Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 1 | /* |
| 2 | * Copyright (c) 2008-2012 Stefan Krah. All rights reserved. |
| 3 | * |
| 4 | * Redistribution and use in source and binary forms, with or without |
| 5 | * modification, are permitted provided that the following conditions |
| 6 | * are met: |
| 7 | * |
| 8 | * 1. Redistributions of source code must retain the above copyright |
| 9 | * notice, this list of conditions and the following disclaimer. |
| 10 | * |
| 11 | * 2. Redistributions in binary form must reproduce the above copyright |
| 12 | * notice, this list of conditions and the following disclaimer in the |
| 13 | * documentation and/or other materials provided with the distribution. |
| 14 | * |
| 15 | * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND |
| 16 | * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| 17 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| 18 | * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE |
| 19 | * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
| 20 | * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
| 21 | * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| 22 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
| 23 | * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
| 24 | * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
| 25 | * SUCH DAMAGE. |
| 26 | */ |
| 27 | |
| 28 | |
| 29 | #include "mpdecimal.h" |
| 30 | #include <stdio.h> |
| 31 | #include <stdlib.h> |
| 32 | #include <string.h> |
| 33 | #include <limits.h> |
| 34 | #include <math.h> |
| 35 | #include "basearith.h" |
| 36 | #include "bits.h" |
| 37 | #include "convolute.h" |
| 38 | #include "crt.h" |
| 39 | #include "errno.h" |
| 40 | #include "memory.h" |
| 41 | #include "typearith.h" |
| 42 | #include "umodarith.h" |
| 43 | |
| 44 | #ifdef PPRO |
| 45 | #if defined(_MSC_VER) |
| 46 | #include <float.h> |
| 47 | #pragma fenv_access(on) |
| 48 | #elif !defined(__OpenBSD__) && !defined(__NetBSD__) |
| 49 | /* C99 */ |
| 50 | #include <fenv.h> |
| 51 | #pragma STDC FENV_ACCESS ON |
| 52 | #endif |
| 53 | #endif |
| 54 | |
| 55 | #if defined(__x86_64__) && defined(__GLIBC__) && !defined(__INTEL_COMPILER) |
| 56 | #define USE_80BIT_LONG_DOUBLE |
| 57 | #endif |
| 58 | |
| 59 | #if defined(_MSC_VER) |
| 60 | #define ALWAYS_INLINE __forceinline |
| 61 | #elif defined(LEGACY_COMPILER) |
| 62 | #define ALWAYS_INLINE |
| 63 | #undef inline |
| 64 | #define inline |
| 65 | #else |
| 66 | #ifdef TEST_COVERAGE |
| 67 | #define ALWAYS_INLINE |
| 68 | #else |
| 69 | #define ALWAYS_INLINE inline __attribute__ ((always_inline)) |
| 70 | #endif |
| 71 | #endif |
| 72 | |
| 73 | |
| 74 | #define MPD_NEWTONDIV_CUTOFF 1024L |
| 75 | |
| 76 | #define MPD_NEW_STATIC(name, flags, exp, digits, len) \ |
| 77 | mpd_uint_t name##_data[MPD_MINALLOC_MAX]; \ |
| 78 | mpd_t name = {flags|MPD_STATIC|MPD_STATIC_DATA, exp, digits, \ |
| 79 | len, MPD_MINALLOC_MAX, name##_data} |
| 80 | |
| 81 | #define MPD_NEW_CONST(name, flags, exp, digits, len, alloc, initval) \ |
| 82 | mpd_uint_t name##_data[alloc] = {initval}; \ |
| 83 | mpd_t name = {flags|MPD_STATIC|MPD_CONST_DATA, exp, digits, \ |
| 84 | len, alloc, name##_data} |
| 85 | |
| 86 | #define MPD_NEW_SHARED(name, a) \ |
| 87 | mpd_t name = {(a->flags&~MPD_DATAFLAGS)|MPD_STATIC|MPD_SHARED_DATA, \ |
| 88 | a->exp, a->digits, a->len, a->alloc, a->data} |
| 89 | |
| 90 | |
| 91 | static mpd_uint_t data_one[1] = {1}; |
| 92 | static mpd_uint_t data_zero[1] = {0}; |
| 93 | static const mpd_t one = {MPD_STATIC|MPD_CONST_DATA, 0, 1, 1, 1, data_one}; |
| 94 | static const mpd_t minus_one = {MPD_NEG|MPD_STATIC|MPD_CONST_DATA, 0, 1, 1, 1, |
| 95 | data_one}; |
| 96 | static const mpd_t zero = {MPD_STATIC|MPD_CONST_DATA, 0, 1, 1, 1, data_zero}; |
| 97 | |
| 98 | static inline void _mpd_check_exp(mpd_t *dec, const mpd_context_t *ctx, |
| 99 | uint32_t *status); |
| 100 | static void _settriple(mpd_t *result, uint8_t sign, mpd_uint_t a, |
| 101 | mpd_ssize_t exp); |
| 102 | static inline mpd_ssize_t _mpd_real_size(mpd_uint_t *data, mpd_ssize_t size); |
| 103 | |
| 104 | static void _mpd_qadd(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 105 | const mpd_context_t *ctx, uint32_t *status); |
| 106 | static inline void _mpd_qmul(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 107 | const mpd_context_t *ctx, uint32_t *status); |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 108 | static void _mpd_base_ndivmod(mpd_t *q, mpd_t *r, const mpd_t *a, |
| 109 | const mpd_t *b, uint32_t *status); |
Stefan Krah | b783293 | 2012-06-12 21:06:06 +0200 | [diff] [blame] | 110 | static inline void _mpd_qpow_uint(mpd_t *result, const mpd_t *base, |
| 111 | mpd_uint_t exp, uint8_t resultsign, |
| 112 | const mpd_context_t *ctx, uint32_t *status); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 113 | |
| 114 | mpd_uint_t mpd_qsshiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n); |
| 115 | |
| 116 | |
| 117 | /******************************************************************************/ |
| 118 | /* Performance critical inline functions */ |
| 119 | /******************************************************************************/ |
| 120 | |
| 121 | #ifdef CONFIG_64 |
| 122 | /* Digits in a word, primarily useful for the most significant word. */ |
| 123 | ALWAYS_INLINE int |
| 124 | mpd_word_digits(mpd_uint_t word) |
| 125 | { |
| 126 | if (word < mpd_pow10[9]) { |
| 127 | if (word < mpd_pow10[4]) { |
| 128 | if (word < mpd_pow10[2]) { |
| 129 | return (word < mpd_pow10[1]) ? 1 : 2; |
| 130 | } |
| 131 | return (word < mpd_pow10[3]) ? 3 : 4; |
| 132 | } |
| 133 | if (word < mpd_pow10[6]) { |
| 134 | return (word < mpd_pow10[5]) ? 5 : 6; |
| 135 | } |
| 136 | if (word < mpd_pow10[8]) { |
| 137 | return (word < mpd_pow10[7]) ? 7 : 8; |
| 138 | } |
| 139 | return 9; |
| 140 | } |
| 141 | if (word < mpd_pow10[14]) { |
| 142 | if (word < mpd_pow10[11]) { |
| 143 | return (word < mpd_pow10[10]) ? 10 : 11; |
| 144 | } |
| 145 | if (word < mpd_pow10[13]) { |
| 146 | return (word < mpd_pow10[12]) ? 12 : 13; |
| 147 | } |
| 148 | return 14; |
| 149 | } |
| 150 | if (word < mpd_pow10[18]) { |
| 151 | if (word < mpd_pow10[16]) { |
| 152 | return (word < mpd_pow10[15]) ? 15 : 16; |
| 153 | } |
| 154 | return (word < mpd_pow10[17]) ? 17 : 18; |
| 155 | } |
| 156 | |
| 157 | return (word < mpd_pow10[19]) ? 19 : 20; |
| 158 | } |
| 159 | #else |
| 160 | ALWAYS_INLINE int |
| 161 | mpd_word_digits(mpd_uint_t word) |
| 162 | { |
| 163 | if (word < mpd_pow10[4]) { |
| 164 | if (word < mpd_pow10[2]) { |
| 165 | return (word < mpd_pow10[1]) ? 1 : 2; |
| 166 | } |
| 167 | return (word < mpd_pow10[3]) ? 3 : 4; |
| 168 | } |
| 169 | if (word < mpd_pow10[6]) { |
| 170 | return (word < mpd_pow10[5]) ? 5 : 6; |
| 171 | } |
| 172 | if (word < mpd_pow10[8]) { |
| 173 | return (word < mpd_pow10[7]) ? 7 : 8; |
| 174 | } |
| 175 | |
| 176 | return (word < mpd_pow10[9]) ? 9 : 10; |
| 177 | } |
| 178 | #endif |
| 179 | |
| 180 | |
| 181 | /* Adjusted exponent */ |
| 182 | ALWAYS_INLINE mpd_ssize_t |
| 183 | mpd_adjexp(const mpd_t *dec) |
| 184 | { |
| 185 | return (dec->exp + dec->digits) - 1; |
| 186 | } |
| 187 | |
| 188 | /* Etiny */ |
| 189 | ALWAYS_INLINE mpd_ssize_t |
| 190 | mpd_etiny(const mpd_context_t *ctx) |
| 191 | { |
| 192 | return ctx->emin - (ctx->prec - 1); |
| 193 | } |
| 194 | |
| 195 | /* Etop: used for folding down in IEEE clamping */ |
| 196 | ALWAYS_INLINE mpd_ssize_t |
| 197 | mpd_etop(const mpd_context_t *ctx) |
| 198 | { |
| 199 | return ctx->emax - (ctx->prec - 1); |
| 200 | } |
| 201 | |
| 202 | /* Most significant word */ |
| 203 | ALWAYS_INLINE mpd_uint_t |
| 204 | mpd_msword(const mpd_t *dec) |
| 205 | { |
| 206 | assert(dec->len > 0); |
| 207 | return dec->data[dec->len-1]; |
| 208 | } |
| 209 | |
| 210 | /* Most significant digit of a word */ |
| 211 | inline mpd_uint_t |
| 212 | mpd_msd(mpd_uint_t word) |
| 213 | { |
| 214 | int n; |
| 215 | |
| 216 | n = mpd_word_digits(word); |
| 217 | return word / mpd_pow10[n-1]; |
| 218 | } |
| 219 | |
| 220 | /* Least significant digit of a word */ |
| 221 | ALWAYS_INLINE mpd_uint_t |
| 222 | mpd_lsd(mpd_uint_t word) |
| 223 | { |
| 224 | return word % 10; |
| 225 | } |
| 226 | |
| 227 | /* Coefficient size needed to store 'digits' */ |
| 228 | ALWAYS_INLINE mpd_ssize_t |
| 229 | mpd_digits_to_size(mpd_ssize_t digits) |
| 230 | { |
| 231 | mpd_ssize_t q, r; |
| 232 | |
| 233 | _mpd_idiv_word(&q, &r, digits, MPD_RDIGITS); |
| 234 | return (r == 0) ? q : q+1; |
| 235 | } |
| 236 | |
| 237 | /* Number of digits in the exponent. Not defined for MPD_SSIZE_MIN. */ |
| 238 | inline int |
| 239 | mpd_exp_digits(mpd_ssize_t exp) |
| 240 | { |
| 241 | exp = (exp < 0) ? -exp : exp; |
| 242 | return mpd_word_digits(exp); |
| 243 | } |
| 244 | |
| 245 | /* Canonical */ |
| 246 | ALWAYS_INLINE int |
| 247 | mpd_iscanonical(const mpd_t *dec UNUSED) |
| 248 | { |
| 249 | return 1; |
| 250 | } |
| 251 | |
| 252 | /* Finite */ |
| 253 | ALWAYS_INLINE int |
| 254 | mpd_isfinite(const mpd_t *dec) |
| 255 | { |
| 256 | return !(dec->flags & MPD_SPECIAL); |
| 257 | } |
| 258 | |
| 259 | /* Infinite */ |
| 260 | ALWAYS_INLINE int |
| 261 | mpd_isinfinite(const mpd_t *dec) |
| 262 | { |
| 263 | return dec->flags & MPD_INF; |
| 264 | } |
| 265 | |
| 266 | /* NaN */ |
| 267 | ALWAYS_INLINE int |
| 268 | mpd_isnan(const mpd_t *dec) |
| 269 | { |
| 270 | return dec->flags & (MPD_NAN|MPD_SNAN); |
| 271 | } |
| 272 | |
| 273 | /* Negative */ |
| 274 | ALWAYS_INLINE int |
| 275 | mpd_isnegative(const mpd_t *dec) |
| 276 | { |
| 277 | return dec->flags & MPD_NEG; |
| 278 | } |
| 279 | |
| 280 | /* Positive */ |
| 281 | ALWAYS_INLINE int |
| 282 | mpd_ispositive(const mpd_t *dec) |
| 283 | { |
| 284 | return !(dec->flags & MPD_NEG); |
| 285 | } |
| 286 | |
| 287 | /* qNaN */ |
| 288 | ALWAYS_INLINE int |
| 289 | mpd_isqnan(const mpd_t *dec) |
| 290 | { |
| 291 | return dec->flags & MPD_NAN; |
| 292 | } |
| 293 | |
| 294 | /* Signed */ |
| 295 | ALWAYS_INLINE int |
| 296 | mpd_issigned(const mpd_t *dec) |
| 297 | { |
| 298 | return dec->flags & MPD_NEG; |
| 299 | } |
| 300 | |
| 301 | /* sNaN */ |
| 302 | ALWAYS_INLINE int |
| 303 | mpd_issnan(const mpd_t *dec) |
| 304 | { |
| 305 | return dec->flags & MPD_SNAN; |
| 306 | } |
| 307 | |
| 308 | /* Special */ |
| 309 | ALWAYS_INLINE int |
| 310 | mpd_isspecial(const mpd_t *dec) |
| 311 | { |
| 312 | return dec->flags & MPD_SPECIAL; |
| 313 | } |
| 314 | |
| 315 | /* Zero */ |
| 316 | ALWAYS_INLINE int |
| 317 | mpd_iszero(const mpd_t *dec) |
| 318 | { |
| 319 | return !mpd_isspecial(dec) && mpd_msword(dec) == 0; |
| 320 | } |
| 321 | |
| 322 | /* Test for zero when specials have been ruled out already */ |
| 323 | ALWAYS_INLINE int |
| 324 | mpd_iszerocoeff(const mpd_t *dec) |
| 325 | { |
| 326 | return mpd_msword(dec) == 0; |
| 327 | } |
| 328 | |
| 329 | /* Normal */ |
| 330 | inline int |
| 331 | mpd_isnormal(const mpd_t *dec, const mpd_context_t *ctx) |
| 332 | { |
| 333 | if (mpd_isspecial(dec)) return 0; |
| 334 | if (mpd_iszerocoeff(dec)) return 0; |
| 335 | |
| 336 | return mpd_adjexp(dec) >= ctx->emin; |
| 337 | } |
| 338 | |
| 339 | /* Subnormal */ |
| 340 | inline int |
| 341 | mpd_issubnormal(const mpd_t *dec, const mpd_context_t *ctx) |
| 342 | { |
| 343 | if (mpd_isspecial(dec)) return 0; |
| 344 | if (mpd_iszerocoeff(dec)) return 0; |
| 345 | |
| 346 | return mpd_adjexp(dec) < ctx->emin; |
| 347 | } |
| 348 | |
| 349 | /* Odd word */ |
| 350 | ALWAYS_INLINE int |
| 351 | mpd_isoddword(mpd_uint_t word) |
| 352 | { |
| 353 | return word & 1; |
| 354 | } |
| 355 | |
| 356 | /* Odd coefficient */ |
| 357 | ALWAYS_INLINE int |
| 358 | mpd_isoddcoeff(const mpd_t *dec) |
| 359 | { |
| 360 | return mpd_isoddword(dec->data[0]); |
| 361 | } |
| 362 | |
| 363 | /* 0 if dec is positive, 1 if dec is negative */ |
| 364 | ALWAYS_INLINE uint8_t |
| 365 | mpd_sign(const mpd_t *dec) |
| 366 | { |
| 367 | return dec->flags & MPD_NEG; |
| 368 | } |
| 369 | |
| 370 | /* 1 if dec is positive, -1 if dec is negative */ |
| 371 | ALWAYS_INLINE int |
| 372 | mpd_arith_sign(const mpd_t *dec) |
| 373 | { |
| 374 | return 1 - 2 * mpd_isnegative(dec); |
| 375 | } |
| 376 | |
| 377 | /* Radix */ |
| 378 | ALWAYS_INLINE long |
| 379 | mpd_radix(void) |
| 380 | { |
| 381 | return 10; |
| 382 | } |
| 383 | |
| 384 | /* Dynamic decimal */ |
| 385 | ALWAYS_INLINE int |
| 386 | mpd_isdynamic(mpd_t *dec) |
| 387 | { |
| 388 | return !(dec->flags & MPD_STATIC); |
| 389 | } |
| 390 | |
| 391 | /* Static decimal */ |
| 392 | ALWAYS_INLINE int |
| 393 | mpd_isstatic(mpd_t *dec) |
| 394 | { |
| 395 | return dec->flags & MPD_STATIC; |
| 396 | } |
| 397 | |
| 398 | /* Data of decimal is dynamic */ |
| 399 | ALWAYS_INLINE int |
| 400 | mpd_isdynamic_data(mpd_t *dec) |
| 401 | { |
| 402 | return !(dec->flags & MPD_DATAFLAGS); |
| 403 | } |
| 404 | |
| 405 | /* Data of decimal is static */ |
| 406 | ALWAYS_INLINE int |
| 407 | mpd_isstatic_data(mpd_t *dec) |
| 408 | { |
| 409 | return dec->flags & MPD_STATIC_DATA; |
| 410 | } |
| 411 | |
| 412 | /* Data of decimal is shared */ |
| 413 | ALWAYS_INLINE int |
| 414 | mpd_isshared_data(mpd_t *dec) |
| 415 | { |
| 416 | return dec->flags & MPD_SHARED_DATA; |
| 417 | } |
| 418 | |
| 419 | /* Data of decimal is const */ |
| 420 | ALWAYS_INLINE int |
| 421 | mpd_isconst_data(mpd_t *dec) |
| 422 | { |
| 423 | return dec->flags & MPD_CONST_DATA; |
| 424 | } |
| 425 | |
| 426 | |
| 427 | /******************************************************************************/ |
| 428 | /* Inline memory handling */ |
| 429 | /******************************************************************************/ |
| 430 | |
| 431 | /* Fill destination with zeros */ |
| 432 | ALWAYS_INLINE void |
| 433 | mpd_uint_zero(mpd_uint_t *dest, mpd_size_t len) |
| 434 | { |
| 435 | mpd_size_t i; |
| 436 | |
| 437 | for (i = 0; i < len; i++) { |
| 438 | dest[i] = 0; |
| 439 | } |
| 440 | } |
| 441 | |
| 442 | /* Free a decimal */ |
| 443 | ALWAYS_INLINE void |
| 444 | mpd_del(mpd_t *dec) |
| 445 | { |
| 446 | if (mpd_isdynamic_data(dec)) { |
| 447 | mpd_free(dec->data); |
| 448 | } |
| 449 | if (mpd_isdynamic(dec)) { |
| 450 | mpd_free(dec); |
| 451 | } |
| 452 | } |
| 453 | |
| 454 | /* |
| 455 | * Resize the coefficient. Existing data up to 'nwords' is left untouched. |
| 456 | * Return 1 on success, 0 otherwise. |
| 457 | * |
Stefan Krah | ec766a6 | 2012-04-10 23:11:54 +0200 | [diff] [blame] | 458 | * Input invariant: MPD_MINALLOC <= result->alloc. |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 459 | * |
Stefan Krah | 7b544ca | 2012-04-10 23:08:29 +0200 | [diff] [blame] | 460 | * Case nwords == result->alloc: |
| 461 | * 'result' is unchanged. Return 1. |
| 462 | * |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 463 | * Case nwords > result->alloc: |
| 464 | * Case realloc success: |
| 465 | * The value of 'result' does not change. Return 1. |
| 466 | * Case realloc failure: |
| 467 | * 'result' is NaN, status is updated with MPD_Malloc_error. Return 0. |
| 468 | * |
| 469 | * Case nwords < result->alloc: |
Stefan Krah | 7b544ca | 2012-04-10 23:08:29 +0200 | [diff] [blame] | 470 | * Case is_static_data or realloc failure [1]: |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 471 | * 'result' is unchanged. Return 1. |
| 472 | * Case realloc success: |
| 473 | * The value of result is undefined (expected). Return 1. |
| 474 | * |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 475 | * |
| 476 | * [1] In that case the old (now oversized) area is still valid. |
| 477 | */ |
| 478 | ALWAYS_INLINE int |
| 479 | mpd_qresize(mpd_t *result, mpd_ssize_t nwords, uint32_t *status) |
| 480 | { |
| 481 | assert(!mpd_isconst_data(result)); /* illegal operation for a const */ |
| 482 | assert(!mpd_isshared_data(result)); /* illegal operation for a shared */ |
Stefan Krah | f69aef7 | 2012-04-09 20:47:57 +0200 | [diff] [blame] | 483 | assert(MPD_MINALLOC <= result->alloc); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 484 | |
Stefan Krah | f69aef7 | 2012-04-09 20:47:57 +0200 | [diff] [blame] | 485 | nwords = (nwords <= MPD_MINALLOC) ? MPD_MINALLOC : nwords; |
| 486 | if (nwords == result->alloc) { |
| 487 | return 1; |
| 488 | } |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 489 | if (mpd_isstatic_data(result)) { |
| 490 | if (nwords > result->alloc) { |
| 491 | return mpd_switch_to_dyn(result, nwords, status); |
| 492 | } |
Stefan Krah | f69aef7 | 2012-04-09 20:47:57 +0200 | [diff] [blame] | 493 | return 1; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 494 | } |
| 495 | |
Stefan Krah | f69aef7 | 2012-04-09 20:47:57 +0200 | [diff] [blame] | 496 | return mpd_realloc_dyn(result, nwords, status); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 497 | } |
| 498 | |
| 499 | /* Same as mpd_qresize, but the complete coefficient (including the old |
| 500 | * memory area!) is initialized to zero. */ |
| 501 | ALWAYS_INLINE int |
| 502 | mpd_qresize_zero(mpd_t *result, mpd_ssize_t nwords, uint32_t *status) |
| 503 | { |
| 504 | assert(!mpd_isconst_data(result)); /* illegal operation for a const */ |
| 505 | assert(!mpd_isshared_data(result)); /* illegal operation for a shared */ |
Stefan Krah | f69aef7 | 2012-04-09 20:47:57 +0200 | [diff] [blame] | 506 | assert(MPD_MINALLOC <= result->alloc); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 507 | |
Stefan Krah | f69aef7 | 2012-04-09 20:47:57 +0200 | [diff] [blame] | 508 | nwords = (nwords <= MPD_MINALLOC) ? MPD_MINALLOC : nwords; |
| 509 | if (nwords != result->alloc) { |
| 510 | if (mpd_isstatic_data(result)) { |
| 511 | if (nwords > result->alloc) { |
| 512 | return mpd_switch_to_dyn_zero(result, nwords, status); |
| 513 | } |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 514 | } |
Stefan Krah | f69aef7 | 2012-04-09 20:47:57 +0200 | [diff] [blame] | 515 | else if (!mpd_realloc_dyn(result, nwords, status)) { |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 516 | return 0; |
| 517 | } |
| 518 | } |
| 519 | |
| 520 | mpd_uint_zero(result->data, nwords); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 521 | return 1; |
| 522 | } |
| 523 | |
| 524 | /* |
| 525 | * Reduce memory size for the coefficient to MPD_MINALLOC. In theory, |
| 526 | * realloc may fail even when reducing the memory size. But in that case |
| 527 | * the old memory area is always big enough, so checking for MPD_Malloc_error |
| 528 | * is not imperative. |
| 529 | */ |
| 530 | ALWAYS_INLINE void |
| 531 | mpd_minalloc(mpd_t *result) |
| 532 | { |
| 533 | assert(!mpd_isconst_data(result)); /* illegal operation for a const */ |
| 534 | assert(!mpd_isshared_data(result)); /* illegal operation for a shared */ |
| 535 | |
| 536 | if (!mpd_isstatic_data(result) && result->alloc > MPD_MINALLOC) { |
| 537 | uint8_t err = 0; |
| 538 | result->data = mpd_realloc(result->data, MPD_MINALLOC, |
| 539 | sizeof *result->data, &err); |
| 540 | if (!err) { |
| 541 | result->alloc = MPD_MINALLOC; |
| 542 | } |
| 543 | } |
| 544 | } |
| 545 | |
| 546 | int |
| 547 | mpd_resize(mpd_t *result, mpd_ssize_t nwords, mpd_context_t *ctx) |
| 548 | { |
| 549 | uint32_t status = 0; |
| 550 | if (!mpd_qresize(result, nwords, &status)) { |
| 551 | mpd_addstatus_raise(ctx, status); |
| 552 | return 0; |
| 553 | } |
| 554 | return 1; |
| 555 | } |
| 556 | |
| 557 | int |
| 558 | mpd_resize_zero(mpd_t *result, mpd_ssize_t nwords, mpd_context_t *ctx) |
| 559 | { |
| 560 | uint32_t status = 0; |
| 561 | if (!mpd_qresize_zero(result, nwords, &status)) { |
| 562 | mpd_addstatus_raise(ctx, status); |
| 563 | return 0; |
| 564 | } |
| 565 | return 1; |
| 566 | } |
| 567 | |
| 568 | |
| 569 | /******************************************************************************/ |
| 570 | /* Set attributes of a decimal */ |
| 571 | /******************************************************************************/ |
| 572 | |
| 573 | /* Set digits. Assumption: result->len is initialized and > 0. */ |
| 574 | inline void |
| 575 | mpd_setdigits(mpd_t *result) |
| 576 | { |
| 577 | mpd_ssize_t wdigits = mpd_word_digits(mpd_msword(result)); |
| 578 | result->digits = wdigits + (result->len-1) * MPD_RDIGITS; |
| 579 | } |
| 580 | |
| 581 | /* Set sign */ |
| 582 | ALWAYS_INLINE void |
| 583 | mpd_set_sign(mpd_t *result, uint8_t sign) |
| 584 | { |
| 585 | result->flags &= ~MPD_NEG; |
| 586 | result->flags |= sign; |
| 587 | } |
| 588 | |
| 589 | /* Copy sign from another decimal */ |
| 590 | ALWAYS_INLINE void |
| 591 | mpd_signcpy(mpd_t *result, mpd_t *a) |
| 592 | { |
| 593 | uint8_t sign = a->flags&MPD_NEG; |
| 594 | |
| 595 | result->flags &= ~MPD_NEG; |
| 596 | result->flags |= sign; |
| 597 | } |
| 598 | |
| 599 | /* Set infinity */ |
| 600 | ALWAYS_INLINE void |
| 601 | mpd_set_infinity(mpd_t *result) |
| 602 | { |
| 603 | result->flags &= ~MPD_SPECIAL; |
| 604 | result->flags |= MPD_INF; |
| 605 | } |
| 606 | |
| 607 | /* Set qNaN */ |
| 608 | ALWAYS_INLINE void |
| 609 | mpd_set_qnan(mpd_t *result) |
| 610 | { |
| 611 | result->flags &= ~MPD_SPECIAL; |
| 612 | result->flags |= MPD_NAN; |
| 613 | } |
| 614 | |
| 615 | /* Set sNaN */ |
| 616 | ALWAYS_INLINE void |
| 617 | mpd_set_snan(mpd_t *result) |
| 618 | { |
| 619 | result->flags &= ~MPD_SPECIAL; |
| 620 | result->flags |= MPD_SNAN; |
| 621 | } |
| 622 | |
| 623 | /* Set to negative */ |
| 624 | ALWAYS_INLINE void |
| 625 | mpd_set_negative(mpd_t *result) |
| 626 | { |
| 627 | result->flags |= MPD_NEG; |
| 628 | } |
| 629 | |
| 630 | /* Set to positive */ |
| 631 | ALWAYS_INLINE void |
| 632 | mpd_set_positive(mpd_t *result) |
| 633 | { |
| 634 | result->flags &= ~MPD_NEG; |
| 635 | } |
| 636 | |
| 637 | /* Set to dynamic */ |
| 638 | ALWAYS_INLINE void |
| 639 | mpd_set_dynamic(mpd_t *result) |
| 640 | { |
| 641 | result->flags &= ~MPD_STATIC; |
| 642 | } |
| 643 | |
| 644 | /* Set to static */ |
| 645 | ALWAYS_INLINE void |
| 646 | mpd_set_static(mpd_t *result) |
| 647 | { |
| 648 | result->flags |= MPD_STATIC; |
| 649 | } |
| 650 | |
| 651 | /* Set data to dynamic */ |
| 652 | ALWAYS_INLINE void |
| 653 | mpd_set_dynamic_data(mpd_t *result) |
| 654 | { |
| 655 | result->flags &= ~MPD_DATAFLAGS; |
| 656 | } |
| 657 | |
| 658 | /* Set data to static */ |
| 659 | ALWAYS_INLINE void |
| 660 | mpd_set_static_data(mpd_t *result) |
| 661 | { |
| 662 | result->flags &= ~MPD_DATAFLAGS; |
| 663 | result->flags |= MPD_STATIC_DATA; |
| 664 | } |
| 665 | |
| 666 | /* Set data to shared */ |
| 667 | ALWAYS_INLINE void |
| 668 | mpd_set_shared_data(mpd_t *result) |
| 669 | { |
| 670 | result->flags &= ~MPD_DATAFLAGS; |
| 671 | result->flags |= MPD_SHARED_DATA; |
| 672 | } |
| 673 | |
| 674 | /* Set data to const */ |
| 675 | ALWAYS_INLINE void |
| 676 | mpd_set_const_data(mpd_t *result) |
| 677 | { |
| 678 | result->flags &= ~MPD_DATAFLAGS; |
| 679 | result->flags |= MPD_CONST_DATA; |
| 680 | } |
| 681 | |
| 682 | /* Clear flags, preserving memory attributes. */ |
| 683 | ALWAYS_INLINE void |
| 684 | mpd_clear_flags(mpd_t *result) |
| 685 | { |
| 686 | result->flags &= (MPD_STATIC|MPD_DATAFLAGS); |
| 687 | } |
| 688 | |
| 689 | /* Set flags, preserving memory attributes. */ |
| 690 | ALWAYS_INLINE void |
| 691 | mpd_set_flags(mpd_t *result, uint8_t flags) |
| 692 | { |
| 693 | result->flags &= (MPD_STATIC|MPD_DATAFLAGS); |
| 694 | result->flags |= flags; |
| 695 | } |
| 696 | |
| 697 | /* Copy flags, preserving memory attributes of result. */ |
| 698 | ALWAYS_INLINE void |
| 699 | mpd_copy_flags(mpd_t *result, const mpd_t *a) |
| 700 | { |
| 701 | uint8_t aflags = a->flags; |
| 702 | result->flags &= (MPD_STATIC|MPD_DATAFLAGS); |
| 703 | result->flags |= (aflags & ~(MPD_STATIC|MPD_DATAFLAGS)); |
| 704 | } |
| 705 | |
| 706 | /* Initialize a workcontext from ctx. Set traps, flags and newtrap to 0. */ |
| 707 | static inline void |
| 708 | mpd_workcontext(mpd_context_t *workctx, const mpd_context_t *ctx) |
| 709 | { |
| 710 | workctx->prec = ctx->prec; |
| 711 | workctx->emax = ctx->emax; |
| 712 | workctx->emin = ctx->emin; |
| 713 | workctx->round = ctx->round; |
| 714 | workctx->traps = 0; |
| 715 | workctx->status = 0; |
| 716 | workctx->newtrap = 0; |
| 717 | workctx->clamp = ctx->clamp; |
| 718 | workctx->allcr = ctx->allcr; |
| 719 | } |
| 720 | |
| 721 | |
| 722 | /******************************************************************************/ |
| 723 | /* Getting and setting parts of decimals */ |
| 724 | /******************************************************************************/ |
| 725 | |
| 726 | /* Flip the sign of a decimal */ |
| 727 | static inline void |
| 728 | _mpd_negate(mpd_t *dec) |
| 729 | { |
| 730 | dec->flags ^= MPD_NEG; |
| 731 | } |
| 732 | |
| 733 | /* Set coefficient to zero */ |
| 734 | void |
| 735 | mpd_zerocoeff(mpd_t *result) |
| 736 | { |
| 737 | mpd_minalloc(result); |
| 738 | result->digits = 1; |
| 739 | result->len = 1; |
| 740 | result->data[0] = 0; |
| 741 | } |
| 742 | |
| 743 | /* Set the coefficient to all nines. */ |
| 744 | void |
| 745 | mpd_qmaxcoeff(mpd_t *result, const mpd_context_t *ctx, uint32_t *status) |
| 746 | { |
| 747 | mpd_ssize_t len, r; |
| 748 | |
| 749 | _mpd_idiv_word(&len, &r, ctx->prec, MPD_RDIGITS); |
| 750 | len = (r == 0) ? len : len+1; |
| 751 | |
| 752 | if (!mpd_qresize(result, len, status)) { |
| 753 | return; |
| 754 | } |
| 755 | |
| 756 | result->len = len; |
| 757 | result->digits = ctx->prec; |
| 758 | |
| 759 | --len; |
| 760 | if (r > 0) { |
| 761 | result->data[len--] = mpd_pow10[r]-1; |
| 762 | } |
| 763 | for (; len >= 0; --len) { |
| 764 | result->data[len] = MPD_RADIX-1; |
| 765 | } |
| 766 | } |
| 767 | |
| 768 | /* |
| 769 | * Cut off the most significant digits so that the rest fits in ctx->prec. |
| 770 | * Cannot fail. |
| 771 | */ |
| 772 | static void |
| 773 | _mpd_cap(mpd_t *result, const mpd_context_t *ctx) |
| 774 | { |
| 775 | uint32_t dummy; |
| 776 | mpd_ssize_t len, r; |
| 777 | |
| 778 | if (result->len > 0 && result->digits > ctx->prec) { |
| 779 | _mpd_idiv_word(&len, &r, ctx->prec, MPD_RDIGITS); |
| 780 | len = (r == 0) ? len : len+1; |
| 781 | |
| 782 | if (r != 0) { |
| 783 | result->data[len-1] %= mpd_pow10[r]; |
| 784 | } |
| 785 | |
| 786 | len = _mpd_real_size(result->data, len); |
| 787 | /* resize to fewer words cannot fail */ |
| 788 | mpd_qresize(result, len, &dummy); |
| 789 | result->len = len; |
| 790 | mpd_setdigits(result); |
| 791 | } |
| 792 | if (mpd_iszero(result)) { |
| 793 | _settriple(result, mpd_sign(result), 0, result->exp); |
| 794 | } |
| 795 | } |
| 796 | |
| 797 | /* |
| 798 | * Cut off the most significant digits of a NaN payload so that the rest |
| 799 | * fits in ctx->prec - ctx->clamp. Cannot fail. |
| 800 | */ |
| 801 | static void |
| 802 | _mpd_fix_nan(mpd_t *result, const mpd_context_t *ctx) |
| 803 | { |
| 804 | uint32_t dummy; |
| 805 | mpd_ssize_t prec; |
| 806 | mpd_ssize_t len, r; |
| 807 | |
| 808 | prec = ctx->prec - ctx->clamp; |
| 809 | if (result->len > 0 && result->digits > prec) { |
| 810 | if (prec == 0) { |
| 811 | mpd_minalloc(result); |
| 812 | result->len = result->digits = 0; |
| 813 | } |
| 814 | else { |
| 815 | _mpd_idiv_word(&len, &r, prec, MPD_RDIGITS); |
| 816 | len = (r == 0) ? len : len+1; |
| 817 | |
| 818 | if (r != 0) { |
| 819 | result->data[len-1] %= mpd_pow10[r]; |
| 820 | } |
| 821 | |
| 822 | len = _mpd_real_size(result->data, len); |
| 823 | /* resize to fewer words cannot fail */ |
| 824 | mpd_qresize(result, len, &dummy); |
| 825 | result->len = len; |
| 826 | mpd_setdigits(result); |
| 827 | if (mpd_iszerocoeff(result)) { |
| 828 | /* NaN0 is not a valid representation */ |
| 829 | result->len = result->digits = 0; |
| 830 | } |
| 831 | } |
| 832 | } |
| 833 | } |
| 834 | |
| 835 | /* |
| 836 | * Get n most significant digits from a decimal, where 0 < n <= MPD_UINT_DIGITS. |
| 837 | * Assumes MPD_UINT_DIGITS == MPD_RDIGITS+1, which is true for 32 and 64 bit |
| 838 | * machines. |
| 839 | * |
| 840 | * The result of the operation will be in lo. If the operation is impossible, |
| 841 | * hi will be nonzero. This is used to indicate an error. |
| 842 | */ |
| 843 | static inline void |
| 844 | _mpd_get_msdigits(mpd_uint_t *hi, mpd_uint_t *lo, const mpd_t *dec, |
| 845 | unsigned int n) |
| 846 | { |
| 847 | mpd_uint_t r, tmp; |
| 848 | |
| 849 | assert(0 < n && n <= MPD_RDIGITS+1); |
| 850 | |
| 851 | _mpd_div_word(&tmp, &r, dec->digits, MPD_RDIGITS); |
| 852 | r = (r == 0) ? MPD_RDIGITS : r; /* digits in the most significant word */ |
| 853 | |
| 854 | *hi = 0; |
| 855 | *lo = dec->data[dec->len-1]; |
| 856 | if (n <= r) { |
| 857 | *lo /= mpd_pow10[r-n]; |
| 858 | } |
| 859 | else if (dec->len > 1) { |
| 860 | /* at this point 1 <= r < n <= MPD_RDIGITS+1 */ |
| 861 | _mpd_mul_words(hi, lo, *lo, mpd_pow10[n-r]); |
| 862 | tmp = dec->data[dec->len-2] / mpd_pow10[MPD_RDIGITS-(n-r)]; |
| 863 | *lo = *lo + tmp; |
| 864 | if (*lo < tmp) (*hi)++; |
| 865 | } |
| 866 | } |
| 867 | |
| 868 | |
| 869 | /******************************************************************************/ |
| 870 | /* Gathering information about a decimal */ |
| 871 | /******************************************************************************/ |
| 872 | |
| 873 | /* The real size of the coefficient without leading zero words. */ |
| 874 | static inline mpd_ssize_t |
| 875 | _mpd_real_size(mpd_uint_t *data, mpd_ssize_t size) |
| 876 | { |
| 877 | while (size > 1 && data[size-1] == 0) { |
| 878 | size--; |
| 879 | } |
| 880 | |
| 881 | return size; |
| 882 | } |
| 883 | |
| 884 | /* Return number of trailing zeros. No errors are possible. */ |
| 885 | mpd_ssize_t |
| 886 | mpd_trail_zeros(const mpd_t *dec) |
| 887 | { |
| 888 | mpd_uint_t word; |
| 889 | mpd_ssize_t i, tz = 0; |
| 890 | |
| 891 | for (i=0; i < dec->len; ++i) { |
| 892 | if (dec->data[i] != 0) { |
| 893 | word = dec->data[i]; |
| 894 | tz = i * MPD_RDIGITS; |
| 895 | while (word % 10 == 0) { |
| 896 | word /= 10; |
| 897 | tz++; |
| 898 | } |
| 899 | break; |
| 900 | } |
| 901 | } |
| 902 | |
| 903 | return tz; |
| 904 | } |
| 905 | |
| 906 | /* Integer: Undefined for specials */ |
| 907 | static int |
| 908 | _mpd_isint(const mpd_t *dec) |
| 909 | { |
| 910 | mpd_ssize_t tz; |
| 911 | |
| 912 | if (mpd_iszerocoeff(dec)) { |
| 913 | return 1; |
| 914 | } |
| 915 | |
| 916 | tz = mpd_trail_zeros(dec); |
| 917 | return (dec->exp + tz >= 0); |
| 918 | } |
| 919 | |
| 920 | /* Integer */ |
| 921 | int |
| 922 | mpd_isinteger(const mpd_t *dec) |
| 923 | { |
| 924 | if (mpd_isspecial(dec)) { |
| 925 | return 0; |
| 926 | } |
| 927 | return _mpd_isint(dec); |
| 928 | } |
| 929 | |
| 930 | /* Word is a power of 10 */ |
| 931 | static int |
| 932 | mpd_word_ispow10(mpd_uint_t word) |
| 933 | { |
| 934 | int n; |
| 935 | |
| 936 | n = mpd_word_digits(word); |
| 937 | if (word == mpd_pow10[n-1]) { |
| 938 | return 1; |
| 939 | } |
| 940 | |
| 941 | return 0; |
| 942 | } |
| 943 | |
| 944 | /* Coefficient is a power of 10 */ |
| 945 | static int |
| 946 | mpd_coeff_ispow10(const mpd_t *dec) |
| 947 | { |
| 948 | if (mpd_word_ispow10(mpd_msword(dec))) { |
| 949 | if (_mpd_isallzero(dec->data, dec->len-1)) { |
| 950 | return 1; |
| 951 | } |
| 952 | } |
| 953 | |
| 954 | return 0; |
| 955 | } |
| 956 | |
| 957 | /* All digits of a word are nines */ |
| 958 | static int |
| 959 | mpd_word_isallnine(mpd_uint_t word) |
| 960 | { |
| 961 | int n; |
| 962 | |
| 963 | n = mpd_word_digits(word); |
| 964 | if (word == mpd_pow10[n]-1) { |
| 965 | return 1; |
| 966 | } |
| 967 | |
| 968 | return 0; |
| 969 | } |
| 970 | |
| 971 | /* All digits of the coefficient are nines */ |
| 972 | static int |
| 973 | mpd_coeff_isallnine(const mpd_t *dec) |
| 974 | { |
| 975 | if (mpd_word_isallnine(mpd_msword(dec))) { |
| 976 | if (_mpd_isallnine(dec->data, dec->len-1)) { |
| 977 | return 1; |
| 978 | } |
| 979 | } |
| 980 | |
| 981 | return 0; |
| 982 | } |
| 983 | |
| 984 | /* Odd decimal: Undefined for non-integers! */ |
| 985 | int |
| 986 | mpd_isodd(const mpd_t *dec) |
| 987 | { |
| 988 | mpd_uint_t q, r; |
| 989 | assert(mpd_isinteger(dec)); |
| 990 | if (mpd_iszerocoeff(dec)) return 0; |
| 991 | if (dec->exp < 0) { |
| 992 | _mpd_div_word(&q, &r, -dec->exp, MPD_RDIGITS); |
| 993 | q = dec->data[q] / mpd_pow10[r]; |
| 994 | return mpd_isoddword(q); |
| 995 | } |
| 996 | return dec->exp == 0 && mpd_isoddword(dec->data[0]); |
| 997 | } |
| 998 | |
| 999 | /* Even: Undefined for non-integers! */ |
| 1000 | int |
| 1001 | mpd_iseven(const mpd_t *dec) |
| 1002 | { |
| 1003 | return !mpd_isodd(dec); |
| 1004 | } |
| 1005 | |
| 1006 | /******************************************************************************/ |
| 1007 | /* Getting and setting decimals */ |
| 1008 | /******************************************************************************/ |
| 1009 | |
| 1010 | /* Internal function: Set a static decimal from a triple, no error checking. */ |
| 1011 | static void |
| 1012 | _ssettriple(mpd_t *result, uint8_t sign, mpd_uint_t a, mpd_ssize_t exp) |
| 1013 | { |
| 1014 | mpd_set_flags(result, sign); |
| 1015 | result->exp = exp; |
| 1016 | _mpd_div_word(&result->data[1], &result->data[0], a, MPD_RADIX); |
| 1017 | result->len = (result->data[1] == 0) ? 1 : 2; |
| 1018 | mpd_setdigits(result); |
| 1019 | } |
| 1020 | |
| 1021 | /* Internal function: Set a decimal from a triple, no error checking. */ |
| 1022 | static void |
| 1023 | _settriple(mpd_t *result, uint8_t sign, mpd_uint_t a, mpd_ssize_t exp) |
| 1024 | { |
| 1025 | mpd_minalloc(result); |
| 1026 | mpd_set_flags(result, sign); |
| 1027 | result->exp = exp; |
| 1028 | _mpd_div_word(&result->data[1], &result->data[0], a, MPD_RADIX); |
| 1029 | result->len = (result->data[1] == 0) ? 1 : 2; |
| 1030 | mpd_setdigits(result); |
| 1031 | } |
| 1032 | |
| 1033 | /* Set a special number from a triple */ |
| 1034 | void |
| 1035 | mpd_setspecial(mpd_t *result, uint8_t sign, uint8_t type) |
| 1036 | { |
| 1037 | mpd_minalloc(result); |
| 1038 | result->flags &= ~(MPD_NEG|MPD_SPECIAL); |
| 1039 | result->flags |= (sign|type); |
| 1040 | result->exp = result->digits = result->len = 0; |
| 1041 | } |
| 1042 | |
| 1043 | /* Set result of NaN with an error status */ |
| 1044 | void |
| 1045 | mpd_seterror(mpd_t *result, uint32_t flags, uint32_t *status) |
| 1046 | { |
| 1047 | mpd_minalloc(result); |
| 1048 | mpd_set_qnan(result); |
| 1049 | mpd_set_positive(result); |
| 1050 | result->exp = result->digits = result->len = 0; |
| 1051 | *status |= flags; |
| 1052 | } |
| 1053 | |
| 1054 | /* quietly set a static decimal from an mpd_ssize_t */ |
| 1055 | void |
| 1056 | mpd_qsset_ssize(mpd_t *result, mpd_ssize_t a, const mpd_context_t *ctx, |
| 1057 | uint32_t *status) |
| 1058 | { |
| 1059 | mpd_uint_t u; |
| 1060 | uint8_t sign = MPD_POS; |
| 1061 | |
| 1062 | if (a < 0) { |
| 1063 | if (a == MPD_SSIZE_MIN) { |
| 1064 | u = (mpd_uint_t)MPD_SSIZE_MAX + |
| 1065 | (-(MPD_SSIZE_MIN+MPD_SSIZE_MAX)); |
| 1066 | } |
| 1067 | else { |
| 1068 | u = -a; |
| 1069 | } |
| 1070 | sign = MPD_NEG; |
| 1071 | } |
| 1072 | else { |
| 1073 | u = a; |
| 1074 | } |
| 1075 | _ssettriple(result, sign, u, 0); |
| 1076 | mpd_qfinalize(result, ctx, status); |
| 1077 | } |
| 1078 | |
| 1079 | /* quietly set a static decimal from an mpd_uint_t */ |
| 1080 | void |
| 1081 | mpd_qsset_uint(mpd_t *result, mpd_uint_t a, const mpd_context_t *ctx, |
| 1082 | uint32_t *status) |
| 1083 | { |
| 1084 | _ssettriple(result, MPD_POS, a, 0); |
| 1085 | mpd_qfinalize(result, ctx, status); |
| 1086 | } |
| 1087 | |
| 1088 | /* quietly set a static decimal from an int32_t */ |
| 1089 | void |
| 1090 | mpd_qsset_i32(mpd_t *result, int32_t a, const mpd_context_t *ctx, |
| 1091 | uint32_t *status) |
| 1092 | { |
| 1093 | mpd_qsset_ssize(result, a, ctx, status); |
| 1094 | } |
| 1095 | |
| 1096 | /* quietly set a static decimal from a uint32_t */ |
| 1097 | void |
| 1098 | mpd_qsset_u32(mpd_t *result, uint32_t a, const mpd_context_t *ctx, |
| 1099 | uint32_t *status) |
| 1100 | { |
