-
Notifications
You must be signed in to change notification settings - Fork 0
/
mpfr.h
1197 lines (1048 loc) · 52.5 KB
/
mpfr.h
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
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
/* mpfr.h -- Include file for mpfr.
Copyright 1999-2020 Free Software Foundation, Inc.
Contributed by the AriC and Caramba 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
https://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
#ifndef __MPFR_H
#define __MPFR_H
/* Define MPFR version number */
#define MPFR_VERSION_MAJOR 4
#define MPFR_VERSION_MINOR 1
#define MPFR_VERSION_PATCHLEVEL 0
#define MPFR_VERSION_STRING "4.1.0-p13"
/* User macros:
MPFR_USE_FILE: Define it to make MPFR define functions dealing
with FILE* (auto-detect).
MPFR_USE_INTMAX_T: Define it to make MPFR define functions dealing
with intmax_t (auto-detect).
MPFR_USE_VA_LIST: Define it to make MPFR define functions dealing
with va_list (auto-detect).
MPFR_USE_C99_FEATURE: Define it to 1 to make MPFR support C99-feature
(auto-detect), to 0 to bypass the detection.
MPFR_USE_EXTENSION: Define it to make MPFR use GCC extension to
reduce warnings.
MPFR_USE_NO_MACRO: Define it to make MPFR remove any overriding
function macro.
*/
/* Macros dealing with MPFR VERSION */
#define MPFR_VERSION_NUM(a,b,c) (((a) << 16L) | ((b) << 8) | (c))
#define MPFR_VERSION \
MPFR_VERSION_NUM(MPFR_VERSION_MAJOR,MPFR_VERSION_MINOR,MPFR_VERSION_PATCHLEVEL)
#ifndef MPFR_USE_MINI_GMP
#include <gmp.h>
#else
#include <mini-gmp.h>
#endif
/* Avoid some problems with macro expansion if the user defines macros
with the same name as keywords. By convention, identifiers and macro
names starting with mpfr_ are reserved by MPFR. */
typedef void mpfr_void;
typedef int mpfr_int;
typedef unsigned int mpfr_uint;
typedef long mpfr_long;
typedef unsigned long mpfr_ulong;
typedef size_t mpfr_size_t;
/* Global (possibly TLS) flags. Might also be used in an mpfr_t in the
future (there would be room as mpfr_sign_t just needs 1 byte).
TODO: The tests currently assume that the flags fits in an unsigned int;
this should be cleaned up, e.g. by defining a function that outputs the
flags as a string or by using the flags_out function (from tests/tests.c
directly). */
typedef unsigned int mpfr_flags_t;
/* Flags macros (in the public API) */
#define MPFR_FLAGS_UNDERFLOW 1
#define MPFR_FLAGS_OVERFLOW 2
#define MPFR_FLAGS_NAN 4
#define MPFR_FLAGS_INEXACT 8
#define MPFR_FLAGS_ERANGE 16
#define MPFR_FLAGS_DIVBY0 32
#define MPFR_FLAGS_ALL (MPFR_FLAGS_UNDERFLOW | \
MPFR_FLAGS_OVERFLOW | \
MPFR_FLAGS_NAN | \
MPFR_FLAGS_INEXACT | \
MPFR_FLAGS_ERANGE | \
MPFR_FLAGS_DIVBY0)
/* Definition of rounding modes (DON'T USE MPFR_RNDNA!).
Warning! Changing the contents of this enum should be seen as an
interface change since the old and the new types are not compatible
(the integer type compatible with the enumerated type can even change,
see ISO C99, 6.7.2.2#4), and in Makefile.am, AGE should be set to 0.
MPFR_RNDU must appear just before MPFR_RNDD (see
MPFR_IS_RNDUTEST_OR_RNDDNOTTEST in mpfr-impl.h).
If you change the order of the rounding modes, please update the routines
in texceptions.c which assume 0=RNDN, 1=RNDZ, 2=RNDU, 3=RNDD, 4=RNDA.
*/
typedef enum {
MPFR_RNDN=0, /* round to nearest, with ties to even */
MPFR_RNDZ, /* round toward zero */
MPFR_RNDU, /* round toward +Inf */
MPFR_RNDD, /* round toward -Inf */
MPFR_RNDA, /* round away from zero */
MPFR_RNDF, /* faithful rounding */
MPFR_RNDNA=-1 /* round to nearest, with ties away from zero (mpfr_round) */
} mpfr_rnd_t;
/* kept for compatibility with MPFR 2.4.x and before */
#define GMP_RNDN MPFR_RNDN
#define GMP_RNDZ MPFR_RNDZ
#define GMP_RNDU MPFR_RNDU
#define GMP_RNDD MPFR_RNDD
/* The _MPFR_PREC_FORMAT and _MPFR_EXP_FORMAT values are automatically
defined below. You MUST NOT force a value (this will break the ABI),
possibly except for a very particular use, in which case you also need
to rebuild the MPFR library with the chosen values; do not install this
rebuilt library in a path that is searched by default, otherwise this
will break applications that are dynamically linked with MPFR.
Using non-default values is not guaranteed to work.
Note: With the following default choices for _MPFR_PREC_FORMAT and
_MPFR_EXP_FORMAT, mpfr_exp_t will be the same as [mp_exp_t] (at least
up to GMP 6). */
/* Define precision: 1 (short), 2 (int) or 3 (long).
DON'T FORCE A VALUE (see above). */
#ifndef _MPFR_PREC_FORMAT
# if __GMP_MP_SIZE_T_INT
# define _MPFR_PREC_FORMAT 2
# else
# define _MPFR_PREC_FORMAT 3
# endif
#endif
/* Define exponent: 1 (short), 2 (int), 3 (long) or 4 (intmax_t).
