Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1 | /**************************************************************** |
| 2 | * |
| 3 | * The author of this software is David M. Gay. |
| 4 | * |
| 5 | * Copyright (c) 1991, 2000, 2001 by Lucent Technologies. |
| 6 | * |
| 7 | * Permission to use, copy, modify, and distribute this software for any |
| 8 | * purpose without fee is hereby granted, provided that this entire notice |
| 9 | * is included in all copies of any software which is or includes a copy |
| 10 | * or modification of this software and in all copies of the supporting |
| 11 | * documentation for such software. |
| 12 | * |
| 13 | * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED |
| 14 | * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY |
| 15 | * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY |
| 16 | * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE. |
| 17 | * |
| 18 | ***************************************************************/ |
| 19 | |
| 20 | /**************************************************************** |
| 21 | * This is dtoa.c by David M. Gay, downloaded from |
| 22 | * http://www.netlib.org/fp/dtoa.c on April 15, 2009 and modified for |
| 23 | * inclusion into the Python core by Mark E. T. Dickinson and Eric V. Smith. |
Mark Dickinson | 7f0ea32 | 2009-04-17 16:06:28 +0000 | [diff] [blame] | 24 | * |
| 25 | * Please remember to check http://www.netlib.org/fp regularly (and especially |
| 26 | * before any Python release) for bugfixes and updates. |
| 27 | * |
| 28 | * The major modifications from Gay's original code are as follows: |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 29 | * |
| 30 | * 0. The original code has been specialized to Python's needs by removing |
| 31 | * many of the #ifdef'd sections. In particular, code to support VAX and |
| 32 | * IBM floating-point formats, hex NaNs, hex floats, locale-aware |
| 33 | * treatment of the decimal point, and setting of the inexact flag have |
| 34 | * been removed. |
| 35 | * |
| 36 | * 1. We use PyMem_Malloc and PyMem_Free in place of malloc and free. |
| 37 | * |
| 38 | * 2. The public functions strtod, dtoa and freedtoa all now have |
| 39 | * a _Py_dg_ prefix. |
| 40 | * |
| 41 | * 3. Instead of assuming that PyMem_Malloc always succeeds, we thread |
| 42 | * PyMem_Malloc failures through the code. The functions |
| 43 | * |
| 44 | * Balloc, multadd, s2b, i2b, mult, pow5mult, lshift, diff, d2b |
| 45 | * |
| 46 | * of return type *Bigint all return NULL to indicate a malloc failure. |
| 47 | * Similarly, rv_alloc and nrv_alloc (return type char *) return NULL on |
| 48 | * failure. bigcomp now has return type int (it used to be void) and |
| 49 | * returns -1 on failure and 0 otherwise. _Py_dg_dtoa returns NULL |
| 50 | * on failure. _Py_dg_strtod indicates failure due to malloc failure |
| 51 | * by returning -1.0, setting errno=ENOMEM and *se to s00. |
| 52 | * |
| 53 | * 4. The static variable dtoa_result has been removed. Callers of |
| 54 | * _Py_dg_dtoa are expected to call _Py_dg_freedtoa to free |
| 55 | * the memory allocated by _Py_dg_dtoa. |
| 56 | * |
| 57 | * 5. The code has been reformatted to better fit with Python's |
| 58 | * C style guide (PEP 7). |
| 59 | * |
Mark Dickinson | 7f0ea32 | 2009-04-17 16:06:28 +0000 | [diff] [blame] | 60 | * 6. A bug in the memory allocation has been fixed: to avoid FREEing memory |
| 61 | * that hasn't been MALLOC'ed, private_mem should only be used when k <= |
| 62 | * Kmax. |
| 63 | * |
Mark Dickinson | 725bfd8 | 2009-05-03 20:33:40 +0000 | [diff] [blame] | 64 | * 7. _Py_dg_strtod has been modified so that it doesn't accept strings with |
| 65 | * leading whitespace. |
| 66 | * |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 67 | ***************************************************************/ |
| 68 | |
| 69 | /* Please send bug reports for the original dtoa.c code to David M. Gay (dmg |
| 70 | * at acm dot org, with " at " changed at "@" and " dot " changed to "."). |
| 71 | * Please report bugs for this modified version using the Python issue tracker |
| 72 | * (http://bugs.python.org). */ |
| 73 | |
| 74 | /* On a machine with IEEE extended-precision registers, it is |
| 75 | * necessary to specify double-precision (53-bit) rounding precision |
| 76 | * before invoking strtod or dtoa. If the machine uses (the equivalent |
| 77 | * of) Intel 80x87 arithmetic, the call |
| 78 | * _control87(PC_53, MCW_PC); |
| 79 | * does this with many compilers. Whether this or another call is |
| 80 | * appropriate depends on the compiler; for this to work, it may be |
| 81 | * necessary to #include "float.h" or another system-dependent header |
| 82 | * file. |
| 83 | */ |
| 84 | |
| 85 | /* strtod for IEEE-, VAX-, and IBM-arithmetic machines. |
| 86 | * |
| 87 | * This strtod returns a nearest machine number to the input decimal |
| 88 | * string (or sets errno to ERANGE). With IEEE arithmetic, ties are |
| 89 | * broken by the IEEE round-even rule. Otherwise ties are broken by |
| 90 | * biased rounding (add half and chop). |
| 91 | * |
| 92 | * Inspired loosely by William D. Clinger's paper "How to Read Floating |
| 93 | * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101]. |
| 94 | * |
| 95 | * Modifications: |
| 96 | * |
| 97 | * 1. We only require IEEE, IBM, or VAX double-precision |
| 98 | * arithmetic (not IEEE double-extended). |
| 99 | * 2. We get by with floating-point arithmetic in a case that |
| 100 | * Clinger missed -- when we're computing d * 10^n |
| 101 | * for a small integer d and the integer n is not too |
| 102 | * much larger than 22 (the maximum integer k for which |
| 103 | * we can represent 10^k exactly), we may be able to |
| 104 | * compute (d*10^k) * 10^(e-k) with just one roundoff. |
| 105 | * 3. Rather than a bit-at-a-time adjustment of the binary |
| 106 | * result in the hard case, we use floating-point |
| 107 | * arithmetic to determine the adjustment to within |
| 108 | * one bit; only in really hard cases do we need to |
| 109 | * compute a second residual. |
| 110 | * 4. Because of 3., we don't need a large table of powers of 10 |
| 111 | * for ten-to-e (just some small tables, e.g. of 10^k |
| 112 | * for 0 <= k <= 22). |
| 113 | */ |
| 114 | |
| 115 | /* Linking of Python's #defines to Gay's #defines starts here. */ |
| 116 | |
| 117 | #include "Python.h" |
| 118 | |
| 119 | /* if PY_NO_SHORT_FLOAT_REPR is defined, then don't even try to compile |
| 120 | the following code */ |
| 121 | #ifndef PY_NO_SHORT_FLOAT_REPR |
| 122 | |
| 123 | #include "float.h" |
| 124 | |
| 125 | #define MALLOC PyMem_Malloc |
| 126 | #define FREE PyMem_Free |
| 127 | |
| 128 | /* This code should also work for ARM mixed-endian format on little-endian |
| 129 | machines, where doubles have byte order 45670123 (in increasing address |
| 130 | order, 0 being the least significant byte). */ |
| 131 | #ifdef DOUBLE_IS_LITTLE_ENDIAN_IEEE754 |
| 132 | # define IEEE_8087 |
| 133 | #endif |
| 134 | #if defined(DOUBLE_IS_BIG_ENDIAN_IEEE754) || \ |
| 135 | defined(DOUBLE_IS_ARM_MIXED_ENDIAN_IEEE754) |
| 136 | # define IEEE_MC68k |
| 137 | #endif |
| 138 | #if defined(IEEE_8087) + defined(IEEE_MC68k) != 1 |
| 139 | #error "Exactly one of IEEE_8087 or IEEE_MC68k should be defined." |
| 140 | #endif |
| 141 | |
| 142 | /* The code below assumes that the endianness of integers matches the |
| 143 | endianness of the two 32-bit words of a double. Check this. */ |
| 144 | #if defined(WORDS_BIGENDIAN) && (defined(DOUBLE_IS_LITTLE_ENDIAN_IEEE754) || \ |
| 145 | defined(DOUBLE_IS_ARM_MIXED_ENDIAN_IEEE754)) |
| 146 | #error "doubles and ints have incompatible endianness" |
| 147 | #endif |
| 148 | |
| 149 | #if !defined(WORDS_BIGENDIAN) && defined(DOUBLE_IS_BIG_ENDIAN_IEEE754) |
| 150 | #error "doubles and ints have incompatible endianness" |
| 151 | #endif |
| 152 | |
| 153 | |
Benjamin Peterson | 4fe5510 | 2016-09-06 11:58:01 -0700 | [diff] [blame^] | 154 | typedef uint32_t ULong; |
| 155 | typedef int32_t Long; |
| 156 | typedef uint64_t ULLong; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 157 | |
| 158 | #undef DEBUG |
| 159 | #ifdef Py_DEBUG |
| 160 | #define DEBUG |
| 161 | #endif |
| 162 | |
| 163 | /* End Python #define linking */ |
| 164 | |
| 165 | #ifdef DEBUG |
| 166 | #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);} |
| 167 | #endif |
| 168 | |
| 169 | #ifndef PRIVATE_MEM |
| 170 | #define PRIVATE_MEM 2304 |
| 171 | #endif |
| 172 | #define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double)) |
| 173 | static double private_mem[PRIVATE_mem], *pmem_next = private_mem; |
| 174 | |
| 175 | #ifdef __cplusplus |
| 176 | extern "C" { |
| 177 | #endif |
| 178 | |
| 179 | typedef union { double d; ULong L[2]; } U; |
| 180 | |
| 181 | #ifdef IEEE_8087 |
| 182 | #define word0(x) (x)->L[1] |
| 183 | #define word1(x) (x)->L[0] |
| 184 | #else |
| 185 | #define word0(x) (x)->L[0] |
| 186 | #define word1(x) (x)->L[1] |
| 187 | #endif |
| 188 | #define dval(x) (x)->d |
| 189 | |
| 190 | #ifndef STRTOD_DIGLIM |
| 191 | #define STRTOD_DIGLIM 40 |
| 192 | #endif |
| 193 | |
Mark Dickinson | 81612e8 | 2010-01-12 23:04:19 +0000 | [diff] [blame] | 194 | /* maximum permitted exponent value for strtod; exponents larger than |
| 195 | MAX_ABS_EXP in absolute value get truncated to +-MAX_ABS_EXP. MAX_ABS_EXP |
| 196 | should fit into an int. */ |
| 197 | #ifndef MAX_ABS_EXP |
Mark Dickinson | f45bbb6 | 2013-11-26 16:19:13 +0000 | [diff] [blame] | 198 | #define MAX_ABS_EXP 1100000000U |
| 199 | #endif |
| 200 | /* Bound on length of pieces of input strings in _Py_dg_strtod; specifically, |
| 201 | this is used to bound the total number of digits ignoring leading zeros and |
| 202 | the number of digits that follow the decimal point. Ideally, MAX_DIGITS |
| 203 | should satisfy MAX_DIGITS + 400 < MAX_ABS_EXP; that ensures that the |
| 204 | exponent clipping in _Py_dg_strtod can't affect the value of the output. */ |
| 205 | #ifndef MAX_DIGITS |
| 206 | #define MAX_DIGITS 1000000000U |
| 207 | #endif |
| 208 | |
| 209 | /* Guard against trying to use the above values on unusual platforms with ints |
| 210 | * of width less than 32 bits. */ |
| 211 | #if MAX_ABS_EXP > INT_MAX |
| 212 | #error "MAX_ABS_EXP should fit in an int" |
| 213 | #endif |
| 214 | #if MAX_DIGITS > INT_MAX |
| 215 | #error "MAX_DIGITS should fit in an int" |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 216 | #endif |
| 217 | |
| 218 | /* The following definition of Storeinc is appropriate for MIPS processors. |
| 219 | * An alternative that might be better on some machines is |
| 220 | * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff) |
| 221 | */ |
| 222 | #if defined(IEEE_8087) |
| 223 | #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \ |
| 224 | ((unsigned short *)a)[0] = (unsigned short)c, a++) |
| 225 | #else |
| 226 | #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \ |
| 227 | ((unsigned short *)a)[1] = (unsigned short)c, a++) |
| 228 | #endif |
| 229 | |
| 230 | /* #define P DBL_MANT_DIG */ |
| 231 | /* Ten_pmax = floor(P*log(2)/log(5)) */ |
| 232 | /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */ |
| 233 | /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */ |
| 234 | /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */ |
| 235 | |
| 236 | #define Exp_shift 20 |
| 237 | #define Exp_shift1 20 |
| 238 | #define Exp_msk1 0x100000 |
| 239 | #define Exp_msk11 0x100000 |
| 240 | #define Exp_mask 0x7ff00000 |
| 241 | #define P 53 |
| 242 | #define Nbits 53 |
| 243 | #define Bias 1023 |
| 244 | #define Emax 1023 |
| 245 | #define Emin (-1022) |
Mark Dickinson | f41d29a | 2010-01-24 10:16:29 +0000 | [diff] [blame] | 246 | #define Etiny (-1074) /* smallest denormal is 2**Etiny */ |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 247 | #define Exp_1 0x3ff00000 |
| 248 | #define Exp_11 0x3ff00000 |
| 249 | #define Ebits 11 |
| 250 | #define Frac_mask 0xfffff |
| 251 | #define Frac_mask1 0xfffff |
| 252 | #define Ten_pmax 22 |
| 253 | #define Bletch 0x10 |
| 254 | #define Bndry_mask 0xfffff |
| 255 | #define Bndry_mask1 0xfffff |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 256 | #define Sign_bit 0x80000000 |
| 257 | #define Log2P 1 |
| 258 | #define Tiny0 0 |
| 259 | #define Tiny1 1 |
| 260 | #define Quick_max 14 |
| 261 | #define Int_max 14 |
| 262 | |
| 263 | #ifndef Flt_Rounds |
| 264 | #ifdef FLT_ROUNDS |
| 265 | #define Flt_Rounds FLT_ROUNDS |
| 266 | #else |
| 267 | #define Flt_Rounds 1 |
| 268 | #endif |
| 269 | #endif /*Flt_Rounds*/ |
| 270 | |
| 271 | #define Rounding Flt_Rounds |
| 272 | |
| 273 | #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1)) |
| 274 | #define Big1 0xffffffff |
| 275 | |
Mark Dickinson | e383e82 | 2012-04-29 15:31:56 +0100 | [diff] [blame] | 276 | /* Standard NaN used by _Py_dg_stdnan. */ |
| 277 | |
| 278 | #define NAN_WORD0 0x7ff80000 |
| 279 | #define NAN_WORD1 0 |
| 280 | |
| 281 | /* Bits of the representation of positive infinity. */ |
| 282 | |
| 283 | #define POSINF_WORD0 0x7ff00000 |
| 284 | #define POSINF_WORD1 0 |
| 285 | |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 286 | /* struct BCinfo is used to pass information from _Py_dg_strtod to bigcomp */ |
| 287 | |
| 288 | typedef struct BCinfo BCinfo; |
| 289 | struct |
| 290 | BCinfo { |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 291 | int e0, nd, nd0, scale; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 292 | }; |
| 293 | |
| 294 | #define FFFFFFFF 0xffffffffUL |
| 295 | |
| 296 | #define Kmax 7 |
| 297 | |
