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GeezerVison is showing github.com — cpython/Python/dtoa.c at main · python/cpython Expand file tree/ Copy pathdtoa.cMore file actions 2855 lines (2579 loc) · 79.3 KB / Copy pathdtoa.cFile metadata and controls2855 lines (2579 loc) · 79.3 KB 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 /**************************************************************** * * The author of this software is David M. Gay. * * Copyright (c) 1991, 2000, 2001 by Lucent Technologies. * * Permission to use, copy, modify, and distribute this software for any * purpose without fee is hereby granted, provided that this entire notice * is included in all copies of any software which is or includes a copy * or modification of this software and in all copies of the supporting * documentation for such software. * * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE. * ***************************************************************/ /**************************************************************** * This is dtoa.c by David M. Gay, downloaded from * http://www.netlib.org/fp/dtoa.c on April 15, 2009 and modified for * inclusion into the Python core by Mark E. T. Dickinson and Eric V. Smith. * * Please remember to check http://www.netlib.org/fp regularly (and especially * before any Python release) for bugfixes and updates. * * The major modifications from Gay's original code are as follows: * * 0. The original code has been specialized to Python's needs by removing * many of the #ifdef'd sections. In particular, code to support VAX and * IBM floating-point formats, hex NaNs, hex floats, locale-aware * treatment of the decimal point, and setting of the inexact flag have * been removed. * * 1. We use PyMem_Malloc and PyMem_Free in place of malloc and free. * * 2. The public functions strtod, dtoa and freedtoa all now have * a _Py_dg_ prefix. * * 3. Instead of assuming that PyMem_Malloc always succeeds, we thread * PyMem_Malloc failures through the code. The functions * * Balloc, multadd, s2b, i2b, mult, pow5mult, lshift, diff, d2b * * of return type *Bigint all return NULL to indicate a malloc failure. * Similarly, rv_alloc and nrv_alloc (return type char *) return NULL on * failure. bigcomp now has return type int (it used to be void) and * returns -1 on failure and 0 otherwise. _Py_dg_dtoa returns NULL * on failure. _Py_dg_strtod indicates failure due to malloc failure * by returning -1.0, setting errno=ENOMEM and *se to s00. * * 4. The static variable dtoa_result has been removed. Callers of * _Py_dg_dtoa are expected to call _Py_dg_freedtoa to free * the memory allocated by _Py_dg_dtoa. * * 5. The code has been reformatted to better fit with Python's * C style guide (PEP 7). * * 6. A bug in the memory allocation has been fixed: to avoid FREEing memory * that hasn't been MALLOC'ed, private_mem should only be used when k <= * Kmax. * * 7. _Py_dg_strtod has been modified so that it doesn't accept strings with * leading whitespace. * * 8. A corner case where _Py_dg_dtoa didn't strip trailing zeros has been * fixed. (bugs.python.org/issue40780) * * 9. _Py_dg_dtoa clamps ndigits in modes 3 and 5 so that its buffer size * arithmetic cannot exceed the int range, and rv_alloc's size doubling * uses size_t. (gh-158446) * ***************************************************************/ /* Please send bug reports for the original dtoa.c code to David M. Gay (dmg * at acm dot org, with " at " changed at "@" and " dot " changed to "."). * Please report bugs for this modified version using the Python issue tracker * as detailed at (https://devguide.python.org/triage/issue-tracker/). */ /* On a machine with IEEE extended-precision registers, it is * necessary to specify double-precision (53-bit) rounding precision * before invoking strtod or dtoa. If the machine uses (the equivalent * of) Intel 80x87 arithmetic, the call * _control87(PC_53, MCW_PC); * does this with many compilers. Whether this or another call is * appropriate depends on the compiler; for this to work, it may be * necessary to #include "float.h" or another system-dependent header * file. */ /* strtod for IEEE-, VAX-, and IBM-arithmetic machines. * * This strtod returns a nearest machine number to the input decimal * string (or sets errno to ERANGE). With IEEE arithmetic, ties are * broken by the IEEE round-even rule. Otherwise ties are broken by * biased rounding (add half and chop). * * Inspired loosely by William D. Clinger's paper "How to Read Floating * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101]. * * Modifications: * * 1. We only require IEEE, IBM, or VAX double-precision * arithmetic (not IEEE double-extended). * 2. We get by with floating-point arithmetic in a case that * Clinger missed -- when we're computing d * 10^n * for a small integer d and the integer n is not too * much larger than 22 (the maximum integer k for which * we can represent 10^k exactly), we may be able to * compute (d*10^k) * 10^(e-k) with just one roundoff. * 3. Rather than a bit-at-a-time adjustment of the binary * result in the hard case, we use floating-point * arithmetic to determine the adjustment to within * one bit; only in really hard cases do we need to * compute a second residual. * 4. Because of 3., we don't need a large table of powers of 10 * for ten-to-e (just some small tables, e.g. of 10^k * for 0 <= k <= 22). */ /* Linking of Python's #defines to Gay's #defines starts here. */ #include "Python.h" #include "pycore_dtoa.h" // _PY_SHORT_FLOAT_REPR #include "pycore_interp_structs.h"// struct Bigint #include "pycore_pystate.h" // _PyInterpreterState_GET() #include <stdlib.h> // exit() /* if _PY_SHORT_FLOAT_REPR == 0, then don't even try to compile the following code */ #if _PY_SHORT_FLOAT_REPR == 1 #include "float.h" #define MALLOC PyMem_Malloc #define FREE PyMem_Free /* This code should also work for ARM mixed-endian format on little-endian machines, where doubles have byte order 45670123 (in increasing address order, 0 being the least significant byte). */ #ifdef DOUBLE_IS_LITTLE_ENDIAN_IEEE754 # define IEEE_8087 #endif #if defined(DOUBLE_IS_BIG_ENDIAN_IEEE754) # define IEEE_MC68k #endif #if defined(IEEE_8087) + defined(IEEE_MC68k) != 1 #error "Exactly one of IEEE_8087 or IEEE_MC68k should be defined." #endif /* The code below assumes that the endianness of integers matches the endianness of the two 32-bit words of a double. Check this. */ #if defined(WORDS_BIGENDIAN) && defined(DOUBLE_IS_LITTLE_ENDIAN_IEEE754) #error "doubles and ints have incompatible endianness" #endif #if !defined(WORDS_BIGENDIAN) && defined(DOUBLE_IS_BIG_ENDIAN_IEEE754) #error "doubles and ints have incompatible endianness" #endif typedef uint32_t ULong; typedef int32_t Long; typedef uint64_t ULLong; #undef DEBUG #ifdef Py_DEBUG #define DEBUG #endif /* End Python #define linking */ #ifdef DEBUG #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);} #endif typedef union { double d; ULong L[2]; } U; #ifdef IEEE_8087 #define word0(x) (x)->L[1] #define word1(x) (x)->L[0] #else #define word0(x) (x)->L[0] #define word1(x) (x)->L[1] #endif #define dval(x) (x)->d #ifndef STRTOD_DIGLIM #define STRTOD_DIGLIM 40 #endif /* maximum permitted exponent value for strtod; exponents larger than MAX_ABS_EXP in absolute value get truncated to +-MAX_ABS_EXP. MAX_ABS_EXP should fit into an int. */ #ifndef MAX_ABS_EXP #define MAX_ABS_EXP 1100000000U #endif /* Bound on length of pieces of input strings in _Py_dg_strtod; specifically, this is used to bound the total number of digits ignoring leading zeros and the number of digits that follow the decimal point. Ideally, MAX_DIGITS should satisfy MAX_DIGITS + 400 < MAX_ABS_EXP; that ensures that the exponent clipping in _Py_dg_strtod can't affect the value of the output. */ #ifndef MAX_DIGITS #define MAX_DIGITS 