DON'T FORCE A VALUE (see above). */
#ifndef _MPFR_EXP_FORMAT
# define _MPFR_EXP_FORMAT _MPFR_PREC_FORMAT
#endif
#if _MPFR_PREC_FORMAT > _MPFR_EXP_FORMAT
# error "mpfr_prec_t must not be larger than mpfr_exp_t"
#endif
/* Let's make mpfr_prec_t signed in order to avoid problems due to the
usual arithmetic conversions when mixing mpfr_prec_t and mpfr_exp_t
in an expression (for error analysis) if casts are forgotten.
Note: mpfr_prec_t is currently limited to "long". This means that
under MS Windows, the precisions are limited to about 2^31; however,
these are already huge precisions, probably sufficient in practice
on this platform. */
#if _MPFR_PREC_FORMAT == 1
typedef short mpfr_prec_t;
typedef unsigned short mpfr_uprec_t;
#elif _MPFR_PREC_FORMAT == 2
typedef int mpfr_prec_t;
typedef unsigned int mpfr_uprec_t;
#elif _MPFR_PREC_FORMAT == 3
/* we could use "long long" under Windows 64 here, which can be tested
with the macro _WIN64 according to
https://sourceforge.net/p/predef/wiki/OperatingSystems/ */
typedef long mpfr_prec_t;
typedef unsigned long mpfr_uprec_t;
#else
# error "Invalid MPFR Prec format"
#endif
/* Definition of precision limits without needing <limits.h> */
/* Note: The casts allows the expression to yield the wanted behavior
for _MPFR_PREC_FORMAT == 1 (due to integer promotion rules). We
also make sure that MPFR_PREC_MIN and MPFR_PREC_MAX have a signed
integer type. The "- 256" allows more security, avoiding some
integer overflows in extreme cases; ideally it should be useless. */
#define MPFR_PREC_MIN 1
#define MPFR_PREC_MAX ((mpfr_prec_t) ((((mpfr_uprec_t) -1) >> 1) - 256))
/* Definition of sign */
typedef int mpfr_sign_t;
/* Definition of the exponent. _MPFR_EXP_FORMAT must be large enough
so that mpfr_exp_t has at least 32 bits. */
#if _MPFR_EXP_FORMAT == 1
typedef short mpfr_exp_t;
typedef unsigned short mpfr_uexp_t;
#elif _MPFR_EXP_FORMAT == 2
typedef int mpfr_exp_t;
typedef unsigned int mpfr_uexp_t;
#elif _MPFR_EXP_FORMAT == 3
typedef long mpfr_exp_t;
typedef unsigned long mpfr_uexp_t;
#elif _MPFR_EXP_FORMAT == 4
/* Note: in this case, intmax_t and uintmax_t must be defined before
the inclusion of mpfr.h (we do not include <stdint.h> here because
of some non-ISO C99 implementations that support these types). */
typedef intmax_t mpfr_exp_t;
typedef uintmax_t mpfr_uexp_t;
#else
# error "Invalid MPFR Exp format"
#endif
/* Definition of the standard exponent limits */
#define MPFR_EMAX_DEFAULT ((mpfr_exp_t) (((mpfr_ulong) 1 << 30) - 1))
#define MPFR_EMIN_DEFAULT (-(MPFR_EMAX_DEFAULT))
/* DON'T USE THIS! (For MPFR-public macros only, see below.)
The mpfr_sgn macro uses the fact that __MPFR_EXP_NAN and __MPFR_EXP_ZERO
are the smallest values. For a n-bit type, EXP_MAX is 2^(n-1)-1,
EXP_ZERO is 1-2^(n-1), EXP_NAN is 2-2^(n-1), EXP_INF is 3-2^(n-1).
This may change in the future. MPFR code should not be based on these
representations (but if this is absolutely needed, protect the code
with a static assertion). */
#define __MPFR_EXP_MAX ((mpfr_exp_t) (((mpfr_uexp_t) -1) >> 1))
#define __MPFR_EXP_NAN (1 - __MPFR_EXP_MAX)
#define __MPFR_EXP_ZERO (0 - __MPFR_EXP_MAX)
#define __MPFR_EXP_INF (2 - __MPFR_EXP_MAX)
/* Definition of the main structure */
typedef struct __mpfr_struct {
mpfr_prec_t _mpfr_prec;
mpfr_sign_t _mpfr_sign;
mpfr_exp_t _mpfr_exp;
mp_limb_t *_mpfr_d;
} __mpfr_struct;
/* Compatibility with previous types of MPFR */
#ifndef mp_rnd_t
# define mp_rnd_t mpfr_rnd_t
#endif
#ifndef mp_prec_t
# define mp_prec_t mpfr_prec_t
#endif
/*
The represented number is
_sign*(_d[k-1]/B+_d[k-2]/B^2+...+_d[0]/B^k)*2^_exp
where k=ceil(_mp_prec/GMP_NUMB_BITS) and B=2^GMP_NUMB_BITS.
For the msb (most significant bit) normalized representation, we must have
_d[k-1]>=B/2, unless the number is singular.
We must also have the last k*GMP_NUMB_BITS-_prec bits set to zero.
*/
typedef __mpfr_struct mpfr_t[1];
typedef __mpfr_struct *mpfr_ptr;
typedef const __mpfr_struct *mpfr_srcptr;
/* For those who need a direct and fast access to the sign field.
However it is not in the API, thus use it at your own risk: it might
not be supported, or change name, in further versions!
Unfortunately, it must be defined here (instead of MPFR's internal
header file mpfr-impl.h) because it is used by some macros below.
*/
#define MPFR_SIGN(x) ((x)->_mpfr_sign)
/* Stack interface */
typedef enum {
MPFR_NAN_KIND = 0,
MPFR_INF_KIND = 1,
MPFR_ZERO_KIND = 2,
MPFR_REGULAR_KIND = 3
} mpfr_kind_t;
/* Free cache policy */
typedef enum {
MPFR_FREE_LOCAL_CACHE = 1, /* 1 << 0 */
MPFR_FREE_GLOBAL_CACHE = 2 /* 1 << 1 */
} mpfr_free_cache_t;
/* GMP defines:
+ size_t: Standard size_t
+ __GMP_NOTHROW For C++: can't throw .
+ __GMP_EXTERN_INLINE Attribute for inline function.
