path: root/src/mpfr-gmp.h

/* Uniform Interface to GMP.

Copyright 2004-2017 Free Software Foundation, Inc.
Contributed by the AriC and Caramba projects, INRIA.

This file is part of the GNU MPFR Library.

The GNU MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or (at your
option) any later version.

The GNU MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */

#ifndef __GMPFR_GMP_H__
#define __GMPFR_GMP_H__

#ifndef __MPFR_IMPL_H__
# error  "mpfr-impl.h not included"
#endif


/******************************************************
 ******************** C++ Compatibility ***************
 ******************************************************/
#if defined (__cplusplus)
extern "C" {
#endif


/******************************************************
 ******************** Identify GMP ********************
 ******************************************************/

/* Macro to detect the GMP version */
#if defined(__GNU_MP_VERSION) && \
    defined(__GNU_MP_VERSION_MINOR) && \
    defined(__GNU_MP_VERSION_PATCHLEVEL)
# define __MPFR_GMP(a,b,c) \
  (MPFR_VERSION_NUM(__GNU_MP_VERSION,__GNU_MP_VERSION_MINOR,__GNU_MP_VERSION_PATCHLEVEL) >= MPFR_VERSION_NUM(a,b,c))
#else
# define __MPFR_GMP(a,b,c) 0
#endif



/******************************************************
 ******************** Check GMP ***********************
 ******************************************************/

#if !__MPFR_GMP(5,0,0) && !defined(MPFR_USE_MINI_GMP)
# error "GMP 5.0.0 or newer is required"
#endif

#if GMP_NAIL_BITS != 0
# error "MPFR doesn't support nonzero values of GMP_NAIL_BITS"
#endif

#if (GMP_NUMB_BITS<32) || (GMP_NUMB_BITS & (GMP_NUMB_BITS - 1))
# error "GMP_NUMB_BITS must be a power of 2, and >= 32"
#endif

#if GMP_NUMB_BITS == 32
# define MPFR_LOG2_GMP_NUMB_BITS 5
#elif GMP_NUMB_BITS == 64
# define MPFR_LOG2_GMP_NUMB_BITS 6
#elif GMP_NUMB_BITS == 128
# define MPFR_LOG2_GMP_NUMB_BITS 7
#elif GMP_NUMB_BITS == 256
# define MPFR_LOG2_GMP_NUMB_BITS 8
#else
# error "Can't compute log2(GMP_NUMB_BITS)"
#endif



/******************************************************
 ************* Define GMP Internal Interface  *********
 ******************************************************/

#ifndef MPFR_HAVE_GMP_IMPL /* Build with gmp internals */

/* The following tries to get a good version of alloca.
   See gmp-impl.h for implementation details and original version */
/* FIXME: the autoconf manual gives a different piece of code under the
   documentation of the AC_FUNC_ALLOCA macro. Should we switch to it? */
#ifndef alloca
# if defined ( __GNUC__ )
#  define alloca __builtin_alloca
# elif defined (__DECC)
#  define alloca(x) __ALLOCA(x)
# elif defined (_MSC_VER)
#  include <malloc.h>
#  define alloca _alloca
# elif defined (HAVE_ALLOCA_H)
#  include <alloca.h>
# elif defined (_AIX) || defined (_IBMR2)
#  pragma alloca
# else
void *alloca (size_t);
# endif
#endif

/* Define some macros */

#define ULONG_HIGHBIT (ULONG_MAX ^ ((unsigned long) ULONG_MAX >> 1))
#define UINT_HIGHBIT  (UINT_MAX ^ ((unsigned) UINT_MAX >> 1))
#define USHRT_HIGHBIT ((unsigned short) (USHRT_MAX ^ ((unsigned short) USHRT_MAX >> 1)))


#if __GMP_MP_SIZE_T_INT
#define MP_SIZE_T_MAX      INT_MAX
#define MP_SIZE_T_MIN      INT_MIN
#else
#define MP_SIZE_T_MAX      LONG_MAX
#define MP_SIZE_T_MIN      LONG_MIN
#endif

