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      1 /* mpfr.h -- Include file for mpfr.
      2 
      3 Copyright 1999-2023 Free Software Foundation, Inc.
      4 Contributed by the AriC and Caramba projects, INRIA.
      5 
      6 This file is part of the GNU MPFR Library.
      7 
      8 The GNU MPFR Library is free software; you can redistribute it and/or modify
      9 it under the terms of the GNU Lesser General Public License as published by
     10 the Free Software Foundation; either version 3 of the License, or (at your
     11 option) any later version.
     12 
     13 The GNU MPFR Library is distributed in the hope that it will be useful, but
     14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
     15 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
     16 License for more details.
     17 
     18 You should have received a copy of the GNU Lesser General Public License
     19 along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
     20 https://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
     21 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
     22 
     23 #ifndef __MPFR_H
     24 #define __MPFR_H
     25 
     26 /* Define MPFR version number */
     27 #define MPFR_VERSION_MAJOR 4
     28 #define MPFR_VERSION_MINOR 2
     29 #define MPFR_VERSION_PATCHLEVEL 1
     30 #define MPFR_VERSION_STRING "4.2.1"
     31 
     32 /* User macros:
     33    MPFR_USE_FILE:        Define it to make MPFR define functions dealing
     34                          with FILE* (auto-detect).
     35    MPFR_USE_INTMAX_T:    Define it to make MPFR define functions dealing
     36                          with intmax_t (auto-detect).
     37    MPFR_USE_VA_LIST:     Define it to make MPFR define functions dealing
     38                          with va_list (auto-detect).
     39    MPFR_USE_C99_FEATURE: Define it to 1 to make MPFR support C99-feature
     40                          (auto-detect), to 0 to bypass the detection.
     41    MPFR_USE_EXTENSION:   Define it to make MPFR use GCC extension to
     42                          reduce warnings.
     43    MPFR_USE_NO_MACRO:    Define it to make MPFR remove any overriding
     44                          function macro.
     45 */
     46 
     47 /* Macros dealing with MPFR VERSION */
     48 #define MPFR_VERSION_NUM(a,b,c) (((a) << 16L) | ((b) << 8) | (c))
     49 #define MPFR_VERSION \
     50 MPFR_VERSION_NUM(MPFR_VERSION_MAJOR,MPFR_VERSION_MINOR,MPFR_VERSION_PATCHLEVEL)
     51 
     52 #ifndef MPFR_USE_MINI_GMP
     53 #include <gmp.h>
     54 #else
     55 #include <mini-gmp.h>
     56 #endif
     57 
     58 /* Avoid some problems with macro expansion if the user defines macros
     59    with the same name as keywords. By convention, identifiers and macro
     60    names starting with mpfr_ are reserved by MPFR. */
     61 typedef void            mpfr_void;
     62 typedef int             mpfr_int;
     63 typedef unsigned int    mpfr_uint;
     64 typedef long            mpfr_long;
     65 typedef unsigned long   mpfr_ulong;
     66 typedef size_t          mpfr_size_t;
     67 
     68 /* Global (possibly TLS) flags. Might also be used in an mpfr_t in the
     69    future (there would be room as mpfr_sign_t just needs 1 byte).
     70    TODO: The tests currently assume that the flags fits in an unsigned int;
     71    this should be cleaned up, e.g. by defining a function that outputs the
     72    flags as a string or by using the flags_out function (from tests/tests.c
     73    directly). */
     74 typedef unsigned int    mpfr_flags_t;
     75 
     76 /* Flags macros (in the public API) */
     77 #define MPFR_FLAGS_UNDERFLOW 1
     78 #define MPFR_FLAGS_OVERFLOW 2
     79 #define MPFR_FLAGS_NAN 4
     80 #define MPFR_FLAGS_INEXACT 8
     81 #define MPFR_FLAGS_ERANGE 16
     82 #define MPFR_FLAGS_DIVBY0 32
     83 #define MPFR_FLAGS_ALL (MPFR_FLAGS_UNDERFLOW | \
     84                         MPFR_FLAGS_OVERFLOW  | \
     85                         MPFR_FLAGS_NAN       | \
     86                         MPFR_FLAGS_INEXACT   | \
     87                         MPFR_FLAGS_ERANGE    | \
     88                         MPFR_FLAGS_DIVBY0)
     89 
     90 /* Definition of rounding modes (DON'T USE MPFR_RNDNA!).
     91    Warning! Changing the contents of this enum should be seen as an
     92    interface change since the old and the new types are not compatible
     93    (the integer type compatible with the enumerated type can even change,
     94    see ISO C99, 6.7.2.2#4), and in Makefile.am, AGE should be set to 0.
     95 
     96    MPFR_RNDU must appear just before MPFR_RNDD (see
     97    MPFR_IS_RNDUTEST_OR_RNDDNOTTEST in mpfr-impl.h).
     98 
     99    If you change the order of the rounding modes, please update the routines
    100    in texceptions.c which assume 0=RNDN, 1=RNDZ, 2=RNDU, 3=RNDD, 4=RNDA.
    101 */
    102 typedef enum {
    103   MPFR_RNDN=0,  /* round to nearest, with ties to even */
    104   MPFR_RNDZ,    /* round toward zero */
    105   MPFR_RNDU,    /* round toward +Inf */
    106   MPFR_RNDD,    /* round toward -Inf */
    107   MPFR_RNDA,    /* round away from zero */
    108   MPFR_RNDF,    /* faithful rounding */
    109   MPFR_RNDNA=-1 /* round to nearest, with ties away from zero (mpfr_round) */
    110 } mpfr_rnd_t;
    111 
    112 /* kept for compatibility with MPFR 2.4.x and before */
    113 #define GMP_RNDN MPFR_RNDN
    114 #define GMP_RNDZ MPFR_RNDZ
    115 #define GMP_RNDU MPFR_RNDU
    116 #define GMP_RNDD MPFR_RNDD
    117 
    118 /* The _MPFR_PREC_FORMAT and _MPFR_EXP_FORMAT values are automatically
    119    defined below. You MUST NOT force a value (this will break the ABI),
    120    possibly except for a very particular use, in which case you also need
    121    to rebuild the MPFR library with the chosen values; do not install this
    122    rebuilt library in a path that is searched by default, otherwise this
    123    will break applications that are dynamically linked with MPFR.
    124 
    125    Using non-default values is not guaranteed to work.
    126 
    127    Note: With the following default choices for _MPFR_PREC_FORMAT and
    128    _MPFR_EXP_FORMAT, mpfr_exp_t will be the same as [mp_exp_t] (at least
    129    up to GMP 6). */
    130 
    131 /* Define precision: 1 (short), 2 (int) or 3 (long).
    132    DON'T FORCE A VALUE (see above). */
    133 #ifndef _MPFR_PREC_FORMAT
    134 # if __GMP_MP_SIZE_T_INT
    135 #  define _MPFR_PREC_FORMAT 2
    136 # else
    137 #  define _MPFR_PREC_FORMAT 3
    138 # endif
    139 #endif
    140 
    141 /* Define exponent: 1 (short), 2 (int), 3 (long) or 4 (intmax_t).
    142    DON'T FORCE A VALUE (see above). */
    143 #ifndef _MPFR_EXP_FORMAT
    144 # define _MPFR_EXP_FORMAT _MPFR_PREC_FORMAT
    145 #endif
    146 
    147 #if _MPFR_PREC_FORMAT > _MPFR_EXP_FORMAT
    148 # error "mpfr_prec_t must not be larger than mpfr_exp_t"
    149 #endif
    150 
    151 /* Let's make mpfr_prec_t signed in order to avoid problems due to the
    152    usual arithmetic conversions when mixing mpfr_prec_t and mpfr_exp_t
    153    in an expression (for error analysis) if casts are forgotten.
    154    Note: mpfr_prec_t is currently limited to "long". This means that
    155    under MS Windows, the precisions are limited to about 2^31; however,
    156    these are already huge precisions, probably sufficient in practice
    157    on this platform. */
    158 #if   _MPFR_PREC_FORMAT == 1
    159 typedef short mpfr_prec_t;
    160 typedef unsigned short mpfr_uprec_t;
    161 #elif _MPFR_PREC_FORMAT == 2
    162 typedef int   mpfr_prec_t;
    163 typedef unsigned int   mpfr_uprec_t;
    164 #elif _MPFR_PREC_FORMAT == 3
    165 typedef long  mpfr_prec_t;
    166 typedef unsigned long  mpfr_uprec_t;
    167 #else
    168 # error "Invalid MPFR Prec format"
    169 #endif
    170 
    171 /* Definition of precision limits without needing <limits.h> */
    172 /* Note: The casts allows the expression to yield the wanted behavior
    173    for _MPFR_PREC_FORMAT == 1 (due to integer promotion rules). We
    174    also make sure that MPFR_PREC_MIN and MPFR_PREC_MAX have a signed
    175    integer type. The "- 256" allows more security, avoiding some
    176    integer overflows in extreme cases; ideally it should be useless. */
    177 #define MPFR_PREC_MIN 1
    178 #define MPFR_PREC_MAX ((mpfr_prec_t) ((((mpfr_uprec_t) -1) >> 1) - 256))
    179 
    180 /* Definition of sign */
    181 typedef int          mpfr_sign_t;
    182 
    183 /* Definition of the exponent. _MPFR_EXP_FORMAT must be large enough
    184    so that mpfr_exp_t has at least 32 bits. */
    185 #if   _MPFR_EXP_FORMAT == 1
    186 typedef short mpfr_exp_t;
    187 typedef unsigned short mpfr_uexp_t;
    188 #elif _MPFR_EXP_FORMAT == 2
    189 typedef int mpfr_exp_t;
    190 typedef unsigned int mpfr_uexp_t;
    191 #elif _MPFR_EXP_FORMAT == 3
    192 typedef long mpfr_exp_t;
    193 typedef unsigned long mpfr_uexp_t;
    194 #elif _MPFR_EXP_FORMAT == 4
    195 /* Note: in this case, intmax_t and uintmax_t must be defined before
    196    the inclusion of mpfr.h (we do not include <stdint.h> here due to
    197    potential issues with non-ISO implementations, on which there are
    198    alternative ways to define these types).
    199    In all known implementations, intmax_t has exactly 64 bits and is
    200    equivalent to long long when defined, but when long has 64 bits,
    201    it may be defined as long by <stdint.h> for better portability
    202    with old compilers, thus offers more flexibility than long long.
