File: | Python/dtoa.c |
Location: | line 1152, column 14 |
Description: | The left operand to '-' is always 0 |
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. | ||
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: | ||
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 | * | ||
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 | * | ||
64 | * 7. _Py_dg_strtod has been modified so that it doesn't accept strings with | ||
65 | * leading whitespace. | ||
66 | * | ||
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 MALLOCPyMem_Malloc PyMem_Malloc | ||
126 | #define FREEPyMem_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 | |||
154 | #if defined(HAVE_UINT32_T1) && defined(HAVE_INT32_T1) | ||
155 | typedef PY_UINT32_Tuint32_t ULong; | ||
156 | typedef PY_INT32_Tint32_t Long; | ||
157 | #else | ||
158 | #error "Failed to find an exact-width 32-bit integer type" | ||
159 | #endif | ||
160 | |||
161 | #if defined(HAVE_UINT64_T1) | ||
162 | #define ULLonguint64_t PY_UINT64_Tuint64_t | ||
163 | #else | ||
164 | #undef ULLonguint64_t | ||
165 | #endif | ||
166 | |||
167 | #undef DEBUG | ||
168 | #ifdef Py_DEBUG1 | ||
169 | #define DEBUG | ||
170 | #endif | ||
171 | |||
172 | /* End Python #define linking */ | ||
173 | |||
174 | #ifdef DEBUG | ||
175 | #define Bug(x){fprintf(__stderrp, "%s\n", x); exit(1);} {fprintf(stderr__stderrp, "%s\n", x); exit(1);} | ||
176 | #endif | ||
177 | |||
178 | #ifndef PRIVATE_MEM2304 | ||
179 | #define PRIVATE_MEM2304 2304 | ||
180 | #endif | ||
181 | #define PRIVATE_mem((2304 +sizeof(double)-1)/sizeof(double)) ((PRIVATE_MEM2304+sizeof(double)-1)/sizeof(double)) | ||
182 | static double private_mem[PRIVATE_mem((2304 +sizeof(double)-1)/sizeof(double))], *pmem_next = private_mem; | ||
183 | |||
184 | #ifdef __cplusplus | ||
185 | extern "C" { | ||
186 | #endif | ||
187 | |||
188 | typedef union { double d; ULong L[2]; } U; | ||
189 | |||
190 | #ifdef IEEE_8087 | ||
191 | #define word0(x)(x)->L[1] (x)->L[1] | ||
192 | #define word1(x)(x)->L[0] (x)->L[0] | ||
193 | #else | ||
194 | #define word0(x)(x)->L[1] (x)->L[0] | ||
195 | #define word1(x)(x)->L[0] (x)->L[1] | ||
196 | #endif | ||
197 | #define dval(x)(x)->d (x)->d | ||
198 | |||
199 | #ifndef STRTOD_DIGLIM40 | ||
200 | #define STRTOD_DIGLIM40 40 | ||
201 | #endif | ||
202 | |||
203 | /* maximum permitted exponent value for strtod; exponents larger than | ||
204 | MAX_ABS_EXP in absolute value get truncated to +-MAX_ABS_EXP. MAX_ABS_EXP | ||
205 | should fit into an int. */ | ||
206 | #ifndef MAX_ABS_EXP19999U | ||
207 | #define MAX_ABS_EXP19999U 19999U | ||
208 | #endif | ||
209 | |||
210 | /* The following definition of Storeinc is appropriate for MIPS processors. | ||
211 | * An alternative that might be better on some machines is | ||
212 | * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff) | ||
213 | */ | ||
214 | #if defined(IEEE_8087) | ||
215 | #define Storeinc(a,b,c)(((unsigned short *)a)[1] = (unsigned short)b, ((unsigned short *)a)[0] = (unsigned short)c, a++) (((unsigned short *)a)[1] = (unsigned short)b, \ | ||
216 | ((unsigned short *)a)[0] = (unsigned short)c, a++) | ||
217 | #else | ||
218 | #define Storeinc(a,b,c)(((unsigned short *)a)[1] = (unsigned short)b, ((unsigned short *)a)[0] = (unsigned short)c, a++) (((unsigned short *)a)[0] = (unsigned short)b, \ | ||
219 | ((unsigned short *)a)[1] = (unsigned short)c, a++) | ||
220 | #endif | ||
221 | |||
222 | /* #define P DBL_MANT_DIG */ | ||
223 | /* Ten_pmax = floor(P*log(2)/log(5)) */ | ||
224 | /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */ | ||
225 | /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */ | ||
226 | /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */ | ||
227 | |||
228 | #define Exp_shift20 20 | ||
229 | #define Exp_shift120 20 | ||
230 | #define Exp_msk10x100000 0x100000 | ||
231 | #define Exp_msk110x100000 0x100000 | ||
232 | #define Exp_mask0x7ff00000 0x7ff00000 | ||
233 | #define P53 53 | ||
234 | #define Nbits53 53 | ||
235 | #define Bias1023 1023 | ||
236 | #define Emax1023 1023 | ||
237 | #define Emin(-1022) (-1022) | ||
238 | #define Etiny(-1074) (-1074) /* smallest denormal is 2**Etiny */ | ||
239 | #define Exp_10x3ff00000 0x3ff00000 | ||
240 | #define Exp_110x3ff00000 0x3ff00000 | ||
241 | #define Ebits11 11 | ||
242 | #define Frac_mask0xfffff 0xfffff | ||
243 | #define Frac_mask10xfffff 0xfffff | ||
244 | #define Ten_pmax22 22 | ||
245 | #define Bletch0x10 0x10 | ||
246 | #define Bndry_mask0xfffff 0xfffff | ||
247 | #define Bndry_mask10xfffff 0xfffff | ||
248 | #define Sign_bit0x80000000 0x80000000 | ||
249 | #define Log2P1 1 | ||
250 | #define Tiny00 0 | ||
251 | #define Tiny11 1 | ||
252 | #define Quick_max14 14 | ||
253 | #define Int_max14 14 | ||
254 | |||
255 | #ifndef Flt_Rounds(__builtin_flt_rounds()) | ||
256 | #ifdef FLT_ROUNDS(__builtin_flt_rounds()) | ||
257 | #define Flt_Rounds(__builtin_flt_rounds()) FLT_ROUNDS(__builtin_flt_rounds()) | ||
258 | #else | ||
259 | #define Flt_Rounds(__builtin_flt_rounds()) 1 | ||
260 | #endif | ||
261 | #endif /*Flt_Rounds*/ | ||
262 | |||
263 | #define Rounding(__builtin_flt_rounds()) Flt_Rounds(__builtin_flt_rounds()) | ||
264 | |||
265 | #define Big0(0xfffff | 0x100000*(1024 +1023 -1)) (Frac_mask10xfffff | Exp_msk10x100000*(DBL_MAX_EXP1024+Bias1023-1)) | ||
266 | #define Big10xffffffff 0xffffffff | ||
267 | |||
268 | /* struct BCinfo is used to pass information from _Py_dg_strtod to bigcomp */ | ||
269 | |||
270 | typedef struct BCinfo BCinfo; | ||
271 | struct | ||
272 | BCinfo { | ||
273 | int e0, nd, nd0, scale; | ||
274 | }; | ||
275 | |||
276 | #define FFFFFFFF0xffffffffUL 0xffffffffUL | ||
277 | |||
278 | #define Kmax7 7 | ||
279 | |||
280 | /* struct Bigint is used to represent arbitrary-precision integers. These | ||
281 | integers are stored in sign-magnitude format, with the magnitude stored as | ||
282 | an array of base 2**32 digits. Bigints are always normalized: if x is a | ||
283 | Bigint then x->wds >= 1, and either x->wds == 1 or x[wds-1] is nonzero. | ||
284 | |||
285 | The Bigint fields are as follows: | ||
286 | |||
287 | - next is a header used by Balloc and Bfree to keep track of lists | ||
288 | of freed Bigints; it's also used for the linked list of | ||
289 | powers of 5 of the form 5**2**i used by pow5mult. | ||
290 | - k indicates which pool this Bigint was allocated from | ||
291 | - maxwds is the maximum number of words space was allocated for | ||
292 | (usually maxwds == 2**k) | ||
293 | - sign is 1 for negative Bigints, 0 for positive. The sign is unused | ||
294 | (ignored on inputs, set to 0 on outputs) in almost all operations | ||
295 | involving Bigints: a notable exception is the diff function, which | ||
296 | ignores signs on inputs but sets the sign of the output correctly. | ||
297 | - wds is the actual number of significant words | ||
298 | - x contains the vector of words (digits) for this Bigint, from least | ||
299 | significant (x[0]) to most significant (x[wds-1]). | ||
300 | */ | ||
301 | |||
302 | struct | ||
303 | Bigint { | ||
304 | struct Bigint *next; | ||
305 | int k, maxwds, sign, wds; | ||
306 | ULong x[1]; | ||
307 | }; | ||
308 | |||
309 | typedef struct Bigint Bigint; | ||
310 | |||
311 | #ifndef Py_USING_MEMORY_DEBUGGER | ||
312 | |||
313 | /* Memory management: memory is allocated from, and returned to, Kmax+1 pools | ||
314 | of memory, where pool k (0 <= k <= Kmax) is for Bigints b with b->maxwds == | ||
315 | 1 << k. These pools are maintained as linked lists, with freelist[k] | ||
316 | pointing to the head of the list for pool k. | ||
317 | |||
318 | On allocation, if there's no free slot in the appropriate pool, MALLOC is | ||
319 | called to get more memory. This memory is not returned to the system until | ||
320 | Python quits. There's also a private memory pool that's allocated from | ||
321 | in preference to using MALLOC. | ||
322 | |||
323 | For Bigints with more than (1 << Kmax) digits (which implies at least 1233 | ||
324 | decimal digits), memory is directly allocated using MALLOC, and freed using | ||
325 | FREE. | ||
326 | |||
327 | XXX: it would be easy to bypass this memory-management system and | ||
328 | translate each call to Balloc into a call to PyMem_Malloc, and each | ||
329 | Bfree to PyMem_Free. Investigate whether this has any significant | ||
330 | performance on impact. */ | ||
331 | |||
332 | static Bigint *freelist[Kmax7+1]; | ||
333 | |||
334 | /* Allocate space for a Bigint with up to 1<<k digits */ | ||
335 | |||
336 | static Bigint * | ||
337 | Balloc(int k) | ||
338 | { | ||
339 | int x; | ||
340 | Bigint *rv; | ||
341 | unsigned int len; | ||
342 | |||
343 | if (k <= Kmax7 && (rv = freelist[k])) | ||
344 | freelist[k] = rv->next; | ||
345 | else { | ||
346 | x = 1 << k; | ||
347 | len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1) | ||
348 | /sizeof(double); | ||
349 | if (k <= Kmax7 && pmem_next - private_mem + len <= PRIVATE_mem((2304 +sizeof(double)-1)/sizeof(double))) { | ||
350 | rv = (Bigint*)pmem_next; | ||
351 | pmem_next += len; | ||
352 | } | ||
353 | else { | ||
354 | rv = (Bigint*)MALLOCPyMem_Malloc(len*sizeof(double)); | ||
355 | if (rv == NULL((void *)0)) | ||
356 | return NULL((void *)0); | ||
357 | } | ||
358 | rv->k = k; | ||
359 | rv->maxwds = x; | ||
360 | } | ||
361 | rv->sign = rv->wds = 0; | ||
362 | return rv; | ||
363 | } | ||
364 | |||
365 | /* Free a Bigint allocated with Balloc */ | ||
366 | |||
367 | static void | ||
368 | Bfree(Bigint *v) | ||
369 | { | ||
370 | if (v) { | ||
371 | if (v->k > Kmax7) | ||
372 | FREEPyMem_Free((void*)v); | ||
373 | else { | ||
374 | v->next = freelist[v->k]; | ||
375 | freelist[v->k] = v; | ||
376 | } | ||
377 | } | ||
378 | } | ||
379 | |||
380 | #else | ||
381 | |||
382 | /* Alternative versions of Balloc and Bfree that use PyMem_Malloc and | ||
383 | PyMem_Free directly in place of the custom memory allocation scheme above. | ||
384 | These are provided for the benefit of memory debugging tools like | ||
385 | Valgrind. */ | ||
386 | |||
387 | /* Allocate space for a Bigint with up to 1<<k digits */ | ||
388 | |||
389 | static Bigint * | ||
390 | Balloc(int k) | ||
391 | { | ||
392 | int x; | ||
393 | Bigint *rv; | ||
394 | unsigned int len; | ||
395 | |||
396 | x = 1 << k; | ||
397 | len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1) | ||
398 | /sizeof(double); | ||
399 | |||
400 | rv = (Bigint*)MALLOCPyMem_Malloc(len*sizeof(double)); | ||
401 | if (rv == NULL((void *)0)) | ||
402 | return NULL((void *)0); | ||
403 | |||
404 | rv->k = k; | ||
405 | rv->maxwds = x; | ||
406 | rv->sign = rv->wds = 0; | ||
407 | return rv; | ||
408 | } | ||
409 | |||
410 | /* Free a Bigint allocated with Balloc */ | ||
411 | |||
412 | static void | ||
413 | Bfree(Bigint *v) | ||
414 | { | ||
415 | if (v) { | ||
416 | FREEPyMem_Free((void*)v); | ||
417 | } | ||
418 | } | ||
419 | |||
420 | #endif /* Py_USING_MEMORY_DEBUGGER */ | ||
421 | |||
422 | #define Bcopy(x,y)((__builtin_object_size ((char *)&x->sign, 0) != (size_t ) -1) ? __builtin___memcpy_chk ((char *)&x->sign, (char *)&y->sign, y->wds*sizeof(Long) + 2*sizeof(int), __builtin_object_size ((char *)&x->sign, 0)) : __inline_memcpy_chk ((char * )&x->sign, (char *)&y->sign, y->wds*sizeof(Long ) + 2*sizeof(int))) memcpy((char *)&x->sign, (char *)&y->sign, \((__builtin_object_size ((char *)&x->sign, 0) != (size_t ) -1) ? __builtin___memcpy_chk ((char *)&x->sign, (char *)&y->sign, y->wds*sizeof(Long) + 2*sizeof(int), __builtin_object_size ((char *)&x->sign, 0)) : __inline_memcpy_chk ((char * )&x->sign, (char *)&y->sign, y->wds*sizeof(Long ) + 2*sizeof(int))) | ||
423 | y->wds*sizeof(Long) + 2*sizeof(int))((__builtin_object_size ((char *)&x->sign, 0) != (size_t ) -1) ? __builtin___memcpy_chk ((char *)&x->sign, (char *)&y->sign, y->wds*sizeof(Long) + 2*sizeof(int), __builtin_object_size ((char *)&x->sign, 0)) : __inline_memcpy_chk ((char * )&x->sign, (char *)&y->sign, y->wds*sizeof(Long ) + 2*sizeof(int))) | ||