| 1101 | mpd_qsset_uint(result, a, ctx, status); |
| 1102 | } |
| 1103 | |
| 1104 | #ifdef CONFIG_64 |
| 1105 | /* quietly set a static decimal from an int64_t */ |
| 1106 | void |
| 1107 | mpd_qsset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx, |
| 1108 | uint32_t *status) |
| 1109 | { |
| 1110 | mpd_qsset_ssize(result, a, ctx, status); |
| 1111 | } |
| 1112 | |
| 1113 | /* quietly set a static decimal from a uint64_t */ |
| 1114 | void |
| 1115 | mpd_qsset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx, |
| 1116 | uint32_t *status) |
| 1117 | { |
| 1118 | mpd_qsset_uint(result, a, ctx, status); |
| 1119 | } |
| 1120 | #endif |
| 1121 | |
| 1122 | /* quietly set a decimal from an mpd_ssize_t */ |
| 1123 | void |
| 1124 | mpd_qset_ssize(mpd_t *result, mpd_ssize_t a, const mpd_context_t *ctx, |
| 1125 | uint32_t *status) |
| 1126 | { |
| 1127 | mpd_minalloc(result); |
| 1128 | mpd_qsset_ssize(result, a, ctx, status); |
| 1129 | } |
| 1130 | |
| 1131 | /* quietly set a decimal from an mpd_uint_t */ |
| 1132 | void |
| 1133 | mpd_qset_uint(mpd_t *result, mpd_uint_t a, const mpd_context_t *ctx, |
| 1134 | uint32_t *status) |
| 1135 | { |
| 1136 | _settriple(result, MPD_POS, a, 0); |
| 1137 | mpd_qfinalize(result, ctx, status); |
| 1138 | } |
| 1139 | |
| 1140 | /* quietly set a decimal from an int32_t */ |
| 1141 | void |
| 1142 | mpd_qset_i32(mpd_t *result, int32_t a, const mpd_context_t *ctx, |
| 1143 | uint32_t *status) |
| 1144 | { |
| 1145 | mpd_qset_ssize(result, a, ctx, status); |
| 1146 | } |
| 1147 | |
| 1148 | /* quietly set a decimal from a uint32_t */ |
| 1149 | void |
| 1150 | mpd_qset_u32(mpd_t *result, uint32_t a, const mpd_context_t *ctx, |
| 1151 | uint32_t *status) |
| 1152 | { |
| 1153 | mpd_qset_uint(result, a, ctx, status); |
| 1154 | } |
| 1155 | |
| 1156 | #if defined(CONFIG_32) && !defined(LEGACY_COMPILER) |
| 1157 | /* set a decimal from a uint64_t */ |
| 1158 | static void |
| 1159 | _c32setu64(mpd_t *result, uint64_t u, uint8_t sign, uint32_t *status) |
| 1160 | { |
| 1161 | mpd_uint_t w[3]; |
| 1162 | uint64_t q; |
| 1163 | int i, len; |
| 1164 | |
| 1165 | len = 0; |
| 1166 | do { |
| 1167 | q = u / MPD_RADIX; |
| 1168 | w[len] = (mpd_uint_t)(u - q * MPD_RADIX); |
| 1169 | u = q; len++; |
| 1170 | } while (u != 0); |
| 1171 | |
| 1172 | if (!mpd_qresize(result, len, status)) { |
| 1173 | return; |
| 1174 | } |
| 1175 | for (i = 0; i < len; i++) { |
| 1176 | result->data[i] = w[i]; |
| 1177 | } |
| 1178 | |
| 1179 | mpd_set_sign(result, sign); |
| 1180 | result->exp = 0; |
| 1181 | result->len = len; |
| 1182 | mpd_setdigits(result); |
| 1183 | } |
| 1184 | |
| 1185 | static void |
| 1186 | _c32_qset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx, |
| 1187 | uint32_t *status) |
| 1188 | { |
| 1189 | _c32setu64(result, a, MPD_POS, status); |
| 1190 | mpd_qfinalize(result, ctx, status); |
| 1191 | } |
| 1192 | |
| 1193 | /* set a decimal from an int64_t */ |
| 1194 | static void |
| 1195 | _c32_qset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx, |
| 1196 | uint32_t *status) |
| 1197 | { |
| 1198 | uint64_t u; |
| 1199 | uint8_t sign = MPD_POS; |
| 1200 | |
| 1201 | if (a < 0) { |
| 1202 | if (a == INT64_MIN) { |
| 1203 | u = (uint64_t)INT64_MAX + (-(INT64_MIN+INT64_MAX)); |
| 1204 | } |
| 1205 | else { |
| 1206 | u = -a; |
| 1207 | } |
| 1208 | sign = MPD_NEG; |
| 1209 | } |
| 1210 | else { |
| 1211 | u = a; |
| 1212 | } |
| 1213 | _c32setu64(result, u, sign, status); |
| 1214 | mpd_qfinalize(result, ctx, status); |
| 1215 | } |
| 1216 | #endif /* CONFIG_32 && !LEGACY_COMPILER */ |
| 1217 | |
| 1218 | #ifndef LEGACY_COMPILER |
| 1219 | /* quietly set a decimal from an int64_t */ |
| 1220 | void |
| 1221 | mpd_qset_i64(mpd_t *result, int64_t a, const mpd_context_t *ctx, |
| 1222 | uint32_t *status) |
| 1223 | { |
| 1224 | #ifdef CONFIG_64 |
| 1225 | mpd_qset_ssize(result, a, ctx, status); |
| 1226 | #else |
| 1227 | _c32_qset_i64(result, a, ctx, status); |
| 1228 | #endif |
| 1229 | } |
| 1230 | |
| 1231 | /* quietly set a decimal from a uint64_t */ |
| 1232 | void |
| 1233 | mpd_qset_u64(mpd_t *result, uint64_t a, const mpd_context_t *ctx, |
| 1234 | uint32_t *status) |
| 1235 | { |
| 1236 | #ifdef CONFIG_64 |
| 1237 | mpd_qset_uint(result, a, ctx, status); |
| 1238 | #else |
| 1239 | _c32_qset_u64(result, a, ctx, status); |
| 1240 | #endif |
| 1241 | } |
| 1242 | #endif /* !LEGACY_COMPILER */ |
| 1243 | |
| 1244 | |
| 1245 | /* |
| 1246 | * Quietly get an mpd_uint_t from a decimal. Assumes |
| 1247 | * MPD_UINT_DIGITS == MPD_RDIGITS+1, which is true for |
| 1248 | * 32 and 64 bit machines. |
| 1249 | * |
| 1250 | * If the operation is impossible, MPD_Invalid_operation is set. |
| 1251 | */ |
| 1252 | static mpd_uint_t |
| 1253 | _mpd_qget_uint(int use_sign, const mpd_t *a, uint32_t *status) |
| 1254 | { |
| 1255 | mpd_t tmp; |
| 1256 | mpd_uint_t tmp_data[2]; |
| 1257 | mpd_uint_t lo, hi; |
| 1258 | |
| 1259 | if (mpd_isspecial(a)) { |
| 1260 | *status |= MPD_Invalid_operation; |
| 1261 | return MPD_UINT_MAX; |
| 1262 | } |
| 1263 | if (mpd_iszero(a)) { |
| 1264 | return 0; |
| 1265 | } |
| 1266 | if (use_sign && mpd_isnegative(a)) { |
| 1267 | *status |= MPD_Invalid_operation; |
| 1268 | return MPD_UINT_MAX; |
| 1269 | } |
| 1270 | |
| 1271 | if (a->digits+a->exp > MPD_RDIGITS+1) { |
| 1272 | *status |= MPD_Invalid_operation; |
| 1273 | return MPD_UINT_MAX; |
| 1274 | } |
| 1275 | |
| 1276 | if (a->exp < 0) { |
| 1277 | if (!_mpd_isint(a)) { |
| 1278 | *status |= MPD_Invalid_operation; |
| 1279 | return MPD_UINT_MAX; |
| 1280 | } |
| 1281 | /* At this point a->digits+a->exp <= MPD_RDIGITS+1, |
| 1282 | * so the shift fits. */ |
| 1283 | tmp.data = tmp_data; |
Stefan Krah | 140893c | 2012-04-18 17:48:34 +0200 | [diff] [blame] | 1284 | tmp.flags = MPD_STATIC|MPD_STATIC_DATA; |
| 1285 | tmp.alloc = 2; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 1286 | mpd_qsshiftr(&tmp, a, -a->exp); |
| 1287 | tmp.exp = 0; |
| 1288 | a = &tmp; |
| 1289 | } |
| 1290 | |
| 1291 | _mpd_get_msdigits(&hi, &lo, a, MPD_RDIGITS+1); |
| 1292 | if (hi) { |
| 1293 | *status |= MPD_Invalid_operation; |
| 1294 | return MPD_UINT_MAX; |
| 1295 | } |
| 1296 | |
| 1297 | if (a->exp > 0) { |
| 1298 | _mpd_mul_words(&hi, &lo, lo, mpd_pow10[a->exp]); |
| 1299 | if (hi) { |
| 1300 | *status |= MPD_Invalid_operation; |
| 1301 | return MPD_UINT_MAX; |
| 1302 | } |
| 1303 | } |
| 1304 | |
| 1305 | return lo; |
| 1306 | } |
| 1307 | |
| 1308 | /* |
| 1309 | * Sets Invalid_operation for: |
| 1310 | * - specials |
| 1311 | * - negative numbers (except negative zero) |
| 1312 | * - non-integers |
| 1313 | * - overflow |
| 1314 | */ |
| 1315 | mpd_uint_t |
| 1316 | mpd_qget_uint(const mpd_t *a, uint32_t *status) |
| 1317 | { |
| 1318 | return _mpd_qget_uint(1, a, status); |
| 1319 | } |
| 1320 | |
| 1321 | /* Same as above, but gets the absolute value, i.e. the sign is ignored. */ |
| 1322 | mpd_uint_t |
| 1323 | mpd_qabs_uint(const mpd_t *a, uint32_t *status) |
| 1324 | { |
| 1325 | return _mpd_qget_uint(0, a, status); |
| 1326 | } |
| 1327 | |
| 1328 | /* quietly get an mpd_ssize_t from a decimal */ |
| 1329 | mpd_ssize_t |
| 1330 | mpd_qget_ssize(const mpd_t *a, uint32_t *status) |
| 1331 | { |
| 1332 | mpd_uint_t u; |
| 1333 | int isneg; |
| 1334 | |
| 1335 | u = mpd_qabs_uint(a, status); |
| 1336 | if (*status&MPD_Invalid_operation) { |
| 1337 | return MPD_SSIZE_MAX; |
| 1338 | } |
| 1339 | |
| 1340 | isneg = mpd_isnegative(a); |
| 1341 | if (u <= MPD_SSIZE_MAX) { |
| 1342 | return isneg ? -((mpd_ssize_t)u) : (mpd_ssize_t)u; |
| 1343 | } |
Stefan Krah | 6369f77 | 2012-04-18 17:57:56 +0200 | [diff] [blame] | 1344 | else if (isneg && u+(MPD_SSIZE_MIN+MPD_SSIZE_MAX) == MPD_SSIZE_MAX) { |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 1345 | return MPD_SSIZE_MIN; |
| 1346 | } |
| 1347 | |
| 1348 | *status |= MPD_Invalid_operation; |
| 1349 | return MPD_SSIZE_MAX; |
| 1350 | } |
| 1351 | |
| 1352 | #ifdef CONFIG_64 |
| 1353 | /* quietly get a uint64_t from a decimal */ |
| 1354 | uint64_t |
| 1355 | mpd_qget_u64(const mpd_t *a, uint32_t *status) |
| 1356 | { |
| 1357 | return mpd_qget_uint(a, status); |
| 1358 | } |
| 1359 | |
| 1360 | /* quietly get an int64_t from a decimal */ |
| 1361 | int64_t |
| 1362 | mpd_qget_i64(const mpd_t *a, uint32_t *status) |
| 1363 | { |
| 1364 | return mpd_qget_ssize(a, status); |
| 1365 | } |
| 1366 | #else |
| 1367 | /* quietly get a uint32_t from a decimal */ |
| 1368 | uint32_t |
| 1369 | mpd_qget_u32(const mpd_t *a, uint32_t *status) |
| 1370 | { |
| 1371 | return mpd_qget_uint(a, status); |
| 1372 | } |
| 1373 | |
| 1374 | /* quietly get an int32_t from a decimal */ |
| 1375 | int32_t |
| 1376 | mpd_qget_i32(const mpd_t *a, uint32_t *status) |
| 1377 | { |
| 1378 | return mpd_qget_ssize(a, status); |
| 1379 | } |
| 1380 | #endif |
| 1381 | |
| 1382 | |
| 1383 | /******************************************************************************/ |
| 1384 | /* Filtering input of functions, finalizing output of functions */ |
| 1385 | /******************************************************************************/ |
| 1386 | |
| 1387 | /* |
| 1388 | * Check if the operand is NaN, copy to result and return 1 if this is |
| 1389 | * the case. Copying can fail since NaNs are allowed to have a payload that |
| 1390 | * does not fit in MPD_MINALLOC. |
| 1391 | */ |
| 1392 | int |
| 1393 | mpd_qcheck_nan(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, |
| 1394 | uint32_t *status) |
| 1395 | { |
| 1396 | if (mpd_isnan(a)) { |
| 1397 | *status |= mpd_issnan(a) ? MPD_Invalid_operation : 0; |
| 1398 | mpd_qcopy(result, a, status); |
| 1399 | mpd_set_qnan(result); |
| 1400 | _mpd_fix_nan(result, ctx); |
| 1401 | return 1; |
| 1402 | } |
| 1403 | return 0; |
| 1404 | } |
| 1405 | |
| 1406 | /* |
| 1407 | * Check if either operand is NaN, copy to result and return 1 if this |
| 1408 | * is the case. Copying can fail since NaNs are allowed to have a payload |
| 1409 | * that does not fit in MPD_MINALLOC. |
| 1410 | */ |
| 1411 | int |
| 1412 | mpd_qcheck_nans(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 1413 | const mpd_context_t *ctx, uint32_t *status) |
| 1414 | { |
| 1415 | if ((a->flags|b->flags)&(MPD_NAN|MPD_SNAN)) { |
| 1416 | const mpd_t *choice = b; |
| 1417 | if (mpd_issnan(a)) { |
| 1418 | choice = a; |
| 1419 | *status |= MPD_Invalid_operation; |
| 1420 | } |
| 1421 | else if (mpd_issnan(b)) { |
| 1422 | *status |= MPD_Invalid_operation; |
| 1423 | } |
| 1424 | else if (mpd_isqnan(a)) { |
| 1425 | choice = a; |
| 1426 | } |
| 1427 | mpd_qcopy(result, choice, status); |
| 1428 | mpd_set_qnan(result); |
| 1429 | _mpd_fix_nan(result, ctx); |
| 1430 | return 1; |
| 1431 | } |
| 1432 | return 0; |
| 1433 | } |
| 1434 | |
| 1435 | /* |
| 1436 | * Check if one of the operands is NaN, copy to result and return 1 if this |
| 1437 | * is the case. Copying can fail since NaNs are allowed to have a payload |
| 1438 | * that does not fit in MPD_MINALLOC. |
| 1439 | */ |
| 1440 | static int |
| 1441 | mpd_qcheck_3nans(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c, |
| 1442 | const mpd_context_t *ctx, uint32_t *status) |
| 1443 | { |
| 1444 | if ((a->flags|b->flags|c->flags)&(MPD_NAN|MPD_SNAN)) { |
| 1445 | const mpd_t *choice = c; |
| 1446 | if (mpd_issnan(a)) { |
| 1447 | choice = a; |
| 1448 | *status |= MPD_Invalid_operation; |
| 1449 | } |
| 1450 | else if (mpd_issnan(b)) { |
| 1451 | choice = b; |
| 1452 | *status |= MPD_Invalid_operation; |
| 1453 | } |
| 1454 | else if (mpd_issnan(c)) { |
| 1455 | *status |= MPD_Invalid_operation; |
| 1456 | } |
| 1457 | else if (mpd_isqnan(a)) { |
| 1458 | choice = a; |
| 1459 | } |
| 1460 | else if (mpd_isqnan(b)) { |
| 1461 | choice = b; |
| 1462 | } |
| 1463 | mpd_qcopy(result, choice, status); |
| 1464 | mpd_set_qnan(result); |
| 1465 | _mpd_fix_nan(result, ctx); |
| 1466 | return 1; |
| 1467 | } |
| 1468 | return 0; |
| 1469 | } |
| 1470 | |
| 1471 | /* Check if rounding digit 'rnd' leads to an increment. */ |
| 1472 | static inline int |
| 1473 | _mpd_rnd_incr(const mpd_t *dec, mpd_uint_t rnd, const mpd_context_t *ctx) |
| 1474 | { |
| 1475 | int ld; |
| 1476 | |
| 1477 | switch (ctx->round) { |
| 1478 | case MPD_ROUND_DOWN: case MPD_ROUND_TRUNC: |
| 1479 | return 0; |
| 1480 | case MPD_ROUND_HALF_UP: |
| 1481 | return (rnd >= 5); |
| 1482 | case MPD_ROUND_HALF_EVEN: |
| 1483 | return (rnd > 5) || ((rnd == 5) && mpd_isoddcoeff(dec)); |
| 1484 | case MPD_ROUND_CEILING: |
| 1485 | return !(rnd == 0 || mpd_isnegative(dec)); |
| 1486 | case MPD_ROUND_FLOOR: |
| 1487 | return !(rnd == 0 || mpd_ispositive(dec)); |
| 1488 | case MPD_ROUND_HALF_DOWN: |
| 1489 | return (rnd > 5); |
| 1490 | case MPD_ROUND_UP: |
| 1491 | return !(rnd == 0); |
| 1492 | case MPD_ROUND_05UP: |
| 1493 | ld = (int)mpd_lsd(dec->data[0]); |
| 1494 | return (!(rnd == 0) && (ld == 0 || ld == 5)); |
| 1495 | default: |
| 1496 | /* Without a valid context, further results will be undefined. */ |
| 1497 | return 0; /* GCOV_NOT_REACHED */ |
| 1498 | } |
| 1499 | } |
| 1500 | |
| 1501 | /* |
| 1502 | * Apply rounding to a decimal that has been right-shifted into a full |
| 1503 | * precision decimal. If an increment leads to an overflow of the precision, |
| 1504 | * adjust the coefficient and the exponent and check the new exponent for |
| 1505 | * overflow. |
| 1506 | */ |
| 1507 | static inline void |
| 1508 | _mpd_apply_round(mpd_t *dec, mpd_uint_t rnd, const mpd_context_t *ctx, |
| 1509 | uint32_t *status) |
| 1510 | { |
| 1511 | if (_mpd_rnd_incr(dec, rnd, ctx)) { |
| 1512 | /* We have a number with exactly ctx->prec digits. The increment |
| 1513 | * can only lead to an overflow if the decimal is all nines. In |
| 1514 | * that case, the result is a power of ten with prec+1 digits. |
| 1515 | * |
| 1516 | * If the precision is a multiple of MPD_RDIGITS, this situation is |
| 1517 | * detected by _mpd_baseincr returning a carry. |
| 1518 | * If the precision is not a multiple of MPD_RDIGITS, we have to |
| 1519 | * check if the result has one digit too many. |
| 1520 | */ |
| 1521 | mpd_uint_t carry = _mpd_baseincr(dec->data, dec->len); |
| 1522 | if (carry) { |
| 1523 | dec->data[dec->len-1] = mpd_pow10[MPD_RDIGITS-1]; |
| 1524 | dec->exp += 1; |
| 1525 | _mpd_check_exp(dec, ctx, status); |
| 1526 | return; |
| 1527 | } |
| 1528 | mpd_setdigits(dec); |
| 1529 | if (dec->digits > ctx->prec) { |
| 1530 | mpd_qshiftr_inplace(dec, 1); |
| 1531 | dec->exp += 1; |
| 1532 | dec->digits = ctx->prec; |
| 1533 | _mpd_check_exp(dec, ctx, status); |
| 1534 | } |
| 1535 | } |
| 1536 | } |
| 1537 | |
| 1538 | /* |
| 1539 | * Apply rounding to a decimal. Allow overflow of the precision. |
| 1540 | */ |
| 1541 | static inline void |
| 1542 | _mpd_apply_round_excess(mpd_t *dec, mpd_uint_t rnd, const mpd_context_t *ctx, |
| 1543 | uint32_t *status) |
| 1544 | { |
| 1545 | if (_mpd_rnd_incr(dec, rnd, ctx)) { |
| 1546 | mpd_uint_t carry = _mpd_baseincr(dec->data, dec->len); |
| 1547 | if (carry) { |
| 1548 | if (!mpd_qresize(dec, dec->len+1, status)) { |
| 1549 | return; |
| 1550 | } |
| 1551 | dec->data[dec->len] = 1; |
| 1552 | dec->len += 1; |
| 1553 | } |
| 1554 | mpd_setdigits(dec); |
| 1555 | } |
| 1556 | } |
| 1557 | |
| 1558 | /* |
| 1559 | * Apply rounding to a decimal that has been right-shifted into a decimal |
| 1560 | * with full precision or less. Return failure if an increment would |
| 1561 | * overflow the precision. |
| 1562 | */ |
| 1563 | static inline int |
| 1564 | _mpd_apply_round_fit(mpd_t *dec, mpd_uint_t rnd, const mpd_context_t *ctx, |
| 1565 | uint32_t *status) |
| 1566 | { |
| 1567 | if (_mpd_rnd_incr(dec, rnd, ctx)) { |
| 1568 | mpd_uint_t carry = _mpd_baseincr(dec->data, dec->len); |
| 1569 | if (carry) { |
| 1570 | if (!mpd_qresize(dec, dec->len+1, status)) { |
| 1571 | return 0; |
| 1572 | } |
| 1573 | dec->data[dec->len] = 1; |
| 1574 | dec->len += 1; |
| 1575 | } |
| 1576 | mpd_setdigits(dec); |
| 1577 | if (dec->digits > ctx->prec) { |
| 1578 | mpd_seterror(dec, MPD_Invalid_operation, status); |
| 1579 | return 0; |
| 1580 | } |
| 1581 | } |
| 1582 | return 1; |
| 1583 | } |
| 1584 | |
| 1585 | /* Check a normal number for overflow, underflow, clamping. If the operand |
| 1586 | is modified, it will be zero, special or (sub)normal with a coefficient |
| 1587 | that fits into the current context precision. */ |
| 1588 | static inline void |
| 1589 | _mpd_check_exp(mpd_t *dec, const mpd_context_t *ctx, uint32_t *status) |
| 1590 | { |
| 1591 | mpd_ssize_t adjexp, etiny, shift; |
| 1592 | int rnd; |
| 1593 | |
| 1594 | adjexp = mpd_adjexp(dec); |
| 1595 | if (adjexp > ctx->emax) { |
| 1596 | |
| 1597 | if (mpd_iszerocoeff(dec)) { |
| 1598 | dec->exp = ctx->emax; |
| 1599 | if (ctx->clamp) { |
| 1600 | dec->exp -= (ctx->prec-1); |
| 1601 | } |
| 1602 | mpd_zerocoeff(dec); |
| 1603 | *status |= MPD_Clamped; |
| 1604 | return; |
| 1605 | } |
| 1606 | |
| 1607 | switch (ctx->round) { |
| 1608 | case MPD_ROUND_HALF_UP: case MPD_ROUND_HALF_EVEN: |
| 1609 | case MPD_ROUND_HALF_DOWN: case MPD_ROUND_UP: |
| 1610 | case MPD_ROUND_TRUNC: |
| 1611 | mpd_setspecial(dec, mpd_sign(dec), MPD_INF); |
| 1612 | break; |
| 1613 | case MPD_ROUND_DOWN: case MPD_ROUND_05UP: |
| 1614 | mpd_qmaxcoeff(dec, ctx, status); |
| 1615 | dec->exp = ctx->emax - ctx->prec + 1; |
| 1616 | break; |
| 1617 | case MPD_ROUND_CEILING: |
| 1618 | if (mpd_isnegative(dec)) { |
| 1619 | mpd_qmaxcoeff(dec, ctx, status); |
| 1620 | dec->exp = ctx->emax - ctx->prec + 1; |
| 1621 | } |
| 1622 | else { |
| 1623 | mpd_setspecial(dec, MPD_POS, MPD_INF); |
| 1624 | } |
| 1625 | break; |
| 1626 | case MPD_ROUND_FLOOR: |
| 1627 | if (mpd_ispositive(dec)) { |
| 1628 | mpd_qmaxcoeff(dec, ctx, status); |
| 1629 | dec->exp = ctx->emax - ctx->prec + 1; |
| 1630 | } |
| 1631 | else { |
| 1632 | mpd_setspecial(dec, MPD_NEG, MPD_INF); |
| 1633 | } |
| 1634 | break; |
| 1635 | default: /* debug */ |
| 1636 | abort(); /* GCOV_NOT_REACHED */ |
| 1637 | } |
| 1638 | |
| 1639 | *status |= MPD_Overflow|MPD_Inexact|MPD_Rounded; |
| 1640 | |
| 1641 | } /* fold down */ |
| 1642 | else if (ctx->clamp && dec->exp > mpd_etop(ctx)) { |
| 1643 | /* At this point adjexp=exp+digits-1 <= emax and exp > etop=emax-prec+1: |
| 1644 | * (1) shift = exp -emax+prec-1 > 0 |
| 1645 | * (2) digits+shift = exp+digits-1 - emax + prec <= prec */ |
| 1646 | shift = dec->exp - mpd_etop(ctx); |
| 1647 | if (!mpd_qshiftl(dec, dec, shift, status)) { |
| 1648 | return; |
| 1649 | } |
| 1650 | dec->exp -= shift; |
| 1651 | *status |= MPD_Clamped; |
| 1652 | if (!mpd_iszerocoeff(dec) && adjexp < ctx->emin) { |
| 1653 | /* Underflow is impossible, since exp < etiny=emin-prec+1 |
| 1654 | * and exp > etop=emax-prec+1 would imply emax < emin. */ |
| 1655 | *status |= MPD_Subnormal; |
| 1656 | } |
| 1657 | } |
| 1658 | else if (adjexp < ctx->emin) { |
| 1659 | |
| 1660 | etiny = mpd_etiny(ctx); |
| 1661 | |
| 1662 | if (mpd_iszerocoeff(dec)) { |
| 1663 | if (dec->exp < etiny) { |
| 1664 | dec->exp = etiny; |
| 1665 | mpd_zerocoeff(dec); |
| 1666 | *status |= MPD_Clamped; |
| 1667 | } |
| 1668 | return; |
| 1669 | } |
| 1670 | |
| 1671 | *status |= MPD_Subnormal; |
| 1672 | if (dec->exp < etiny) { |
| 1673 | /* At this point adjexp=exp+digits-1 < emin and exp < etiny=emin-prec+1: |
| 1674 | * (1) shift = emin-prec+1 - exp > 0 |
| 1675 | * (2) digits-shift = exp+digits-1 - emin + prec < prec */ |
| 1676 | shift = etiny - dec->exp; |
| 1677 | rnd = (int)mpd_qshiftr_inplace(dec, shift); |
| 1678 | dec->exp = etiny; |
| 1679 | /* We always have a spare digit in case of an increment. */ |
| 1680 | _mpd_apply_round_excess(dec, rnd, ctx, status); |
| 1681 | *status |= MPD_Rounded; |
| 1682 | if (rnd) { |
| 1683 | *status |= (MPD_Inexact|MPD_Underflow); |
| 1684 | if (mpd_iszerocoeff(dec)) { |
| 1685 | mpd_zerocoeff(dec); |
| 1686 | *status |= MPD_Clamped; |
| 1687 | } |
| 1688 | } |
| 1689 | } |
| 1690 | /* Case exp >= etiny=emin-prec+1: |
| 1691 | * (1) adjexp=exp+digits-1 < emin |
| 1692 | * (2) digits < emin-exp+1 <= prec */ |
| 1693 | } |
| 1694 | } |
| 1695 | |
| 1696 | /* Transcendental functions do not always set Underflow reliably, |
| 1697 | * since they only use as much precision as is necessary for correct |
| 1698 | * rounding. If a result like 1.0000000000e-101 is finalized, there |
| 1699 | * is no rounding digit that would trigger Underflow. But we can |
| 1700 | * assume Inexact, so a short check suffices. */ |
| 1701 | static inline void |
| 1702 | mpd_check_underflow(mpd_t *dec, const mpd_context_t *ctx, uint32_t *status) |
| 1703 | { |
| 1704 | if (mpd_adjexp(dec) < ctx->emin && !mpd_iszero(dec) && |
| 1705 | dec->exp < mpd_etiny(ctx)) { |
| 1706 | *status |= MPD_Underflow; |
| 1707 | } |
| 1708 | } |
| 1709 | |
| 1710 | /* Check if a normal number must be rounded after the exponent has been checked. */ |
| 1711 | static inline void |
| 1712 | _mpd_check_round(mpd_t *dec, const mpd_context_t *ctx, uint32_t *status) |
| 1713 | { |
| 1714 | mpd_uint_t rnd; |
| 1715 | mpd_ssize_t shift; |
| 1716 | |
| 1717 | /* must handle specials: _mpd_check_exp() can produce infinities or NaNs */ |
| 1718 | if (mpd_isspecial(dec)) { |
| 1719 | return; |
| 1720 | } |
| 1721 | |
| 1722 | if (dec->digits > ctx->prec) { |
| 1723 | shift = dec->digits - ctx->prec; |
| 1724 | rnd = mpd_qshiftr_inplace(dec, shift); |
| 1725 | dec->exp += shift; |
| 1726 | _mpd_apply_round(dec, rnd, ctx, status); |
| 1727 | *status |= MPD_Rounded; |
| 1728 | if (rnd) { |
| 1729 | *status |= MPD_Inexact; |
| 1730 | } |
| 1731 | } |
| 1732 | } |
| 1733 | |
| 1734 | /* Finalize all operations. */ |
| 1735 | void |
| 1736 | mpd_qfinalize(mpd_t *result, const mpd_context_t *ctx, uint32_t *status) |
| 1737 | { |
| 1738 | if (mpd_isspecial(result)) { |
| 1739 | if (mpd_isnan(result)) { |
| 1740 | _mpd_fix_nan(result, ctx); |
| 1741 | } |
| 1742 | return; |
| 1743 | } |
| 1744 | |
| 1745 | _mpd_check_exp(result, ctx, status); |
| 1746 | _mpd_check_round(result, ctx, status); |
| 1747 | } |
| 1748 | |
| 1749 | |
| 1750 | /******************************************************************************/ |
| 1751 | /* Copying */ |
| 1752 | /******************************************************************************/ |
| 1753 | |
| 1754 | /* Internal function: Copy a decimal, share data with src: USE WITH CARE! */ |
| 1755 | static inline void |
| 1756 | _mpd_copy_shared(mpd_t *dest, const mpd_t *src) |
| 1757 | { |
| 1758 | dest->flags = src->flags; |
| 1759 | dest->exp = src->exp; |
| 1760 | dest->digits = src->digits; |
| 1761 | dest->len = src->len; |
| 1762 | dest->alloc = src->alloc; |
| 1763 | dest->data = src->data; |
| 1764 | |
| 1765 | mpd_set_shared_data(dest); |
| 1766 | } |
| 1767 | |
| 1768 | /* |
| 1769 | * Copy a decimal. In case of an error, status is set to MPD_Malloc_error. |
| 1770 | */ |
| 1771 | int |
| 1772 | mpd_qcopy(mpd_t *result, const mpd_t *a, uint32_t *status) |
| 1773 | { |
| 1774 | if (result == a) return 1; |
| 1775 | |
| 1776 | if (!mpd_qresize(result, a->len, status)) { |
| 1777 | return 0; |
| 1778 | } |
| 1779 | |
| 1780 | mpd_copy_flags(result, a); |
| 1781 | result->exp = a->exp; |
| 1782 | result->digits = a->digits; |
| 1783 | result->len = a->len; |
| 1784 | memcpy(result->data, a->data, a->len * (sizeof *result->data)); |
| 1785 | |
| 1786 | return 1; |
| 1787 | } |
| 1788 | |
| 1789 | /* |
| 1790 | * Copy to a decimal with a static buffer. The caller has to make sure that |
| 1791 | * the buffer is big enough. Cannot fail. |
| 1792 | */ |
| 1793 | static void |
| 1794 | mpd_qcopy_static(mpd_t *result, const mpd_t *a) |
| 1795 | { |
| 1796 | if (result == a) return; |
| 1797 | |
| 1798 | memcpy(result->data, a->data, a->len * (sizeof *result->data)); |
| 1799 | |
| 1800 | mpd_copy_flags(result, a); |
| 1801 | result->exp = a->exp; |
| 1802 | result->digits = a->digits; |
| 1803 | result->len = a->len; |
| 1804 | } |
| 1805 | |
| 1806 | /* |
| 1807 | * Return a newly allocated copy of the operand. In case of an error, |
| 1808 | * status is set to MPD_Malloc_error and the return value is NULL. |
| 1809 | */ |
| 1810 | mpd_t * |
| 1811 | mpd_qncopy(const mpd_t *a) |
| 1812 | { |
| 1813 | mpd_t *result; |
| 1814 | |
| 1815 | if ((result = mpd_qnew_size(a->len)) == NULL) { |
| 1816 | return NULL; |
| 1817 | } |
| 1818 | memcpy(result->data, a->data, a->len * (sizeof *result->data)); |
| 1819 | mpd_copy_flags(result, a); |
| 1820 | result->exp = a->exp; |
| 1821 | result->digits = a->digits; |
| 1822 | result->len = a->len; |
| 1823 | |
| 1824 | return result; |
| 1825 | } |
| 1826 | |
| 1827 | /* |
| 1828 | * Copy a decimal and set the sign to positive. In case of an error, the |
| 1829 | * status is set to MPD_Malloc_error. |
| 1830 | */ |
| 1831 | int |
| 1832 | mpd_qcopy_abs(mpd_t *result, const mpd_t *a, uint32_t *status) |
| 1833 | { |
| 1834 | if (!mpd_qcopy(result, a, status)) { |
| 1835 | return 0; |
| 1836 | } |
| 1837 | mpd_set_positive(result); |
| 1838 | return 1; |
| 1839 | } |
| 1840 | |
| 1841 | /* |
| 1842 | * Copy a decimal and negate the sign. In case of an error, the |
| 1843 | * status is set to MPD_Malloc_error. |
| 1844 | */ |
| 1845 | int |
| 1846 | mpd_qcopy_negate(mpd_t *result, const mpd_t *a, uint32_t *status) |
| 1847 | { |
| 1848 | if (!mpd_qcopy(result, a, status)) { |
| 1849 | return 0; |
| 1850 | } |
| 1851 | _mpd_negate(result); |
| 1852 | return 1; |
| 1853 | } |
| 1854 | |
| 1855 | /* |
| 1856 | * Copy a decimal, setting the sign of the first operand to the sign of the |
| 1857 | * second operand. In case of an error, the status is set to MPD_Malloc_error. |
| 1858 | */ |
| 1859 | int |
| 1860 | mpd_qcopy_sign(mpd_t *result, const mpd_t *a, const mpd_t *b, uint32_t *status) |
| 1861 | { |
| 1862 | uint8_t sign_b = mpd_sign(b); /* result may equal b! */ |
| 1863 | |
| 1864 | if (!mpd_qcopy(result, a, status)) { |
| 1865 | return 0; |
| 1866 | } |
| 1867 | mpd_set_sign(result, sign_b); |
| 1868 | return 1; |
| 1869 | } |
| 1870 | |
| 1871 | |
| 1872 | /******************************************************************************/ |
| 1873 | /* Comparisons */ |
| 1874 | /******************************************************************************/ |
| 1875 | |
| 1876 | /* |
| 1877 | * For all functions that compare two operands and return an int the usual |
| 1878 | * convention applies to the return value: |
| 1879 | * |
| 1880 | * -1 if op1 < op2 |
| 1881 | * 0 if op1 == op2 |
| 1882 | * 1 if op1 > op2 |
| 1883 | * |
| 1884 | * INT_MAX for error |
| 1885 | */ |
| 1886 | |
| 1887 | |
| 1888 | /* Convenience macro. If a and b are not equal, return from the calling |
| 1889 | * function with the correct comparison value. */ |
| 1890 | #define CMP_EQUAL_OR_RETURN(a, b) \ |
| 1891 | if (a != b) { \ |
| 1892 | if (a < b) { \ |
| 1893 | return -1; \ |
| 1894 | } \ |
| 1895 | return 1; \ |
| 1896 | } |
| 1897 | |
| 1898 | /* |
| 1899 | * Compare the data of big and small. This function does the equivalent |
| 1900 | * of first shifting small to the left and then comparing the data of |
| 1901 | * big and small, except that no allocation for the left shift is needed. |
| 1902 | */ |
| 1903 | static int |
| 1904 | _mpd_basecmp(mpd_uint_t *big, mpd_uint_t *small, mpd_size_t n, mpd_size_t m, |
| 1905 | mpd_size_t shift) |
| 1906 | { |
| 1907 | #if defined(__GNUC__) && !defined(__INTEL_COMPILER) && !defined(__clang__) |
| 1908 | /* spurious uninitialized warnings */ |
| 1909 | mpd_uint_t l=l, lprev=lprev, h=h; |
| 1910 | #else |
| 1911 | mpd_uint_t l, lprev, h; |
| 1912 | #endif |
| 1913 | mpd_uint_t q, r; |
| 1914 | mpd_uint_t ph, x; |
| 1915 | |
| 1916 | assert(m > 0 && n >= m && shift > 0); |
| 1917 | |
| 1918 | _mpd_div_word(&q, &r, (mpd_uint_t)shift, MPD_RDIGITS); |
| 1919 | |
| 1920 | if (r != 0) { |
| 1921 | |
| 1922 | ph = mpd_pow10[r]; |
| 1923 | |
| 1924 | --m; --n; |
| 1925 | _mpd_divmod_pow10(&h, &lprev, small[m--], MPD_RDIGITS-r); |
| 1926 | if (h != 0) { |
| 1927 | CMP_EQUAL_OR_RETURN(big[n], h) |
| 1928 | --n; |
| 1929 | } |
| 1930 | for (; m != MPD_SIZE_MAX; m--,n--) { |
| 1931 | _mpd_divmod_pow10(&h, &l, small[m], MPD_RDIGITS-r); |
| 1932 | x = ph * lprev + h; |
| 1933 | CMP_EQUAL_OR_RETURN(big[n], x) |
| 1934 | lprev = l; |
| 1935 | } |
| 1936 | x = ph * lprev; |
| 1937 | CMP_EQUAL_OR_RETURN(big[q], x) |
| 1938 | } |
| 1939 | else { |
| 1940 | while (--m != MPD_SIZE_MAX) { |
| 1941 | CMP_EQUAL_OR_RETURN(big[m+q], small[m]) |
| 1942 | } |
| 1943 | } |
| 1944 | |
| 1945 | return !_mpd_isallzero(big, q); |
| 1946 | } |
| 1947 | |
| 1948 | /* Compare two decimals with the same adjusted exponent. */ |
| 1949 | static int |
| 1950 | _mpd_cmp_same_adjexp(const mpd_t *a, const mpd_t *b) |
| 1951 | { |
| 1952 | mpd_ssize_t shift, i; |
| 1953 | |
| 1954 | if (a->exp != b->exp) { |
| 1955 | /* Cannot wrap: a->exp + a->digits = b->exp + b->digits, so |
| 1956 | * a->exp - b->exp = b->digits - a->digits. */ |
| 1957 | shift = a->exp - b->exp; |
| 1958 | if (shift > 0) { |
| 1959 | return -1 * _mpd_basecmp(b->data, a->data, b->len, a->len, shift); |
| 1960 | } |
| 1961 | else { |
| 1962 | return _mpd_basecmp(a->data, b->data, a->len, b->len, -shift); |
| 1963 | } |
| 1964 | } |
| 1965 | |
| 1966 | /* |
| 1967 | * At this point adjexp(a) == adjexp(b) and a->exp == b->exp, |
| 1968 | * so a->digits == b->digits, therefore a->len == b->len. |
| 1969 | */ |
| 1970 | for (i = a->len-1; i >= 0; --i) { |
| 1971 | CMP_EQUAL_OR_RETURN(a->data[i], b->data[i]) |
| 1972 | } |
| 1973 | |
| 1974 | return 0; |
| 1975 | } |
| 1976 | |
| 1977 | /* Compare two numerical values. */ |
| 1978 | static int |
| 1979 | _mpd_cmp(const mpd_t *a, const mpd_t *b) |
| 1980 | { |
| 1981 | mpd_ssize_t adjexp_a, adjexp_b; |
| 1982 | |
| 1983 | /* equal pointers */ |
| 1984 | if (a == b) { |
| 1985 | return 0; |
| 1986 | } |
| 1987 | |
| 1988 | /* infinities */ |
| 1989 | if (mpd_isinfinite(a)) { |
| 1990 | if (mpd_isinfinite(b)) { |
| 1991 | return mpd_isnegative(b) - mpd_isnegative(a); |
| 1992 | } |
| 1993 | return mpd_arith_sign(a); |
| 1994 | } |
| 1995 | if (mpd_isinfinite(b)) { |
| 1996 | return -mpd_arith_sign(b); |
| 1997 | } |
| 1998 | |
| 1999 | /* zeros */ |
| 2000 | if (mpd_iszerocoeff(a)) { |
| 2001 | if (mpd_iszerocoeff(b)) { |
| 2002 | return 0; |
| 2003 | } |
| 2004 | return -mpd_arith_sign(b); |
| 2005 | } |
| 2006 | if (mpd_iszerocoeff(b)) { |
| 2007 | return mpd_arith_sign(a); |
| 2008 | } |
| 2009 | |
| 2010 | /* different signs */ |
| 2011 | if (mpd_sign(a) != mpd_sign(b)) { |
| 2012 | return mpd_sign(b) - mpd_sign(a); |
| 2013 | } |
| 2014 | |
| 2015 | /* different adjusted exponents */ |
| 2016 | adjexp_a = mpd_adjexp(a); |
| 2017 | adjexp_b = mpd_adjexp(b); |
| 2018 | if (adjexp_a != adjexp_b) { |
| 2019 | if (adjexp_a < adjexp_b) { |
| 2020 | return -1 * mpd_arith_sign(a); |
| 2021 | } |
| 2022 | return mpd_arith_sign(a); |
| 2023 | } |
| 2024 | |
| 2025 | /* same adjusted exponents */ |
| 2026 | return _mpd_cmp_same_adjexp(a, b) * mpd_arith_sign(a); |
| 2027 | } |
| 2028 | |
| 2029 | /* Compare the absolutes of two numerical values. */ |
| 2030 | static int |
| 2031 | _mpd_cmp_abs(const mpd_t *a, const mpd_t *b) |
| 2032 | { |
| 2033 | mpd_ssize_t adjexp_a, adjexp_b; |
| 2034 | |
| 2035 | /* equal pointers */ |
| 2036 | if (a == b) { |
| 2037 | return 0; |
| 2038 | } |
| 2039 | |
| 2040 | /* infinities */ |
| 2041 | if (mpd_isinfinite(a)) { |
| 2042 | if (mpd_isinfinite(b)) { |
| 2043 | return 0; |
| 2044 | } |
| 2045 | return 1; |
| 2046 | } |
| 2047 | if (mpd_isinfinite(b)) { |
| 2048 | return -1; |
| 2049 | } |
| 2050 | |
| 2051 | /* zeros */ |
| 2052 | if (mpd_iszerocoeff(a)) { |
| 2053 | if (mpd_iszerocoeff(b)) { |
| 2054 | return 0; |
| 2055 | } |
| 2056 | return -1; |
| 2057 | } |
| 2058 | if (mpd_iszerocoeff(b)) { |
| 2059 | return 1; |
| 2060 | } |
| 2061 | |
| 2062 | /* different adjusted exponents */ |
| 2063 | adjexp_a = mpd_adjexp(a); |
| 2064 | adjexp_b = mpd_adjexp(b); |
| 2065 | if (adjexp_a != adjexp_b) { |
| 2066 | if (adjexp_a < adjexp_b) { |
| 2067 | return -1; |
| 2068 | } |
| 2069 | return 1; |
| 2070 | } |
| 2071 | |
| 2072 | /* same adjusted exponents */ |
| 2073 | return _mpd_cmp_same_adjexp(a, b); |
| 2074 | } |
| 2075 | |
| 2076 | /* Compare two values and return an integer result. */ |
| 2077 | int |
| 2078 | mpd_qcmp(const mpd_t *a, const mpd_t *b, uint32_t *status) |
| 2079 | { |
| 2080 | if (mpd_isspecial(a) || mpd_isspecial(b)) { |
| 2081 | if (mpd_isnan(a) || mpd_isnan(b)) { |
| 2082 | *status |= MPD_Invalid_operation; |
| 2083 | return INT_MAX; |
| 2084 | } |
| 2085 | } |
| 2086 | |
| 2087 | return _mpd_cmp(a, b); |
| 2088 | } |
| 2089 | |
| 2090 | /* |
| 2091 | * Compare a and b, convert the the usual integer result to a decimal and |
| 2092 | * store it in 'result'. For convenience, the integer result of the comparison |
| 2093 | * is returned. Comparisons involving NaNs return NaN/INT_MAX. |
| 2094 | */ |
| 2095 | int |
| 2096 | mpd_qcompare(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 2097 | const mpd_context_t *ctx, uint32_t *status) |
| 2098 | { |
| 2099 | int c; |
| 2100 | |
| 2101 | if (mpd_isspecial(a) || mpd_isspecial(b)) { |
| 2102 | if (mpd_qcheck_nans(result, a, b, ctx, status)) { |
| 2103 | return INT_MAX; |
| 2104 | } |
| 2105 | } |
| 2106 | |
| 2107 | c = _mpd_cmp(a, b); |
| 2108 | _settriple(result, (c < 0), (c != 0), 0); |
| 2109 | return c; |
| 2110 | } |
| 2111 | |
| 2112 | /* Same as mpd_compare(), but signal for all NaNs, i.e. also for quiet NaNs. */ |
| 2113 | int |
| 2114 | mpd_qcompare_signal(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 2115 | const mpd_context_t *ctx, uint32_t *status) |
| 2116 | { |
| 2117 | int c; |
| 2118 | |
| 2119 | if (mpd_isspecial(a) || mpd_isspecial(b)) { |
| 2120 | if (mpd_qcheck_nans(result, a, b, ctx, status)) { |
| 2121 | *status |= MPD_Invalid_operation; |
| 2122 | return INT_MAX; |
| 2123 | } |
| 2124 | } |
| 2125 | |
| 2126 | c = _mpd_cmp(a, b); |
| 2127 | _settriple(result, (c < 0), (c != 0), 0); |
| 2128 | return c; |
| 2129 | } |
| 2130 | |
| 2131 | /* Compare the operands using a total order. */ |
| 2132 | int |
| 2133 | mpd_cmp_total(const mpd_t *a, const mpd_t *b) |
| 2134 | { |
| 2135 | mpd_t aa, bb; |
| 2136 | int nan_a, nan_b; |
| 2137 | int c; |
| 2138 | |
| 2139 | if (mpd_sign(a) != mpd_sign(b)) { |
| 2140 | return mpd_sign(b) - mpd_sign(a); |
| 2141 | } |
| 2142 | |
| 2143 | |
| 2144 | if (mpd_isnan(a)) { |
| 2145 | c = 1; |
| 2146 | if (mpd_isnan(b)) { |
| 2147 | nan_a = (mpd_isqnan(a)) ? 1 : 0; |
| 2148 | nan_b = (mpd_isqnan(b)) ? 1 : 0; |
| 2149 | if (nan_b == nan_a) { |
| 2150 | if (a->len > 0 && b->len > 0) { |
| 2151 | _mpd_copy_shared(&aa, a); |
| 2152 | _mpd_copy_shared(&bb, b); |
| 2153 | aa.exp = bb.exp = 0; |
| 2154 | /* compare payload */ |
| 2155 | c = _mpd_cmp_abs(&aa, &bb); |
| 2156 | } |
| 2157 | else { |
| 2158 | c = (a->len > 0) - (b->len > 0); |
| 2159 | } |
| 2160 | } |
| 2161 | else { |
| 2162 | c = nan_a - nan_b; |
| 2163 | } |
| 2164 | } |
| 2165 | } |
| 2166 | else if (mpd_isnan(b)) { |
| 2167 | c = -1; |
| 2168 | } |
| 2169 | else { |
| 2170 | c = _mpd_cmp_abs(a, b); |
| 2171 | if (c == 0 && a->exp != b->exp) { |
| 2172 | c = (a->exp < b->exp) ? -1 : 1; |
| 2173 | } |
| 2174 | } |
| 2175 | |
| 2176 | return c * mpd_arith_sign(a); |
| 2177 | } |
| 2178 | |
| 2179 | /* |
| 2180 | * Compare a and b according to a total order, convert the usual integer result |
| 2181 | * to a decimal and store it in 'result'. For convenience, the integer result |
| 2182 | * of the comparison is returned. |
| 2183 | */ |
| 2184 | int |
| 2185 | mpd_compare_total(mpd_t *result, const mpd_t *a, const mpd_t *b) |
| 2186 | { |
| 2187 | int c; |
| 2188 | |
| 2189 | c = mpd_cmp_total(a, b); |
| 2190 | _settriple(result, (c < 0), (c != 0), 0); |
| 2191 | return c; |
| 2192 | } |
| 2193 | |
| 2194 | /* Compare the magnitude of the operands using a total order. */ |
| 2195 | int |
| 2196 | mpd_cmp_total_mag(const mpd_t *a, const mpd_t *b) |
| 2197 | { |
