* -Infinity */ |
| 1353 status|=DEC_Division_by_zero; /* as per 754 */ |
| 1354 } |
| 1355 else { /* finite non-zero */ |
| 1356 Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */ |
| 1357 uprv_decNumberFromInt32(res, ae); /* lay it out */ |
| 1358 } |
| 1359 |
| 1360 if (status!=0) decStatus(res, status, set); |
| 1361 return res; |
| 1362 } /* decNumberLogB */ |
| 1363 |
| 1364 /* ------------------------------------------------------------------ */ |
| 1365 /* decNumberLog10 -- logarithm in base 10 */ |
| 1366 /* */ |
| 1367 /* This computes C = log10(A) */ |
| 1368 /* */ |
| 1369 /* res is C, the result. C may be A */ |
| 1370 /* rhs is A */ |
| 1371 /* set is the context; note that rounding mode has no effect */ |
| 1372 /* */ |
| 1373 /* C must have space for set->digits digits. */ |
| 1374 /* */ |
| 1375 /* Notable cases: */ |
| 1376 /* A<0 -> Invalid */ |
| 1377 /* A=0 -> -Infinity (Exact) */ |
| 1378 /* A=+Infinity -> +Infinity (Exact) */ |
| 1379 /* A=10**n (if n is an integer) -> n (Exact) */ |
| 1380 /* */ |
| 1381 /* Mathematical function restrictions apply (see above); a NaN is */ |
| 1382 /* returned with Invalid_operation if a restriction is violated. */ |
| 1383 /* */ |
| 1384 /* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ |
| 1385 /* almost always be correctly rounded, but may be up to 1 ulp in */ |
| 1386 /* error in rare cases. */ |
| 1387 /* ------------------------------------------------------------------ */ |
| 1388 /* This calculates ln(A)/ln(10) using appropriate precision. For */ |
| 1389 /* ln(A) this is the max(p, rhs->digits + t) + 3, where p is the */ |
| 1390 /* requested digits and t is the number of digits in the exponent */ |
| 1391 /* (maximum 6). For ln(10) it is p + 3; this is often handled by the */ |
| 1392 /* fastpath in decLnOp. The final division is done to the requested */ |
| 1393 /* precision. */ |
| 1394 /* ------------------------------------------------------------------ */ |
| 1395 U_CAPI decNumber * U_EXPORT2 uprv_decNumberLog10(decNumber *res, const decNumber
*rhs, |
| 1396 decContext *set) { |
| 1397 uInt status=0, ignore=0; /* status accumulators */ |
| 1398 uInt needbytes; /* for space calculations */ |
| 1399 Int p; /* working precision */ |
| 1400 Int t; /* digits in exponent of A */ |
| 1401 |
| 1402 /* buffers for a and b working decimals */ |
| 1403 /* (adjustment calculator, same size) */ |
| 1404 decNumber bufa[D2N(DECBUFFER+2)]; |
| 1405 decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ |
| 1406 decNumber *a=bufa; /* temporary a */ |
| 1407 decNumber bufb[D2N(DECBUFFER+2)]; |
| 1408 decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */ |
| 1409 decNumber *b=bufb; /* temporary b */ |
| 1410 decNumber bufw[D2N(10)]; /* working 2-10 digit number */ |
| 1411 decNumber *w=bufw; /* .. */ |
| 1412 #if DECSUBSET |
| 1413 decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ |
| 1414 #endif |
| 1415 |
| 1416 decContext aset; /* working context */ |
| 1417 |
| 1418 #if DECCHECK |
| 1419 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
| 1420 #endif |
| 1421 |
| 1422 /* Check restrictions; this is a math function; if not violated */ |
| 1423 /* then carry out the operation. */ |
| 1424 if (!decCheckMath(rhs, set, &status)) do { /* protect malloc */ |
| 1425 #if DECSUBSET |
| 1426 if (!set->extended) { |
| 1427 /* reduce operand and set lostDigits status, as needed */ |
| 1428 if (rhs->digits>set->digits) { |
| 1429 allocrhs=decRoundOperand(rhs, set, &status); |
| 1430 if (allocrhs==NULL) break; |
| 1431 rhs=allocrhs; |
| 1432 } |
| 1433 /* special check in subset for rhs=0 */ |
| 1434 if (ISZERO(rhs)) { /* +/- zeros -> error */ |
| 1435 status|=DEC_Invalid_operation; |
| 1436 break;} |
| 1437 } /* extended=0 */ |
| 1438 #endif |
| 1439 |
| 1440 uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */ |
| 1441 |
| 1442 /* handle exact powers of 10; only check if +ve finite */ |
| 1443 if (!(rhs->bits&(DECNEG|DECSPECIAL)) && !ISZERO(rhs)) { |
| 1444 Int residue=0; /* (no residue) */ |
| 1445 uInt copystat=0; /* clean status */ |
| 1446 |
| 1447 /* round to a single digit... */ |
| 1448 aset.digits=1; |
| 1449 decCopyFit(w, rhs, &aset, &residue, ©stat); /* copy & shorten */ |
| 1450 /* if exact and the digit is 1, rhs is a power of 10 */ |
| 1451 if (!(copystat&DEC_Inexact) && w->lsu[0]==1) { |
| 1452 /* the exponent, conveniently, is the power of 10; making */ |
| 1453 /* this the result needs a little care as it might not fit, */ |
| 1454 /* so first convert it into the working number, and then move */ |
| 1455 /* to res */ |
| 1456 uprv_decNumberFromInt32(w, w->exponent); |
| 1457 residue=0; |
| 1458 decCopyFit(res, w, set, &residue, &status); /* copy & round */ |
| 1459 decFinish(res, set, &residue, &status); /* cleanup/set flags */ |
| 1460 break; |
| 1461 } /* not a power of 10 */ |
| 1462 } /* not a candidate for exact */ |
| 1463 |
| 1464 /* simplify the information-content calculation to use 'total */ |
| 1465 /* number of digits in a, including exponent' as compared to the */ |
| 1466 /* requested digits, as increasing this will only rarely cost an */ |
| 1467 /* iteration in ln(a) anyway */ |
| 1468 t=6; /* it can never be >6 */ |
| 1469 |
| 1470 /* allocate space when needed... */ |
| 1471 p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3; |
| 1472 needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit); |
| 1473 if (needbytes>sizeof(bufa)) { /* need malloc space */ |
| 1474 allocbufa=(decNumber *)malloc(needbytes); |
| 1475 if (allocbufa==NULL) { /* hopeless -- abandon */ |
| 1476 status|=DEC_Insufficient_storage; |
| 1477 break;} |
| 1478 a=allocbufa; /* use the allocated space */ |
| 1479 } |
| 1480 aset.digits=p; /* as calculated */ |
| 1481 aset.emax=DEC_MAX_MATH; /* usual bounds */ |
| 1482 aset.emin=-DEC_MAX_MATH; /* .. */ |
| 1483 aset.clamp=0; /* and no concrete format */ |
| 1484 decLnOp(a, rhs, &aset, &status); /* a=ln(rhs) */ |
| 1485 |
| 1486 /* skip the division if the result so far is infinite, NaN, or */ |
| 1487 /* zero, or there was an error; note NaN from sNaN needs copy */ |
| 1488 if (status&DEC_NaNs && !(status&DEC_sNaN)) break; |
| 1489 if (a->bits&DECSPECIAL || ISZERO(a)) { |
| 1490 uprv_decNumberCopy(res, a); /* [will fit] */ |
| 1491 break;} |
| 1492 |
| 1493 /* for ln(10) an extra 3 digits of precision are needed */ |
| 1494 p=set->digits+3; |
| 1495 needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit); |
| 1496 if (needbytes>sizeof(bufb)) { /* need malloc space */ |
| 1497 allocbufb=(decNumber *)malloc(needbytes); |
| 1498 if (allocbufb==NULL) { /* hopeless -- abandon */ |
| 1499 status|=DEC_Insufficient_storage; |
| 1500 break;} |
| 1501 b=allocbufb; /* use the allocated space */ |
| 1502 } |
| 1503 uprv_decNumberZero(w); /* set up 10... */ |
| 1504 #if DECDPUN==1 |
| 1505 w->lsu[1]=1; w->lsu[0]=0; /* .. */ |
| 1506 #else |
| 1507 w->lsu[0]=10; /* .. */ |
| 1508 #endif |
| 1509 w->digits=2; /* .. */ |
| 1510 |
| 1511 aset.digits=p; |
| 1512 decLnOp(b, w, &aset, &ignore); /* b=ln(10) */ |
| 1513 |
| 1514 aset.digits=set->digits; /* for final divide */ |
| 1515 decDivideOp(res, a, b, &aset, DIVIDE, &status); /* into result */ |
| 1516 } while(0); /* [for break] */ |
| 1517 |
| 1518 if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ |
| 1519 if (allocbufb!=NULL) free(allocbufb); /* .. */ |
| 1520 #if DECSUBSET |
| 1521 if (allocrhs !=NULL) free(allocrhs); /* .. */ |
| 1522 #endif |
| 1523 /* apply significant status */ |
| 1524 if (status!=0) decStatus(res, status, set); |
| 1525 #if DECCHECK |
| 1526 decCheckInexact(res, set); |
| 1527 #endif |
| 1528 return res; |
| 1529 } /* decNumberLog10 */ |
| 1530 |
| 1531 /* ------------------------------------------------------------------ */ |
| 1532 /* decNumberMax -- compare two Numbers and return the maximum */ |
| 1533 /* */ |
| 1534 /* This computes C = A ? B, returning the maximum by 754 rules */ |
| 1535 /* */ |
| 1536 /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ |
| 1537 /* lhs is A */ |
| 1538 /* rhs is B */ |
| 1539 /* set is the context */ |
| 1540 /* */ |
| 1541 /* C must have space for set->digits digits. */ |
| 1542 /* ------------------------------------------------------------------ */ |
| 1543 U_CAPI decNumber * U_EXPORT2 uprv_decNumberMax(decNumber *res, const decNumber *
lhs, |
| 1544 const decNumber *rhs, decContext *set) { |
| 1545 uInt status=0; /* accumulator */ |
| 1546 decCompareOp(res, lhs, rhs, set, COMPMAX, &status); |
| 1547 if (status!=0) decStatus(res, status, set); |
| 1548 #if DECCHECK |
| 1549 decCheckInexact(res, set); |
| 1550 #endif |
| 1551 return res; |
| 1552 } /* decNumberMax */ |
| 1553 |
| 1554 /* ------------------------------------------------------------------ */ |
| 1555 /* decNumberMaxMag -- compare and return the maximum by magnitude */ |
| 1556 /* */ |
| 1557 /* This computes C = A ? B, returning the maximum by 754 rules */ |
| 1558 /* */ |
| 1559 /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ |
| 1560 /* lhs is A */ |
| 1561 /* rhs is B */ |
| 1562 /* set is the context */ |
| 1563 /* */ |
| 1564 /* C must have space for set->digits digits. */ |
| 1565 /* ------------------------------------------------------------------ */ |
| 1566 U_CAPI decNumber * U_EXPORT2 uprv_decNumberMaxMag(decNumber *res, const decNumbe
r *lhs, |
| 1567 const decNumber *rhs, decContext *set) { |
| 1568 uInt status=0; /* accumulator */ |
| 1569 decCompareOp(res, lhs, rhs, set, COMPMAXMAG, &status); |
| 1570 if (status!=0) decStatus(res, status, set); |
| 1571 #if DECCHECK |
| 1572 decCheckInexact(res, set); |
| 1573 #endif |
| 1574 return res; |
| 1575 } /* decNumberMaxMag */ |
| 1576 |
| 1577 /* ------------------------------------------------------------------ */ |
| 1578 /* decNumberMin -- compare two Numbers and return the minimum */ |
| 1579 /* */ |
| 1580 /* This computes C = A ? B, returning the minimum by 754 rules */ |
| 1581 /* */ |
| 1582 /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ |
| 1583 /* lhs is A */ |
| 1584 /* rhs is B */ |
| 1585 /* set is the context */ |
| 1586 /* */ |
| 1587 /* C must have space for set->digits digits. */ |
| 1588 /* ------------------------------------------------------------------ */ |
| 1589 U_CAPI decNumber * U_EXPORT2 uprv_decNumberMin(decNumber *res, const decNumber *
lhs, |
| 1590 const decNumber *rhs, decContext *set) { |
| 1591 uInt status=0; /* accumulator */ |
| 1592 decCompareOp(res, lhs, rhs, set, COMPMIN, &status); |
| 1593 if (status!=0) decStatus(res, status, set); |
| 1594 #if DECCHECK |
| 1595 decCheckInexact(res, set); |
| 1596 #endif |
| 1597 return res; |
| 1598 } /* decNumberMin */ |
| 1599 |
| 1600 /* ------------------------------------------------------------------ */ |
| 1601 /* decNumberMinMag -- compare and return the minimum by magnitude */ |
| 1602 /* */ |
| 1603 /* This computes C = A ? B, returning the minimum by 754 rules */ |
| 1604 /* */ |
| 1605 /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ |
| 1606 /* lhs is A */ |
| 1607 /* rhs is B */ |
| 1608 /* set is the context */ |
| 1609 /* */ |
| 1610 /* C must have space for set->digits digits. */ |
| 1611 /* ------------------------------------------------------------------ */ |
| 1612 U_CAPI decNumber * U_EXPORT2 uprv_decNumberMinMag(decNumber *res, const decNumbe
r *lhs, |
| 1613 const decNumber *rhs, decContext *set) { |
| 1614 uInt status=0; /* accumulator */ |
| 1615 decCompareOp(res, lhs, rhs, set, COMPMINMAG, &status); |
| 1616 if (status!=0) decStatus(res, status, set); |
| 1617 #if DECCHECK |
| 1618 decCheckInexact(res, set); |
| 1619 #endif |
| 1620 return res; |
| 1621 } /* decNumberMinMag */ |
| 1622 |
| 1623 /* ------------------------------------------------------------------ */ |
| 1624 /* decNumberMinus -- prefix minus operator */ |
| 1625 /* */ |
| 1626 /* This computes C = 0 - A */ |
| 1627 /* */ |
| 1628 /* res is C, the result. C may be A */ |
| 1629 /* rhs is A */ |
| 1630 /* set is the context */ |
| 1631 /* */ |
| 1632 /* See also decNumberCopyNegate for a quiet bitwise version of this. */ |
| 1633 /* C must have space for set->digits digits. */ |
| 1634 /* ------------------------------------------------------------------ */ |
| 1635 /* Simply use AddOp for the subtract, which will do the necessary. */ |
| 1636 /* ------------------------------------------------------------------ */ |
| 1637 U_CAPI decNumber * U_EXPORT2 uprv_decNumberMinus(decNumber *res, const decNumber
*rhs, |
| 1638 decContext *set) { |
| 1639 decNumber dzero; |
| 1640 uInt status=0; /* accumulator */ |
| 1641 |
| 1642 #if DECCHECK |
| 1643 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
| 1644 #endif |
| 1645 |
| 1646 uprv_decNumberZero(&dzero); /* make 0 */ |
| 1647 dzero.exponent=rhs->exponent; /* [no coefficient expansion] */ |
| 1648 decAddOp(res, &dzero, rhs, set, DECNEG, &status); |
| 1649 if (status!=0) decStatus(res, status, set); |
| 1650 #if DECCHECK |
| 1651 decCheckInexact(res, set); |
| 1652 #endif |
| 1653 return res; |
| 1654 } /* decNumberMinus */ |
| 1655 |
| 1656 /* ------------------------------------------------------------------ */ |
| 1657 /* decNumberNextMinus -- next towards -Infinity */ |
| 1658 /* */ |
| 1659 /* This computes C = A - infinitesimal, rounded towards -Infinity */ |
| 1660 /* */ |
| 1661 /* res is C, the result. C may be A */ |
| 1662 /* rhs is A */ |
| 1663 /* set is the context */ |
| 1664 /* */ |
| 1665 /* This is a generalization of 754 NextDown. */ |
| 1666 /* ------------------------------------------------------------------ */ |
| 1667 U_CAPI decNumber * U_EXPORT2 uprv_decNumberNextMinus(decNumber *res, const decNu
mber *rhs, |
| 1668 decContext *set) { |
| 1669 decNumber dtiny; /* constant */ |
| 1670 decContext workset=*set; /* work */ |
| 1671 uInt status=0; /* accumulator */ |
| 1672 #if DECCHECK |
| 1673 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
| 1674 #endif |
| 1675 |
| 1676 /* +Infinity is the special case */ |
| 1677 if ((rhs->bits&(DECINF|DECNEG))==DECINF) { |
| 1678 decSetMaxValue(res, set); /* is +ve */ |
| 1679 /* there is no status to set */ |
| 1680 return res; |
| 1681 } |
| 1682 uprv_decNumberZero(&dtiny); /* start with 0 */ |
| 1683 dtiny.lsu[0]=1; /* make number that is .. */ |
| 1684 dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */ |
| 1685 workset.round=DEC_ROUND_FLOOR; |
| 1686 decAddOp(res, rhs, &dtiny, &workset, DECNEG, &status); |
| 1687 status&=DEC_Invalid_operation|DEC_sNaN; /* only sNaN Invalid please */ |
| 1688 if (status!=0) decStatus(res, status, set); |
| 1689 return res; |
| 1690 } /* decNumberNextMinus */ |
| 1691 |
| 1692 /* ------------------------------------------------------------------ */ |
| 1693 /* decNumberNextPlus -- next towards +Infinity */ |
| 1694 /* */ |
| 1695 /* This computes C = A + infinitesimal, rounded towards +Infinity */ |
| 1696 /* */ |
| 1697 /* res is C, the result. C may be A */ |
| 1698 /* rhs is A */ |
| 1699 /* set is the context */ |
| 1700 /* */ |
| 1701 /* This is a generalization of 754 NextUp. */ |
| 1702 /* ------------------------------------------------------------------ */ |
| 1703 U_CAPI decNumber * U_EXPORT2 uprv_decNumberNextPlus(decNumber *res, const decNum
ber *rhs, |
| 1704 decContext *set) { |
| 1705 decNumber dtiny; /* constant */ |
| 1706 decContext workset=*set; /* work */ |
| 1707 uInt status=0; /* accumulator */ |
| 1708 #if DECCHECK |
| 1709 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
| 1710 #endif |
| 1711 |
| 1712 /* -Infinity is the special case */ |
| 1713 if ((rhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) { |
| 1714 decSetMaxValue(res, set); |
| 1715 res->bits=DECNEG; /* negative */ |
| 1716 /* there is no status to set */ |
| 1717 return res; |
| 1718 } |
| 1719 uprv_decNumberZero(&dtiny); /* start with 0 */ |
| 1720 dtiny.lsu[0]=1; /* make number that is .. */ |
| 1721 dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */ |
| 1722 workset.round=DEC_ROUND_CEILING; |
| 1723 decAddOp(res, rhs, &dtiny, &workset, 0, &status); |
| 1724 status&=DEC_Invalid_operation|DEC_sNaN; /* only sNaN Invalid please */ |
| 1725 if (status!=0) decStatus(res, status, set); |
| 1726 return res; |
| 1727 } /* decNumberNextPlus */ |
| 1728 |
| 1729 /* ------------------------------------------------------------------ */ |
| 1730 /* decNumberNextToward -- next towards rhs */ |
| 1731 /* */ |
| 1732 /* This computes C = A +/- infinitesimal, rounded towards */ |
| 1733 /* +/-Infinity in the direction of B, as per 754-1985 nextafter */ |
| 1734 /* modified during revision but dropped from 754-2008. */ |
| 1735 /* */ |
| 1736 /* res is C, the result. C may be A or B. */ |
| 1737 /* lhs is A */ |
| 1738 /* rhs is B */ |
| 1739 /* set is the context */ |
| 1740 /* */ |
| 1741 /* This is a generalization of 754-1985 NextAfter. */ |
| 1742 /* ------------------------------------------------------------------ */ |
| 1743 U_CAPI decNumber * U_EXPORT2 uprv_decNumberNextToward(decNumber *res, const decN
umber *lhs, |
| 1744 const decNumber *rhs, decContext *set) { |
| 1745 decNumber dtiny; /* constant */ |
| 1746 decContext workset=*set; /* work */ |
| 1747 Int result; /* .. */ |
| 1748 uInt status=0; /* accumulator */ |
| 1749 #if DECCHECK |
| 1750 if (decCheckOperands(res, lhs, rhs, set)) return res; |
| 1751 #endif |
| 1752 |
| 1753 if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { |
| 1754 decNaNs(res, lhs, rhs, set, &status); |
| 1755 } |
| 1756 else { /* Is numeric, so no chance of sNaN Invalid, etc. */ |
| 1757 result=decCompare(lhs, rhs, 0); /* sign matters */ |
| 1758 if (result==BADINT) status|=DEC_Insufficient_storage; /* rare */ |
| 1759 else { /* valid compare */ |
| 1760 if (result==0) uprv_decNumberCopySign(res, lhs, rhs); /* easy */ |
| 1761 else { /* differ: need NextPlus or NextMinus */ |
| 1762 uByte sub; /* add or subtract */ |
| 1763 if (result<0) { /* lhs<rhs, do nextplus */ |
| 1764 /* -Infinity is the special case */ |
| 1765 if ((lhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) { |
| 1766 decSetMaxValue(res, set); |
| 1767 res->bits=DECNEG; /* negative */ |
| 1768 return res; /* there is no status to set */ |
| 1769 } |
| 1770 workset.round=DEC_ROUND_CEILING; |
| 1771 sub=0; /* add, please */ |
| 1772 } /* plus */ |
| 1773 else { /* lhs>rhs, do nextminus */ |
| 1774 /* +Infinity is the special case */ |
| 1775 if ((lhs->bits&(DECINF|DECNEG))==DECINF) { |
| 1776 decSetMaxValue(res, set); |
| 1777 return res; /* there is no status to set */ |
| 1778 } |
| 1779 workset.round=DEC_ROUND_FLOOR; |
| 1780 sub=DECNEG; /* subtract, please */ |
| 1781 } /* minus */ |
| 1782 uprv_decNumberZero(&dtiny); /* start with 0 */ |
| 1783 dtiny.lsu[0]=1; /* make number that is .. */ |
| 1784 dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */ |
| 1785 decAddOp(res, lhs, &dtiny, &workset, sub, &status); /* + or - */ |
| 1786 /* turn off exceptions if the result is a normal number */ |
| 1787 /* (including Nmin), otherwise let all status through */ |
| 1788 if (uprv_decNumberIsNormal(res, set)) status=0; |
| 1789 } /* unequal */ |
| 1790 } /* compare OK */ |
| 1791 } /* numeric */ |
| 1792 if (status!=0) decStatus(res, status, set); |
| 1793 return res; |
| 1794 } /* decNumberNextToward */ |
| 1795 |
| 1796 /* ------------------------------------------------------------------ */ |
| 1797 /* decNumberOr -- OR two Numbers, digitwise */ |
| 1798 /* */ |
| 1799 /* This computes C = A | B */ |
| 1800 /* */ |
| 1801 /* res is C, the result. C may be A and/or B (e.g., X=X|X) */ |
| 1802 /* lhs is A */ |
| 1803 /* rhs is B */ |
| 1804 /* set is the context (used for result length and error report) */ |
| 1805 /* */ |
| 1806 /* C must have space for set->digits digits. */ |
| 1807 /* */ |
| 1808 /* Logical function restrictions apply (see above); a NaN is */ |
| 1809 /* returned with Invalid_operation if a restriction is violated. */ |
| 1810 /* ------------------------------------------------------------------ */ |
| 1811 U_CAPI decNumber * U_EXPORT2 uprv_decNumberOr(decNumber *res, const decNumber *l
hs, |
| 1812 const decNumber *rhs, decContext *set) { |
| 1813 const Unit *ua, *ub; /* -> operands */ |
| 1814 const Unit *msua, *msub; /* -> operand msus */ |
| 1815 Unit *uc, *msuc; /* -> result and its msu */ |
| 1816 Int msudigs; /* digits in res msu */ |
| 1817 #if DECCHECK |
| 1818 if (decCheckOperands(res, lhs, rhs, set)) return res; |
| 1819 #endif |
| 1820 |
| 1821 if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) |
| 1822 || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { |
| 1823 decStatus(res, DEC_Invalid_operation, set); |
| 1824 return res; |
| 1825 } |
| 1826 /* operands are valid */ |
| 1827 ua=lhs->lsu; /* bottom-up */ |
| 1828 ub=rhs->lsu; /* .. */ |
| 1829 uc=res->lsu; /* .. */ |
| 1830 msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */ |
| 1831 msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */ |
| 1832 msuc=uc+D2U(set->digits)-1; /* -> msu of result */ |
| 1833 msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ |
| 1834 for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */ |
| 1835 Unit a, b; /* extract units */ |
| 1836 if (ua>msua) a=0; |
| 1837 else a=*ua; |
| 1838 if (ub>msub) b=0; |
| 1839 else b=*ub; |
| 1840 *uc=0; /* can now write back */ |
| 1841 if (a|b) { /* maybe 1 bits to examine */ |
| 1842 Int i, j; |
| 1843 /* This loop could be unrolled and/or use BIN2BCD tables */ |
| 1844 for (i=0; i<DECDPUN; i++) { |
| 1845 if ((a|b)&1) *uc=*uc+(Unit)powers[i]; /* effect OR */ |
| 1846 j=a%10; |
| 1847 a=a/10; |
| 1848 j|=b%10; |
| 1849 b=b/10; |
| 1850 if (j>1) { |
| 1851 decStatus(res, DEC_Invalid_operation, set); |
| 1852 return res; |
| 1853 } |
| 1854 if (uc==msuc && i==msudigs-1) break; /* just did final digit */ |
| 1855 } /* each digit */ |
| 1856 } /* non-zero */ |
| 1857 } /* each unit */ |
| 1858 /* [here uc-1 is the msu of the result] */ |
| 1859 res->digits=decGetDigits(res->lsu, uc-res->lsu); |
| 1860 res->exponent=0; /* integer */ |
| 1861 res->bits=0; /* sign=0 */ |
| 1862 return res; /* [no status to set] */ |
| 1863 } /* decNumberOr */ |
| 1864 |
| 1865 /* ------------------------------------------------------------------ */ |
| 1866 /* decNumberPlus -- prefix plus operator */ |
| 1867 /* */ |
| 1868 /* This computes C = 0 + A */ |
| 1869 /* */ |
| 1870 /* res is C, the result. C may be A */ |
| 1871 /* rhs is A */ |
| 1872 /* set is the context */ |
| 1873 /* */ |
| 1874 /* See also decNumberCopy for a quiet bitwise version of this. */ |
| 1875 /* C must have space for set->digits digits. */ |
| 1876 /* ------------------------------------------------------------------ */ |
| 1877 /* This simply uses AddOp; Add will take fast path after preparing A. */ |
| 1878 /* Performance is a concern here, as this routine is often used to */ |
| 1879 /* check operands and apply rounding and overflow/underflow testing. */ |
| 1880 /* ------------------------------------------------------------------ */ |
| 1881 U_CAPI decNumber * U_EXPORT2 uprv_decNumberPlus(decNumber *res, const decNumber
*rhs, |
| 1882 decContext *set) { |
| 1883 decNumber dzero; |
| 1884 uInt status=0; /* accumulator */ |
| 1885 #if DECCHECK |
| 1886 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
| 1887 #endif |
| 1888 |
| 1889 uprv_decNumberZero(&dzero); /* make 0 */ |
| 1890 dzero.exponent=rhs->exponent; /* [no coefficient expansion] */ |
| 1891 decAddOp(res, &dzero, rhs, set, 0, &status); |
| 1892 if (status!=0) decStatus(res, status, set); |
| 1893 #if DECCHECK |
| 1894 decCheckInexact(res, set); |
| 1895 #endif |
| 1896 return res; |
| 1897 } /* decNumberPlus */ |
| 1898 |
| 1899 /* ------------------------------------------------------------------ */ |
| 1900 /* decNumberMultiply -- multiply two Numbers */ |
| 1901 /* */ |
| 1902 /* This computes C = A x B */ |
| 1903 /* */ |
| 1904 /* res is C, the result. C may be A and/or B (e.g., X=X+X) */ |
| 1905 /* lhs is A */ |
| 1906 /* rhs is B */ |
| 1907 /* set is the context */ |
| 1908 /* */ |
| 1909 /* C must have space for set->digits digits. */ |
| 1910 /* ------------------------------------------------------------------ */ |
| 1911 U_CAPI decNumber * U_EXPORT2 uprv_decNumberMultiply(decNumber *res, const decNum
ber *lhs, |
| 1912 const decNumber *rhs, decContext *set) { |
| 1913 uInt status=0; /* accumulator */ |
| 1914 decMultiplyOp(res, lhs, rhs, set, &status); |
| 1915 if (status!=0) decStatus(res, status, set); |
| 1916 #if DECCHECK |
| 1917 decCheckInexact(res, set); |
| 1918 #endif |
| 1919 return res; |
| 1920 } /* decNumberMultiply */ |
| 1921 |
| 1922 /* ------------------------------------------------------------------ */ |
| 1923 /* decNumberPower -- raise a number to a power */ |
| 1924 /* */ |
| 1925 /* This computes C = A ** B */ |
| 1926 /* */ |
| 1927 /* res is C, the result. C may be A and/or B (e.g., X=X**X) */ |
| 1928 /* lhs is A */ |
| 1929 /* rhs is B */ |
| 1930 /* set is the context */ |
| 1931 /* */ |
| 1932 /* C must have space for set->digits digits. */ |
| 1933 /* */ |
| 1934 /* Mathematical function restrictions apply (see above); a NaN is */ |
| 1935 /* returned with Invalid_operation if a restriction is violated. */ |
| 1936 /* */ |
| 1937 /* However, if 1999999997<=B<=999999999 and B is an integer then the */ |
| 1938 /* restrictions on A and the context are relaxed to the usual bounds, */ |
| 1939 /* for compatibility with the earlier (integer power only) version */ |
| 1940 /* of this function. */ |
| 1941 /* */ |
| 1942 /* When B is an integer, the result may be exact, even if rounded. */ |
| 1943 /* */ |
| 1944 /* The final result is rounded according to the context; it will */ |
| 1945 /* almost always be correctly rounded, but may be up to 1 ulp in */ |
| 1946 /* error in rare cases. */ |
| 1947 /* ------------------------------------------------------------------ */ |
| 1948 U_CAPI decNumber * U_EXPORT2 uprv_decNumberPower(decNumber *res, const decNumber
*lhs, |
| 1949 const decNumber *rhs, decContext *set) { |
| 1950 #if DECSUBSET |
| 1951 decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ |
| 1952 decNumber *allocrhs=NULL; /* .., rhs */ |
| 1953 #endif |
| 1954 decNumber *allocdac=NULL; /* -> allocated acc buffer, iff used */ |
| 1955 decNumber *allocinv=NULL; /* -> allocated 1/x buffer, iff used */ |
| 1956 Int reqdigits=set->digits; /* requested DIGITS */ |
| 1957 Int n; /* rhs in binary */ |
| 1958 Flag rhsint=0; /* 1 if rhs is an integer */ |
| 1959 Flag useint=0; /* 1 if can use integer calculation */ |
| 1960 Flag isoddint=0; /* 1 if rhs is an integer and odd */ |
| 1961 Int i; /* work */ |
| 1962 #if DECSUBSET |
| 1963 Int dropped; /* .. */ |
| 1964 #endif |
| 1965 uInt needbytes; /* buffer size needed */ |
| 1966 Flag seenbit; /* seen a bit while powering */ |
| 1967 Int residue=0; /* rounding residue */ |
| 1968 uInt status=0; /* accumulators */ |
| 1969 uByte bits=0; /* result sign if errors */ |
| 1970 decContext aset; /* working context */ |
| 1971 decNumber dnOne; /* work value 1... */ |
| 1972 /* local accumulator buffer [a decNumber, with digits+elength+1 digits] */ |
| 1973 decNumber dacbuff[D2N(DECBUFFER+9)]; |
| 1974 decNumber *dac=dacbuff; /* -> result accumulator */ |
| 1975 /* same again for possible 1/lhs calculation */ |
| 1976 decNumber invbuff[D2N(DECBUFFER+9)]; |
| 1977 |
| 1978 #if DECCHECK |
| 1979 if (decCheckOperands(res, lhs, rhs, set)) return res; |
| 1980 #endif |
| 1981 |
| 1982 do { /* protect allocated storage */ |
| 1983 #if DECSUBSET |
| 1984 if (!set->extended) { /* reduce operands and set status, as needed */ |
| 1985 if (lhs->digits>reqdigits) { |
| 1986 alloclhs=decRoundOperand(lhs, set, &status); |
| 1987 if (alloclhs==NULL) break; |
| 1988 lhs=alloclhs; |
| 1989 } |
| 1990 if (rhs->digits>reqdigits) { |
| 1991 allocrhs=decRoundOperand(rhs, set, &status); |
| 1992 if (allocrhs==NULL) break; |
| 1993 rhs=allocrhs; |
| 1994 } |
| 1995 } |
| 1996 #endif |
| 1997 /* [following code does not require input rounding] */ |
| 1998 |
| 1999 /* handle NaNs and rhs Infinity (lhs infinity is harder) */ |
| 2000 if (SPECIALARGS) { |
| 2001 if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { /* NaNs */ |
| 2002 decNaNs(res, lhs, rhs, set, &status); |
| 2003 break;} |
| 2004 if (decNumberIsInfinite(rhs)) { /* rhs Infinity */ |
| 2005 Flag rhsneg=rhs->bits&DECNEG; /* save rhs sign */ |
| 2006 if (decNumberIsNegative(lhs) /* lhs<0 */ |
| 2007 && !decNumberIsZero(lhs)) /* .. */ |
| 2008 status|=DEC_Invalid_operation; |
| 2009 else { /* lhs >=0 */ |
| 2010 uprv_decNumberZero(&dnOne); /* set up 1 */ |
| 2011 dnOne.lsu[0]=1; |
| 2012 uprv_decNumberCompare(dac, lhs, &dnOne, set); /* lhs ? 1 */ |
| 2013 uprv_decNumberZero(res); /* prepare for 0/1/Infinity */ |
| 2014 if (decNumberIsNegative(dac)) { /* lhs<1 */ |
| 2015 if (rhsneg) res->bits|=DECINF; /* +Infinity [else is +0] */ |
| 2016 } |
| 2017 else if (dac->lsu[0]==0) { /* lhs=1 */ |
| 2018 /* 1**Infinity is inexact, so return fully-padded 1.0000 */ |
| 2019 Int shift=set->digits-1; |
| 2020 *res->lsu=1; /* was 0, make int 1 */ |
| 2021 res->digits=decShiftToMost(res->lsu, 1, shift); |
| 2022 res->exponent=-shift; /* make 1.0000... */ |
| 2023 status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */ |
| 2024 } |
| 2025 else { /* lhs>1 */ |
| 2026 if (!rhsneg) res->bits|=DECINF; /* +Infinity [else is +0] */ |
| 2027 } |
| 2028 } /* lhs>=0 */ |
| 2029 break;} |
| 2030 /* [lhs infinity drops through] */ |
| 2031 } /* specials */ |
| 2032 |
| 2033 /* Original rhs may be an integer that fits and is in range */ |
| 2034 n=decGetInt(rhs); |
| 2035 if (n!=BADINT) { /* it is an integer */ |
| 2036 rhsint=1; /* record the fact for 1**n */ |
| 2037 isoddint=(Flag)n&1; /* [works even if big] */ |
| 2038 if (n!=BIGEVEN && n!=BIGODD) /* can use integer path? */ |
| 2039 useint=1; /* looks good */ |
| 2040 } |
| 2041 |
| 2042 if (decNumberIsNegative(lhs) /* -x .. */ |
| 2043 && isoddint) bits=DECNEG; /* .. to an odd power */ |
| 2044 |
| 2045 /* handle LHS infinity */ |
| 2046 if (decNumberIsInfinite(lhs)) { /* [NaNs already handled] */ |
| 2047 uByte rbits=rhs->bits; /* save */ |
| 2048 uprv_decNumberZero(res); /* prepare */ |
| 2049 if (n==0) *res->lsu=1; /* [-]Inf**0 => 1 */ |
| 2050 else { |
| 2051 /* -Inf**nonint -> error */ |
| 2052 if (!rhsint && decNumberIsNegative(lhs)) { |
| 2053 status|=DEC_Invalid_operation; /* -Inf**nonint is error */ |
| 2054 break;} |
| 2055 if (!(rbits & DECNEG)) bits|=DECINF; /* was not a **-n */ |
| 2056 /* [otherwise will be 0 or -0] */ |
| 2057 res->bits=bits; |
| 2058 } |
| 2059 break;} |
| 2060 |
| 2061 /* similarly handle LHS zero */ |
| 2062 if (decNumberIsZero(lhs)) { |
| 2063 if (n==0) { /* 0**0 => Error */ |
| 2064 #if DECSUBSET |
| 2065 if (!set->extended) { /* [unless subset] */ |
| 2066 uprv_decNumberZero(res); |
| 2067 *res->lsu=1; /* return 1 */ |
| 2068 break;} |
| 2069 #endif |
| 2070 status|=DEC_Invalid_operation; |
| 2071 } |
| 2072 else { /* 0**x */ |
| 2073 uByte rbits=rhs->bits; /* save */ |
| 2074 if (rbits & DECNEG) { /* was a 0**(-n) */ |
| 2075 #if DECSUBSET |
| 2076 if (!set->extended) { /* [bad if subset] */ |
| 2077 status|=DEC_Invalid_operation; |
| 2078 break;} |
| 2079 #endif |
| 2080 bits|=DECINF; |
| 2081 } |
| 2082 uprv_decNumberZero(res); /* prepare */ |
| 2083 /* [otherwise will be 0 or -0] */ |
| 2084 res->bits=bits; |
| 2085 } |
| 2086 break;} |
| 2087 |
| 2088 /* here both lhs and rhs are finite; rhs==0 is handled in the */ |
| 2089 /* integer path. Next handle the non-integer cases */ |
| 2090 if (!useint) { /* non-integral rhs */ |
| 2091 /* any -ve lhs is bad, as is either operand or context out of */ |
| 2092 /* bounds */ |
| 2093 if (decNumberIsNegative(lhs)) { |
| 2094 status|=DEC_Invalid_operation; |
| 2095 break;} |
| 2096 if (decCheckMath(lhs, set, &status) |
| 2097 || decCheckMath(rhs, set, &status)) break; /* variable status */ |
| 2098 |
| 2099 uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */ |
| 2100 aset.emax=DEC_MAX_MATH; /* usual bounds */ |
| 2101 aset.emin=-DEC_MAX_MATH; /* .. */ |
| 2102 aset.clamp=0; /* and no concrete format */ |
| 2103 |
| 2104 /* calculate the result using exp(ln(lhs)*rhs), which can */ |
| 2105 /* all be done into the accumulator, dac. The precision needed */ |
| 2106 /* is enough to contain the full information in the lhs (which */ |
| 2107 /* is the total digits, including exponent), or the requested */ |
| 2108 /* precision, if larger, + 4; 6 is used for the exponent */ |
| 2109 /* maximum length, and this is also used when it is shorter */ |
| 2110 /* than the requested digits as it greatly reduces the >0.5 ulp */ |
| 2111 /* cases at little cost (because Ln doubles digits each */ |
| 2112 /* iteration so a few extra digits rarely causes an extra */ |
| 2113 /* iteration) */ |
| 2114 aset.digits=MAXI(lhs->digits, set->digits)+6+4; |
| 2115 } /* non-integer rhs */ |
| 2116 |
| 2117 else { /* rhs is in-range integer */ |
| 2118 if (n==0) { /* x**0 = 1 */ |
| 2119 /* (0**0 was handled above) */ |
| 2120 uprv_decNumberZero(res); /* result=1 */ |
| 2121 *res->lsu=1; /* .. */ |
| 2122 break;} |
| 2123 /* rhs is a non-zero integer */ |
| 2124 if (n<0) n=-n; /* use abs(n) */ |
| 2125 |
| 2126 aset=*set; /* clone the context */ |
| 2127 aset.round=DEC_ROUND_HALF_EVEN; /* internally use balanced */ |
| 2128 /* calculate the working DIGITS */ |
| 2129 aset.digits=reqdigits+(rhs->digits+rhs->exponent)+2; |
| 2130 #if DECSUBSET |
| 2131 if (!set->extended) aset.digits--; /* use classic precision */ |
| 2132 #endif |
| 2133 /* it's an error if this is more than can be handled */ |
| 2134 if (aset.digits>DECNUMMAXP) {status|=DEC_Invalid_operation; break;} |
| 2135 } /* integer path */ |
| 2136 |
| 2137 /* aset.digits is the count of digits for the accumulator needed */ |
| 2138 /* if accumulator is too long for local storage, then allocate */ |
| 2139 needbytes=sizeof(decNumber)+(D2U(aset.digits)-1)*sizeof(Unit); |
| 2140 /* [needbytes also used below if 1/lhs needed] */ |
| 2141 if (needbytes>sizeof(dacbuff)) { |
| 2142 allocdac=(decNumber *)malloc(needbytes); |
| 2143 if (allocdac==NULL) { /* hopeless -- abandon */ |
| 2144 status|=DEC_Insufficient_storage; |
| 2145 break;} |
| 2146 dac=allocdac; /* use the allocated space */ |
| 2147 } |
| 2148 /* here, aset is set up and accumulator is ready for use */ |
| 2149 |
| 2150 if (!useint) { /* non-integral rhs */ |
| 2151 /* x ** y; special-case x=1 here as it will otherwise always */ |
| 2152 /* reduce to integer 1; decLnOp has a fastpath which detects */ |
| 2153 /* the case of x=1 */ |
| 2154 decLnOp(dac, lhs, &aset, &status); /* dac=ln(lhs) */ |
| 2155 /* [no error possible, as lhs 0 already handled] */ |
| 2156 if (ISZERO(dac)) { /* x==1, 1.0, etc. */ |
| 2157 /* need to return fully-padded 1.0000 etc., but rhsint->1 */ |
| 2158 *dac->lsu=1; /* was 0, make int 1 */ |
| 2159 if (!rhsint) { /* add padding */ |
| 2160 Int shift=set->digits-1; |
| 2161 dac->digits=decShiftToMost(dac->lsu, 1, shift); |
| 2162 dac->exponent=-shift; /* make 1.0000... */ |
| 2163 status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */ |
| 2164 } |
| 2165 } |
| 2166 else { |
| 2167 decMultiplyOp(dac, dac, rhs, &aset, &status); /* dac=dac*rhs */ |
| 2168 decExpOp(dac, dac, &aset, &status); /* dac=exp(dac) */ |
| 2169 } |
| 2170 /* and drop through for final rounding */ |
| 2171 } /* non-integer rhs */ |
| 2172 |
| 2173 else { /* carry on with integer */ |
| 2174 uprv_decNumberZero(dac); /* acc=1 */ |
| 2175 *dac->lsu=1; /* .. */ |
| 2176 |
| 2177 /* if a negative power the constant 1 is needed, and if not subset */ |
| 2178 /* invert the lhs now rather than inverting the result later */ |
| 2179 if (decNumberIsNegative(rhs)) { /* was a **-n [hence digits>0] */ |
| 2180 decNumber *inv=invbuff; /* asssume use fixed buffer */ |
| 2181 uprv_decNumberCopy(&dnOne, dac); /* dnOne=1; [needed now or later]
*/ |
| 2182 #if DECSUBSET |
| 2183 if (set->extended) { /* need to calculate 1/lhs */ |
| 2184 #endif |
| 2185 /* divide lhs into 1, putting result in dac [dac=1/dac] */ |
| 2186 decDivideOp(dac, &dnOne, lhs, &aset, DIVIDE, &status); |
| 2187 /* now locate or allocate space for the inverted lhs */ |
| 2188 if (needbytes>sizeof(invbuff)) { |
| 2189 allocinv=(decNumber *)malloc(needbytes); |
| 2190 if (allocinv==NULL) { /* hopeless -- abandon */ |
| 2191 status|=DEC_Insufficient_storage; |
| 2192 break;} |
| 2193 inv=allocinv; /* use the allocated space */ |
| 2194 } |
| 2195 /* [inv now points to big-enough buffer or allocated storage] */ |
| 2196 uprv_decNumberCopy(inv, dac); /* copy the 1/lhs */ |
| 2197 uprv_decNumberCopy(dac, &dnOne); /* restore acc=1 */ |
| 2198 lhs=inv; /* .. and go forward with new lhs */ |
| 2199 #if DECSUBSET |
| 2200 } |
| 2201 #endif |
| 2202 } |
| 2203 |
| 2204 /* Raise-to-the-power loop... */ |
| 2205 seenbit=0; /* set once a 1-bit is encountered */ |
| 2206 for (i=1;;i++){ /* for each bit [top bit ignored] */ |
| 2207 /* abandon if had overflow or terminal underflow */ |
| 2208 if (status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */ |
| 2209 if (status&DEC_Overflow || ISZERO(dac)) break; |
| 2210 } |
| 2211 /* [the following two lines revealed an optimizer bug in a C++ */ |
| 2212 /* compiler, with symptom: 5**3 -> 25, when n=n+n was used] */ |
| 2213 n=n<<1; /* move next bit to testable position */ |
| 2214 if (n<0) { /* top bit is set */ |
| 2215 seenbit=1; /* OK, significant bit seen */ |
| 2216 decMultiplyOp(dac, dac, lhs, &aset, &status); /* dac=dac*x */ |
| 2217 } |
| 2218 if (i==31) break; /* that was the last bit */ |