424 | |||
425 | /* Multiply a Bigint b by m and add a. Either modifies b in place and returns | ||
426 | a pointer to the modified b, or Bfrees b and returns a pointer to a copy. | ||
427 | On failure, return NULL. In this case, b will have been already freed. */ | ||
428 | |||
429 | static Bigint * | ||
430 | multadd(Bigint *b, int m, int a) /* multiply by m and add a */ | ||
431 | { | ||
432 | int i, wds; | ||
433 | #ifdef ULLonguint64_t | ||
434 | ULong *x; | ||
435 | ULLonguint64_t carry, y; | ||
436 | #else | ||
437 | ULong carry, *x, y; | ||
438 | ULong xi, z; | ||
439 | #endif | ||
440 | Bigint *b1; | ||
441 | |||
442 | wds = b->wds; | ||
443 | x = b->x; | ||
444 | i = 0; | ||
445 | carry = a; | ||
446 | do { | ||
447 | #ifdef ULLonguint64_t | ||
448 | y = *x * (ULLonguint64_t)m + carry; | ||
449 | carry = y >> 32; | ||
450 | *x++ = (ULong)(y & FFFFFFFF0xffffffffUL); | ||
451 | #else | ||
452 | xi = *x; | ||
453 | y = (xi & 0xffff) * m + carry; | ||
454 | z = (xi >> 16) * m + (y >> 16); | ||
455 | carry = z >> 16; | ||
456 | *x++ = (z << 16) + (y & 0xffff); | ||
457 | #endif | ||
458 | } | ||
459 | while(++i < wds); | ||
460 | if (carry) { | ||
461 | if (wds >= b->maxwds) { | ||
462 | b1 = Balloc(b->k+1); | ||
463 | if (b1 == NULL((void *)0)){ | ||
464 | Bfree(b); | ||
465 | return NULL((void *)0); | ||
466 | } | ||
467 | Bcopy(b1, b)((__builtin_object_size ((char *)&b1->sign, 0) != (size_t ) -1) ? __builtin___memcpy_chk ((char *)&b1->sign, (char *)&b->sign, b->wds*sizeof(Long) + 2*sizeof(int), __builtin_object_size ((char *)&b1->sign, 0)) : __inline_memcpy_chk ((char * )&b1->sign, (char *)&b->sign, b->wds*sizeof( Long) + 2*sizeof(int))); | ||
468 | Bfree(b); | ||
469 | b = b1; | ||
470 | } | ||
471 | b->x[wds++] = (ULong)carry; | ||
472 | b->wds = wds; | ||
473 | } | ||
474 | return b; | ||
475 | } | ||
476 | |||
477 | /* convert a string s containing nd decimal digits (possibly containing a | ||
478 | decimal separator at position nd0, which is ignored) to a Bigint. This | ||
479 | function carries on where the parsing code in _Py_dg_strtod leaves off: on | ||
480 | entry, y9 contains the result of converting the first 9 digits. Returns | ||
481 | NULL on failure. */ | ||
482 | |||
483 | static Bigint * | ||
484 | s2b(const char *s, int nd0, int nd, ULong y9) | ||
485 | { | ||
486 | Bigint *b; | ||
487 | int i, k; | ||
488 | Long x, y; | ||
489 | |||
490 | x = (nd + 8) / 9; | ||
491 | for(k = 0, y = 1; x > y; y <<= 1, k++) ; | ||
492 | b = Balloc(k); | ||
493 | if (b == NULL((void *)0)) | ||
494 | return NULL((void *)0); | ||
495 | b->x[0] = y9; | ||
496 | b->wds = 1; | ||
497 | |||
498 | if (nd <= 9) | ||
499 | return b; | ||
500 | |||
501 | s += 9; | ||
502 | for (i = 9; i < nd0; i++) { | ||
503 | b = multadd(b, 10, *s++ - '0'); | ||
504 | if (b == NULL((void *)0)) | ||
505 | return NULL((void *)0); | ||
506 | } | ||
507 | s++; | ||
508 | for(; i < nd; i++) { | ||
509 | b = multadd(b, 10, *s++ - '0'); | ||
510 | if (b == NULL((void *)0)) | ||
511 | return NULL((void *)0); | ||
512 | } | ||
513 | return b; | ||
514 | } | ||
515 | |||
516 | /* count leading 0 bits in the 32-bit integer x. */ | ||
517 | |||
518 | static int | ||
519 | hi0bits(ULong x) | ||
520 | { | ||
521 | int k = 0; | ||
522 | |||
523 | if (!(x & 0xffff0000)) { | ||
524 | k = 16; | ||
525 | x <<= 16; | ||
526 | } | ||
527 | if (!(x & 0xff000000)) { | ||
528 | k += 8; | ||
529 | x <<= 8; | ||
530 | } | ||
531 | if (!(x & 0xf0000000)) { | ||
532 | k += 4; | ||
533 | x <<= 4; | ||
534 | } | ||
535 | if (!(x & 0xc0000000)) { | ||
536 | k += 2; | ||
537 | x <<= 2; | ||
538 | } | ||
539 | if (!(x & 0x80000000)) { | ||
540 | k++; | ||
541 | if (!(x & 0x40000000)) | ||
542 | return 32; | ||
543 | } | ||
544 | return k; | ||
545 | } | ||
546 | |||
547 | /* count trailing 0 bits in the 32-bit integer y, and shift y right by that | ||
548 | number of bits. */ | ||
549 | |||
550 | static int | ||
551 | lo0bits(ULong *y) | ||
552 | { | ||
553 | int k; | ||
554 | ULong x = *y; | ||
555 | |||
556 | if (x & 7) { | ||
557 | if (x & 1) | ||
558 | return 0; | ||
559 | if (x & 2) { | ||
560 | *y = x >> 1; | ||
561 | return 1; | ||
562 | } | ||
563 | *y = x >> 2; | ||
564 | return 2; | ||
565 | } | ||
566 | k = 0; | ||
567 | if (!(x & 0xffff)) { | ||
568 | k = 16; | ||
569 | x >>= 16; | ||
570 | } | ||
571 | if (!(x & 0xff)) { | ||
572 | k += 8; | ||
573 | x >>= 8; | ||
574 | } | ||
575 | if (!(x & 0xf)) { | ||
576 | k += 4; | ||
577 | x >>= 4; | ||
578 | } | ||
579 | if (!(x & 0x3)) { | ||
580 | k += 2; | ||
581 | x >>= 2; | ||
582 | } | ||
583 | if (!(x & 1)) { | ||
584 | k++; | ||
585 | x >>= 1; | ||
586 | if (!x) | ||
587 | return 32; | ||
588 | } | ||
589 | *y = x; | ||
590 | return k; | ||
591 | } | ||
592 | |||
593 | /* convert a small nonnegative integer to a Bigint */ | ||
594 | |||
595 | static Bigint * | ||
596 | i2b(int i) | ||
597 | { | ||
598 | Bigint *b; | ||
599 | |||
600 | b = Balloc(1); | ||
601 | if (b == NULL((void *)0)) | ||
602 | return NULL((void *)0); | ||
603 | b->x[0] = i; | ||
604 | b->wds = 1; | ||
605 | return b; | ||
606 | } | ||
607 | |||
608 | /* multiply two Bigints. Returns a new Bigint, or NULL on failure. Ignores | ||
609 | the signs of a and b. */ | ||
610 | |||
611 | static Bigint * | ||
612 | mult(Bigint *a, Bigint *b) | ||
613 | { | ||
614 | Bigint *c; | ||
615 | int k, wa, wb, wc; | ||
616 | ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0; | ||
617 | ULong y; | ||
618 | #ifdef ULLonguint64_t | ||
619 | ULLonguint64_t carry, z; | ||
620 | #else | ||
621 | ULong carry, z; | ||
622 | ULong z2; | ||
623 | #endif | ||
624 | |||
625 | if ((!a->x[0] && a->wds == 1) || (!b->x[0] && b->wds == 1)) { | ||
626 | c = Balloc(0); | ||
627 | if (c == NULL((void *)0)) | ||
628 | return NULL((void *)0); | ||
629 | c->wds = 1; | ||
630 | c->x[0] = 0; | ||
631 | return c; | ||
632 | } | ||
633 | |||
634 | if (a->wds < b->wds) { | ||
635 | c = a; | ||
636 | a = b; | ||
637 | b = c; | ||
638 | } | ||
639 | k = a->k; | ||
640 | wa = a->wds; | ||
641 | wb = b->wds; | ||
642 | wc = wa + wb; | ||
643 | if (wc > a->maxwds) | ||
644 | k++; | ||
645 | c = Balloc(k); | ||
646 | if (c == NULL((void *)0)) | ||
647 | return NULL((void *)0); | ||
648 | for(x = c->x, xa = x + wc; x < xa; x++) | ||
649 | *x = 0; | ||
650 | xa = a->x; | ||
651 | xae = xa + wa; | ||
652 | xb = b->x; | ||
653 | xbe = xb + wb; | ||
654 | xc0 = c->x; | ||
655 | #ifdef ULLonguint64_t | ||
656 | for(; xb < xbe; xc0++) { | ||
657 | if ((y = *xb++)) { | ||
658 | x = xa; | ||
659 | xc = xc0; | ||
660 | carry = 0; | ||
661 | do { | ||
662 | z = *x++ * (ULLonguint64_t)y + *xc + carry; | ||
663 | carry = z >> 32; | ||
664 | *xc++ = (ULong)(z & FFFFFFFF0xffffffffUL); | ||
665 | } | ||
666 | while(x < xae); | ||
667 | *xc = (ULong)carry; | ||
668 | } | ||
669 | } | ||
670 | #else | ||
671 | for(; xb < xbe; xb++, xc0++) { | ||
672 | if (y = *xb & 0xffff) { | ||
673 | x = xa; | ||
674 | xc = xc0; | ||
675 | carry = 0; | ||
676 | do { | ||
677 | z = (*x & 0xffff) * y + (*xc & 0xffff) + carry; | ||
678 | carry = z >> 16; | ||
679 | z2 = (*x++ >> 16) * y + (*xc >> 16) + carry; | ||
680 | carry = z2 >> 16; | ||
681 | Storeinc(xc, z2, z)(((unsigned short *)xc)[1] = (unsigned short)z2, ((unsigned short *)xc)[0] = (unsigned short)z, xc++); | ||
682 | } | ||
683 | while(x < xae); | ||
684 | *xc = carry; | ||
685 | } | ||
686 | if (y = *xb >> 16) { | ||
687 | x = xa; | ||
688 | xc = xc0; | ||
689 | carry = 0; | ||
690 | z2 = *xc; | ||
691 | do { | ||
692 | z = (*x & 0xffff) * y + (*xc >> 16) + carry; | ||
693 | carry = z >> 16; | ||
694 | Storeinc(xc, z, z2)(((unsigned short *)xc)[1] = (unsigned short)z, ((unsigned short *)xc)[0] = (unsigned short)z2, xc++); | ||
695 | z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry; | ||
696 | carry = z2 >> 16; | ||
697 | } | ||
698 | while(x < xae); | ||
699 | *xc = z2; | ||
700 | } | ||
701 | } | ||
702 | #endif | ||
703 | for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ; | ||
704 | c->wds = wc; | ||
705 | return c; | ||
706 | } | ||
707 | |||
708 | #ifndef Py_USING_MEMORY_DEBUGGER | ||
709 | |||
710 | /* p5s is a linked list of powers of 5 of the form 5**(2**i), i >= 2 */ | ||
711 | |||
712 | static Bigint *p5s; | ||
713 | |||
714 | /* multiply the Bigint b by 5**k. Returns a pointer to the result, or NULL on | ||
715 | failure; if the returned pointer is distinct from b then the original | ||
716 | Bigint b will have been Bfree'd. Ignores the sign of b. */ | ||
717 | |||
718 | static Bigint * | ||
719 | pow5mult(Bigint *b, int k) | ||
720 | { | ||
721 | Bigint *b1, *p5, *p51; | ||
722 | int i; | ||
723 | static int p05[3] = { 5, 25, 125 }; | ||
724 | |||
725 | if ((i = k & 3)) { | ||
726 | b = multadd(b, p05[i-1], 0); | ||
727 | if (b == NULL((void *)0)) | ||
728 | return NULL((void *)0); | ||
729 | } | ||
730 | |||
731 | if (!(k >>= 2)) | ||
732 | return b; | ||
733 | p5 = p5s; | ||
734 | if (!p5) { | ||
735 | /* first time */ | ||
736 | p5 = i2b(625); | ||
737 | if (p5 == NULL((void *)0)) { | ||
738 | Bfree(b); | ||
739 | return NULL((void *)0); | ||
740 | } | ||
741 | p5s = p5; | ||
742 | p5->next = 0; | ||
743 | } | ||
744 | for(;;) { | ||
745 | if (k & 1) { | ||
746 | b1 = mult(b, p5); | ||
747 | Bfree(b); | ||
748 | b = b1; | ||
749 | if (b == NULL((void *)0)) | ||
750 | return NULL((void *)0); | ||
751 | } | ||
752 | if (!(k >>= 1)) | ||
753 | break; | ||
754 | p51 = p5->next; | ||
755 | if (!p51) { | ||
756 | p51 = mult(p5,p5); | ||
757 | if (p51 == NULL((void *)0)) { | ||
758 | Bfree(b); | ||
759 | return NULL((void *)0); | ||
760 | } | ||
761 | p51->next = 0; | ||
762 | p5->next = p51; | ||
763 | } | ||
764 | p5 = p51; | ||
765 | } | ||
766 | return b; | ||
767 | } | ||
768 | |||
769 | #else | ||
770 | |||
771 | /* Version of pow5mult that doesn't cache powers of 5. Provided for | ||
772 | the benefit of memory debugging tools like Valgrind. */ | ||
773 | |||
774 | static Bigint * | ||
775 | pow5mult(Bigint *b, int k) | ||
776 | { | ||
777 | Bigint *b1, *p5, *p51; | ||
778 | int i; | ||
779 | static int p05[3] = { 5, 25, 125 }; | ||
780 | |||
781 | if ((i = k & 3)) { | ||
782 | b = multadd(b, p05[i-1], 0); | ||
783 | if (b == NULL((void *)0)) | ||
784 | return NULL((void *)0); | ||
785 | } | ||
786 | |||
787 | if (!(k >>= 2)) | ||
788 | return b; | ||
789 | p5 = i2b(625); | ||
790 | if (p5 == NULL((void *)0)) { | ||
791 | Bfree(b); | ||
792 | return NULL((void *)0); | ||
793 | } | ||
794 | |||
795 | for(;;) { | ||
796 | if (k & 1) { | ||
797 | b1 = mult(b, p5); | ||
798 | Bfree(b); | ||
799 | b = b1; | ||
800 | if (b == NULL((void *)0)) { | ||
801 | Bfree(p5); | ||
802 | return NULL((void *)0); | ||
803 | } | ||
804 | } | ||
805 | if (!(k >>= 1)) | ||
806 | break; | ||
807 | p51 = mult(p5, p5); | ||
808 | Bfree(p5); | ||
809 | p5 = p51; | ||
810 | if (p5 == NULL((void *)0)) { | ||
811 | Bfree(b); | ||
812 | return NULL((void *)0); | ||
813 | } | ||
814 | } | ||
815 | Bfree(p5); | ||
816 | return b; | ||
817 | } | ||
818 | |||
819 | #endif /* Py_USING_MEMORY_DEBUGGER */ | ||
820 | |||
821 | /* shift a Bigint b left by k bits. Return a pointer to the shifted result, | ||
822 | or NULL on failure. If the returned pointer is distinct from b then the | ||
823 | original b will have been Bfree'd. Ignores the sign of b. */ | ||
824 | |||
825 | static Bigint * | ||
826 | lshift(Bigint *b, int k) | ||
827 | { | ||
828 | int i, k1, n, n1; | ||
829 | Bigint *b1; | ||
830 | ULong *x, *x1, *xe, z; | ||
831 | |||
832 | if (!k || (!b->x[0] && b->wds == 1)) | ||
833 | return b; | ||
834 | |||
835 | n = k >> 5; | ||
836 | k1 = b->k; | ||
837 | n1 = n + b->wds + 1; | ||
838 | for(i = b->maxwds; n1 > i; i <<= 1) | ||
839 | k1++; | ||
840 | b1 = Balloc(k1); | ||