| 2198 | mpd_t aa, bb; |
| 2199 | |
| 2200 | _mpd_copy_shared(&aa, a); |
| 2201 | _mpd_copy_shared(&bb, b); |
| 2202 | |
| 2203 | mpd_set_positive(&aa); |
| 2204 | mpd_set_positive(&bb); |
| 2205 | |
| 2206 | return mpd_cmp_total(&aa, &bb); |
| 2207 | } |
| 2208 | |
| 2209 | /* |
| 2210 | * Compare the magnitude of a and b according to a total order, convert the |
| 2211 | * the usual integer result to a decimal and store it in 'result'. |
| 2212 | * For convenience, the integer result of the comparison is returned. |
| 2213 | */ |
| 2214 | int |
| 2215 | mpd_compare_total_mag(mpd_t *result, const mpd_t *a, const mpd_t *b) |
| 2216 | { |
| 2217 | int c; |
| 2218 | |
| 2219 | c = mpd_cmp_total_mag(a, b); |
| 2220 | _settriple(result, (c < 0), (c != 0), 0); |
| 2221 | return c; |
| 2222 | } |
| 2223 | |
| 2224 | /* Determine an ordering for operands that are numerically equal. */ |
| 2225 | static inline int |
| 2226 | _mpd_cmp_numequal(const mpd_t *a, const mpd_t *b) |
| 2227 | { |
| 2228 | int sign_a, sign_b; |
| 2229 | int c; |
| 2230 | |
| 2231 | sign_a = mpd_sign(a); |
| 2232 | sign_b = mpd_sign(b); |
| 2233 | if (sign_a != sign_b) { |
| 2234 | c = sign_b - sign_a; |
| 2235 | } |
| 2236 | else { |
| 2237 | c = (a->exp < b->exp) ? -1 : 1; |
| 2238 | c *= mpd_arith_sign(a); |
| 2239 | } |
| 2240 | |
| 2241 | return c; |
| 2242 | } |
| 2243 | |
| 2244 | |
| 2245 | /******************************************************************************/ |
| 2246 | /* Shifting the coefficient */ |
| 2247 | /******************************************************************************/ |
| 2248 | |
| 2249 | /* |
| 2250 | * Shift the coefficient of the operand to the left, no check for specials. |
| 2251 | * Both operands may be the same pointer. If the result length has to be |
| 2252 | * increased, mpd_qresize() might fail with MPD_Malloc_error. |
| 2253 | */ |
| 2254 | int |
| 2255 | mpd_qshiftl(mpd_t *result, const mpd_t *a, mpd_ssize_t n, uint32_t *status) |
| 2256 | { |
| 2257 | mpd_ssize_t size; |
| 2258 | |
Stefan Krah | dc36efa | 2012-04-07 15:57:59 +0200 | [diff] [blame] | 2259 | assert(!mpd_isspecial(a)); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 2260 | assert(n >= 0); |
| 2261 | |
| 2262 | if (mpd_iszerocoeff(a) || n == 0) { |
| 2263 | return mpd_qcopy(result, a, status); |
| 2264 | } |
| 2265 | |
| 2266 | size = mpd_digits_to_size(a->digits+n); |
| 2267 | if (!mpd_qresize(result, size, status)) { |
| 2268 | return 0; /* result is NaN */ |
| 2269 | } |
| 2270 | |
| 2271 | _mpd_baseshiftl(result->data, a->data, size, a->len, n); |
| 2272 | |
| 2273 | mpd_copy_flags(result, a); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 2274 | result->exp = a->exp; |
| 2275 | result->digits = a->digits+n; |
Stefan Krah | dc36efa | 2012-04-07 15:57:59 +0200 | [diff] [blame] | 2276 | result->len = size; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 2277 | |
| 2278 | return 1; |
| 2279 | } |
| 2280 | |
| 2281 | /* Determine the rounding indicator if all digits of the coefficient are shifted |
| 2282 | * out of the picture. */ |
| 2283 | static mpd_uint_t |
| 2284 | _mpd_get_rnd(const mpd_uint_t *data, mpd_ssize_t len, int use_msd) |
| 2285 | { |
| 2286 | mpd_uint_t rnd = 0, rest = 0, word; |
| 2287 | |
| 2288 | word = data[len-1]; |
| 2289 | /* special treatment for the most significant digit if shift == digits */ |
| 2290 | if (use_msd) { |
| 2291 | _mpd_divmod_pow10(&rnd, &rest, word, mpd_word_digits(word)-1); |
| 2292 | if (len > 1 && rest == 0) { |
| 2293 | rest = !_mpd_isallzero(data, len-1); |
| 2294 | } |
| 2295 | } |
| 2296 | else { |
| 2297 | rest = !_mpd_isallzero(data, len); |
| 2298 | } |
| 2299 | |
| 2300 | return (rnd == 0 || rnd == 5) ? rnd + !!rest : rnd; |
| 2301 | } |
| 2302 | |
| 2303 | /* |
Stefan Krah | dc36efa | 2012-04-07 15:57:59 +0200 | [diff] [blame] | 2304 | * Same as mpd_qshiftr(), but 'result' is an mpd_t with a static coefficient. |
| 2305 | * It is the caller's responsibility to ensure that the coefficient is big |
| 2306 | * enough. The function cannot fail. |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 2307 | */ |
| 2308 | mpd_uint_t |
| 2309 | mpd_qsshiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n) |
| 2310 | { |
| 2311 | mpd_uint_t rnd; |
| 2312 | mpd_ssize_t size; |
| 2313 | |
Stefan Krah | dc36efa | 2012-04-07 15:57:59 +0200 | [diff] [blame] | 2314 | assert(!mpd_isspecial(a)); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 2315 | assert(n >= 0); |
| 2316 | |
| 2317 | if (mpd_iszerocoeff(a) || n == 0) { |
| 2318 | mpd_qcopy_static(result, a); |
| 2319 | return 0; |
| 2320 | } |
| 2321 | |
| 2322 | if (n >= a->digits) { |
| 2323 | rnd = _mpd_get_rnd(a->data, a->len, (n==a->digits)); |
| 2324 | mpd_zerocoeff(result); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 2325 | } |
| 2326 | else { |
| 2327 | result->digits = a->digits-n; |
| 2328 | size = mpd_digits_to_size(result->digits); |
| 2329 | rnd = _mpd_baseshiftr(result->data, a->data, a->len, n); |
Stefan Krah | dc36efa | 2012-04-07 15:57:59 +0200 | [diff] [blame] | 2330 | result->len = size; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 2331 | } |
| 2332 | |
| 2333 | mpd_copy_flags(result, a); |
| 2334 | result->exp = a->exp; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 2335 | |
| 2336 | return rnd; |
| 2337 | } |
| 2338 | |
| 2339 | /* |
| 2340 | * Inplace shift of the coefficient to the right, no check for specials. |
| 2341 | * Returns the rounding indicator for mpd_rnd_incr(). |
| 2342 | * The function cannot fail. |
| 2343 | */ |
| 2344 | mpd_uint_t |
| 2345 | mpd_qshiftr_inplace(mpd_t *result, mpd_ssize_t n) |
| 2346 | { |
| 2347 | uint32_t dummy; |
| 2348 | mpd_uint_t rnd; |
| 2349 | mpd_ssize_t size; |
| 2350 | |
Stefan Krah | dc36efa | 2012-04-07 15:57:59 +0200 | [diff] [blame] | 2351 | assert(!mpd_isspecial(result)); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 2352 | assert(n >= 0); |
| 2353 | |
| 2354 | if (mpd_iszerocoeff(result) || n == 0) { |
| 2355 | return 0; |
| 2356 | } |
| 2357 | |
| 2358 | if (n >= result->digits) { |
| 2359 | rnd = _mpd_get_rnd(result->data, result->len, (n==result->digits)); |
| 2360 | mpd_zerocoeff(result); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 2361 | } |
| 2362 | else { |
| 2363 | rnd = _mpd_baseshiftr(result->data, result->data, result->len, n); |
| 2364 | result->digits -= n; |
| 2365 | size = mpd_digits_to_size(result->digits); |
| 2366 | /* reducing the size cannot fail */ |
| 2367 | mpd_qresize(result, size, &dummy); |
Stefan Krah | dc36efa | 2012-04-07 15:57:59 +0200 | [diff] [blame] | 2368 | result->len = size; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 2369 | } |
| 2370 | |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 2371 | return rnd; |
| 2372 | } |
| 2373 | |
| 2374 | /* |
| 2375 | * Shift the coefficient of the operand to the right, no check for specials. |
| 2376 | * Both operands may be the same pointer. Returns the rounding indicator to |
| 2377 | * be used by mpd_rnd_incr(). If the result length has to be increased, |
| 2378 | * mpd_qcopy() or mpd_qresize() might fail with MPD_Malloc_error. In those |
| 2379 | * cases, MPD_UINT_MAX is returned. |
| 2380 | */ |
| 2381 | mpd_uint_t |
| 2382 | mpd_qshiftr(mpd_t *result, const mpd_t *a, mpd_ssize_t n, uint32_t *status) |
| 2383 | { |
| 2384 | mpd_uint_t rnd; |
| 2385 | mpd_ssize_t size; |
| 2386 | |
Stefan Krah | dc36efa | 2012-04-07 15:57:59 +0200 | [diff] [blame] | 2387 | assert(!mpd_isspecial(a)); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 2388 | assert(n >= 0); |
| 2389 | |
| 2390 | if (mpd_iszerocoeff(a) || n == 0) { |
| 2391 | if (!mpd_qcopy(result, a, status)) { |
| 2392 | return MPD_UINT_MAX; |
| 2393 | } |
| 2394 | return 0; |
| 2395 | } |
| 2396 | |
| 2397 | if (n >= a->digits) { |
| 2398 | rnd = _mpd_get_rnd(a->data, a->len, (n==a->digits)); |
| 2399 | mpd_zerocoeff(result); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 2400 | } |
| 2401 | else { |
| 2402 | result->digits = a->digits-n; |
| 2403 | size = mpd_digits_to_size(result->digits); |
| 2404 | if (result == a) { |
| 2405 | rnd = _mpd_baseshiftr(result->data, a->data, a->len, n); |
| 2406 | /* reducing the size cannot fail */ |
| 2407 | mpd_qresize(result, size, status); |
| 2408 | } |
| 2409 | else { |
| 2410 | if (!mpd_qresize(result, size, status)) { |
| 2411 | return MPD_UINT_MAX; |
| 2412 | } |
| 2413 | rnd = _mpd_baseshiftr(result->data, a->data, a->len, n); |
| 2414 | } |
Stefan Krah | dc36efa | 2012-04-07 15:57:59 +0200 | [diff] [blame] | 2415 | result->len = size; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 2416 | } |
| 2417 | |
| 2418 | mpd_copy_flags(result, a); |
| 2419 | result->exp = a->exp; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 2420 | |
| 2421 | return rnd; |
| 2422 | } |
| 2423 | |
| 2424 | |
| 2425 | /******************************************************************************/ |
| 2426 | /* Miscellaneous operations */ |
| 2427 | /******************************************************************************/ |
| 2428 | |
| 2429 | /* Logical And */ |
| 2430 | void |
| 2431 | mpd_qand(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 2432 | const mpd_context_t *ctx, uint32_t *status) |
| 2433 | { |
| 2434 | const mpd_t *big = a, *small = b; |
| 2435 | mpd_uint_t x, y, z, xbit, ybit; |
| 2436 | int k, mswdigits; |
| 2437 | mpd_ssize_t i; |
| 2438 | |
| 2439 | if (mpd_isspecial(a) || mpd_isspecial(b) || |
| 2440 | mpd_isnegative(a) || mpd_isnegative(b) || |
| 2441 | a->exp != 0 || b->exp != 0) { |
| 2442 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 2443 | return; |
| 2444 | } |
| 2445 | if (b->digits > a->digits) { |
| 2446 | big = b; |
| 2447 | small = a; |
| 2448 | } |
| 2449 | if (!mpd_qresize(result, big->len, status)) { |
| 2450 | return; |
| 2451 | } |
| 2452 | |
| 2453 | |
| 2454 | /* full words */ |
| 2455 | for (i = 0; i < small->len-1; i++) { |
| 2456 | x = small->data[i]; |
| 2457 | y = big->data[i]; |
| 2458 | z = 0; |
| 2459 | for (k = 0; k < MPD_RDIGITS; k++) { |
| 2460 | xbit = x % 10; |
| 2461 | x /= 10; |
| 2462 | ybit = y % 10; |
| 2463 | y /= 10; |
| 2464 | if (xbit > 1 || ybit > 1) { |
| 2465 | goto invalid_operation; |
| 2466 | } |
| 2467 | z += (xbit&ybit) ? mpd_pow10[k] : 0; |
| 2468 | } |
| 2469 | result->data[i] = z; |
| 2470 | } |
| 2471 | /* most significant word of small */ |
| 2472 | x = small->data[i]; |
| 2473 | y = big->data[i]; |
| 2474 | z = 0; |
| 2475 | mswdigits = mpd_word_digits(x); |
| 2476 | for (k = 0; k < mswdigits; k++) { |
| 2477 | xbit = x % 10; |
| 2478 | x /= 10; |
| 2479 | ybit = y % 10; |
| 2480 | y /= 10; |
| 2481 | if (xbit > 1 || ybit > 1) { |
| 2482 | goto invalid_operation; |
| 2483 | } |
| 2484 | z += (xbit&ybit) ? mpd_pow10[k] : 0; |
| 2485 | } |
| 2486 | result->data[i++] = z; |
| 2487 | |
Stefan Krah | aecaf0b | 2012-04-18 18:08:20 +0200 | [diff] [blame] | 2488 | /* scan the rest of y for digits > 1 */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 2489 | for (; k < MPD_RDIGITS; k++) { |
| 2490 | ybit = y % 10; |
| 2491 | y /= 10; |
| 2492 | if (ybit > 1) { |
| 2493 | goto invalid_operation; |
| 2494 | } |
| 2495 | } |
Stefan Krah | aecaf0b | 2012-04-18 18:08:20 +0200 | [diff] [blame] | 2496 | /* scan the rest of big for digits > 1 */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 2497 | for (; i < big->len; i++) { |
| 2498 | y = big->data[i]; |
| 2499 | for (k = 0; k < MPD_RDIGITS; k++) { |
| 2500 | ybit = y % 10; |
| 2501 | y /= 10; |
| 2502 | if (ybit > 1) { |
| 2503 | goto invalid_operation; |
| 2504 | } |
| 2505 | } |
| 2506 | } |
| 2507 | |
| 2508 | mpd_clear_flags(result); |
| 2509 | result->exp = 0; |
| 2510 | result->len = _mpd_real_size(result->data, small->len); |
| 2511 | mpd_qresize(result, result->len, status); |
| 2512 | mpd_setdigits(result); |
| 2513 | _mpd_cap(result, ctx); |
| 2514 | return; |
| 2515 | |
| 2516 | invalid_operation: |
| 2517 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 2518 | } |
| 2519 | |
| 2520 | /* Class of an operand. Returns a pointer to the constant name. */ |
| 2521 | const char * |
| 2522 | mpd_class(const mpd_t *a, const mpd_context_t *ctx) |
| 2523 | { |
| 2524 | if (mpd_isnan(a)) { |
| 2525 | if (mpd_isqnan(a)) |
| 2526 | return "NaN"; |
| 2527 | else |
| 2528 | return "sNaN"; |
| 2529 | } |
| 2530 | else if (mpd_ispositive(a)) { |
| 2531 | if (mpd_isinfinite(a)) |
| 2532 | return "+Infinity"; |
| 2533 | else if (mpd_iszero(a)) |
| 2534 | return "+Zero"; |
| 2535 | else if (mpd_isnormal(a, ctx)) |
| 2536 | return "+Normal"; |
| 2537 | else |
| 2538 | return "+Subnormal"; |
| 2539 | } |
| 2540 | else { |
| 2541 | if (mpd_isinfinite(a)) |
| 2542 | return "-Infinity"; |
| 2543 | else if (mpd_iszero(a)) |
| 2544 | return "-Zero"; |
| 2545 | else if (mpd_isnormal(a, ctx)) |
| 2546 | return "-Normal"; |
| 2547 | else |
| 2548 | return "-Subnormal"; |
| 2549 | } |
| 2550 | } |
| 2551 | |
| 2552 | /* Logical Xor */ |
| 2553 | void |
| 2554 | mpd_qinvert(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, |
| 2555 | uint32_t *status) |
| 2556 | { |
| 2557 | mpd_uint_t x, z, xbit; |
| 2558 | mpd_ssize_t i, digits, len; |
| 2559 | mpd_ssize_t q, r; |
| 2560 | int k; |
| 2561 | |
| 2562 | if (mpd_isspecial(a) || mpd_isnegative(a) || a->exp != 0) { |
| 2563 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 2564 | return; |
| 2565 | } |
| 2566 | |
| 2567 | digits = (a->digits < ctx->prec) ? ctx->prec : a->digits; |
| 2568 | _mpd_idiv_word(&q, &r, digits, MPD_RDIGITS); |
| 2569 | len = (r == 0) ? q : q+1; |
| 2570 | if (!mpd_qresize(result, len, status)) { |
| 2571 | return; |
| 2572 | } |
| 2573 | |
| 2574 | for (i = 0; i < len; i++) { |
Stefan Krah | aecaf0b | 2012-04-18 18:08:20 +0200 | [diff] [blame] | 2575 | x = (i < a->len) ? a->data[i] : 0; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 2576 | z = 0; |
| 2577 | for (k = 0; k < MPD_RDIGITS; k++) { |
| 2578 | xbit = x % 10; |
| 2579 | x /= 10; |
| 2580 | if (xbit > 1) { |
| 2581 | goto invalid_operation; |
| 2582 | } |
| 2583 | z += !xbit ? mpd_pow10[k] : 0; |
| 2584 | } |
| 2585 | result->data[i] = z; |
| 2586 | } |
| 2587 | |
| 2588 | mpd_clear_flags(result); |
| 2589 | result->exp = 0; |
| 2590 | result->len = _mpd_real_size(result->data, len); |
| 2591 | mpd_qresize(result, result->len, status); |
| 2592 | mpd_setdigits(result); |
| 2593 | _mpd_cap(result, ctx); |
| 2594 | return; |
| 2595 | |
| 2596 | invalid_operation: |
| 2597 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 2598 | } |
| 2599 | |
| 2600 | /* Exponent of the magnitude of the most significant digit of the operand. */ |
| 2601 | void |
| 2602 | mpd_qlogb(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, |
| 2603 | uint32_t *status) |
| 2604 | { |
| 2605 | if (mpd_isspecial(a)) { |
| 2606 | if (mpd_qcheck_nan(result, a, ctx, status)) { |
| 2607 | return; |
| 2608 | } |
| 2609 | mpd_setspecial(result, MPD_POS, MPD_INF); |
| 2610 | } |
| 2611 | else if (mpd_iszerocoeff(a)) { |
| 2612 | mpd_setspecial(result, MPD_NEG, MPD_INF); |
| 2613 | *status |= MPD_Division_by_zero; |
| 2614 | } |
| 2615 | else { |
| 2616 | mpd_qset_ssize(result, mpd_adjexp(a), ctx, status); |
| 2617 | } |
| 2618 | } |
| 2619 | |
| 2620 | /* Logical Or */ |
| 2621 | void |
| 2622 | mpd_qor(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 2623 | const mpd_context_t *ctx, uint32_t *status) |
| 2624 | { |
| 2625 | const mpd_t *big = a, *small = b; |
| 2626 | mpd_uint_t x, y, z, xbit, ybit; |
| 2627 | int k, mswdigits; |
| 2628 | mpd_ssize_t i; |
| 2629 | |
| 2630 | if (mpd_isspecial(a) || mpd_isspecial(b) || |
| 2631 | mpd_isnegative(a) || mpd_isnegative(b) || |
| 2632 | a->exp != 0 || b->exp != 0) { |
| 2633 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 2634 | return; |
| 2635 | } |
| 2636 | if (b->digits > a->digits) { |
| 2637 | big = b; |
| 2638 | small = a; |
| 2639 | } |
| 2640 | if (!mpd_qresize(result, big->len, status)) { |
| 2641 | return; |
| 2642 | } |
| 2643 | |
| 2644 | |
| 2645 | /* full words */ |
| 2646 | for (i = 0; i < small->len-1; i++) { |
| 2647 | x = small->data[i]; |
| 2648 | y = big->data[i]; |
| 2649 | z = 0; |
| 2650 | for (k = 0; k < MPD_RDIGITS; k++) { |
| 2651 | xbit = x % 10; |
| 2652 | x /= 10; |
| 2653 | ybit = y % 10; |
| 2654 | y /= 10; |
| 2655 | if (xbit > 1 || ybit > 1) { |
| 2656 | goto invalid_operation; |
| 2657 | } |
| 2658 | z += (xbit|ybit) ? mpd_pow10[k] : 0; |
| 2659 | } |
| 2660 | result->data[i] = z; |
| 2661 | } |
| 2662 | /* most significant word of small */ |
| 2663 | x = small->data[i]; |
| 2664 | y = big->data[i]; |
| 2665 | z = 0; |
| 2666 | mswdigits = mpd_word_digits(x); |
| 2667 | for (k = 0; k < mswdigits; k++) { |
| 2668 | xbit = x % 10; |
| 2669 | x /= 10; |
| 2670 | ybit = y % 10; |
| 2671 | y /= 10; |
| 2672 | if (xbit > 1 || ybit > 1) { |
| 2673 | goto invalid_operation; |
| 2674 | } |
| 2675 | z += (xbit|ybit) ? mpd_pow10[k] : 0; |
| 2676 | } |
| 2677 | |
Stefan Krah | aecaf0b | 2012-04-18 18:08:20 +0200 | [diff] [blame] | 2678 | /* scan for digits > 1 and copy the rest of y */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 2679 | for (; k < MPD_RDIGITS; k++) { |
| 2680 | ybit = y % 10; |
| 2681 | y /= 10; |
| 2682 | if (ybit > 1) { |
| 2683 | goto invalid_operation; |
| 2684 | } |
| 2685 | z += ybit*mpd_pow10[k]; |
| 2686 | } |
| 2687 | result->data[i++] = z; |
Stefan Krah | aecaf0b | 2012-04-18 18:08:20 +0200 | [diff] [blame] | 2688 | /* scan for digits > 1 and copy the rest of big */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 2689 | for (; i < big->len; i++) { |
| 2690 | y = big->data[i]; |
| 2691 | for (k = 0; k < MPD_RDIGITS; k++) { |
| 2692 | ybit = y % 10; |
| 2693 | y /= 10; |
| 2694 | if (ybit > 1) { |
| 2695 | goto invalid_operation; |
| 2696 | } |
| 2697 | } |
| 2698 | result->data[i] = big->data[i]; |
| 2699 | } |
| 2700 | |
| 2701 | mpd_clear_flags(result); |
| 2702 | result->exp = 0; |
| 2703 | result->len = _mpd_real_size(result->data, big->len); |
| 2704 | mpd_qresize(result, result->len, status); |
| 2705 | mpd_setdigits(result); |
| 2706 | _mpd_cap(result, ctx); |
| 2707 | return; |
| 2708 | |
| 2709 | invalid_operation: |
| 2710 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 2711 | } |
| 2712 | |
| 2713 | /* |
Stefan Krah | aecaf0b | 2012-04-18 18:08:20 +0200 | [diff] [blame] | 2714 | * Rotate the coefficient of 'a' by 'b' digits. 'b' must be an integer with |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 2715 | * exponent 0. |
| 2716 | */ |
| 2717 | void |
| 2718 | mpd_qrotate(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 2719 | const mpd_context_t *ctx, uint32_t *status) |
| 2720 | { |
| 2721 | uint32_t workstatus = 0; |
| 2722 | MPD_NEW_STATIC(tmp,0,0,0,0); |
| 2723 | MPD_NEW_STATIC(big,0,0,0,0); |
| 2724 | MPD_NEW_STATIC(small,0,0,0,0); |
| 2725 | mpd_ssize_t n, lshift, rshift; |
| 2726 | |
| 2727 | if (mpd_isspecial(a) || mpd_isspecial(b)) { |
| 2728 | if (mpd_qcheck_nans(result, a, b, ctx, status)) { |
| 2729 | return; |
| 2730 | } |
| 2731 | } |
| 2732 | if (b->exp != 0 || mpd_isinfinite(b)) { |
| 2733 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 2734 | return; |
| 2735 | } |
| 2736 | |
| 2737 | n = mpd_qget_ssize(b, &workstatus); |
| 2738 | if (workstatus&MPD_Invalid_operation) { |
| 2739 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 2740 | return; |
| 2741 | } |
| 2742 | if (n > ctx->prec || n < -ctx->prec) { |
| 2743 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 2744 | return; |
| 2745 | } |
| 2746 | if (mpd_isinfinite(a)) { |
| 2747 | mpd_qcopy(result, a, status); |
| 2748 | return; |
| 2749 | } |
| 2750 | |
| 2751 | if (n >= 0) { |
| 2752 | lshift = n; |
| 2753 | rshift = ctx->prec-n; |
| 2754 | } |
| 2755 | else { |
| 2756 | lshift = ctx->prec+n; |
| 2757 | rshift = -n; |
| 2758 | } |
| 2759 | |
| 2760 | if (a->digits > ctx->prec) { |
| 2761 | if (!mpd_qcopy(&tmp, a, status)) { |
| 2762 | mpd_seterror(result, MPD_Malloc_error, status); |
| 2763 | goto finish; |
| 2764 | } |
| 2765 | _mpd_cap(&tmp, ctx); |
| 2766 | a = &tmp; |
| 2767 | } |
| 2768 | |
| 2769 | if (!mpd_qshiftl(&big, a, lshift, status)) { |
| 2770 | mpd_seterror(result, MPD_Malloc_error, status); |
| 2771 | goto finish; |
| 2772 | } |
| 2773 | _mpd_cap(&big, ctx); |
| 2774 | |
| 2775 | if (mpd_qshiftr(&small, a, rshift, status) == MPD_UINT_MAX) { |
| 2776 | mpd_seterror(result, MPD_Malloc_error, status); |
| 2777 | goto finish; |
| 2778 | } |
| 2779 | _mpd_qadd(result, &big, &small, ctx, status); |
| 2780 | |
| 2781 | |
| 2782 | finish: |
| 2783 | mpd_del(&tmp); |
| 2784 | mpd_del(&big); |
| 2785 | mpd_del(&small); |
| 2786 | } |
| 2787 | |
| 2788 | /* |
| 2789 | * b must be an integer with exponent 0 and in the range +-2*(emax + prec). |
| 2790 | * XXX: In my opinion +-(2*emax + prec) would be more sensible. |
| 2791 | * The result is a with the value of b added to its exponent. |
| 2792 | */ |
| 2793 | void |
| 2794 | mpd_qscaleb(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 2795 | const mpd_context_t *ctx, uint32_t *status) |
| 2796 | { |
| 2797 | uint32_t workstatus = 0; |
| 2798 | mpd_uint_t n, maxjump; |
| 2799 | #ifndef LEGACY_COMPILER |
| 2800 | int64_t exp; |
| 2801 | #else |
| 2802 | mpd_uint_t x; |
| 2803 | int x_sign, n_sign; |
| 2804 | mpd_ssize_t exp; |
| 2805 | #endif |
| 2806 | |
| 2807 | if (mpd_isspecial(a) || mpd_isspecial(b)) { |
| 2808 | if (mpd_qcheck_nans(result, a, b, ctx, status)) { |
| 2809 | return; |
| 2810 | } |
| 2811 | } |
| 2812 | if (b->exp != 0 || mpd_isinfinite(b)) { |
| 2813 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 2814 | return; |
| 2815 | } |
| 2816 | |
| 2817 | n = mpd_qabs_uint(b, &workstatus); |
| 2818 | /* the spec demands this */ |
| 2819 | maxjump = 2 * (mpd_uint_t)(ctx->emax + ctx->prec); |
| 2820 | |
| 2821 | if (n > maxjump || workstatus&MPD_Invalid_operation) { |
| 2822 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 2823 | return; |
| 2824 | } |
| 2825 | if (mpd_isinfinite(a)) { |
| 2826 | mpd_qcopy(result, a, status); |
| 2827 | return; |
| 2828 | } |
| 2829 | |
| 2830 | #ifndef LEGACY_COMPILER |
| 2831 | exp = a->exp + (int64_t)n * mpd_arith_sign(b); |
| 2832 | exp = (exp > MPD_EXP_INF) ? MPD_EXP_INF : exp; |
| 2833 | exp = (exp < MPD_EXP_CLAMP) ? MPD_EXP_CLAMP : exp; |
| 2834 | #else |
| 2835 | x = (a->exp < 0) ? -a->exp : a->exp; |
| 2836 | x_sign = (a->exp < 0) ? 1 : 0; |
| 2837 | n_sign = mpd_isnegative(b) ? 1 : 0; |
| 2838 | |
| 2839 | if (x_sign == n_sign) { |
| 2840 | x = x + n; |
| 2841 | if (x < n) x = MPD_UINT_MAX; |
| 2842 | } |
| 2843 | else { |
| 2844 | x_sign = (x >= n) ? x_sign : n_sign; |
| 2845 | x = (x >= n) ? x - n : n - x; |
| 2846 | } |
| 2847 | if (!x_sign && x > MPD_EXP_INF) x = MPD_EXP_INF; |
| 2848 | if (x_sign && x > -MPD_EXP_CLAMP) x = -MPD_EXP_CLAMP; |
| 2849 | exp = x_sign ? -((mpd_ssize_t)x) : (mpd_ssize_t)x; |
| 2850 | #endif |
| 2851 | |
| 2852 | mpd_qcopy(result, a, status); |
| 2853 | result->exp = (mpd_ssize_t)exp; |
| 2854 | |
| 2855 | mpd_qfinalize(result, ctx, status); |
| 2856 | } |
| 2857 | |
| 2858 | /* |
| 2859 | * Shift the coefficient by n digits, positive n is a left shift. In the case |
| 2860 | * of a left shift, the result is decapitated to fit the context precision. If |
| 2861 | * you don't want that, use mpd_shiftl(). |
| 2862 | */ |
| 2863 | void |
| 2864 | mpd_qshiftn(mpd_t *result, const mpd_t *a, mpd_ssize_t n, const mpd_context_t *ctx, |
| 2865 | uint32_t *status) |
| 2866 | { |
| 2867 | if (mpd_isspecial(a)) { |
| 2868 | if (mpd_qcheck_nan(result, a, ctx, status)) { |
| 2869 | return; |
| 2870 | } |
| 2871 | mpd_qcopy(result, a, status); |
| 2872 | return; |
| 2873 | } |
| 2874 | |
| 2875 | if (n >= 0 && n <= ctx->prec) { |
| 2876 | mpd_qshiftl(result, a, n, status); |
| 2877 | _mpd_cap(result, ctx); |
| 2878 | } |
| 2879 | else if (n < 0 && n >= -ctx->prec) { |
| 2880 | if (!mpd_qcopy(result, a, status)) { |
| 2881 | return; |
| 2882 | } |
| 2883 | _mpd_cap(result, ctx); |
| 2884 | mpd_qshiftr_inplace(result, -n); |
| 2885 | } |
| 2886 | else { |
| 2887 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 2888 | } |
| 2889 | } |
| 2890 | |
| 2891 | /* |
| 2892 | * Same as mpd_shiftn(), but the shift is specified by the decimal b, which |
| 2893 | * must be an integer with a zero exponent. Infinities remain infinities. |
| 2894 | */ |
| 2895 | void |
| 2896 | mpd_qshift(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, |
| 2897 | uint32_t *status) |
| 2898 | { |
| 2899 | uint32_t workstatus = 0; |
| 2900 | mpd_ssize_t n; |
| 2901 | |
| 2902 | if (mpd_isspecial(a) || mpd_isspecial(b)) { |
| 2903 | if (mpd_qcheck_nans(result, a, b, ctx, status)) { |
| 2904 | return; |
| 2905 | } |
| 2906 | } |
| 2907 | if (b->exp != 0 || mpd_isinfinite(b)) { |
| 2908 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 2909 | return; |
| 2910 | } |
| 2911 | |
| 2912 | n = mpd_qget_ssize(b, &workstatus); |
| 2913 | if (workstatus&MPD_Invalid_operation) { |
| 2914 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 2915 | return; |
| 2916 | } |
| 2917 | if (n > ctx->prec || n < -ctx->prec) { |
| 2918 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 2919 | return; |
| 2920 | } |
| 2921 | if (mpd_isinfinite(a)) { |
| 2922 | mpd_qcopy(result, a, status); |
| 2923 | return; |
| 2924 | } |
| 2925 | |
| 2926 | if (n >= 0) { |
| 2927 | mpd_qshiftl(result, a, n, status); |
| 2928 | _mpd_cap(result, ctx); |
| 2929 | } |
| 2930 | else { |
| 2931 | if (!mpd_qcopy(result, a, status)) { |
| 2932 | return; |
| 2933 | } |
| 2934 | _mpd_cap(result, ctx); |
| 2935 | mpd_qshiftr_inplace(result, -n); |
| 2936 | } |
| 2937 | } |
| 2938 | |
| 2939 | /* Logical Xor */ |
| 2940 | void |
| 2941 | mpd_qxor(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 2942 | const mpd_context_t *ctx, uint32_t *status) |
| 2943 | { |
| 2944 | const mpd_t *big = a, *small = b; |
| 2945 | mpd_uint_t x, y, z, xbit, ybit; |
| 2946 | int k, mswdigits; |
| 2947 | mpd_ssize_t i; |
| 2948 | |
| 2949 | if (mpd_isspecial(a) || mpd_isspecial(b) || |
| 2950 | mpd_isnegative(a) || mpd_isnegative(b) || |
| 2951 | a->exp != 0 || b->exp != 0) { |
| 2952 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 2953 | return; |
| 2954 | } |
| 2955 | if (b->digits > a->digits) { |
| 2956 | big = b; |
| 2957 | small = a; |
| 2958 | } |
| 2959 | if (!mpd_qresize(result, big->len, status)) { |
| 2960 | return; |
| 2961 | } |
| 2962 | |
| 2963 | |
| 2964 | /* full words */ |
| 2965 | for (i = 0; i < small->len-1; i++) { |
| 2966 | x = small->data[i]; |
| 2967 | y = big->data[i]; |
| 2968 | z = 0; |
| 2969 | for (k = 0; k < MPD_RDIGITS; k++) { |
| 2970 | xbit = x % 10; |
| 2971 | x /= 10; |
| 2972 | ybit = y % 10; |
| 2973 | y /= 10; |
| 2974 | if (xbit > 1 || ybit > 1) { |
| 2975 | goto invalid_operation; |
| 2976 | } |
| 2977 | z += (xbit^ybit) ? mpd_pow10[k] : 0; |
| 2978 | } |
| 2979 | result->data[i] = z; |
| 2980 | } |
| 2981 | /* most significant word of small */ |
| 2982 | x = small->data[i]; |
| 2983 | y = big->data[i]; |
| 2984 | z = 0; |
| 2985 | mswdigits = mpd_word_digits(x); |
| 2986 | for (k = 0; k < mswdigits; k++) { |
| 2987 | xbit = x % 10; |
| 2988 | x /= 10; |
| 2989 | ybit = y % 10; |
| 2990 | y /= 10; |
| 2991 | if (xbit > 1 || ybit > 1) { |
| 2992 | goto invalid_operation; |
| 2993 | } |
| 2994 | z += (xbit^ybit) ? mpd_pow10[k] : 0; |
| 2995 | } |
| 2996 | |
Stefan Krah | aecaf0b | 2012-04-18 18:08:20 +0200 | [diff] [blame] | 2997 | /* scan for digits > 1 and copy the rest of y */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 2998 | for (; k < MPD_RDIGITS; k++) { |
| 2999 | ybit = y % 10; |
| 3000 | y /= 10; |
| 3001 | if (ybit > 1) { |
| 3002 | goto invalid_operation; |
| 3003 | } |
| 3004 | z += ybit*mpd_pow10[k]; |
| 3005 | } |
| 3006 | result->data[i++] = z; |
Stefan Krah | aecaf0b | 2012-04-18 18:08:20 +0200 | [diff] [blame] | 3007 | /* scan for digits > 1 and copy the rest of big */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3008 | for (; i < big->len; i++) { |
| 3009 | y = big->data[i]; |
| 3010 | for (k = 0; k < MPD_RDIGITS; k++) { |
| 3011 | ybit = y % 10; |
| 3012 | y /= 10; |
| 3013 | if (ybit > 1) { |
| 3014 | goto invalid_operation; |
| 3015 | } |
| 3016 | } |
| 3017 | result->data[i] = big->data[i]; |
| 3018 | } |
| 3019 | |
| 3020 | mpd_clear_flags(result); |
| 3021 | result->exp = 0; |
| 3022 | result->len = _mpd_real_size(result->data, big->len); |
| 3023 | mpd_qresize(result, result->len, status); |
| 3024 | mpd_setdigits(result); |
| 3025 | _mpd_cap(result, ctx); |
| 3026 | return; |
| 3027 | |
| 3028 | invalid_operation: |
| 3029 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 3030 | } |
| 3031 | |
| 3032 | |
| 3033 | /******************************************************************************/ |
| 3034 | /* Arithmetic operations */ |
| 3035 | /******************************************************************************/ |
| 3036 | |
| 3037 | /* |
| 3038 | * The absolute value of a. If a is negative, the result is the same |
| 3039 | * as the result of the minus operation. Otherwise, the result is the |
| 3040 | * result of the plus operation. |
| 3041 | */ |
| 3042 | void |
| 3043 | mpd_qabs(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, |
| 3044 | uint32_t *status) |
| 3045 | { |
| 3046 | if (mpd_isspecial(a)) { |
| 3047 | if (mpd_qcheck_nan(result, a, ctx, status)) { |
| 3048 | return; |
| 3049 | } |
| 3050 | } |
| 3051 | |
| 3052 | if (mpd_isnegative(a)) { |
| 3053 | mpd_qminus(result, a, ctx, status); |
| 3054 | } |
| 3055 | else { |
| 3056 | mpd_qplus(result, a, ctx, status); |
| 3057 | } |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3058 | } |
| 3059 | |
| 3060 | static inline void |
| 3061 | _mpd_ptrswap(mpd_t **a, mpd_t **b) |
| 3062 | { |
| 3063 | mpd_t *t = *a; |
| 3064 | *a = *b; |
| 3065 | *b = t; |
| 3066 | } |
| 3067 | |
| 3068 | /* Add or subtract infinities. */ |
| 3069 | static void |
| 3070 | _mpd_qaddsub_inf(mpd_t *result, const mpd_t *a, const mpd_t *b, uint8_t sign_b, |
| 3071 | uint32_t *status) |
| 3072 | { |
| 3073 | if (mpd_isinfinite(a)) { |
| 3074 | if (mpd_sign(a) != sign_b && mpd_isinfinite(b)) { |
| 3075 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 3076 | } |
| 3077 | else { |
| 3078 | mpd_setspecial(result, mpd_sign(a), MPD_INF); |
| 3079 | } |
| 3080 | return; |
| 3081 | } |
| 3082 | assert(mpd_isinfinite(b)); |
| 3083 | mpd_setspecial(result, sign_b, MPD_INF); |
| 3084 | } |
| 3085 | |
| 3086 | /* Add or subtract non-special numbers. */ |
| 3087 | static void |
| 3088 | _mpd_qaddsub(mpd_t *result, const mpd_t *a, const mpd_t *b, uint8_t sign_b, |
| 3089 | const mpd_context_t *ctx, uint32_t *status) |
| 3090 | { |
| 3091 | mpd_t *big, *small; |
| 3092 | MPD_NEW_STATIC(big_aligned,0,0,0,0); |
Stefan Krah | ed4b21f | 2012-04-18 18:45:22 +0200 | [diff] [blame] | 3093 | MPD_NEW_CONST(tiny,0,0,1,1,1,1); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3094 | mpd_uint_t carry; |
| 3095 | mpd_ssize_t newsize, shift; |
| 3096 | mpd_ssize_t exp, i; |
| 3097 | int swap = 0; |
| 3098 | |
| 3099 | |
| 3100 | /* compare exponents */ |
| 3101 | big = (mpd_t *)a; small = (mpd_t *)b; |
| 3102 | if (big->exp != small->exp) { |
| 3103 | if (small->exp > big->exp) { |
| 3104 | _mpd_ptrswap(&big, &small); |
| 3105 | swap++; |
| 3106 | } |
Stefan Krah | 5d0d2e2 | 2012-04-18 18:59:56 +0200 | [diff] [blame] | 3107 | /* align the coefficients */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3108 | if (!mpd_iszerocoeff(big)) { |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3109 | exp = big->exp - 1; |
| 3110 | exp += (big->digits > ctx->prec) ? 0 : big->digits-ctx->prec-1; |
| 3111 | if (mpd_adjexp(small) < exp) { |
Stefan Krah | 5d0d2e2 | 2012-04-18 18:59:56 +0200 | [diff] [blame] | 3112 | /* |
| 3113 | * Avoid huge shifts by substituting a value for small that is |
| 3114 | * guaranteed to produce the same results. |
| 3115 | * |
| 3116 | * adjexp(small) < exp if and only if: |
| 3117 | * |
| 3118 | * bdigits <= prec AND |
| 3119 | * bdigits+shift >= prec+2+sdigits AND |
| 3120 | * exp = bexp+bdigits-prec-2 |
| 3121 | * |
| 3122 | * 1234567000000000 -> bdigits + shift |
| 3123 | * ----------XX1234 -> sdigits |
| 3124 | * ----------X1 -> tiny-digits |
| 3125 | * |- prec -| |
| 3126 | * |
| 3127 | * OR |
| 3128 | * |
| 3129 | * bdigits > prec AND |
| 3130 | * shift > sdigits AND |
| 3131 | * exp = bexp-1 |
| 3132 | * |
| 3133 | * 1234567892100000 -> bdigits + shift |
| 3134 | * ----------XX1234 -> sdigits |
| 3135 | * ----------X1 -> tiny-digits |
| 3136 | * |- prec -| |
| 3137 | * |
| 3138 | * If tiny is zero, adding or subtracting is a no-op. |
| 3139 | * Otherwise, adding tiny generates a non-zero digit either |
| 3140 | * below the rounding digit or the least significant digit |
| 3141 | * of big. When subtracting, tiny is in the same position as |
| 3142 | * the carry that would be generated by subtracting sdigits. |
| 3143 | */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3144 | mpd_copy_flags(&tiny, small); |
| 3145 | tiny.exp = exp; |
| 3146 | tiny.digits = 1; |
| 3147 | tiny.len = 1; |
| 3148 | tiny.data[0] = mpd_iszerocoeff(small) ? 0 : 1; |
| 3149 | small = &tiny; |
| 3150 | } |
Stefan Krah | 5d0d2e2 | 2012-04-18 18:59:56 +0200 | [diff] [blame] | 3151 | /* This cannot wrap: the difference is positive and <= maxprec */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3152 | shift = big->exp - small->exp; |
| 3153 | if (!mpd_qshiftl(&big_aligned, big, shift, status)) { |
| 3154 | mpd_seterror(result, MPD_Malloc_error, status); |
| 3155 | goto finish; |
| 3156 | } |
| 3157 | big = &big_aligned; |
| 3158 | } |
| 3159 | } |
| 3160 | result->exp = small->exp; |
| 3161 | |
| 3162 | |
| 3163 | /* compare length of coefficients */ |
| 3164 | if (big->len < small->len) { |
| 3165 | _mpd_ptrswap(&big, &small); |
| 3166 | swap++; |
| 3167 | } |
| 3168 | |
| 3169 | newsize = big->len; |
| 3170 | if (!mpd_qresize(result, newsize, status)) { |
| 3171 | goto finish; |
| 3172 | } |
| 3173 | |
| 3174 | if (mpd_sign(a) == sign_b) { |
| 3175 | |
| 3176 | carry = _mpd_baseadd(result->data, big->data, small->data, |
| 3177 | big->len, small->len); |
| 3178 | |
| 3179 | if (carry) { |
| 3180 | newsize = big->len + 1; |
| 3181 | if (!mpd_qresize(result, newsize, status)) { |
| 3182 | goto finish; |
| 3183 | } |
| 3184 | result->data[newsize-1] = carry; |
| 3185 | } |
| 3186 | |
| 3187 | result->len = newsize; |
| 3188 | mpd_set_flags(result, sign_b); |
| 3189 | } |
| 3190 | else { |
| 3191 | if (big->len == small->len) { |
| 3192 | for (i=big->len-1; i >= 0; --i) { |
| 3193 | if (big->data[i] != small->data[i]) { |
| 3194 | if (big->data[i] < small->data[i]) { |
| 3195 | _mpd_ptrswap(&big, &small); |
| 3196 | swap++; |
| 3197 | } |
| 3198 | break; |
| 3199 | } |
| 3200 | } |
| 3201 | } |
| 3202 | |
| 3203 | _mpd_basesub(result->data, big->data, small->data, |
| 3204 | big->len, small->len); |
| 3205 | newsize = _mpd_real_size(result->data, big->len); |
| 3206 | /* resize to smaller cannot fail */ |
| 3207 | (void)mpd_qresize(result, newsize, status); |
| 3208 | |
| 3209 | result->len = newsize; |
| 3210 | sign_b = (swap & 1) ? sign_b : mpd_sign(a); |
| 3211 | mpd_set_flags(result, sign_b); |
| 3212 | |
| 3213 | if (mpd_iszerocoeff(result)) { |
| 3214 | mpd_set_positive(result); |
| 3215 | if (ctx->round == MPD_ROUND_FLOOR) { |
| 3216 | mpd_set_negative(result); |
| 3217 | } |
| 3218 | } |
| 3219 | } |
| 3220 | |
| 3221 | mpd_setdigits(result); |
| 3222 | |
| 3223 | finish: |
| 3224 | mpd_del(&big_aligned); |
| 3225 | } |
| 3226 | |
| 3227 | /* Add a and b. No specials, no finalizing. */ |
| 3228 | static void |
| 3229 | _mpd_qadd(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 3230 | const mpd_context_t *ctx, uint32_t *status) |
| 3231 | { |
| 3232 | _mpd_qaddsub(result, a, b, mpd_sign(b), ctx, status); |
| 3233 | } |
| 3234 | |
| 3235 | /* Subtract b from a. No specials, no finalizing. */ |