/* MP_LIMB macros */
#define MPN_ZERO(dst, n) memset((dst), 0, (n)*MPFR_BYTES_PER_MP_LIMB)
/* TODO: add MPFR_ASSERTD assertions for MPN_COPY_DECR and MPN_COPY_INCR,
   even though memmove works with any overlapping. Useful to detect bugs! */
#define MPN_COPY_DECR(dst,src,n) memmove((dst),(src),(n)*MPFR_BYTES_PER_MP_LIMB)
#define MPN_COPY_INCR(dst,src,n) memmove((dst),(src),(n)*MPFR_BYTES_PER_MP_LIMB)
#define MPN_COPY(dst,src,n) \
  do                                                                  \
    {                                                                 \
      if ((dst) != (src))                                             \
        {                                                             \
          MPFR_ASSERTD ((char *) (dst) >= (char *) (src) +            \
                                     (n) * MPFR_BYTES_PER_MP_LIMB ||  \
                        (char *) (src) >= (char *) (dst) +            \
                                     (n) * MPFR_BYTES_PER_MP_LIMB);   \
          memcpy ((dst), (src), (n) * MPFR_BYTES_PER_MP_LIMB);        \
        }                                                             \
    }                                                                 \
  while (0)

/* MPN macros taken from gmp-impl.h */
#define MPN_NORMALIZE(DST, NLIMBS) \
  do {                                        \
    while (NLIMBS > 0)                        \
      {                                       \
        if ((DST)[(NLIMBS) - 1] != 0)         \
          break;                              \
        NLIMBS--;                             \
      }                                       \
  } while (0)
#define MPN_NORMALIZE_NOT_ZERO(DST, NLIMBS)     \
  do {                                          \
    MPFR_ASSERTD ((NLIMBS) >= 1);               \
    while (1)                                   \
      {                                         \
        if ((DST)[(NLIMBS) - 1] != 0)           \
          break;                                \
        NLIMBS--;                               \
      }                                         \
  } while (0)
#define MPN_OVERLAP_P(xp, xsize, yp, ysize) \
  ((xp) + (xsize) > (yp) && (yp) + (ysize) > (xp))
#define MPN_SAME_OR_INCR2_P(dst, dsize, src, ssize)             \
  ((dst) <= (src) || ! MPN_OVERLAP_P (dst, dsize, src, ssize))
#define MPN_SAME_OR_INCR_P(dst, src, size)      \
  MPN_SAME_OR_INCR2_P(dst, size, src, size)
#define MPN_SAME_OR_DECR2_P(dst, dsize, src, ssize)             \
  ((dst) >= (src) || ! MPN_OVERLAP_P (dst, dsize, src, ssize))
#define MPN_SAME_OR_DECR_P(dst, src, size)      \
  MPN_SAME_OR_DECR2_P(dst, size, src, size)

/* If mul_basecase or mpn_sqr_basecase are not exported, used mpn_mul instead */
#ifndef mpn_mul_basecase
# define mpn_mul_basecase(dst,s1,n1,s2,n2) mpn_mul((dst),(s1),(n1),(s2),(n2))
#endif
#ifndef mpn_sqr_basecase
# define mpn_sqr_basecase(dst,src,n) mpn_mul((dst),(src),(n),(src),(n))
#endif

/* ASSERT */
__MPFR_DECLSPEC void mpfr_assert_fail (const char *, int,
                                       const char *);

#define ASSERT_FAIL(expr)  mpfr_assert_fail (__FILE__, __LINE__, #expr)
/* ASSERT() is for mpfr-longlong.h only. */
#define ASSERT(expr)       MPFR_ASSERTD(expr)

/* Access fields of GMP struct */
#define SIZ(x) ((x)->_mp_size)
#define ABSIZ(x) ABS (SIZ (x))
#define PTR(x) ((x)->_mp_d)
#define EXP(x) ((x)->_mp_exp)
#define PREC(x) ((x)->_mp_prec)
#define ALLOC(x) ((x)->_mp_alloc)