| 298 | /* struct Bigint is used to represent arbitrary-precision integers. These |
| 299 | integers are stored in sign-magnitude format, with the magnitude stored as |
| 300 | an array of base 2**32 digits. Bigints are always normalized: if x is a |
| 301 | Bigint then x->wds >= 1, and either x->wds == 1 or x[wds-1] is nonzero. |
| 302 | |
| 303 | The Bigint fields are as follows: |
| 304 | |
| 305 | - next is a header used by Balloc and Bfree to keep track of lists |
| 306 | of freed Bigints; it's also used for the linked list of |
| 307 | powers of 5 of the form 5**2**i used by pow5mult. |
| 308 | - k indicates which pool this Bigint was allocated from |
| 309 | - maxwds is the maximum number of words space was allocated for |
| 310 | (usually maxwds == 2**k) |
| 311 | - sign is 1 for negative Bigints, 0 for positive. The sign is unused |
| 312 | (ignored on inputs, set to 0 on outputs) in almost all operations |
| 313 | involving Bigints: a notable exception is the diff function, which |
| 314 | ignores signs on inputs but sets the sign of the output correctly. |
| 315 | - wds is the actual number of significant words |
| 316 | - x contains the vector of words (digits) for this Bigint, from least |
| 317 | significant (x[0]) to most significant (x[wds-1]). |
| 318 | */ |
| 319 | |
| 320 | struct |
| 321 | Bigint { |
| 322 | struct Bigint *next; |
| 323 | int k, maxwds, sign, wds; |
| 324 | ULong x[1]; |
| 325 | }; |
| 326 | |
| 327 | typedef struct Bigint Bigint; |
| 328 | |
Mark Dickinson | de50800 | 2010-01-17 21:02:55 +0000 | [diff] [blame] | 329 | #ifndef Py_USING_MEMORY_DEBUGGER |
| 330 | |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 331 | /* Memory management: memory is allocated from, and returned to, Kmax+1 pools |
| 332 | of memory, where pool k (0 <= k <= Kmax) is for Bigints b with b->maxwds == |
| 333 | 1 << k. These pools are maintained as linked lists, with freelist[k] |
| 334 | pointing to the head of the list for pool k. |
| 335 | |
| 336 | On allocation, if there's no free slot in the appropriate pool, MALLOC is |
| 337 | called to get more memory. This memory is not returned to the system until |
| 338 | Python quits. There's also a private memory pool that's allocated from |
| 339 | in preference to using MALLOC. |
| 340 | |
| 341 | For Bigints with more than (1 << Kmax) digits (which implies at least 1233 |
| 342 | decimal digits), memory is directly allocated using MALLOC, and freed using |
| 343 | FREE. |
| 344 | |
| 345 | XXX: it would be easy to bypass this memory-management system and |
| 346 | translate each call to Balloc into a call to PyMem_Malloc, and each |
| 347 | Bfree to PyMem_Free. Investigate whether this has any significant |
| 348 | performance on impact. */ |
| 349 | |
| 350 | static Bigint *freelist[Kmax+1]; |
| 351 | |
| 352 | /* Allocate space for a Bigint with up to 1<<k digits */ |
| 353 | |
| 354 | static Bigint * |
| 355 | Balloc(int k) |
| 356 | { |
| 357 | int x; |
| 358 | Bigint *rv; |
| 359 | unsigned int len; |
| 360 | |
| 361 | if (k <= Kmax && (rv = freelist[k])) |
| 362 | freelist[k] = rv->next; |
| 363 | else { |
| 364 | x = 1 << k; |
| 365 | len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1) |
| 366 | /sizeof(double); |
Victor Stinner | 938b0b9 | 2015-03-18 15:01:44 +0100 | [diff] [blame] | 367 | if (k <= Kmax && pmem_next - private_mem + len <= (Py_ssize_t)PRIVATE_mem) { |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 368 | rv = (Bigint*)pmem_next; |
| 369 | pmem_next += len; |
| 370 | } |
| 371 | else { |
| 372 | rv = (Bigint*)MALLOC(len*sizeof(double)); |
| 373 | if (rv == NULL) |
| 374 | return NULL; |
| 375 | } |
| 376 | rv->k = k; |
| 377 | rv->maxwds = x; |
| 378 | } |
| 379 | rv->sign = rv->wds = 0; |
| 380 | return rv; |
| 381 | } |
| 382 | |
| 383 | /* Free a Bigint allocated with Balloc */ |
| 384 | |
| 385 | static void |
| 386 | Bfree(Bigint *v) |
| 387 | { |
| 388 | if (v) { |
| 389 | if (v->k > Kmax) |
| 390 | FREE((void*)v); |
| 391 | else { |
| 392 | v->next = freelist[v->k]; |
| 393 | freelist[v->k] = v; |
| 394 | } |
| 395 | } |
| 396 | } |
| 397 | |
Mark Dickinson | de50800 | 2010-01-17 21:02:55 +0000 | [diff] [blame] | 398 | #else |
| 399 | |
| 400 | /* Alternative versions of Balloc and Bfree that use PyMem_Malloc and |
| 401 | PyMem_Free directly in place of the custom memory allocation scheme above. |
| 402 | These are provided for the benefit of memory debugging tools like |
| 403 | Valgrind. */ |
| 404 | |
| 405 | /* Allocate space for a Bigint with up to 1<<k digits */ |
| 406 | |
| 407 | static Bigint * |
| 408 | Balloc(int k) |
| 409 | { |
| 410 | int x; |
| 411 | Bigint *rv; |
| 412 | unsigned int len; |
| 413 | |
| 414 | x = 1 << k; |
| 415 | len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1) |
| 416 | /sizeof(double); |
| 417 | |
| 418 | rv = (Bigint*)MALLOC(len*sizeof(double)); |
| 419 | if (rv == NULL) |
| 420 | return NULL; |
| 421 | |
| 422 | rv->k = k; |
| 423 | rv->maxwds = x; |
| 424 | rv->sign = rv->wds = 0; |
| 425 | return rv; |
| 426 | } |
| 427 | |
| 428 | /* Free a Bigint allocated with Balloc */ |
| 429 | |
| 430 | static void |
| 431 | Bfree(Bigint *v) |
| 432 | { |
| 433 | if (v) { |
| 434 | FREE((void*)v); |
| 435 | } |
| 436 | } |
| 437 | |
| 438 | #endif /* Py_USING_MEMORY_DEBUGGER */ |
| 439 | |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 440 | #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \ |
| 441 | y->wds*sizeof(Long) + 2*sizeof(int)) |
| 442 | |
| 443 | /* Multiply a Bigint b by m and add a. Either modifies b in place and returns |
| 444 | a pointer to the modified b, or Bfrees b and returns a pointer to a copy. |
| 445 | On failure, return NULL. In this case, b will have been already freed. */ |
| 446 | |
| 447 | static Bigint * |
| 448 | multadd(Bigint *b, int m, int a) /* multiply by m and add a */ |
| 449 | { |
| 450 | int i, wds; |
| 451 | #ifdef ULLong |
| 452 | ULong *x; |
| 453 | ULLong carry, y; |
| 454 | #else |
| 455 | ULong carry, *x, y; |
| 456 | ULong xi, z; |
| 457 | #endif |
| 458 | Bigint *b1; |
| 459 | |
| 460 | wds = b->wds; |
| 461 | x = b->x; |
| 462 | i = 0; |
| 463 | carry = a; |
| 464 | do { |
| 465 | #ifdef ULLong |
| 466 | y = *x * (ULLong)m + carry; |
| 467 | carry = y >> 32; |
Mark Dickinson | fd2ad8b | 2009-04-17 19:29:46 +0000 | [diff] [blame] | 468 | *x++ = (ULong)(y & FFFFFFFF); |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 469 | #else |
| 470 | xi = *x; |
| 471 | y = (xi & 0xffff) * m + carry; |
| 472 | z = (xi >> 16) * m + (y >> 16); |
| 473 | carry = z >> 16; |
| 474 | *x++ = (z << 16) + (y & 0xffff); |
| 475 | #endif |
| 476 | } |
| 477 | while(++i < wds); |
| 478 | if (carry) { |
| 479 | if (wds >= b->maxwds) { |
| 480 | b1 = Balloc(b->k+1); |
| 481 | if (b1 == NULL){ |
| 482 | Bfree(b); |
| 483 | return NULL; |
| 484 | } |
| 485 | Bcopy(b1, b); |
| 486 | Bfree(b); |
| 487 | b = b1; |
| 488 | } |
| 489 | b->x[wds++] = (ULong)carry; |
| 490 | b->wds = wds; |
| 491 | } |
| 492 | return b; |
| 493 | } |
| 494 | |
| 495 | /* convert a string s containing nd decimal digits (possibly containing a |
| 496 | decimal separator at position nd0, which is ignored) to a Bigint. This |
| 497 | function carries on where the parsing code in _Py_dg_strtod leaves off: on |
| 498 | entry, y9 contains the result of converting the first 9 digits. Returns |
| 499 | NULL on failure. */ |
| 500 | |
| 501 | static Bigint * |
Mark Dickinson | 853c3bb | 2010-01-14 15:37:49 +0000 | [diff] [blame] | 502 | s2b(const char *s, int nd0, int nd, ULong y9) |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 503 | { |
| 504 | Bigint *b; |
| 505 | int i, k; |
| 506 | Long x, y; |
| 507 | |
| 508 | x = (nd + 8) / 9; |
| 509 | for(k = 0, y = 1; x > y; y <<= 1, k++) ; |
| 510 | b = Balloc(k); |
| 511 | if (b == NULL) |
| 512 | return NULL; |
| 513 | b->x[0] = y9; |
| 514 | b->wds = 1; |
| 515 | |
Mark Dickinson | 853c3bb | 2010-01-14 15:37:49 +0000 | [diff] [blame] | 516 | if (nd <= 9) |
| 517 | return b; |
| 518 | |
| 519 | s += 9; |
| 520 | for (i = 9; i < nd0; i++) { |
| 521 | b = multadd(b, 10, *s++ - '0'); |
| 522 | if (b == NULL) |
| 523 | return NULL; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 524 | } |
Mark Dickinson | 853c3bb | 2010-01-14 15:37:49 +0000 | [diff] [blame] | 525 | s++; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 526 | for(; i < nd; i++) { |
| 527 | b = multadd(b, 10, *s++ - '0'); |
| 528 | if (b == NULL) |
| 529 | return NULL; |
| 530 | } |
| 531 | return b; |
| 532 | } |
| 533 | |
| 534 | /* count leading 0 bits in the 32-bit integer x. */ |
| 535 | |
| 536 | static int |
| 537 | hi0bits(ULong x) |
| 538 | { |
| 539 | int k = 0; |
| 540 | |
| 541 | if (!(x & 0xffff0000)) { |
| 542 | k = 16; |
| 543 | x <<= 16; |
| 544 | } |
| 545 | if (!(x & 0xff000000)) { |
| 546 | k += 8; |
| 547 | x <<= 8; |
| 548 | } |
| 549 | if (!(x & 0xf0000000)) { |
| 550 | k += 4; |
| 551 | x <<= 4; |
| 552 | } |
| 553 | if (!(x & 0xc0000000)) { |
| 554 | k += 2; |
| 555 | x <<= 2; |
| 556 | } |
| 557 | if (!(x & 0x80000000)) { |
| 558 | k++; |
| 559 | if (!(x & 0x40000000)) |
| 560 | return 32; |
| 561 | } |
| 562 | return k; |
| 563 | } |
| 564 | |
| 565 | /* count trailing 0 bits in the 32-bit integer y, and shift y right by that |
| 566 | number of bits. */ |
| 567 | |
| 568 | static int |
| 569 | lo0bits(ULong *y) |
| 570 | { |
| 571 | int k; |
| 572 | ULong x = *y; |
| 573 | |
| 574 | if (x & 7) { |
| 575 | if (x & 1) |
| 576 | return 0; |
| 577 | if (x & 2) { |
| 578 | *y = x >> 1; |
| 579 | return 1; |
| 580 | } |
| 581 | *y = x >> 2; |
| 582 | return 2; |
| 583 | } |
| 584 | k = 0; |
| 585 | if (!(x & 0xffff)) { |
| 586 | k = 16; |
| 587 | x >>= 16; |
| 588 | } |
| 589 | if (!(x & 0xff)) { |
| 590 | k += 8; |
| 591 | x >>= 8; |
| 592 | } |
| 593 | if (!(x & 0xf)) { |
| 594 | k += 4; |
| 595 | x >>= 4; |
| 596 | } |
| 597 | if (!(x & 0x3)) { |
| 598 | k += 2; |
| 599 | x >>= 2; |
| 600 | } |
| 601 | if (!(x & 1)) { |
| 602 | k++; |
| 603 | x >>= 1; |
| 604 | if (!x) |
| 605 | return 32; |
| 606 | } |
| 607 | *y = x; |
| 608 | return k; |
| 609 | } |
| 610 | |
| 611 | /* convert a small nonnegative integer to a Bigint */ |
| 612 | |
| 613 | static Bigint * |
| 614 | i2b(int i) |
| 615 | { |
| 616 | Bigint *b; |
| 617 | |
| 618 | b = Balloc(1); |
| 619 | if (b == NULL) |
| 620 | return NULL; |
| 621 | b->x[0] = i; |
| 622 | b->wds = 1; |
| 623 | return b; |
| 624 | } |
| 625 | |
| 626 | /* multiply two Bigints. Returns a new Bigint, or NULL on failure. Ignores |
| 627 | the signs of a and b. */ |
| 628 | |
| 629 | static Bigint * |
| 630 | mult(Bigint *a, Bigint *b) |
| 631 | { |
| 632 | Bigint *c; |
| 633 | int k, wa, wb, wc; |
| 634 | ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0; |
| 635 | ULong y; |
| 636 | #ifdef ULLong |
| 637 | ULLong carry, z; |
| 638 | #else |
| 639 | ULong carry, z; |
| 640 | ULong z2; |
| 641 | #endif |
| 642 | |
Mark Dickinson | f41d29a | 2010-01-24 10:16:29 +0000 | [diff] [blame] | 643 | if ((!a->x[0] && a->wds == 1) || (!b->x[0] && b->wds == 1)) { |
| 644 | c = Balloc(0); |
| 645 | if (c == NULL) |
| 646 | return NULL; |
| 647 | c->wds = 1; |
| 648 | c->x[0] = 0; |
| 649 | return c; |
| 650 | } |
| 651 | |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 652 | if (a->wds < b->wds) { |
| 653 | c = a; |
| 654 | a = b; |
| 655 | b = c; |
| 656 | } |
| 657 | k = a->k; |
| 658 | wa = a->wds; |
| 659 | wb = b->wds; |
| 660 | wc = wa + wb; |
| 661 | if (wc > a->maxwds) |
| 662 | k++; |
| 663 | c = Balloc(k); |
| 664 | if (c == NULL) |
| 665 | return NULL; |
| 666 | for(x = c->x, xa = x + wc; x < xa; x++) |
| 667 | *x = 0; |
| 668 | xa = a->x; |
| 669 | xae = xa + wa; |
| 670 | xb = b->x; |
| 671 | xbe = xb + wb; |
| 672 | xc0 = c->x; |
| 673 | #ifdef ULLong |
| 674 | for(; xb < xbe; xc0++) { |
| 675 | if ((y = *xb++)) { |
| 676 | x = xa; |
| 677 | xc = xc0; |
| 678 | carry = 0; |
| 679 | do { |
| 680 | z = *x++ * (ULLong)y + *xc + carry; |
| 681 | carry = z >> 32; |
Mark Dickinson | fd2ad8b | 2009-04-17 19:29:46 +0000 | [diff] [blame] | 682 | *xc++ = (ULong)(z & FFFFFFFF); |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 683 | } |
| 684 | while(x < xae); |
| 685 | *xc = (ULong)carry; |
| 686 | } |
| 687 | } |
| 688 | #else |
| 689 | for(; xb < xbe; xb++, xc0++) { |
| 690 | if (y = *xb & 0xffff) { |
| 691 | x = xa; |
| 692 | xc = xc0; |
| 693 | carry = 0; |
| 694 | do { |
| 695 | z = (*x & 0xffff) * y + (*xc & 0xffff) + carry; |
| 696 | carry = z >> 16; |
| 697 | z2 = (*x++ >> 16) * y + (*xc >> 16) + carry; |
| 698 | carry = z2 >> 16; |
| 699 | Storeinc(xc, z2, z); |
| 700 | } |
| 701 | while(x < xae); |
| 702 | *xc = carry; |
| 703 | } |
| 704 | if (y = *xb >> 16) { |
| 705 | x = xa; |
| 706 | xc = xc0; |
| 707 | carry = 0; |
| 708 | z2 = *xc; |
| 709 | do { |
| 710 | z = (*x & 0xffff) * y + (*xc >> 16) + carry; |
| 711 | carry = z >> 16; |
| 712 | Storeinc(xc, z, z2); |
| 713 | z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry; |
| 714 | carry = z2 >> 16; |
| 715 | } |
| 716 | while(x < xae); |
| 717 | *xc = z2; |
| 718 | } |
| 719 | } |
| 720 | #endif |
| 721 | for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ; |
| 722 | c->wds = wc; |
| 723 | return c; |
| 724 | } |
| 725 | |
Mark Dickinson | de50800 | 2010-01-17 21:02:55 +0000 | [diff] [blame] | 726 | #ifndef Py_USING_MEMORY_DEBUGGER |
| 727 | |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 728 | /* p5s is a linked list of powers of 5 of the form 5**(2**i), i >= 2 */ |
| 729 | |
| 730 | static Bigint *p5s; |
| 731 | |
| 732 | /* multiply the Bigint b by 5**k. Returns a pointer to the result, or NULL on |