    203    This may change in the future.
    204    This _MPFR_EXP_FORMAT value is currently not supported since the
    205    MPFR code assumes that mpfr_exp_t fits in a long. Some examples
    206    of problematic code can be obtained with:
    207      grep -E 'mpfr_cmp_[su]i *\(.*__gmpfr_em' *.c
    208 */
    209 typedef intmax_t mpfr_exp_t;
    210 typedef uintmax_t mpfr_uexp_t;
    211 #else
    212 # error "Invalid MPFR Exp format"
    213 #endif
    214 
    215 /* Definition of the standard exponent limits */
    216 #define MPFR_EMAX_DEFAULT ((mpfr_exp_t) (((mpfr_ulong) 1 << 30) - 1))
    217 #define MPFR_EMIN_DEFAULT (-(MPFR_EMAX_DEFAULT))
    218 
    219 /* DON'T USE THIS! (For MPFR-public macros only, see below.)
    220    The mpfr_sgn macro uses the fact that __MPFR_EXP_NAN and __MPFR_EXP_ZERO
    221    are the smallest values. For a n-bit type, EXP_MAX is 2^(n-1)-1,
    222    EXP_ZERO is 1-2^(n-1), EXP_NAN is 2-2^(n-1), EXP_INF is 3-2^(n-1).
    223    This may change in the future. MPFR code should not be based on these
    224    representations (but if this is absolutely needed, protect the code
    225    with a static assertion). */
    226 #define __MPFR_EXP_MAX ((mpfr_exp_t) (((mpfr_uexp_t) -1) >> 1))
    227 #define __MPFR_EXP_NAN  (1 - __MPFR_EXP_MAX)
    228 #define __MPFR_EXP_ZERO (0 - __MPFR_EXP_MAX)
    229 #define __MPFR_EXP_INF  (2 - __MPFR_EXP_MAX)
    230 
    231 /* Definition of the main structure */
    232 typedef struct {
    233   mpfr_prec_t  _mpfr_prec;
    234   mpfr_sign_t  _mpfr_sign;
    235   mpfr_exp_t   _mpfr_exp;
    236   mp_limb_t   *_mpfr_d;
    237 } __mpfr_struct;
    238 
    239 /* Compatibility with previous types of MPFR */
    240 #ifndef mp_rnd_t
    241 # define mp_rnd_t  mpfr_rnd_t
    242 #endif
    243 #ifndef mp_prec_t
    244 # define mp_prec_t mpfr_prec_t
    245 #endif
    246 
    247 /*
    248    The represented number is
    249       _sign*(_d[k-1]/B+_d[k-2]/B^2+...+_d[0]/B^k)*2^_exp
    250    where k=ceil(_mp_prec/GMP_NUMB_BITS) and B=2^GMP_NUMB_BITS.
    251 
    252    For the msb (most significant bit) normalized representation, we must have
    253       _d[k-1]>=B/2, unless the number is singular.
    254 
    255    We must also have the last k*GMP_NUMB_BITS-_prec bits set to zero.
    256 */
    257 
    258 typedef __mpfr_struct mpfr_t[1];
    259 typedef __mpfr_struct *mpfr_ptr;
    260 typedef const __mpfr_struct *mpfr_srcptr;
    261 
    262 /* For those who need a direct and fast access to the sign field.
    263    However, it is not in the API, thus use it at your own risk: it
    264    might not be supported, or change name, in further versions!
    265    Unfortunately, it must be defined here (instead of MPFR's internal
    266    header file mpfr-impl.h) because it is used by some macros below.
    267 */
    268 #define MPFR_SIGN(x) ((x)->_mpfr_sign)
    269 
    270 /* Custom interface */
    271 typedef enum {
    272   MPFR_NAN_KIND     = 0,
    273   MPFR_INF_KIND     = 1,
    274   MPFR_ZERO_KIND    = 2,
    275   MPFR_REGULAR_KIND = 3
    276 } mpfr_kind_t;
    277 
    278 /* Free cache policy */
    279 typedef enum {
    280   MPFR_FREE_LOCAL_CACHE  = 1,  /* 1 << 0 */
    281   MPFR_FREE_GLOBAL_CACHE = 2   /* 1 << 1 */
    282 } mpfr_free_cache_t;
    283 
    284 /* GMP defines:
    285     + size_t:                Standard size_t
    286     + __GMP_NOTHROW          For C++: can't throw .
    287     + __GMP_EXTERN_INLINE    Attribute for inline function.
    288     + __GMP_DECLSPEC_EXPORT  compiling to go into a DLL
    289     + __GMP_DECLSPEC_IMPORT  compiling to go into a application
    290 */
    291 /* Extra MPFR defines */
    292 #define __MPFR_SENTINEL_ATTR
    293 #if defined (__GNUC__)
    294 # if __GNUC__ >= 4
    295 #  undef __MPFR_SENTINEL_ATTR
    296 #  define __MPFR_SENTINEL_ATTR __attribute__ ((__sentinel__))
    297 # endif
    298 #endif
    299 
    300 /* If the user hasn't requested his/her preference
    301    and if the intention of support by the compiler is C99
    302    and if the compiler is known to support the C99 feature
    303    then we can auto-detect the C99 support as OK.
    304    __GNUC__ is used to detect GNU-C, ICC & CLANG compilers.
    305    Currently we need only variadic macros, and they are present
    306    since GCC >= 3. We don't test library version since we don't
    307    use any feature present in the library too (except intmax_t,
    308    but they use another detection).*/
    309 #ifndef MPFR_USE_C99_FEATURE
    310 # if defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901L)
    311 #  if defined (__GNUC__)
    312 #   if __GNUC__ >= 3
    313 #    define MPFR_USE_C99_FEATURE 1
    314 #   endif
    315 #  endif
    316 # endif
    317 # ifndef MPFR_USE_C99_FEATURE
    318 #  define MPFR_USE_C99_FEATURE 0
    319 # endif
    320 #endif
    321 
    322 /* Support for WINDOWS Dll:
    323    Check if we are inside a MPFR build, and if so export the functions.
    324    Otherwise does the same thing as GMP */
    325 #if defined(__MPFR_WITHIN_MPFR) && __GMP_LIBGMP_DLL
    326 # define __MPFR_DECLSPEC __GMP_DECLSPEC_EXPORT
    327 #else
    328 # ifndef __GMP_DECLSPEC
    329 #  define __GMP_DECLSPEC
    330 # endif
    331 # define __MPFR_DECLSPEC __GMP_DECLSPEC
    332 #endif
    333 
    334 /* Use MPFR_DEPRECATED to mark MPFR functions, types or variables as
    335    deprecated. Code inspired by Apache Subversion's svn_types.h file.
    336    For compatibility with MSVC, MPFR_DEPRECATED must be put before
    337    __MPFR_DECLSPEC (not at the end of the function declaration as
    338    documented in the GCC manual); GCC does not seem to care.
    339    Moreover, in order to avoid a warning when testing such functions,
    340    do something like:
    341      +------------------------------------------
    342      |#ifndef _MPFR_NO_DEPRECATED_funcname
    343      |MPFR_DEPRECATED
    344      |#endif
    345      |__MPFR_DECLSPEC int mpfr_funcname (...);
    346      +------------------------------------------
    347    and in the corresponding test program:
    348      +------------------------------------------
    349      |#define _MPFR_NO_DEPRECATED_funcname
    350      |#include "mpfr-test.h"
    351      +------------------------------------------
    352 */
    353 #if defined(__GNUC__) && \
    354   (__GNUC__ >= 4 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1))
    355 # define MPFR_DEPRECATED __attribute__ ((__deprecated__))
    356 #elif defined(_MSC_VER) && _MSC_VER >= 1300
    357 # define MPFR_DEPRECATED __declspec(deprecated)
    358 #else
    359 # define MPFR_DEPRECATED
    360 #endif
    361 /* TODO: Also define MPFR_EXPERIMENTAL for experimental functions?