| 2219 if (!seenbit) continue; /* no need to square 1 */ |
| 2220 decMultiplyOp(dac, dac, dac, &aset, &status); /* dac=dac*dac [square] *
/ |
| 2221 } /*i*/ /* 32 bits */ |
| 2222 |
| 2223 /* complete internal overflow or underflow processing */ |
| 2224 if (status & (DEC_Overflow|DEC_Underflow)) { |
| 2225 #if DECSUBSET |
| 2226 /* If subset, and power was negative, reverse the kind of -erflow */ |
| 2227 /* [1/x not yet done] */ |
| 2228 if (!set->extended && decNumberIsNegative(rhs)) { |
| 2229 if (status & DEC_Overflow) |
| 2230 status^=DEC_Overflow | DEC_Underflow | DEC_Subnormal; |
| 2231 else { /* trickier -- Underflow may or may not be set */ |
| 2232 status&=~(DEC_Underflow | DEC_Subnormal); /* [one or both] */ |
| 2233 status|=DEC_Overflow; |
| 2234 } |
| 2235 } |
| 2236 #endif |
| 2237 dac->bits=(dac->bits & ~DECNEG) | bits; /* force correct sign */ |
| 2238 /* round subnormals [to set.digits rather than aset.digits] */ |
| 2239 /* or set overflow result similarly as required */ |
| 2240 decFinalize(dac, set, &residue, &status); |
| 2241 uprv_decNumberCopy(res, dac); /* copy to result (is now OK length) */ |
| 2242 break; |
| 2243 } |
| 2244 |
| 2245 #if DECSUBSET |
| 2246 if (!set->extended && /* subset math */ |
| 2247 decNumberIsNegative(rhs)) { /* was a **-n [hence digits>0] */ |
| 2248 /* so divide result into 1 [dac=1/dac] */ |
| 2249 decDivideOp(dac, &dnOne, dac, &aset, DIVIDE, &status); |
| 2250 } |
| 2251 #endif |
| 2252 } /* rhs integer path */ |
| 2253 |
| 2254 /* reduce result to the requested length and copy to result */ |
| 2255 decCopyFit(res, dac, set, &residue, &status); |
| 2256 decFinish(res, set, &residue, &status); /* final cleanup */ |
| 2257 #if DECSUBSET |
| 2258 if (!set->extended) decTrim(res, set, 0, 1, &dropped); /* trailing zeros */ |
| 2259 #endif |
| 2260 } while(0); /* end protected */ |
| 2261 |
| 2262 if (allocdac!=NULL) free(allocdac); /* drop any storage used */ |
| 2263 if (allocinv!=NULL) free(allocinv); /* .. */ |
| 2264 #if DECSUBSET |
| 2265 if (alloclhs!=NULL) free(alloclhs); /* .. */ |
| 2266 if (allocrhs!=NULL) free(allocrhs); /* .. */ |
| 2267 #endif |
| 2268 if (status!=0) decStatus(res, status, set); |
| 2269 #if DECCHECK |
| 2270 decCheckInexact(res, set); |
| 2271 #endif |
| 2272 return res; |
| 2273 } /* decNumberPower */ |
| 2274 |
| 2275 /* ------------------------------------------------------------------ */ |
| 2276 /* decNumberQuantize -- force exponent to requested value */ |
| 2277 /* */ |
| 2278 /* This computes C = op(A, B), where op adjusts the coefficient */ |
| 2279 /* of C (by rounding or shifting) such that the exponent (-scale) */ |
| 2280 /* of C has exponent of B. The numerical value of C will equal A, */ |
| 2281 /* except for the effects of any rounding that occurred. */ |
| 2282 /* */ |
| 2283 /* res is C, the result. C may be A or B */ |
| 2284 /* lhs is A, the number to adjust */ |
| 2285 /* rhs is B, the number with exponent to match */ |
| 2286 /* set is the context */ |
| 2287 /* */ |
| 2288 /* C must have space for set->digits digits. */ |
| 2289 /* */ |
| 2290 /* Unless there is an error or the result is infinite, the exponent */ |
| 2291 /* after the operation is guaranteed to be equal to that of B. */ |
| 2292 /* ------------------------------------------------------------------ */ |
| 2293 U_CAPI decNumber * U_EXPORT2 uprv_decNumberQuantize(decNumber *res, const decNum
ber *lhs, |
| 2294 const decNumber *rhs, decContext *set) { |
| 2295 uInt status=0; /* accumulator */ |
| 2296 decQuantizeOp(res, lhs, rhs, set, 1, &status); |
| 2297 if (status!=0) decStatus(res, status, set); |
| 2298 return res; |
| 2299 } /* decNumberQuantize */ |
| 2300 |
| 2301 /* ------------------------------------------------------------------ */ |
| 2302 /* decNumberReduce -- remove trailing zeros */ |
| 2303 /* */ |
| 2304 /* This computes C = 0 + A, and normalizes the result */ |
| 2305 /* */ |
| 2306 /* res is C, the result. C may be A */ |
| 2307 /* rhs is A */ |
| 2308 /* set is the context */ |
| 2309 /* */ |
| 2310 /* C must have space for set->digits digits. */ |
| 2311 /* ------------------------------------------------------------------ */ |
| 2312 /* Previously known as Normalize */ |
| 2313 U_CAPI decNumber * U_EXPORT2 uprv_decNumberNormalize(decNumber *res, const decNu
mber *rhs, |
| 2314 decContext *set) { |
| 2315 return uprv_decNumberReduce(res, rhs, set); |
| 2316 } /* decNumberNormalize */ |
| 2317 |
| 2318 U_CAPI decNumber * U_EXPORT2 uprv_decNumberReduce(decNumber *res, const decNumbe
r *rhs, |
| 2319 decContext *set) { |
| 2320 #if DECSUBSET |
| 2321 decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ |
| 2322 #endif |
| 2323 uInt status=0; /* as usual */ |
| 2324 Int residue=0; /* as usual */ |
| 2325 Int dropped; /* work */ |
| 2326 |
| 2327 #if DECCHECK |
| 2328 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
| 2329 #endif |
| 2330 |
| 2331 do { /* protect allocated storage */ |
| 2332 #if DECSUBSET |
| 2333 if (!set->extended) { |
| 2334 /* reduce operand and set lostDigits status, as needed */ |
| 2335 if (rhs->digits>set->digits) { |
| 2336 allocrhs=decRoundOperand(rhs, set, &status); |
| 2337 if (allocrhs==NULL) break; |
| 2338 rhs=allocrhs; |
| 2339 } |
| 2340 } |
| 2341 #endif |
| 2342 /* [following code does not require input rounding] */ |
| 2343 |
| 2344 /* Infinities copy through; NaNs need usual treatment */ |
| 2345 if (decNumberIsNaN(rhs)) { |
| 2346 decNaNs(res, rhs, NULL, set, &status); |
| 2347 break; |
| 2348 } |
| 2349 |
| 2350 /* reduce result to the requested length and copy to result */ |
| 2351 decCopyFit(res, rhs, set, &residue, &status); /* copy & round */ |
| 2352 decFinish(res, set, &residue, &status); /* cleanup/set flags */ |
| 2353 decTrim(res, set, 1, 0, &dropped); /* normalize in place */ |
| 2354 /* [may clamp] */ |
| 2355 } while(0); /* end protected */ |
| 2356 |
| 2357 #if DECSUBSET |
| 2358 if (allocrhs !=NULL) free(allocrhs); /* .. */ |
| 2359 #endif |
| 2360 if (status!=0) decStatus(res, status, set);/* then report status */ |
| 2361 return res; |
| 2362 } /* decNumberReduce */ |
| 2363 |
| 2364 /* ------------------------------------------------------------------ */ |
| 2365 /* decNumberRescale -- force exponent to requested value */ |
| 2366 /* */ |
| 2367 /* This computes C = op(A, B), where op adjusts the coefficient */ |
| 2368 /* of C (by rounding or shifting) such that the exponent (-scale) */ |
| 2369 /* of C has the value B. The numerical value of C will equal A, */ |
| 2370 /* except for the effects of any rounding that occurred. */ |
| 2371 /* */ |
| 2372 /* res is C, the result. C may be A or B */ |
| 2373 /* lhs is A, the number to adjust */ |
| 2374 /* rhs is B, the requested exponent */ |
| 2375 /* set is the context */ |
| 2376 /* */ |
| 2377 /* C must have space for set->digits digits. */ |
| 2378 /* */ |
| 2379 /* Unless there is an error or the result is infinite, the exponent */ |
| 2380 /* after the operation is guaranteed to be equal to B. */ |
| 2381 /* ------------------------------------------------------------------ */ |
| 2382 U_CAPI decNumber * U_EXPORT2 uprv_decNumberRescale(decNumber *res, const decNumb
er *lhs, |
| 2383 const decNumber *rhs, decContext *set) { |
| 2384 uInt status=0; /* accumulator */ |
| 2385 decQuantizeOp(res, lhs, rhs, set, 0, &status); |
| 2386 if (status!=0) decStatus(res, status, set); |
| 2387 return res; |
| 2388 } /* decNumberRescale */ |
| 2389 |
| 2390 /* ------------------------------------------------------------------ */ |
| 2391 /* decNumberRemainder -- divide and return remainder */ |
| 2392 /* */ |
| 2393 /* This computes C = A % B */ |
| 2394 /* */ |
| 2395 /* res is C, the result. C may be A and/or B (e.g., X=X%X) */ |
| 2396 /* lhs is A */ |
| 2397 /* rhs is B */ |
| 2398 /* set is the context */ |
| 2399 /* */ |
| 2400 /* C must have space for set->digits digits. */ |
| 2401 /* ------------------------------------------------------------------ */ |
| 2402 U_CAPI decNumber * U_EXPORT2 uprv_decNumberRemainder(decNumber *res, const decNu
mber *lhs, |
| 2403 const decNumber *rhs, decContext *set) { |
| 2404 uInt status=0; /* accumulator */ |
| 2405 decDivideOp(res, lhs, rhs, set, REMAINDER, &status); |
| 2406 if (status!=0) decStatus(res, status, set); |
| 2407 #if DECCHECK |
| 2408 decCheckInexact(res, set); |
| 2409 #endif |
| 2410 return res; |
| 2411 } /* decNumberRemainder */ |
| 2412 |
| 2413 /* ------------------------------------------------------------------ */ |
| 2414 /* decNumberRemainderNear -- divide and return remainder from nearest */ |
| 2415 /* */ |
| 2416 /* This computes C = A % B, where % is the IEEE remainder operator */ |
| 2417 /* */ |
| 2418 /* res is C, the result. C may be A and/or B (e.g., X=X%X) */ |
| 2419 /* lhs is A */ |
| 2420 /* rhs is B */ |
| 2421 /* set is the context */ |
| 2422 /* */ |
| 2423 /* C must have space for set->digits digits. */ |
| 2424 /* ------------------------------------------------------------------ */ |
| 2425 U_CAPI decNumber * U_EXPORT2 uprv_decNumberRemainderNear(decNumber *res, const d
ecNumber *lhs, |
| 2426 const decNumber *rhs, decContext *set) { |
| 2427 uInt status=0; /* accumulator */ |
| 2428 decDivideOp(res, lhs, rhs, set, REMNEAR, &status); |
| 2429 if (status!=0) decStatus(res, status, set); |
| 2430 #if DECCHECK |
| 2431 decCheckInexact(res, set); |
| 2432 #endif |
| 2433 return res; |
| 2434 } /* decNumberRemainderNear */ |
| 2435 |
| 2436 /* ------------------------------------------------------------------ */ |
| 2437 /* decNumberRotate -- rotate the coefficient of a Number left/right */ |
| 2438 /* */ |
| 2439 /* This computes C = A rot B (in base ten and rotating set->digits */ |
| 2440 /* digits). */ |
| 2441 /* */ |
| 2442 /* res is C, the result. C may be A and/or B (e.g., X=XrotX) */ |
| 2443 /* lhs is A */ |
| 2444 /* rhs is B, the number of digits to rotate (-ve to right) */ |
| 2445 /* set is the context */ |
| 2446 /* */ |
| 2447 /* The digits of the coefficient of A are rotated to the left (if B */ |
| 2448 /* is positive) or to the right (if B is negative) without adjusting */ |
| 2449 /* the exponent or the sign of A. If lhs->digits is less than */ |
| 2450 /* set->digits the coefficient is padded with zeros on the left */ |
| 2451 /* before the rotate. Any leading zeros in the result are removed */ |
| 2452 /* as usual. */ |
| 2453 /* */ |
| 2454 /* B must be an integer (q=0) and in the range -set->digits through */ |
| 2455 /* +set->digits. */ |
| 2456 /* C must have space for set->digits digits. */ |
| 2457 /* NaNs are propagated as usual. Infinities are unaffected (but */ |
| 2458 /* B must be valid). No status is set unless B is invalid or an */ |
| 2459 /* operand is an sNaN. */ |
| 2460 /* ------------------------------------------------------------------ */ |
| 2461 U_CAPI decNumber * U_EXPORT2 uprv_decNumberRotate(decNumber *res, const decNumbe
r *lhs, |
| 2462 const decNumber *rhs, decContext *set) { |
| 2463 uInt status=0; /* accumulator */ |
| 2464 Int rotate; /* rhs as an Int */ |
| 2465 |
| 2466 #if DECCHECK |
| 2467 if (decCheckOperands(res, lhs, rhs, set)) return res; |
| 2468 #endif |
| 2469 |
| 2470 /* NaNs propagate as normal */ |
| 2471 if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) |
| 2472 decNaNs(res, lhs, rhs, set, &status); |
| 2473 /* rhs must be an integer */ |
| 2474 else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) |
| 2475 status=DEC_Invalid_operation; |
| 2476 else { /* both numeric, rhs is an integer */ |
| 2477 rotate=decGetInt(rhs); /* [cannot fail] */ |
| 2478 if (rotate==BADINT /* something bad .. */ |
| 2479 || rotate==BIGODD || rotate==BIGEVEN /* .. very big .. */ |
| 2480 || abs(rotate)>set->digits) /* .. or out of range */ |
| 2481 status=DEC_Invalid_operation; |
| 2482 else { /* rhs is OK */ |
| 2483 uprv_decNumberCopy(res, lhs); |
| 2484 /* convert -ve rotate to equivalent positive rotation */ |
| 2485 if (rotate<0) rotate=set->digits+rotate; |
| 2486 if (rotate!=0 && rotate!=set->digits /* zero or full rotation */ |
| 2487 && !decNumberIsInfinite(res)) { /* lhs was infinite */ |
| 2488 /* left-rotate to do; 0 < rotate < set->digits */ |
| 2489 uInt units, shift; /* work */ |
| 2490 uInt msudigits; /* digits in result msu */ |
| 2491 Unit *msu=res->lsu+D2U(res->digits)-1; /* current msu */ |
| 2492 Unit *msumax=res->lsu+D2U(set->digits)-1; /* rotation msu */ |
| 2493 for (msu++; msu<=msumax; msu++) *msu=0; /* ensure high units=0 */ |
| 2494 res->digits=set->digits; /* now full-length */ |
| 2495 msudigits=MSUDIGITS(res->digits); /* actual digits in msu */ |
| 2496 |
| 2497 /* rotation here is done in-place, in three steps */ |
| 2498 /* 1. shift all to least up to one unit to unit-align final */ |
| 2499 /* lsd [any digits shifted out are rotated to the left, */ |
| 2500 /* abutted to the original msd (which may require split)] */ |
| 2501 /* */ |
| 2502 /* [if there are no whole units left to rotate, the */ |
| 2503 /* rotation is now complete] */ |
| 2504 /* */ |
| 2505 /* 2. shift to least, from below the split point only, so that */ |
| 2506 /* the final msd is in the right place in its Unit [any */ |
| 2507 /* digits shifted out will fit exactly in the current msu, */ |
| 2508 /* left aligned, no split required] */ |
| 2509 /* */ |
| 2510 /* 3. rotate all the units by reversing left part, right */ |
| 2511 /* part, and then whole */ |
| 2512 /* */ |
| 2513 /* example: rotate right 8 digits (2 units + 2), DECDPUN=3. */ |
| 2514 /* */ |
| 2515 /* start: 00a bcd efg hij klm npq */ |
| 2516 /* */ |
| 2517 /* 1a 000 0ab cde fgh|ijk lmn [pq saved] */ |
| 2518 /* 1b 00p qab cde fgh|ijk lmn */ |
| 2519 /* */ |
| 2520 /* 2a 00p qab cde fgh|00i jkl [mn saved] */ |
| 2521 /* 2b mnp qab cde fgh|00i jkl */ |
| 2522 /* */ |
| 2523 /* 3a fgh cde qab mnp|00i jkl */ |
| 2524 /* 3b fgh cde qab mnp|jkl 00i */ |
| 2525 /* 3c 00i jkl mnp qab cde fgh */ |
| 2526 |
| 2527 /* Step 1: amount to shift is the partial right-rotate count */ |
| 2528 rotate=set->digits-rotate; /* make it right-rotate */ |
| 2529 units=rotate/DECDPUN; /* whole units to rotate */ |
| 2530 shift=rotate%DECDPUN; /* left-over digits count */ |
| 2531 if (shift>0) { /* not an exact number of units */ |
| 2532 uInt save=res->lsu[0]%powers[shift]; /* save low digit(s) */ |
| 2533 decShiftToLeast(res->lsu, D2U(res->digits), shift); |
| 2534 if (shift>msudigits) { /* msumax-1 needs >0 digits */ |
| 2535 uInt rem=save%powers[shift-msudigits];/* split save */ |
| 2536 *msumax=(Unit)(save/powers[shift-msudigits]); /* and insert */ |
| 2537 *(msumax-1)=*(msumax-1) |
| 2538 +(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); /* .. */ |
| 2539 } |
| 2540 else { /* all fits in msumax */ |
| 2541 *msumax=*msumax+(Unit)(save*powers[msudigits-shift]); /* [maybe *1]
*/ |
| 2542 } |
| 2543 } /* digits shift needed */ |
| 2544 |
| 2545 /* If whole units to rotate... */ |
| 2546 if (units>0) { /* some to do */ |
| 2547 /* Step 2: the units to touch are the whole ones in rotate, */ |
| 2548 /* if any, and the shift is DECDPUN-msudigits (which may be */ |
| 2549 /* 0, again) */ |
| 2550 shift=DECDPUN-msudigits; |
| 2551 if (shift>0) { /* not an exact number of units */ |
| 2552 uInt save=res->lsu[0]%powers[shift]; /* save low digit(s) */ |
| 2553 decShiftToLeast(res->lsu, units, shift); |
| 2554 *msumax=*msumax+(Unit)(save*powers[msudigits]); |
| 2555 } /* partial shift needed */ |
| 2556 |
| 2557 /* Step 3: rotate the units array using triple reverse */ |
| 2558 /* (reversing is easy and fast) */ |
| 2559 decReverse(res->lsu+units, msumax); /* left part */ |
| 2560 decReverse(res->lsu, res->lsu+units-1); /* right part */ |
| 2561 decReverse(res->lsu, msumax); /* whole */ |
| 2562 } /* whole units to rotate */ |
| 2563 /* the rotation may have left an undetermined number of zeros */ |
| 2564 /* on the left, so true length needs to be calculated */ |
| 2565 res->digits=decGetDigits(res->lsu, msumax-res->lsu+1); |
| 2566 } /* rotate needed */ |
| 2567 } /* rhs OK */ |
| 2568 } /* numerics */ |
| 2569 if (status!=0) decStatus(res, status, set); |
| 2570 return res; |
| 2571 } /* decNumberRotate */ |
| 2572 |
| 2573 /* ------------------------------------------------------------------ */ |
| 2574 /* decNumberSameQuantum -- test for equal exponents */ |
| 2575 /* */ |
| 2576 /* res is the result number, which will contain either 0 or 1 */ |
| 2577 /* lhs is a number to test */ |
| 2578 /* rhs is the second (usually a pattern) */ |
| 2579 /* */ |
| 2580 /* No errors are possible and no context is needed. */ |
| 2581 /* ------------------------------------------------------------------ */ |
| 2582 U_CAPI decNumber * U_EXPORT2 uprv_decNumberSameQuantum(decNumber *res, const dec
Number *lhs, |
| 2583 const decNumber *rhs) { |
| 2584 Unit ret=0; /* return value */ |
| 2585 |
| 2586 #if DECCHECK |
| 2587 if (decCheckOperands(res, lhs, rhs, DECUNCONT)) return res; |
| 2588 #endif |
| 2589 |
| 2590 if (SPECIALARGS) { |
| 2591 if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1; |
| 2592 else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1; |
| 2593 /* [anything else with a special gives 0] */ |
| 2594 } |
| 2595 else if (lhs->exponent==rhs->exponent) ret=1; |
| 2596 |
| 2597 uprv_decNumberZero(res); /* OK to overwrite an operand now */ |
| 2598 *res->lsu=ret; |
| 2599 return res; |
| 2600 } /* decNumberSameQuantum */ |
| 2601 |
| 2602 /* ------------------------------------------------------------------ */ |
| 2603 /* decNumberScaleB -- multiply by a power of 10 */ |
| 2604 /* */ |
| 2605 /* This computes C = A x 10**B where B is an integer (q=0) with */ |
| 2606 /* maximum magnitude 2*(emax+digits) */ |
| 2607 /* */ |
| 2608 /* res is C, the result. C may be A or B */ |
| 2609 /* lhs is A, the number to adjust */ |
| 2610 /* rhs is B, the requested power of ten to use */ |
| 2611 /* set is the context */ |
| 2612 /* */ |
| 2613 /* C must have space for set->digits digits. */ |
| 2614 /* */ |
| 2615 /* The result may underflow or overflow. */ |
| 2616 /* ------------------------------------------------------------------ */ |
| 2617 U_CAPI decNumber * U_EXPORT2 uprv_decNumberScaleB(decNumber *res, const decNumbe
r *lhs, |
| 2618 const decNumber *rhs, decContext *set) { |
| 2619 Int reqexp; /* requested exponent change [B] */ |
| 2620 uInt status=0; /* accumulator */ |
| 2621 Int residue; /* work */ |
| 2622 |
| 2623 #if DECCHECK |
| 2624 if (decCheckOperands(res, lhs, rhs, set)) return res; |
| 2625 #endif |
| 2626 |
| 2627 /* Handle special values except lhs infinite */ |
| 2628 if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) |
| 2629 decNaNs(res, lhs, rhs, set, &status); |
| 2630 /* rhs must be an integer */ |
| 2631 else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) |
| 2632 status=DEC_Invalid_operation; |
| 2633 else { |
| 2634 /* lhs is a number; rhs is a finite with q==0 */ |
| 2635 reqexp=decGetInt(rhs); /* [cannot fail] */ |
| 2636 if (reqexp==BADINT /* something bad .. */ |
| 2637 || reqexp==BIGODD || reqexp==BIGEVEN /* .. very big .. */ |
| 2638 || abs(reqexp)>(2*(set->digits+set->emax))) /* .. or out of range */ |
| 2639 status=DEC_Invalid_operation; |
| 2640 else { /* rhs is OK */ |
| 2641 uprv_decNumberCopy(res, lhs); /* all done if infinite lhs *
/ |
| 2642 if (!decNumberIsInfinite(res)) { /* prepare to scale */ |
| 2643 res->exponent+=reqexp; /* adjust the exponent */ |
| 2644 residue=0; |
| 2645 decFinalize(res, set, &residue, &status); /* .. and check */ |
| 2646 } /* finite LHS */ |
| 2647 } /* rhs OK */ |
| 2648 } /* rhs finite */ |
| 2649 if (status!=0) decStatus(res, status, set); |
| 2650 return res; |
| 2651 } /* decNumberScaleB */ |
| 2652 |
| 2653 /* ------------------------------------------------------------------ */ |
| 2654 /* decNumberShift -- shift the coefficient of a Number left or right */ |
| 2655 /* */ |
| 2656 /* This computes C = A << B or C = A >> -B (in base ten). */ |
| 2657 /* */ |
| 2658 /* res is C, the result. C may be A and/or B (e.g., X=X<<X) */ |
| 2659 /* lhs is A */ |
| 2660 /* rhs is B, the number of digits to shift (-ve to right) */ |
| 2661 /* set is the context */ |
| 2662 /* */ |
| 2663 /* The digits of the coefficient of A are shifted to the left (if B */ |
| 2664 /* is positive) or to the right (if B is negative) without adjusting */ |
| 2665 /* the exponent or the sign of A. */ |
| 2666 /* */ |
| 2667 /* B must be an integer (q=0) and in the range -set->digits through */ |
| 2668 /* +set->digits. */ |
| 2669 /* C must have space for set->digits digits. */ |
| 2670 /* NaNs are propagated as usual. Infinities are unaffected (but */ |
| 2671 /* B must be valid). No status is set unless B is invalid or an */ |
| 2672 /* operand is an sNaN. */ |
| 2673 /* ------------------------------------------------------------------ */ |
| 2674 U_CAPI decNumber * U_EXPORT2 uprv_decNumberShift(decNumber *res, const decNumber
*lhs, |
| 2675 const decNumber *rhs, decContext *set) { |
| 2676 uInt status=0; /* accumulator */ |
| 2677 Int shift; /* rhs as an Int */ |
| 2678 |
| 2679 #if DECCHECK |
| 2680 if (decCheckOperands(res, lhs, rhs, set)) return res; |
| 2681 #endif |
| 2682 |
| 2683 /* NaNs propagate as normal */ |
| 2684 if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) |
| 2685 decNaNs(res, lhs, rhs, set, &status); |
| 2686 /* rhs must be an integer */ |
| 2687 else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) |
| 2688 status=DEC_Invalid_operation; |
| 2689 else { /* both numeric, rhs is an integer */ |
| 2690 shift=decGetInt(rhs); /* [cannot fail] */ |
| 2691 if (shift==BADINT /* something bad .. */ |
| 2692 || shift==BIGODD || shift==BIGEVEN /* .. very big .. */ |
| 2693 || abs(shift)>set->digits) /* .. or out of range */ |
| 2694 status=DEC_Invalid_operation; |
| 2695 else { /* rhs is OK */ |
| 2696 uprv_decNumberCopy(res, lhs); |
| 2697 if (shift!=0 && !decNumberIsInfinite(res)) { /* something to do */ |
| 2698 if (shift>0) { /* to left */ |
| 2699 if (shift==set->digits) { /* removing all */ |
| 2700 *res->lsu=0; /* so place 0 */ |
| 2701 res->digits=1; /* .. */ |
| 2702 } |
| 2703 else { /* */ |
| 2704 /* first remove leading digits if necessary */ |
| 2705 if (res->digits+shift>set->digits) { |
| 2706 decDecap(res, res->digits+shift-set->digits); |
| 2707 /* that updated res->digits; may have gone to 1 (for a */ |
| 2708 /* single digit or for zero */ |
| 2709 } |
| 2710 if (res->digits>1 || *res->lsu) /* if non-zero.. */ |
| 2711 res->digits=decShiftToMost(res->lsu, res->digits, shift); |
| 2712 } /* partial left */ |
| 2713 } /* left */ |
| 2714 else { /* to right */ |
| 2715 if (-shift>=res->digits) { /* discarding all */ |
| 2716 *res->lsu=0; /* so place 0 */ |
| 2717 res->digits=1; /* .. */ |
| 2718 } |
| 2719 else { |
| 2720 decShiftToLeast(res->lsu, D2U(res->digits), -shift); |
| 2721 res->digits-=(-shift); |
| 2722 } |
| 2723 } /* to right */ |
| 2724 } /* non-0 non-Inf shift */ |
| 2725 } /* rhs OK */ |
| 2726 } /* numerics */ |
| 2727 if (status!=0) decStatus(res, status, set); |
| 2728 return res; |
| 2729 } /* decNumberShift */ |
| 2730 |
| 2731 /* ------------------------------------------------------------------ */ |
| 2732 /* decNumberSquareRoot -- square root operator */ |
| 2733 /* */ |
| 2734 /* This computes C = squareroot(A) */ |
| 2735 /* */ |
| 2736 /* res is C, the result. C may be A */ |
| 2737 /* rhs is A */ |
| 2738 /* set is the context; note that rounding mode has no effect */ |
| 2739 /* */ |
| 2740 /* C must have space for set->digits digits. */ |
| 2741 /* ------------------------------------------------------------------ */ |
| 2742 /* This uses the following varying-precision algorithm in: */ |
| 2743 /* */ |
| 2744 /* Properly Rounded Variable Precision Square Root, T. E. Hull and */ |
| 2745 /* A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */ |
| 2746 /* pp229-237, ACM, September 1985. */ |
| 2747 /* */ |
| 2748 /* The square-root is calculated using Newton's method, after which */ |
| 2749 /* a check is made to ensure the result is correctly rounded. */ |
| 2750 /* */ |
| 2751 /* % [Reformatted original Numerical Turing source code follows.] */ |
| 2752 /* function sqrt(x : real) : real */ |
| 2753 /* % sqrt(x) returns the properly rounded approximation to the square */ |
| 2754 /* % root of x, in the precision of the calling environment, or it */ |
| 2755 /* % fails if x < 0. */ |
| 2756 /* % t e hull and a abrham, august, 1984 */ |
| 2757 /* if x <= 0 then */ |
| 2758 /* if x < 0 then */ |
| 2759 /* assert false */ |
| 2760 /* else */ |
| 2761 /* result 0 */ |
| 2762 /* end if */ |
| 2763 /* end if */ |
| 2764 /* var f := setexp(x, 0) % fraction part of x [0.1 <= x < 1] */ |
| 2765 /* var e := getexp(x) % exponent part of x */ |
| 2766 /* var approx : real */ |
| 2767 /* if e mod 2 = 0 then */ |
| 2768 /* approx := .259 + .819 * f % approx to root of f */ |
| 2769 /* else */ |
| 2770 /* f := f/l0 % adjustments */ |
| 2771 /* e := e + 1 % for odd */ |
| 2772 /* approx := .0819 + 2.59 * f % exponent */ |
| 2773 /* end if */ |
| 2774 /* */ |
| 2775 /* var p:= 3 */ |
| 2776 /* const maxp := currentprecision + 2 */ |
| 2777 /* loop */ |
| 2778 /* p := min(2*p - 2, maxp) % p = 4,6,10, . . . , maxp */ |
| 2779 /* precision p */ |
| 2780 /* approx := .5 * (approx + f/approx) */ |
| 2781 /* exit when p = maxp */ |
| 2782 /* end loop */ |
| 2783 /* */ |
| 2784 /* % approx is now within 1 ulp of the properly rounded square root */ |
| 2785 /* % of f; to ensure proper rounding, compare squares of (approx - */ |
| 2786 /* % l/2 ulp) and (approx + l/2 ulp) with f. */ |
| 2787 /* p := currentprecision */ |
| 2788 /* begin */ |
| 2789 /* precision p + 2 */ |
| 2790 /* const approxsubhalf := approx - setexp(.5, -p) */ |
| 2791 /* if mulru(approxsubhalf, approxsubhalf) > f then */ |
| 2792 /* approx := approx - setexp(.l, -p + 1) */ |
| 2793 /* else */ |
| 2794 /* const approxaddhalf := approx + setexp(.5, -p) */ |
| 2795 /* if mulrd(approxaddhalf, approxaddhalf) < f then */ |
| 2796 /* approx := approx + setexp(.l, -p + 1) */ |
| 2797 /* end if */ |
| 2798 /* end if */ |
| 2799 /* end */ |
| 2800 /* result setexp(approx, e div 2) % fix exponent */ |
| 2801 /* end sqrt */ |
| 2802 /* ------------------------------------------------------------------ */ |
| 2803 U_CAPI decNumber * U_EXPORT2 uprv_decNumberSquareRoot(decNumber *res, const decN
umber *rhs, |
| 2804 decContext *set) { |
| 2805 decContext workset, approxset; /* work contexts */ |
| 2806 decNumber dzero; /* used for constant zero */ |
| 2807 Int maxp; /* largest working precision */ |
| 2808 Int workp; /* working precision */ |
| 2809 Int residue=0; /* rounding residue */ |
| 2810 uInt status=0, ignore=0; /* status accumulators */ |
| 2811 uInt rstatus; /* .. */ |
| 2812 Int exp; /* working exponent */ |
| 2813 Int ideal; /* ideal (preferred) exponent */ |
| 2814 Int needbytes; /* work */ |
| 2815 Int dropped; /* .. */ |
| 2816 |
| 2817 #if DECSUBSET |
| 2818 decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ |
| 2819 #endif |
| 2820 /* buffer for f [needs +1 in case DECBUFFER 0] */ |
| 2821 decNumber buff[D2N(DECBUFFER+1)]; |
| 2822 /* buffer for a [needs +2 to match likely maxp] */ |
| 2823 decNumber bufa[D2N(DECBUFFER+2)]; |
| 2824 /* buffer for temporary, b [must be same size as a] */ |
| 2825 decNumber bufb[D2N(DECBUFFER+2)]; |
| 2826 decNumber *allocbuff=NULL; /* -> allocated buff, iff allocated */ |
| 2827 decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ |
| 2828 decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */ |
| 2829 decNumber *f=buff; /* reduced fraction */ |
| 2830 decNumber *a=bufa; /* approximation to result */ |
| 2831 decNumber *b=bufb; /* intermediate result */ |
| 2832 /* buffer for temporary variable, up to 3 digits */ |
| 2833 decNumber buft[D2N(3)]; |
| 2834 decNumber *t=buft; /* up-to-3-digit constant or work */ |
| 2835 |
| 2836 #if DECCHECK |
| 2837 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
| 2838 #endif |
| 2839 |
| 2840 do { /* protect allocated storage */ |
| 2841 #if DECSUBSET |
| 2842 if (!set->extended) { |
| 2843 /* reduce operand and set lostDigits status, as needed */ |
| 2844 if (rhs->digits>set->digits) { |
| 2845 allocrhs=decRoundOperand(rhs, set, &status); |
| 2846 if (allocrhs==NULL) break; |
| 2847 /* [Note: 'f' allocation below could reuse this buffer if */ |
| 2848 /* used, but as this is rare they are kept separate for clarity.] */ |
| 2849 rhs=allocrhs; |
| 2850 } |
| 2851 } |
| 2852 #endif |
| 2853 /* [following code does not require input rounding] */ |
| 2854 |
| 2855 /* handle infinities and NaNs */ |
| 2856 if (SPECIALARG) { |
| 2857 if (decNumberIsInfinite(rhs)) { /* an infinity */ |
| 2858 if (decNumberIsNegative(rhs)) status|=DEC_Invalid_operation; |
| 2859 else uprv_decNumberCopy(res, rhs); /* +Infinity */ |
| 2860 } |
| 2861 else decNaNs(res, rhs, NULL, set, &status); /* a NaN */ |
| 2862 break; |
| 2863 } |
| 2864 |
| 2865 /* calculate the ideal (preferred) exponent [floor(exp/2)] */ |
| 2866 /* [It would be nicer to write: ideal=rhs->exponent>>1, but this */ |
| 2867 /* generates a compiler warning. Generated code is the same.] */ |
| 2868 ideal=(rhs->exponent&~1)/2; /* target */ |
| 2869 |
| 2870 /* handle zeros */ |
| 2871 if (ISZERO(rhs)) { |
| 2872 uprv_decNumberCopy(res, rhs); /* could be 0 or -0 */ |
| 2873 res->exponent=ideal; /* use the ideal [safe] */ |
| 2874 /* use decFinish to clamp any out-of-range exponent, etc. */ |
| 2875 decFinish(res, set, &residue, &status); |
| 2876 break; |
| 2877 } |
| 2878 |
| 2879 /* any other -x is an oops */ |
| 2880 if (decNumberIsNegative(rhs)) { |
| 2881 status|=DEC_Invalid_operation; |
| 2882 break; |
| 2883 } |
| 2884 |
| 2885 /* space is needed for three working variables */ |
| 2886 /* f -- the same precision as the RHS, reduced to 0.01->0.99... */ |
| 2887 /* a -- Hull's approximation -- precision, when assigned, is */ |
| 2888 /* currentprecision+1 or the input argument precision, */ |
| 2889 /* whichever is larger (+2 for use as temporary) */ |
| 2890 /* b -- intermediate temporary result (same size as a) */ |
| 2891 /* if any is too long for local storage, then allocate */ |
| 2892 workp=MAXI(set->digits+1, rhs->digits); /* actual rounding precision */ |
| 2893 workp=MAXI(workp, 7); /* at least 7 for low cases */ |
| 2894 maxp=workp+2; /* largest working precision */ |
| 2895 |
| 2896 needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); |
| 2897 if (needbytes>(Int)sizeof(buff)) { |
| 2898 allocbuff=(decNumber *)malloc(needbytes); |
| 2899 if (allocbuff==NULL) { /* hopeless -- abandon */ |
| 2900 status|=DEC_Insufficient_storage; |
| 2901 break;} |
| 2902 f=allocbuff; /* use the allocated space */ |
| 2903 } |
| 2904 /* a and b both need to be able to hold a maxp-length number */ |
| 2905 needbytes=sizeof(decNumber)+(D2U(maxp)-1)*sizeof(Unit); |
| 2906 if (needbytes>(Int)sizeof(bufa)) { /* [same applies to b] */ |
| 2907 allocbufa=(decNumber *)malloc(needbytes); |
| 2908 allocbufb=(decNumber *)malloc(needbytes); |
| 2909 if (allocbufa==NULL || allocbufb==NULL) { /* hopeless */ |
| 2910 status|=DEC_Insufficient_storage; |
| 2911 break;} |
| 2912 a=allocbufa; /* use the allocated spaces */ |
| 2913 b=allocbufb; /* .. */ |
| 2914 } |
| 2915 |
| 2916 /* copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1 */ |
| 2917 uprv_decNumberCopy(f, rhs); |
| 2918 exp=f->exponent+f->digits; /* adjusted to Hull rules */ |
| 2919 f->exponent=-(f->digits); /* to range */ |
| 2920 |
| 2921 /* set up working context */ |
| 2922 uprv_decContextDefault(&workset, DEC_INIT_DECIMAL64); |
| 2923 workset.emax=DEC_MAX_EMAX; |
| 2924 workset.emin=DEC_MIN_EMIN; |
| 2925 |
| 2926 /* [Until further notice, no error is possible and status bits */ |
| 2927 /* (Rounded, etc.) should be ignored, not accumulated.] */ |
| 2928 |
| 2929 /* Calculate initial approximation, and allow for odd exponent */ |
| 2930 workset.digits=workp; /* p for initial calculation */ |
| 2931 t->bits=0; t->digits=3; |
| 2932 a->bits=0; a->digits=3; |
| 2933 if ((exp & 1)==0) { /* even exponent */ |
| 2934 /* Set t=0.259, a=0.819 */ |
| 2935 t->exponent=-3; |
| 2936 a->exponent=-3; |
| 2937 #if DECDPUN>=3 |
| 2938 t->lsu[0]=259; |
| 2939 a->lsu[0]=819; |
| 2940 #elif DECDPUN==2 |
| 2941 t->lsu[0]=59; t->lsu[1]=2; |
| 2942 a->lsu[0]=19; a->lsu[1]=8; |
| 2943 #else |
| 2944 t->lsu[0]=9; t->lsu[1]=5; t->lsu[2]=2; |
| 2945 a->lsu[0]=9; a->lsu[1]=1; a->lsu[2]=8; |
| 2946 #endif |
| 2947 } |
| 2948 else { /* odd exponent */ |
| 2949 /* Set t=0.0819, a=2.59 */ |
| 2950 f->exponent--; /* f=f/10 */ |
| 2951 exp++; /* e=e+1 */ |
| 2952 t->exponent=-4; |
| 2953 a->exponent=-2; |
| 2954 #if DECDPUN>=3 |
| 2955 t->lsu[0]=819; |
| 2956 a->lsu[0]=259; |
| 2957 #elif DECDPUN==2 |
| 2958 t->lsu[0]=19; t->lsu[1]=8; |
| 2959 a->lsu[0]=59; a->lsu[1]=2; |
| 2960 #else |
| 2961 t->lsu[0]=9; t->lsu[1]=1; t->lsu[2]=8; |
| 2962 a->lsu[0]=9; a->lsu[1]=5; a->lsu[2]=2; |
| 2963 #endif |
| 2964 } |
| 2965 |
| 2966 decMultiplyOp(a, a, f, &workset, &ignore); /* a=a*f */ |
| 2967 decAddOp(a, a, t, &workset, 0, &ignore); /* ..+t */ |
| 2968 /* [a is now the initial approximation for sqrt(f), calculated with */ |
| 2969 /* currentprecision, which is also a's precision.] */ |
| 2970 |
| 2971 /* the main calculation loop */ |
| 2972 uprv_decNumberZero(&dzero); /* make 0 */ |
| 2973 uprv_decNumberZero(t); /* set t = 0.5 */ |
| 2974 t->lsu[0]=5; /* .. */ |
| 2975 t->exponent=-1; /* .. */ |
| 2976 workset.digits=3; /* initial p */ |
| 2977 for (; workset.digits<maxp;) { |
| 2978 /* set p to min(2*p - 2, maxp) [hence 3; or: 4, 6, 10, ... , maxp] */ |
| 2979 workset.digits=MINI(workset.digits*2-2, maxp); |
| 2980 /* a = 0.5 * (a + f/a) */ |
| 2981 /* [calculated at p then rounded to currentprecision] */ |
| 2982 decDivideOp(b, f, a, &workset, DIVIDE, &ignore); /* b=f/a */ |
| 2983 decAddOp(b, b, a, &workset, 0, &ignore); /* b=b+a */ |
| 2984 decMultiplyOp(a, b, t, &workset, &ignore); /* a=b*0.5 */ |
| 2985 } /* loop */ |
| 2986 |
| 2987 /* Here, 0.1 <= a < 1 [Hull], and a has maxp digits */ |
| 2988 /* now reduce to length, etc.; this needs to be done with a */ |
| 2989 /* having the correct exponent so as to handle subnormals */ |
| 2990 /* correctly */ |
| 2991 approxset=*set; /* get emin, emax, etc. */ |
| 2992 approxset.round=DEC_ROUND_HALF_EVEN; |
| 2993 a->exponent+=exp/2; /* set correct exponent */ |
| 2994 rstatus=0; /* clear status */ |
| 2995 residue=0; /* .. and accumulator */ |
| 2996 decCopyFit(a, a, &approxset, &residue, &rstatus); /* reduce (if needed) */ |
| 2997 decFinish(a, &approxset, &residue, &rstatus); /* clean and finalize */ |
| 2998 |
| 2999 /* Overflow was possible if the input exponent was out-of-range, */ |
| 3000 /* in which case quit */ |
| 3001 if (rstatus&DEC_Overflow) { |
| 3002 status=rstatus; /* use the status as-is */ |
| 3003 uprv_decNumberCopy(res, a); /* copy to result */ |
| 3004 break; |
| 3005 } |
| 3006 |
| 3007 /* Preserve status except Inexact/Rounded */ |
| 3008 status|=(rstatus & ~(DEC_Rounded|DEC_Inexact)); |
| 3009 |
| 3010 /* Carry out the Hull correction */ |
| 3011 a->exponent-=exp/2; /* back to 0.1->1 */ |
| 3012 |
| 3013 /* a is now at final precision and within 1 ulp of the properly */ |
| 3014 /* rounded square root of f; to ensure proper rounding, compare */ |
| 3015 /* squares of (a - l/2 ulp) and (a + l/2 ulp) with f. */ |
| 3016 /* Here workset.digits=maxp and t=0.5, and a->digits determines */ |
| 3017 /* the ulp */ |
| 3018 workset.digits--; /* maxp-1 is OK now */ |
| 3019 t->exponent=-a->digits-1; /* make 0.5 ulp */ |
| 3020 decAddOp(b, a, t, &workset, DECNEG, &ignore); /* b = a - 0.5 ulp */ |
| 3021 workset.round=DEC_ROUND_UP; |
| 3022 decMultiplyOp(b, b, b, &workset, &ignore); /* b = mulru(b, b) */ |
| 3023 decCompareOp(b, f, b, &workset, COMPARE, &ignore); /* b ? f, reversed */ |
| 3024 if (decNumberIsNegative(b)) { /* f < b [i.e., b > f] */ |
| 3025 /* this is the more common adjustment, though both are rare */ |
| 3026 t->exponent++; /* make 1.0 ulp */ |
| 3027 t->lsu[0]=1; /* .. */ |
| 3028 decAddOp(a, a, t, &workset, DECNEG, &ignore); /* a = a - 1 ulp */ |
| 3029 /* assign to approx [round to length] */ |
| 3030 approxset.emin-=exp/2; /* adjust to match a */ |
| 3031 approxset.emax-=exp/2; |
| 3032 decAddOp(a, &dzero, a, &approxset, 0, &ignore); |
| 3033 } |
| 3034 else { |
| 3035 decAddOp(b, a, t, &workset, 0, &ignore); /* b = a + 0.5 ulp */ |
| 3036 workset.round=DEC_ROUND_DOWN; |
| 3037 decMultiplyOp(b, b, b, &workset, &ignore); /* b = mulrd(b, b) */ |
| 3038 decCompareOp(b, b, f, &workset, COMPARE, &ignore); /* b ? f */ |
| 3039 if (decNumberIsNegative(b)) { /* b < f */ |
| 3040 t->exponent++; /* make 1.0 ulp */ |
| 3041 t->lsu[0]=1; /* .. */ |
| 3042 decAddOp(a, a, t, &workset, 0, &ignore); /* a = a + 1 ulp */ |
| 3043 /* assign to approx [round to length] */ |
| 3044 approxset.emin-=exp/2; /* adjust to match a */ |
| 3045 approxset.emax-=exp/2; |
| 3046 decAddOp(a, &dzero, a, &approxset, 0, &ignore); |
| 3047 } |
| 3048 } |
| 3049 /* [no errors are possible in the above, and rounding/inexact during */ |
| 3050 /* estimation are irrelevant, so status was not accumulated] */ |
| 3051 |
| 3052 /* Here, 0.1 <= a < 1 (still), so adjust back */ |
| 3053 a->exponent+=exp/2; /* set correct exponent */ |
| 3054 |
| 3055 /* count droppable zeros [after any subnormal rounding] by */ |
| 3056 /* trimming a copy */ |
| 3057 uprv_decNumberCopy(b, a); |
| 3058 decTrim(b, set, 1, 1, &dropped); /* [drops trailing zeros] */ |
| 3059 |
