### Bug Summary

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

### Annotated Source Code

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 */