src/mpfr-impl.h - master - niceSOFT/mpfr

src/mpfr-impl.h
2 867 строк129 KB
Vincent Lefevre
[src/mpfr-impl.h] Updated comment about UBF and aliasing issues.
17 июл 2026, 15:10
17 июл 2026, 15:102be4ee7
/* Utilities for MPFR developers, not exported.

Copyright 1999-2026 Free Software Foundation, Inc.
Contributed by the Pascaline 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/>. */

#ifndef __MPFR_IMPL_H__
#define __MPFR_IMPL_H__

/* Include config.h before using ANY configure macros if needed. */
#ifdef HAVE_CONFIG_H
# include "config.h"
#endif


/******************************************************
 *****************  Standard headers  *****************
 ******************************************************/

/* Let's include some standard headers unconditionally as they are
   already needed by several source files or when some options are
   enabled/disabled, and it is easy to forget them (some configure
   options may hide the error).
   Note: If some source file must not have such a header included
   (which is very unlikely and probably means something broken in
   this source file), we should do that with some macro (that would
   also force to disable incompatible features). */

#if defined (__cplusplus)
# include <cstdio>
# include <cstring>
#else
# include <stdio.h>
# include <string.h>
#endif

/* Since <stdio.h> (<cstdio> for C++) is unconditionally included... */
#define MPFR_USE_FILE

#include <stdlib.h>
#include <limits.h>
#include <float.h>  /* for FLT_RADIX, etc., tested below */


/******************************************************
 *****************  Include files  ********************
 ******************************************************/

/* The macros defined in mpfr-cvers.h do not depend on anything,
   so that it is better to include this header file early: then
   it can be used by any other header. */
#include "mpfr-cvers.h"

#if defined(_MPFR_EXP_FORMAT) && _MPFR_EXP_FORMAT == 4
/* mpfr_exp_t will be defined as intmax_t */
# undef MPFR_NEED_INTMAX_H
# define MPFR_NEED_INTMAX_H 1
#endif

#ifdef MPFR_NEED_INTMAX_H
# include "mpfr-intmax.h"
#endif

/* Check if we are inside a build of MPFR or inside the test suite.
   This is needed in mpfr.h to export or import the functions.
   It matters only for Windows DLL */
#ifndef __MPFR_TEST_H__
# define __MPFR_WITHIN_MPFR 1
#endif

/* For the definition of MPFR_THREAD_ATTR. GCC/ICC detection macros are
   no longer used, as they sometimes gave incorrect information about
   the support of thread-local variables. A configure check is now done.
   Also defines macros related to thread locking. */
#if defined(MPFR_WANT_SHARED_CACHE)
# define MPFR_NEED_THREAD_LOCK 1
#endif
#include "mpfr-thread.h"

#ifndef MPFR_USE_MINI_GMP
#include "gmp.h"
#else
#include "mini-gmp.h"
#endif

/* With the current code, MPFR_LONG_WITHIN_LIMB must be defined if an
   unsigned long fits in a limb. Since one cannot rely on the configure
   tests entirely (in particular when GMP is involved) and some platforms
   may not use configure, handle this definition here. A limb (mp_limb_t)
   is normally defined as an unsigned long, but this may not be the case
   with mini-gmp (and we can't rely on __GMP_SHORT_LIMB for this reason).
   So, concerning mp_limb_t, we can only test GMP_NUMB_BITS.
   Chosen heuristic: define MPFR_LONG_WITHIN_LIMB only when
     * mp_limb_t and unsigned long have both 32 bits exactly, or
     * mp_limb_t has at least 64 bits.
   Since we require that mp_limb_t have a size that is a power of 2, we
   can currently be wrong only if mini-gmp is used and unsigned long has
   more than 64 bits, which is unlikely to occur. */
#if GMP_NUMB_BITS >= 64 || (GMP_NUMB_BITS == 32 && ULONG_MAX == 0xffffffff)
# undef MPFR_LONG_WITHIN_LIMB
# define MPFR_LONG_WITHIN_LIMB 1
#endif

#ifdef MPFR_HAVE_GMP_IMPL /* Build with gmp internals */

# ifdef MPFR_USE_MINI_GMP
#  error "MPFR_HAVE_GMP_IMPL and MPFR_USE_MINI_GMP must not be both defined"
# endif
# include "gmp-impl.h"
# ifdef MPFR_NEED_LONGLONG_H
#  include "longlong.h"
# endif
# include "mpfr.h"
# include "mpfr-gmp.h"

#else /* Build without gmp internals */

/* if using mini-gmp, include missing definitions in mini-gmp */
# ifdef MPFR_USE_MINI_GMP
#  include "mpfr-mini-gmp.h"
# endif
# include "mpfr.h"
# include "mpfr-gmp.h"
# ifdef MPFR_LONG_WITHIN_LIMB /* longlong.h is not valid otherwise */
#  ifdef MPFR_NEED_LONGLONG_H
#   define LONGLONG_STANDALONE
#   include "mpfr-longlong.h"
#  endif
# endif

#endif

#undef MPFR_NEED_LONGLONG_H


/******************************************************
 *************  Attribute definitions  ****************
 ******************************************************/

#if defined(MPFR_HAVE_NORETURN)
/* _Noreturn is specified by ISO C11 (Section 6.7.4);
   in GCC, it is supported as of version 4.7. */
# define MPFR_NORETURN _Noreturn
#elif !defined(noreturn)
/* A noreturn macro could be defined if <stdnoreturn.h> has been included,
   in which case it would make sense to #define MPFR_NORETURN noreturn.
   But this is unlikely, as MPFR_HAVE_NORETURN should have been defined
   in such a case. So, in doubt, let us avoid any code that would use a
   noreturn macro, since it could be invalid. */
# if __MPFR_GNUC(3,0) || __MPFR_ICC(8,1,0)
#  define MPFR_NORETURN __attribute__ ((noreturn))
# elif defined(_MSC_VER) && defined(_WIN32) && (_MSC_VER >= 1200)
#  define MPFR_NORETURN __declspec (noreturn)
# endif
#endif
#ifndef MPFR_NORETURN
# define MPFR_NORETURN
#endif

#if __MPFR_GNUC(3,0) || __MPFR_ICC(8,1,0)
# define MPFR_CONST_FUNCTION_ATTR   __attribute__ ((const))
#else
# define MPFR_CONST_FUNCTION_ATTR
#endif

#if __MPFR_GNUC(3,0) || __MPFR_ICC(8,1,0)
# define MPFR_PURE_FUNCTION_ATTR    __attribute__ ((pure))
#else
# define MPFR_PURE_FUNCTION_ATTR
#endif

/* The hot attribute on a function is used to inform the compiler
   that the function is a hot spot of the compiled program. */
#if __MPFR_GNUC(4,3)
# define MPFR_HOT_FUNCTION_ATTR     __attribute__ ((hot))
#else
# define MPFR_HOT_FUNCTION_ATTR
#endif

/* The cold attribute on functions is used to inform the compiler
   that the function is unlikely to be executed. */
#if __MPFR_GNUC(4,3)
# define MPFR_COLD_FUNCTION_ATTR    __attribute__ ((cold))
#else
# define MPFR_COLD_FUNCTION_ATTR
#endif

/* Add MPFR_MAYBE_UNUSED after a variable declaration to avoid compiler
   warnings if it is not used.
   TODO: To be replaced by the future maybe_unused attribute (C2x) once
   supported. */
#if __MPFR_GNUC(3,4)
#define MPFR_MAYBE_UNUSED __attribute__ ((unused))
#else
#define MPFR_MAYBE_UNUSED
#endif

/* This MPFR_FALLTHROUGH macro allows one to make fallthrough in switch case
   explicit. Use this macro at the end of a switch case if it falls through,
   in order to avoid a -Wimplicit-fallthrough warning. */
#if __MPFR_GNUC(7,0)
#define MPFR_FALLTHROUGH __attribute__ ((fallthrough))
#else
#define MPFR_FALLTHROUGH
#endif



/******************************************************
 ***  Global internal variables and related macros  ***
 ******************************************************/

#if defined (__cplusplus)
extern "C" {
#endif

#if defined(MPFR_WANT_SHARED_CACHE)
# define MPFR_CACHE_ATTR
#else
# define MPFR_CACHE_ATTR MPFR_THREAD_ATTR
#endif

/* Note: The following structure and types depend on the MPFR build options
   (including compiler options), due to the various locking methods affecting
   MPFR_DEFERRED_INIT_SLAVE_DECL and MPFR_LOCK_DECL. But since this is only
   internal, that's OK. */
struct __gmpfr_cache_s {
  mpfr_t x;
  int inexact;
  int (*func)(mpfr_ptr, mpfr_rnd_t);
  MPFR_DEFERRED_INIT_SLAVE_DECL()
  MPFR_LOCK_DECL(lock)
};
typedef struct __gmpfr_cache_s mpfr_cache_t[1];
typedef struct __gmpfr_cache_s *mpfr_cache_ptr;

#if __GMP_LIBGMP_DLL
# define MPFR_WIN_THREAD_SAFE_DLL 1
#endif

#if defined(__MPFR_WITHIN_MPFR) || !defined(MPFR_WIN_THREAD_SAFE_DLL)
extern MPFR_THREAD_ATTR mpfr_flags_t __gmpfr_flags;
extern MPFR_THREAD_ATTR mpfr_exp_t   __gmpfr_emin;
extern MPFR_THREAD_ATTR mpfr_exp_t   __gmpfr_emax;
extern MPFR_THREAD_ATTR mpfr_prec_t  __gmpfr_default_fp_bit_precision;
extern MPFR_THREAD_ATTR mpfr_rnd_t   __gmpfr_default_rounding_mode;
extern MPFR_CACHE_ATTR  mpfr_cache_t __gmpfr_cache_const_euler;
extern MPFR_CACHE_ATTR  mpfr_cache_t __gmpfr_cache_const_catalan;
# ifndef MPFR_USE_LOGGING
extern MPFR_CACHE_ATTR  mpfr_cache_t __gmpfr_cache_const_pi;
extern MPFR_CACHE_ATTR  mpfr_cache_t __gmpfr_cache_const_log2;
# else
/* Two constants are used by the logging functions (via mpfr_fprintf,
   then mpfr_log, for the base conversion): pi and log(2). Since the
   mpfr_cache function isn't re-entrant when working on the same cache,
   we need to define two caches for each constant. */
extern MPFR_CACHE_ATTR  mpfr_cache_t   __gmpfr_normal_pi;
extern MPFR_CACHE_ATTR  mpfr_cache_t   __gmpfr_normal_log2;
extern MPFR_CACHE_ATTR  mpfr_cache_t   __gmpfr_logging_pi;
extern MPFR_CACHE_ATTR  mpfr_cache_t   __gmpfr_logging_log2;
extern MPFR_CACHE_ATTR  mpfr_cache_ptr __gmpfr_cache_const_pi;
extern MPFR_CACHE_ATTR  mpfr_cache_ptr __gmpfr_cache_const_log2;
# endif
#endif

#ifdef MPFR_WIN_THREAD_SAFE_DLL
# define MPFR_MAKE_VARFCT(T,N) T * N ## _f (void) { return &N; }
__MPFR_DECLSPEC mpfr_flags_t * __gmpfr_flags_f (void);
__MPFR_DECLSPEC mpfr_exp_t *   __gmpfr_emin_f (void);
__MPFR_DECLSPEC mpfr_exp_t *   __gmpfr_emax_f (void);
__MPFR_DECLSPEC mpfr_prec_t *  __gmpfr_default_fp_bit_precision_f (void);
__MPFR_DECLSPEC mpfr_rnd_t *   __gmpfr_default_rounding_mode_f (void);
__MPFR_DECLSPEC mpfr_cache_t * __gmpfr_cache_const_euler_f (void);
__MPFR_DECLSPEC mpfr_cache_t * __gmpfr_cache_const_catalan_f (void);
# ifndef MPFR_USE_LOGGING
__MPFR_DECLSPEC mpfr_cache_t * __gmpfr_cache_const_pi_f (void);
__MPFR_DECLSPEC mpfr_cache_t * __gmpfr_cache_const_log2_f (void);
# else
__MPFR_DECLSPEC mpfr_cache_t *   __gmpfr_normal_pi_f (void);
__MPFR_DECLSPEC mpfr_cache_t *   __gmpfr_normal_log2_f (void);
__MPFR_DECLSPEC mpfr_cache_t *   __gmpfr_logging_pi_f (void);
__MPFR_DECLSPEC mpfr_cache_t *   __gmpfr_logging_log2_f (void);
__MPFR_DECLSPEC mpfr_cache_ptr * __gmpfr_cache_const_pi_f (void);
__MPFR_DECLSPEC mpfr_cache_ptr * __gmpfr_cache_const_log2_f (void);
# endif
# ifndef __MPFR_WITHIN_MPFR
#  define __gmpfr_flags                    (*__gmpfr_flags_f())
#  define __gmpfr_emin                     (*__gmpfr_emin_f())
#  define __gmpfr_emax                     (*__gmpfr_emax_f())
#  define __gmpfr_default_fp_bit_precision (*__gmpfr_default_fp_bit_precision_f())
#  define __gmpfr_default_rounding_mode    (*__gmpfr_default_rounding_mode_f())
#  define __gmpfr_cache_const_euler        (*__gmpfr_cache_const_euler_f())
#  define __gmpfr_cache_const_catalan      (*__gmpfr_cache_const_catalan_f())
#  ifndef MPFR_USE_LOGGING
#   define __gmpfr_cache_const_pi         (*__gmpfr_cache_const_pi_f())
#   define __gmpfr_cache_const_log2       (*__gmpfr_cache_const_log2_f())
#  else
#   define __gmpfr_normal_pi              (*__gmpfr_normal_pi_f())
#   define __gmpfr_logging_pi             (*__gmpfr_logging_pi_f())
#   define __gmpfr_logging_log2           (*__gmpfr_logging_log2_f())
#   define __gmpfr_cache_const_pi         (*__gmpfr_cache_const_pi_f())
#   define __gmpfr_cache_const_log2       (*__gmpfr_cache_const_log2_f())
#  endif
# endif
#else
# define MPFR_MAKE_VARFCT(T,N)
#endif

# define MPFR_THREAD_VAR(T,N,V)    \
  MPFR_THREAD_ATTR T N = (V);      \
  MPFR_MAKE_VARFCT (T,N)

#define BASE_MAX 62
__MPFR_DECLSPEC extern const __mpfr_struct __gmpfr_l2b[BASE_MAX-1][2];

/* Warning! These constants may be out of range if the exponent range is
   very reduced. Do not use them in such a case, except when explicitly
   allowed (e.g., see comments in cmp.c, cmpabs.c and comparisons.c). */
__MPFR_DECLSPEC extern const mpfr_t __gmpfr_one;
__MPFR_DECLSPEC extern const mpfr_t __gmpfr_two;
__MPFR_DECLSPEC extern const mpfr_t __gmpfr_four;
__MPFR_DECLSPEC extern const mpfr_t __gmpfr_mone;
__MPFR_DECLSPEC extern const mpfr_t __gmpfr_const_log2_RNDD;
__MPFR_DECLSPEC extern const mpfr_t __gmpfr_const_log2_RNDU;

#if defined (__cplusplus)
 }
#endif

/* Replace some common functions for direct access to the global vars.
   The casts prevent these macros from being used as a lvalue (and this
   method makes sure that the expressions have the correct type). */

#define mpfr_get_emin() ((mpfr_exp_t) __gmpfr_emin)
#define mpfr_get_emax() ((mpfr_exp_t) __gmpfr_emax)
#define mpfr_get_default_rounding_mode() \
  ((mpfr_rnd_t) __gmpfr_default_rounding_mode)
#define mpfr_get_default_prec() \
  ((mpfr_prec_t) __gmpfr_default_fp_bit_precision)

/* Flags related macros. */
/* Note: Function-like macros that modify __gmpfr_flags are not defined
   because of the risk to break the sequence point rules if two such
   macros are used in the same expression (without a sequence point
   between). For instance, mpfr_sgn currently uses mpfr_set_erangeflag,
   which mustn't be implemented as a macro for this reason. */

#define mpfr_flags_test(mask) \
  (__gmpfr_flags & (mpfr_flags_t) (mask))

#if MPFR_FLAGS_ALL <= INT_MAX
#define mpfr_underflow_p() \
  ((int) (__gmpfr_flags & MPFR_FLAGS_UNDERFLOW))
#define mpfr_overflow_p() \
  ((int) (__gmpfr_flags & MPFR_FLAGS_OVERFLOW))
#define mpfr_nanflag_p() \
  ((int) (__gmpfr_flags & MPFR_FLAGS_NAN))
#define mpfr_inexflag_p() \
  ((int) (__gmpfr_flags & MPFR_FLAGS_INEXACT))
#define mpfr_erangeflag_p() \
  ((int) (__gmpfr_flags & MPFR_FLAGS_ERANGE))
#define mpfr_divby0_p() \
  ((int) (__gmpfr_flags & MPFR_FLAGS_DIVBY0))
#endif