841 | if (b1 == NULL((void *)0)) { | ||
842 | Bfree(b); | ||
843 | return NULL((void *)0); | ||
844 | } | ||
845 | x1 = b1->x; | ||
846 | for(i = 0; i < n; i++) | ||
847 | *x1++ = 0; | ||
848 | x = b->x; | ||
849 | xe = x + b->wds; | ||
850 | if (k &= 0x1f) { | ||
851 | k1 = 32 - k; | ||
852 | z = 0; | ||
853 | do { | ||
854 | *x1++ = *x << k | z; | ||
855 | z = *x++ >> k1; | ||
856 | } | ||
857 | while(x < xe); | ||
858 | if ((*x1 = z)) | ||
859 | ++n1; | ||
860 | } | ||
861 | else do | ||
862 | *x1++ = *x++; | ||
863 | while(x < xe); | ||
864 | b1->wds = n1 - 1; | ||
865 | Bfree(b); | ||
866 | return b1; | ||
867 | } | ||
868 | |||
869 | /* Do a three-way compare of a and b, returning -1 if a < b, 0 if a == b and | ||
870 | 1 if a > b. Ignores signs of a and b. */ | ||
871 | |||
872 | static int | ||
873 | cmp(Bigint *a, Bigint *b) | ||
874 | { | ||
875 | ULong *xa, *xa0, *xb, *xb0; | ||
876 | int i, j; | ||
877 | |||
878 | i = a->wds; | ||
879 | j = b->wds; | ||
880 | #ifdef DEBUG | ||
881 | if (i > 1 && !a->x[i-1]) | ||
882 | Bug("cmp called with a->x[a->wds-1] == 0"){fprintf(__stderrp, "%s\n", "cmp called with a->x[a->wds-1] == 0" ); exit(1);}; | ||
883 | if (j > 1 && !b->x[j-1]) | ||
884 | Bug("cmp called with b->x[b->wds-1] == 0"){fprintf(__stderrp, "%s\n", "cmp called with b->x[b->wds-1] == 0" ); exit(1);}; | ||
885 | #endif | ||
886 | if (i -= j) | ||
887 | return i; | ||
888 | xa0 = a->x; | ||
889 | xa = xa0 + j; | ||
890 | xb0 = b->x; | ||
891 | xb = xb0 + j; | ||
892 | for(;;) { | ||
893 | if (*--xa != *--xb) | ||
894 | return *xa < *xb ? -1 : 1; | ||
895 | if (xa <= xa0) | ||
896 | break; | ||
897 | } | ||
898 | return 0; | ||
899 | } | ||
900 | |||
901 | /* Take the difference of Bigints a and b, returning a new Bigint. Returns | ||
902 | NULL on failure. The signs of a and b are ignored, but the sign of the | ||
903 | result is set appropriately. */ | ||
904 | |||
905 | static Bigint * | ||
906 | diff(Bigint *a, Bigint *b) | ||
907 | { | ||
908 | Bigint *c; | ||
909 | int i, wa, wb; | ||
910 | ULong *xa, *xae, *xb, *xbe, *xc; | ||
911 | #ifdef ULLonguint64_t | ||
912 | ULLonguint64_t borrow, y; | ||
913 | #else | ||
914 | ULong borrow, y; | ||
915 | ULong z; | ||
916 | #endif | ||
917 | |||
918 | i = cmp(a,b); | ||
919 | if (!i) { | ||
920 | c = Balloc(0); | ||
921 | if (c == NULL((void *)0)) | ||
922 | return NULL((void *)0); | ||
923 | c->wds = 1; | ||
924 | c->x[0] = 0; | ||
925 | return c; | ||
926 | } | ||
927 | if (i < 0) { | ||
928 | c = a; | ||
929 | a = b; | ||
930 | b = c; | ||
931 | i = 1; | ||
932 | } | ||
933 | else | ||
934 | i = 0; | ||
935 | c = Balloc(a->k); | ||
936 | if (c == NULL((void *)0)) | ||
937 | return NULL((void *)0); | ||
938 | c->sign = i; | ||
939 | wa = a->wds; | ||
940 | xa = a->x; | ||
941 | xae = xa + wa; | ||
942 | wb = b->wds; | ||
943 | xb = b->x; | ||
944 | xbe = xb + wb; | ||
945 | xc = c->x; | ||
946 | borrow = 0; | ||
947 | #ifdef ULLonguint64_t | ||
948 | do { | ||
949 | y = (ULLonguint64_t)*xa++ - *xb++ - borrow; | ||
950 | borrow = y >> 32 & (ULong)1; | ||
951 | *xc++ = (ULong)(y & FFFFFFFF0xffffffffUL); | ||
952 | } | ||
953 | while(xb < xbe); | ||
954 | while(xa < xae) { | ||
955 | y = *xa++ - borrow; | ||
956 | borrow = y >> 32 & (ULong)1; | ||
957 | *xc++ = (ULong)(y & FFFFFFFF0xffffffffUL); | ||
958 | } | ||
959 | #else | ||
960 | do { | ||
961 | y = (*xa & 0xffff) - (*xb & 0xffff) - borrow; | ||
962 | borrow = (y & 0x10000) >> 16; | ||
963 | z = (*xa++ >> 16) - (*xb++ >> 16) - borrow; | ||
964 | borrow = (z & 0x10000) >> 16; | ||
965 | Storeinc(xc, z, y)(((unsigned short *)xc)[1] = (unsigned short)z, ((unsigned short *)xc)[0] = (unsigned short)y, xc++); | ||
966 | } | ||
967 | while(xb < xbe); | ||
968 | while(xa < xae) { | ||
969 | y = (*xa & 0xffff) - borrow; | ||
970 | borrow = (y & 0x10000) >> 16; | ||
971 | z = (*xa++ >> 16) - borrow; | ||
972 | borrow = (z & 0x10000) >> 16; | ||
973 | Storeinc(xc, z, y)(((unsigned short *)xc)[1] = (unsigned short)z, ((unsigned short *)xc)[0] = (unsigned short)y, xc++); | ||
974 | } | ||
975 | #endif | ||
976 | while(!*--xc) | ||
977 | wa--; | ||
978 | c->wds = wa; | ||
979 | return c; | ||
980 | } | ||
981 | |||
982 | /* Given a positive normal double x, return the difference between x and the | ||
983 | next double up. Doesn't give correct results for subnormals. */ | ||
984 | |||
985 | static double | ||
986 | ulp(U *x) | ||
987 | { | ||
988 | Long L; | ||
989 | U u; | ||
990 | |||
991 | L = (word0(x)(x)->L[1] & Exp_mask0x7ff00000) - (P53-1)*Exp_msk10x100000; | ||
992 | word0(&u)(&u)->L[1] = L; | ||
993 | word1(&u)(&u)->L[0] = 0; | ||
994 | return dval(&u)(&u)->d; | ||
995 | } | ||
996 | |||
997 | /* Convert a Bigint to a double plus an exponent */ | ||
998 | |||
999 | static double | ||
1000 | b2d(Bigint *a, int *e) | ||
1001 | { | ||
1002 | ULong *xa, *xa0, w, y, z; | ||
1003 | int k; | ||
1004 | U d; | ||
1005 | |||
1006 | xa0 = a->x; | ||
1007 | xa = xa0 + a->wds; | ||
1008 | y = *--xa; | ||
1009 | #ifdef DEBUG | ||
1010 | if (!y) Bug("zero y in b2d"){fprintf(__stderrp, "%s\n", "zero y in b2d"); exit(1);}; | ||
1011 | #endif | ||
1012 | k = hi0bits(y); | ||
1013 | *e = 32 - k; | ||
1014 | if (k < Ebits11) { | ||
1015 | word0(&d)(&d)->L[1] = Exp_10x3ff00000 | y >> (Ebits11 - k); | ||
1016 | w = xa > xa0 ? *--xa : 0; | ||
1017 | word1(&d)(&d)->L[0] = y << ((32-Ebits11) + k) | w >> (Ebits11 - k); | ||
1018 | goto ret_d; | ||
1019 | } | ||
1020 | z = xa > xa0 ? *--xa : 0; | ||
1021 | if (k -= Ebits11) { | ||
1022 | word0(&d)(&d)->L[1] = Exp_10x3ff00000 | y << k | z >> (32 - k); | ||
1023 | y = xa > xa0 ? *--xa : 0; | ||
1024 | word1(&d)(&d)->L[0] = z << k | y >> (32 - k); | ||
1025 | } | ||
1026 | else { | ||
1027 | word0(&d)(&d)->L[1] = Exp_10x3ff00000 | y; | ||
1028 | word1(&d)(&d)->L[0] = z; | ||
1029 | } | ||
1030 | ret_d: | ||
1031 | return dval(&d)(&d)->d; | ||
1032 | } | ||
1033 | |||
1034 | /* Convert a scaled double to a Bigint plus an exponent. Similar to d2b, | ||
1035 | except that it accepts the scale parameter used in _Py_dg_strtod (which | ||
1036 | should be either 0 or 2*P), and the normalization for the return value is | ||
1037 | different (see below). On input, d should be finite and nonnegative, and d | ||
1038 | / 2**scale should be exactly representable as an IEEE 754 double. | ||
1039 | |||
1040 | Returns a Bigint b and an integer e such that | ||
1041 | |||
1042 | dval(d) / 2**scale = b * 2**e. | ||
1043 | |||
1044 | Unlike d2b, b is not necessarily odd: b and e are normalized so | ||
1045 | that either 2**(P-1) <= b < 2**P and e >= Etiny, or b < 2**P | ||
1046 | and e == Etiny. This applies equally to an input of 0.0: in that | ||
1047 | case the return values are b = 0 and e = Etiny. | ||
1048 | |||
1049 | The above normalization ensures that for all possible inputs d, | ||
1050 | 2**e gives ulp(d/2**scale). | ||
1051 | |||
1052 | Returns NULL on failure. | ||
1053 | */ | ||
1054 | |||
1055 | static Bigint * | ||
1056 | sd2b(U *d, int scale, int *e) | ||
1057 | { | ||
1058 | Bigint *b; | ||
1059 | |||
1060 | b = Balloc(1); | ||
1061 | if (b == NULL((void *)0)) | ||
1062 | return NULL((void *)0); | ||
1063 | |||
1064 | /* First construct b and e assuming that scale == 0. */ | ||
1065 | b->wds = 2; | ||
1066 | b->x[0] = word1(d)(d)->L[0]; | ||
1067 | b->x[1] = word0(d)(d)->L[1] & Frac_mask0xfffff; | ||
1068 | *e = Etiny(-1074) - 1 + (int)((word0(d)(d)->L[1] & Exp_mask0x7ff00000) >> Exp_shift20); | ||
1069 | if (*e < Etiny(-1074)) | ||
1070 | *e = Etiny(-1074); | ||
1071 | else | ||
1072 | b->x[1] |= Exp_msk10x100000; | ||
1073 | |||
1074 | /* Now adjust for scale, provided that b != 0. */ | ||
1075 | if (scale && (b->x[0] || b->x[1])) { | ||
1076 | *e -= scale; | ||
1077 | if (*e < Etiny(-1074)) { | ||
1078 | scale = Etiny(-1074) - *e; | ||
1079 | *e = Etiny(-1074); | ||
1080 | /* We can't shift more than P-1 bits without shifting out a 1. */ | ||
1081 | assert(0 < scale && scale <= P - 1)(__builtin_expect(!(0 < scale && scale <= 53 - 1 ), 0) ? __assert_rtn(__func__, "Python/dtoa.c", 1081, "0 < scale && scale <= P - 1" ) : (void)0); | ||
1082 | if (scale >= 32) { | ||
1083 | /* The bits shifted out should all be zero. */ | ||
1084 | assert(b->x[0] == 0)(__builtin_expect(!(b->x[0] == 0), 0) ? __assert_rtn(__func__ , "Python/dtoa.c", 1084, "b->x[0] == 0") : (void)0); | ||
1085 | b->x[0] = b->x[1]; | ||
1086 | b->x[1] = 0; | ||
1087 | scale -= 32; | ||
1088 | } | ||
1089 | if (scale) { | ||
1090 | /* The bits shifted out should all be zero. */ | ||
1091 | assert(b->x[0] << (32 - scale) == 0)(__builtin_expect(!(b->x[0] << (32 - scale) == 0), 0 ) ? __assert_rtn(__func__, "Python/dtoa.c", 1091, "b->x[0] << (32 - scale) == 0" ) : (void)0); | ||
1092 | b->x[0] = (b->x[0] >> scale) | (b->x[1] << (32 - scale)); | ||
1093 | b->x[1] >>= scale; | ||
1094 | } | ||
1095 | } | ||
1096 | } | ||
1097 | /* Ensure b is normalized. */ | ||
1098 | if (!b->x[1]) | ||
1099 | b->wds = 1; | ||
1100 | |||
1101 | return b; | ||
1102 | } | ||
1103 | |||
1104 | /* Convert a double to a Bigint plus an exponent. Return NULL on failure. | ||
1105 | |||
1106 | Given a finite nonzero double d, return an odd Bigint b and exponent *e | ||
1107 | such that fabs(d) = b * 2**e. On return, *bbits gives the number of | ||
1108 | significant bits of b; that is, 2**(*bbits-1) <= b < 2**(*bbits). | ||
1109 | |||
1110 | If d is zero, then b == 0, *e == -1010, *bbits = 0. | ||
1111 | */ | ||
1112 | |||
1113 | static Bigint * | ||
1114 | d2b(U *d, int *e, int *bits) | ||
1115 | { | ||
1116 | Bigint *b; | ||
1117 | int de, k; | ||
1118 | ULong *x, y, z; | ||
1119 | int i; | ||
1120 | |||
1121 | b = Balloc(1); | ||
1122 | if (b == NULL((void *)0)) | ||
| |||
1123 | return NULL((void *)0); | ||
1124 | x = b->x; | ||
1125 | |||
1126 | z = word0(d)(d)->L[1] & Frac_mask0xfffff; | ||
1127 | word0(d)(d)->L[1] &= 0x7fffffff; /* clear sign bit, which we ignore */ | ||
1128 | if ((de = (int)(word0(d)(d)->L[1] >> Exp_shift20))) | ||
| |||
1129 | z |= Exp_msk10x100000; | ||
1130 | if ((y = word1(d)(d)->L[0])) { | ||
| |||
1131 | if ((k = lo0bits(&y))) { | ||
1132 | x[0] = y | z << (32 - k); | ||
1133 | z >>= k; | ||
1134 | } | ||
1135 | else | ||
1136 | x[0] = y; | ||
1137 | i = | ||
1138 | b->wds = (x[1] = z) ? 2 : 1; | ||
1139 | } | ||
1140 | else { | ||
1141 | k = lo0bits(&z); | ||
1142 | x[0] = z; | ||
1143 | i = | ||
1144 | b->wds = 1; | ||
1145 | k += 32; | ||
1146 | } | ||
1147 | if (de) { | ||
| |||
1148 | *e = de - Bias1023 - (P53-1) + k; | ||
1149 | *bits = P53 - k; | ||
1150 | } | ||
1151 | else { | ||
1152 | *e = de - Bias1023 - (P53-1) + 1 + k; | ||
| |||
1153 | *bits = 32*i - hi0bits(x[i-1]); | ||
1154 | } | ||
1155 | return b; | ||
1156 | } | ||
1157 | |||
1158 | /* Compute the ratio of two Bigints, as a double. The result may have an | ||
1159 | error of up to 2.5 ulps. */ | ||
1160 | |||
1161 | static double | ||
1162 | ratio(Bigint *a, Bigint *b) | ||
1163 | { | ||
1164 | U da, db; | ||
1165 | int k, ka, kb; | ||
1166 | |||
1167 | dval(&da)(&da)->d = b2d(a, &ka); | ||
1168 | dval(&db)(&db)->d = b2d(b, &kb); | ||
1169 | k = ka - kb + 32*(a->wds - b->wds); | ||
1170 | if (k > 0) | ||
1171 | word0(&da)(&da)->L[1] += k*Exp_msk10x100000; | ||
1172 | else { | ||
1173 | k = -k; | ||
1174 | word0(&db)(&db)->L[1] += k*Exp_msk10x100000; | ||
1175 | } | ||
1176 | return dval(&da)(&da)->d / dval(&db)(&db)->d; | ||
1177 | } | ||
1178 | |||
1179 | static const double | ||
1180 | tens[] = { | ||
1181 | 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, | ||
1182 | 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, | ||
1183 | 1e20, 1e21, 1e22 | ||
1184 | }; | ||
1185 | |||
1186 | static const double | ||
1187 | bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 }; | ||
1188 | static const double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, | ||
1189 | 9007199254740992.*9007199254740992.e-256 | ||