1000000000U #endif /* Guard against trying to use the above values on unusual platforms with ints * of width less than 32 bits. */ #if MAX_ABS_EXP > INT_MAX #error "MAX_ABS_EXP should fit in an int" #endif #if MAX_DIGITS > INT_MAX #error "MAX_DIGITS should fit in an int" #endif /* The following definition of Storeinc is appropriate for MIPS processors. * An alternative that might be better on some machines is * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff) */ #if defined(IEEE_8087) #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \ ((unsigned short *)a)[0] = (unsigned short)c, a++) #else #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \ ((unsigned short *)a)[1] = (unsigned short)c, a++) #endif /* #define P DBL_MANT_DIG */ /* Ten_pmax = floor(P*log(2)/log(5)) */ /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */ /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */ /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */ #define Exp_shift 20 #define Exp_shift1 20 #define Exp_msk1 0x100000 #define Exp_msk11 0x100000 #define Exp_mask 0x7ff00000 #define P 53 #define Nbits 53 #define Bias 1023 #define Emax 1023 #define Emin (-1022) #define Etiny (-1074) /* smallest denormal is 2**Etiny */ #define Exp_1 0x3ff00000 #define Exp_11 0x3ff00000 #define Ebits 11 #define Frac_mask 0xfffff #define Frac_mask1 0xfffff #define Ten_pmax 22 #define Bletch 0x10 #define Bndry_mask 0xfffff #define Bndry_mask1 0xfffff #define Sign_bit 0x80000000 #define Log2P 1 #define Tiny0 0 #define Tiny1 1 #define Quick_max 14 #define Int_max 14 #ifndef Flt_Rounds #ifdef FLT_ROUNDS #define Flt_Rounds FLT_ROUNDS #else #define Flt_Rounds 1 #endif #endif /*Flt_Rounds*/ #define Rounding Flt_Rounds #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1)) #define Big1 0xffffffff /* Bits of the representation of positive infinity. */ #define POSINF_WORD0 0x7ff00000 #define POSINF_WORD1 0 /* struct BCinfo is used to pass information from _Py_dg_strtod to bigcomp */ typedef struct BCinfo BCinfo; struct BCinfo { int e0, nd, nd0, scale; }; #define FFFFFFFF 0xffffffffUL /* struct Bigint is used to represent arbitrary-precision integers. These integers are stored in sign-magnitude format, with the magnitude stored as an array of base 2**32 digits. Bigints are always normalized: if x is a Bigint then x->wds >= 1, and either x->wds == 1 or x[wds-1] is nonzero. The Bigint fields are as follows: - next is a header used by Balloc and Bfree to keep track of lists of freed Bigints; it's also used for the linked list of powers of 5 of the form 5**2**i used by pow5mult. - k indicates which pool this Bigint was allocated from - maxwds is the maximum number of words space was allocated for (usually maxwds == 2**k) - sign is 1 for negative Bigints, 0 for positive. The sign is unused (ignored on inputs, set to 0 on outputs) in almost all operations involving Bigints: a notable exception is the diff function, which ignores signs on inputs but sets the sign of the output correctly. - wds is the actual number of significant words - x contains the vector of words (digits) for this Bigint, from least significant (x[0]) to most significant (x[wds-1]). */ // struct Bigint is defined in pycore_dtoa.h. typedef struct Bigint Bigint; #if !defined(Py_GIL_DISABLED) && !defined(Py_USING_MEMORY_DEBUGGER) /* Memory management: memory is allocated from, and returned to, Kmax+1 pools of memory, where pool k (0 <= k <= Kmax) is for Bigints b with b->maxwds == 1 << k. These pools are maintained as linked lists, with freelist[k] pointing to the head of the list for pool k. On allocation, if there's no free slot in the appropriate pool, MALLOC is called to get more memory. This memory is not returned to the system until Python quits. There's also a private memory pool that's allocated from in preference to using MALLOC. For Bigints with more than (1 << Kmax) digits (which implies at least 1233 