/* Use a do-while statement for the following macros in order to prevent
   one from using them in an expression, as the sequence point rules could
   be broken if __gmpfr_flags is assigned twice in the same expression
   (via macro expansions). For instance, the mpfr_sgn macro currently uses
   mpfr_set_erangeflag, which mustn't be implemented as a function-like
   macro for this reason. It is not clear whether an expression with
   sequence points, like (void) (0, __gmpfr_flags = 0), would avoid UB. */
#define MPFR_CLEAR_FLAGS() \
  do __gmpfr_flags = 0; while (0)
#define MPFR_CLEAR_UNDERFLOW() \
  do __gmpfr_flags &= MPFR_FLAGS_ALL ^ MPFR_FLAGS_UNDERFLOW; while (0)
#define MPFR_CLEAR_OVERFLOW() \
  do __gmpfr_flags &= MPFR_FLAGS_ALL ^ MPFR_FLAGS_OVERFLOW; while (0)
#define MPFR_CLEAR_DIVBY0() \
  do __gmpfr_flags &= MPFR_FLAGS_ALL ^ MPFR_FLAGS_DIVBY0; while (0)
#define MPFR_CLEAR_NANFLAG() \
  do __gmpfr_flags &= MPFR_FLAGS_ALL ^ MPFR_FLAGS_NAN; while (0)
#define MPFR_CLEAR_INEXFLAG() \
  do __gmpfr_flags &= MPFR_FLAGS_ALL ^ MPFR_FLAGS_INEXACT; while (0)
#define MPFR_CLEAR_ERANGEFLAG() \
  do __gmpfr_flags &= MPFR_FLAGS_ALL ^ MPFR_FLAGS_ERANGE; while (0)
#define MPFR_SET_UNDERFLOW() \
  do __gmpfr_flags |= MPFR_FLAGS_UNDERFLOW; while (0)
#define MPFR_SET_OVERFLOW() \
  do __gmpfr_flags |= MPFR_FLAGS_OVERFLOW; while (0)
#define MPFR_SET_DIVBY0() \
  do __gmpfr_flags |= MPFR_FLAGS_DIVBY0; while (0)
#define MPFR_SET_NANFLAG() \
  do __gmpfr_flags |= MPFR_FLAGS_NAN; while (0)
#define MPFR_SET_INEXFLAG() \
  do __gmpfr_flags |= MPFR_FLAGS_INEXACT; while (0)
#define MPFR_SET_ERANGEFLAG() \
  do __gmpfr_flags |= MPFR_FLAGS_ERANGE; while (0)

/* Testing an exception flag correctly is tricky. There are mainly two
   pitfalls: First, one needs to remember to clear the corresponding
   flag, in case it was set before the function call or during some
   intermediate computations (in practice, one can clear all the flags).
   Secondly, one needs to test the flag early enough, i.e. before it
   can be modified by another function. Moreover, it is quite difficult
   (if not impossible) to reliably check problems with "make check". To
   avoid these pitfalls, it is recommended to use the following macros.
   Other use of the exception-flag predicate functions/macros will be
   detected by mpfrlint.
   Note: _op can be either a statement or an expression.
   MPFR_BLOCK_EXCEP should be used only inside a block; it is useful to
   detect some exception in order to exit the block as soon as possible. */
#define MPFR_BLOCK_DECL(_flags) mpfr_flags_t _flags
/* The (void) (_flags) makes sure that _flags is read at least once (it
   makes sense to use MPFR_BLOCK while _flags will never be read in the
   source, so that we wish to avoid the corresponding warning). */
#define MPFR_BLOCK(_flags,_op)          \
  do                                    \
    {                                   \
      MPFR_CLEAR_FLAGS ();              \
      _op;                              \
      (_flags) = __gmpfr_flags;         \
      (void) (_flags);                  \
    }                                   \
  while (0)
#define MPFR_BLOCK_TEST(_flags,_f) MPFR_UNLIKELY ((_flags) & (_f))
#define MPFR_BLOCK_EXCEP (__gmpfr_flags & (MPFR_FLAGS_UNDERFLOW | \
                                           MPFR_FLAGS_OVERFLOW | \
                                           MPFR_FLAGS_DIVBY0 | \
                                           MPFR_FLAGS_NAN))
/* Let's use a MPFR_ prefix, because e.g. OVERFLOW is defined by glibc's
   math.h, though this is not a reserved identifier! */
#define MPFR_UNDERFLOW(_flags)  MPFR_BLOCK_TEST (_flags, MPFR_FLAGS_UNDERFLOW)
#define MPFR_OVERFLOW(_flags)   MPFR_BLOCK_TEST (_flags, MPFR_FLAGS_OVERFLOW)
#define MPFR_NANFLAG(_flags)    MPFR_BLOCK_TEST (_flags, MPFR_FLAGS_NAN)
#define MPFR_INEXFLAG(_flags)   MPFR_BLOCK_TEST (_flags, MPFR_FLAGS_INEXACT)
#define MPFR_ERANGEFLAG(_flags) MPFR_BLOCK_TEST (_flags, MPFR_FLAGS_ERANGE)
#define MPFR_DIVBY0(_flags)     MPFR_BLOCK_TEST (_flags, MPFR_FLAGS_DIVBY0)


/******************************************************
 *******************  Assertions  *********************
 ******************************************************/

/* MPFR_WANT_ASSERT can take 4 values (the default value is 0):
   -1 (or below): Do not check any assertion. Discouraged, in particular
     for a shared library (for time-critical applications, LTO with a
     static library should also be used anyway).
   0: Check normal assertions.
   1: Check debugging assertions too.
   2 (or above): Additional checks that may take time. For instance,
     some functions may be tested by using two different implementations
     and comparing the results.
*/

/* Note: do not use GMP macros ASSERT_ALWAYS and ASSERT as they are not
   expressions, and as a consequence, they cannot be used in a for(),
   with a comma operator and so on. */

/* MPFR_ASSERTN(expr): assertions that should normally be checked,
     otherwise give a hint to the compiler.
   MPFR_ASSERTD(expr): assertions that should be checked when testing,
     otherwise give a hint to the compiler.
   MPFR_DBGRES(assignment): to be used when the result is tested only
     in an MPFR_ASSERTD expression (in order to avoid a warning, e.g.
     with GCC's -Wunused-but-set-variable, in non-debug mode).
     Note: WG14/N2270 proposed a maybe_unused attribute, which could
     be useful to avoid MPFR_DBGRES. See:
       https://www.open-std.org/jtc1/sc22/wg14/www/docs/n2270.pdf
   Note: Evaluating expr might yield side effects, but such side effects
   must not change the results (except by yielding an assertion failure).
   If MPFR_ASSERT* is used as a left expression of a comma operator, make
   sure to protect the full expression with parentheses in order to avoid
   a compilation error when it appears in a function or macro argument.
   For instance, do not write
     bp[MPFR_ASSERTD (k >= 0), k]
   but
     bp[(MPFR_ASSERTD (k >= 0), k)]
   because
     MPFR_UNLIKELY (bp[MPFR_ASSERTD (k >= 0), k] == 0)
   would be invalid (it may also be better to put the assertion earlier
   to improve the readability of the code, if possible).
*/
#ifndef MPFR_WANT_ASSERT
# define MPFR_WANT_ASSERT 0
#endif

#if MPFR_WANT_ASSERT < 0
# undef MPFR_EXP_CHECK
# define MPFR_ASSERTN(expr)  MPFR_ASSUME (expr)
#else
# define MPFR_ASSERTN(expr)  \
  ((void) ((MPFR_LIKELY(expr)) || (ASSERT_FAIL(expr),MPFR_ASSUME(expr),0)))
/* Some explanations: mpfr_assert_fail is not marked as "no return",
   so that ((void) ((MPFR_LIKELY(expr)) || (ASSERT_FAIL(expr),0)))
   cannot be a way to tell the compiler that after this code, expr is
   necessarily true. The MPFR_ASSUME(expr) is a way to tell the compiler
   that if expr is false, then ASSERT_FAIL(expr) does not return
   (otherwise they would be a contradiction / UB when MPFR_ASSUME(expr)
   is reached). Such information is useful to avoid warnings like those
   from -Wmaybe-uninitialized, e.g. in tests/turandom.c r11663 on t[0]
   from "mpfr_equal_p (y, t[0])".
   TODO: Remove the MPFR_ASSUME(expr) once mpfr_assert_fail is marked as
   "no return".
 */
#endif

#if MPFR_WANT_ASSERT > 0
# define MPFR_EXP_CHECK 1
# define MPFR_ASSERTD(expr)  MPFR_ASSERTN (expr)
# define MPFR_DBGRES(A)      (A)
#else
# define MPFR_ASSERTD(expr)  MPFR_ASSUME (expr)
# define MPFR_DBGRES(A)      ((void) (A))
#endif

/* MPFR_ASSUME is like assert(), but it is a hint to a compiler about a
   statement of fact in a function call free expression, which allows
   the compiler to generate better machine code.
   __builtin_unreachable has been introduced in GCC 4.5 but it works
   fine since 4.8 only (before it may generate unoptimized code if there
   are more than one decision).
   Note:
     The goal of MPFR_ASSUME() is to allow the compiler to optimize even
     more. Thus we need to make sure that its use in MPFR will never yield
     code generation. Since MPFR_ASSUME() may be used by MPFR_ASSERTN()
     and MPFR_ASSERTD(), whose expression might have side effects, we need
     to make sure that the expression x is not evaluated in such a case.
     This is done with __builtin_constant_p (!!(x) || !(x)), whose value
     is 0 if x has side effects, and normally 1 if the compiler knows that
     x has no side effects (since here, it can deduce that !!(x) || !(x)
     is equivalent to the constant 1). In the former case, MPFR_ASSUME(x)
     will give (void) 0, and in the latter case, it will give:
       (x) ? (void) 0 : __builtin_unreachable()
   In the development code, it is better to use MPFR_ASSERTD than
   MPFR_ASSUME, since it'll check if the condition is true in debug
   build.
*/
#if defined(MPFR_HAVE_BUILTIN_UNREACHABLE) && __MPFR_GNUC(4, 8)
# define MPFR_ASSUME(x)                                 \
    (! __builtin_constant_p (!!(x) || !(x)) || (x) ?    \
     (void) 0 : __builtin_unreachable())
#elif defined(_MSC_VER)
# define MPFR_ASSUME(x) __assume(x)
#else
# define MPFR_ASSUME(x) ((void) 0)
#endif

#include "mpfr-sassert.h"

/* Code to deal with impossible, for functions returning an int.
   The "return 0;" avoids an error with current GCC versions and
   "-Werror=return-type".
   WARNING: It doesn't use do { } while (0) for Insure++ */
#if defined(HAVE_BUILTIN_UNREACHABLE)
# define MPFR_RET_NEVER_GO_HERE() do { __builtin_unreachable(); } while (0)
#else
# define MPFR_RET_NEVER_GO_HERE() do { MPFR_ASSERTN(0); return 0; } while (0)
#endif


/******************************************************
 *******************  Warnings  ***********************
 ******************************************************/

/* MPFR_WARNING is no longer useful, but let's keep the macro in case
   it needs to be used again in the future. */

#ifdef MPFR_USE_WARNINGS
# define MPFR_WARNING(W)                    \
  do                                        \
    {                                       \
      char *q = getenv ("MPFR_QUIET");      \
      if (q == NULL || *q == 0)             \
        fprintf (stderr, "MPFR: %s\n", W);  \
    }                                       \
  while (0)
#else
# define MPFR_WARNING(W)  ((void) 0)
#endif


/******************************************************
 *****************  double macros  ********************
 ******************************************************/

/* Precision used for lower precision computations */
#define MPFR_SMALL_PRECISION 32

/* Definition of constants */
#define LOG2 0.69314718055994528622 /* log(2) rounded to zero on 53 bits */

/* MPFR_DOUBLE_SPEC = 1 if the C type 'double' corresponds to IEEE-754
   double precision, 0 if it doesn't, and undefined if one doesn't know.
   On all the tested machines, MPFR_DOUBLE_SPEC = 1. To have this macro
   defined here, #include <float.h> is needed. If need be, other values
   could be defined for other specs (once they are known). */
#if !defined(MPFR_DOUBLE_SPEC) && defined(FLT_RADIX) && \
    defined(DBL_MANT_DIG) && defined(DBL_MIN_EXP) && defined(DBL_MAX_EXP)
# if FLT_RADIX == 2 && DBL_MANT_DIG == 53 && \
     DBL_MIN_EXP == -1021 && DBL_MAX_EXP == 1024
#  define MPFR_DOUBLE_SPEC 1
# else
#  define MPFR_DOUBLE_SPEC 0
# endif
#endif

/* With -DMPFR_DISABLE_IEEE_FLOATS, exercise non IEEE floats */
#ifdef MPFR_DISABLE_IEEE_FLOATS
# ifdef _MPFR_IEEE_FLOATS
#  undef _MPFR_IEEE_FLOATS
# endif
# define _MPFR_IEEE_FLOATS 0
# undef HAVE_LDOUBLE_IS_DOUBLE
# undef HAVE_LDOUBLE_IEEE_EXT_LITTLE
# undef HAVE_LDOUBLE_IEEE_EXT_BIG
# undef HAVE_LDOUBLE_IEEE_QUAD_BIG
# undef HAVE_LDOUBLE_IEEE_QUAD_LITTLE
#endif

#ifndef IEEE_DBL_MANT_DIG
#define IEEE_DBL_MANT_DIG 53
#endif
#define MPFR_LIMBS_PER_DOUBLE ((IEEE_DBL_MANT_DIG-1)/GMP_NUMB_BITS+1)

#ifndef IEEE_FLT_MANT_DIG
#define IEEE_FLT_MANT_DIG 24
#endif
#define MPFR_LIMBS_PER_FLT ((IEEE_FLT_MANT_DIG-1)/GMP_NUMB_BITS+1)

/* Visual C++ doesn't support +1.0/0.0, -1.0/0.0 and 0.0/0.0
   at compile time.
   Clang with -fsanitize=undefined is a bit similar due to a bug:
     https://llvm.org/bugs/show_bug.cgi?id=17381 (fixed on 2015-12-03)
   but even without its sanitizer, it may be better to use the
   double_zero version until IEEE 754 division by zero is properly
   supported:
     https://llvm.org/bugs/show_bug.cgi?id=17005
   Note: DBL_NAN is 0/0, thus its value is a quiet NaN (qNAN).
*/
#if (defined(_MSC_VER) && defined(_WIN32) && (_MSC_VER >= 1200)) || \
    defined(__clang__)
static double double_zero = 0.0;
# define DBL_NAN (double_zero/double_zero)
# define DBL_POS_INF ((double) 1.0/double_zero)
# define DBL_NEG_INF ((double)-1.0/double_zero)
# define DBL_NEG_ZERO (-double_zero)
#else
# define DBL_POS_INF ((double) 1.0/0.0)
# define DBL_NEG_INF ((double)-1.0/0.0)
# define DBL_NAN     ((double) 0.0/0.0)
# define DBL_NEG_ZERO (-0.0)
#endif

/* Note: In the past, there was specific code for _MPFR_IEEE_FLOATS, which
   was based on NaN and Inf memory representations. This code was breaking
   the aliasing rules (see ISO C99, 6.5#6 and 6.5#7 on the effective type)
   and for this reason it did not behave correctly with GCC 4.5.0 20091119.
   The code needed a memory transfer and was probably not better than the
   macros below with a good compiler (a fix based on the NaN / Inf memory
   representation would be even worse due to C limitations), and this code
   could be selected only when MPFR was built with --with-gmp-build, thus
   introducing a difference (bad for maintaining/testing MPFR); therefore
   it has been removed. The old code required that the argument x be an
   lvalue of type double. We still require that, in case one would need
   to change the macros below, e.g. for some broken compiler. But the
   LVALUE(x) condition could be removed if really necessary. */
/* Below, the &(x) == &(x) || &(x) != &(x) allows to make sure that x
   is a lvalue without (probably) any warning from the compiler.  The
   &(x) != &(x) is needed to avoid a failure under Mac OS X 10.4.11
   (with Xcode 2.4.1, i.e. the latest one). */
#define LVALUE(x) (&(x) == &(x) || &(x) != &(x))
#define DOUBLE_ISINF(x) (LVALUE(x) && ((x) > DBL_MAX || (x) < -DBL_MAX))
/* The DOUBLE_ISNAN(x) macro must be valid with any real floating type,
   thus constants must be of integer type (e.g. 0). */
#if defined(MPFR_NANISNAN) || (__MPFR_GNUC(1,0) && !defined(__STRICT_ANSI__))
/* Avoid MIPSpro / IRIX64 / GCC (incorrect) optimizations.
   The + must not be replaced by a ||. With gcc -ffast-math, NaN is
   regarded as a positive number or something like that; the second
   test catches this case.
   [2016-03-01] Various tests now fail with gcc -ffast-math or just
   -ffinite-math-only; such options are not supported, but this makes
   difficult to test MPFR assuming x == x optimization to 1. Anyway
   support of functions/tests of using native FP and special values for
   non-IEEE-754 environment will always be on a case-by-case basis.
   [2018-06-02] Let's use this macro instead of the usual (x) != (x) test
   with all GCC versions except in ISO C mode[*], as due to
     https://gcc.gnu.org/bugzilla/show_bug.cgi?id=323
   there is no guarantee that (x) != (x) will be true only for NaN.
   Testing __STRICT_ANSI__ is suggested in:
     https://gcc.gnu.org/bugzilla/show_bug.cgi?id=85995
   but this is not safe if the user adds a -f option affecting conformance,
   in which case this would be a user error (however, note that the
   configure test associated with MPFR_NANISNAN will catch some issues).
   Note that this macro may raise FP flags due to the multiplication.
   See <https://gitlab.inria.fr/mpfr/mpfr/-/issues/2>.
*/
# define DOUBLE_ISNAN(x) \
    (LVALUE(x) && !((((x) >= 0) + ((x) <= 0)) && -(x)*(x) <= 0))
#else
# define DOUBLE_ISNAN(x) (LVALUE(x) && (x) != (x))
#endif


/******************************************************
 **********  long double macros and typedef  **********
 ******************************************************/

/* We try to get the exact value of the precision of long double
   (provided by the implementation) in order to provide correct
   rounding in this case (not guaranteed if the C implementation
   does not have an adequate long double arithmetic). Note that
   it may be lower than the precision of some numbers that can
   be represented in a long double; e.g. on FreeBSD/x86, it is
   53 because the processor is configured to round in double
   precision (even when using the long double type -- this is a
   limitation of the x87 arithmetic), and on Mac OS X, it is 106
   because the implementation is a double-double arithmetic.
   Otherwise (e.g. in base 10), we get an upper bound of the
   precision, and correct rounding isn't currently provided.
*/