| 3236 | static void |
| 3237 | _mpd_qsub(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 3238 | const mpd_context_t *ctx, uint32_t *status) |
| 3239 | { |
| 3240 | _mpd_qaddsub(result, a, b, !mpd_sign(b), ctx, status); |
| 3241 | } |
| 3242 | |
| 3243 | /* Add a and b. */ |
| 3244 | void |
| 3245 | mpd_qadd(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 3246 | const mpd_context_t *ctx, uint32_t *status) |
| 3247 | { |
| 3248 | if (mpd_isspecial(a) || mpd_isspecial(b)) { |
| 3249 | if (mpd_qcheck_nans(result, a, b, ctx, status)) { |
| 3250 | return; |
| 3251 | } |
| 3252 | _mpd_qaddsub_inf(result, a, b, mpd_sign(b), status); |
| 3253 | return; |
| 3254 | } |
| 3255 | |
| 3256 | _mpd_qaddsub(result, a, b, mpd_sign(b), ctx, status); |
| 3257 | mpd_qfinalize(result, ctx, status); |
| 3258 | } |
| 3259 | |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 3260 | /* Add a and b. Set NaN/Invalid_operation if the result is inexact. */ |
| 3261 | static void |
| 3262 | _mpd_qadd_exact(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 3263 | const mpd_context_t *ctx, uint32_t *status) |
| 3264 | { |
| 3265 | uint32_t workstatus = 0; |
| 3266 | |
| 3267 | mpd_qadd(result, a, b, ctx, &workstatus); |
| 3268 | *status |= workstatus; |
| 3269 | if (workstatus & (MPD_Inexact|MPD_Rounded|MPD_Clamped)) { |
| 3270 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 3271 | } |
| 3272 | } |
| 3273 | |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3274 | /* Subtract b from a. */ |
| 3275 | void |
| 3276 | mpd_qsub(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 3277 | const mpd_context_t *ctx, uint32_t *status) |
| 3278 | { |
| 3279 | if (mpd_isspecial(a) || mpd_isspecial(b)) { |
| 3280 | if (mpd_qcheck_nans(result, a, b, ctx, status)) { |
| 3281 | return; |
| 3282 | } |
| 3283 | _mpd_qaddsub_inf(result, a, b, !mpd_sign(b), status); |
| 3284 | return; |
| 3285 | } |
| 3286 | |
| 3287 | _mpd_qaddsub(result, a, b, !mpd_sign(b), ctx, status); |
| 3288 | mpd_qfinalize(result, ctx, status); |
| 3289 | } |
| 3290 | |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 3291 | /* Subtract b from a. Set NaN/Invalid_operation if the result is inexact. */ |
| 3292 | static void |
| 3293 | _mpd_qsub_exact(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 3294 | const mpd_context_t *ctx, uint32_t *status) |
| 3295 | { |
| 3296 | uint32_t workstatus = 0; |
| 3297 | |
| 3298 | mpd_qsub(result, a, b, ctx, &workstatus); |
| 3299 | *status |= workstatus; |
| 3300 | if (workstatus & (MPD_Inexact|MPD_Rounded|MPD_Clamped)) { |
| 3301 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 3302 | } |
| 3303 | } |
| 3304 | |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3305 | /* Add decimal and mpd_ssize_t. */ |
| 3306 | void |
| 3307 | mpd_qadd_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, |
| 3308 | const mpd_context_t *ctx, uint32_t *status) |
| 3309 | { |
| 3310 | mpd_context_t maxcontext; |
| 3311 | MPD_NEW_STATIC(bb,0,0,0,0); |
| 3312 | |
| 3313 | mpd_maxcontext(&maxcontext); |
| 3314 | mpd_qsset_ssize(&bb, b, &maxcontext, status); |
| 3315 | mpd_qadd(result, a, &bb, ctx, status); |
| 3316 | mpd_del(&bb); |
| 3317 | } |
| 3318 | |
| 3319 | /* Add decimal and mpd_uint_t. */ |
| 3320 | void |
| 3321 | mpd_qadd_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, |
| 3322 | const mpd_context_t *ctx, uint32_t *status) |
| 3323 | { |
| 3324 | mpd_context_t maxcontext; |
| 3325 | MPD_NEW_STATIC(bb,0,0,0,0); |
| 3326 | |
| 3327 | mpd_maxcontext(&maxcontext); |
| 3328 | mpd_qsset_uint(&bb, b, &maxcontext, status); |
| 3329 | mpd_qadd(result, a, &bb, ctx, status); |
| 3330 | mpd_del(&bb); |
| 3331 | } |
| 3332 | |
| 3333 | /* Subtract mpd_ssize_t from decimal. */ |
| 3334 | void |
| 3335 | mpd_qsub_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, |
| 3336 | const mpd_context_t *ctx, uint32_t *status) |
| 3337 | { |
| 3338 | mpd_context_t maxcontext; |
| 3339 | MPD_NEW_STATIC(bb,0,0,0,0); |
| 3340 | |
| 3341 | mpd_maxcontext(&maxcontext); |
| 3342 | mpd_qsset_ssize(&bb, b, &maxcontext, status); |
| 3343 | mpd_qsub(result, a, &bb, ctx, status); |
| 3344 | mpd_del(&bb); |
| 3345 | } |
| 3346 | |
| 3347 | /* Subtract mpd_uint_t from decimal. */ |
| 3348 | void |
| 3349 | mpd_qsub_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, |
| 3350 | const mpd_context_t *ctx, uint32_t *status) |
| 3351 | { |
| 3352 | mpd_context_t maxcontext; |
| 3353 | MPD_NEW_STATIC(bb,0,0,0,0); |
| 3354 | |
| 3355 | mpd_maxcontext(&maxcontext); |
| 3356 | mpd_qsset_uint(&bb, b, &maxcontext, status); |
| 3357 | mpd_qsub(result, a, &bb, ctx, status); |
| 3358 | mpd_del(&bb); |
| 3359 | } |
| 3360 | |
| 3361 | /* Add decimal and int32_t. */ |
| 3362 | void |
| 3363 | mpd_qadd_i32(mpd_t *result, const mpd_t *a, int32_t b, |
| 3364 | const mpd_context_t *ctx, uint32_t *status) |
| 3365 | { |
| 3366 | mpd_qadd_ssize(result, a, b, ctx, status); |
| 3367 | } |
| 3368 | |
| 3369 | /* Add decimal and uint32_t. */ |
| 3370 | void |
| 3371 | mpd_qadd_u32(mpd_t *result, const mpd_t *a, uint32_t b, |
| 3372 | const mpd_context_t *ctx, uint32_t *status) |
| 3373 | { |
| 3374 | mpd_qadd_uint(result, a, b, ctx, status); |
| 3375 | } |
| 3376 | |
| 3377 | #ifdef CONFIG_64 |
| 3378 | /* Add decimal and int64_t. */ |
| 3379 | void |
| 3380 | mpd_qadd_i64(mpd_t *result, const mpd_t *a, int64_t b, |
| 3381 | const mpd_context_t *ctx, uint32_t *status) |
| 3382 | { |
| 3383 | mpd_qadd_ssize(result, a, b, ctx, status); |
| 3384 | } |
| 3385 | |
| 3386 | /* Add decimal and uint64_t. */ |
| 3387 | void |
| 3388 | mpd_qadd_u64(mpd_t *result, const mpd_t *a, uint64_t b, |
| 3389 | const mpd_context_t *ctx, uint32_t *status) |
| 3390 | { |
| 3391 | mpd_qadd_uint(result, a, b, ctx, status); |
| 3392 | } |
| 3393 | #endif |
| 3394 | |
| 3395 | /* Subtract int32_t from decimal. */ |
| 3396 | void |
| 3397 | mpd_qsub_i32(mpd_t *result, const mpd_t *a, int32_t b, |
| 3398 | const mpd_context_t *ctx, uint32_t *status) |
| 3399 | { |
| 3400 | mpd_qsub_ssize(result, a, b, ctx, status); |
| 3401 | } |
| 3402 | |
| 3403 | /* Subtract uint32_t from decimal. */ |
| 3404 | void |
| 3405 | mpd_qsub_u32(mpd_t *result, const mpd_t *a, uint32_t b, |
| 3406 | const mpd_context_t *ctx, uint32_t *status) |
| 3407 | { |
| 3408 | mpd_qsub_uint(result, a, b, ctx, status); |
| 3409 | } |
| 3410 | |
| 3411 | #ifdef CONFIG_64 |
| 3412 | /* Subtract int64_t from decimal. */ |
| 3413 | void |
| 3414 | mpd_qsub_i64(mpd_t *result, const mpd_t *a, int64_t b, |
| 3415 | const mpd_context_t *ctx, uint32_t *status) |
| 3416 | { |
| 3417 | mpd_qsub_ssize(result, a, b, ctx, status); |
| 3418 | } |
| 3419 | |
| 3420 | /* Subtract uint64_t from decimal. */ |
| 3421 | void |
| 3422 | mpd_qsub_u64(mpd_t *result, const mpd_t *a, uint64_t b, |
| 3423 | const mpd_context_t *ctx, uint32_t *status) |
| 3424 | { |
| 3425 | mpd_qsub_uint(result, a, b, ctx, status); |
| 3426 | } |
| 3427 | #endif |
| 3428 | |
| 3429 | |
| 3430 | /* Divide infinities. */ |
| 3431 | static void |
| 3432 | _mpd_qdiv_inf(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 3433 | const mpd_context_t *ctx, uint32_t *status) |
| 3434 | { |
| 3435 | if (mpd_isinfinite(a)) { |
| 3436 | if (mpd_isinfinite(b)) { |
| 3437 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 3438 | return; |
| 3439 | } |
| 3440 | mpd_setspecial(result, mpd_sign(a)^mpd_sign(b), MPD_INF); |
| 3441 | return; |
| 3442 | } |
| 3443 | assert(mpd_isinfinite(b)); |
| 3444 | _settriple(result, mpd_sign(a)^mpd_sign(b), 0, mpd_etiny(ctx)); |
| 3445 | *status |= MPD_Clamped; |
| 3446 | } |
| 3447 | |
| 3448 | enum {NO_IDEAL_EXP, SET_IDEAL_EXP}; |
| 3449 | /* Divide a by b. */ |
| 3450 | static void |
| 3451 | _mpd_qdiv(int action, mpd_t *q, const mpd_t *a, const mpd_t *b, |
| 3452 | const mpd_context_t *ctx, uint32_t *status) |
| 3453 | { |
| 3454 | MPD_NEW_STATIC(aligned,0,0,0,0); |
| 3455 | mpd_uint_t ld; |
| 3456 | mpd_ssize_t shift, exp, tz; |
| 3457 | mpd_ssize_t newsize; |
| 3458 | mpd_ssize_t ideal_exp; |
| 3459 | mpd_uint_t rem; |
| 3460 | uint8_t sign_a = mpd_sign(a); |
| 3461 | uint8_t sign_b = mpd_sign(b); |
| 3462 | |
| 3463 | |
| 3464 | if (mpd_isspecial(a) || mpd_isspecial(b)) { |
| 3465 | if (mpd_qcheck_nans(q, a, b, ctx, status)) { |
| 3466 | return; |
| 3467 | } |
| 3468 | _mpd_qdiv_inf(q, a, b, ctx, status); |
| 3469 | return; |
| 3470 | } |
| 3471 | if (mpd_iszerocoeff(b)) { |
| 3472 | if (mpd_iszerocoeff(a)) { |
| 3473 | mpd_seterror(q, MPD_Division_undefined, status); |
| 3474 | } |
| 3475 | else { |
| 3476 | mpd_setspecial(q, sign_a^sign_b, MPD_INF); |
| 3477 | *status |= MPD_Division_by_zero; |
| 3478 | } |
| 3479 | return; |
| 3480 | } |
| 3481 | if (mpd_iszerocoeff(a)) { |
| 3482 | exp = a->exp - b->exp; |
| 3483 | _settriple(q, sign_a^sign_b, 0, exp); |
| 3484 | mpd_qfinalize(q, ctx, status); |
| 3485 | return; |
| 3486 | } |
| 3487 | |
| 3488 | shift = (b->digits - a->digits) + ctx->prec + 1; |
| 3489 | ideal_exp = a->exp - b->exp; |
| 3490 | exp = ideal_exp - shift; |
| 3491 | if (shift > 0) { |
| 3492 | if (!mpd_qshiftl(&aligned, a, shift, status)) { |
| 3493 | mpd_seterror(q, MPD_Malloc_error, status); |
| 3494 | goto finish; |
| 3495 | } |
| 3496 | a = &aligned; |
| 3497 | } |
| 3498 | else if (shift < 0) { |
| 3499 | shift = -shift; |
| 3500 | if (!mpd_qshiftl(&aligned, b, shift, status)) { |
| 3501 | mpd_seterror(q, MPD_Malloc_error, status); |
| 3502 | goto finish; |
| 3503 | } |
| 3504 | b = &aligned; |
| 3505 | } |
| 3506 | |
| 3507 | |
| 3508 | newsize = a->len - b->len + 1; |
| 3509 | if ((q != b && q != a) || (q == b && newsize > b->len)) { |
| 3510 | if (!mpd_qresize(q, newsize, status)) { |
| 3511 | mpd_seterror(q, MPD_Malloc_error, status); |
| 3512 | goto finish; |
| 3513 | } |
| 3514 | } |
| 3515 | |
| 3516 | |
| 3517 | if (b->len == 1) { |
| 3518 | rem = _mpd_shortdiv(q->data, a->data, a->len, b->data[0]); |
| 3519 | } |
| 3520 | else if (a->len < 2*MPD_NEWTONDIV_CUTOFF && |
| 3521 | b->len < MPD_NEWTONDIV_CUTOFF) { |
| 3522 | int ret = _mpd_basedivmod(q->data, NULL, a->data, b->data, |
| 3523 | a->len, b->len); |
| 3524 | if (ret < 0) { |
| 3525 | mpd_seterror(q, MPD_Malloc_error, status); |
| 3526 | goto finish; |
| 3527 | } |
| 3528 | rem = ret; |
| 3529 | } |
| 3530 | else { |
| 3531 | MPD_NEW_STATIC(r,0,0,0,0); |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 3532 | _mpd_base_ndivmod(q, &r, a, b, status); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3533 | if (mpd_isspecial(q) || mpd_isspecial(&r)) { |
Stefan Krah | 9d3a5ae | 2012-04-20 21:00:31 +0200 | [diff] [blame] | 3534 | mpd_setspecial(q, MPD_POS, MPD_NAN); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3535 | mpd_del(&r); |
| 3536 | goto finish; |
| 3537 | } |
| 3538 | rem = !mpd_iszerocoeff(&r); |
| 3539 | mpd_del(&r); |
| 3540 | newsize = q->len; |
| 3541 | } |
| 3542 | |
| 3543 | newsize = _mpd_real_size(q->data, newsize); |
| 3544 | /* resize to smaller cannot fail */ |
| 3545 | mpd_qresize(q, newsize, status); |
Stefan Krah | dc36efa | 2012-04-07 15:57:59 +0200 | [diff] [blame] | 3546 | mpd_set_flags(q, sign_a^sign_b); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3547 | q->len = newsize; |
| 3548 | mpd_setdigits(q); |
| 3549 | |
| 3550 | shift = ideal_exp - exp; |
| 3551 | if (rem) { |
| 3552 | ld = mpd_lsd(q->data[0]); |
| 3553 | if (ld == 0 || ld == 5) { |
| 3554 | q->data[0] += 1; |
| 3555 | } |
| 3556 | } |
| 3557 | else if (action == SET_IDEAL_EXP && shift > 0) { |
| 3558 | tz = mpd_trail_zeros(q); |
| 3559 | shift = (tz > shift) ? shift : tz; |
| 3560 | mpd_qshiftr_inplace(q, shift); |
| 3561 | exp += shift; |
| 3562 | } |
| 3563 | |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3564 | q->exp = exp; |
| 3565 | |
| 3566 | |
| 3567 | finish: |
| 3568 | mpd_del(&aligned); |
| 3569 | mpd_qfinalize(q, ctx, status); |
| 3570 | } |
| 3571 | |
| 3572 | /* Divide a by b. */ |
| 3573 | void |
| 3574 | mpd_qdiv(mpd_t *q, const mpd_t *a, const mpd_t *b, |
| 3575 | const mpd_context_t *ctx, uint32_t *status) |
| 3576 | { |
| 3577 | _mpd_qdiv(SET_IDEAL_EXP, q, a, b, ctx, status); |
| 3578 | } |
| 3579 | |
| 3580 | /* Internal function. */ |
| 3581 | static void |
| 3582 | _mpd_qdivmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b, |
Stefan Krah | 5d0d2e2 | 2012-04-18 18:59:56 +0200 | [diff] [blame] | 3583 | const mpd_context_t *ctx, uint32_t *status) |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3584 | { |
| 3585 | MPD_NEW_STATIC(aligned,0,0,0,0); |
| 3586 | mpd_ssize_t qsize, rsize; |
| 3587 | mpd_ssize_t ideal_exp, expdiff, shift; |
| 3588 | uint8_t sign_a = mpd_sign(a); |
| 3589 | uint8_t sign_ab = mpd_sign(a)^mpd_sign(b); |
| 3590 | |
| 3591 | |
| 3592 | ideal_exp = (a->exp > b->exp) ? b->exp : a->exp; |
| 3593 | if (mpd_iszerocoeff(a)) { |
| 3594 | if (!mpd_qcopy(r, a, status)) { |
| 3595 | goto nanresult; /* GCOV_NOT_REACHED */ |
| 3596 | } |
| 3597 | r->exp = ideal_exp; |
| 3598 | _settriple(q, sign_ab, 0, 0); |
| 3599 | return; |
| 3600 | } |
| 3601 | |
| 3602 | expdiff = mpd_adjexp(a) - mpd_adjexp(b); |
| 3603 | if (expdiff < 0) { |
| 3604 | if (a->exp > b->exp) { |
| 3605 | /* positive and less than b->digits - a->digits */ |
| 3606 | shift = a->exp - b->exp; |
| 3607 | if (!mpd_qshiftl(r, a, shift, status)) { |
| 3608 | goto nanresult; |
| 3609 | } |
| 3610 | r->exp = ideal_exp; |
| 3611 | } |
| 3612 | else { |
| 3613 | if (!mpd_qcopy(r, a, status)) { |
| 3614 | goto nanresult; |
| 3615 | } |
| 3616 | } |
| 3617 | _settriple(q, sign_ab, 0, 0); |
| 3618 | return; |
| 3619 | } |
| 3620 | if (expdiff > ctx->prec) { |
| 3621 | *status |= MPD_Division_impossible; |
| 3622 | goto nanresult; |
| 3623 | } |
| 3624 | |
| 3625 | |
| 3626 | /* |
| 3627 | * At this point we have: |
| 3628 | * (1) 0 <= a->exp + a->digits - b->exp - b->digits <= prec |
| 3629 | * (2) a->exp - b->exp >= b->digits - a->digits |
| 3630 | * (3) a->exp - b->exp <= prec + b->digits - a->digits |
| 3631 | */ |
| 3632 | if (a->exp != b->exp) { |
| 3633 | shift = a->exp - b->exp; |
| 3634 | if (shift > 0) { |
| 3635 | /* by (3), after the shift a->digits <= prec + b->digits */ |
| 3636 | if (!mpd_qshiftl(&aligned, a, shift, status)) { |
| 3637 | goto nanresult; |
| 3638 | } |
| 3639 | a = &aligned; |
| 3640 | } |
| 3641 | else { |
| 3642 | shift = -shift; |
| 3643 | /* by (2), after the shift b->digits <= a->digits */ |
| 3644 | if (!mpd_qshiftl(&aligned, b, shift, status)) { |
| 3645 | goto nanresult; |
| 3646 | } |
| 3647 | b = &aligned; |
| 3648 | } |
| 3649 | } |
| 3650 | |
| 3651 | |
| 3652 | qsize = a->len - b->len + 1; |
| 3653 | if (!(q == a && qsize < a->len) && !(q == b && qsize < b->len)) { |
| 3654 | if (!mpd_qresize(q, qsize, status)) { |
| 3655 | goto nanresult; |
| 3656 | } |
| 3657 | } |
| 3658 | |
| 3659 | rsize = b->len; |
| 3660 | if (!(r == a && rsize < a->len)) { |
| 3661 | if (!mpd_qresize(r, rsize, status)) { |
| 3662 | goto nanresult; |
| 3663 | } |
| 3664 | } |
| 3665 | |
| 3666 | if (b->len == 1) { |
| 3667 | if (a->len == 1) { |
| 3668 | _mpd_div_word(&q->data[0], &r->data[0], a->data[0], b->data[0]); |
| 3669 | } |
| 3670 | else { |
| 3671 | r->data[0] = _mpd_shortdiv(q->data, a->data, a->len, b->data[0]); |
| 3672 | } |
| 3673 | } |
| 3674 | else if (a->len < 2*MPD_NEWTONDIV_CUTOFF && |
| 3675 | b->len < MPD_NEWTONDIV_CUTOFF) { |
| 3676 | int ret; |
| 3677 | ret = _mpd_basedivmod(q->data, r->data, a->data, b->data, |
| 3678 | a->len, b->len); |
| 3679 | if (ret == -1) { |
| 3680 | *status |= MPD_Malloc_error; |
| 3681 | goto nanresult; |
| 3682 | } |
| 3683 | } |
| 3684 | else { |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 3685 | _mpd_base_ndivmod(q, r, a, b, status); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3686 | if (mpd_isspecial(q) || mpd_isspecial(r)) { |
| 3687 | goto nanresult; |
| 3688 | } |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3689 | qsize = q->len; |
| 3690 | rsize = r->len; |
| 3691 | } |
| 3692 | |
| 3693 | qsize = _mpd_real_size(q->data, qsize); |
| 3694 | /* resize to smaller cannot fail */ |
| 3695 | mpd_qresize(q, qsize, status); |
| 3696 | q->len = qsize; |
| 3697 | mpd_setdigits(q); |
| 3698 | mpd_set_flags(q, sign_ab); |
| 3699 | q->exp = 0; |
| 3700 | if (q->digits > ctx->prec) { |
| 3701 | *status |= MPD_Division_impossible; |
| 3702 | goto nanresult; |
| 3703 | } |
| 3704 | |
| 3705 | rsize = _mpd_real_size(r->data, rsize); |
| 3706 | /* resize to smaller cannot fail */ |
| 3707 | mpd_qresize(r, rsize, status); |
| 3708 | r->len = rsize; |
| 3709 | mpd_setdigits(r); |
| 3710 | mpd_set_flags(r, sign_a); |
| 3711 | r->exp = ideal_exp; |
| 3712 | |
| 3713 | out: |
| 3714 | mpd_del(&aligned); |
| 3715 | return; |
| 3716 | |
| 3717 | nanresult: |
| 3718 | mpd_setspecial(q, MPD_POS, MPD_NAN); |
| 3719 | mpd_setspecial(r, MPD_POS, MPD_NAN); |
| 3720 | goto out; |
| 3721 | } |
| 3722 | |
| 3723 | /* Integer division with remainder. */ |
| 3724 | void |
| 3725 | mpd_qdivmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b, |
| 3726 | const mpd_context_t *ctx, uint32_t *status) |
| 3727 | { |
| 3728 | uint8_t sign = mpd_sign(a)^mpd_sign(b); |
| 3729 | |
| 3730 | if (mpd_isspecial(a) || mpd_isspecial(b)) { |
| 3731 | if (mpd_qcheck_nans(q, a, b, ctx, status)) { |
| 3732 | mpd_qcopy(r, q, status); |
| 3733 | return; |
| 3734 | } |
| 3735 | if (mpd_isinfinite(a)) { |
| 3736 | if (mpd_isinfinite(b)) { |
| 3737 | mpd_setspecial(q, MPD_POS, MPD_NAN); |
| 3738 | } |
| 3739 | else { |
| 3740 | mpd_setspecial(q, sign, MPD_INF); |
| 3741 | } |
| 3742 | mpd_setspecial(r, MPD_POS, MPD_NAN); |
| 3743 | *status |= MPD_Invalid_operation; |
| 3744 | return; |
| 3745 | } |
| 3746 | if (mpd_isinfinite(b)) { |
| 3747 | if (!mpd_qcopy(r, a, status)) { |
| 3748 | mpd_seterror(q, MPD_Malloc_error, status); |
| 3749 | return; |
| 3750 | } |
| 3751 | mpd_qfinalize(r, ctx, status); |
| 3752 | _settriple(q, sign, 0, 0); |
| 3753 | return; |
| 3754 | } |
| 3755 | /* debug */ |
| 3756 | abort(); /* GCOV_NOT_REACHED */ |
| 3757 | } |
| 3758 | if (mpd_iszerocoeff(b)) { |
| 3759 | if (mpd_iszerocoeff(a)) { |
| 3760 | mpd_setspecial(q, MPD_POS, MPD_NAN); |
| 3761 | mpd_setspecial(r, MPD_POS, MPD_NAN); |
| 3762 | *status |= MPD_Division_undefined; |
| 3763 | } |
| 3764 | else { |
| 3765 | mpd_setspecial(q, sign, MPD_INF); |
| 3766 | mpd_setspecial(r, MPD_POS, MPD_NAN); |
| 3767 | *status |= (MPD_Division_by_zero|MPD_Invalid_operation); |
| 3768 | } |
| 3769 | return; |
| 3770 | } |
| 3771 | |
| 3772 | _mpd_qdivmod(q, r, a, b, ctx, status); |
| 3773 | mpd_qfinalize(q, ctx, status); |
| 3774 | mpd_qfinalize(r, ctx, status); |
| 3775 | } |
| 3776 | |
| 3777 | void |
| 3778 | mpd_qdivint(mpd_t *q, const mpd_t *a, const mpd_t *b, |
| 3779 | const mpd_context_t *ctx, uint32_t *status) |
| 3780 | { |
| 3781 | MPD_NEW_STATIC(r,0,0,0,0); |
| 3782 | uint8_t sign = mpd_sign(a)^mpd_sign(b); |
| 3783 | |
| 3784 | if (mpd_isspecial(a) || mpd_isspecial(b)) { |
| 3785 | if (mpd_qcheck_nans(q, a, b, ctx, status)) { |
| 3786 | return; |
| 3787 | } |
| 3788 | if (mpd_isinfinite(a) && mpd_isinfinite(b)) { |
| 3789 | mpd_seterror(q, MPD_Invalid_operation, status); |
| 3790 | return; |
| 3791 | } |
| 3792 | if (mpd_isinfinite(a)) { |
| 3793 | mpd_setspecial(q, sign, MPD_INF); |
| 3794 | return; |
| 3795 | } |
| 3796 | if (mpd_isinfinite(b)) { |
| 3797 | _settriple(q, sign, 0, 0); |
| 3798 | return; |
| 3799 | } |
| 3800 | /* debug */ |
| 3801 | abort(); /* GCOV_NOT_REACHED */ |
| 3802 | } |
| 3803 | if (mpd_iszerocoeff(b)) { |
| 3804 | if (mpd_iszerocoeff(a)) { |
| 3805 | mpd_seterror(q, MPD_Division_undefined, status); |
| 3806 | } |
| 3807 | else { |
| 3808 | mpd_setspecial(q, sign, MPD_INF); |
| 3809 | *status |= MPD_Division_by_zero; |
| 3810 | } |
| 3811 | return; |
| 3812 | } |
| 3813 | |
| 3814 | |
| 3815 | _mpd_qdivmod(q, &r, a, b, ctx, status); |
| 3816 | mpd_del(&r); |
| 3817 | mpd_qfinalize(q, ctx, status); |
| 3818 | } |
| 3819 | |
| 3820 | /* Divide decimal by mpd_ssize_t. */ |
| 3821 | void |
| 3822 | mpd_qdiv_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, |
| 3823 | const mpd_context_t *ctx, uint32_t *status) |
| 3824 | { |
| 3825 | mpd_context_t maxcontext; |
| 3826 | MPD_NEW_STATIC(bb,0,0,0,0); |
| 3827 | |
| 3828 | mpd_maxcontext(&maxcontext); |
| 3829 | mpd_qsset_ssize(&bb, b, &maxcontext, status); |
| 3830 | mpd_qdiv(result, a, &bb, ctx, status); |
| 3831 | mpd_del(&bb); |
| 3832 | } |
| 3833 | |
| 3834 | /* Divide decimal by mpd_uint_t. */ |
| 3835 | void |
| 3836 | mpd_qdiv_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, |
| 3837 | const mpd_context_t *ctx, uint32_t *status) |
| 3838 | { |
| 3839 | mpd_context_t maxcontext; |
| 3840 | MPD_NEW_STATIC(bb,0,0,0,0); |
| 3841 | |
| 3842 | mpd_maxcontext(&maxcontext); |
| 3843 | mpd_qsset_uint(&bb, b, &maxcontext, status); |
| 3844 | mpd_qdiv(result, a, &bb, ctx, status); |
| 3845 | mpd_del(&bb); |
| 3846 | } |
| 3847 | |
| 3848 | /* Divide decimal by int32_t. */ |
| 3849 | void |
| 3850 | mpd_qdiv_i32(mpd_t *result, const mpd_t *a, int32_t b, |
| 3851 | const mpd_context_t *ctx, uint32_t *status) |
| 3852 | { |
| 3853 | mpd_qdiv_ssize(result, a, b, ctx, status); |
| 3854 | } |
| 3855 | |
| 3856 | /* Divide decimal by uint32_t. */ |
| 3857 | void |
| 3858 | mpd_qdiv_u32(mpd_t *result, const mpd_t *a, uint32_t b, |
| 3859 | const mpd_context_t *ctx, uint32_t *status) |
| 3860 | { |
| 3861 | mpd_qdiv_uint(result, a, b, ctx, status); |
| 3862 | } |
| 3863 | |
| 3864 | #ifdef CONFIG_64 |
| 3865 | /* Divide decimal by int64_t. */ |
| 3866 | void |
| 3867 | mpd_qdiv_i64(mpd_t *result, const mpd_t *a, int64_t b, |
| 3868 | const mpd_context_t *ctx, uint32_t *status) |
| 3869 | { |
| 3870 | mpd_qdiv_ssize(result, a, b, ctx, status); |
| 3871 | } |
| 3872 | |
| 3873 | /* Divide decimal by uint64_t. */ |
| 3874 | void |
| 3875 | mpd_qdiv_u64(mpd_t *result, const mpd_t *a, uint64_t b, |
| 3876 | const mpd_context_t *ctx, uint32_t *status) |
| 3877 | { |
| 3878 | mpd_qdiv_uint(result, a, b, ctx, status); |
| 3879 | } |
| 3880 | #endif |
| 3881 | |
Stefan Krah | 696d10f | 2012-05-16 20:10:21 +0200 | [diff] [blame] | 3882 | /* Pad the result with trailing zeros if it has fewer digits than prec. */ |
| 3883 | static void |
| 3884 | _mpd_zeropad(mpd_t *result, const mpd_context_t *ctx, uint32_t *status) |
| 3885 | { |
| 3886 | if (!mpd_isspecial(result) && !mpd_iszero(result) && |
| 3887 | result->digits < ctx->prec) { |
| 3888 | mpd_ssize_t shift = ctx->prec - result->digits; |
| 3889 | mpd_qshiftl(result, result, shift, status); |
| 3890 | result->exp -= shift; |
| 3891 | } |
| 3892 | } |
| 3893 | |
| 3894 | /* Check if the result is guaranteed to be one. */ |
| 3895 | static int |
| 3896 | _mpd_qexp_check_one(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, |
| 3897 | uint32_t *status) |
| 3898 | { |
| 3899 | MPD_NEW_CONST(lim,0,-(ctx->prec+1),1,1,1,9); |
| 3900 | MPD_NEW_SHARED(aa, a); |
| 3901 | |
| 3902 | mpd_set_positive(&aa); |
| 3903 | |
| 3904 | /* abs(a) <= 9 * 10**(-prec-1) */ |
| 3905 | if (_mpd_cmp(&aa, &lim) <= 0) { |
| 3906 | _settriple(result, 0, 1, 0); |
Stefan Krah | 30c35e8 | 2012-05-31 15:09:27 +0200 | [diff] [blame] | 3907 | *status |= MPD_Rounded|MPD_Inexact; |
Stefan Krah | 696d10f | 2012-05-16 20:10:21 +0200 | [diff] [blame] | 3908 | return 1; |
| 3909 | } |
| 3910 | |
| 3911 | return 0; |
| 3912 | } |
| 3913 | |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3914 | /* |
| 3915 | * Get the number of iterations for the Horner scheme in _mpd_qexp(). |
| 3916 | */ |
| 3917 | static inline mpd_ssize_t |
Stefan Krah | 696d10f | 2012-05-16 20:10:21 +0200 | [diff] [blame] | 3918 | _mpd_get_exp_iterations(const mpd_t *r, mpd_ssize_t p) |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3919 | { |
Stefan Krah | 696d10f | 2012-05-16 20:10:21 +0200 | [diff] [blame] | 3920 | mpd_ssize_t log10pbyr; /* lower bound for log10(p / abs(r)) */ |
| 3921 | mpd_ssize_t n; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3922 | |
Stefan Krah | 696d10f | 2012-05-16 20:10:21 +0200 | [diff] [blame] | 3923 | assert(p >= 10); |
| 3924 | assert(!mpd_iszero(r)); |
| 3925 | assert(-p < mpd_adjexp(r) && mpd_adjexp(r) <= -1); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3926 | |
| 3927 | #ifdef CONFIG_64 |
Stefan Krah | 696d10f | 2012-05-16 20:10:21 +0200 | [diff] [blame] | 3928 | if (p > (mpd_ssize_t)(1ULL<<52)) { |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3929 | return MPD_SSIZE_MAX; |
| 3930 | } |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3931 | #endif |
Stefan Krah | 696d10f | 2012-05-16 20:10:21 +0200 | [diff] [blame] | 3932 | |
| 3933 | /* |
| 3934 | * Lower bound for log10(p / abs(r)): adjexp(p) - (adjexp(r) + 1) |
| 3935 | * At this point (for CONFIG_64, CONFIG_32 is not problematic): |
| 3936 | * 1) 10 <= p <= 2**52 |
| 3937 | * 2) -p < adjexp(r) <= -1 |
| 3938 | * 3) 1 <= log10pbyr <= 2**52 + 14 |
| 3939 | */ |
| 3940 | log10pbyr = (mpd_word_digits(p)-1) - (mpd_adjexp(r)+1); |
| 3941 | |
| 3942 | /* |
| 3943 | * The numerator in the paper is 1.435 * p - 1.182, calculated |
| 3944 | * exactly. We compensate for rounding errors by using 1.43503. |
| 3945 | * ACL2 proofs: |
| 3946 | * 1) exp-iter-approx-lower-bound: The term below evaluated |
| 3947 | * in 53-bit floating point arithmetic is greater than or |
| 3948 | * equal to the exact term used in the paper. |
| 3949 | * 2) exp-iter-approx-upper-bound: The term below is less than |
| 3950 | * or equal to 3/2 * p <= 3/2 * 2**52. |
| 3951 | */ |
| 3952 | n = (mpd_ssize_t)ceil((1.43503*(double)p - 1.182) / (double)log10pbyr); |
| 3953 | return n >= 3 ? n : 3; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3954 | } |
| 3955 | |
| 3956 | /* |
Stefan Krah | 9a5beec | 2012-05-31 16:21:34 +0200 | [diff] [blame] | 3957 | * Internal function, specials have been dealt with. Apart from Overflow |
| 3958 | * and Underflow, two cases must be considered for the error of the result: |
| 3959 | * |
| 3960 | * 1) abs(a) <= 9 * 10**(-prec-1) ==> result == 1 |
| 3961 | * |
| 3962 | * Absolute error: abs(1 - e**x) < 10**(-prec) |
| 3963 | * ------------------------------------------- |
| 3964 | * |
| 3965 | * 2) abs(a) > 9 * 10**(-prec-1) |
| 3966 | * |
| 3967 | * Relative error: abs(result - e**x) < 0.5 * 10**(-prec) * e**x |
| 3968 | * ------------------------------------------------------------- |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3969 | * |
| 3970 | * The algorithm is from Hull&Abrham, Variable Precision Exponential Function, |
| 3971 | * ACM Transactions on Mathematical Software, Vol. 12, No. 2, June 1986. |
| 3972 | * |
| 3973 | * Main differences: |
| 3974 | * |
Stefan Krah | 696d10f | 2012-05-16 20:10:21 +0200 | [diff] [blame] | 3975 | * - The number of iterations for the Horner scheme is calculated using |
| 3976 | * 53-bit floating point arithmetic. |
| 3977 | * |
| 3978 | * - In the error analysis for ER (relative error accumulated in the |
| 3979 | * evaluation of the truncated series) the reduced operand r may |
| 3980 | * have any number of digits. |
| 3981 | * ACL2 proof: exponent-relative-error |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3982 | * |
| 3983 | * - The analysis for early abortion has been adapted for the mpd_t |
| 3984 | * ranges. |
| 3985 | */ |
| 3986 | static void |
| 3987 | _mpd_qexp(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, |
| 3988 | uint32_t *status) |
| 3989 | { |
| 3990 | mpd_context_t workctx; |
| 3991 | MPD_NEW_STATIC(tmp,0,0,0,0); |
| 3992 | MPD_NEW_STATIC(sum,0,0,0,0); |
Stefan Krah | 67ee1d0 | 2012-06-01 10:58:16 +0200 | [diff] [blame] | 3993 | MPD_NEW_CONST(word,0,0,1,1,1,1); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 3994 | mpd_ssize_t j, n, t; |
| 3995 | |
| 3996 | assert(!mpd_isspecial(a)); |
| 3997 | |
Stefan Krah | 696d10f | 2012-05-16 20:10:21 +0200 | [diff] [blame] | 3998 | if (mpd_iszerocoeff(a)) { |
| 3999 | _settriple(result, MPD_POS, 1, 0); |
| 4000 | return; |
| 4001 | } |
| 4002 | |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4003 | /* |
Stefan Krah | 696d10f | 2012-05-16 20:10:21 +0200 | [diff] [blame] | 4004 | * We are calculating e^x = e^(r*10^t) = (e^r)^(10^t), where abs(r) < 1 and t >= 0. |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4005 | * |
| 4006 | * If t > 0, we have: |
| 4007 | * |
Stefan Krah | 696d10f | 2012-05-16 20:10:21 +0200 | [diff] [blame] | 4008 | * (1) 0.1 <= r < 1, so e^0.1 <= e^r. If t > MAX_T, overflow occurs: |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4009 | * |
Stefan Krah | 696d10f | 2012-05-16 20:10:21 +0200 | [diff] [blame] | 4010 | * MAX-EMAX+1 < log10(e^(0.1*10*t)) <= log10(e^(r*10^t)) < adjexp(e^(r*10^t))+1 |
| 4011 | * |
Stefan Krah | 9a5beec | 2012-05-31 16:21:34 +0200 | [diff] [blame] | 4012 | * (2) -1 < r <= -0.1, so e^r <= e^-0.1. If t > MAX_T, underflow occurs: |
Stefan Krah | 696d10f | 2012-05-16 20:10:21 +0200 | [diff] [blame] | 4013 | * |
Stefan Krah | 9a5beec | 2012-05-31 16:21:34 +0200 | [diff] [blame] | 4014 | * adjexp(e^(r*10^t)) <= log10(e^(r*10^t)) <= log10(e^(-0.1*10^t)) < MIN-ETINY |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4015 | */ |
| 4016 | #if defined(CONFIG_64) |
| 4017 | #define MPD_EXP_MAX_T 19 |
| 4018 | #elif defined(CONFIG_32) |
| 4019 | #define MPD_EXP_MAX_T 10 |
| 4020 | #endif |
| 4021 | t = a->digits + a->exp; |
| 4022 | t = (t > 0) ? t : 0; |
| 4023 | if (t > MPD_EXP_MAX_T) { |
| 4024 | if (mpd_ispositive(a)) { |
| 4025 | mpd_setspecial(result, MPD_POS, MPD_INF); |
| 4026 | *status |= MPD_Overflow|MPD_Inexact|MPD_Rounded; |
| 4027 | } |
| 4028 | else { |
| 4029 | _settriple(result, MPD_POS, 0, mpd_etiny(ctx)); |
| 4030 | *status |= (MPD_Inexact|MPD_Rounded|MPD_Subnormal| |
| 4031 | MPD_Underflow|MPD_Clamped); |
| 4032 | } |
| 4033 | return; |
| 4034 | } |
| 4035 | |
Stefan Krah | 696d10f | 2012-05-16 20:10:21 +0200 | [diff] [blame] | 4036 | /* abs(a) <= 9 * 10**(-prec-1) */ |
| 4037 | if (_mpd_qexp_check_one(result, a, ctx, status)) { |
| 4038 | return; |
| 4039 | } |
| 4040 | |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4041 | mpd_maxcontext(&workctx); |
| 4042 | workctx.prec = ctx->prec + t + 2; |
Stefan Krah | 696d10f | 2012-05-16 20:10:21 +0200 | [diff] [blame] | 4043 | workctx.prec = (workctx.prec < 10) ? 10 : workctx.prec; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4044 | workctx.round = MPD_ROUND_HALF_EVEN; |
| 4045 | |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4046 | if (!mpd_qcopy(result, a, status)) { |
Stefan Krah | 696d10f | 2012-05-16 20:10:21 +0200 | [diff] [blame] | 4047 | return; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4048 | } |
| 4049 | result->exp -= t; |
| 4050 | |
Stefan Krah | 696d10f | 2012-05-16 20:10:21 +0200 | [diff] [blame] | 4051 | /* |
| 4052 | * At this point: |
| 4053 | * 1) 9 * 10**(-prec-1) < abs(a) |
| 4054 | * 2) 9 * 10**(-prec-t-1) < abs(r) |
| 4055 | * 3) log10(9) - prec - t - 1 < log10(abs(r)) < adjexp(abs(r)) + 1 |
| 4056 | * 4) - prec - t - 2 < adjexp(abs(r)) <= -1 |
| 4057 | */ |
| 4058 | n = _mpd_get_exp_iterations(result, workctx.prec); |
| 4059 | if (n == MPD_SSIZE_MAX) { |
| 4060 | mpd_seterror(result, MPD_Invalid_operation, status); /* GCOV_UNLIKELY */ |
| 4061 | return; /* GCOV_UNLIKELY */ |
| 4062 | } |
| 4063 | |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4064 | _settriple(&sum, MPD_POS, 1, 0); |
| 4065 | |
| 4066 | for (j = n-1; j >= 1; j--) { |
| 4067 | word.data[0] = j; |
| 4068 | mpd_setdigits(&word); |
| 4069 | mpd_qdiv(&tmp, result, &word, &workctx, &workctx.status); |
Stefan Krah | 696d10f | 2012-05-16 20:10:21 +0200 | [diff] [blame] | 4070 | mpd_qfma(&sum, &sum, &tmp, &one, &workctx, &workctx.status); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4071 | } |
| 4072 | |
| 4073 | #ifdef CONFIG_64 |
| 4074 | _mpd_qpow_uint(result, &sum, mpd_pow10[t], MPD_POS, &workctx, status); |
| 4075 | #else |
| 4076 | if (t <= MPD_MAX_POW10) { |
| 4077 | _mpd_qpow_uint(result, &sum, mpd_pow10[t], MPD_POS, &workctx, status); |
| 4078 | } |
| 4079 | else { |
| 4080 | t -= MPD_MAX_POW10; |
| 4081 | _mpd_qpow_uint(&tmp, &sum, mpd_pow10[MPD_MAX_POW10], MPD_POS, |
| 4082 | &workctx, status); |
| 4083 | _mpd_qpow_uint(result, &tmp, mpd_pow10[t], MPD_POS, &workctx, status); |
| 4084 | } |
| 4085 | #endif |
| 4086 | |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4087 | mpd_del(&tmp); |
| 4088 | mpd_del(&sum); |
| 4089 | *status |= (workctx.status&MPD_Errors); |
| 4090 | *status |= (MPD_Inexact|MPD_Rounded); |
| 4091 | } |
| 4092 | |
| 4093 | /* exp(a) */ |
| 4094 | void |
| 4095 | mpd_qexp(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, |
| 4096 | uint32_t *status) |
| 4097 | { |
| 4098 | mpd_context_t workctx; |
| 4099 | |
| 4100 | if (mpd_isspecial(a)) { |
| 4101 | if (mpd_qcheck_nan(result, a, ctx, status)) { |
| 4102 | return; |
| 4103 | } |
| 4104 | if (mpd_isnegative(a)) { |
| 4105 | _settriple(result, MPD_POS, 0, 0); |
| 4106 | } |
| 4107 | else { |
| 4108 | mpd_setspecial(result, MPD_POS, MPD_INF); |
| 4109 | } |
| 4110 | return; |
| 4111 | } |
| 4112 | if (mpd_iszerocoeff(a)) { |
| 4113 | _settriple(result, MPD_POS, 1, 0); |
| 4114 | return; |
| 4115 | } |
| 4116 | |
| 4117 | workctx = *ctx; |
| 4118 | workctx.round = MPD_ROUND_HALF_EVEN; |
| 4119 | |
| 4120 | if (ctx->allcr) { |
| 4121 | MPD_NEW_STATIC(t1, 0,0,0,0); |
| 4122 | MPD_NEW_STATIC(t2, 0,0,0,0); |
| 4123 | MPD_NEW_STATIC(ulp, 0,0,0,0); |
| 4124 | MPD_NEW_STATIC(aa, 0,0,0,0); |
| 4125 | mpd_ssize_t prec; |
Stefan Krah | 4d3e0a6 | 2012-05-31 20:01:05 +0200 | [diff] [blame] | 4126 | mpd_ssize_t ulpexp; |
| 4127 | uint32_t workstatus; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4128 | |
| 4129 | if (result == a) { |
| 4130 | if (!mpd_qcopy(&aa, a, status)) { |
| 4131 | mpd_seterror(result, MPD_Malloc_error, status); |
| 4132 | return; |
| 4133 | } |
| 4134 | a = &aa; |
| 4135 | } |
| 4136 | |
| 4137 | workctx.clamp = 0; |
| 4138 | prec = ctx->prec + 3; |
| 4139 | while (1) { |
| 4140 | workctx.prec = prec; |
Stefan Krah | 4d3e0a6 | 2012-05-31 20:01:05 +0200 | [diff] [blame] | 4141 | workstatus = 0; |
| 4142 | |
| 4143 | _mpd_qexp(result, a, &workctx, &workstatus); |
| 4144 | *status |= workstatus; |
| 4145 | |
| 4146 | ulpexp = result->exp + result->digits - workctx.prec; |
| 4147 | if (workstatus & MPD_Underflow) { |
| 4148 | /* The effective work precision is result->digits. */ |
| 4149 | ulpexp = result->exp; |
| 4150 | } |
| 4151 | _ssettriple(&ulp, MPD_POS, 1, ulpexp); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4152 | |
Stefan Krah | 696d10f | 2012-05-16 20:10:21 +0200 | [diff] [blame] | 4153 | /* |
Stefan Krah | 4d3e0a6 | 2012-05-31 20:01:05 +0200 | [diff] [blame] | 4154 | * At this point [1]: |
Stefan Krah | 696d10f | 2012-05-16 20:10:21 +0200 | [diff] [blame] | 4155 | * 1) abs(result - e**x) < 0.5 * 10**(-prec) * e**x |
| 4156 | * 2) result - ulp < e**x < result + ulp |
| 4157 | * 3) result - ulp < result < result + ulp |
| 4158 | * |
| 4159 | * If round(result-ulp)==round(result+ulp), then |
| 4160 | * round(result)==round(e**x). Therefore the result |
| 4161 | * is correctly rounded. |
Stefan Krah | 4d3e0a6 | 2012-05-31 20:01:05 +0200 | [diff] [blame] | 4162 | * |
| 4163 | * [1] If abs(a) <= 9 * 10**(-prec-1), use the absolute |
| 4164 | * error for a similar argument. |
Stefan Krah | 696d10f | 2012-05-16 20:10:21 +0200 | [diff] [blame] | 4165 | */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4166 | workctx.prec = ctx->prec; |
| 4167 | mpd_qadd(&t1, result, &ulp, &workctx, &workctx.status); |
| 4168 | mpd_qsub(&t2, result, &ulp, &workctx, &workctx.status); |
| 4169 | if (mpd_isspecial(result) || mpd_iszerocoeff(result) || |
| 4170 | mpd_qcmp(&t1, &t2, status) == 0) { |
| 4171 | workctx.clamp = ctx->clamp; |
Stefan Krah | 0271766 | 2012-05-31 20:49:24 +0200 | [diff] [blame] | 4172 | _mpd_zeropad(result, &workctx, status); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4173 | mpd_check_underflow(result, &workctx, status); |
| 4174 | mpd_qfinalize(result, &workctx, status); |
| 4175 | break; |
| 4176 | } |