| 733 | failure; if the returned pointer is distinct from b then the original |
| 734 | Bigint b will have been Bfree'd. Ignores the sign of b. */ |
| 735 | |
| 736 | static Bigint * |
| 737 | pow5mult(Bigint *b, int k) |
| 738 | { |
| 739 | Bigint *b1, *p5, *p51; |
| 740 | int i; |
Serhiy Storchaka | 2d06e84 | 2015-12-25 19:53:18 +0200 | [diff] [blame] | 741 | static const int p05[3] = { 5, 25, 125 }; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 742 | |
| 743 | if ((i = k & 3)) { |
| 744 | b = multadd(b, p05[i-1], 0); |
| 745 | if (b == NULL) |
| 746 | return NULL; |
| 747 | } |
| 748 | |
| 749 | if (!(k >>= 2)) |
| 750 | return b; |
| 751 | p5 = p5s; |
| 752 | if (!p5) { |
| 753 | /* first time */ |
| 754 | p5 = i2b(625); |
| 755 | if (p5 == NULL) { |
| 756 | Bfree(b); |
| 757 | return NULL; |
| 758 | } |
| 759 | p5s = p5; |
| 760 | p5->next = 0; |
| 761 | } |
| 762 | for(;;) { |
| 763 | if (k & 1) { |
| 764 | b1 = mult(b, p5); |
| 765 | Bfree(b); |
| 766 | b = b1; |
| 767 | if (b == NULL) |
| 768 | return NULL; |
| 769 | } |
| 770 | if (!(k >>= 1)) |
| 771 | break; |
| 772 | p51 = p5->next; |
| 773 | if (!p51) { |
| 774 | p51 = mult(p5,p5); |
| 775 | if (p51 == NULL) { |
| 776 | Bfree(b); |
| 777 | return NULL; |
| 778 | } |
| 779 | p51->next = 0; |
| 780 | p5->next = p51; |
| 781 | } |
| 782 | p5 = p51; |
| 783 | } |
| 784 | return b; |
| 785 | } |
| 786 | |
Mark Dickinson | de50800 | 2010-01-17 21:02:55 +0000 | [diff] [blame] | 787 | #else |
| 788 | |
| 789 | /* Version of pow5mult that doesn't cache powers of 5. Provided for |
| 790 | the benefit of memory debugging tools like Valgrind. */ |
| 791 | |
| 792 | static Bigint * |
| 793 | pow5mult(Bigint *b, int k) |
| 794 | { |
| 795 | Bigint *b1, *p5, *p51; |
| 796 | int i; |
Serhiy Storchaka | 2d06e84 | 2015-12-25 19:53:18 +0200 | [diff] [blame] | 797 | static const int p05[3] = { 5, 25, 125 }; |
Mark Dickinson | de50800 | 2010-01-17 21:02:55 +0000 | [diff] [blame] | 798 | |
| 799 | if ((i = k & 3)) { |
| 800 | b = multadd(b, p05[i-1], 0); |
| 801 | if (b == NULL) |
| 802 | return NULL; |
| 803 | } |
| 804 | |
| 805 | if (!(k >>= 2)) |
| 806 | return b; |
| 807 | p5 = i2b(625); |
| 808 | if (p5 == NULL) { |
| 809 | Bfree(b); |
| 810 | return NULL; |
| 811 | } |
| 812 | |
| 813 | for(;;) { |
| 814 | if (k & 1) { |
| 815 | b1 = mult(b, p5); |
| 816 | Bfree(b); |
| 817 | b = b1; |
| 818 | if (b == NULL) { |
| 819 | Bfree(p5); |
| 820 | return NULL; |
| 821 | } |
| 822 | } |
| 823 | if (!(k >>= 1)) |
| 824 | break; |
| 825 | p51 = mult(p5, p5); |
| 826 | Bfree(p5); |
| 827 | p5 = p51; |
| 828 | if (p5 == NULL) { |
| 829 | Bfree(b); |
| 830 | return NULL; |
| 831 | } |
| 832 | } |
| 833 | Bfree(p5); |
| 834 | return b; |
| 835 | } |
| 836 | |
| 837 | #endif /* Py_USING_MEMORY_DEBUGGER */ |
| 838 | |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 839 | /* shift a Bigint b left by k bits. Return a pointer to the shifted result, |
| 840 | or NULL on failure. If the returned pointer is distinct from b then the |
| 841 | original b will have been Bfree'd. Ignores the sign of b. */ |
| 842 | |
| 843 | static Bigint * |
| 844 | lshift(Bigint *b, int k) |
| 845 | { |
| 846 | int i, k1, n, n1; |
| 847 | Bigint *b1; |
| 848 | ULong *x, *x1, *xe, z; |
| 849 | |
Mark Dickinson | f41d29a | 2010-01-24 10:16:29 +0000 | [diff] [blame] | 850 | if (!k || (!b->x[0] && b->wds == 1)) |
| 851 | return b; |
| 852 | |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 853 | n = k >> 5; |
| 854 | k1 = b->k; |
| 855 | n1 = n + b->wds + 1; |
| 856 | for(i = b->maxwds; n1 > i; i <<= 1) |
| 857 | k1++; |
| 858 | b1 = Balloc(k1); |
| 859 | if (b1 == NULL) { |
| 860 | Bfree(b); |
| 861 | return NULL; |
| 862 | } |
| 863 | x1 = b1->x; |
| 864 | for(i = 0; i < n; i++) |
| 865 | *x1++ = 0; |
| 866 | x = b->x; |
| 867 | xe = x + b->wds; |
| 868 | if (k &= 0x1f) { |
| 869 | k1 = 32 - k; |
| 870 | z = 0; |
| 871 | do { |
| 872 | *x1++ = *x << k | z; |
| 873 | z = *x++ >> k1; |
| 874 | } |
| 875 | while(x < xe); |
| 876 | if ((*x1 = z)) |
| 877 | ++n1; |
| 878 | } |
| 879 | else do |
| 880 | *x1++ = *x++; |
| 881 | while(x < xe); |
| 882 | b1->wds = n1 - 1; |
| 883 | Bfree(b); |
| 884 | return b1; |
| 885 | } |
| 886 | |
| 887 | /* Do a three-way compare of a and b, returning -1 if a < b, 0 if a == b and |
| 888 | 1 if a > b. Ignores signs of a and b. */ |
| 889 | |
| 890 | static int |
| 891 | cmp(Bigint *a, Bigint *b) |
| 892 | { |
| 893 | ULong *xa, *xa0, *xb, *xb0; |
| 894 | int i, j; |
| 895 | |
| 896 | i = a->wds; |
| 897 | j = b->wds; |
| 898 | #ifdef DEBUG |
| 899 | if (i > 1 && !a->x[i-1]) |
| 900 | Bug("cmp called with a->x[a->wds-1] == 0"); |
| 901 | if (j > 1 && !b->x[j-1]) |
| 902 | Bug("cmp called with b->x[b->wds-1] == 0"); |
| 903 | #endif |
| 904 | if (i -= j) |
| 905 | return i; |
| 906 | xa0 = a->x; |
| 907 | xa = xa0 + j; |
| 908 | xb0 = b->x; |
| 909 | xb = xb0 + j; |
| 910 | for(;;) { |
| 911 | if (*--xa != *--xb) |
| 912 | return *xa < *xb ? -1 : 1; |
| 913 | if (xa <= xa0) |
| 914 | break; |
| 915 | } |
| 916 | return 0; |
| 917 | } |
| 918 | |
| 919 | /* Take the difference of Bigints a and b, returning a new Bigint. Returns |
| 920 | NULL on failure. The signs of a and b are ignored, but the sign of the |
| 921 | result is set appropriately. */ |
| 922 | |
| 923 | static Bigint * |
| 924 | diff(Bigint *a, Bigint *b) |
| 925 | { |
| 926 | Bigint *c; |
| 927 | int i, wa, wb; |
| 928 | ULong *xa, *xae, *xb, *xbe, *xc; |
| 929 | #ifdef ULLong |
| 930 | ULLong borrow, y; |
| 931 | #else |
| 932 | ULong borrow, y; |
| 933 | ULong z; |
| 934 | #endif |
| 935 | |
| 936 | i = cmp(a,b); |
| 937 | if (!i) { |
| 938 | c = Balloc(0); |
| 939 | if (c == NULL) |
| 940 | return NULL; |
| 941 | c->wds = 1; |
| 942 | c->x[0] = 0; |
| 943 | return c; |
| 944 | } |
| 945 | if (i < 0) { |
| 946 | c = a; |
| 947 | a = b; |
| 948 | b = c; |
| 949 | i = 1; |
| 950 | } |
| 951 | else |
| 952 | i = 0; |
| 953 | c = Balloc(a->k); |
| 954 | if (c == NULL) |
| 955 | return NULL; |
| 956 | c->sign = i; |
| 957 | wa = a->wds; |
| 958 | xa = a->x; |
| 959 | xae = xa + wa; |
| 960 | wb = b->wds; |
| 961 | xb = b->x; |
| 962 | xbe = xb + wb; |
| 963 | xc = c->x; |
| 964 | borrow = 0; |
| 965 | #ifdef ULLong |
| 966 | do { |
| 967 | y = (ULLong)*xa++ - *xb++ - borrow; |
| 968 | borrow = y >> 32 & (ULong)1; |
Mark Dickinson | fd2ad8b | 2009-04-17 19:29:46 +0000 | [diff] [blame] | 969 | *xc++ = (ULong)(y & FFFFFFFF); |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 970 | } |
| 971 | while(xb < xbe); |
| 972 | while(xa < xae) { |
| 973 | y = *xa++ - borrow; |
| 974 | borrow = y >> 32 & (ULong)1; |
Mark Dickinson | fd2ad8b | 2009-04-17 19:29:46 +0000 | [diff] [blame] | 975 | *xc++ = (ULong)(y & FFFFFFFF); |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 976 | } |
| 977 | #else |
| 978 | do { |
| 979 | y = (*xa & 0xffff) - (*xb & 0xffff) - borrow; |
| 980 | borrow = (y & 0x10000) >> 16; |
| 981 | z = (*xa++ >> 16) - (*xb++ >> 16) - borrow; |
| 982 | borrow = (z & 0x10000) >> 16; |
| 983 | Storeinc(xc, z, y); |
| 984 | } |
| 985 | while(xb < xbe); |
| 986 | while(xa < xae) { |
| 987 | y = (*xa & 0xffff) - borrow; |
| 988 | borrow = (y & 0x10000) >> 16; |
| 989 | z = (*xa++ >> 16) - borrow; |
| 990 | borrow = (z & 0x10000) >> 16; |
| 991 | Storeinc(xc, z, y); |
| 992 | } |
| 993 | #endif |
| 994 | while(!*--xc) |
| 995 | wa--; |
| 996 | c->wds = wa; |
| 997 | return c; |
| 998 | } |
| 999 | |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1000 | /* Given a positive normal double x, return the difference between x and the |
| 1001 | next double up. Doesn't give correct results for subnormals. */ |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1002 | |
| 1003 | static double |
| 1004 | ulp(U *x) |
| 1005 | { |
| 1006 | Long L; |
| 1007 | U u; |
| 1008 | |
| 1009 | L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1; |
| 1010 | word0(&u) = L; |
| 1011 | word1(&u) = 0; |
| 1012 | return dval(&u); |
| 1013 | } |
| 1014 | |
| 1015 | /* Convert a Bigint to a double plus an exponent */ |
| 1016 | |
| 1017 | static double |
| 1018 | b2d(Bigint *a, int *e) |
| 1019 | { |
| 1020 | ULong *xa, *xa0, w, y, z; |
| 1021 | int k; |
| 1022 | U d; |
| 1023 | |
| 1024 | xa0 = a->x; |
| 1025 | xa = xa0 + a->wds; |
| 1026 | y = *--xa; |
| 1027 | #ifdef DEBUG |
| 1028 | if (!y) Bug("zero y in b2d"); |
| 1029 | #endif |
| 1030 | k = hi0bits(y); |
| 1031 | *e = 32 - k; |
| 1032 | if (k < Ebits) { |
| 1033 | word0(&d) = Exp_1 | y >> (Ebits - k); |
| 1034 | w = xa > xa0 ? *--xa : 0; |
| 1035 | word1(&d) = y << ((32-Ebits) + k) | w >> (Ebits - k); |
| 1036 | goto ret_d; |
| 1037 | } |
| 1038 | z = xa > xa0 ? *--xa : 0; |
| 1039 | if (k -= Ebits) { |
| 1040 | word0(&d) = Exp_1 | y << k | z >> (32 - k); |
| 1041 | y = xa > xa0 ? *--xa : 0; |
| 1042 | word1(&d) = z << k | y >> (32 - k); |
| 1043 | } |
| 1044 | else { |
| 1045 | word0(&d) = Exp_1 | y; |
| 1046 | word1(&d) = z; |
| 1047 | } |
| 1048 | ret_d: |
| 1049 | return dval(&d); |
| 1050 | } |
| 1051 | |
Mark Dickinson | f41d29a | 2010-01-24 10:16:29 +0000 | [diff] [blame] | 1052 | /* Convert a scaled double to a Bigint plus an exponent. Similar to d2b, |
| 1053 | except that it accepts the scale parameter used in _Py_dg_strtod (which |
| 1054 | should be either 0 or 2*P), and the normalization for the return value is |
| 1055 | different (see below). On input, d should be finite and nonnegative, and d |
| 1056 | / 2**scale should be exactly representable as an IEEE 754 double. |
| 1057 | |
| 1058 | Returns a Bigint b and an integer e such that |
| 1059 | |
| 1060 | dval(d) / 2**scale = b * 2**e. |
| 1061 | |
| 1062 | Unlike d2b, b is not necessarily odd: b and e are normalized so |
| 1063 | that either 2**(P-1) <= b < 2**P and e >= Etiny, or b < 2**P |
| 1064 | and e == Etiny. This applies equally to an input of 0.0: in that |
| 1065 | case the return values are b = 0 and e = Etiny. |
| 1066 | |
| 1067 | The above normalization ensures that for all possible inputs d, |
| 1068 | 2**e gives ulp(d/2**scale). |
| 1069 | |
| 1070 | Returns NULL on failure. |
| 1071 | */ |
| 1072 | |
| 1073 | static Bigint * |
| 1074 | sd2b(U *d, int scale, int *e) |
| 1075 | { |
| 1076 | Bigint *b; |
| 1077 | |
| 1078 | b = Balloc(1); |
| 1079 | if (b == NULL) |
| 1080 | return NULL; |
Victor Stinner | 938b0b9 | 2015-03-18 15:01:44 +0100 | [diff] [blame] | 1081 | |
Mark Dickinson | f41d29a | 2010-01-24 10:16:29 +0000 | [diff] [blame] | 1082 | /* First construct b and e assuming that scale == 0. */ |
| 1083 | b->wds = 2; |
| 1084 | b->x[0] = word1(d); |
| 1085 | b->x[1] = word0(d) & Frac_mask; |
| 1086 | *e = Etiny - 1 + (int)((word0(d) & Exp_mask) >> Exp_shift); |
| 1087 | if (*e < Etiny) |
| 1088 | *e = Etiny; |
| 1089 | else |
| 1090 | b->x[1] |= Exp_msk1; |
| 1091 | |
| 1092 | /* Now adjust for scale, provided that b != 0. */ |
| 1093 | if (scale && (b->x[0] || b->x[1])) { |
| 1094 | *e -= scale; |
| 1095 | if (*e < Etiny) { |
| 1096 | scale = Etiny - *e; |
| 1097 | *e = Etiny; |
| 1098 | /* We can't shift more than P-1 bits without shifting out a 1. */ |
| 1099 | assert(0 < scale && scale <= P - 1); |
| 1100 | if (scale >= 32) { |
| 1101 | /* The bits shifted out should all be zero. */ |
| 1102 | assert(b->x[0] == 0); |
| 1103 | b->x[0] = b->x[1]; |
| 1104 | b->x[1] = 0; |
| 1105 | scale -= 32; |
| 1106 | } |
| 1107 | if (scale) { |
| 1108 | /* The bits shifted out should all be zero. */ |
| 1109 | assert(b->x[0] << (32 - scale) == 0); |
| 1110 | b->x[0] = (b->x[0] >> scale) | (b->x[1] << (32 - scale)); |
| 1111 | b->x[1] >>= scale; |
| 1112 | } |
| 1113 | } |
| 1114 | } |
| 1115 | /* Ensure b is normalized. */ |
| 1116 | if (!b->x[1]) |
| 1117 | b->wds = 1; |
| 1118 | |
| 1119 | return b; |
| 1120 | } |
| 1121 | |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1122 | /* Convert a double to a Bigint plus an exponent. Return NULL on failure. |
| 1123 | |
| 1124 | Given a finite nonzero double d, return an odd Bigint b and exponent *e |
| 1125 | such that fabs(d) = b * 2**e. On return, *bbits gives the number of |
Mark Dickinson | 180e4cd | 2010-01-04 21:33:31 +0000 | [diff] [blame] | 1126 | significant bits of b; that is, 2**(*bbits-1) <= b < 2**(*bbits). |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1127 | |
| 1128 | If d is zero, then b == 0, *e == -1010, *bbits = 0. |
| 1129 | */ |
| 1130 | |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1131 | static Bigint * |
| 1132 | d2b(U *d, int *e, int *bits) |
| 1133 | { |
| 1134 | Bigint *b; |
| 1135 | int de, k; |
| 1136 | ULong *x, y, z; |
| 1137 | int i; |
| 1138 | |
| 1139 | b = Balloc(1); |
| 1140 | if (b == NULL) |
| 1141 | return NULL; |
| 1142 | x = b->x; |
| 1143 | |
| 1144 | z = word0(d) & Frac_mask; |
| 1145 | word0(d) &= 0x7fffffff; /* clear sign bit, which we ignore */ |
| 1146 | if ((de = (int)(word0(d) >> Exp_shift))) |
| 1147 | z |= Exp_msk1; |
| 1148 | if ((y = word1(d))) { |
| 1149 | if ((k = lo0bits(&y))) { |
| 1150 | x[0] = y | z << (32 - k); |
| 1151 | z >>= k; |
| 1152 | } |
| 1153 | else |
| 1154 | x[0] = y; |
| 1155 | i = |
| 1156 | b->wds = (x[1] = z) ? 2 : 1; |
| 1157 | } |
| 1158 | else { |
| 1159 | k = lo0bits(&z); |
| 1160 | x[0] = z; |
| 1161 | i = |
| 1162 | b->wds = 1; |
| 1163 | k += 32; |
| 1164 | } |
| 1165 | if (de) { |
| 1166 | *e = de - Bias - (P-1) + k; |
| 1167 | *bits = P - k; |
| 1168 | } |
| 1169 | else { |
| 1170 | *e = de - Bias - (P-1) + 1 + k; |
| 1171 | *bits = 32*i - hi0bits(x[i-1]); |
| 1172 | } |
| 1173 | return b; |
| 1174 | } |
| 1175 | |
| 1176 | /* Compute the ratio of two Bigints, as a double. The result may have an |