| 3060 /* Set Inexact and Rounded. The answer can only be exact if */ |
| 3061 /* it is short enough so that squaring it could fit in workp */ |
| 3062 /* digits, so this is the only (relatively rare) condition that */ |
| 3063 /* a careful check is needed */ |
| 3064 if (b->digits*2-1 > workp) { /* cannot fit */ |
| 3065 status|=DEC_Inexact|DEC_Rounded; |
| 3066 } |
| 3067 else { /* could be exact/unrounded */ |
| 3068 uInt mstatus=0; /* local status */ |
| 3069 decMultiplyOp(b, b, b, &workset, &mstatus); /* try the multiply */ |
| 3070 if (mstatus&DEC_Overflow) { /* result just won't fit */ |
| 3071 status|=DEC_Inexact|DEC_Rounded; |
| 3072 } |
| 3073 else { /* plausible */ |
| 3074 decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); /* b ? rhs */ |
| 3075 if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; /* not equal */ |
| 3076 else { /* is Exact */ |
| 3077 /* here, dropped is the count of trailing zeros in 'a' */ |
| 3078 /* use closest exponent to ideal... */ |
| 3079 Int todrop=ideal-a->exponent; /* most that can be dropped */ |
| 3080 if (todrop<0) status|=DEC_Rounded; /* ideally would add 0s */ |
| 3081 else { /* unrounded */ |
| 3082 /* there are some to drop, but emax may not allow all */ |
| 3083 Int maxexp=set->emax-set->digits+1; |
| 3084 Int maxdrop=maxexp-a->exponent; |
| 3085 if (todrop>maxdrop && set->clamp) { /* apply clamping */ |
| 3086 todrop=maxdrop; |
| 3087 status|=DEC_Clamped; |
| 3088 } |
| 3089 if (dropped<todrop) { /* clamp to those available */ |
| 3090 todrop=dropped; |
| 3091 status|=DEC_Clamped; |
| 3092 } |
| 3093 if (todrop>0) { /* have some to drop */ |
| 3094 decShiftToLeast(a->lsu, D2U(a->digits), todrop); |
| 3095 a->exponent+=todrop; /* maintain numerical value */ |
| 3096 a->digits-=todrop; /* new length */ |
| 3097 } |
| 3098 } |
| 3099 } |
| 3100 } |
| 3101 } |
| 3102 |
| 3103 /* double-check Underflow, as perhaps the result could not have */ |
| 3104 /* been subnormal (initial argument too big), or it is now Exact */ |
| 3105 if (status&DEC_Underflow) { |
| 3106 Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */ |
| 3107 /* check if truly subnormal */ |
| 3108 #if DECEXTFLAG /* DEC_Subnormal too */ |
| 3109 if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow); |
| 3110 #else |
| 3111 if (ae>=set->emin*2) status&=~DEC_Underflow; |
| 3112 #endif |
| 3113 /* check if truly inexact */ |
| 3114 if (!(status&DEC_Inexact)) status&=~DEC_Underflow; |
| 3115 } |
| 3116 |
| 3117 uprv_decNumberCopy(res, a); /* a is now the result */ |
| 3118 } while(0); /* end protected */ |
| 3119 |
| 3120 if (allocbuff!=NULL) free(allocbuff); /* drop any storage used */ |
| 3121 if (allocbufa!=NULL) free(allocbufa); /* .. */ |
| 3122 if (allocbufb!=NULL) free(allocbufb); /* .. */ |
| 3123 #if DECSUBSET |
| 3124 if (allocrhs !=NULL) free(allocrhs); /* .. */ |
| 3125 #endif |
| 3126 if (status!=0) decStatus(res, status, set);/* then report status */ |
| 3127 #if DECCHECK |
| 3128 decCheckInexact(res, set); |
| 3129 #endif |
| 3130 return res; |
| 3131 } /* decNumberSquareRoot */ |
| 3132 |
| 3133 /* ------------------------------------------------------------------ */ |
| 3134 /* decNumberSubtract -- subtract two Numbers */ |
| 3135 /* */ |
| 3136 /* This computes C = A - B */ |
| 3137 /* */ |
| 3138 /* res is C, the result. C may be A and/or B (e.g., X=X-X) */ |
| 3139 /* lhs is A */ |
| 3140 /* rhs is B */ |
| 3141 /* set is the context */ |
| 3142 /* */ |
| 3143 /* C must have space for set->digits digits. */ |
| 3144 /* ------------------------------------------------------------------ */ |
| 3145 U_CAPI decNumber * U_EXPORT2 uprv_decNumberSubtract(decNumber *res, const decNum
ber *lhs, |
| 3146 const decNumber *rhs, decContext *set) { |
| 3147 uInt status=0; /* accumulator */ |
| 3148 |
| 3149 decAddOp(res, lhs, rhs, set, DECNEG, &status); |
| 3150 if (status!=0) decStatus(res, status, set); |
| 3151 #if DECCHECK |
| 3152 decCheckInexact(res, set); |
| 3153 #endif |
| 3154 return res; |
| 3155 } /* decNumberSubtract */ |
| 3156 |
| 3157 /* ------------------------------------------------------------------ */ |
| 3158 /* decNumberToIntegralExact -- round-to-integral-value with InExact */ |
| 3159 /* decNumberToIntegralValue -- round-to-integral-value */ |
| 3160 /* */ |
| 3161 /* res is the result */ |
| 3162 /* rhs is input number */ |
| 3163 /* set is the context */ |
| 3164 /* */ |
| 3165 /* res must have space for any value of rhs. */ |
| 3166 /* */ |
| 3167 /* This implements the IEEE special operators and therefore treats */ |
| 3168 /* special values as valid. For finite numbers it returns */ |
| 3169 /* rescale(rhs, 0) if rhs->exponent is <0. */ |
| 3170 /* Otherwise the result is rhs (so no error is possible, except for */ |
| 3171 /* sNaN). */ |
| 3172 /* */ |
| 3173 /* The context is used for rounding mode and status after sNaN, but */ |
| 3174 /* the digits setting is ignored. The Exact version will signal */ |
| 3175 /* Inexact if the result differs numerically from rhs; the other */ |
| 3176 /* never signals Inexact. */ |
| 3177 /* ------------------------------------------------------------------ */ |
| 3178 U_CAPI decNumber * U_EXPORT2 uprv_decNumberToIntegralExact(decNumber *res, const
decNumber *rhs, |
| 3179 decContext *set) { |
| 3180 decNumber dn; |
| 3181 decContext workset; /* working context */ |
| 3182 uInt status=0; /* accumulator */ |
| 3183 |
| 3184 #if DECCHECK |
| 3185 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
| 3186 #endif |
| 3187 |
| 3188 /* handle infinities and NaNs */ |
| 3189 if (SPECIALARG) { |
| 3190 if (decNumberIsInfinite(rhs)) uprv_decNumberCopy(res, rhs); /* an Infinity
*/ |
| 3191 else decNaNs(res, rhs, NULL, set, &status); /* a NaN */ |
| 3192 } |
| 3193 else { /* finite */ |
| 3194 /* have a finite number; no error possible (res must be big enough) */ |
| 3195 if (rhs->exponent>=0) return uprv_decNumberCopy(res, rhs); |
| 3196 /* that was easy, but if negative exponent there is work to do... */ |
| 3197 workset=*set; /* clone rounding, etc. */ |
| 3198 workset.digits=rhs->digits; /* no length rounding */ |
| 3199 workset.traps=0; /* no traps */ |
| 3200 uprv_decNumberZero(&dn); /* make a number with exponent 0 */ |
| 3201 uprv_decNumberQuantize(res, rhs, &dn, &workset); |
| 3202 status|=workset.status; |
| 3203 } |
| 3204 if (status!=0) decStatus(res, status, set); |
| 3205 return res; |
| 3206 } /* decNumberToIntegralExact */ |
| 3207 |
| 3208 U_CAPI decNumber * U_EXPORT2 uprv_decNumberToIntegralValue(decNumber *res, const
decNumber *rhs, |
| 3209 decContext *set) { |
| 3210 decContext workset=*set; /* working context */ |
| 3211 workset.traps=0; /* no traps */ |
| 3212 uprv_decNumberToIntegralExact(res, rhs, &workset); |
| 3213 /* this never affects set, except for sNaNs; NaN will have been set */ |
| 3214 /* or propagated already, so no need to call decStatus */ |
| 3215 set->status|=workset.status&DEC_Invalid_operation; |
| 3216 return res; |
| 3217 } /* decNumberToIntegralValue */ |
| 3218 |
| 3219 /* ------------------------------------------------------------------ */ |
| 3220 /* decNumberXor -- XOR two Numbers, digitwise */ |
| 3221 /* */ |
| 3222 /* This computes C = A ^ B */ |
| 3223 /* */ |
| 3224 /* res is C, the result. C may be A and/or B (e.g., X=X^X) */ |
| 3225 /* lhs is A */ |
| 3226 /* rhs is B */ |
| 3227 /* set is the context (used for result length and error report) */ |
| 3228 /* */ |
| 3229 /* C must have space for set->digits digits. */ |
| 3230 /* */ |
| 3231 /* Logical function restrictions apply (see above); a NaN is */ |
| 3232 /* returned with Invalid_operation if a restriction is violated. */ |
| 3233 /* ------------------------------------------------------------------ */ |
| 3234 U_CAPI decNumber * U_EXPORT2 uprv_decNumberXor(decNumber *res, const decNumber *
lhs, |
| 3235 const decNumber *rhs, decContext *set) { |
| 3236 const Unit *ua, *ub; /* -> operands */ |
| 3237 const Unit *msua, *msub; /* -> operand msus */ |
| 3238 Unit *uc, *msuc; /* -> result and its msu */ |
| 3239 Int msudigs; /* digits in res msu */ |
| 3240 #if DECCHECK |
| 3241 if (decCheckOperands(res, lhs, rhs, set)) return res; |
| 3242 #endif |
| 3243 |
| 3244 if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) |
| 3245 || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { |
| 3246 decStatus(res, DEC_Invalid_operation, set); |
| 3247 return res; |
| 3248 } |
| 3249 /* operands are valid */ |
| 3250 ua=lhs->lsu; /* bottom-up */ |
| 3251 ub=rhs->lsu; /* .. */ |
| 3252 uc=res->lsu; /* .. */ |
| 3253 msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */ |
| 3254 msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */ |
| 3255 msuc=uc+D2U(set->digits)-1; /* -> msu of result */ |
| 3256 msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ |
| 3257 for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */ |
| 3258 Unit a, b; /* extract units */ |
| 3259 if (ua>msua) a=0; |
| 3260 else a=*ua; |
| 3261 if (ub>msub) b=0; |
| 3262 else b=*ub; |
| 3263 *uc=0; /* can now write back */ |
| 3264 if (a|b) { /* maybe 1 bits to examine */ |
| 3265 Int i, j; |
| 3266 /* This loop could be unrolled and/or use BIN2BCD tables */ |
| 3267 for (i=0; i<DECDPUN; i++) { |
| 3268 if ((a^b)&1) *uc=*uc+(Unit)powers[i]; /* effect XOR */ |
| 3269 j=a%10; |
| 3270 a=a/10; |
| 3271 j|=b%10; |
| 3272 b=b/10; |
| 3273 if (j>1) { |
| 3274 decStatus(res, DEC_Invalid_operation, set); |
| 3275 return res; |
| 3276 } |
| 3277 if (uc==msuc && i==msudigs-1) break; /* just did final digit */ |
| 3278 } /* each digit */ |
| 3279 } /* non-zero */ |
| 3280 } /* each unit */ |
| 3281 /* [here uc-1 is the msu of the result] */ |
| 3282 res->digits=decGetDigits(res->lsu, uc-res->lsu); |
| 3283 res->exponent=0; /* integer */ |
| 3284 res->bits=0; /* sign=0 */ |
| 3285 return res; /* [no status to set] */ |
| 3286 } /* decNumberXor */ |
| 3287 |
| 3288 |
| 3289 /* ================================================================== */ |
| 3290 /* Utility routines */ |
| 3291 /* ================================================================== */ |
| 3292 |
| 3293 /* ------------------------------------------------------------------ */ |
| 3294 /* decNumberClass -- return the decClass of a decNumber */ |
| 3295 /* dn -- the decNumber to test */ |
| 3296 /* set -- the context to use for Emin */ |
| 3297 /* returns the decClass enum */ |
| 3298 /* ------------------------------------------------------------------ */ |
| 3299 enum decClass uprv_decNumberClass(const decNumber *dn, decContext *set) { |
| 3300 if (decNumberIsSpecial(dn)) { |
| 3301 if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN; |
| 3302 if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN; |
| 3303 /* must be an infinity */ |
| 3304 if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF; |
| 3305 return DEC_CLASS_POS_INF; |
| 3306 } |
| 3307 /* is finite */ |
| 3308 if (uprv_decNumberIsNormal(dn, set)) { /* most common */ |
| 3309 if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL; |
| 3310 return DEC_CLASS_POS_NORMAL; |
| 3311 } |
| 3312 /* is subnormal or zero */ |
| 3313 if (decNumberIsZero(dn)) { /* most common */ |
| 3314 if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO; |
| 3315 return DEC_CLASS_POS_ZERO; |
| 3316 } |
| 3317 if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL; |
| 3318 return DEC_CLASS_POS_SUBNORMAL; |
| 3319 } /* decNumberClass */ |
| 3320 |
| 3321 /* ------------------------------------------------------------------ */ |
| 3322 /* decNumberClassToString -- convert decClass to a string */ |
| 3323 /* */ |
| 3324 /* eclass is a valid decClass */ |
| 3325 /* returns a constant string describing the class (max 13+1 chars) */ |
| 3326 /* ------------------------------------------------------------------ */ |
| 3327 const char *uprv_decNumberClassToString(enum decClass eclass) { |
| 3328 if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN; |
| 3329 if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN; |
| 3330 if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ; |
| 3331 if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ; |
| 3332 if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS; |
| 3333 if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS; |
| 3334 if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI; |
| 3335 if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI; |
| 3336 if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN; |
| 3337 if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN; |
| 3338 return DEC_ClassString_UN; /* Unknown */ |
| 3339 } /* decNumberClassToString */ |
| 3340 |
| 3341 /* ------------------------------------------------------------------ */ |
| 3342 /* decNumberCopy -- copy a number */ |
| 3343 /* */ |
| 3344 /* dest is the target decNumber */ |
| 3345 /* src is the source decNumber */ |
| 3346 /* returns dest */ |
| 3347 /* */ |
| 3348 /* (dest==src is allowed and is a no-op) */ |
| 3349 /* All fields are updated as required. This is a utility operation, */ |
| 3350 /* so special values are unchanged and no error is possible. */ |
| 3351 /* ------------------------------------------------------------------ */ |
| 3352 U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopy(decNumber *dest, const decNumber
*src) { |
| 3353 |
| 3354 #if DECCHECK |
| 3355 if (src==NULL) return uprv_decNumberZero(dest); |
| 3356 #endif |
| 3357 |
| 3358 if (dest==src) return dest; /* no copy required */ |
| 3359 |
| 3360 /* Use explicit assignments here as structure assignment could copy */ |
| 3361 /* more than just the lsu (for small DECDPUN). This would not affect */ |
| 3362 /* the value of the results, but could disturb test harness spill */ |
| 3363 /* checking. */ |
| 3364 dest->bits=src->bits; |
| 3365 dest->exponent=src->exponent; |
| 3366 dest->digits=src->digits; |
| 3367 dest->lsu[0]=src->lsu[0]; |
| 3368 if (src->digits>DECDPUN) { /* more Units to come */ |
| 3369 const Unit *smsup, *s; /* work */ |
| 3370 Unit *d; /* .. */ |
| 3371 /* memcpy for the remaining Units would be safe as they cannot */ |
| 3372 /* overlap. However, this explicit loop is faster in short cases. */ |
| 3373 d=dest->lsu+1; /* -> first destination */ |
| 3374 smsup=src->lsu+D2U(src->digits); /* -> source msu+1 */ |
| 3375 for (s=src->lsu+1; s<smsup; s++, d++) *d=*s; |
| 3376 } |
| 3377 return dest; |
| 3378 } /* decNumberCopy */ |
| 3379 |
| 3380 /* ------------------------------------------------------------------ */ |
| 3381 /* decNumberCopyAbs -- quiet absolute value operator */ |
| 3382 /* */ |
| 3383 /* This sets C = abs(A) */ |
| 3384 /* */ |
| 3385 /* res is C, the result. C may be A */ |
| 3386 /* rhs is A */ |
| 3387 /* */ |
| 3388 /* C must have space for set->digits digits. */ |
| 3389 /* No exception or error can occur; this is a quiet bitwise operation.*/ |
| 3390 /* See also decNumberAbs for a checking version of this. */ |
| 3391 /* ------------------------------------------------------------------ */ |
| 3392 U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopyAbs(decNumber *res, const decNumb
er *rhs) { |
| 3393 #if DECCHECK |
| 3394 if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; |
| 3395 #endif |
| 3396 uprv_decNumberCopy(res, rhs); |
| 3397 res->bits&=~DECNEG; /* turn off sign */ |
| 3398 return res; |
| 3399 } /* decNumberCopyAbs */ |
| 3400 |
| 3401 /* ------------------------------------------------------------------ */ |
| 3402 /* decNumberCopyNegate -- quiet negate value operator */ |
| 3403 /* */ |
| 3404 /* This sets C = negate(A) */ |
| 3405 /* */ |
| 3406 /* res is C, the result. C may be A */ |
| 3407 /* rhs is A */ |
| 3408 /* */ |
| 3409 /* C must have space for set->digits digits. */ |
| 3410 /* No exception or error can occur; this is a quiet bitwise operation.*/ |
| 3411 /* See also decNumberMinus for a checking version of this. */ |
| 3412 /* ------------------------------------------------------------------ */ |
| 3413 U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopyNegate(decNumber *res, const decN
umber *rhs) { |
| 3414 #if DECCHECK |
| 3415 if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; |
| 3416 #endif |
| 3417 uprv_decNumberCopy(res, rhs); |
| 3418 res->bits^=DECNEG; /* invert the sign */ |
| 3419 return res; |
| 3420 } /* decNumberCopyNegate */ |
| 3421 |
| 3422 /* ------------------------------------------------------------------ */ |
| 3423 /* decNumberCopySign -- quiet copy and set sign operator */ |
| 3424 /* */ |
| 3425 /* This sets C = A with the sign of B */ |
| 3426 /* */ |
| 3427 /* res is C, the result. C may be A */ |
| 3428 /* lhs is A */ |
| 3429 /* rhs is B */ |
| 3430 /* */ |
| 3431 /* C must have space for set->digits digits. */ |
| 3432 /* No exception or error can occur; this is a quiet bitwise operation.*/ |
| 3433 /* ------------------------------------------------------------------ */ |
| 3434 U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopySign(decNumber *res, const decNum
ber *lhs, |
| 3435 const decNumber *rhs) { |
| 3436 uByte sign; /* rhs sign */ |
| 3437 #if DECCHECK |
| 3438 if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; |
| 3439 #endif |
| 3440 sign=rhs->bits & DECNEG; /* save sign bit */ |
| 3441 uprv_decNumberCopy(res, lhs); |
| 3442 res->bits&=~DECNEG; /* clear the sign */ |
| 3443 res->bits|=sign; /* set from rhs */ |
| 3444 return res; |
| 3445 } /* decNumberCopySign */ |
| 3446 |
| 3447 /* ------------------------------------------------------------------ */ |
| 3448 /* decNumberGetBCD -- get the coefficient in BCD8 */ |
| 3449 /* dn is the source decNumber */ |
| 3450 /* bcd is the uInt array that will receive dn->digits BCD bytes, */ |
| 3451 /* most-significant at offset 0 */ |
| 3452 /* returns bcd */ |
| 3453 /* */ |
| 3454 /* bcd must have at least dn->digits bytes. No error is possible; if */ |
| 3455 /* dn is a NaN or Infinite, digits must be 1 and the coefficient 0. */ |
| 3456 /* ------------------------------------------------------------------ */ |
| 3457 U_CAPI uByte * U_EXPORT2 uprv_decNumberGetBCD(const decNumber *dn, uByte *bcd) { |
| 3458 uByte *ub=bcd+dn->digits-1; /* -> lsd */ |
| 3459 const Unit *up=dn->lsu; /* Unit pointer, -> lsu */ |
| 3460 |
| 3461 #if DECDPUN==1 /* trivial simple copy */ |
| 3462 for (; ub>=bcd; ub--, up++) *ub=*up; |
| 3463 #else /* chopping needed */ |
| 3464 uInt u=*up; /* work */ |
| 3465 uInt cut=DECDPUN; /* downcounter through unit */ |
| 3466 for (; ub>=bcd; ub--) { |
| 3467 *ub=(uByte)(u%10); /* [*6554 trick inhibits, here] */ |
| 3468 u=u/10; |
| 3469 cut--; |
| 3470 if (cut>0) continue; /* more in this unit */ |
| 3471 up++; |
| 3472 u=*up; |
| 3473 cut=DECDPUN; |
| 3474 } |
| 3475 #endif |
| 3476 return bcd; |
| 3477 } /* decNumberGetBCD */ |
| 3478 |
| 3479 /* ------------------------------------------------------------------ */ |
| 3480 /* decNumberSetBCD -- set (replace) the coefficient from BCD8 */ |
| 3481 /* dn is the target decNumber */ |
| 3482 /* bcd is the uInt array that will source n BCD bytes, most- */ |
| 3483 /* significant at offset 0 */ |
| 3484 /* n is the number of digits in the source BCD array (bcd) */ |
| 3485 /* returns dn */ |
| 3486 /* */ |
| 3487 /* dn must have space for at least n digits. No error is possible; */ |
| 3488 /* if dn is a NaN, or Infinite, or is to become a zero, n must be 1 */ |
| 3489 /* and bcd[0] zero. */ |
| 3490 /* ------------------------------------------------------------------ */ |
| 3491 U_CAPI decNumber * U_EXPORT2 uprv_decNumberSetBCD(decNumber *dn, const uByte *bc
d, uInt n) { |
| 3492 Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [target pointer] */ |
| 3493 const uByte *ub=bcd; /* -> source msd */ |
| 3494 |
| 3495 #if DECDPUN==1 /* trivial simple copy */ |
| 3496 for (; ub<bcd+n; ub++, up--) *up=*ub; |
| 3497 #else /* some assembly needed */ |
| 3498 /* calculate how many digits in msu, and hence first cut */ |
| 3499 Int cut=MSUDIGITS(n); /* [faster than remainder] */ |
| 3500 for (;up>=dn->lsu; up--) { /* each Unit from msu */ |
| 3501 *up=0; /* will take <=DECDPUN digits */ |
| 3502 for (; cut>0; ub++, cut--) *up=X10(*up)+*ub; |
| 3503 cut=DECDPUN; /* next Unit has all digits */ |
| 3504 } |
| 3505 #endif |
| 3506 dn->digits=n; /* set digit count */ |
| 3507 return dn; |
| 3508 } /* decNumberSetBCD */ |
| 3509 |
| 3510 /* ------------------------------------------------------------------ */ |
| 3511 /* decNumberIsNormal -- test normality of a decNumber */ |
| 3512 /* dn is the decNumber to test */ |
| 3513 /* set is the context to use for Emin */ |
| 3514 /* returns 1 if |dn| is finite and >=Nmin, 0 otherwise */ |
| 3515 /* ------------------------------------------------------------------ */ |
| 3516 Int uprv_decNumberIsNormal(const decNumber *dn, decContext *set) { |
| 3517 Int ae; /* adjusted exponent */ |
| 3518 #if DECCHECK |
| 3519 if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; |
| 3520 #endif |
| 3521 |
| 3522 if (decNumberIsSpecial(dn)) return 0; /* not finite */ |
| 3523 if (decNumberIsZero(dn)) return 0; /* not non-zero */ |
| 3524 |
| 3525 ae=dn->exponent+dn->digits-1; /* adjusted exponent */ |
| 3526 if (ae<set->emin) return 0; /* is subnormal */ |
| 3527 return 1; |
| 3528 } /* decNumberIsNormal */ |
| 3529 |
| 3530 /* ------------------------------------------------------------------ */ |
| 3531 /* decNumberIsSubnormal -- test subnormality of a decNumber */ |
| 3532 /* dn is the decNumber to test */ |
| 3533 /* set is the context to use for Emin */ |
| 3534 /* returns 1 if |dn| is finite, non-zero, and <Nmin, 0 otherwise */ |
| 3535 /* ------------------------------------------------------------------ */ |
| 3536 Int uprv_decNumberIsSubnormal(const decNumber *dn, decContext *set) { |
| 3537 Int ae; /* adjusted exponent */ |
| 3538 #if DECCHECK |
| 3539 if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; |
| 3540 #endif |
| 3541 |
| 3542 if (decNumberIsSpecial(dn)) return 0; /* not finite */ |
| 3543 if (decNumberIsZero(dn)) return 0; /* not non-zero */ |
| 3544 |
| 3545 ae=dn->exponent+dn->digits-1; /* adjusted exponent */ |
| 3546 if (ae<set->emin) return 1; /* is subnormal */ |
| 3547 return 0; |
| 3548 } /* decNumberIsSubnormal */ |
| 3549 |
| 3550 /* ------------------------------------------------------------------ */ |
| 3551 /* decNumberTrim -- remove insignificant zeros */ |
| 3552 /* */ |
| 3553 /* dn is the number to trim */ |
| 3554 /* returns dn */ |
| 3555 /* */ |
| 3556 /* All fields are updated as required. This is a utility operation, */ |
| 3557 /* so special values are unchanged and no error is possible. The */ |
| 3558 /* zeros are removed unconditionally. */ |
| 3559 /* ------------------------------------------------------------------ */ |
| 3560 U_CAPI decNumber * U_EXPORT2 uprv_decNumberTrim(decNumber *dn) { |
| 3561 Int dropped; /* work */ |
| 3562 decContext set; /* .. */ |
| 3563 #if DECCHECK |
| 3564 if (decCheckOperands(DECUNRESU, DECUNUSED, dn, DECUNCONT)) return dn; |
| 3565 #endif |
| 3566 uprv_decContextDefault(&set, DEC_INIT_BASE); /* clamp=0 */ |
| 3567 return decTrim(dn, &set, 0, 1, &dropped); |
| 3568 } /* decNumberTrim */ |
| 3569 |
| 3570 /* ------------------------------------------------------------------ */ |
| 3571 /* decNumberVersion -- return the name and version of this module */ |
| 3572 /* */ |
| 3573 /* No error is possible. */ |
| 3574 /* ------------------------------------------------------------------ */ |
| 3575 const char * uprv_decNumberVersion(void) { |
| 3576 return DECVERSION; |
| 3577 } /* decNumberVersion */ |
| 3578 |
| 3579 /* ------------------------------------------------------------------ */ |
| 3580 /* decNumberZero -- set a number to 0 */ |
| 3581 /* */ |
| 3582 /* dn is the number to set, with space for one digit */ |
| 3583 /* returns dn */ |
| 3584 /* */ |
| 3585 /* No error is possible. */ |
| 3586 /* ------------------------------------------------------------------ */ |
| 3587 /* Memset is not used as it is much slower in some environments. */ |
| 3588 U_CAPI decNumber * U_EXPORT2 uprv_decNumberZero(decNumber *dn) { |
| 3589 |
| 3590 #if DECCHECK |
| 3591 if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn; |
| 3592 #endif |
| 3593 |
| 3594 dn->bits=0; |
| 3595 dn->exponent=0; |
| 3596 dn->digits=1; |
| 3597 dn->lsu[0]=0; |
| 3598 return dn; |
| 3599 } /* decNumberZero */ |
| 3600 |
| 3601 /* ================================================================== */ |
| 3602 /* Local routines */ |
| 3603 /* ================================================================== */ |
| 3604 |
| 3605 /* ------------------------------------------------------------------ */ |
| 3606 /* decToString -- lay out a number into a string */ |
| 3607 /* */ |
| 3608 /* dn is the number to lay out */ |
| 3609 /* string is where to lay out the number */ |
| 3610 /* eng is 1 if Engineering, 0 if Scientific */ |
| 3611 /* */ |
| 3612 /* string must be at least dn->digits+14 characters long */ |
| 3613 /* No error is possible. */ |
| 3614 /* */ |
| 3615 /* Note that this routine can generate a -0 or 0.000. These are */ |
| 3616 /* never generated in subset to-number or arithmetic, but can occur */ |
| 3617 /* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234). */ |
| 3618 /* ------------------------------------------------------------------ */ |
| 3619 /* If DECCHECK is enabled the string "?" is returned if a number is */ |
| 3620 /* invalid. */ |
| 3621 static void decToString(const decNumber *dn, char *string, Flag eng) { |
| 3622 Int exp=dn->exponent; /* local copy */ |
| 3623 Int e; /* E-part value */ |
| 3624 Int pre; /* digits before the '.' */ |
| 3625 Int cut; /* for counting digits in a Unit */ |
| 3626 char *c=string; /* work [output pointer] */ |
| 3627 const Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [input pointer] */ |
| 3628 uInt u, pow; /* work */ |
| 3629 |
| 3630 #if DECCHECK |
| 3631 if (decCheckOperands(DECUNRESU, dn, DECUNUSED, DECUNCONT)) { |
| 3632 strcpy(string, "?"); |
| 3633 return;} |
| 3634 #endif |
| 3635 |
| 3636 if (decNumberIsNegative(dn)) { /* Negatives get a minus */ |
| 3637 *c='-'; |
| 3638 c++; |
| 3639 } |
| 3640 if (dn->bits&DECSPECIAL) { /* Is a special value */ |
| 3641 if (decNumberIsInfinite(dn)) { |
| 3642 strcpy(c, "Inf"); |
| 3643 strcpy(c+3, "inity"); |
| 3644 return;} |
| 3645 /* a NaN */ |
| 3646 if (dn->bits&DECSNAN) { /* signalling NaN */ |
| 3647 *c='s'; |
| 3648 c++; |
| 3649 } |
| 3650 strcpy(c, "NaN"); |
| 3651 c+=3; /* step past */ |
| 3652 /* if not a clean non-zero coefficient, that's all there is in a */ |
| 3653 /* NaN string */ |
| 3654 if (exp!=0 || (*dn->lsu==0 && dn->digits==1)) return; |
| 3655 /* [drop through to add integer] */ |
| 3656 } |
| 3657 |
| 3658 /* calculate how many digits in msu, and hence first cut */ |
| 3659 cut=MSUDIGITS(dn->digits); /* [faster than remainder] */ |
| 3660 cut--; /* power of ten for digit */ |
| 3661 |
| 3662 if (exp==0) { /* simple integer [common fastpath] */ |
| 3663 for (;up>=dn->lsu; up--) { /* each Unit from msu */ |
| 3664 u=*up; /* contains DECDPUN digits to lay out */ |
| 3665 for (; cut>=0; c++, cut--) TODIGIT(u, cut, c, pow); |
| 3666 cut=DECDPUN-1; /* next Unit has all digits */ |
| 3667 } |
| 3668 *c='\0'; /* terminate the string */ |
| 3669 return;} |
| 3670 |
| 3671 /* non-0 exponent -- assume plain form */ |
| 3672 pre=dn->digits+exp; /* digits before '.' */ |
| 3673 e=0; /* no E */ |
| 3674 if ((exp>0) || (pre<-5)) { /* need exponential form */ |
| 3675 e=exp+dn->digits-1; /* calculate E value */ |
| 3676 pre=1; /* assume one digit before '.' */ |
| 3677 if (eng && (e!=0)) { /* engineering: may need to adjust */ |
| 3678 Int adj; /* adjustment */ |
| 3679 /* The C remainder operator is undefined for negative numbers, so */ |
| 3680 /* a positive remainder calculation must be used here */ |
| 3681 if (e<0) { |
| 3682 adj=(-e)%3; |
| 3683 if (adj!=0) adj=3-adj; |
| 3684 } |
| 3685 else { /* e>0 */ |
| 3686 adj=e%3; |
| 3687 } |
| 3688 e=e-adj; |
| 3689 /* if dealing with zero still produce an exponent which is a */ |
| 3690 /* multiple of three, as expected, but there will only be the */ |
| 3691 /* one zero before the E, still. Otherwise note the padding. */ |
| 3692 if (!ISZERO(dn)) pre+=adj; |
| 3693 else { /* is zero */ |
| 3694 if (adj!=0) { /* 0.00Esnn needed */ |
| 3695 e=e+3; |
| 3696 pre=-(2-adj); |
| 3697 } |
| 3698 } /* zero */ |
| 3699 } /* eng */ |
| 3700 } /* need exponent */ |
| 3701 |
| 3702 /* lay out the digits of the coefficient, adding 0s and . as needed */ |
| 3703 u=*up; |
| 3704 if (pre>0) { /* xxx.xxx or xx00 (engineering) form */ |
| 3705 Int n=pre; |
| 3706 for (; pre>0; pre--, c++, cut--) { |
| 3707 if (cut<0) { /* need new Unit */ |
| 3708 if (up==dn->lsu) break; /* out of input digits (pre>digits) */ |
| 3709 up--; |
| 3710 cut=DECDPUN-1; |
| 3711 u=*up; |
| 3712 } |
| 3713 TODIGIT(u, cut, c, pow); |
| 3714 } |
| 3715 if (n<dn->digits) { /* more to come, after '.' */ |
| 3716 *c='.'; c++; |
| 3717 for (;; c++, cut--) { |
| 3718 if (cut<0) { /* need new Unit */ |
| 3719 if (up==dn->lsu) break; /* out of input digits */ |
| 3720 up--; |
| 3721 cut=DECDPUN-1; |
| 3722 u=*up; |
| 3723 } |
| 3724 TODIGIT(u, cut, c, pow); |
| 3725 } |
| 3726 } |
| 3727 else for (; pre>0; pre--, c++) *c='0'; /* 0 padding (for engineering) neede
d */ |
| 3728 } |
| 3729 else { /* 0.xxx or 0.000xxx form */ |
| 3730 *c='0'; c++; |
| 3731 *c='.'; c++; |
| 3732 for (; pre<0; pre++, c++) *c='0'; /* add any 0's after '.' */ |
| 3733 for (; ; c++, cut--) { |
| 3734 if (cut<0) { /* need new Unit */ |
| 3735 if (up==dn->lsu) break; /* out of input digits */ |
| 3736 up--; |
| 3737 cut=DECDPUN-1; |
| 3738 u=*up; |
| 3739 } |
| 3740 TODIGIT(u, cut, c, pow); |
| 3741 } |
| 3742 } |
| 3743 |
| 3744 /* Finally add the E-part, if needed. It will never be 0, has a |
| 3745 base maximum and minimum of +999999999 through -999999999, but |
| 3746 could range down to -1999999998 for anormal numbers */ |
| 3747 if (e!=0) { |
| 3748 Flag had=0; /* 1=had non-zero */ |
| 3749 *c='E'; c++; |
| 3750 *c='+'; c++; /* assume positive */ |
| 3751 u=e; /* .. */ |
| 3752 if (e<0) { |
| 3753 *(c-1)='-'; /* oops, need - */ |
| 3754 u=-e; /* uInt, please */ |
| 3755 } |
| 3756 /* lay out the exponent [_itoa or equivalent is not ANSI C] */ |
| 3757 for (cut=9; cut>=0; cut--) { |
| 3758 TODIGIT(u, cut, c, pow); |
| 3759 if (*c=='0' && !had) continue; /* skip leading zeros */ |
| 3760 had=1; /* had non-0 */ |
| 3761 c++; /* step for next */ |
| 3762 } /* cut */ |
| 3763 } |
| 3764 *c='\0'; /* terminate the string (all paths) */ |
| 3765 return; |
| 3766 } /* decToString */ |
| 3767 |
| 3768 /* ------------------------------------------------------------------ */ |
| 3769 /* decAddOp -- add/subtract operation */ |
| 3770 /* */ |
| 3771 /* This computes C = A + B */ |
| 3772 /* */ |
| 3773 /* res is C, the result. C may be A and/or B (e.g., X=X+X) */ |
| 3774 /* lhs is A */ |
| 3775 /* rhs is B */ |
| 3776 /* set is the context */ |
| 3777 /* negate is DECNEG if rhs should be negated, or 0 otherwise */ |
| 3778 /* status accumulates status for the caller */ |
| 3779 /* */ |
| 3780 /* C must have space for set->digits digits. */ |
| 3781 /* Inexact in status must be 0 for correct Exact zero sign in result */ |
| 3782 /* ------------------------------------------------------------------ */ |
| 3783 /* If possible, the coefficient is calculated directly into C. */ |
| 3784 /* However, if: */ |
| 3785 /* -- a digits+1 calculation is needed because the numbers are */ |
| 3786 /* unaligned and span more than set->digits digits */ |
| 3787 /* -- a carry to digits+1 digits looks possible */ |
| 3788 /* -- C is the same as A or B, and the result would destructively */ |
| 3789 /* overlap the A or B coefficient */ |
| 3790 /* then the result must be calculated into a temporary buffer. In */ |
| 3791 /* this case a local (stack) buffer is used if possible, and only if */ |
| 3792 /* too long for that does malloc become the final resort. */ |
| 3793 /* */ |
| 3794 /* Misalignment is handled as follows: */ |
| 3795 /* Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp. */ |
| 3796 /* BPad: Apply the padding by a combination of shifting (whole */ |
| 3797 /* units) and multiplication (part units). */ |
| 3798 /* */ |
| 3799 /* Addition, especially x=x+1, is speed-critical. */ |
| 3800 /* The static buffer is larger than might be expected to allow for */ |
| 3801 /* calls from higher-level funtions (notable exp). */ |
| 3802 /* ------------------------------------------------------------------ */ |
| 3803 static decNumber * decAddOp(decNumber *res, const decNumber *lhs, |
| 3804 const decNumber *rhs, decContext *set, |
| 3805 uByte negate, uInt *status) { |
| 3806 #if DECSUBSET |
| 3807 decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ |
| 3808 decNumber *allocrhs=NULL; /* .., rhs */ |
| 3809 #endif |
| 3810 Int rhsshift; /* working shift (in Units) */ |
| 3811 Int maxdigits; /* longest logical length */ |
| 3812 Int mult; /* multiplier */ |
| 3813 Int residue; /* rounding accumulator */ |
| 3814 uByte bits; /* result bits */ |
| 3815 Flag diffsign; /* non-0 if arguments have different sign */ |
| 3816 Unit *acc; /* accumulator for result */ |
| 3817 Unit accbuff[SD2U(DECBUFFER*2+20)]; /* local buffer [*2+20 reduces many */ |
| 3818 /* allocations when called from */ |
| 3819 /* other operations, notable exp] */ |
| 3820 Unit *allocacc=NULL; /* -> allocated acc buffer, iff allocated */ |
| 3821 Int reqdigits=set->digits; /* local copy; requested DIGITS */ |
| 3822 Int padding; /* work */ |
| 3823 |
| 3824 #if DECCHECK |
| 3825 if (decCheckOperands(res, lhs, rhs, set)) return res; |
| 3826 #endif |
| 3827 |
| 3828 do { /* protect allocated storage */ |
| 3829 #if DECSUBSET |
| 3830 if (!set->extended) { |
| 3831 /* reduce operands and set lostDigits status, as needed */ |
| 3832 if (lhs->digits>reqdigits) { |
| 3833 alloclhs=decRoundOperand(lhs, set, status); |
| 3834 if (alloclhs==NULL) break; |
| 3835 lhs=alloclhs; |
| 3836 } |
| 3837 if (rhs->digits>reqdigits) { |
| 3838 allocrhs=decRoundOperand(rhs, set, status); |
| 3839 if (allocrhs==NULL) break; |
| 3840 rhs=allocrhs; |
| 3841 } |
| 3842 } |
| 3843 #endif |
| 3844 /* [following code does not require input rounding] */ |
| 3845 |
| 3846 /* note whether signs differ [used all paths] */ |
| 3847 diffsign=(Flag)((lhs->bits^rhs->bits^negate)&DECNEG); |
| 3848 |
| 3849 /* handle infinities and NaNs */ |
| 3850 if (SPECIALARGS) { /* a special bit set */ |
| 3851 if (SPECIALARGS & (DECSNAN | DECNAN)) /* a NaN */ |
| 3852 decNaNs(res, lhs, rhs, set, status); |
| 3853 else { /* one or two infinities */ |
| 3854 if (decNumberIsInfinite(lhs)) { /* LHS is infinity */ |
| 3855 /* two infinities with different signs is invalid */ |
| 3856 if (decNumberIsInfinite(rhs) && diffsign) { |
| 3857 *status|=DEC_Invalid_operation; |
| 3858 break; |
| 3859 } |
| 3860 bits=lhs->bits & DECNEG; /* get sign from LHS */ |
| 3861 } |
| 3862 else bits=(rhs->bits^negate) & DECNEG;/* RHS must be Infinity */ |
| 3863 bits|=DECINF; |
| 3864 uprv_decNumberZero(res); |
| 3865 res->bits=bits; /* set +/- infinity */ |
| 3866 } /* an infinity */ |
| 3867 break; |
| 3868 } |
| 3869 |
| 3870 /* Quick exit for add 0s; return the non-0, modified as need be */ |
| 3871 if (ISZERO(lhs)) { |
| 3872 Int adjust; /* work */ |
| 3873 Int lexp=lhs->exponent; /* save in case LHS==RES */ |
| 3874 bits=lhs->bits; /* .. */ |
| 3875 residue=0; /* clear accumulator */ |
| 3876 decCopyFit(res, rhs, set, &residue, status); /* copy (as needed) */ |
| 3877 res->bits^=negate; /* flip if rhs was negated */ |
| 3878 #if DECSUBSET |
| 3879 if (set->extended) { /* exponents on zeros count */ |
| 3880 #endif |
| 3881 /* exponent will be the lower of the two */ |
| 3882 adjust=lexp-res->exponent; /* adjustment needed [if -ve] */ |
| 3883 if (ISZERO(res)) { /* both 0: special IEEE 754 rules */ |
| 3884 if (adjust<0) res->exponent=lexp; /* set exponent */ |
| 3885 /* 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0 */ |
| 3886 if (diffsign) { |
| 3887 if (set->round!=DEC_ROUND_FLOOR) res->bits=0; |
| 3888 else res->bits=DECNEG; /* preserve 0 sign */ |
| 3889 } |
| 3890 } |
| 3891 else { /* non-0 res */ |
| 3892 if (adjust<0) { /* 0-padding needed */ |
| 3893 if ((res->digits-adjust)>set->digits) { |
| 3894 adjust=res->digits-set->digits; /* to fit exactly */ |
| 3895 *status|=DEC_Rounded; /* [but exact] */ |
| 3896 } |
| 3897 res->digits=decShiftToMost(res->lsu, res->digits, -adjust); |
| 3898 res->exponent+=adjust; /* set the exponent. */ |
| 3899 } |
| 3900 } /* non-0 res */ |
| 3901 #if DECSUBSET |
| 3902 } /* extended */ |
| 3903 #endif |
| 3904 decFinish(res, set, &residue, status); /* clean and finalize */ |
| 3905 break;} |
| 3906 |
| 3907 if (ISZERO(rhs)) { /* [lhs is non-zero] */ |
| 3908 Int adjust; /* work */ |
| 3909 Int rexp=rhs->exponent; /* save in case RHS==RES */ |
| 3910 bits=rhs->bits; /* be clean */ |
| 3911 residue=0; /* clear accumulator */ |
| 3912 decCopyFit(res, lhs, set, &residue, status); /* copy (as needed) */ |
| 3913 #if DECSUBSET |
| 3914 if (set->extended) { /* exponents on zeros count */ |
| 3915 #endif |
| 3916 /* exponent will be the lower of the two */ |
| 3917 /* [0-0 case handled above] */ |
| 3918 adjust=rexp-res->exponent; /* adjustment needed [if -ve] */ |
| 3919 if (adjust<0) { /* 0-padding needed */ |
| 3920 if ((res->digits-adjust)>set->digits) { |
| 3921 adjust=res->digits-set->digits; /* to fit exactly */ |
| 3922 *status|=DEC_Rounded; /* [but exact] */ |
| 3923 } |