    362    See SVN_EXPERIMENTAL in Subversion 1.9+ as an example:
    363    __attribute__((__warning__("..."))) can be used with GCC 4.3.1+ but
    364    not __llvm__, and __declspec(deprecated("...")) can be used with
    365    MSC as above. */
    366 
    367 /* ICC up to 19.1.3.304 at least declares itself as interoperable with
    368    GCC 4.9, but does not support the returns_nonnull attribute, thus
    369    outputs warning #1292. This minor issue has been reported in 2019-04:
    370    https://community.intel.com/t5/Intel-C-Compiler/Missing-support-for-returns-nonnull-attribute/td-p/1183013 */
    371 #if defined(__GNUC__) && \
    372   (__GNUC__ >= 5 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 9))
    373 # define MPFR_RETURNS_NONNULL __attribute__ ((__returns_nonnull__))
    374 #else
    375 # define MPFR_RETURNS_NONNULL
    376 #endif
    377 
    378 /* Note: In order to be declared, some functions need a specific
    379    system header to be included *before* "mpfr.h". If the user
    380    forgets to include the header, the MPFR function prototype in
    381    the user object file is not correct. To avoid wrong results,
    382    we raise a linker error in that case by changing their internal
    383    name in the library (prefixed by __gmpfr instead of mpfr). See
    384    the lines of the form "#define mpfr_xxx __gmpfr_xxx" below. */
    385 
    386 #if defined (__cplusplus)
    387 extern "C" {
    388 #endif
    389 
    390 __MPFR_DECLSPEC MPFR_RETURNS_NONNULL const char * mpfr_get_version (void);
    391 __MPFR_DECLSPEC MPFR_RETURNS_NONNULL const char * mpfr_get_patches (void);
    392 
    393 __MPFR_DECLSPEC int mpfr_buildopt_tls_p          (void);
    394 __MPFR_DECLSPEC int mpfr_buildopt_float128_p     (void);
    395 __MPFR_DECLSPEC int mpfr_buildopt_decimal_p      (void);
    396 __MPFR_DECLSPEC int mpfr_buildopt_gmpinternals_p (void);
    397 __MPFR_DECLSPEC int mpfr_buildopt_sharedcache_p  (void);
    398 __MPFR_DECLSPEC MPFR_RETURNS_NONNULL const char *
    399   mpfr_buildopt_tune_case (void);
    400 
    401 __MPFR_DECLSPEC mpfr_exp_t mpfr_get_emin     (void);
    402 __MPFR_DECLSPEC int        mpfr_set_emin     (mpfr_exp_t);
    403 __MPFR_DECLSPEC mpfr_exp_t mpfr_get_emin_min (void);
    404 __MPFR_DECLSPEC mpfr_exp_t mpfr_get_emin_max (void);
    405 __MPFR_DECLSPEC mpfr_exp_t mpfr_get_emax     (void);
    406 __MPFR_DECLSPEC int        mpfr_set_emax     (mpfr_exp_t);
    407 __MPFR_DECLSPEC mpfr_exp_t mpfr_get_emax_min (void);
    408 __MPFR_DECLSPEC mpfr_exp_t mpfr_get_emax_max (void);
    409 
    410 __MPFR_DECLSPEC void mpfr_set_default_rounding_mode (mpfr_rnd_t);
    411 __MPFR_DECLSPEC mpfr_rnd_t mpfr_get_default_rounding_mode (void);
    412 __MPFR_DECLSPEC const char * mpfr_print_rnd_mode (mpfr_rnd_t);
    413 
    414 __MPFR_DECLSPEC void mpfr_clear_flags (void);
    415 __MPFR_DECLSPEC void mpfr_clear_underflow (void);
    416 __MPFR_DECLSPEC void mpfr_clear_overflow (void);
    417 __MPFR_DECLSPEC void mpfr_clear_divby0 (void);
    418 __MPFR_DECLSPEC void mpfr_clear_nanflag (void);
    419 __MPFR_DECLSPEC void mpfr_clear_inexflag (void);
    420 __MPFR_DECLSPEC void mpfr_clear_erangeflag (void);
    421 
    422 __MPFR_DECLSPEC void mpfr_set_underflow (void);
    423 __MPFR_DECLSPEC void mpfr_set_overflow (void);
    424 __MPFR_DECLSPEC void mpfr_set_divby0 (void);
    425 __MPFR_DECLSPEC void mpfr_set_nanflag (void);
    426 __MPFR_DECLSPEC void mpfr_set_inexflag (void);
    427 __MPFR_DECLSPEC void mpfr_set_erangeflag (void);
    428 
    429 __MPFR_DECLSPEC int mpfr_underflow_p (void);
    430 __MPFR_DECLSPEC int mpfr_overflow_p (void);
    431 __MPFR_DECLSPEC int mpfr_divby0_p (void);
    432 __MPFR_DECLSPEC int mpfr_nanflag_p (void);
    433 __MPFR_DECLSPEC int mpfr_inexflag_p (void);
    434 __MPFR_DECLSPEC int mpfr_erangeflag_p (void);
    435 
    436 __MPFR_DECLSPEC void mpfr_flags_clear (mpfr_flags_t);
    437 __MPFR_DECLSPEC void mpfr_flags_set (mpfr_flags_t);
    438 __MPFR_DECLSPEC mpfr_flags_t mpfr_flags_test (mpfr_flags_t);
    439 __MPFR_DECLSPEC mpfr_flags_t mpfr_flags_save (void);
    440 __MPFR_DECLSPEC void mpfr_flags_restore (mpfr_flags_t,
    441                                          mpfr_flags_t);
    442 
    443 __MPFR_DECLSPEC int mpfr_check_range (mpfr_ptr, int, mpfr_rnd_t);
    444 
    445 __MPFR_DECLSPEC void mpfr_init2 (mpfr_ptr, mpfr_prec_t);
    446 __MPFR_DECLSPEC void mpfr_init (mpfr_ptr);
    447 __MPFR_DECLSPEC void mpfr_clear (mpfr_ptr);
    448 
    449 __MPFR_DECLSPEC void
    450   mpfr_inits2 (mpfr_prec_t, mpfr_ptr, ...) __MPFR_SENTINEL_ATTR;
    451 __MPFR_DECLSPEC void
    452   mpfr_inits (mpfr_ptr, ...) __MPFR_SENTINEL_ATTR;
    453 __MPFR_DECLSPEC void
    454   mpfr_clears (mpfr_ptr, ...) __MPFR_SENTINEL_ATTR;
    455 
    456 __MPFR_DECLSPEC int mpfr_prec_round (mpfr_ptr, mpfr_prec_t, mpfr_rnd_t);
    457 __MPFR_DECLSPEC int mpfr_can_round (mpfr_srcptr, mpfr_exp_t, mpfr_rnd_t,
    458                                     mpfr_rnd_t, mpfr_prec_t);
    459 __MPFR_DECLSPEC mpfr_prec_t mpfr_min_prec (mpfr_srcptr);
    460 
    461 __MPFR_DECLSPEC mpfr_exp_t mpfr_get_exp (mpfr_srcptr);
    462 __MPFR_DECLSPEC int mpfr_set_exp (mpfr_ptr, mpfr_exp_t);
    463 __MPFR_DECLSPEC mpfr_prec_t mpfr_get_prec (mpfr_srcptr);
    464 __MPFR_DECLSPEC void mpfr_set_prec (mpfr_ptr, mpfr_prec_t);
    465 __MPFR_DECLSPEC void mpfr_set_prec_raw (mpfr_ptr, mpfr_prec_t);
    466 __MPFR_DECLSPEC void mpfr_set_default_prec (mpfr_prec_t);
    467 __MPFR_DECLSPEC mpfr_prec_t mpfr_get_default_prec (void);
    468 
    469 __MPFR_DECLSPEC int mpfr_set_d (mpfr_ptr, double, mpfr_rnd_t);
    470 __MPFR_DECLSPEC int mpfr_set_flt (mpfr_ptr, float, mpfr_rnd_t);
    471 #ifdef MPFR_WANT_DECIMAL_FLOATS
    472 /* _Decimal64 is not defined in C++,
    473    cf https://gcc.gnu.org/bugzilla/show_bug.cgi?id=51364 */
    474 __MPFR_DECLSPEC int mpfr_set_decimal64 (mpfr_ptr, _Decimal64, mpfr_rnd_t);
    475 __MPFR_DECLSPEC int mpfr_set_decimal128 (mpfr_ptr, _Decimal128, mpfr_rnd_t);
    476 #endif
    477 __MPFR_DECLSPEC int mpfr_set_ld (mpfr_ptr, long double, mpfr_rnd_t);
    478 #ifdef MPFR_WANT_FLOAT128
    479 __MPFR_DECLSPEC int mpfr_set_float128 (mpfr_ptr, _Float128, mpfr_rnd_t);
    480 __MPFR_DECLSPEC _Float128 mpfr_get_float128 (mpfr_srcptr, mpfr_rnd_t);
    481 #endif
    482 __MPFR_DECLSPEC int mpfr_set_z (mpfr_ptr, mpz_srcptr, mpfr_rnd_t);
    483 __MPFR_DECLSPEC int mpfr_set_z_2exp (mpfr_ptr, mpz_srcptr, mpfr_exp_t,
    484                                      mpfr_rnd_t);
    485 __MPFR_DECLSPEC void mpfr_set_nan (mpfr_ptr);
    486 __MPFR_DECLSPEC void mpfr_set_inf (mpfr_ptr, int);
    487 __MPFR_DECLSPEC void mpfr_set_zero (mpfr_ptr, int);
    488 
    489 #ifndef MPFR_USE_MINI_GMP
    490   /* mini-gmp does not provide mpf_t, we disable the following functions */
    491 __MPFR_DECLSPEC int mpfr_set_f (mpfr_ptr, mpf_srcptr, mpfr_rnd_t);
    492 __MPFR_DECLSPEC int mpfr_cmp_f (mpfr_srcptr, mpf_srcptr);
    493 __MPFR_DECLSPEC int mpfr_get_f (mpf_ptr, mpfr_srcptr, mpfr_rnd_t);
    494 #endif
    495 __MPFR_DECLSPEC int mpfr_set_si (mpfr_ptr, long, mpfr_rnd_t);
    496 __MPFR_DECLSPEC int mpfr_set_ui (mpfr_ptr, unsigned long, mpfr_rnd_t);
    497 __MPFR_DECLSPEC int mpfr_set_si_2exp (mpfr_ptr, long, mpfr_exp_t, mpfr_rnd_t);
    498 __MPFR_DECLSPEC int mpfr_set_ui_2exp (mpfr_ptr, unsigned long, mpfr_exp_t,
    499                                       mpfr_rnd_t);
    500 #ifndef MPFR_USE_MINI_GMP
    501   /* mini-gmp does not provide mpq_t, we disable the following functions */
    502 __MPFR_DECLSPEC int mpfr_set_q (mpfr_ptr, mpq_srcptr, mpfr_rnd_t);
    503 __MPFR_DECLSPEC int mpfr_mul_q (mpfr_ptr, mpfr_srcptr, mpq_srcptr, mpfr_rnd_t);
    504 __MPFR_DECLSPEC int mpfr_div_q (mpfr_ptr, mpfr_srcptr, mpq_srcptr, mpfr_rnd_t);
    505 __MPFR_DECLSPEC int mpfr_add_q (mpfr_ptr, mpfr_srcptr, mpq_srcptr, mpfr_rnd_t);
    506 __MPFR_DECLSPEC int mpfr_sub_q (mpfr_ptr, mpfr_srcptr, mpq_srcptr, mpfr_rnd_t);
    507 __MPFR_DECLSPEC int mpfr_cmp_q (mpfr_srcptr, mpq_srcptr);
    508 __MPFR_DECLSPEC void mpfr_get_q (mpq_ptr q, mpfr_srcptr f);
    509 #endif
    510 __MPFR_DECLSPEC int mpfr_set_str (mpfr_ptr, const char *, int, mpfr_rnd_t);
    511 __MPFR_DECLSPEC int mpfr_init_set_str (mpfr_ptr, const char *, int,
    512                                        mpfr_rnd_t);
    513 __MPFR_DECLSPEC int mpfr_set4 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t, int);
    514 __MPFR_DECLSPEC int mpfr_abs (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    515 __MPFR_DECLSPEC int mpfr_set (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    516 __MPFR_DECLSPEC int mpfr_neg (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    517 __MPFR_DECLSPEC int mpfr_signbit (mpfr_srcptr);
    518 __MPFR_DECLSPEC int mpfr_setsign (mpfr_ptr, mpfr_srcptr, int, mpfr_rnd_t);
