1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
|
/* Exception flags and utilities. Constructors and destructors (debug).
Copyright 2001-2014 Free Software Foundation, Inc.
Contributed by the AriC and Caramel projects, INRIA.
This file is part of the GNU MPFR Library.
The GNU MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or (at your
option) any later version.
The GNU MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see
http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
#include "mpfr-impl.h"
MPFR_THREAD_ATTR mpfr_flags_t __gmpfr_flags = 0;
MPFR_THREAD_ATTR mpfr_exp_t __gmpfr_emin = MPFR_EMIN_DEFAULT;
MPFR_THREAD_ATTR mpfr_exp_t __gmpfr_emax = MPFR_EMAX_DEFAULT;
#undef mpfr_get_emin
MPFR_COLD_FUNCTION_ATTR mpfr_exp_t
mpfr_get_emin (void)
{
return __gmpfr_emin;
}
#undef mpfr_set_emin
int
mpfr_set_emin (mpfr_exp_t exponent)
{
if (MPFR_LIKELY (exponent >= MPFR_EMIN_MIN && exponent <= MPFR_EMIN_MAX))
{
__gmpfr_emin = exponent;
return 0;
}
else
{
return 1;
}
}
MPFR_COLD_FUNCTION_ATTR mpfr_exp_t
mpfr_get_emin_min (void)
{
return MPFR_EMIN_MIN;
}
MPFR_COLD_FUNCTION_ATTR mpfr_exp_t
mpfr_get_emin_max (void)
{
return MPFR_EMIN_MAX;
}
#undef mpfr_get_emax
MPFR_COLD_FUNCTION_ATTR mpfr_exp_t
mpfr_get_emax (void)
{
return __gmpfr_emax;
}
#undef mpfr_set_emax
int
mpfr_set_emax (mpfr_exp_t exponent)
{
if (MPFR_LIKELY (exponent >= MPFR_EMAX_MIN && exponent <= MPFR_EMAX_MAX))
{
__gmpfr_emax = exponent;
return 0;
}
else
{
return 1;
}
}
MPFR_COLD_FUNCTION_ATTR mpfr_exp_t
mpfr_get_emax_min (void)
{
return MPFR_EMAX_MIN;
}
MPFR_COLD_FUNCTION_ATTR mpfr_exp_t
mpfr_get_emax_max (void)
{
return MPFR_EMAX_MAX;
}
#undef mpfr_flags_clear
MPFR_COLD_FUNCTION_ATTR void
mpfr_flags_clear (mpfr_flags_t mask)
{
__gmpfr_flags &= MPFR_FLAGS_ALL ^ mask;
}
#undef mpfr_flags_set
MPFR_COLD_FUNCTION_ATTR void
mpfr_flags_set (mpfr_flags_t mask)
{
__gmpfr_flags |= mask;
}
#undef mpfr_flags_test
MPFR_COLD_FUNCTION_ATTR mpfr_flags_t
mpfr_flags_test (mpfr_flags_t mask)
{
return __gmpfr_flags & mask;
}
#undef mpfr_flags_save
MPFR_COLD_FUNCTION_ATTR mpfr_flags_t
mpfr_flags_save (void)
{
return __gmpfr_flags;
}
#undef mpfr_flags_restore
MPFR_COLD_FUNCTION_ATTR void
mpfr_flags_restore (mpfr_flags_t flags, mpfr_flags_t mask)
{
__gmpfr_flags =
(__gmpfr_flags & (MPFR_FLAGS_ALL ^ mask)) |
(flags & mask);
}
#undef mpfr_clear_flags
void
mpfr_clear_flags (void)
{
__gmpfr_flags = 0;
}
#undef mpfr_clear_underflow
MPFR_COLD_FUNCTION_ATTR void
mpfr_clear_underflow (void)
{
__gmpfr_flags &= MPFR_FLAGS_ALL ^ MPFR_FLAGS_UNDERFLOW;
}
#undef mpfr_clear_overflow
MPFR_COLD_FUNCTION_ATTR void
mpfr_clear_overflow (void)
{
__gmpfr_flags &= MPFR_FLAGS_ALL ^ MPFR_FLAGS_OVERFLOW;
}
#undef mpfr_clear_divby0
MPFR_COLD_FUNCTION_ATTR void
mpfr_clear_divby0 (void)
{
__gmpfr_flags &= MPFR_FLAGS_ALL ^ MPFR_FLAGS_DIVBY0;
}
#undef mpfr_clear_nanflag
MPFR_COLD_FUNCTION_ATTR void
mpfr_clear_nanflag (void)
{
__gmpfr_flags &= MPFR_FLAGS_ALL ^ MPFR_FLAGS_NAN;
}
#undef mpfr_clear_inexflag
MPFR_COLD_FUNCTION_ATTR void
mpfr_clear_inexflag (void)