decimal digits), memory is directly allocated using MALLOC, and freed using FREE. XXX: it would be easy to bypass this memory-management system and translate each call to Balloc into a call to PyMem_Malloc, and each Bfree to PyMem_Free. Investigate whether this has any significant performance on impact. */ #define freelist interp->dtoa.freelist #define private_mem interp->dtoa.preallocated #define pmem_next interp->dtoa.preallocated_next /* Allocate space for a Bigint with up to 1<<k digits */ static Bigint * Balloc(int k) { int x; Bigint *rv; unsigned int len; PyInterpreterState *interp = _PyInterpreterState_GET(); if (k <= Bigint_Kmax && (rv = freelist[k])) freelist[k] = rv->next; else { x = 1 << k; len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1) /sizeof(double); if (k <= Bigint_Kmax && pmem_next - private_mem + len <= (Py_ssize_t)Bigint_PREALLOC_SIZE ) { rv = (Bigint*)pmem_next; pmem_next += len; } else { rv = (Bigint*)MALLOC(len*sizeof(double)); if (rv == NULL) return NULL; } rv->k = k; rv->maxwds = x; } rv->sign = rv->wds = 0; return rv; } /* Free a Bigint allocated with Balloc */ static void Bfree(Bigint *v) { if (v) { if (v->k > Bigint_Kmax) FREE((void*)v); else { PyInterpreterState *interp = _PyInterpreterState_GET(); v->next = freelist[v->k]; freelist[v->k] = v; } } } #undef pmem_next #undef private_mem #undef freelist #else /* Alternative versions of Balloc and Bfree that use PyMem_Malloc and PyMem_Free directly in place of the custom memory allocation scheme above. These are provided for the benefit of memory debugging tools like Valgrind. */ /* Allocate space for a Bigint with up to 1<<k digits */ static Bigint * Balloc(int k) { int x; Bigint *rv; unsigned int len; x = 1 << k; len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1) /sizeof(double); rv = (Bigint*)MALLOC(len*sizeof(double)); if (rv == NULL) return NULL; rv->k = k; rv->maxwds = x; rv->sign = rv->wds = 0; return rv; } /* Free a Bigint allocated with Balloc */ static void Bfree(Bigint *v) { if (v) { FREE((void*)v); } } #endif /* !defined(Py_GIL_DISABLED) && !defined(Py_USING_MEMORY_DEBUGGER) */ #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \ y->wds*sizeof(Long) + 2*sizeof(int)) /* Multiply a Bigint b by m and add a. Either modifies b in place and returns a pointer to the modified b, or Bfrees b and returns a pointer to a copy. On failure, return NULL. In this case, b will have been already freed. */ static Bigint * multadd(Bigint *b, int m, int a) /* multiply by m and add a */ { int i, wds; ULong *x; ULLong carry, y; Bigint *b1; wds = b->wds; x = b->x; i = 0; carry = a; do { y = *x * (ULLong)m + carry; carry = y >> 32; *x++ = (ULong)(y & FFFFFFFF); } while(++i < wds); if (carry) { if (wds >= b->maxwds) { b1 = Balloc(b->k+1); if (b1 == NULL){ Bfree(b); return NULL; } Bcopy(b1, b); Bfree(b); b = b1; } b->x[wds++] = (ULong)carry; b->wds = wds; } return b; } /* convert a string s containing nd decimal digits (possibly containing a decimal separator at position nd0, which is ignored) to a Bigint. This function carries on where the parsing code in _Py_dg_strtod leaves off: on entry, y9 contains the result of converting the first 9 digits. Returns NULL on failure. */ static Bigint * s2b(const char *s, int nd0, int nd, ULong y9) { Bigint *b; int i, k; Long x, y; x = (nd + 8) / 9; for(k = 0, y = 1; x > y; y <<= 1, k++) ; b = Balloc(k); if (b == NULL) return NULL; b->x[0] = y9; b->wds = 1; if (nd <= 9) return b; s += 9; for (i = 9; i < nd0; i++) { b = multadd(b, 10, *s++ - '0'); if (b == NULL) return NULL; } s++; for(; i < nd; i++) { b = multadd(b, 10, *s++ - '0'); if (b == NULL) return NULL; } return b; } /* count leading 0 bits in the 32-bit integer x. */ static int hi0bits(ULong x) { int k = 0; if (!(x & 0xffff0000)) { k = 16; x <<= 16; } if (!(x & 0xff000000)) { k += 8; x <<= 8; } if (!(x & 0xf0000000)) { k += 4; x <<= 4; } if (!(x & 0xc0000000)) { k += 2; x <<= 2; } if (!