| 1177 | error of up to 2.5 ulps. */ |
| 1178 | |
| 1179 | static double |
| 1180 | ratio(Bigint *a, Bigint *b) |
| 1181 | { |
| 1182 | U da, db; |
| 1183 | int k, ka, kb; |
| 1184 | |
| 1185 | dval(&da) = b2d(a, &ka); |
| 1186 | dval(&db) = b2d(b, &kb); |
| 1187 | k = ka - kb + 32*(a->wds - b->wds); |
| 1188 | if (k > 0) |
| 1189 | word0(&da) += k*Exp_msk1; |
| 1190 | else { |
| 1191 | k = -k; |
| 1192 | word0(&db) += k*Exp_msk1; |
| 1193 | } |
| 1194 | return dval(&da) / dval(&db); |
| 1195 | } |
| 1196 | |
| 1197 | static const double |
| 1198 | tens[] = { |
| 1199 | 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, |
| 1200 | 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, |
| 1201 | 1e20, 1e21, 1e22 |
| 1202 | }; |
| 1203 | |
| 1204 | static const double |
| 1205 | bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 }; |
| 1206 | static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, |
| 1207 | 9007199254740992.*9007199254740992.e-256 |
| 1208 | /* = 2^106 * 1e-256 */ |
| 1209 | }; |
| 1210 | /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */ |
| 1211 | /* flag unnecessarily. It leads to a song and dance at the end of strtod. */ |
| 1212 | #define Scale_Bit 0x10 |
| 1213 | #define n_bigtens 5 |
| 1214 | |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1215 | #define ULbits 32 |
| 1216 | #define kshift 5 |
| 1217 | #define kmask 31 |
| 1218 | |
| 1219 | |
| 1220 | static int |
| 1221 | dshift(Bigint *b, int p2) |
| 1222 | { |
| 1223 | int rv = hi0bits(b->x[b->wds-1]) - 4; |
| 1224 | if (p2 > 0) |
| 1225 | rv -= p2; |
| 1226 | return rv & kmask; |
| 1227 | } |
| 1228 | |
| 1229 | /* special case of Bigint division. The quotient is always in the range 0 <= |
| 1230 | quotient < 10, and on entry the divisor S is normalized so that its top 4 |
| 1231 | bits (28--31) are zero and bit 27 is set. */ |
| 1232 | |
| 1233 | static int |
| 1234 | quorem(Bigint *b, Bigint *S) |
| 1235 | { |
| 1236 | int n; |
| 1237 | ULong *bx, *bxe, q, *sx, *sxe; |
| 1238 | #ifdef ULLong |
| 1239 | ULLong borrow, carry, y, ys; |
| 1240 | #else |
| 1241 | ULong borrow, carry, y, ys; |
| 1242 | ULong si, z, zs; |
| 1243 | #endif |
| 1244 | |
| 1245 | n = S->wds; |
| 1246 | #ifdef DEBUG |
| 1247 | /*debug*/ if (b->wds > n) |
| 1248 | /*debug*/ Bug("oversize b in quorem"); |
| 1249 | #endif |
| 1250 | if (b->wds < n) |
| 1251 | return 0; |
| 1252 | sx = S->x; |
| 1253 | sxe = sx + --n; |
| 1254 | bx = b->x; |
| 1255 | bxe = bx + n; |
| 1256 | q = *bxe / (*sxe + 1); /* ensure q <= true quotient */ |
| 1257 | #ifdef DEBUG |
| 1258 | /*debug*/ if (q > 9) |
| 1259 | /*debug*/ Bug("oversized quotient in quorem"); |
| 1260 | #endif |
| 1261 | if (q) { |
| 1262 | borrow = 0; |
| 1263 | carry = 0; |
| 1264 | do { |
| 1265 | #ifdef ULLong |
| 1266 | ys = *sx++ * (ULLong)q + carry; |
| 1267 | carry = ys >> 32; |
| 1268 | y = *bx - (ys & FFFFFFFF) - borrow; |
| 1269 | borrow = y >> 32 & (ULong)1; |
Mark Dickinson | fd2ad8b | 2009-04-17 19:29:46 +0000 | [diff] [blame] | 1270 | *bx++ = (ULong)(y & FFFFFFFF); |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1271 | #else |
| 1272 | si = *sx++; |
| 1273 | ys = (si & 0xffff) * q + carry; |
| 1274 | zs = (si >> 16) * q + (ys >> 16); |
| 1275 | carry = zs >> 16; |
| 1276 | y = (*bx & 0xffff) - (ys & 0xffff) - borrow; |
| 1277 | borrow = (y & 0x10000) >> 16; |
| 1278 | z = (*bx >> 16) - (zs & 0xffff) - borrow; |
| 1279 | borrow = (z & 0x10000) >> 16; |
| 1280 | Storeinc(bx, z, y); |
| 1281 | #endif |
| 1282 | } |
| 1283 | while(sx <= sxe); |
| 1284 | if (!*bxe) { |
| 1285 | bx = b->x; |
| 1286 | while(--bxe > bx && !*bxe) |
| 1287 | --n; |
| 1288 | b->wds = n; |
| 1289 | } |
| 1290 | } |
| 1291 | if (cmp(b, S) >= 0) { |
| 1292 | q++; |
| 1293 | borrow = 0; |
| 1294 | carry = 0; |
| 1295 | bx = b->x; |
| 1296 | sx = S->x; |
| 1297 | do { |
| 1298 | #ifdef ULLong |
| 1299 | ys = *sx++ + carry; |
| 1300 | carry = ys >> 32; |
| 1301 | y = *bx - (ys & FFFFFFFF) - borrow; |
| 1302 | borrow = y >> 32 & (ULong)1; |
Mark Dickinson | fd2ad8b | 2009-04-17 19:29:46 +0000 | [diff] [blame] | 1303 | *bx++ = (ULong)(y & FFFFFFFF); |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1304 | #else |
| 1305 | si = *sx++; |
| 1306 | ys = (si & 0xffff) + carry; |
| 1307 | zs = (si >> 16) + (ys >> 16); |
| 1308 | carry = zs >> 16; |
| 1309 | y = (*bx & 0xffff) - (ys & 0xffff) - borrow; |
| 1310 | borrow = (y & 0x10000) >> 16; |
| 1311 | z = (*bx >> 16) - (zs & 0xffff) - borrow; |
| 1312 | borrow = (z & 0x10000) >> 16; |
| 1313 | Storeinc(bx, z, y); |
| 1314 | #endif |
| 1315 | } |
| 1316 | while(sx <= sxe); |
| 1317 | bx = b->x; |
| 1318 | bxe = bx + n; |
| 1319 | if (!*bxe) { |
| 1320 | while(--bxe > bx && !*bxe) |
| 1321 | --n; |
| 1322 | b->wds = n; |
| 1323 | } |
| 1324 | } |
| 1325 | return q; |
| 1326 | } |
| 1327 | |
Mark Dickinson | 853c3bb | 2010-01-14 15:37:49 +0000 | [diff] [blame] | 1328 | /* sulp(x) is a version of ulp(x) that takes bc.scale into account. |
Mark Dickinson | 81612e8 | 2010-01-12 23:04:19 +0000 | [diff] [blame] | 1329 | |
Mark Dickinson | 853c3bb | 2010-01-14 15:37:49 +0000 | [diff] [blame] | 1330 | Assuming that x is finite and nonnegative (positive zero is fine |
| 1331 | here) and x / 2^bc.scale is exactly representable as a double, |
| 1332 | sulp(x) is equivalent to 2^bc.scale * ulp(x / 2^bc.scale). */ |
Mark Dickinson | 81612e8 | 2010-01-12 23:04:19 +0000 | [diff] [blame] | 1333 | |
| 1334 | static double |
| 1335 | sulp(U *x, BCinfo *bc) |
| 1336 | { |
| 1337 | U u; |
| 1338 | |
Mark Dickinson | 853c3bb | 2010-01-14 15:37:49 +0000 | [diff] [blame] | 1339 | if (bc->scale && 2*P + 1 > (int)((word0(x) & Exp_mask) >> Exp_shift)) { |
Mark Dickinson | 81612e8 | 2010-01-12 23:04:19 +0000 | [diff] [blame] | 1340 | /* rv/2^bc->scale is subnormal */ |
| 1341 | word0(&u) = (P+2)*Exp_msk1; |
| 1342 | word1(&u) = 0; |
| 1343 | return u.d; |
| 1344 | } |
Mark Dickinson | 853c3bb | 2010-01-14 15:37:49 +0000 | [diff] [blame] | 1345 | else { |
| 1346 | assert(word0(x) || word1(x)); /* x != 0.0 */ |
Mark Dickinson | 81612e8 | 2010-01-12 23:04:19 +0000 | [diff] [blame] | 1347 | return ulp(x); |
Mark Dickinson | 853c3bb | 2010-01-14 15:37:49 +0000 | [diff] [blame] | 1348 | } |
Mark Dickinson | 81612e8 | 2010-01-12 23:04:19 +0000 | [diff] [blame] | 1349 | } |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1350 | |
Mark Dickinson | 853c3bb | 2010-01-14 15:37:49 +0000 | [diff] [blame] | 1351 | /* The bigcomp function handles some hard cases for strtod, for inputs |
| 1352 | with more than STRTOD_DIGLIM digits. It's called once an initial |
| 1353 | estimate for the double corresponding to the input string has |
| 1354 | already been obtained by the code in _Py_dg_strtod. |
| 1355 | |
| 1356 | The bigcomp function is only called after _Py_dg_strtod has found a |
| 1357 | double value rv such that either rv or rv + 1ulp represents the |
| 1358 | correctly rounded value corresponding to the original string. It |
| 1359 | determines which of these two values is the correct one by |
| 1360 | computing the decimal digits of rv + 0.5ulp and comparing them with |
| 1361 | the corresponding digits of s0. |
| 1362 | |
| 1363 | In the following, write dv for the absolute value of the number represented |
| 1364 | by the input string. |
| 1365 | |
| 1366 | Inputs: |
| 1367 | |
| 1368 | s0 points to the first significant digit of the input string. |
| 1369 | |
| 1370 | rv is a (possibly scaled) estimate for the closest double value to the |
| 1371 | value represented by the original input to _Py_dg_strtod. If |
| 1372 | bc->scale is nonzero, then rv/2^(bc->scale) is the approximation to |
| 1373 | the input value. |
| 1374 | |
| 1375 | bc is a struct containing information gathered during the parsing and |
| 1376 | estimation steps of _Py_dg_strtod. Description of fields follows: |
| 1377 | |
Mark Dickinson | 853c3bb | 2010-01-14 15:37:49 +0000 | [diff] [blame] | 1378 | bc->e0 gives the exponent of the input value, such that dv = (integer |
| 1379 | given by the bd->nd digits of s0) * 10**e0 |
| 1380 | |
| 1381 | bc->nd gives the total number of significant digits of s0. It will |
| 1382 | be at least 1. |
| 1383 | |
| 1384 | bc->nd0 gives the number of significant digits of s0 before the |
| 1385 | decimal separator. If there's no decimal separator, bc->nd0 == |
| 1386 | bc->nd. |
| 1387 | |
| 1388 | bc->scale is the value used to scale rv to avoid doing arithmetic with |
| 1389 | subnormal values. It's either 0 or 2*P (=106). |
| 1390 | |
| 1391 | Outputs: |
| 1392 | |
| 1393 | On successful exit, rv/2^(bc->scale) is the closest double to dv. |
| 1394 | |
| 1395 | Returns 0 on success, -1 on failure (e.g., due to a failed malloc call). */ |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1396 | |
| 1397 | static int |
| 1398 | bigcomp(U *rv, const char *s0, BCinfo *bc) |
| 1399 | { |
| 1400 | Bigint *b, *d; |
Mark Dickinson | f41d29a | 2010-01-24 10:16:29 +0000 | [diff] [blame] | 1401 | int b2, d2, dd, i, nd, nd0, odd, p2, p5; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1402 | |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1403 | nd = bc->nd; |
| 1404 | nd0 = bc->nd0; |
Mark Dickinson | 81612e8 | 2010-01-12 23:04:19 +0000 | [diff] [blame] | 1405 | p5 = nd + bc->e0; |
Mark Dickinson | f41d29a | 2010-01-24 10:16:29 +0000 | [diff] [blame] | 1406 | b = sd2b(rv, bc->scale, &p2); |
Mark Dickinson | 853c3bb | 2010-01-14 15:37:49 +0000 | [diff] [blame] | 1407 | if (b == NULL) |
| 1408 | return -1; |
Mark Dickinson | f41d29a | 2010-01-24 10:16:29 +0000 | [diff] [blame] | 1409 | |
Mark Dickinson | 853c3bb | 2010-01-14 15:37:49 +0000 | [diff] [blame] | 1410 | /* record whether the lsb of rv/2^(bc->scale) is odd: in the exact halfway |
| 1411 | case, this is used for round to even. */ |
Mark Dickinson | f41d29a | 2010-01-24 10:16:29 +0000 | [diff] [blame] | 1412 | odd = b->x[0] & 1; |
Mark Dickinson | 853c3bb | 2010-01-14 15:37:49 +0000 | [diff] [blame] | 1413 | |
Mark Dickinson | f41d29a | 2010-01-24 10:16:29 +0000 | [diff] [blame] | 1414 | /* left shift b by 1 bit and or a 1 into the least significant bit; |
| 1415 | this gives us b * 2**p2 = rv/2^(bc->scale) + 0.5 ulp. */ |
| 1416 | b = lshift(b, 1); |
| 1417 | if (b == NULL) |
| 1418 | return -1; |
| 1419 | b->x[0] |= 1; |
| 1420 | p2--; |
| 1421 | |
| 1422 | p2 -= p5; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1423 | d = i2b(1); |
| 1424 | if (d == NULL) { |
| 1425 | Bfree(b); |
| 1426 | return -1; |
| 1427 | } |
| 1428 | /* Arrange for convenient computation of quotients: |
| 1429 | * shift left if necessary so divisor has 4 leading 0 bits. |
| 1430 | */ |
| 1431 | if (p5 > 0) { |
| 1432 | d = pow5mult(d, p5); |
| 1433 | if (d == NULL) { |
| 1434 | Bfree(b); |
| 1435 | return -1; |
| 1436 | } |
| 1437 | } |
| 1438 | else if (p5 < 0) { |
| 1439 | b = pow5mult(b, -p5); |
| 1440 | if (b == NULL) { |
| 1441 | Bfree(d); |
| 1442 | return -1; |
| 1443 | } |
| 1444 | } |
| 1445 | if (p2 > 0) { |
| 1446 | b2 = p2; |
| 1447 | d2 = 0; |
| 1448 | } |
| 1449 | else { |
| 1450 | b2 = 0; |
| 1451 | d2 = -p2; |
| 1452 | } |
| 1453 | i = dshift(d, d2); |
| 1454 | if ((b2 += i) > 0) { |
| 1455 | b = lshift(b, b2); |
| 1456 | if (b == NULL) { |
| 1457 | Bfree(d); |
| 1458 | return -1; |
| 1459 | } |
| 1460 | } |
| 1461 | if ((d2 += i) > 0) { |
| 1462 | d = lshift(d, d2); |
| 1463 | if (d == NULL) { |
| 1464 | Bfree(b); |
| 1465 | return -1; |
| 1466 | } |
| 1467 | } |
| 1468 | |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1469 | /* Compare s0 with b/d: set dd to -1, 0, or 1 according as s0 < b/d, s0 == |
| 1470 | * b/d, or s0 > b/d. Here the digits of s0 are thought of as representing |
| 1471 | * a number in the range [0.1, 1). */ |
| 1472 | if (cmp(b, d) >= 0) |
| 1473 | /* b/d >= 1 */ |
Mark Dickinson | 81612e8 | 2010-01-12 23:04:19 +0000 | [diff] [blame] | 1474 | dd = -1; |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1475 | else { |
| 1476 | i = 0; |
| 1477 | for(;;) { |
| 1478 | b = multadd(b, 10, 0); |
| 1479 | if (b == NULL) { |
| 1480 | Bfree(d); |
| 1481 | return -1; |
| 1482 | } |
| 1483 | dd = s0[i < nd0 ? i : i+1] - '0' - quorem(b, d); |
| 1484 | i++; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1485 | |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1486 | if (dd) |
| 1487 | break; |
| 1488 | if (!b->x[0] && b->wds == 1) { |
| 1489 | /* b/d == 0 */ |
| 1490 | dd = i < nd; |
| 1491 | break; |
| 1492 | } |
| 1493 | if (!(i < nd)) { |
| 1494 | /* b/d != 0, but digits of s0 exhausted */ |
| 1495 | dd = -1; |
| 1496 | break; |
| 1497 | } |
Mark Dickinson | 853c3bb | 2010-01-14 15:37:49 +0000 | [diff] [blame] | 1498 | } |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1499 | } |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1500 | Bfree(b); |
| 1501 | Bfree(d); |
Mark Dickinson | 853c3bb | 2010-01-14 15:37:49 +0000 | [diff] [blame] | 1502 | if (dd > 0 || (dd == 0 && odd)) |
| 1503 | dval(rv) += sulp(rv, bc); |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1504 | return 0; |
| 1505 | } |
| 1506 | |
Mark Dickinson | e383e82 | 2012-04-29 15:31:56 +0100 | [diff] [blame] | 1507 | /* Return a 'standard' NaN value. |
| 1508 | |
| 1509 | There are exactly two quiet NaNs that don't arise by 'quieting' signaling |
| 1510 | NaNs (see IEEE 754-2008, section 6.2.1). If sign == 0, return the one whose |
| 1511 | sign bit is cleared. Otherwise, return the one whose sign bit is set. |
| 1512 | */ |
| 1513 | |
| 1514 | double |
| 1515 | _Py_dg_stdnan(int sign) |
| 1516 | { |
| 1517 | U rv; |
| 1518 | word0(&rv) = NAN_WORD0; |
| 1519 | word1(&rv) = NAN_WORD1; |
| 1520 | if (sign) |