/* Definitions are enabled only if <float.h> is included. */
#if defined (FLT_RADIX)

#if defined(LDBL_MANT_DIG) && FLT_RADIX == 2
# define MPFR_LDBL_MANT_DIG LDBL_MANT_DIG
#else
# define MPFR_LDBL_MANT_DIG \
  (sizeof(long double)*GMP_NUMB_BITS/sizeof(mp_limb_t))
#endif

/* LONGDOUBLE_NAN_ACTION executes the code "action" if x is a NaN. */

/* On hppa2.0n-hp-hpux10 with the unbundled HP cc, the test x!=x on a NaN
   has been seen false, meaning NaNs are not detected.  This seemed to
   happen only after other comparisons, not sure what's really going on.  In
   any case we can pick apart the bytes to identify a NaN.  */
#ifdef HAVE_LDOUBLE_IEEE_QUAD_BIG
# define LONGDOUBLE_NAN_ACTION(x, action)                       \
  do {                                                          \
    union {                                                     \
      long double    ld;                                        \
      struct {                                                  \
        unsigned int sign : 1;                                  \
        unsigned int exp  : 15;                                 \
        unsigned int man3 : 16;                                 \
        unsigned int man2 : 32;                                 \
        unsigned int man1 : 32;                                 \
        unsigned int man0 : 32;                                 \
      } s;                                                      \
    } u;                                                        \
    u.ld = (x);                                                 \
    if (u.s.exp == 0x7FFFL                                      \
        && (u.s.man0 | u.s.man1 | u.s.man2 | u.s.man3) != 0)    \
      { action; }                                               \
  } while (0)
#endif

#ifdef HAVE_LDOUBLE_IEEE_QUAD_LITTLE
# define LONGDOUBLE_NAN_ACTION(x, action)                       \
  do {                                                          \
    union {                                                     \
      long double    ld;                                        \
      struct {                                                  \
        unsigned int man0 : 32;                                 \
        unsigned int man1 : 32;                                 \
        unsigned int man2 : 32;                                 \
        unsigned int man3 : 16;                                 \
        unsigned int exp  : 15;                                 \
        unsigned int sign : 1;                                  \
      } s;                                                      \
    } u;                                                        \
    u.ld = (x);                                                 \
    if (u.s.exp == 0x7FFFL                                      \
        && (u.s.man0 | u.s.man1 | u.s.man2 | u.s.man3) != 0)    \
      { action; }                                               \
  } while (0)
#endif

/* Under IEEE rules, NaN is not equal to anything, including itself.
   "volatile" here stops "cc" on mips64-sgi-irix6.5 from optimizing away
   x!=x. */
#ifndef LONGDOUBLE_NAN_ACTION
# define LONGDOUBLE_NAN_ACTION(x, action)               \
  do {                                                  \
    volatile long double __x = LONGDOUBLE_VOLATILE (x); \
    if ((x) != __x)                                     \
      { action; }                                       \
  } while (0)

/* Some compilers do not have a proper "volatile" and #define volatile
   to empty (to avoid a build failure with programs using "volatile"),
   i.e. "volatile" is just ignored and will not prevent optimizations
   that could potentially break the IEEE rules. In this case, call an
   external function, hoping that the compiler will not optimize. */
# ifdef volatile
__MPFR_DECLSPEC long double
  __gmpfr_longdouble_volatile (long double) MPFR_CONST_FUNCTION_ATTR;
#  define LONGDOUBLE_VOLATILE(x)  (__gmpfr_longdouble_volatile (x))
#  define WANT_GMPFR_LONGDOUBLE_VOLATILE 1
# else
#  define LONGDOUBLE_VOLATILE(x)  (x)
# endif
#endif

/* Some special case for IEEE_EXT Little Endian */
#if HAVE_LDOUBLE_IEEE_EXT_LITTLE

typedef union {
  long double    ld;
  struct {
    unsigned int manl : 32;
    unsigned int manh : 32;
    unsigned int expl : 8 ;
    unsigned int exph : 7;
    unsigned int sign : 1;
  } s;
} mpfr_long_double_t;

#endif /* HAVE_LDOUBLE_IEEE_EXT_LITTLE */

#endif  /* long double macros and typedef */


/******************************************************
 ******************  _FloatN support  *****************
 ******************************************************/

/* This is standardized by IEEE 754-2019 (binary16 and binary128). */
#define IEEE_FLOAT16_MANT_DIG 11
#define IEEE_FLOAT128_MANT_DIG 113


/******************************************************
 ******************  Decimal support  *****************
 ******************************************************/

#ifdef MPFR_WANT_DECIMAL_FLOATS

#if defined(__GNUC__) && \
    __FLT64_DECIMAL_DIG__ == 17 && \
    __FLT128_DECIMAL_DIG__ == 36

/* GCC has standard _Decimal64 and _Decimal128 support.
   We may be able to detect the encoding here at compile time.

   Note: GCC may define __FLT64_DECIMAL_DIG__ and __FLT128_DECIMAL_DIG__
   even when it does not support _Decimal64 and _Decimal128, e.g. on
   aarch64 and sparc64. But since MPFR_WANT_DECIMAL_FLOATS has been
   defined, we already know that these types should be supported.

   Determining which encoding is used via macros is not documented, and
   there is the risk of being wrong. Currently __DECIMAL_BID_FORMAT__ is
   defined on x86, where the BID encoding is used. But on PowerPC, where
   the DPD encoding is used, nothing indicating the encoding is defined.
   A possible reason may be that the decimal support is provided by the
   hardware (in this case), so that GCC does not need to care about the
   encoding. Thus the absence of a __DECIMAL_BID_FORMAT__ macro would
   not necessarily imply DPD, as similarly in the future, GCC could
   support an ISA-level implementation using the BID encoding. */

#ifdef __DECIMAL_BID_FORMAT__

#if defined(DECIMAL_DPD_FORMAT)
# error "Decimal encoding mismatch (DPD assumed, BID detected)"
#elif !defined(DECIMAL_GENERIC_CODE)
# define DECIMAL_BID_FORMAT 1
#endif

#endif  /* __DECIMAL_BID_FORMAT__ */

#endif  /* __GNUC__ */

#if defined(DECIMAL_GENERIC_CODE)
# if defined(DECIMAL_BID_FORMAT)
#  error "DECIMAL_BID_FORMAT and DECIMAL_GENERIC_CODE both defined"
# endif
# if defined(DECIMAL_DPD_FORMAT)
#  error "DECIMAL_DPD_FORMAT and DECIMAL_GENERIC_CODE both defined"
# endif
#elif defined(DECIMAL_BID_FORMAT) || defined(DECIMAL_DPD_FORMAT)
# if defined(DECIMAL_BID_FORMAT) && defined(DECIMAL_DPD_FORMAT)
#  error "DECIMAL_BID_FORMAT and DECIMAL_DPD_FORMAT both defined"
# endif
#else
# define DECIMAL_GENERIC_CODE 1
#endif

/* TODO: The following is ugly and possibly wrong on some platforms.
   Do something like union ieee_decimal128. */
MPFR_EXTENSION
union ieee_double_decimal64 { double d; _Decimal64 d64; };

/* FIXME: There's no reason to make the _Decimal128 code depend on
   whether _MPFR_IEEE_FLOATS is defined or not, as _MPFR_IEEE_FLOATS
   is about binary IEEE-754 floating point only. */
#if _MPFR_IEEE_FLOATS
/* TODO: It would be better to define a different structure for DPD,
   where the t* bit-fields correspond to the declets. And to avoid
   confusion and detect coding errors, these bit-fields should have
   different names for BID and DPD. */
MPFR_EXTENSION
union ieee_decimal128
{
  struct
    {
      /* Assume little-endian double implies little-endian for bit-field
         allocation (C99 says: "The order of allocation of bit-fields
         within a unit (high-order to low-order or low-order to high-order)
         is implementation-defined.") */
#if defined(HAVE_DECIMAL128_IEEE_LITTLE_ENDIAN)
#define HAVE_DECIMAL128_IEEE 1
      unsigned int t3:32;
      unsigned int t2:32;
      unsigned int t1:32;
      unsigned int t0:14;
      unsigned int comb:17;
      unsigned int sig:1;
#elif defined(HAVE_DECIMAL128_IEEE_BIG_ENDIAN)
#define HAVE_DECIMAL128_IEEE 1
      unsigned int sig:1;
      unsigned int comb:17;
      unsigned int t0:14;
      unsigned int t1:32;
      unsigned int t2:32;
      unsigned int t3:32;
#else /* unknown bit-field ordering */
      /* This will not be used as HAVE_DECIMAL128_IEEE is not defined. */
      unsigned int dummy;
#endif
    } s;
  _Decimal128 d128;
};
#endif /* _MPFR_IEEE_FLOATS */

#endif /* MPFR_WANT_DECIMAL_FLOATS */


/******************************************************
 ****************  mpfr_t properties  *****************
 ******************************************************/

#define MPFR_PREC_COND(p) ((p) >= MPFR_PREC_MIN && (p) <= MPFR_PREC_MAX)
#define MPFR_PREC_IN_RANGE(p) (MPFR_ASSERTD (MPFR_PREC_COND(p)), (p))

/* In the following macro, p is usually a mpfr_prec_t, but this macro
   works with other integer types (without integer overflow). Checking
   that p >= 1 in debug mode is useful here because this macro can be
   used on a computed precision (in particular, this formula does not
   work for a degenerate case p = 0, and could give different results
   on different platforms). But let us not use an assertion checking
   in the MPFR_LAST_LIMB() and MPFR_LIMB_SIZE() macros below to avoid
   too much expansion for assertions (in practice, this should be a
   problem just when testing MPFR with the --enable-assert configure
   option and the -ansi -pedantic-errors gcc compiler flags). */
#define MPFR_PREC2LIMBS(p) \
  (MPFR_ASSERTD ((p) >= 1), ((p) - 1) / GMP_NUMB_BITS + 1)

#define MPFR_PREC(x)      ((x)->_mpfr_prec)
#define MPFR_EXP(x)       ((x)->_mpfr_exp)
#define MPFR_MANT(x)      ((x)->_mpfr_d)
#define MPFR_GET_PREC(x)  MPFR_PREC_IN_RANGE (MPFR_PREC (x))
#define MPFR_LAST_LIMB(x) ((MPFR_GET_PREC (x) - 1) / GMP_NUMB_BITS)
#define MPFR_LIMB_SIZE(x) (MPFR_LAST_LIMB (x) + 1)


/******************************************************
 ***************  Exponent properties  ****************
 ******************************************************/

/* Limits of the mpfr_exp_t type (NOT those of valid exponent values).
   These macros can be used in preprocessor directives. */
#if   _MPFR_EXP_FORMAT == 1
# define MPFR_EXP_MAX (SHRT_MAX)
# define MPFR_EXP_MIN (SHRT_MIN)
#elif _MPFR_EXP_FORMAT == 2
# define MPFR_EXP_MAX (INT_MAX)
# define MPFR_EXP_MIN (INT_MIN)
#elif _MPFR_EXP_FORMAT == 3
# define MPFR_EXP_MAX (LONG_MAX)
# define MPFR_EXP_MIN (LONG_MIN)
#elif _MPFR_EXP_FORMAT == 4
/* Note: MPFR_EXP_MAX and MPFR_EXP_MIN must not be used in #if directives
   if _MPFR_EXP_FORMAT == 4 and MPFR_HAVE_INTMAX_MAX is not defined. */
# define MPFR_EXP_MAX (MPFR_INTMAX_MAX)
# define MPFR_EXP_MIN (MPFR_INTMAX_MIN)
#else
# error "Invalid MPFR Exp format"
#endif

/* Before doing a cast to mpfr_uexp_t, make sure that the value is
   non-negative. */
#define MPFR_UEXP(X) (MPFR_ASSERTD ((X) >= 0), (mpfr_uexp_t) (X))

/* Define mpfr_eexp_t, mpfr_ueexp_t and MPFR_EXP_FSPEC.
   Warning! MPFR_EXP_FSPEC is the length modifier associated with
   these types mpfr_eexp_t / mpfr_ueexp_t, not with mpfr_exp_t.
   (Should we change that, or is this safer to detect bugs, e.g.
   in the context of an expression with computations with long?)
*/
#if _MPFR_EXP_FORMAT <= 3
typedef long mpfr_eexp_t;
typedef unsigned long mpfr_ueexp_t;
# define mpfr_get_exp_t(x,r) mpfr_get_si((x),(r))
# define mpfr_set_exp_t(x,e,r) mpfr_set_si((x),(e),(r))
# define MPFR_EXP_FSPEC "l"
#else
typedef intmax_t mpfr_eexp_t;
typedef uintmax_t mpfr_ueexp_t;
# define mpfr_get_exp_t(x,r) mpfr_get_sj((x),(r))
# define mpfr_set_exp_t(x,e,r) mpfr_set_sj((x),(e),(r))
# define MPFR_EXP_FSPEC "j"
#endif

/* Size of mpfr_exp_t in limbs */
#define MPFR_EXP_LIMB_SIZE \
  ((sizeof (mpfr_exp_t) - 1) / MPFR_BYTES_PER_MP_LIMB + 1)

/* Invalid exponent value (to track bugs...).
   MPFR_EXP_MAX has the form 2^n-1; MPFR_EXP_INVALID is 2^(n-1). */
#define MPFR_EXP_INVALID (MPFR_EXP_MAX / 2 + 1)

/* Definition of the exponent limits for MPFR numbers.
 * These limits are chosen so that if e is such an exponent, then 2e-1 and
 * 2e+1 are representable. This is useful for intermediate computations,
 * in particular the multiplication.
 */
#undef MPFR_EMIN_MIN
#undef MPFR_EMIN_MAX
#undef MPFR_EMAX_MIN
#undef MPFR_EMAX_MAX
#define MPFR_EMIN_MIN (1-MPFR_EXP_INVALID)
#define MPFR_EMIN_MAX (MPFR_EXP_INVALID-1)
#define MPFR_EMAX_MIN (1-MPFR_EXP_INVALID)
#define MPFR_EMAX_MAX (MPFR_EXP_INVALID-1)

/* Use MPFR_GET_EXP and MPFR_SET_EXP instead of MPFR_EXP directly, unless
   the exponent may be invalid (or out of range in case of MPFR_SET_EXP),
   for instance when setting the exponent before calling mpfr_check_range.
   MPFR_EXP_CHECK is defined when MPFR_WANT_ASSERT is defined, but if you
   don't use MPFR_WANT_ASSERT (for speed reasons), you can still define
   MPFR_EXP_CHECK by setting -DMPFR_EXP_CHECK in $CFLAGS.
   Note about MPFR_EXP_IN_RANGE and MPFR_SET_EXP:
     The exp expression is required to have a signed type. To avoid spurious
     failures, we could cast (e) to mpfr_exp_t, but this would not allow us
     to detect some bugs that can occur on particular platforms. Anyway, an
     unsigned type for exp is suspicious and should be regarded as a bug.
*/

#define MPFR_EXP_IN_RANGE(e)                                          \
  (MPFR_ASSERTD (IS_SIGNED (e)), (e) >= __gmpfr_emin && (e) <= __gmpfr_emax)

#ifdef MPFR_EXP_CHECK
# define MPFR_GET_EXP(x)          (mpfr_get_exp) (x)
# define MPFR_SET_EXP(x,e)        (MPFR_ASSERTN (MPFR_EXP_IN_RANGE (e)), \
                                   (void) (MPFR_EXP (x) = (e)))
# define MPFR_SET_INVALID_EXP(x)  ((void) (MPFR_EXP (x) = MPFR_EXP_INVALID))
#else
# define MPFR_GET_EXP(x)          MPFR_EXP (x)
# define MPFR_SET_EXP(x,e)        ((void) (MPFR_EXP (x) = (e)))
# define MPFR_SET_INVALID_EXP(x)  ((void) 0)
#endif

/* Compare the exponents of two numbers, which can be either MPFR numbers
   or UBF numbers. */
#define MPFR_UBF_EXP_LESS_P(x,y) \
  (MPFR_UNLIKELY (MPFR_IS_UBF (x) || MPFR_IS_UBF (y)) ? \
   mpfr_ubf_exp_less_p (x, y) : MPFR_GET_EXP (x) < MPFR_GET_EXP (y))


/******************************************************
 *********  Singular values (NAN, INF, ZERO)  *********
 ******************************************************/

/* Enum special value of exponent. */
# define MPFR_EXP_ZERO (MPFR_EXP_MIN+1)
# define MPFR_EXP_NAN  (MPFR_EXP_MIN+2)
# define MPFR_EXP_INF  (MPFR_EXP_MIN+3)
# define MPFR_EXP_UBF  (MPFR_EXP_MIN+4)

#define MPFR_IS_NAN(x)   (MPFR_EXP(x) == MPFR_EXP_NAN)
#define MPFR_SET_NAN(x)  (MPFR_EXP(x) =  MPFR_EXP_NAN)
#define MPFR_IS_INF(x)   (MPFR_EXP(x) == MPFR_EXP_INF)
#define MPFR_SET_INF(x)  (MPFR_EXP(x) =  MPFR_EXP_INF)
#define MPFR_IS_ZERO(x)  (MPFR_EXP(x) == MPFR_EXP_ZERO)
#define MPFR_SET_ZERO(x) (MPFR_EXP(x) =  MPFR_EXP_ZERO)
#define MPFR_NOTZERO(x)  (MPFR_EXP(x) != MPFR_EXP_ZERO)
#define MPFR_IS_UBF(x)   (MPFR_EXP(x) == MPFR_EXP_UBF)
#define MPFR_SET_UBF(x)  (MPFR_EXP(x) =  MPFR_EXP_UBF)