/* For longlong.h */
#ifdef HAVE_ATTRIBUTE_MODE
typedef unsigned int UQItype    __attribute__ ((mode (QI)));
typedef          int SItype     __attribute__ ((mode (SI)));
typedef unsigned int USItype    __attribute__ ((mode (SI)));
typedef          int DItype     __attribute__ ((mode (DI)));
typedef unsigned int UDItype    __attribute__ ((mode (DI)));
#else
typedef unsigned char UQItype;
typedef          long SItype;
typedef unsigned long USItype;
#ifdef HAVE_LONG_LONG
typedef long long int DItype;
typedef unsigned long long int UDItype;
#else /* Assume `long' gives us a wide enough type.  Needed for hppa2.0w.  */
typedef long int DItype;
typedef unsigned long int UDItype;
#endif
#endif
typedef mp_limb_t UWtype;
typedef unsigned int UHWtype;
#define W_TYPE_SIZE GMP_NUMB_BITS

/* Remap names of internal mpn functions (for longlong.h).  */
#undef  __clz_tab
#define __clz_tab               mpfr_clz_tab

/* Use (4.0 * ...) instead of (2.0 * ...) to work around buggy compilers
   that don't convert ulong->double correctly (eg. SunOS 4 native cc).  */
#undef MP_BASE_AS_DOUBLE
#define MP_BASE_AS_DOUBLE (4.0 * (MPFR_LIMB_ONE << (GMP_NUMB_BITS - 2)))

/* Structure for conversion between internal binary format and
   strings in base 2..36.  */
struct bases
{
  /* log(2)/log(conversion_base) */
  double chars_per_bit_exactly;
};
#undef  __mp_bases
#define __mp_bases mpfr_bases
__MPFR_DECLSPEC extern const struct bases mpfr_bases[257];

/* Standard macros */
#undef ABS
#undef MIN
#undef MAX
#define ABS(x) ((x) >= 0 ? (x) : -(x))
#define MIN(l,o) ((l) < (o) ? (l) : (o))
#define MAX(h,i) ((h) > (i) ? (h) : (i))

/* 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. */
#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);                                          \
      numberof_const (x);                                               \
    }) )
#else
# define numberof(x)                                    \
  (MPFR_ASSERTN ((void *) &(x) == (void *) &(x)[0]),    \
   numberof_const (x))
#endif

/* Allocate func are defined in gmp-impl.h.
   Warning: the code below fetches the GMP memory allocation functions the first
   time one allocates some mpfr_t, and then always uses those initial functions,
   even if the user later changes the GMP memory allocation functions with
   mp_set_memory_functions(). This is fine as long as the user who wants to use
   different memory allocation functions first calls mp_set_memory_functions()
   before any call to mpfr_init or mpfr_init2.
   For more complex usages, change #if 1 into #if 0. Warning! But in this
   case, the user must make sure that there are no data internal to MPFR
   allocated with the previous allocator. Freeing all the caches may be
   necessary, but this is not guaranteed to be sufficient. */

#if 1
#undef __gmp_allocate_func
#undef __gmp_reallocate_func
#undef __gmp_free_func
#define MPFR_GET_MEMFUNC                                        \
  ((void) (MPFR_LIKELY (mpfr_allocate_func != 0) ||             \
           (mp_get_memory_functions(&mpfr_allocate_func,        \
                                    &mpfr_reallocate_func,      \
                                    &mpfr_free_func), 1)))
#define __gmp_allocate_func   (MPFR_GET_MEMFUNC, mpfr_allocate_func)
#define __gmp_reallocate_func (MPFR_GET_MEMFUNC, mpfr_reallocate_func)
#define __gmp_free_func       (MPFR_GET_MEMFUNC, mpfr_free_func)
#else
extern void * (*__gmp_allocate_func) (size_t);
extern void * (*__gmp_reallocate_func) (void *, size_t, size_t);
extern void (*__gmp_free_func) (void *, size_t);
#endif

__MPFR_DECLSPEC extern MPFR_THREAD_ATTR void * (*mpfr_allocate_func)   (size_t);
__MPFR_DECLSPEC extern MPFR_THREAD_ATTR void * (*mpfr_reallocate_func) (void *, size_t, size_t);
__MPFR_DECLSPEC extern MPFR_THREAD_ATTR void   (*mpfr_free_func)       (void *, size_t);

#if defined(WANT_GMP_INTERNALS) && defined(HAVE___GMPN_SBPI1_DIVAPPR_Q)
#ifndef __gmpn_sbpi1_divappr_q
__MPFR_DECLSPEC mp_limb_t __gmpn_sbpi1_divappr_q (mp_limb_t*,
                mp_limb_t*, mp_size_t, mp_limb_t*, mp_size_t, mp_limb_t);
#endif
#endif