| 3924 res->digits=decShiftToMost(res->lsu, res->digits, -adjust); |
| 3925 res->exponent+=adjust; /* set the exponent. */ |
| 3926 } |
| 3927 #if DECSUBSET |
| 3928 } /* extended */ |
| 3929 #endif |
| 3930 decFinish(res, set, &residue, status); /* clean and finalize */ |
| 3931 break;} |
| 3932 |
| 3933 /* [NB: both fastpath and mainpath code below assume these cases */ |
| 3934 /* (notably 0-0) have already been handled] */ |
| 3935 |
| 3936 /* calculate the padding needed to align the operands */ |
| 3937 padding=rhs->exponent-lhs->exponent; |
| 3938 |
| 3939 /* Fastpath cases where the numbers are aligned and normal, the RHS */ |
| 3940 /* is all in one unit, no operand rounding is needed, and no carry, */ |
| 3941 /* lengthening, or borrow is needed */ |
| 3942 if (padding==0 |
| 3943 && rhs->digits<=DECDPUN |
| 3944 && rhs->exponent>=set->emin /* [some normals drop through] */ |
| 3945 && rhs->exponent<=set->emax-set->digits+1 /* [could clamp] */ |
| 3946 && rhs->digits<=reqdigits |
| 3947 && lhs->digits<=reqdigits) { |
| 3948 Int partial=*lhs->lsu; |
| 3949 if (!diffsign) { /* adding */ |
| 3950 partial+=*rhs->lsu; |
| 3951 if ((partial<=DECDPUNMAX) /* result fits in unit */ |
| 3952 && (lhs->digits>=DECDPUN || /* .. and no digits-count change */ |
| 3953 partial<(Int)powers[lhs->digits])) { /* .. */ |
| 3954 if (res!=lhs) uprv_decNumberCopy(res, lhs); /* not in place */ |
| 3955 *res->lsu=(Unit)partial; /* [copy could have overwritten RHS] */ |
| 3956 break; |
| 3957 } |
| 3958 /* else drop out for careful add */ |
| 3959 } |
| 3960 else { /* signs differ */ |
| 3961 partial-=*rhs->lsu; |
| 3962 if (partial>0) { /* no borrow needed, and non-0 result */ |
| 3963 if (res!=lhs) uprv_decNumberCopy(res, lhs); /* not in place */ |
| 3964 *res->lsu=(Unit)partial; |
| 3965 /* this could have reduced digits [but result>0] */ |
| 3966 res->digits=decGetDigits(res->lsu, D2U(res->digits)); |
| 3967 break; |
| 3968 } |
| 3969 /* else drop out for careful subtract */ |
| 3970 } |
| 3971 } |
| 3972 |
| 3973 /* Now align (pad) the lhs or rhs so they can be added or */ |
| 3974 /* subtracted, as necessary. If one number is much larger than */ |
| 3975 /* the other (that is, if in plain form there is a least one */ |
| 3976 /* digit between the lowest digit of one and the highest of the */ |
| 3977 /* other) padding with up to DIGITS-1 trailing zeros may be */ |
| 3978 /* needed; then apply rounding (as exotic rounding modes may be */ |
| 3979 /* affected by the residue). */ |
| 3980 rhsshift=0; /* rhs shift to left (padding) in Units */ |
| 3981 bits=lhs->bits; /* assume sign is that of LHS */ |
| 3982 mult=1; /* likely multiplier */ |
| 3983 |
| 3984 /* [if padding==0 the operands are aligned; no padding is needed] */ |
| 3985 if (padding!=0) { |
| 3986 /* some padding needed; always pad the RHS, as any required */ |
| 3987 /* padding can then be effected by a simple combination of */ |
| 3988 /* shifts and a multiply */ |
| 3989 Flag swapped=0; |
| 3990 if (padding<0) { /* LHS needs the padding */ |
| 3991 const decNumber *t; |
| 3992 padding=-padding; /* will be +ve */ |
| 3993 bits=(uByte)(rhs->bits^negate); /* assumed sign is now that of RHS */ |
| 3994 t=lhs; lhs=rhs; rhs=t; |
| 3995 swapped=1; |
| 3996 } |
| 3997 |
| 3998 /* If, after pad, rhs would be longer than lhs by digits+1 or */ |
| 3999 /* more then lhs cannot affect the answer, except as a residue, */ |
| 4000 /* so only need to pad up to a length of DIGITS+1. */ |
| 4001 if (rhs->digits+padding > lhs->digits+reqdigits+1) { |
| 4002 /* The RHS is sufficient */ |
| 4003 /* for residue use the relative sign indication... */ |
| 4004 Int shift=reqdigits-rhs->digits; /* left shift needed */ |
| 4005 residue=1; /* residue for rounding */ |
| 4006 if (diffsign) residue=-residue; /* signs differ */ |
| 4007 /* copy, shortening if necessary */ |
| 4008 decCopyFit(res, rhs, set, &residue, status); |
| 4009 /* if it was already shorter, then need to pad with zeros */ |
| 4010 if (shift>0) { |
| 4011 res->digits=decShiftToMost(res->lsu, res->digits, shift); |
| 4012 res->exponent-=shift; /* adjust the exponent. */ |
| 4013 } |
| 4014 /* flip the result sign if unswapped and rhs was negated */ |
| 4015 if (!swapped) res->bits^=negate; |
| 4016 decFinish(res, set, &residue, status); /* done */ |
| 4017 break;} |
| 4018 |
| 4019 /* LHS digits may affect result */ |
| 4020 rhsshift=D2U(padding+1)-1; /* this much by Unit shift .. */ |
| 4021 mult=powers[padding-(rhsshift*DECDPUN)]; /* .. this by multiplication */ |
| 4022 } /* padding needed */ |
| 4023 |
| 4024 if (diffsign) mult=-mult; /* signs differ */ |
| 4025 |
| 4026 /* determine the longer operand */ |
| 4027 maxdigits=rhs->digits+padding; /* virtual length of RHS */ |
| 4028 if (lhs->digits>maxdigits) maxdigits=lhs->digits; |
| 4029 |
| 4030 /* Decide on the result buffer to use; if possible place directly */ |
| 4031 /* into result. */ |
| 4032 acc=res->lsu; /* assume add direct to result */ |
| 4033 /* If destructive overlap, or the number is too long, or a carry or */ |
| 4034 /* borrow to DIGITS+1 might be possible, a buffer must be used. */ |
| 4035 /* [Might be worth more sophisticated tests when maxdigits==reqdigits] */ |
| 4036 if ((maxdigits>=reqdigits) /* is, or could be, too large */ |
| 4037 || (res==rhs && rhsshift>0)) { /* destructive overlap */ |
| 4038 /* buffer needed, choose it; units for maxdigits digits will be */ |
| 4039 /* needed, +1 Unit for carry or borrow */ |
| 4040 Int need=D2U(maxdigits)+1; |
| 4041 acc=accbuff; /* assume use local buffer */ |
| 4042 if (need*sizeof(Unit)>sizeof(accbuff)) { |
| 4043 /* printf("malloc add %ld %ld\n", need, sizeof(accbuff)); */ |
| 4044 allocacc=(Unit *)malloc(need*sizeof(Unit)); |
| 4045 if (allocacc==NULL) { /* hopeless -- abandon */ |
| 4046 *status|=DEC_Insufficient_storage; |
| 4047 break;} |
| 4048 acc=allocacc; |
| 4049 } |
| 4050 } |
| 4051 |
| 4052 res->bits=(uByte)(bits&DECNEG); /* it's now safe to overwrite.. */ |
| 4053 res->exponent=lhs->exponent; /* .. operands (even if aliased) */ |
| 4054 |
| 4055 #if DECTRACE |
| 4056 decDumpAr('A', lhs->lsu, D2U(lhs->digits)); |
| 4057 decDumpAr('B', rhs->lsu, D2U(rhs->digits)); |
| 4058 printf(" :h: %ld %ld\n", rhsshift, mult); |
| 4059 #endif |
| 4060 |
| 4061 /* add [A+B*m] or subtract [A+B*(-m)] */ |
| 4062 res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits), |
| 4063 rhs->lsu, D2U(rhs->digits), |
| 4064 rhsshift, acc, mult) |
| 4065 *DECDPUN; /* [units -> digits] */ |
| 4066 if (res->digits<0) { /* borrowed... */ |
| 4067 res->digits=-res->digits; |
| 4068 res->bits^=DECNEG; /* flip the sign */ |
| 4069 } |
| 4070 #if DECTRACE |
| 4071 decDumpAr('+', acc, D2U(res->digits)); |
| 4072 #endif |
| 4073 |
| 4074 /* If a buffer was used the result must be copied back, possibly */ |
| 4075 /* shortening. (If no buffer was used then the result must have */ |
| 4076 /* fit, so can't need rounding and residue must be 0.) */ |
| 4077 residue=0; /* clear accumulator */ |
| 4078 if (acc!=res->lsu) { |
| 4079 #if DECSUBSET |
| 4080 if (set->extended) { /* round from first significant digit */ |
| 4081 #endif |
| 4082 /* remove leading zeros that were added due to rounding up to */ |
| 4083 /* integral Units -- before the test for rounding. */ |
| 4084 if (res->digits>reqdigits) |
| 4085 res->digits=decGetDigits(acc, D2U(res->digits)); |
| 4086 decSetCoeff(res, set, acc, res->digits, &residue, status); |
| 4087 #if DECSUBSET |
| 4088 } |
| 4089 else { /* subset arithmetic rounds from original significant digit */ |
| 4090 /* May have an underestimate. This only occurs when both */ |
| 4091 /* numbers fit in DECDPUN digits and are padding with a */ |
| 4092 /* negative multiple (-10, -100...) and the top digit(s) become */ |
| 4093 /* 0. (This only matters when using X3.274 rules where the */ |
| 4094 /* leading zero could be included in the rounding.) */ |
| 4095 if (res->digits<maxdigits) { |
| 4096 *(acc+D2U(res->digits))=0; /* ensure leading 0 is there */ |
| 4097 res->digits=maxdigits; |
| 4098 } |
| 4099 else { |
| 4100 /* remove leading zeros that added due to rounding up to */ |
| 4101 /* integral Units (but only those in excess of the original */ |
| 4102 /* maxdigits length, unless extended) before test for rounding. */ |
| 4103 if (res->digits>reqdigits) { |
| 4104 res->digits=decGetDigits(acc, D2U(res->digits)); |
| 4105 if (res->digits<maxdigits) res->digits=maxdigits; |
| 4106 } |
| 4107 } |
| 4108 decSetCoeff(res, set, acc, res->digits, &residue, status); |
| 4109 /* Now apply rounding if needed before removing leading zeros. */ |
| 4110 /* This is safe because subnormals are not a possibility */ |
| 4111 if (residue!=0) { |
| 4112 decApplyRound(res, set, residue, status); |
| 4113 residue=0; /* did what needed to be done */ |
| 4114 } |
| 4115 } /* subset */ |
| 4116 #endif |
| 4117 } /* used buffer */ |
| 4118 |
| 4119 /* strip leading zeros [these were left on in case of subset subtract] */ |
| 4120 res->digits=decGetDigits(res->lsu, D2U(res->digits)); |
| 4121 |
| 4122 /* apply checks and rounding */ |
| 4123 decFinish(res, set, &residue, status); |
| 4124 |
| 4125 /* "When the sum of two operands with opposite signs is exactly */ |
| 4126 /* zero, the sign of that sum shall be '+' in all rounding modes */ |
| 4127 /* except round toward -Infinity, in which mode that sign shall be */ |
| 4128 /* '-'." [Subset zeros also never have '-', set by decFinish.] */ |
| 4129 if (ISZERO(res) && diffsign |
| 4130 #if DECSUBSET |
| 4131 && set->extended |
| 4132 #endif |
| 4133 && (*status&DEC_Inexact)==0) { |
| 4134 if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG; /* sign - */ |
| 4135 else res->bits&=~DECNEG; /* sign + */ |
| 4136 } |
| 4137 } while(0); /* end protected */ |
| 4138 |
| 4139 if (allocacc!=NULL) free(allocacc); /* drop any storage used */ |
| 4140 #if DECSUBSET |
| 4141 if (allocrhs!=NULL) free(allocrhs); /* .. */ |
| 4142 if (alloclhs!=NULL) free(alloclhs); /* .. */ |
| 4143 #endif |
| 4144 return res; |
| 4145 } /* decAddOp */ |
| 4146 |
| 4147 /* ------------------------------------------------------------------ */ |
| 4148 /* decDivideOp -- division operation */ |
| 4149 /* */ |
| 4150 /* This routine performs the calculations for all four division */ |
| 4151 /* operators (divide, divideInteger, remainder, remainderNear). */ |
| 4152 /* */ |
| 4153 /* C=A op B */ |
| 4154 /* */ |
| 4155 /* res is C, the result. C may be A and/or B (e.g., X=X/X) */ |
| 4156 /* lhs is A */ |
| 4157 /* rhs is B */ |
| 4158 /* set is the context */ |
| 4159 /* op is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively. */ |
| 4160 /* status is the usual accumulator */ |
| 4161 /* */ |
| 4162 /* C must have space for set->digits digits. */ |
| 4163 /* */ |
| 4164 /* ------------------------------------------------------------------ */ |
| 4165 /* The underlying algorithm of this routine is the same as in the */ |
| 4166 /* 1981 S/370 implementation, that is, non-restoring long division */ |
| 4167 /* with bi-unit (rather than bi-digit) estimation for each unit */ |
| 4168 /* multiplier. In this pseudocode overview, complications for the */ |
| 4169 /* Remainder operators and division residues for exact rounding are */ |
| 4170 /* omitted for clarity. */ |
| 4171 /* */ |
| 4172 /* Prepare operands and handle special values */ |
| 4173 /* Test for x/0 and then 0/x */ |
| 4174 /* Exp =Exp1 - Exp2 */ |
| 4175 /* Exp =Exp +len(var1) -len(var2) */ |
| 4176 /* Sign=Sign1 * Sign2 */ |
| 4177 /* Pad accumulator (Var1) to double-length with 0's (pad1) */ |
| 4178 /* Pad Var2 to same length as Var1 */ |
| 4179 /* msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round */ |
| 4180 /* have=0 */ |
| 4181 /* Do until (have=digits+1 OR residue=0) */ |
| 4182 /* if exp<0 then if integer divide/residue then leave */ |
| 4183 /* this_unit=0 */ |
| 4184 /* Do forever */ |
| 4185 /* compare numbers */ |
| 4186 /* if <0 then leave inner_loop */ |
| 4187 /* if =0 then (* quick exit without subtract *) do */ |
| 4188 /* this_unit=this_unit+1; output this_unit */ |
| 4189 /* leave outer_loop; end */ |
| 4190 /* Compare lengths of numbers (mantissae): */ |
| 4191 /* If same then tops2=msu2pair -- {units 1&2 of var2} */ |
| 4192 /* else tops2=msu2plus -- {0, unit 1 of var2} */ |
| 4193 /* tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */ |
| 4194 /* mult=tops1/tops2 -- Good and safe guess at divisor */ |
| 4195 /* if mult=0 then mult=1 */ |
| 4196 /* this_unit=this_unit+mult */ |
| 4197 /* subtract */ |
| 4198 /* end inner_loop */ |
| 4199 /* if have\=0 | this_unit\=0 then do */ |
| 4200 /* output this_unit */ |
| 4201 /* have=have+1; end */ |
| 4202 /* var2=var2/10 */ |
| 4203 /* exp=exp-1 */ |
| 4204 /* end outer_loop */ |
| 4205 /* exp=exp+1 -- set the proper exponent */ |
| 4206 /* if have=0 then generate answer=0 */ |
| 4207 /* Return (Result is defined by Var1) */ |
| 4208 /* */ |
| 4209 /* ------------------------------------------------------------------ */ |
| 4210 /* Two working buffers are needed during the division; one (digits+ */ |
| 4211 /* 1) to accumulate the result, and the other (up to 2*digits+1) for */ |
| 4212 /* long subtractions. These are acc and var1 respectively. */ |
| 4213 /* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/ |
| 4214 /* The static buffers may be larger than might be expected to allow */ |
| 4215 /* for calls from higher-level funtions (notable exp). */ |
| 4216 /* ------------------------------------------------------------------ */ |
| 4217 static decNumber * decDivideOp(decNumber *res, |
| 4218 const decNumber *lhs, const decNumber *rhs, |
| 4219 decContext *set, Flag op, uInt *status) { |
| 4220 #if DECSUBSET |
| 4221 decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ |
| 4222 decNumber *allocrhs=NULL; /* .., rhs */ |
| 4223 #endif |
| 4224 Unit accbuff[SD2U(DECBUFFER+DECDPUN+10)]; /* local buffer */ |
| 4225 Unit *acc=accbuff; /* -> accumulator array for result */ |
| 4226 Unit *allocacc=NULL; /* -> allocated buffer, iff allocated */ |
| 4227 Unit *accnext; /* -> where next digit will go */ |
| 4228 Int acclength; /* length of acc needed [Units] */ |
| 4229 Int accunits; /* count of units accumulated */ |
| 4230 Int accdigits; /* count of digits accumulated */ |
| 4231 |
| 4232 Unit varbuff[SD2U(DECBUFFER*2+DECDPUN)]; /* buffer for var1 */ |
| 4233 Unit *var1=varbuff; /* -> var1 array for long subtraction */ |
| 4234 Unit *varalloc=NULL; /* -> allocated buffer, iff used */ |
| 4235 Unit *msu1; /* -> msu of var1 */ |
| 4236 |
| 4237 const Unit *var2; /* -> var2 array */ |
| 4238 const Unit *msu2; /* -> msu of var2 */ |
| 4239 Int msu2plus; /* msu2 plus one [does not vary] */ |
| 4240 eInt msu2pair; /* msu2 pair plus one [does not vary] */ |
| 4241 |
| 4242 Int var1units, var2units; /* actual lengths */ |
| 4243 Int var2ulen; /* logical length (units) */ |
| 4244 Int var1initpad=0; /* var1 initial padding (digits) */ |
| 4245 Int maxdigits; /* longest LHS or required acc length */ |
| 4246 Int mult; /* multiplier for subtraction */ |
| 4247 Unit thisunit; /* current unit being accumulated */ |
| 4248 Int residue; /* for rounding */ |
| 4249 Int reqdigits=set->digits; /* requested DIGITS */ |
| 4250 Int exponent; /* working exponent */ |
| 4251 Int maxexponent=0; /* DIVIDE maximum exponent if unrounded */ |
| 4252 uByte bits; /* working sign */ |
| 4253 Unit *target; /* work */ |
| 4254 const Unit *source; /* .. */ |
| 4255 uInt const *pow; /* .. */ |
| 4256 Int shift, cut; /* .. */ |
| 4257 #if DECSUBSET |
| 4258 Int dropped; /* work */ |
| 4259 #endif |
| 4260 |
| 4261 #if DECCHECK |
| 4262 if (decCheckOperands(res, lhs, rhs, set)) return res; |
| 4263 #endif |
| 4264 |
| 4265 do { /* protect allocated storage */ |
| 4266 #if DECSUBSET |
| 4267 if (!set->extended) { |
| 4268 /* reduce operands and set lostDigits status, as needed */ |
| 4269 if (lhs->digits>reqdigits) { |
| 4270 alloclhs=decRoundOperand(lhs, set, status); |
| 4271 if (alloclhs==NULL) break; |
| 4272 lhs=alloclhs; |
| 4273 } |
| 4274 if (rhs->digits>reqdigits) { |
| 4275 allocrhs=decRoundOperand(rhs, set, status); |
| 4276 if (allocrhs==NULL) break; |
| 4277 rhs=allocrhs; |
| 4278 } |
| 4279 } |
| 4280 #endif |
| 4281 /* [following code does not require input rounding] */ |
| 4282 |
| 4283 bits=(lhs->bits^rhs->bits)&DECNEG; /* assumed sign for divisions */ |
| 4284 |
| 4285 /* handle infinities and NaNs */ |
| 4286 if (SPECIALARGS) { /* a special bit set */ |
| 4287 if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */ |
| 4288 decNaNs(res, lhs, rhs, set, status); |
| 4289 break; |
| 4290 } |
| 4291 /* one or two infinities */ |
| 4292 if (decNumberIsInfinite(lhs)) { /* LHS (dividend) is infinite */ |
| 4293 if (decNumberIsInfinite(rhs) || /* two infinities are invalid .. */ |
| 4294 op & (REMAINDER | REMNEAR)) { /* as is remainder of infinity */ |
| 4295 *status|=DEC_Invalid_operation; |
| 4296 break; |
| 4297 } |
| 4298 /* [Note that infinity/0 raises no exceptions] */ |
| 4299 uprv_decNumberZero(res); |
| 4300 res->bits=bits|DECINF; /* set +/- infinity */ |
| 4301 break; |
| 4302 } |
| 4303 else { /* RHS (divisor) is infinite */ |
| 4304 residue=0; |
| 4305 if (op&(REMAINDER|REMNEAR)) { |
| 4306 /* result is [finished clone of] lhs */ |
| 4307 decCopyFit(res, lhs, set, &residue, status); |
| 4308 } |
| 4309 else { /* a division */ |
| 4310 uprv_decNumberZero(res); |
| 4311 res->bits=bits; /* set +/- zero */ |
| 4312 /* for DIVIDEINT the exponent is always 0. For DIVIDE, result */ |
| 4313 /* is a 0 with infinitely negative exponent, clamped to minimum */ |
| 4314 if (op&DIVIDE) { |
| 4315 res->exponent=set->emin-set->digits+1; |
| 4316 *status|=DEC_Clamped; |
| 4317 } |
| 4318 } |
| 4319 decFinish(res, set, &residue, status); |
| 4320 break; |
| 4321 } |
| 4322 } |
| 4323 |
| 4324 /* handle 0 rhs (x/0) */ |
| 4325 if (ISZERO(rhs)) { /* x/0 is always exceptional */ |
| 4326 if (ISZERO(lhs)) { |
| 4327 uprv_decNumberZero(res); /* [after lhs test] */ |
| 4328 *status|=DEC_Division_undefined;/* 0/0 will become NaN */ |
| 4329 } |
| 4330 else { |
| 4331 uprv_decNumberZero(res); |
| 4332 if (op&(REMAINDER|REMNEAR)) *status|=DEC_Invalid_operation; |
| 4333 else { |
| 4334 *status|=DEC_Division_by_zero; /* x/0 */ |
| 4335 res->bits=bits|DECINF; /* .. is +/- Infinity */ |
| 4336 } |
| 4337 } |
| 4338 break;} |
| 4339 |
| 4340 /* handle 0 lhs (0/x) */ |
| 4341 if (ISZERO(lhs)) { /* 0/x [x!=0] */ |
| 4342 #if DECSUBSET |
| 4343 if (!set->extended) uprv_decNumberZero(res); |
| 4344 else { |
| 4345 #endif |
| 4346 if (op&DIVIDE) { |
| 4347 residue=0; |
| 4348 exponent=lhs->exponent-rhs->exponent; /* ideal exponent */ |
| 4349 uprv_decNumberCopy(res, lhs); /* [zeros always fit] */ |
| 4350 res->bits=bits; /* sign as computed */ |
| 4351 res->exponent=exponent; /* exponent, too */ |
| 4352 decFinalize(res, set, &residue, status); /* check exponent */ |
| 4353 } |
| 4354 else if (op&DIVIDEINT) { |
| 4355 uprv_decNumberZero(res); /* integer 0 */ |
| 4356 res->bits=bits; /* sign as computed */ |
| 4357 } |
| 4358 else { /* a remainder */ |
| 4359 exponent=rhs->exponent; /* [save in case overwrite] */ |
| 4360 uprv_decNumberCopy(res, lhs); /* [zeros always fit] */ |
| 4361 if (exponent<res->exponent) res->exponent=exponent; /* use lower */ |
| 4362 } |
| 4363 #if DECSUBSET |
| 4364 } |
| 4365 #endif |
| 4366 break;} |
| 4367 |
| 4368 /* Precalculate exponent. This starts off adjusted (and hence fits */ |
| 4369 /* in 31 bits) and becomes the usual unadjusted exponent as the */ |
| 4370 /* division proceeds. The order of evaluation is important, here, */ |
| 4371 /* to avoid wrap. */ |
| 4372 exponent=(lhs->exponent+lhs->digits)-(rhs->exponent+rhs->digits); |
| 4373 |
| 4374 /* If the working exponent is -ve, then some quick exits are */ |
| 4375 /* possible because the quotient is known to be <1 */ |
| 4376 /* [for REMNEAR, it needs to be < -1, as -0.5 could need work] */ |
| 4377 if (exponent<0 && !(op==DIVIDE)) { |
| 4378 if (op&DIVIDEINT) { |
| 4379 uprv_decNumberZero(res); /* integer part is 0 */ |
| 4380 #if DECSUBSET |
| 4381 if (set->extended) |
| 4382 #endif |
| 4383 res->bits=bits; /* set +/- zero */ |
| 4384 break;} |
| 4385 /* fastpath remainders so long as the lhs has the smaller */ |
| 4386 /* (or equal) exponent */ |
| 4387 if (lhs->exponent<=rhs->exponent) { |
| 4388 if (op&REMAINDER || exponent<-1) { |
| 4389 /* It is REMAINDER or safe REMNEAR; result is [finished */ |
| 4390 /* clone of] lhs (r = x - 0*y) */ |
| 4391 residue=0; |
| 4392 decCopyFit(res, lhs, set, &residue, status); |
| 4393 decFinish(res, set, &residue, status); |
| 4394 break; |
| 4395 } |
| 4396 /* [unsafe REMNEAR drops through] */ |
| 4397 } |
| 4398 } /* fastpaths */ |
| 4399 |
| 4400 /* Long (slow) division is needed; roll up the sleeves... */ |
| 4401 |
| 4402 /* The accumulator will hold the quotient of the division. */ |
| 4403 /* If it needs to be too long for stack storage, then allocate. */ |
| 4404 acclength=D2U(reqdigits+DECDPUN); /* in Units */ |
| 4405 if (acclength*sizeof(Unit)>sizeof(accbuff)) { |
| 4406 /* printf("malloc dvacc %ld units\n", acclength); */ |
| 4407 allocacc=(Unit *)malloc(acclength*sizeof(Unit)); |
| 4408 if (allocacc==NULL) { /* hopeless -- abandon */ |
| 4409 *status|=DEC_Insufficient_storage; |
| 4410 break;} |
| 4411 acc=allocacc; /* use the allocated space */ |
| 4412 } |
| 4413 |
| 4414 /* var1 is the padded LHS ready for subtractions. */ |
| 4415 /* If it needs to be too long for stack storage, then allocate. */ |
| 4416 /* The maximum units needed for var1 (long subtraction) is: */ |
| 4417 /* Enough for */ |
| 4418 /* (rhs->digits+reqdigits-1) -- to allow full slide to right */ |
| 4419 /* or (lhs->digits) -- to allow for long lhs */ |
| 4420 /* whichever is larger */ |
| 4421 /* +1 -- for rounding of slide to right */ |
| 4422 /* +1 -- for leading 0s */ |
| 4423 /* +1 -- for pre-adjust if a remainder or DIVIDEINT */ |
| 4424 /* [Note: unused units do not participate in decUnitAddSub data] */ |
| 4425 maxdigits=rhs->digits+reqdigits-1; |
| 4426 if (lhs->digits>maxdigits) maxdigits=lhs->digits; |
| 4427 var1units=D2U(maxdigits)+2; |
| 4428 /* allocate a guard unit above msu1 for REMAINDERNEAR */ |
| 4429 if (!(op&DIVIDE)) var1units++; |
| 4430 if ((var1units+1)*sizeof(Unit)>sizeof(varbuff)) { |
| 4431 /* printf("malloc dvvar %ld units\n", var1units+1); */ |
| 4432 varalloc=(Unit *)malloc((var1units+1)*sizeof(Unit)); |
| 4433 if (varalloc==NULL) { /* hopeless -- abandon */ |
| 4434 *status|=DEC_Insufficient_storage; |
| 4435 break;} |
| 4436 var1=varalloc; /* use the allocated space */ |
| 4437 } |
| 4438 |
| 4439 /* Extend the lhs and rhs to full long subtraction length. The lhs */ |
| 4440 /* is truly extended into the var1 buffer, with 0 padding, so a */ |
| 4441 /* subtract in place is always possible. The rhs (var2) has */ |
| 4442 /* virtual padding (implemented by decUnitAddSub). */ |
| 4443 /* One guard unit was allocated above msu1 for rem=rem+rem in */ |
| 4444 /* REMAINDERNEAR. */ |
| 4445 msu1=var1+var1units-1; /* msu of var1 */ |
| 4446 source=lhs->lsu+D2U(lhs->digits)-1; /* msu of input array */ |
| 4447 for (target=msu1; source>=lhs->lsu; source--, target--) *target=*source; |
| 4448 for (; target>=var1; target--) *target=0; |
| 4449 |
| 4450 /* rhs (var2) is left-aligned with var1 at the start */ |
| 4451 var2ulen=var1units; /* rhs logical length (units) */ |
| 4452 var2units=D2U(rhs->digits); /* rhs actual length (units) */ |
| 4453 var2=rhs->lsu; /* -> rhs array */ |
| 4454 msu2=var2+var2units-1; /* -> msu of var2 [never changes] */ |
| 4455 /* now set up the variables which will be used for estimating the */ |
| 4456 /* multiplication factor. If these variables are not exact, add */ |
| 4457 /* 1 to make sure that the multiplier is never overestimated. */ |
| 4458 msu2plus=*msu2; /* it's value .. */ |
| 4459 if (var2units>1) msu2plus++; /* .. +1 if any more */ |
| 4460 msu2pair=(eInt)*msu2*(DECDPUNMAX+1);/* top two pair .. */ |
| 4461 if (var2units>1) { /* .. [else treat 2nd as 0] */ |
| 4462 msu2pair+=*(msu2-1); /* .. */ |
| 4463 if (var2units>2) msu2pair++; /* .. +1 if any more */ |
| 4464 } |
| 4465 |
| 4466 /* The calculation is working in units, which may have leading zeros, */ |
| 4467 /* but the exponent was calculated on the assumption that they are */ |
| 4468 /* both left-aligned. Adjust the exponent to compensate: add the */ |
| 4469 /* number of leading zeros in var1 msu and subtract those in var2 msu. */ |
| 4470 /* [This is actually done by counting the digits and negating, as */ |
| 4471 /* lead1=DECDPUN-digits1, and similarly for lead2.] */ |
| 4472 for (pow=&powers[1]; *msu1>=*pow; pow++) exponent--; |
| 4473 for (pow=&powers[1]; *msu2>=*pow; pow++) exponent++; |
| 4474 |
| 4475 /* Now, if doing an integer divide or remainder, ensure that */ |
| 4476 /* the result will be Unit-aligned. To do this, shift the var1 */ |
| 4477 /* accumulator towards least if need be. (It's much easier to */ |
| 4478 /* do this now than to reassemble the residue afterwards, if */ |
| 4479 /* doing a remainder.) Also ensure the exponent is not negative. */ |
| 4480 if (!(op&DIVIDE)) { |
| 4481 Unit *u; /* work */ |
| 4482 /* save the initial 'false' padding of var1, in digits */ |
| 4483 var1initpad=(var1units-D2U(lhs->digits))*DECDPUN; |
| 4484 /* Determine the shift to do. */ |
| 4485 if (exponent<0) cut=-exponent; |
| 4486 else cut=DECDPUN-exponent%DECDPUN; |
| 4487 decShiftToLeast(var1, var1units, cut); |
| 4488 exponent+=cut; /* maintain numerical value */ |
| 4489 var1initpad-=cut; /* .. and reduce padding */ |
| 4490 /* clean any most-significant units which were just emptied */ |
| 4491 for (u=msu1; cut>=DECDPUN; cut-=DECDPUN, u--) *u=0; |
| 4492 } /* align */ |
| 4493 else { /* is DIVIDE */ |
| 4494 maxexponent=lhs->exponent-rhs->exponent; /* save */ |
| 4495 /* optimization: if the first iteration will just produce 0, */ |
| 4496 /* preadjust to skip it [valid for DIVIDE only] */ |
| 4497 if (*msu1<*msu2) { |
| 4498 var2ulen--; /* shift down */ |
| 4499 exponent-=DECDPUN; /* update the exponent */ |
| 4500 } |
| 4501 } |
| 4502 |
| 4503 /* ---- start the long-division loops ------------------------------ */ |
| 4504 accunits=0; /* no units accumulated yet */ |
| 4505 accdigits=0; /* .. or digits */ |
| 4506 accnext=acc+acclength-1; /* -> msu of acc [NB: allows digits+1]
*/ |
| 4507 for (;;) { /* outer forever loop */ |
| 4508 thisunit=0; /* current unit assumed 0 */ |
| 4509 /* find the next unit */ |
| 4510 for (;;) { /* inner forever loop */ |
| 4511 /* strip leading zero units [from either pre-adjust or from */ |
| 4512 /* subtract last time around]. Leave at least one unit. */ |
| 4513 for (; *msu1==0 && msu1>var1; msu1--) var1units--; |
| 4514 |
| 4515 if (var1units<var2ulen) break; /* var1 too low for subtract */ |
| 4516 if (var1units==var2ulen) { /* unit-by-unit compare needed */ |
| 4517 /* compare the two numbers, from msu */ |
| 4518 const Unit *pv1, *pv2; |
| 4519 Unit v2; /* units to compare */ |
| 4520 pv2=msu2; /* -> msu */ |
| 4521 for (pv1=msu1; ; pv1--, pv2--) { |
| 4522 /* v1=*pv1 -- always OK */ |
| 4523 v2=0; /* assume in padding */ |
| 4524 if (pv2>=var2) v2=*pv2; /* in range */ |
| 4525 if (*pv1!=v2) break; /* no longer the same */ |
| 4526 if (pv1==var1) break; /* done; leave pv1 as is */ |
| 4527 } |
| 4528 /* here when all inspected or a difference seen */ |
| 4529 if (*pv1<v2) break; /* var1 too low to subtract */ |
| 4530 if (*pv1==v2) { /* var1 == var2 */ |
| 4531 /* reach here if var1 and var2 are identical; subtraction */ |
| 4532 /* would increase digit by one, and the residue will be 0 so */ |
| 4533 /* the calculation is done; leave the loop with residue=0. */ |
| 4534 thisunit++; /* as though subtracted */ |
| 4535 *var1=0; /* set var1 to 0 */ |
| 4536 var1units=1; /* .. */ |
| 4537 break; /* from inner */ |
| 4538 } /* var1 == var2 */ |
| 4539 /* *pv1>v2. Prepare for real subtraction; the lengths are equal */ |
| 4540 /* Estimate the multiplier (there's always a msu1-1)... */ |
| 4541 /* Bring in two units of var2 to provide a good estimate. */ |
| 4542 mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2pair); |
| 4543 } /* lengths the same */ |
| 4544 else { /* var1units > var2ulen, so subtraction is safe */ |
| 4545 /* The var2 msu is one unit towards the lsu of the var1 msu, */ |
| 4546 /* so only one unit for var2 can be used. */ |
| 4547 mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2plus); |
| 4548 } |
| 4549 if (mult==0) mult=1; /* must always be at least 1 */ |
| 4550 /* subtraction needed; var1 is > var2 */ |
| 4551 thisunit=(Unit)(thisunit+mult); /* accumulate */ |
| 4552 /* subtract var1-var2, into var1; only the overlap needs */ |
| 4553 /* processing, as this is an in-place calculation */ |
| 4554 shift=var2ulen-var2units; |
| 4555 #if DECTRACE |
| 4556 decDumpAr('1', &var1[shift], var1units-shift); |
| 4557 decDumpAr('2', var2, var2units); |
| 4558 printf("m=%ld\n", -mult); |
| 4559 #endif |
| 4560 decUnitAddSub(&var1[shift], var1units-shift, |
| 4561 var2, var2units, 0, |
| 4562 &var1[shift], -mult); |
| 4563 #if DECTRACE |
| 4564 decDumpAr('#', &var1[shift], var1units-shift); |
| 4565 #endif |
| 4566 /* var1 now probably has leading zeros; these are removed at the */ |
| 4567 /* top of the inner loop. */ |
| 4568 } /* inner loop */ |
| 4569 |
| 4570 /* The next unit has been calculated in full; unless it's a */ |
| 4571 /* leading zero, add to acc */ |
| 4572 if (accunits!=0 || thisunit!=0) { /* is first or non-zero */ |
| 4573 *accnext=thisunit; /* store in accumulator */ |
| 4574 /* account exactly for the new digits */ |
| 4575 if (accunits==0) { |
| 4576 accdigits++; /* at least one */ |
| 4577 for (pow=&powers[1]; thisunit>=*pow; pow++) accdigits++; |
| 4578 } |
| 4579 else accdigits+=DECDPUN; |
| 4580 accunits++; /* update count */ |
| 4581 accnext--; /* ready for next */ |
| 4582 if (accdigits>reqdigits) break; /* have enough digits */ |
| 4583 } |
| 4584 |
| 4585 /* if the residue is zero, the operation is done (unless divide */ |
| 4586 /* or divideInteger and still not enough digits yet) */ |
| 4587 if (*var1==0 && var1units==1) { /* residue is 0 */ |
| 4588 if (op&(REMAINDER|REMNEAR)) break; |
| 4589 if ((op&DIVIDE) && (exponent<=maxexponent)) break; |
| 4590 /* [drop through if divideInteger] */ |
| 4591 } |
| 4592 /* also done enough if calculating remainder or integer */ |
| 4593 /* divide and just did the last ('units') unit */ |
| 4594 if (exponent==0 && !(op&DIVIDE)) break; |
| 4595 |
| 4596 /* to get here, var1 is less than var2, so divide var2 by the per- */ |
| 4597 /* Unit power of ten and go for the next digit */ |
| 4598 var2ulen--; /* shift down */ |
| 4599 exponent-=DECDPUN; /* update the exponent */ |
| 4600 } /* outer loop */ |
| 4601 |
| 4602 /* ---- division is complete --------------------------------------- */ |
| 4603 /* here: acc has at least reqdigits+1 of good results (or fewer */ |
| 4604 /* if early stop), starting at accnext+1 (its lsu) */ |
| 4605 /* var1 has any residue at the stopping point */ |
| 4606 /* accunits is the number of digits collected in acc */ |
| 4607 if (accunits==0) { /* acc is 0 */ |
| 4608 accunits=1; /* show have a unit .. */ |
| 4609 accdigits=1; /* .. */ |
| 4610 *accnext=0; /* .. whose value is 0 */ |
| 4611 } |
| 4612 else accnext++; /* back to last placed */ |
| 4613 /* accnext now -> lowest unit of result */ |
| 4614 |
| 4615 residue=0; /* assume no residue */ |
| 4616 if (op&DIVIDE) { |
| 4617 /* record the presence of any residue, for rounding */ |
| 4618 if (*var1!=0 || var1units>1) residue=1; |
| 4619 else { /* no residue */ |
| 4620 /* Had an exact division; clean up spurious trailing 0s. */ |
| 4621 /* There will be at most DECDPUN-1, from the final multiply, */ |
| 4622 /* and then only if the result is non-0 (and even) and the */ |
| 4623 /* exponent is 'loose'. */ |
| 4624 #if DECDPUN>1 |
| 4625 Unit lsu=*accnext; |
| 4626 if (!(lsu&0x01) && (lsu!=0)) { |
| 4627 /* count the trailing zeros */ |
| 4628 Int drop=0; |
| 4629 for (;; drop++) { /* [will terminate because lsu!=0] */ |
| 4630 if (exponent>=maxexponent) break; /* don't chop real 0s */ |
| 4631 #if DECDPUN<=4 |
| 4632 if ((lsu-QUOT10(lsu, drop+1) |
| 4633 *powers[drop+1])!=0) break; /* found non-0 digit */ |
| 4634 #else |
| 4635 if (lsu%powers[drop+1]!=0) break; /* found non-0 digit */ |
| 4636 #endif |
| 4637 exponent++; |
| 4638 } |
| 4639 if (drop>0) { |
| 4640 accunits=decShiftToLeast(accnext, accunits, drop); |
| 4641 accdigits=decGetDigits(accnext, accunits); |
| 4642 accunits=D2U(accdigits); |
| 4643 /* [exponent was adjusted in the loop] */ |
| 4644 } |
| 4645 } /* neither odd nor 0 */ |
| 4646 #endif |
| 4647 } /* exact divide */ |
| 4648 } /* divide */ |
| 4649 else /* op!=DIVIDE */ { |
| 4650 /* check for coefficient overflow */ |
| 4651 if (accdigits+exponent>reqdigits) { |
| 4652 *status|=DEC_Division_impossible; |
| 4653 break; |
| 4654 } |
| 4655 if (op & (REMAINDER|REMNEAR)) { |
| 4656 /* [Here, the exponent will be 0, because var1 was adjusted */ |
| 4657 /* appropriately.] */ |
| 4658 Int postshift; /* work */ |
| 4659 Flag wasodd=0; /* integer was odd */ |
| 4660 Unit *quotlsu; /* for save */ |
| 4661 Int quotdigits; /* .. */ |
| 4662 |
| 4663 bits=lhs->bits; /* remainder sign is always as lhs
*/ |
| 4664 |
| 4665 /* Fastpath when residue is truly 0 is worthwhile [and */ |
| 4666 /* simplifies the code below] */ |
| 4667 if (*var1==0 && var1units==1) { /* residue is 0 */ |
| 4668 Int exp=lhs->exponent; /* save min(exponents) */ |
| 4669 if (rhs->exponent<exp) exp=rhs->exponent; |
| 4670 uprv_decNumberZero(res); /* 0 coefficient */ |
| 4671 #if DECSUBSET |
| 4672 if (set->extended) |
| 4673 #endif |
| 4674 res->exponent=exp; /* .. with proper exponent */ |
| 4675 res->bits=(uByte)(bits&DECNEG); /* [cleaned] */ |
| 4676 decFinish(res, set, &residue, status); /* might clamp */ |
| 4677 break; |
| 4678 } |
| 4679 /* note if the quotient was odd */ |
| 4680 if (*accnext & 0x01) wasodd=1; /* acc is odd */ |
| 4681 quotlsu=accnext; /* save in case need to reinspect
*/ |
| 4682 quotdigits=accdigits; /* .. */ |
| 4683 |
| 4684 /* treat the residue, in var1, as the value to return, via acc */ |
| 4685 /* calculate the unused zero digits. This is the smaller of: */ |
| 4686 /* var1 initial padding (saved above) */ |
| 4687 /* var2 residual padding, which happens to be given by: */ |
| 4688 postshift=var1initpad+exponent-lhs->exponent+rhs->exponent; |
| 4689 /* [the 'exponent' term accounts for the shifts during divide] */ |
| 4690 if (var1initpad<postshift) postshift=var1initpad; |
| 4691 |
| 4692 /* shift var1 the requested amount, and adjust its digits */ |
| 4693 var1units=decShiftToLeast(var1, var1units, postshift); |
| 4694 accnext=var1; |
| 4695 accdigits=decGetDigits(var1, var1units); |
| 4696 accunits=D2U(accdigits); |
| 4697 |
| 4698 exponent=lhs->exponent; /* exponent is smaller of lhs & rhs */ |
| 4699 if (rhs->exponent<exponent) exponent=rhs->exponent; |
| 4700 |
| 4701 /* Now correct the result if doing remainderNear; if it */ |
| 4702 /* (looking just at coefficients) is > rhs/2, or == rhs/2 and */ |
| 4703 /* the integer was odd then the result should be rem-rhs. */ |
| 4704 if (op&REMNEAR) { |
| 4705 Int compare, tarunits; /* work */ |
| 4706 Unit *up; /* .. */ |
| 4707 /* calculate remainder*2 into the var1 buffer (which has */ |
| 4708 /* 'headroom' of an extra unit and hence enough space) */ |
| 4709 /* [a dedicated 'double' loop would be faster, here] */ |
| 4710 tarunits=decUnitAddSub(accnext, accunits, accnext, accunits, |
| 4711 0, accnext, 1); |
| 4712 /* decDumpAr('r', accnext, tarunits); */ |
| 4713 |
| 4714 /* Here, accnext (var1) holds tarunits Units with twice the */ |
| 4715 /* remainder's coefficient, which must now be compared to the */ |
| 4716 /* RHS. The remainder's exponent may be smaller than the RHS's. */ |
| 4717 compare=decUnitCompare(accnext, tarunits, rhs->lsu, D2U(rhs->digits), |
| 4718 rhs->exponent-exponent); |
| 4719 if (compare==BADINT) { /* deep trouble */ |
| 4720 *status|=DEC_Insufficient_storage; |
| 4721 break;} |
| 4722 |
| 4723 /* now restore the remainder by dividing by two; the lsu */ |
| 4724 /* is known to be even. */ |
| 4725 for (up=accnext; up<accnext+tarunits; up++) { |
| 4726 Int half; /* half to add to lower unit */ |
| 4727 half=*up & 0x01; |
| 4728 *up/=2; /* [shift] */ |
| 4729 if (!half) continue; |
| 4730 *(up-1)+=(DECDPUNMAX+1)/2; |
| 4731 } |
| 4732 /* [accunits still describes the original remainder length] */ |
| 4733 |
| 4734 if (compare>0 || (compare==0 && wasodd)) { /* adjustment needed */ |
| 4735 Int exp, expunits, exprem; /* work */ |
| 4736 /* This is effectively causing round-up of the quotient, */ |
| 4737 /* so if it was the rare case where it was full and all */ |
| 4738 /* nines, it would overflow and hence division-impossible */ |
| 4739 /* should be raised */ |
| 4740 Flag allnines=0; /* 1 if quotient all nines */ |
| 4741 if (quotdigits==reqdigits) { /* could be borderline */ |
| 4742 for (up=quotlsu; ; up++) { |
| 4743 if (quotdigits>DECDPUN) { |
| 4744 if (*up!=DECDPUNMAX) break;/* non-nines */ |
| 4745 } |
| 4746 else { /* this is the last Unit */ |
| 4747 if (*up==powers[quotdigits]-1) allnines=1; |
| 4748 break; |
| 4749 } |
| 4750 quotdigits-=DECDPUN; /* checked those digits */ |
| 4751 } /* up */ |
| 4752 } /* borderline check */ |
| 4753 if (allnines) { |
| 4754 *status|=DEC_Division_impossible; |
| 4755 break;} |
| 4756 |
| 4757 /* rem-rhs is needed; the sign will invert. Again, var1 */ |