+ __GMP_DECLSPEC_EXPORT compiling to go into a DLL
+ __GMP_DECLSPEC_IMPORT compiling to go into a application
*/
/* Extra MPFR defines */
#define __MPFR_SENTINEL_ATTR
#if defined (__GNUC__)
# if __GNUC__ >= 4
# undef __MPFR_SENTINEL_ATTR
# define __MPFR_SENTINEL_ATTR __attribute__ ((__sentinel__))
# endif
#endif
/* If the user hasn't requested his/her preference
and if the intention of support by the compiler is C99
and if the compiler is known to support the C99 feature
then we can auto-detect the C99 support as OK.
__GNUC__ is used to detect GNU-C, ICC & CLANG compilers.
Currently we need only variadic macros, and they are present
since GCC >= 3. We don't test library version since we don't
use any feature present in the library too (except intmax_t,
but they use another detection).*/
#ifndef MPFR_USE_C99_FEATURE
# if defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901L)
# if defined (__GNUC__)
# if __GNUC__ >= 3
# define MPFR_USE_C99_FEATURE 1
# endif
# endif
# endif
# ifndef MPFR_USE_C99_FEATURE
# define MPFR_USE_C99_FEATURE 0
# endif
#endif
/* Support for WINDOWS Dll:
Check if we are inside a MPFR build, and if so export the functions.
Otherwise does the same thing as GMP */
#if defined(__MPFR_WITHIN_MPFR) && __GMP_LIBGMP_DLL
# define __MPFR_DECLSPEC __GMP_DECLSPEC_EXPORT
#else
# ifndef __GMP_DECLSPEC
# define __GMP_DECLSPEC
# endif
# define __MPFR_DECLSPEC __GMP_DECLSPEC
#endif
/* Use MPFR_DEPRECATED to mark MPFR functions, types or variables as
deprecated. Code inspired by Apache Subversion's svn_types.h file.
For compatibility with MSVC, MPFR_DEPRECATED must be put before
__MPFR_DECLSPEC (not at the end of the function declaration as
documented in the GCC manual); GCC does not seem to care.
Moreover, in order to avoid a warning when testing such functions,
do something like:
+------------------------------------------
|#ifndef _MPFR_NO_DEPRECATED_funcname
|MPFR_DEPRECATED
|#endif
|__MPFR_DECLSPEC int mpfr_funcname (...);
+------------------------------------------
and in the corresponding test program:
+------------------------------------------
|#define _MPFR_NO_DEPRECATED_funcname
|#include "mpfr-test.h"
+------------------------------------------
*/
#if defined(__GNUC__) && \
(__GNUC__ >= 4 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1))
# define MPFR_DEPRECATED __attribute__ ((__deprecated__))
#elif defined(_MSC_VER) && _MSC_VER >= 1300
# define MPFR_DEPRECATED __declspec(deprecated)
#else
# define MPFR_DEPRECATED
#endif
/* TODO: Also define MPFR_EXPERIMENTAL for experimental functions?
See SVN_EXPERIMENTAL in Subversion 1.9+ as an example:
__attribute__((__warning__("..."))) can be used with GCC 4.3.1+ but
not __llvm__, and __declspec(deprecated("...")) can be used with
MSC as above. */
#if defined(__GNUC__) && \
(__GNUC__ >= 5 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 9))
# define MPFR_RETURNS_NONNULL __attribute__ ((__returns_nonnull__))
#else
# define MPFR_RETURNS_NONNULL
#endif
/* Note: In order to be declared, some functions need a specific
system header to be included *before* "mpfr.h". If the user
forgets to include the header, the MPFR function prototype in
the user object file is not correct. To avoid wrong results,
we raise a linker error in that case by changing their internal
name in the library (prefixed by __gmpfr instead of mpfr). See
the lines of the form "#define mpfr_xxx __gmpfr_xxx" below. */
#if defined (__cplusplus)
extern "C" {
#endif
__MPFR_DECLSPEC MPFR_RETURNS_NONNULL const char * mpfr_get_version (void);
__MPFR_DECLSPEC MPFR_RETURNS_NONNULL const char * mpfr_get_patches (void);
__MPFR_DECLSPEC int mpfr_buildopt_tls_p (void);
__MPFR_DECLSPEC int mpfr_buildopt_float128_p (void);
__MPFR_DECLSPEC int mpfr_buildopt_decimal_p (void);
__MPFR_DECLSPEC int mpfr_buildopt_gmpinternals_p (void);
__MPFR_DECLSPEC int mpfr_buildopt_sharedcache_p (void);
__MPFR_DECLSPEC MPFR_RETURNS_NONNULL const char *
mpfr_buildopt_tune_case (void);
__MPFR_DECLSPEC mpfr_exp_t mpfr_get_emin (void);
__MPFR_DECLSPEC int mpfr_set_emin (mpfr_exp_t);
__MPFR_DECLSPEC mpfr_exp_t mpfr_get_emin_min (void);
__MPFR_DECLSPEC mpfr_exp_t mpfr_get_emin_max (void);
__MPFR_DECLSPEC mpfr_exp_t mpfr_get_emax (void);
__MPFR_DECLSPEC int mpfr_set_emax (mpfr_exp_t);
__MPFR_DECLSPEC mpfr_exp_t mpfr_get_emax_min (void);
__MPFR_DECLSPEC mpfr_exp_t mpfr_get_emax_max (void);
__MPFR_DECLSPEC void mpfr_set_default_rounding_mode (mpfr_rnd_t);
__MPFR_DECLSPEC mpfr_rnd_t mpfr_get_default_rounding_mode (void);
__MPFR_DECLSPEC const char * mpfr_print_rnd_mode (mpfr_rnd_t);
__MPFR_DECLSPEC void mpfr_clear_flags (void);
__MPFR_DECLSPEC void mpfr_clear_underflow (void);
__MPFR_DECLSPEC void mpfr_clear_overflow (void);
__MPFR_DECLSPEC void mpfr_clear_divby0 (void);
__MPFR_DECLSPEC void mpfr_clear_nanflag (void);
__MPFR_DECLSPEC void mpfr_clear_inexflag (void);
__MPFR_DECLSPEC void mpfr_clear_erangeflag (void);
__MPFR_DECLSPEC void mpfr_set_underflow (void);
__MPFR_DECLSPEC void mpfr_set_overflow (void);
__MPFR_DECLSPEC void mpfr_set_divby0 (void);
__MPFR_DECLSPEC void mpfr_set_nanflag (void);
__MPFR_DECLSPEC void mpfr_set_inexflag (void);
__MPFR_DECLSPEC void mpfr_set_erangeflag (void);
__MPFR_DECLSPEC int mpfr_underflow_p (void);
__MPFR_DECLSPEC int mpfr_overflow_p (void);
__MPFR_DECLSPEC int mpfr_divby0_p (void);
__MPFR_DECLSPEC int mpfr_nanflag_p (void);
__MPFR_DECLSPEC int mpfr_inexflag_p (void);
__MPFR_DECLSPEC int mpfr_erangeflag_p (void);
__MPFR_DECLSPEC void mpfr_flags_clear (mpfr_flags_t);
__MPFR_DECLSPEC void mpfr_flags_set (mpfr_flags_t);
__MPFR_DECLSPEC mpfr_flags_t mpfr_flags_test (mpfr_flags_t);
__MPFR_DECLSPEC mpfr_flags_t mpfr_flags_save (void);
__MPFR_DECLSPEC void mpfr_flags_restore (mpfr_flags_t,
mpfr_flags_t);
__MPFR_DECLSPEC int mpfr_check_range (mpfr_ptr, int, mpfr_rnd_t);
__MPFR_DECLSPEC void mpfr_init2 (mpfr_ptr, mpfr_prec_t);
__MPFR_DECLSPEC void mpfr_init (mpfr_ptr);
__MPFR_DECLSPEC void mpfr_clear (mpfr_ptr);
__MPFR_DECLSPEC void
mpfr_inits2 (mpfr_prec_t, mpfr_ptr, ...) __MPFR_SENTINEL_ATTR;
__MPFR_DECLSPEC void
mpfr_inits (mpfr_ptr, ...) __MPFR_SENTINEL_ATTR;
__MPFR_DECLSPEC void
mpfr_clears (mpfr_ptr, ...) __MPFR_SENTINEL_ATTR;
__MPFR_DECLSPEC int mpfr_prec_round (mpfr_ptr, mpfr_prec_t, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_can_round (mpfr_srcptr, mpfr_exp_t, mpfr_rnd_t,
mpfr_rnd_t, mpfr_prec_t);