| 1521 | word0(&rv) |= Sign_bit; |
| 1522 | return dval(&rv); |
| 1523 | } |
| 1524 | |
| 1525 | /* Return positive or negative infinity, according to the given sign (0 for |
| 1526 | * positive infinity, 1 for negative infinity). */ |
| 1527 | |
| 1528 | double |
| 1529 | _Py_dg_infinity(int sign) |
| 1530 | { |
| 1531 | U rv; |
| 1532 | word0(&rv) = POSINF_WORD0; |
| 1533 | word1(&rv) = POSINF_WORD1; |
| 1534 | return sign ? -dval(&rv) : dval(&rv); |
| 1535 | } |
| 1536 | |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1537 | double |
| 1538 | _Py_dg_strtod(const char *s00, char **se) |
| 1539 | { |
Mark Dickinson | f41d29a | 2010-01-24 10:16:29 +0000 | [diff] [blame] | 1540 | int bb2, bb5, bbe, bd2, bd5, bs2, c, dsign, e, e1, error; |
| 1541 | int esign, i, j, k, lz, nd, nd0, odd, sign; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1542 | const char *s, *s0, *s1; |
| 1543 | double aadj, aadj1; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1544 | U aadj2, adj, rv, rv0; |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1545 | ULong y, z, abs_exp; |
Mark Dickinson | 45b6365 | 2010-01-16 18:10:25 +0000 | [diff] [blame] | 1546 | Long L; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1547 | BCinfo bc; |
| 1548 | Bigint *bb, *bb1, *bd, *bd0, *bs, *delta; |
Mark Dickinson | f45bbb6 | 2013-11-26 16:19:13 +0000 | [diff] [blame] | 1549 | size_t ndigits, fraclen; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1550 | |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1551 | dval(&rv) = 0.; |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1552 | |
| 1553 | /* Start parsing. */ |
| 1554 | c = *(s = s00); |
| 1555 | |
| 1556 | /* Parse optional sign, if present. */ |
| 1557 | sign = 0; |
| 1558 | switch (c) { |
| 1559 | case '-': |
| 1560 | sign = 1; |
| 1561 | /* no break */ |
| 1562 | case '+': |
| 1563 | c = *++s; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1564 | } |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1565 | |
| 1566 | /* Skip leading zeros: lz is true iff there were leading zeros. */ |
| 1567 | s1 = s; |
| 1568 | while (c == '0') |
| 1569 | c = *++s; |
| 1570 | lz = s != s1; |
| 1571 | |
Mark Dickinson | f45bbb6 | 2013-11-26 16:19:13 +0000 | [diff] [blame] | 1572 | /* Point s0 at the first nonzero digit (if any). fraclen will be the |
| 1573 | number of digits between the decimal point and the end of the |
| 1574 | digit string. ndigits will be the total number of digits ignoring |
| 1575 | leading zeros. */ |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1576 | s0 = s1 = s; |
| 1577 | while ('0' <= c && c <= '9') |
| 1578 | c = *++s; |
Mark Dickinson | f45bbb6 | 2013-11-26 16:19:13 +0000 | [diff] [blame] | 1579 | ndigits = s - s1; |
| 1580 | fraclen = 0; |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1581 | |
| 1582 | /* Parse decimal point and following digits. */ |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1583 | if (c == '.') { |
| 1584 | c = *++s; |
Mark Dickinson | f45bbb6 | 2013-11-26 16:19:13 +0000 | [diff] [blame] | 1585 | if (!ndigits) { |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1586 | s1 = s; |
| 1587 | while (c == '0') |
| 1588 | c = *++s; |
| 1589 | lz = lz || s != s1; |
Mark Dickinson | f45bbb6 | 2013-11-26 16:19:13 +0000 | [diff] [blame] | 1590 | fraclen += (s - s1); |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1591 | s0 = s; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1592 | } |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1593 | s1 = s; |
| 1594 | while ('0' <= c && c <= '9') |
| 1595 | c = *++s; |
Mark Dickinson | f45bbb6 | 2013-11-26 16:19:13 +0000 | [diff] [blame] | 1596 | ndigits += s - s1; |
| 1597 | fraclen += s - s1; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1598 | } |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1599 | |
Mark Dickinson | f45bbb6 | 2013-11-26 16:19:13 +0000 | [diff] [blame] | 1600 | /* Now lz is true if and only if there were leading zero digits, and |
| 1601 | ndigits gives the total number of digits ignoring leading zeros. A |
| 1602 | valid input must have at least one digit. */ |
| 1603 | if (!ndigits && !lz) { |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1604 | if (se) |
| 1605 | *se = (char *)s00; |
| 1606 | goto parse_error; |
| 1607 | } |
| 1608 | |
Mark Dickinson | f45bbb6 | 2013-11-26 16:19:13 +0000 | [diff] [blame] | 1609 | /* Range check ndigits and fraclen to make sure that they, and values |
| 1610 | computed with them, can safely fit in an int. */ |
| 1611 | if (ndigits > MAX_DIGITS || fraclen > MAX_DIGITS) { |
| 1612 | if (se) |
| 1613 | *se = (char *)s00; |
| 1614 | goto parse_error; |
| 1615 | } |
| 1616 | nd = (int)ndigits; |
| 1617 | nd0 = (int)ndigits - (int)fraclen; |
| 1618 | |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1619 | /* Parse exponent. */ |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1620 | e = 0; |
| 1621 | if (c == 'e' || c == 'E') { |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1622 | s00 = s; |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1623 | c = *++s; |
| 1624 | |
| 1625 | /* Exponent sign. */ |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1626 | esign = 0; |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1627 | switch (c) { |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1628 | case '-': |
| 1629 | esign = 1; |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1630 | /* no break */ |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1631 | case '+': |
| 1632 | c = *++s; |
| 1633 | } |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1634 | |
| 1635 | /* Skip zeros. lz is true iff there are leading zeros. */ |
| 1636 | s1 = s; |
| 1637 | while (c == '0') |
| 1638 | c = *++s; |
| 1639 | lz = s != s1; |
| 1640 | |
| 1641 | /* Get absolute value of the exponent. */ |
| 1642 | s1 = s; |
| 1643 | abs_exp = 0; |
| 1644 | while ('0' <= c && c <= '9') { |
| 1645 | abs_exp = 10*abs_exp + (c - '0'); |
| 1646 | c = *++s; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1647 | } |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1648 | |
| 1649 | /* abs_exp will be correct modulo 2**32. But 10**9 < 2**32, so if |
| 1650 | there are at most 9 significant exponent digits then overflow is |
| 1651 | impossible. */ |
| 1652 | if (s - s1 > 9 || abs_exp > MAX_ABS_EXP) |
| 1653 | e = (int)MAX_ABS_EXP; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1654 | else |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1655 | e = (int)abs_exp; |
| 1656 | if (esign) |
| 1657 | e = -e; |
| 1658 | |
| 1659 | /* A valid exponent must have at least one digit. */ |
| 1660 | if (s == s1 && !lz) |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1661 | s = s00; |
| 1662 | } |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1663 | |
| 1664 | /* Adjust exponent to take into account position of the point. */ |
| 1665 | e -= nd - nd0; |
| 1666 | if (nd0 <= 0) |
Mark Dickinson | 45b6365 | 2010-01-16 18:10:25 +0000 | [diff] [blame] | 1667 | nd0 = nd; |
| 1668 | |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1669 | /* Finished parsing. Set se to indicate how far we parsed */ |
| 1670 | if (se) |
| 1671 | *se = (char *)s; |
| 1672 | |
| 1673 | /* If all digits were zero, exit with return value +-0.0. Otherwise, |
| 1674 | strip trailing zeros: scan back until we hit a nonzero digit. */ |
| 1675 | if (!nd) |
| 1676 | goto ret; |
Mark Dickinson | 45b6365 | 2010-01-16 18:10:25 +0000 | [diff] [blame] | 1677 | for (i = nd; i > 0; ) { |
Mark Dickinson | 45b6365 | 2010-01-16 18:10:25 +0000 | [diff] [blame] | 1678 | --i; |
| 1679 | if (s0[i < nd0 ? i : i+1] != '0') { |
| 1680 | ++i; |
| 1681 | break; |
| 1682 | } |
| 1683 | } |
| 1684 | e += nd - i; |
| 1685 | nd = i; |
| 1686 | if (nd0 > nd) |
| 1687 | nd0 = nd; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1688 | |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1689 | /* Summary of parsing results. After parsing, and dealing with zero |
| 1690 | * inputs, we have values s0, nd0, nd, e, sign, where: |
Mark Dickinson | 45b6365 | 2010-01-16 18:10:25 +0000 | [diff] [blame] | 1691 | * |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1692 | * - s0 points to the first significant digit of the input string |
Mark Dickinson | 45b6365 | 2010-01-16 18:10:25 +0000 | [diff] [blame] | 1693 | * |
| 1694 | * - nd is the total number of significant digits (here, and |
| 1695 | * below, 'significant digits' means the set of digits of the |
| 1696 | * significand of the input that remain after ignoring leading |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1697 | * and trailing zeros). |
Mark Dickinson | 45b6365 | 2010-01-16 18:10:25 +0000 | [diff] [blame] | 1698 | * |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1699 | * - nd0 indicates the position of the decimal point, if present; it |
| 1700 | * satisfies 1 <= nd0 <= nd. The nd significant digits are in |
| 1701 | * s0[0:nd0] and s0[nd0+1:nd+1] using the usual Python half-open slice |
| 1702 | * notation. (If nd0 < nd, then s0[nd0] contains a '.' character; if |
| 1703 | * nd0 == nd, then s0[nd0] could be any non-digit character.) |
Mark Dickinson | 45b6365 | 2010-01-16 18:10:25 +0000 | [diff] [blame] | 1704 | * |
| 1705 | * - e is the adjusted exponent: the absolute value of the number |
| 1706 | * represented by the original input string is n * 10**e, where |
| 1707 | * n is the integer represented by the concatenation of |
| 1708 | * s0[0:nd0] and s0[nd0+1:nd+1] |
| 1709 | * |
| 1710 | * - sign gives the sign of the input: 1 for negative, 0 for positive |
| 1711 | * |
| 1712 | * - the first and last significant digits are nonzero |
| 1713 | */ |
| 1714 | |
| 1715 | /* put first DBL_DIG+1 digits into integer y and z. |
| 1716 | * |
| 1717 | * - y contains the value represented by the first min(9, nd) |
| 1718 | * significant digits |
| 1719 | * |
| 1720 | * - if nd > 9, z contains the value represented by significant digits |
| 1721 | * with indices in [9, min(16, nd)). So y * 10**(min(16, nd) - 9) + z |
| 1722 | * gives the value represented by the first min(16, nd) sig. digits. |
| 1723 | */ |
| 1724 | |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1725 | bc.e0 = e1 = e; |
Mark Dickinson | 45b6365 | 2010-01-16 18:10:25 +0000 | [diff] [blame] | 1726 | y = z = 0; |
| 1727 | for (i = 0; i < nd; i++) { |
| 1728 | if (i < 9) |
| 1729 | y = 10*y + s0[i < nd0 ? i : i+1] - '0'; |
| 1730 | else if (i < DBL_DIG+1) |
| 1731 | z = 10*z + s0[i < nd0 ? i : i+1] - '0'; |
| 1732 | else |
| 1733 | break; |
| 1734 | } |
| 1735 | |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1736 | k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1; |
| 1737 | dval(&rv) = y; |
| 1738 | if (k > 9) { |
| 1739 | dval(&rv) = tens[k - 9] * dval(&rv) + z; |
| 1740 | } |
| 1741 | bd0 = 0; |
| 1742 | if (nd <= DBL_DIG |
| 1743 | && Flt_Rounds == 1 |
| 1744 | ) { |
| 1745 | if (!e) |
| 1746 | goto ret; |
| 1747 | if (e > 0) { |
| 1748 | if (e <= Ten_pmax) { |
| 1749 | dval(&rv) *= tens[e]; |
| 1750 | goto ret; |
| 1751 | } |
| 1752 | i = DBL_DIG - nd; |
| 1753 | if (e <= Ten_pmax + i) { |
| 1754 | /* A fancier test would sometimes let us do |
| 1755 | * this for larger i values. |
| 1756 | */ |
| 1757 | e -= i; |
| 1758 | dval(&rv) *= tens[i]; |
| 1759 | dval(&rv) *= tens[e]; |
| 1760 | goto ret; |
| 1761 | } |
| 1762 | } |
| 1763 | else if (e >= -Ten_pmax) { |
| 1764 | dval(&rv) /= tens[-e]; |
| 1765 | goto ret; |
| 1766 | } |
| 1767 | } |
| 1768 | e1 += nd - k; |
| 1769 | |
| 1770 | bc.scale = 0; |
| 1771 | |
| 1772 | /* Get starting approximation = rv * 10**e1 */ |
| 1773 | |
| 1774 | if (e1 > 0) { |
| 1775 | if ((i = e1 & 15)) |
| 1776 | dval(&rv) *= tens[i]; |
| 1777 | if (e1 &= ~15) { |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1778 | if (e1 > DBL_MAX_10_EXP) |
| 1779 | goto ovfl; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1780 | e1 >>= 4; |
| 1781 | for(j = 0; e1 > 1; j++, e1 >>= 1) |
| 1782 | if (e1 & 1) |
| 1783 | dval(&rv) *= bigtens[j]; |
| 1784 | /* The last multiplication could overflow. */ |
| 1785 | word0(&rv) -= P*Exp_msk1; |
| 1786 | dval(&rv) *= bigtens[j]; |
| 1787 | if ((z = word0(&rv) & Exp_mask) |
| 1788 | > Exp_msk1*(DBL_MAX_EXP+Bias-P)) |
| 1789 | goto ovfl; |
| 1790 | if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) { |
| 1791 | /* set to largest number */ |
| 1792 | /* (Can't trust DBL_MAX) */ |
| 1793 | word0(&rv) = Big0; |
| 1794 | word1(&rv) = Big1; |
| 1795 | } |
| 1796 | else |
| 1797 | word0(&rv) += P*Exp_msk1; |
| 1798 | } |
| 1799 | } |
| 1800 | else if (e1 < 0) { |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1801 | /* The input decimal value lies in [10**e1, 10**(e1+16)). |
| 1802 | |
| 1803 | If e1 <= -512, underflow immediately. |
| 1804 | If e1 <= -256, set bc.scale to 2*P. |
| 1805 | |
| 1806 | So for input value < 1e-256, bc.scale is always set; |
| 1807 | for input value >= 1e-240, bc.scale is never set. |
| 1808 | For input values in [1e-256, 1e-240), bc.scale may or may |
| 1809 | not be set. */ |
| 1810 | |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1811 | e1 = -e1; |
| 1812 | if ((i = e1 & 15)) |
| 1813 | dval(&rv) /= tens[i]; |
| 1814 | if (e1 >>= 4) { |
| 1815 | if (e1 >= 1 << n_bigtens) |
| 1816 | goto undfl; |
| 1817 | if (e1 & Scale_Bit) |
| 1818 | bc.scale = 2*P; |
| 1819 | for(j = 0; e1 > 0; j++, e1 >>= 1) |
| 1820 | if (e1 & 1) |
| 1821 | dval(&rv) *= tinytens[j]; |
| 1822 | if (bc.scale && (j = 2*P + 1 - ((word0(&rv) & Exp_mask) |
| 1823 | >> Exp_shift)) > 0) { |
| 1824 | /* scaled rv is denormal; clear j low bits */ |
| 1825 | if (j >= 32) { |