#if defined(WANT_GMP_INTERNALS) && defined(HAVE___GMPN_INVERT_LIMB)
#ifndef __gmpn_invert_limb
__MPFR_DECLSPEC mp_limb_t __gmpn_invert_limb (mp_limb_t);
#endif
#endif

/* Temp memory allocate */
struct tmp_marker
{
  void *ptr;
  size_t size;
  struct tmp_marker *next;
};

__MPFR_DECLSPEC void *mpfr_tmp_allocate (struct tmp_marker **,
                                         size_t);
__MPFR_DECLSPEC void mpfr_tmp_free (struct tmp_marker *);

/* Can be overriden at configure time. Useful for checking buffer overflow. */
#ifndef MPFR_ALLOCA_MAX
# define MPFR_ALLOCA_MAX 16384
#endif

/* Do not define TMP_SALLOC (see the test in mpfr-impl.h)! */
#define TMP_ALLOC(n) (MPFR_LIKELY ((n) <= MPFR_ALLOCA_MAX) ?       \
                      alloca (n) : mpfr_tmp_allocate (&tmp_marker, (n)))
#define TMP_DECL(m) struct tmp_marker *tmp_marker
#define TMP_MARK(m) (tmp_marker = 0)
/* Note about TMP_FREE: For small precisions, tmp_marker is null as
   the allocation is done on the stack (see TMP_ALLOC above). */
#define TMP_FREE(m) \
  (MPFR_LIKELY (tmp_marker == NULL) ? (void) 0 : mpfr_tmp_free (tmp_marker))

#endif /* GMP Internal replacement */



/******************************************************
 ****** GMP Interface which changes with versions *****
 ****** to other versions of GMP. Add missing     *****
 ****** interfaces.                               *****
 ******************************************************/

/* If a mpn_sqr_n macro is not defined, use mpn_mul. GMP 4.x defines a
   mpn_sqr_n macro in gmp-impl.h (and this macro disappeared in GMP 5),
   so that GMP's macro can only be used when MPFR has been configured
   with --with-gmp-build (and only with GMP 4.x). */
#ifndef mpn_sqr_n
# define mpn_sqr_n(dst,src,n) mpn_mul((dst),(src),(n),(src),(n))
#endif

/* invert_limb macro, copied from GMP 5.0.2, file gmp-impl.h.
   It returns invxl = floor((B^2-1)/xl)-B, where B=2^BITS_PER_LIMB,
   assuming the most significant bit of xl is set. */
#ifndef invert_limb
#if defined(WANT_GMP_INTERNALS) && defined(HAVE___GMPN_INVERT_LIMB)
#define invert_limb(invxl,xl)                             \
  do {                                                    \
    invxl = __gmpn_invert_limb (xl);                      \
  } while (0)
#else
#define invert_limb(invxl,xl)                             \
  do {                                                    \
    mp_limb_t dummy MPFR_MAYBE_UNUSED;                    \
    MPFR_ASSERTD ((xl) != 0);                             \
    udiv_qrnnd (invxl, dummy, ~(xl), MPFR_LIMB_MAX, xl);  \
  } while (0)
#endif /* defined(WANT_GMP_INTERNALS) && defined(HAVE___GMPN_INVERT_LIMB) */
#endif /* ifndef invert_limb */

/* udiv_qr_3by2 macro, adapted from GMP 5.0.2, file gmp-impl.h.
   Compute quotient the quotient and remainder for n / d. Requires d
   >= B^2 / 2 and n < d B. dinv is the inverse

     floor ((B^3 - 1) / (d0 + d1 B)) - B.