    519 __MPFR_DECLSPEC int mpfr_copysign (mpfr_ptr, mpfr_srcptr, mpfr_srcptr,
    520                                    mpfr_rnd_t);
    521 
    522 __MPFR_DECLSPEC mpfr_exp_t mpfr_get_z_2exp (mpz_ptr, mpfr_srcptr);
    523 __MPFR_DECLSPEC float mpfr_get_flt (mpfr_srcptr, mpfr_rnd_t);
    524 __MPFR_DECLSPEC double mpfr_get_d (mpfr_srcptr, mpfr_rnd_t);
    525 #ifdef MPFR_WANT_DECIMAL_FLOATS
    526 __MPFR_DECLSPEC _Decimal64 mpfr_get_decimal64 (mpfr_srcptr, mpfr_rnd_t);
    527 __MPFR_DECLSPEC _Decimal128 mpfr_get_decimal128 (mpfr_srcptr, mpfr_rnd_t);
    528 #endif
    529 __MPFR_DECLSPEC long double mpfr_get_ld (mpfr_srcptr, mpfr_rnd_t);
    530 __MPFR_DECLSPEC double mpfr_get_d1 (mpfr_srcptr);
    531 __MPFR_DECLSPEC double mpfr_get_d_2exp (long*, mpfr_srcptr, mpfr_rnd_t);
    532 __MPFR_DECLSPEC long double mpfr_get_ld_2exp (long*, mpfr_srcptr, mpfr_rnd_t);
    533 __MPFR_DECLSPEC int mpfr_frexp (mpfr_exp_t*, mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    534 __MPFR_DECLSPEC long mpfr_get_si (mpfr_srcptr, mpfr_rnd_t);
    535 __MPFR_DECLSPEC unsigned long mpfr_get_ui (mpfr_srcptr, mpfr_rnd_t);
    536 __MPFR_DECLSPEC size_t mpfr_get_str_ndigits (int, mpfr_prec_t);
    537 __MPFR_DECLSPEC char * mpfr_get_str (char*, mpfr_exp_t*, int, size_t,
    538                                      mpfr_srcptr, mpfr_rnd_t);
    539 __MPFR_DECLSPEC int mpfr_get_z (mpz_ptr z, mpfr_srcptr f, mpfr_rnd_t);
    540 
    541 __MPFR_DECLSPEC void mpfr_free_str (char *);
    542 
    543 __MPFR_DECLSPEC int mpfr_urandom (mpfr_ptr, gmp_randstate_t, mpfr_rnd_t);
    544 #ifndef _MPFR_NO_DEPRECATED_GRANDOM /* for the test of this function */
    545 MPFR_DEPRECATED
    546 #endif
    547 __MPFR_DECLSPEC int mpfr_grandom (mpfr_ptr, mpfr_ptr, gmp_randstate_t,
    548                                   mpfr_rnd_t);
    549 __MPFR_DECLSPEC int mpfr_nrandom (mpfr_ptr, gmp_randstate_t, mpfr_rnd_t);
    550 __MPFR_DECLSPEC int mpfr_erandom (mpfr_ptr, gmp_randstate_t, mpfr_rnd_t);
    551 __MPFR_DECLSPEC int mpfr_urandomb (mpfr_ptr, gmp_randstate_t);
    552 
    553 __MPFR_DECLSPEC void mpfr_nextabove (mpfr_ptr);
    554 __MPFR_DECLSPEC void mpfr_nextbelow (mpfr_ptr);
    555 __MPFR_DECLSPEC void mpfr_nexttoward (mpfr_ptr, mpfr_srcptr);
    556 
    557 #ifndef MPFR_USE_MINI_GMP
    558 __MPFR_DECLSPEC int mpfr_printf (const char*, ...);
    559 __MPFR_DECLSPEC int mpfr_asprintf (char**, const char*, ...);
    560 __MPFR_DECLSPEC int mpfr_sprintf (char*, const char*, ...);
    561 __MPFR_DECLSPEC int mpfr_snprintf (char*, size_t, const char*, ...);
    562 #endif
    563 
    564 __MPFR_DECLSPEC int mpfr_pow (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
    565 __MPFR_DECLSPEC int mpfr_powr (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
    566 __MPFR_DECLSPEC int mpfr_pow_si (mpfr_ptr, mpfr_srcptr, long, mpfr_rnd_t);
    567 __MPFR_DECLSPEC int mpfr_compound_si (mpfr_ptr, mpfr_srcptr, long, mpfr_rnd_t);
    568 __MPFR_DECLSPEC int mpfr_pow_ui (mpfr_ptr, mpfr_srcptr, unsigned long,
    569                                  mpfr_rnd_t);
    570 __MPFR_DECLSPEC int mpfr_ui_pow_ui (mpfr_ptr, unsigned long, unsigned long,
    571                                     mpfr_rnd_t);
    572 __MPFR_DECLSPEC int mpfr_ui_pow (mpfr_ptr, unsigned long, mpfr_srcptr,
    573                                  mpfr_rnd_t);
    574 __MPFR_DECLSPEC int mpfr_pow_z (mpfr_ptr, mpfr_srcptr, mpz_srcptr, mpfr_rnd_t);
    575 
    576 __MPFR_DECLSPEC int mpfr_sqrt (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    577 __MPFR_DECLSPEC int mpfr_sqrt_ui (mpfr_ptr, unsigned long, mpfr_rnd_t);
    578 __MPFR_DECLSPEC int mpfr_rec_sqrt (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    579 
    580 __MPFR_DECLSPEC int mpfr_add (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
    581 __MPFR_DECLSPEC int mpfr_sub (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
    582 __MPFR_DECLSPEC int mpfr_mul (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
    583 __MPFR_DECLSPEC int mpfr_div (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
    584 
    585 __MPFR_DECLSPEC int mpfr_add_ui (mpfr_ptr, mpfr_srcptr, unsigned long,
    586                                  mpfr_rnd_t);
    587 __MPFR_DECLSPEC int mpfr_sub_ui (mpfr_ptr, mpfr_srcptr, unsigned long,
    588                                  mpfr_rnd_t);
    589 __MPFR_DECLSPEC int mpfr_ui_sub (mpfr_ptr, unsigned long, mpfr_srcptr,
    590                                  mpfr_rnd_t);
    591 __MPFR_DECLSPEC int mpfr_mul_ui (mpfr_ptr, mpfr_srcptr, unsigned long,
    592                                  mpfr_rnd_t);
    593 __MPFR_DECLSPEC int mpfr_div_ui (mpfr_ptr, mpfr_srcptr, unsigned long,
    594                                  mpfr_rnd_t);
    595 __MPFR_DECLSPEC int mpfr_ui_div (mpfr_ptr, unsigned long, mpfr_srcptr,
    596                                  mpfr_rnd_t);
    597 
    598 __MPFR_DECLSPEC int mpfr_add_si (mpfr_ptr, mpfr_srcptr, long, mpfr_rnd_t);
    599 __MPFR_DECLSPEC int mpfr_sub_si (mpfr_ptr, mpfr_srcptr, long, mpfr_rnd_t);
    600 __MPFR_DECLSPEC int mpfr_si_sub (mpfr_ptr, long, mpfr_srcptr, mpfr_rnd_t);
    601 __MPFR_DECLSPEC int mpfr_mul_si (mpfr_ptr, mpfr_srcptr, long, mpfr_rnd_t);
    602 __MPFR_DECLSPEC int mpfr_div_si (mpfr_ptr, mpfr_srcptr, long, mpfr_rnd_t);
    603 __MPFR_DECLSPEC int mpfr_si_div (mpfr_ptr, long, mpfr_srcptr, mpfr_rnd_t);
    604 
    605 __MPFR_DECLSPEC int mpfr_add_d (mpfr_ptr, mpfr_srcptr, double, mpfr_rnd_t);
    606 __MPFR_DECLSPEC int mpfr_sub_d (mpfr_ptr, mpfr_srcptr, double, mpfr_rnd_t);
    607 __MPFR_DECLSPEC int mpfr_d_sub (mpfr_ptr, double, mpfr_srcptr, mpfr_rnd_t);
    608 __MPFR_DECLSPEC int mpfr_mul_d (mpfr_ptr, mpfr_srcptr, double, mpfr_rnd_t);
    609 __MPFR_DECLSPEC int mpfr_div_d (mpfr_ptr, mpfr_srcptr, double, mpfr_rnd_t);
    610 __MPFR_DECLSPEC int mpfr_d_div (mpfr_ptr, double, mpfr_srcptr, mpfr_rnd_t);
    611 
    612 __MPFR_DECLSPEC int mpfr_sqr (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    613 
    614 __MPFR_DECLSPEC int mpfr_const_pi (mpfr_ptr, mpfr_rnd_t);
    615 __MPFR_DECLSPEC int mpfr_const_log2 (mpfr_ptr, mpfr_rnd_t);
    616 __MPFR_DECLSPEC int mpfr_const_euler (mpfr_ptr, mpfr_rnd_t);
    617 __MPFR_DECLSPEC int mpfr_const_catalan (mpfr_ptr, mpfr_rnd_t);
    618 
    619 __MPFR_DECLSPEC int mpfr_agm (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
    620 
    621 __MPFR_DECLSPEC int mpfr_log (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    622 __MPFR_DECLSPEC int mpfr_log2 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    623 __MPFR_DECLSPEC int mpfr_log10 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    624 __MPFR_DECLSPEC int mpfr_log1p (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    625 __MPFR_DECLSPEC int mpfr_log2p1 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    626 __MPFR_DECLSPEC int mpfr_log10p1 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    627 __MPFR_DECLSPEC int mpfr_log_ui (mpfr_ptr, unsigned long, mpfr_rnd_t);
    628 
    629 __MPFR_DECLSPEC int mpfr_exp (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    630 __MPFR_DECLSPEC int mpfr_exp2 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    631 __MPFR_DECLSPEC int mpfr_exp10 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    632 __MPFR_DECLSPEC int mpfr_expm1 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    633 __MPFR_DECLSPEC int mpfr_exp2m1 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    634 __MPFR_DECLSPEC int mpfr_exp10m1 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    635 __MPFR_DECLSPEC int mpfr_eint (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    636 __MPFR_DECLSPEC int mpfr_li2 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    637 
    638 __MPFR_DECLSPEC int mpfr_cmp  (mpfr_srcptr, mpfr_srcptr);
    639 __MPFR_DECLSPEC int mpfr_cmp3 (mpfr_srcptr, mpfr_srcptr, int);
    640 __MPFR_DECLSPEC int mpfr_cmp_d (mpfr_srcptr, double);
    641 __MPFR_DECLSPEC int mpfr_cmp_ld (mpfr_srcptr, long double);
    642 __MPFR_DECLSPEC int mpfr_cmp_ui (mpfr_srcptr, unsigned long);
    643 __MPFR_DECLSPEC int mpfr_cmp_si (mpfr_srcptr, long);
    644 __MPFR_DECLSPEC int mpfr_cmp_ui_2exp (mpfr_srcptr, unsigned long, mpfr_exp_t);
    645 __MPFR_DECLSPEC int mpfr_cmp_si_2exp (mpfr_srcptr, long, mpfr_exp_t);
    646 __MPFR_DECLSPEC int mpfr_cmpabs (mpfr_srcptr, mpfr_srcptr);
    647 __MPFR_DECLSPEC int mpfr_cmpabs_ui (mpfr_srcptr, unsigned long);
    648 __MPFR_DECLSPEC void mpfr_reldiff (mpfr_ptr, mpfr_srcptr, mpfr_srcptr,
    649                                    mpfr_rnd_t);
    650 __MPFR_DECLSPEC int mpfr_eq (mpfr_srcptr, mpfr_srcptr, unsigned long);
    651 __MPFR_DECLSPEC int mpfr_sgn (mpfr_srcptr);
    652 
    653 __MPFR_DECLSPEC int mpfr_mul_2exp (mpfr_ptr, mpfr_srcptr, unsigned long,
    654                                    mpfr_rnd_t);