| 1826 | word1(&rv) = 0; |
| 1827 | if (j >= 53) |
| 1828 | word0(&rv) = (P+2)*Exp_msk1; |
| 1829 | else |
| 1830 | word0(&rv) &= 0xffffffff << (j-32); |
| 1831 | } |
| 1832 | else |
| 1833 | word1(&rv) &= 0xffffffff << j; |
| 1834 | } |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1835 | if (!dval(&rv)) |
| 1836 | goto undfl; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1837 | } |
| 1838 | } |
| 1839 | |
| 1840 | /* Now the hard part -- adjusting rv to the correct value.*/ |
| 1841 | |
| 1842 | /* Put digits into bd: true value = bd * 10^e */ |
| 1843 | |
| 1844 | bc.nd = nd; |
Mark Dickinson | 81612e8 | 2010-01-12 23:04:19 +0000 | [diff] [blame] | 1845 | bc.nd0 = nd0; /* Only needed if nd > STRTOD_DIGLIM, but done here */ |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1846 | /* to silence an erroneous warning about bc.nd0 */ |
| 1847 | /* possibly not being initialized. */ |
Mark Dickinson | 81612e8 | 2010-01-12 23:04:19 +0000 | [diff] [blame] | 1848 | if (nd > STRTOD_DIGLIM) { |
| 1849 | /* ASSERT(STRTOD_DIGLIM >= 18); 18 == one more than the */ |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1850 | /* minimum number of decimal digits to distinguish double values */ |
| 1851 | /* in IEEE arithmetic. */ |
Mark Dickinson | 45b6365 | 2010-01-16 18:10:25 +0000 | [diff] [blame] | 1852 | |
| 1853 | /* Truncate input to 18 significant digits, then discard any trailing |
| 1854 | zeros on the result by updating nd, nd0, e and y suitably. (There's |
| 1855 | no need to update z; it's not reused beyond this point.) */ |
| 1856 | for (i = 18; i > 0; ) { |
| 1857 | /* scan back until we hit a nonzero digit. significant digit 'i' |
| 1858 | is s0[i] if i < nd0, s0[i+1] if i >= nd0. */ |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1859 | --i; |
Mark Dickinson | 45b6365 | 2010-01-16 18:10:25 +0000 | [diff] [blame] | 1860 | if (s0[i < nd0 ? i : i+1] != '0') { |
| 1861 | ++i; |
| 1862 | break; |
| 1863 | } |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1864 | } |
| 1865 | e += nd - i; |
| 1866 | nd = i; |
| 1867 | if (nd0 > nd) |
| 1868 | nd0 = nd; |
| 1869 | if (nd < 9) { /* must recompute y */ |
| 1870 | y = 0; |
| 1871 | for(i = 0; i < nd0; ++i) |
| 1872 | y = 10*y + s0[i] - '0'; |
Mark Dickinson | 45b6365 | 2010-01-16 18:10:25 +0000 | [diff] [blame] | 1873 | for(; i < nd; ++i) |
| 1874 | y = 10*y + s0[i+1] - '0'; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1875 | } |
| 1876 | } |
Mark Dickinson | 853c3bb | 2010-01-14 15:37:49 +0000 | [diff] [blame] | 1877 | bd0 = s2b(s0, nd0, nd, y); |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1878 | if (bd0 == NULL) |
| 1879 | goto failed_malloc; |
| 1880 | |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1881 | /* Notation for the comments below. Write: |
| 1882 | |
| 1883 | - dv for the absolute value of the number represented by the original |
| 1884 | decimal input string. |
| 1885 | |
| 1886 | - if we've truncated dv, write tdv for the truncated value. |
| 1887 | Otherwise, set tdv == dv. |
| 1888 | |
| 1889 | - srv for the quantity rv/2^bc.scale; so srv is the current binary |
| 1890 | approximation to tdv (and dv). It should be exactly representable |
| 1891 | in an IEEE 754 double. |
| 1892 | */ |
| 1893 | |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1894 | for(;;) { |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1895 | |
| 1896 | /* This is the main correction loop for _Py_dg_strtod. |
| 1897 | |
| 1898 | We've got a decimal value tdv, and a floating-point approximation |
| 1899 | srv=rv/2^bc.scale to tdv. The aim is to determine whether srv is |
| 1900 | close enough (i.e., within 0.5 ulps) to tdv, and to compute a new |
| 1901 | approximation if not. |
| 1902 | |
| 1903 | To determine whether srv is close enough to tdv, compute integers |
| 1904 | bd, bb and bs proportional to tdv, srv and 0.5 ulp(srv) |
| 1905 | respectively, and then use integer arithmetic to determine whether |
| 1906 | |tdv - srv| is less than, equal to, or greater than 0.5 ulp(srv). |
| 1907 | */ |
| 1908 | |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1909 | bd = Balloc(bd0->k); |
| 1910 | if (bd == NULL) { |
| 1911 | Bfree(bd0); |
| 1912 | goto failed_malloc; |
| 1913 | } |
| 1914 | Bcopy(bd, bd0); |
Mark Dickinson | f41d29a | 2010-01-24 10:16:29 +0000 | [diff] [blame] | 1915 | bb = sd2b(&rv, bc.scale, &bbe); /* srv = bb * 2^bbe */ |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1916 | if (bb == NULL) { |
| 1917 | Bfree(bd); |
| 1918 | Bfree(bd0); |
| 1919 | goto failed_malloc; |
| 1920 | } |
Mark Dickinson | f41d29a | 2010-01-24 10:16:29 +0000 | [diff] [blame] | 1921 | /* Record whether lsb of bb is odd, in case we need this |
| 1922 | for the round-to-even step later. */ |
| 1923 | odd = bb->x[0] & 1; |
| 1924 | |
| 1925 | /* tdv = bd * 10**e; srv = bb * 2**bbe */ |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1926 | bs = i2b(1); |
| 1927 | if (bs == NULL) { |
| 1928 | Bfree(bb); |
| 1929 | Bfree(bd); |
| 1930 | Bfree(bd0); |
| 1931 | goto failed_malloc; |
| 1932 | } |
| 1933 | |
| 1934 | if (e >= 0) { |
| 1935 | bb2 = bb5 = 0; |
| 1936 | bd2 = bd5 = e; |
| 1937 | } |
| 1938 | else { |
| 1939 | bb2 = bb5 = -e; |
| 1940 | bd2 = bd5 = 0; |
| 1941 | } |
| 1942 | if (bbe >= 0) |
| 1943 | bb2 += bbe; |
| 1944 | else |
| 1945 | bd2 -= bbe; |
| 1946 | bs2 = bb2; |
Mark Dickinson | f41d29a | 2010-01-24 10:16:29 +0000 | [diff] [blame] | 1947 | bb2++; |
| 1948 | bd2++; |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1949 | |
Mark Dickinson | f41d29a | 2010-01-24 10:16:29 +0000 | [diff] [blame] | 1950 | /* At this stage bd5 - bb5 == e == bd2 - bb2 + bbe, bb2 - bs2 == 1, |
Mark Dickinson | e383e82 | 2012-04-29 15:31:56 +0100 | [diff] [blame] | 1951 | and bs == 1, so: |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1952 | |
Mark Dickinson | f41d29a | 2010-01-24 10:16:29 +0000 | [diff] [blame] | 1953 | tdv == bd * 10**e = bd * 2**(bbe - bb2 + bd2) * 5**(bd5 - bb5) |
| 1954 | srv == bb * 2**bbe = bb * 2**(bbe - bb2 + bb2) |
Mark Dickinson | e383e82 | 2012-04-29 15:31:56 +0100 | [diff] [blame] | 1955 | 0.5 ulp(srv) == 2**(bbe-1) = bs * 2**(bbe - bb2 + bs2) |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1956 | |
Mark Dickinson | e383e82 | 2012-04-29 15:31:56 +0100 | [diff] [blame] | 1957 | It follows that: |
Mark Dickinson | f41d29a | 2010-01-24 10:16:29 +0000 | [diff] [blame] | 1958 | |
| 1959 | M * tdv = bd * 2**bd2 * 5**bd5 |
| 1960 | M * srv = bb * 2**bb2 * 5**bb5 |
| 1961 | M * 0.5 ulp(srv) = bs * 2**bs2 * 5**bb5 |
| 1962 | |
Mark Dickinson | e383e82 | 2012-04-29 15:31:56 +0100 | [diff] [blame] | 1963 | for some constant M. (Actually, M == 2**(bb2 - bbe) * 5**bb5, but |
| 1964 | this fact is not needed below.) |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1965 | */ |
| 1966 | |
Mark Dickinson | f41d29a | 2010-01-24 10:16:29 +0000 | [diff] [blame] | 1967 | /* Remove factor of 2**i, where i = min(bb2, bd2, bs2). */ |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1968 | i = bb2 < bd2 ? bb2 : bd2; |
| 1969 | if (i > bs2) |
| 1970 | i = bs2; |
| 1971 | if (i > 0) { |
| 1972 | bb2 -= i; |
| 1973 | bd2 -= i; |
| 1974 | bs2 -= i; |
| 1975 | } |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 1976 | |
| 1977 | /* Scale bb, bd, bs by the appropriate powers of 2 and 5. */ |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 1978 | if (bb5 > 0) { |
| 1979 | bs = pow5mult(bs, bb5); |
| 1980 | if (bs == NULL) { |
| 1981 | Bfree(bb); |
| 1982 | Bfree(bd); |
| 1983 | Bfree(bd0); |
| 1984 | goto failed_malloc; |
| 1985 | } |
| 1986 | bb1 = mult(bs, bb); |
| 1987 | Bfree(bb); |
| 1988 | bb = bb1; |
| 1989 | if (bb == NULL) { |
| 1990 | Bfree(bs); |
| 1991 | Bfree(bd); |
| 1992 | Bfree(bd0); |
| 1993 | goto failed_malloc; |
| 1994 | } |
| 1995 | } |
| 1996 | if (bb2 > 0) { |
| 1997 | bb = lshift(bb, bb2); |
| 1998 | if (bb == NULL) { |
| 1999 | Bfree(bs); |
| 2000 | Bfree(bd); |
| 2001 | Bfree(bd0); |
| 2002 | goto failed_malloc; |
| 2003 | } |
| 2004 | } |
| 2005 | if (bd5 > 0) { |
| 2006 | bd = pow5mult(bd, bd5); |
| 2007 | if (bd == NULL) { |
| 2008 | Bfree(bb); |
| 2009 | Bfree(bs); |
| 2010 | Bfree(bd0); |
| 2011 | goto failed_malloc; |
| 2012 | } |
| 2013 | } |
| 2014 | if (bd2 > 0) { |
| 2015 | bd = lshift(bd, bd2); |
| 2016 | if (bd == NULL) { |
| 2017 | Bfree(bb); |
| 2018 | Bfree(bs); |
| 2019 | Bfree(bd0); |
| 2020 | goto failed_malloc; |
| 2021 | } |
| 2022 | } |
| 2023 | if (bs2 > 0) { |
| 2024 | bs = lshift(bs, bs2); |
| 2025 | if (bs == NULL) { |
| 2026 | Bfree(bb); |
| 2027 | Bfree(bd); |
| 2028 | Bfree(bd0); |
| 2029 | goto failed_malloc; |
| 2030 | } |
| 2031 | } |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 2032 | |
| 2033 | /* Now bd, bb and bs are scaled versions of tdv, srv and 0.5 ulp(srv), |
| 2034 | respectively. Compute the difference |tdv - srv|, and compare |
| 2035 | with 0.5 ulp(srv). */ |
| 2036 | |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2037 | delta = diff(bb, bd); |
| 2038 | if (delta == NULL) { |
| 2039 | Bfree(bb); |
| 2040 | Bfree(bs); |
| 2041 | Bfree(bd); |
| 2042 | Bfree(bd0); |
| 2043 | goto failed_malloc; |
| 2044 | } |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 2045 | dsign = delta->sign; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2046 | delta->sign = 0; |
| 2047 | i = cmp(delta, bs); |
| 2048 | if (bc.nd > nd && i <= 0) { |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 2049 | if (dsign) |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2050 | break; /* Must use bigcomp(). */ |
Mark Dickinson | 853c3bb | 2010-01-14 15:37:49 +0000 | [diff] [blame] | 2051 | |
| 2052 | /* Here rv overestimates the truncated decimal value by at most |
| 2053 | 0.5 ulp(rv). Hence rv either overestimates the true decimal |
| 2054 | value by <= 0.5 ulp(rv), or underestimates it by some small |
| 2055 | amount (< 0.1 ulp(rv)); either way, rv is within 0.5 ulps of |
| 2056 | the true decimal value, so it's possible to exit. |
| 2057 | |
| 2058 | Exception: if scaled rv is a normal exact power of 2, but not |
| 2059 | DBL_MIN, then rv - 0.5 ulp(rv) takes us all the way down to the |
| 2060 | next double, so the correctly rounded result is either rv - 0.5 |
| 2061 | ulp(rv) or rv; in this case, use bigcomp to distinguish. */ |
| 2062 | |
| 2063 | if (!word1(&rv) && !(word0(&rv) & Bndry_mask)) { |
| 2064 | /* rv can't be 0, since it's an overestimate for some |
| 2065 | nonzero value. So rv is a normal power of 2. */ |
| 2066 | j = (int)(word0(&rv) & Exp_mask) >> Exp_shift; |
| 2067 | /* rv / 2^bc.scale = 2^(j - 1023 - bc.scale); use bigcomp if |
| 2068 | rv / 2^bc.scale >= 2^-1021. */ |
| 2069 | if (j - bc.scale >= 2) { |
| 2070 | dval(&rv) -= 0.5 * sulp(&rv, &bc); |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 2071 | break; /* Use bigcomp. */ |
Mark Dickinson | 853c3bb | 2010-01-14 15:37:49 +0000 | [diff] [blame] | 2072 | } |
| 2073 | } |
| 2074 | |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2075 | { |
| 2076 | bc.nd = nd; |
| 2077 | i = -1; /* Discarded digits make delta smaller. */ |
| 2078 | } |
| 2079 | } |
| 2080 | |
| 2081 | if (i < 0) { |
| 2082 | /* Error is less than half an ulp -- check for |
| 2083 | * special case of mantissa a power of two. |
| 2084 | */ |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 2085 | if (dsign || word1(&rv) || word0(&rv) & Bndry_mask |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2086 | || (word0(&rv) & Exp_mask) <= (2*P+1)*Exp_msk1 |
| 2087 | ) { |
| 2088 | break; |
| 2089 | } |
| 2090 | if (!delta->x[0] && delta->wds <= 1) { |
| 2091 | /* exact result */ |
| 2092 | break; |
| 2093 | } |
| 2094 | delta = lshift(delta,Log2P); |
| 2095 | if (delta == NULL) { |
| 2096 | Bfree(bb); |
| 2097 | Bfree(bs); |
| 2098 | Bfree(bd); |
| 2099 | Bfree(bd0); |
| 2100 | goto failed_malloc; |
| 2101 | } |
| 2102 | if (cmp(delta, bs) > 0) |
| 2103 | goto drop_down; |
| 2104 | break; |
| 2105 | } |
| 2106 | if (i == 0) { |
| 2107 | /* exactly half-way between */ |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 2108 | if (dsign) { |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2109 | if ((word0(&rv) & Bndry_mask1) == Bndry_mask1 |
| 2110 | && word1(&rv) == ( |
| 2111 | (bc.scale && |
| 2112 | (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1) ? |
| 2113 | (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) : |
| 2114 | 0xffffffff)) { |
| 2115 | /*boundary case -- increment exponent*/ |
| 2116 | word0(&rv) = (word0(&rv) & Exp_mask) |
| 2117 | + Exp_msk1 |
| 2118 | ; |
| 2119 | word1(&rv) = 0; |
Brett Cannon | b94767f | 2011-02-22 20:15:44 +0000 | [diff] [blame] | 2120 | /* dsign = 0; */ |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2121 | break; |
| 2122 | } |
| 2123 | } |
| 2124 | else if (!(word0(&rv) & Bndry_mask) && !word1(&rv)) { |
| 2125 | drop_down: |
| 2126 | /* boundary case -- decrement exponent */ |
| 2127 | if (bc.scale) { |
| 2128 | L = word0(&rv) & Exp_mask; |
| 2129 | if (L <= (2*P+1)*Exp_msk1) { |
| 2130 | if (L > (P+2)*Exp_msk1) |
| 2131 | /* round even ==> */ |
| 2132 | /* accept rv */ |
| 2133 | break; |
| 2134 | /* rv = smallest denormal */ |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 2135 | if (bc.nd > nd) |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2136 | break; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2137 | goto undfl; |
| 2138 | } |
| 2139 | } |
| 2140 | L = (word0(&rv) & Exp_mask) - Exp_msk1; |
| 2141 | word0(&rv) = L | Bndry_mask1; |
| 2142 | word1(&rv) = 0xffffffff; |
| 2143 | break; |
| 2144 | } |