   NOTE: Output variables are updated multiple times. Only some inputs
   and outputs may overlap.
*/
#ifndef udiv_qr_3by2
#define udiv_qr_3by2(q, r1, r0, n2, n1, n0, d1, d0, dinv)               \
  do {                                                                  \
    mp_limb_t _q0, _t1, _t0, _mask;                                     \
    umul_ppmm ((q), _q0, (n2), (dinv));                                 \
    add_ssaaaa ((q), _q0, (q), _q0, (n2), (n1));                        \
                                                                        \
    /* Compute the two most significant limbs of n - q'd */             \
    (r1) = (n1) - (d1) * (q);                                           \
    (r0) = (n0);                                                        \
    sub_ddmmss ((r1), (r0), (r1), (r0), (d1), (d0));                    \
    umul_ppmm (_t1, _t0, (d0), (q));                                    \
    sub_ddmmss ((r1), (r0), (r1), (r0), _t1, _t0);                      \
    (q)++;                                                              \
                                                                        \
    /* Conditionally adjust q and the remainders */                     \
    _mask = - (mp_limb_t) ((r1) >= _q0);                                \
    (q) += _mask;                                                       \
    add_ssaaaa ((r1), (r0), (r1), (r0), _mask & (d1), _mask & (d0));    \
    if (MPFR_UNLIKELY ((r1) >= (d1)))                                   \
      {                                                                 \
        if ((r1) > (d1) || (r0) >= (d0))                                \
          {                                                             \
            (q)++;                                                      \
            sub_ddmmss ((r1), (r0), (r1), (r0), (d1), (d0));            \
          }                                                             \
      }                                                                 \
  } while (0)
#endif

/* invert_pi1 macro adapted from GMP 5 */
typedef struct {mp_limb_t inv32;} mpfr_pi1_t;
#ifndef invert_pi1
#define invert_pi1(dinv, d1, d0)                                        \
  do {                                                                  \
    mp_limb_t _v, _p, _t1, _t0, _mask;                                  \
    invert_limb (_v, d1);                                               \
    _p = (d1) * _v;                                                     \
    _p += (d0);                                                         \
    if (_p < (d0))                                                      \
      {                                                                 \
        _v--;                                                           \
        _mask = -(mp_limb_t) (_p >= (d1));                              \
        _p -= (d1);                                                     \
        _v += _mask;                                                    \
        _p -= _mask & (d1);                                             \
      }                                                                 \
    umul_ppmm (_t1, _t0, d0, _v);                                       \
    _p += _t1;                                                          \
    if (_p < _t1)                                                       \
      {                                                                 \
        _v--;                                                           \
        if (MPFR_UNLIKELY (_p >= (d1)))                                 \
          {                                                             \
            if (_p > (d1) || _t0 >= (d0))                               \
              _v--;                                                     \
          }                                                             \
      }                                                                 \
    (dinv).inv32 = _v;                                                  \
  } while (0)
#endif

/* mpn_copyd is a new exported function in GMP 5.
   It existed in GMP 4 in the internal header, but still may not be
   defined if HAVE_NATIVE_mpn_copyd is not defined */
#if !__MPFR_GMP(5,0,0)
# undef  mpn_copyd
# define mpn_copyd MPN_COPY
#endif

/* The following macro is copied from GMP-6.1.1, file gmp-impl.h,
   macro udiv_qrnnd_preinv.
   It computes q and r such that nh*2^GMP_NUMB_BITS + nl = q*d + r,
   with 0 <= r < d, assuming di = __gmpn_invert_limb (d). */
#define __udiv_qrnnd_preinv(q, r, nh, nl, d, di)                        \
  do {                                                                  \
    mp_limb_t _qh, _ql, _r, _mask;                                      \
    umul_ppmm (_qh, _ql, (nh), (di));                                   \
    if (__builtin_constant_p (nl) && (nl) == 0)                         \
      {                                                                 \
        _qh += (nh) + 1;                                                \
        _r = - _qh * (d);                                               \
        _mask = -(mp_limb_t) (_r > _ql); /* both > and >= are OK */     \
        _qh += _mask;                                                   \
        _r += _mask & (d);                                              \
      }                                                                 \
    else                                                                \
      {                                                                 \
        add_ssaaaa (_qh, _ql, _qh, _ql, (nh) + 1, (nl));                \
        _r = (nl) - _qh * (d);                                          \
        _mask = -(mp_limb_t) (_r > _ql); /* both > and >= are OK */     \
        _qh += _mask;                                                   \
        _r += _mask & (d);                                              \
        if (MPFR_UNLIKELY (_r >= (d)))                                  \
          {                                                             \
            _r -= (d);                                                  \
            _qh++;                                                      \
          }                                                             \
      }                                                                 \
    (r) = _r;                                                           \
    (q) = _qh;                                                          \
  } while (0)