#define MPFR_IS_NORMALIZED(x) \
  (MPFR_LIMB_MSB (MPFR_MANT(x)[MPFR_LAST_LIMB(x)]) != 0)

#define MPFR_IS_FP(x)       (!MPFR_IS_NAN(x) && !MPFR_IS_INF(x))

/* Note: Contrary to the MPFR_IS_PURE_*(x) macros, the MPFR_IS_SINGULAR*(x)
   macros may be used even when x is being constructed, e.g. by a low-level
   algorithm. The exponent field of x must already be set, but it may have
   any value, even less than MPFR_EMIN_MIN or larger than MPFR_EMAX_MAX.
   Any real exponent value must obviously be larger than MPFR_EXP_INF,
   though. The significand field may still contain arbitrary data. Thus
   MPFR_IS_PURE_FP(x) is not always equivalent to !MPFR_IS_SINGULAR(x);
   see the code below. */
#define MPFR_IS_SINGULAR(x) (MPFR_EXP(x) <= MPFR_EXP_INF)
#define MPFR_IS_SINGULAR_OR_UBF(x) (MPFR_EXP(x) <= MPFR_EXP_UBF)

/* The following two macros return true iff the value is a regular number,
   i.e. it is not a singular number. In debug mode, the format is also
   checked: the exponent must be valid, but potentially out of range,
   since such numbers may be acceptable as inputs by some functions
   (e.g. comparisons with constants); the significand must be normalized
   (all functions return numbers with a normalized significand; otherwise
   this indicates a bug). In contexts where UBFs are not accepted or
   not possible, MPFR_IS_PURE_FP is preferable. If UBFs are accepted,
   MPFR_IS_PURE_UBF must be used. */
#define MPFR_IS_PURE_FP(x)                          \
  (!MPFR_IS_SINGULAR(x) &&                          \
   (MPFR_ASSERTD (MPFR_EXP (x) >= MPFR_EMIN_MIN &&  \
                  MPFR_EXP (x) <= MPFR_EMAX_MAX &&  \
                  MPFR_IS_NORMALIZED (x)), 1))
#define MPFR_IS_PURE_UBF(x)                             \
  (!MPFR_IS_SINGULAR(x) &&                              \
   (MPFR_ASSERTD ((MPFR_IS_UBF (x) ||                   \
                   (MPFR_EXP (x) >= MPFR_EMIN_MIN &&    \
                    MPFR_EXP (x) <= MPFR_EMAX_MAX)) &&  \
                  MPFR_IS_NORMALIZED (x)), 1))

/* Ditto for 2 numbers. */
#define MPFR_ARE_SINGULAR(x,y) \
  (MPFR_UNLIKELY(MPFR_IS_SINGULAR(x)) || MPFR_UNLIKELY(MPFR_IS_SINGULAR(y)))
#define MPFR_ARE_SINGULAR_OR_UBF(x,y)           \
  (MPFR_UNLIKELY(MPFR_IS_SINGULAR_OR_UBF(x)) || \
   MPFR_UNLIKELY(MPFR_IS_SINGULAR_OR_UBF(y)))


/******************************************************
 ********************  Sign macros  *******************
 ******************************************************/

/* These are sign macros for MPFR numbers only. */

#define MPFR_SIGN_POS (1)
#define MPFR_SIGN_NEG (-1)

#define MPFR_IS_STRICTPOS(x)  (MPFR_NOTZERO (x) && MPFR_IS_POS (x))
#define MPFR_IS_STRICTNEG(x)  (MPFR_NOTZERO (x) && MPFR_IS_NEG (x))

#define MPFR_IS_NEG(x) (MPFR_SIGN(x) < 0)
#define MPFR_IS_POS(x) (MPFR_SIGN(x) > 0)

#define MPFR_SET_POS(x) (MPFR_SIGN(x) = MPFR_SIGN_POS)
#define MPFR_SET_NEG(x) (MPFR_SIGN(x) = MPFR_SIGN_NEG)

#define MPFR_CHANGE_SIGN(x) (MPFR_SIGN(x) = -MPFR_SIGN(x))
#define MPFR_SET_SAME_SIGN(x, y) (MPFR_SIGN(x) = MPFR_SIGN(y))
#define MPFR_SET_OPPOSITE_SIGN(x, y) (MPFR_SIGN(x) = -MPFR_SIGN(y))
#define MPFR_ASSERT_SIGN(s) \
 (MPFR_ASSERTD((s) == MPFR_SIGN_POS || (s) == MPFR_SIGN_NEG))
#define MPFR_SET_SIGN(x, s) \
  (MPFR_ASSERT_SIGN(s), MPFR_SIGN(x) = s)
#define MPFR_IS_POS_SIGN(s1) ((s1) > 0)
#define MPFR_IS_NEG_SIGN(s1) ((s1) < 0)
#define MPFR_MULT_SIGN(s1, s2) ((s1) * (s2))
/* Transform a sign to 1 or -1 */
#define MPFR_FROM_SIGN_TO_INT(s) (s)
#define MPFR_INT_SIGN(x) MPFR_FROM_SIGN_TO_INT(MPFR_SIGN(x))


/******************************************************
 ***************  Ternary value macros  ***************
 ******************************************************/

/* Special inexact value */
#define MPFR_EVEN_INEX 2

/* Note: the addition/subtraction of 2 comparisons below instead of the
   use of the ?: operator allows GCC and Clang to generate better code
   in general; this is the case at least with GCC on x86 (32 & 64 bits),
   PowerPC and Aarch64 (64-bit ARM), and with Clang on x86_64.
   VSIGN code based on mini-gmp's GMP_CMP macro; adapted for INEXPOS. */

/* Macros for functions returning two inexact values in an 'int'
   (exact = 0, positive = 1, negative = 2) */
#define INEXPOS(y) (((y) != 0) + ((y) < 0))
#define INEX(y,z) (INEXPOS(y) | (INEXPOS(z) << 2))

/* When returning the ternary inexact value, ALWAYS use one of the
   following two macros, unless the flag comes from another function
   returning the ternary inexact value */
#define MPFR_RET(I) return \
  (I) != 0 ? ((__gmpfr_flags |= MPFR_FLAGS_INEXACT), (I)) : 0
#define MPFR_RET_NAN return (__gmpfr_flags |= MPFR_FLAGS_NAN), 0

/* Sign of a native value. */
#define VSIGN(I) (((I) > 0) - ((I) < 0))
#define SAME_SIGN(I1,I2) (VSIGN (I1) == VSIGN (I2))


/******************************************************
 ***************  Rounding mode macros  ***************
 ******************************************************/

/* MPFR_RND_MAX gives the number of supported rounding modes by all functions.
 */
#define MPFR_RND_MAX ((mpfr_rnd_t)((MPFR_RNDF)+1))

/* We want to test this :
 *  (rnd == MPFR_RNDU && test) || (rnd == RNDD && !test)
 * i.e. it transforms RNDU or RNDD to away or zero according to the sign.
 * The argument test must be 0 or 1. */
#define MPFR_IS_RNDUTEST_OR_RNDDNOTTEST(rnd, test) \
  (MPFR_ASSERTD ((test) == 0 || (test) == 1),      \
   ((rnd) + (test)) == MPFR_RNDD)

/* We want to test if rnd rounds toward zero or away from zero.
   'neg' is 1 if negative, and 0 if positive. */
#define MPFR_IS_LIKE_RNDZ(rnd, neg) \
  ((rnd) == MPFR_RNDZ || MPFR_IS_RNDUTEST_OR_RNDDNOTTEST (rnd, neg))
#define MPFR_IS_LIKE_RNDA(rnd, neg) \
  ((rnd) == MPFR_RNDA || MPFR_IS_RNDUTEST_OR_RNDDNOTTEST (rnd, (neg) == 0))

#define MPFR_IS_LIKE_RNDU(rnd, sign)                    \
  (((rnd) == MPFR_RNDU) ||                              \
   ((rnd) == MPFR_RNDZ && MPFR_IS_NEG_SIGN (sign)) ||   \
   ((rnd) == MPFR_RNDA && MPFR_IS_POS_SIGN (sign)))

#define MPFR_IS_LIKE_RNDD(rnd, sign)                    \
  (((rnd) == MPFR_RNDD) ||                              \
   ((rnd) == MPFR_RNDZ && MPFR_IS_POS_SIGN (sign)) ||   \
   ((rnd) == MPFR_RNDA && MPFR_IS_NEG_SIGN (sign)))

/* Invert RNDU and RNDD; the other rounding modes are unchanged. */
#define MPFR_INVERT_RND(rnd) ((rnd) == MPFR_RNDU ? MPFR_RNDD :          \
                              (rnd) == MPFR_RNDD ? MPFR_RNDU : (rnd))

/* Transform RNDU and RNDD to RNDZ according to test */
#define MPFR_UPDATE_RND_MODE(rnd, test)                             \
  do {                                                              \
    if (MPFR_UNLIKELY(MPFR_IS_RNDUTEST_OR_RNDDNOTTEST(rnd, test)))  \
      rnd = MPFR_RNDZ;                                              \
  } while (0)

/* Transform RNDU and RNDD to RNDZ or RNDA according to sign;
   leave the other modes unchanged.
   Usage: MPFR_UPDATE2_RND_MODE (rnd_mode, MPFR_SIGN (x)) */
#define MPFR_UPDATE2_RND_MODE(rnd, sign)                       \
  do {                                                         \
    if (rnd == MPFR_RNDU)                                      \
      rnd = MPFR_IS_POS_SIGN (sign) ? MPFR_RNDA : MPFR_RNDZ;   \
    else if (rnd == MPFR_RNDD)                                 \
      rnd = MPFR_IS_NEG_SIGN (sign) ? MPFR_RNDA : MPFR_RNDZ;   \
  } while (0)


/******************************************************
 ******************  Limb macros  *********************
 ******************************************************/

/* MPFR_LIMB: Cast to mp_limb_t, assuming that x is based on mp_limb_t
   variables (needed when mp_limb_t is defined as an integer type shorter
   than int, due to the integer promotion rules, which is possible only
   if MPFR_LONG_WITHIN_LIMB is not defined). Warning! This will work
   only when the computed value x is congruent to the expected value
   modulo MPFR_LIMB_MAX + 1. Be aware that this macro may not solve all
   the problems related to the integer promotion rules, because it won't
   have an influence on the evaluation of x itself. Hence the need for...

   MPFR_LIMB_LSHIFT: Left shift by making sure that the shifted argument
   is unsigned (use unsigned long due to the MPFR_LONG_WITHIN_LIMB test).
   For instance, due to the integer promotion rules, if mp_limb_t is
   defined as a 16-bit unsigned short and an int has 32 bits, then a
   mp_limb_t will be converted to an int, which is signed.
*/
#ifdef MPFR_LONG_WITHIN_LIMB
#define MPFR_LIMB(x) (x)
#define MPFR_LIMB_LSHIFT(x,c) ((x) << (c))
#else
#define MPFR_LIMB(x) ((mp_limb_t) (x))
#define MPFR_LIMB_LSHIFT(x,c) MPFR_LIMB((unsigned long) (x) << (c))
#endif

/* Definition of simple mp_limb_t constants */
#define MPFR_LIMB_ZERO    ((mp_limb_t) 0)
#define MPFR_LIMB_ONE     ((mp_limb_t) 1)
#define MPFR_LIMB_HIGHBIT MPFR_LIMB_LSHIFT (MPFR_LIMB_ONE, GMP_NUMB_BITS - 1)
#define MPFR_LIMB_MAX     ((mp_limb_t) -1)

/* Mask to get the Most Significant Bit of a limb */
#define MPFR_LIMB_MSB(l) ((mp_limb_t) ((l) & MPFR_LIMB_HIGHBIT))

/* Mask for the low 's' bits of a limb */
#define MPFR_LIMB_MASK(s)                                               \
  (MPFR_ASSERTD (s >= 0 && s <= GMP_NUMB_BITS),                         \
   s == GMP_NUMB_BITS ? MPFR_LIMB_MAX :                                 \
   (mp_limb_t) (MPFR_LIMB_LSHIFT (MPFR_LIMB_ONE, s) - MPFR_LIMB_ONE))

/******************************************************
 **********************  Memory  **********************
 ******************************************************/

#define MPFR_BYTES_PER_MP_LIMB (GMP_NUMB_BITS/CHAR_BIT)

/* Heap memory handling
   --------------------
   Memory allocated for a significand (mantissa) has the following
   format:
     * A mp_size_t in a mpfr_size_limb_t union (see below).
     * An array of mp_limb_t (not all of them are necessarily used,
       as the precision can change without a reallocation).
   The goal of the mpfr_size_limb_t union is to make sure that
   size and alignment requirements are satisfied if mp_size_t and
   mp_limb_t have different sizes and/or alignment requirements.
   And the casts to void * prevents the compiler from emitting a
   warning (or error), such as:
     cast increases required alignment of target type
   with the -Wcast-align GCC option. Correct alignment is checked
   by MPFR_SET_MANT_PTR (when setting MPFR_MANT(x), the MPFR code
   should use this macro or guarantee a correct alignment at this
   time).
   Moreover, pointer conversions are not fully specified by the
   C standard, and the use of a union (and the double casts below)
   might help even if mp_size_t and mp_limb_t have the same size
   and the same alignment requirements. Still, there is currently
   no guarantee that this code is portable. Note that union members
   are not used at all.
*/
typedef union { mp_size_t s; mp_limb_t l; } mpfr_size_limb_t;
#define MPFR_GET_ALLOC_SIZE(x) \
  (((mp_size_t *) (void *) MPFR_MANT(x))[-1] + 0)
#define MPFR_SET_ALLOC_SIZE(x, n) \
  (((mp_size_t *) (void *) MPFR_MANT(x))[-1] = (n))
#define MPFR_MALLOC_SIZE(s) \
  (sizeof(mpfr_size_limb_t) + MPFR_BYTES_PER_MP_LIMB * (size_t) (s))
#define MPFR_SET_MANT_PTR(x,p) \
  (MPFR_MANT(x) = (mp_limb_t *) ((mpfr_size_limb_t *) (p) + 1))
#define MPFR_GET_REAL_PTR(x) \
  ((void *) ((mpfr_size_limb_t *) (void *) MPFR_MANT(x) - 1))

/* Temporary memory handling */
#ifndef TMP_SALLOC
/* GMP 4.1.x or below or internals */
#define MPFR_TMP_DECL TMP_DECL
#define MPFR_TMP_MARK TMP_MARK
#define MPFR_TMP_ALLOC TMP_ALLOC
#define MPFR_TMP_FREE TMP_FREE
#else
#define MPFR_TMP_DECL(x) TMP_DECL
#define MPFR_TMP_MARK(x) TMP_MARK
#define MPFR_TMP_ALLOC(s) TMP_ALLOC(s)
#define MPFR_TMP_FREE(x) TMP_FREE
#endif

#define MPFR_TMP_LIMBS_ALLOC(N)                                         \
  (MPFR_ASSERTD ((N) > 0),                                              \
   (mp_limb_t *) MPFR_TMP_ALLOC ((size_t) (N) * MPFR_BYTES_PER_MP_LIMB))

/* The temporary var doesn't have any size field, but it doesn't matter
 * since only functions dealing with the Heap care about it */
#define MPFR_TMP_INIT1(xp, x, p)                                     \
 ( MPFR_PREC(x) = (p),                                               \
   MPFR_MANT(x) = (xp),                                              \
   MPFR_SET_POS(x),                                                  \
   MPFR_SET_INVALID_EXP(x))

#define MPFR_TMP_INIT(xp, x, p, s)                                   \
  (xp = MPFR_TMP_LIMBS_ALLOC(s),                                     \
   MPFR_TMP_INIT1(xp, x, p))

/* Set y to s*significand(x)*2^e, for example MPFR_ALIAS(y,x,1,MPFR_EXP(x))
   sets y to |x|, and MPFR_ALIAS(y,x,MPFR_SIGN(x),0) sets y to x*2^f such
   that 1/2 <= |y| < 1. Does not check y is in the valid exponent range.
   WARNING! x and y share the same significand. So, some operations are
   not valid if x has been provided via an argument, e.g., trying to
   modify the significand of y, even temporarily, or calling mpfr_clear
   on y. An alias may also break the detection of reuse of an argument
   for the destination (since the pointers to the numbers are different,
   the detection of reuse by a comparison of these pointers will fail).
*/
#define MPFR_ALIAS(y,x,s,e)                     \
  (MPFR_PREC(y) = MPFR_PREC(x),                 \
   MPFR_SIGN(y) = (s),                          \
   MPFR_EXP(y) = (e),                           \
   MPFR_MANT(y) = MPFR_MANT(x))

#define MPFR_TMP_INIT_ABS(y,x) \
  MPFR_ALIAS (y, x, MPFR_SIGN_POS, MPFR_EXP (x))

#define MPFR_TMP_INIT_NEG(y,x) \
  MPFR_ALIAS (y, x, - MPFR_SIGN (x), MPFR_EXP (x))


/******************************************************
 *******************  Cache macros  *******************
 ******************************************************/

/* Cache struct */
#define mpfr_const_pi(_d,_r)    mpfr_cache(_d, __gmpfr_cache_const_pi,_r)
#define mpfr_const_log2(_d,_r)  mpfr_cache(_d, __gmpfr_cache_const_log2, _r)
#define mpfr_const_euler(_d,_r) mpfr_cache(_d, __gmpfr_cache_const_euler, _r)
#define mpfr_const_catalan(_d,_r) mpfr_cache(_d,__gmpfr_cache_const_catalan,_r)