1190 | /* = 2^106 * 1e-256 */ | ||
1191 | }; | ||
1192 | /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */ | ||
1193 | /* flag unnecessarily. It leads to a song and dance at the end of strtod. */ | ||
1194 | #define Scale_Bit0x10 0x10 | ||
1195 | #define n_bigtens5 5 | ||
1196 | |||
1197 | #define ULbits32 32 | ||
1198 | #define kshift5 5 | ||
1199 | #define kmask31 31 | ||
1200 | |||
1201 | |||
1202 | static int | ||
1203 | dshift(Bigint *b, int p2) | ||
1204 | { | ||
1205 | int rv = hi0bits(b->x[b->wds-1]) - 4; | ||
1206 | if (p2 > 0) | ||
1207 | rv -= p2; | ||
1208 | return rv & kmask31; | ||
1209 | } | ||
1210 | |||
1211 | /* special case of Bigint division. The quotient is always in the range 0 <= | ||
1212 | quotient < 10, and on entry the divisor S is normalized so that its top 4 | ||
1213 | bits (28--31) are zero and bit 27 is set. */ | ||
1214 | |||
1215 | static int | ||
1216 | quorem(Bigint *b, Bigint *S) | ||
1217 | { | ||
1218 | int n; | ||
1219 | ULong *bx, *bxe, q, *sx, *sxe; | ||
1220 | #ifdef ULLonguint64_t | ||
1221 | ULLonguint64_t borrow, carry, y, ys; | ||
1222 | #else | ||
1223 | ULong borrow, carry, y, ys; | ||
1224 | ULong si, z, zs; | ||
1225 | #endif | ||
1226 | |||
1227 | n = S->wds; | ||
1228 | #ifdef DEBUG | ||
1229 | /*debug*/ if (b->wds > n) | ||
1230 | /*debug*/ Bug("oversize b in quorem"){fprintf(__stderrp, "%s\n", "oversize b in quorem"); exit(1); }; | ||
1231 | #endif | ||
1232 | if (b->wds < n) | ||
1233 | return 0; | ||
1234 | sx = S->x; | ||
1235 | sxe = sx + --n; | ||
1236 | bx = b->x; | ||
1237 | bxe = bx + n; | ||
1238 | q = *bxe / (*sxe + 1); /* ensure q <= true quotient */ | ||
1239 | #ifdef DEBUG | ||
1240 | /*debug*/ if (q > 9) | ||
1241 | /*debug*/ Bug("oversized quotient in quorem"){fprintf(__stderrp, "%s\n", "oversized quotient in quorem"); exit (1);}; | ||
1242 | #endif | ||
1243 | if (q) { | ||
1244 | borrow = 0; | ||
1245 | carry = 0; | ||
1246 | do { | ||
1247 | #ifdef ULLonguint64_t | ||
1248 | ys = *sx++ * (ULLonguint64_t)q + carry; | ||
1249 | carry = ys >> 32; | ||
1250 | y = *bx - (ys & FFFFFFFF0xffffffffUL) - borrow; | ||
1251 | borrow = y >> 32 & (ULong)1; | ||
1252 | *bx++ = (ULong)(y & FFFFFFFF0xffffffffUL); | ||
1253 | #else | ||
1254 | si = *sx++; | ||
1255 | ys = (si & 0xffff) * q + carry; | ||
1256 | zs = (si >> 16) * q + (ys >> 16); | ||
1257 | carry = zs >> 16; | ||
1258 | y = (*bx & 0xffff) - (ys & 0xffff) - borrow; | ||
1259 | borrow = (y & 0x10000) >> 16; | ||
1260 | z = (*bx >> 16) - (zs & 0xffff) - borrow; | ||
1261 | borrow = (z & 0x10000) >> 16; | ||
1262 | Storeinc(bx, z, y)(((unsigned short *)bx)[1] = (unsigned short)z, ((unsigned short *)bx)[0] = (unsigned short)y, bx++); | ||
1263 | #endif | ||
1264 | } | ||
1265 | while(sx <= sxe); | ||
1266 | if (!*bxe) { | ||
1267 | bx = b->x; | ||
1268 | while(--bxe > bx && !*bxe) | ||
1269 | --n; | ||
1270 | b->wds = n; | ||
1271 | } | ||
1272 | } | ||
1273 | if (cmp(b, S) >= 0) { | ||
1274 | q++; | ||
1275 | borrow = 0; | ||
1276 | carry = 0; | ||
1277 | bx = b->x; | ||
1278 | sx = S->x; | ||
1279 | do { | ||
1280 | #ifdef ULLonguint64_t | ||
1281 | ys = *sx++ + carry; | ||
1282 | carry = ys >> 32; | ||
1283 | y = *bx - (ys & FFFFFFFF0xffffffffUL) - borrow; | ||
1284 | borrow = y >> 32 & (ULong)1; | ||
1285 | *bx++ = (ULong)(y & FFFFFFFF0xffffffffUL); | ||
1286 | #else | ||
1287 | si = *sx++; | ||
1288 | ys = (si & 0xffff) + carry; | ||
1289 | zs = (si >> 16) + (ys >> 16); | ||
1290 | carry = zs >> 16; | ||
1291 | y = (*bx & 0xffff) - (ys & 0xffff) - borrow; | ||
1292 | borrow = (y & 0x10000) >> 16; | ||
1293 | z = (*bx >> 16) - (zs & 0xffff) - borrow; | ||
1294 | borrow = (z & 0x10000) >> 16; | ||
1295 | Storeinc(bx, z, y)(((unsigned short *)bx)[1] = (unsigned short)z, ((unsigned short *)bx)[0] = (unsigned short)y, bx++); | ||
1296 | #endif | ||
1297 | } | ||
1298 | while(sx <= sxe); | ||
1299 | bx = b->x; | ||
1300 | bxe = bx + n; | ||
1301 | if (!*bxe) { | ||
1302 | while(--bxe > bx && !*bxe) | ||
1303 | --n; | ||
1304 | b->wds = n; | ||
1305 | } | ||
1306 | } | ||
1307 | return q; | ||
1308 | } | ||
1309 | |||
1310 | /* sulp(x) is a version of ulp(x) that takes bc.scale into account. | ||
1311 | |||
1312 | Assuming that x is finite and nonnegative (positive zero is fine | ||
1313 | here) and x / 2^bc.scale is exactly representable as a double, | ||
1314 | sulp(x) is equivalent to 2^bc.scale * ulp(x / 2^bc.scale). */ | ||
1315 | |||
1316 | static double | ||
1317 | sulp(U *x, BCinfo *bc) | ||
1318 | { | ||
1319 | U u; | ||
1320 | |||
1321 | if (bc->scale && 2*P53 + 1 > (int)((word0(x)(x)->L[1] & Exp_mask0x7ff00000) >> Exp_shift20)) { | ||
1322 | /* rv/2^bc->scale is subnormal */ | ||
1323 | word0(&u)(&u)->L[1] = (P53+2)*Exp_msk10x100000; | ||
1324 | word1(&u)(&u)->L[0] = 0; | ||
1325 | return u.d; | ||
1326 | } | ||
1327 | else { | ||
1328 | assert(word0(x) || word1(x))(__builtin_expect(!((x)->L[1] || (x)->L[0]), 0) ? __assert_rtn (__func__, "Python/dtoa.c", 1328, "word0(x) || word1(x)") : ( void)0); /* x != 0.0 */ | ||
1329 | return ulp(x); | ||
1330 | } | ||
1331 | } | ||
1332 | |||
1333 | /* The bigcomp function handles some hard cases for strtod, for inputs | ||
1334 | with more than STRTOD_DIGLIM digits. It's called once an initial | ||
1335 | estimate for the double corresponding to the input string has | ||
1336 | already been obtained by the code in _Py_dg_strtod. | ||
1337 | |||
1338 | The bigcomp function is only called after _Py_dg_strtod has found a | ||
1339 | double value rv such that either rv or rv + 1ulp represents the | ||
1340 | correctly rounded value corresponding to the original string. It | ||
1341 | determines which of these two values is the correct one by | ||
1342 | computing the decimal digits of rv + 0.5ulp and comparing them with | ||
1343 | the corresponding digits of s0. | ||
1344 | |||
1345 | In the following, write dv for the absolute value of the number represented | ||
1346 | by the input string. | ||
1347 | |||
1348 | Inputs: | ||
1349 | |||
1350 | s0 points to the first significant digit of the input string. | ||
1351 | |||
1352 | rv is a (possibly scaled) estimate for the closest double value to the | ||
1353 | value represented by the original input to _Py_dg_strtod. If | ||
1354 | bc->scale is nonzero, then rv/2^(bc->scale) is the approximation to | ||
1355 | the input value. | ||
1356 | |||
1357 | bc is a struct containing information gathered during the parsing and | ||
1358 | estimation steps of _Py_dg_strtod. Description of fields follows: | ||
1359 | |||
1360 | bc->e0 gives the exponent of the input value, such that dv = (integer | ||
1361 | given by the bd->nd digits of s0) * 10**e0 | ||
1362 | |||
1363 | bc->nd gives the total number of significant digits of s0. It will | ||
1364 | be at least 1. | ||
1365 | |||
1366 | bc->nd0 gives the number of significant digits of s0 before the | ||
1367 | decimal separator. If there's no decimal separator, bc->nd0 == | ||
1368 | bc->nd. | ||
1369 | |||
1370 | bc->scale is the value used to scale rv to avoid doing arithmetic with | ||
1371 | subnormal values. It's either 0 or 2*P (=106). | ||
1372 | |||
1373 | Outputs: | ||
1374 | |||
1375 | On successful exit, rv/2^(bc->scale) is the closest double to dv. | ||
1376 | |||
1377 | Returns 0 on success, -1 on failure (e.g., due to a failed malloc call). */ | ||
1378 | |||
1379 | static int | ||
1380 | bigcomp(U *rv, const char *s0, BCinfo *bc) | ||
1381 | { | ||
1382 | Bigint *b, *d; | ||
1383 | int b2, d2, dd, i, nd, nd0, odd, p2, p5; | ||
1384 | |||
1385 | nd = bc->nd; | ||
1386 | nd0 = bc->nd0; | ||
1387 | p5 = nd + bc->e0; | ||
1388 | b = sd2b(rv, bc->scale, &p2); | ||
1389 | if (b == NULL((void *)0)) | ||
1390 | return -1; | ||
1391 | |||
1392 | /* record whether the lsb of rv/2^(bc->scale) is odd: in the exact halfway | ||
1393 | case, this is used for round to even. */ | ||
1394 | odd = b->x[0] & 1; | ||
1395 | |||
1396 | /* left shift b by 1 bit and or a 1 into the least significant bit; | ||
1397 | this gives us b * 2**p2 = rv/2^(bc->scale) + 0.5 ulp. */ | ||
1398 | b = lshift(b, 1); | ||
1399 | if (b == NULL((void *)0)) | ||
1400 | return -1; | ||
1401 | b->x[0] |= 1; | ||
1402 | p2--; | ||
1403 | |||
1404 | p2 -= p5; | ||
1405 | d = i2b(1); | ||
1406 | if (d == NULL((void *)0)) { | ||
1407 | Bfree(b); | ||
1408 | return -1; | ||
1409 | } | ||
1410 | /* Arrange for convenient computation of quotients: | ||
1411 | * shift left if necessary so divisor has 4 leading 0 bits. | ||
1412 | */ | ||
1413 | if (p5 > 0) { | ||
1414 | d = pow5mult(d, p5); | ||
1415 | if (d == NULL((void *)0)) { | ||
1416 | Bfree(b); | ||
1417 | return -1; | ||
1418 | } | ||
1419 | } | ||
1420 | else if (p5 < 0) { | ||
1421 | b = pow5mult(b, -p5); | ||
1422 | if (b == NULL((void *)0)) { | ||
1423 | Bfree(d); | ||
1424 | return -1; | ||
1425 | } | ||
1426 | } | ||
1427 | if (p2 > 0) { | ||
1428 | b2 = p2; | ||
1429 | d2 = 0; | ||
1430 | } | ||
1431 | else { | ||
1432 | b2 = 0; | ||
1433 | d2 = -p2; | ||
1434 | } | ||
1435 | i = dshift(d, d2); | ||
1436 | if ((b2 += i) > 0) { | ||
1437 | b = lshift(b, b2); | ||
1438 | if (b == NULL((void *)0)) { | ||
1439 | Bfree(d); | ||
1440 | return -1; | ||
1441 | } | ||
1442 | } | ||
1443 | if ((d2 += i) > 0) { | ||
1444 | d = lshift(d, d2); | ||
1445 | if (d == NULL((void *)0)) { | ||
1446 | Bfree(b); | ||
1447 | return -1; | ||
1448 | } | ||
1449 | } | ||
1450 | |||
1451 | /* Compare s0 with b/d: set dd to -1, 0, or 1 according as s0 < b/d, s0 == | ||
1452 | * b/d, or s0 > b/d. Here the digits of s0 are thought of as representing | ||
1453 | * a number in the range [0.1, 1). */ | ||
1454 | if (cmp(b, d) >= 0) | ||
1455 | /* b/d >= 1 */ | ||
1456 | dd = -1; | ||
1457 | else { | ||
1458 | i = 0; | ||
1459 | for(;;) { | ||
1460 | b = multadd(b, 10, 0); | ||
1461 | if (b == NULL((void *)0)) { | ||
1462 | Bfree(d); | ||
1463 | return -1; | ||
1464 | } | ||
1465 | dd = s0[i < nd0 ? i : i+1] - '0' - quorem(b, d); | ||
1466 | i++; | ||
1467 | |||
1468 | if (dd) | ||
1469 | break; | ||
1470 | if (!b->x[0] && b->wds == 1) { | ||
1471 | /* b/d == 0 */ | ||
1472 | dd = i < nd; | ||
1473 | break; | ||
1474 | } | ||
1475 | if (!(i < nd)) { | ||
1476 | /* b/d != 0, but digits of s0 exhausted */ | ||
1477 | dd = -1; | ||
1478 | break; | ||
1479 | } | ||
1480 | } | ||
1481 | } | ||
1482 | Bfree(b); | ||
1483 | Bfree(d); | ||
1484 | if (dd > 0 || (dd == 0 && odd)) | ||
1485 | dval(rv)(rv)->d += sulp(rv, bc); | ||
1486 | return 0; | ||
1487 | } | ||
1488 | |||
1489 | double | ||
1490 | _Py_dg_strtod(const char *s00, char **se) | ||
1491 | { | ||
1492 | int bb2, bb5, bbe, bd2, bd5, bs2, c, dsign, e, e1, error; | ||
1493 | int esign, i, j, k, lz, nd, nd0, odd, sign; | ||
1494 | const char *s, *s0, *s1; | ||
1495 | double aadj, aadj1; | ||
1496 | U aadj2, adj, rv, rv0; | ||
1497 | ULong y, z, abs_exp; | ||
1498 | Long L; | ||
1499 | BCinfo bc; | ||
1500 | Bigint *bb, *bb1, *bd, *bd0, *bs, *delta; | ||
1501 | |||
1502 | dval(&rv)(&rv)->d = 0.; | ||
1503 | |||
1504 | /* Start parsing. */ | ||
1505 | c = *(s = s00); | ||
1506 | |||
1507 | /* Parse optional sign, if present. */ | ||
1508 | sign = 0; | ||
1509 | switch (c) { | ||
1510 | case '-': | ||
1511 | sign = 1; | ||
1512 | /* no break */ | ||
1513 | case '+': | ||
1514 | c = *++s; | ||
1515 | } | ||
1516 | |||
1517 | /* Skip leading zeros: lz is true iff there were leading zeros. */ | ||
1518 | s1 = s; | ||
1519 | while (c == '0') | ||
1520 | c = *++s; | ||
1521 | lz = s != s1; | ||
1522 | |||
1523 | /* Point s0 at the first nonzero digit (if any). nd0 will be the position | ||
1524 | of the point relative to s0. nd will be the total number of digits | ||
1525 | ignoring leading zeros. */ | ||
1526 | s0 = s1 = s; | ||
1527 | while ('0' <= c && c <= '9') | ||
1528 | c = *++s; | ||
1529 | nd0 = nd = s - s1; | ||
1530 | |||