| 4177 | prec += MPD_RDIGITS; |
| 4178 | } |
| 4179 | mpd_del(&t1); |
| 4180 | mpd_del(&t2); |
| 4181 | mpd_del(&ulp); |
| 4182 | mpd_del(&aa); |
| 4183 | } |
| 4184 | else { |
| 4185 | _mpd_qexp(result, a, &workctx, status); |
Stefan Krah | 0271766 | 2012-05-31 20:49:24 +0200 | [diff] [blame] | 4186 | _mpd_zeropad(result, &workctx, status); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4187 | mpd_check_underflow(result, &workctx, status); |
| 4188 | mpd_qfinalize(result, &workctx, status); |
| 4189 | } |
| 4190 | } |
| 4191 | |
| 4192 | /* Fused multiply-add: (a * b) + c, with a single final rounding. */ |
| 4193 | void |
| 4194 | mpd_qfma(mpd_t *result, const mpd_t *a, const mpd_t *b, const mpd_t *c, |
| 4195 | const mpd_context_t *ctx, uint32_t *status) |
| 4196 | { |
| 4197 | uint32_t workstatus = 0; |
| 4198 | mpd_t *cc = (mpd_t *)c; |
| 4199 | |
| 4200 | if (result == c) { |
| 4201 | if ((cc = mpd_qncopy(c)) == NULL) { |
| 4202 | mpd_seterror(result, MPD_Malloc_error, status); |
| 4203 | return; |
| 4204 | } |
| 4205 | } |
| 4206 | |
| 4207 | _mpd_qmul(result, a, b, ctx, &workstatus); |
| 4208 | if (!(workstatus&MPD_Invalid_operation)) { |
| 4209 | mpd_qadd(result, result, cc, ctx, &workstatus); |
| 4210 | } |
| 4211 | |
| 4212 | if (cc != c) mpd_del(cc); |
| 4213 | *status |= workstatus; |
| 4214 | } |
| 4215 | |
Stefan Krah | a3394bc | 2012-06-06 15:57:18 +0200 | [diff] [blame] | 4216 | /* |
| 4217 | * Schedule the optimal precision increase for the Newton iteration. |
| 4218 | * v := input operand |
| 4219 | * z_0 := initial approximation |
| 4220 | * initprec := natural number such that abs(log(v) - z_0) < 10**-initprec |
| 4221 | * maxprec := target precision |
| 4222 | * |
| 4223 | * For convenience the output klist contains the elements in reverse order: |
| 4224 | * klist := [k_n-1, ..., k_0], where |
| 4225 | * 1) k_0 <= initprec and |
| 4226 | * 2) abs(log(v) - result) < 10**(-2*k_n-1 + 1) <= 10**-maxprec. |
| 4227 | */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4228 | static inline int |
| 4229 | ln_schedule_prec(mpd_ssize_t klist[MPD_MAX_PREC_LOG2], mpd_ssize_t maxprec, |
| 4230 | mpd_ssize_t initprec) |
| 4231 | { |
| 4232 | mpd_ssize_t k; |
| 4233 | int i; |
| 4234 | |
| 4235 | assert(maxprec >= 2 && initprec >= 2); |
| 4236 | if (maxprec <= initprec) return -1; |
| 4237 | |
| 4238 | i = 0; k = maxprec; |
| 4239 | do { |
| 4240 | k = (k+2) / 2; |
| 4241 | klist[i++] = k; |
| 4242 | } while (k > initprec); |
| 4243 | |
| 4244 | return i-1; |
| 4245 | } |
| 4246 | |
Stefan Krah | a3394bc | 2012-06-06 15:57:18 +0200 | [diff] [blame] | 4247 | /* The constants have been verified with both decimal.py and mpfr. */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4248 | #ifdef CONFIG_64 |
| 4249 | #if MPD_RDIGITS != 19 |
| 4250 | #error "mpdecimal.c: MPD_RDIGITS must be 19." |
| 4251 | #endif |
| 4252 | static const mpd_uint_t mpd_ln10_data[MPD_MINALLOC_MAX] = { |
| 4253 | 6983716328982174407ULL, 9089704281976336583ULL, 1515961135648465461ULL, |
| 4254 | 4416816335727555703ULL, 2900988039194170265ULL, 2307925037472986509ULL, |
| 4255 | 107598438319191292ULL, 3466624107184669231ULL, 4450099781311469159ULL, |
| 4256 | 9807828059751193854ULL, 7713456862091670584ULL, 1492198849978748873ULL, |
| 4257 | 6528728696511086257ULL, 2385392051446341972ULL, 8692180205189339507ULL, |
| 4258 | 6518769751037497088ULL, 2375253577097505395ULL, 9095610299291824318ULL, |
| 4259 | 982748238504564801ULL, 5438635917781170543ULL, 7547331541421808427ULL, |
| 4260 | 752371033310119785ULL, 3171643095059950878ULL, 9785265383207606726ULL, |
| 4261 | 2932258279850258550ULL, 5497347726624257094ULL, 2976979522110718264ULL, |
| 4262 | 9221477656763693866ULL, 1979650047149510504ULL, 6674183485704422507ULL, |
| 4263 | 9702766860595249671ULL, 9278096762712757753ULL, 9314848524948644871ULL, |
| 4264 | 6826928280848118428ULL, 754403708474699401ULL, 230105703089634572ULL, |
| 4265 | 1929203337658714166ULL, 7589402567763113569ULL, 4208241314695689016ULL, |
| 4266 | 2922455440575892572ULL, 9356734206705811364ULL, 2684916746550586856ULL, |
| 4267 | 644507064800027750ULL, 9476834636167921018ULL, 5659121373450747856ULL, |
| 4268 | 2835522011480466371ULL, 6470806855677432162ULL, 7141748003688084012ULL, |
| 4269 | 9619404400222105101ULL, 5504893431493939147ULL, 6674744042432743651ULL, |
| 4270 | 2287698219886746543ULL, 7773262884616336622ULL, 1985283935053089653ULL, |
| 4271 | 4680843799894826233ULL, 8168948290720832555ULL, 8067566662873690987ULL, |
| 4272 | 6248633409525465082ULL, 9829834196778404228ULL, 3524802359972050895ULL, |
| 4273 | 3327900967572609677ULL, 110148862877297603ULL, 179914546843642076ULL, |
| 4274 | 2302585092994045684ULL |
| 4275 | }; |
| 4276 | #else |
| 4277 | #if MPD_RDIGITS != 9 |
| 4278 | #error "mpdecimal.c: MPD_RDIGITS must be 9." |
| 4279 | #endif |
| 4280 | static const mpd_uint_t mpd_ln10_data[MPD_MINALLOC_MAX] = { |
| 4281 | 401682692UL, 708474699UL, 720754403UL, 30896345UL, 602301057UL, 765871416UL, |
| 4282 | 192920333UL, 763113569UL, 589402567UL, 956890167UL, 82413146UL, 589257242UL, |
| 4283 | 245544057UL, 811364292UL, 734206705UL, 868569356UL, 167465505UL, 775026849UL, |
| 4284 | 706480002UL, 18064450UL, 636167921UL, 569476834UL, 734507478UL, 156591213UL, |
| 4285 | 148046637UL, 283552201UL, 677432162UL, 470806855UL, 880840126UL, 417480036UL, |
| 4286 | 210510171UL, 940440022UL, 939147961UL, 893431493UL, 436515504UL, 440424327UL, |
| 4287 | 654366747UL, 821988674UL, 622228769UL, 884616336UL, 537773262UL, 350530896UL, |
| 4288 | 319852839UL, 989482623UL, 468084379UL, 720832555UL, 168948290UL, 736909878UL, |
| 4289 | 675666628UL, 546508280UL, 863340952UL, 404228624UL, 834196778UL, 508959829UL, |
| 4290 | 23599720UL, 967735248UL, 96757260UL, 603332790UL, 862877297UL, 760110148UL, |
| 4291 | 468436420UL, 401799145UL, 299404568UL, 230258509UL |
| 4292 | }; |
| 4293 | #endif |
| 4294 | /* _mpd_ln10 is used directly for precisions smaller than MINALLOC_MAX*RDIGITS. |
| 4295 | Otherwise, it serves as the initial approximation for calculating ln(10). */ |
| 4296 | static const mpd_t _mpd_ln10 = { |
| 4297 | MPD_STATIC|MPD_CONST_DATA, -(MPD_MINALLOC_MAX*MPD_RDIGITS-1), |
| 4298 | MPD_MINALLOC_MAX*MPD_RDIGITS, MPD_MINALLOC_MAX, MPD_MINALLOC_MAX, |
| 4299 | (mpd_uint_t *)mpd_ln10_data |
| 4300 | }; |
| 4301 | |
Stefan Krah | 1cf6dfc | 2012-06-08 18:41:33 +0200 | [diff] [blame] | 4302 | /* |
| 4303 | * Set 'result' to log(10). |
| 4304 | * Ulp error: abs(result - log(10)) < ulp(log(10)) |
| 4305 | * Relative error : abs(result - log(10)) < 5 * 10**-prec * log(10) |
| 4306 | * |
| 4307 | * NOTE: The relative error is not derived from the ulp error, but |
| 4308 | * calculated separately using the fact that 23/10 < log(10) < 24/10. |
| 4309 | */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4310 | void |
| 4311 | mpd_qln10(mpd_t *result, mpd_ssize_t prec, uint32_t *status) |
| 4312 | { |
| 4313 | mpd_context_t varcontext, maxcontext; |
| 4314 | MPD_NEW_STATIC(tmp, 0,0,0,0); |
| 4315 | MPD_NEW_CONST(static10, 0,0,2,1,1,10); |
| 4316 | mpd_ssize_t klist[MPD_MAX_PREC_LOG2]; |
| 4317 | mpd_uint_t rnd; |
| 4318 | mpd_ssize_t shift; |
| 4319 | int i; |
| 4320 | |
| 4321 | assert(prec >= 1); |
| 4322 | |
| 4323 | shift = MPD_MINALLOC_MAX*MPD_RDIGITS-prec; |
| 4324 | shift = shift < 0 ? 0 : shift; |
| 4325 | |
| 4326 | rnd = mpd_qshiftr(result, &_mpd_ln10, shift, status); |
| 4327 | if (rnd == MPD_UINT_MAX) { |
| 4328 | mpd_seterror(result, MPD_Malloc_error, status); |
| 4329 | return; |
| 4330 | } |
| 4331 | result->exp = -(result->digits-1); |
| 4332 | |
| 4333 | mpd_maxcontext(&maxcontext); |
| 4334 | if (prec < MPD_MINALLOC_MAX*MPD_RDIGITS) { |
| 4335 | maxcontext.prec = prec; |
| 4336 | _mpd_apply_round_excess(result, rnd, &maxcontext, status); |
| 4337 | *status |= (MPD_Inexact|MPD_Rounded); |
| 4338 | return; |
| 4339 | } |
| 4340 | |
| 4341 | mpd_maxcontext(&varcontext); |
| 4342 | varcontext.round = MPD_ROUND_TRUNC; |
| 4343 | |
Stefan Krah | a3394bc | 2012-06-06 15:57:18 +0200 | [diff] [blame] | 4344 | i = ln_schedule_prec(klist, prec+2, -result->exp); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4345 | for (; i >= 0; i--) { |
| 4346 | varcontext.prec = 2*klist[i]+3; |
| 4347 | result->flags ^= MPD_NEG; |
| 4348 | _mpd_qexp(&tmp, result, &varcontext, status); |
| 4349 | result->flags ^= MPD_NEG; |
| 4350 | mpd_qmul(&tmp, &static10, &tmp, &varcontext, status); |
| 4351 | mpd_qsub(&tmp, &tmp, &one, &maxcontext, status); |
| 4352 | mpd_qadd(result, result, &tmp, &maxcontext, status); |
| 4353 | if (mpd_isspecial(result)) { |
| 4354 | break; |
| 4355 | } |
| 4356 | } |
| 4357 | |
| 4358 | mpd_del(&tmp); |
| 4359 | maxcontext.prec = prec; |
| 4360 | mpd_qfinalize(result, &maxcontext, status); |
| 4361 | } |
| 4362 | |
Stefan Krah | a3394bc | 2012-06-06 15:57:18 +0200 | [diff] [blame] | 4363 | /* |
| 4364 | * Initial approximations for the ln() iteration. The values have the |
| 4365 | * following properties (established with both decimal.py and mpfr): |
| 4366 | * |
| 4367 | * Index 0 - 400, logarithms of x in [1.00, 5.00]: |
| 4368 | * abs(lnapprox[i] * 10**-3 - log((i+100)/100)) < 10**-2 |
| 4369 | * abs(lnapprox[i] * 10**-3 - log((i+1+100)/100)) < 10**-2 |
| 4370 | * |
| 4371 | * Index 401 - 899, logarithms of x in (0.500, 0.999]: |
| 4372 | * abs(-lnapprox[i] * 10**-3 - log((i+100)/1000)) < 10**-2 |
| 4373 | * abs(-lnapprox[i] * 10**-3 - log((i+1+100)/1000)) < 10**-2 |
| 4374 | */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4375 | static const uint16_t lnapprox[900] = { |
| 4376 | /* index 0 - 400: log((i+100)/100) * 1000 */ |
| 4377 | 0, 10, 20, 30, 39, 49, 58, 68, 77, 86, 95, 104, 113, 122, 131, 140, 148, 157, |
| 4378 | 166, 174, 182, 191, 199, 207, 215, 223, 231, 239, 247, 255, 262, 270, 278, |
| 4379 | 285, 293, 300, 308, 315, 322, 329, 336, 344, 351, 358, 365, 372, 378, 385, |
| 4380 | 392, 399, 406, 412, 419, 425, 432, 438, 445, 451, 457, 464, 470, 476, 482, |
| 4381 | 489, 495, 501, 507, 513, 519, 525, 531, 536, 542, 548, 554, 560, 565, 571, |
| 4382 | 577, 582, 588, 593, 599, 604, 610, 615, 621, 626, 631, 637, 642, 647, 652, |
| 4383 | 658, 663, 668, 673, 678, 683, 688, 693, 698, 703, 708, 713, 718, 723, 728, |
| 4384 | 732, 737, 742, 747, 751, 756, 761, 766, 770, 775, 779, 784, 788, 793, 798, |
| 4385 | 802, 806, 811, 815, 820, 824, 829, 833, 837, 842, 846, 850, 854, 859, 863, |
| 4386 | 867, 871, 876, 880, 884, 888, 892, 896, 900, 904, 908, 912, 916, 920, 924, |
| 4387 | 928, 932, 936, 940, 944, 948, 952, 956, 959, 963, 967, 971, 975, 978, 982, |
| 4388 | 986, 990, 993, 997, 1001, 1004, 1008, 1012, 1015, 1019, 1022, 1026, 1030, |
| 4389 | 1033, 1037, 1040, 1044, 1047, 1051, 1054, 1058, 1061, 1065, 1068, 1072, 1075, |
| 4390 | 1078, 1082, 1085, 1089, 1092, 1095, 1099, 1102, 1105, 1109, 1112, 1115, 1118, |
| 4391 | 1122, 1125, 1128, 1131, 1135, 1138, 1141, 1144, 1147, 1151, 1154, 1157, 1160, |
| 4392 | 1163, 1166, 1169, 1172, 1176, 1179, 1182, 1185, 1188, 1191, 1194, 1197, 1200, |
| 4393 | 1203, 1206, 1209, 1212, 1215, 1218, 1221, 1224, 1227, 1230, 1233, 1235, 1238, |
| 4394 | 1241, 1244, 1247, 1250, 1253, 1256, 1258, 1261, 1264, 1267, 1270, 1273, 1275, |
| 4395 | 1278, 1281, 1284, 1286, 1289, 1292, 1295, 1297, 1300, 1303, 1306, 1308, 1311, |
| 4396 | 1314, 1316, 1319, 1322, 1324, 1327, 1330, 1332, 1335, 1338, 1340, 1343, 1345, |
| 4397 | 1348, 1351, 1353, 1356, 1358, 1361, 1364, 1366, 1369, 1371, 1374, 1376, 1379, |
| 4398 | 1381, 1384, 1386, 1389, 1391, 1394, 1396, 1399, 1401, 1404, 1406, 1409, 1411, |
| 4399 | 1413, 1416, 1418, 1421, 1423, 1426, 1428, 1430, 1433, 1435, 1437, 1440, 1442, |
| 4400 | 1445, 1447, 1449, 1452, 1454, 1456, 1459, 1461, 1463, 1466, 1468, 1470, 1472, |
| 4401 | 1475, 1477, 1479, 1482, 1484, 1486, 1488, 1491, 1493, 1495, 1497, 1500, 1502, |
| 4402 | 1504, 1506, 1509, 1511, 1513, 1515, 1517, 1520, 1522, 1524, 1526, 1528, 1530, |
| 4403 | 1533, 1535, 1537, 1539, 1541, 1543, 1545, 1548, 1550, 1552, 1554, 1556, 1558, |
| 4404 | 1560, 1562, 1564, 1567, 1569, 1571, 1573, 1575, 1577, 1579, 1581, 1583, 1585, |
| 4405 | 1587, 1589, 1591, 1593, 1595, 1597, 1599, 1601, 1603, 1605, 1607, 1609, |
| 4406 | /* index 401 - 899: -log((i+100)/1000) * 1000 */ |
| 4407 | 691, 689, 687, 685, 683, 681, 679, 677, 675, 673, 671, 669, 668, 666, 664, |
| 4408 | 662, 660, 658, 656, 654, 652, 650, 648, 646, 644, 642, 641, 639, 637, 635, |
| 4409 | 633, 631, 629, 627, 626, 624, 622, 620, 618, 616, 614, 612, 611, 609, 607, |
| 4410 | 605, 603, 602, 600, 598, 596, 594, 592, 591, 589, 587, 585, 583, 582, 580, |
| 4411 | 578, 576, 574, 573, 571, 569, 567, 566, 564, 562, 560, 559, 557, 555, 553, |
| 4412 | 552, 550, 548, 546, 545, 543, 541, 540, 538, 536, 534, 533, 531, 529, 528, |
| 4413 | 526, 524, 523, 521, 519, 518, 516, 514, 512, 511, 509, 508, 506, 504, 502, |
| 4414 | 501, 499, 498, 496, 494, 493, 491, 489, 488, 486, 484, 483, 481, 480, 478, |
| 4415 | 476, 475, 473, 472, 470, 468, 467, 465, 464, 462, 460, 459, 457, 456, 454, |
| 4416 | 453, 451, 449, 448, 446, 445, 443, 442, 440, 438, 437, 435, 434, 432, 431, |
| 4417 | 429, 428, 426, 425, 423, 422, 420, 419, 417, 416, 414, 412, 411, 410, 408, |
| 4418 | 406, 405, 404, 402, 400, 399, 398, 396, 394, 393, 392, 390, 389, 387, 386, |
| 4419 | 384, 383, 381, 380, 378, 377, 375, 374, 372, 371, 370, 368, 367, 365, 364, |
| 4420 | 362, 361, 360, 358, 357, 355, 354, 352, 351, 350, 348, 347, 345, 344, 342, |
| 4421 | 341, 340, 338, 337, 336, 334, 333, 331, 330, 328, 327, 326, 324, 323, 322, |
| 4422 | 320, 319, 318, 316, 315, 313, 312, 311, 309, 308, 306, 305, 304, 302, 301, |
| 4423 | 300, 298, 297, 296, 294, 293, 292, 290, 289, 288, 286, 285, 284, 282, 281, |
| 4424 | 280, 278, 277, 276, 274, 273, 272, 270, 269, 268, 267, 265, 264, 263, 261, |
| 4425 | 260, 259, 258, 256, 255, 254, 252, 251, 250, 248, 247, 246, 245, 243, 242, |
| 4426 | 241, 240, 238, 237, 236, 234, 233, 232, 231, 229, 228, 227, 226, 224, 223, |
| 4427 | 222, 221, 219, 218, 217, 216, 214, 213, 212, 211, 210, 208, 207, 206, 205, |
| 4428 | 203, 202, 201, 200, 198, 197, 196, 195, 194, 192, 191, 190, 189, 188, 186, |
| 4429 | 185, 184, 183, 182, 180, 179, 178, 177, 176, 174, 173, 172, 171, 170, 168, |
| 4430 | 167, 166, 165, 164, 162, 161, 160, 159, 158, 157, 156, 154, 153, 152, 151, |
| 4431 | 150, 148, 147, 146, 145, 144, 143, 142, 140, 139, 138, 137, 136, 135, 134, |
| 4432 | 132, 131, 130, 129, 128, 127, 126, 124, 123, 122, 121, 120, 119, 118, 116, |
| 4433 | 115, 114, 113, 112, 111, 110, 109, 108, 106, 105, 104, 103, 102, 101, 100, |
| 4434 | 99, 98, 97, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 84, 83, 82, 81, 80, 79, |
| 4435 | 78, 77, 76, 75, 74, 73, 72, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, |
| 4436 | 58, 57, 56, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, |
| 4437 | 38, 37, 36, 35, 34, 33, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, |
| 4438 | 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 |
| 4439 | }; |
| 4440 | |
Stefan Krah | a3394bc | 2012-06-06 15:57:18 +0200 | [diff] [blame] | 4441 | /* |
| 4442 | * Internal ln() function that does not check for specials, zero or one. |
| 4443 | * Relative error: abs(result - log(a)) < 0.1 * 10**-prec * abs(log(a)) |
| 4444 | */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4445 | static void |
| 4446 | _mpd_qln(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, |
| 4447 | uint32_t *status) |
| 4448 | { |
| 4449 | mpd_context_t varcontext, maxcontext; |
| 4450 | mpd_t *z = (mpd_t *) result; |
| 4451 | MPD_NEW_STATIC(v,0,0,0,0); |
| 4452 | MPD_NEW_STATIC(vtmp,0,0,0,0); |
| 4453 | MPD_NEW_STATIC(tmp,0,0,0,0); |
| 4454 | mpd_ssize_t klist[MPD_MAX_PREC_LOG2]; |
| 4455 | mpd_ssize_t maxprec, shift, t; |
| 4456 | mpd_ssize_t a_digits, a_exp; |
| 4457 | mpd_uint_t dummy, x; |
| 4458 | int i; |
| 4459 | |
| 4460 | assert(!mpd_isspecial(a) && !mpd_iszerocoeff(a)); |
| 4461 | |
| 4462 | /* |
| 4463 | * We are calculating ln(a) = ln(v * 10^t) = ln(v) + t*ln(10), |
| 4464 | * where 0.5 < v <= 5. |
| 4465 | */ |
| 4466 | if (!mpd_qcopy(&v, a, status)) { |
| 4467 | mpd_seterror(result, MPD_Malloc_error, status); |
| 4468 | goto finish; |
| 4469 | } |
| 4470 | |
| 4471 | /* Initial approximation: we have at least one non-zero digit */ |
| 4472 | _mpd_get_msdigits(&dummy, &x, &v, 3); |
| 4473 | if (x < 10) x *= 10; |
| 4474 | if (x < 100) x *= 10; |
| 4475 | x -= 100; |
| 4476 | |
| 4477 | /* a may equal z */ |
| 4478 | a_digits = a->digits; |
| 4479 | a_exp = a->exp; |
| 4480 | |
| 4481 | mpd_minalloc(z); |
| 4482 | mpd_clear_flags(z); |
| 4483 | z->data[0] = lnapprox[x]; |
| 4484 | z->len = 1; |
| 4485 | z->exp = -3; |
| 4486 | mpd_setdigits(z); |
| 4487 | |
| 4488 | if (x <= 400) { |
Stefan Krah | a3394bc | 2012-06-06 15:57:18 +0200 | [diff] [blame] | 4489 | /* Reduce the input operand to 1.00 <= v <= 5.00. Let y = x + 100, |
| 4490 | * so 100 <= y <= 500. Since y contains the most significant digits |
| 4491 | * of v, y/100 <= v < (y+1)/100 and abs(z - log(v)) < 10**-2. */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4492 | v.exp = -(a_digits - 1); |
| 4493 | t = a_exp + a_digits - 1; |
| 4494 | } |
| 4495 | else { |
Stefan Krah | a3394bc | 2012-06-06 15:57:18 +0200 | [diff] [blame] | 4496 | /* Reduce the input operand to 0.500 < v <= 0.999. Let y = x + 100, |
| 4497 | * so 500 < y <= 999. Since y contains the most significant digits |
| 4498 | * of v, y/1000 <= v < (y+1)/1000 and abs(z - log(v)) < 10**-2. */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4499 | v.exp = -a_digits; |
| 4500 | t = a_exp + a_digits; |
| 4501 | mpd_set_negative(z); |
| 4502 | } |
| 4503 | |
| 4504 | mpd_maxcontext(&maxcontext); |
| 4505 | mpd_maxcontext(&varcontext); |
| 4506 | varcontext.round = MPD_ROUND_TRUNC; |
| 4507 | |
| 4508 | maxprec = ctx->prec + 2; |
Stefan Krah | a3394bc | 2012-06-06 15:57:18 +0200 | [diff] [blame] | 4509 | if (t == 0 && (x <= 15 || x >= 800)) { |
| 4510 | /* 0.900 <= v <= 1.15: Estimate the magnitude of the logarithm. |
| 4511 | * If ln(v) will underflow, skip the loop. Otherwise, adjust the |
| 4512 | * precision upwards in order to obtain a sufficient number of |
| 4513 | * significant digits. |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4514 | * |
Stefan Krah | a3394bc | 2012-06-06 15:57:18 +0200 | [diff] [blame] | 4515 | * Case v > 1: |
| 4516 | * abs((v-1)/10) < abs((v-1)/v) < abs(ln(v)) < abs(v-1) |
| 4517 | * Case v < 1: |
| 4518 | * abs(v-1) < abs(ln(v)) < abs((v-1)/v) < abs((v-1)*10) |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4519 | */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4520 | int cmp = _mpd_cmp(&v, &one); |
| 4521 | |
Stefan Krah | a3394bc | 2012-06-06 15:57:18 +0200 | [diff] [blame] | 4522 | /* Upper bound (assume v > 1): abs(v-1), unrounded */ |
| 4523 | _mpd_qsub(&tmp, &v, &one, &maxcontext, &maxcontext.status); |
| 4524 | if (maxcontext.status & MPD_Errors) { |
| 4525 | mpd_seterror(result, MPD_Malloc_error, status); |
| 4526 | goto finish; |
| 4527 | } |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4528 | |
| 4529 | if (cmp < 0) { |
Stefan Krah | a3394bc | 2012-06-06 15:57:18 +0200 | [diff] [blame] | 4530 | /* v < 1: abs((v-1)*10) */ |
| 4531 | tmp.exp += 1; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4532 | } |
Stefan Krah | a3394bc | 2012-06-06 15:57:18 +0200 | [diff] [blame] | 4533 | if (mpd_adjexp(&tmp) < mpd_etiny(ctx)) { |
| 4534 | /* The upper bound is less than etiny: Underflow to zero */ |
| 4535 | _settriple(result, (cmp<0), 1, mpd_etiny(ctx)-1); |
| 4536 | goto finish; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4537 | } |
Stefan Krah | a3394bc | 2012-06-06 15:57:18 +0200 | [diff] [blame] | 4538 | /* Lower bound: abs((v-1)/10) or abs(v-1) */ |
| 4539 | tmp.exp -= 1; |
| 4540 | if (mpd_adjexp(&tmp) < 0) { |
| 4541 | /* Absolute error of the loop: abs(z - log(v)) < 10**-p. If |
| 4542 | * p = ctx->prec+2-adjexp(lower), then the relative error of |
| 4543 | * the result is (using 10**adjexp(x) <= abs(x)): |
| 4544 | * |
| 4545 | * abs(z - log(v)) / abs(log(v)) < 10**-p / abs(log(v)) |
| 4546 | * <= 10**(-ctx->prec-2) |
| 4547 | */ |
| 4548 | maxprec = maxprec - mpd_adjexp(&tmp); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4549 | } |
| 4550 | } |
| 4551 | |
| 4552 | i = ln_schedule_prec(klist, maxprec, 2); |
| 4553 | for (; i >= 0; i--) { |
| 4554 | varcontext.prec = 2*klist[i]+3; |
| 4555 | z->flags ^= MPD_NEG; |
| 4556 | _mpd_qexp(&tmp, z, &varcontext, status); |
| 4557 | z->flags ^= MPD_NEG; |
| 4558 | |
| 4559 | if (v.digits > varcontext.prec) { |
| 4560 | shift = v.digits - varcontext.prec; |
| 4561 | mpd_qshiftr(&vtmp, &v, shift, status); |
| 4562 | vtmp.exp += shift; |
| 4563 | mpd_qmul(&tmp, &vtmp, &tmp, &varcontext, status); |
| 4564 | } |
| 4565 | else { |
| 4566 | mpd_qmul(&tmp, &v, &tmp, &varcontext, status); |
| 4567 | } |
| 4568 | |
| 4569 | mpd_qsub(&tmp, &tmp, &one, &maxcontext, status); |
| 4570 | mpd_qadd(z, z, &tmp, &maxcontext, status); |
| 4571 | if (mpd_isspecial(z)) { |
| 4572 | break; |
| 4573 | } |
| 4574 | } |
| 4575 | |
Stefan Krah | a3394bc | 2012-06-06 15:57:18 +0200 | [diff] [blame] | 4576 | /* |
| 4577 | * Case t == 0: |
| 4578 | * t * log(10) == 0, the result does not change and the analysis |
| 4579 | * above applies. If v < 0.900 or v > 1.15, the relative error is |
| 4580 | * less than 10**(-ctx.prec-1). |
| 4581 | * Case t != 0: |
| 4582 | * z := approx(log(v)) |
| 4583 | * y := approx(log(10)) |
| 4584 | * p := maxprec = ctx->prec + 2 |
| 4585 | * Absolute errors: |
| 4586 | * 1) abs(z - log(v)) < 10**-p |
| 4587 | * 2) abs(y - log(10)) < 10**-p |
| 4588 | * The multiplication is exact, so: |
| 4589 | * 3) abs(t*y - t*log(10)) < t*10**-p |
| 4590 | * The sum is exact, so: |
| 4591 | * 4) abs((z + t*y) - (log(v) + t*log(10))) < (abs(t) + 1) * 10**-p |
| 4592 | * Bounds for log(v) and log(10): |
| 4593 | * 5) -7/10 < log(v) < 17/10 |
| 4594 | * 6) 23/10 < log(10) < 24/10 |
| 4595 | * Using 4), 5), 6) and t != 0, the relative error is: |
| 4596 | * |
| 4597 | * 7) relerr < ((abs(t) + 1)*10**-p) / abs(log(v) + t*log(10)) |
| 4598 | * < 0.5 * 10**(-p + 1) = 0.5 * 10**(-ctx->prec-1) |
| 4599 | */ |
| 4600 | mpd_qln10(&v, maxprec+1, status); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4601 | mpd_qmul_ssize(&tmp, &v, t, &maxcontext, status); |
Stefan Krah | a3394bc | 2012-06-06 15:57:18 +0200 | [diff] [blame] | 4602 | mpd_qadd(result, &tmp, z, &maxcontext, status); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4603 | |
| 4604 | |
| 4605 | finish: |
Stefan Krah | a3394bc | 2012-06-06 15:57:18 +0200 | [diff] [blame] | 4606 | *status |= (MPD_Inexact|MPD_Rounded); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4607 | mpd_del(&v); |
| 4608 | mpd_del(&vtmp); |
| 4609 | mpd_del(&tmp); |
| 4610 | } |
| 4611 | |
| 4612 | /* ln(a) */ |
| 4613 | void |
| 4614 | mpd_qln(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, |
| 4615 | uint32_t *status) |
| 4616 | { |
| 4617 | mpd_context_t workctx; |
| 4618 | mpd_ssize_t adjexp, t; |
| 4619 | |
| 4620 | if (mpd_isspecial(a)) { |
| 4621 | if (mpd_qcheck_nan(result, a, ctx, status)) { |
| 4622 | return; |
| 4623 | } |
| 4624 | if (mpd_isnegative(a)) { |
| 4625 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 4626 | return; |
| 4627 | } |
| 4628 | mpd_setspecial(result, MPD_POS, MPD_INF); |
| 4629 | return; |
| 4630 | } |
| 4631 | if (mpd_iszerocoeff(a)) { |
| 4632 | mpd_setspecial(result, MPD_NEG, MPD_INF); |
| 4633 | return; |
| 4634 | } |
| 4635 | if (mpd_isnegative(a)) { |
| 4636 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 4637 | return; |
| 4638 | } |
| 4639 | if (_mpd_cmp(a, &one) == 0) { |
| 4640 | _settriple(result, MPD_POS, 0, 0); |
| 4641 | return; |
| 4642 | } |
Stefan Krah | 7bda265 | 2012-06-07 17:48:47 +0200 | [diff] [blame] | 4643 | /* |
| 4644 | * Check if the result will overflow (0 < x, x != 1): |
| 4645 | * 1) log10(x) < 0 iff adjexp(x) < 0 |
| 4646 | * 2) 0 < x /\ x <= y ==> adjexp(x) <= adjexp(y) |
| 4647 | * 3) 0 < x /\ x != 1 ==> 2 * abs(log10(x)) < abs(log(x)) |
| 4648 | * 4) adjexp(x) <= log10(x) < adjexp(x) + 1 |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4649 | * |
Stefan Krah | 7bda265 | 2012-06-07 17:48:47 +0200 | [diff] [blame] | 4650 | * Case adjexp(x) >= 0: |
| 4651 | * 5) 2 * adjexp(x) < abs(log(x)) |
| 4652 | * Case adjexp(x) > 0: |
| 4653 | * 6) adjexp(2 * adjexp(x)) <= adjexp(abs(log(x))) |
| 4654 | * Case adjexp(x) == 0: |
| 4655 | * mpd_exp_digits(t)-1 == 0 <= emax (the shortcut is not triggered) |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4656 | * |
Stefan Krah | 7bda265 | 2012-06-07 17:48:47 +0200 | [diff] [blame] | 4657 | * Case adjexp(x) < 0: |
| 4658 | * 7) 2 * (-adjexp(x) - 1) < abs(log(x)) |
| 4659 | * Case adjexp(x) < -1: |
| 4660 | * 8) adjexp(2 * (-adjexp(x) - 1)) <= adjexp(abs(log(x))) |
| 4661 | * Case adjexp(x) == -1: |
| 4662 | * mpd_exp_digits(t)-1 == 0 <= emax (the shortcut is not triggered) |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4663 | */ |
| 4664 | adjexp = mpd_adjexp(a); |
| 4665 | t = (adjexp < 0) ? -adjexp-1 : adjexp; |
| 4666 | t *= 2; |
| 4667 | if (mpd_exp_digits(t)-1 > ctx->emax) { |
| 4668 | *status |= MPD_Overflow|MPD_Inexact|MPD_Rounded; |
| 4669 | mpd_setspecial(result, (adjexp<0), MPD_INF); |
| 4670 | return; |
| 4671 | } |
| 4672 | |
| 4673 | workctx = *ctx; |
| 4674 | workctx.round = MPD_ROUND_HALF_EVEN; |
| 4675 | |
| 4676 | if (ctx->allcr) { |
| 4677 | MPD_NEW_STATIC(t1, 0,0,0,0); |
| 4678 | MPD_NEW_STATIC(t2, 0,0,0,0); |
| 4679 | MPD_NEW_STATIC(ulp, 0,0,0,0); |
| 4680 | MPD_NEW_STATIC(aa, 0,0,0,0); |
| 4681 | mpd_ssize_t prec; |
| 4682 | |
| 4683 | if (result == a) { |
| 4684 | if (!mpd_qcopy(&aa, a, status)) { |
| 4685 | mpd_seterror(result, MPD_Malloc_error, status); |
| 4686 | return; |
| 4687 | } |
| 4688 | a = &aa; |
| 4689 | } |
| 4690 | |
| 4691 | workctx.clamp = 0; |
| 4692 | prec = ctx->prec + 3; |
| 4693 | while (1) { |
| 4694 | workctx.prec = prec; |
| 4695 | _mpd_qln(result, a, &workctx, status); |
| 4696 | _ssettriple(&ulp, MPD_POS, 1, |
Stefan Krah | 7bda265 | 2012-06-07 17:48:47 +0200 | [diff] [blame] | 4697 | result->exp + result->digits-workctx.prec); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4698 | |
| 4699 | workctx.prec = ctx->prec; |
| 4700 | mpd_qadd(&t1, result, &ulp, &workctx, &workctx.status); |
| 4701 | mpd_qsub(&t2, result, &ulp, &workctx, &workctx.status); |
| 4702 | if (mpd_isspecial(result) || mpd_iszerocoeff(result) || |
| 4703 | mpd_qcmp(&t1, &t2, status) == 0) { |
| 4704 | workctx.clamp = ctx->clamp; |
| 4705 | mpd_check_underflow(result, &workctx, status); |
| 4706 | mpd_qfinalize(result, &workctx, status); |
| 4707 | break; |
| 4708 | } |
| 4709 | prec += MPD_RDIGITS; |
| 4710 | } |
| 4711 | mpd_del(&t1); |
| 4712 | mpd_del(&t2); |
| 4713 | mpd_del(&ulp); |
| 4714 | mpd_del(&aa); |
| 4715 | } |
| 4716 | else { |
| 4717 | _mpd_qln(result, a, &workctx, status); |
| 4718 | mpd_check_underflow(result, &workctx, status); |
| 4719 | mpd_qfinalize(result, &workctx, status); |
| 4720 | } |
| 4721 | } |
| 4722 | |
Stefan Krah | 1cf6dfc | 2012-06-08 18:41:33 +0200 | [diff] [blame] | 4723 | /* |
| 4724 | * Internal log10() function that does not check for specials, zero or one. |
| 4725 | * Case SKIP_FINALIZE: |
| 4726 | * Relative error: abs(result - log10(a)) < 0.1 * 10**-prec * abs(log10(a)) |
| 4727 | * Case DO_FINALIZE: |
| 4728 | * Ulp error: abs(result - log10(a)) < ulp(log10(a)) |
| 4729 | */ |
| 4730 | enum {SKIP_FINALIZE, DO_FINALIZE}; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4731 | static void |
Stefan Krah | 1cf6dfc | 2012-06-08 18:41:33 +0200 | [diff] [blame] | 4732 | _mpd_qlog10(int action, mpd_t *result, const mpd_t *a, |
| 4733 | const mpd_context_t *ctx, uint32_t *status) |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4734 | { |
| 4735 | mpd_context_t workctx; |
| 4736 | MPD_NEW_STATIC(ln10,0,0,0,0); |
| 4737 | |
| 4738 | mpd_maxcontext(&workctx); |
| 4739 | workctx.prec = ctx->prec + 3; |
Stefan Krah | 1cf6dfc | 2012-06-08 18:41:33 +0200 | [diff] [blame] | 4740 | /* relative error: 0.1 * 10**(-p-3). The specific underflow shortcut |
| 4741 | * in _mpd_qln() does not change the final result. */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4742 | _mpd_qln(result, a, &workctx, status); |
Stefan Krah | 1cf6dfc | 2012-06-08 18:41:33 +0200 | [diff] [blame] | 4743 | /* relative error: 5 * 10**(-p-3) */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4744 | mpd_qln10(&ln10, workctx.prec, status); |
| 4745 | |
Stefan Krah | 1cf6dfc | 2012-06-08 18:41:33 +0200 | [diff] [blame] | 4746 | if (action == DO_FINALIZE) { |
| 4747 | workctx = *ctx; |
| 4748 | workctx.round = MPD_ROUND_HALF_EVEN; |
| 4749 | } |
| 4750 | /* SKIP_FINALIZE: relative error: 5 * 10**(-p-3) */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4751 | _mpd_qdiv(NO_IDEAL_EXP, result, result, &ln10, &workctx, status); |
| 4752 | |
| 4753 | mpd_del(&ln10); |
| 4754 | } |
| 4755 | |
| 4756 | /* log10(a) */ |
| 4757 | void |
| 4758 | mpd_qlog10(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, |
| 4759 | uint32_t *status) |
| 4760 | { |
| 4761 | mpd_context_t workctx; |
| 4762 | mpd_ssize_t adjexp, t; |
| 4763 | |
| 4764 | workctx = *ctx; |
| 4765 | workctx.round = MPD_ROUND_HALF_EVEN; |
| 4766 | |
| 4767 | if (mpd_isspecial(a)) { |
| 4768 | if (mpd_qcheck_nan(result, a, ctx, status)) { |
| 4769 | return; |
| 4770 | } |
| 4771 | if (mpd_isnegative(a)) { |
| 4772 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 4773 | return; |
| 4774 | } |
| 4775 | mpd_setspecial(result, MPD_POS, MPD_INF); |
| 4776 | return; |
| 4777 | } |
| 4778 | if (mpd_iszerocoeff(a)) { |
| 4779 | mpd_setspecial(result, MPD_NEG, MPD_INF); |
| 4780 | return; |
| 4781 | } |
| 4782 | if (mpd_isnegative(a)) { |
| 4783 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 4784 | return; |
| 4785 | } |
| 4786 | if (mpd_coeff_ispow10(a)) { |
| 4787 | uint8_t sign = 0; |
| 4788 | adjexp = mpd_adjexp(a); |
| 4789 | if (adjexp < 0) { |
| 4790 | sign = 1; |
| 4791 | adjexp = -adjexp; |
| 4792 | } |
| 4793 | _settriple(result, sign, adjexp, 0); |
| 4794 | mpd_qfinalize(result, &workctx, status); |
| 4795 | return; |
| 4796 | } |
Stefan Krah | 5248a2d | 2012-06-09 00:01:28 +0200 | [diff] [blame] | 4797 | /* |
| 4798 | * Check if the result will overflow (0 < x, x != 1): |
| 4799 | * 1) log10(x) < 0 iff adjexp(x) < 0 |
| 4800 | * 2) 0 < x /\ x <= y ==> adjexp(x) <= adjexp(y) |
| 4801 | * 3) adjexp(x) <= log10(x) < adjexp(x) + 1 |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4802 | * |
Stefan Krah | 5248a2d | 2012-06-09 00:01:28 +0200 | [diff] [blame] | 4803 | * Case adjexp(x) >= 0: |
| 4804 | * 4) adjexp(x) <= abs(log10(x)) |
| 4805 | * Case adjexp(x) > 0: |
| 4806 | * 5) adjexp(adjexp(x)) <= adjexp(abs(log10(x))) |
| 4807 | * Case adjexp(x) == 0: |
| 4808 | * mpd_exp_digits(t)-1 == 0 <= emax (the shortcut is not triggered) |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4809 | * |
Stefan Krah | 5248a2d | 2012-06-09 00:01:28 +0200 | [diff] [blame] | 4810 | * Case adjexp(x) < 0: |
| 4811 | * 6) -adjexp(x) - 1 < abs(log10(x)) |
| 4812 | * Case adjexp(x) < -1: |
| 4813 | * 7) adjexp(-adjexp(x) - 1) <= adjexp(abs(log(x))) |
| 4814 | * Case adjexp(x) == -1: |
| 4815 | * mpd_exp_digits(t)-1 == 0 <= emax (the shortcut is not triggered) |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4816 | */ |
| 4817 | adjexp = mpd_adjexp(a); |
| 4818 | t = (adjexp < 0) ? -adjexp-1 : adjexp; |
| 4819 | if (mpd_exp_digits(t)-1 > ctx->emax) { |
| 4820 | *status |= MPD_Overflow|MPD_Inexact|MPD_Rounded; |
| 4821 | mpd_setspecial(result, (adjexp<0), MPD_INF); |
| 4822 | return; |
| 4823 | } |
| 4824 | |
| 4825 | if (ctx->allcr) { |
| 4826 | MPD_NEW_STATIC(t1, 0,0,0,0); |
| 4827 | MPD_NEW_STATIC(t2, 0,0,0,0); |
| 4828 | MPD_NEW_STATIC(ulp, 0,0,0,0); |
| 4829 | MPD_NEW_STATIC(aa, 0,0,0,0); |
| 4830 | mpd_ssize_t prec; |
| 4831 | |
| 4832 | if (result == a) { |
| 4833 | if (!mpd_qcopy(&aa, a, status)) { |
| 4834 | mpd_seterror(result, MPD_Malloc_error, status); |
| 4835 | return; |
| 4836 | } |
| 4837 | a = &aa; |
| 4838 | } |
| 4839 | |
| 4840 | workctx.clamp = 0; |
| 4841 | prec = ctx->prec + 3; |
| 4842 | while (1) { |
| 4843 | workctx.prec = prec; |
Stefan Krah | 1cf6dfc | 2012-06-08 18:41:33 +0200 | [diff] [blame] | 4844 | _mpd_qlog10(SKIP_FINALIZE, result, a, &workctx, status); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4845 | _ssettriple(&ulp, MPD_POS, 1, |
Stefan Krah | 1cf6dfc | 2012-06-08 18:41:33 +0200 | [diff] [blame] | 4846 | result->exp + result->digits-workctx.prec); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4847 | |
| 4848 | workctx.prec = ctx->prec; |
| 4849 | mpd_qadd(&t1, result, &ulp, &workctx, &workctx.status); |
| 4850 | mpd_qsub(&t2, result, &ulp, &workctx, &workctx.status); |
| 4851 | if (mpd_isspecial(result) || mpd_iszerocoeff(result) || |
| 4852 | mpd_qcmp(&t1, &t2, status) == 0) { |
| 4853 | workctx.clamp = ctx->clamp; |
| 4854 | mpd_check_underflow(result, &workctx, status); |
| 4855 | mpd_qfinalize(result, &workctx, status); |
| 4856 | break; |
| 4857 | } |
| 4858 | prec += MPD_RDIGITS; |
| 4859 | } |
| 4860 | mpd_del(&t1); |
| 4861 | mpd_del(&t2); |
| 4862 | mpd_del(&ulp); |
| 4863 | mpd_del(&aa); |
| 4864 | } |
| 4865 | else { |
Stefan Krah | 1cf6dfc | 2012-06-08 18:41:33 +0200 | [diff] [blame] | 4866 | _mpd_qlog10(DO_FINALIZE, result, a, &workctx, status); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 4867 | mpd_check_underflow(result, &workctx, status); |
| 4868 | } |
| 4869 | } |
| 4870 | |
| 4871 | /* |
| 4872 | * Maximum of the two operands. Attention: If one operand is a quiet NaN and the |
| 4873 | * other is numeric, the numeric operand is returned. This may not be what one |
| 4874 | * expects. |
| 4875 | */ |
| 4876 | void |
| 4877 | mpd_qmax(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 4878 | const mpd_context_t *ctx, uint32_t *status) |
| 4879 | { |
| 4880 | int c; |
| 4881 | |
| 4882 | if (mpd_isqnan(a) && !mpd_isnan(b)) { |
| 4883 | mpd_qcopy(result, b, status); |
| 4884 | } |
| 4885 | else if (mpd_isqnan(b) && !mpd_isnan(a)) { |
| 4886 | mpd_qcopy(result, a, status); |
| 4887 | } |
| 4888 | else if (mpd_qcheck_nans(result, a, b, ctx, status)) { |
| 4889 | return; |
| 4890 | } |
| 4891 | else { |
| 4892 | c = _mpd_cmp(a, b); |
| 4893 | if (c == 0) { |
| 4894 | c = _mpd_cmp_numequal(a, b); |
| 4895 | } |
| 4896 | |
| 4897 | if (c < 0) { |
| 4898 | mpd_qcopy(result, b, status); |
| 4899 | } |
| 4900 | else { |
| 4901 | mpd_qcopy(result, a, status); |
| 4902 | } |
| 4903 | } |
| 4904 | |
| 4905 | mpd_qfinalize(result, ctx, status); |
| 4906 | } |
| 4907 | |
| 4908 | /* |
| 4909 | * Maximum magnitude: Same as mpd_max(), but compares the operands with their |
| 4910 | * sign ignored. |
| 4911 | */ |
| 4912 | void |
| 4913 | mpd_qmax_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 4914 | const mpd_context_t *ctx, uint32_t *status) |
| 4915 | { |
| 4916 | int c; |
| 4917 | |
| 4918 | if (mpd_isqnan(a) && !mpd_isnan(b)) { |
| 4919 | mpd_qcopy(result, b, status); |
| 4920 | } |
| 4921 | else if (mpd_isqnan(b) && !mpd_isnan(a)) { |
| 4922 | mpd_qcopy(result, a, status); |
| 4923 | } |
| 4924 | else if (mpd_qcheck_nans(result, a, b, ctx, status)) { |
| 4925 | return; |
| 4926 | } |
| 4927 | else { |
| 4928 | c = _mpd_cmp_abs(a, b); |
| 4929 | if (c == 0) { |
| 4930 | c = _mpd_cmp_numequal(a, b); |
| 4931 | } |
| 4932 | |
| 4933 | if (c < 0) { |
| 4934 | mpd_qcopy(result, b, status); |
| 4935 | } |
| 4936 | else { |
| 4937 | mpd_qcopy(result, a, status); |
| 4938 | } |
| 4939 | } |
| 4940 | |
| 4941 | mpd_qfinalize(result, ctx, status); |
| 4942 | } |
| 4943 | |
| 4944 | /* |
| 4945 | * Minimum of the two operands. Attention: If one operand is a quiet NaN and the |
| 4946 | * other is numeric, the numeric operand is returned. This may not be what one |
| 4947 | * expects. |
| 4948 | */ |
| 4949 | void |