    655 __MPFR_DECLSPEC int mpfr_div_2exp (mpfr_ptr, mpfr_srcptr, unsigned long,
    656                                    mpfr_rnd_t);
    657 __MPFR_DECLSPEC int mpfr_mul_2ui (mpfr_ptr, mpfr_srcptr, unsigned long,
    658                                   mpfr_rnd_t);
    659 __MPFR_DECLSPEC int mpfr_div_2ui (mpfr_ptr, mpfr_srcptr, unsigned long,
    660                                   mpfr_rnd_t);
    661 __MPFR_DECLSPEC int mpfr_mul_2si (mpfr_ptr, mpfr_srcptr, long, mpfr_rnd_t);
    662 __MPFR_DECLSPEC int mpfr_div_2si (mpfr_ptr, mpfr_srcptr, long, mpfr_rnd_t);
    663 
    664 __MPFR_DECLSPEC int mpfr_rint (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    665 __MPFR_DECLSPEC int mpfr_roundeven (mpfr_ptr, mpfr_srcptr);
    666 __MPFR_DECLSPEC int mpfr_round (mpfr_ptr, mpfr_srcptr);
    667 __MPFR_DECLSPEC int mpfr_trunc (mpfr_ptr, mpfr_srcptr);
    668 __MPFR_DECLSPEC int mpfr_ceil (mpfr_ptr, mpfr_srcptr);
    669 __MPFR_DECLSPEC int mpfr_floor (mpfr_ptr, mpfr_srcptr);
    670 __MPFR_DECLSPEC int mpfr_rint_roundeven (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    671 __MPFR_DECLSPEC int mpfr_rint_round (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    672 __MPFR_DECLSPEC int mpfr_rint_trunc (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    673 __MPFR_DECLSPEC int mpfr_rint_ceil (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    674 __MPFR_DECLSPEC int mpfr_rint_floor (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    675 __MPFR_DECLSPEC int mpfr_frac (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    676 __MPFR_DECLSPEC int mpfr_modf (mpfr_ptr, mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    677 __MPFR_DECLSPEC int mpfr_remquo (mpfr_ptr, long*, mpfr_srcptr, mpfr_srcptr,
    678                                  mpfr_rnd_t);
    679 __MPFR_DECLSPEC int mpfr_remainder (mpfr_ptr, mpfr_srcptr, mpfr_srcptr,
    680                                     mpfr_rnd_t);
    681 __MPFR_DECLSPEC int mpfr_fmod (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
    682 __MPFR_DECLSPEC int mpfr_fmod_ui (mpfr_ptr, mpfr_srcptr, unsigned long,
    683                                   mpfr_rnd_t);
    684 __MPFR_DECLSPEC int mpfr_fmodquo (mpfr_ptr, long*, mpfr_srcptr, mpfr_srcptr,
    685                                   mpfr_rnd_t);
    686 
    687 __MPFR_DECLSPEC int mpfr_fits_ulong_p (mpfr_srcptr, mpfr_rnd_t);
    688 __MPFR_DECLSPEC int mpfr_fits_slong_p (mpfr_srcptr, mpfr_rnd_t);
    689 __MPFR_DECLSPEC int mpfr_fits_uint_p (mpfr_srcptr, mpfr_rnd_t);
    690 __MPFR_DECLSPEC int mpfr_fits_sint_p (mpfr_srcptr, mpfr_rnd_t);
    691 __MPFR_DECLSPEC int mpfr_fits_ushort_p (mpfr_srcptr, mpfr_rnd_t);
    692 __MPFR_DECLSPEC int mpfr_fits_sshort_p (mpfr_srcptr, mpfr_rnd_t);
    693 __MPFR_DECLSPEC int mpfr_fits_uintmax_p (mpfr_srcptr, mpfr_rnd_t);
    694 __MPFR_DECLSPEC int mpfr_fits_intmax_p (mpfr_srcptr, mpfr_rnd_t);
    695 
    696 __MPFR_DECLSPEC void mpfr_extract (mpz_ptr, mpfr_srcptr, unsigned int);
    697 __MPFR_DECLSPEC void mpfr_swap (mpfr_ptr, mpfr_ptr);
    698 __MPFR_DECLSPEC void mpfr_dump (mpfr_srcptr);
    699 
    700 __MPFR_DECLSPEC int mpfr_nan_p (mpfr_srcptr);
    701 __MPFR_DECLSPEC int mpfr_inf_p (mpfr_srcptr);
    702 __MPFR_DECLSPEC int mpfr_number_p (mpfr_srcptr);
    703 __MPFR_DECLSPEC int mpfr_integer_p (mpfr_srcptr);
    704 __MPFR_DECLSPEC int mpfr_zero_p (mpfr_srcptr);
    705 __MPFR_DECLSPEC int mpfr_regular_p (mpfr_srcptr);
    706 
    707 __MPFR_DECLSPEC int mpfr_greater_p (mpfr_srcptr, mpfr_srcptr);
    708 __MPFR_DECLSPEC int mpfr_greaterequal_p (mpfr_srcptr, mpfr_srcptr);
    709 __MPFR_DECLSPEC int mpfr_less_p (mpfr_srcptr, mpfr_srcptr);
    710 __MPFR_DECLSPEC int mpfr_lessequal_p (mpfr_srcptr, mpfr_srcptr);
    711 __MPFR_DECLSPEC int mpfr_lessgreater_p (mpfr_srcptr, mpfr_srcptr);
    712 __MPFR_DECLSPEC int mpfr_equal_p (mpfr_srcptr, mpfr_srcptr);
    713 __MPFR_DECLSPEC int mpfr_unordered_p (mpfr_srcptr, mpfr_srcptr);
    714 
    715 __MPFR_DECLSPEC int mpfr_atanh (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    716 __MPFR_DECLSPEC int mpfr_acosh (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    717 __MPFR_DECLSPEC int mpfr_asinh (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    718 __MPFR_DECLSPEC int mpfr_cosh (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    719 __MPFR_DECLSPEC int mpfr_sinh (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    720 __MPFR_DECLSPEC int mpfr_tanh (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    721 __MPFR_DECLSPEC int mpfr_sinh_cosh (mpfr_ptr, mpfr_ptr, mpfr_srcptr,
    722                                     mpfr_rnd_t);
    723 
    724 __MPFR_DECLSPEC int mpfr_sech (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    725 __MPFR_DECLSPEC int mpfr_csch (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    726 __MPFR_DECLSPEC int mpfr_coth (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    727 
    728 __MPFR_DECLSPEC int mpfr_acos (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    729 __MPFR_DECLSPEC int mpfr_asin (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    730 __MPFR_DECLSPEC int mpfr_atan (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    731 __MPFR_DECLSPEC int mpfr_sin (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    732 __MPFR_DECLSPEC int mpfr_sin_cos (mpfr_ptr, mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    733 __MPFR_DECLSPEC int mpfr_cos (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    734 __MPFR_DECLSPEC int mpfr_tan (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    735 __MPFR_DECLSPEC int mpfr_atan2 (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
    736 __MPFR_DECLSPEC int mpfr_sec (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    737 __MPFR_DECLSPEC int mpfr_csc (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    738 __MPFR_DECLSPEC int mpfr_cot (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    739 
    740 __MPFR_DECLSPEC int mpfr_sinu (mpfr_ptr, mpfr_srcptr, unsigned long, mpfr_rnd_t);
    741 __MPFR_DECLSPEC int mpfr_cosu (mpfr_ptr, mpfr_srcptr, unsigned long, mpfr_rnd_t);
    742 __MPFR_DECLSPEC int mpfr_tanu (mpfr_ptr, mpfr_srcptr, unsigned long, mpfr_rnd_t);
    743 __MPFR_DECLSPEC int mpfr_acosu (mpfr_ptr, mpfr_srcptr, unsigned long, mpfr_rnd_t);
    744 __MPFR_DECLSPEC int mpfr_asinu (mpfr_ptr, mpfr_srcptr, unsigned long, mpfr_rnd_t);
    745 __MPFR_DECLSPEC int mpfr_atanu (mpfr_ptr, mpfr_srcptr, unsigned long, mpfr_rnd_t);
    746 __MPFR_DECLSPEC int mpfr_atan2u (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, unsigned long, mpfr_rnd_t);
    747 __MPFR_DECLSPEC int mpfr_acospi (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    748 __MPFR_DECLSPEC int mpfr_asinpi (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    749 __MPFR_DECLSPEC int mpfr_atanpi (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    750 __MPFR_DECLSPEC int mpfr_atan2pi (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
    751 
    752 __MPFR_DECLSPEC int mpfr_sinpi (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    753 __MPFR_DECLSPEC int mpfr_cospi (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    754 __MPFR_DECLSPEC int mpfr_tanpi (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    755 
    756 __MPFR_DECLSPEC int mpfr_hypot (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
    757 __MPFR_DECLSPEC int mpfr_erf (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    758 __MPFR_DECLSPEC int mpfr_erfc (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    759 __MPFR_DECLSPEC int mpfr_cbrt (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    760 #ifndef _MPFR_NO_DEPRECATED_ROOT /* for the test of this function */
    761 MPFR_DEPRECATED
    762 #endif
    763 __MPFR_DECLSPEC int mpfr_root (mpfr_ptr, mpfr_srcptr, unsigned long,
    764                                mpfr_rnd_t);
    765 __MPFR_DECLSPEC int mpfr_rootn_ui (mpfr_ptr, mpfr_srcptr, unsigned long,
    766                                    mpfr_rnd_t);
    767 __MPFR_DECLSPEC int mpfr_rootn_si (mpfr_ptr, mpfr_srcptr, long, mpfr_rnd_t);
    768 __MPFR_DECLSPEC int mpfr_gamma (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    769 __MPFR_DECLSPEC int mpfr_gamma_inc (mpfr_ptr, mpfr_srcptr, mpfr_srcptr,
    770                                     mpfr_rnd_t);
    771 __MPFR_DECLSPEC int mpfr_beta (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
    772 __MPFR_DECLSPEC int mpfr_lngamma (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    773 __MPFR_DECLSPEC int mpfr_lgamma (mpfr_ptr, int *, mpfr_srcptr, mpfr_rnd_t);
    774 __MPFR_DECLSPEC int mpfr_digamma (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    775 __MPFR_DECLSPEC int mpfr_zeta (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    776 __MPFR_DECLSPEC int mpfr_zeta_ui (mpfr_ptr, unsigned long, mpfr_rnd_t);