1531 | /* Parse decimal point and following digits. */ | ||
1532 | if (c == '.') { | ||
1533 | c = *++s; | ||
1534 | if (!nd) { | ||
1535 | s1 = s; | ||
1536 | while (c == '0') | ||
1537 | c = *++s; | ||
1538 | lz = lz || s != s1; | ||
1539 | nd0 -= s - s1; | ||
1540 | s0 = s; | ||
1541 | } | ||
1542 | s1 = s; | ||
1543 | while ('0' <= c && c <= '9') | ||
1544 | c = *++s; | ||
1545 | nd += s - s1; | ||
1546 | } | ||
1547 | |||
1548 | /* Now lz is true if and only if there were leading zero digits, and nd | ||
1549 | gives the total number of digits ignoring leading zeros. A valid input | ||
1550 | must have at least one digit. */ | ||
1551 | if (!nd && !lz) { | ||
1552 | if (se) | ||
1553 | *se = (char *)s00; | ||
1554 | goto parse_error; | ||
1555 | } | ||
1556 | |||
1557 | /* Parse exponent. */ | ||
1558 | e = 0; | ||
1559 | if (c == 'e' || c == 'E') { | ||
1560 | s00 = s; | ||
1561 | c = *++s; | ||
1562 | |||
1563 | /* Exponent sign. */ | ||
1564 | esign = 0; | ||
1565 | switch (c) { | ||
1566 | case '-': | ||
1567 | esign = 1; | ||
1568 | /* no break */ | ||
1569 | case '+': | ||
1570 | c = *++s; | ||
1571 | } | ||
1572 | |||
1573 | /* Skip zeros. lz is true iff there are leading zeros. */ | ||
1574 | s1 = s; | ||
1575 | while (c == '0') | ||
1576 | c = *++s; | ||
1577 | lz = s != s1; | ||
1578 | |||
1579 | /* Get absolute value of the exponent. */ | ||
1580 | s1 = s; | ||
1581 | abs_exp = 0; | ||
1582 | while ('0' <= c && c <= '9') { | ||
1583 | abs_exp = 10*abs_exp + (c - '0'); | ||
1584 | c = *++s; | ||
1585 | } | ||
1586 | |||
1587 | /* abs_exp will be correct modulo 2**32. But 10**9 < 2**32, so if | ||
1588 | there are at most 9 significant exponent digits then overflow is | ||
1589 | impossible. */ | ||
1590 | if (s - s1 > 9 || abs_exp > MAX_ABS_EXP19999U) | ||
1591 | e = (int)MAX_ABS_EXP19999U; | ||
1592 | else | ||
1593 | e = (int)abs_exp; | ||
1594 | if (esign) | ||
1595 | e = -e; | ||
1596 | |||
1597 | /* A valid exponent must have at least one digit. */ | ||
1598 | if (s == s1 && !lz) | ||
1599 | s = s00; | ||
1600 | } | ||
1601 | |||
1602 | /* Adjust exponent to take into account position of the point. */ | ||
1603 | e -= nd - nd0; | ||
1604 | if (nd0 <= 0) | ||
1605 | nd0 = nd; | ||
1606 | |||
1607 | /* Finished parsing. Set se to indicate how far we parsed */ | ||
1608 | if (se) | ||
1609 | *se = (char *)s; | ||
1610 | |||
1611 | /* If all digits were zero, exit with return value +-0.0. Otherwise, | ||
1612 | strip trailing zeros: scan back until we hit a nonzero digit. */ | ||
1613 | if (!nd) | ||
1614 | goto ret; | ||
1615 | for (i = nd; i > 0; ) { | ||
1616 | --i; | ||
1617 | if (s0[i < nd0 ? i : i+1] != '0') { | ||
1618 | ++i; | ||
1619 | break; | ||
1620 | } | ||
1621 | } | ||
1622 | e += nd - i; | ||
1623 | nd = i; | ||
1624 | if (nd0 > nd) | ||
1625 | nd0 = nd; | ||
1626 | |||
1627 | /* Summary of parsing results. After parsing, and dealing with zero | ||
1628 | * inputs, we have values s0, nd0, nd, e, sign, where: | ||
1629 | * | ||
1630 | * - s0 points to the first significant digit of the input string | ||
1631 | * | ||
1632 | * - nd is the total number of significant digits (here, and | ||
1633 | * below, 'significant digits' means the set of digits of the | ||
1634 | * significand of the input that remain after ignoring leading | ||
1635 | * and trailing zeros). | ||
1636 | * | ||
1637 | * - nd0 indicates the position of the decimal point, if present; it | ||
1638 | * satisfies 1 <= nd0 <= nd. The nd significant digits are in | ||
1639 | * s0[0:nd0] and s0[nd0+1:nd+1] using the usual Python half-open slice | ||
1640 | * notation. (If nd0 < nd, then s0[nd0] contains a '.' character; if | ||
1641 | * nd0 == nd, then s0[nd0] could be any non-digit character.) | ||
1642 | * | ||
1643 | * - e is the adjusted exponent: the absolute value of the number | ||
1644 | * represented by the original input string is n * 10**e, where | ||
1645 | * n is the integer represented by the concatenation of | ||
1646 | * s0[0:nd0] and s0[nd0+1:nd+1] | ||
1647 | * | ||
1648 | * - sign gives the sign of the input: 1 for negative, 0 for positive | ||
1649 | * | ||
1650 | * - the first and last significant digits are nonzero | ||
1651 | */ | ||
1652 | |||
1653 | /* put first DBL_DIG+1 digits into integer y and z. | ||
1654 | * | ||
1655 | * - y contains the value represented by the first min(9, nd) | ||
1656 | * significant digits | ||
1657 | * | ||
1658 | * - if nd > 9, z contains the value represented by significant digits | ||
1659 | * with indices in [9, min(16, nd)). So y * 10**(min(16, nd) - 9) + z | ||
1660 | * gives the value represented by the first min(16, nd) sig. digits. | ||
1661 | */ | ||
1662 | |||
1663 | bc.e0 = e1 = e; | ||
1664 | y = z = 0; | ||
1665 | for (i = 0; i < nd; i++) { | ||
1666 | if (i < 9) | ||
1667 | y = 10*y + s0[i < nd0 ? i : i+1] - '0'; | ||
1668 | else if (i < DBL_DIG15+1) | ||
1669 | z = 10*z + s0[i < nd0 ? i : i+1] - '0'; | ||
1670 | else | ||
1671 | break; | ||
1672 | } | ||
1673 | |||
1674 | k = nd < DBL_DIG15 + 1 ? nd : DBL_DIG15 + 1; | ||
1675 | dval(&rv)(&rv)->d = y; | ||
1676 | if (k > 9) { | ||
1677 | dval(&rv)(&rv)->d = tens[k - 9] * dval(&rv)(&rv)->d + z; | ||
1678 | } | ||
1679 | bd0 = 0; | ||
1680 | if (nd <= DBL_DIG15 | ||
1681 | && Flt_Rounds(__builtin_flt_rounds()) == 1 | ||
1682 | ) { | ||
1683 | if (!e) | ||
1684 | goto ret; | ||
1685 | if (e > 0) { | ||
1686 | if (e <= Ten_pmax22) { | ||
1687 | dval(&rv)(&rv)->d *= tens[e]; | ||
1688 | goto ret; | ||
1689 | } | ||
1690 | i = DBL_DIG15 - nd; | ||
1691 | if (e <= Ten_pmax22 + i) { | ||
1692 | /* A fancier test would sometimes let us do | ||
1693 | * this for larger i values. | ||
1694 | */ | ||
1695 | e -= i; | ||
1696 | dval(&rv)(&rv)->d *= tens[i]; | ||
1697 | dval(&rv)(&rv)->d *= tens[e]; | ||
1698 | goto ret; | ||
1699 | } | ||
1700 | } | ||
1701 | else if (e >= -Ten_pmax22) { | ||
1702 | dval(&rv)(&rv)->d /= tens[-e]; | ||
1703 | goto ret; | ||
1704 | } | ||
1705 | } | ||
1706 | e1 += nd - k; | ||
1707 | |||
1708 | bc.scale = 0; | ||
1709 | |||
1710 | /* Get starting approximation = rv * 10**e1 */ | ||
1711 | |||
1712 | if (e1 > 0) { | ||
1713 | if ((i = e1 & 15)) | ||
1714 | dval(&rv)(&rv)->d *= tens[i]; | ||
1715 | if (e1 &= ~15) { | ||
1716 | if (e1 > DBL_MAX_10_EXP308) | ||
1717 | goto ovfl; | ||
1718 | e1 >>= 4; | ||
1719 | for(j = 0; e1 > 1; j++, e1 >>= 1) | ||
1720 | if (e1 & 1) | ||
1721 | dval(&rv)(&rv)->d *= bigtens[j]; | ||
1722 | /* The last multiplication could overflow. */ | ||
1723 | word0(&rv)(&rv)->L[1] -= P53*Exp_msk10x100000; | ||
1724 | dval(&rv)(&rv)->d *= bigtens[j]; | ||
1725 | if ((z = word0(&rv)(&rv)->L[1] & Exp_mask0x7ff00000) | ||
1726 | > Exp_msk10x100000*(DBL_MAX_EXP1024+Bias1023-P53)) | ||
1727 | goto ovfl; | ||
1728 | if (z > Exp_msk10x100000*(DBL_MAX_EXP1024+Bias1023-1-P53)) { | ||
1729 | /* set to largest number */ | ||
1730 | /* (Can't trust DBL_MAX) */ | ||
1731 | word0(&rv)(&rv)->L[1] = Big0(0xfffff | 0x100000*(1024 +1023 -1)); | ||
1732 | word1(&rv)(&rv)->L[0] = Big10xffffffff; | ||
1733 | } | ||
1734 | else | ||
1735 | word0(&rv)(&rv)->L[1] += P53*Exp_msk10x100000; | ||
1736 | } | ||
1737 | } | ||
1738 | else if (e1 < 0) { | ||
1739 | /* The input decimal value lies in [10**e1, 10**(e1+16)). | ||
1740 | |||
1741 | If e1 <= -512, underflow immediately. | ||
1742 | If e1 <= -256, set bc.scale to 2*P. | ||
1743 | |||
1744 | So for input value < 1e-256, bc.scale is always set; | ||
1745 | for input value >= 1e-240, bc.scale is never set. | ||
1746 | For input values in [1e-256, 1e-240), bc.scale may or may | ||
1747 | not be set. */ | ||
1748 | |||
1749 | e1 = -e1; | ||
1750 | if ((i = e1 & 15)) | ||
1751 | dval(&rv)(&rv)->d /= tens[i]; | ||
1752 | if (e1 >>= 4) { | ||
1753 | if (e1 >= 1 << n_bigtens5) | ||
1754 | goto undfl; | ||
1755 | if (e1 & Scale_Bit0x10) | ||
1756 | bc.scale = 2*P53; | ||
1757 | for(j = 0; e1 > 0; j++, e1 >>= 1) | ||
1758 | if (e1 & 1) | ||
1759 | dval(&rv)(&rv)->d *= tinytens[j]; | ||
1760 | if (bc.scale && (j = 2*P53 + 1 - ((word0(&rv)(&rv)->L[1] & Exp_mask0x7ff00000) | ||
1761 | >> Exp_shift20)) > 0) { | ||
1762 | /* scaled rv is denormal; clear j low bits */ | ||
1763 | if (j >= 32) { | ||
1764 | word1(&rv)(&rv)->L[0] = 0; | ||
1765 | if (j >= 53) | ||
1766 | word0(&rv)(&rv)->L[1] = (P53+2)*Exp_msk10x100000; | ||
1767 | else | ||
1768 | word0(&rv)(&rv)->L[1] &= 0xffffffff << (j-32); | ||
1769 | } | ||
1770 | else | ||
1771 | word1(&rv)(&rv)->L[0] &= 0xffffffff << j; | ||
1772 | } | ||
1773 | if (!dval(&rv)(&rv)->d) | ||
1774 | goto undfl; | ||
1775 | } | ||
1776 | } | ||
1777 | |||
1778 | /* Now the hard part -- adjusting rv to the correct value.*/ | ||
1779 | |||
1780 | /* Put digits into bd: true value = bd * 10^e */ | ||
1781 | |||
1782 | bc.nd = nd; | ||
1783 | bc.nd0 = nd0; /* Only needed if nd > STRTOD_DIGLIM, but done here */ | ||
1784 | /* to silence an erroneous warning about bc.nd0 */ | ||
1785 | /* possibly not being initialized. */ | ||
1786 | if (nd > STRTOD_DIGLIM40) { | ||
1787 | /* ASSERT(STRTOD_DIGLIM >= 18); 18 == one more than the */ | ||
1788 | /* minimum number of decimal digits to distinguish double values */ | ||
1789 | /* in IEEE arithmetic. */ | ||
1790 | |||
1791 | /* Truncate input to 18 significant digits, then discard any trailing | ||
1792 | zeros on the result by updating nd, nd0, e and y suitably. (There's | ||
1793 | no need to update z; it's not reused beyond this point.) */ | ||
1794 | for (i = 18; i > 0; ) { | ||
1795 | /* scan back until we hit a nonzero digit. significant digit 'i' | ||
1796 | is s0[i] if i < nd0, s0[i+1] if i >= nd0. */ | ||
1797 | --i; | ||
1798 | if (s0[i < nd0 ? i : i+1] != '0') { | ||
1799 | ++i; | ||
1800 | break; | ||
1801 | } | ||
1802 | } | ||
1803 | e += nd - i; | ||
1804 | nd = i; | ||
1805 | if (nd0 > nd) | ||
1806 | nd0 = nd; | ||
1807 | if (nd < 9) { /* must recompute y */ | ||
1808 | y = 0; | ||
1809 | for(i = 0; i < nd0; ++i) | ||
1810 | y = 10*y + s0[i] - '0'; | ||
1811 | for(; i < nd; ++i) | ||
1812 | y = 10*y + s0[i+1] - '0'; | ||
1813 | } | ||
1814 | } | ||
1815 | bd0 = s2b(s0, nd0, nd, y); | ||
1816 | if (bd0 == NULL((void *)0)) | ||
1817 | goto failed_malloc; | ||
1818 | |||
1819 | /* Notation for the comments below. Write: | ||
1820 | |||
1821 | - dv for the absolute value of the number represented by the original | ||
1822 | decimal input string. | ||
1823 | |||
1824 | - if we've truncated dv, write tdv for the truncated value. | ||
1825 | Otherwise, set tdv == dv. | ||
1826 | |||
1827 | - srv for the quantity rv/2^bc.scale; so srv is the current binary | ||
1828 | approximation to tdv (and dv). It should be exactly representable | ||
1829 | in an IEEE 754 double. | ||
1830 | */ | ||
1831 | |||
1832 | for(;;) { | ||
1833 | |||
1834 | /* This is the main correction loop for _Py_dg_strtod. | ||
1835 | |||
1836 | We've got a decimal value tdv, and a floating-point approximation | ||
1837 | srv=rv/2^bc.scale to tdv. The aim is to determine whether srv is | ||
1838 | close enough (i.e., within 0.5 ulps) to tdv, and to compute a new | ||
1839 | approximation if not. | ||
1840 | |||
1841 | To determine whether srv is close enough to tdv, compute integers | ||
1842 | bd, bb and bs proportional to tdv, srv and 0.5 ulp(srv) | ||
1843 | respectively, and then use integer arithmetic to determine whether | ||
1844 | |tdv - srv| is less than, equal to, or greater than 0.5 ulp(srv). | ||
1845 | */ | ||
1846 | |||
1847 | bd = Balloc(bd0->k); | ||
1848 | if (bd == NULL((void *)0)) { | ||
1849 | Bfree(bd0); | ||
1850 | goto failed_malloc; | ||
1851 | } | ||
1852 | Bcopy(bd, bd0)((__builtin_object_size ((char *)&bd->sign, 0) != (size_t ) -1) ? __builtin___memcpy_chk ((char *)&bd->sign, (char *)&bd0->sign, bd0->wds*sizeof(Long) + 2*sizeof(int ), __builtin_object_size ((char *)&bd->sign, 0)) : __inline_memcpy_chk ((char *)&bd->sign, (char *)&bd0->sign, bd0-> wds*sizeof(Long) + 2*sizeof(int))); | ||