#if GMP_NUMB_BITS == 64
/* specialized version for nl = 0, with di computed inside */
#define __udiv_qrnd_preinv(q, r, nh, d)                                 \
  do {                                                                  \
    mp_limb_t _di;                                                      \
                                                                        \
    MPFR_ASSERTD ((d) != 0);                                            \
    MPFR_ASSERTD ((nh) < (d));                                          \
    MPFR_ASSERTD ((d) & MPFR_LIMB_HIGHBIT);                             \
                                                                        \
    __gmpfr_invert_limb (_di, d);                                       \
    __udiv_qrnnd_preinv (q, r, nh, 0, d, _di);                          \
  } while (0)
#elif defined(WANT_GMP_INTERNALS) && defined(HAVE___GMPN_INVERT_LIMB)
/* specialized version for nl = 0, with di computed inside */
#define __udiv_qrnd_preinv(q, r, nh, d)                                 \
  do {                                                                  \
    mp_limb_t _di;                                                      \
                                                                        \
    MPFR_ASSERTD ((d) != 0);                                            \
    MPFR_ASSERTD ((nh) < (d));                                          \
    MPFR_ASSERTD ((d) & MPFR_LIMB_HIGHBIT);                             \
                                                                        \
    _di = __gmpn_invert_limb (d);                                       \
    __udiv_qrnnd_preinv (q, r, nh, 0, d, _di);                          \
  } while (0)
#else
/* Same as __udiv_qrnnd_c from longlong.h, but using a single UWType/UWtype
   division instead of two, and with n0=0. The analysis below assumes a limb
   has 64 bits for simplicity. */
#define __udiv_qrnd_preinv(q, r, n1, d)                                 \
  do {                                                                  \
    UWtype __d1, __d0, __q1, __q0, __r1, __r0, __i;                     \
                                                                        \
    MPFR_ASSERTD ((d) != 0);                                            \
    MPFR_ASSERTD ((n1) < (d));                                          \
    MPFR_ASSERTD ((d) & MPFR_LIMB_HIGHBIT);                             \
                                                                        \
    __d1 = __ll_highpart (d);                                           \
    /* 2^31 <= d1 < 2^32 */                                             \
    __d0 = __ll_lowpart (d);                                            \
    /* 0 <= d0 < 2^32 */                                                \
    __i = ~(UWtype) 0 / __d1;                                           \
    /* 2^32 < i < 2^33 with i < 2^64/d1 */                              \
                                                                        \
    __q1 = (((n1) / __ll_B) * __i) / __ll_B;                            \
    /* Since n1 < d, high(n1) <= d1 = high(d), thus */                  \
    /* q1 <= high(n1) * (2^64/d1) / 2^32 <= 2^32 */                     \
    /* and also q1 <= n1/d1 thus r1 >= 0 below */                       \
    __r1 = (n1) - __q1 * __d1;                                          \
    while (__r1 >= __d1)                                                \
      __q1 ++, __r1 -= __d1;                                            \
    /* by construction, we have n1 = q1*d1+r1, and 0 <= r1 < d1 */      \
    /* thus q1 <= n1/d1 < 2^32+2 */                                     \
    /* q1*d0 <= (2^32+1)*(2^32-1) <= 2^64-1 thus it fits in a limb. */  \
    __r0 = __r1 * __ll_B;                                               \
    __r1 = __r0 - __q1 * __d0;                                          \
    /* At most two corrections are needed like in __udiv_qrnnd_c. */    \
    if (__r1 > __r0) /* borrow when subtracting q1*d0 */                \
      {                                                                 \
        __q1--, __r1 += (d);                                            \
        if (__r1 > (d)) /* no carry when adding d */                    \
          __q1--, __r1 += (d);                                          \
      }                                                                 \
    /* We can have r1 < m here, but in this case the true remainder */  \
    /* is 2^64+r1, which is > m (same analysis as below for r0). */     \
    /* Now we have n1*2^32 = q1*d + r1, with 0 <= r1 < d. */            \
    MPFR_ASSERTD(__r1 < (d));                                           \
                                                                        \
    /* The same analysis as above applies, with n1 replaced by r1, */   \
    /* q1 by q0, r1 by r0. */                                           \
    __q0 = ((__r1 / __ll_B) * __i) / __ll_B;                            \
    __r0 = __r1  - __q0 * __d1;                                         \
    while (__r0 >= __d1)                                                \
      __q0 ++, __r0 -= __d1;                                            \
    __r1 = __r0 * __ll_B;                                               \
    __r0 = __r1 - __q0 * __d0;                                          \
    /* We know the quotient floor(r1*2^64/d) is q0, q0-1 or q0-2.*/     \
    if (__r0 > __r1) /* borrow when subtracting q0*d0 */                \
      {                                                                 \
        /* The quotient is either q0-1 or q0-2. */                      \
        __q0--, __r0 += (d);                                            \
        if (__r0 > (d)) /* no carry when adding d */                    \
          __q0--, __r0 += (d);                                          \
      }                                                                 \
    /* Now we have n1*2^64 = (q1*2^32+q0)*d + r0, with 0 <= r0 < d. */  \
    MPFR_ASSERTD(__r0 < (d));                                           \
                                                                        \
    (q) = __q1 * __ll_B | __q0;                                         \
    (r) = __r0;                                                         \
  } while (0)
#endif