| 4758 /* can safely be used for the working Units array. */ |
| 4759 exp=rhs->exponent-exponent; /* RHS padding needed */ |
| 4760 /* Calculate units and remainder from exponent. */ |
| 4761 expunits=exp/DECDPUN; |
| 4762 exprem=exp%DECDPUN; |
| 4763 /* subtract [A+B*(-m)]; the result will always be negative */ |
| 4764 accunits=-decUnitAddSub(accnext, accunits, |
| 4765 rhs->lsu, D2U(rhs->digits), |
| 4766 expunits, accnext, -(Int)powers[exprem]); |
| 4767 accdigits=decGetDigits(accnext, accunits); /* count digits exactly
*/ |
| 4768 accunits=D2U(accdigits); /* and recalculate the units for copy *
/ |
| 4769 /* [exponent is as for original remainder] */ |
| 4770 bits^=DECNEG; /* flip the sign */ |
| 4771 } |
| 4772 } /* REMNEAR */ |
| 4773 } /* REMAINDER or REMNEAR */ |
| 4774 } /* not DIVIDE */ |
| 4775 |
| 4776 /* Set exponent and bits */ |
| 4777 res->exponent=exponent; |
| 4778 res->bits=(uByte)(bits&DECNEG); /* [cleaned] */ |
| 4779 |
| 4780 /* Now the coefficient. */ |
| 4781 decSetCoeff(res, set, accnext, accdigits, &residue, status); |
| 4782 |
| 4783 decFinish(res, set, &residue, status); /* final cleanup */ |
| 4784 |
| 4785 #if DECSUBSET |
| 4786 /* If a divide then strip trailing zeros if subset [after round] */ |
| 4787 if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, 1, &dropped); |
| 4788 #endif |
| 4789 } while(0); /* end protected */ |
| 4790 |
| 4791 if (varalloc!=NULL) free(varalloc); /* drop any storage used */ |
| 4792 if (allocacc!=NULL) free(allocacc); /* .. */ |
| 4793 #if DECSUBSET |
| 4794 if (allocrhs!=NULL) free(allocrhs); /* .. */ |
| 4795 if (alloclhs!=NULL) free(alloclhs); /* .. */ |
| 4796 #endif |
| 4797 return res; |
| 4798 } /* decDivideOp */ |
| 4799 |
| 4800 /* ------------------------------------------------------------------ */ |
| 4801 /* decMultiplyOp -- multiplication operation */ |
| 4802 /* */ |
| 4803 /* This routine performs the multiplication C=A x B. */ |
| 4804 /* */ |
| 4805 /* res is C, the result. C may be A and/or B (e.g., X=X*X) */ |
| 4806 /* lhs is A */ |
| 4807 /* rhs is B */ |
| 4808 /* set is the context */ |
| 4809 /* status is the usual accumulator */ |
| 4810 /* */ |
| 4811 /* C must have space for set->digits digits. */ |
| 4812 /* */ |
| 4813 /* ------------------------------------------------------------------ */ |
| 4814 /* 'Classic' multiplication is used rather than Karatsuba, as the */ |
| 4815 /* latter would give only a minor improvement for the short numbers */ |
| 4816 /* expected to be handled most (and uses much more memory). */ |
| 4817 /* */ |
| 4818 /* There are two major paths here: the general-purpose ('old code') */ |
| 4819 /* path which handles all DECDPUN values, and a fastpath version */ |
| 4820 /* which is used if 64-bit ints are available, DECDPUN<=4, and more */ |
| 4821 /* than two calls to decUnitAddSub would be made. */ |
| 4822 /* */ |
| 4823 /* The fastpath version lumps units together into 8-digit or 9-digit */ |
| 4824 /* chunks, and also uses a lazy carry strategy to minimise expensive */ |
| 4825 /* 64-bit divisions. The chunks are then broken apart again into */ |
| 4826 /* units for continuing processing. Despite this overhead, the */ |
| 4827 /* fastpath can speed up some 16-digit operations by 10x (and much */ |
| 4828 /* more for higher-precision calculations). */ |
| 4829 /* */ |
| 4830 /* A buffer always has to be used for the accumulator; in the */ |
| 4831 /* fastpath, buffers are also always needed for the chunked copies of */ |
| 4832 /* of the operand coefficients. */ |
| 4833 /* Static buffers are larger than needed just for multiply, to allow */ |
| 4834 /* for calls from other operations (notably exp). */ |
| 4835 /* ------------------------------------------------------------------ */ |
| 4836 #define FASTMUL (DECUSE64 && DECDPUN<5) |
| 4837 static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs, |
| 4838 const decNumber *rhs, decContext *set, |
| 4839 uInt *status) { |
| 4840 Int accunits; /* Units of accumulator in use */ |
| 4841 Int exponent; /* work */ |
| 4842 Int residue=0; /* rounding residue */ |
| 4843 uByte bits; /* result sign */ |
| 4844 Unit *acc; /* -> accumulator Unit array */ |
| 4845 Int needbytes; /* size calculator */ |
| 4846 void *allocacc=NULL; /* -> allocated accumulator, iff allocated *
/ |
| 4847 Unit accbuff[SD2U(DECBUFFER*4+1)]; /* buffer (+1 for DECBUFFER==0, */ |
| 4848 /* *4 for calls from other operations) */ |
| 4849 const Unit *mer, *mermsup; /* work */ |
| 4850 Int madlength; /* Units in multiplicand */ |
| 4851 Int shift; /* Units to shift multiplicand by */ |
| 4852 |
| 4853 #if FASTMUL |
| 4854 /* if DECDPUN is 1 or 3 work in base 10**9, otherwise */ |
| 4855 /* (DECDPUN is 2 or 4) then work in base 10**8 */ |
| 4856 #if DECDPUN & 1 /* odd */ |
| 4857 #define FASTBASE 1000000000 /* base */ |
| 4858 #define FASTDIGS 9 /* digits in base */ |
| 4859 #define FASTLAZY 18 /* carry resolution point [1->18] */ |
| 4860 #else |
| 4861 #define FASTBASE 100000000 |
| 4862 #define FASTDIGS 8 |
| 4863 #define FASTLAZY 1844 /* carry resolution point [1->1844] */ |
| 4864 #endif |
| 4865 /* three buffers are used, two for chunked copies of the operands */ |
| 4866 /* (base 10**8 or base 10**9) and one base 2**64 accumulator with */ |
| 4867 /* lazy carry evaluation */ |
| 4868 uInt zlhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */ |
| 4869 uInt *zlhi=zlhibuff; /* -> lhs array */ |
| 4870 uInt *alloclhi=NULL; /* -> allocated buffer, iff allocated
*/ |
| 4871 uInt zrhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */ |
| 4872 uInt *zrhi=zrhibuff; /* -> rhs array */ |
| 4873 uInt *allocrhi=NULL; /* -> allocated buffer, iff allocated
*/ |
| 4874 uLong zaccbuff[(DECBUFFER*2+1)/4+2]; /* buffer (+1 for DECBUFFER==0) */ |
| 4875 /* [allocacc is shared for both paths, as only one will run] */ |
| 4876 uLong *zacc=zaccbuff; /* -> accumulator array for exact result */ |
| 4877 #if DECDPUN==1 |
| 4878 Int zoff; /* accumulator offset */ |
| 4879 #endif |
| 4880 uInt *lip, *rip; /* item pointers */ |
| 4881 uInt *lmsi, *rmsi; /* most significant items */ |
| 4882 Int ilhs, irhs, iacc; /* item counts in the arrays */ |
| 4883 Int lazy; /* lazy carry counter */ |
| 4884 uLong lcarry; /* uLong carry */ |
| 4885 uInt carry; /* carry (NB not uLong) */ |
| 4886 Int count; /* work */ |
| 4887 const Unit *cup; /* .. */ |
| 4888 Unit *up; /* .. */ |
| 4889 uLong *lp; /* .. */ |
| 4890 Int p; /* .. */ |
| 4891 #endif |
| 4892 |
| 4893 #if DECSUBSET |
| 4894 decNumber *alloclhs=NULL; /* -> allocated buffer, iff allocated */ |
| 4895 decNumber *allocrhs=NULL; /* -> allocated buffer, iff allocated */ |
| 4896 #endif |
| 4897 |
| 4898 #if DECCHECK |
| 4899 if (decCheckOperands(res, lhs, rhs, set)) return res; |
| 4900 #endif |
| 4901 |
| 4902 /* precalculate result sign */ |
| 4903 bits=(uByte)((lhs->bits^rhs->bits)&DECNEG); |
| 4904 |
| 4905 /* handle infinities and NaNs */ |
| 4906 if (SPECIALARGS) { /* a special bit set */ |
| 4907 if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */ |
| 4908 decNaNs(res, lhs, rhs, set, status); |
| 4909 return res;} |
| 4910 /* one or two infinities; Infinity * 0 is invalid */ |
| 4911 if (((lhs->bits & DECINF)==0 && ISZERO(lhs)) |
| 4912 ||((rhs->bits & DECINF)==0 && ISZERO(rhs))) { |
| 4913 *status|=DEC_Invalid_operation; |
| 4914 return res;} |
| 4915 uprv_decNumberZero(res); |
| 4916 res->bits=bits|DECINF; /* infinity */ |
| 4917 return res;} |
| 4918 |
| 4919 /* For best speed, as in DMSRCN [the original Rexx numerics */ |
| 4920 /* module], use the shorter number as the multiplier (rhs) and */ |
| 4921 /* the longer as the multiplicand (lhs) to minimise the number of */ |
| 4922 /* adds (partial products) */ |
| 4923 if (lhs->digits<rhs->digits) { /* swap... */ |
| 4924 const decNumber *hold=lhs; |
| 4925 lhs=rhs; |
| 4926 rhs=hold; |
| 4927 } |
| 4928 |
| 4929 do { /* protect allocated storage */ |
| 4930 #if DECSUBSET |
| 4931 if (!set->extended) { |
| 4932 /* reduce operands and set lostDigits status, as needed */ |
| 4933 if (lhs->digits>set->digits) { |
| 4934 alloclhs=decRoundOperand(lhs, set, status); |
| 4935 if (alloclhs==NULL) break; |
| 4936 lhs=alloclhs; |
| 4937 } |
| 4938 if (rhs->digits>set->digits) { |
| 4939 allocrhs=decRoundOperand(rhs, set, status); |
| 4940 if (allocrhs==NULL) break; |
| 4941 rhs=allocrhs; |
| 4942 } |
| 4943 } |
| 4944 #endif |
| 4945 /* [following code does not require input rounding] */ |
| 4946 |
| 4947 #if FASTMUL /* fastpath can be used */ |
| 4948 /* use the fast path if there are enough digits in the shorter */ |
| 4949 /* operand to make the setup and takedown worthwhile */ |
| 4950 #define NEEDTWO (DECDPUN*2) /* within two decUnitAddSub calls */ |
| 4951 if (rhs->digits>NEEDTWO) { /* use fastpath... */ |
| 4952 /* calculate the number of elements in each array */ |
| 4953 ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; /* [ceiling] */ |
| 4954 irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; /* .. */ |
| 4955 iacc=ilhs+irhs; |
| 4956 |
| 4957 /* allocate buffers if required, as usual */ |
| 4958 needbytes=ilhs*sizeof(uInt); |
| 4959 if (needbytes>(Int)sizeof(zlhibuff)) { |
| 4960 alloclhi=(uInt *)malloc(needbytes); |
| 4961 zlhi=alloclhi;} |
| 4962 needbytes=irhs*sizeof(uInt); |
| 4963 if (needbytes>(Int)sizeof(zrhibuff)) { |
| 4964 allocrhi=(uInt *)malloc(needbytes); |
| 4965 zrhi=allocrhi;} |
| 4966 |
| 4967 /* Allocating the accumulator space needs a special case when */ |
| 4968 /* DECDPUN=1 because when converting the accumulator to Units */ |
| 4969 /* after the multiplication each 8-byte item becomes 9 1-byte */ |
| 4970 /* units. Therefore iacc extra bytes are needed at the front */ |
| 4971 /* (rounded up to a multiple of 8 bytes), and the uLong */ |
| 4972 /* accumulator starts offset the appropriate number of units */ |
| 4973 /* to the right to avoid overwrite during the unchunking. */ |
| 4974 needbytes=iacc*sizeof(uLong); |
| 4975 #if DECDPUN==1 |
| 4976 zoff=(iacc+7)/8; /* items to offset by */ |
| 4977 needbytes+=zoff*8; |
| 4978 #endif |
| 4979 if (needbytes>(Int)sizeof(zaccbuff)) { |
| 4980 allocacc=(uLong *)malloc(needbytes); |
| 4981 zacc=(uLong *)allocacc;} |
| 4982 if (zlhi==NULL||zrhi==NULL||zacc==NULL) { |
| 4983 *status|=DEC_Insufficient_storage; |
| 4984 break;} |
| 4985 |
| 4986 acc=(Unit *)zacc; /* -> target Unit array */ |
| 4987 #if DECDPUN==1 |
| 4988 zacc+=zoff; /* start uLong accumulator to right */ |
| 4989 #endif |
| 4990 |
| 4991 /* assemble the chunked copies of the left and right sides */ |
| 4992 for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++) |
| 4993 for (p=0, *lip=0; p<FASTDIGS && count>0; |
| 4994 p+=DECDPUN, cup++, count-=DECDPUN) |
| 4995 *lip+=*cup*powers[p]; |
| 4996 lmsi=lip-1; /* save -> msi */ |
| 4997 for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++) |
| 4998 for (p=0, *rip=0; p<FASTDIGS && count>0; |
| 4999 p+=DECDPUN, cup++, count-=DECDPUN) |
| 5000 *rip+=*cup*powers[p]; |
| 5001 rmsi=rip-1; /* save -> msi */ |
| 5002 |
| 5003 /* zero the accumulator */ |
| 5004 for (lp=zacc; lp<zacc+iacc; lp++) *lp=0; |
| 5005 |
| 5006 /* Start the multiplication */ |
| 5007 /* Resolving carries can dominate the cost of accumulating the */ |
| 5008 /* partial products, so this is only done when necessary. */ |
| 5009 /* Each uLong item in the accumulator can hold values up to */ |
| 5010 /* 2**64-1, and each partial product can be as large as */ |
| 5011 /* (10**FASTDIGS-1)**2. When FASTDIGS=9, this can be added to */ |
| 5012 /* itself 18.4 times in a uLong without overflowing, so during */ |
| 5013 /* the main calculation resolution is carried out every 18th */ |
| 5014 /* add -- every 162 digits. Similarly, when FASTDIGS=8, the */ |
| 5015 /* partial products can be added to themselves 1844.6 times in */ |
| 5016 /* a uLong without overflowing, so intermediate carry */ |
| 5017 /* resolution occurs only every 14752 digits. Hence for common */ |
| 5018 /* short numbers usually only the one final carry resolution */ |
| 5019 /* occurs. */ |
| 5020 /* (The count is set via FASTLAZY to simplify experiments to */ |
| 5021 /* measure the value of this approach: a 35% improvement on a */ |
| 5022 /* [34x34] multiply.) */ |
| 5023 lazy=FASTLAZY; /* carry delay count */ |
| 5024 for (rip=zrhi; rip<=rmsi; rip++) { /* over each item in rhs */ |
| 5025 lp=zacc+(rip-zrhi); /* where to add the lhs */ |
| 5026 for (lip=zlhi; lip<=lmsi; lip++, lp++) { /* over each item in lhs */ |
| 5027 *lp+=(uLong)(*lip)*(*rip); /* [this should in-line] */ |
| 5028 } /* lip loop */ |
| 5029 lazy--; |
| 5030 if (lazy>0 && rip!=rmsi) continue; |
| 5031 lazy=FASTLAZY; /* reset delay count */ |
| 5032 /* spin up the accumulator resolving overflows */ |
| 5033 for (lp=zacc; lp<zacc+iacc; lp++) { |
| 5034 if (*lp<FASTBASE) continue; /* it fits */ |
| 5035 lcarry=*lp/FASTBASE; /* top part [slow divide] */ |
| 5036 /* lcarry can exceed 2**32-1, so check again; this check */ |
| 5037 /* and occasional extra divide (slow) is well worth it, as */ |
| 5038 /* it allows FASTLAZY to be increased to 18 rather than 4 */ |
| 5039 /* in the FASTDIGS=9 case */ |
| 5040 if (lcarry<FASTBASE) carry=(uInt)lcarry; /* [usual] */ |
| 5041 else { /* two-place carry [fairly rare] */ |
| 5042 uInt carry2=(uInt)(lcarry/FASTBASE); /* top top part */ |
| 5043 *(lp+2)+=carry2; /* add to item+2 */ |
| 5044 *lp-=((uLong)FASTBASE*FASTBASE*carry2); /* [slow] */ |
| 5045 carry=(uInt)(lcarry-((uLong)FASTBASE*carry2)); /* [inline] */ |
| 5046 } |
| 5047 *(lp+1)+=carry; /* add to item above [inline] */ |
| 5048 *lp-=((uLong)FASTBASE*carry); /* [inline] */ |
| 5049 } /* carry resolution */ |
| 5050 } /* rip loop */ |
| 5051 |
| 5052 /* The multiplication is complete; time to convert back into */ |
| 5053 /* units. This can be done in-place in the accumulator and in */ |
| 5054 /* 32-bit operations, because carries were resolved after the */ |
| 5055 /* final add. This needs N-1 divides and multiplies for */ |
| 5056 /* each item in the accumulator (which will become up to N */ |
| 5057 /* units, where 2<=N<=9). */ |
| 5058 for (lp=zacc, up=acc; lp<zacc+iacc; lp++) { |
| 5059 uInt item=(uInt)*lp; /* decapitate to uInt */ |
| 5060 for (p=0; p<FASTDIGS-DECDPUN; p+=DECDPUN, up++) { |
| 5061 uInt part=item/(DECDPUNMAX+1); |
| 5062 *up=(Unit)(item-(part*(DECDPUNMAX+1))); |
| 5063 item=part; |
| 5064 } /* p */ |
| 5065 *up=(Unit)item; up++; /* [final needs no division] */ |
| 5066 } /* lp */ |
| 5067 accunits=up-acc; /* count of units */ |
| 5068 } |
| 5069 else { /* here to use units directly, without chunking ['old code'] */ |
| 5070 #endif |
| 5071 |
| 5072 /* if accumulator will be too long for local storage, then allocate */ |
| 5073 acc=accbuff; /* -> assume buffer for accumulator */ |
| 5074 needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit); |
| 5075 if (needbytes>(Int)sizeof(accbuff)) { |
| 5076 allocacc=(Unit *)malloc(needbytes); |
| 5077 if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;} |
| 5078 acc=(Unit *)allocacc; /* use the allocated space */ |
| 5079 } |
| 5080 |
| 5081 /* Now the main long multiplication loop */ |
| 5082 /* Unlike the equivalent in the IBM Java implementation, there */ |
| 5083 /* is no advantage in calculating from msu to lsu. So, do it */ |
| 5084 /* by the book, as it were. */ |
| 5085 /* Each iteration calculates ACC=ACC+MULTAND*MULT */ |
| 5086 accunits=1; /* accumulator starts at '0' */ |
| 5087 *acc=0; /* .. (lsu=0) */ |
| 5088 shift=0; /* no multiplicand shift at first */ |
| 5089 madlength=D2U(lhs->digits); /* this won't change */ |
| 5090 mermsup=rhs->lsu+D2U(rhs->digits); /* -> msu+1 of multiplier */ |
| 5091 |
| 5092 for (mer=rhs->lsu; mer<mermsup; mer++) { |
| 5093 /* Here, *mer is the next Unit in the multiplier to use */ |
| 5094 /* If non-zero [optimization] add it... */ |
| 5095 if (*mer!=0) accunits=decUnitAddSub(&acc[shift], accunits-shift, |
| 5096 lhs->lsu, madlength, 0, |
| 5097 &acc[shift], *mer) |
| 5098 + shift; |
| 5099 else { /* extend acc with a 0; it will be used shortly */ |
| 5100 *(acc+accunits)=0; /* [this avoids length of <=0 later] */ |
| 5101 accunits++; |
| 5102 } |
| 5103 /* multiply multiplicand by 10**DECDPUN for next Unit to left */ |
| 5104 shift++; /* add this for 'logical length' */ |
| 5105 } /* n */ |
| 5106 #if FASTMUL |
| 5107 } /* unchunked units */ |
| 5108 #endif |
| 5109 /* common end-path */ |
| 5110 #if DECTRACE |
| 5111 decDumpAr('*', acc, accunits); /* Show exact result */ |
| 5112 #endif |
| 5113 |
| 5114 /* acc now contains the exact result of the multiplication, */ |
| 5115 /* possibly with a leading zero unit; build the decNumber from */ |
| 5116 /* it, noting if any residue */ |
| 5117 res->bits=bits; /* set sign */ |
| 5118 res->digits=decGetDigits(acc, accunits); /* count digits exactly */ |
| 5119 |
| 5120 /* There can be a 31-bit wrap in calculating the exponent. */ |
| 5121 /* This can only happen if both input exponents are negative and */ |
| 5122 /* both their magnitudes are large. If there was a wrap, set a */ |
| 5123 /* safe very negative exponent, from which decFinalize() will */ |
| 5124 /* raise a hard underflow shortly. */ |
| 5125 exponent=lhs->exponent+rhs->exponent; /* calculate exponent */ |
| 5126 if (lhs->exponent<0 && rhs->exponent<0 && exponent>0) |
| 5127 exponent=-2*DECNUMMAXE; /* force underflow */ |
| 5128 res->exponent=exponent; /* OK to overwrite now */ |
| 5129 |
| 5130 |
| 5131 /* Set the coefficient. If any rounding, residue records */ |
| 5132 decSetCoeff(res, set, acc, res->digits, &residue, status); |
| 5133 decFinish(res, set, &residue, status); /* final cleanup */ |
| 5134 } while(0); /* end protected */ |
| 5135 |
| 5136 if (allocacc!=NULL) free(allocacc); /* drop any storage used */ |
| 5137 #if DECSUBSET |
| 5138 if (allocrhs!=NULL) free(allocrhs); /* .. */ |
| 5139 if (alloclhs!=NULL) free(alloclhs); /* .. */ |
| 5140 #endif |
| 5141 #if FASTMUL |
| 5142 if (allocrhi!=NULL) free(allocrhi); /* .. */ |
| 5143 if (alloclhi!=NULL) free(alloclhi); /* .. */ |
| 5144 #endif |
| 5145 return res; |
| 5146 } /* decMultiplyOp */ |
| 5147 |
| 5148 /* ------------------------------------------------------------------ */ |
| 5149 /* decExpOp -- effect exponentiation */ |
| 5150 /* */ |
| 5151 /* This computes C = exp(A) */ |
| 5152 /* */ |
| 5153 /* res is C, the result. C may be A */ |
| 5154 /* rhs is A */ |
| 5155 /* set is the context; note that rounding mode has no effect */ |
| 5156 /* */ |
| 5157 /* C must have space for set->digits digits. status is updated but */ |
| 5158 /* not set. */ |
| 5159 /* */ |
| 5160 /* Restrictions: */ |
| 5161 /* */ |
| 5162 /* digits, emax, and -emin in the context must be less than */ |
| 5163 /* 2*DEC_MAX_MATH (1999998), and the rhs must be within these */ |
| 5164 /* bounds or a zero. This is an internal routine, so these */ |
| 5165 /* restrictions are contractual and not enforced. */ |
| 5166 /* */ |
| 5167 /* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */ |
| 5168 /* almost always be correctly rounded, but may be up to 1 ulp in */ |
| 5169 /* error in rare cases. */ |
| 5170 /* */ |
| 5171 /* Finite results will always be full precision and Inexact, except */ |
| 5172 /* when A is a zero or -Infinity (giving 1 or 0 respectively). */ |
| 5173 /* ------------------------------------------------------------------ */ |
| 5174 /* This approach used here is similar to the algorithm described in */ |
| 5175 /* */ |
| 5176 /* Variable Precision Exponential Function, T. E. Hull and */ |
| 5177 /* A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */ |
| 5178 /* pp79-91, ACM, June 1986. */ |
| 5179 /* */ |
| 5180 /* with the main difference being that the iterations in the series */ |
| 5181 /* evaluation are terminated dynamically (which does not require the */ |
| 5182 /* extra variable-precision variables which are expensive in this */ |
| 5183 /* context). */ |
| 5184 /* */ |
| 5185 /* The error analysis in Hull & Abrham's paper applies except for the */ |
| 5186 /* round-off error accumulation during the series evaluation. This */ |
| 5187 /* code does not precalculate the number of iterations and so cannot */ |
| 5188 /* use Horner's scheme. Instead, the accumulation is done at double- */ |
| 5189 /* precision, which ensures that the additions of the terms are exact */ |
| 5190 /* and do not accumulate round-off (and any round-off errors in the */ |
| 5191 /* terms themselves move 'to the right' faster than they can */ |
| 5192 /* accumulate). This code also extends the calculation by allowing, */ |
| 5193 /* in the spirit of other decNumber operators, the input to be more */ |
| 5194 /* precise than the result (the precision used is based on the more */ |
| 5195 /* precise of the input or requested result). */ |
| 5196 /* */ |
| 5197 /* Implementation notes: */ |
| 5198 /* */ |
| 5199 /* 1. This is separated out as decExpOp so it can be called from */ |
| 5200 /* other Mathematical functions (notably Ln) with a wider range */ |
| 5201 /* than normal. In particular, it can handle the slightly wider */ |
| 5202 /* (double) range needed by Ln (which has to be able to calculate */ |
| 5203 /* exp(-x) where x can be the tiniest number (Ntiny). */ |
| 5204 /* */ |
| 5205 /* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop */ |
| 5206 /* iterations by appoximately a third with additional (although */ |
| 5207 /* diminishing) returns as the range is reduced to even smaller */ |
| 5208 /* fractions. However, h (the power of 10 used to correct the */ |
| 5209 /* result at the end, see below) must be kept <=8 as otherwise */ |
| 5210 /* the final result cannot be computed. Hence the leverage is a */ |
| 5211 /* sliding value (8-h), where potentially the range is reduced */ |
| 5212 /* more for smaller values. */ |
| 5213 /* */ |
| 5214 /* The leverage that can be applied in this way is severely */ |
| 5215 /* limited by the cost of the raise-to-the power at the end, */ |
| 5216 /* which dominates when the number of iterations is small (less */ |
| 5217 /* than ten) or when rhs is short. As an example, the adjustment */ |
| 5218 /* x**10,000,000 needs 31 multiplications, all but one full-width. */ |
| 5219 /* */ |
| 5220 /* 3. The restrictions (especially precision) could be raised with */ |
| 5221 /* care, but the full decNumber range seems very hard within the */ |
| 5222 /* 32-bit limits. */ |
| 5223 /* */ |
| 5224 /* 4. The working precisions for the static buffers are twice the */ |
| 5225 /* obvious size to allow for calls from decNumberPower. */ |
| 5226 /* ------------------------------------------------------------------ */ |
| 5227 decNumber * decExpOp(decNumber *res, const decNumber *rhs, |
| 5228 decContext *set, uInt *status) { |
| 5229 uInt ignore=0; /* working status */ |
| 5230 Int h; /* adjusted exponent for 0.xxxx */ |
| 5231 Int p; /* working precision */ |
| 5232 Int residue; /* rounding residue */ |
| 5233 uInt needbytes; /* for space calculations */ |
| 5234 const decNumber *x=rhs; /* (may point to safe copy later) */ |
| 5235 decContext aset, tset, dset; /* working contexts */ |
| 5236 Int comp; /* work */ |
| 5237 |
| 5238 /* the argument is often copied to normalize it, so (unusually) it */ |
| 5239 /* is treated like other buffers, using DECBUFFER, +1 in case */ |
| 5240 /* DECBUFFER is 0 */ |
| 5241 decNumber bufr[D2N(DECBUFFER*2+1)]; |
| 5242 decNumber *allocrhs=NULL; /* non-NULL if rhs buffer allocated */ |
| 5243 |
| 5244 /* the working precision will be no more than set->digits+8+1 */ |
| 5245 /* so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER */ |
| 5246 /* is 0 (and twice that for the accumulator) */ |
| 5247 |
| 5248 /* buffer for t, term (working precision plus) */ |
| 5249 decNumber buft[D2N(DECBUFFER*2+9+1)]; |
| 5250 decNumber *allocbuft=NULL; /* -> allocated buft, iff allocated */ |
| 5251 decNumber *t=buft; /* term */ |
| 5252 /* buffer for a, accumulator (working precision * 2), at least 9 */ |
| 5253 decNumber bufa[D2N(DECBUFFER*4+18+1)]; |
| 5254 decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ |
| 5255 decNumber *a=bufa; /* accumulator */ |
| 5256 /* decNumber for the divisor term; this needs at most 9 digits */ |
| 5257 /* and so can be fixed size [16 so can use standard context] */ |
| 5258 decNumber bufd[D2N(16)]; |
| 5259 decNumber *d=bufd; /* divisor */ |
| 5260 decNumber numone; /* constant 1 */ |
| 5261 |
| 5262 #if DECCHECK |
| 5263 Int iterations=0; /* for later sanity check */ |
| 5264 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
| 5265 #endif |
| 5266 |
| 5267 do { /* protect allocated storage */ |
| 5268 if (SPECIALARG) { /* handle infinities and NaNs */ |
| 5269 if (decNumberIsInfinite(rhs)) { /* an infinity */ |
| 5270 if (decNumberIsNegative(rhs)) /* -Infinity -> +0 */ |
| 5271 uprv_decNumberZero(res); |
| 5272 else uprv_decNumberCopy(res, rhs); /* +Infinity -> self */ |
| 5273 } |
| 5274 else decNaNs(res, rhs, NULL, set, status); /* a NaN */ |
| 5275 break;} |
| 5276 |
| 5277 if (ISZERO(rhs)) { /* zeros -> exact 1 */ |
| 5278 uprv_decNumberZero(res); /* make clean 1 */ |
| 5279 *res->lsu=1; /* .. */ |
| 5280 break;} /* [no status to set] */ |
| 5281 |
| 5282 /* e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path */ |
| 5283 /* positive and negative tiny cases which will result in inexact */ |
| 5284 /* 1. This also allows the later add-accumulate to always be */ |
| 5285 /* exact (because its length will never be more than twice the */ |
| 5286 /* working precision). */ |
| 5287 /* The comparator (tiny) needs just one digit, so use the */ |
| 5288 /* decNumber d for it (reused as the divisor, etc., below); its */ |
| 5289 /* exponent is such that if x is positive it will have */ |
| 5290 /* set->digits-1 zeros between the decimal point and the digit, */ |
| 5291 /* which is 4, and if x is negative one more zero there as the */ |
| 5292 /* more precise result will be of the form 0.9999999 rather than */ |
| 5293 /* 1.0000001. Hence, tiny will be 0.0000004 if digits=7 and x>0 */ |
| 5294 /* or 0.00000004 if digits=7 and x<0. If RHS not larger than */ |
| 5295 /* this then the result will be 1.000000 */ |
| 5296 uprv_decNumberZero(d); /* clean */ |
| 5297 *d->lsu=4; /* set 4 .. */ |
| 5298 d->exponent=-set->digits; /* * 10**(-d) */ |
| 5299 if (decNumberIsNegative(rhs)) d->exponent--; /* negative case */ |
| 5300 comp=decCompare(d, rhs, 1); /* signless compare */ |
| 5301 if (comp==BADINT) { |
| 5302 *status|=DEC_Insufficient_storage; |
| 5303 break;} |
| 5304 if (comp>=0) { /* rhs < d */ |
| 5305 Int shift=set->digits-1; |
| 5306 uprv_decNumberZero(res); /* set 1 */ |
| 5307 *res->lsu=1; /* .. */ |
| 5308 res->digits=decShiftToMost(res->lsu, 1, shift); |
| 5309 res->exponent=-shift; /* make 1.0000... */ |
| 5310 *status|=DEC_Inexact | DEC_Rounded; /* .. inexactly */ |
| 5311 break;} /* tiny */ |
| 5312 |
| 5313 /* set up the context to be used for calculating a, as this is */ |
| 5314 /* used on both paths below */ |
| 5315 uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); |
| 5316 /* accumulator bounds are as requested (could underflow) */ |
| 5317 aset.emax=set->emax; /* usual bounds */ |
| 5318 aset.emin=set->emin; /* .. */ |
| 5319 aset.clamp=0; /* and no concrete format */ |
| 5320 |
| 5321 /* calculate the adjusted (Hull & Abrham) exponent (where the */ |
| 5322 /* decimal point is just to the left of the coefficient msd) */ |
| 5323 h=rhs->exponent+rhs->digits; |
| 5324 /* if h>8 then 10**h cannot be calculated safely; however, when */ |
| 5325 /* h=8 then exp(|rhs|) will be at least exp(1E+7) which is at */ |
| 5326 /* least 6.59E+4342944, so (due to the restriction on Emax/Emin) */ |
| 5327 /* overflow (or underflow to 0) is guaranteed -- so this case can */ |
| 5328 /* be handled by simply forcing the appropriate excess */ |
| 5329 if (h>8) { /* overflow/underflow */ |
| 5330 /* set up here so Power call below will over or underflow to */ |
| 5331 /* zero; set accumulator to either 2 or 0.02 */ |
| 5332 /* [stack buffer for a is always big enough for this] */ |
| 5333 uprv_decNumberZero(a); |
| 5334 *a->lsu=2; /* not 1 but < exp(1) */ |
| 5335 if (decNumberIsNegative(rhs)) a->exponent=-2; /* make 0.02 */ |
| 5336 h=8; /* clamp so 10**h computable */ |
| 5337 p=9; /* set a working precision */ |
| 5338 } |
| 5339 else { /* h<=8 */ |
| 5340 Int maxlever=(rhs->digits>8?1:0); |
| 5341 /* [could/should increase this for precisions >40 or so, too] */ |
| 5342 |
| 5343 /* if h is 8, cannot normalize to a lower upper limit because */ |
| 5344 /* the final result will not be computable (see notes above), */ |
| 5345 /* but leverage can be applied whenever h is less than 8. */ |
| 5346 /* Apply as much as possible, up to a MAXLEVER digits, which */ |
| 5347 /* sets the tradeoff against the cost of the later a**(10**h). */ |
| 5348 /* As h is increased, the working precision below also */ |
| 5349 /* increases to compensate for the "constant digits at the */ |
| 5350 /* front" effect. */ |
| 5351 Int lever=MINI(8-h, maxlever); /* leverage attainable */ |
| 5352 Int use=-rhs->digits-lever; /* exponent to use for RHS */ |
| 5353 h+=lever; /* apply leverage selected */ |
| 5354 if (h<0) { /* clamp */ |
| 5355 use+=h; /* [may end up subnormal] */ |
| 5356 h=0; |
| 5357 } |
| 5358 /* Take a copy of RHS if it needs normalization (true whenever x>=1) */ |
| 5359 if (rhs->exponent!=use) { |
| 5360 decNumber *newrhs=bufr; /* assume will fit on stack */ |
| 5361 needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); |
| 5362 if (needbytes>sizeof(bufr)) { /* need malloc space */ |
| 5363 allocrhs=(decNumber *)malloc(needbytes); |
| 5364 if (allocrhs==NULL) { /* hopeless -- abandon */ |
| 5365 *status|=DEC_Insufficient_storage; |
| 5366 break;} |
| 5367 newrhs=allocrhs; /* use the allocated space */ |
| 5368 } |
| 5369 uprv_decNumberCopy(newrhs, rhs); /* copy to safe space */ |
| 5370 newrhs->exponent=use; /* normalize; now <1 */ |
| 5371 x=newrhs; /* ready for use */ |
| 5372 /* decNumberShow(x); */ |
| 5373 } |
| 5374 |
| 5375 /* Now use the usual power series to evaluate exp(x). The */ |
| 5376 /* series starts as 1 + x + x^2/2 ... so prime ready for the */ |
| 5377 /* third term by setting the term variable t=x, the accumulator */ |
| 5378 /* a=1, and the divisor d=2. */ |
| 5379 |
| 5380 /* First determine the working precision. From Hull & Abrham */ |
| 5381 /* this is set->digits+h+2. However, if x is 'over-precise' we */ |
| 5382 /* need to allow for all its digits to potentially participate */ |
| 5383 /* (consider an x where all the excess digits are 9s) so in */ |
| 5384 /* this case use x->digits+h+2 */ |
| 5385 p=MAXI(x->digits, set->digits)+h+2; /* [h<=8] */ |
| 5386 |
| 5387 /* a and t are variable precision, and depend on p, so space */ |
| 5388 /* must be allocated for them if necessary */ |
| 5389 |
| 5390 /* the accumulator needs to be able to hold 2p digits so that */ |
| 5391 /* the additions on the second and subsequent iterations are */ |
| 5392 /* sufficiently exact. */ |
| 5393 needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit); |
| 5394 if (needbytes>sizeof(bufa)) { /* need malloc space */ |
| 5395 allocbufa=(decNumber *)malloc(needbytes); |
| 5396 if (allocbufa==NULL) { /* hopeless -- abandon */ |
| 5397 *status|=DEC_Insufficient_storage; |
| 5398 break;} |
| 5399 a=allocbufa; /* use the allocated space */ |
| 5400 } |
| 5401 /* the term needs to be able to hold p digits (which is */ |
| 5402 /* guaranteed to be larger than x->digits, so the initial copy */ |
| 5403 /* is safe); it may also be used for the raise-to-power */ |
| 5404 /* calculation below, which needs an extra two digits */ |
| 5405 needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit); |
| 5406 if (needbytes>sizeof(buft)) { /* need malloc space */ |
| 5407 allocbuft=(decNumber *)malloc(needbytes); |
| 5408 if (allocbuft==NULL) { /* hopeless -- abandon */ |
| 5409 *status|=DEC_Insufficient_storage; |
| 5410 break;} |
| 5411 t=allocbuft; /* use the allocated space */ |
| 5412 } |
| 5413 |
| 5414 uprv_decNumberCopy(t, x); /* term=x */ |
| 5415 uprv_decNumberZero(a); *a->lsu=1; /* accumulator=1 */ |
| 5416 uprv_decNumberZero(d); *d->lsu=2; /* divisor=2 */ |
| 5417 uprv_decNumberZero(&numone); *numone.lsu=1; /* constant 1 for increment *
/ |
| 5418 |
| 5419 /* set up the contexts for calculating a, t, and d */ |
| 5420 uprv_decContextDefault(&tset, DEC_INIT_DECIMAL64); |
| 5421 dset=tset; |
| 5422 /* accumulator bounds are set above, set precision now */ |
| 5423 aset.digits=p*2; /* double */ |
| 5424 /* term bounds avoid any underflow or overflow */ |
| 5425 tset.digits=p; |
| 5426 tset.emin=DEC_MIN_EMIN; /* [emax is plenty] */ |
| 5427 /* [dset.digits=16, etc., are sufficient] */ |
| 5428 |
| 5429 /* finally ready to roll */ |
| 5430 for (;;) { |
| 5431 #if DECCHECK |
| 5432 iterations++; |
| 5433 #endif |
| 5434 /* only the status from the accumulation is interesting */ |
| 5435 /* [but it should remain unchanged after first add] */ |
| 5436 decAddOp(a, a, t, &aset, 0, status); /* a=a+t */ |
| 5437 decMultiplyOp(t, t, x, &tset, &ignore); /* t=t*x */ |
| 5438 decDivideOp(t, t, d, &tset, DIVIDE, &ignore); /* t=t/d */ |
| 5439 /* the iteration ends when the term cannot affect the result, */ |
| 5440 /* if rounded to p digits, which is when its value is smaller */ |
| 5441 /* than the accumulator by p+1 digits. There must also be */ |
| 5442 /* full precision in a. */ |
| 5443 if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1)) |
| 5444 && (a->digits>=p)) break; |
| 5445 decAddOp(d, d, &numone, &dset, 0, &ignore); /* d=d+1 */ |
| 5446 } /* iterate */ |
| 5447 |
| 5448 #if DECCHECK |
| 5449 /* just a sanity check; comment out test to show always */ |
| 5450 if (iterations>p+3) |
| 5451 printf("Exp iterations=%ld, status=%08lx, p=%ld, d=%ld\n", |
| 5452 (LI)iterations, (LI)*status, (LI)p, (LI)x->digits); |
| 5453 #endif |
| 5454 } /* h<=8 */ |
| 5455 |
| 5456 /* apply postconditioning: a=a**(10**h) -- this is calculated */ |
| 5457 /* at a slightly higher precision than Hull & Abrham suggest */ |
| 5458 if (h>0) { |
| 5459 Int seenbit=0; /* set once a 1-bit is seen */ |
| 5460 Int i; /* counter */ |
| 5461 Int n=powers[h]; /* always positive */ |
| 5462 aset.digits=p+2; /* sufficient precision */ |
| 5463 /* avoid the overhead and many extra digits of decNumberPower */ |
| 5464 /* as all that is needed is the short 'multipliers' loop; here */ |
| 5465 /* accumulate the answer into t */ |
| 5466 uprv_decNumberZero(t); *t->lsu=1; /* acc=1 */ |
| 5467 for (i=1;;i++){ /* for each bit [top bit ignored] */ |
| 5468 /* abandon if have had overflow or terminal underflow */ |
| 5469 if (*status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */ |
| 5470 if (*status&DEC_Overflow || ISZERO(t)) break;} |
| 5471 n=n<<1; /* move next bit to testable position */ |
| 5472 if (n<0) { /* top bit is set */ |
| 5473 seenbit=1; /* OK, have a significant bit */ |
| 5474 decMultiplyOp(t, t, a, &aset, status); /* acc=acc*x */ |
| 5475 } |
| 5476 if (i==31) break; /* that was the last bit */ |
| 5477 if (!seenbit) continue; /* no need to square 1 */ |
| 5478 decMultiplyOp(t, t, t, &aset, status); /* acc=acc*acc [square] */ |
| 5479 } /*i*/ /* 32 bits */ |
| 5480 /* decNumberShow(t); */ |
| 5481 a=t; /* and carry on using t instead of a */ |
| 5482 } |
| 5483 |
| 5484 /* Copy and round the result to res */ |
| 5485 residue=1; /* indicate dirt to right .. */ |
| 5486 if (ISZERO(a)) residue=0; /* .. unless underflowed to 0 */ |
| 5487 aset.digits=set->digits; /* [use default rounding] */ |
| 5488 decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */ |
| 5489 decFinish(res, set, &residue, status); /* cleanup/set flags */ |
| 5490 } while(0); /* end protected */ |
| 5491 |
| 5492 if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */ |
| 5493 if (allocbufa!=NULL) free(allocbufa); /* .. */ |
| 5494 if (allocbuft!=NULL) free(allocbuft); /* .. */ |
| 5495 /* [status is handled by caller] */ |
| 5496 return res; |
| 5497 } /* decExpOp */ |
| 5498 |
| 5499 /* ------------------------------------------------------------------ */ |
| 5500 /* Initial-estimate natural logarithm table */ |
| 5501 /* */ |
| 5502 /* LNnn -- 90-entry 16-bit table for values from .10 through .99. */ |
| 5503 /* The result is a 4-digit encode of the coefficient (c=the */ |
| 5504 /* top 14 bits encoding 0-9999) and a 2-digit encode of the */ |
| 5505 /* exponent (e=the bottom 2 bits encoding 0-3) */ |
| 5506 /* */ |
| 5507 /* The resulting value is given by: */ |
| 5508 /* */ |
| 5509 /* v = -c * 10**(-e-3) */ |
| 5510 /* */ |
| 5511 /* where e and c are extracted from entry k = LNnn[x-10] */ |
| 5512 /* where x is truncated (NB) into the range 10 through 99, */ |
| 5513 /* and then c = k>>2 and e = k&3. */ |
| 5514 /* ------------------------------------------------------------------ */ |
| 5515 const uShort LNnn[90]={9016, 8652, 8316, 8008, 7724, 7456, 7208, |
| 5516 6972, 6748, 6540, 6340, 6148, 5968, 5792, 5628, 5464, 5312, |
| 5517 5164, 5020, 4884, 4748, 4620, 4496, 4376, 4256, 4144, 4032, |
| 5518 39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629, |
| 5519 29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837, |
| 5520 22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321, |
| 5521 15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717, |
| 5522 10197, 9685, 9177, 8677, 8185, 7697, 7213, 6737, 6269, 5801, |
| 5523 5341, 4889, 4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254, |
| 5524 10130, 6046, 20055}; |
| 5525 |