1853 | bb = sd2b(&rv, bc.scale, &bbe); /* srv = bb * 2^bbe */ | ||
1854 | if (bb == NULL((void *)0)) { | ||
1855 | Bfree(bd); | ||
1856 | Bfree(bd0); | ||
1857 | goto failed_malloc; | ||
1858 | } | ||
1859 | /* Record whether lsb of bb is odd, in case we need this | ||
1860 | for the round-to-even step later. */ | ||
1861 | odd = bb->x[0] & 1; | ||
1862 | |||
1863 | /* tdv = bd * 10**e; srv = bb * 2**bbe */ | ||
1864 | bs = i2b(1); | ||
1865 | if (bs == NULL((void *)0)) { | ||
1866 | Bfree(bb); | ||
1867 | Bfree(bd); | ||
1868 | Bfree(bd0); | ||
1869 | goto failed_malloc; | ||
1870 | } | ||
1871 | |||
1872 | if (e >= 0) { | ||
1873 | bb2 = bb5 = 0; | ||
1874 | bd2 = bd5 = e; | ||
1875 | } | ||
1876 | else { | ||
1877 | bb2 = bb5 = -e; | ||
1878 | bd2 = bd5 = 0; | ||
1879 | } | ||
1880 | if (bbe >= 0) | ||
1881 | bb2 += bbe; | ||
1882 | else | ||
1883 | bd2 -= bbe; | ||
1884 | bs2 = bb2; | ||
1885 | bb2++; | ||
1886 | bd2++; | ||
1887 | |||
1888 | /* At this stage bd5 - bb5 == e == bd2 - bb2 + bbe, bb2 - bs2 == 1, | ||
1889 | and bs == 1, so: | ||
1890 | |||
1891 | tdv == bd * 10**e = bd * 2**(bbe - bb2 + bd2) * 5**(bd5 - bb5) | ||
1892 | srv == bb * 2**bbe = bb * 2**(bbe - bb2 + bb2) | ||
1893 | 0.5 ulp(srv) == 2**(bbe-1) = bs * 2**(bbe - bb2 + bs2) | ||
1894 | |||
1895 | It follows that: | ||
1896 | |||
1897 | M * tdv = bd * 2**bd2 * 5**bd5 | ||
1898 | M * srv = bb * 2**bb2 * 5**bb5 | ||
1899 | M * 0.5 ulp(srv) = bs * 2**bs2 * 5**bb5 | ||
1900 | |||
1901 | for some constant M. (Actually, M == 2**(bb2 - bbe) * 5**bb5, but | ||
1902 | this fact is not needed below.) | ||
1903 | */ | ||
1904 | |||
1905 | /* Remove factor of 2**i, where i = min(bb2, bd2, bs2). */ | ||
1906 | i = bb2 < bd2 ? bb2 : bd2; | ||
1907 | if (i > bs2) | ||
1908 | i = bs2; | ||
1909 | if (i > 0) { | ||
1910 | bb2 -= i; | ||
1911 | bd2 -= i; | ||
1912 | bs2 -= i; | ||
1913 | } | ||
1914 | |||
1915 | /* Scale bb, bd, bs by the appropriate powers of 2 and 5. */ | ||
1916 | if (bb5 > 0) { | ||
1917 | bs = pow5mult(bs, bb5); | ||
1918 | if (bs == NULL((void *)0)) { | ||
1919 | Bfree(bb); | ||
1920 | Bfree(bd); | ||
1921 | Bfree(bd0); | ||
1922 | goto failed_malloc; | ||
1923 | } | ||
1924 | bb1 = mult(bs, bb); | ||
1925 | Bfree(bb); | ||
1926 | bb = bb1; | ||
1927 | if (bb == NULL((void *)0)) { | ||
1928 | Bfree(bs); | ||
1929 | Bfree(bd); | ||
1930 | Bfree(bd0); | ||
1931 | goto failed_malloc; | ||
1932 | } | ||
1933 | } | ||
1934 | if (bb2 > 0) { | ||
1935 | bb = lshift(bb, bb2); | ||
1936 | if (bb == NULL((void *)0)) { | ||
1937 | Bfree(bs); | ||
1938 | Bfree(bd); | ||
1939 | Bfree(bd0); | ||
1940 | goto failed_malloc; | ||
1941 | } | ||
1942 | } | ||
1943 | if (bd5 > 0) { | ||
1944 | bd = pow5mult(bd, bd5); | ||
1945 | if (bd == NULL((void *)0)) { | ||
1946 | Bfree(bb); | ||
1947 | Bfree(bs); | ||
1948 | Bfree(bd0); | ||
1949 | goto failed_malloc; | ||
1950 | } | ||
1951 | } | ||
1952 | if (bd2 > 0) { | ||
1953 | bd = lshift(bd, bd2); | ||
1954 | if (bd == NULL((void *)0)) { | ||
1955 | Bfree(bb); | ||
1956 | Bfree(bs); | ||
1957 | Bfree(bd0); | ||
1958 | goto failed_malloc; | ||
1959 | } | ||
1960 | } | ||
1961 | if (bs2 > 0) { | ||
1962 | bs = lshift(bs, bs2); | ||
1963 | if (bs == NULL((void *)0)) { | ||
1964 | Bfree(bb); | ||
1965 | Bfree(bd); | ||
1966 | Bfree(bd0); | ||
1967 | goto failed_malloc; | ||
1968 | } | ||
1969 | } | ||
1970 | |||
1971 | /* Now bd, bb and bs are scaled versions of tdv, srv and 0.5 ulp(srv), | ||
1972 | respectively. Compute the difference |tdv - srv|, and compare | ||
1973 | with 0.5 ulp(srv). */ | ||
1974 | |||
1975 | delta = diff(bb, bd); | ||
1976 | if (delta == NULL((void *)0)) { | ||
1977 | Bfree(bb); | ||
1978 | Bfree(bs); | ||
1979 | Bfree(bd); | ||
1980 | Bfree(bd0); | ||
1981 | goto failed_malloc; | ||
1982 | } | ||
1983 | dsign = delta->sign; | ||
1984 | delta->sign = 0; | ||
1985 | i = cmp(delta, bs); | ||
1986 | if (bc.nd > nd && i <= 0) { | ||
1987 | if (dsign) | ||
1988 | break; /* Must use bigcomp(). */ | ||
1989 | |||
1990 | /* Here rv overestimates the truncated decimal value by at most | ||
1991 | 0.5 ulp(rv). Hence rv either overestimates the true decimal | ||
1992 | value by <= 0.5 ulp(rv), or underestimates it by some small | ||
1993 | amount (< 0.1 ulp(rv)); either way, rv is within 0.5 ulps of | ||
1994 | the true decimal value, so it's possible to exit. | ||
1995 | |||
1996 | Exception: if scaled rv is a normal exact power of 2, but not | ||
1997 | DBL_MIN, then rv - 0.5 ulp(rv) takes us all the way down to the | ||
1998 | next double, so the correctly rounded result is either rv - 0.5 | ||
1999 | ulp(rv) or rv; in this case, use bigcomp to distinguish. */ | ||
2000 | |||
2001 | if (!word1(&rv)(&rv)->L[0] && !(word0(&rv)(&rv)->L[1] & Bndry_mask0xfffff)) { | ||
2002 | /* rv can't be 0, since it's an overestimate for some | ||
2003 | nonzero value. So rv is a normal power of 2. */ | ||
2004 | j = (int)(word0(&rv)(&rv)->L[1] & Exp_mask0x7ff00000) >> Exp_shift20; | ||
2005 | /* rv / 2^bc.scale = 2^(j - 1023 - bc.scale); use bigcomp if | ||
2006 | rv / 2^bc.scale >= 2^-1021. */ | ||
2007 | if (j - bc.scale >= 2) { | ||
2008 | dval(&rv)(&rv)->d -= 0.5 * sulp(&rv, &bc); | ||
2009 | break; /* Use bigcomp. */ | ||
2010 | } | ||
2011 | } | ||
2012 | |||
2013 | { | ||
2014 | bc.nd = nd; | ||
2015 | i = -1; /* Discarded digits make delta smaller. */ | ||
2016 | } | ||
2017 | } | ||
2018 | |||
2019 | if (i < 0) { | ||
2020 | /* Error is less than half an ulp -- check for | ||
2021 | * special case of mantissa a power of two. | ||
2022 | */ | ||
2023 | if (dsign || word1(&rv)(&rv)->L[0] || word0(&rv)(&rv)->L[1] & Bndry_mask0xfffff | ||
2024 | || (word0(&rv)(&rv)->L[1] & Exp_mask0x7ff00000) <= (2*P53+1)*Exp_msk10x100000 | ||
2025 | ) { | ||
2026 | break; | ||
2027 | } | ||
2028 | if (!delta->x[0] && delta->wds <= 1) { | ||
2029 | /* exact result */ | ||
2030 | break; | ||
2031 | } | ||
2032 | delta = lshift(delta,Log2P1); | ||
2033 | if (delta == NULL((void *)0)) { | ||
2034 | Bfree(bb); | ||
2035 | Bfree(bs); | ||
2036 | Bfree(bd); | ||
2037 | Bfree(bd0); | ||
2038 | goto failed_malloc; | ||
2039 | } | ||
2040 | if (cmp(delta, bs) > 0) | ||
2041 | goto drop_down; | ||
2042 | break; | ||
2043 | } | ||
2044 | if (i == 0) { | ||
2045 | /* exactly half-way between */ | ||
2046 | if (dsign) { | ||
2047 | if ((word0(&rv)(&rv)->L[1] & Bndry_mask10xfffff) == Bndry_mask10xfffff | ||
2048 | && word1(&rv)(&rv)->L[0] == ( | ||
2049 | (bc.scale && | ||
2050 | (y = word0(&rv)(&rv)->L[1] & Exp_mask0x7ff00000) <= 2*P53*Exp_msk10x100000) ? | ||
2051 | (0xffffffff & (0xffffffff << (2*P53+1-(y>>Exp_shift20)))) : | ||
2052 | 0xffffffff)) { | ||
2053 | /*boundary case -- increment exponent*/ | ||
2054 | word0(&rv)(&rv)->L[1] = (word0(&rv)(&rv)->L[1] & Exp_mask0x7ff00000) | ||
2055 | + Exp_msk10x100000 | ||
2056 | ; | ||
2057 | word1(&rv)(&rv)->L[0] = 0; | ||
2058 | dsign = 0; | ||
2059 | break; | ||
2060 | } | ||
2061 | } | ||
2062 | else if (!(word0(&rv)(&rv)->L[1] & Bndry_mask0xfffff) && !word1(&rv)(&rv)->L[0]) { | ||
2063 | drop_down: | ||
2064 | /* boundary case -- decrement exponent */ | ||
2065 | if (bc.scale) { | ||
2066 | L = word0(&rv)(&rv)->L[1] & Exp_mask0x7ff00000; | ||
2067 | if (L <= (2*P53+1)*Exp_msk10x100000) { | ||
2068 | if (L > (P53+2)*Exp_msk10x100000) | ||
2069 | /* round even ==> */ | ||
2070 | /* accept rv */ | ||
2071 | break; | ||
2072 | /* rv = smallest denormal */ | ||
2073 | if (bc.nd > nd) | ||
2074 | break; | ||
2075 | goto undfl; | ||
2076 | } | ||
2077 | } | ||
2078 | L = (word0(&rv)(&rv)->L[1] & Exp_mask0x7ff00000) - Exp_msk10x100000; | ||
2079 | word0(&rv)(&rv)->L[1] = L | Bndry_mask10xfffff; | ||
2080 | word1(&rv)(&rv)->L[0] = 0xffffffff; | ||
2081 | break; | ||
2082 | } | ||
2083 | if (!odd) | ||
2084 | break; | ||
2085 | if (dsign) | ||
2086 | dval(&rv)(&rv)->d += sulp(&rv, &bc); | ||
2087 | else { | ||
2088 | dval(&rv)(&rv)->d -= sulp(&rv, &bc); | ||
2089 | if (!dval(&rv)(&rv)->d) { | ||
2090 | if (bc.nd >nd) | ||
2091 | break; | ||
2092 | goto undfl; | ||
2093 | } | ||
2094 | } | ||
2095 | /* dsign = 1 - dsign; */ | ||
2096 | break; | ||
2097 | } | ||
2098 | if ((aadj = ratio(delta, bs)) <= 2.) { | ||
2099 | if (dsign) | ||
2100 | aadj = aadj1 = 1.; | ||
2101 | else if (word1(&rv)(&rv)->L[0] || word0(&rv)(&rv)->L[1] & Bndry_mask0xfffff) { | ||
2102 | if (word1(&rv)(&rv)->L[0] == Tiny11 && !word0(&rv)(&rv)->L[1]) { | ||
2103 | if (bc.nd >nd) | ||
2104 | break; | ||
2105 | goto undfl; | ||
2106 | } | ||
2107 | aadj = 1.; | ||
2108 | aadj1 = -1.; | ||
2109 | } | ||
2110 | else { | ||
2111 | /* special case -- power of FLT_RADIX to be */ | ||
2112 | /* rounded down... */ | ||
2113 | |||
2114 | if (aadj < 2./FLT_RADIX2) | ||
2115 | aadj = 1./FLT_RADIX2; | ||
2116 | else | ||
2117 | aadj *= 0.5; | ||
2118 | aadj1 = -aadj; | ||
2119 | } | ||
2120 | } | ||
2121 | else { | ||
2122 | aadj *= 0.5; | ||
2123 | aadj1 = dsign ? aadj : -aadj; | ||
2124 | if (Flt_Rounds(__builtin_flt_rounds()) == 0) | ||
2125 | aadj1 += 0.5; | ||
2126 | } | ||
2127 | y = word0(&rv)(&rv)->L[1] & Exp_mask0x7ff00000; | ||
2128 | |||
2129 | /* Check for overflow */ | ||
2130 | |||
2131 | if (y == Exp_msk10x100000*(DBL_MAX_EXP1024+Bias1023-1)) { | ||
2132 | dval(&rv0)(&rv0)->d = dval(&rv)(&rv)->d; | ||
2133 | word0(&rv)(&rv)->L[1] -= P53*Exp_msk10x100000; | ||
2134 | adj.d = aadj1 * ulp(&rv); | ||
2135 | dval(&rv)(&rv)->d += adj.d; | ||
2136 | if ((word0(&rv)(&rv)->L[1] & Exp_mask0x7ff00000) >= | ||
2137 | Exp_msk10x100000*(DBL_MAX_EXP1024+Bias1023-P53)) { | ||
2138 | if (word0(&rv0)(&rv0)->L[1] == Big0(0xfffff | 0x100000*(1024 +1023 -1)) && word1(&rv0)(&rv0)->L[0] == Big10xffffffff) { | ||
2139 | Bfree(bb); | ||
2140 | Bfree(bd); | ||
2141 | Bfree(bs); | ||
2142 | Bfree(bd0); | ||
2143 | Bfree(delta); | ||
2144 | goto ovfl; | ||
2145 | } | ||
2146 | word0(&rv)(&rv)->L[1] = Big0(0xfffff | 0x100000*(1024 +1023 -1)); | ||
2147 | word1(&rv)(&rv)->L[0] = Big10xffffffff; | ||
2148 | goto cont; | ||
2149 | } | ||
2150 | else | ||
2151 | word0(&rv)(&rv)->L[1] += P53*Exp_msk10x100000; | ||
2152 | } | ||
2153 | else { | ||
2154 | if (bc.scale && y <= 2*P53*Exp_msk10x100000) { | ||
2155 | if (aadj <= 0x7fffffff) { | ||
2156 | if ((z = (ULong)aadj) <= 0) | ||
2157 | z = 1; | ||
2158 | aadj = z; | ||
2159 | aadj1 = dsign ? aadj : -aadj; | ||
2160 | } | ||
2161 | dval(&aadj2)(&aadj2)->d = aadj1; | ||
2162 | word0(&aadj2)(&aadj2)->L[1] += (2*P53+1)*Exp_msk10x100000 - y; | ||
2163 | aadj1 = dval(&aadj2)(&aadj2)->d; | ||
2164 | } | ||
2165 | adj.d = aadj1 * ulp(&rv); | ||
2166 | dval(&rv)(&rv)->d += adj.d; | ||
2167 | } | ||
2168 | z = word0(&rv)(&rv)->L[1] & Exp_mask0x7ff00000; | ||
2169 | if (bc.nd == nd) { | ||
2170 | if (!bc.scale) | ||
2171 | if (y == z) { | ||
2172 | /* Can we stop now? */ | ||
2173 | L = (Long)aadj; | ||
2174 | aadj -= L; | ||
2175 | /* The tolerances below are conservative. */ | ||
2176 | if (dsign || word1(&rv)(&rv)->L[0] || word0(&rv)(&rv)->L[1] & Bndry_mask0xfffff) { | ||
2177 | if (aadj < .4999999 || aadj > .5000001) | ||
2178 | break; | ||
2179 | } | ||
2180 | else if (aadj < .4999999/FLT_RADIX2) | ||
2181 | break; | ||
2182 | } | ||
2183 | } | ||
2184 | cont: | ||
2185 | Bfree(bb); | ||
2186 | Bfree(bd); | ||
2187 | Bfree(bs); | ||
2188 | Bfree(delta); | ||
2189 | } | ||
2190 | Bfree(bb); | ||
2191 | Bfree(bd); | ||
2192 | Bfree(bs); | ||
2193 | Bfree(bd0); | ||
2194 | Bfree(delta); | ||
2195 | if (bc.nd > nd) { | ||
2196 | error = bigcomp(&rv, s0, &bc); | ||
2197 | if (error) | ||
2198 | goto failed_malloc; | ||
2199 | } | ||
2200 | |||
2201 | if (bc.scale) { | ||
2202 | word0(&rv0)(&rv0)->L[1] = Exp_10x3ff00000 - 2*P53*Exp_msk10x100000; | ||
2203 | word1(&rv0)(&rv0)->L[0] = 0; | ||
2204 | dval(&rv)(&rv)->d *= dval(&rv0)(&rv0)->d; | ||
2205 | } | ||
2206 | |||
2207 | ret: | ||