__MPFR_DECLSPEC mpfr_prec_t mpfr_min_prec (mpfr_srcptr);
__MPFR_DECLSPEC mpfr_exp_t mpfr_get_exp (mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_set_exp (mpfr_ptr, mpfr_exp_t);
__MPFR_DECLSPEC mpfr_prec_t mpfr_get_prec (mpfr_srcptr);
__MPFR_DECLSPEC void mpfr_set_prec (mpfr_ptr, mpfr_prec_t);
__MPFR_DECLSPEC void mpfr_set_prec_raw (mpfr_ptr, mpfr_prec_t);
__MPFR_DECLSPEC void mpfr_set_default_prec (mpfr_prec_t);
__MPFR_DECLSPEC mpfr_prec_t mpfr_get_default_prec (void);
__MPFR_DECLSPEC int mpfr_set_d (mpfr_ptr, double, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_set_flt (mpfr_ptr, float, mpfr_rnd_t);
#ifdef MPFR_WANT_DECIMAL_FLOATS
/* _Decimal64 is not defined in C++,
cf https://gcc.gnu.org/bugzilla/show_bug.cgi?id=51364 */
__MPFR_DECLSPEC int mpfr_set_decimal64 (mpfr_ptr, _Decimal64, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_set_decimal128 (mpfr_ptr, _Decimal128, mpfr_rnd_t);
#endif
__MPFR_DECLSPEC int mpfr_set_ld (mpfr_ptr, long double, mpfr_rnd_t);
#ifdef MPFR_WANT_FLOAT128
__MPFR_DECLSPEC int mpfr_set_float128 (mpfr_ptr, _Float128, mpfr_rnd_t);
__MPFR_DECLSPEC _Float128 mpfr_get_float128 (mpfr_srcptr, mpfr_rnd_t);
#endif
__MPFR_DECLSPEC int mpfr_set_z (mpfr_ptr, mpz_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_set_z_2exp (mpfr_ptr, mpz_srcptr, mpfr_exp_t,
mpfr_rnd_t);
__MPFR_DECLSPEC void mpfr_set_nan (mpfr_ptr);
__MPFR_DECLSPEC void mpfr_set_inf (mpfr_ptr, int);
__MPFR_DECLSPEC void mpfr_set_zero (mpfr_ptr, int);
#ifndef MPFR_USE_MINI_GMP
/* mini-gmp does not provide mpf_t, we disable the following functions */
__MPFR_DECLSPEC int mpfr_set_f (mpfr_ptr, mpf_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_cmp_f (mpfr_srcptr, mpf_srcptr);
__MPFR_DECLSPEC int mpfr_get_f (mpf_ptr, mpfr_srcptr, mpfr_rnd_t);
#endif
__MPFR_DECLSPEC int mpfr_set_si (mpfr_ptr, long, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_set_ui (mpfr_ptr, unsigned long, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_set_si_2exp (mpfr_ptr, long, mpfr_exp_t, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_set_ui_2exp (mpfr_ptr, unsigned long, mpfr_exp_t,
mpfr_rnd_t);
#ifndef MPFR_USE_MINI_GMP
/* mini-gmp does not provide mpq_t, we disable the following functions */
__MPFR_DECLSPEC int mpfr_set_q (mpfr_ptr, mpq_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_mul_q (mpfr_ptr, mpfr_srcptr, mpq_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_div_q (mpfr_ptr, mpfr_srcptr, mpq_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_add_q (mpfr_ptr, mpfr_srcptr, mpq_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_sub_q (mpfr_ptr, mpfr_srcptr, mpq_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_cmp_q (mpfr_srcptr, mpq_srcptr);
__MPFR_DECLSPEC void mpfr_get_q (mpq_ptr q, mpfr_srcptr f);
#endif
__MPFR_DECLSPEC int mpfr_set_str (mpfr_ptr, const char *, int, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_init_set_str (mpfr_ptr, const char *, int,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_set4 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t, int);
__MPFR_DECLSPEC int mpfr_abs (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_set (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_neg (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_signbit (mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_setsign (mpfr_ptr, mpfr_srcptr, int, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_copysign (mpfr_ptr, mpfr_srcptr, mpfr_srcptr,
mpfr_rnd_t);
__MPFR_DECLSPEC mpfr_exp_t mpfr_get_z_2exp (mpz_ptr, mpfr_srcptr);
__MPFR_DECLSPEC float mpfr_get_flt (mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC double mpfr_get_d (mpfr_srcptr, mpfr_rnd_t);
#ifdef MPFR_WANT_DECIMAL_FLOATS
__MPFR_DECLSPEC _Decimal64 mpfr_get_decimal64 (mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC _Decimal128 mpfr_get_decimal128 (mpfr_srcptr, mpfr_rnd_t);
#endif
__MPFR_DECLSPEC long double mpfr_get_ld (mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC double mpfr_get_d1 (mpfr_srcptr);
__MPFR_DECLSPEC double mpfr_get_d_2exp (long*, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC long double mpfr_get_ld_2exp (long*, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_frexp (mpfr_exp_t*, mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC long mpfr_get_si (mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC unsigned long mpfr_get_ui (mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC size_t mpfr_get_str_ndigits (int, mpfr_prec_t);
__MPFR_DECLSPEC char * mpfr_get_str (char*, mpfr_exp_t*, int, size_t,
mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_get_z (mpz_ptr z, mpfr_srcptr f, mpfr_rnd_t);
__MPFR_DECLSPEC void mpfr_free_str (char *);
__MPFR_DECLSPEC int mpfr_urandom (mpfr_ptr, gmp_randstate_t, mpfr_rnd_t);
#ifndef _MPFR_NO_DEPRECATED_GRANDOM /* for the test of this function */
MPFR_DEPRECATED
#endif
__MPFR_DECLSPEC int mpfr_grandom (mpfr_ptr, mpfr_ptr, gmp_randstate_t,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_nrandom (mpfr_ptr, gmp_randstate_t, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_erandom (mpfr_ptr, gmp_randstate_t, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_urandomb (mpfr_ptr, gmp_randstate_t);
__MPFR_DECLSPEC void mpfr_nextabove (mpfr_ptr);
__MPFR_DECLSPEC void mpfr_nextbelow (mpfr_ptr);
__MPFR_DECLSPEC void mpfr_nexttoward (mpfr_ptr, mpfr_srcptr);
#ifndef MPFR_USE_MINI_GMP
__MPFR_DECLSPEC int mpfr_printf (const char*, ...);
__MPFR_DECLSPEC int mpfr_asprintf (char**, const char*, ...);
__MPFR_DECLSPEC int mpfr_sprintf (char*, const char*, ...);
__MPFR_DECLSPEC int mpfr_snprintf (char*, size_t, const char*, ...);
#endif