| 5526 /* ------------------------------------------------------------------ */ |
| 5527 /* decLnOp -- effect natural logarithm */ |
| 5528 /* */ |
| 5529 /* This computes C = ln(A) */ |
| 5530 /* */ |
| 5531 /* res is C, the result. C may be A */ |
| 5532 /* rhs is A */ |
| 5533 /* set is the context; note that rounding mode has no effect */ |
| 5534 /* */ |
| 5535 /* C must have space for set->digits digits. */ |
| 5536 /* */ |
| 5537 /* Notable cases: */ |
| 5538 /* A<0 -> Invalid */ |
| 5539 /* A=0 -> -Infinity (Exact) */ |
| 5540 /* A=+Infinity -> +Infinity (Exact) */ |
| 5541 /* A=1 exactly -> 0 (Exact) */ |
| 5542 /* */ |
| 5543 /* Restrictions (as for Exp): */ |
| 5544 /* */ |
| 5545 /* digits, emax, and -emin in the context must be less than */ |
| 5546 /* DEC_MAX_MATH+11 (1000010), and the rhs must be within these */ |
| 5547 /* bounds or a zero. This is an internal routine, so these */ |
| 5548 /* restrictions are contractual and not enforced. */ |
| 5549 /* */ |
| 5550 /* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */ |
| 5551 /* almost always be correctly rounded, but may be up to 1 ulp in */ |
| 5552 /* error in rare cases. */ |
| 5553 /* ------------------------------------------------------------------ */ |
| 5554 /* The result is calculated using Newton's method, with each */ |
| 5555 /* iteration calculating a' = a + x * exp(-a) - 1. See, for example, */ |
| 5556 /* Epperson 1989. */ |
| 5557 /* */ |
| 5558 /* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */ |
| 5559 /* This has to be calculated at the sum of the precision of x and the */ |
| 5560 /* working precision. */ |
| 5561 /* */ |
| 5562 /* Implementation notes: */ |
| 5563 /* */ |
| 5564 /* 1. This is separated out as decLnOp so it can be called from */ |
| 5565 /* other Mathematical functions (e.g., Log 10) with a wider range */ |
| 5566 /* than normal. In particular, it can handle the slightly wider */ |
| 5567 /* (+9+2) range needed by a power function. */ |
| 5568 /* */ |
| 5569 /* 2. The speed of this function is about 10x slower than exp, as */ |
| 5570 /* it typically needs 4-6 iterations for short numbers, and the */ |
| 5571 /* extra precision needed adds a squaring effect, twice. */ |
| 5572 /* */ |
| 5573 /* 3. Fastpaths are included for ln(10) and ln(2), up to length 40, */ |
| 5574 /* as these are common requests. ln(10) is used by log10(x). */ |
| 5575 /* */ |
| 5576 /* 4. An iteration might be saved by widening the LNnn table, and */ |
| 5577 /* would certainly save at least one if it were made ten times */ |
| 5578 /* bigger, too (for truncated fractions 0.100 through 0.999). */ |
| 5579 /* However, for most practical evaluations, at least four or five */ |
| 5580 /* iterations will be neede -- so this would only speed up by */ |
| 5581 /* 20-25% and that probably does not justify increasing the table */ |
| 5582 /* size. */ |
| 5583 /* */ |
| 5584 /* 5. The static buffers are larger than might be expected to allow */ |
| 5585 /* for calls from decNumberPower. */ |
| 5586 /* ------------------------------------------------------------------ */ |
| 5587 decNumber * decLnOp(decNumber *res, const decNumber *rhs, |
| 5588 decContext *set, uInt *status) { |
| 5589 uInt ignore=0; /* working status accumulator */ |
| 5590 uInt needbytes; /* for space calculations */ |
| 5591 Int residue; /* rounding residue */ |
| 5592 Int r; /* rhs=f*10**r [see below] */ |
| 5593 Int p; /* working precision */ |
| 5594 Int pp; /* precision for iteration */ |
| 5595 Int t; /* work */ |
| 5596 |
| 5597 /* buffers for a (accumulator, typically precision+2) and b */ |
| 5598 /* (adjustment calculator, same size) */ |
| 5599 decNumber bufa[D2N(DECBUFFER+12)]; |
| 5600 decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ |
| 5601 decNumber *a=bufa; /* accumulator/work */ |
| 5602 decNumber bufb[D2N(DECBUFFER*2+2)]; |
| 5603 decNumber *allocbufb=NULL; /* -> allocated bufa, iff allocated */ |
| 5604 decNumber *b=bufb; /* adjustment/work */ |
| 5605 |
| 5606 decNumber numone; /* constant 1 */ |
| 5607 decNumber cmp; /* work */ |
| 5608 decContext aset, bset; /* working contexts */ |
| 5609 |
| 5610 #if DECCHECK |
| 5611 Int iterations=0; /* for later sanity check */ |
| 5612 if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; |
| 5613 #endif |
| 5614 |
| 5615 do { /* protect allocated storage */ |
| 5616 if (SPECIALARG) { /* handle infinities and NaNs */ |
| 5617 if (decNumberIsInfinite(rhs)) { /* an infinity */ |
| 5618 if (decNumberIsNegative(rhs)) /* -Infinity -> error */ |
| 5619 *status|=DEC_Invalid_operation; |
| 5620 else uprv_decNumberCopy(res, rhs); /* +Infinity -> self */ |
| 5621 } |
| 5622 else decNaNs(res, rhs, NULL, set, status); /* a NaN */ |
| 5623 break;} |
| 5624 |
| 5625 if (ISZERO(rhs)) { /* +/- zeros -> -Infinity */ |
| 5626 uprv_decNumberZero(res); /* make clean */ |
| 5627 res->bits=DECINF|DECNEG; /* set - infinity */ |
| 5628 break;} /* [no status to set] */ |
| 5629 |
| 5630 /* Non-zero negatives are bad... */ |
| 5631 if (decNumberIsNegative(rhs)) { /* -x -> error */ |
| 5632 *status|=DEC_Invalid_operation; |
| 5633 break;} |
| 5634 |
| 5635 /* Here, rhs is positive, finite, and in range */ |
| 5636 |
| 5637 /* lookaside fastpath code for ln(2) and ln(10) at common lengths */ |
| 5638 if (rhs->exponent==0 && set->digits<=40) { |
| 5639 #if DECDPUN==1 |
| 5640 if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { /* ln(10) */ |
| 5641 #else |
| 5642 if (rhs->lsu[0]==10 && rhs->digits==2) { /* ln(10) */ |
| 5643 #endif |
| 5644 aset=*set; aset.round=DEC_ROUND_HALF_EVEN; |
| 5645 #define LN10 "2.302585092994045684017991454684364207601" |
| 5646 uprv_decNumberFromString(res, LN10, &aset); |
| 5647 *status|=(DEC_Inexact | DEC_Rounded); /* is inexact */ |
| 5648 break;} |
| 5649 if (rhs->lsu[0]==2 && rhs->digits==1) { /* ln(2) */ |
| 5650 aset=*set; aset.round=DEC_ROUND_HALF_EVEN; |
| 5651 #define LN2 "0.6931471805599453094172321214581765680755" |
| 5652 uprv_decNumberFromString(res, LN2, &aset); |
| 5653 *status|=(DEC_Inexact | DEC_Rounded); |
| 5654 break;} |
| 5655 } /* integer and short */ |
| 5656 |
| 5657 /* Determine the working precision. This is normally the */ |
| 5658 /* requested precision + 2, with a minimum of 9. However, if */ |
| 5659 /* the rhs is 'over-precise' then allow for all its digits to */ |
| 5660 /* potentially participate (consider an rhs where all the excess */ |
| 5661 /* digits are 9s) so in this case use rhs->digits+2. */ |
| 5662 p=MAXI(rhs->digits, MAXI(set->digits, 7))+2; |
| 5663 |
| 5664 /* Allocate space for the accumulator and the high-precision */ |
| 5665 /* adjustment calculator, if necessary. The accumulator must */ |
| 5666 /* be able to hold p digits, and the adjustment up to */ |
| 5667 /* rhs->digits+p digits. They are also made big enough for 16 */ |
| 5668 /* digits so that they can be used for calculating the initial */ |
| 5669 /* estimate. */ |
| 5670 needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit); |
| 5671 if (needbytes>sizeof(bufa)) { /* need malloc space */ |
| 5672 allocbufa=(decNumber *)malloc(needbytes); |
| 5673 if (allocbufa==NULL) { /* hopeless -- abandon */ |
| 5674 *status|=DEC_Insufficient_storage; |
| 5675 break;} |
| 5676 a=allocbufa; /* use the allocated space */ |
| 5677 } |
| 5678 pp=p+rhs->digits; |
| 5679 needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit); |
| 5680 if (needbytes>sizeof(bufb)) { /* need malloc space */ |
| 5681 allocbufb=(decNumber *)malloc(needbytes); |
| 5682 if (allocbufb==NULL) { /* hopeless -- abandon */ |
| 5683 *status|=DEC_Insufficient_storage; |
| 5684 break;} |
| 5685 b=allocbufb; /* use the allocated space */ |
| 5686 } |
| 5687 |
| 5688 /* Prepare an initial estimate in acc. Calculate this by */ |
| 5689 /* considering the coefficient of x to be a normalized fraction, */ |
| 5690 /* f, with the decimal point at far left and multiplied by */ |
| 5691 /* 10**r. Then, rhs=f*10**r and 0.1<=f<1, and */ |
| 5692 /* ln(x) = ln(f) + ln(10)*r */ |
| 5693 /* Get the initial estimate for ln(f) from a small lookup */ |
| 5694 /* table (see above) indexed by the first two digits of f, */ |
| 5695 /* truncated. */ |
| 5696 |
| 5697 uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); /* 16-digit extended */ |
| 5698 r=rhs->exponent+rhs->digits; /* 'normalised' exponent */ |
| 5699 uprv_decNumberFromInt32(a, r); /* a=r */ |
| 5700 uprv_decNumberFromInt32(b, 2302585); /* b=ln(10) (2.302585) */ |
| 5701 b->exponent=-6; /* .. */ |
| 5702 decMultiplyOp(a, a, b, &aset, &ignore); /* a=a*b */ |
| 5703 /* now get top two digits of rhs into b by simple truncate and */ |
| 5704 /* force to integer */ |
| 5705 residue=0; /* (no residue) */ |
| 5706 aset.digits=2; aset.round=DEC_ROUND_DOWN; |
| 5707 decCopyFit(b, rhs, &aset, &residue, &ignore); /* copy & shorten */ |
| 5708 b->exponent=0; /* make integer */ |
| 5709 t=decGetInt(b); /* [cannot fail] */ |
| 5710 if (t<10) t=X10(t); /* adjust single-digit b */ |
| 5711 t=LNnn[t-10]; /* look up ln(b) */ |
| 5712 uprv_decNumberFromInt32(b, t>>2); /* b=ln(b) coefficient */ |
| 5713 b->exponent=-(t&3)-3; /* set exponent */ |
| 5714 b->bits=DECNEG; /* ln(0.10)->ln(0.99) always -ve */ |
| 5715 aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; /* restore */ |
| 5716 decAddOp(a, a, b, &aset, 0, &ignore); /* acc=a+b */ |
| 5717 /* the initial estimate is now in a, with up to 4 digits correct. */ |
| 5718 /* When rhs is at or near Nmax the estimate will be low, so we */ |
| 5719 /* will approach it from below, avoiding overflow when calling exp. */ |
| 5720 |
| 5721 uprv_decNumberZero(&numone); *numone.lsu=1; /* constant 1 for adjustment
*/ |
| 5722 |
| 5723 /* accumulator bounds are as requested (could underflow, but */ |
| 5724 /* cannot overflow) */ |
| 5725 aset.emax=set->emax; |
| 5726 aset.emin=set->emin; |
| 5727 aset.clamp=0; /* no concrete format */ |
| 5728 /* set up a context to be used for the multiply and subtract */ |
| 5729 bset=aset; |
| 5730 bset.emax=DEC_MAX_MATH*2; /* use double bounds for the */ |
| 5731 bset.emin=-DEC_MAX_MATH*2; /* adjustment calculation */ |
| 5732 /* [see decExpOp call below] */ |
| 5733 /* for each iteration double the number of digits to calculate, */ |
| 5734 /* up to a maximum of p */ |
| 5735 pp=9; /* initial precision */ |
| 5736 /* [initially 9 as then the sequence starts 7+2, 16+2, and */ |
| 5737 /* 34+2, which is ideal for standard-sized numbers] */ |
| 5738 aset.digits=pp; /* working context */ |
| 5739 bset.digits=pp+rhs->digits; /* wider context */ |
| 5740 for (;;) { /* iterate */ |
| 5741 #if DECCHECK |
| 5742 iterations++; |
| 5743 if (iterations>24) break; /* consider 9 * 2**24 */ |
| 5744 #endif |
| 5745 /* calculate the adjustment (exp(-a)*x-1) into b. This is a */ |
| 5746 /* catastrophic subtraction but it really is the difference */ |
| 5747 /* from 1 that is of interest. */ |
| 5748 /* Use the internal entry point to Exp as it allows the double */ |
| 5749 /* range for calculating exp(-a) when a is the tiniest subnormal. */ |
| 5750 a->bits^=DECNEG; /* make -a */ |
| 5751 decExpOp(b, a, &bset, &ignore); /* b=exp(-a) */ |
| 5752 a->bits^=DECNEG; /* restore sign of a */ |
| 5753 /* now multiply by rhs and subtract 1, at the wider precision */ |
| 5754 decMultiplyOp(b, b, rhs, &bset, &ignore); /* b=b*rhs */ |
| 5755 decAddOp(b, b, &numone, &bset, DECNEG, &ignore); /* b=b-1 */ |
| 5756 |
| 5757 /* the iteration ends when the adjustment cannot affect the */ |
| 5758 /* result by >=0.5 ulp (at the requested digits), which */ |
| 5759 /* is when its value is smaller than the accumulator by */ |
| 5760 /* set->digits+1 digits (or it is zero) -- this is a looser */ |
| 5761 /* requirement than for Exp because all that happens to the */ |
| 5762 /* accumulator after this is the final rounding (but note that */ |
| 5763 /* there must also be full precision in a, or a=0). */ |
| 5764 |
| 5765 if (decNumberIsZero(b) || |
| 5766 (a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) { |
| 5767 if (a->digits==p) break; |
| 5768 if (decNumberIsZero(a)) { |
| 5769 decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); /* rhs=1 ?
*/ |
| 5770 if (cmp.lsu[0]==0) a->exponent=0; /* yes, exact 0 */ |
| 5771 else *status|=(DEC_Inexact | DEC_Rounded); /* no, inexact */ |
| 5772 break; |
| 5773 } |
| 5774 /* force padding if adjustment has gone to 0 before full length */ |
| 5775 if (decNumberIsZero(b)) b->exponent=a->exponent-p; |
| 5776 } |
| 5777 |
| 5778 /* not done yet ... */ |
| 5779 decAddOp(a, a, b, &aset, 0, &ignore); /* a=a+b for next estimate */ |
| 5780 if (pp==p) continue; /* precision is at maximum */ |
| 5781 /* lengthen the next calculation */ |
| 5782 pp=pp*2; /* double precision */ |
| 5783 if (pp>p) pp=p; /* clamp to maximum */ |
| 5784 aset.digits=pp; /* working context */ |
| 5785 bset.digits=pp+rhs->digits; /* wider context */ |
| 5786 } /* Newton's iteration */ |
| 5787 |
| 5788 #if DECCHECK |
| 5789 /* just a sanity check; remove the test to show always */ |
| 5790 if (iterations>24) |
| 5791 printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n", |
| 5792 (LI)iterations, (LI)*status, (LI)p, (LI)rhs->digits); |
| 5793 #endif |
| 5794 |
| 5795 /* Copy and round the result to res */ |
| 5796 residue=1; /* indicate dirt to right */ |
| 5797 if (ISZERO(a)) residue=0; /* .. unless underflowed to 0 */ |
| 5798 aset.digits=set->digits; /* [use default rounding] */ |
| 5799 decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */ |
| 5800 decFinish(res, set, &residue, status); /* cleanup/set flags */ |
| 5801 } while(0); /* end protected */ |
| 5802 |
| 5803 if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ |
| 5804 if (allocbufb!=NULL) free(allocbufb); /* .. */ |
| 5805 /* [status is handled by caller] */ |
| 5806 return res; |
| 5807 } /* decLnOp */ |
| 5808 |
| 5809 /* ------------------------------------------------------------------ */ |
| 5810 /* decQuantizeOp -- force exponent to requested value */ |
| 5811 /* */ |
| 5812 /* This computes C = op(A, B), where op adjusts the coefficient */ |
| 5813 /* of C (by rounding or shifting) such that the exponent (-scale) */ |
| 5814 /* of C has the value B or matches the exponent of B. */ |
| 5815 /* The numerical value of C will equal A, except for the effects of */ |
| 5816 /* any rounding that occurred. */ |
| 5817 /* */ |
| 5818 /* res is C, the result. C may be A or B */ |
| 5819 /* lhs is A, the number to adjust */ |
| 5820 /* rhs is B, the requested exponent */ |
| 5821 /* set is the context */ |
| 5822 /* quant is 1 for quantize or 0 for rescale */ |
| 5823 /* status is the status accumulator (this can be called without */ |
| 5824 /* risk of control loss) */ |
| 5825 /* */ |
| 5826 /* C must have space for set->digits digits. */ |
| 5827 /* */ |
| 5828 /* Unless there is an error or the result is infinite, the exponent */ |
| 5829 /* after the operation is guaranteed to be that requested. */ |
| 5830 /* ------------------------------------------------------------------ */ |
| 5831 static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs, |
| 5832 const decNumber *rhs, decContext *set, |
| 5833 Flag quant, uInt *status) { |
| 5834 #if DECSUBSET |
| 5835 decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ |
| 5836 decNumber *allocrhs=NULL; /* .., rhs */ |
| 5837 #endif |
| 5838 const decNumber *inrhs=rhs; /* save original rhs */ |
| 5839 Int reqdigits=set->digits; /* requested DIGITS */ |
| 5840 Int reqexp; /* requested exponent [-scale] */ |
| 5841 Int residue=0; /* rounding residue */ |
| 5842 Int etiny=set->emin-(reqdigits-1); |
| 5843 |
| 5844 #if DECCHECK |
| 5845 if (decCheckOperands(res, lhs, rhs, set)) return res; |
| 5846 #endif |
| 5847 |
| 5848 do { /* protect allocated storage */ |
| 5849 #if DECSUBSET |
| 5850 if (!set->extended) { |
| 5851 /* reduce operands and set lostDigits status, as needed */ |
| 5852 if (lhs->digits>reqdigits) { |
| 5853 alloclhs=decRoundOperand(lhs, set, status); |
| 5854 if (alloclhs==NULL) break; |
| 5855 lhs=alloclhs; |
| 5856 } |
| 5857 if (rhs->digits>reqdigits) { /* [this only checks lostDigits] */ |
| 5858 allocrhs=decRoundOperand(rhs, set, status); |
| 5859 if (allocrhs==NULL) break; |
| 5860 rhs=allocrhs; |
| 5861 } |
| 5862 } |
| 5863 #endif |
| 5864 /* [following code does not require input rounding] */ |
| 5865 |
| 5866 /* Handle special values */ |
| 5867 if (SPECIALARGS) { |
| 5868 /* NaNs get usual processing */ |
| 5869 if (SPECIALARGS & (DECSNAN | DECNAN)) |
| 5870 decNaNs(res, lhs, rhs, set, status); |
| 5871 /* one infinity but not both is bad */ |
| 5872 else if ((lhs->bits ^ rhs->bits) & DECINF) |
| 5873 *status|=DEC_Invalid_operation; |
| 5874 /* both infinity: return lhs */ |
| 5875 else uprv_decNumberCopy(res, lhs); /* [nop if in place] */ |
| 5876 break; |
| 5877 } |
| 5878 |
| 5879 /* set requested exponent */ |
| 5880 if (quant) reqexp=inrhs->exponent; /* quantize -- match exponents */ |
| 5881 else { /* rescale -- use value of rhs */ |
| 5882 /* Original rhs must be an integer that fits and is in range, */ |
| 5883 /* which could be from -1999999997 to +999999999, thanks to */ |
| 5884 /* subnormals */ |
| 5885 reqexp=decGetInt(inrhs); /* [cannot fail] */ |
| 5886 } |
| 5887 |
| 5888 #if DECSUBSET |
| 5889 if (!set->extended) etiny=set->emin; /* no subnormals */ |
| 5890 #endif |
| 5891 |
| 5892 if (reqexp==BADINT /* bad (rescale only) or .. */ |
| 5893 || reqexp==BIGODD || reqexp==BIGEVEN /* very big (ditto) or .. */ |
| 5894 || (reqexp<etiny) /* < lowest */ |
| 5895 || (reqexp>set->emax)) { /* > emax */ |
| 5896 *status|=DEC_Invalid_operation; |
| 5897 break;} |
| 5898 |
| 5899 /* the RHS has been processed, so it can be overwritten now if necessary */ |
| 5900 if (ISZERO(lhs)) { /* zero coefficient unchanged */ |
| 5901 uprv_decNumberCopy(res, lhs); /* [nop if in place] */ |
| 5902 res->exponent=reqexp; /* .. just set exponent */ |
| 5903 #if DECSUBSET |
| 5904 if (!set->extended) res->bits=0; /* subset specification; no -0 */ |
| 5905 #endif |
| 5906 } |
| 5907 else { /* non-zero lhs */ |
| 5908 Int adjust=reqexp-lhs->exponent; /* digit adjustment needed */ |
| 5909 /* if adjusted coefficient will definitely not fit, give up now */ |
| 5910 if ((lhs->digits-adjust)>reqdigits) { |
| 5911 *status|=DEC_Invalid_operation; |
| 5912 break; |
| 5913 } |
| 5914 |
| 5915 if (adjust>0) { /* increasing exponent */ |
| 5916 /* this will decrease the length of the coefficient by adjust */ |
| 5917 /* digits, and must round as it does so */ |
| 5918 decContext workset; /* work */ |
| 5919 workset=*set; /* clone rounding, etc. */ |
| 5920 workset.digits=lhs->digits-adjust; /* set requested length */ |
| 5921 /* [note that the latter can be <1, here] */ |
| 5922 decCopyFit(res, lhs, &workset, &residue, status); /* fit to result */ |
| 5923 decApplyRound(res, &workset, residue, status); /* .. and round */ |
| 5924 residue=0; /* [used] */ |
| 5925 /* If just rounded a 999s case, exponent will be off by one; */ |
| 5926 /* adjust back (after checking space), if so. */ |
| 5927 if (res->exponent>reqexp) { |
| 5928 /* re-check needed, e.g., for quantize(0.9999, 0.001) under */ |
| 5929 /* set->digits==3 */ |
| 5930 if (res->digits==reqdigits) { /* cannot shift by 1 */ |
| 5931 *status&=~(DEC_Inexact | DEC_Rounded); /* [clean these] */ |
| 5932 *status|=DEC_Invalid_operation; |
| 5933 break; |
| 5934 } |
| 5935 res->digits=decShiftToMost(res->lsu, res->digits, 1); /* shift */ |
| 5936 res->exponent--; /* (re)adjust the exponent. */ |
| 5937 } |
| 5938 #if DECSUBSET |
| 5939 if (ISZERO(res) && !set->extended) res->bits=0; /* subset; no -0 */ |
| 5940 #endif |
| 5941 } /* increase */ |
| 5942 else /* adjust<=0 */ { /* decreasing or = exponent */ |
| 5943 /* this will increase the length of the coefficient by -adjust */ |
| 5944 /* digits, by adding zero or more trailing zeros; this is */ |
| 5945 /* already checked for fit, above */ |
| 5946 uprv_decNumberCopy(res, lhs); /* [it will fit] */ |
| 5947 /* if padding needed (adjust<0), add it now... */ |
| 5948 if (adjust<0) { |
| 5949 res->digits=decShiftToMost(res->lsu, res->digits, -adjust); |
| 5950 res->exponent+=adjust; /* adjust the exponent */ |
| 5951 } |
| 5952 } /* decrease */ |
| 5953 } /* non-zero */ |
| 5954 |
| 5955 /* Check for overflow [do not use Finalize in this case, as an */ |
| 5956 /* overflow here is a "don't fit" situation] */ |
| 5957 if (res->exponent>set->emax-res->digits+1) { /* too big */ |
| 5958 *status|=DEC_Invalid_operation; |
| 5959 break; |
| 5960 } |
| 5961 else { |
| 5962 decFinalize(res, set, &residue, status); /* set subnormal flags */ |
| 5963 *status&=~DEC_Underflow; /* suppress Underflow [as per 754] */ |
| 5964 } |
| 5965 } while(0); /* end protected */ |
| 5966 |
| 5967 #if DECSUBSET |
| 5968 if (allocrhs!=NULL) free(allocrhs); /* drop any storage used */ |
| 5969 if (alloclhs!=NULL) free(alloclhs); /* .. */ |
| 5970 #endif |
| 5971 return res; |
| 5972 } /* decQuantizeOp */ |
| 5973 |
| 5974 /* ------------------------------------------------------------------ */ |
| 5975 /* decCompareOp -- compare, min, or max two Numbers */ |
| 5976 /* */ |
| 5977 /* This computes C = A ? B and carries out one of four operations: */ |
| 5978 /* COMPARE -- returns the signum (as a number) giving the */ |
| 5979 /* result of a comparison unless one or both */ |
| 5980 /* operands is a NaN (in which case a NaN results) */ |
| 5981 /* COMPSIG -- as COMPARE except that a quiet NaN raises */ |
| 5982 /* Invalid operation. */ |
| 5983 /* COMPMAX -- returns the larger of the operands, using the */ |
| 5984 /* 754 maxnum operation */ |
| 5985 /* COMPMAXMAG -- ditto, comparing absolute values */ |
| 5986 /* COMPMIN -- the 754 minnum operation */ |
| 5987 /* COMPMINMAG -- ditto, comparing absolute values */ |
| 5988 /* COMTOTAL -- returns the signum (as a number) giving the */ |
| 5989 /* result of a comparison using 754 total ordering */ |
| 5990 /* */ |
| 5991 /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ |
| 5992 /* lhs is A */ |
| 5993 /* rhs is B */ |
| 5994 /* set is the context */ |
| 5995 /* op is the operation flag */ |
| 5996 /* status is the usual accumulator */ |
| 5997 /* */ |
| 5998 /* C must have space for one digit for COMPARE or set->digits for */ |
| 5999 /* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG. */ |
| 6000 /* ------------------------------------------------------------------ */ |
| 6001 /* The emphasis here is on speed for common cases, and avoiding */ |
| 6002 /* coefficient comparison if possible. */ |
| 6003 /* ------------------------------------------------------------------ */ |
| 6004 static decNumber * decCompareOp(decNumber *res, const decNumber *lhs, |
| 6005 const decNumber *rhs, decContext *set, |
| 6006 Flag op, uInt *status) { |
| 6007 #if DECSUBSET |
| 6008 decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ |
| 6009 decNumber *allocrhs=NULL; /* .., rhs */ |
| 6010 #endif |
| 6011 Int result=0; /* default result value */ |
| 6012 uByte merged; /* work */ |
| 6013 |
| 6014 #if DECCHECK |
| 6015 if (decCheckOperands(res, lhs, rhs, set)) return res; |
| 6016 #endif |
| 6017 |
| 6018 do { /* protect allocated storage */ |
| 6019 #if DECSUBSET |
| 6020 if (!set->extended) { |
| 6021 /* reduce operands and set lostDigits status, as needed */ |
| 6022 if (lhs->digits>set->digits) { |
| 6023 alloclhs=decRoundOperand(lhs, set, status); |
| 6024 if (alloclhs==NULL) {result=BADINT; break;} |
| 6025 lhs=alloclhs; |
| 6026 } |
| 6027 if (rhs->digits>set->digits) { |
| 6028 allocrhs=decRoundOperand(rhs, set, status); |
| 6029 if (allocrhs==NULL) {result=BADINT; break;} |
| 6030 rhs=allocrhs; |
| 6031 } |
| 6032 } |
| 6033 #endif |
| 6034 /* [following code does not require input rounding] */ |
| 6035 |
| 6036 /* If total ordering then handle differing signs 'up front' */ |
| 6037 if (op==COMPTOTAL) { /* total ordering */ |
| 6038 if (decNumberIsNegative(lhs) & !decNumberIsNegative(rhs)) { |
| 6039 result=-1; |
| 6040 break; |
| 6041 } |
| 6042 if (!decNumberIsNegative(lhs) & decNumberIsNegative(rhs)) { |
| 6043 result=+1; |
| 6044 break; |
| 6045 } |
| 6046 } |
| 6047 |
| 6048 /* handle NaNs specially; let infinities drop through */ |
| 6049 /* This assumes sNaN (even just one) leads to NaN. */ |
| 6050 merged=(lhs->bits | rhs->bits) & (DECSNAN | DECNAN); |
| 6051 if (merged) { /* a NaN bit set */ |
| 6052 if (op==COMPARE); /* result will be NaN */ |
| 6053 else if (op==COMPSIG) /* treat qNaN as sNaN */ |
| 6054 *status|=DEC_Invalid_operation | DEC_sNaN; |
| 6055 else if (op==COMPTOTAL) { /* total ordering, always finite */ |
| 6056 /* signs are known to be the same; compute the ordering here */ |
| 6057 /* as if the signs are both positive, then invert for negatives */ |
| 6058 if (!decNumberIsNaN(lhs)) result=-1; |
| 6059 else if (!decNumberIsNaN(rhs)) result=+1; |
| 6060 /* here if both NaNs */ |
| 6061 else if (decNumberIsSNaN(lhs) && decNumberIsQNaN(rhs)) result=-1; |
| 6062 else if (decNumberIsQNaN(lhs) && decNumberIsSNaN(rhs)) result=+1; |
| 6063 else { /* both NaN or both sNaN */ |
| 6064 /* now it just depends on the payload */ |
| 6065 result=decUnitCompare(lhs->lsu, D2U(lhs->digits), |
| 6066 rhs->lsu, D2U(rhs->digits), 0); |
| 6067 /* [Error not possible, as these are 'aligned'] */ |
| 6068 } /* both same NaNs */ |
| 6069 if (decNumberIsNegative(lhs)) result=-result; |
| 6070 break; |
| 6071 } /* total order */ |
| 6072 |
| 6073 else if (merged & DECSNAN); /* sNaN -> qNaN */ |
| 6074 else { /* here if MIN or MAX and one or two quiet NaNs */ |
| 6075 /* min or max -- 754 rules ignore single NaN */ |
| 6076 if (!decNumberIsNaN(lhs) || !decNumberIsNaN(rhs)) { |
| 6077 /* just one NaN; force choice to be the non-NaN operand */ |
| 6078 op=COMPMAX; |
| 6079 if (lhs->bits & DECNAN) result=-1; /* pick rhs */ |
| 6080 else result=+1; /* pick lhs */ |
| 6081 break; |
| 6082 } |
| 6083 } /* max or min */ |
| 6084 op=COMPNAN; /* use special path */ |
| 6085 decNaNs(res, lhs, rhs, set, status); /* propagate NaN */ |
| 6086 break; |
| 6087 } |
| 6088 /* have numbers */ |
| 6089 if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1); |
| 6090 else result=decCompare(lhs, rhs, 0); /* sign matters */ |
| 6091 } while(0); /* end protected */ |
| 6092 |
| 6093 if (result==BADINT) *status|=DEC_Insufficient_storage; /* rare */ |
| 6094 else { |
| 6095 if (op==COMPARE || op==COMPSIG ||op==COMPTOTAL) { /* returning signum */ |
| 6096 if (op==COMPTOTAL && result==0) { |
| 6097 /* operands are numerically equal or same NaN (and same sign, */ |
| 6098 /* tested first); if identical, leave result 0 */ |
| 6099 if (lhs->exponent!=rhs->exponent) { |
| 6100 if (lhs->exponent<rhs->exponent) result=-1; |
| 6101 else result=+1; |
| 6102 if (decNumberIsNegative(lhs)) result=-result; |
| 6103 } /* lexp!=rexp */ |
| 6104 } /* total-order by exponent */ |
| 6105 uprv_decNumberZero(res); /* [always a valid result] */ |
| 6106 if (result!=0) { /* must be -1 or +1 */ |
| 6107 *res->lsu=1; |
| 6108 if (result<0) res->bits=DECNEG; |
| 6109 } |
| 6110 } |
| 6111 else if (op==COMPNAN); /* special, drop through */ |
| 6112 else { /* MAX or MIN, non-NaN result */ |
| 6113 Int residue=0; /* rounding accumulator */ |
| 6114 /* choose the operand for the result */ |
| 6115 const decNumber *choice; |
| 6116 if (result==0) { /* operands are numerically equal */ |
| 6117 /* choose according to sign then exponent (see 754) */ |
| 6118 uByte slhs=(lhs->bits & DECNEG); |
| 6119 uByte srhs=(rhs->bits & DECNEG); |
| 6120 #if DECSUBSET |
| 6121 if (!set->extended) { /* subset: force left-hand */ |
| 6122 op=COMPMAX; |
| 6123 result=+1; |
| 6124 } |
| 6125 else |
| 6126 #endif |
| 6127 if (slhs!=srhs) { /* signs differ */ |
| 6128 if (slhs) result=-1; /* rhs is max */ |
| 6129 else result=+1; /* lhs is max */ |
| 6130 } |
| 6131 else if (slhs && srhs) { /* both negative */ |
| 6132 if (lhs->exponent<rhs->exponent) result=+1; |
| 6133 else result=-1; |
| 6134 /* [if equal, use lhs, technically identical] */ |
| 6135 } |
| 6136 else { /* both positive */ |
| 6137 if (lhs->exponent>rhs->exponent) result=+1; |
| 6138 else result=-1; |
| 6139 /* [ditto] */ |
| 6140 } |
| 6141 } /* numerically equal */ |
| 6142 /* here result will be non-0; reverse if looking for MIN */ |
| 6143 if (op==COMPMIN || op==COMPMINMAG) result=-result; |
| 6144 choice=(result>0 ? lhs : rhs); /* choose */ |
| 6145 /* copy chosen to result, rounding if need be */ |
| 6146 decCopyFit(res, choice, set, &residue, status); |
| 6147 decFinish(res, set, &residue, status); |
| 6148 } |
| 6149 } |
| 6150 #if DECSUBSET |
| 6151 if (allocrhs!=NULL) free(allocrhs); /* free any storage used */ |
| 6152 if (alloclhs!=NULL) free(alloclhs); /* .. */ |
| 6153 #endif |
| 6154 return res; |
| 6155 } /* decCompareOp */ |
| 6156 |
| 6157 /* ------------------------------------------------------------------ */ |
| 6158 /* decCompare -- compare two decNumbers by numerical value */ |
| 6159 /* */ |
| 6160 /* This routine compares A ? B without altering them. */ |
| 6161 /* */ |
| 6162 /* Arg1 is A, a decNumber which is not a NaN */ |
| 6163 /* Arg2 is B, a decNumber which is not a NaN */ |
| 6164 /* Arg3 is 1 for a sign-independent compare, 0 otherwise */ |
| 6165 /* */ |
| 6166 /* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */ |
| 6167 /* (the only possible failure is an allocation error) */ |
| 6168 /* ------------------------------------------------------------------ */ |
| 6169 static Int decCompare(const decNumber *lhs, const decNumber *rhs, |
| 6170 Flag abs_c) { |
| 6171 Int result; /* result value */ |
| 6172 Int sigr; /* rhs signum */ |
| 6173 Int compare; /* work */ |
| 6174 |
| 6175 result=1; /* assume signum(lhs) */ |
| 6176 if (ISZERO(lhs)) result=0; |
| 6177 if (abs_c) { |
| 6178 if (ISZERO(rhs)) return result; /* LHS wins or both 0 */ |
| 6179 /* RHS is non-zero */ |
| 6180 if (result==0) return -1; /* LHS is 0; RHS wins */ |
| 6181 /* [here, both non-zero, result=1] */ |
| 6182 } |
| 6183 else { /* signs matter */ |
| 6184 if (result && decNumberIsNegative(lhs)) result=-1; |
| 6185 sigr=1; /* compute signum(rhs) */ |
| 6186 if (ISZERO(rhs)) sigr=0; |
| 6187 else if (decNumberIsNegative(rhs)) sigr=-1; |
| 6188 if (result > sigr) return +1; /* L > R, return 1 */ |
| 6189 if (result < sigr) return -1; /* L < R, return -1 */ |
| 6190 if (result==0) return 0; /* both 0 */ |
| 6191 } |
| 6192 |
| 6193 /* signums are the same; both are non-zero */ |
| 6194 if ((lhs->bits | rhs->bits) & DECINF) { /* one or more infinities */ |
| 6195 if (decNumberIsInfinite(rhs)) { |
| 6196 if (decNumberIsInfinite(lhs)) result=0;/* both infinite */ |
| 6197 else result=-result; /* only rhs infinite */ |
| 6198 } |
| 6199 return result; |
| 6200 } |
| 6201 /* must compare the coefficients, allowing for exponents */ |
| 6202 if (lhs->exponent>rhs->exponent) { /* LHS exponent larger */ |
| 6203 /* swap sides, and sign */ |
| 6204 const decNumber *temp=lhs; |
| 6205 lhs=rhs; |
| 6206 rhs=temp; |
| 6207 result=-result; |
| 6208 } |
| 6209 compare=decUnitCompare(lhs->lsu, D2U(lhs->digits), |
| 6210 rhs->lsu, D2U(rhs->digits), |
| 6211 rhs->exponent-lhs->exponent); |
| 6212 if (compare!=BADINT) compare*=result; /* comparison succeeded */ |
| 6213 return compare; |
| 6214 } /* decCompare */ |
| 6215 |
| 6216 /* ------------------------------------------------------------------ */ |
| 6217 /* decUnitCompare -- compare two >=0 integers in Unit arrays */ |
| 6218 /* */ |
| 6219 /* This routine compares A ? B*10**E where A and B are unit arrays */ |
| 6220 /* A is a plain integer */ |
| 6221 /* B has an exponent of E (which must be non-negative) */ |
| 6222 /* */ |
| 6223 /* Arg1 is A first Unit (lsu) */ |
| 6224 /* Arg2 is A length in Units */ |
| 6225 /* Arg3 is B first Unit (lsu) */ |
| 6226 /* Arg4 is B length in Units */ |
| 6227 /* Arg5 is E (0 if the units are aligned) */ |
| 6228 /* */ |
| 6229 /* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */ |
| 6230 /* (the only possible failure is an allocation error, which can */ |
| 6231 /* only occur if E!=0) */ |
| 6232 /* ------------------------------------------------------------------ */ |
| 6233 static Int decUnitCompare(const Unit *a, Int alength, |
| 6234 const Unit *b, Int blength, Int exp) { |
| 6235 Unit *acc; /* accumulator for result */ |
| 6236 Unit accbuff[SD2U(DECBUFFER*2+1)]; /* local buffer */ |
| 6237 Unit *allocacc=NULL; /* -> allocated acc buffer, iff allocated */ |
| 6238 Int accunits, need; /* units in use or needed for acc */ |
| 6239 const Unit *l, *r, *u; /* work */ |
| 6240 Int expunits, exprem, result; /* .. */ |
| 6241 |
| 6242 if (exp==0) { /* aligned; fastpath */ |
| 6243 if (alength>blength) return 1; |
| 6244 if (alength<blength) return -1; |
| 6245 /* same number of units in both -- need unit-by-unit compare */ |
| 6246 l=a+alength-1; |
| 6247 r=b+alength-1; |
| 6248 for (;l>=a; l--, r--) { |
| 6249 if (*l>*r) return 1; |
| 6250 if (*l<*r) return -1; |
| 6251 } |
| 6252 return 0; /* all units match */ |
| 6253 } /* aligned */ |
| 6254 |
| 6255 /* Unaligned. If one is >1 unit longer than the other, padded */ |
| 6256 /* approximately, then can return easily */ |
| 6257 if (alength>blength+(Int)D2U(exp)) return 1; |
| 6258 if (alength+1<blength+(Int)D2U(exp)) return -1; |
| 6259 |
| 6260 /* Need to do a real subtract. For this, a result buffer is needed */ |
| 6261 /* even though only the sign is of interest. Its length needs */ |
| 6262 /* to be the larger of alength and padded blength, +2 */ |
| 6263 need=blength+D2U(exp); /* maximum real length of B */ |
| 6264 if (need<alength) need=alength; |
| 6265 need+=2; |
| 6266 acc=accbuff; /* assume use local buffer */ |
| 6267 if (need*sizeof(Unit)>sizeof(accbuff)) { |
| 6268 allocacc=(Unit *)malloc(need*sizeof(Unit)); |
| 6269 if (allocacc==NULL) return BADINT; /* hopeless -- abandon */ |
| 6270 acc=allocacc; |
| 6271 } |
| 6272 /* Calculate units and remainder from exponent. */ |
| 6273 expunits=exp/DECDPUN; |
| 6274 exprem=exp%DECDPUN; |
| 6275 /* subtract [A+B*(-m)] */ |
| 6276 accunits=decUnitAddSub(a, alength, b, blength, expunits, acc, |
| 6277 -(Int)powers[exprem]); |
| 6278 /* [UnitAddSub result may have leading zeros, even on zero] */ |
| 6279 if (accunits<0) result=-1; /* negative result */ |
| 6280 else { /* non-negative result */ |
| 6281 /* check units of the result before freeing any storage */ |
| 6282 for (u=acc; u<acc+accunits-1 && *u==0;) u++; |
| 6283 result=(*u==0 ? 0 : +1); |
| 6284 } |
| 6285 /* clean up and return the result */ |
| 6286 if (allocacc!=NULL) free(allocacc); /* drop any storage used */ |
| 6287 return result; |
| 6288 } /* decUnitCompare */ |
| 6289 |
| 6290 /* ------------------------------------------------------------------ */ |
| 6291 /* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays */ |
| 6292 /* */ |
| 6293 /* This routine performs the calculation: */ |
| 6294 /* */ |
| 6295 /* C=A+(B*M) */ |
| 6296 /* */ |
| 6297 /* Where M is in the range -DECDPUNMAX through +DECDPUNMAX. */ |
| 6298 /* */ |
| 6299 /* A may be shorter or longer than B. */ |
| 6300 /* */ |
| 6301 /* Leading zeros are not removed after a calculation. The result is */ |
| 6302 /* either the same length as the longer of A and B (adding any */ |
| 6303 /* shift), or one Unit longer than that (if a Unit carry occurred). */ |
| 6304 /* */ |
| 6305 /* A and B content are not altered unless C is also A or B. */ |
| 6306 /* C may be the same array as A or B, but only if no zero padding is */ |
| 6307 /* requested (that is, C may be B only if bshift==0). */ |
| 6308 /* C is filled from the lsu; only those units necessary to complete */ |
| 6309 /* the calculation are referenced. */ |
| 6310 /* */ |
| 6311 /* Arg1 is A first Unit (lsu) */ |
| 6312 /* Arg2 is A length in Units */ |
| 6313 /* Arg3 is B first Unit (lsu) */ |
| 6314 /* Arg4 is B length in Units */ |
| 6315 /* Arg5 is B shift in Units (>=0; pads with 0 units if positive) */ |
| 6316 /* Arg6 is C first Unit (lsu) */ |
| 6317 /* Arg7 is M, the multiplier */ |
| 6318 /* */ |
| 6319 /* returns the count of Units written to C, which will be non-zero */ |
| 6320 /* and negated if the result is negative. That is, the sign of the */ |
| 6321 /* returned Int is the sign of the result (positive for zero) and */ |
| 6322 /* the absolute value of the Int is the count of Units. */ |
| 6323 /* */ |
| 6324 /* It is the caller's responsibility to make sure that C size is */ |
| 6325 /* safe, allowing space if necessary for a one-Unit carry. */ |
| 6326 /* */ |
| 6327 /* This routine is severely performance-critical; *any* change here */ |
| 6328 /* must be measured (timed) to assure no performance degradation. */ |
| 6329 /* In particular, trickery here tends to be counter-productive, as */ |
| 6330 /* increased complexity of code hurts register optimizations on */ |
| 6331 /* register-poor architectures. Avoiding divisions is nearly */ |
| 6332 /* always a Good Idea, however. */ |
| 6333 /* */ |
| 6334 /* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark */ |
| 6335 /* (IBM Warwick, UK) for some of the ideas used in this routine. */ |
| 6336 /* ------------------------------------------------------------------ */ |
| 6337 static Int decUnitAddSub(const Unit *a, Int alength, |
| 6338 const Unit *b, Int blength, Int bshift, |
| 6339 Unit *c, Int m) { |
| 6340 const Unit *alsu=a; /* A lsu [need to remember it] */ |
| 6341 Unit *clsu=c; /* C ditto */ |
| 6342 Unit *minC; /* low water mark for C */ |
| 6343 Unit *maxC; /* high water mark for C */ |
| 6344 eInt carry=0; /* carry integer (could be Long) */ |
| 6345 Int add; /* work */ |