2208 | return sign ? -dval(&rv)(&rv)->d : dval(&rv)(&rv)->d; | ||
2209 | |||
2210 | parse_error: | ||
2211 | return 0.0; | ||
2212 | |||
2213 | failed_malloc: | ||
2214 | errno(*__error()) = ENOMEM12; | ||
2215 | return -1.0; | ||
2216 | |||
2217 | undfl: | ||
2218 | return sign ? -0.0 : 0.0; | ||
2219 | |||
2220 | ovfl: | ||
2221 | errno(*__error()) = ERANGE34; | ||
2222 | /* Can't trust HUGE_VAL */ | ||
2223 | word0(&rv)(&rv)->L[1] = Exp_mask0x7ff00000; | ||
2224 | word1(&rv)(&rv)->L[0] = 0; | ||
2225 | return sign ? -dval(&rv)(&rv)->d : dval(&rv)(&rv)->d; | ||
2226 | |||
2227 | } | ||
2228 | |||
2229 | static char * | ||
2230 | rv_alloc(int i) | ||
2231 | { | ||
2232 | int j, k, *r; | ||
2233 | |||
2234 | j = sizeof(ULong); | ||
2235 | for(k = 0; | ||
2236 | sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= (unsigned)i; | ||
2237 | j <<= 1) | ||
2238 | k++; | ||
2239 | r = (int*)Balloc(k); | ||
2240 | if (r == NULL((void *)0)) | ||
2241 | return NULL((void *)0); | ||
2242 | *r = k; | ||
2243 | return (char *)(r+1); | ||
2244 | } | ||
2245 | |||
2246 | static char * | ||
2247 | nrv_alloc(char *s, char **rve, int n) | ||
2248 | { | ||
2249 | char *rv, *t; | ||
2250 | |||
2251 | rv = rv_alloc(n); | ||
2252 | if (rv == NULL((void *)0)) | ||
2253 | return NULL((void *)0); | ||
2254 | t = rv; | ||
2255 | while((*t = *s++)) t++; | ||
2256 | if (rve) | ||
2257 | *rve = t; | ||
2258 | return rv; | ||
2259 | } | ||
2260 | |||
2261 | /* freedtoa(s) must be used to free values s returned by dtoa | ||
2262 | * when MULTIPLE_THREADS is #defined. It should be used in all cases, | ||
2263 | * but for consistency with earlier versions of dtoa, it is optional | ||
2264 | * when MULTIPLE_THREADS is not defined. | ||
2265 | */ | ||
2266 | |||
2267 | void | ||
2268 | _Py_dg_freedtoa(char *s) | ||
2269 | { | ||
2270 | Bigint *b = (Bigint *)((int *)s - 1); | ||
2271 | b->maxwds = 1 << (b->k = *(int*)b); | ||
2272 | Bfree(b); | ||
2273 | } | ||
2274 | |||
2275 | /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string. | ||
2276 | * | ||
2277 | * Inspired by "How to Print Floating-Point Numbers Accurately" by | ||
2278 | * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126]. | ||
2279 | * | ||
2280 | * Modifications: | ||
2281 | * 1. Rather than iterating, we use a simple numeric overestimate | ||
2282 | * to determine k = floor(log10(d)). We scale relevant | ||
2283 | * quantities using O(log2(k)) rather than O(k) multiplications. | ||
2284 | * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't | ||
2285 | * try to generate digits strictly left to right. Instead, we | ||
2286 | * compute with fewer bits and propagate the carry if necessary | ||
2287 | * when rounding the final digit up. This is often faster. | ||
2288 | * 3. Under the assumption that input will be rounded nearest, | ||
2289 | * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22. | ||
2290 | * That is, we allow equality in stopping tests when the | ||
2291 | * round-nearest rule will give the same floating-point value | ||
2292 | * as would satisfaction of the stopping test with strict | ||
2293 | * inequality. | ||
2294 | * 4. We remove common factors of powers of 2 from relevant | ||
2295 | * quantities. | ||
2296 | * 5. When converting floating-point integers less than 1e16, | ||
2297 | * we use floating-point arithmetic rather than resorting | ||
2298 | * to multiple-precision integers. | ||
2299 | * 6. When asked to produce fewer than 15 digits, we first try | ||
2300 | * to get by with floating-point arithmetic; we resort to | ||
2301 | * multiple-precision integer arithmetic only if we cannot | ||
2302 | * guarantee that the floating-point calculation has given | ||
2303 | * the correctly rounded result. For k requested digits and | ||
2304 | * "uniformly" distributed input, the probability is | ||
2305 | * something like 10^(k-15) that we must resort to the Long | ||
2306 | * calculation. | ||
2307 | */ | ||
2308 | |||
2309 | /* Additional notes (METD): (1) returns NULL on failure. (2) to avoid memory | ||
2310 | leakage, a successful call to _Py_dg_dtoa should always be matched by a | ||
2311 | call to _Py_dg_freedtoa. */ | ||
2312 | |||
2313 | char * | ||
2314 | _Py_dg_dtoa(double dd, int mode, int ndigits, | ||
2315 | int *decpt, int *sign, char **rve) | ||
2316 | { | ||
2317 | /* Arguments ndigits, decpt, sign are similar to those | ||
2318 | of ecvt and fcvt; trailing zeros are suppressed from | ||
2319 | the returned string. If not null, *rve is set to point | ||
2320 | to the end of the return value. If d is +-Infinity or NaN, | ||
2321 | then *decpt is set to 9999. | ||
2322 | |||
2323 | mode: | ||
2324 | 0 ==> shortest string that yields d when read in | ||
2325 | and rounded to nearest. | ||
2326 | 1 ==> like 0, but with Steele & White stopping rule; | ||
2327 | e.g. with IEEE P754 arithmetic , mode 0 gives | ||
2328 | 1e23 whereas mode 1 gives 9.999999999999999e22. | ||
2329 | 2 ==> max(1,ndigits) significant digits. This gives a | ||
2330 | return value similar to that of ecvt, except | ||
2331 | that trailing zeros are suppressed. | ||
2332 | 3 ==> through ndigits past the decimal point. This | ||
2333 | gives a return value similar to that from fcvt, | ||
2334 | except that trailing zeros are suppressed, and | ||
2335 | ndigits can be negative. | ||
2336 | 4,5 ==> similar to 2 and 3, respectively, but (in | ||
2337 | round-nearest mode) with the tests of mode 0 to | ||
2338 | possibly return a shorter string that rounds to d. | ||
2339 | With IEEE arithmetic and compilation with | ||
2340 | -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same | ||
2341 | as modes 2 and 3 when FLT_ROUNDS != 1. | ||
2342 | 6-9 ==> Debugging modes similar to mode - 4: don't try | ||
2343 | fast floating-point estimate (if applicable). | ||
2344 | |||
2345 | Values of mode other than 0-9 are treated as mode 0. | ||
2346 | |||
2347 | Sufficient space is allocated to the return value | ||
2348 | to hold the suppressed trailing zeros. | ||
2349 | */ | ||
2350 | |||
2351 | int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1, | ||
2352 | j, j1, k, k0, k_check, leftright, m2, m5, s2, s5, | ||
2353 | spec_case, try_quick; | ||
2354 | Long L; | ||
2355 | int denorm; | ||
2356 | ULong x; | ||
2357 | Bigint *b, *b1, *delta, *mlo, *mhi, *S; | ||
2358 | U d2, eps, u; | ||
2359 | double ds; | ||
2360 | char *s, *s0; | ||
2361 | |||
2362 | /* set pointers to NULL, to silence gcc compiler warnings and make | ||
2363 | cleanup easier on error */ | ||
2364 | mlo = mhi = S = 0; | ||
2365 | s0 = 0; | ||
2366 | |||
2367 | u.d = dd; | ||
2368 | if (word0(&u)(&u)->L[1] & Sign_bit0x80000000) { | ||
2369 | /* set sign for everything, including 0's and NaNs */ | ||
2370 | *sign = 1; | ||
2371 | word0(&u)(&u)->L[1] &= ~Sign_bit0x80000000; /* clear sign bit */ | ||
2372 | } | ||
2373 | else | ||
2374 | *sign = 0; | ||
2375 | |||
2376 | /* quick return for Infinities, NaNs and zeros */ | ||
2377 | if ((word0(&u)(&u)->L[1] & Exp_mask0x7ff00000) == Exp_mask0x7ff00000) | ||
2378 | { | ||
2379 | /* Infinity or NaN */ | ||
2380 | *decpt = 9999; | ||
2381 | if (!word1(&u)(&u)->L[0] && !(word0(&u)(&u)->L[1] & 0xfffff)) | ||
2382 | return nrv_alloc("Infinity", rve, 8); | ||
2383 | return nrv_alloc("NaN", rve, 3); | ||
2384 | } | ||
2385 | if (!dval(&u)(&u)->d) { | ||
2386 | *decpt = 1; | ||
2387 | return nrv_alloc("0", rve, 1); | ||
2388 | } | ||
2389 | |||
2390 | /* compute k = floor(log10(d)). The computation may leave k | ||
2391 | one too large, but should never leave k too small. */ | ||
2392 | b = d2b(&u, &be, &bbits); | ||
2393 | if (b == NULL((void *)0)) | ||
2394 | goto failed_malloc; | ||
2395 | if ((i = (int)(word0(&u)(&u)->L[1] >> Exp_shift120 & (Exp_mask0x7ff00000>>Exp_shift120)))) { | ||
2396 | dval(&d2)(&d2)->d = dval(&u)(&u)->d; | ||
2397 | word0(&d2)(&d2)->L[1] &= Frac_mask10xfffff; | ||
2398 | word0(&d2)(&d2)->L[1] |= Exp_110x3ff00000; | ||
2399 | |||
2400 | /* log(x) ~=~ log(1.5) + (x-1.5)/1.5 | ||
2401 | * log10(x) = log(x) / log(10) | ||
2402 | * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10)) | ||
2403 | * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2) | ||
2404 | * | ||
2405 | * This suggests computing an approximation k to log10(d) by | ||
2406 | * | ||
2407 | * k = (i - Bias)*0.301029995663981 | ||
2408 | * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 ); | ||
2409 | * | ||
2410 | * We want k to be too large rather than too small. | ||
2411 | * The error in the first-order Taylor series approximation | ||
2412 | * is in our favor, so we just round up the constant enough | ||
2413 | * to compensate for any error in the multiplication of | ||
2414 | * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077, | ||
2415 | * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14, | ||
2416 | * adding 1e-13 to the constant term more than suffices. | ||
2417 | * Hence we adjust the constant term to 0.1760912590558. | ||
2418 | * (We could get a more accurate k by invoking log10, | ||
2419 | * but this is probably not worthwhile.) | ||
2420 | */ | ||
2421 | |||
2422 | i -= Bias1023; | ||
2423 | denorm = 0; | ||
2424 | } | ||
2425 | else { | ||
2426 | /* d is denormalized */ | ||
2427 | |||
2428 | i = bbits + be + (Bias1023 + (P53-1) - 1); | ||
2429 | x = i > 32 ? word0(&u)(&u)->L[1] << (64 - i) | word1(&u)(&u)->L[0] >> (i - 32) | ||
2430 | : word1(&u)(&u)->L[0] << (32 - i); | ||
2431 | dval(&d2)(&d2)->d = x; | ||
2432 | word0(&d2)(&d2)->L[1] -= 31*Exp_msk10x100000; /* adjust exponent */ | ||
2433 | i -= (Bias1023 + (P53-1) - 1) + 1; | ||
2434 | denorm = 1; | ||
2435 | } | ||
2436 | ds = (dval(&d2)(&d2)->d-1.5)*0.289529654602168 + 0.1760912590558 + | ||
2437 | i*0.301029995663981; | ||
2438 | k = (int)ds; | ||
2439 | if (ds < 0. && ds != k) | ||
2440 | k--; /* want k = floor(ds) */ | ||
2441 | k_check = 1; | ||
2442 | if (k >= 0 && k <= Ten_pmax22) { | ||
2443 | if (dval(&u)(&u)->d < tens[k]) | ||
2444 | k--; | ||
2445 | k_check = 0; | ||
2446 | } | ||
2447 | j = bbits - i - 1; | ||
2448 | if (j >= 0) { | ||
2449 | b2 = 0; | ||
2450 | s2 = j; | ||
2451 | } | ||
2452 | else { | ||
2453 | b2 = -j; | ||
2454 | s2 = 0; | ||
2455 | } | ||
2456 | if (k >= 0) { | ||
2457 | b5 = 0; | ||
2458 | s5 = k; | ||
2459 | s2 += k; | ||
2460 | } | ||
2461 | else { | ||
2462 | b2 -= k; | ||
2463 | b5 = -k; | ||
2464 | s5 = 0; | ||
2465 | } | ||
2466 | if (mode < 0 || mode > 9) | ||
2467 | mode = 0; | ||
2468 | |||
2469 | try_quick = 1; | ||
2470 | |||
2471 | if (mode > 5) { | ||
2472 | mode -= 4; | ||
2473 | try_quick = 0; | ||
2474 | } | ||
2475 | leftright = 1; | ||
2476 | ilim = ilim1 = -1; /* Values for cases 0 and 1; done here to */ | ||
2477 | /* silence erroneous "gcc -Wall" warning. */ | ||
2478 | switch(mode) { | ||
2479 | case 0: | ||
2480 | case 1: | ||
2481 | i = 18; | ||
2482 | ndigits = 0; | ||
2483 | break; | ||
2484 | case 2: | ||
2485 | leftright = 0; | ||
2486 | /* no break */ | ||
2487 | case 4: | ||
2488 | if (ndigits <= 0) | ||
2489 | ndigits = 1; | ||
2490 | ilim = ilim1 = i = ndigits; | ||
2491 | break; | ||
2492 | case 3: | ||
2493 | leftright = 0; | ||
2494 | /* no break */ | ||
2495 | case 5: | ||
2496 | i = ndigits + k + 1; | ||
2497 | ilim = i; | ||
2498 | ilim1 = i - 1; | ||
2499 | if (i <= 0) | ||
2500 | i = 1; | ||
2501 | } | ||
2502 | s0 = rv_alloc(i); | ||
2503 | if (s0 == NULL((void *)0)) | ||
2504 | goto failed_malloc; | ||
2505 | s = s0; | ||
2506 | |||
2507 | |||
2508 | if (ilim >= 0 && ilim <= Quick_max14 && try_quick) { | ||
2509 | |||
2510 | /* Try to get by with floating-point arithmetic. */ | ||
2511 | |||
2512 | i = 0; | ||
2513 | dval(&d2)(&d2)->d = dval(&u)(&u)->d; | ||
2514 | k0 = k; | ||
2515 | ilim0 = ilim; | ||
2516 | ieps = 2; /* conservative */ | ||
2517 | if (k > 0) { | ||
2518 | ds = tens[k&0xf]; | ||
2519 | j = k >> 4; | ||
2520 | if (j & Bletch0x10) { | ||