    777 __MPFR_DECLSPEC int mpfr_fac_ui (mpfr_ptr, unsigned long, mpfr_rnd_t);
    778 __MPFR_DECLSPEC int mpfr_j0 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    779 __MPFR_DECLSPEC int mpfr_j1 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    780 __MPFR_DECLSPEC int mpfr_jn (mpfr_ptr, long, mpfr_srcptr, mpfr_rnd_t);
    781 __MPFR_DECLSPEC int mpfr_y0 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    782 __MPFR_DECLSPEC int mpfr_y1 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    783 __MPFR_DECLSPEC int mpfr_yn (mpfr_ptr, long, mpfr_srcptr, mpfr_rnd_t);
    784 
    785 __MPFR_DECLSPEC int mpfr_ai (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
    786 
    787 __MPFR_DECLSPEC int mpfr_min (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
    788 __MPFR_DECLSPEC int mpfr_max (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
    789 __MPFR_DECLSPEC int mpfr_dim (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
    790 
    791 __MPFR_DECLSPEC int mpfr_mul_z (mpfr_ptr, mpfr_srcptr, mpz_srcptr, mpfr_rnd_t);
    792 __MPFR_DECLSPEC int mpfr_div_z (mpfr_ptr, mpfr_srcptr, mpz_srcptr, mpfr_rnd_t);
    793 __MPFR_DECLSPEC int mpfr_add_z (mpfr_ptr, mpfr_srcptr, mpz_srcptr, mpfr_rnd_t);
    794 __MPFR_DECLSPEC int mpfr_sub_z (mpfr_ptr, mpfr_srcptr, mpz_srcptr, mpfr_rnd_t);
    795 __MPFR_DECLSPEC int mpfr_z_sub (mpfr_ptr, mpz_srcptr, mpfr_srcptr, mpfr_rnd_t);
    796 __MPFR_DECLSPEC int mpfr_cmp_z (mpfr_srcptr, mpz_srcptr);
    797 
    798 __MPFR_DECLSPEC int mpfr_fma (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_srcptr,
    799                               mpfr_rnd_t);
    800 __MPFR_DECLSPEC int mpfr_fms (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_srcptr,
    801                               mpfr_rnd_t);
    802 __MPFR_DECLSPEC int mpfr_fmma (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_srcptr,
    803                                mpfr_srcptr, mpfr_rnd_t);
    804 __MPFR_DECLSPEC int mpfr_fmms (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_srcptr,
    805                                mpfr_srcptr, mpfr_rnd_t);
    806 __MPFR_DECLSPEC int mpfr_sum (mpfr_ptr, const mpfr_ptr *, unsigned long,
    807                               mpfr_rnd_t);
    808 __MPFR_DECLSPEC int mpfr_dot (mpfr_ptr, const mpfr_ptr *, const mpfr_ptr *,
    809                               unsigned long, mpfr_rnd_t);
    810 
    811 __MPFR_DECLSPEC void mpfr_free_cache (void);
    812 __MPFR_DECLSPEC void mpfr_free_cache2 (mpfr_free_cache_t);
    813 __MPFR_DECLSPEC void mpfr_free_pool (void);
    814 __MPFR_DECLSPEC int mpfr_mp_memory_cleanup (void);
    815 
    816 __MPFR_DECLSPEC int mpfr_subnormalize (mpfr_ptr, int, mpfr_rnd_t);
    817 
    818 __MPFR_DECLSPEC int mpfr_strtofr (mpfr_ptr, const char *, char **, int,
    819                                   mpfr_rnd_t);
    820 
    821 __MPFR_DECLSPEC void mpfr_round_nearest_away_begin (mpfr_ptr);
    822 __MPFR_DECLSPEC int mpfr_round_nearest_away_end (mpfr_ptr, int);
    823 
    824 __MPFR_DECLSPEC size_t mpfr_custom_get_size (mpfr_prec_t);
    825 __MPFR_DECLSPEC void mpfr_custom_init (void *, mpfr_prec_t);
    826 __MPFR_DECLSPEC MPFR_RETURNS_NONNULL void *
    827   mpfr_custom_get_significand (mpfr_srcptr);
    828 __MPFR_DECLSPEC mpfr_exp_t mpfr_custom_get_exp (mpfr_srcptr);
    829 __MPFR_DECLSPEC void mpfr_custom_move (mpfr_ptr, void *);
    830 __MPFR_DECLSPEC void mpfr_custom_init_set (mpfr_ptr, int, mpfr_exp_t,
    831                                            mpfr_prec_t, void *);
    832 __MPFR_DECLSPEC int mpfr_custom_get_kind (mpfr_srcptr);
    833 
    834 __MPFR_DECLSPEC int mpfr_total_order_p (mpfr_srcptr, mpfr_srcptr);
    835 
    836 #if defined (__cplusplus)
    837 }
    838 #endif
    839 
    840 /* Define MPFR_USE_EXTENSION to avoid "gcc -pedantic" warnings. */
    841 #ifndef MPFR_EXTENSION
    842 # if defined(MPFR_USE_EXTENSION)
    843 #  define MPFR_EXTENSION __extension__
    844 # else
    845 #  define MPFR_EXTENSION
    846 # endif
    847 #endif
    848 
    849 /* Warning! This macro doesn't work with K&R C (e.g., compare the "gcc -E"
    850    output with and without -traditional) and shouldn't be used internally.
    851    For public use only, but see the MPFR manual. */
    852 #define MPFR_DECL_INIT(_x, _p)                                        \
    853   MPFR_EXTENSION mp_limb_t __gmpfr_local_tab_##_x[((_p)-1)/GMP_NUMB_BITS+1]; \
    854   MPFR_EXTENSION mpfr_t _x = {{(_p),1,__MPFR_EXP_NAN,__gmpfr_local_tab_##_x}}
    855 
    856 #if MPFR_USE_C99_FEATURE
    857 /* C99 & C11 version: functions with multiple inputs supported */
    858 #define mpfr_round_nearest_away(func, rop, ...)                         \
    859   (mpfr_round_nearest_away_begin(rop),                                  \
    860    mpfr_round_nearest_away_end((rop), func((rop), __VA_ARGS__, MPFR_RNDN)))
    861 #else
    862 /* C90 version: function with one input supported */
    863 #define mpfr_round_nearest_away(func, rop, op)                          \
    864   (mpfr_round_nearest_away_begin(rop),                                  \
    865    mpfr_round_nearest_away_end((rop), func((rop), (op), MPFR_RNDN)))
    866 #endif
    867 
    868 /* Fast access macros to replace function interface.
    869    If the user doesn't want to use the macro interface, let him make happy
    870    even if it produces faster and smaller code. */
    871 #ifndef MPFR_USE_NO_MACRO
    872 
    873 /* In the implementation of these macros, we need to make sure that the
    874    arguments are evaluated one time exactly and that type conversion is
    875    done as it would be with a function. Tests should be added to ensure
    876    that. */
    877 
    878 /* Prevent x from being used as an lvalue.
    879    Thanks to Wojtek Lerch and Tim Rentsch for the idea. */
    880 #define MPFR_VALUE_OF(x)  (0 ? (x) : (x))
    881 
    882 /* The following macro converts the argument to mpfr_srcptr, as in type
    883    conversion for function parameters. But it will detect disallowed
    884    implicit conversions, e.g. when the argument has an integer type. */
    885 #define MPFR_SRCPTR(x) ((mpfr_srcptr) (0 ? (x) : (mpfr_srcptr) (x)))
    886 #define MPFR_GET_SIGN(_x) MPFR_VALUE_OF(MPFR_SIGN(MPFR_SRCPTR(_x)))
    887 
    888 #define mpfr_nan_p(_x)      (MPFR_SRCPTR(_x)->_mpfr_exp == __MPFR_EXP_NAN)
    889 #define mpfr_inf_p(_x)      (MPFR_SRCPTR(_x)->_mpfr_exp == __MPFR_EXP_INF)
    890 #define mpfr_zero_p(_x)     (MPFR_SRCPTR(_x)->_mpfr_exp == __MPFR_EXP_ZERO)
    891 #define mpfr_regular_p(_x)  (MPFR_SRCPTR(_x)->_mpfr_exp >  __MPFR_EXP_INF)
    892 
    893 /* mpfr_sgn is documented as a macro, thus the following code is fine.
    894    But it would be safer to regard it as a function in some future
    895    MPFR version. */
    896 #define mpfr_sgn(_x)                                               \
    897   ((_x)->_mpfr_exp < __MPFR_EXP_INF ?                              \
    898    (mpfr_nan_p (_x) ? mpfr_set_erangeflag () : (mpfr_void) 0), 0 : \
    899    MPFR_SIGN (_x))
    900 
    901 #define mpfr_get_prec(_x) MPFR_VALUE_OF(MPFR_SRCPTR(_x)->_mpfr_prec)
    902 #define mpfr_get_exp(_x)  MPFR_VALUE_OF(MPFR_SRCPTR(_x)->_mpfr_exp)
    903 /* Note: Defining mpfr_get_exp() as a macro has the effect to disable
    904    the check that the argument is a pure FP number (done in the function);
    905    this increases the risk of undetected error and makes debugging more
    906    complex. Is it really worth in practice? (Potential FIXME) */
    907 
    908 #define mpfr_round(a,b) mpfr_rint((a), (b), MPFR_RNDNA)
    909 #define mpfr_trunc(a,b) mpfr_rint((a), (b), MPFR_RNDZ)
    910 #define mpfr_ceil(a,b)  mpfr_rint((a), (b), MPFR_RNDU)
    911 #define mpfr_floor(a,b) mpfr_rint((a), (b), MPFR_RNDD)
    912 
    913 #define mpfr_cmp_ui(b,i) mpfr_cmp_ui_2exp((b),(i),0)
    914 #define mpfr_cmp_si(b,i) mpfr_cmp_si_2exp((b),(i),0)
    915 #if __GNUC__ > 2 || __GNUC_MINOR__ >= 95
    916 #define mpfr_set(a,b,r)                         \
    917   __extension__ ({                              \
    918       mpfr_srcptr _p = (b);                     \
    919       mpfr_set4(a,_p,r,MPFR_SIGN(_p));          \
    920     })
    921 #endif
    922 #define mpfr_abs(a,b,r)  mpfr_set4(a,b,r,1)
    923 #define mpfr_copysign(a,b,c,r) mpfr_set4(a,b,r,MPFR_GET_SIGN(c))
    924 #define mpfr_setsign(a,b,s,r) mpfr_set4(a,b,r,(s) ? -1 : 1)
    925 #define mpfr_signbit(x)  (MPFR_GET_SIGN(x) < 0)
    926 #define mpfr_cmp(b, c)   mpfr_cmp3(b, c, 1)
    927 #define mpfr_mul_2exp(y,x,n,r) mpfr_mul_2ui((y),(x),(n),(r))
    928 #define mpfr_div_2exp(y,x,n,r) mpfr_div_2ui((y),(x),(n),(r))
    929 
    930 
    931 /* When using GCC or ICC, optimize certain common comparisons and affectations.