/* Declare a global cache for a MPFR constant.
   If the shared cache is enabled, and if the constructor/destructor
   attributes are available, we need to initialize the shared lock of
   the cache with a constructor. It is the goal of the macro
   MPFR_DEFERRED_INIT_MASTER_DECL.
   FIXME: When MPFR is built with shared cache, the field "lock" is
   not explicitly initialized, which can yield a warning, e.g. with
   GCC's -Wmissing-field-initializers (and an error with -Werror).
   Since one does not know what is behind the associated typedef name,
   one cannot provide an explicit initialization for such a type. Two
   possible solutions:
     1. Encapsulate the type in a structure or a union and use the
        universal zero initializer: { 0 }
        But: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=80454
     2. Use designated initializers when supported. But this needs a
        configure test.
   Using a diagnostic pragma to ignore the warning in this particular case
   is not really possible, because the warning occurs when the macro is
   expanded and one cannot put a pragma in the contents of a #define.
*/
#define MPFR_DECL_INIT_CACHE(_cache,_func)                           \
  MPFR_DEFERRED_INIT_MASTER_DECL(_func,                              \
                                 MPFR_LOCK_INIT( (_cache)->lock),    \
                                 MPFR_LOCK_CLEAR((_cache)->lock))    \
  MPFR_CACHE_ATTR mpfr_cache_t _cache = {{                           \
      {{ 0, MPFR_SIGN_POS, 0, (mp_limb_t *) 0 }}, 0, _func           \
      MPFR_DEFERRED_INIT_SLAVE_VALUE(_func)                          \
    }};                                                              \
  MPFR_MAKE_VARFCT (mpfr_cache_t,_cache)

/******************************************************
 ***************  Threshold parameters  ***************
 ******************************************************/

#include "mparam.h"


/******************************************************
 ******************  Useful macros  *******************
 ******************************************************/

/* The MAX, MIN and ABS macros may already be defined if gmp-impl.h has
   been included. They have the same semantics as in gmp-impl.h, but the
   expressions may be slightly different. So, it's better to undefine
   them first, as required by the ISO C standard. */
#undef MAX
#undef MIN
#undef ABS
#define MAX(a, b) (((a) > (b)) ? (a) : (b))
#define MIN(a, b) (((a) < (b)) ? (a) : (b))
#define ABS(x) (((x)>0) ? (x) : -(x))

/* These macros help the compiler to determine if a test is
   likely or unlikely. The !! is necessary in case x is larger
   than a long. */
#if defined MPFR_DEBUG_PREDICTION && __MPFR_GNUC(3,0)

/* Code to debug branch prediction, based on Ulrich Drepper's paper
 * "What Every Programmer Should Know About Memory":
 *   https://people.freebsd.org/~lstewart/articles/cpumemory.pdf
 */
asm (".section predict_data, \"aw\"; .previous\n"
     ".section predict_line, \"a\"; .previous\n"
     ".section predict_file, \"a\"; .previous");
# if defined __x86_64__
#  define MPFR_DEBUGPRED__(e,E)                                         \
  ({ long _e = !!(e);                                                   \
    asm volatile (".pushsection predict_data\n"                         \
                  "..predictcnt%=: .quad 0; .quad 0\n"                  \
                  ".section predict_line; .quad %c1\n"                  \
                  ".section predict_file; .quad %c2; .popsection\n"     \
                  "addq $1,..predictcnt%=(,%0,8)"                       \
                  : : "r" (_e == E), "i" (__LINE__), "i" (__FILE__));   \
    __builtin_expect (_e, E);                                           \
  })
# elif defined __i386__
#  define MPFR_DEBUGPRED__(e,E)                                         \
  ({ long _e = !!(e);                                                   \
    asm volatile (".pushsection predict_data\n"                         \
                  "..predictcnt%=: .long 0; .long 0\n"                  \
                  ".section predict_line; .long %c1\n"                  \
                  ".section predict_file; .long %c2; .popsection\n"     \
                  "incl ..predictcnt%=(,%0,4)"                          \
                  : : "r" (_e == E), "i" (__LINE__), "i" (__FILE__));   \
    __builtin_expect (_e, E);                                           \
  })
# else
#  error "MPFR_DEBUGPRED__ definition missing"
# endif

# define MPFR_LIKELY(x) MPFR_DEBUGPRED__ ((x), 1)
# define MPFR_UNLIKELY(x) MPFR_DEBUGPRED__ ((x), 0)

#elif __MPFR_GNUC(3,0) || __MPFR_ICC(8,1,0)

# define MPFR_LIKELY(x) (__builtin_expect(!!(x), 1))
# define MPFR_UNLIKELY(x) (__builtin_expect(!!(x), 0))

#else

# define MPFR_LIKELY(x) (x)
# define MPFR_UNLIKELY(x) (x)

#endif

/* Declare that some variable is initialized before being used (without a
   dummy initialization) in order to avoid some compiler warnings. Use the
   VAR = VAR trick (see https://gcc.gnu.org/bugzilla/show_bug.cgi?id=36296#c3)
   only with gcc as this is undefined behavior, and we don't know what other
   compilers do (they may also be smarter). This self-initialization trick
   could be disabled with future gcc versions. It can explicitly be disabled
   by defining NO_INITIALIZED_TRICK (useful for testing). */
#if defined(__GNUC__) && !defined(NO_INITIALIZED_TRICK)
# define INITIALIZED(VAR) VAR = VAR
#else
# define INITIALIZED(VAR) VAR
#endif

/* Ceil log 2: If GCC, uses a GCC extension, otherwise calls a function */
/* Warning:
 *   Needs to define MPFR_NEED_LONGLONG.
 *   Computes ceil(log2(x)) only for x integer (unsigned long)
 *   Undefined if x is 0 */
#if __MPFR_GNUC(2,95) || __MPFR_ICC(8,1,0)
/* Note: This macro MPFR_INT_CEIL_LOG2 shouldn't be used in an MPFR_ASSERT*
   macro, either directly or indirectly via other macros, otherwise it can
   yield an error due to a too large stringized expression in ASSERT_FAIL.
   A static inline function could be a better solution than this macro. */
/* FIXME: The current code assumes that x fits in an unsigned long
   (used by __gmpfr_int_ceil_log2) while MPFR_INT_CEIL_LOG2 is used on
   values that might be larger than ULONG_MAX on some platforms and/or
   with some build options; a loop could be used if x > ULONG_MAX. If
   the type of x is <= unsigned long, then no additional code will be
   generated thanks to obvious compiler optimization. */
#ifdef MPFR_LONG_WITHIN_LIMB
# define MPFR_INT_CEIL_LOG2(x)                            \
    (MPFR_UNLIKELY ((x) == 1) ? 0 :                       \
     __extension__ ({ int _b; mp_limb_t _limb;            \
      MPFR_ASSERTN ((x) > 1);                             \
      _limb = (x) - 1;                                    \
      MPFR_ASSERTN (_limb == (x) - 1);                    \
      count_leading_zeros (_b, _limb);                    \
      _b = GMP_NUMB_BITS - _b;                            \
      MPFR_ASSERTD (_b >= 0);                             \
      _b; }))
#else
# define MPFR_INT_CEIL_LOG2(x)                              \
  (MPFR_UNLIKELY ((x) == 1) ? 0 :                           \
   __extension__ ({ int _c = 0; unsigned long _x = (x) - 1; \
       MPFR_ASSERTN ((x) > 1);                              \
       while (_x != 0)                                      \
         {                                                  \
           _x = _x >> 1;                                    \
           _c ++;                                           \
         };                                                 \
       MPFR_ASSERTD (_c >= 0);                              \
       _c; }))
#endif /* MPFR_LONG_WITHIN_LIMB */
#else
# define MPFR_INT_CEIL_LOG2(x) \
  (MPFR_ASSERTN (x <= ULONG_MAX), __gmpfr_int_ceil_log2(x))
#endif /* __MPFR_GNUC(2,95) || __MPFR_ICC(8,1,0) */

/* Add two integers with overflow handling */
/* Example: MPFR_SADD_OVERFLOW (c, a, b, long, unsigned long,
 *                              LONG_MIN, LONG_MAX,
 *                              goto overflow, goto underflow); */
#define MPFR_UADD_OVERFLOW(c,a,b,ACTION_IF_OVERFLOW)                  \
 do {                                                                 \
  (c) = (a) + (b);                                                    \
  if ((c) < (a)) ACTION_IF_OVERFLOW;                                  \
 } while (0)

/* FIXME:
   This macro should currently be called in such a way that MIN is the
   minimum value of the type and MAX is the maximum value of the type.
   Otherwise the last "else" case does not ensure that MIN <= c <= MAX.
   However, this is not how it is always called in strtofr.c: there's
   sometimes MPFR_EXP_MIN+2 and MPFR_EXP_MAX-2 (this is not always
   optimal, but some adjustments are needed).
   Then (a) >= 0 && (b) >= 0 could be changed to (a) > 0 && (b) > 0
   so that when one of the arguments is 0, one would use the simple
   addition (last "else"). But the strtofr.c code needs to be fixed
   first.
*/
#define MPFR_SADD_OVERFLOW(c,a,b,STYPE,UTYPE,MIN,MAX,ACTION_IF_POS_OVERFLOW,ACTION_IF_NEG_OVERFLOW) \
  do {                                                                \
  if ((a) >= 0 && (b) >= 0) {                                         \
         UTYPE uc,ua,ub;                                              \
         ua = (UTYPE) (a); ub = (UTYPE) (b);                          \
         MPFR_UADD_OVERFLOW (uc, ua, ub, ACTION_IF_POS_OVERFLOW);     \
         if (uc > (UTYPE)(MAX)) ACTION_IF_POS_OVERFLOW;               \
         else (c) = (STYPE) uc;                                       \
  } else if ((a) < 0 && (b) < 0) {                                    \
         UTYPE uc,ua,ub;                                              \
         ua = -(UTYPE) (a); ub = -(UTYPE) (b);                        \
         MPFR_UADD_OVERFLOW (uc, ua, ub, ACTION_IF_NEG_OVERFLOW);     \
         if (uc >= -(UTYPE)(MIN) || uc > (UTYPE)(MAX)) {              \
           if (uc ==  -(UTYPE)(MIN)) (c) = (MIN);                     \
           else  ACTION_IF_NEG_OVERFLOW; }                            \
         else (c) = -(STYPE) uc;                                      \
  } else (c) = (a) + (b);                                             \
 } while (0)


/* Set a number to 1 (Fast) - It doesn't check if 1 is in the exponent range */
#define MPFR_SET_ONE(x)                                               \
do {                                                                  \
  mp_size_t _size = MPFR_LAST_LIMB(x);                                \
  MPFR_SET_POS(x);                                                    \
  MPFR_EXP(x) = 1;                                                    \
  MPN_ZERO ( MPFR_MANT(x), _size);                                    \
  MPFR_MANT(x)[_size] = MPFR_LIMB_HIGHBIT;                            \
} while (0)

/* Compute s = (-a) % GMP_NUMB_BITS as unsigned */
#define MPFR_UNSIGNED_MINUS_MODULO(s, a)                              \
  do                                                                  \
    {                                                                 \
      if (IS_POW2 (GMP_NUMB_BITS))                                    \
        (s) = (- (unsigned int) (a)) % GMP_NUMB_BITS;                 \
      else                                                            \
        {                                                             \
          (s) = (a) % GMP_NUMB_BITS;                                  \
          if ((s) != 0)                                               \
            (s) = GMP_NUMB_BITS - (s);                                \
        }                                                             \
      MPFR_ASSERTD ((s) >= 0 && (s) < GMP_NUMB_BITS);                 \
    }                                                                 \
  while (0)

/* Test if X (positive) is a power of 2 */
#define IS_POW2(X) (((X) & ((X) - 1)) == 0)
#define NOT_POW2(X) (((X) & ((X) - 1)) != 0)

/* Safe absolute value and difference (to avoid possible integer overflow) */
/* type is the target (unsigned) type */
#define SAFE_ABS(type,x) ((x) >= 0 ? (type)(x) : -(type)(x))
#define SAFE_DIFF(type,x,y) (MPFR_ASSERTD((x) >= (y)), (type)(x) - (type)(y))

#define ULONG2LONG(U) ((U) > LONG_MAX ? -1 - (long) ~(U) : (long) (U))

/* Check whether an integer type (after integer promotion) is signed.
   This can be determined at compilation time, but unfortunately,
   when used in practice, this is not a constant expression (because
   the argument X is not a constant expression, even though the result
   does not depend on its value), so that this cannot be used for a
   static assertion. */
#define IS_SIGNED(X) ((X) * 0 - 1 < 0)

#define mpfr_get_d1(x) mpfr_get_d((x), __gmpfr_default_rounding_mode)

/* Store in r the size in bits of the mpz_t z */
#define MPFR_MPZ_SIZEINBASE2(r, z)                      \
  do {                                                  \
    int _cnt;                                           \
    mp_size_t _size;                                    \
    MPFR_ASSERTD (mpz_sgn (z) != 0);                    \
    _size = ABSIZ(z);                                   \
    MPFR_ASSERTD (_size >= 1);                          \
    count_leading_zeros (_cnt, PTR(z)[_size-1]);        \
    (r) = (mp_bitcnt_t) _size * GMP_NUMB_BITS - _cnt;   \
  } while (0)

/* MPFR_LCONV_DPTS can also be forced to 0 or 1 by the user. */
#ifndef MPFR_LCONV_DPTS
# if defined(HAVE_LOCALE_H) && \
     defined(HAVE_STRUCT_LCONV_DECIMAL_POINT) && \
     defined(HAVE_STRUCT_LCONV_THOUSANDS_SEP)
#  define MPFR_LCONV_DPTS 1
# else
#  define MPFR_LCONV_DPTS 0
# endif
#endif

/* FIXME: Add support for multibyte decimal_point and thousands_sep since
   this can be found in practice: https://reviews.llvm.org/D27167 says:
   "I found this problem on FreeBSD 11, where thousands_sep in fr_FR.UTF-8
   is a no-break space (U+00A0)."
   Under Linux, this is U+202F NARROW NO-BREAK SPACE (e2 80 af).
   And in the ps_AF locale,
     decimal_point = U+066B ARABIC DECIMAL SEPARATOR (d9 ab)
     thousands_sep = U+066C ARABIC THOUSANDS SEPARATOR (d9 ac)
   In the mean time, in case of non-single-byte character, revert to the
   default value. Note that the GNU C Library doesn't handle a multibyte
   decimal_point or thousands_sep correctly (with the specification of
   ISO C for decimal_point and POSIX for both):
     https://sourceware.org/bugzilla/show_bug.cgi?id=30883
     https://sourceware.org/bugzilla/show_bug.cgi?id=28943
*/
#if MPFR_LCONV_DPTS
#include <locale.h>
/* Warning! In case of signed char, the value of MPFR_DECIMAL_POINT may
   be negative (the ISO C99 does not seem to forbid negative values). */
#define MPFR_DECIMAL_POINT                      \
  (localeconv()->decimal_point[1] != '\0' ?     \
   (char) '.' : localeconv()->decimal_point[0])
#define MPFR_THOUSANDS_SEPARATOR                \
  (localeconv()->thousands_sep[0] == '\0' ||    \
   localeconv()->thousands_sep[1] != '\0' ?     \
   (char) '\0' : localeconv()->thousands_sep[0])
#else
#define MPFR_DECIMAL_POINT ((char) '.')
#define MPFR_THOUSANDS_SEPARATOR ((char) '\0')
#endif

/* Size of an array, as a constant expression. */
#define numberof_const(x)  (sizeof (x) / sizeof ((x)[0]))

/* Size of an array, safe version but not a constant expression:
   Since an array can silently be converted to a pointer, we check
   that this macro is applied on an array, not a pointer.
   Also make sure that the type is signed ("long" is sufficient
   in practice since the sizes come from the MPFR source), so that
   the value can be used in arbitrary expressions without the risk
   of silently switching to unsigned arithmetic. */
/* TODO: Make numberof() a constant expression and always use it in
   the MPFR code instead of numberof_const(). See the tricks at
     https://gcc.gnu.org/pipermail/gcc/2020-September/233763.html
     "[PATCH v2] <sys/param.h>: Add nitems() and snitems() macros"
     by Alejandro Colomar
   but this needs to be fully tested on various platforms and with
   various compilers and compilation options.
   Moreover, change "long" to "ptrdiff_t", as used at the above URL? */
#undef numberof
#if 0
/* The following should work with GCC as documented in its manual,
   but fails: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=38377#c10
   Thus disabled for now. */
# define numberof(x)                                                    \
  ( __extension__ ({                                                    \
      int is_array = (void *) &(x) == (void *) &(x)[0];                 \
      MPFR_STAT_STATIC_ASSERT (__builtin_constant_p (is_array) ?        \
                               is_array : 1);                           \
      MPFR_ASSERTN (is_array);                                          \
      (long) numberof_const (x);                                        \
    }) )
#else
# define numberof(x)                                    \
  (MPFR_ASSERTN ((void *) &(x) == (void *) &(x)[0]),    \
   (long) numberof_const (x))
#endif

/* Addition with carry (detected by GCC and other good compilers). */
#define ADD_LIMB(u,v,c) ((u) += (v), (c) = (u) < (v))

/* umul_hi(h, x, y) puts in h the high part of x*y */
/* MPFR_NEED_LONGLONG_H needs to be defined to use it. */
#define umul_hi(h, x, y)                        \
  do {                                          \
    mp_limb_t _l;                               \
    umul_ppmm (h, _l, x, y);                    \
    (void) _l;  /* unused variable */           \
  } while (0)


/******************************************************
 ************  Save exponent/flags macros  ************
 ******************************************************/

/* See README.dev for details on how to use the macros.
   They are used to set the exponent range to the maximum
   temporarily */

typedef struct {
  mpfr_flags_t saved_flags;
  mpfr_exp_t saved_emin;
  mpfr_exp_t saved_emax;
} mpfr_save_expo_t;

