File: | Python/dtoa.c |
Location: | line 2058, column 21 |
Description: | Value stored to 'dsign' is never read |
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; |
Value stored to 'dsign' is never read | |
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 */ |