__MPFR_DECLSPEC int mpfr_pow (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_pow_si (mpfr_ptr, mpfr_srcptr, long, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_pow_ui (mpfr_ptr, mpfr_srcptr, unsigned long,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_ui_pow_ui (mpfr_ptr, unsigned long, unsigned long,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_ui_pow (mpfr_ptr, unsigned long, mpfr_srcptr,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_pow_z (mpfr_ptr, mpfr_srcptr, mpz_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_sqrt (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_sqrt_ui (mpfr_ptr, unsigned long, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_rec_sqrt (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_add (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_sub (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_mul (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_div (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_add_ui (mpfr_ptr, mpfr_srcptr, unsigned long,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_sub_ui (mpfr_ptr, mpfr_srcptr, unsigned long,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_ui_sub (mpfr_ptr, unsigned long, mpfr_srcptr,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_mul_ui (mpfr_ptr, mpfr_srcptr, unsigned long,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_div_ui (mpfr_ptr, mpfr_srcptr, unsigned long,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_ui_div (mpfr_ptr, unsigned long, mpfr_srcptr,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_add_si (mpfr_ptr, mpfr_srcptr, long, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_sub_si (mpfr_ptr, mpfr_srcptr, long, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_si_sub (mpfr_ptr, long, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_mul_si (mpfr_ptr, mpfr_srcptr, long, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_div_si (mpfr_ptr, mpfr_srcptr, long, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_si_div (mpfr_ptr, long, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_add_d (mpfr_ptr, mpfr_srcptr, double, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_sub_d (mpfr_ptr, mpfr_srcptr, double, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_d_sub (mpfr_ptr, double, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_mul_d (mpfr_ptr, mpfr_srcptr, double, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_div_d (mpfr_ptr, mpfr_srcptr, double, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_d_div (mpfr_ptr, double, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_sqr (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_const_pi (mpfr_ptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_const_log2 (mpfr_ptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_const_euler (mpfr_ptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_const_catalan (mpfr_ptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_agm (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_log (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_log2 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_log10 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_log1p (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_log_ui (mpfr_ptr, unsigned long, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_exp (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_exp2 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_exp10 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_expm1 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_eint (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_li2 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_cmp (mpfr_srcptr, mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_cmp3 (mpfr_srcptr, mpfr_srcptr, int);
__MPFR_DECLSPEC int mpfr_cmp_d (mpfr_srcptr, double);
__MPFR_DECLSPEC int mpfr_cmp_ld (mpfr_srcptr, long double);
__MPFR_DECLSPEC int mpfr_cmp_ui (mpfr_srcptr, unsigned long);
__MPFR_DECLSPEC int mpfr_cmp_si (mpfr_srcptr, long);
__MPFR_DECLSPEC int mpfr_cmp_ui_2exp (mpfr_srcptr, unsigned long, mpfr_exp_t);
__MPFR_DECLSPEC int mpfr_cmp_si_2exp (mpfr_srcptr, long, mpfr_exp_t);
__MPFR_DECLSPEC int mpfr_cmpabs (mpfr_srcptr, mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_cmpabs_ui (mpfr_srcptr, unsigned long);
__MPFR_DECLSPEC void mpfr_reldiff (mpfr_ptr, mpfr_srcptr, mpfr_srcptr,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_eq (mpfr_srcptr, mpfr_srcptr, unsigned long);
__MPFR_DECLSPEC int mpfr_sgn (mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_mul_2exp (mpfr_ptr, mpfr_srcptr, unsigned long,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_div_2exp (mpfr_ptr, mpfr_srcptr, unsigned long,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_mul_2ui (mpfr_ptr, mpfr_srcptr, unsigned long,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_div_2ui (mpfr_ptr, mpfr_srcptr, unsigned long,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_mul_2si (mpfr_ptr, mpfr_srcptr, long, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_div_2si (mpfr_ptr, mpfr_srcptr, long, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_rint (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_roundeven (mpfr_ptr, mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_round (mpfr_ptr, mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_trunc (mpfr_ptr, mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_ceil (mpfr_ptr, mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_floor (mpfr_ptr, mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_rint_roundeven (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_rint_round (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_rint_trunc (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_rint_ceil (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_rint_floor (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_frac (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_modf (mpfr_ptr, mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_remquo (mpfr_ptr, long*, mpfr_srcptr, mpfr_srcptr,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_remainder (mpfr_ptr, mpfr_srcptr, mpfr_srcptr,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_fmod (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_fmodquo (mpfr_ptr, long*, mpfr_srcptr, mpfr_srcptr,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_fits_ulong_p (mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_fits_slong_p (mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_fits_uint_p (mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_fits_sint_p (mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_fits_ushort_p (mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_fits_sshort_p (mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_fits_uintmax_p (mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_fits_intmax_p (mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC void mpfr_extract (mpz_ptr, mpfr_srcptr, unsigned int);
__MPFR_DECLSPEC void mpfr_swap (mpfr_ptr, mpfr_ptr);
__MPFR_DECLSPEC void mpfr_dump (mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_nan_p (mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_inf_p (mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_number_p (mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_integer_p (mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_zero_p (mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_regular_p (mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_greater_p (mpfr_srcptr, mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_greaterequal_p (mpfr_srcptr, mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_less_p (mpfr_srcptr, mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_lessequal_p (mpfr_srcptr, mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_lessgreater_p (mpfr_srcptr, mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_equal_p (mpfr_srcptr, mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_unordered_p (mpfr_srcptr, mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_atanh (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_acosh (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_asinh (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_cosh (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_sinh (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_tanh (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_sinh_cosh (mpfr_ptr, mpfr_ptr, mpfr_srcptr,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_sech (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_csch (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_coth (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_acos (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_asin (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_atan (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_sin (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_sin_cos (mpfr_ptr, mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_cos (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_tan (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_atan2 (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_sec (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_csc (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_cot (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_hypot (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_erf (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_erfc (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_cbrt (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
#ifndef _MPFR_NO_DEPRECATED_ROOT /* for the test of this function */
MPFR_DEPRECATED
#endif
__MPFR_DECLSPEC int mpfr_root (mpfr_ptr, mpfr_srcptr, unsigned long,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_rootn_ui (mpfr_ptr, mpfr_srcptr, unsigned long,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_gamma (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_gamma_inc (mpfr_ptr, mpfr_srcptr, mpfr_srcptr,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_beta (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_lngamma (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_lgamma (mpfr_ptr, int *, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_digamma (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_zeta (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_zeta_ui (mpfr_ptr, unsigned long, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_fac_ui (mpfr_ptr, unsigned long, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_j0 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_j1 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_jn (mpfr_ptr, long, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_y0 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_y1 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_yn (mpfr_ptr, long, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_ai (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_min (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_max (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_dim (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_mul_z (mpfr_ptr, mpfr_srcptr, mpz_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_div_z (mpfr_ptr, mpfr_srcptr, mpz_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_add_z (mpfr_ptr, mpfr_srcptr, mpz_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_sub_z (mpfr_ptr, mpfr_srcptr, mpz_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_z_sub (mpfr_ptr, mpz_srcptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_cmp_z (mpfr_srcptr, mpz_srcptr);
__MPFR_DECLSPEC int mpfr_fma (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_srcptr,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_fms (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_srcptr,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_fmma (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_srcptr,
mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_fmms (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_srcptr,
mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_sum (mpfr_ptr, const mpfr_ptr *, unsigned long,
mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_dot (mpfr_ptr, const mpfr_ptr *, const mpfr_ptr *,
unsigned long, mpfr_rnd_t);
__MPFR_DECLSPEC void mpfr_free_cache (void);
__MPFR_DECLSPEC void mpfr_free_cache2 (mpfr_free_cache_t);
__MPFR_DECLSPEC void mpfr_free_pool (void);
__MPFR_DECLSPEC int mpfr_mp_memory_cleanup (void);
__MPFR_DECLSPEC int mpfr_subnormalize (mpfr_ptr, int, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_strtofr (mpfr_ptr, const char *, char **, int,
mpfr_rnd_t);
__MPFR_DECLSPEC void mpfr_round_nearest_away_begin (mpfr_ptr);
__MPFR_DECLSPEC int mpfr_round_nearest_away_end (mpfr_ptr, int);
__MPFR_DECLSPEC size_t mpfr_custom_get_size (mpfr_prec_t);
__MPFR_DECLSPEC void mpfr_custom_init (void *, mpfr_prec_t);
__MPFR_DECLSPEC MPFR_RETURNS_NONNULL void *
mpfr_custom_get_significand (mpfr_srcptr);
__MPFR_DECLSPEC mpfr_exp_t mpfr_custom_get_exp (mpfr_srcptr);
__MPFR_DECLSPEC void mpfr_custom_move (mpfr_ptr, void *);
__MPFR_DECLSPEC void mpfr_custom_init_set (mpfr_ptr, int, mpfr_exp_t,
mpfr_prec_t, void *);
__MPFR_DECLSPEC int mpfr_custom_get_kind (mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_total_order_p (mpfr_srcptr, mpfr_srcptr);
#if defined (__cplusplus)
}
#endif
/* Define MPFR_USE_EXTENSION to avoid "gcc -pedantic" warnings. */
#ifndef MPFR_EXTENSION
# if defined(MPFR_USE_EXTENSION)
# define MPFR_EXTENSION __extension__
# else
# define MPFR_EXTENSION
# endif
#endif
/* Warning! This macro doesn't work with K&R C (e.g., compare the "gcc -E"
output with and without -traditional) and shouldn't be used internally.