{
__gmpfr_flags &= MPFR_FLAGS_ALL ^ MPFR_FLAGS_INEXACT;
}
#undef mpfr_clear_erangeflag
MPFR_COLD_FUNCTION_ATTR void
mpfr_clear_erangeflag (void)
{
__gmpfr_flags &= MPFR_FLAGS_ALL ^ MPFR_FLAGS_ERANGE;
}
#undef mpfr_set_underflow
MPFR_COLD_FUNCTION_ATTR void
mpfr_set_underflow (void)
{
__gmpfr_flags |= MPFR_FLAGS_UNDERFLOW;
}
#undef mpfr_set_overflow
MPFR_COLD_FUNCTION_ATTR void
mpfr_set_overflow (void)
{
__gmpfr_flags |= MPFR_FLAGS_OVERFLOW;
}
#undef mpfr_set_divby0
MPFR_COLD_FUNCTION_ATTR void
mpfr_set_divby0 (void)
{
__gmpfr_flags |= MPFR_FLAGS_DIVBY0;
}
#undef mpfr_set_nanflag
MPFR_COLD_FUNCTION_ATTR void
mpfr_set_nanflag (void)
{
__gmpfr_flags |= MPFR_FLAGS_NAN;
}
#undef mpfr_set_inexflag
MPFR_COLD_FUNCTION_ATTR void
mpfr_set_inexflag (void)
{
__gmpfr_flags |= MPFR_FLAGS_INEXACT;
}
#undef mpfr_set_erangeflag
MPFR_COLD_FUNCTION_ATTR void
mpfr_set_erangeflag (void)
{
__gmpfr_flags |= MPFR_FLAGS_ERANGE;
}
#undef mpfr_check_range
int
mpfr_check_range (mpfr_ptr x, int t, mpfr_rnd_t rnd_mode)
{
if (MPFR_LIKELY( MPFR_IS_PURE_FP(x)) )
{ /* x is a non-zero FP */
mpfr_exp_t exp = MPFR_EXP (x); /* Do not use MPFR_GET_EXP */
/* Even if it is unlikely that exp is lower than emin,
this function is called by MPFR functions only if it is
already the case (or if exp is greater than emax) */
if (exp < __gmpfr_emin)
{
/* The following test is necessary because in the rounding to the
* nearest mode, mpfr_underflow always rounds away from 0. In
* this rounding mode, we need to round to 0 if:
* _ |x| < 2^(emin-2), or
* _ |x| = 2^(emin-2) and the absolute value of the exact
* result is <= 2^(emin-2).
*/
if (rnd_mode == MPFR_RNDN &&
(exp + 1 < __gmpfr_emin ||
(mpfr_powerof2_raw(x) &&
(MPFR_IS_NEG(x) ? t <= 0 : t >= 0))))
rnd_mode = MPFR_RNDZ;
return mpfr_underflow(x, rnd_mode, MPFR_SIGN(x));
}
if (exp > __gmpfr_emax)
return mpfr_overflow (x, rnd_mode, MPFR_SIGN(x));
}
else if (MPFR_UNLIKELY (t != 0 && MPFR_IS_INF (x)))
{
/* We need to do the following because most MPFR functions are
* implemented in the following way:
* Ziv's loop:
* | Compute an approximation to the result and an error bound.
* | Possible underflow/overflow detection -> return.
* | If can_round, break (exit the loop).
* | Otherwise, increase the working precision and loop.
* Round the approximation in the target precision. <== See below
* Restore the flags (that could have been set due to underflows
* or overflows during the internal computations).
* Execute: return mpfr_check_range (...).
* The problem is that an overflow could be generated when rounding the
* approximation (in general, such an overflow could not be detected
* earlier), and the overflow flag is lost when the flags are restored.
* This can occur only when the rounding yields an exponent change
* and the new exponent is larger than the maximum exponent, so that
* an infinity is necessarily obtained.
* So, the simplest solution is to detect this overflow case here in
* mpfr_check_range, which is easy to do since the rounded result is
* necessarily an inexact infinity.