| 4950 | mpd_qmin(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 4951 | const mpd_context_t *ctx, uint32_t *status) |
| 4952 | { |
| 4953 | int c; |
| 4954 | |
| 4955 | if (mpd_isqnan(a) && !mpd_isnan(b)) { |
| 4956 | mpd_qcopy(result, b, status); |
| 4957 | } |
| 4958 | else if (mpd_isqnan(b) && !mpd_isnan(a)) { |
| 4959 | mpd_qcopy(result, a, status); |
| 4960 | } |
| 4961 | else if (mpd_qcheck_nans(result, a, b, ctx, status)) { |
| 4962 | return; |
| 4963 | } |
| 4964 | else { |
| 4965 | c = _mpd_cmp(a, b); |
| 4966 | if (c == 0) { |
| 4967 | c = _mpd_cmp_numequal(a, b); |
| 4968 | } |
| 4969 | |
| 4970 | if (c < 0) { |
| 4971 | mpd_qcopy(result, a, status); |
| 4972 | } |
| 4973 | else { |
| 4974 | mpd_qcopy(result, b, status); |
| 4975 | } |
| 4976 | } |
| 4977 | |
| 4978 | mpd_qfinalize(result, ctx, status); |
| 4979 | } |
| 4980 | |
| 4981 | /* |
| 4982 | * Minimum magnitude: Same as mpd_min(), but compares the operands with their |
| 4983 | * sign ignored. |
| 4984 | */ |
| 4985 | void |
| 4986 | mpd_qmin_mag(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 4987 | const mpd_context_t *ctx, uint32_t *status) |
| 4988 | { |
| 4989 | int c; |
| 4990 | |
| 4991 | if (mpd_isqnan(a) && !mpd_isnan(b)) { |
| 4992 | mpd_qcopy(result, b, status); |
| 4993 | } |
| 4994 | else if (mpd_isqnan(b) && !mpd_isnan(a)) { |
| 4995 | mpd_qcopy(result, a, status); |
| 4996 | } |
| 4997 | else if (mpd_qcheck_nans(result, a, b, ctx, status)) { |
| 4998 | return; |
| 4999 | } |
| 5000 | else { |
| 5001 | c = _mpd_cmp_abs(a, b); |
| 5002 | if (c == 0) { |
| 5003 | c = _mpd_cmp_numequal(a, b); |
| 5004 | } |
| 5005 | |
| 5006 | if (c < 0) { |
| 5007 | mpd_qcopy(result, a, status); |
| 5008 | } |
| 5009 | else { |
| 5010 | mpd_qcopy(result, b, status); |
| 5011 | } |
| 5012 | } |
| 5013 | |
| 5014 | mpd_qfinalize(result, ctx, status); |
| 5015 | } |
| 5016 | |
| 5017 | /* Minimum space needed for the result array in _karatsuba_rec(). */ |
| 5018 | static inline mpd_size_t |
| 5019 | _kmul_resultsize(mpd_size_t la, mpd_size_t lb) |
| 5020 | { |
| 5021 | mpd_size_t n, m; |
| 5022 | |
| 5023 | n = add_size_t(la, lb); |
| 5024 | n = add_size_t(n, 1); |
| 5025 | |
| 5026 | m = (la+1)/2 + 1; |
| 5027 | m = mul_size_t(m, 3); |
| 5028 | |
| 5029 | return (m > n) ? m : n; |
| 5030 | } |
| 5031 | |
| 5032 | /* Work space needed in _karatsuba_rec(). lim >= 4 */ |
| 5033 | static inline mpd_size_t |
| 5034 | _kmul_worksize(mpd_size_t n, mpd_size_t lim) |
| 5035 | { |
| 5036 | mpd_size_t m; |
| 5037 | |
| 5038 | if (n <= lim) { |
| 5039 | return 0; |
| 5040 | } |
| 5041 | |
| 5042 | m = (n+1)/2 + 1; |
| 5043 | |
| 5044 | return add_size_t(mul_size_t(m, 2), _kmul_worksize(m, lim)); |
| 5045 | } |
| 5046 | |
| 5047 | |
| 5048 | #define MPD_KARATSUBA_BASECASE 16 /* must be >= 4 */ |
| 5049 | |
| 5050 | /* |
| 5051 | * Add the product of a and b to c. |
| 5052 | * c must be _kmul_resultsize(la, lb) in size. |
| 5053 | * w is used as a work array and must be _kmul_worksize(a, lim) in size. |
| 5054 | * Roman E. Maeder, Storage Allocation for the Karatsuba Integer Multiplication |
| 5055 | * Algorithm. In "Design and implementation of symbolic computation systems", |
| 5056 | * Springer, 1993, ISBN 354057235X, 9783540572350. |
| 5057 | */ |
| 5058 | static void |
| 5059 | _karatsuba_rec(mpd_uint_t *c, const mpd_uint_t *a, const mpd_uint_t *b, |
| 5060 | mpd_uint_t *w, mpd_size_t la, mpd_size_t lb) |
| 5061 | { |
| 5062 | mpd_size_t m, lt; |
| 5063 | |
| 5064 | assert(la >= lb && lb > 0); |
| 5065 | assert(la <= MPD_KARATSUBA_BASECASE || w != NULL); |
| 5066 | |
| 5067 | if (la <= MPD_KARATSUBA_BASECASE) { |
| 5068 | _mpd_basemul(c, a, b, la, lb); |
| 5069 | return; |
| 5070 | } |
| 5071 | |
| 5072 | m = (la+1)/2; // ceil(la/2) |
| 5073 | |
| 5074 | /* lb <= m < la */ |
| 5075 | if (lb <= m) { |
| 5076 | |
| 5077 | /* lb can now be larger than la-m */ |
| 5078 | if (lb > la-m) { |
| 5079 | lt = lb + lb + 1; // space needed for result array |
| 5080 | mpd_uint_zero(w, lt); // clear result array |
| 5081 | _karatsuba_rec(w, b, a+m, w+lt, lb, la-m); // b*ah |
| 5082 | } |
| 5083 | else { |
| 5084 | lt = (la-m) + (la-m) + 1; // space needed for result array |
| 5085 | mpd_uint_zero(w, lt); // clear result array |
| 5086 | _karatsuba_rec(w, a+m, b, w+lt, la-m, lb); // ah*b |
| 5087 | } |
| 5088 | _mpd_baseaddto(c+m, w, (la-m)+lb); // add ah*b*B**m |
| 5089 | |
| 5090 | lt = m + m + 1; // space needed for the result array |
| 5091 | mpd_uint_zero(w, lt); // clear result array |
| 5092 | _karatsuba_rec(w, a, b, w+lt, m, lb); // al*b |
| 5093 | _mpd_baseaddto(c, w, m+lb); // add al*b |
| 5094 | |
| 5095 | return; |
| 5096 | } |
| 5097 | |
| 5098 | /* la >= lb > m */ |
| 5099 | memcpy(w, a, m * sizeof *w); |
| 5100 | w[m] = 0; |
| 5101 | _mpd_baseaddto(w, a+m, la-m); |
| 5102 | |
| 5103 | memcpy(w+(m+1), b, m * sizeof *w); |
| 5104 | w[m+1+m] = 0; |
| 5105 | _mpd_baseaddto(w+(m+1), b+m, lb-m); |
| 5106 | |
| 5107 | _karatsuba_rec(c+m, w, w+(m+1), w+2*(m+1), m+1, m+1); |
| 5108 | |
| 5109 | lt = (la-m) + (la-m) + 1; |
| 5110 | mpd_uint_zero(w, lt); |
| 5111 | |
| 5112 | _karatsuba_rec(w, a+m, b+m, w+lt, la-m, lb-m); |
| 5113 | |
| 5114 | _mpd_baseaddto(c+2*m, w, (la-m) + (lb-m)); |
| 5115 | _mpd_basesubfrom(c+m, w, (la-m) + (lb-m)); |
| 5116 | |
| 5117 | lt = m + m + 1; |
| 5118 | mpd_uint_zero(w, lt); |
| 5119 | |
| 5120 | _karatsuba_rec(w, a, b, w+lt, m, m); |
| 5121 | _mpd_baseaddto(c, w, m+m); |
| 5122 | _mpd_basesubfrom(c+m, w, m+m); |
| 5123 | |
| 5124 | return; |
| 5125 | } |
| 5126 | |
| 5127 | /* |
| 5128 | * Multiply u and v, using Karatsuba multiplication. Returns a pointer |
| 5129 | * to the result or NULL in case of failure (malloc error). |
| 5130 | * Conditions: ulen >= vlen, ulen >= 4 |
| 5131 | */ |
| 5132 | mpd_uint_t * |
| 5133 | _mpd_kmul(const mpd_uint_t *u, const mpd_uint_t *v, |
| 5134 | mpd_size_t ulen, mpd_size_t vlen, |
| 5135 | mpd_size_t *rsize) |
| 5136 | { |
| 5137 | mpd_uint_t *result = NULL, *w = NULL; |
| 5138 | mpd_size_t m; |
| 5139 | |
| 5140 | assert(ulen >= 4); |
| 5141 | assert(ulen >= vlen); |
| 5142 | |
| 5143 | *rsize = _kmul_resultsize(ulen, vlen); |
| 5144 | if ((result = mpd_calloc(*rsize, sizeof *result)) == NULL) { |
| 5145 | return NULL; |
| 5146 | } |
| 5147 | |
| 5148 | m = _kmul_worksize(ulen, MPD_KARATSUBA_BASECASE); |
| 5149 | if (m && ((w = mpd_calloc(m, sizeof *w)) == NULL)) { |
| 5150 | mpd_free(result); |
| 5151 | return NULL; |
| 5152 | } |
| 5153 | |
| 5154 | _karatsuba_rec(result, u, v, w, ulen, vlen); |
| 5155 | |
| 5156 | |
| 5157 | if (w) mpd_free(w); |
| 5158 | return result; |
| 5159 | } |
| 5160 | |
| 5161 | |
Stefan Krah | 9253862 | 2012-06-10 16:50:55 +0200 | [diff] [blame] | 5162 | /* |
| 5163 | * Determine the minimum length for the number theoretic transform. Valid |
| 5164 | * transform lengths are 2**n or 3*2**n, where 2**n <= MPD_MAXTRANSFORM_2N. |
| 5165 | * The function finds the shortest length m such that rsize <= m. |
| 5166 | */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5167 | static inline mpd_size_t |
| 5168 | _mpd_get_transform_len(mpd_size_t rsize) |
| 5169 | { |
| 5170 | mpd_size_t log2rsize; |
| 5171 | mpd_size_t x, step; |
| 5172 | |
| 5173 | assert(rsize >= 4); |
| 5174 | log2rsize = mpd_bsr(rsize); |
| 5175 | |
| 5176 | if (rsize <= 1024) { |
Stefan Krah | 9253862 | 2012-06-10 16:50:55 +0200 | [diff] [blame] | 5177 | /* 2**n is faster in this range. */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5178 | x = ((mpd_size_t)1)<<log2rsize; |
| 5179 | return (rsize == x) ? x : x<<1; |
| 5180 | } |
| 5181 | else if (rsize <= MPD_MAXTRANSFORM_2N) { |
| 5182 | x = ((mpd_size_t)1)<<log2rsize; |
| 5183 | if (rsize == x) return x; |
| 5184 | step = x>>1; |
| 5185 | x += step; |
| 5186 | return (rsize <= x) ? x : x + step; |
| 5187 | } |
| 5188 | else if (rsize <= MPD_MAXTRANSFORM_2N+MPD_MAXTRANSFORM_2N/2) { |
| 5189 | return MPD_MAXTRANSFORM_2N+MPD_MAXTRANSFORM_2N/2; |
| 5190 | } |
| 5191 | else if (rsize <= 3*MPD_MAXTRANSFORM_2N) { |
| 5192 | return 3*MPD_MAXTRANSFORM_2N; |
| 5193 | } |
| 5194 | else { |
| 5195 | return MPD_SIZE_MAX; |
| 5196 | } |
| 5197 | } |
| 5198 | |
| 5199 | #ifdef PPRO |
| 5200 | #ifndef _MSC_VER |
| 5201 | static inline unsigned short |
| 5202 | _mpd_get_control87(void) |
| 5203 | { |
| 5204 | unsigned short cw; |
| 5205 | |
| 5206 | __asm__ __volatile__ ("fnstcw %0" : "=m" (cw)); |
| 5207 | return cw; |
| 5208 | } |
| 5209 | |
| 5210 | static inline void |
| 5211 | _mpd_set_control87(unsigned short cw) |
| 5212 | { |
| 5213 | __asm__ __volatile__ ("fldcw %0" : : "m" (cw)); |
| 5214 | } |
| 5215 | #endif |
| 5216 | |
| 5217 | unsigned int |
| 5218 | mpd_set_fenv(void) |
| 5219 | { |
| 5220 | unsigned int cw; |
| 5221 | #ifdef _MSC_VER |
| 5222 | unsigned int flags = |
| 5223 | _EM_INVALID|_EM_DENORMAL|_EM_ZERODIVIDE|_EM_OVERFLOW| |
| 5224 | _EM_UNDERFLOW|_EM_INEXACT|_RC_CHOP|_PC_64; |
| 5225 | unsigned int mask = _MCW_EM|_MCW_RC|_MCW_PC; |
| 5226 | unsigned int dummy; |
| 5227 | |
| 5228 | __control87_2(0, 0, &cw, NULL); |
| 5229 | __control87_2(flags, mask, &dummy, NULL); |
| 5230 | #else |
| 5231 | cw = _mpd_get_control87(); |
| 5232 | _mpd_set_control87(cw|0xF3F); |
| 5233 | #endif |
| 5234 | return cw; |
| 5235 | } |
| 5236 | |
| 5237 | void |
| 5238 | mpd_restore_fenv(unsigned int cw) |
| 5239 | { |
| 5240 | #ifdef _MSC_VER |
| 5241 | unsigned int mask = _MCW_EM|_MCW_RC|_MCW_PC; |
| 5242 | unsigned int dummy; |
| 5243 | |
| 5244 | __control87_2(cw, mask, &dummy, NULL); |
| 5245 | #else |
| 5246 | _mpd_set_control87((unsigned short)cw); |
| 5247 | #endif |
| 5248 | } |
| 5249 | #endif /* PPRO */ |
| 5250 | |
| 5251 | /* |
| 5252 | * Multiply u and v, using the fast number theoretic transform. Returns |
| 5253 | * a pointer to the result or NULL in case of failure (malloc error). |
| 5254 | */ |
| 5255 | mpd_uint_t * |
| 5256 | _mpd_fntmul(const mpd_uint_t *u, const mpd_uint_t *v, |
| 5257 | mpd_size_t ulen, mpd_size_t vlen, |
| 5258 | mpd_size_t *rsize) |
| 5259 | { |
| 5260 | mpd_uint_t *c1 = NULL, *c2 = NULL, *c3 = NULL, *vtmp = NULL; |
| 5261 | mpd_size_t n; |
| 5262 | |
| 5263 | #ifdef PPRO |
| 5264 | unsigned int cw; |
| 5265 | cw = mpd_set_fenv(); |
| 5266 | #endif |
| 5267 | |
| 5268 | *rsize = add_size_t(ulen, vlen); |
| 5269 | if ((n = _mpd_get_transform_len(*rsize)) == MPD_SIZE_MAX) { |
| 5270 | goto malloc_error; |
| 5271 | } |
| 5272 | |
Stefan Krah | 9253862 | 2012-06-10 16:50:55 +0200 | [diff] [blame] | 5273 | if ((c1 = mpd_calloc(n, sizeof *c1)) == NULL) { |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5274 | goto malloc_error; |
| 5275 | } |
Stefan Krah | 9253862 | 2012-06-10 16:50:55 +0200 | [diff] [blame] | 5276 | if ((c2 = mpd_calloc(n, sizeof *c2)) == NULL) { |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5277 | goto malloc_error; |
| 5278 | } |
Stefan Krah | 9253862 | 2012-06-10 16:50:55 +0200 | [diff] [blame] | 5279 | if ((c3 = mpd_calloc(n, sizeof *c3)) == NULL) { |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5280 | goto malloc_error; |
| 5281 | } |
| 5282 | |
| 5283 | memcpy(c1, u, ulen * (sizeof *c1)); |
| 5284 | memcpy(c2, u, ulen * (sizeof *c2)); |
| 5285 | memcpy(c3, u, ulen * (sizeof *c3)); |
| 5286 | |
| 5287 | if (u == v) { |
| 5288 | if (!fnt_autoconvolute(c1, n, P1) || |
| 5289 | !fnt_autoconvolute(c2, n, P2) || |
| 5290 | !fnt_autoconvolute(c3, n, P3)) { |
| 5291 | goto malloc_error; |
| 5292 | } |
| 5293 | } |
| 5294 | else { |
Stefan Krah | 9253862 | 2012-06-10 16:50:55 +0200 | [diff] [blame] | 5295 | if ((vtmp = mpd_calloc(n, sizeof *vtmp)) == NULL) { |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5296 | goto malloc_error; |
| 5297 | } |
| 5298 | |
| 5299 | memcpy(vtmp, v, vlen * (sizeof *vtmp)); |
| 5300 | if (!fnt_convolute(c1, vtmp, n, P1)) { |
| 5301 | mpd_free(vtmp); |
| 5302 | goto malloc_error; |
| 5303 | } |
| 5304 | |
| 5305 | memcpy(vtmp, v, vlen * (sizeof *vtmp)); |
| 5306 | mpd_uint_zero(vtmp+vlen, n-vlen); |
| 5307 | if (!fnt_convolute(c2, vtmp, n, P2)) { |
| 5308 | mpd_free(vtmp); |
| 5309 | goto malloc_error; |
| 5310 | } |
| 5311 | |
| 5312 | memcpy(vtmp, v, vlen * (sizeof *vtmp)); |
| 5313 | mpd_uint_zero(vtmp+vlen, n-vlen); |
| 5314 | if (!fnt_convolute(c3, vtmp, n, P3)) { |
| 5315 | mpd_free(vtmp); |
| 5316 | goto malloc_error; |
| 5317 | } |
| 5318 | |
| 5319 | mpd_free(vtmp); |
| 5320 | } |
| 5321 | |
| 5322 | crt3(c1, c2, c3, *rsize); |
| 5323 | |
| 5324 | out: |
| 5325 | #ifdef PPRO |
| 5326 | mpd_restore_fenv(cw); |
| 5327 | #endif |
| 5328 | if (c2) mpd_free(c2); |
| 5329 | if (c3) mpd_free(c3); |
| 5330 | return c1; |
| 5331 | |
| 5332 | malloc_error: |
| 5333 | if (c1) mpd_free(c1); |
| 5334 | c1 = NULL; |
| 5335 | goto out; |
| 5336 | } |
| 5337 | |
| 5338 | |
| 5339 | /* |
| 5340 | * Karatsuba multiplication with FNT/basemul as the base case. |
| 5341 | */ |
| 5342 | static int |
| 5343 | _karatsuba_rec_fnt(mpd_uint_t *c, const mpd_uint_t *a, const mpd_uint_t *b, |
| 5344 | mpd_uint_t *w, mpd_size_t la, mpd_size_t lb) |
| 5345 | { |
| 5346 | mpd_size_t m, lt; |
| 5347 | |
| 5348 | assert(la >= lb && lb > 0); |
| 5349 | assert(la <= 3*(MPD_MAXTRANSFORM_2N/2) || w != NULL); |
| 5350 | |
| 5351 | if (la <= 3*(MPD_MAXTRANSFORM_2N/2)) { |
| 5352 | |
| 5353 | if (lb <= 192) { |
| 5354 | _mpd_basemul(c, b, a, lb, la); |
| 5355 | } |
| 5356 | else { |
| 5357 | mpd_uint_t *result; |
| 5358 | mpd_size_t dummy; |
| 5359 | |
| 5360 | if ((result = _mpd_fntmul(a, b, la, lb, &dummy)) == NULL) { |
| 5361 | return 0; |
| 5362 | } |
| 5363 | memcpy(c, result, (la+lb) * (sizeof *result)); |
| 5364 | mpd_free(result); |
| 5365 | } |
| 5366 | return 1; |
| 5367 | } |
| 5368 | |
| 5369 | m = (la+1)/2; // ceil(la/2) |
| 5370 | |
| 5371 | /* lb <= m < la */ |
| 5372 | if (lb <= m) { |
| 5373 | |
| 5374 | /* lb can now be larger than la-m */ |
| 5375 | if (lb > la-m) { |
| 5376 | lt = lb + lb + 1; // space needed for result array |
| 5377 | mpd_uint_zero(w, lt); // clear result array |
| 5378 | if (!_karatsuba_rec_fnt(w, b, a+m, w+lt, lb, la-m)) { // b*ah |
| 5379 | return 0; /* GCOV_UNLIKELY */ |
| 5380 | } |
| 5381 | } |
| 5382 | else { |
| 5383 | lt = (la-m) + (la-m) + 1; // space needed for result array |
| 5384 | mpd_uint_zero(w, lt); // clear result array |
| 5385 | if (!_karatsuba_rec_fnt(w, a+m, b, w+lt, la-m, lb)) { // ah*b |
| 5386 | return 0; /* GCOV_UNLIKELY */ |
| 5387 | } |
| 5388 | } |
| 5389 | _mpd_baseaddto(c+m, w, (la-m)+lb); // add ah*b*B**m |
| 5390 | |
| 5391 | lt = m + m + 1; // space needed for the result array |
| 5392 | mpd_uint_zero(w, lt); // clear result array |
| 5393 | if (!_karatsuba_rec_fnt(w, a, b, w+lt, m, lb)) { // al*b |
| 5394 | return 0; /* GCOV_UNLIKELY */ |
| 5395 | } |
| 5396 | _mpd_baseaddto(c, w, m+lb); // add al*b |
| 5397 | |
| 5398 | return 1; |
| 5399 | } |
| 5400 | |
| 5401 | /* la >= lb > m */ |
| 5402 | memcpy(w, a, m * sizeof *w); |
| 5403 | w[m] = 0; |
| 5404 | _mpd_baseaddto(w, a+m, la-m); |
| 5405 | |
| 5406 | memcpy(w+(m+1), b, m * sizeof *w); |
| 5407 | w[m+1+m] = 0; |
| 5408 | _mpd_baseaddto(w+(m+1), b+m, lb-m); |
| 5409 | |
| 5410 | if (!_karatsuba_rec_fnt(c+m, w, w+(m+1), w+2*(m+1), m+1, m+1)) { |
| 5411 | return 0; /* GCOV_UNLIKELY */ |
| 5412 | } |
| 5413 | |
| 5414 | lt = (la-m) + (la-m) + 1; |
| 5415 | mpd_uint_zero(w, lt); |
| 5416 | |
| 5417 | if (!_karatsuba_rec_fnt(w, a+m, b+m, w+lt, la-m, lb-m)) { |
| 5418 | return 0; /* GCOV_UNLIKELY */ |
| 5419 | } |
| 5420 | |
| 5421 | _mpd_baseaddto(c+2*m, w, (la-m) + (lb-m)); |
| 5422 | _mpd_basesubfrom(c+m, w, (la-m) + (lb-m)); |
| 5423 | |
| 5424 | lt = m + m + 1; |
| 5425 | mpd_uint_zero(w, lt); |
| 5426 | |
| 5427 | if (!_karatsuba_rec_fnt(w, a, b, w+lt, m, m)) { |
| 5428 | return 0; /* GCOV_UNLIKELY */ |
| 5429 | } |
| 5430 | _mpd_baseaddto(c, w, m+m); |
| 5431 | _mpd_basesubfrom(c+m, w, m+m); |
| 5432 | |
| 5433 | return 1; |
| 5434 | } |
| 5435 | |
| 5436 | /* |
| 5437 | * Multiply u and v, using Karatsuba multiplication with the FNT as the |
| 5438 | * base case. Returns a pointer to the result or NULL in case of failure |
| 5439 | * (malloc error). Conditions: ulen >= vlen, ulen >= 4. |
| 5440 | */ |
| 5441 | mpd_uint_t * |
| 5442 | _mpd_kmul_fnt(const mpd_uint_t *u, const mpd_uint_t *v, |
| 5443 | mpd_size_t ulen, mpd_size_t vlen, |
| 5444 | mpd_size_t *rsize) |
| 5445 | { |
| 5446 | mpd_uint_t *result = NULL, *w = NULL; |
| 5447 | mpd_size_t m; |
| 5448 | |
| 5449 | assert(ulen >= 4); |
| 5450 | assert(ulen >= vlen); |
| 5451 | |
| 5452 | *rsize = _kmul_resultsize(ulen, vlen); |
| 5453 | if ((result = mpd_calloc(*rsize, sizeof *result)) == NULL) { |
| 5454 | return NULL; |
| 5455 | } |
| 5456 | |
| 5457 | m = _kmul_worksize(ulen, 3*(MPD_MAXTRANSFORM_2N/2)); |
| 5458 | if (m && ((w = mpd_calloc(m, sizeof *w)) == NULL)) { |
| 5459 | mpd_free(result); /* GCOV_UNLIKELY */ |
| 5460 | return NULL; /* GCOV_UNLIKELY */ |
| 5461 | } |
| 5462 | |
| 5463 | if (!_karatsuba_rec_fnt(result, u, v, w, ulen, vlen)) { |
| 5464 | mpd_free(result); |
| 5465 | result = NULL; |
| 5466 | } |
| 5467 | |
| 5468 | |
| 5469 | if (w) mpd_free(w); |
| 5470 | return result; |
| 5471 | } |
| 5472 | |
| 5473 | |
| 5474 | /* Deal with the special cases of multiplying infinities. */ |
| 5475 | static void |
| 5476 | _mpd_qmul_inf(mpd_t *result, const mpd_t *a, const mpd_t *b, uint32_t *status) |
| 5477 | { |
| 5478 | if (mpd_isinfinite(a)) { |
| 5479 | if (mpd_iszero(b)) { |
| 5480 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 5481 | } |
| 5482 | else { |
| 5483 | mpd_setspecial(result, mpd_sign(a)^mpd_sign(b), MPD_INF); |
| 5484 | } |
| 5485 | return; |
| 5486 | } |
| 5487 | assert(mpd_isinfinite(b)); |
| 5488 | if (mpd_iszero(a)) { |
| 5489 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 5490 | } |
| 5491 | else { |
| 5492 | mpd_setspecial(result, mpd_sign(a)^mpd_sign(b), MPD_INF); |
| 5493 | } |
| 5494 | } |
| 5495 | |
| 5496 | /* |
| 5497 | * Internal function: Multiply a and b. _mpd_qmul deals with specials but |
| 5498 | * does NOT finalize the result. This is for use in mpd_fma(). |
| 5499 | */ |
| 5500 | static inline void |
| 5501 | _mpd_qmul(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 5502 | const mpd_context_t *ctx, uint32_t *status) |
| 5503 | { |
| 5504 | mpd_t *big = (mpd_t *)a, *small = (mpd_t *)b; |
| 5505 | mpd_uint_t *rdata = NULL; |
| 5506 | mpd_uint_t rbuf[MPD_MINALLOC_MAX]; |
| 5507 | mpd_size_t rsize, i; |
| 5508 | |
| 5509 | |
| 5510 | if (mpd_isspecial(a) || mpd_isspecial(b)) { |
| 5511 | if (mpd_qcheck_nans(result, a, b, ctx, status)) { |
| 5512 | return; |
| 5513 | } |
| 5514 | _mpd_qmul_inf(result, a, b, status); |
| 5515 | return; |
| 5516 | } |
| 5517 | |
| 5518 | if (small->len > big->len) { |
| 5519 | _mpd_ptrswap(&big, &small); |
| 5520 | } |
| 5521 | |
| 5522 | rsize = big->len + small->len; |
| 5523 | |
| 5524 | if (big->len == 1) { |
| 5525 | _mpd_singlemul(result->data, big->data[0], small->data[0]); |
| 5526 | goto finish; |
| 5527 | } |
| 5528 | if (rsize <= (mpd_size_t)MPD_MINALLOC_MAX) { |
| 5529 | if (big->len == 2) { |
| 5530 | _mpd_mul_2_le2(rbuf, big->data, small->data, small->len); |
| 5531 | } |
| 5532 | else { |
| 5533 | mpd_uint_zero(rbuf, rsize); |
| 5534 | if (small->len == 1) { |
| 5535 | _mpd_shortmul(rbuf, big->data, big->len, small->data[0]); |
| 5536 | } |
| 5537 | else { |
| 5538 | _mpd_basemul(rbuf, small->data, big->data, small->len, big->len); |
| 5539 | } |
| 5540 | } |
| 5541 | if (!mpd_qresize(result, rsize, status)) { |
| 5542 | return; |
| 5543 | } |
| 5544 | for(i = 0; i < rsize; i++) { |
| 5545 | result->data[i] = rbuf[i]; |
| 5546 | } |
| 5547 | goto finish; |
| 5548 | } |
| 5549 | |
| 5550 | |
| 5551 | if (small->len == 1) { |
Stefan Krah | afc0c77 | 2012-06-09 15:28:36 +0200 | [diff] [blame] | 5552 | rdata = mpd_calloc(rsize, sizeof *rdata); |
| 5553 | if (rdata != NULL) { |
| 5554 | _mpd_shortmul(rdata, big->data, big->len, small->data[0]); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5555 | } |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5556 | } |
| 5557 | else if (rsize <= 1024) { |
| 5558 | rdata = _mpd_kmul(big->data, small->data, big->len, small->len, &rsize); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5559 | } |
| 5560 | else if (rsize <= 3*MPD_MAXTRANSFORM_2N) { |
| 5561 | rdata = _mpd_fntmul(big->data, small->data, big->len, small->len, &rsize); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5562 | } |
| 5563 | else { |
| 5564 | rdata = _mpd_kmul_fnt(big->data, small->data, big->len, small->len, &rsize); |
Stefan Krah | afc0c77 | 2012-06-09 15:28:36 +0200 | [diff] [blame] | 5565 | } |
| 5566 | |
| 5567 | if (rdata == NULL) { |
| 5568 | mpd_seterror(result, MPD_Malloc_error, status); |
| 5569 | return; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5570 | } |
| 5571 | |
| 5572 | if (mpd_isdynamic_data(result)) { |
| 5573 | mpd_free(result->data); |
| 5574 | } |
| 5575 | result->data = rdata; |
| 5576 | result->alloc = rsize; |
| 5577 | mpd_set_dynamic_data(result); |
| 5578 | |
| 5579 | |
| 5580 | finish: |
| 5581 | mpd_set_flags(result, mpd_sign(a)^mpd_sign(b)); |
| 5582 | result->exp = big->exp + small->exp; |
| 5583 | result->len = _mpd_real_size(result->data, rsize); |
| 5584 | /* resize to smaller cannot fail */ |
| 5585 | mpd_qresize(result, result->len, status); |
| 5586 | mpd_setdigits(result); |
| 5587 | } |
| 5588 | |
| 5589 | /* Multiply a and b. */ |
| 5590 | void |
| 5591 | mpd_qmul(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 5592 | const mpd_context_t *ctx, uint32_t *status) |
| 5593 | { |
| 5594 | _mpd_qmul(result, a, b, ctx, status); |
| 5595 | mpd_qfinalize(result, ctx, status); |
| 5596 | } |
| 5597 | |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 5598 | /* Multiply a and b. Set NaN/Invalid_operation if the result is inexact. */ |
| 5599 | static void |
| 5600 | _mpd_qmul_exact(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 5601 | const mpd_context_t *ctx, uint32_t *status) |
| 5602 | { |
| 5603 | uint32_t workstatus = 0; |
| 5604 | |
| 5605 | mpd_qmul(result, a, b, ctx, &workstatus); |
| 5606 | *status |= workstatus; |
| 5607 | if (workstatus & (MPD_Inexact|MPD_Rounded|MPD_Clamped)) { |
| 5608 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 5609 | } |
| 5610 | } |
| 5611 | |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5612 | /* Multiply decimal and mpd_ssize_t. */ |
| 5613 | void |
| 5614 | mpd_qmul_ssize(mpd_t *result, const mpd_t *a, mpd_ssize_t b, |
| 5615 | const mpd_context_t *ctx, uint32_t *status) |
| 5616 | { |
| 5617 | mpd_context_t maxcontext; |
| 5618 | MPD_NEW_STATIC(bb,0,0,0,0); |
| 5619 | |
| 5620 | mpd_maxcontext(&maxcontext); |
| 5621 | mpd_qsset_ssize(&bb, b, &maxcontext, status); |
| 5622 | mpd_qmul(result, a, &bb, ctx, status); |
| 5623 | mpd_del(&bb); |
| 5624 | } |
| 5625 | |
| 5626 | /* Multiply decimal and mpd_uint_t. */ |
| 5627 | void |
| 5628 | mpd_qmul_uint(mpd_t *result, const mpd_t *a, mpd_uint_t b, |
| 5629 | const mpd_context_t *ctx, uint32_t *status) |
| 5630 | { |
| 5631 | mpd_context_t maxcontext; |
| 5632 | MPD_NEW_STATIC(bb,0,0,0,0); |
| 5633 | |
| 5634 | mpd_maxcontext(&maxcontext); |
| 5635 | mpd_qsset_uint(&bb, b, &maxcontext, status); |
| 5636 | mpd_qmul(result, a, &bb, ctx, status); |
| 5637 | mpd_del(&bb); |
| 5638 | } |
| 5639 | |
| 5640 | void |
| 5641 | mpd_qmul_i32(mpd_t *result, const mpd_t *a, int32_t b, |
| 5642 | const mpd_context_t *ctx, uint32_t *status) |
| 5643 | { |
| 5644 | mpd_qmul_ssize(result, a, b, ctx, status); |
| 5645 | } |
| 5646 | |
| 5647 | void |
| 5648 | mpd_qmul_u32(mpd_t *result, const mpd_t *a, uint32_t b, |
| 5649 | const mpd_context_t *ctx, uint32_t *status) |
| 5650 | { |
| 5651 | mpd_qmul_uint(result, a, b, ctx, status); |
| 5652 | } |
| 5653 | |
| 5654 | #ifdef CONFIG_64 |
| 5655 | void |
| 5656 | mpd_qmul_i64(mpd_t *result, const mpd_t *a, int64_t b, |
| 5657 | const mpd_context_t *ctx, uint32_t *status) |
| 5658 | { |
| 5659 | mpd_qmul_ssize(result, a, b, ctx, status); |
| 5660 | } |
| 5661 | |
| 5662 | void |
| 5663 | mpd_qmul_u64(mpd_t *result, const mpd_t *a, uint64_t b, |
| 5664 | const mpd_context_t *ctx, uint32_t *status) |
| 5665 | { |
| 5666 | mpd_qmul_uint(result, a, b, ctx, status); |
| 5667 | } |
| 5668 | #endif |
| 5669 | |
| 5670 | /* Like the minus operator. */ |
| 5671 | void |
| 5672 | mpd_qminus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, |
| 5673 | uint32_t *status) |
| 5674 | { |
| 5675 | if (mpd_isspecial(a)) { |
| 5676 | if (mpd_qcheck_nan(result, a, ctx, status)) { |
| 5677 | return; |
| 5678 | } |
| 5679 | } |
| 5680 | |
| 5681 | if (mpd_iszero(a) && ctx->round != MPD_ROUND_FLOOR) { |
| 5682 | mpd_qcopy_abs(result, a, status); |
| 5683 | } |
| 5684 | else { |
| 5685 | mpd_qcopy_negate(result, a, status); |
| 5686 | } |
| 5687 | |
| 5688 | mpd_qfinalize(result, ctx, status); |
| 5689 | } |
| 5690 | |
| 5691 | /* Like the plus operator. */ |
| 5692 | void |
| 5693 | mpd_qplus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, |
| 5694 | uint32_t *status) |
| 5695 | { |
| 5696 | if (mpd_isspecial(a)) { |
| 5697 | if (mpd_qcheck_nan(result, a, ctx, status)) { |
| 5698 | return; |
| 5699 | } |
| 5700 | } |
| 5701 | |
| 5702 | if (mpd_iszero(a) && ctx->round != MPD_ROUND_FLOOR) { |
| 5703 | mpd_qcopy_abs(result, a, status); |
| 5704 | } |
| 5705 | else { |
| 5706 | mpd_qcopy(result, a, status); |
| 5707 | } |
| 5708 | |
| 5709 | mpd_qfinalize(result, ctx, status); |
| 5710 | } |
| 5711 | |
| 5712 | /* The largest representable number that is smaller than the operand. */ |
| 5713 | void |
| 5714 | mpd_qnext_minus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, |
| 5715 | uint32_t *status) |
| 5716 | { |
Stefan Krah | 88e1977 | 2012-06-11 08:57:17 +0200 | [diff] [blame] | 5717 | mpd_context_t workctx; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5718 | MPD_NEW_CONST(tiny,MPD_POS,mpd_etiny(ctx)-1,1,1,1,1); |
| 5719 | |
| 5720 | if (mpd_isspecial(a)) { |
| 5721 | if (mpd_qcheck_nan(result, a, ctx, status)) { |
| 5722 | return; |
| 5723 | } |
Stefan Krah | 88e1977 | 2012-06-11 08:57:17 +0200 | [diff] [blame] | 5724 | |
| 5725 | assert(mpd_isinfinite(a)); |
| 5726 | if (mpd_isnegative(a)) { |
| 5727 | mpd_qcopy(result, a, status); |
| 5728 | return; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5729 | } |
Stefan Krah | 88e1977 | 2012-06-11 08:57:17 +0200 | [diff] [blame] | 5730 | else { |
| 5731 | mpd_clear_flags(result); |
| 5732 | mpd_qmaxcoeff(result, ctx, status); |
| 5733 | if (mpd_isnan(result)) { |
| 5734 | return; |
| 5735 | } |
| 5736 | result->exp = mpd_etop(ctx); |
| 5737 | return; |
| 5738 | } |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5739 | } |
| 5740 | |
| 5741 | mpd_workcontext(&workctx, ctx); |
| 5742 | workctx.round = MPD_ROUND_FLOOR; |
| 5743 | |
| 5744 | if (!mpd_qcopy(result, a, status)) { |
| 5745 | return; |
| 5746 | } |
| 5747 | |
| 5748 | mpd_qfinalize(result, &workctx, &workctx.status); |
| 5749 | if (workctx.status&(MPD_Inexact|MPD_Errors)) { |
| 5750 | *status |= (workctx.status&MPD_Errors); |
| 5751 | return; |
| 5752 | } |
| 5753 | |
| 5754 | workctx.status = 0; |
| 5755 | mpd_qsub(result, a, &tiny, &workctx, &workctx.status); |
| 5756 | *status |= (workctx.status&MPD_Errors); |
| 5757 | } |
| 5758 | |
| 5759 | /* The smallest representable number that is larger than the operand. */ |
| 5760 | void |
| 5761 | mpd_qnext_plus(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, |
| 5762 | uint32_t *status) |
| 5763 | { |
| 5764 | mpd_context_t workctx; |
| 5765 | MPD_NEW_CONST(tiny,MPD_POS,mpd_etiny(ctx)-1,1,1,1,1); |
| 5766 | |
| 5767 | if (mpd_isspecial(a)) { |
| 5768 | if (mpd_qcheck_nan(result, a, ctx, status)) { |
| 5769 | return; |
| 5770 | } |
Stefan Krah | 88e1977 | 2012-06-11 08:57:17 +0200 | [diff] [blame] | 5771 | |
| 5772 | assert(mpd_isinfinite(a)); |
| 5773 | if (mpd_ispositive(a)) { |
| 5774 | mpd_qcopy(result, a, status); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5775 | } |
Stefan Krah | 88e1977 | 2012-06-11 08:57:17 +0200 | [diff] [blame] | 5776 | else { |
| 5777 | mpd_clear_flags(result); |
| 5778 | mpd_qmaxcoeff(result, ctx, status); |
| 5779 | if (mpd_isnan(result)) { |
| 5780 | return; |
| 5781 | } |
| 5782 | mpd_set_flags(result, MPD_NEG); |
| 5783 | result->exp = mpd_etop(ctx); |
| 5784 | } |
| 5785 | return; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5786 | } |
| 5787 | |
| 5788 | mpd_workcontext(&workctx, ctx); |
| 5789 | workctx.round = MPD_ROUND_CEILING; |
| 5790 | |
| 5791 | if (!mpd_qcopy(result, a, status)) { |
| 5792 | return; |
| 5793 | } |
| 5794 | |
| 5795 | mpd_qfinalize(result, &workctx, &workctx.status); |
| 5796 | if (workctx.status & (MPD_Inexact|MPD_Errors)) { |
| 5797 | *status |= (workctx.status&MPD_Errors); |
| 5798 | return; |
| 5799 | } |
| 5800 | |
| 5801 | workctx.status = 0; |
| 5802 | mpd_qadd(result, a, &tiny, &workctx, &workctx.status); |
| 5803 | *status |= (workctx.status&MPD_Errors); |
| 5804 | } |
| 5805 | |
| 5806 | /* |
| 5807 | * The number closest to the first operand that is in the direction towards |
| 5808 | * the second operand. |
| 5809 | */ |
| 5810 | void |
| 5811 | mpd_qnext_toward(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 5812 | const mpd_context_t *ctx, uint32_t *status) |
| 5813 | { |
| 5814 | int c; |
| 5815 | |
Stefan Krah | 88e1977 | 2012-06-11 08:57:17 +0200 | [diff] [blame] | 5816 | if (mpd_qcheck_nans(result, a, b, ctx, status)) { |
| 5817 | return; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5818 | } |
| 5819 | |
| 5820 | c = _mpd_cmp(a, b); |
| 5821 | if (c == 0) { |
| 5822 | mpd_qcopy_sign(result, a, b, status); |
| 5823 | return; |
| 5824 | } |
| 5825 | |
| 5826 | if (c < 0) { |
| 5827 | mpd_qnext_plus(result, a, ctx, status); |
| 5828 | } |
| 5829 | else { |
| 5830 | mpd_qnext_minus(result, a, ctx, status); |
| 5831 | } |
| 5832 | |
| 5833 | if (mpd_isinfinite(result)) { |
| 5834 | *status |= (MPD_Overflow|MPD_Rounded|MPD_Inexact); |
| 5835 | } |
| 5836 | else if (mpd_adjexp(result) < ctx->emin) { |
| 5837 | *status |= (MPD_Underflow|MPD_Subnormal|MPD_Rounded|MPD_Inexact); |
| 5838 | if (mpd_iszero(result)) { |
| 5839 | *status |= MPD_Clamped; |
| 5840 | } |
| 5841 | } |
| 5842 | } |
| 5843 | |
| 5844 | /* |
Stefan Krah | b783293 | 2012-06-12 21:06:06 +0200 | [diff] [blame] | 5845 | * Internal function: Integer power with mpd_uint_t exponent. The function |
| 5846 | * can fail with MPD_Malloc_error. |
Stefan Krah | c62bd13 | 2012-06-16 19:45:35 +0200 | [diff] [blame] | 5847 | * |
| 5848 | * The error is equal to the error incurred in k-1 multiplications. Assuming |
| 5849 | * the upper bound for the relative error in each operation: |
| 5850 | * |
| 5851 | * abs(err) = 5 * 10**-prec |
| 5852 | * result = x**k * (1 + err)**(k-1) |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5853 | */ |
| 5854 | static inline void |
Stefan Krah | b783293 | 2012-06-12 21:06:06 +0200 | [diff] [blame] | 5855 | _mpd_qpow_uint(mpd_t *result, const mpd_t *base, mpd_uint_t exp, |
| 5856 | uint8_t resultsign, const mpd_context_t *ctx, uint32_t *status) |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5857 | { |
| 5858 | uint32_t workstatus = 0; |
| 5859 | mpd_uint_t n; |
| 5860 | |
| 5861 | if (exp == 0) { |
| 5862 | _settriple(result, resultsign, 1, 0); /* GCOV_NOT_REACHED */ |
| 5863 | return; /* GCOV_NOT_REACHED */ |
| 5864 | } |
| 5865 | |
| 5866 | if (!mpd_qcopy(result, base, status)) { |
| 5867 | return; |
| 5868 | } |
| 5869 | |
| 5870 | n = mpd_bits[mpd_bsr(exp)]; |
| 5871 | while (n >>= 1) { |
| 5872 | mpd_qmul(result, result, result, ctx, &workstatus); |
| 5873 | if (exp & n) { |
| 5874 | mpd_qmul(result, result, base, ctx, &workstatus); |
| 5875 | } |
Stefan Krah | b783293 | 2012-06-12 21:06:06 +0200 | [diff] [blame] | 5876 | if (mpd_isspecial(result) || |
| 5877 | (mpd_iszerocoeff(result) && (workstatus & MPD_Clamped))) { |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5878 | break; |
| 5879 | } |
| 5880 | } |
| 5881 | |
| 5882 | *status |= workstatus; |
| 5883 | mpd_set_sign(result, resultsign); |
| 5884 | } |
| 5885 | |
| 5886 | /* |
| 5887 | * Internal function: Integer power with mpd_t exponent, tbase and texp |
| 5888 | * are modified!! Function can fail with MPD_Malloc_error. |
Stefan Krah | c62bd13 | 2012-06-16 19:45:35 +0200 | [diff] [blame] | 5889 | * |
| 5890 | * The error is equal to the error incurred in k multiplications. Assuming |
| 5891 | * the upper bound for the relative error in each operation: |
| 5892 | * |
| 5893 | * abs(err) = 5 * 10**-prec |
| 5894 | * result = x**k * (1 + err)**k |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5895 | */ |
| 5896 | static inline void |
| 5897 | _mpd_qpow_mpd(mpd_t *result, mpd_t *tbase, mpd_t *texp, uint8_t resultsign, |
| 5898 | const mpd_context_t *ctx, uint32_t *status) |
| 5899 | { |
| 5900 | uint32_t workstatus = 0; |
| 5901 | mpd_context_t maxctx; |
| 5902 | MPD_NEW_CONST(two,0,0,1,1,1,2); |
| 5903 | |
| 5904 | |
| 5905 | mpd_maxcontext(&maxctx); |
| 5906 | |
| 5907 | /* resize to smaller cannot fail */ |
| 5908 | mpd_qcopy(result, &one, status); |
| 5909 | |
| 5910 | while (!mpd_iszero(texp)) { |
| 5911 | if (mpd_isodd(texp)) { |
| 5912 | mpd_qmul(result, result, tbase, ctx, &workstatus); |
| 5913 | *status |= workstatus; |
Stefan Krah | c62bd13 | 2012-06-16 19:45:35 +0200 | [diff] [blame] | 5914 | if (mpd_isspecial(result) || |
| 5915 | (mpd_iszerocoeff(result) && (workstatus & MPD_Clamped))) { |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5916 | break; |
| 5917 | } |
| 5918 | } |
| 5919 | mpd_qmul(tbase, tbase, tbase, ctx, &workstatus); |
| 5920 | mpd_qdivint(texp, texp, &two, &maxctx, &workstatus); |
| 5921 | if (mpd_isnan(tbase) || mpd_isnan(texp)) { |
| 5922 | mpd_seterror(result, workstatus&MPD_Errors, status); |
| 5923 | return; |
| 5924 | } |
| 5925 | } |
| 5926 | mpd_set_sign(result, resultsign); |
| 5927 | } |
| 5928 | |
| 5929 | /* |
Stefan Krah | c62bd13 | 2012-06-16 19:45:35 +0200 | [diff] [blame] | 5930 | * The power function for integer exponents. Relative error _before_ the |
| 5931 | * final rounding to prec: |
| 5932 | * abs(result - base**exp) < 0.1 * 10**-prec * abs(base**exp) |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5933 | */ |
| 5934 | static void |
| 5935 | _mpd_qpow_int(mpd_t *result, const mpd_t *base, const mpd_t *exp, |
| 5936 | uint8_t resultsign, |
| 5937 | const mpd_context_t *ctx, uint32_t *status) |
| 5938 | { |
| 5939 | mpd_context_t workctx; |
| 5940 | MPD_NEW_STATIC(tbase,0,0,0,0); |
| 5941 | MPD_NEW_STATIC(texp,0,0,0,0); |
| 5942 | mpd_ssize_t n; |
| 5943 | |
| 5944 | |
| 5945 | mpd_workcontext(&workctx, ctx); |
| 5946 | workctx.prec += (exp->digits + exp->exp + 2); |
| 5947 | workctx.round = MPD_ROUND_HALF_EVEN; |
| 5948 | workctx.clamp = 0; |
| 5949 | if (mpd_isnegative(exp)) { |
Stefan Krah | c62bd13 | 2012-06-16 19:45:35 +0200 | [diff] [blame] | 5950 | workctx.prec += 1; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5951 | mpd_qdiv(&tbase, &one, base, &workctx, status); |
| 5952 | if (*status&MPD_Errors) { |
| 5953 | mpd_setspecial(result, MPD_POS, MPD_NAN); |
| 5954 | goto finish; |
| 5955 | } |
| 5956 | } |
| 5957 | else { |
| 5958 | if (!mpd_qcopy(&tbase, base, status)) { |
| 5959 | mpd_setspecial(result, MPD_POS, MPD_NAN); |
| 5960 | goto finish; |
| 5961 | } |
| 5962 | } |
| 5963 | |
| 5964 | n = mpd_qabs_uint(exp, &workctx.status); |
| 5965 | if (workctx.status&MPD_Invalid_operation) { |
| 5966 | if (!mpd_qcopy(&texp, exp, status)) { |
| 5967 | mpd_setspecial(result, MPD_POS, MPD_NAN); /* GCOV_UNLIKELY */ |
| 5968 | goto finish; /* GCOV_UNLIKELY */ |
| 5969 | } |
| 5970 | _mpd_qpow_mpd(result, &tbase, &texp, resultsign, &workctx, status); |
| 5971 | } |
| 5972 | else { |
| 5973 | _mpd_qpow_uint(result, &tbase, n, resultsign, &workctx, status); |
| 5974 | } |
| 5975 | |
| 5976 | if (mpd_isinfinite(result)) { |
| 5977 | /* for ROUND_DOWN, ROUND_FLOOR, etc. */ |
| 5978 | _settriple(result, resultsign, 1, MPD_EXP_INF); |
| 5979 | } |
| 5980 | |