    932    Added casts to improve robustness in case of undefined behavior and
    933    compiler extensions based on UB (in particular -fwrapv). MPFR doesn't
    934    use such extensions, but these macros will be used by 3rd-party code,
    935    where such extensions may be required.
    936    Moreover casts to unsigned long have been added to avoid warnings in
    937    programs that use MPFR and are compiled with -Wconversion; such casts
    938    are OK since if X is a constant expression, then (unsigned long) X is
    939    also a constant expression, so that the optimizations still work. The
    940    warnings are probably related to the following two bugs:
    941      https://gcc.gnu.org/bugzilla/show_bug.cgi?id=4210
    942      https://gcc.gnu.org/bugzilla/show_bug.cgi?id=38470 (possibly a variant)
    943    and the casts could be removed once these bugs are fixed.
    944    Casts shouldn't be used on the generic calls (to the ..._2exp functions),
    945    where implicit conversions are performed. Indeed, having at least one
    946    implicit conversion in the macro allows the compiler to emit diagnostics
    947    when normally expected, for instance in the following call:
    948      mpfr_set_ui (x, "foo", MPFR_RNDN);
    949    If this is not possible (for future macros), one of the tricks described on
    950    https://groups.google.com/g/comp.std.c/c/9Jl0giNILfg/m/e6-evyS9KukJ?pli=1
    951    could be used. */
    952 #if defined (__GNUC__) && !defined(__cplusplus)
    953 #if (__GNUC__ >= 2)
    954 
    955 #undef mpfr_cmp_ui
    956 /* We use the fact that mpfr_sgn on NaN sets the erange flag and returns 0.
    957    But warning! mpfr_sgn is specified as a macro in the API, thus the macro
    958    mustn't be used if side effects are possible, like here. */
    959 #define mpfr_cmp_ui(_f,_u)                                      \
    960   (__builtin_constant_p (_u) && (mpfr_ulong) (_u) == 0 ?        \
    961    (mpfr_sgn) (_f) :                                            \
    962    mpfr_cmp_ui_2exp ((_f), (_u), 0))
    963 
    964 #undef mpfr_cmp_si
    965 #define mpfr_cmp_si(_f,_s)                                      \
    966   (__builtin_constant_p (_s) && (mpfr_long) (_s) >= 0 ?         \
    967    mpfr_cmp_ui ((_f), (mpfr_ulong) (mpfr_long) (_s)) :          \
    968    mpfr_cmp_si_2exp ((_f), (_s), 0))
    969 
    970 #if __GNUC__ > 2 || __GNUC_MINOR__ >= 95
    971 #undef mpfr_set_ui
    972 #define mpfr_set_ui(_f,_u,_r)                                   \
    973   (__builtin_constant_p (_u) && (mpfr_ulong) (_u) == 0 ?        \
    974    __extension__ ({                                             \
    975        mpfr_ptr _p = (_f);                                      \
    976        _p->_mpfr_sign = 1;                                      \
    977        _p->_mpfr_exp = __MPFR_EXP_ZERO;                         \
    978        (mpfr_void) (_r); 0; }) :                                \
    979    mpfr_set_ui_2exp ((_f), (_u), 0, (_r)))
    980 #endif
    981 
    982 #undef mpfr_set_si
    983 #define mpfr_set_si(_f,_s,_r)                                   \
    984   (__builtin_constant_p (_s) && (mpfr_long) (_s) >= 0 ?         \
    985    mpfr_set_ui ((_f), (mpfr_ulong) (mpfr_long) (_s), (_r)) :    \
    986    mpfr_set_si_2exp ((_f), (_s), 0, (_r)))
    987 
    988 #if __GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 4)
    989 /* If the source is a constant number that is a power of 2,
    990    optimize the call */
    991 #undef mpfr_mul_ui
    992 #define mpfr_mul_ui(_f, _g, _u,_r)                              \
    993   (__builtin_constant_p (_u) && (mpfr_ulong) (_u) >= 1 &&       \
    994    ((mpfr_ulong) (_u) & ((mpfr_ulong) (_u) - 1)) == 0 ?         \
    995    mpfr_mul_2si((_f), (_g), __builtin_ctzl (_u), (_r)) :        \
    996    mpfr_mul_ui ((_f), (_g), (_u), (_r)))
    997 #undef mpfr_div_ui
    998 #define mpfr_div_ui(_f, _g, _u,_r)                              \
    999   (__builtin_constant_p (_u) && (mpfr_ulong) (_u) >= 1 &&       \
   1000    ((mpfr_ulong) (_u) & ((mpfr_ulong) (_u) - 1)) == 0 ?         \
   1001    mpfr_mul_2si((_f), (_g), - __builtin_ctzl (_u), (_r)) :      \
   1002    mpfr_div_ui ((_f), (_g), (_u), (_r)))
   1003 #endif
   1004 
   1005 /* If the source is a constant number that is non-negative,
   1006    optimize the call */
   1007 #undef mpfr_mul_si
   1008 #define mpfr_mul_si(_f, _g, _s,_r)                                      \
   1009   (__builtin_constant_p (_s) && (mpfr_long) (_s) >= 0 ?                 \
   1010    mpfr_mul_ui ((_f), (_g), (mpfr_ulong) (mpfr_long) (_s), (_r)) :      \
   1011    mpfr_mul_si ((_f), (_g), (_s), (_r)))
   1012 #undef mpfr_div_si
   1013 #define mpfr_div_si(_f, _g, _s,_r)                                      \
   1014   (__builtin_constant_p (_s) && (mpfr_long) (_s) >= 0 ?                 \
   1015    mpfr_div_ui ((_f), (_g), (mpfr_ulong) (mpfr_long) (_s), (_r)) :      \
   1016    mpfr_div_si ((_f), (_g), (_s), (_r)))
   1017 
   1018 #endif
   1019 #endif
   1020 
   1021 /* Macro versions of the custom interface for fast access. */
   1022 
   1023 /* The internal cast to mpfr_size_t will silent a warning with
   1024    GCC's -Wsign-conversion that could occur with user code, as
   1025    sizeof is of type size_t, which is unsigned. */
   1026 #define mpfr_custom_get_size(p)                                             \
   1027   ((mpfr_size_t)                                                            \
   1028    ((mpfr_size_t) (((mpfr_prec_t)(p) + GMP_NUMB_BITS - 1) / GMP_NUMB_BITS)  \
   1029     * sizeof (mp_limb_t)))
   1030 
   1031 #define mpfr_custom_init(m,p) ((void) (m), (void) (p))
   1032 
   1033 #define mpfr_custom_get_significand(x) \
   1034   ((mpfr_void *) MPFR_VALUE_OF(MPFR_SRCPTR(x)->_mpfr_d))
   1035 
   1036 #define mpfr_custom_get_exp(x) MPFR_VALUE_OF(MPFR_SRCPTR(x)->_mpfr_exp)
   1037 
   1038 #define mpfr_custom_move(x,m) (((mpfr_ptr) (x))->_mpfr_d = (mp_limb_t *) (m))
   1039 
   1040 /* Note: the following macro is not usable in contexts where an expression
   1041    is expected. */
   1042 #define mpfr_custom_init_set(x,k,e,p,m) do {                   \
   1043   mpfr_ptr _x = (x);                                           \
   1044   mpfr_exp_t _e = (e);                                         \
   1045   mpfr_kind_t _t;                                              \
   1046   mpfr_int _s, _k;                                             \
   1047   _k = (k);                                                    \
   1048   if (_k >= 0)  {                                              \
   1049     _t = (mpfr_kind_t) _k;                                     \
   1050     _s = 1;                                                    \
   1051   } else {                                                     \
   1052     _t = (mpfr_kind_t) - _k;                                   \
   1053     _s = -1;                                                   \
   1054   }                                                            \
   1055   _e = _t == MPFR_REGULAR_KIND ? _e :                          \
   1056     _t == MPFR_NAN_KIND ? __MPFR_EXP_NAN :                     \
   1057     _t == MPFR_INF_KIND ? __MPFR_EXP_INF : __MPFR_EXP_ZERO;    \
   1058   _x->_mpfr_prec = (p);                                        \
   1059   _x->_mpfr_sign = _s;                                         \
   1060   _x->_mpfr_exp  = _e;                                         \
   1061   _x->_mpfr_d    = (mp_limb_t*) (m);                           \
   1062  } while (0)
   1063 
   1064 #if __GNUC__ > 2 || __GNUC_MINOR__ >= 95
   1065 #define mpfr_custom_get_kind(x)                                         \
   1066   __extension__ ({                                                      \
   1067     mpfr_srcptr _x = (x);                                               \
   1068     _x->_mpfr_exp >  __MPFR_EXP_INF ?                                   \
   1069       (mpfr_int) MPFR_REGULAR_KIND * MPFR_SIGN (_x)                     \
   1070       : _x->_mpfr_exp == __MPFR_EXP_INF ?                               \
   1071       (mpfr_int) MPFR_INF_KIND * MPFR_SIGN (_x)                         \
   1072       : _x->_mpfr_exp == __MPFR_EXP_NAN ? (mpfr_int) MPFR_NAN_KIND      \
   1073       : (mpfr_int) MPFR_ZERO_KIND * MPFR_SIGN (_x);                     \
   1074   })
   1075 #else
   1076 #define mpfr_custom_get_kind(x) ((mpfr_custom_get_kind)(x))
   1077 #endif
   1078 
   1079 /* End of the macro versions of the custom interface. */
   1080 
   1081 #endif /* MPFR_USE_NO_MACRO */
   1082 
   1083 /* These are defined to be macros */
   1084 #define mpfr_init_set_si(x, i, rnd) \
   1085  ( mpfr_init(x), mpfr_set_si((x), (i), (rnd)) )
   1086 #define mpfr_init_set_ui(x, i, rnd) \
   1087  ( mpfr_init(x), mpfr_set_ui((x), (i), (rnd)) )
   1088 #define mpfr_init_set_d(x, d, rnd) \
   1089  ( mpfr_init(x), mpfr_set_d((x), (d), (rnd)) )
   1090 #define mpfr_init_set_ld(x, d, rnd) \
   1091  ( mpfr_init(x), mpfr_set_ld((x), (d), (rnd)) )
   1092 #define mpfr_init_set_z(x, i, rnd) \
   1093  ( mpfr_init(x), mpfr_set_z((x), (i), (rnd)) )
   1094 #ifndef MPFR_USE_MINI_GMP
   1095 #define mpfr_init_set_q(x, i, rnd) \
   1096  ( mpfr_init(x), mpfr_set_q((x), (i), (rnd)) )
   1097 #define mpfr_init_set_f(x, y, rnd) \
   1098  ( mpfr_init(x), mpfr_set_f((x), (y), (rnd)) )
   1099 #endif
   1100 #define mpfr_init_set(x, y, rnd) \
   1101  ( mpfr_init(x), mpfr_set((x), (y), (rnd)) )
   1102 
   1103 /* Compatibility layer -- obsolete functions and macros */
   1104 /* Note: it is not possible to output warnings, unless one defines
   1105  * a deprecated variable and uses it, e.g.