#define MPFR_SAVE_EXPO_DECL(x) mpfr_save_expo_t x
#define MPFR_SAVE_EXPO_MARK(x)     \
 ((x).saved_flags = __gmpfr_flags, \
  (x).saved_emin = __gmpfr_emin,   \
  (x).saved_emax = __gmpfr_emax,   \
  __gmpfr_emin = MPFR_EMIN_MIN,    \
  __gmpfr_emax = MPFR_EMAX_MAX)
#define MPFR_SAVE_EXPO_FREE(x)     \
 (__gmpfr_flags = (x).saved_flags, \
  __gmpfr_emin = (x).saved_emin,   \
  __gmpfr_emax = (x).saved_emax)
#define MPFR_SAVE_EXPO_UPDATE_FLAGS(x, flags)  \
  (x).saved_flags |= (flags)

/* Speed up final checking */
#define mpfr_check_range(x,t,r) \
  (MPFR_LIKELY (MPFR_EXP_IN_RANGE (MPFR_EXP (x)))                \
   ? ((t) ? (__gmpfr_flags |= MPFR_FLAGS_INEXACT, (t)) : 0)      \
   : mpfr_check_range(x,t,r))


/******************************************************
 *****************  Inline rounding  ******************
 ******************************************************/

/*
 * Note: due to the labels, one cannot use a macro MPFR_RNDRAW* more than
 * once in a function (otherwise these labels would not be unique).
 *
 * Moreover, these macros have "complex" arguments (handlers and extra),
 * which can take code. One should make sure that such code does not use
 * commas that are not inside parentheses (this must be parentheses, not
 * brackets); otherwise the comma just separates the macro arguments,
 * and the compilation would fail as there would be more arguments than
 * expected by the macro definition.
 */

/*
 * Round mantissa (srcp, sprec) to mpfr_t dest using rounding mode rnd
 * assuming dest's sign is sign.
 * In rounding to nearest mode, execute MIDDLE_HANDLER when the value
 * is the middle of two consecutive numbers in dest precision.
 * Execute OVERFLOW_HANDLER in case of overflow when rounding.
 *
 * Note: the exponent field of dest is not used, possibly except by the
 * handlers. It is the caller (via the handlers) who entirely decides
 * how to handle it.
 */
#define MPFR_RNDRAW_GEN(inexact, dest, srcp, sprec, rnd, sign,              \
                        MIDDLE_HANDLER, OVERFLOW_HANDLER)                   \
  do {                                                                      \
    mp_size_t _dests, _srcs;                                                \
    mp_limb_t *_destp;                                                      \
    mpfr_prec_t _destprec, _srcprec;                                        \
                                                                            \
    /* Check Trivial Case when Dest Mantissa has more bits than source */   \
    _srcprec = (sprec);                                                     \
    _destprec = MPFR_PREC (dest);                                           \
    MPFR_ASSERTD (_srcprec >= MPFR_PREC_MIN);                               \
    MPFR_ASSERTD (_destprec >= MPFR_PREC_MIN);                              \
    _destp = MPFR_MANT (dest);                                              \
    if (MPFR_UNLIKELY (_destprec >= _srcprec))                              \
      {                                                                     \
        _srcs  = MPFR_PREC2LIMBS (_srcprec);                                \
        _dests = MPFR_PREC2LIMBS (_destprec) - _srcs;                       \
        MPN_COPY (_destp + _dests, srcp, _srcs);                            \
        MPN_ZERO (_destp, _dests);                                          \
        inexact = 0;                                                        \
      }                                                                     \
    else                                                                    \
      {                                                                     \
        /* Non trivial case: rounding needed */                             \
        mpfr_prec_t _sh;                                                    \
        mp_limb_t *_sp;                                                     \
        mp_limb_t _rb, _sb, _ulp;                                           \
                                                                            \
        /* Compute Position and shift */                                    \
        _srcs  = MPFR_PREC2LIMBS (_srcprec);                                \
        _dests = MPFR_PREC2LIMBS (_destprec);                               \
        MPFR_UNSIGNED_MINUS_MODULO (_sh, _destprec);                        \
        _sp = (srcp) + _srcs - _dests;                                      \
                                                                            \
        /* General case when prec % GMP_NUMB_BITS != 0 */                   \
        if (MPFR_LIKELY (_sh != 0))                                         \
          {                                                                 \
            mp_limb_t _mask;                                                \
            /* Compute Rounding Bit and Sticky Bit */                       \
            /* Note: in directed rounding modes, if the rounding bit */     \
            /* is 1, the behavior does not depend on the sticky bit; */     \
            /* thus we will not try to compute it in this case (this */     \
            /* can be much faster and avoids to read uninitialized   */     \
            /* data in the current mpfr_mul implementation). We just */     \
            /* make sure that _sb is initialized.                    */     \
            _mask = MPFR_LIMB_ONE << (_sh - 1);                             \
            _rb = _sp[0] & _mask;                                           \
            _sb = _sp[0] & (_mask - 1);                                     \
            if ((rnd) == MPFR_RNDN || _rb == 0)                             \
              {                                                             \
                mp_limb_t *_tmp;                                            \
                mp_size_t _n;                                               \
                for (_tmp = _sp, _n = _srcs - _dests ;                      \
                     _n != 0 && _sb == 0 ; _n--)                            \
                  _sb = *--_tmp;                                            \
              }                                                             \
            _ulp = 2 * _mask;                                               \
          }                                                                 \
        else /* _sh == 0 */                                                 \
          {                                                                 \
            MPFR_ASSERTD (_dests < _srcs);                                  \
            /* Compute Rounding Bit and Sticky Bit - see note above */      \
            _rb = _sp[-1] & MPFR_LIMB_HIGHBIT;                              \
            _sb = _sp[-1] & (MPFR_LIMB_HIGHBIT-1);                          \
            if ((rnd) == MPFR_RNDN || _rb == 0)                             \
              {                                                             \
                mp_limb_t *_tmp;                                            \
                mp_size_t _n;                                               \
                for (_tmp = _sp - 1, _n = _srcs - _dests - 1 ;              \
                     _n != 0 && _sb == 0 ; _n--)                            \
                  _sb = *--_tmp;                                            \
              }                                                             \
            _ulp = MPFR_LIMB_ONE;                                           \
          }                                                                 \
        /* Rounding */                                                      \
        if (rnd == MPFR_RNDF)                                               \
          {                                                                 \
            inexact = 0;                                                    \
            goto trunc_doit;                                                \
          }                                                                 \
        else if (rnd == MPFR_RNDN)                                          \
          {                                                                 \
            if (_rb == 0)                                                   \
              {                                                             \
              trunc:                                                        \
                inexact = MPFR_LIKELY ((_sb | _rb) != 0) ? -sign : 0;       \
              trunc_doit:                                                   \
                MPN_COPY (_destp, _sp, _dests);                             \
                _destp[0] &= ~(_ulp - 1);                                   \
              }                                                             \
            else if (MPFR_UNLIKELY (_sb == 0))                              \
              { /* Middle of two consecutive representable numbers */       \
                MIDDLE_HANDLER;                                             \
              }                                                             \
            else                                                            \
              {                                                             \
                if (0)                                                      \
                  goto addoneulp_doit; /* dummy code to avoid warning */    \
              addoneulp:                                                    \
                inexact = sign;                                             \
              addoneulp_doit:                                               \
                if (MPFR_UNLIKELY (mpn_add_1 (_destp, _sp, _dests, _ulp)))  \
                  {                                                         \
                    _destp[_dests - 1] = MPFR_LIMB_HIGHBIT;                 \
                    OVERFLOW_HANDLER;                                       \
                  }                                                         \
                _destp[0] &= ~(_ulp - 1);                                   \
              }                                                             \
          }                                                                 \
        else                                                                \
          { /* Directed rounding mode */                                    \
            if (MPFR_IS_LIKE_RNDZ (rnd, MPFR_IS_NEG_SIGN (sign)))           \
              goto trunc;                                                   \
             else if (MPFR_UNLIKELY ((_sb | _rb) == 0))                     \
               {                                                            \
                 inexact = 0;                                               \
                 goto trunc_doit;                                           \
               }                                                            \
             else                                                           \
              goto addoneulp;                                               \
          }                                                                 \
      }                                                                     \
  } while (0)

/*
 * Round mantissa (srcp, sprec) to mpfr_t dest using rounding mode rnd
 * assuming dest's sign is sign.
 * Execute OVERFLOW_HANDLER in case of overflow when rounding.
 */
#define MPFR_RNDRAW(inexact, dest, srcp, sprec, rnd, sign, OVERFLOW_HANDLER) \
   MPFR_RNDRAW_GEN (inexact, dest, srcp, sprec, rnd, sign,                   \
     if ((_sp[0] & _ulp) == 0)                                               \
       {                                                                     \
         inexact = -sign;                                                    \
         goto trunc_doit;                                                    \
       }                                                                     \
     else                                                                    \
       goto addoneulp;                                                       \
     , OVERFLOW_HANDLER)

/*
 * Round mantissa (srcp, sprec) to mpfr_t dest using rounding mode rnd
 * assuming dest's sign is sign.
 * Execute OVERFLOW_HANDLER in case of overflow when rounding.
 * Set inexact to +/- MPFR_EVEN_INEX in case of even rounding.
 */
#define MPFR_RNDRAW_EVEN(inexact, dest, srcp, sprec, rnd, sign, \
                         OVERFLOW_HANDLER)                      \
   MPFR_RNDRAW_GEN (inexact, dest, srcp, sprec, rnd, sign,      \
     if ((_sp[0] & _ulp) == 0)                                  \
       {                                                        \
         inexact = -MPFR_EVEN_INEX * sign;                      \
         goto trunc_doit;                                       \
       }                                                        \
     else                                                       \
       {                                                        \
         inexact = MPFR_EVEN_INEX * sign;                       \
         goto addoneulp_doit;                                   \
       }                                                        \
     , OVERFLOW_HANDLER)

/* Return TRUE if b is non singular and we can round it to precision 'prec'
   and determine the ternary value, with rounding mode 'rnd', and with
   error at most 2^(EXP(b)-correct_bits). */
#define MPFR_CAN_ROUND(b,correct_bits,prec,rnd)                 \
  (!MPFR_IS_SINGULAR (b) &&                                     \
   mpfr_round_p (MPFR_MANT (b), MPFR_LIMB_SIZE (b),             \
                 (correct_bits), (prec) + ((rnd)==MPFR_RNDN)))

/* Copy the sign and the significand, and handle the exponent in exp. */
#define MPFR_SETRAW(inexact,dest,src,exp,rnd)                           \
  if (dest != src)                                                      \
    {                                                                   \
      MPFR_SET_SIGN (dest, MPFR_SIGN (src));                            \
      if (MPFR_PREC (dest) == MPFR_PREC (src))                          \
        {                                                               \
          MPN_COPY (MPFR_MANT (dest), MPFR_MANT (src),                  \
                    MPFR_LIMB_SIZE (src));                              \
          inexact = 0;                                                  \
        }                                                               \
      else                                                              \
        {                                                               \
          MPFR_RNDRAW (inexact, dest, MPFR_MANT (src), MPFR_PREC (src), \
                       rnd, MPFR_SIGN (src), exp++);                    \
        }                                                               \
    }                                                                   \
  else                                                                  \
    inexact = 0;

/* TODO: fix this description (see round_near_x.c). */
/* Assuming that the function has a Taylor expansion which looks like:
    y=o(f(x)) = o(v + g(x)) with |g(x)| <= 2^(EXP(v)-err)
   we can quickly set y to v if x is small (ie err > prec(y)+1) in most
   cases. It assumes that f(x) is not representable exactly as a FP number.
   v must not be a singular value (NAN, INF or ZERO); usual values are
   v=1 or v=x.

   y is the destination (a mpfr_t), v the value to set (a mpfr_t),
   err1+err2 with 0 <= err2 <= 3 the error term (mpfr_exp_t's), dir (an int)
   is the direction of the committed error (if dir = 0, it rounds toward 0,
   if dir=1, it rounds away from 0), rnd the rounding mode.

   It returns from the function a ternary value in case of success.
   If you want to free something, you must fill the "extra" field
   in consequences, otherwise put nothing in it.

   The test is less restrictive than necessary, but the function
   will finish the check itself.

   Note: err1 + err2 is allowed to overflow as mpfr_exp_t, but it must give
   its real value as mpfr_uexp_t.
*/
#define MPFR_FAST_COMPUTE_IF_SMALL_INPUT(y,v,err1,err2,dir,rnd,extra)   \
  do {                                                                  \
    mpfr_ptr _y = (y);                                                  \
    mpfr_exp_t _err1 = (err1);                                          \
    mpfr_exp_t _err2 = (err2);                                          \
    if (_err1 > 0)                                                      \
      {                                                                 \
        mpfr_uexp_t _err = (mpfr_uexp_t) _err1 + _err2;                 \
        if (MPFR_UNLIKELY (_err > MPFR_PREC (_y) + 1))                  \
          {                                                             \
            int _inexact = mpfr_round_near_x (_y,(v),_err,(dir),(rnd)); \
            if (_inexact != 0)                                          \
              {                                                         \
                extra;                                                  \
                return _inexact;                                        \
              }                                                         \
          }                                                             \
      }                                                                 \
  } while (0)

/* Variant, to be called somewhere after MPFR_SAVE_EXPO_MARK. This variant
   is needed when there are some computations before or when some non-zero
   real constant is used, such as __gmpfr_one for mpfr_cos. */
#define MPFR_SMALL_INPUT_AFTER_SAVE_EXPO(y,v,err1,err2,dir,rnd,expo,extra) \
  do {                                                                  \
    mpfr_ptr _y = (y);                                                  \
    mpfr_exp_t _err1 = (err1);                                          \
    mpfr_exp_t _err2 = (err2);                                          \
    if (_err1 > 0)                                                      \
      {                                                                 \
        mpfr_uexp_t _err = (mpfr_uexp_t) _err1 + _err2;                 \
        if (MPFR_UNLIKELY (_err > MPFR_PREC (_y) + 1))                  \
          {                                                             \
            int _inexact;                                               \
            MPFR_CLEAR_FLAGS ();                                        \
            _inexact = mpfr_round_near_x (_y,(v),_err,(dir),(rnd));     \
            if (_inexact != 0)                                          \
              {                                                         \
                extra;                                                  \
                MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags);      \
                MPFR_SAVE_EXPO_FREE (expo);                             \
                return mpfr_check_range (_y, _inexact, (rnd));          \
              }                                                         \
          }                                                             \
      }                                                                 \
  } while (0)


/******************************************************
 *****************  Ziv loop macros  ******************
 ******************************************************/

/* To safely increase some precision, detecting integer overflows.
   This macro is particularly useful when determining the initial
   working precision before Ziv's loop. P is a precision, X is an
   arbitrary non-negative integer.
   Note: On 2012-02-23, the MPFR_PREC_MAX value has been decreased
   by 256 from the maximum value representable in the mpfr_prec_t
   type, in order to avoid some integer overflows when this macro
   is not used (if the result is larger than MPFR_PREC_MAX, this
   should be detected with a later assertion, e.g. in mpfr_init2).
   But this change is mainly for existing code that has not been
   updated yet. So, it is advised to always use MPFR_ADD_PREC or
   MPFR_INC_PREC if the result can be larger than MPFR_PREC_MAX. */
#define MPFR_ADD_PREC(P,X) \
  (MPFR_ASSERTN ((X) <= MPFR_PREC_MAX - (P)), (P) + (X))
#define MPFR_INC_PREC(P,X) \
  (MPFR_ASSERTN ((X) <= MPFR_PREC_MAX - (P)), (P) += (X))

#ifndef MPFR_USE_LOGGING

#define MPFR_ZIV_DECL(_x) mpfr_prec_t _x
#define MPFR_ZIV_INIT(_x, _p) (_x) = GMP_NUMB_BITS
#define MPFR_ZIV_NEXT(_x, _p) (MPFR_INC_PREC (_p, _x), (_x) = (_p)/2)
#define MPFR_ZIV_FREE(x)

#else

/* The following test on glibc is there mainly for Darwin (Mac OS X), to
   obtain a better error message. The real test should have been a test
   concerning nested functions in gcc, which are disabled by default on
   Darwin; but it is not possible to do that without a configure test. */
# if defined (__cplusplus) || !(__MPFR_GNUC(3,0) && __MPFR_GLIBC(2,0))
#  error "Logging not supported (needs gcc >= 3.0 and GNU C Library >= 2.0)."
# endif

/* Use LOGGING */

/* Note: the mpfr_log_level >= 0 below avoids to take into account
   Ziv loops used by the MPFR functions called by the mpfr_fprintf
   in LOG_PRINT. */

#define MPFR_ZIV_DECL(_x)                                               \
  mpfr_prec_t _x;                                                       \
  int _x ## _cpt = 1;                                                   \
  static unsigned long  _x ## _loop = 0, _x ## _bad = 0;                \
  static const char *_x ## _fname = __func__;                           \
  auto void __attribute__ ((destructor)) x ## _f  (void);               \
  void __attribute__ ((destructor)) x ## _f  (void) {                   \
    if (_x ## _loop != 0 && (MPFR_LOG_STAT_F & mpfr_log_type)) {        \
      fprintf (mpfr_log_file,                                           \
               "%s: Ziv failed %2.2f%% (%lu bad cases / %lu calls)\n",  \
               _x ## _fname, (double) 100.0 * _x ## _bad / _x ## _loop, \
               _x ## _bad, _x ## _loop );                               \
      if (mpfr_log_flush)                                               \
        fflush (mpfr_log_file);                                         \
    }                                                                   \
  }