| 5981 | finish: |
| 5982 | mpd_del(&tbase); |
| 5983 | mpd_del(&texp); |
| 5984 | mpd_qfinalize(result, ctx, status); |
| 5985 | } |
| 5986 | |
Stefan Krah | 9c1feb8 | 2012-06-18 19:57:23 +0200 | [diff] [blame] | 5987 | /* |
| 5988 | * If the exponent is infinite and base equals one, the result is one |
| 5989 | * with a coefficient of length prec. Otherwise, result is undefined. |
| 5990 | * Return the value of the comparison against one. |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 5991 | */ |
| 5992 | static int |
| 5993 | _qcheck_pow_one_inf(mpd_t *result, const mpd_t *base, uint8_t resultsign, |
| 5994 | const mpd_context_t *ctx, uint32_t *status) |
| 5995 | { |
| 5996 | mpd_ssize_t shift; |
| 5997 | int cmp; |
| 5998 | |
| 5999 | if ((cmp = _mpd_cmp(base, &one)) == 0) { |
| 6000 | shift = ctx->prec-1; |
| 6001 | mpd_qshiftl(result, &one, shift, status); |
| 6002 | result->exp = -shift; |
| 6003 | mpd_set_flags(result, resultsign); |
| 6004 | *status |= (MPD_Inexact|MPD_Rounded); |
| 6005 | } |
| 6006 | |
| 6007 | return cmp; |
| 6008 | } |
| 6009 | |
| 6010 | /* |
Stefan Krah | 9c1feb8 | 2012-06-18 19:57:23 +0200 | [diff] [blame] | 6011 | * If abs(base) equals one, calculate the correct power of one result. |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6012 | * Otherwise, result is undefined. Return the value of the comparison |
| 6013 | * against 1. |
| 6014 | * |
| 6015 | * This is an internal function that does not check for specials. |
| 6016 | */ |
| 6017 | static int |
| 6018 | _qcheck_pow_one(mpd_t *result, const mpd_t *base, const mpd_t *exp, |
| 6019 | uint8_t resultsign, |
| 6020 | const mpd_context_t *ctx, uint32_t *status) |
| 6021 | { |
| 6022 | uint32_t workstatus = 0; |
| 6023 | mpd_ssize_t shift; |
| 6024 | int cmp; |
| 6025 | |
| 6026 | if ((cmp = _mpd_cmp_abs(base, &one)) == 0) { |
| 6027 | if (_mpd_isint(exp)) { |
| 6028 | if (mpd_isnegative(exp)) { |
| 6029 | _settriple(result, resultsign, 1, 0); |
| 6030 | return 0; |
| 6031 | } |
| 6032 | /* 1.000**3 = 1.000000000 */ |
| 6033 | mpd_qmul_ssize(result, exp, -base->exp, ctx, &workstatus); |
| 6034 | if (workstatus&MPD_Errors) { |
| 6035 | *status |= (workstatus&MPD_Errors); |
| 6036 | return 0; |
| 6037 | } |
| 6038 | /* digits-1 after exponentiation */ |
| 6039 | shift = mpd_qget_ssize(result, &workstatus); |
| 6040 | /* shift is MPD_SSIZE_MAX if result is too large */ |
| 6041 | if (shift > ctx->prec-1) { |
| 6042 | shift = ctx->prec-1; |
| 6043 | *status |= MPD_Rounded; |
| 6044 | } |
| 6045 | } |
| 6046 | else if (mpd_ispositive(base)) { |
| 6047 | shift = ctx->prec-1; |
| 6048 | *status |= (MPD_Inexact|MPD_Rounded); |
| 6049 | } |
| 6050 | else { |
| 6051 | return -2; /* GCOV_NOT_REACHED */ |
| 6052 | } |
| 6053 | if (!mpd_qshiftl(result, &one, shift, status)) { |
| 6054 | return 0; |
| 6055 | } |
| 6056 | result->exp = -shift; |
| 6057 | mpd_set_flags(result, resultsign); |
| 6058 | } |
| 6059 | |
| 6060 | return cmp; |
| 6061 | } |
| 6062 | |
| 6063 | /* |
| 6064 | * Detect certain over/underflow of x**y. |
Stefan Krah | 9c1feb8 | 2012-06-18 19:57:23 +0200 | [diff] [blame] | 6065 | * ACL2 proof: pow-bounds.lisp. |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6066 | * |
| 6067 | * Symbols: |
| 6068 | * |
| 6069 | * e: EXP_INF or EXP_CLAMP |
| 6070 | * x: base |
| 6071 | * y: exponent |
| 6072 | * |
| 6073 | * omega(e) = log10(abs(e)) |
| 6074 | * zeta(x) = log10(abs(log10(x))) |
| 6075 | * theta(y) = log10(abs(y)) |
| 6076 | * |
| 6077 | * Upper and lower bounds: |
| 6078 | * |
| 6079 | * ub_omega(e) = ceil(log10(abs(e))) |
| 6080 | * lb_theta(y) = floor(log10(abs(y))) |
| 6081 | * |
| 6082 | * | floor(log10(floor(abs(log10(x))))) if x < 1/10 or x >= 10 |
| 6083 | * lb_zeta(x) = | floor(log10(abs(x-1)/10)) if 1/10 <= x < 1 |
| 6084 | * | floor(log10(abs((x-1)/100))) if 1 < x < 10 |
| 6085 | * |
| 6086 | * ub_omega(e) and lb_theta(y) are obviously upper and lower bounds |
| 6087 | * for omega(e) and theta(y). |
| 6088 | * |
| 6089 | * lb_zeta is a lower bound for zeta(x): |
| 6090 | * |
| 6091 | * x < 1/10 or x >= 10: |
| 6092 | * |
| 6093 | * abs(log10(x)) >= 1, so the outer log10 is well defined. Since log10 |
| 6094 | * is strictly increasing, the end result is a lower bound. |
| 6095 | * |
| 6096 | * 1/10 <= x < 1: |
| 6097 | * |
| 6098 | * We use: log10(x) <= (x-1)/log(10) |
| 6099 | * abs(log10(x)) >= abs(x-1)/log(10) |
| 6100 | * abs(log10(x)) >= abs(x-1)/10 |
| 6101 | * |
| 6102 | * 1 < x < 10: |
| 6103 | * |
| 6104 | * We use: (x-1)/(x*log(10)) < log10(x) |
| 6105 | * abs((x-1)/100) < abs(log10(x)) |
| 6106 | * |
| 6107 | * XXX: abs((x-1)/10) would work, need ACL2 proof. |
| 6108 | * |
| 6109 | * |
| 6110 | * Let (0 < x < 1 and y < 0) or (x > 1 and y > 0). (H1) |
| 6111 | * Let ub_omega(exp_inf) < lb_zeta(x) + lb_theta(y) (H2) |
| 6112 | * |
| 6113 | * Then: |
| 6114 | * log10(abs(exp_inf)) < log10(abs(log10(x))) + log10(abs(y)). (1) |
| 6115 | * exp_inf < log10(x) * y (2) |
| 6116 | * 10**exp_inf < x**y (3) |
| 6117 | * |
| 6118 | * Let (0 < x < 1 and y > 0) or (x > 1 and y < 0). (H3) |
| 6119 | * Let ub_omega(exp_clamp) < lb_zeta(x) + lb_theta(y) (H4) |
| 6120 | * |
| 6121 | * Then: |
| 6122 | * log10(abs(exp_clamp)) < log10(abs(log10(x))) + log10(abs(y)). (4) |
| 6123 | * log10(x) * y < exp_clamp (5) |
| 6124 | * x**y < 10**exp_clamp (6) |
| 6125 | * |
| 6126 | */ |
| 6127 | static mpd_ssize_t |
| 6128 | _lower_bound_zeta(const mpd_t *x, uint32_t *status) |
| 6129 | { |
| 6130 | mpd_context_t maxctx; |
| 6131 | MPD_NEW_STATIC(scratch,0,0,0,0); |
| 6132 | mpd_ssize_t t, u; |
| 6133 | |
| 6134 | t = mpd_adjexp(x); |
| 6135 | if (t > 0) { |
Stefan Krah | cd9e1d0 | 2012-03-23 16:22:05 +0100 | [diff] [blame] | 6136 | /* x >= 10 -> floor(log10(floor(abs(log10(x))))) */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6137 | return mpd_exp_digits(t) - 1; |
| 6138 | } |
| 6139 | else if (t < -1) { |
| 6140 | /* x < 1/10 -> floor(log10(floor(abs(log10(x))))) */ |
| 6141 | return mpd_exp_digits(t+1) - 1; |
| 6142 | } |
| 6143 | else { |
| 6144 | mpd_maxcontext(&maxctx); |
| 6145 | mpd_qsub(&scratch, x, &one, &maxctx, status); |
| 6146 | if (mpd_isspecial(&scratch)) { |
| 6147 | mpd_del(&scratch); |
| 6148 | return MPD_SSIZE_MAX; |
| 6149 | } |
| 6150 | u = mpd_adjexp(&scratch); |
| 6151 | mpd_del(&scratch); |
| 6152 | |
| 6153 | /* t == -1, 1/10 <= x < 1 -> floor(log10(abs(x-1)/10)) |
| 6154 | * t == 0, 1 < x < 10 -> floor(log10(abs(x-1)/100)) */ |
| 6155 | return (t == 0) ? u-2 : u-1; |
| 6156 | } |
| 6157 | } |
| 6158 | |
| 6159 | /* |
| 6160 | * Detect cases of certain overflow/underflow in the power function. |
| 6161 | * Assumptions: x != 1, y != 0. The proof above is for positive x. |
| 6162 | * If x is negative and y is an odd integer, x**y == -(abs(x)**y), |
| 6163 | * so the analysis does not change. |
| 6164 | */ |
| 6165 | static int |
| 6166 | _qcheck_pow_bounds(mpd_t *result, const mpd_t *x, const mpd_t *y, |
| 6167 | uint8_t resultsign, |
| 6168 | const mpd_context_t *ctx, uint32_t *status) |
| 6169 | { |
| 6170 | MPD_NEW_SHARED(abs_x, x); |
| 6171 | mpd_ssize_t ub_omega, lb_zeta, lb_theta; |
| 6172 | uint8_t sign; |
| 6173 | |
| 6174 | mpd_set_positive(&abs_x); |
| 6175 | |
| 6176 | lb_theta = mpd_adjexp(y); |
| 6177 | lb_zeta = _lower_bound_zeta(&abs_x, status); |
| 6178 | if (lb_zeta == MPD_SSIZE_MAX) { |
| 6179 | mpd_seterror(result, MPD_Malloc_error, status); |
| 6180 | return 1; |
| 6181 | } |
| 6182 | |
| 6183 | sign = (mpd_adjexp(&abs_x) < 0) ^ mpd_sign(y); |
| 6184 | if (sign == 0) { |
| 6185 | /* (0 < |x| < 1 and y < 0) or (|x| > 1 and y > 0) */ |
| 6186 | ub_omega = mpd_exp_digits(ctx->emax); |
| 6187 | if (ub_omega < lb_zeta + lb_theta) { |
| 6188 | _settriple(result, resultsign, 1, MPD_EXP_INF); |
| 6189 | mpd_qfinalize(result, ctx, status); |
| 6190 | return 1; |
| 6191 | } |
| 6192 | } |
| 6193 | else { |
Stefan Krah | cd9e1d0 | 2012-03-23 16:22:05 +0100 | [diff] [blame] | 6194 | /* (0 < |x| < 1 and y > 0) or (|x| > 1 and y < 0). */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6195 | ub_omega = mpd_exp_digits(mpd_etiny(ctx)); |
| 6196 | if (ub_omega < lb_zeta + lb_theta) { |
| 6197 | _settriple(result, resultsign, 1, mpd_etiny(ctx)-1); |
| 6198 | mpd_qfinalize(result, ctx, status); |
| 6199 | return 1; |
| 6200 | } |
| 6201 | } |
| 6202 | |
| 6203 | return 0; |
| 6204 | } |
| 6205 | |
| 6206 | /* |
| 6207 | * TODO: Implement algorithm for computing exact powers from decimal.py. |
| 6208 | * In order to prevent infinite loops, this has to be called before |
| 6209 | * using Ziv's strategy for correct rounding. |
| 6210 | */ |
| 6211 | /* |
| 6212 | static int |
| 6213 | _mpd_qpow_exact(mpd_t *result, const mpd_t *base, const mpd_t *exp, |
| 6214 | const mpd_context_t *ctx, uint32_t *status) |
| 6215 | { |
| 6216 | return 0; |
| 6217 | } |
| 6218 | */ |
| 6219 | |
Stefan Krah | 9c1feb8 | 2012-06-18 19:57:23 +0200 | [diff] [blame] | 6220 | /* |
| 6221 | * The power function for real exponents. |
| 6222 | * Relative error: abs(result - e**y) < e**y * 1/5 * 10**(-prec - 1) |
| 6223 | */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6224 | static void |
| 6225 | _mpd_qpow_real(mpd_t *result, const mpd_t *base, const mpd_t *exp, |
| 6226 | const mpd_context_t *ctx, uint32_t *status) |
| 6227 | { |
| 6228 | mpd_context_t workctx; |
| 6229 | MPD_NEW_STATIC(texp,0,0,0,0); |
| 6230 | |
| 6231 | if (!mpd_qcopy(&texp, exp, status)) { |
| 6232 | mpd_seterror(result, MPD_Malloc_error, status); |
| 6233 | return; |
| 6234 | } |
| 6235 | |
| 6236 | mpd_maxcontext(&workctx); |
| 6237 | workctx.prec = (base->digits > ctx->prec) ? base->digits : ctx->prec; |
| 6238 | workctx.prec += (4 + MPD_EXPDIGITS); |
| 6239 | workctx.round = MPD_ROUND_HALF_EVEN; |
| 6240 | workctx.allcr = ctx->allcr; |
| 6241 | |
Stefan Krah | 9c1feb8 | 2012-06-18 19:57:23 +0200 | [diff] [blame] | 6242 | /* |
| 6243 | * extra := MPD_EXPDIGITS = MPD_EXP_MAX_T |
| 6244 | * wp := prec + 4 + extra |
| 6245 | * abs(err) < 5 * 10**-wp |
| 6246 | * y := log(base) * exp |
| 6247 | * Calculate: |
| 6248 | * 1) e**(y * (1 + err)**2) * (1 + err) |
| 6249 | * = e**y * e**(y * (2*err + err**2)) * (1 + err) |
| 6250 | * ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ |
| 6251 | * Relative error of the underlined term: |
| 6252 | * 2) abs(e**(y * (2*err + err**2)) - 1) |
| 6253 | * Case abs(y) >= 10**extra: |
| 6254 | * 3) adjexp(y)+1 > log10(abs(y)) >= extra |
| 6255 | * This triggers the Overflow/Underflow shortcut in _mpd_qexp(), |
| 6256 | * so no further analysis is necessary. |
| 6257 | * Case abs(y) < 10**extra: |
| 6258 | * 4) abs(y * (2*err + err**2)) < 1/5 * 10**(-prec - 2) |
| 6259 | * Use (see _mpd_qexp): |
| 6260 | * 5) abs(x) <= 9/10 * 10**-p ==> abs(e**x - 1) < 10**-p |
| 6261 | * With 2), 4) and 5): |
| 6262 | * 6) abs(e**(y * (2*err + err**2)) - 1) < 10**(-prec - 2) |
| 6263 | * The complete relative error of 1) is: |
| 6264 | * 7) abs(result - e**y) < e**y * 1/5 * 10**(-prec - 1) |
| 6265 | */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6266 | mpd_qln(result, base, &workctx, &workctx.status); |
| 6267 | mpd_qmul(result, result, &texp, &workctx, &workctx.status); |
| 6268 | mpd_qexp(result, result, &workctx, status); |
| 6269 | |
| 6270 | mpd_del(&texp); |
| 6271 | *status |= (workctx.status&MPD_Errors); |
| 6272 | *status |= (MPD_Inexact|MPD_Rounded); |
| 6273 | } |
| 6274 | |
| 6275 | /* The power function: base**exp */ |
| 6276 | void |
| 6277 | mpd_qpow(mpd_t *result, const mpd_t *base, const mpd_t *exp, |
| 6278 | const mpd_context_t *ctx, uint32_t *status) |
| 6279 | { |
| 6280 | uint8_t resultsign = 0; |
| 6281 | int intexp = 0; |
| 6282 | int cmp; |
| 6283 | |
| 6284 | if (mpd_isspecial(base) || mpd_isspecial(exp)) { |
| 6285 | if (mpd_qcheck_nans(result, base, exp, ctx, status)) { |
| 6286 | return; |
| 6287 | } |
| 6288 | } |
| 6289 | if (mpd_isinteger(exp)) { |
| 6290 | intexp = 1; |
| 6291 | resultsign = mpd_isnegative(base) && mpd_isodd(exp); |
| 6292 | } |
| 6293 | |
| 6294 | if (mpd_iszero(base)) { |
| 6295 | if (mpd_iszero(exp)) { |
| 6296 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 6297 | } |
| 6298 | else if (mpd_isnegative(exp)) { |
| 6299 | mpd_setspecial(result, resultsign, MPD_INF); |
| 6300 | } |
| 6301 | else { |
| 6302 | _settriple(result, resultsign, 0, 0); |
| 6303 | } |
| 6304 | return; |
| 6305 | } |
| 6306 | if (mpd_isnegative(base)) { |
| 6307 | if (!intexp || mpd_isinfinite(exp)) { |
| 6308 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 6309 | return; |
| 6310 | } |
| 6311 | } |
| 6312 | if (mpd_isinfinite(exp)) { |
| 6313 | /* power of one */ |
| 6314 | cmp = _qcheck_pow_one_inf(result, base, resultsign, ctx, status); |
| 6315 | if (cmp == 0) { |
| 6316 | return; |
| 6317 | } |
| 6318 | else { |
| 6319 | cmp *= mpd_arith_sign(exp); |
| 6320 | if (cmp < 0) { |
| 6321 | _settriple(result, resultsign, 0, 0); |
| 6322 | } |
| 6323 | else { |
| 6324 | mpd_setspecial(result, resultsign, MPD_INF); |
| 6325 | } |
| 6326 | } |
| 6327 | return; |
| 6328 | } |
| 6329 | if (mpd_isinfinite(base)) { |
| 6330 | if (mpd_iszero(exp)) { |
| 6331 | _settriple(result, resultsign, 1, 0); |
| 6332 | } |
| 6333 | else if (mpd_isnegative(exp)) { |
| 6334 | _settriple(result, resultsign, 0, 0); |
| 6335 | } |
| 6336 | else { |
| 6337 | mpd_setspecial(result, resultsign, MPD_INF); |
| 6338 | } |
| 6339 | return; |
| 6340 | } |
| 6341 | if (mpd_iszero(exp)) { |
| 6342 | _settriple(result, resultsign, 1, 0); |
| 6343 | return; |
| 6344 | } |
| 6345 | if (_qcheck_pow_one(result, base, exp, resultsign, ctx, status) == 0) { |
| 6346 | return; |
| 6347 | } |
| 6348 | if (_qcheck_pow_bounds(result, base, exp, resultsign, ctx, status)) { |
| 6349 | return; |
| 6350 | } |
| 6351 | |
| 6352 | if (intexp) { |
| 6353 | _mpd_qpow_int(result, base, exp, resultsign, ctx, status); |
| 6354 | } |
| 6355 | else { |
| 6356 | _mpd_qpow_real(result, base, exp, ctx, status); |
| 6357 | if (!mpd_isspecial(result) && _mpd_cmp(result, &one) == 0) { |
| 6358 | mpd_ssize_t shift = ctx->prec-1; |
| 6359 | mpd_qshiftl(result, &one, shift, status); |
| 6360 | result->exp = -shift; |
| 6361 | } |
| 6362 | if (mpd_isinfinite(result)) { |
| 6363 | /* for ROUND_DOWN, ROUND_FLOOR, etc. */ |
| 6364 | _settriple(result, MPD_POS, 1, MPD_EXP_INF); |
| 6365 | } |
| 6366 | mpd_qfinalize(result, ctx, status); |
| 6367 | } |
| 6368 | } |
| 6369 | |
| 6370 | /* |
| 6371 | * Internal function: Integer powmod with mpd_uint_t exponent, base is modified! |
| 6372 | * Function can fail with MPD_Malloc_error. |
| 6373 | */ |
| 6374 | static inline void |
| 6375 | _mpd_qpowmod_uint(mpd_t *result, mpd_t *base, mpd_uint_t exp, |
| 6376 | mpd_t *mod, uint32_t *status) |
| 6377 | { |
| 6378 | mpd_context_t maxcontext; |
| 6379 | |
| 6380 | mpd_maxcontext(&maxcontext); |
| 6381 | |
| 6382 | /* resize to smaller cannot fail */ |
| 6383 | mpd_qcopy(result, &one, status); |
| 6384 | |
| 6385 | while (exp > 0) { |
| 6386 | if (exp & 1) { |
| 6387 | mpd_qmul(result, result, base, &maxcontext, status); |
| 6388 | mpd_qrem(result, result, mod, &maxcontext, status); |
| 6389 | } |
| 6390 | mpd_qmul(base, base, base, &maxcontext, status); |
| 6391 | mpd_qrem(base, base, mod, &maxcontext, status); |
| 6392 | exp >>= 1; |
| 6393 | } |
| 6394 | } |
| 6395 | |
| 6396 | /* The powmod function: (base**exp) % mod */ |
| 6397 | void |
| 6398 | mpd_qpowmod(mpd_t *result, const mpd_t *base, const mpd_t *exp, |
| 6399 | const mpd_t *mod, |
| 6400 | const mpd_context_t *ctx, uint32_t *status) |
| 6401 | { |
| 6402 | mpd_context_t maxcontext; |
| 6403 | MPD_NEW_STATIC(tbase,0,0,0,0); |
| 6404 | MPD_NEW_STATIC(texp,0,0,0,0); |
| 6405 | MPD_NEW_STATIC(tmod,0,0,0,0); |
| 6406 | MPD_NEW_STATIC(tmp,0,0,0,0); |
| 6407 | MPD_NEW_CONST(two,0,0,1,1,1,2); |
| 6408 | mpd_ssize_t tbase_exp, texp_exp; |
| 6409 | mpd_ssize_t i; |
| 6410 | mpd_t t; |
| 6411 | mpd_uint_t r; |
| 6412 | uint8_t sign; |
| 6413 | |
| 6414 | |
| 6415 | if (mpd_isspecial(base) || mpd_isspecial(exp) || mpd_isspecial(mod)) { |
| 6416 | if (mpd_qcheck_3nans(result, base, exp, mod, ctx, status)) { |
| 6417 | return; |
| 6418 | } |
| 6419 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 6420 | return; |
| 6421 | } |
| 6422 | |
| 6423 | |
| 6424 | if (!_mpd_isint(base) || !_mpd_isint(exp) || !_mpd_isint(mod)) { |
| 6425 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 6426 | return; |
| 6427 | } |
| 6428 | if (mpd_iszerocoeff(mod)) { |
| 6429 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 6430 | return; |
| 6431 | } |
| 6432 | if (mod->digits+mod->exp > ctx->prec) { |
| 6433 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 6434 | return; |
| 6435 | } |
| 6436 | |
| 6437 | sign = (mpd_isnegative(base)) && (mpd_isodd(exp)); |
| 6438 | if (mpd_iszerocoeff(exp)) { |
| 6439 | if (mpd_iszerocoeff(base)) { |
| 6440 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 6441 | return; |
| 6442 | } |
| 6443 | r = (_mpd_cmp_abs(mod, &one)==0) ? 0 : 1; |
| 6444 | _settriple(result, sign, r, 0); |
| 6445 | return; |
| 6446 | } |
| 6447 | if (mpd_isnegative(exp)) { |
| 6448 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 6449 | return; |
| 6450 | } |
| 6451 | if (mpd_iszerocoeff(base)) { |
| 6452 | _settriple(result, sign, 0, 0); |
| 6453 | return; |
| 6454 | } |
| 6455 | |
| 6456 | if (!mpd_qcopy(&tmod, mod, status)) { |
| 6457 | goto mpd_errors; |
| 6458 | } |
| 6459 | mpd_set_positive(&tmod); |
| 6460 | |
| 6461 | mpd_maxcontext(&maxcontext); |
| 6462 | |
| 6463 | mpd_qround_to_int(&tbase, base, &maxcontext, status); |
| 6464 | mpd_qround_to_int(&texp, exp, &maxcontext, status); |
| 6465 | mpd_qround_to_int(&tmod, &tmod, &maxcontext, status); |
| 6466 | |
| 6467 | tbase_exp = tbase.exp; |
| 6468 | tbase.exp = 0; |
| 6469 | texp_exp = texp.exp; |
| 6470 | texp.exp = 0; |
| 6471 | |
| 6472 | /* base = (base.int % modulo * pow(10, base.exp, modulo)) % modulo */ |
| 6473 | mpd_qrem(&tbase, &tbase, &tmod, &maxcontext, status); |
| 6474 | _settriple(result, MPD_POS, 1, tbase_exp); |
| 6475 | mpd_qrem(result, result, &tmod, &maxcontext, status); |
| 6476 | mpd_qmul(&tbase, &tbase, result, &maxcontext, status); |
| 6477 | mpd_qrem(&tbase, &tbase, &tmod, &maxcontext, status); |
| 6478 | if (mpd_isspecial(&tbase) || |
| 6479 | mpd_isspecial(&texp) || |
| 6480 | mpd_isspecial(&tmod)) { |
| 6481 | goto mpd_errors; |
| 6482 | } |
| 6483 | |
| 6484 | for (i = 0; i < texp_exp; i++) { |
| 6485 | _mpd_qpowmod_uint(&tmp, &tbase, 10, &tmod, status); |
| 6486 | t = tmp; |
| 6487 | tmp = tbase; |
| 6488 | tbase = t; |
| 6489 | } |
| 6490 | if (mpd_isspecial(&tbase)) { |
| 6491 | goto mpd_errors; /* GCOV_UNLIKELY */ |
| 6492 | } |
| 6493 | |
| 6494 | /* resize to smaller cannot fail */ |
| 6495 | mpd_qcopy(result, &one, status); |
| 6496 | while (mpd_isfinite(&texp) && !mpd_iszero(&texp)) { |
| 6497 | if (mpd_isodd(&texp)) { |
| 6498 | mpd_qmul(result, result, &tbase, &maxcontext, status); |
| 6499 | mpd_qrem(result, result, &tmod, &maxcontext, status); |
| 6500 | } |
| 6501 | mpd_qmul(&tbase, &tbase, &tbase, &maxcontext, status); |
| 6502 | mpd_qrem(&tbase, &tbase, &tmod, &maxcontext, status); |
| 6503 | mpd_qdivint(&texp, &texp, &two, &maxcontext, status); |
| 6504 | } |
| 6505 | if (mpd_isspecial(&texp) || mpd_isspecial(&tbase) || |
Stefan Krah | 7cc5521 | 2012-03-21 20:21:20 +0100 | [diff] [blame] | 6506 | mpd_isspecial(&tmod) || mpd_isspecial(result)) { |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6507 | /* MPD_Malloc_error */ |
| 6508 | goto mpd_errors; |
| 6509 | } |
| 6510 | else { |
| 6511 | mpd_set_sign(result, sign); |
| 6512 | } |
| 6513 | |
| 6514 | out: |
| 6515 | mpd_del(&tbase); |
| 6516 | mpd_del(&texp); |
| 6517 | mpd_del(&tmod); |
| 6518 | mpd_del(&tmp); |
| 6519 | mpd_qfinalize(result, ctx, status); |
| 6520 | return; |
| 6521 | |
| 6522 | mpd_errors: |
| 6523 | mpd_setspecial(result, MPD_POS, MPD_NAN); |
| 6524 | goto out; |
| 6525 | } |
| 6526 | |
| 6527 | void |
| 6528 | mpd_qquantize(mpd_t *result, const mpd_t *a, const mpd_t *b, |
| 6529 | const mpd_context_t *ctx, uint32_t *status) |
| 6530 | { |
| 6531 | uint32_t workstatus = 0; |
| 6532 | mpd_ssize_t b_exp = b->exp; |
| 6533 | mpd_ssize_t expdiff, shift; |
| 6534 | mpd_uint_t rnd; |
| 6535 | |
| 6536 | if (mpd_isspecial(a) || mpd_isspecial(b)) { |
| 6537 | if (mpd_qcheck_nans(result, a, b, ctx, status)) { |
| 6538 | return; |
| 6539 | } |
| 6540 | if (mpd_isinfinite(a) && mpd_isinfinite(b)) { |
| 6541 | mpd_qcopy(result, a, status); |
| 6542 | return; |
| 6543 | } |
| 6544 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 6545 | return; |
| 6546 | } |
| 6547 | |
| 6548 | if (b->exp > ctx->emax || b->exp < mpd_etiny(ctx)) { |
| 6549 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 6550 | return; |
| 6551 | } |
| 6552 | |
| 6553 | if (mpd_iszero(a)) { |
| 6554 | _settriple(result, mpd_sign(a), 0, b->exp); |
| 6555 | mpd_qfinalize(result, ctx, status); |
| 6556 | return; |
| 6557 | } |
| 6558 | |
| 6559 | |
| 6560 | expdiff = a->exp - b->exp; |
| 6561 | if (a->digits + expdiff > ctx->prec) { |
| 6562 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 6563 | return; |
| 6564 | } |
| 6565 | |
| 6566 | if (expdiff >= 0) { |
| 6567 | shift = expdiff; |
| 6568 | if (!mpd_qshiftl(result, a, shift, status)) { |
| 6569 | return; |
| 6570 | } |
| 6571 | result->exp = b_exp; |
| 6572 | } |
| 6573 | else { |
| 6574 | /* At this point expdiff < 0 and a->digits+expdiff <= prec, |
| 6575 | * so the shift before an increment will fit in prec. */ |
| 6576 | shift = -expdiff; |
| 6577 | rnd = mpd_qshiftr(result, a, shift, status); |
| 6578 | if (rnd == MPD_UINT_MAX) { |
| 6579 | return; |
| 6580 | } |
| 6581 | result->exp = b_exp; |
| 6582 | if (!_mpd_apply_round_fit(result, rnd, ctx, status)) { |
| 6583 | return; |
| 6584 | } |
| 6585 | workstatus |= MPD_Rounded; |
| 6586 | if (rnd) { |
| 6587 | workstatus |= MPD_Inexact; |
| 6588 | } |
| 6589 | } |
| 6590 | |
| 6591 | if (mpd_adjexp(result) > ctx->emax || |
| 6592 | mpd_adjexp(result) < mpd_etiny(ctx)) { |
| 6593 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 6594 | return; |
| 6595 | } |
| 6596 | |
| 6597 | *status |= workstatus; |
| 6598 | mpd_qfinalize(result, ctx, status); |
| 6599 | } |
| 6600 | |
| 6601 | void |
| 6602 | mpd_qreduce(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, |
| 6603 | uint32_t *status) |
| 6604 | { |
| 6605 | mpd_ssize_t shift, maxexp, maxshift; |
| 6606 | uint8_t sign_a = mpd_sign(a); |
| 6607 | |
| 6608 | if (mpd_isspecial(a)) { |
| 6609 | if (mpd_qcheck_nan(result, a, ctx, status)) { |
| 6610 | return; |
| 6611 | } |
| 6612 | mpd_qcopy(result, a, status); |
| 6613 | return; |
| 6614 | } |
| 6615 | |
| 6616 | if (!mpd_qcopy(result, a, status)) { |
| 6617 | return; |
| 6618 | } |
| 6619 | mpd_qfinalize(result, ctx, status); |
| 6620 | if (mpd_isspecial(result)) { |
| 6621 | return; |
| 6622 | } |
| 6623 | if (mpd_iszero(result)) { |
| 6624 | _settriple(result, sign_a, 0, 0); |
| 6625 | return; |
| 6626 | } |
| 6627 | |
| 6628 | shift = mpd_trail_zeros(result); |
| 6629 | maxexp = (ctx->clamp) ? mpd_etop(ctx) : ctx->emax; |
| 6630 | /* After the finalizing above result->exp <= maxexp. */ |
| 6631 | maxshift = maxexp - result->exp; |
| 6632 | shift = (shift > maxshift) ? maxshift : shift; |
| 6633 | |
| 6634 | mpd_qshiftr_inplace(result, shift); |
| 6635 | result->exp += shift; |
| 6636 | } |
| 6637 | |
| 6638 | void |
| 6639 | mpd_qrem(mpd_t *r, const mpd_t *a, const mpd_t *b, const mpd_context_t *ctx, |
| 6640 | uint32_t *status) |
| 6641 | { |
| 6642 | MPD_NEW_STATIC(q,0,0,0,0); |
| 6643 | |
| 6644 | if (mpd_isspecial(a) || mpd_isspecial(b)) { |
| 6645 | if (mpd_qcheck_nans(r, a, b, ctx, status)) { |
| 6646 | return; |
| 6647 | } |
| 6648 | if (mpd_isinfinite(a)) { |
| 6649 | mpd_seterror(r, MPD_Invalid_operation, status); |
| 6650 | return; |
| 6651 | } |
| 6652 | if (mpd_isinfinite(b)) { |
| 6653 | mpd_qcopy(r, a, status); |
| 6654 | mpd_qfinalize(r, ctx, status); |
| 6655 | return; |
| 6656 | } |
| 6657 | /* debug */ |
| 6658 | abort(); /* GCOV_NOT_REACHED */ |
| 6659 | } |
| 6660 | if (mpd_iszerocoeff(b)) { |
| 6661 | if (mpd_iszerocoeff(a)) { |
| 6662 | mpd_seterror(r, MPD_Division_undefined, status); |
| 6663 | } |
| 6664 | else { |
| 6665 | mpd_seterror(r, MPD_Invalid_operation, status); |
| 6666 | } |
| 6667 | return; |
| 6668 | } |
| 6669 | |
| 6670 | _mpd_qdivmod(&q, r, a, b, ctx, status); |
| 6671 | mpd_del(&q); |
| 6672 | mpd_qfinalize(r, ctx, status); |
| 6673 | } |
| 6674 | |
| 6675 | void |
| 6676 | mpd_qrem_near(mpd_t *r, const mpd_t *a, const mpd_t *b, |
| 6677 | const mpd_context_t *ctx, uint32_t *status) |
| 6678 | { |
| 6679 | mpd_context_t workctx; |
| 6680 | MPD_NEW_STATIC(btmp,0,0,0,0); |
| 6681 | MPD_NEW_STATIC(q,0,0,0,0); |
Stefan Krah | 2238501 | 2012-06-20 23:34:58 +0200 | [diff] [blame] | 6682 | mpd_ssize_t expdiff, qdigits; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6683 | int cmp, isodd, allnine; |
| 6684 | |
| 6685 | if (mpd_isspecial(a) || mpd_isspecial(b)) { |
| 6686 | if (mpd_qcheck_nans(r, a, b, ctx, status)) { |
| 6687 | return; |
| 6688 | } |
| 6689 | if (mpd_isinfinite(a)) { |
| 6690 | mpd_seterror(r, MPD_Invalid_operation, status); |
| 6691 | return; |
| 6692 | } |
| 6693 | if (mpd_isinfinite(b)) { |
| 6694 | mpd_qcopy(r, a, status); |
| 6695 | mpd_qfinalize(r, ctx, status); |
| 6696 | return; |
| 6697 | } |
| 6698 | /* debug */ |
| 6699 | abort(); /* GCOV_NOT_REACHED */ |
| 6700 | } |
| 6701 | if (mpd_iszerocoeff(b)) { |
| 6702 | if (mpd_iszerocoeff(a)) { |
| 6703 | mpd_seterror(r, MPD_Division_undefined, status); |
| 6704 | } |
| 6705 | else { |
| 6706 | mpd_seterror(r, MPD_Invalid_operation, status); |
| 6707 | } |
| 6708 | return; |
| 6709 | } |
| 6710 | |
| 6711 | if (r == b) { |
| 6712 | if (!mpd_qcopy(&btmp, b, status)) { |
| 6713 | mpd_seterror(r, MPD_Malloc_error, status); |
| 6714 | return; |
| 6715 | } |
| 6716 | b = &btmp; |
| 6717 | } |
| 6718 | |
Stefan Krah | 2238501 | 2012-06-20 23:34:58 +0200 | [diff] [blame] | 6719 | _mpd_qdivmod(&q, r, a, b, ctx, status); |
| 6720 | if (mpd_isnan(&q) || mpd_isnan(r)) { |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6721 | goto finish; |
| 6722 | } |
| 6723 | if (mpd_iszerocoeff(r)) { |
| 6724 | goto finish; |
| 6725 | } |
| 6726 | |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6727 | expdiff = mpd_adjexp(b) - mpd_adjexp(r); |
| 6728 | if (-1 <= expdiff && expdiff <= 1) { |
| 6729 | |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6730 | allnine = mpd_coeff_isallnine(&q); |
Stefan Krah | 2238501 | 2012-06-20 23:34:58 +0200 | [diff] [blame] | 6731 | qdigits = q.digits; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6732 | isodd = mpd_isodd(&q); |
| 6733 | |
| 6734 | mpd_maxcontext(&workctx); |
| 6735 | if (mpd_sign(a) == mpd_sign(b)) { |
Stefan Krah | 2238501 | 2012-06-20 23:34:58 +0200 | [diff] [blame] | 6736 | /* sign(r) == sign(b) */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6737 | _mpd_qsub(&q, r, b, &workctx, &workctx.status); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6738 | } |
| 6739 | else { |
Stefan Krah | 2238501 | 2012-06-20 23:34:58 +0200 | [diff] [blame] | 6740 | /* sign(r) != sign(b) */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6741 | _mpd_qadd(&q, r, b, &workctx, &workctx.status); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6742 | } |
| 6743 | |
Stefan Krah | 2238501 | 2012-06-20 23:34:58 +0200 | [diff] [blame] | 6744 | if (workctx.status&MPD_Errors) { |
| 6745 | mpd_seterror(r, workctx.status&MPD_Errors, status); |
| 6746 | goto finish; |
| 6747 | } |
| 6748 | |
| 6749 | cmp = _mpd_cmp_abs(&q, r); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6750 | if (cmp < 0 || (cmp == 0 && isodd)) { |
Stefan Krah | 2238501 | 2012-06-20 23:34:58 +0200 | [diff] [blame] | 6751 | /* abs(r) > abs(b)/2 or abs(r) == abs(b)/2 and isodd(quotient) */ |
| 6752 | if (allnine && qdigits == ctx->prec) { |
| 6753 | /* abs(quotient) + 1 == 10**prec */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6754 | mpd_seterror(r, MPD_Division_impossible, status); |
| 6755 | goto finish; |
| 6756 | } |
| 6757 | mpd_qcopy(r, &q, status); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6758 | } |
| 6759 | } |
| 6760 | |
| 6761 | |
| 6762 | finish: |
| 6763 | mpd_del(&btmp); |
| 6764 | mpd_del(&q); |
| 6765 | mpd_qfinalize(r, ctx, status); |
| 6766 | } |
| 6767 | |
| 6768 | static void |
| 6769 | _mpd_qrescale(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, |
| 6770 | const mpd_context_t *ctx, uint32_t *status) |
| 6771 | { |
| 6772 | mpd_ssize_t expdiff, shift; |
| 6773 | mpd_uint_t rnd; |
| 6774 | |
| 6775 | if (mpd_isspecial(a)) { |
| 6776 | mpd_qcopy(result, a, status); |
| 6777 | return; |
| 6778 | } |
| 6779 | |
| 6780 | if (mpd_iszero(a)) { |
| 6781 | _settriple(result, mpd_sign(a), 0, exp); |
| 6782 | return; |
| 6783 | } |
| 6784 | |
| 6785 | expdiff = a->exp - exp; |
| 6786 | if (expdiff >= 0) { |
| 6787 | shift = expdiff; |
| 6788 | if (a->digits + shift > MPD_MAX_PREC+1) { |
| 6789 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 6790 | return; |
| 6791 | } |
| 6792 | if (!mpd_qshiftl(result, a, shift, status)) { |
| 6793 | return; |
| 6794 | } |
| 6795 | result->exp = exp; |
| 6796 | } |
| 6797 | else { |
| 6798 | shift = -expdiff; |
| 6799 | rnd = mpd_qshiftr(result, a, shift, status); |
| 6800 | if (rnd == MPD_UINT_MAX) { |
| 6801 | return; |
| 6802 | } |
| 6803 | result->exp = exp; |
| 6804 | _mpd_apply_round_excess(result, rnd, ctx, status); |
| 6805 | *status |= MPD_Rounded; |
| 6806 | if (rnd) { |
| 6807 | *status |= MPD_Inexact; |
| 6808 | } |
| 6809 | } |
| 6810 | |
| 6811 | if (mpd_issubnormal(result, ctx)) { |
| 6812 | *status |= MPD_Subnormal; |
| 6813 | } |
| 6814 | } |
| 6815 | |
| 6816 | /* |
| 6817 | * Rescale a number so that it has exponent 'exp'. Does not regard context |
| 6818 | * precision, emax, emin, but uses the rounding mode. Special numbers are |
| 6819 | * quietly copied. Restrictions: |
| 6820 | * |
| 6821 | * MPD_MIN_ETINY <= exp <= MPD_MAX_EMAX+1 |
| 6822 | * result->digits <= MPD_MAX_PREC+1 |
| 6823 | */ |
| 6824 | void |
| 6825 | mpd_qrescale(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, |
| 6826 | const mpd_context_t *ctx, uint32_t *status) |
| 6827 | { |
| 6828 | if (exp > MPD_MAX_EMAX+1 || exp < MPD_MIN_ETINY) { |
| 6829 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 6830 | return; |
| 6831 | } |
| 6832 | |
| 6833 | _mpd_qrescale(result, a, exp, ctx, status); |
| 6834 | } |
| 6835 | |
| 6836 | /* |
| 6837 | * Same as mpd_qrescale, but with relaxed restrictions. The result of this |
| 6838 | * function should only be used for formatting a number and never as input |
| 6839 | * for other operations. |
| 6840 | * |
| 6841 | * MPD_MIN_ETINY-MPD_MAX_PREC <= exp <= MPD_MAX_EMAX+1 |
| 6842 | * result->digits <= MPD_MAX_PREC+1 |
| 6843 | */ |
| 6844 | void |
| 6845 | mpd_qrescale_fmt(mpd_t *result, const mpd_t *a, mpd_ssize_t exp, |
| 6846 | const mpd_context_t *ctx, uint32_t *status) |
| 6847 | { |
| 6848 | if (exp > MPD_MAX_EMAX+1 || exp < MPD_MIN_ETINY-MPD_MAX_PREC) { |
| 6849 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 6850 | return; |
| 6851 | } |
| 6852 | |
| 6853 | _mpd_qrescale(result, a, exp, ctx, status); |
| 6854 | } |
| 6855 | |
| 6856 | /* Round to an integer according to 'action' and ctx->round. */ |
| 6857 | enum {TO_INT_EXACT, TO_INT_SILENT, TO_INT_TRUNC}; |
| 6858 | static void |
| 6859 | _mpd_qround_to_integral(int action, mpd_t *result, const mpd_t *a, |
| 6860 | const mpd_context_t *ctx, uint32_t *status) |
| 6861 | { |
| 6862 | mpd_uint_t rnd; |
| 6863 | |
| 6864 | if (mpd_isspecial(a)) { |
| 6865 | if (mpd_qcheck_nan(result, a, ctx, status)) { |
| 6866 | return; |
| 6867 | } |
| 6868 | mpd_qcopy(result, a, status); |
| 6869 | return; |
| 6870 | } |
| 6871 | if (a->exp >= 0) { |
| 6872 | mpd_qcopy(result, a, status); |
| 6873 | return; |
| 6874 | } |
| 6875 | if (mpd_iszerocoeff(a)) { |
| 6876 | _settriple(result, mpd_sign(a), 0, 0); |
| 6877 | return; |
| 6878 | } |
| 6879 | |
| 6880 | rnd = mpd_qshiftr(result, a, -a->exp, status); |
| 6881 | if (rnd == MPD_UINT_MAX) { |
| 6882 | return; |
| 6883 | } |
| 6884 | result->exp = 0; |
| 6885 | |
| 6886 | if (action == TO_INT_EXACT || action == TO_INT_SILENT) { |
| 6887 | _mpd_apply_round_excess(result, rnd, ctx, status); |
| 6888 | if (action == TO_INT_EXACT) { |
| 6889 | *status |= MPD_Rounded; |
| 6890 | if (rnd) { |
| 6891 | *status |= MPD_Inexact; |
| 6892 | } |
| 6893 | } |
| 6894 | } |
| 6895 | } |
| 6896 | |
| 6897 | void |
| 6898 | mpd_qround_to_intx(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, |
| 6899 | uint32_t *status) |
| 6900 | { |
| 6901 | (void)_mpd_qround_to_integral(TO_INT_EXACT, result, a, ctx, status); |
| 6902 | } |
| 6903 | |
| 6904 | void |
| 6905 | mpd_qround_to_int(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, |
| 6906 | uint32_t *status) |
| 6907 | { |
| 6908 | (void)_mpd_qround_to_integral(TO_INT_SILENT, result, a, ctx, status); |
| 6909 | } |
| 6910 | |
| 6911 | void |
| 6912 | mpd_qtrunc(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, |
Stefan Krah | 3077ab8 | 2012-06-23 00:31:04 +0200 | [diff] [blame] | 6913 | uint32_t *status) |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6914 | { |
| 6915 | (void)_mpd_qround_to_integral(TO_INT_TRUNC, result, a, ctx, status); |
| 6916 | } |
| 6917 | |
| 6918 | void |
| 6919 | mpd_qfloor(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, |
| 6920 | uint32_t *status) |
| 6921 | { |
| 6922 | mpd_context_t workctx = *ctx; |
| 6923 | workctx.round = MPD_ROUND_FLOOR; |
| 6924 | (void)_mpd_qround_to_integral(TO_INT_SILENT, result, a, |
| 6925 | &workctx, status); |
| 6926 | } |
| 6927 | |
| 6928 | void |
| 6929 | mpd_qceil(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, |
| 6930 | uint32_t *status) |
| 6931 | { |
| 6932 | mpd_context_t workctx = *ctx; |
| 6933 | workctx.round = MPD_ROUND_CEILING; |
| 6934 | (void)_mpd_qround_to_integral(TO_INT_SILENT, result, a, |
| 6935 | &workctx, status); |
| 6936 | } |
| 6937 | |
| 6938 | int |
| 6939 | mpd_same_quantum(const mpd_t *a, const mpd_t *b) |
| 6940 | { |
| 6941 | if (mpd_isspecial(a) || mpd_isspecial(b)) { |
| 6942 | return ((mpd_isnan(a) && mpd_isnan(b)) || |
Stefan Krah | cd9e1d0 | 2012-03-23 16:22:05 +0100 | [diff] [blame] | 6943 | (mpd_isinfinite(a) && mpd_isinfinite(b))); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6944 | } |
| 6945 | |
| 6946 | return a->exp == b->exp; |
| 6947 | } |
| 6948 | |
| 6949 | /* Schedule the increase in precision for the Newton iteration. */ |
| 6950 | static inline int |
| 6951 | recpr_schedule_prec(mpd_ssize_t klist[MPD_MAX_PREC_LOG2], |
| 6952 | mpd_ssize_t maxprec, mpd_ssize_t initprec) |
| 6953 | { |
| 6954 | mpd_ssize_t k; |
| 6955 | int i; |
| 6956 | |
| 6957 | assert(maxprec > 0 && initprec > 0); |
| 6958 | if (maxprec <= initprec) return -1; |
| 6959 | |
| 6960 | i = 0; k = maxprec; |
| 6961 | do { |
| 6962 | k = (k+1) / 2; |
| 6963 | klist[i++] = k; |
| 6964 | } while (k > initprec); |
| 6965 | |
| 6966 | return i-1; |
| 6967 | } |
| 6968 | |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 6969 | /* |
| 6970 | * Initial approximation for the reciprocal: |
| 6971 | * k_0 := MPD_RDIGITS-2 |
| 6972 | * z_0 := 10**(-k_0) * floor(10**(2*k_0 + 2) / floor(v * 10**(k_0 + 2))) |
| 6973 | * Absolute error: |
| 6974 | * |1/v - z_0| < 10**(-k_0) |
| 6975 | * ACL2 proof: maxerror-inverse-approx |
| 6976 | */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6977 | static void |
| 6978 | _mpd_qreciprocal_approx(mpd_t *z, const mpd_t *v, uint32_t *status) |
| 6979 | { |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 6980 | mpd_uint_t p10data[2] = {0, mpd_pow10[MPD_RDIGITS-2]}; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6981 | mpd_uint_t dummy, word; |
| 6982 | int n; |
| 6983 | |
Stefan Krah | c51b7fd | 2012-04-18 19:27:32 +0200 | [diff] [blame] | 6984 | assert(v->exp == -v->digits); |