/******************************************************
 ************* GMP Basic Pointer Types ****************
 ******************************************************/
/* Compatibility with old GMP versions. */
#if !__MPFR_GMP(5,0,0)
typedef unsigned long mp_bitcnt_t;
#endif

typedef mp_limb_t *mpfr_limb_ptr;
typedef const mp_limb_t *mpfr_limb_srcptr;

/* mpfr_ieee_double_extract structure (copied from GMP 6.1.0, gmp-impl.h, with
   ieee_double_extract changed into mpfr_ieee_double_extract, and
   _GMP_IEEE_FLOATS changed into _MPFR_IEEE_FLOATS). */

/* Define mpfr_ieee_double_extract and _MPFR_IEEE_FLOATS.

   Bit field packing is "implementation defined" according to C99, which
   leaves us at the compiler's mercy here.  For some systems packing is
   defined in the ABI (eg. x86).  In any case so far it seems universal that
   little endian systems pack from low to high, and big endian from high to
   low within the given type.

   Within the fields we rely on the integer endianness being the same as the
   float endianness, this is true everywhere we know of and it'd be a fairly
   strange system that did anything else.  */

/* Note for MPFR: building with "gcc -std=c89 -pedantic -pedantic-errors"
   fails if the bit-field type is unsigned long:

     error: type of bit-field '...' is a GCC extension [-Wpedantic]

   Though with -std=c99 no errors are obtained, this is still an extension
   in C99, which says:

     A bit-field shall have a type that is a qualified or unqualified version
     of _Bool, signed int, unsigned int, or some other implementation-defined
     type.

   So, unsigned int should be better. This will fail with implementations
   having 16-bit int's, but such implementations are not required to
   support bit-fields of size > 16 anyway; if ever an implementation with
   16-bit int's is found, the appropriate minimal changes could still be
   done in the future.
*/

#ifndef _MPFR_IEEE_FLOATS

#ifdef HAVE_DOUBLE_IEEE_LITTLE_ENDIAN
#define _MPFR_IEEE_FLOATS 1
union mpfr_ieee_double_extract
{
  struct
    {
      unsigned int manl:32;
      unsigned int manh:20;
      unsigned int exp:11;
      unsigned int sig:1;
    } s;
  double d;
};
#endif

#ifdef HAVE_DOUBLE_IEEE_BIG_ENDIAN
#define _MPFR_IEEE_FLOATS 1
union mpfr_ieee_double_extract
{
  struct
    {
      unsigned int sig:1;
      unsigned int exp:11;
      unsigned int manh:20;
      unsigned int manl:32;
    } s;
  double d;
};
#endif

#endif /* _MPFR_IEEE_FLOATS */

/******************************************************
 ******************** C++ Compatibility ***************
 ******************************************************/
#if defined (__cplusplus)
}
#endif

#endif /* Gmp internal emulator */