For public use only, but see the MPFR manual. */
#define MPFR_DECL_INIT(_x, _p) \
MPFR_EXTENSION mp_limb_t __gmpfr_local_tab_##_x[((_p)-1)/GMP_NUMB_BITS+1]; \
MPFR_EXTENSION mpfr_t _x = {{(_p),1,__MPFR_EXP_NAN,__gmpfr_local_tab_##_x}}
#if MPFR_USE_C99_FEATURE
/* C99 & C11 version: functions with multiple inputs supported */
#define mpfr_round_nearest_away(func, rop, ...) \
(mpfr_round_nearest_away_begin(rop), \
mpfr_round_nearest_away_end((rop), func((rop), __VA_ARGS__, MPFR_RNDN)))
#else
/* C89 version: function with one input supported */
#define mpfr_round_nearest_away(func, rop, op) \
(mpfr_round_nearest_away_begin(rop), \
mpfr_round_nearest_away_end((rop), func((rop), (op), MPFR_RNDN)))
#endif
/* Fast access macros to replace function interface.
If the USER don't want to use the macro interface, let him make happy
even if it produces faster and smaller code. */
#ifndef MPFR_USE_NO_MACRO
/* In the implementation of these macros, we need to make sure that the
arguments are evaluated one time exactly and that type conversion is
done as it would be with a function. Tests should be added to ensure
that.
Note that the macros for the custom interface are not concerned; the
MPFR manual has been clarified. */
/* Prevent x from being used as an lvalue.
Thanks to Wojtek Lerch and Tim Rentsch for the idea. */
#define MPFR_VALUE_OF(x) (0 ? (x) : (x))
/* The following macro converts the argument to mpfr_srcptr, as in type
conversion for function parameters. But it will detect disallowed
implicit conversions, e.g. when the argument has an integer type. */
#define MPFR_SRCPTR(x) ((mpfr_srcptr) (0 ? (x) : (mpfr_srcptr) (x)))
#define MPFR_GET_SIGN(_x) MPFR_VALUE_OF(MPFR_SIGN(MPFR_SRCPTR(_x)))
#define mpfr_nan_p(_x) (MPFR_SRCPTR(_x)->_mpfr_exp == __MPFR_EXP_NAN)
#define mpfr_inf_p(_x) (MPFR_SRCPTR(_x)->_mpfr_exp == __MPFR_EXP_INF)
#define mpfr_zero_p(_x) (MPFR_SRCPTR(_x)->_mpfr_exp == __MPFR_EXP_ZERO)
#define mpfr_regular_p(_x) (MPFR_SRCPTR(_x)->_mpfr_exp > __MPFR_EXP_INF)
/* mpfr_sgn is documented as a macro, thus the following code is fine.
But it would be safer to regard it as a function in some future
MPFR version. */
#define mpfr_sgn(_x) \
((_x)->_mpfr_exp < __MPFR_EXP_INF ? \
(mpfr_nan_p (_x) ? mpfr_set_erangeflag () : (mpfr_void) 0), 0 : \
MPFR_SIGN (_x))
#define mpfr_get_prec(_x) MPFR_VALUE_OF(MPFR_SRCPTR(_x)->_mpfr_prec)
#define mpfr_get_exp(_x) MPFR_VALUE_OF(MPFR_SRCPTR(_x)->_mpfr_exp)
/* Note: Defining mpfr_get_exp() as a macro has the effect to disable
the check that the argument is a pure FP number (done in the function);
this increases the risk of undetected error and makes debugging more
complex. Is it really worth in practice? (Potential FIXME) */
#define mpfr_round(a,b) mpfr_rint((a), (b), MPFR_RNDNA)
#define mpfr_trunc(a,b) mpfr_rint((a), (b), MPFR_RNDZ)
#define mpfr_ceil(a,b) mpfr_rint((a), (b), MPFR_RNDU)
#define mpfr_floor(a,b) mpfr_rint((a), (b), MPFR_RNDD)
#define mpfr_cmp_ui(b,i) mpfr_cmp_ui_2exp((b),(i),0)
#define mpfr_cmp_si(b,i) mpfr_cmp_si_2exp((b),(i),0)
#if __GNUC__ > 2 || __GNUC_MINOR__ >= 95
#define mpfr_set(a,b,r) \
__extension__ ({ \
mpfr_srcptr _p = (b); \
mpfr_set4(a,_p,r,MPFR_SIGN(_p)); \
})
#endif
#define mpfr_abs(a,b,r) mpfr_set4(a,b,r,1)
#define mpfr_copysign(a,b,c,r) mpfr_set4(a,b,r,MPFR_GET_SIGN(c))
#define mpfr_setsign(a,b,s,r) mpfr_set4(a,b,r,(s) ? -1 : 1)
#define mpfr_signbit(x) (MPFR_GET_SIGN(x) < 0)
#define mpfr_cmp(b, c) mpfr_cmp3(b, c, 1)
#define mpfr_mul_2exp(y,x,n,r) mpfr_mul_2ui((y),(x),(n),(r))
#define mpfr_div_2exp(y,x,n,r) mpfr_div_2ui((y),(x),(n),(r))
/* When using GCC or ICC, optimize certain common comparisons and affectations.