Mark Dickinson | f41d29a | 2010-01-24 10:16:29 +0000 | [diff] [blame] | 2145 | if (!odd) |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2146 | break; |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 2147 | if (dsign) |
Mark Dickinson | f41d29a | 2010-01-24 10:16:29 +0000 | [diff] [blame] | 2148 | dval(&rv) += sulp(&rv, &bc); |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2149 | else { |
Mark Dickinson | f41d29a | 2010-01-24 10:16:29 +0000 | [diff] [blame] | 2150 | dval(&rv) -= sulp(&rv, &bc); |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2151 | if (!dval(&rv)) { |
Mark Dickinson | 81612e8 | 2010-01-12 23:04:19 +0000 | [diff] [blame] | 2152 | if (bc.nd >nd) |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2153 | break; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2154 | goto undfl; |
| 2155 | } |
| 2156 | } |
Brett Cannon | b94767f | 2011-02-22 20:15:44 +0000 | [diff] [blame] | 2157 | /* dsign = 1 - dsign; */ |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2158 | break; |
| 2159 | } |
| 2160 | if ((aadj = ratio(delta, bs)) <= 2.) { |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 2161 | if (dsign) |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2162 | aadj = aadj1 = 1.; |
| 2163 | else if (word1(&rv) || word0(&rv) & Bndry_mask) { |
| 2164 | if (word1(&rv) == Tiny1 && !word0(&rv)) { |
Mark Dickinson | 81612e8 | 2010-01-12 23:04:19 +0000 | [diff] [blame] | 2165 | if (bc.nd >nd) |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2166 | break; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2167 | goto undfl; |
| 2168 | } |
| 2169 | aadj = 1.; |
| 2170 | aadj1 = -1.; |
| 2171 | } |
| 2172 | else { |
| 2173 | /* special case -- power of FLT_RADIX to be */ |
| 2174 | /* rounded down... */ |
| 2175 | |
| 2176 | if (aadj < 2./FLT_RADIX) |
| 2177 | aadj = 1./FLT_RADIX; |
| 2178 | else |
| 2179 | aadj *= 0.5; |
| 2180 | aadj1 = -aadj; |
| 2181 | } |
| 2182 | } |
| 2183 | else { |
| 2184 | aadj *= 0.5; |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 2185 | aadj1 = dsign ? aadj : -aadj; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2186 | if (Flt_Rounds == 0) |
| 2187 | aadj1 += 0.5; |
| 2188 | } |
| 2189 | y = word0(&rv) & Exp_mask; |
| 2190 | |
| 2191 | /* Check for overflow */ |
| 2192 | |
| 2193 | if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) { |
| 2194 | dval(&rv0) = dval(&rv); |
| 2195 | word0(&rv) -= P*Exp_msk1; |
| 2196 | adj.d = aadj1 * ulp(&rv); |
| 2197 | dval(&rv) += adj.d; |
| 2198 | if ((word0(&rv) & Exp_mask) >= |
| 2199 | Exp_msk1*(DBL_MAX_EXP+Bias-P)) { |
Mark Dickinson | c4f1868 | 2010-01-17 14:39:12 +0000 | [diff] [blame] | 2200 | if (word0(&rv0) == Big0 && word1(&rv0) == Big1) { |
| 2201 | Bfree(bb); |
| 2202 | Bfree(bd); |
| 2203 | Bfree(bs); |
| 2204 | Bfree(bd0); |
| 2205 | Bfree(delta); |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2206 | goto ovfl; |
Mark Dickinson | c4f1868 | 2010-01-17 14:39:12 +0000 | [diff] [blame] | 2207 | } |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2208 | word0(&rv) = Big0; |
| 2209 | word1(&rv) = Big1; |
| 2210 | goto cont; |
| 2211 | } |
| 2212 | else |
| 2213 | word0(&rv) += P*Exp_msk1; |
| 2214 | } |
| 2215 | else { |
| 2216 | if (bc.scale && y <= 2*P*Exp_msk1) { |
| 2217 | if (aadj <= 0x7fffffff) { |
| 2218 | if ((z = (ULong)aadj) <= 0) |
| 2219 | z = 1; |
| 2220 | aadj = z; |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 2221 | aadj1 = dsign ? aadj : -aadj; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2222 | } |
| 2223 | dval(&aadj2) = aadj1; |
| 2224 | word0(&aadj2) += (2*P+1)*Exp_msk1 - y; |
| 2225 | aadj1 = dval(&aadj2); |
| 2226 | } |
| 2227 | adj.d = aadj1 * ulp(&rv); |
| 2228 | dval(&rv) += adj.d; |
| 2229 | } |
| 2230 | z = word0(&rv) & Exp_mask; |
| 2231 | if (bc.nd == nd) { |
| 2232 | if (!bc.scale) |
| 2233 | if (y == z) { |
| 2234 | /* Can we stop now? */ |
| 2235 | L = (Long)aadj; |
| 2236 | aadj -= L; |
| 2237 | /* The tolerances below are conservative. */ |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 2238 | if (dsign || word1(&rv) || word0(&rv) & Bndry_mask) { |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2239 | if (aadj < .4999999 || aadj > .5000001) |
| 2240 | break; |
| 2241 | } |
| 2242 | else if (aadj < .4999999/FLT_RADIX) |
| 2243 | break; |
| 2244 | } |
| 2245 | } |
| 2246 | cont: |
| 2247 | Bfree(bb); |
| 2248 | Bfree(bd); |
| 2249 | Bfree(bs); |
| 2250 | Bfree(delta); |
| 2251 | } |
| 2252 | Bfree(bb); |
| 2253 | Bfree(bd); |
| 2254 | Bfree(bs); |
| 2255 | Bfree(bd0); |
| 2256 | Bfree(delta); |
| 2257 | if (bc.nd > nd) { |
| 2258 | error = bigcomp(&rv, s0, &bc); |
| 2259 | if (error) |
| 2260 | goto failed_malloc; |
| 2261 | } |
| 2262 | |
| 2263 | if (bc.scale) { |
| 2264 | word0(&rv0) = Exp_1 - 2*P*Exp_msk1; |
| 2265 | word1(&rv0) = 0; |
| 2266 | dval(&rv) *= dval(&rv0); |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2267 | } |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 2268 | |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2269 | ret: |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2270 | return sign ? -dval(&rv) : dval(&rv); |
| 2271 | |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 2272 | parse_error: |
| 2273 | return 0.0; |
| 2274 | |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2275 | failed_malloc: |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2276 | errno = ENOMEM; |
| 2277 | return -1.0; |
Mark Dickinson | add2823 | 2010-01-21 19:51:08 +0000 | [diff] [blame] | 2278 | |
| 2279 | undfl: |
| 2280 | return sign ? -0.0 : 0.0; |
| 2281 | |
| 2282 | ovfl: |
| 2283 | errno = ERANGE; |
| 2284 | /* Can't trust HUGE_VAL */ |
| 2285 | word0(&rv) = Exp_mask; |
| 2286 | word1(&rv) = 0; |
| 2287 | return sign ? -dval(&rv) : dval(&rv); |
| 2288 | |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2289 | } |
| 2290 | |
| 2291 | static char * |
| 2292 | rv_alloc(int i) |
| 2293 | { |
| 2294 | int j, k, *r; |
| 2295 | |
| 2296 | j = sizeof(ULong); |
| 2297 | for(k = 0; |
| 2298 | sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (unsigned)i; |
| 2299 | j <<= 1) |
| 2300 | k++; |
| 2301 | r = (int*)Balloc(k); |
| 2302 | if (r == NULL) |
| 2303 | return NULL; |
| 2304 | *r = k; |
| 2305 | return (char *)(r+1); |
| 2306 | } |
| 2307 | |
| 2308 | static char * |
Serhiy Storchaka | ef1585e | 2015-12-25 20:01:53 +0200 | [diff] [blame] | 2309 | nrv_alloc(const char *s, char **rve, int n) |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2310 | { |
| 2311 | char *rv, *t; |
| 2312 | |
| 2313 | rv = rv_alloc(n); |
| 2314 | if (rv == NULL) |
| 2315 | return NULL; |
| 2316 | t = rv; |
| 2317 | while((*t = *s++)) t++; |
| 2318 | if (rve) |
| 2319 | *rve = t; |
| 2320 | return rv; |
| 2321 | } |
| 2322 | |
| 2323 | /* freedtoa(s) must be used to free values s returned by dtoa |
| 2324 | * when MULTIPLE_THREADS is #defined. It should be used in all cases, |
| 2325 | * but for consistency with earlier versions of dtoa, it is optional |
| 2326 | * when MULTIPLE_THREADS is not defined. |
| 2327 | */ |
| 2328 | |
| 2329 | void |
| 2330 | _Py_dg_freedtoa(char *s) |
| 2331 | { |
| 2332 | Bigint *b = (Bigint *)((int *)s - 1); |
| 2333 | b->maxwds = 1 << (b->k = *(int*)b); |
| 2334 | Bfree(b); |
| 2335 | } |
| 2336 | |
| 2337 | /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string. |
| 2338 | * |
| 2339 | * Inspired by "How to Print Floating-Point Numbers Accurately" by |
| 2340 | * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126]. |
| 2341 | * |
| 2342 | * Modifications: |
| 2343 | * 1. Rather than iterating, we use a simple numeric overestimate |
| 2344 | * to determine k = floor(log10(d)). We scale relevant |
| 2345 | * quantities using O(log2(k)) rather than O(k) multiplications. |
| 2346 | * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't |
| 2347 | * try to generate digits strictly left to right. Instead, we |
| 2348 | * compute with fewer bits and propagate the carry if necessary |
| 2349 | * when rounding the final digit up. This is often faster. |
| 2350 | * 3. Under the assumption that input will be rounded nearest, |
| 2351 | * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22. |
| 2352 | * That is, we allow equality in stopping tests when the |
| 2353 | * round-nearest rule will give the same floating-point value |
| 2354 | * as would satisfaction of the stopping test with strict |
| 2355 | * inequality. |
| 2356 | * 4. We remove common factors of powers of 2 from relevant |
| 2357 | * quantities. |
| 2358 | * 5. When converting floating-point integers less than 1e16, |
| 2359 | * we use floating-point arithmetic rather than resorting |
| 2360 | * to multiple-precision integers. |
| 2361 | * 6. When asked to produce fewer than 15 digits, we first try |
| 2362 | * to get by with floating-point arithmetic; we resort to |
| 2363 | * multiple-precision integer arithmetic only if we cannot |
| 2364 | * guarantee that the floating-point calculation has given |
| 2365 | * the correctly rounded result. For k requested digits and |
| 2366 | * "uniformly" distributed input, the probability is |
| 2367 | * something like 10^(k-15) that we must resort to the Long |
| 2368 | * calculation. |
| 2369 | */ |
| 2370 | |
| 2371 | /* Additional notes (METD): (1) returns NULL on failure. (2) to avoid memory |
| 2372 | leakage, a successful call to _Py_dg_dtoa should always be matched by a |
| 2373 | call to _Py_dg_freedtoa. */ |
| 2374 | |
| 2375 | char * |
| 2376 | _Py_dg_dtoa(double dd, int mode, int ndigits, |
| 2377 | int *decpt, int *sign, char **rve) |
| 2378 | { |
| 2379 | /* Arguments ndigits, decpt, sign are similar to those |
| 2380 | of ecvt and fcvt; trailing zeros are suppressed from |
| 2381 | the returned string. If not null, *rve is set to point |
| 2382 | to the end of the return value. If d is +-Infinity or NaN, |
| 2383 | then *decpt is set to 9999. |
| 2384 | |
| 2385 | mode: |
| 2386 | 0 ==> shortest string that yields d when read in |
| 2387 | and rounded to nearest. |
| 2388 | 1 ==> like 0, but with Steele & White stopping rule; |
| 2389 | e.g. with IEEE P754 arithmetic , mode 0 gives |
| 2390 | 1e23 whereas mode 1 gives 9.999999999999999e22. |
| 2391 | 2 ==> max(1,ndigits) significant digits. This gives a |
| 2392 | return value similar to that of ecvt, except |
| 2393 | that trailing zeros are suppressed. |
| 2394 | 3 ==> through ndigits past the decimal point. This |
| 2395 | gives a return value similar to that from fcvt, |
| 2396 | except that trailing zeros are suppressed, and |
| 2397 | ndigits can be negative. |
| 2398 | 4,5 ==> similar to 2 and 3, respectively, but (in |
| 2399 | round-nearest mode) with the tests of mode 0 to |
| 2400 | possibly return a shorter string that rounds to d. |
| 2401 | With IEEE arithmetic and compilation with |
| 2402 | -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same |
| 2403 | as modes 2 and 3 when FLT_ROUNDS != 1. |
| 2404 | 6-9 ==> Debugging modes similar to mode - 4: don't try |
| 2405 | fast floating-point estimate (if applicable). |
| 2406 | |
| 2407 | Values of mode other than 0-9 are treated as mode 0. |
| 2408 | |
| 2409 | Sufficient space is allocated to the return value |
| 2410 | to hold the suppressed trailing zeros. |
| 2411 | */ |
| 2412 | |
| 2413 | int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1, |
| 2414 | j, j1, k, k0, k_check, leftright, m2, m5, s2, s5, |
| 2415 | spec_case, try_quick; |
| 2416 | Long L; |
| 2417 | int denorm; |
| 2418 | ULong x; |
| 2419 | Bigint *b, *b1, *delta, *mlo, *mhi, *S; |
| 2420 | U d2, eps, u; |
| 2421 | double ds; |
| 2422 | char *s, *s0; |
| 2423 | |
| 2424 | /* set pointers to NULL, to silence gcc compiler warnings and make |
| 2425 | cleanup easier on error */ |
Mark Dickinson | d369726 | 2010-05-13 11:52:22 +0000 | [diff] [blame] | 2426 | mlo = mhi = S = 0; |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2427 | s0 = 0; |
| 2428 | |
| 2429 | u.d = dd; |
| 2430 | if (word0(&u) & Sign_bit) { |
| 2431 | /* set sign for everything, including 0's and NaNs */ |
| 2432 | *sign = 1; |
| 2433 | word0(&u) &= ~Sign_bit; /* clear sign bit */ |
| 2434 | } |
| 2435 | else |
| 2436 | *sign = 0; |
| 2437 | |
| 2438 | /* quick return for Infinities, NaNs and zeros */ |
| 2439 | if ((word0(&u) & Exp_mask) == Exp_mask) |
| 2440 | { |
| 2441 | /* Infinity or NaN */ |
| 2442 | *decpt = 9999; |
| 2443 | if (!word1(&u) && !(word0(&u) & 0xfffff)) |
| 2444 | return nrv_alloc("Infinity", rve, 8); |
| 2445 | return nrv_alloc("NaN", rve, 3); |
| 2446 | } |
| 2447 | if (!dval(&u)) { |
| 2448 | *decpt = 1; |
| 2449 | return nrv_alloc("0", rve, 1); |
| 2450 | } |
| 2451 | |
| 2452 | /* compute k = floor(log10(d)). The computation may leave k |
| 2453 | one too large, but should never leave k too small. */ |
| 2454 | b = d2b(&u, &be, &bbits); |
| 2455 | if (b == NULL) |
| 2456 | goto failed_malloc; |
| 2457 | if ((i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) { |
| 2458 | dval(&d2) = dval(&u); |
| 2459 | word0(&d2) &= Frac_mask1; |
| 2460 | word0(&d2) |= Exp_11; |
| 2461 | |
| 2462 | /* log(x) ~=~ log(1.5) + (x-1.5)/1.5 |
| 2463 | * log10(x) = log(x) / log(10) |
| 2464 | * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10)) |
| 2465 | * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2) |
| 2466 | * |
| 2467 | * This suggests computing an approximation k to log10(d) by |
| 2468 | * |
| 2469 | * k = (i - Bias)*0.301029995663981 |
| 2470 | * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 ); |
| 2471 | * |
| 2472 | * We want k to be too large rather than too small. |
| 2473 | * The error in the first-order Taylor series approximation |
| 2474 | * is in our favor, so we just round up the constant enough |