| 6346 #if DECDPUN<=4 /* myriadal, millenary, etc. */ |
| 6347 Int est; /* estimated quotient */ |
| 6348 #endif |
| 6349 |
| 6350 #if DECTRACE |
| 6351 if (alength<1 || blength<1) |
| 6352 printf("decUnitAddSub: alen blen m %ld %ld [%ld]\n", alength, blength, m); |
| 6353 #endif |
| 6354 |
| 6355 maxC=c+alength; /* A is usually the longer */ |
| 6356 minC=c+blength; /* .. and B the shorter */ |
| 6357 if (bshift!=0) { /* B is shifted; low As copy across */ |
| 6358 minC+=bshift; |
| 6359 /* if in place [common], skip copy unless there's a gap [rare] */ |
| 6360 if (a==c && bshift<=alength) { |
| 6361 c+=bshift; |
| 6362 a+=bshift; |
| 6363 } |
| 6364 else for (; c<clsu+bshift; a++, c++) { /* copy needed */ |
| 6365 if (a<alsu+alength) *c=*a; |
| 6366 else *c=0; |
| 6367 } |
| 6368 } |
| 6369 if (minC>maxC) { /* swap */ |
| 6370 Unit *hold=minC; |
| 6371 minC=maxC; |
| 6372 maxC=hold; |
| 6373 } |
| 6374 |
| 6375 /* For speed, do the addition as two loops; the first where both A */ |
| 6376 /* and B contribute, and the second (if necessary) where only one or */ |
| 6377 /* other of the numbers contribute. */ |
| 6378 /* Carry handling is the same (i.e., duplicated) in each case. */ |
| 6379 for (; c<minC; c++) { |
| 6380 carry+=*a; |
| 6381 a++; |
| 6382 carry+=((eInt)*b)*m; /* [special-casing m=1/-1 */ |
| 6383 b++; /* here is not a win] */ |
| 6384 /* here carry is new Unit of digits; it could be +ve or -ve */ |
| 6385 if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */ |
| 6386 *c=(Unit)carry; |
| 6387 carry=0; |
| 6388 continue; |
| 6389 } |
| 6390 #if DECDPUN==4 /* use divide-by-multiply */ |
| 6391 if (carry>=0) { |
| 6392 est=(((ueInt)carry>>11)*53687)>>18; |
| 6393 *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ |
| 6394 carry=est; /* likely quotient [89%] */ |
| 6395 if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ |
| 6396 carry++; |
| 6397 *c-=DECDPUNMAX+1; |
| 6398 continue; |
| 6399 } |
| 6400 /* negative case */ |
| 6401 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ |
| 6402 est=(((ueInt)carry>>11)*53687)>>18; |
| 6403 *c=(Unit)(carry-est*(DECDPUNMAX+1)); |
| 6404 carry=est-(DECDPUNMAX+1); /* correctly negative */ |
| 6405 if (*c<DECDPUNMAX+1) continue; /* was OK */ |
| 6406 carry++; |
| 6407 *c-=DECDPUNMAX+1; |
| 6408 #elif DECDPUN==3 |
| 6409 if (carry>=0) { |
| 6410 est=(((ueInt)carry>>3)*16777)>>21; |
| 6411 *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ |
| 6412 carry=est; /* likely quotient [99%] */ |
| 6413 if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ |
| 6414 carry++; |
| 6415 *c-=DECDPUNMAX+1; |
| 6416 continue; |
| 6417 } |
| 6418 /* negative case */ |
| 6419 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ |
| 6420 est=(((ueInt)carry>>3)*16777)>>21; |
| 6421 *c=(Unit)(carry-est*(DECDPUNMAX+1)); |
| 6422 carry=est-(DECDPUNMAX+1); /* correctly negative */ |
| 6423 if (*c<DECDPUNMAX+1) continue; /* was OK */ |
| 6424 carry++; |
| 6425 *c-=DECDPUNMAX+1; |
| 6426 #elif DECDPUN<=2 |
| 6427 /* Can use QUOT10 as carry <= 4 digits */ |
| 6428 if (carry>=0) { |
| 6429 est=QUOT10(carry, DECDPUN); |
| 6430 *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ |
| 6431 carry=est; /* quotient */ |
| 6432 continue; |
| 6433 } |
| 6434 /* negative case */ |
| 6435 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ |
| 6436 est=QUOT10(carry, DECDPUN); |
| 6437 *c=(Unit)(carry-est*(DECDPUNMAX+1)); |
| 6438 carry=est-(DECDPUNMAX+1); /* correctly negative */ |
| 6439 #else |
| 6440 /* remainder operator is undefined if negative, so must test */ |
| 6441 if ((ueInt)carry<(DECDPUNMAX+1)*2) { /* fastpath carry +1 */ |
| 6442 *c=(Unit)(carry-(DECDPUNMAX+1)); /* [helps additions] */ |
| 6443 carry=1; |
| 6444 continue; |
| 6445 } |
| 6446 if (carry>=0) { |
| 6447 *c=(Unit)(carry%(DECDPUNMAX+1)); |
| 6448 carry=carry/(DECDPUNMAX+1); |
| 6449 continue; |
| 6450 } |
| 6451 /* negative case */ |
| 6452 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ |
| 6453 *c=(Unit)(carry%(DECDPUNMAX+1)); |
| 6454 carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1); |
| 6455 #endif |
| 6456 } /* c */ |
| 6457 |
| 6458 /* now may have one or other to complete */ |
| 6459 /* [pretest to avoid loop setup/shutdown] */ |
| 6460 if (c<maxC) for (; c<maxC; c++) { |
| 6461 if (a<alsu+alength) { /* still in A */ |
| 6462 carry+=*a; |
| 6463 a++; |
| 6464 } |
| 6465 else { /* inside B */ |
| 6466 carry+=((eInt)*b)*m; |
| 6467 b++; |
| 6468 } |
| 6469 /* here carry is new Unit of digits; it could be +ve or -ve and */ |
| 6470 /* magnitude up to DECDPUNMAX squared */ |
| 6471 if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */ |
| 6472 *c=(Unit)carry; |
| 6473 carry=0; |
| 6474 continue; |
| 6475 } |
| 6476 /* result for this unit is negative or >DECDPUNMAX */ |
| 6477 #if DECDPUN==4 /* use divide-by-multiply */ |
| 6478 if (carry>=0) { |
| 6479 est=(((ueInt)carry>>11)*53687)>>18; |
| 6480 *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ |
| 6481 carry=est; /* likely quotient [79.7%] */ |
| 6482 if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ |
| 6483 carry++; |
| 6484 *c-=DECDPUNMAX+1; |
| 6485 continue; |
| 6486 } |
| 6487 /* negative case */ |
| 6488 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ |
| 6489 est=(((ueInt)carry>>11)*53687)>>18; |
| 6490 *c=(Unit)(carry-est*(DECDPUNMAX+1)); |
| 6491 carry=est-(DECDPUNMAX+1); /* correctly negative */ |
| 6492 if (*c<DECDPUNMAX+1) continue; /* was OK */ |
| 6493 carry++; |
| 6494 *c-=DECDPUNMAX+1; |
| 6495 #elif DECDPUN==3 |
| 6496 if (carry>=0) { |
| 6497 est=(((ueInt)carry>>3)*16777)>>21; |
| 6498 *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ |
| 6499 carry=est; /* likely quotient [99%] */ |
| 6500 if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ |
| 6501 carry++; |
| 6502 *c-=DECDPUNMAX+1; |
| 6503 continue; |
| 6504 } |
| 6505 /* negative case */ |
| 6506 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ |
| 6507 est=(((ueInt)carry>>3)*16777)>>21; |
| 6508 *c=(Unit)(carry-est*(DECDPUNMAX+1)); |
| 6509 carry=est-(DECDPUNMAX+1); /* correctly negative */ |
| 6510 if (*c<DECDPUNMAX+1) continue; /* was OK */ |
| 6511 carry++; |
| 6512 *c-=DECDPUNMAX+1; |
| 6513 #elif DECDPUN<=2 |
| 6514 if (carry>=0) { |
| 6515 est=QUOT10(carry, DECDPUN); |
| 6516 *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ |
| 6517 carry=est; /* quotient */ |
| 6518 continue; |
| 6519 } |
| 6520 /* negative case */ |
| 6521 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ |
| 6522 est=QUOT10(carry, DECDPUN); |
| 6523 *c=(Unit)(carry-est*(DECDPUNMAX+1)); |
| 6524 carry=est-(DECDPUNMAX+1); /* correctly negative */ |
| 6525 #else |
| 6526 if ((ueInt)carry<(DECDPUNMAX+1)*2){ /* fastpath carry 1 */ |
| 6527 *c=(Unit)(carry-(DECDPUNMAX+1)); |
| 6528 carry=1; |
| 6529 continue; |
| 6530 } |
| 6531 /* remainder operator is undefined if negative, so must test */ |
| 6532 if (carry>=0) { |
| 6533 *c=(Unit)(carry%(DECDPUNMAX+1)); |
| 6534 carry=carry/(DECDPUNMAX+1); |
| 6535 continue; |
| 6536 } |
| 6537 /* negative case */ |
| 6538 carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ |
| 6539 *c=(Unit)(carry%(DECDPUNMAX+1)); |
| 6540 carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1); |
| 6541 #endif |
| 6542 } /* c */ |
| 6543 |
| 6544 /* OK, all A and B processed; might still have carry or borrow */ |
| 6545 /* return number of Units in the result, negated if a borrow */ |
| 6546 if (carry==0) return c-clsu; /* no carry, so no more to do */ |
| 6547 if (carry>0) { /* positive carry */ |
| 6548 *c=(Unit)carry; /* place as new unit */ |
| 6549 c++; /* .. */ |
| 6550 return c-clsu; |
| 6551 } |
| 6552 /* -ve carry: it's a borrow; complement needed */ |
| 6553 add=1; /* temporary carry... */ |
| 6554 for (c=clsu; c<maxC; c++) { |
| 6555 add=DECDPUNMAX+add-*c; |
| 6556 if (add<=DECDPUNMAX) { |
| 6557 *c=(Unit)add; |
| 6558 add=0; |
| 6559 } |
| 6560 else { |
| 6561 *c=0; |
| 6562 add=1; |
| 6563 } |
| 6564 } |
| 6565 /* add an extra unit iff it would be non-zero */ |
| 6566 #if DECTRACE |
| 6567 printf("UAS borrow: add %ld, carry %ld\n", add, carry); |
| 6568 #endif |
| 6569 if ((add-carry-1)!=0) { |
| 6570 *c=(Unit)(add-carry-1); |
| 6571 c++; /* interesting, include it */ |
| 6572 } |
| 6573 return clsu-c; /* -ve result indicates borrowed */ |
| 6574 } /* decUnitAddSub */ |
| 6575 |
| 6576 /* ------------------------------------------------------------------ */ |
| 6577 /* decTrim -- trim trailing zeros or normalize */ |
| 6578 /* */ |
| 6579 /* dn is the number to trim or normalize */ |
| 6580 /* set is the context to use to check for clamp */ |
| 6581 /* all is 1 to remove all trailing zeros, 0 for just fraction ones */ |
| 6582 /* noclamp is 1 to unconditional (unclamped) trim */ |
| 6583 /* dropped returns the number of discarded trailing zeros */ |
| 6584 /* returns dn */ |
| 6585 /* */ |
| 6586 /* If clamp is set in the context then the number of zeros trimmed */ |
| 6587 /* may be limited if the exponent is high. */ |
| 6588 /* All fields are updated as required. This is a utility operation, */ |
| 6589 /* so special values are unchanged and no error is possible. */ |
| 6590 /* ------------------------------------------------------------------ */ |
| 6591 static decNumber * decTrim(decNumber *dn, decContext *set, Flag all, |
| 6592 Flag noclamp, Int *dropped) { |
| 6593 Int d, exp; /* work */ |
| 6594 uInt cut; /* .. */ |
| 6595 Unit *up; /* -> current Unit */ |
| 6596 |
| 6597 #if DECCHECK |
| 6598 if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn; |
| 6599 #endif |
| 6600 |
| 6601 *dropped=0; /* assume no zeros dropped */ |
| 6602 if ((dn->bits & DECSPECIAL) /* fast exit if special .. */ |
| 6603 || (*dn->lsu & 0x01)) return dn; /* .. or odd */ |
| 6604 if (ISZERO(dn)) { /* .. or 0 */ |
| 6605 dn->exponent=0; /* (sign is preserved) */ |
| 6606 return dn; |
| 6607 } |
| 6608 |
| 6609 /* have a finite number which is even */ |
| 6610 exp=dn->exponent; |
| 6611 cut=1; /* digit (1-DECDPUN) in Unit */ |
| 6612 up=dn->lsu; /* -> current Unit */ |
| 6613 for (d=0; d<dn->digits-1; d++) { /* [don't strip the final digit] */ |
| 6614 /* slice by powers */ |
| 6615 #if DECDPUN<=4 |
| 6616 uInt quot=QUOT10(*up, cut); |
| 6617 if ((*up-quot*powers[cut])!=0) break; /* found non-0 digit */ |
| 6618 #else |
| 6619 if (*up%powers[cut]!=0) break; /* found non-0 digit */ |
| 6620 #endif |
| 6621 /* have a trailing 0 */ |
| 6622 if (!all) { /* trimming */ |
| 6623 /* [if exp>0 then all trailing 0s are significant for trim] */ |
| 6624 if (exp<=0) { /* if digit might be significant */ |
| 6625 if (exp==0) break; /* then quit */ |
| 6626 exp++; /* next digit might be significant */ |
| 6627 } |
| 6628 } |
| 6629 cut++; /* next power */ |
| 6630 if (cut>DECDPUN) { /* need new Unit */ |
| 6631 up++; |
| 6632 cut=1; |
| 6633 } |
| 6634 } /* d */ |
| 6635 if (d==0) return dn; /* none to drop */ |
| 6636 |
| 6637 /* may need to limit drop if clamping */ |
| 6638 if (set->clamp && !noclamp) { |
| 6639 Int maxd=set->emax-set->digits+1-dn->exponent; |
| 6640 if (maxd<=0) return dn; /* nothing possible */ |
| 6641 if (d>maxd) d=maxd; |
| 6642 } |
| 6643 |
| 6644 /* effect the drop */ |
| 6645 decShiftToLeast(dn->lsu, D2U(dn->digits), d); |
| 6646 dn->exponent+=d; /* maintain numerical value */ |
| 6647 dn->digits-=d; /* new length */ |
| 6648 *dropped=d; /* report the count */ |
| 6649 return dn; |
| 6650 } /* decTrim */ |
| 6651 |
| 6652 /* ------------------------------------------------------------------ */ |
| 6653 /* decReverse -- reverse a Unit array in place */ |
| 6654 /* */ |
| 6655 /* ulo is the start of the array */ |
| 6656 /* uhi is the end of the array (highest Unit to include) */ |
| 6657 /* */ |
| 6658 /* The units ulo through uhi are reversed in place (if the number */ |
| 6659 /* of units is odd, the middle one is untouched). Note that the */ |
| 6660 /* digit(s) in each unit are unaffected. */ |
| 6661 /* ------------------------------------------------------------------ */ |
| 6662 static void decReverse(Unit *ulo, Unit *uhi) { |
| 6663 Unit temp; |
| 6664 for (; ulo<uhi; ulo++, uhi--) { |
| 6665 temp=*ulo; |
| 6666 *ulo=*uhi; |
| 6667 *uhi=temp; |
| 6668 } |
| 6669 return; |
| 6670 } /* decReverse */ |
| 6671 |
| 6672 /* ------------------------------------------------------------------ */ |
| 6673 /* decShiftToMost -- shift digits in array towards most significant */ |
| 6674 /* */ |
| 6675 /* uar is the array */ |
| 6676 /* digits is the count of digits in use in the array */ |
| 6677 /* shift is the number of zeros to pad with (least significant); */ |
| 6678 /* it must be zero or positive */ |
| 6679 /* */ |
| 6680 /* returns the new length of the integer in the array, in digits */ |
| 6681 /* */ |
| 6682 /* No overflow is permitted (that is, the uar array must be known to */ |
| 6683 /* be large enough to hold the result, after shifting). */ |
| 6684 /* ------------------------------------------------------------------ */ |
| 6685 static Int decShiftToMost(Unit *uar, Int digits, Int shift) { |
| 6686 Unit *target, *source, *first; /* work */ |
| 6687 Int cut; /* odd 0's to add */ |
| 6688 uInt next; /* work */ |
| 6689 |
| 6690 if (shift==0) return digits; /* [fastpath] nothing to do */ |
| 6691 if ((digits+shift)<=DECDPUN) { /* [fastpath] single-unit case */ |
| 6692 *uar=(Unit)(*uar*powers[shift]); |
| 6693 return digits+shift; |
| 6694 } |
| 6695 |
| 6696 next=0; /* all paths */ |
| 6697 source=uar+D2U(digits)-1; /* where msu comes from */ |
| 6698 target=source+D2U(shift); /* where upper part of first cut goes */ |
| 6699 cut=DECDPUN-MSUDIGITS(shift); /* where to slice */ |
| 6700 if (cut==0) { /* unit-boundary case */ |
| 6701 for (; source>=uar; source--, target--) *target=*source; |
| 6702 } |
| 6703 else { |
| 6704 first=uar+D2U(digits+shift)-1; /* where msu of source will end up */ |
| 6705 for (; source>=uar; source--, target--) { |
| 6706 /* split the source Unit and accumulate remainder for next */ |
| 6707 #if DECDPUN<=4 |
| 6708 uInt quot=QUOT10(*source, cut); |
| 6709 uInt rem=*source-quot*powers[cut]; |
| 6710 next+=quot; |
| 6711 #else |
| 6712 uInt rem=*source%powers[cut]; |
| 6713 next+=*source/powers[cut]; |
| 6714 #endif |
| 6715 if (target<=first) *target=(Unit)next; /* write to target iff valid */ |
| 6716 next=rem*powers[DECDPUN-cut]; /* save remainder for next Unit
*/ |
| 6717 } |
| 6718 } /* shift-move */ |
| 6719 |
| 6720 /* propagate any partial unit to one below and clear the rest */ |
| 6721 for (; target>=uar; target--) { |
| 6722 *target=(Unit)next; |
| 6723 next=0; |
| 6724 } |
| 6725 return digits+shift; |
| 6726 } /* decShiftToMost */ |
| 6727 |
| 6728 /* ------------------------------------------------------------------ */ |
| 6729 /* decShiftToLeast -- shift digits in array towards least significant */ |
| 6730 /* */ |
| 6731 /* uar is the array */ |
| 6732 /* units is length of the array, in units */ |
| 6733 /* shift is the number of digits to remove from the lsu end; it */ |
| 6734 /* must be zero or positive and <= than units*DECDPUN. */ |
| 6735 /* */ |
| 6736 /* returns the new length of the integer in the array, in units */ |
| 6737 /* */ |
| 6738 /* Removed digits are discarded (lost). Units not required to hold */ |
| 6739 /* the final result are unchanged. */ |
| 6740 /* ------------------------------------------------------------------ */ |
| 6741 static Int decShiftToLeast(Unit *uar, Int units, Int shift) { |
| 6742 Unit *target, *up; /* work */ |
| 6743 Int cut, count; /* work */ |
| 6744 Int quot, rem; /* for division */ |
| 6745 |
| 6746 if (shift==0) return units; /* [fastpath] nothing to do */ |
| 6747 if (shift==units*DECDPUN) { /* [fastpath] little to do */ |
| 6748 *uar=0; /* all digits cleared gives zero */ |
| 6749 return 1; /* leaves just the one */ |
| 6750 } |
| 6751 |
| 6752 target=uar; /* both paths */ |
| 6753 cut=MSUDIGITS(shift); |
| 6754 if (cut==DECDPUN) { /* unit-boundary case; easy */ |
| 6755 up=uar+D2U(shift); |
| 6756 for (; up<uar+units; target++, up++) *target=*up; |
| 6757 return target-uar; |
| 6758 } |
| 6759 |
| 6760 /* messier */ |
| 6761 up=uar+D2U(shift-cut); /* source; correct to whole Units */ |
| 6762 count=units*DECDPUN-shift; /* the maximum new length */ |
| 6763 #if DECDPUN<=4 |
| 6764 quot=QUOT10(*up, cut); |
| 6765 #else |
| 6766 quot=*up/powers[cut]; |
| 6767 #endif |
| 6768 for (; ; target++) { |
| 6769 *target=(Unit)quot; |
| 6770 count-=(DECDPUN-cut); |
| 6771 if (count<=0) break; |
| 6772 up++; |
| 6773 quot=*up; |
| 6774 #if DECDPUN<=4 |
| 6775 quot=QUOT10(quot, cut); |
| 6776 rem=*up-quot*powers[cut]; |
| 6777 #else |
| 6778 rem=quot%powers[cut]; |
| 6779 quot=quot/powers[cut]; |
| 6780 #endif |
| 6781 *target=(Unit)(*target+rem*powers[DECDPUN-cut]); |
| 6782 count-=cut; |
| 6783 if (count<=0) break; |
| 6784 } |
| 6785 return target-uar+1; |
| 6786 } /* decShiftToLeast */ |
| 6787 |
| 6788 #if DECSUBSET |
| 6789 /* ------------------------------------------------------------------ */ |
| 6790 /* decRoundOperand -- round an operand [used for subset only] */ |
| 6791 /* */ |
| 6792 /* dn is the number to round (dn->digits is > set->digits) */ |
| 6793 /* set is the relevant context */ |
| 6794 /* status is the status accumulator */ |
| 6795 /* */ |
| 6796 /* returns an allocated decNumber with the rounded result. */ |
| 6797 /* */ |
| 6798 /* lostDigits and other status may be set by this. */ |
| 6799 /* */ |
| 6800 /* Since the input is an operand, it must not be modified. */ |
| 6801 /* Instead, return an allocated decNumber, rounded as required. */ |
| 6802 /* It is the caller's responsibility to free the allocated storage. */ |
| 6803 /* */ |
| 6804 /* If no storage is available then the result cannot be used, so NULL */ |
| 6805 /* is returned. */ |
| 6806 /* ------------------------------------------------------------------ */ |
| 6807 static decNumber *decRoundOperand(const decNumber *dn, decContext *set, |
| 6808 uInt *status) { |
| 6809 decNumber *res; /* result structure */ |
| 6810 uInt newstatus=0; /* status from round */ |
| 6811 Int residue=0; /* rounding accumulator */ |
| 6812 |
| 6813 /* Allocate storage for the returned decNumber, big enough for the */ |
| 6814 /* length specified by the context */ |
| 6815 res=(decNumber *)malloc(sizeof(decNumber) |
| 6816 +(D2U(set->digits)-1)*sizeof(Unit)); |
| 6817 if (res==NULL) { |
| 6818 *status|=DEC_Insufficient_storage; |
| 6819 return NULL; |
| 6820 } |
| 6821 decCopyFit(res, dn, set, &residue, &newstatus); |
| 6822 decApplyRound(res, set, residue, &newstatus); |
| 6823 |
| 6824 /* If that set Inexact then "lost digits" is raised... */ |
| 6825 if (newstatus & DEC_Inexact) newstatus|=DEC_Lost_digits; |
| 6826 *status|=newstatus; |
| 6827 return res; |
| 6828 } /* decRoundOperand */ |
| 6829 #endif |
| 6830 |
| 6831 /* ------------------------------------------------------------------ */ |
| 6832 /* decCopyFit -- copy a number, truncating the coefficient if needed */ |
| 6833 /* */ |
| 6834 /* dest is the target decNumber */ |
| 6835 /* src is the source decNumber */ |
| 6836 /* set is the context [used for length (digits) and rounding mode] */ |
| 6837 /* residue is the residue accumulator */ |
| 6838 /* status contains the current status to be updated */ |
| 6839 /* */ |
| 6840 /* (dest==src is allowed and will be a no-op if fits) */ |
| 6841 /* All fields are updated as required. */ |
| 6842 /* ------------------------------------------------------------------ */ |
| 6843 static void decCopyFit(decNumber *dest, const decNumber *src, |
| 6844 decContext *set, Int *residue, uInt *status) { |
| 6845 dest->bits=src->bits; |
| 6846 dest->exponent=src->exponent; |
| 6847 decSetCoeff(dest, set, src->lsu, src->digits, residue, status); |
| 6848 } /* decCopyFit */ |
| 6849 |
| 6850 /* ------------------------------------------------------------------ */ |
| 6851 /* decSetCoeff -- set the coefficient of a number */ |
| 6852 /* */ |
| 6853 /* dn is the number whose coefficient array is to be set. */ |
| 6854 /* It must have space for set->digits digits */ |
| 6855 /* set is the context [for size] */ |
| 6856 /* lsu -> lsu of the source coefficient [may be dn->lsu] */ |
| 6857 /* len is digits in the source coefficient [may be dn->digits] */ |
| 6858 /* residue is the residue accumulator. This has values as in */ |
| 6859 /* decApplyRound, and will be unchanged unless the */ |
| 6860 /* target size is less than len. In this case, the */ |
| 6861 /* coefficient is truncated and the residue is updated to */ |
| 6862 /* reflect the previous residue and the dropped digits. */ |
| 6863 /* status is the status accumulator, as usual */ |
| 6864 /* */ |
| 6865 /* The coefficient may already be in the number, or it can be an */ |
| 6866 /* external intermediate array. If it is in the number, lsu must == */ |
| 6867 /* dn->lsu and len must == dn->digits. */ |
| 6868 /* */ |
| 6869 /* Note that the coefficient length (len) may be < set->digits, and */ |
| 6870 /* in this case this merely copies the coefficient (or is a no-op */ |
| 6871 /* if dn->lsu==lsu). */ |
| 6872 /* */ |
| 6873 /* Note also that (only internally, from decQuantizeOp and */ |
| 6874 /* decSetSubnormal) the value of set->digits may be less than one, */ |
| 6875 /* indicating a round to left. This routine handles that case */ |
| 6876 /* correctly; caller ensures space. */ |
| 6877 /* */ |
| 6878 /* dn->digits, dn->lsu (and as required), and dn->exponent are */ |
| 6879 /* updated as necessary. dn->bits (sign) is unchanged. */ |
| 6880 /* */ |
| 6881 /* DEC_Rounded status is set if any digits are discarded. */ |
| 6882 /* DEC_Inexact status is set if any non-zero digits are discarded, or */ |
| 6883 /* incoming residue was non-0 (implies rounded) */ |
| 6884 /* ------------------------------------------------------------------ */ |
| 6885 /* mapping array: maps 0-9 to canonical residues, so that a residue */ |
| 6886 /* can be adjusted in the range [-1, +1] and achieve correct rounding */ |
| 6887 /* 0 1 2 3 4 5 6 7 8 9 */ |
| 6888 static const uByte resmap[10]={0, 3, 3, 3, 3, 5, 7, 7, 7, 7}; |
| 6889 static void decSetCoeff(decNumber *dn, decContext *set, const Unit *lsu, |
| 6890 Int len, Int *residue, uInt *status) { |
| 6891 Int discard; /* number of digits to discard */ |
| 6892 uInt cut; /* cut point in Unit */ |
| 6893 const Unit *up; /* work */ |
| 6894 Unit *target; /* .. */ |
| 6895 Int count; /* .. */ |
| 6896 #if DECDPUN<=4 |
| 6897 uInt temp; /* .. */ |
| 6898 #endif |
| 6899 |
| 6900 discard=len-set->digits; /* digits to discard */ |
| 6901 if (discard<=0) { /* no digits are being discarded */ |
| 6902 if (dn->lsu!=lsu) { /* copy needed */ |
| 6903 /* copy the coefficient array to the result number; no shift needed */ |
| 6904 count=len; /* avoids D2U */ |
| 6905 up=lsu; |
| 6906 for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN) |
| 6907 *target=*up; |
| 6908 dn->digits=len; /* set the new length */ |
| 6909 } |
| 6910 /* dn->exponent and residue are unchanged, record any inexactitude */ |
| 6911 if (*residue!=0) *status|=(DEC_Inexact | DEC_Rounded); |
| 6912 return; |
| 6913 } |
| 6914 |
| 6915 /* some digits must be discarded ... */ |
| 6916 dn->exponent+=discard; /* maintain numerical value */ |
| 6917 *status|=DEC_Rounded; /* accumulate Rounded status */ |
| 6918 if (*residue>1) *residue=1; /* previous residue now to right, so reduce */ |
| 6919 |
| 6920 if (discard>len) { /* everything, +1, is being discarded */ |
| 6921 /* guard digit is 0 */ |
| 6922 /* residue is all the number [NB could be all 0s] */ |
| 6923 if (*residue<=0) { /* not already positive */ |
| 6924 count=len; /* avoids D2U */ |
| 6925 for (up=lsu; count>0; up++, count-=DECDPUN) if (*up!=0) { /* found non-0
*/ |
| 6926 *residue=1; |
| 6927 break; /* no need to check any others */ |
| 6928 } |
| 6929 } |
| 6930 if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */ |
| 6931 *dn->lsu=0; /* coefficient will now be 0 */ |
| 6932 dn->digits=1; /* .. */ |
| 6933 return; |
| 6934 } /* total discard */ |
| 6935 |
| 6936 /* partial discard [most common case] */ |
| 6937 /* here, at least the first (most significant) discarded digit exists */ |
| 6938 |
| 6939 /* spin up the number, noting residue during the spin, until get to */ |
| 6940 /* the Unit with the first discarded digit. When reach it, extract */ |
| 6941 /* it and remember its position */ |
| 6942 count=0; |
| 6943 for (up=lsu;; up++) { |
| 6944 count+=DECDPUN; |
| 6945 if (count>=discard) break; /* full ones all checked */ |
| 6946 if (*up!=0) *residue=1; |
| 6947 } /* up */ |
| 6948 |
| 6949 /* here up -> Unit with first discarded digit */ |
| 6950 cut=discard-(count-DECDPUN)-1; |
| 6951 if (cut==DECDPUN-1) { /* unit-boundary case (fast) */ |
| 6952 Unit half=(Unit)powers[DECDPUN]>>1; |
| 6953 /* set residue directly */ |
| 6954 if (*up>=half) { |
| 6955 if (*up>half) *residue=7; |
| 6956 else *residue+=5; /* add sticky bit */ |
| 6957 } |
| 6958 else { /* <half */ |
| 6959 if (*up!=0) *residue=3; /* [else is 0, leave as sticky bit] */ |
| 6960 } |
| 6961 if (set->digits<=0) { /* special for Quantize/Subnormal :-( */ |
| 6962 *dn->lsu=0; /* .. result is 0 */ |
| 6963 dn->digits=1; /* .. */ |
| 6964 } |
| 6965 else { /* shift to least */ |
| 6966 count=set->digits; /* now digits to end up with */ |
| 6967 dn->digits=count; /* set the new length */ |
| 6968 up++; /* move to next */ |
| 6969 /* on unit boundary, so shift-down copy loop is simple */ |
| 6970 for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN) |
| 6971 *target=*up; |
| 6972 } |
| 6973 } /* unit-boundary case */ |
| 6974 |
| 6975 else { /* discard digit is in low digit(s), and not top digit */ |
| 6976 uInt discard1; /* first discarded digit */ |
| 6977 uInt quot, rem; /* for divisions */ |
| 6978 if (cut==0) quot=*up; /* is at bottom of unit */ |
| 6979 else /* cut>0 */ { /* it's not at bottom of unit */ |
| 6980 #if DECDPUN<=4 |
| 6981 quot=QUOT10(*up, cut); |
| 6982 rem=*up-quot*powers[cut]; |
| 6983 #else |
| 6984 rem=*up%powers[cut]; |
| 6985 quot=*up/powers[cut]; |
| 6986 #endif |
| 6987 if (rem!=0) *residue=1; |
| 6988 } |
| 6989 /* discard digit is now at bottom of quot */ |
| 6990 #if DECDPUN<=4 |
| 6991 temp=(quot*6554)>>16; /* fast /10 */ |
| 6992 /* Vowels algorithm here not a win (9 instructions) */ |
| 6993 discard1=quot-X10(temp); |
| 6994 quot=temp; |
| 6995 #else |
| 6996 discard1=quot%10; |
| 6997 quot=quot/10; |
| 6998 #endif |
| 6999 /* here, discard1 is the guard digit, and residue is everything */ |
| 7000 /* else [use mapping array to accumulate residue safely] */ |
| 7001 *residue+=resmap[discard1]; |
| 7002 cut++; /* update cut */ |
| 7003 /* here: up -> Unit of the array with bottom digit */ |
| 7004 /* cut is the division point for each Unit */ |
| 7005 /* quot holds the uncut high-order digits for the current unit */ |
| 7006 if (set->digits<=0) { /* special for Quantize/Subnormal :-( */ |
| 7007 *dn->lsu=0; /* .. result is 0 */ |
| 7008 dn->digits=1; /* .. */ |
| 7009 } |
| 7010 else { /* shift to least needed */ |
| 7011 count=set->digits; /* now digits to end up with */ |
| 7012 dn->digits=count; /* set the new length */ |
| 7013 /* shift-copy the coefficient array to the result number */ |
| 7014 for (target=dn->lsu; ; target++) { |
| 7015 *target=(Unit)quot; |
| 7016 count-=(DECDPUN-cut); |
| 7017 if (count<=0) break; |
| 7018 up++; |
| 7019 quot=*up; |
| 7020 #if DECDPUN<=4 |
| 7021 quot=QUOT10(quot, cut); |
| 7022 rem=*up-quot*powers[cut]; |
| 7023 #else |
| 7024 rem=quot%powers[cut]; |
| 7025 quot=quot/powers[cut]; |
| 7026 #endif |
| 7027 *target=(Unit)(*target+rem*powers[DECDPUN-cut]); |
| 7028 count-=cut; |
| 7029 if (count<=0) break; |
| 7030 } /* shift-copy loop */ |
| 7031 } /* shift to least */ |
| 7032 } /* not unit boundary */ |
| 7033 |
| 7034 if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */ |
| 7035 return; |
| 7036 } /* decSetCoeff */ |
| 7037 |
| 7038 /* ------------------------------------------------------------------ */ |
| 7039 /* decApplyRound -- apply pending rounding to a number */ |
| 7040 /* */ |
| 7041 /* dn is the number, with space for set->digits digits */ |
| 7042 /* set is the context [for size and rounding mode] */ |
| 7043 /* residue indicates pending rounding, being any accumulated */ |
| 7044 /* guard and sticky information. It may be: */ |
| 7045 /* 6-9: rounding digit is >5 */ |
| 7046 /* 5: rounding digit is exactly half-way */ |
| 7047 /* 1-4: rounding digit is <5 and >0 */ |
| 7048 /* 0: the coefficient is exact */ |
| 7049 /* -1: as 1, but the hidden digits are subtractive, that */ |
| 7050 /* is, of the opposite sign to dn. In this case the */ |
| 7051 /* coefficient must be non-0. This case occurs when */ |
| 7052 /* subtracting a small number (which can be reduced to */ |
| 7053 /* a sticky bit); see decAddOp. */ |
| 7054 /* status is the status accumulator, as usual */ |
| 7055 /* */ |
| 7056 /* This routine applies rounding while keeping the length of the */ |
| 7057 /* coefficient constant. The exponent and status are unchanged */ |
| 7058 /* except if: */ |
| 7059 /* */ |
| 7060 /* -- the coefficient was increased and is all nines (in which */ |
| 7061 /* case Overflow could occur, and is handled directly here so */ |
| 7062 /* the caller does not need to re-test for overflow) */ |
| 7063 /* */ |
| 7064 /* -- the coefficient was decreased and becomes all nines (in which */ |
| 7065 /* case Underflow could occur, and is also handled directly). */ |
| 7066 /* */ |
| 7067 /* All fields in dn are updated as required. */ |
| 7068 /* */ |
| 7069 /* ------------------------------------------------------------------ */ |
| 7070 static void decApplyRound(decNumber *dn, decContext *set, Int residue, |
| 7071 uInt *status) { |
| 7072 Int bump; /* 1 if coefficient needs to be incremented */ |
| 7073 /* -1 if coefficient needs to be decremented */ |
| 7074 |
| 7075 if (residue==0) return; /* nothing to apply */ |
| 7076 |
| 7077 bump=0; /* assume a smooth ride */ |
| 7078 |
| 7079 /* now decide whether, and how, to round, depending on mode */ |
| 7080 switch (set->round) { |
| 7081 case DEC_ROUND_05UP: { /* round zero or five up (for reround) */ |
| 7082 /* This is the same as DEC_ROUND_DOWN unless there is a */ |
| 7083 /* positive residue and the lsd of dn is 0 or 5, in which case */ |
| 7084 /* it is bumped; when residue is <0, the number is therefore */ |
| 7085 /* bumped down unless the final digit was 1 or 6 (in which */ |
| 7086 /* case it is bumped down and then up -- a no-op) */ |
| 7087 Int lsd5=*dn->lsu%5; /* get lsd and quintate */ |
| 7088 if (residue<0 && lsd5!=1) bump=-1; |
| 7089 else if (residue>0 && lsd5==0) bump=1; |
| 7090 /* [bump==1 could be applied directly; use common path for clarity] */ |
| 7091 break;} /* r-05 */ |
| 7092 |
| 7093 case DEC_ROUND_DOWN: { |
| 7094 /* no change, except if negative residue */ |
| 7095 if (residue<0) bump=-1; |
| 7096 break;} /* r-d */ |
| 7097 |
| 7098 case DEC_ROUND_HALF_DOWN: { |
| 7099 if (residue>5) bump=1; |
| 7100 break;} /* r-h-d */ |
| 7101 |
| 7102 case DEC_ROUND_HALF_EVEN: { |
| 7103 if (residue>5) bump=1; /* >0.5 goes up */ |
| 7104 else if (residue==5) { /* exactly 0.5000... */ |
| 7105 /* 0.5 goes up iff [new] lsd is odd */ |
| 7106 if (*dn->lsu & 0x01) bump=1; |
| 7107 } |
| 7108 break;} /* r-h-e */ |
| 7109 |
| 7110 case DEC_ROUND_HALF_UP: { |
| 7111 if (residue>=5) bump=1; |
| 7112 break;} /* r-h-u */ |
| 7113 |
| 7114 case DEC_ROUND_UP: { |
| 7115 if (residue>0) bump=1; |
| 7116 break;} /* r-u */ |
| 7117 |
| 7118 case DEC_ROUND_CEILING: { |
| 7119 /* same as _UP for positive numbers, and as _DOWN for negatives */ |
| 7120 /* [negative residue cannot occur on 0] */ |
| 7121 if (decNumberIsNegative(dn)) { |
| 7122 if (residue<0) bump=-1; |
| 7123 } |
| 7124 else { |
| 7125 if (residue>0) bump=1; |
| 7126 } |
| 7127 break;} /* r-c */ |
| 7128 |
| 7129 case DEC_ROUND_FLOOR: { |
| 7130 /* same as _UP for negative numbers, and as _DOWN for positive */ |
| 7131 /* [negative residue cannot occur on 0] */ |
| 7132 if (!decNumberIsNegative(dn)) { |
| 7133 if (residue<0) bump=-1; |
| 7134 } |
| 7135 else { |
| 7136 if (residue>0) bump=1; |
| 7137 } |
| 7138 break;} /* r-f */ |
| 7139 |
| 7140 default: { /* e.g., DEC_ROUND_MAX */ |
| 7141 *status|=DEC_Invalid_context; |
| 7142 #if DECTRACE || (DECCHECK && DECVERB) |
| 7143 printf("Unknown rounding mode: %d\n", set->round); |
| 7144 #endif |
| 7145 break;} |
| 7146 } /* switch */ |
| 7147 |
| 7148 /* now bump the number, up or down, if need be */ |
| 7149 if (bump==0) return; /* no action required */ |
| 7150 |
| 7151 /* Simply use decUnitAddSub unless bumping up and the number is */ |
| 7152 /* all nines. In this special case set to 100... explicitly */ |
| 7153 /* and adjust the exponent by one (as otherwise could overflow */ |
| 7154 /* the array) */ |
| 7155 /* Similarly handle all-nines result if bumping down. */ |
| 7156 if (bump>0) { |
| 7157 Unit *up; /* work */ |
| 7158 uInt count=dn->digits; /* digits to be checked */ |
| 7159 for (up=dn->lsu; ; up++) { |
| 7160 if (count<=DECDPUN) { |
| 7161 /* this is the last Unit (the msu) */ |
| 7162 if (*up!=powers[count]-1) break; /* not still 9s */ |
| 7163 /* here if it, too, is all nines */ |
| 7164 *up=(Unit)powers[count-1]; /* here 999 -> 100 etc. */ |
| 7165 for (up=up-1; up>=dn->lsu; up--) *up=0; /* others all to 0 */ |
| 7166 dn->exponent++; /* and bump exponent */ |
| 7167 /* [which, very rarely, could cause Overflow...] */ |
| 7168 if ((dn->exponent+dn->digits)>set->emax+1) { |
| 7169 decSetOverflow(dn, set, status); |
| 7170 } |
| 7171 return; /* done */ |
| 7172 } |
| 7173 /* a full unit to check, with more to come */ |
| 7174 if (*up!=DECDPUNMAX) break; /* not still 9s */ |
| 7175 count-=DECDPUN; |
| 7176 } /* up */ |
| 7177 } /* bump>0 */ |
| 7178 else { /* -1 */ |
| 7179 /* here checking for a pre-bump of 1000... (leading 1, all */ |
| 7180 /* other digits zero) */ |
| 7181 Unit *up, *sup; /* work */ |
| 7182 uInt count=dn->digits; /* digits to be checked */ |
| 7183 for (up=dn->lsu; ; up++) { |
| 7184 if (count<=DECDPUN) { |
| 7185 /* this is the last Unit (the msu) */ |
| 7186 if (*up!=powers[count-1]) break; /* not 100.. */ |
| 7187 /* here if have the 1000... case */ |
| 7188 sup=up; /* save msu pointer */ |
| 7189 *up=(Unit)powers[count]-1; /* here 100 in msu -> 999 */ |
| 7190 /* others all to all-nines, too */ |
| 7191 for (up=up-1; up>=dn->lsu; up--) *up=(Unit)powers[DECDPUN]-1; |
| 7192 dn->exponent--; /* and bump exponent */ |
| 7193 |
| 7194 /* iff the number was at the subnormal boundary (exponent=etiny) */ |
| 7195 /* then the exponent is now out of range, so it will in fact get */ |
| 7196 /* clamped to etiny and the final 9 dropped. */ |
| 7197 /* printf(">> emin=%d exp=%d sdig=%d\n", set->emin, */ |
| 7198 /* dn->exponent, set->digits); */ |
| 7199 if (dn->exponent+1==set->emin-set->digits+1) { |
| 7200 if (count==1 && dn->digits==1) *sup=0; /* here 9 -> 0[.9] */ |
| 7201 else { |
| 7202 *sup=(Unit)powers[count-1]-1; /* here 999.. in msu -> 99.. */ |
| 7203 dn->digits--; |
| 7204 } |
| 7205 dn->exponent++; |
| 7206 *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded; |
| 7207 } |
| 7208 return; /* done */ |
| 7209 } |
| 7210 |
| 7211 /* a full unit to check, with more to come */ |
| 7212 if (*up!=0) break; /* not still 0s */ |
| 7213 count-=DECDPUN; |
| 7214 } /* up */ |
| 7215 |
| 7216 } /* bump<0 */ |
| 7217 |
| 7218 /* Actual bump needed. Do it. */ |
| 7219 decUnitAddSub(dn->lsu, D2U(dn->digits), uarrone, 1, 0, dn->lsu, bump); |
| 7220 } /* decApplyRound */ |
| 7221 |
| 7222 #if DECSUBSET |
| 7223 /* ------------------------------------------------------------------ */ |
| 7224 /* decFinish -- finish processing a number */ |
| 7225 /* */ |
| 7226 /* dn is the number */ |
| 7227 /* set is the context */ |
| 7228 /* residue is the rounding accumulator (as in decApplyRound) */ |
| 7229 /* status is the accumulator */ |
| 7230 /* */ |
| 7231 /* This finishes off the current number by: */ |
| 7232 /* 1. If not extended: */ |
| 7233 /* a. Converting a zero result to clean '0' */ |
| 7234 /* b. Reducing positive exponents to 0, if would fit in digits */ |
| 7235 /* 2. Checking for overflow and subnormals (always) */ |
| 7236 /* Note this is just Finalize when no subset arithmetic. */ |
| 7237 /* All fields are updated as required. */ |
| 7238 /* ------------------------------------------------------------------ */ |
| 7239 static void decFinish(decNumber *dn, decContext *set, Int *residue, |
| 7240 uInt *status) { |
| 7241 if (!set->extended) { |
| 7242 if ISZERO(dn) { /* value is zero */ |
| 7243 dn->exponent=0; /* clean exponent .. */ |
| 7244 dn->bits=0; /* .. and sign */ |
| 7245 return; /* no error possible */ |
| 7246 } |
| 7247 if (dn->exponent>=0) { /* non-negative exponent */ |
| 7248 /* >0; reduce to integer if possible */ |
| 7249 if (set->digits >= (dn->exponent+dn->digits)) { |
| 7250 dn->digits=decShiftToMost(dn->lsu, dn->digits, dn->exponent); |
| 7251 dn->exponent=0; |
| 7252 } |
| 7253 } |
| 7254 } /* !extended */ |
| 7255 |
| 7256 decFinalize(dn, set, residue, status); |
| 7257 } /* decFinish */ |
| 7258 #endif |
| 7259 |
| 7260 /* ------------------------------------------------------------------ */ |
| 7261 /* decFinalize -- final check, clamp, and round of a number */ |
| 7262 /* */ |
| 7263 /* dn is the number */ |
| 7264 /* set is the context */ |
| 7265 /* residue is the rounding accumulator (as in decApplyRound) */ |
| 7266 /* status is the status accumulator */ |
| 7267 /* */ |