2521 | /* prevent overflows */ | ||
2522 | j &= Bletch0x10 - 1; | ||
2523 | dval(&u)(&u)->d /= bigtens[n_bigtens5-1]; | ||
2524 | ieps++; | ||
2525 | } | ||
2526 | for(; j; j >>= 1, i++) | ||
2527 | if (j & 1) { | ||
2528 | ieps++; | ||
2529 | ds *= bigtens[i]; | ||
2530 | } | ||
2531 | dval(&u)(&u)->d /= ds; | ||
2532 | } | ||
2533 | else if ((j1 = -k)) { | ||
2534 | dval(&u)(&u)->d *= tens[j1 & 0xf]; | ||
2535 | for(j = j1 >> 4; j; j >>= 1, i++) | ||
2536 | if (j & 1) { | ||
2537 | ieps++; | ||
2538 | dval(&u)(&u)->d *= bigtens[i]; | ||
2539 | } | ||
2540 | } | ||
2541 | if (k_check && dval(&u)(&u)->d < 1. && ilim > 0) { | ||
2542 | if (ilim1 <= 0) | ||
2543 | goto fast_failed; | ||
2544 | ilim = ilim1; | ||
2545 | k--; | ||
2546 | dval(&u)(&u)->d *= 10.; | ||
2547 | ieps++; | ||
2548 | } | ||
2549 | dval(&eps)(&eps)->d = ieps*dval(&u)(&u)->d + 7.; | ||
2550 | word0(&eps)(&eps)->L[1] -= (P53-1)*Exp_msk10x100000; | ||
2551 | if (ilim == 0) { | ||
2552 | S = mhi = 0; | ||
2553 | dval(&u)(&u)->d -= 5.; | ||
2554 | if (dval(&u)(&u)->d > dval(&eps)(&eps)->d) | ||
2555 | goto one_digit; | ||
2556 | if (dval(&u)(&u)->d < -dval(&eps)(&eps)->d) | ||
2557 | goto no_digits; | ||
2558 | goto fast_failed; | ||
2559 | } | ||
2560 | if (leftright) { | ||
2561 | /* Use Steele & White method of only | ||
2562 | * generating digits needed. | ||
2563 | */ | ||
2564 | dval(&eps)(&eps)->d = 0.5/tens[ilim-1] - dval(&eps)(&eps)->d; | ||
2565 | for(i = 0;;) { | ||
2566 | L = (Long)dval(&u)(&u)->d; | ||
2567 | dval(&u)(&u)->d -= L; | ||
2568 | *s++ = '0' + (int)L; | ||
2569 | if (dval(&u)(&u)->d < dval(&eps)(&eps)->d) | ||
2570 | goto ret1; | ||
2571 | if (1. - dval(&u)(&u)->d < dval(&eps)(&eps)->d) | ||
2572 | goto bump_up; | ||
2573 | if (++i >= ilim) | ||
2574 | break; | ||
2575 | dval(&eps)(&eps)->d *= 10.; | ||
2576 | dval(&u)(&u)->d *= 10.; | ||
2577 | } | ||
2578 | } | ||
2579 | else { | ||
2580 | /* Generate ilim digits, then fix them up. */ | ||
2581 | dval(&eps)(&eps)->d *= tens[ilim-1]; | ||
2582 | for(i = 1;; i++, dval(&u)(&u)->d *= 10.) { | ||
2583 | L = (Long)(dval(&u)(&u)->d); | ||
2584 | if (!(dval(&u)(&u)->d -= L)) | ||
2585 | ilim = i; | ||
2586 | *s++ = '0' + (int)L; | ||
2587 | if (i == ilim) { | ||
2588 | if (dval(&u)(&u)->d > 0.5 + dval(&eps)(&eps)->d) | ||
2589 | goto bump_up; | ||
2590 | else if (dval(&u)(&u)->d < 0.5 - dval(&eps)(&eps)->d) { | ||
2591 | while(*--s == '0'); | ||
2592 | s++; | ||
2593 | goto ret1; | ||
2594 | } | ||
2595 | break; | ||
2596 | } | ||
2597 | } | ||
2598 | } | ||
2599 | fast_failed: | ||
2600 | s = s0; | ||
2601 | dval(&u)(&u)->d = dval(&d2)(&d2)->d; | ||
2602 | k = k0; | ||
2603 | ilim = ilim0; | ||
2604 | } | ||
2605 | |||
2606 | /* Do we have a "small" integer? */ | ||
2607 | |||
2608 | if (be >= 0 && k <= Int_max14) { | ||
2609 | /* Yes. */ | ||
2610 | ds = tens[k]; | ||
2611 | if (ndigits < 0 && ilim <= 0) { | ||
2612 | S = mhi = 0; | ||
2613 | if (ilim < 0 || dval(&u)(&u)->d <= 5*ds) | ||
2614 | goto no_digits; | ||
2615 | goto one_digit; | ||
2616 | } | ||
2617 | for(i = 1;; i++, dval(&u)(&u)->d *= 10.) { | ||
2618 | L = (Long)(dval(&u)(&u)->d / ds); | ||
2619 | dval(&u)(&u)->d -= L*ds; | ||
2620 | *s++ = '0' + (int)L; | ||
2621 | if (!dval(&u)(&u)->d) { | ||
2622 | break; | ||
2623 | } | ||
2624 | if (i == ilim) { | ||
2625 | dval(&u)(&u)->d += dval(&u)(&u)->d; | ||
2626 | if (dval(&u)(&u)->d > ds || (dval(&u)(&u)->d == ds && L & 1)) { | ||
2627 | bump_up: | ||
2628 | while(*--s == '9') | ||
2629 | if (s == s0) { | ||
2630 | k++; | ||
2631 | *s = '0'; | ||
2632 | break; | ||
2633 | } | ||
2634 | ++*s++; | ||
2635 | } | ||
2636 | break; | ||
2637 | } | ||
2638 | } | ||
2639 | goto ret1; | ||
2640 | } | ||
2641 | |||
2642 | m2 = b2; | ||
2643 | m5 = b5; | ||
2644 | if (leftright) { | ||
2645 | i = | ||
2646 | denorm ? be + (Bias1023 + (P53-1) - 1 + 1) : | ||
2647 | 1 + P53 - bbits; | ||
2648 | b2 += i; | ||
2649 | s2 += i; | ||
2650 | mhi = i2b(1); | ||
2651 | if (mhi == NULL((void *)0)) | ||
2652 | goto failed_malloc; | ||
2653 | } | ||
2654 | if (m2 > 0 && s2 > 0) { | ||
2655 | i = m2 < s2 ? m2 : s2; | ||
2656 | b2 -= i; | ||
2657 | m2 -= i; | ||
2658 | s2 -= i; | ||
2659 | } | ||
2660 | if (b5 > 0) { | ||
2661 | if (leftright) { | ||
2662 | if (m5 > 0) { | ||
2663 | mhi = pow5mult(mhi, m5); | ||
2664 | if (mhi == NULL((void *)0)) | ||
2665 | goto failed_malloc; | ||
2666 | b1 = mult(mhi, b); | ||
2667 | Bfree(b); | ||
2668 | b = b1; | ||
2669 | if (b == NULL((void *)0)) | ||
2670 | goto failed_malloc; | ||
2671 | } | ||
2672 | if ((j = b5 - m5)) { | ||
2673 | b = pow5mult(b, j); | ||
2674 | if (b == NULL((void *)0)) | ||
2675 | goto failed_malloc; | ||
2676 | } | ||
2677 | } | ||
2678 | else { | ||
2679 | b = pow5mult(b, b5); | ||
2680 | if (b == NULL((void *)0)) | ||
2681 | goto failed_malloc; | ||
2682 | } | ||
2683 | } | ||
2684 | S = i2b(1); | ||
2685 | if (S == NULL((void *)0)) | ||
2686 | goto failed_malloc; | ||
2687 | if (s5 > 0) { | ||
2688 | S = pow5mult(S, s5); | ||
2689 | if (S == NULL((void *)0)) | ||
2690 | goto failed_malloc; | ||
2691 | } | ||
2692 | |||
2693 | /* Check for special case that d is a normalized power of 2. */ | ||
2694 | |||
2695 | spec_case = 0; | ||
2696 | if ((mode < 2 || leftright) | ||
2697 | ) { | ||
2698 | if (!word1(&u)(&u)->L[0] && !(word0(&u)(&u)->L[1] & Bndry_mask0xfffff) | ||
2699 | && word0(&u)(&u)->L[1] & (Exp_mask0x7ff00000 & ~Exp_msk10x100000) | ||
2700 | ) { | ||
2701 | /* The special case */ | ||
2702 | b2 += Log2P1; | ||
2703 | s2 += Log2P1; | ||
2704 | spec_case = 1; | ||
2705 | } | ||
2706 | } | ||
2707 | |||
2708 | /* Arrange for convenient computation of quotients: | ||
2709 | * shift left if necessary so divisor has 4 leading 0 bits. | ||
2710 | * | ||
2711 | * Perhaps we should just compute leading 28 bits of S once | ||
2712 | * and for all and pass them and a shift to quorem, so it | ||
2713 | * can do shifts and ors to compute the numerator for q. | ||
2714 | */ | ||
2715 | #define iInc28 28 | ||
2716 | i = dshift(S, s2); | ||
2717 | b2 += i; | ||
2718 | m2 += i; | ||
2719 | s2 += i; | ||
2720 | if (b2 > 0) { | ||
2721 | b = lshift(b, b2); | ||
2722 | if (b == NULL((void *)0)) | ||
2723 | goto failed_malloc; | ||
2724 | } | ||
2725 | if (s2 > 0) { | ||
2726 | S = lshift(S, s2); | ||
2727 | if (S == NULL((void *)0)) | ||
2728 | goto failed_malloc; | ||
2729 | } | ||
2730 | if (k_check) { | ||
2731 | if (cmp(b,S) < 0) { | ||
2732 | k--; | ||
2733 | b = multadd(b, 10, 0); /* we botched the k estimate */ | ||
2734 | if (b == NULL((void *)0)) | ||
2735 | goto failed_malloc; | ||
2736 | if (leftright) { | ||
2737 | mhi = multadd(mhi, 10, 0); | ||
2738 | if (mhi == NULL((void *)0)) | ||
2739 | goto failed_malloc; | ||
2740 | } | ||
2741 | ilim = ilim1; | ||
2742 | } | ||
2743 | } | ||
2744 | if (ilim <= 0 && (mode == 3 || mode == 5)) { | ||
2745 | if (ilim < 0) { | ||
2746 | /* no digits, fcvt style */ | ||
2747 | no_digits: | ||
2748 | k = -1 - ndigits; | ||
2749 | goto ret; | ||
2750 | } | ||
2751 | else { | ||
2752 | S = multadd(S, 5, 0); | ||
2753 | if (S == NULL((void *)0)) | ||
2754 | goto failed_malloc; | ||
2755 | if (cmp(b, S) <= 0) | ||
2756 | goto no_digits; | ||
2757 | } | ||
2758 | one_digit: | ||
2759 | *s++ = '1'; | ||
2760 | k++; | ||
2761 | goto ret; | ||
2762 | } | ||
2763 | if (leftright) { | ||
2764 | if (m2 > 0) { | ||
2765 | mhi = lshift(mhi, m2); | ||
2766 | if (mhi == NULL((void *)0)) | ||
2767 | goto failed_malloc; | ||
2768 | } | ||
2769 | |||
2770 | /* Compute mlo -- check for special case | ||
2771 | * that d is a normalized power of 2. | ||
2772 | */ | ||
2773 | |||
2774 | mlo = mhi; | ||
2775 | if (spec_case) { | ||
2776 | mhi = Balloc(mhi->k); | ||
2777 | if (mhi == NULL((void *)0)) | ||
2778 | goto failed_malloc; | ||
2779 | Bcopy(mhi, mlo)((__builtin_object_size ((char *)&mhi->sign, 0) != (size_t ) -1) ? __builtin___memcpy_chk ((char *)&mhi->sign, (char *)&mlo->sign, mlo->wds*sizeof(Long) + 2*sizeof(int ), __builtin_object_size ((char *)&mhi->sign, 0)) : __inline_memcpy_chk ((char *)&mhi->sign, (char *)&mlo->sign, mlo-> wds*sizeof(Long) + 2*sizeof(int))); | ||
2780 | mhi = lshift(mhi, Log2P1); | ||
2781 | if (mhi == NULL((void *)0)) | ||
2782 | goto failed_malloc; | ||
2783 | } | ||
2784 | |||
2785 | for(i = 1;;i++) { | ||
2786 | dig = quorem(b,S) + '0'; | ||
2787 | /* Do we yet have the shortest decimal string | ||
2788 | * that will round to d? | ||
2789 | */ | ||
2790 | j = cmp(b, mlo); | ||
2791 | delta = diff(S, mhi); | ||
2792 | if (delta == NULL((void *)0)) | ||
2793 | goto failed_malloc; | ||
2794 | j1 = delta->sign ? 1 : cmp(b, delta); | ||
2795 | Bfree(delta); | ||
2796 | if (j1 == 0 && mode != 1 && !(word1(&u)(&u)->L[0] & 1) | ||
2797 | ) { | ||
2798 | if (dig == '9') | ||
2799 | goto round_9_up; | ||
2800 | if (j > 0) | ||
2801 | dig++; | ||
2802 | *s++ = dig; | ||
2803 | goto ret; | ||
2804 | } | ||
2805 | if (j < 0 || (j == 0 && mode != 1 | ||
2806 | && !(word1(&u)(&u)->L[0] & 1) | ||
2807 | )) { | ||
2808 | if (!b->x[0] && b->wds <= 1) { | ||
2809 | goto accept_dig; | ||
2810 | } | ||
2811 | if (j1 > 0) { | ||
2812 | b = lshift(b, 1); | ||
2813 | if (b == NULL((void *)0)) | ||
2814 | goto failed_malloc; | ||
2815 | j1 = cmp(b, S); | ||
2816 | if ((j1 > 0 || (j1 == 0 && dig & 1)) | ||
2817 | && dig++ == '9') | ||
2818 | goto round_9_up; | ||
2819 | } | ||
2820 | accept_dig: | ||
2821 | *s++ = dig; | ||
2822 | goto ret; | ||
2823 | } | ||
2824 | if (j1 > 0) { | ||
2825 | if (dig == '9') { /* possible if i == 1 */ | ||
2826 | round_9_up: | ||
2827 | *s++ = '9'; | ||
2828 | goto roundoff; | ||
2829 | } | ||
2830 | *s++ = dig + 1; | ||
2831 | goto ret; | ||
2832 | } | ||
2833 | *s++ = dig; | ||
2834 | if (i == ilim) | ||
2835 | break; | ||
2836 | b = multadd(b, 10, 0); | ||
2837 | if (b == NULL((void *)0)) | ||
2838 | goto failed_malloc; | ||
2839 | if (mlo == mhi) { | ||
2840 | mlo = mhi = multadd(mhi, 10, 0); | ||
2841 | if (mlo == NULL((void *)0)) | ||
2842 | goto failed_malloc; | ||
2843 | } | ||
2844 | else { | ||
2845 | mlo = multadd(mlo, 10, 0); | ||
2846 | if (mlo == NULL((void *)0)) | ||
2847 | goto failed_malloc; | ||
2848 | mhi = multadd(mhi, 10, 0); | ||
2849 | if (mhi == NULL((void *)0)) | ||
2850 | goto failed_malloc; | ||
2851 | } | ||
2852 | } | ||
2853 | } | ||
2854 | else | ||
2855 | for(i = 1;; i++) { | ||
2856 | *s++ = dig = quorem(b,S) + '0'; | ||
2857 | if (!b->x[0] && b->wds <= 1) { | ||
2858 | goto ret; | ||
2859 | } | ||
2860 | if (i >= ilim) | ||
2861 | break; | ||
2862 | b = multadd(b, 10, 0); | ||
2863 | if (b == NULL((void *)0)) | ||
2864 | goto failed_malloc; | ||
2865 | } | ||
2866 | |||
2867 | /* Round off last digit */ | ||
2868 | |||
2869 | b = lshift(b, 1); | ||
2870 | if (b == NULL((void *)0)) | ||
2871 | goto failed_malloc; | ||
2872 | j = cmp(b, S); | ||
2873 | if (j > 0 || (j == 0 && dig & 1)) { | ||
2874 | roundoff: | ||
2875 | while(*--s == '9') | ||
2876 | if (s == s0) { | ||
2877 | k++; | ||
2878 | *s++ = '1'; | ||
2879 | goto ret; | ||
2880 | } | ||
2881 | ++*s++; | ||
2882 | } | ||
2883 | else { | ||
2884 | while(*--s == '0'); | ||
2885 | s++; | ||
2886 | } | ||
2887 | ret: | ||
2888 | Bfree(S); | ||
2889 | if (mhi) { | ||
2890 | if (mlo && mlo != mhi) | ||
2891 | Bfree(mlo); | ||
2892 | Bfree(mhi); | ||
2893 | } | ||
2894 | ret1: | ||
2895 | Bfree(b); | ||
2896 | *s = 0; | ||
2897 | *decpt = k + 1; | ||
2898 | if (rve) | ||
2899 | *rve = s; | ||
2900 | return s0; | ||
2901 | failed_malloc: | ||
2902 | if (S) | ||
2903 | Bfree(S); | ||
2904 | if (mlo && mlo != mhi) | ||
2905 | Bfree(mlo); | ||
2906 | if (mhi) | ||
2907 | Bfree(mhi); | ||
2908 | if (b) | ||
2909 | Bfree(b); | ||
2910 | if (s0) | ||
2911 | _Py_dg_freedtoa(s0); | ||
2912 | return NULL((void *)0); | ||
2913 | } | ||
2914 | #ifdef __cplusplus | ||
2915 | } | ||
2916 | #endif | ||
2917 | |||
2918 | #endif /* PY_NO_SHORT_FLOAT_REPR */ |