| 2475 | * to compensate for any error in the multiplication of |
| 2476 | * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077, |
| 2477 | * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14, |
| 2478 | * adding 1e-13 to the constant term more than suffices. |
| 2479 | * Hence we adjust the constant term to 0.1760912590558. |
| 2480 | * (We could get a more accurate k by invoking log10, |
| 2481 | * but this is probably not worthwhile.) |
| 2482 | */ |
| 2483 | |
| 2484 | i -= Bias; |
| 2485 | denorm = 0; |
| 2486 | } |
| 2487 | else { |
| 2488 | /* d is denormalized */ |
| 2489 | |
| 2490 | i = bbits + be + (Bias + (P-1) - 1); |
| 2491 | x = i > 32 ? word0(&u) << (64 - i) | word1(&u) >> (i - 32) |
| 2492 | : word1(&u) << (32 - i); |
| 2493 | dval(&d2) = x; |
| 2494 | word0(&d2) -= 31*Exp_msk1; /* adjust exponent */ |
| 2495 | i -= (Bias + (P-1) - 1) + 1; |
| 2496 | denorm = 1; |
| 2497 | } |
| 2498 | ds = (dval(&d2)-1.5)*0.289529654602168 + 0.1760912590558 + |
| 2499 | i*0.301029995663981; |
| 2500 | k = (int)ds; |
| 2501 | if (ds < 0. && ds != k) |
| 2502 | k--; /* want k = floor(ds) */ |
| 2503 | k_check = 1; |
| 2504 | if (k >= 0 && k <= Ten_pmax) { |
| 2505 | if (dval(&u) < tens[k]) |
| 2506 | k--; |
| 2507 | k_check = 0; |
| 2508 | } |
| 2509 | j = bbits - i - 1; |
| 2510 | if (j >= 0) { |
| 2511 | b2 = 0; |
| 2512 | s2 = j; |
| 2513 | } |
| 2514 | else { |
| 2515 | b2 = -j; |
| 2516 | s2 = 0; |
| 2517 | } |
| 2518 | if (k >= 0) { |
| 2519 | b5 = 0; |
| 2520 | s5 = k; |
| 2521 | s2 += k; |
| 2522 | } |
| 2523 | else { |
| 2524 | b2 -= k; |
| 2525 | b5 = -k; |
| 2526 | s5 = 0; |
| 2527 | } |
| 2528 | if (mode < 0 || mode > 9) |
| 2529 | mode = 0; |
| 2530 | |
| 2531 | try_quick = 1; |
| 2532 | |
| 2533 | if (mode > 5) { |
| 2534 | mode -= 4; |
| 2535 | try_quick = 0; |
| 2536 | } |
| 2537 | leftright = 1; |
| 2538 | ilim = ilim1 = -1; /* Values for cases 0 and 1; done here to */ |
| 2539 | /* silence erroneous "gcc -Wall" warning. */ |
| 2540 | switch(mode) { |
| 2541 | case 0: |
| 2542 | case 1: |
| 2543 | i = 18; |
| 2544 | ndigits = 0; |
| 2545 | break; |
| 2546 | case 2: |
| 2547 | leftright = 0; |
| 2548 | /* no break */ |
| 2549 | case 4: |
| 2550 | if (ndigits <= 0) |
| 2551 | ndigits = 1; |
| 2552 | ilim = ilim1 = i = ndigits; |
| 2553 | break; |
| 2554 | case 3: |
| 2555 | leftright = 0; |
| 2556 | /* no break */ |
| 2557 | case 5: |
| 2558 | i = ndigits + k + 1; |
| 2559 | ilim = i; |
| 2560 | ilim1 = i - 1; |
| 2561 | if (i <= 0) |
| 2562 | i = 1; |
| 2563 | } |
| 2564 | s0 = rv_alloc(i); |
| 2565 | if (s0 == NULL) |
| 2566 | goto failed_malloc; |
| 2567 | s = s0; |
| 2568 | |
| 2569 | |
| 2570 | if (ilim >= 0 && ilim <= Quick_max && try_quick) { |
| 2571 | |
| 2572 | /* Try to get by with floating-point arithmetic. */ |
| 2573 | |
| 2574 | i = 0; |
| 2575 | dval(&d2) = dval(&u); |
| 2576 | k0 = k; |
| 2577 | ilim0 = ilim; |
| 2578 | ieps = 2; /* conservative */ |
| 2579 | if (k > 0) { |
| 2580 | ds = tens[k&0xf]; |
| 2581 | j = k >> 4; |
| 2582 | if (j & Bletch) { |
| 2583 | /* prevent overflows */ |
| 2584 | j &= Bletch - 1; |
| 2585 | dval(&u) /= bigtens[n_bigtens-1]; |
| 2586 | ieps++; |
| 2587 | } |
| 2588 | for(; j; j >>= 1, i++) |
| 2589 | if (j & 1) { |
| 2590 | ieps++; |
| 2591 | ds *= bigtens[i]; |
| 2592 | } |
| 2593 | dval(&u) /= ds; |
| 2594 | } |
| 2595 | else if ((j1 = -k)) { |
| 2596 | dval(&u) *= tens[j1 & 0xf]; |
| 2597 | for(j = j1 >> 4; j; j >>= 1, i++) |
| 2598 | if (j & 1) { |
| 2599 | ieps++; |
| 2600 | dval(&u) *= bigtens[i]; |
| 2601 | } |
| 2602 | } |
| 2603 | if (k_check && dval(&u) < 1. && ilim > 0) { |
| 2604 | if (ilim1 <= 0) |
| 2605 | goto fast_failed; |
| 2606 | ilim = ilim1; |
| 2607 | k--; |
| 2608 | dval(&u) *= 10.; |
| 2609 | ieps++; |
| 2610 | } |
| 2611 | dval(&eps) = ieps*dval(&u) + 7.; |
| 2612 | word0(&eps) -= (P-1)*Exp_msk1; |
| 2613 | if (ilim == 0) { |
| 2614 | S = mhi = 0; |
| 2615 | dval(&u) -= 5.; |
| 2616 | if (dval(&u) > dval(&eps)) |
| 2617 | goto one_digit; |
| 2618 | if (dval(&u) < -dval(&eps)) |
| 2619 | goto no_digits; |
| 2620 | goto fast_failed; |
| 2621 | } |
| 2622 | if (leftright) { |
| 2623 | /* Use Steele & White method of only |
| 2624 | * generating digits needed. |
| 2625 | */ |
| 2626 | dval(&eps) = 0.5/tens[ilim-1] - dval(&eps); |
| 2627 | for(i = 0;;) { |
| 2628 | L = (Long)dval(&u); |
| 2629 | dval(&u) -= L; |
| 2630 | *s++ = '0' + (int)L; |
| 2631 | if (dval(&u) < dval(&eps)) |
| 2632 | goto ret1; |
| 2633 | if (1. - dval(&u) < dval(&eps)) |
| 2634 | goto bump_up; |
| 2635 | if (++i >= ilim) |
| 2636 | break; |
| 2637 | dval(&eps) *= 10.; |
| 2638 | dval(&u) *= 10.; |
| 2639 | } |
| 2640 | } |
| 2641 | else { |
| 2642 | /* Generate ilim digits, then fix them up. */ |
| 2643 | dval(&eps) *= tens[ilim-1]; |
| 2644 | for(i = 1;; i++, dval(&u) *= 10.) { |
| 2645 | L = (Long)(dval(&u)); |
| 2646 | if (!(dval(&u) -= L)) |
| 2647 | ilim = i; |
| 2648 | *s++ = '0' + (int)L; |
| 2649 | if (i == ilim) { |
| 2650 | if (dval(&u) > 0.5 + dval(&eps)) |
| 2651 | goto bump_up; |
| 2652 | else if (dval(&u) < 0.5 - dval(&eps)) { |
| 2653 | while(*--s == '0'); |
| 2654 | s++; |
| 2655 | goto ret1; |
| 2656 | } |
| 2657 | break; |
| 2658 | } |
| 2659 | } |
| 2660 | } |
| 2661 | fast_failed: |
| 2662 | s = s0; |
| 2663 | dval(&u) = dval(&d2); |
| 2664 | k = k0; |
| 2665 | ilim = ilim0; |
| 2666 | } |
| 2667 | |
| 2668 | /* Do we have a "small" integer? */ |
| 2669 | |
| 2670 | if (be >= 0 && k <= Int_max) { |
| 2671 | /* Yes. */ |
| 2672 | ds = tens[k]; |
| 2673 | if (ndigits < 0 && ilim <= 0) { |
| 2674 | S = mhi = 0; |
| 2675 | if (ilim < 0 || dval(&u) <= 5*ds) |
| 2676 | goto no_digits; |
| 2677 | goto one_digit; |
| 2678 | } |
| 2679 | for(i = 1;; i++, dval(&u) *= 10.) { |
| 2680 | L = (Long)(dval(&u) / ds); |
| 2681 | dval(&u) -= L*ds; |
| 2682 | *s++ = '0' + (int)L; |
| 2683 | if (!dval(&u)) { |
| 2684 | break; |
| 2685 | } |
| 2686 | if (i == ilim) { |
| 2687 | dval(&u) += dval(&u); |
| 2688 | if (dval(&u) > ds || (dval(&u) == ds && L & 1)) { |
| 2689 | bump_up: |
| 2690 | while(*--s == '9') |
| 2691 | if (s == s0) { |
| 2692 | k++; |
| 2693 | *s = '0'; |
| 2694 | break; |
| 2695 | } |
| 2696 | ++*s++; |
| 2697 | } |
| 2698 | break; |
| 2699 | } |
| 2700 | } |
| 2701 | goto ret1; |
| 2702 | } |
| 2703 | |
| 2704 | m2 = b2; |
| 2705 | m5 = b5; |
| 2706 | if (leftright) { |
| 2707 | i = |
| 2708 | denorm ? be + (Bias + (P-1) - 1 + 1) : |
| 2709 | 1 + P - bbits; |
| 2710 | b2 += i; |
| 2711 | s2 += i; |
| 2712 | mhi = i2b(1); |
| 2713 | if (mhi == NULL) |
| 2714 | goto failed_malloc; |
| 2715 | } |
| 2716 | if (m2 > 0 && s2 > 0) { |
| 2717 | i = m2 < s2 ? m2 : s2; |
| 2718 | b2 -= i; |
| 2719 | m2 -= i; |
| 2720 | s2 -= i; |
| 2721 | } |
| 2722 | if (b5 > 0) { |
| 2723 | if (leftright) { |
| 2724 | if (m5 > 0) { |
| 2725 | mhi = pow5mult(mhi, m5); |
| 2726 | if (mhi == NULL) |
| 2727 | goto failed_malloc; |
| 2728 | b1 = mult(mhi, b); |
| 2729 | Bfree(b); |
| 2730 | b = b1; |
| 2731 | if (b == NULL) |
| 2732 | goto failed_malloc; |
| 2733 | } |
| 2734 | if ((j = b5 - m5)) { |
| 2735 | b = pow5mult(b, j); |
| 2736 | if (b == NULL) |
| 2737 | goto failed_malloc; |
| 2738 | } |
| 2739 | } |
| 2740 | else { |
| 2741 | b = pow5mult(b, b5); |
| 2742 | if (b == NULL) |
| 2743 | goto failed_malloc; |
| 2744 | } |
| 2745 | } |
| 2746 | S = i2b(1); |
| 2747 | if (S == NULL) |
| 2748 | goto failed_malloc; |
| 2749 | if (s5 > 0) { |
| 2750 | S = pow5mult(S, s5); |
| 2751 | if (S == NULL) |
| 2752 | goto failed_malloc; |
| 2753 | } |
| 2754 | |
| 2755 | /* Check for special case that d is a normalized power of 2. */ |
| 2756 | |
| 2757 | spec_case = 0; |
| 2758 | if ((mode < 2 || leftright) |
| 2759 | ) { |
| 2760 | if (!word1(&u) && !(word0(&u) & Bndry_mask) |
| 2761 | && word0(&u) & (Exp_mask & ~Exp_msk1) |
| 2762 | ) { |
| 2763 | /* The special case */ |
| 2764 | b2 += Log2P; |
| 2765 | s2 += Log2P; |
| 2766 | spec_case = 1; |
| 2767 | } |
| 2768 | } |
| 2769 | |
| 2770 | /* Arrange for convenient computation of quotients: |
| 2771 | * shift left if necessary so divisor has 4 leading 0 bits. |
| 2772 | * |
| 2773 | * Perhaps we should just compute leading 28 bits of S once |
| 2774 | * and for all and pass them and a shift to quorem, so it |
| 2775 | * can do shifts and ors to compute the numerator for q. |
| 2776 | */ |
Mark Dickinson | b08a53a | 2009-04-16 19:52:09 +0000 | [diff] [blame] | 2777 | #define iInc 28 |
| 2778 | i = dshift(S, s2); |
| 2779 | b2 += i; |
| 2780 | m2 += i; |
| 2781 | s2 += i; |
| 2782 | if (b2 > 0) { |
| 2783 | b = lshift(b, b2); |
| 2784 | if (b == NULL) |
| 2785 | goto failed_malloc; |
| 2786 | } |
| 2787 | if (s2 > 0) { |
| 2788 | S = lshift(S, s2); |
| 2789 | if (S == NULL) |
| 2790 | goto failed_malloc; |
| 2791 | } |
| 2792 | if (k_check) { |
| 2793 | if (cmp(b,S) < 0) { |
| 2794 | k--; |
| 2795 | b = multadd(b, 10, 0); /* we botched the k estimate */ |
| 2796 | if (b == NULL) |
| 2797 | goto failed_malloc; |
| 2798 | if (leftright) { |
| 2799 | mhi = multadd(mhi, 10, 0); |
| 2800 | if (mhi == NULL) |
| 2801 | goto failed_malloc; |
| 2802 | } |
| 2803 | ilim = ilim1; |
| 2804 | } |
| 2805 | } |
| 2806 | if (ilim <= 0 && (mode == 3 || mode == 5)) { |
| 2807 | if (ilim < 0) { |
| 2808 | /* no digits, fcvt style */ |
| 2809 | no_digits: |
| 2810 | k = -1 - ndigits; |
| 2811 | goto ret; |
| 2812 | } |
| 2813 | else { |
| 2814 | S = multadd(S, 5, 0); |
| 2815 | if (S == NULL) |
| 2816 | goto failed_malloc; |
| 2817 | if (cmp(b, S) <= 0) |
| 2818 | goto no_digits; |
| 2819 | } |
| 2820 | one_digit: |
| 2821 | *s++ = '1'; |
| 2822 | k++; |
| 2823 | goto ret; |
| 2824 | } |
| 2825 | if (leftright) { |
| 2826 | if (m2 > 0) { |
| 2827 | mhi = lshift(mhi, m2); |
| 2828 | if (mhi == NULL) |
| 2829 | goto failed_malloc; |
| 2830 | } |
| 2831 | |
| 2832 | /* Compute mlo -- check for special case |
| 2833 | * that d is a normalized power of 2. |
| 2834 | */ |
| 2835 | |
| 2836 | mlo = mhi; |
| 2837 | if (spec_case) { |
| 2838 | mhi = Balloc(mhi->k); |
| 2839 | if (mhi == NULL) |
| 2840 | goto failed_malloc; |
| 2841 | Bcopy(mhi, mlo); |
| 2842 | mhi = lshift(mhi, Log2P); |
| 2843 | if (mhi == NULL) |
| 2844 | goto failed_malloc; |
| 2845 | } |
| 2846 | |
| 2847 | for(i = 1;;i++) { |
| 2848 | dig = quorem(b,S) + '0'; |
| 2849 | /* Do we yet have the shortest decimal string |
| 2850 | * that will round to d? |
| 2851 | */ |
| 2852 | j = cmp(b, mlo); |
| 2853 | delta = diff(S, mhi); |
| 2854 | if (delta == NULL) |
| 2855 | goto failed_malloc; |
| 2856 | j1 = delta->sign ? 1 : cmp(b, delta); |
| 2857 | Bfree(delta); |
| 2858 | if (j1 == 0 && mode != 1 && !(word1(&u) & 1) |
| 2859 | ) { |
| 2860 | if (dig == '9') |
| 2861 | goto round_9_up; |
| 2862 | if (j > 0) |
| 2863 | dig++; |
| 2864 | *s++ = dig; |
| 2865 | goto ret; |
| 2866 | } |
| 2867 | if (j < 0 || (j == 0 && mode != 1 |
| 2868 | && !(word1(&u) & 1) |
| 2869 | )) { |
| 2870 | if (!b->x[0] && b->wds <= 1) { |
| 2871 | goto accept_dig; |
| 2872 | } |
| 2873 | if (j1 > 0) { |
| 2874 | b = lshift(b, 1); |
| 2875 | if (b == NULL) |
| 2876 | goto failed_malloc; |
| 2877 | j1 = cmp(b, S); |
| 2878 | if ((j1 > 0 || (j1 == 0 && dig & 1)) |
| 2879 | && dig++ == '9') |
| 2880 | goto round_9_up; |
| 2881 | } |
| 2882 | accept_dig: |
| 2883 | *s++ = dig; |
| 2884 | goto ret; |
| 2885 | } |
| 2886 | if (j1 > 0) { |
| 2887 | if (dig == '9') { /* possible if i == 1 */ |
| 2888 | round_9_up: |
| 2889 | *s++ = '9'; |
| 2890 | goto roundoff; |
| 2891 | } |
| 2892 | *s++ = dig + 1; |
| 2893 | goto ret; |
| 2894 | } |
| 2895 | *s++ = dig; |
| 2896 | if (i == ilim) |
| 2897 | break; |
| 2898 | b = multadd(b, 10, 0); |
| 2899 | if (b == NULL) |
| 2900 | goto failed_malloc; |
| 2901 | if (mlo == mhi) { |
| 2902 | mlo = mhi = multadd(mhi, 10, 0); |
| 2903 | if (mlo == NULL) |
| 2904 | goto failed_malloc; |
| 2905 | } |
| 2906 | else { |
| 2907 | mlo = multadd(mlo, 10, 0); |
| 2908 | if (mlo == NULL) |
| 2909 | goto failed_malloc; |
| 2910 | mhi = multadd(mhi, 10, 0); |
| 2911 | if (mhi == NULL) |
| 2912 | goto failed_malloc; |
| 2913 | } |
| 2914 | } |
| 2915 | } |
| 2916 | else |
| 2917 | for(i = 1;; i++) { |
| 2918 | *s++ = dig = quorem(b,S) + '0'; |
| 2919 | if (!b->x[0] && b->wds <= 1) { |
| 2920 | goto ret; |
| 2921 | } |
| 2922 | if (i >= ilim) |
| 2923 | break; |
| 2924 | b = multadd(b, 10, 0); |
| 2925 | if (b == NULL) |
| 2926 | goto failed_malloc; |
| 2927 | } |
| 2928 | |
| 2929 | /* Round off last digit */ |
| 2930 | |
| 2931 | b = lshift(b, 1); |
| 2932 | if (b == NULL) |
| 2933 | goto failed_malloc; |
| 2934 | j = cmp(b, S); |
| 2935 | if (j > 0 || (j == 0 && dig & 1)) { |
| 2936 | roundoff: |
| 2937 | while(*--s == '9') |
| 2938 | if (s == s0) { |
| 2939 | k++; |
| 2940 | *s++ = '1'; |
| 2941 | goto ret; |
| 2942 | } |
| 2943 | ++*s++; |
| 2944 | } |
| 2945 | else { |
| 2946 | while(*--s == '0'); |
| 2947 | s++; |
| 2948 | } |
| 2949 | ret: |
| 2950 | Bfree(S); |
| 2951 | if (mhi) { |
| 2952 | if (mlo && mlo != mhi) |
| 2953 | Bfree(mlo); |
| 2954 | Bfree(mhi); |
| 2955 | } |
| 2956 | ret1: |
| 2957 | Bfree(b); |
| 2958 | *s = 0; |
| 2959 | *decpt = k + 1; |
| 2960 | if (rve) |
| 2961 | *rve = s; |
| 2962 | return s0; |
| 2963 | failed_malloc: |
| 2964 | if (S) |
| 2965 | Bfree(S); |
| 2966 | if (mlo && mlo != mhi) |
| 2967 | Bfree(mlo); |
| 2968 | if (mhi) |
| 2969 | Bfree(mhi); |
| 2970 | if (b) |
| 2971 | Bfree(b); |
| 2972 | if (s0) |
| 2973 | _Py_dg_freedtoa(s0); |
| 2974 | return NULL; |
| 2975 | } |
| 2976 | #ifdef __cplusplus |
| 2977 | } |
| 2978 | #endif |
| 2979 | |
| 2980 | #endif /* PY_NO_SHORT_FLOAT_REPR */ |