Added casts to improve robustness in case of undefined behavior and
compiler extensions based on UB (in particular -fwrapv). MPFR doesn't
use such extensions, but these macros will be used by 3rd-party code,
where such extensions may be required.
Moreover casts to unsigned long have been added to avoid warnings in
programs that use MPFR and are compiled with -Wconversion; such casts
are OK since if X is a constant expression, then (unsigned long) X is
also a constant expression, so that the optimizations still work. The
warnings are probably related to the following two bugs:
https://gcc.gnu.org/bugzilla/show_bug.cgi?id=4210
https://gcc.gnu.org/bugzilla/show_bug.cgi?id=38470 (possibly a variant)
and the casts could be removed once these bugs are fixed.
Casts shouldn't be used on the generic calls (to the ..._2exp functions),
where implicit conversions are performed. Indeed, having at least one
implicit conversion in the macro allows the compiler to emit diagnostics
when normally expected, for instance in the following call:
mpfr_set_ui (x, "foo", MPFR_RNDN);
If this is not possible (for future macros), one of the tricks described
on http://groups.google.com/group/comp.std.c/msg/e92abd24bf9eaf7b could
be used. */
#if defined (__GNUC__) && !defined(__cplusplus)
#if (__GNUC__ >= 2)
#undef mpfr_cmp_ui
/* We use the fact that mpfr_sgn on NaN sets the erange flag and returns 0.
But warning! mpfr_sgn is specified as a macro in the API, thus the macro
mustn't be used if side effects are possible, like here. */
#define mpfr_cmp_ui(_f,_u) \
(__builtin_constant_p (_u) && (mpfr_ulong) (_u) == 0 ? \
(mpfr_sgn) (_f) : \
mpfr_cmp_ui_2exp ((_f), (_u), 0))
#undef mpfr_cmp_si
#define mpfr_cmp_si(_f,_s) \
(__builtin_constant_p (_s) && (mpfr_long) (_s) >= 0 ? \
mpfr_cmp_ui ((_f), (mpfr_ulong) (mpfr_long) (_s)) : \
mpfr_cmp_si_2exp ((_f), (_s), 0))
#if __GNUC__ > 2 || __GNUC_MINOR__ >= 95
#undef mpfr_set_ui
#define mpfr_set_ui(_f,_u,_r) \
(__builtin_constant_p (_u) && (mpfr_ulong) (_u) == 0 ? \
__extension__ ({ \
mpfr_ptr _p = (_f); \
_p->_mpfr_sign = 1; \
_p->_mpfr_exp = __MPFR_EXP_ZERO; \
(mpfr_void) (_r); 0; }) : \
mpfr_set_ui_2exp ((_f), (_u), 0, (_r)))
#endif
#undef mpfr_set_si
#define mpfr_set_si(_f,_s,_r) \
(__builtin_constant_p (_s) && (mpfr_long) (_s) >= 0 ? \
mpfr_set_ui ((_f), (mpfr_ulong) (mpfr_long) (_s), (_r)) : \
mpfr_set_si_2exp ((_f), (_s), 0, (_r)))
#if __GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 4)
/* If the source is a constant number that is a power of 2,
optimize the call */
#undef mpfr_mul_ui
#define mpfr_mul_ui(_f, _g, _u,_r) \
(__builtin_constant_p (_u) && (mpfr_ulong) (_u) >= 1 && \
((mpfr_ulong) (_u) & ((mpfr_ulong) (_u) - 1)) == 0 ? \
mpfr_mul_2si((_f), (_g), __builtin_ctzl (_u), (_r)) : \
mpfr_mul_ui ((_f), (_g), (_u), (_r)))
#undef mpfr_div_ui
#define mpfr_div_ui(_f, _g, _u,_r) \
(__builtin_constant_p (_u) && (mpfr_ulong) (_u) >= 1 && \
((mpfr_ulong) (_u) & ((mpfr_ulong) (_u) - 1)) == 0 ? \
mpfr_mul_2si((_f), (_g), - __builtin_ctzl (_u), (_r)) : \
mpfr_div_ui ((_f), (_g), (_u), (_r)))
#endif
/* If the source is a constant number that is non-negative,
optimize the call */
#undef mpfr_mul_si
#define mpfr_mul_si(_f, _g, _s,_r) \
(__builtin_constant_p (_s) && (mpfr_long) (_s) >= 0 ? \
mpfr_mul_ui ((_f), (_g), (mpfr_ulong) (mpfr_long) (_s), (_r)) : \
mpfr_mul_si ((_f), (_g), (_s), (_r)))
#undef mpfr_div_si
#define mpfr_div_si(_f, _g, _s,_r) \
(__builtin_constant_p (_s) && (mpfr_long) (_s) >= 0 ? \
mpfr_div_ui ((_f), (_g), (mpfr_ulong) (mpfr_long) (_s), (_r)) : \
mpfr_div_si ((_f), (_g), (_s), (_r)))
#endif
#endif
/* Macro version of mpfr_stack interface for fast access */
#define mpfr_custom_get_size(p) ((mpfr_size_t) \
(((p)+GMP_NUMB_BITS-1)/GMP_NUMB_BITS*sizeof (mp_limb_t)))
#define mpfr_custom_init(m,p) do {} while (0)
#define mpfr_custom_get_significand(x) ((mpfr_void*)((x)->_mpfr_d))
#define mpfr_custom_get_exp(x) ((x)->_mpfr_exp)
#define mpfr_custom_move(x,m) do { ((x)->_mpfr_d = (mp_limb_t*)(m)); } while (0)
#define mpfr_custom_init_set(x,k,e,p,m) do { \
mpfr_ptr _x = (x); \
mpfr_exp_t _e; \
mpfr_kind_t _t; \
mpfr_int _s, _k; \
_k = (k); \
if (_k >= 0) { \
_t = (mpfr_kind_t) _k; \