(x & 0x80000000)) { k++; if (!(x & 0x40000000)) return 32; } return k; } /* count trailing 0 bits in the 32-bit integer y, and shift y right by that number of bits. */ static int lo0bits(ULong *y) { int k; ULong x = *y; if (x & 7) { if (x & 1) return 0; if (x & 2) { *y = x >> 1; return 1; } *y = x >> 2; return 2; } k = 0; if (!(x & 0xffff)) { k = 16; x >>= 16; } if (!(x & 0xff)) { k += 8; x >>= 8; } if (!(x & 0xf)) { k += 4; x >>= 4; } if (!(x & 0x3)) { k += 2; x >>= 2; } if (!(x & 1)) { k++; x >>= 1; if (!x) return 32; } *y = x; return k; } /* convert a small nonnegative integer to a Bigint */ static Bigint * i2b(int i) { Bigint *b; b = Balloc(1); if (b == NULL) return NULL; b->x[0] = i; b->wds = 1; return b; } /* multiply two Bigints. Returns a new Bigint, or NULL on failure. Ignores the signs of a and b. */ static Bigint * mult(Bigint *a, Bigint *b) { Bigint *c; int k, wa, wb, wc; ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0; ULong y; ULLong carry, z; if ((!a->x[0] && a->wds == 1) || (!b->x[0] && b->wds == 1)) { c = Balloc(0); if (c == NULL) return NULL; c->wds = 1; c->x[0] = 0; return c; } if (a->wds < b->wds) { c = a; a = b; b = c; } k = a->k; wa = a->wds; wb = b->wds; wc = wa + wb; if (wc > a->maxwds) k++; c = Balloc(k); if (c == NULL) return NULL; for(x = c->x, xa = x + wc; x < xa; x++) *x = 0; xa = a->x; xae = xa + wa; xb = b->x; xbe = xb + wb; xc0 = c->x; for(; xb < xbe; xc0++) { if ((y = *xb++)) { x = xa; xc = xc0; carry = 0; do { z = *x++ * (ULLong)y + *xc + carry; carry = z >> 32; *xc++ = (ULong)(z & FFFFFFFF); } while(x < xae); *xc = (ULong)carry; } } for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ; c->wds = wc; return c; } #ifndef Py_USING_MEMORY_DEBUGGER /* multiply the Bigint b by 5**k. Returns a pointer to the result, or NULL on failure; if the returned pointer is distinct from b then the original Bigint b will have been Bfree'd. Ignores the sign of b. */ static Bigint * pow5mult(Bigint *b, int k) { Bigint *b1, *p5, **p5s; int i; static const int p05[3] = { 5, 25, 125 }; // For double-to-string conversion, the maximum value of k is limited by // DBL_MAX_10_EXP (308), the maximum decimal base-10 exponent for binary64. // For string-to-double conversion, the extreme case is constrained by our // hardcoded exponent limit before we underflow of -512, adjusted by // STRTOD_DIGLIM-DBL_DIG-1, giving a maximum of k=535. assert(0 <= k && k < 1024); if ((i = k & 3)) { b = multadd(b, p05[i-1], 0); if (b == NULL) return NULL; } if (!(k >>= 2)) return b; PyInterpreterState *interp = _PyInterpreterState_GET(); p5s = interp->dtoa.p5s; for(;;) { assert(p5s != interp->dtoa.p5s + Bigint_Pow5size); p5 = *p5s; p5s++; if (k & 1) { b1 = mult(b, p5); Bfree(b); b = b1; if (b == NULL) return NULL; } if (!(k >>= 1)) break; } return b; } #else /* Version of pow5mult that doesn't cache powers of 5. Provided for the benefit of memory debugging tools like Valgrind. */ static Bigint * pow5mult(Bigint *b, int k) { Bigint *b1, *p5, *p51; int i; static const int p05[3] = { 5, 25, 125 }; if ((i = k & 3)) { b = multadd(b, p05[i-1], 0); if (b == NULL) return NULL; } if (!(k >>= 2)) return b; p5 = i2b(625); if (p5 == NULL) { Bfree(b); return NULL; } for(;;) { if (k & 1) { b1 = mult(b, p5); Bfree(b); b = b1; if (b == NULL) { Bfree(p5); return NULL; } } if (!(k >>= 1)) break; p51 = mult(p5, p5); Bfree(p5); p5 = p51; if (p5 == NULL) { Bfree(b); return NULL; } } Bfree(p5); return b; } #endif /* Py_USING_MEMORY_DEBUGGER */ /* shift a Bigint b left by k bits. Return a pointer to the shifted result, or NULL on failure. If the returned pointer is distinct from b then the original b will have been Bfree'd. Ignores the sign of b. */ static Bigint * lshift(Bigint *b, int k) { int i, k1, n, n1; Bigint *b1; ULong *x, *x1, *xe, z; if (!k || (!b->x[0] && b->wds == 1)) return b; n = k >> 5; k1 = b->k; n1 = n + b->wds + 1; for(i = b->maxwds; n1 > i; i <<= 1) k1++; b1 = Balloc(k1); if (b1 == NULL) { Bfree(b); return NULL; } x1 = b1->x; for(i = 0; i < n; i++) *x1++ = 0; x = b->x; xe = x + b->wds; if (k &= 0x1f) { k1 = 32 - k; z = 0; do { *x1++ = *x << k | z; z = *x++ >> k1; } while(x < xe); if ((*x1 = z)) ++n1; } else do *x1++ = *x++; while(x < xe); b1->wds = n1 - 1; Bfree(b); return b1; } /* Do a three-way compare of a and b, returning -1 if a < b, 0 if a == b and 1 if a > b. Ignores signs of a and b. */ static int cmp(Bigint *a, Bigint *b) { ULong *xa, *xa0, *xb, *xb0; int i, j; i = a->wds; j = b->wds; #ifdef DEBUG if (i > 1 && !a->x[i-1]) Bug("cmp called with a->x[a->wds-1] == 0"); if (j > 1 && !b->x[j-1]) Bug("cmp called with b->x[b->wds-1] == 0"); #endif if (i -= j) return i; xa0 = a->x; xa = xa0 + j; xb0 = b->x; xb = xb0 + j; for(;;) { if (*--xa != *--xb) return *xa < *xb ? -1 : 1; if (xa <= xa0) break; } return 0; } /* Take the difference of Bigints a and b, returning a new Bigint. Returns NULL on failure. The signs of a and b are ignored, but the sign of the result is set appropriately. */ static Bigint * diff(Bigint *a, Bigint *b) { Bigint *c; int i, wa, wb; ULong *xa, *xae, *xb, *xbe, *xc; ULLong borrow, y; i = cmp(a,b); if (!i) { c = Balloc(0); if (c == NULL) return NULL; c->wds = 1; c->x[0] = 0; return c; } if (i < 0) { c = a; a = b; b = c; i = 1; } else i = 0; c = Balloc(a->k); if (c == NULL) return NULL; c->sign = i; wa = a->wds; xa = a->x; xae = xa + wa; wb = b->wds; xb = b->x; xbe = xb + wb; xc = c->x; borrow = 0; do { y = (ULLong)*xa++ - *xb++ - borrow; borrow = y >> 32 & (ULong)1; *xc++ = (ULong)(y & FFFFFFFF); } while(xb < xbe); while(xa < xae) { y = *xa++ - borrow; borrow = y >> 32 & (ULong)1; *xc++ = (ULong)(y & FFFFFFFF); } while(!*--xc) wa--; c->wds = wa; return c; } /* Given a positive normal double x, return the difference between x and the next double up. Doesn't give correct results for subnormals. */ static double ulp(U *x) { Long L; U u; L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1; word0(&u) = L; word1(&u) = 0; return dval(&u); } /* Convert a Bigint to a double plus an exponent */ static double b2d(Bigint *a, int *e) { ULong *xa, *xa0, w, y, z; int k; U d; xa0 = a->x; xa = xa0 + a->wds; y = *--xa; #ifdef DEBUG if (!y) Bug("zero y in b2d"); #endif k = hi0bits(y); *e = 32 - k; if (k < Ebits) { word0(&d) = Exp_1 | y >> (Ebits - k); w = xa > xa0 ? *--xa : 0; word1(&d) = y << ((32-Ebits) + k) | w >> (Ebits - k); goto ret_d; } z = xa > xa0 ? *--xa : 0; if (k -= Ebits) { word0(&d) = Exp_1 | y << k | z >> (32 - k); y = xa > xa0 ? *--xa : 0; word1(&d) = z << k | y >> (32 - k); } else { word0(&d) = Exp_1 | y; word1(&d) = z; } ret_d: return dval(&d); } /* Convert a scaled double to a Bigint plus an exponent. Similar to d2b, except that it accepts the scale parameter used in _Py_dg_strtod (which should be either 0 or 2*P), and the normalization for the return value is different (see below). On input, d should be finite and nonnegative, and d / 2**scale should be exactly representable as an IEEE 754 double. Returns a Bigint b and an integer e such that dval(d) / 2**scale = b * 2**e. Unlike d2b, b is not necessarily odd: b and e are normalized so that either 2**(P-1) <= b < 2**P and e >= Etiny, or b < 2**P and e == Etiny. This applies equally to an input of 0.0: in that case the return values are b = 0 and e = Etiny. The above normalization ensures that for all possible inputs d, 2**e gives ulp(d/2**scale). Returns NULL on failure. */ static Bigint * sd2b(U *d, int scale, int *e) { Bigint *b; b = Balloc(1); if (b == NULL) return NULL; /* First construct b and e assuming that scale == 0. */ b->wds = 2; b->x[0] = word1(d); b->x[1] = word0(d) & Frac_mask; *e = Etiny - 1 + (int)((word0(d) & Exp_mask) >> Exp_shift); if (*e < Etiny) *e = Etiny; else b->x[1] |= Exp_msk1; /* Now adjust for scale, provided that b != 0. */ |
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