*/
__gmpfr_flags |= MPFR_FLAGS_OVERFLOW;
}
MPFR_RET (t); /* propagate inexact ternary value, unlike most functions */
}
#undef mpfr_underflow_p
MPFR_COLD_FUNCTION_ATTR int
mpfr_underflow_p (void)
{
MPFR_STAT_STATIC_ASSERT (MPFR_FLAGS_UNDERFLOW <= INT_MAX);
return __gmpfr_flags & MPFR_FLAGS_UNDERFLOW;
}
#undef mpfr_overflow_p
MPFR_COLD_FUNCTION_ATTR int
mpfr_overflow_p (void)
{
MPFR_STAT_STATIC_ASSERT (MPFR_FLAGS_OVERFLOW <= INT_MAX);
return __gmpfr_flags & MPFR_FLAGS_OVERFLOW;
}
#undef mpfr_divby0_p
MPFR_COLD_FUNCTION_ATTR int
mpfr_divby0_p (void)
{
MPFR_STAT_STATIC_ASSERT (MPFR_FLAGS_DIVBY0 <= INT_MAX);
return __gmpfr_flags & MPFR_FLAGS_DIVBY0;
}
#undef mpfr_nanflag_p
MPFR_COLD_FUNCTION_ATTR int
mpfr_nanflag_p (void)
{
MPFR_STAT_STATIC_ASSERT (MPFR_FLAGS_NAN <= INT_MAX);
return __gmpfr_flags & MPFR_FLAGS_NAN;
}
#undef mpfr_inexflag_p
MPFR_COLD_FUNCTION_ATTR int
mpfr_inexflag_p (void)
{
MPFR_STAT_STATIC_ASSERT (MPFR_FLAGS_INEXACT <= INT_MAX);
return __gmpfr_flags & MPFR_FLAGS_INEXACT;
}
#undef mpfr_erangeflag_p
MPFR_COLD_FUNCTION_ATTR int
mpfr_erangeflag_p (void)
{
MPFR_STAT_STATIC_ASSERT (MPFR_FLAGS_ERANGE <= INT_MAX);
return __gmpfr_flags & MPFR_FLAGS_ERANGE;
}
/* #undef mpfr_underflow */
/* Note: In the rounding to the nearest mode, mpfr_underflow
always rounds away from 0. In this rounding mode, you must call
mpfr_underflow with rnd_mode = MPFR_RNDZ if the exact result
is <= 2^(emin-2) in absolute value. */
MPFR_COLD_FUNCTION_ATTR int
mpfr_underflow (mpfr_ptr x, mpfr_rnd_t rnd_mode, int sign)
{
int inex;
MPFR_ASSERT_SIGN (sign);
if (MPFR_IS_LIKE_RNDZ(rnd_mode, sign < 0))
{
MPFR_SET_ZERO(x);
inex = -1;
}
else
{
mpfr_setmin (x, __gmpfr_emin);
inex = 1;
}
MPFR_SET_SIGN(x, sign);
__gmpfr_flags |= MPFR_FLAGS_INEXACT | MPFR_FLAGS_UNDERFLOW;
return sign > 0 ? inex : -inex;
}
/* #undef mpfr_overflow */
MPFR_COLD_FUNCTION_ATTR int
mpfr_overflow (mpfr_ptr x, mpfr_rnd_t rnd_mode, int sign)
{
int inex;
MPFR_ASSERT_SIGN(sign);
if (MPFR_IS_LIKE_RNDZ(rnd_mode, sign < 0))
{
mpfr_setmax (x, __gmpfr_emax);
inex = -1;
}
else
{
MPFR_SET_INF(x);
inex = 1;
}
MPFR_SET_SIGN(x, sign);
__gmpfr_flags |= MPFR_FLAGS_INEXACT | MPFR_FLAGS_OVERFLOW;
return sign > 0 ? inex : -inex;
}
/**************************************************************************/
/* Code related to constructors and destructors (for debugging) should
be put here. The reason is that such code must be in an object file
that will be kept by the linker for symbol resolution, and symbols
__gmpfr_emin and __gmpfr_emax from this file will be used by every
program calling a MPFR math function (where rounding is involved). */
#if defined MPFR_DEBUG_PREDICTION
/* Print prediction statistics at the end of a program.
*
* Code to debug branch prediction, based on Ulrich Drepper's paper
* "What Every Programmer Should Know About Memory":
* http://people.freebsd.org/~lstewart/articles/cpumemory.pdf
*/
extern long int __start_predict_data;
extern long int __stop_predict_data;
extern long int __start_predict_line;
extern const char *__start_predict_file;
static void __attribute__ ((destructor))
predprint (void)
{
long int *s = &__start_predict_data;
long int *e = &__stop_predict_data;
long int *sl = &__start_predict_line;
const char **sf = &__start_predict_file;
while (s < e)
{
printf("%s:%ld: incorrect=%ld, correct=%ld%s\n",
*sf, *sl, s[0], s[1],
s[0] > s[1] ? " <==== WARNING" : "");
++sl;
++sf;
s += 2;
}
}
#endif
|