| 6985 | |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6986 | _mpd_get_msdigits(&dummy, &word, v, MPD_RDIGITS); |
| 6987 | n = mpd_word_digits(word); |
| 6988 | word *= mpd_pow10[MPD_RDIGITS-n]; |
| 6989 | |
| 6990 | mpd_qresize(z, 2, status); |
| 6991 | (void)_mpd_shortdiv(z->data, p10data, 2, word); |
| 6992 | |
| 6993 | mpd_clear_flags(z); |
Stefan Krah | c51b7fd | 2012-04-18 19:27:32 +0200 | [diff] [blame] | 6994 | z->exp = -(MPD_RDIGITS-2); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 6995 | z->len = (z->data[1] == 0) ? 1 : 2; |
| 6996 | mpd_setdigits(z); |
| 6997 | } |
| 6998 | |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 6999 | /* |
| 7000 | * Reciprocal, calculated with Newton's Method. Assumption: result != a. |
| 7001 | * NOTE: The comments in the function show that certain operations are |
| 7002 | * exact. The proof for the maximum error is too long to fit in here. |
| 7003 | * ACL2 proof: maxerror-inverse-complete |
| 7004 | */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7005 | static void |
| 7006 | _mpd_qreciprocal(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, |
| 7007 | uint32_t *status) |
| 7008 | { |
| 7009 | mpd_context_t varcontext, maxcontext; |
| 7010 | mpd_t *z = result; /* current approximation */ |
| 7011 | mpd_t *v; /* a, normalized to a number between 0.1 and 1 */ |
Stefan Krah | c51b7fd | 2012-04-18 19:27:32 +0200 | [diff] [blame] | 7012 | MPD_NEW_SHARED(vtmp, a); /* v shares data with a */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7013 | MPD_NEW_STATIC(s,0,0,0,0); /* temporary variable */ |
| 7014 | MPD_NEW_STATIC(t,0,0,0,0); /* temporary variable */ |
| 7015 | MPD_NEW_CONST(two,0,0,1,1,1,2); /* const 2 */ |
| 7016 | mpd_ssize_t klist[MPD_MAX_PREC_LOG2]; |
| 7017 | mpd_ssize_t adj, maxprec, initprec; |
| 7018 | uint8_t sign = mpd_sign(a); |
| 7019 | int i; |
| 7020 | |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7021 | assert(result != a); |
| 7022 | |
Stefan Krah | c51b7fd | 2012-04-18 19:27:32 +0200 | [diff] [blame] | 7023 | v = &vtmp; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7024 | mpd_clear_flags(v); |
| 7025 | adj = v->digits + v->exp; |
| 7026 | v->exp = -v->digits; |
| 7027 | |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 7028 | /* Initial approximation */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7029 | _mpd_qreciprocal_approx(z, v, status); |
| 7030 | |
| 7031 | mpd_maxcontext(&varcontext); |
| 7032 | mpd_maxcontext(&maxcontext); |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 7033 | varcontext.round = maxcontext.round = MPD_ROUND_TRUNC; |
| 7034 | varcontext.emax = maxcontext.emax = MPD_MAX_EMAX + 100; |
| 7035 | varcontext.emin = maxcontext.emin = MPD_MIN_EMIN - 100; |
| 7036 | maxcontext.prec = MPD_MAX_PREC + 100; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7037 | |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 7038 | maxprec = ctx->prec; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7039 | maxprec += 2; |
| 7040 | initprec = MPD_RDIGITS-3; |
| 7041 | |
| 7042 | i = recpr_schedule_prec(klist, maxprec, initprec); |
| 7043 | for (; i >= 0; i--) { |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 7044 | /* Loop invariant: z->digits <= klist[i]+7 */ |
| 7045 | /* Let s := z**2, exact result */ |
| 7046 | _mpd_qmul_exact(&s, z, z, &maxcontext, status); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7047 | varcontext.prec = 2*klist[i] + 5; |
| 7048 | if (v->digits > varcontext.prec) { |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 7049 | /* Let t := v, truncated to n >= 2*k+5 fraction digits */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7050 | mpd_qshiftr(&t, v, v->digits-varcontext.prec, status); |
| 7051 | t.exp = -varcontext.prec; |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 7052 | /* Let t := trunc(v)*s, truncated to n >= 2*k+1 fraction digits */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7053 | mpd_qmul(&t, &t, &s, &varcontext, status); |
| 7054 | } |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 7055 | else { /* v->digits <= 2*k+5 */ |
| 7056 | /* Let t := v*s, truncated to n >= 2*k+1 fraction digits */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7057 | mpd_qmul(&t, v, &s, &varcontext, status); |
| 7058 | } |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 7059 | /* Let s := 2*z, exact result */ |
| 7060 | _mpd_qmul_exact(&s, z, &two, &maxcontext, status); |
| 7061 | /* s.digits < t.digits <= 2*k+5, |adjexp(s)-adjexp(t)| <= 1, |
| 7062 | * so the subtraction generates at most 2*k+6 <= klist[i+1]+7 |
| 7063 | * digits. The loop invariant is preserved. */ |
| 7064 | _mpd_qsub_exact(z, &s, &t, &maxcontext, status); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7065 | } |
| 7066 | |
| 7067 | if (!mpd_isspecial(z)) { |
| 7068 | z->exp -= adj; |
| 7069 | mpd_set_flags(z, sign); |
| 7070 | } |
| 7071 | |
| 7072 | mpd_del(&s); |
| 7073 | mpd_del(&t); |
| 7074 | mpd_qfinalize(z, ctx, status); |
| 7075 | } |
| 7076 | |
| 7077 | /* |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 7078 | * Internal function for large numbers: |
| 7079 | * |
| 7080 | * q, r = divmod(coeff(a), coeff(b)) |
| 7081 | * |
| 7082 | * Strategy: Multiply the dividend by the reciprocal of the divisor. The |
Stefan Krah | 50b0a36 | 2012-06-20 23:38:51 +0200 | [diff] [blame] | 7083 | * inexact result is fixed by a small loop, using at most one iteration. |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 7084 | * |
| 7085 | * ACL2 proofs: |
| 7086 | * ------------ |
| 7087 | * 1) q is a natural number. (ndivmod-quotient-natp) |
| 7088 | * 2) r is a natural number. (ndivmod-remainder-natp) |
| 7089 | * 3) a = q * b + r (ndivmod-q*b+r==a) |
| 7090 | * 4) r < b (ndivmod-remainder-<-b) |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7091 | */ |
| 7092 | static void |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 7093 | _mpd_base_ndivmod(mpd_t *q, mpd_t *r, const mpd_t *a, const mpd_t *b, |
| 7094 | uint32_t *status) |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7095 | { |
| 7096 | mpd_context_t workctx; |
| 7097 | mpd_t *qq = q, *rr = r; |
| 7098 | mpd_t aa, bb; |
| 7099 | int k; |
| 7100 | |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7101 | _mpd_copy_shared(&aa, a); |
| 7102 | _mpd_copy_shared(&bb, b); |
| 7103 | |
| 7104 | mpd_set_positive(&aa); |
| 7105 | mpd_set_positive(&bb); |
| 7106 | aa.exp = 0; |
| 7107 | bb.exp = 0; |
| 7108 | |
| 7109 | if (q == a || q == b) { |
| 7110 | if ((qq = mpd_qnew()) == NULL) { |
| 7111 | *status |= MPD_Malloc_error; |
| 7112 | goto nanresult; |
| 7113 | } |
| 7114 | } |
| 7115 | if (r == a || r == b) { |
| 7116 | if ((rr = mpd_qnew()) == NULL) { |
| 7117 | *status |= MPD_Malloc_error; |
| 7118 | goto nanresult; |
| 7119 | } |
| 7120 | } |
| 7121 | |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 7122 | mpd_maxcontext(&workctx); |
| 7123 | |
| 7124 | /* Let prec := adigits - bdigits + 4 */ |
| 7125 | workctx.prec = a->digits - b->digits + 1 + 3; |
| 7126 | if (a->digits > MPD_MAX_PREC || workctx.prec > MPD_MAX_PREC) { |
| 7127 | *status |= MPD_Division_impossible; |
| 7128 | goto nanresult; |
| 7129 | } |
| 7130 | |
| 7131 | /* Let x := _mpd_qreciprocal(b, prec) |
| 7132 | * Then x is bounded by: |
| 7133 | * 1) 1/b - 10**(-prec - bdigits) < x < 1/b + 10**(-prec - bdigits) |
| 7134 | * 2) 1/b - 10**(-adigits - 4) < x < 1/b + 10**(-adigits - 4) |
| 7135 | */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7136 | _mpd_qreciprocal(rr, &bb, &workctx, &workctx.status); |
| 7137 | |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 7138 | /* Get an estimate for the quotient. Let q := a * x |
| 7139 | * Then q is bounded by: |
| 7140 | * 3) a/b - 10**-4 < q < a/b + 10**-4 |
| 7141 | */ |
| 7142 | _mpd_qmul(qq, &aa, rr, &workctx, &workctx.status); |
| 7143 | /* Truncate q to an integer: |
| 7144 | * 4) a/b - 2 < trunc(q) < a/b + 1 |
| 7145 | */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7146 | mpd_qtrunc(qq, qq, &workctx, &workctx.status); |
| 7147 | |
| 7148 | workctx.prec = aa.digits + 3; |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 7149 | workctx.emax = MPD_MAX_EMAX + 3; |
| 7150 | workctx.emin = MPD_MIN_EMIN - 3; |
| 7151 | /* Multiply the estimate for q by b: |
| 7152 | * 5) a - 2 * b < trunc(q) * b < a + b |
| 7153 | */ |
| 7154 | _mpd_qmul(rr, &bb, qq, &workctx, &workctx.status); |
| 7155 | /* Get the estimate for r such that a = q * b + r. */ |
| 7156 | _mpd_qsub_exact(rr, &aa, rr, &workctx, &workctx.status); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7157 | |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 7158 | /* Fix the result. At this point -b < r < 2*b, so the correction loop |
| 7159 | takes at most one iteration. */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7160 | for (k = 0;; k++) { |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 7161 | if (mpd_isspecial(qq) || mpd_isspecial(rr)) { |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7162 | *status |= (workctx.status&MPD_Errors); |
| 7163 | goto nanresult; |
| 7164 | } |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 7165 | if (k > 2) { /* Allow two iterations despite the proof. */ |
| 7166 | mpd_err_warn("libmpdec: internal error in " /* GCOV_NOT_REACHED */ |
| 7167 | "_mpd_base_ndivmod: please report"); /* GCOV_NOT_REACHED */ |
| 7168 | *status |= MPD_Invalid_operation; /* GCOV_NOT_REACHED */ |
| 7169 | goto nanresult; /* GCOV_NOT_REACHED */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7170 | } |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 7171 | /* r < 0 */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7172 | else if (_mpd_cmp(&zero, rr) == 1) { |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 7173 | _mpd_qadd_exact(rr, rr, &bb, &workctx, &workctx.status); |
| 7174 | _mpd_qadd_exact(qq, qq, &minus_one, &workctx, &workctx.status); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7175 | } |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 7176 | /* 0 <= r < b */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7177 | else if (_mpd_cmp(rr, &bb) == -1) { |
| 7178 | break; |
| 7179 | } |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 7180 | /* r >= b */ |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7181 | else { |
Stefan Krah | 3c23a87 | 2012-04-20 19:59:20 +0200 | [diff] [blame] | 7182 | _mpd_qsub_exact(rr, rr, &bb, &workctx, &workctx.status); |
| 7183 | _mpd_qadd_exact(qq, qq, &one, &workctx, &workctx.status); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7184 | } |
| 7185 | } |
| 7186 | |
| 7187 | if (qq != q) { |
| 7188 | if (!mpd_qcopy(q, qq, status)) { |
| 7189 | goto nanresult; /* GCOV_UNLIKELY */ |
| 7190 | } |
| 7191 | mpd_del(qq); |
| 7192 | } |
| 7193 | if (rr != r) { |
| 7194 | if (!mpd_qcopy(r, rr, status)) { |
| 7195 | goto nanresult; /* GCOV_UNLIKELY */ |
| 7196 | } |
| 7197 | mpd_del(rr); |
| 7198 | } |
| 7199 | |
| 7200 | *status |= (workctx.status&MPD_Errors); |
| 7201 | return; |
| 7202 | |
| 7203 | |
| 7204 | nanresult: |
| 7205 | if (qq && qq != q) mpd_del(qq); |
| 7206 | if (rr && rr != r) mpd_del(rr); |
| 7207 | mpd_setspecial(q, MPD_POS, MPD_NAN); |
| 7208 | mpd_setspecial(r, MPD_POS, MPD_NAN); |
| 7209 | } |
| 7210 | |
| 7211 | static inline int |
| 7212 | invroot_schedule_prec(mpd_ssize_t klist[MPD_MAX_PREC_LOG2], |
| 7213 | mpd_ssize_t maxprec, mpd_ssize_t initprec) |
| 7214 | { |
| 7215 | mpd_ssize_t k; |
| 7216 | int i; |
| 7217 | |
| 7218 | assert(maxprec >= 3 && initprec >= 3); |
| 7219 | if (maxprec <= initprec) return -1; |
| 7220 | |
| 7221 | i = 0; k = maxprec; |
| 7222 | do { |
| 7223 | k = (k+3) / 2; |
| 7224 | klist[i++] = k; |
| 7225 | } while (k > initprec); |
| 7226 | |
| 7227 | return i-1; |
| 7228 | } |
| 7229 | |
| 7230 | /* |
| 7231 | * Initial approximation for the inverse square root. |
| 7232 | * |
| 7233 | * Input: |
| 7234 | * v := 7 or 8 decimal digits with an implicit exponent of 10**-6, |
| 7235 | * representing a number 1 <= x < 100. |
| 7236 | * |
| 7237 | * Output: |
| 7238 | * An approximation to 1/sqrt(v) |
| 7239 | */ |
| 7240 | static inline void |
| 7241 | _invroot_init_approx(mpd_t *z, mpd_uint_t v) |
| 7242 | { |
| 7243 | mpd_uint_t lo = 1000; |
| 7244 | mpd_uint_t hi = 10000; |
| 7245 | mpd_uint_t a, sq; |
| 7246 | |
| 7247 | assert(v >= lo*lo && v < (hi+1)*(hi+1)); |
| 7248 | |
| 7249 | for(;;) { |
| 7250 | a = (lo + hi) / 2; |
| 7251 | sq = a * a; |
| 7252 | if (v >= sq) { |
| 7253 | if (v < sq + 2*a + 1) { |
| 7254 | break; |
| 7255 | } |
| 7256 | lo = a + 1; |
| 7257 | } |
| 7258 | else { |
| 7259 | hi = a - 1; |
| 7260 | } |
| 7261 | } |
| 7262 | |
| 7263 | /* At this point a/1000 is an approximation to sqrt(v). */ |
| 7264 | mpd_minalloc(z); |
| 7265 | mpd_clear_flags(z); |
| 7266 | z->data[0] = 1000000000UL / a; |
| 7267 | z->len = 1; |
| 7268 | z->exp = -6; |
| 7269 | mpd_setdigits(z); |
| 7270 | } |
| 7271 | |
| 7272 | static void |
| 7273 | _mpd_qinvroot(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, |
| 7274 | uint32_t *status) |
| 7275 | { |
| 7276 | uint32_t workstatus = 0; |
| 7277 | mpd_context_t varcontext, maxcontext; |
| 7278 | mpd_t *z = result; /* current approximation */ |
| 7279 | mpd_t *v; /* a, normalized to a number between 1 and 100 */ |
| 7280 | MPD_NEW_SHARED(vtmp, a); /* by default v will share data with a */ |
| 7281 | MPD_NEW_STATIC(s,0,0,0,0); /* temporary variable */ |
| 7282 | MPD_NEW_STATIC(t,0,0,0,0); /* temporary variable */ |
| 7283 | MPD_NEW_CONST(one_half,0,-1,1,1,1,5); |
| 7284 | MPD_NEW_CONST(three,0,0,1,1,1,3); |
| 7285 | mpd_ssize_t klist[MPD_MAX_PREC_LOG2]; |
| 7286 | mpd_ssize_t ideal_exp, shift; |
| 7287 | mpd_ssize_t adj, tz; |
| 7288 | mpd_ssize_t maxprec, fracdigits; |
| 7289 | mpd_uint_t x, dummy; |
| 7290 | int i, n; |
| 7291 | |
| 7292 | |
| 7293 | ideal_exp = -(a->exp - (a->exp & 1)) / 2; |
| 7294 | |
| 7295 | v = &vtmp; |
| 7296 | if (result == a) { |
| 7297 | if ((v = mpd_qncopy(a)) == NULL) { |
| 7298 | mpd_seterror(result, MPD_Malloc_error, status); |
| 7299 | return; |
| 7300 | } |
| 7301 | } |
| 7302 | |
| 7303 | /* normalize a to 1 <= v < 100 */ |
| 7304 | if ((v->digits+v->exp) & 1) { |
| 7305 | fracdigits = v->digits - 1; |
| 7306 | v->exp = -fracdigits; |
| 7307 | n = (v->digits > 7) ? 7 : (int)v->digits; |
| 7308 | _mpd_get_msdigits(&dummy, &x, v, n); |
| 7309 | if (n < 7) { |
| 7310 | x *= mpd_pow10[7-n]; |
| 7311 | } |
| 7312 | } |
| 7313 | else { |
| 7314 | fracdigits = v->digits - 2; |
| 7315 | v->exp = -fracdigits; |
| 7316 | n = (v->digits > 8) ? 8 : (int)v->digits; |
| 7317 | _mpd_get_msdigits(&dummy, &x, v, n); |
| 7318 | if (n < 8) { |
| 7319 | x *= mpd_pow10[8-n]; |
| 7320 | } |
| 7321 | } |
| 7322 | adj = (a->exp-v->exp) / 2; |
| 7323 | |
| 7324 | /* initial approximation */ |
| 7325 | _invroot_init_approx(z, x); |
| 7326 | |
| 7327 | mpd_maxcontext(&maxcontext); |
| 7328 | mpd_maxcontext(&varcontext); |
| 7329 | varcontext.round = MPD_ROUND_TRUNC; |
| 7330 | maxprec = ctx->prec + 2; |
| 7331 | |
| 7332 | i = invroot_schedule_prec(klist, maxprec, 3); |
| 7333 | for (; i >= 0; i--) { |
| 7334 | varcontext.prec = 2*klist[i]+2; |
| 7335 | mpd_qmul(&s, z, z, &maxcontext, &workstatus); |
| 7336 | if (v->digits > varcontext.prec) { |
| 7337 | shift = v->digits - varcontext.prec; |
| 7338 | mpd_qshiftr(&t, v, shift, &workstatus); |
| 7339 | t.exp += shift; |
| 7340 | mpd_qmul(&t, &t, &s, &varcontext, &workstatus); |
| 7341 | } |
| 7342 | else { |
| 7343 | mpd_qmul(&t, v, &s, &varcontext, &workstatus); |
| 7344 | } |
| 7345 | mpd_qsub(&t, &three, &t, &maxcontext, &workstatus); |
| 7346 | mpd_qmul(z, z, &t, &varcontext, &workstatus); |
| 7347 | mpd_qmul(z, z, &one_half, &maxcontext, &workstatus); |
| 7348 | } |
| 7349 | |
| 7350 | z->exp -= adj; |
| 7351 | |
| 7352 | tz = mpd_trail_zeros(result); |
| 7353 | shift = ideal_exp - result->exp; |
| 7354 | shift = (tz > shift) ? shift : tz; |
| 7355 | if (shift > 0) { |
| 7356 | mpd_qshiftr_inplace(result, shift); |
| 7357 | result->exp += shift; |
| 7358 | } |
| 7359 | |
| 7360 | |
| 7361 | mpd_del(&s); |
| 7362 | mpd_del(&t); |
| 7363 | if (v != &vtmp) mpd_del(v); |
| 7364 | *status |= (workstatus&MPD_Errors); |
| 7365 | varcontext = *ctx; |
| 7366 | varcontext.round = MPD_ROUND_HALF_EVEN; |
| 7367 | mpd_qfinalize(result, &varcontext, status); |
| 7368 | } |
| 7369 | |
| 7370 | void |
| 7371 | mpd_qinvroot(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, |
| 7372 | uint32_t *status) |
| 7373 | { |
| 7374 | |
| 7375 | if (mpd_isspecial(a)) { |
| 7376 | if (mpd_qcheck_nan(result, a, ctx, status)) { |
| 7377 | return; |
| 7378 | } |
| 7379 | if (mpd_isnegative(a)) { |
| 7380 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 7381 | return; |
| 7382 | } |
| 7383 | /* positive infinity */ |
| 7384 | _settriple(result, MPD_POS, 0, mpd_etiny(ctx)); |
| 7385 | *status |= MPD_Clamped; |
| 7386 | return; |
| 7387 | } |
| 7388 | if (mpd_iszero(a)) { |
| 7389 | mpd_setspecial(result, mpd_sign(a), MPD_INF); |
| 7390 | *status |= MPD_Division_by_zero; |
| 7391 | return; |
| 7392 | } |
| 7393 | if (mpd_isnegative(a)) { |
| 7394 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 7395 | return; |
| 7396 | } |
| 7397 | |
| 7398 | _mpd_qinvroot(result, a, ctx, status); |
| 7399 | } |
| 7400 | |
| 7401 | /* |
| 7402 | * Ensure correct rounding. Algorithm after Hull & Abrham, "Properly Rounded |
| 7403 | * Variable Precision Square Root", ACM Transactions on Mathematical Software, |
| 7404 | * Vol. 11, No. 3. |
| 7405 | */ |
| 7406 | static void |
| 7407 | _mpd_fix_sqrt(mpd_t *result, const mpd_t *a, mpd_t *tmp, |
| 7408 | const mpd_context_t *ctx, uint32_t *status) |
| 7409 | { |
| 7410 | mpd_context_t maxctx; |
| 7411 | MPD_NEW_CONST(u,0,0,1,1,1,5); |
| 7412 | |
| 7413 | mpd_maxcontext(&maxctx); |
| 7414 | u.exp = u.digits - ctx->prec + result->exp - 1; |
| 7415 | |
| 7416 | _mpd_qsub(tmp, result, &u, &maxctx, status); |
Stefan Krah | cd9e1d0 | 2012-03-23 16:22:05 +0100 | [diff] [blame] | 7417 | if (*status&MPD_Errors) goto nanresult; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7418 | |
| 7419 | _mpd_qmul(tmp, tmp, tmp, &maxctx, status); |
Stefan Krah | cd9e1d0 | 2012-03-23 16:22:05 +0100 | [diff] [blame] | 7420 | if (*status&MPD_Errors) goto nanresult; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7421 | |
| 7422 | if (_mpd_cmp(tmp, a) == 1) { |
| 7423 | u.exp += 1; |
| 7424 | u.data[0] = 1; |
| 7425 | _mpd_qsub(result, result, &u, &maxctx, status); |
| 7426 | } |
| 7427 | else { |
| 7428 | _mpd_qadd(tmp, result, &u, &maxctx, status); |
Stefan Krah | cd9e1d0 | 2012-03-23 16:22:05 +0100 | [diff] [blame] | 7429 | if (*status&MPD_Errors) goto nanresult; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7430 | |
| 7431 | _mpd_qmul(tmp, tmp, tmp, &maxctx, status); |
Stefan Krah | cd9e1d0 | 2012-03-23 16:22:05 +0100 | [diff] [blame] | 7432 | if (*status&MPD_Errors) goto nanresult; |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7433 | |
| 7434 | if (_mpd_cmp(tmp, a) == -1) { |
| 7435 | u.exp += 1; |
| 7436 | u.data[0] = 1; |
| 7437 | _mpd_qadd(result, result, &u, &maxctx, status); |
| 7438 | } |
| 7439 | } |
| 7440 | |
| 7441 | return; |
| 7442 | |
| 7443 | nanresult: |
| 7444 | mpd_setspecial(result, MPD_POS, MPD_NAN); |
| 7445 | } |
| 7446 | |
| 7447 | void |
| 7448 | mpd_qsqrt(mpd_t *result, const mpd_t *a, const mpd_context_t *ctx, |
| 7449 | uint32_t *status) |
| 7450 | { |
| 7451 | uint32_t workstatus = 0; |
| 7452 | mpd_context_t varcontext; |
| 7453 | mpd_t *z = result; /* current approximation */ |
| 7454 | MPD_NEW_STATIC(v,0,0,0,0); /* a, normalized to a number between 1 and 10 */ |
| 7455 | MPD_NEW_STATIC(vtmp,0,0,0,0); |
| 7456 | MPD_NEW_STATIC(tmp,0,0,0,0); |
| 7457 | mpd_ssize_t ideal_exp, shift; |
| 7458 | mpd_ssize_t target_prec, fracdigits; |
| 7459 | mpd_ssize_t a_exp, a_digits; |
| 7460 | mpd_ssize_t adj, tz; |
| 7461 | mpd_uint_t dummy, t; |
| 7462 | int exact = 0; |
| 7463 | |
| 7464 | |
| 7465 | varcontext = *ctx; |
| 7466 | varcontext.round = MPD_ROUND_HALF_EVEN; |
| 7467 | ideal_exp = (a->exp - (a->exp & 1)) / 2; |
| 7468 | |
| 7469 | if (mpd_isspecial(a)) { |
| 7470 | if (mpd_qcheck_nan(result, a, ctx, status)) { |
| 7471 | return; |
| 7472 | } |
| 7473 | if (mpd_isnegative(a)) { |
| 7474 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 7475 | return; |
| 7476 | } |
| 7477 | mpd_setspecial(result, MPD_POS, MPD_INF); |
| 7478 | return; |
| 7479 | } |
| 7480 | if (mpd_iszero(a)) { |
| 7481 | _settriple(result, mpd_sign(a), 0, ideal_exp); |
| 7482 | mpd_qfinalize(result, ctx, status); |
| 7483 | return; |
| 7484 | } |
| 7485 | if (mpd_isnegative(a)) { |
| 7486 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 7487 | return; |
| 7488 | } |
| 7489 | |
| 7490 | if (!mpd_qcopy(&v, a, status)) { |
| 7491 | mpd_seterror(result, MPD_Malloc_error, status); |
| 7492 | goto finish; |
| 7493 | } |
| 7494 | |
| 7495 | a_exp = a->exp; |
| 7496 | a_digits = a->digits; |
| 7497 | |
| 7498 | /* normalize a to 1 <= v < 100 */ |
| 7499 | if ((v.digits+v.exp) & 1) { |
| 7500 | fracdigits = v.digits - 1; |
| 7501 | v.exp = -fracdigits; |
| 7502 | _mpd_get_msdigits(&dummy, &t, &v, 3); |
| 7503 | t = t < 100 ? t*10 : t; |
| 7504 | t = t < 100 ? t*10 : t; |
| 7505 | } |
| 7506 | else { |
| 7507 | fracdigits = v.digits - 2; |
| 7508 | v.exp = -fracdigits; |
| 7509 | _mpd_get_msdigits(&dummy, &t, &v, 4); |
| 7510 | t = t < 1000 ? t*10 : t; |
| 7511 | t = t < 1000 ? t*10 : t; |
| 7512 | t = t < 1000 ? t*10 : t; |
| 7513 | } |
| 7514 | adj = (a_exp-v.exp) / 2; |
| 7515 | |
| 7516 | |
| 7517 | /* use excess digits */ |
| 7518 | target_prec = (a_digits > ctx->prec) ? a_digits : ctx->prec; |
| 7519 | target_prec += 2; |
| 7520 | varcontext.prec = target_prec + 3; |
| 7521 | |
| 7522 | /* invroot is much faster for large numbers */ |
| 7523 | _mpd_qinvroot(&tmp, &v, &varcontext, &workstatus); |
| 7524 | |
| 7525 | varcontext.prec = target_prec; |
| 7526 | _mpd_qdiv(NO_IDEAL_EXP, z, &one, &tmp, &varcontext, &workstatus); |
| 7527 | |
| 7528 | |
| 7529 | tz = mpd_trail_zeros(result); |
| 7530 | if ((result->digits-tz)*2-1 <= v.digits) { |
| 7531 | _mpd_qmul(&tmp, result, result, &varcontext, &workstatus); |
| 7532 | if (workstatus&MPD_Errors) { |
| 7533 | mpd_seterror(result, workstatus&MPD_Errors, status); |
| 7534 | goto finish; |
| 7535 | } |
| 7536 | exact = (_mpd_cmp(&tmp, &v) == 0); |
| 7537 | } |
| 7538 | *status |= (workstatus&MPD_Errors); |
| 7539 | |
| 7540 | if (!exact && !mpd_isspecial(result) && !mpd_iszero(result)) { |
| 7541 | _mpd_fix_sqrt(result, &v, &tmp, &varcontext, status); |
| 7542 | if (mpd_isspecial(result)) goto finish; |
| 7543 | *status |= (MPD_Rounded|MPD_Inexact); |
| 7544 | } |
| 7545 | |
| 7546 | result->exp += adj; |
| 7547 | if (exact) { |
| 7548 | shift = ideal_exp - result->exp; |
| 7549 | shift = (tz > shift) ? shift : tz; |
| 7550 | if (shift > 0) { |
| 7551 | mpd_qshiftr_inplace(result, shift); |
| 7552 | result->exp += shift; |
| 7553 | } |
| 7554 | } |
| 7555 | |
| 7556 | |
| 7557 | finish: |
| 7558 | mpd_del(&v); |
| 7559 | mpd_del(&vtmp); |
| 7560 | mpd_del(&tmp); |
| 7561 | varcontext.prec = ctx->prec; |
| 7562 | mpd_qfinalize(result, &varcontext, status); |
| 7563 | } |
| 7564 | |
| 7565 | |
| 7566 | /******************************************************************************/ |
| 7567 | /* Base conversions */ |
| 7568 | /******************************************************************************/ |
| 7569 | |
| 7570 | /* |
| 7571 | * Returns the space needed to represent an integer mpd_t in base 'base'. |
| 7572 | * The result is undefined for non-integers. |
| 7573 | * |
| 7574 | * Max space needed: |
| 7575 | * |
| 7576 | * base^n >= 10^(digits+exp) |
| 7577 | * n >= log10(10^(digits+exp))/log10(base) = (digits+exp) / log10(base) |
| 7578 | */ |
| 7579 | size_t |
| 7580 | mpd_sizeinbase(mpd_t *a, uint32_t base) |
| 7581 | { |
| 7582 | size_t x; |
| 7583 | |
| 7584 | assert(mpd_isinteger(a)); |
| 7585 | if (mpd_iszero(a)) { |
| 7586 | return 1; |
| 7587 | } |
| 7588 | |
| 7589 | x = a->digits+a->exp; |
| 7590 | |
| 7591 | #ifdef CONFIG_64 |
| 7592 | #ifdef USE_80BIT_LONG_DOUBLE |
| 7593 | return (long double)x / log10(base) + 3; |
| 7594 | #else |
| 7595 | /* x > floor(((1ULL<<53)-3) * log10(2)) */ |
| 7596 | if (x > 2711437152599294ULL) { |
| 7597 | return SIZE_MAX; |
| 7598 | } |
Stefan Krah | e34a209 | 2012-05-16 20:20:03 +0200 | [diff] [blame] | 7599 | return (size_t)((double)x / log10(base) + 3); |
Stefan Krah | 1919b7e | 2012-03-21 18:25:23 +0100 | [diff] [blame] | 7600 | #endif |
| 7601 | #else /* CONFIG_32 */ |
| 7602 | { |
| 7603 | double y = x / log10(base) + 3; |
| 7604 | return (y > SIZE_MAX) ? SIZE_MAX : (size_t)y; |
| 7605 | } |
| 7606 | #endif |
| 7607 | } |
| 7608 | |
| 7609 | /* |
| 7610 | * Returns the space needed to import a base 'base' integer of length 'srclen'. |
| 7611 | */ |
| 7612 | static inline mpd_ssize_t |
| 7613 | _mpd_importsize(size_t srclen, uint32_t base) |
| 7614 | { |
| 7615 | #if SIZE_MAX == UINT64_MAX |
| 7616 | #ifdef USE_80BIT_LONG_DOUBLE |
| 7617 | long double x = (long double)srclen * (log10(base)/MPD_RDIGITS) + 3; |
| 7618 | #else |
| 7619 | double x; |
| 7620 | if (srclen > (1ULL<<53)) { |
| 7621 | return MPD_SSIZE_MAX; |
| 7622 | } |
| 7623 | x = (double)srclen * (log10(base)/MPD_RDIGITS) + 3; |
| 7624 | #endif |
| 7625 | #else |
| 7626 | double x = srclen * (log10(base)/MPD_RDIGITS) + 3; |
| 7627 | #endif |
| 7628 | return (x > MPD_MAXIMPORT) ? MPD_SSIZE_MAX : (mpd_ssize_t)x; |
| 7629 | } |
| 7630 | |
| 7631 | |
| 7632 | static inline size_t |
| 7633 | _to_base_u16(uint16_t *w, size_t wlen, mpd_uint_t wbase, |
| 7634 | mpd_uint_t *u, mpd_ssize_t ulen) |
| 7635 | { |
| 7636 | size_t n = 0; |
| 7637 | |
| 7638 | assert(wlen > 0 && ulen > 0); |
| 7639 | |
| 7640 | do { |
| 7641 | w[n++] = (uint16_t)_mpd_shortdiv(u, u, ulen, wbase); |
| 7642 | /* ulen will be at least 1. u[ulen-1] can only be zero if ulen == 1 */ |
| 7643 | ulen = _mpd_real_size(u, ulen); |
| 7644 | |
| 7645 | } while (u[ulen-1] != 0 && n < wlen); |
| 7646 | |
| 7647 | /* proper termination condition */ |
| 7648 | assert(u[ulen-1] == 0); |
| 7649 | |
| 7650 | return n; |
| 7651 | } |
| 7652 | |
| 7653 | static inline void |
| 7654 | _from_base_u16(mpd_uint_t *w, mpd_ssize_t wlen, |
| 7655 | const mpd_uint_t *u, size_t ulen, uint32_t ubase) |
| 7656 | { |
| 7657 | mpd_ssize_t m = 1; |
| 7658 | mpd_uint_t carry; |
| 7659 | |
| 7660 | assert(wlen > 0 && ulen > 0); |
| 7661 | |
| 7662 | w[0] = u[--ulen]; |
| 7663 | while (--ulen != SIZE_MAX && m < wlen) { |
| 7664 | _mpd_shortmul(w, w, m, ubase); |
| 7665 | m = _mpd_real_size(w, m+1); |
| 7666 | carry = _mpd_shortadd(w, m, u[ulen]); |
| 7667 | if (carry) w[m++] = carry; |
| 7668 | } |
| 7669 | |
| 7670 | /* proper termination condition */ |
| 7671 | assert(ulen == SIZE_MAX); |
| 7672 | } |
| 7673 | |
| 7674 | /* target base wbase <= source base ubase */ |
| 7675 | static inline size_t |
| 7676 | _baseconv_to_smaller(uint32_t *w, size_t wlen, mpd_uint_t wbase, |
| 7677 | mpd_uint_t *u, mpd_ssize_t ulen, mpd_uint_t ubase) |
| 7678 | { |
| 7679 | size_t n = 0; |
| 7680 | |
| 7681 | assert(wlen > 0 && ulen > 0); |
| 7682 | |
| 7683 | do { |
| 7684 | w[n++] = (uint32_t)_mpd_shortdiv_b(u, u, ulen, wbase, ubase); |
| 7685 | /* ulen will be at least 1. u[ulen-1] can only be zero if ulen == 1 */ |
| 7686 | ulen = _mpd_real_size(u, ulen); |
| 7687 | |
| 7688 | } while (u[ulen-1] != 0 && n < wlen); |
| 7689 | |
| 7690 | /* proper termination condition */ |
| 7691 | assert(u[ulen-1] == 0); |
| 7692 | |
| 7693 | return n; |
| 7694 | } |
| 7695 | |
| 7696 | /* target base wbase >= source base ubase */ |
| 7697 | static inline void |
| 7698 | _baseconv_to_larger(mpd_uint_t *w, mpd_ssize_t wlen, mpd_uint_t wbase, |
| 7699 | const mpd_uint_t *u, size_t ulen, mpd_uint_t ubase) |
| 7700 | { |
| 7701 | mpd_ssize_t m = 1; |
| 7702 | mpd_uint_t carry; |
| 7703 | |
| 7704 | assert(wlen > 0 && ulen > 0); |
| 7705 | |
| 7706 | w[0] = u[--ulen]; |
| 7707 | while (--ulen != SIZE_MAX && m < wlen) { |
| 7708 | _mpd_shortmul_b(w, w, m, ubase, wbase); |
| 7709 | m = _mpd_real_size(w, m+1); |
| 7710 | carry = _mpd_shortadd_b(w, m, u[ulen], wbase); |
| 7711 | if (carry) w[m++] = carry; |
| 7712 | } |
| 7713 | |
| 7714 | /* proper termination condition */ |
| 7715 | assert(ulen == SIZE_MAX); |
| 7716 | } |
| 7717 | |
| 7718 | |
| 7719 | /* |
| 7720 | * Converts an integer mpd_t to a multiprecision integer with |
| 7721 | * base <= UINT16_MAX+1. The least significant word of the result |
| 7722 | * is rdata[0]. |
| 7723 | */ |
| 7724 | size_t |
| 7725 | mpd_qexport_u16(uint16_t *rdata, size_t rlen, uint32_t rbase, |
| 7726 | const mpd_t *src, uint32_t *status) |
| 7727 | { |
| 7728 | mpd_t *tsrc; |
| 7729 | size_t n; |
| 7730 | |
| 7731 | assert(rbase <= (1U<<16)); |
| 7732 | assert(rlen <= SIZE_MAX/(sizeof *rdata)); |
| 7733 | |
| 7734 | if (mpd_isspecial(src) || !_mpd_isint(src)) { |
| 7735 | *status |= MPD_Invalid_operation; |
| 7736 | return SIZE_MAX; |
| 7737 | } |
| 7738 | |
| 7739 | memset(rdata, 0, rlen * (sizeof *rdata)); |
| 7740 | |
| 7741 | if (mpd_iszero(src)) { |
| 7742 | return 1; |
| 7743 | } |
| 7744 | |
| 7745 | if ((tsrc = mpd_qnew()) == NULL) { |
| 7746 | *status |= MPD_Malloc_error; |
| 7747 | return SIZE_MAX; |
| 7748 | } |
| 7749 | |
| 7750 | if (src->exp >= 0) { |
| 7751 | if (!mpd_qshiftl(tsrc, src, src->exp, status)) { |
| 7752 | mpd_del(tsrc); |
| 7753 | return SIZE_MAX; |
| 7754 | } |
| 7755 | } |
| 7756 | else { |
| 7757 | if (mpd_qshiftr(tsrc, src, -src->exp, status) == MPD_UINT_MAX) { |
| 7758 | mpd_del(tsrc); |
| 7759 | return SIZE_MAX; |
| 7760 | } |
| 7761 | } |
| 7762 | |
| 7763 | n = _to_base_u16(rdata, rlen, rbase, tsrc->data, tsrc->len); |
| 7764 | |
| 7765 | mpd_del(tsrc); |
| 7766 | return n; |
| 7767 | } |
| 7768 | |
| 7769 | /* |
| 7770 | * Converts an integer mpd_t to a multiprecision integer with |
| 7771 | * base <= UINT32_MAX. The least significant word of the result |
| 7772 | * is rdata[0]. |
| 7773 | */ |
| 7774 | size_t |
| 7775 | mpd_qexport_u32(uint32_t *rdata, size_t rlen, uint32_t rbase, |
| 7776 | const mpd_t *src, uint32_t *status) |
| 7777 | { |
| 7778 | mpd_t *tsrc; |
| 7779 | size_t n; |
| 7780 | |
| 7781 | if (mpd_isspecial(src) || !_mpd_isint(src)) { |
| 7782 | *status |= MPD_Invalid_operation; |
| 7783 | return SIZE_MAX; |
| 7784 | } |
| 7785 | #if MPD_SIZE_MAX < SIZE_MAX |
| 7786 | if (rlen > MPD_SSIZE_MAX) { |
| 7787 | *status |= MPD_Invalid_operation; |
| 7788 | return SIZE_MAX; |
| 7789 | } |
| 7790 | #endif |
| 7791 | |
| 7792 | assert(rlen <= SIZE_MAX/(sizeof *rdata)); |
| 7793 | memset(rdata, 0, rlen * (sizeof *rdata)); |
| 7794 | |
| 7795 | if (mpd_iszero(src)) { |
| 7796 | return 1; |
| 7797 | } |
| 7798 | |
| 7799 | if ((tsrc = mpd_qnew()) == NULL) { |
| 7800 | *status |= MPD_Malloc_error; |
| 7801 | return SIZE_MAX; |
| 7802 | } |
| 7803 | |
| 7804 | if (src->exp >= 0) { |
| 7805 | if (!mpd_qshiftl(tsrc, src, src->exp, status)) { |
| 7806 | mpd_del(tsrc); |
| 7807 | return SIZE_MAX; |
| 7808 | } |
| 7809 | } |
| 7810 | else { |
| 7811 | if (mpd_qshiftr(tsrc, src, -src->exp, status) == MPD_UINT_MAX) { |
| 7812 | mpd_del(tsrc); |
| 7813 | return SIZE_MAX; |
| 7814 | } |
| 7815 | } |
| 7816 | |
| 7817 | #ifdef CONFIG_64 |
| 7818 | n = _baseconv_to_smaller(rdata, rlen, rbase, |
| 7819 | tsrc->data, tsrc->len, MPD_RADIX); |
| 7820 | #else |
| 7821 | if (rbase <= MPD_RADIX) { |
| 7822 | n = _baseconv_to_smaller(rdata, rlen, rbase, |
| 7823 | tsrc->data, tsrc->len, MPD_RADIX); |
| 7824 | } |
| 7825 | else { |
| 7826 | _baseconv_to_larger(rdata, (mpd_ssize_t)rlen, rbase, |
| 7827 | tsrc->data, tsrc->len, MPD_RADIX); |
| 7828 | n = _mpd_real_size(rdata, (mpd_ssize_t)rlen); |
| 7829 | } |
| 7830 | #endif |
| 7831 | |
| 7832 | mpd_del(tsrc); |
| 7833 | return n; |
| 7834 | } |
| 7835 | |
| 7836 | |
| 7837 | /* |
| 7838 | * Converts a multiprecision integer with base <= UINT16_MAX+1 to an mpd_t. |
| 7839 | * The least significant word of the source is srcdata[0]. |
| 7840 | */ |
| 7841 | void |
| 7842 | mpd_qimport_u16(mpd_t *result, |
| 7843 | const uint16_t *srcdata, size_t srclen, |
| 7844 | uint8_t srcsign, uint32_t srcbase, |
| 7845 | const mpd_context_t *ctx, uint32_t *status) |
| 7846 | { |
| 7847 | mpd_uint_t *usrc; /* uint16_t src copied to an mpd_uint_t array */ |
| 7848 | mpd_ssize_t rlen; /* length of the result */ |
| 7849 | size_t n = 0; |
| 7850 | |
| 7851 | assert(srclen > 0); |
| 7852 | assert(srcbase <= (1U<<16)); |
| 7853 | |
| 7854 | if ((rlen = _mpd_importsize(srclen, srcbase)) == MPD_SSIZE_MAX) { |
| 7855 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 7856 | return; |
| 7857 | } |
| 7858 | if (srclen > MPD_SIZE_MAX/(sizeof *usrc)) { |
| 7859 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 7860 | return; |
| 7861 | } |
| 7862 | if ((usrc = mpd_alloc((mpd_size_t)srclen, sizeof *usrc)) == NULL) { |
| 7863 | mpd_seterror(result, MPD_Malloc_error, status); |
| 7864 | return; |
| 7865 | } |
| 7866 | for (n = 0; n < srclen; n++) { |
| 7867 | usrc[n] = srcdata[n]; |
| 7868 | } |
| 7869 | |
| 7870 | /* result->data is initialized to zero */ |
| 7871 | if (!mpd_qresize_zero(result, rlen, status)) { |
| 7872 | goto finish; |
| 7873 | } |
| 7874 | |
| 7875 | _from_base_u16(result->data, rlen, usrc, srclen, srcbase); |
| 7876 | |
| 7877 | mpd_set_flags(result, srcsign); |
| 7878 | result->exp = 0; |
| 7879 | result->len = _mpd_real_size(result->data, rlen); |
| 7880 | mpd_setdigits(result); |
| 7881 | |
| 7882 | mpd_qresize(result, result->len, status); |
| 7883 | mpd_qfinalize(result, ctx, status); |
| 7884 | |
| 7885 | |
| 7886 | finish: |
| 7887 | mpd_free(usrc); |
| 7888 | } |
| 7889 | |
| 7890 | /* |
| 7891 | * Converts a multiprecision integer with base <= UINT32_MAX to an mpd_t. |
| 7892 | * The least significant word of the source is srcdata[0]. |
| 7893 | */ |
| 7894 | void |
| 7895 | mpd_qimport_u32(mpd_t *result, |
| 7896 | const uint32_t *srcdata, size_t srclen, |
| 7897 | uint8_t srcsign, uint32_t srcbase, |
| 7898 | const mpd_context_t *ctx, uint32_t *status) |
| 7899 | { |
| 7900 | mpd_uint_t *usrc; /* uint32_t src copied to an mpd_uint_t array */ |
| 7901 | mpd_ssize_t rlen; /* length of the result */ |
| 7902 | size_t n = 0; |
| 7903 | |
| 7904 | assert(srclen > 0); |
| 7905 | |
| 7906 | if ((rlen = _mpd_importsize(srclen, srcbase)) == MPD_SSIZE_MAX) { |
| 7907 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 7908 | return; |
| 7909 | } |
| 7910 | if (srclen > MPD_SIZE_MAX/(sizeof *usrc)) { |
| 7911 | mpd_seterror(result, MPD_Invalid_operation, status); |
| 7912 | return; |
| 7913 | } |
| 7914 | if ((usrc = mpd_alloc((mpd_size_t)srclen, sizeof *usrc)) == NULL) { |
| 7915 | mpd_seterror(result, MPD_Malloc_error, status); |
| 7916 | return; |
| 7917 | } |
| 7918 | for (n = 0; n < srclen; n++) { |
| 7919 | usrc[n] = srcdata[n]; |
| 7920 | } |
| 7921 | |
| 7922 | /* result->data is initialized to zero */ |
| 7923 | if (!mpd_qresize_zero(result, rlen, status)) { |
| 7924 | goto finish; |
| 7925 | } |
| 7926 | |
| 7927 | #ifdef CONFIG_64 |
| 7928 | _baseconv_to_larger(result->data, rlen, MPD_RADIX, |
| 7929 | usrc, srclen, srcbase); |
| 7930 | #else |
| 7931 | if (srcbase <= MPD_RADIX) { |
| 7932 | _baseconv_to_larger(result->data, rlen, MPD_RADIX, |
| 7933 | usrc, srclen, srcbase); |
| 7934 | } |
| 7935 | else { |
| 7936 | _baseconv_to_smaller(result->data, rlen, MPD_RADIX, |
| 7937 | usrc, (mpd_ssize_t)srclen, srcbase); |
| 7938 | } |
| 7939 | #endif |
| 7940 | |
| 7941 | mpd_set_flags(result, srcsign); |
| 7942 | result->exp = 0; |
| 7943 | result->len = _mpd_real_size(result->data, rlen); |
| 7944 | mpd_setdigits(result); |
| 7945 | |
| 7946 | mpd_qresize(result, result->len, status); |
| 7947 | mpd_qfinalize(result, ctx, status); |
| 7948 | |
| 7949 | |
| 7950 | finish: |
| 7951 | mpd_free(usrc); |
| 7952 | } |
| 7953 | |
| 7954 | |
| 7955 | |