   1106  *   MPFR_DEPRECATED extern int mpfr_deprecated_feature;
   1107  *   #define MPFR_EMIN_MIN ((void)mpfr_deprecated_feature,mpfr_get_emin_min())
   1108  * (the cast to void avoids a warning because the left-hand operand
   1109  * has no effect).
   1110  */
   1111 #define mpfr_cmp_abs mpfr_cmpabs
   1112 #define mpfr_round_prec(x,r,p) mpfr_prec_round(x,p,r)
   1113 #define __gmp_default_rounding_mode (mpfr_get_default_rounding_mode())
   1114 #define __mpfr_emin (mpfr_get_emin())
   1115 #define __mpfr_emax (mpfr_get_emax())
   1116 #define __mpfr_default_fp_bit_precision (mpfr_get_default_fp_bit_precision())
   1117 #define MPFR_EMIN_MIN mpfr_get_emin_min()
   1118 #define MPFR_EMIN_MAX mpfr_get_emin_max()
   1119 #define MPFR_EMAX_MIN mpfr_get_emax_min()
   1120 #define MPFR_EMAX_MAX mpfr_get_emax_max()
   1121 #define mpfr_version (mpfr_get_version())
   1122 #ifndef mpz_set_fr
   1123 # define mpz_set_fr mpfr_get_z
   1124 #endif
   1125 #define mpfr_get_z_exp mpfr_get_z_2exp
   1126 #define mpfr_custom_get_mantissa mpfr_custom_get_significand
   1127 
   1128 #endif /* __MPFR_H */
   1129 
   1130 
   1131 /* Check if <stdint.h> / <inttypes.h> is included or if the user
   1132    explicitly wants intmax_t. Automatic detection is done by
   1133    checking:
   1134      - INTMAX_C and UINTMAX_C, but not if the compiler is a C++ one
   1135        (as suggested by Patrick Pelissier) because the test does not
   1136        work well in this case. See:
   1137          https://sympa.inria.fr/sympa/arc/mpfr/2010-02/msg00025.html
   1138        We do not check INTMAX_MAX and UINTMAX_MAX because under Solaris,
   1139        these macros are always defined by <limits.h> (i.e. even when
   1140        <stdint.h> and <inttypes.h> are not included).
   1141      - _STDINT_H (defined by the glibc), _STDINT_H_ (defined under
   1142        Mac OS X) and _STDINT (defined under MS Visual Studio), but
   1143        this test may not work with all implementations.
   1144        Portable software should not rely on these tests.
   1145 */
   1146 #if (defined (INTMAX_C) && defined (UINTMAX_C) && !defined(__cplusplus)) || \
   1147   defined (MPFR_USE_INTMAX_T) || \
   1148   defined (_STDINT_H) || defined (_STDINT_H_) || defined (_STDINT) || \
   1149   defined (_SYS_STDINT_H_) /* needed for FreeBSD */
   1150 # ifndef _MPFR_H_HAVE_INTMAX_T
   1151 # define _MPFR_H_HAVE_INTMAX_T 1
   1152 
   1153 #if defined (__cplusplus)
   1154 extern "C" {
   1155 #endif
   1156 
   1157 #define mpfr_set_sj __gmpfr_set_sj
   1158 #define mpfr_set_sj_2exp __gmpfr_set_sj_2exp
   1159 #define mpfr_set_uj __gmpfr_set_uj
   1160 #define mpfr_set_uj_2exp __gmpfr_set_uj_2exp
   1161 #define mpfr_get_sj __gmpfr_mpfr_get_sj
   1162 #define mpfr_get_uj __gmpfr_mpfr_get_uj
   1163 #define mpfr_pow_uj __gmpfr_mpfr_pow_uj
   1164 #define mpfr_pow_sj __gmpfr_mpfr_pow_sj
   1165 __MPFR_DECLSPEC int mpfr_set_sj (mpfr_ptr, intmax_t, mpfr_rnd_t);
   1166 __MPFR_DECLSPEC int mpfr_set_sj_2exp (mpfr_ptr, intmax_t, intmax_t,
   1167                                       mpfr_rnd_t);
   1168 __MPFR_DECLSPEC int mpfr_set_uj (mpfr_ptr, uintmax_t, mpfr_rnd_t);
   1169 __MPFR_DECLSPEC int mpfr_set_uj_2exp (mpfr_ptr, uintmax_t, intmax_t,
   1170                                       mpfr_rnd_t);
   1171 __MPFR_DECLSPEC intmax_t mpfr_get_sj (mpfr_srcptr, mpfr_rnd_t);
   1172 __MPFR_DECLSPEC uintmax_t mpfr_get_uj (mpfr_srcptr, mpfr_rnd_t);
   1173 __MPFR_DECLSPEC int mpfr_pow_uj (mpfr_ptr, mpfr_srcptr, uintmax_t, mpfr_rnd_t);
   1174 __MPFR_DECLSPEC int mpfr_pow_sj (mpfr_ptr, mpfr_srcptr, intmax_t, mpfr_rnd_t);
   1175 /* define mpfr_pown (defined in IEEE 754-2019) as an alias for mpfr_pow_sj.
   1176    It is currently implemented as a macro, but this may change in the future
   1177    (it could be implemented as an inline function); in case of change, update
   1178    the manual. */
   1179 #define mpfr_pown mpfr_pow_sj
   1180 
   1181 #if defined (__cplusplus)
   1182 }
   1183 #endif
   1184 
   1185 # endif /* _MPFR_H_HAVE_INTMAX_T */
   1186 #endif
   1187 
   1188 
   1189 /* Check if <stdio.h> has been included or if the user wants FILE */
   1190 #if defined (_GMP_H_HAVE_FILE) || defined (MPFR_USE_FILE)
   1191 # ifndef _MPFR_H_HAVE_FILE
   1192 # define _MPFR_H_HAVE_FILE 1
   1193 
   1194 #if defined (__cplusplus)
   1195 extern "C" {
   1196 #endif
   1197 
   1198 #define mpfr_inp_str __gmpfr_inp_str
   1199 #define mpfr_out_str __gmpfr_out_str
   1200 __MPFR_DECLSPEC size_t mpfr_inp_str (mpfr_ptr, FILE*, int, mpfr_rnd_t);
   1201 __MPFR_DECLSPEC size_t mpfr_out_str (FILE*, int, size_t, mpfr_srcptr,
   1202                                      mpfr_rnd_t);
   1203 #ifndef MPFR_USE_MINI_GMP
   1204 #define mpfr_fprintf __gmpfr_fprintf
   1205 __MPFR_DECLSPEC int mpfr_fprintf (FILE*, const char*, ...);
   1206 #endif
   1207 #define mpfr_fpif_export __gmpfr_fpif_export
   1208 #define mpfr_fpif_import __gmpfr_fpif_import
   1209 __MPFR_DECLSPEC int mpfr_fpif_export (FILE*, mpfr_ptr);
   1210 __MPFR_DECLSPEC int mpfr_fpif_import (mpfr_ptr, FILE*);
   1211 
   1212 #if defined (__cplusplus)
   1213 }
   1214 #endif
   1215 
   1216 # endif /* _MPFR_H_HAVE_FILE */
   1217 #endif
   1218 
   1219 
   1220 /* check if <stdarg.h> has been included or if the user wants va_list */
   1221 #if defined (_GMP_H_HAVE_VA_LIST) || defined (MPFR_USE_VA_LIST)
   1222 # ifndef _MPFR_H_HAVE_VA_LIST
   1223 # define _MPFR_H_HAVE_VA_LIST 1
   1224 
   1225 #if defined (__cplusplus)
   1226 extern "C" {
   1227 #endif
   1228 
   1229 #define mpfr_vprintf __gmpfr_vprintf
   1230 #define mpfr_vasprintf __gmpfr_vasprintf
   1231 #define mpfr_vsprintf __gmpfr_vsprintf
   1232 #define mpfr_vsnprintf __gmpfr_vsnprintf
   1233 __MPFR_DECLSPEC int mpfr_vprintf (const char*, va_list);
   1234 __MPFR_DECLSPEC int mpfr_vasprintf (char**, const char*, va_list);
   1235 __MPFR_DECLSPEC int mpfr_vsprintf (char*, const char*, va_list);
   1236 __MPFR_DECLSPEC int mpfr_vsnprintf (char*, size_t, const char*, va_list);
   1237 
   1238 #if defined (__cplusplus)
   1239 }
   1240 #endif
   1241 
   1242 # endif /* _MPFR_H_HAVE_VA_LIST */
   1243 #endif
   1244 
   1245 
   1246 /* check if <stdarg.h> has been included and if FILE is available
   1247    (see above) */
   1248 #if defined (_MPFR_H_HAVE_VA_LIST) && defined (_MPFR_H_HAVE_FILE)
   1249 # ifndef _MPFR_H_HAVE_VA_LIST_FILE
   1250 # define _MPFR_H_HAVE_VA_LIST_FILE 1
   1251 
   1252 #if defined (__cplusplus)
   1253 extern "C" {
   1254 #endif
   1255 
   1256 #define mpfr_vfprintf __gmpfr_vfprintf
   1257 __MPFR_DECLSPEC int mpfr_vfprintf (FILE*, const char*, va_list);
   1258 
   1259 #if defined (__cplusplus)
   1260 }
   1261 #endif
   1262 
   1263 # endif /* _MPFR_H_HAVE_VA_LIST_FILE */
   1264 #endif
   1265