#define MPFR_ZIV_INIT(_x, _p)                                           \
  do                                                                    \
    {                                                                   \
      (_x) = GMP_NUMB_BITS;                                             \
      if (mpfr_log_level >= 0)                                          \
        _x ## _loop ++;                                                 \
      LOG_PRINT (MPFR_LOG_ZIV_F, "%s:ZIV 1st prec=%Pd\n",               \
                 __func__, (mpfr_prec_t) (_p));                         \
    }                                                                   \
  while (0)

#define MPFR_ZIV_NEXT(_x, _p)                                           \
  do                                                                    \
    {                                                                   \
      MPFR_INC_PREC (_p, _x);                                           \
      (_x) = (_p) / 2;                                                  \
      if (mpfr_log_level >= 0)                                          \
        _x ## _bad += (_x ## _cpt == 1);                                \
      _x ## _cpt ++;                                                    \
      LOG_PRINT (MPFR_LOG_ZIV_F, "%s:ZIV new prec=%Pd\n",               \
                 __func__, (mpfr_prec_t) (_p));                         \
    }                                                                   \
  while (0)

#define MPFR_ZIV_FREE(_x)                                               \
  do                                                                    \
    if (_x ## _cpt > 1)                                                 \
      LOG_PRINT (MPFR_LOG_ZIV_F, "%s:ZIV %d loops\n",                   \
                 __func__, _x ## _cpt);                                 \
  while (0)

#endif


/******************************************************
 ******************  Logging macros  ******************
 ******************************************************/

/* The different kind of LOG */
#define MPFR_LOG_INPUT_F    1
#define MPFR_LOG_OUTPUT_F   2
#define MPFR_LOG_INTERNAL_F 4
#define MPFR_LOG_TIME_F     8
#define MPFR_LOG_ZIV_F      16
#define MPFR_LOG_MSG_F      32
#define MPFR_LOG_STAT_F     64
#define MPFR_LOG_ALLOCA_F   128

#ifdef MPFR_USE_LOGGING

/* Check if we can support this feature */
# ifdef MPFR_USE_THREAD_SAFE
#  error "Enable either `Logging' or `thread-safe', not both"
# endif
# if !__MPFR_GNUC(3,0)
#  error "Logging not supported (GCC >= 3.0)"
# endif

#if defined (__cplusplus)
extern "C" {
#endif

__MPFR_DECLSPEC extern FILE *mpfr_log_file;
__MPFR_DECLSPEC extern int   mpfr_log_flush;
__MPFR_DECLSPEC extern int   mpfr_log_level;
__MPFR_DECLSPEC extern int   mpfr_log_current;
__MPFR_DECLSPEC extern mpfr_prec_t mpfr_log_prec;
__MPFR_DECLSPEC extern unsigned int mpfr_log_type;

#if defined (__cplusplus)
 }
#endif

/* LOG_PRINT calls mpfr_fprintf on mpfr_log_file with logging disabled
   (recursive logging is not wanted and freezes MPFR). */
#define LOG_PRINT(type, format, ...)                                    \
  do                                                                    \
    if ((mpfr_log_type & (type)) && mpfr_log_current <= mpfr_log_level) \
      {                                                                 \
        int old_level = mpfr_log_level;                                 \
        mpfr_log_level = -1;  /* disable logging in mpfr_fprintf */     \
        __gmpfr_cache_const_pi = __gmpfr_logging_pi;                    \
        __gmpfr_cache_const_log2 = __gmpfr_logging_log2;                \
        mpfr_fprintf (mpfr_log_file, format, __VA_ARGS__);              \
        if (mpfr_log_flush)                                             \
          fflush (mpfr_log_file);                                       \
        mpfr_log_level = old_level;                                     \
        __gmpfr_cache_const_pi = __gmpfr_normal_pi;                     \
        __gmpfr_cache_const_log2 = __gmpfr_normal_log2;                 \
      }                                                                 \
  while (0)

#define MPFR_LOG_VAR(x)                                                 \
  LOG_PRINT (MPFR_LOG_INTERNAL_F, "%s.%d:%s[%#Pd]=%.*Rg\n", __func__,   \
             (int) __LINE__, #x, mpfr_get_prec (x), mpfr_log_prec, x)

#define MPFR_LOG_MSG2(format, ...)                                      \
  LOG_PRINT (MPFR_LOG_MSG_F, "%s.%d: "format, __func__, (int) __LINE__, \
             __VA_ARGS__)
#define MPFR_LOG_MSG(x) MPFR_LOG_MSG2 x

#define MPFR_LOG_BEGIN2(format, ...)                                    \
  mpfr_log_current ++;                                                  \
  LOG_PRINT (MPFR_LOG_INPUT_F, "%s:IN  flags=%x "format"\n", __func__,  \
             (unsigned int) __gmpfr_flags, __VA_ARGS__);                \
  if ((MPFR_LOG_TIME_F & mpfr_log_type) &&                              \
      (mpfr_log_current <= mpfr_log_level))                             \
    __gmpfr_log_time = mpfr_get_cputime ();
#define MPFR_LOG_BEGIN(x)                                               \
  int __gmpfr_log_time = 0;                                             \
  MPFR_LOG_BEGIN2 x

#define MPFR_LOG_END2(format, ...)                                      \
  LOG_PRINT (MPFR_LOG_TIME_F, "%s:TIM %dms\n", __mpfr_log_fname,        \
             mpfr_get_cputime () - __gmpfr_log_time);                   \
  LOG_PRINT (MPFR_LOG_OUTPUT_F, "%s:OUT flags=%x "format"\n",           \
             __mpfr_log_fname, (unsigned int) __gmpfr_flags,            \
             __VA_ARGS__);                                              \
  mpfr_log_current --;
#define MPFR_LOG_END(x)                                                 \
  static const char *__mpfr_log_fname = __func__;                       \
  MPFR_LOG_END2 x

/* Note about the implementation of alloca() logging: In each function
   where a TMP_ALLOC() is done, a variable __gmpfr_log_alloca_size needs
   to be declared. In order to ensure that only one variable is declared
   (even when several markers are used), we do this in MPFR_LOG_FUNC.
   This means that the function needs to be logged with MPFR_LOG_FUNC
   (otherwise, there will be a compilation error when logging is enabled).
*/
#define MPFR_LOG_FUNC(begin,end)                                        \
  static const char *__mpfr_log_fname = __func__;                       \
  auto void __mpfr_log_cleanup (int *time);                             \
  void __mpfr_log_cleanup (int *time) {                                 \
    int __gmpfr_log_time = *time;                                       \
    MPFR_LOG_END2 end; }                                                \
  int __gmpfr_log_time __attribute__ ((cleanup (__mpfr_log_cleanup)));  \
  size_t __gmpfr_log_alloca_size = 0;                                   \
  __gmpfr_log_time = 0;                                                 \
  (void) __gmpfr_log_alloca_size;  /* use it to avoid warnings */       \
  MPFR_LOG_BEGIN2 begin

#else /* MPFR_USE_LOGGING */

/* Define void macro for logging */

#define MPFR_LOG_VAR(x)
#define MPFR_LOG_BEGIN(x)
#define MPFR_LOG_END(x)
#define MPFR_LOG_MSG(x)
#define MPFR_LOG_FUNC(x,y)

#endif /* MPFR_USE_LOGGING */


/**************************************************************
 ************  Group Initialize Functions Macros  *************
 **************************************************************/

#ifndef MPFR_GROUP_STATIC_SIZE
# define MPFR_GROUP_STATIC_SIZE 16
#endif

struct mpfr_group_t {
  size_t     alloc;
  mp_limb_t *mant;
#if MPFR_GROUP_STATIC_SIZE != 0
  mp_limb_t  tab[MPFR_GROUP_STATIC_SIZE];
#else
  /* In order to detect memory leaks when testing, MPFR_GROUP_STATIC_SIZE
     can be set to 0, in which case tab will not be used. ISO C does not
     support zero-length arrays[*], thus let's use a flexible array member
     (which will be equivalent here). Note: this is new in C99, but this
     is just used for testing.
     [*] Zero-length arrays are a GNU extension:
           https://gcc.gnu.org/onlinedocs/gcc/Zero-Length.html
         and as such an extension is forbidden in ISO C, it triggers an
         error with -Werror=pedantic.
  */
  mp_limb_t  tab[];
#endif
};

#define MPFR_GROUP_DECL(g) struct mpfr_group_t g
#define MPFR_GROUP_CLEAR(g) do {                                 \
 MPFR_LOG_MSG (("GROUP_CLEAR: ptr = 0x%lX, size = %lu\n",        \
                (unsigned long) (g).mant,                        \
                (unsigned long) (g).alloc));                     \
 if ((g).alloc != 0) {                                           \
   MPFR_ASSERTD ((g).mant != (g).tab);                           \
   mpfr_free_func ((g).mant, (g).alloc);                         \
 }} while (0)

#define MPFR_GROUP_INIT_TEMPLATE(g, prec, num, handler) do {            \
 mpfr_prec_t _prec = (prec);                                            \
 mp_size_t _size;                                                       \
 MPFR_ASSERTD (_prec >= MPFR_PREC_MIN);                                 \
 if (MPFR_UNLIKELY (_prec > MPFR_PREC_MAX))                             \
   mpfr_abort_prec_max ();                                              \
 _size = MPFR_PREC2LIMBS (_prec);                                       \
 if (_size * (num) > MPFR_GROUP_STATIC_SIZE)                            \
   {                                                                    \
     (g).alloc = (num) * _size * sizeof (mp_limb_t);                    \
     (g).mant = (mp_limb_t *) mpfr_allocate_func ((g).alloc);           \
   }                                                                    \
 else                                                                   \
   {                                                                    \
     (g).alloc = 0;                                                     \
     (g).mant = (g).tab;                                                \
   }                                                                    \
 MPFR_LOG_MSG (("GROUP_INIT: ptr = 0x%lX, size = %lu\n",                \
                (unsigned long) (g).mant, (unsigned long) (g).alloc));  \
 handler;                                                               \
 } while (0)
#define MPFR_GROUP_TINIT(g, n, x)                       \
  MPFR_TMP_INIT1 ((g).mant + _size * (n), x, _prec)

#define MPFR_GROUP_INIT_1(g, prec, x)                            \
 MPFR_GROUP_INIT_TEMPLATE(g, prec, 1, MPFR_GROUP_TINIT(g, 0, x))
#define MPFR_GROUP_INIT_2(g, prec, x, y)                         \
 MPFR_GROUP_INIT_TEMPLATE(g, prec, 2,                            \
   MPFR_GROUP_TINIT(g, 0, x);MPFR_GROUP_TINIT(g, 1, y))
#define MPFR_GROUP_INIT_3(g, prec, x, y, z)                      \
 MPFR_GROUP_INIT_TEMPLATE(g, prec, 3,                            \
   MPFR_GROUP_TINIT(g, 0, x);MPFR_GROUP_TINIT(g, 1, y);          \
   MPFR_GROUP_TINIT(g, 2, z))
#define MPFR_GROUP_INIT_4(g, prec, x, y, z, t)                   \
 MPFR_GROUP_INIT_TEMPLATE(g, prec, 4,                            \
   MPFR_GROUP_TINIT(g, 0, x);MPFR_GROUP_TINIT(g, 1, y);          \
   MPFR_GROUP_TINIT(g, 2, z);MPFR_GROUP_TINIT(g, 3, t))
#define MPFR_GROUP_INIT_5(g, prec, x, y, z, t, a)                \
 MPFR_GROUP_INIT_TEMPLATE(g, prec, 5,                            \
   MPFR_GROUP_TINIT(g, 0, x);MPFR_GROUP_TINIT(g, 1, y);          \
   MPFR_GROUP_TINIT(g, 2, z);MPFR_GROUP_TINIT(g, 3, t);          \
   MPFR_GROUP_TINIT(g, 4, a))
#define MPFR_GROUP_INIT_6(g, prec, x, y, z, t, a, b)             \
 MPFR_GROUP_INIT_TEMPLATE(g, prec, 6,                            \
   MPFR_GROUP_TINIT(g, 0, x);MPFR_GROUP_TINIT(g, 1, y);          \
   MPFR_GROUP_TINIT(g, 2, z);MPFR_GROUP_TINIT(g, 3, t);          \
   MPFR_GROUP_TINIT(g, 4, a);MPFR_GROUP_TINIT(g, 5, b))

#define MPFR_GROUP_REPREC_TEMPLATE(g, prec, num, handler) do {          \
 mpfr_prec_t _prec = (prec);                                            \
 size_t    _oalloc = (g).alloc;                                         \
 mp_size_t _size;                                                       \
 MPFR_LOG_MSG (("GROUP_REPREC: oldptr = 0x%lX, oldsize = %lu\n",        \
                (unsigned long) (g).mant, (unsigned long) _oalloc));    \
 MPFR_ASSERTD (_prec >= MPFR_PREC_MIN);                                 \
 if (MPFR_UNLIKELY (_prec > MPFR_PREC_MAX))                             \
   mpfr_abort_prec_max ();                                              \
 _size = MPFR_PREC2LIMBS (_prec);                                       \
 (g).alloc = (num) * _size * sizeof (mp_limb_t);                        \
 if (_oalloc == 0)                                                      \
   (g).mant = (mp_limb_t *) mpfr_allocate_func ((g).alloc);             \
 else                                                                   \
   (g).mant = (mp_limb_t *)                                             \
     mpfr_reallocate_func ((g).mant, _oalloc, (g).alloc);               \
 MPFR_LOG_MSG (("GROUP_REPREC: newptr = 0x%lX, newsize = %lu\n",        \
                (unsigned long) (g).mant, (unsigned long) (g).alloc));  \
 handler;                                                               \
 } while (0)

#define MPFR_GROUP_REPREC_1(g, prec, x)                          \
 MPFR_GROUP_REPREC_TEMPLATE(g, prec, 1, MPFR_GROUP_TINIT(g, 0, x))
#define MPFR_GROUP_REPREC_2(g, prec, x, y)                       \
 MPFR_GROUP_REPREC_TEMPLATE(g, prec, 2,                          \
   MPFR_GROUP_TINIT(g, 0, x);MPFR_GROUP_TINIT(g, 1, y))
#define MPFR_GROUP_REPREC_3(g, prec, x, y, z)                    \
 MPFR_GROUP_REPREC_TEMPLATE(g, prec, 3,                          \
   MPFR_GROUP_TINIT(g, 0, x);MPFR_GROUP_TINIT(g, 1, y);          \
   MPFR_GROUP_TINIT(g, 2, z))
#define MPFR_GROUP_REPREC_4(g, prec, x, y, z, t)                 \
 MPFR_GROUP_REPREC_TEMPLATE(g, prec, 4,                          \
   MPFR_GROUP_TINIT(g, 0, x);MPFR_GROUP_TINIT(g, 1, y);          \
   MPFR_GROUP_TINIT(g, 2, z);MPFR_GROUP_TINIT(g, 3, t))
#define MPFR_GROUP_REPREC_5(g, prec, x, y, z, t, a)              \
 MPFR_GROUP_REPREC_TEMPLATE(g, prec, 5,                          \
   MPFR_GROUP_TINIT(g, 0, x);MPFR_GROUP_TINIT(g, 1, y);          \
   MPFR_GROUP_TINIT(g, 2, z);MPFR_GROUP_TINIT(g, 3, t);          \
   MPFR_GROUP_TINIT(g, 4, a))
#define MPFR_GROUP_REPREC_6(g, prec, x, y, z, t, a, b)           \
 MPFR_GROUP_REPREC_TEMPLATE(g, prec, 6,                          \
   MPFR_GROUP_TINIT(g, 0, x);MPFR_GROUP_TINIT(g, 1, y);          \
   MPFR_GROUP_TINIT(g, 2, z);MPFR_GROUP_TINIT(g, 3, t);          \
   MPFR_GROUP_TINIT(g, 4, a);MPFR_GROUP_TINIT(g, 5, b))


/******************************************************
 ***************  Internal functions  *****************
 ******************************************************/

#if defined (__cplusplus)
extern "C" {
#endif

MPFR_COLD_FUNCTION_ATTR __MPFR_DECLSPEC int
  mpfr_underflow (mpfr_ptr, mpfr_rnd_t, int);
MPFR_COLD_FUNCTION_ATTR __MPFR_DECLSPEC int
  mpfr_overflow (mpfr_ptr, mpfr_rnd_t, int);

__MPFR_DECLSPEC int mpfr_add1 (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_sub1 (mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_add1sp (mpfr_ptr, mpfr_srcptr, mpfr_srcptr,
                                 mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_sub1sp (mpfr_ptr, mpfr_srcptr, mpfr_srcptr,
                                 mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_can_round_raw (const mp_limb_t *,
             mp_size_t, int, mpfr_exp_t, mpfr_rnd_t, mpfr_rnd_t, mpfr_prec_t);

__MPFR_DECLSPEC int mpfr_set_1_2 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t, int);

__MPFR_DECLSPEC int mpfr_cmp2 (mpfr_srcptr, mpfr_srcptr, mpfr_prec_t *);

__MPFR_DECLSPEC long          __gmpfr_ceil_log2     (double);
__MPFR_DECLSPEC long          __gmpfr_floor_log2    (double);
__MPFR_DECLSPEC double        __gmpfr_ceil_exp2     (double);
__MPFR_DECLSPEC unsigned long __gmpfr_isqrt     (unsigned long);
__MPFR_DECLSPEC unsigned long __gmpfr_cuberoot  (unsigned long);
__MPFR_DECLSPEC int       __gmpfr_int_ceil_log2 (unsigned long);

__MPFR_DECLSPEC mpfr_exp_t mpfr_ceil_mul (mpfr_exp_t, int, int);

__MPFR_DECLSPEC int mpfr_exp_2 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_exp_3 (mpfr_ptr, mpfr_srcptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_powerof2_raw (mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_powerof2_raw2 (const mp_limb_t *, mp_size_t);

__MPFR_DECLSPEC int mpfr_pow_general (mpfr_ptr, mpfr_srcptr, mpfr_srcptr,
                                      mpfr_rnd_t, int, mpfr_save_expo_t *);