| 7268 /* This finishes off the current number by checking for subnormal */ |
| 7269 /* results, applying any pending rounding, checking for overflow, */ |
| 7270 /* and applying any clamping. */ |
| 7271 /* Underflow and overflow conditions are raised as appropriate. */ |
| 7272 /* All fields are updated as required. */ |
| 7273 /* ------------------------------------------------------------------ */ |
| 7274 static void decFinalize(decNumber *dn, decContext *set, Int *residue, |
| 7275 uInt *status) { |
| 7276 Int shift; /* shift needed if clamping */ |
| 7277 Int tinyexp=set->emin-dn->digits+1; /* precalculate subnormal boundary */ |
| 7278 |
| 7279 /* Must be careful, here, when checking the exponent as the */ |
| 7280 /* adjusted exponent could overflow 31 bits [because it may already */ |
| 7281 /* be up to twice the expected]. */ |
| 7282 |
| 7283 /* First test for subnormal. This must be done before any final */ |
| 7284 /* round as the result could be rounded to Nmin or 0. */ |
| 7285 if (dn->exponent<=tinyexp) { /* prefilter */ |
| 7286 Int comp; |
| 7287 decNumber nmin; |
| 7288 /* A very nasty case here is dn == Nmin and residue<0 */ |
| 7289 if (dn->exponent<tinyexp) { |
| 7290 /* Go handle subnormals; this will apply round if needed. */ |
| 7291 decSetSubnormal(dn, set, residue, status); |
| 7292 return; |
| 7293 } |
| 7294 /* Equals case: only subnormal if dn=Nmin and negative residue */ |
| 7295 uprv_decNumberZero(&nmin); |
| 7296 nmin.lsu[0]=1; |
| 7297 nmin.exponent=set->emin; |
| 7298 comp=decCompare(dn, &nmin, 1); /* (signless compare) */ |
| 7299 if (comp==BADINT) { /* oops */ |
| 7300 *status|=DEC_Insufficient_storage; /* abandon... */ |
| 7301 return; |
| 7302 } |
| 7303 if (*residue<0 && comp==0) { /* neg residue and dn==Nmin *
/ |
| 7304 decApplyRound(dn, set, *residue, status); /* might force down */ |
| 7305 decSetSubnormal(dn, set, residue, status); |
| 7306 return; |
| 7307 } |
| 7308 } |
| 7309 |
| 7310 /* now apply any pending round (this could raise overflow). */ |
| 7311 if (*residue!=0) decApplyRound(dn, set, *residue, status); |
| 7312 |
| 7313 /* Check for overflow [redundant in the 'rare' case] or clamp */ |
| 7314 if (dn->exponent<=set->emax-set->digits+1) return; /* neither needed */ |
| 7315 |
| 7316 |
| 7317 /* here when might have an overflow or clamp to do */ |
| 7318 if (dn->exponent>set->emax-dn->digits+1) { /* too big */ |
| 7319 decSetOverflow(dn, set, status); |
| 7320 return; |
| 7321 } |
| 7322 /* here when the result is normal but in clamp range */ |
| 7323 if (!set->clamp) return; |
| 7324 |
| 7325 /* here when need to apply the IEEE exponent clamp (fold-down) */ |
| 7326 shift=dn->exponent-(set->emax-set->digits+1); |
| 7327 |
| 7328 /* shift coefficient (if non-zero) */ |
| 7329 if (!ISZERO(dn)) { |
| 7330 dn->digits=decShiftToMost(dn->lsu, dn->digits, shift); |
| 7331 } |
| 7332 dn->exponent-=shift; /* adjust the exponent to match */ |
| 7333 *status|=DEC_Clamped; /* and record the dirty deed */ |
| 7334 return; |
| 7335 } /* decFinalize */ |
| 7336 |
| 7337 /* ------------------------------------------------------------------ */ |
| 7338 /* decSetOverflow -- set number to proper overflow value */ |
| 7339 /* */ |
| 7340 /* dn is the number (used for sign [only] and result) */ |
| 7341 /* set is the context [used for the rounding mode, etc.] */ |
| 7342 /* status contains the current status to be updated */ |
| 7343 /* */ |
| 7344 /* This sets the sign of a number and sets its value to either */ |
| 7345 /* Infinity or the maximum finite value, depending on the sign of */ |
| 7346 /* dn and the rounding mode, following IEEE 754 rules. */ |
| 7347 /* ------------------------------------------------------------------ */ |
| 7348 static void decSetOverflow(decNumber *dn, decContext *set, uInt *status) { |
| 7349 Flag needmax=0; /* result is maximum finite value */ |
| 7350 uByte sign=dn->bits&DECNEG; /* clean and save sign bit */ |
| 7351 |
| 7352 if (ISZERO(dn)) { /* zero does not overflow magnitude */ |
| 7353 Int emax=set->emax; /* limit value */ |
| 7354 if (set->clamp) emax-=set->digits-1; /* lower if clamping */ |
| 7355 if (dn->exponent>emax) { /* clamp required */ |
| 7356 dn->exponent=emax; |
| 7357 *status|=DEC_Clamped; |
| 7358 } |
| 7359 return; |
| 7360 } |
| 7361 |
| 7362 uprv_decNumberZero(dn); |
| 7363 switch (set->round) { |
| 7364 case DEC_ROUND_DOWN: { |
| 7365 needmax=1; /* never Infinity */ |
| 7366 break;} /* r-d */ |
| 7367 case DEC_ROUND_05UP: { |
| 7368 needmax=1; /* never Infinity */ |
| 7369 break;} /* r-05 */ |
| 7370 case DEC_ROUND_CEILING: { |
| 7371 if (sign) needmax=1; /* Infinity if non-negative */ |
| 7372 break;} /* r-c */ |
| 7373 case DEC_ROUND_FLOOR: { |
| 7374 if (!sign) needmax=1; /* Infinity if negative */ |
| 7375 break;} /* r-f */ |
| 7376 default: break; /* Infinity in all other cases */ |
| 7377 } |
| 7378 if (needmax) { |
| 7379 decSetMaxValue(dn, set); |
| 7380 dn->bits=sign; /* set sign */ |
| 7381 } |
| 7382 else dn->bits=sign|DECINF; /* Value is +/-Infinity */ |
| 7383 *status|=DEC_Overflow | DEC_Inexact | DEC_Rounded; |
| 7384 } /* decSetOverflow */ |
| 7385 |
| 7386 /* ------------------------------------------------------------------ */ |
| 7387 /* decSetMaxValue -- set number to +Nmax (maximum normal value) */ |
| 7388 /* */ |
| 7389 /* dn is the number to set */ |
| 7390 /* set is the context [used for digits and emax] */ |
| 7391 /* */ |
| 7392 /* This sets the number to the maximum positive value. */ |
| 7393 /* ------------------------------------------------------------------ */ |
| 7394 static void decSetMaxValue(decNumber *dn, decContext *set) { |
| 7395 Unit *up; /* work */ |
| 7396 Int count=set->digits; /* nines to add */ |
| 7397 dn->digits=count; |
| 7398 /* fill in all nines to set maximum value */ |
| 7399 for (up=dn->lsu; ; up++) { |
| 7400 if (count>DECDPUN) *up=DECDPUNMAX; /* unit full o'nines */ |
| 7401 else { /* this is the msu */ |
| 7402 *up=(Unit)(powers[count]-1); |
| 7403 break; |
| 7404 } |
| 7405 count-=DECDPUN; /* filled those digits */ |
| 7406 } /* up */ |
| 7407 dn->bits=0; /* + sign */ |
| 7408 dn->exponent=set->emax-set->digits+1; |
| 7409 } /* decSetMaxValue */ |
| 7410 |
| 7411 /* ------------------------------------------------------------------ */ |
| 7412 /* decSetSubnormal -- process value whose exponent is <Emin */ |
| 7413 /* */ |
| 7414 /* dn is the number (used as input as well as output; it may have */ |
| 7415 /* an allowed subnormal value, which may need to be rounded) */ |
| 7416 /* set is the context [used for the rounding mode] */ |
| 7417 /* residue is any pending residue */ |
| 7418 /* status contains the current status to be updated */ |
| 7419 /* */ |
| 7420 /* If subset mode, set result to zero and set Underflow flags. */ |
| 7421 /* */ |
| 7422 /* Value may be zero with a low exponent; this does not set Subnormal */ |
| 7423 /* but the exponent will be clamped to Etiny. */ |
| 7424 /* */ |
| 7425 /* Otherwise ensure exponent is not out of range, and round as */ |
| 7426 /* necessary. Underflow is set if the result is Inexact. */ |
| 7427 /* ------------------------------------------------------------------ */ |
| 7428 static void decSetSubnormal(decNumber *dn, decContext *set, Int *residue, |
| 7429 uInt *status) { |
| 7430 decContext workset; /* work */ |
| 7431 Int etiny, adjust; /* .. */ |
| 7432 |
| 7433 #if DECSUBSET |
| 7434 /* simple set to zero and 'hard underflow' for subset */ |
| 7435 if (!set->extended) { |
| 7436 uprv_decNumberZero(dn); |
| 7437 /* always full overflow */ |
| 7438 *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded; |
| 7439 return; |
| 7440 } |
| 7441 #endif |
| 7442 |
| 7443 /* Full arithmetic -- allow subnormals, rounded to minimum exponent */ |
| 7444 /* (Etiny) if needed */ |
| 7445 etiny=set->emin-(set->digits-1); /* smallest allowed exponent */ |
| 7446 |
| 7447 if ISZERO(dn) { /* value is zero */ |
| 7448 /* residue can never be non-zero here */ |
| 7449 #if DECCHECK |
| 7450 if (*residue!=0) { |
| 7451 printf("++ Subnormal 0 residue %ld\n", (LI)*residue); |
| 7452 *status|=DEC_Invalid_operation; |
| 7453 } |
| 7454 #endif |
| 7455 if (dn->exponent<etiny) { /* clamp required */ |
| 7456 dn->exponent=etiny; |
| 7457 *status|=DEC_Clamped; |
| 7458 } |
| 7459 return; |
| 7460 } |
| 7461 |
| 7462 *status|=DEC_Subnormal; /* have a non-zero subnormal */ |
| 7463 adjust=etiny-dn->exponent; /* calculate digits to remove */ |
| 7464 if (adjust<=0) { /* not out of range; unrounded */ |
| 7465 /* residue can never be non-zero here, except in the Nmin-residue */ |
| 7466 /* case (which is a subnormal result), so can take fast-path here */ |
| 7467 /* it may already be inexact (from setting the coefficient) */ |
| 7468 if (*status&DEC_Inexact) *status|=DEC_Underflow; |
| 7469 return; |
| 7470 } |
| 7471 |
| 7472 /* adjust>0, so need to rescale the result so exponent becomes Etiny */ |
| 7473 /* [this code is similar to that in rescale] */ |
| 7474 workset=*set; /* clone rounding, etc. */ |
| 7475 workset.digits=dn->digits-adjust; /* set requested length */ |
| 7476 workset.emin-=adjust; /* and adjust emin to match */ |
| 7477 /* [note that the latter can be <1, here, similar to Rescale case] */ |
| 7478 decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status); |
| 7479 decApplyRound(dn, &workset, *residue, status); |
| 7480 |
| 7481 /* Use 754 default rule: Underflow is set iff Inexact */ |
| 7482 /* [independent of whether trapped] */ |
| 7483 if (*status&DEC_Inexact) *status|=DEC_Underflow; |
| 7484 |
| 7485 /* if rounded up a 999s case, exponent will be off by one; adjust */ |
| 7486 /* back if so [it will fit, because it was shortened earlier] */ |
| 7487 if (dn->exponent>etiny) { |
| 7488 dn->digits=decShiftToMost(dn->lsu, dn->digits, 1); |
| 7489 dn->exponent--; /* (re)adjust the exponent. */ |
| 7490 } |
| 7491 |
| 7492 /* if rounded to zero, it is by definition clamped... */ |
| 7493 if (ISZERO(dn)) *status|=DEC_Clamped; |
| 7494 } /* decSetSubnormal */ |
| 7495 |
| 7496 /* ------------------------------------------------------------------ */ |
| 7497 /* decCheckMath - check entry conditions for a math function */ |
| 7498 /* */ |
| 7499 /* This checks the context and the operand */ |
| 7500 /* */ |
| 7501 /* rhs is the operand to check */ |
| 7502 /* set is the context to check */ |
| 7503 /* status is unchanged if both are good */ |
| 7504 /* */ |
| 7505 /* returns non-zero if status is changed, 0 otherwise */ |
| 7506 /* */ |
| 7507 /* Restrictions enforced: */ |
| 7508 /* */ |
| 7509 /* digits, emax, and -emin in the context must be less than */ |
| 7510 /* DEC_MAX_MATH (999999), and A must be within these bounds if */ |
| 7511 /* non-zero. Invalid_operation is set in the status if a */ |
| 7512 /* restriction is violated. */ |
| 7513 /* ------------------------------------------------------------------ */ |
| 7514 static uInt decCheckMath(const decNumber *rhs, decContext *set, |
| 7515 uInt *status) { |
| 7516 uInt save=*status; /* record */ |
| 7517 if (set->digits>DEC_MAX_MATH |
| 7518 || set->emax>DEC_MAX_MATH |
| 7519 || -set->emin>DEC_MAX_MATH) *status|=DEC_Invalid_context; |
| 7520 else if ((rhs->digits>DEC_MAX_MATH |
| 7521 || rhs->exponent+rhs->digits>DEC_MAX_MATH+1 |
| 7522 || rhs->exponent+rhs->digits<2*(1-DEC_MAX_MATH)) |
| 7523 && !ISZERO(rhs)) *status|=DEC_Invalid_operation; |
| 7524 return (*status!=save); |
| 7525 } /* decCheckMath */ |
| 7526 |
| 7527 /* ------------------------------------------------------------------ */ |
| 7528 /* decGetInt -- get integer from a number */ |
| 7529 /* */ |
| 7530 /* dn is the number [which will not be altered] */ |
| 7531 /* */ |
| 7532 /* returns one of: */ |
| 7533 /* BADINT if there is a non-zero fraction */ |
| 7534 /* the converted integer */ |
| 7535 /* BIGEVEN if the integer is even and magnitude > 2*10**9 */ |
| 7536 /* BIGODD if the integer is odd and magnitude > 2*10**9 */ |
| 7537 /* */ |
| 7538 /* This checks and gets a whole number from the input decNumber. */ |
| 7539 /* The sign can be determined from dn by the caller when BIGEVEN or */ |
| 7540 /* BIGODD is returned. */ |
| 7541 /* ------------------------------------------------------------------ */ |
| 7542 static Int decGetInt(const decNumber *dn) { |
| 7543 Int theInt; /* result accumulator */ |
| 7544 const Unit *up; /* work */ |
| 7545 Int got; /* digits (real or not) processed */ |
| 7546 Int ilength=dn->digits+dn->exponent; /* integral length */ |
| 7547 Flag neg=decNumberIsNegative(dn); /* 1 if -ve */ |
| 7548 |
| 7549 /* The number must be an integer that fits in 10 digits */ |
| 7550 /* Assert, here, that 10 is enough for any rescale Etiny */ |
| 7551 #if DEC_MAX_EMAX > 999999999 |
| 7552 #error GetInt may need updating [for Emax] |
| 7553 #endif |
| 7554 #if DEC_MIN_EMIN < -999999999 |
| 7555 #error GetInt may need updating [for Emin] |
| 7556 #endif |
| 7557 if (ISZERO(dn)) return 0; /* zeros are OK, with any exponent */ |
| 7558 |
| 7559 up=dn->lsu; /* ready for lsu */ |
| 7560 theInt=0; /* ready to accumulate */ |
| 7561 if (dn->exponent>=0) { /* relatively easy */ |
| 7562 /* no fractional part [usual]; allow for positive exponent */ |
| 7563 got=dn->exponent; |
| 7564 } |
| 7565 else { /* -ve exponent; some fractional part to check and discard */ |
| 7566 Int count=-dn->exponent; /* digits to discard */ |
| 7567 /* spin up whole units until reach the Unit with the unit digit */ |
| 7568 for (; count>=DECDPUN; up++) { |
| 7569 if (*up!=0) return BADINT; /* non-zero Unit to discard */ |
| 7570 count-=DECDPUN; |
| 7571 } |
| 7572 if (count==0) got=0; /* [a multiple of DECDPUN] */ |
| 7573 else { /* [not multiple of DECDPUN] */ |
| 7574 Int rem; /* work */ |
| 7575 /* slice off fraction digits and check for non-zero */ |
| 7576 #if DECDPUN<=4 |
| 7577 theInt=QUOT10(*up, count); |
| 7578 rem=*up-theInt*powers[count]; |
| 7579 #else |
| 7580 rem=*up%powers[count]; /* slice off discards */ |
| 7581 theInt=*up/powers[count]; |
| 7582 #endif |
| 7583 if (rem!=0) return BADINT; /* non-zero fraction */ |
| 7584 /* it looks good */ |
| 7585 got=DECDPUN-count; /* number of digits so far */ |
| 7586 up++; /* ready for next */ |
| 7587 } |
| 7588 } |
| 7589 /* now it's known there's no fractional part */ |
| 7590 |
| 7591 /* tricky code now, to accumulate up to 9.3 digits */ |
| 7592 if (got==0) {theInt=*up; got+=DECDPUN; up++;} /* ensure lsu is there */ |
| 7593 |
| 7594 if (ilength<11) { |
| 7595 Int save=theInt; |
| 7596 /* collect any remaining unit(s) */ |
| 7597 for (; got<ilength; up++) { |
| 7598 theInt+=*up*powers[got]; |
| 7599 got+=DECDPUN; |
| 7600 } |
| 7601 if (ilength==10) { /* need to check for wrap */ |
| 7602 if (theInt/(Int)powers[got-DECDPUN]!=(Int)*(up-1)) ilength=11; |
| 7603 /* [that test also disallows the BADINT result case] */ |
| 7604 else if (neg && theInt>1999999997) ilength=11; |
| 7605 else if (!neg && theInt>999999999) ilength=11; |
| 7606 if (ilength==11) theInt=save; /* restore correct low bit */ |
| 7607 } |
| 7608 } |
| 7609 |
| 7610 if (ilength>10) { /* too big */ |
| 7611 if (theInt&1) return BIGODD; /* bottom bit 1 */ |
| 7612 return BIGEVEN; /* bottom bit 0 */ |
| 7613 } |
| 7614 |
| 7615 if (neg) theInt=-theInt; /* apply sign */ |
| 7616 return theInt; |
| 7617 } /* decGetInt */ |
| 7618 |
| 7619 /* ------------------------------------------------------------------ */ |
| 7620 /* decDecap -- decapitate the coefficient of a number */ |
| 7621 /* */ |
| 7622 /* dn is the number to be decapitated */ |
| 7623 /* drop is the number of digits to be removed from the left of dn; */ |
| 7624 /* this must be <= dn->digits (if equal, the coefficient is */ |
| 7625 /* set to 0) */ |
| 7626 /* */ |
| 7627 /* Returns dn; dn->digits will be <= the initial digits less drop */ |
| 7628 /* (after removing drop digits there may be leading zero digits */ |
| 7629 /* which will also be removed). Only dn->lsu and dn->digits change. */ |
| 7630 /* ------------------------------------------------------------------ */ |
| 7631 static decNumber *decDecap(decNumber *dn, Int drop) { |
| 7632 Unit *msu; /* -> target cut point */ |
| 7633 Int cut; /* work */ |
| 7634 if (drop>=dn->digits) { /* losing the whole thing */ |
| 7635 #if DECCHECK |
| 7636 if (drop>dn->digits) |
| 7637 printf("decDecap called with drop>digits [%ld>%ld]\n", |
| 7638 (LI)drop, (LI)dn->digits); |
| 7639 #endif |
| 7640 dn->lsu[0]=0; |
| 7641 dn->digits=1; |
| 7642 return dn; |
| 7643 } |
| 7644 msu=dn->lsu+D2U(dn->digits-drop)-1; /* -> likely msu */ |
| 7645 cut=MSUDIGITS(dn->digits-drop); /* digits to be in use in msu */ |
| 7646 if (cut!=DECDPUN) *msu%=powers[cut]; /* clear left digits */ |
| 7647 /* that may have left leading zero digits, so do a proper count... */ |
| 7648 dn->digits=decGetDigits(dn->lsu, msu-dn->lsu+1); |
| 7649 return dn; |
| 7650 } /* decDecap */ |
| 7651 |
| 7652 /* ------------------------------------------------------------------ */ |
| 7653 /* decBiStr -- compare string with pairwise options */ |
| 7654 /* */ |
| 7655 /* targ is the string to compare */ |
| 7656 /* str1 is one of the strings to compare against (length may be 0) */ |
| 7657 /* str2 is the other; it must be the same length as str1 */ |
| 7658 /* */ |
| 7659 /* returns 1 if strings compare equal, (that is, it is the same */ |
| 7660 /* length as str1 and str2, and each character of targ is in either */ |
| 7661 /* str1 or str2 in the corresponding position), or 0 otherwise */ |
| 7662 /* */ |
| 7663 /* This is used for generic caseless compare, including the awkward */ |
| 7664 /* case of the Turkish dotted and dotless Is. Use as (for example): */ |
| 7665 /* if (decBiStr(test, "mike", "MIKE")) ... */ |
| 7666 /* ------------------------------------------------------------------ */ |
| 7667 static Flag decBiStr(const char *targ, const char *str1, const char *str2) { |
| 7668 for (;;targ++, str1++, str2++) { |
| 7669 if (*targ!=*str1 && *targ!=*str2) return 0; |
| 7670 /* *targ has a match in one (or both, if terminator) */ |
| 7671 if (*targ=='\0') break; |
| 7672 } /* forever */ |
| 7673 return 1; |
| 7674 } /* decBiStr */ |
| 7675 |
| 7676 /* ------------------------------------------------------------------ */ |
| 7677 /* decNaNs -- handle NaN operand or operands */ |
| 7678 /* */ |
| 7679 /* res is the result number */ |
| 7680 /* lhs is the first operand */ |
| 7681 /* rhs is the second operand, or NULL if none */ |
| 7682 /* context is used to limit payload length */ |
| 7683 /* status contains the current status */ |
| 7684 /* returns res in case convenient */ |
| 7685 /* */ |
| 7686 /* Called when one or both operands is a NaN, and propagates the */ |
| 7687 /* appropriate result to res. When an sNaN is found, it is changed */ |
| 7688 /* to a qNaN and Invalid operation is set. */ |
| 7689 /* ------------------------------------------------------------------ */ |
| 7690 static decNumber * decNaNs(decNumber *res, const decNumber *lhs, |
| 7691 const decNumber *rhs, decContext *set, |
| 7692 uInt *status) { |
| 7693 /* This decision tree ends up with LHS being the source pointer, */ |
| 7694 /* and status updated if need be */ |
| 7695 if (lhs->bits & DECSNAN) |
| 7696 *status|=DEC_Invalid_operation | DEC_sNaN; |
| 7697 else if (rhs==NULL); |
| 7698 else if (rhs->bits & DECSNAN) { |
| 7699 lhs=rhs; |
| 7700 *status|=DEC_Invalid_operation | DEC_sNaN; |
| 7701 } |
| 7702 else if (lhs->bits & DECNAN); |
| 7703 else lhs=rhs; |
| 7704 |
| 7705 /* propagate the payload */ |
| 7706 if (lhs->digits<=set->digits) uprv_decNumberCopy(res, lhs); /* easy */ |
| 7707 else { /* too long */ |
| 7708 const Unit *ul; |
| 7709 Unit *ur, *uresp1; |
| 7710 /* copy safe number of units, then decapitate */ |
| 7711 res->bits=lhs->bits; /* need sign etc. */ |
| 7712 uresp1=res->lsu+D2U(set->digits); |
| 7713 for (ur=res->lsu, ul=lhs->lsu; ur<uresp1; ur++, ul++) *ur=*ul; |
| 7714 res->digits=D2U(set->digits)*DECDPUN; |
| 7715 /* maybe still too long */ |
| 7716 if (res->digits>set->digits) decDecap(res, res->digits-set->digits); |
| 7717 } |
| 7718 |
| 7719 res->bits&=~DECSNAN; /* convert any sNaN to NaN, while */ |
| 7720 res->bits|=DECNAN; /* .. preserving sign */ |
| 7721 res->exponent=0; /* clean exponent */ |
| 7722 /* [coefficient was copied/decapitated] */ |
| 7723 return res; |
| 7724 } /* decNaNs */ |
| 7725 |
| 7726 /* ------------------------------------------------------------------ */ |
| 7727 /* decStatus -- apply non-zero status */ |
| 7728 /* */ |
| 7729 /* dn is the number to set if error */ |
| 7730 /* status contains the current status (not yet in context) */ |
| 7731 /* set is the context */ |
| 7732 /* */ |
| 7733 /* If the status is an error status, the number is set to a NaN, */ |
| 7734 /* unless the error was an overflow, divide-by-zero, or underflow, */ |
| 7735 /* in which case the number will have already been set. */ |
| 7736 /* */ |
| 7737 /* The context status is then updated with the new status. Note that */ |
| 7738 /* this may raise a signal, so control may never return from this */ |
| 7739 /* routine (hence resources must be recovered before it is called). */ |
| 7740 /* ------------------------------------------------------------------ */ |
| 7741 static void decStatus(decNumber *dn, uInt status, decContext *set) { |
| 7742 if (status & DEC_NaNs) { /* error status -> NaN */ |
| 7743 /* if cause was an sNaN, clear and propagate [NaN is already set up] */ |
| 7744 if (status & DEC_sNaN) status&=~DEC_sNaN; |
| 7745 else { |
| 7746 uprv_decNumberZero(dn); /* other error: clean throughout *
/ |
| 7747 dn->bits=DECNAN; /* and make a quiet NaN */ |
| 7748 } |
| 7749 } |
| 7750 uprv_decContextSetStatus(set, status); /* [may not return] */ |
| 7751 return; |
| 7752 } /* decStatus */ |
| 7753 |
| 7754 /* ------------------------------------------------------------------ */ |
| 7755 /* decGetDigits -- count digits in a Units array */ |
| 7756 /* */ |
| 7757 /* uar is the Unit array holding the number (this is often an */ |
| 7758 /* accumulator of some sort) */ |
| 7759 /* len is the length of the array in units [>=1] */ |
| 7760 /* */ |
| 7761 /* returns the number of (significant) digits in the array */ |
| 7762 /* */ |
| 7763 /* All leading zeros are excluded, except the last if the array has */ |
| 7764 /* only zero Units. */ |
| 7765 /* ------------------------------------------------------------------ */ |
| 7766 /* This may be called twice during some operations. */ |
| 7767 static Int decGetDigits(Unit *uar, Int len) { |
| 7768 Unit *up=uar+(len-1); /* -> msu */ |
| 7769 Int digits=(len-1)*DECDPUN+1; /* possible digits excluding msu */ |
| 7770 #if DECDPUN>4 |
| 7771 uInt const *pow; /* work */ |
| 7772 #endif |
| 7773 /* (at least 1 in final msu) */ |
| 7774 #if DECCHECK |
| 7775 if (len<1) printf("decGetDigits called with len<1 [%ld]\n", (LI)len); |
| 7776 #endif |
| 7777 |
| 7778 for (; up>=uar; up--) { |
| 7779 if (*up==0) { /* unit is all 0s */ |
| 7780 if (digits==1) break; /* a zero has one digit */ |
| 7781 digits-=DECDPUN; /* adjust for 0 unit */ |
| 7782 continue;} |
| 7783 /* found the first (most significant) non-zero Unit */ |
| 7784 #if DECDPUN>1 /* not done yet */ |
| 7785 if (*up<10) break; /* is 1-9 */ |
| 7786 digits++; |
| 7787 #if DECDPUN>2 /* not done yet */ |
| 7788 if (*up<100) break; /* is 10-99 */ |
| 7789 digits++; |
| 7790 #if DECDPUN>3 /* not done yet */ |
| 7791 if (*up<1000) break; /* is 100-999 */ |
| 7792 digits++; |
| 7793 #if DECDPUN>4 /* count the rest ... */ |
| 7794 for (pow=&powers[4]; *up>=*pow; pow++) digits++; |
| 7795 #endif |
| 7796 #endif |
| 7797 #endif |
| 7798 #endif |
| 7799 break; |
| 7800 } /* up */ |
| 7801 return digits; |
| 7802 } /* decGetDigits */ |
| 7803 |
| 7804 #if DECTRACE | DECCHECK |
| 7805 /* ------------------------------------------------------------------ */ |
| 7806 /* decNumberShow -- display a number [debug aid] */ |
| 7807 /* dn is the number to show */ |
| 7808 /* */ |
| 7809 /* Shows: sign, exponent, coefficient (msu first), digits */ |
| 7810 /* or: sign, special-value */ |
| 7811 /* ------------------------------------------------------------------ */ |
| 7812 /* this is public so other modules can use it */ |
| 7813 void uprv_decNumberShow(const decNumber *dn) { |
| 7814 const Unit *up; /* work */ |
| 7815 uInt u, d; /* .. */ |
| 7816 Int cut; /* .. */ |
| 7817 char isign='+'; /* main sign */ |
| 7818 if (dn==NULL) { |
| 7819 printf("NULL\n"); |
| 7820 return;} |
| 7821 if (decNumberIsNegative(dn)) isign='-'; |
| 7822 printf(" >> %c ", isign); |
| 7823 if (dn->bits&DECSPECIAL) { /* Is a special value */ |
| 7824 if (decNumberIsInfinite(dn)) printf("Infinity"); |
| 7825 else { /* a NaN */ |
| 7826 if (dn->bits&DECSNAN) printf("sNaN"); /* signalling NaN */ |
| 7827 else printf("NaN"); |
| 7828 } |
| 7829 /* if coefficient and exponent are 0, no more to do */ |
| 7830 if (dn->exponent==0 && dn->digits==1 && *dn->lsu==0) { |
| 7831 printf("\n"); |
| 7832 return;} |
| 7833 /* drop through to report other information */ |
| 7834 printf(" "); |
| 7835 } |
| 7836 |
| 7837 /* now carefully display the coefficient */ |
| 7838 up=dn->lsu+D2U(dn->digits)-1; /* msu */ |
| 7839 printf("%ld", (LI)*up); |
| 7840 for (up=up-1; up>=dn->lsu; up--) { |
| 7841 u=*up; |
| 7842 printf(":"); |
| 7843 for (cut=DECDPUN-1; cut>=0; cut--) { |
| 7844 d=u/powers[cut]; |
| 7845 u-=d*powers[cut]; |
| 7846 printf("%ld", (LI)d); |
| 7847 } /* cut */ |
| 7848 } /* up */ |
| 7849 if (dn->exponent!=0) { |
| 7850 char esign='+'; |
| 7851 if (dn->exponent<0) esign='-'; |
| 7852 printf(" E%c%ld", esign, (LI)abs(dn->exponent)); |
| 7853 } |
| 7854 printf(" [%ld]\n", (LI)dn->digits); |
| 7855 } /* decNumberShow */ |
| 7856 #endif |
| 7857 |
| 7858 #if DECTRACE || DECCHECK |
| 7859 /* ------------------------------------------------------------------ */ |
| 7860 /* decDumpAr -- display a unit array [debug/check aid] */ |
| 7861 /* name is a single-character tag name */ |
| 7862 /* ar is the array to display */ |
| 7863 /* len is the length of the array in Units */ |
| 7864 /* ------------------------------------------------------------------ */ |
| 7865 static void decDumpAr(char name, const Unit *ar, Int len) { |
| 7866 Int i; |
| 7867 const char *spec; |
| 7868 #if DECDPUN==9 |
| 7869 spec="%09d "; |
| 7870 #elif DECDPUN==8 |
| 7871 spec="%08d "; |
| 7872 #elif DECDPUN==7 |
| 7873 spec="%07d "; |
| 7874 #elif DECDPUN==6 |
| 7875 spec="%06d "; |
| 7876 #elif DECDPUN==5 |
| 7877 spec="%05d "; |
| 7878 #elif DECDPUN==4 |
| 7879 spec="%04d "; |
| 7880 #elif DECDPUN==3 |
| 7881 spec="%03d "; |
| 7882 #elif DECDPUN==2 |
| 7883 spec="%02d "; |
| 7884 #else |
| 7885 spec="%d "; |
| 7886 #endif |
| 7887 printf(" :%c: ", name); |
| 7888 for (i=len-1; i>=0; i--) { |
| 7889 if (i==len-1) printf("%ld ", (LI)ar[i]); |
| 7890 else printf(spec, ar[i]); |
| 7891 } |
| 7892 printf("\n"); |
| 7893 return;} |
| 7894 #endif |
| 7895 |
| 7896 #if DECCHECK |
| 7897 /* ------------------------------------------------------------------ */ |
| 7898 /* decCheckOperands -- check operand(s) to a routine */ |
| 7899 /* res is the result structure (not checked; it will be set to */ |
| 7900 /* quiet NaN if error found (and it is not NULL)) */ |
| 7901 /* lhs is the first operand (may be DECUNRESU) */ |
| 7902 /* rhs is the second (may be DECUNUSED) */ |
| 7903 /* set is the context (may be DECUNCONT) */ |
| 7904 /* returns 0 if both operands, and the context are clean, or 1 */ |
| 7905 /* otherwise (in which case the context will show an error, */ |
| 7906 /* unless NULL). Note that res is not cleaned; caller should */ |
| 7907 /* handle this so res=NULL case is safe. */ |
| 7908 /* The caller is expected to abandon immediately if 1 is returned. */ |
| 7909 /* ------------------------------------------------------------------ */ |
| 7910 static Flag decCheckOperands(decNumber *res, const decNumber *lhs, |
| 7911 const decNumber *rhs, decContext *set) { |
| 7912 Flag bad=0; |
| 7913 if (set==NULL) { /* oops; hopeless */ |
| 7914 #if DECTRACE || DECVERB |
| 7915 printf("Reference to context is NULL.\n"); |
| 7916 #endif |
| 7917 bad=1; |
| 7918 return 1;} |
| 7919 else if (set!=DECUNCONT |
| 7920 && (set->digits<1 || set->round>=DEC_ROUND_MAX)) { |
| 7921 bad=1; |
| 7922 #if DECTRACE || DECVERB |
| 7923 printf("Bad context [digits=%ld round=%ld].\n", |
| 7924 (LI)set->digits, (LI)set->round); |
| 7925 #endif |
| 7926 } |
| 7927 else { |
| 7928 if (res==NULL) { |
| 7929 bad=1; |
| 7930 #if DECTRACE |
| 7931 /* this one not DECVERB as standard tests include NULL */ |
| 7932 printf("Reference to result is NULL.\n"); |
| 7933 #endif |
| 7934 } |
| 7935 if (!bad && lhs!=DECUNUSED) bad=(decCheckNumber(lhs)); |
| 7936 if (!bad && rhs!=DECUNUSED) bad=(decCheckNumber(rhs)); |
| 7937 } |
| 7938 if (bad) { |
| 7939 if (set!=DECUNCONT) uprv_decContextSetStatus(set, DEC_Invalid_operation); |
| 7940 if (res!=DECUNRESU && res!=NULL) { |
| 7941 uprv_decNumberZero(res); |
| 7942 res->bits=DECNAN; /* qNaN */ |
| 7943 } |
| 7944 } |
| 7945 return bad; |
| 7946 } /* decCheckOperands */ |
| 7947 |
| 7948 /* ------------------------------------------------------------------ */ |
| 7949 /* decCheckNumber -- check a number */ |
| 7950 /* dn is the number to check */ |
| 7951 /* returns 0 if the number is clean, or 1 otherwise */ |
| 7952 /* */ |
| 7953 /* The number is considered valid if it could be a result from some */ |
| 7954 /* operation in some valid context. */ |
| 7955 /* ------------------------------------------------------------------ */ |
| 7956 static Flag decCheckNumber(const decNumber *dn) { |
| 7957 const Unit *up; /* work */ |
| 7958 uInt maxuint; /* .. */ |
| 7959 Int ae, d, digits; /* .. */ |
| 7960 Int emin, emax; /* .. */ |
| 7961 |
| 7962 if (dn==NULL) { /* hopeless */ |
| 7963 #if DECTRACE |
| 7964 /* this one not DECVERB as standard tests include NULL */ |
| 7965 printf("Reference to decNumber is NULL.\n"); |
| 7966 #endif |
| 7967 return 1;} |
| 7968 |
| 7969 /* check special values */ |
| 7970 if (dn->bits & DECSPECIAL) { |
| 7971 if (dn->exponent!=0) { |
| 7972 #if DECTRACE || DECVERB |
| 7973 printf("Exponent %ld (not 0) for a special value [%02x].\n", |
| 7974 (LI)dn->exponent, dn->bits); |
| 7975 #endif |
| 7976 return 1;} |
| 7977 |
| 7978 /* 2003.09.08: NaNs may now have coefficients, so next tests Inf only */ |
| 7979 if (decNumberIsInfinite(dn)) { |
| 7980 if (dn->digits!=1) { |
| 7981 #if DECTRACE || DECVERB |
| 7982 printf("Digits %ld (not 1) for an infinity.\n", (LI)dn->digits); |
| 7983 #endif |
| 7984 return 1;} |
| 7985 if (*dn->lsu!=0) { |
| 7986 #if DECTRACE || DECVERB |
| 7987 printf("LSU %ld (not 0) for an infinity.\n", (LI)*dn->lsu); |
| 7988 #endif |
| 7989 decDumpAr('I', dn->lsu, D2U(dn->digits)); |
| 7990 return 1;} |
| 7991 } /* Inf */ |
| 7992 /* 2002.12.26: negative NaNs can now appear through proposed IEEE */ |
| 7993 /* concrete formats (decimal64, etc.). */ |
| 7994 return 0; |
| 7995 } |
| 7996 |
| 7997 /* check the coefficient */ |
| 7998 if (dn->digits<1 || dn->digits>DECNUMMAXP) { |
| 7999 #if DECTRACE || DECVERB |
| 8000 printf("Digits %ld in number.\n", (LI)dn->digits); |
| 8001 #endif |
| 8002 return 1;} |
| 8003 |
| 8004 d=dn->digits; |
| 8005 |
| 8006 for (up=dn->lsu; d>0; up++) { |
| 8007 if (d>DECDPUN) maxuint=DECDPUNMAX; |
| 8008 else { /* reached the msu */ |
| 8009 maxuint=powers[d]-1; |
| 8010 if (dn->digits>1 && *up<powers[d-1]) { |
| 8011 #if DECTRACE || DECVERB |
| 8012 printf("Leading 0 in number.\n"); |
| 8013 uprv_decNumberShow(dn); |
| 8014 #endif |
| 8015 return 1;} |
| 8016 } |
| 8017 if (*up>maxuint) { |
| 8018 #if DECTRACE || DECVERB |
| 8019 printf("Bad Unit [%08lx] in %ld-digit number at offset %ld [maxuint %ld].\
n", |
| 8020 (LI)*up, (LI)dn->digits, (LI)(up-dn->lsu), (LI)maxuint); |
| 8021 #endif |
| 8022 return 1;} |
| 8023 d-=DECDPUN; |
| 8024 } |
| 8025 |
| 8026 /* check the exponent. Note that input operands can have exponents */ |
| 8027 /* which are out of the set->emin/set->emax and set->digits range */ |
| 8028 /* (just as they can have more digits than set->digits). */ |
| 8029 ae=dn->exponent+dn->digits-1; /* adjusted exponent */ |
| 8030 emax=DECNUMMAXE; |
| 8031 emin=DECNUMMINE; |
| 8032 digits=DECNUMMAXP; |
| 8033 if (ae<emin-(digits-1)) { |
| 8034 #if DECTRACE || DECVERB |
| 8035 printf("Adjusted exponent underflow [%ld].\n", (LI)ae); |
| 8036 uprv_decNumberShow(dn); |
| 8037 #endif |
| 8038 return 1;} |
| 8039 if (ae>+emax) { |
| 8040 #if DECTRACE || DECVERB |
| 8041 printf("Adjusted exponent overflow [%ld].\n", (LI)ae); |
| 8042 uprv_decNumberShow(dn); |
| 8043 #endif |
| 8044 return 1;} |
| 8045 |
| 8046 return 0; /* it's OK */ |
| 8047 } /* decCheckNumber */ |
| 8048 |
| 8049 /* ------------------------------------------------------------------ */ |
| 8050 /* decCheckInexact -- check a normal finite inexact result has digits */ |
| 8051 /* dn is the number to check */ |
| 8052 /* set is the context (for status and precision) */ |
| 8053 /* sets Invalid operation, etc., if some digits are missing */ |
| 8054 /* [this check is not made for DECSUBSET compilation or when */ |
| 8055 /* subnormal is not set] */ |
| 8056 /* ------------------------------------------------------------------ */ |
| 8057 static void decCheckInexact(const decNumber *dn, decContext *set) { |
| 8058 #if !DECSUBSET && DECEXTFLAG |
| 8059 if ((set->status & (DEC_Inexact|DEC_Subnormal))==DEC_Inexact |
| 8060 && (set->digits!=dn->digits) && !(dn->bits & DECSPECIAL)) { |
| 8061 #if DECTRACE || DECVERB |
| 8062 printf("Insufficient digits [%ld] on normal Inexact result.\n", |
| 8063 (LI)dn->digits); |
| 8064 uprv_decNumberShow(dn); |
| 8065 #endif |
| 8066 uprv_decContextSetStatus(set, DEC_Invalid_operation); |
| 8067 } |
| 8068 #else |
| 8069 /* next is a noop for quiet compiler */ |
| 8070 if (dn!=NULL && dn->digits==0) set->status|=DEC_Invalid_operation; |
| 8071 #endif |
| 8072 return; |
| 8073 } /* decCheckInexact */ |
| 8074 #endif |
| 8075 |
| 8076 #if DECALLOC |
| 8077 #undef malloc |
| 8078 #undef free |
| 8079 /* ------------------------------------------------------------------ */ |
| 8080 /* decMalloc -- accountable allocation routine */ |
| 8081 /* n is the number of bytes to allocate */ |
| 8082 /* */ |
| 8083 /* Semantics is the same as the stdlib malloc routine, but bytes */ |
| 8084 /* allocated are accounted for globally, and corruption fences are */ |
| 8085 /* added before and after the 'actual' storage. */ |
| 8086 /* ------------------------------------------------------------------ */ |
| 8087 /* This routine allocates storage with an extra twelve bytes; 8 are */ |
| 8088 /* at the start and hold: */ |
| 8089 /* 0-3 the original length requested */ |
| 8090 /* 4-7 buffer corruption detection fence (DECFENCE, x4) */ |
| 8091 /* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */ |
| 8092 /* ------------------------------------------------------------------ */ |
| 8093 static void *decMalloc(size_t n) { |
| 8094 uInt size=n+12; /* true size */ |
| 8095 void *alloc; /* -> allocated storage */ |
| 8096 uByte *b, *b0; /* work */ |
| 8097 uInt uiwork; /* for macros */ |
| 8098 |
| 8099 alloc=malloc(size); /* -> allocated storage */ |
| 8100 if (alloc==NULL) return NULL; /* out of strorage */ |
| 8101 b0=(uByte *)alloc; /* as bytes */ |
| 8102 decAllocBytes+=n; /* account for storage */ |
| 8103 UBFROMUI(alloc, n); /* save n */ |
| 8104 /* printf(" alloc ++ dAB: %ld (%ld)\n", (LI)decAllocBytes, (LI)n); */ |
| 8105 for (b=b0+4; b<b0+8; b++) *b=DECFENCE; |
| 8106 for (b=b0+n+8; b<b0+n+12; b++) *b=DECFENCE; |
| 8107 return b0+8; /* -> play area */ |
| 8108 } /* decMalloc */ |
| 8109 |
| 8110 /* ------------------------------------------------------------------ */ |
| 8111 /* decFree -- accountable free routine */ |
| 8112 /* alloc is the storage to free */ |
| 8113 /* */ |
| 8114 /* Semantics is the same as the stdlib malloc routine, except that */ |
| 8115 /* the global storage accounting is updated and the fences are */ |
| 8116 /* checked to ensure that no routine has written 'out of bounds'. */ |
| 8117 /* ------------------------------------------------------------------ */ |
| 8118 /* This routine first checks that the fences have not been corrupted. */ |
| 8119 /* It then frees the storage using the 'truw' storage address (that */ |
| 8120 /* is, offset by 8). */ |
| 8121 /* ------------------------------------------------------------------ */ |
| 8122 static void decFree(void *alloc) { |
| 8123 uInt n; /* original length */ |
| 8124 uByte *b, *b0; /* work */ |
| 8125 uInt uiwork; /* for macros */ |
| 8126 |
| 8127 if (alloc==NULL) return; /* allowed; it's a nop */ |
| 8128 b0=(uByte *)alloc; /* as bytes */ |
| 8129 b0-=8; /* -> true start of storage */ |
| 8130 n=UBTOUI(b0); /* lift length */ |
| 8131 for (b=b0+4; b<b0+8; b++) if (*b!=DECFENCE) |
| 8132 printf("=== Corrupt byte [%02x] at offset %d from %ld ===\n", *b, |
| 8133 b-b0-8, (LI)b0); |
| 8134 for (b=b0+n+8; b<b0+n+12; b++) if (*b!=DECFENCE) |
| 8135 printf("=== Corrupt byte [%02x] at offset +%d from %ld, n=%ld ===\n", *b, |
| 8136 b-b0-8, (LI)b0, (LI)n); |
| 8137 free(b0); /* drop the storage */ |
| 8138 decAllocBytes-=n; /* account for storage */ |
| 8139 /* printf(" free -- dAB: %d (%d)\n", decAllocBytes, -n); */ |
| 8140 } /* decFree */ |
| 8141 #define malloc(a) decMalloc(a) |
| 8142 #define free(a) decFree(a) |
| 8143 #endif |
| OLD | NEW |
|---|
Chromium Code Reviews
Issue 5516007:
Check in the pristine copy of ICU 4.6... (Closed)
Base URL: svn://chrome-svn/chrome/trunk/deps/third_party/