__MPFR_DECLSPEC void mpfr_setmax (mpfr_ptr, mpfr_exp_t);
__MPFR_DECLSPEC void mpfr_setmin (mpfr_ptr, mpfr_exp_t);

__MPFR_DECLSPEC int mpfr_mpn_exp (mp_limb_t *, mpfr_exp_t *, int,
                                  mpfr_exp_t, size_t);

#ifdef _MPFR_H_HAVE_FILE
__MPFR_DECLSPEC void mpfr_fdump (FILE *, mpfr_srcptr);
#endif
__MPFR_DECLSPEC void mpfr_print_mant_binary (const char*, const mp_limb_t*,
                                             mpfr_prec_t);
__MPFR_DECLSPEC void mpfr_set_str_binary (mpfr_ptr, const char*);

__MPFR_DECLSPEC int mpfr_round_raw (mp_limb_t *,
       const mp_limb_t *, mpfr_prec_t, int, mpfr_prec_t, mpfr_rnd_t, int *);
__MPFR_DECLSPEC int mpfr_round_raw_2 (const mp_limb_t *, mpfr_prec_t, int,
                                      mpfr_prec_t, mpfr_rnd_t);
/* No longer defined (see round_prec.c).
   Uncomment if it needs to be defined again.
__MPFR_DECLSPEC int mpfr_round_raw_3 (const mp_limb_t *,
             mpfr_prec_t, int, mpfr_prec_t, mpfr_rnd_t, int *);
*/
__MPFR_DECLSPEC int mpfr_round_raw_4 (mp_limb_t *,
       const mp_limb_t *, mpfr_prec_t, int, mpfr_prec_t, mpfr_rnd_t);

#define mpfr_round_raw2(xp, xn, neg, r, prec) \
  mpfr_round_raw_2((xp),(xn)*GMP_NUMB_BITS,(neg),(prec),(r))

__MPFR_DECLSPEC int mpfr_check (mpfr_srcptr);

__MPFR_DECLSPEC int mpfr_get_cputime (void);

__MPFR_DECLSPEC void mpfr_nexttozero (mpfr_ptr);
__MPFR_DECLSPEC void mpfr_nexttoinf (mpfr_ptr);

__MPFR_DECLSPEC int mpfr_const_pi_internal (mpfr_ptr,mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_const_log2_internal (mpfr_ptr,mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_const_euler_internal (mpfr_ptr, mpfr_rnd_t);
__MPFR_DECLSPEC int mpfr_const_catalan_internal (mpfr_ptr, mpfr_rnd_t);

#if 0
__MPFR_DECLSPEC void mpfr_init_cache (mpfr_cache_t,
                                      int(*)(mpfr_ptr,mpfr_rnd_t));
#endif
__MPFR_DECLSPEC void mpfr_clear_cache (mpfr_cache_t);
__MPFR_DECLSPEC int  mpfr_cache (mpfr_ptr, mpfr_cache_t, mpfr_rnd_t);

__MPFR_DECLSPEC void mpfr_mulhigh_n (mpfr_limb_ptr, mpfr_limb_srcptr,
                                     mpfr_limb_srcptr, mp_size_t);
__MPFR_DECLSPEC void mpfr_mullow_n  (mpfr_limb_ptr, mpfr_limb_srcptr,
                                     mpfr_limb_srcptr, mp_size_t);
__MPFR_DECLSPEC void mpfr_sqrhigh_n (mpfr_limb_ptr, mpfr_limb_srcptr,
                                     mp_size_t);
__MPFR_DECLSPEC mp_limb_t mpfr_divhigh_n (mpfr_limb_ptr, mpfr_limb_ptr,
                                          mpfr_limb_ptr, mp_size_t);

__MPFR_DECLSPEC int mpfr_round_p (mp_limb_t *, mp_size_t, mpfr_exp_t,
                                  mpfr_prec_t);

__MPFR_DECLSPEC int mpfr_round_near_x (mpfr_ptr, mpfr_srcptr, mpfr_uexp_t, int,
                                       mpfr_rnd_t);
__MPFR_DECLSPEC MPFR_COLD_FUNCTION_ATTR MPFR_NORETURN void
  mpfr_abort_prec_max (void);

__MPFR_DECLSPEC void mpfr_rand_raw (mpfr_limb_ptr, gmp_randstate_t,
                                    mpfr_prec_t);

__MPFR_DECLSPEC mpz_srcptr mpfr_bernoulli_cache (unsigned long);
__MPFR_DECLSPEC void mpfr_bernoulli_freecache (void);

__MPFR_DECLSPEC int mpfr_sincos_fast (mpfr_ptr, mpfr_ptr, mpfr_srcptr,
                                      mpfr_rnd_t);

__MPFR_DECLSPEC double mpfr_scale2 (double, int);

__MPFR_DECLSPEC void mpfr_div_ui2 (mpfr_ptr, mpfr_srcptr, unsigned long,
                                   unsigned long, mpfr_rnd_t);

__MPFR_DECLSPEC void mpfr_gamma_one_and_two_third (mpfr_ptr, mpfr_ptr,
                                                   mpfr_prec_t);

__MPFR_DECLSPEC void mpfr_mpz_init (mpz_ptr);
__MPFR_DECLSPEC void mpfr_mpz_init2 (mpz_ptr, mp_bitcnt_t);
__MPFR_DECLSPEC void mpfr_mpz_clear (mpz_ptr);

__MPFR_DECLSPEC int mpfr_odd_p (mpfr_srcptr);

__MPFR_DECLSPEC int mpfr_nbits_ulong (unsigned long);
#ifdef _MPFR_H_HAVE_INTMAX_T
__MPFR_DECLSPEC int mpfr_nbits_uj (uintmax_t);
#endif

#ifdef _MPFR_H_HAVE_VA_LIST
/* Declared only if <stdarg.h> has been included. */
__MPFR_DECLSPEC int mpfr_vasnprintf_aux (char**, char*, size_t, const char*,
                                         va_list);
#endif

#if MPFR_WANT_ASSERT >= 2
__MPFR_DECLSPEC void flags_fout (FILE *, mpfr_flags_t);
#endif

#if defined (__cplusplus)
}
#endif


/*****************************************************
 ***************  Internal mpz_t pool  ***************
 *****************************************************/

/* don't use the mpz_t pool with mini-gmp */
#ifdef MPFR_USE_MINI_GMP
# define MPFR_POOL_NENTRIES 0
#endif

#ifndef MPFR_POOL_NENTRIES
# define MPFR_POOL_NENTRIES 32  /* default number of entries of the pool */
#endif

#if MPFR_POOL_NENTRIES && !defined(MPFR_POOL_DONT_REDEFINE)
# undef mpz_init
# undef mpz_init2
# undef mpz_clear
# undef mpz_init_set_ui
# undef mpz_init_set
# define mpz_init mpfr_mpz_init
# define mpz_init2 mpfr_mpz_init2
# define mpz_clear mpfr_mpz_clear
# define mpz_init_set_ui(a,b) do { mpz_init (a); mpz_set_ui (a, b); } while (0)
# define mpz_init_set(a,b) do { mpz_init (a); mpz_set (a, b); } while (0)
#endif


/******************************************************
 ********  Compute LOG2(LOG2(MPFR_PREC_MAX))  *********
 ******************************************************/

#if   _MPFR_PREC_FORMAT == 1
# define MPFR_PREC_MAX_TEMP USHRT_MAX
#elif _MPFR_PREC_FORMAT == 2
# define MPFR_PREC_MAX_TEMP UINT_MAX
#elif _MPFR_PREC_FORMAT == 3
# define MPFR_PREC_MAX_TEMP ULONG_MAX
#else
# error "Invalid MPFR Prec format"
#endif

/* Note: In the constants below, it is sufficient to use the suffix U.
 * A large enough unsigned type will be chosen automatically, but the
 * exact type doesn't matter here.
 */

#if MPFR_PREC_MAX_TEMP == 255U
# define MPFR_PREC_BITS 8
# define MPFR_LOG2_PREC_BITS 3
#elif MPFR_PREC_MAX_TEMP == 65535U
# define MPFR_PREC_BITS 16
# define MPFR_LOG2_PREC_BITS 4
#elif MPFR_PREC_MAX_TEMP == 4294967295U
# define MPFR_PREC_BITS 32
# define MPFR_LOG2_PREC_BITS 5
#elif MPFR_PREC_MAX_TEMP == 18446744073709551615U
# define MPFR_PREC_BITS 64
# define MPFR_LOG2_PREC_BITS 6
#else
# error "Unsupported MPFR_PREC_MAX_TEMP value"
#endif


/******************************************************
 *************  Value coverage checking  **************
 ******************************************************/

#ifdef MPFR_COV_CHECK

/* Variable names should start with the __gmpfr_cov_ prefix. */

#define MPFR_COV_SET(X) (__gmpfr_cov_ ## X = 1)

#if defined (__cplusplus)
extern "C" {
#endif

__MPFR_DECLSPEC extern int __gmpfr_cov_div_ui_sb[10][2];
__MPFR_DECLSPEC extern int __gmpfr_cov_sum_tmd[MPFR_RND_MAX][2][2][3][2][2];

#if defined (__cplusplus)
}
#endif

#else /* MPFR_COV_CHECK */

#define MPFR_COV_SET(X) ((void) 0)

#endif /* MPFR_COV_CHECK */


/******************************************************
 *****************  Unbounded Floats  *****************
 ******************************************************/

#if defined (__cplusplus)
extern "C" {
#endif

/* An UBF is like a MPFR number, but with an additional mpz_t member,
   which is assumed to be present (with a value in it) when the usual
   exponent field has the value MPFR_EXP_UBF. The goal of this compatible
   representation is to easily be able to support UBF in "normal" code
   using the public API. This is some form of "subtyping".

   Unfortunately this breaks aliasing rules, and C does not provide any way
   to avoid that (except with additional syntax ugliness and API breakage,
   though there is a workaround -- see the end of this comment):

     https://news.ycombinator.com/item?id=11753236

   The alignment requirement for __mpfr_ubf_struct (UBF) needs to be at least
   as strong as the one for __mpfr_struct (MPFR number); this is not required
   by the C standard, but this should always be the case in practice, since
   __mpfr_ubf_struct starts with the same members as those of __mpfr_struct.
   If ever this would not be the case with some particular C implementation,
   an _Alignas alignment attribute (C11) could be added for UBF.

   When an input of a public function is an UBF, the semantic remains
   internal to MPFR and can change in the future. UBF arguments need
   to be explicitly converted to mpfr_ptr (or mpfr_srcptr); be careful
   with variadic functions, as the compiler will not be able to check
   in general. See fmma.c as an example of usage.

   In general, the type used for values that may be UBF must be either
   mpfr_ubf_t or mpfr_ubf_ptr. The type mpfr_ptr or mpfr_srcptr may be
   used for UBF only in the case where the pointer has been converted
   from mpfr_ubf_ptr, in order to ensure valid alignment. For instance,
   in mpfr_fmma_aux, one uses mpfr_ubf_t to generate the exact products
   as UBF; then the corresponding pointers are converted to mpfr_srcptr
   for mpfr_add (even though they point to UBF).

   Functions that can accept either MPFR arguments (mpfr_ptr type) or
   UBF arguments (mpfr_ubf_ptr type) must use a pointer type that can
   always be converted from both, typically mpfr_ptr or mpfr_srcptr.
   For instance, that's why mpfr_ubf_exp_less_p uses mpfr_srcptr.
   Note: "void *" could also be used, but mpfr_ptr is more meaningful
   and practical.

   Note that functions used for logging need to support UBF (currently
   done by printing that a number is an UBF, as it may be difficult to
   do more without significant changes).

   --------

   [NOTE] Added on 2020-03-26 (commit 98d053b0bc)

   A workaround to avoid breaking aliasing rules should be to use mpfr_ptr
   to access the usual mpfr_t members and mpfr_ubf_ptr to access the
   additional member _mpfr_zexp. And never use __mpfr_ubf_struct as a
   declared type; otherwise this would force __mpfr_ubf_struct to be the
   effective type of the whole object. Thus instead of

     typedef __mpfr_ubf_struct mpfr_ubf_t[1];

   one could use the following definition as a trick to allocate an UBF as
   an automatic variable with the required alignment but without forcing
   the effective type to __mpfr_ubf_struct.

      typedef union {
        __mpfr_ubf_struct u[1];
        __mpfr_struct m[1];
      } mpfr_ubf_t;

   Then adapt the related code to select to right member, depending on the
   context. Unfortunately, this triggers -Wstrict-aliasing false positives
   with GCC in the MPFR_UBF_CLEAR_EXP expansion:

     https://gcc.gnu.org/bugzilla/show_bug.cgi?id=94337

   (see changeset r13820 in the ubf2 branch). So, for the time being,
   as long as the code does not break, do not change anything.

   [NOTE] Added on 2020-10-21 (commit 6d782e61bf)

   Note: The condition "use mpfr_ptr to access the usual mpfr_t members and
   mpfr_ubf_ptr to access the additional member _mpfr_zexp" may be ignored
   if the union type is visible within the function (see ISO C99 6.5.2.3#5
   and 6.5.2.3#8 for the example, this implementation being very similar to
   the valid fragment of this example), which must be the case as the union
   is declared globally. However, this seems to be buggy in GCC:

     https://gcc.gnu.org/bugzilla/show_bug.cgi?id=14319
     https://gcc.gnu.org/bugzilla/show_bug.cgi?id=65892

   [NOTE] Updated on 2020-10-21 (commit e045753e5d)

   Alternatively, GCC's may_alias attribute could conditionally be used
   on the __mpfr_ubf_struct and __mpfr_struct types (though it would be
   much stronger than needed since only these two types may alias each
   other).

   --------

   [NOTE] Added then updated on
      2024-09-30 02:22:29 +0000 (commit 7348bb03e5)
      2025-03-28 14:17:25 +0000 (commit e04e5ed3ca)
      2025-03-28 15:54:36 +0000 (commit 0b869c1d5c)

   The above suggestion may not be correct. Any use of __mpfr_ubf_struct
   will lead to a break of the aliasing rules at some point. A solution
   might be to define something like
     typedef struct {
       __mpfr_struct _mpfr_m;
       mpz_t _mpfr_zexp;
     } __mpfr_ubf_struct;
   and manipulate it with a mpfr_ptr pointer to the member _mpfr_m.
   This would be very similar to
     https://stackoverflow.com/questions/63518693/struct-extension-in-c
     https://www.codementor.io/@arpitbhayani/powering-inheritance-in-c-using-structure-composition-176sygr724

   The drawback is that if the compiler does not support type-generic
   expressions (with _Generic, new in ISO C11), it seems no longer
   possible to do pointer type checking with a type-generic macros,
   previously done with code like

   | #define MPFR_ZEXP(x)                            \
   |   ((void) sizeof ((x)->_mpfr_exp),              \
   |    ((mpfr_ubf_ptr) (x))->_mpfr_zexp)

   That said, a version with _Generic could be used conditionally (with
   support detected at configure time), and as long as one develops and/or
   tests MPFR with at least a compiler that supports _Generic, type issues
   with such macros will be detected. Moreover, the use of _Generic would
   be cleaner and give a clearer error message if an incorrect type is
   provided.
*/

typedef struct {
  mpfr_prec_t  _mpfr_prec;
  mpfr_sign_t  _mpfr_sign;
  mpfr_exp_t   _mpfr_exp;
  mp_limb_t   *_mpfr_d;
  mpz_t        _mpfr_zexp;
} __mpfr_ubf_struct;

typedef __mpfr_ubf_struct mpfr_ubf_t[1];
typedef __mpfr_ubf_struct *mpfr_ubf_ptr;

__MPFR_DECLSPEC void mpfr_ubf_mul_exact (mpfr_ubf_ptr,
                                         mpfr_srcptr, mpfr_srcptr);
__MPFR_DECLSPEC int mpfr_ubf_exp_less_p (mpfr_srcptr, mpfr_srcptr);
__MPFR_DECLSPEC mpfr_exp_t mpfr_ubf_zexp2exp (mpz_ptr);
__MPFR_DECLSPEC mpfr_exp_t mpfr_ubf_diff_exp (mpfr_srcptr, mpfr_srcptr);

#if defined (__cplusplus)
}
#endif

/* Get the _mpfr_zexp field (pointer to a mpz_t) of an UBF object.
   For practical reasons, the type of the argument x can be either
   mpfr_ubf_ptr or mpfr_ptr, since the latter is used in functions
   that accept both MPFR numbers and UBFs; this is checked by the
   code "(x)->_mpfr_exp" (the "sizeof" prevents an access, which
   could be invalid when MPFR_ZEXP(x) is used for an assignment,
   and also avoids breaking the aliasing rules if they are dealt
   with in the future).
   This macro can be used when building an UBF. So we do not check
   that the _mpfr_exp field has the value MPFR_EXP_UBF. */
#define MPFR_ZEXP(x)                            \
  ((void) sizeof ((x)->_mpfr_exp),              \
   ((mpfr_ubf_ptr) (x))->_mpfr_zexp)

/* If x is an UBF, clear its mpz_t exponent. */
#define MPFR_UBF_CLEAR_EXP(x) \
  ((void) (MPFR_IS_UBF (x) && (mpz_clear (MPFR_ZEXP (x)), 0)))

/* Like MPFR_GET_EXP, but accepts UBF (with exponent saturated to
   the interval [MPFR_EXP_MIN,MPFR_EXP_MAX]). */
#define MPFR_UBF_GET_EXP(x)                                     \
  (MPFR_IS_UBF (x) ? mpfr_ubf_zexp2exp (MPFR_ZEXP (x)) :        \
   MPFR_GET_EXP ((mpfr_ptr) (x)))

#endif /* __MPFR_IMPL_H__ */