Add configury for GMP library

* configure.ac (GMP_LIB, GMP_OBJ): New substs.
* src/Makefile.in (GMP_OBJ, GMP_OBJ): New variables.
(base_obj): Add GMP_OBJ.
(LIBES): Add GMP_LIB.
* src/mini-gmp.h: New file.
* src/mini-gmp.c: New file.

4 files changed, 4772 insertions, 2 deletions

diff --git a/configure.ac b/configure.ac
index 6613ce1eaaf..e202acf8cd2 100644
--- a/configure.ac
+++ b/configure.ac
@@ -4302,6 +4302,20 @@ AC_SUBST(KRB5LIB)
 AC_SUBST(DESLIB)
 AC_SUBST(KRB4LIB)
 
+GMP_LIB=
+GMP_OBJ=
+HAVE_GMP=no
+AC_CHECK_LIB(gmp, __gmpz_init, [
+  AC_CHECK_HEADERS(gmp.h, [
+    GMP_LIB=-lgmp
+    HAVE_GMP=yes
+    AC_DEFINE(HAVE_GMP, 1, [Define to 1 if you have gmp.h and -lgmp])])])
+if test $HAVE_GMP = no; then
+   GMP_OBJ=mini-gmp.o
+fi
+AC_SUBST(GMP_LIB)
+AC_SUBST(GMP_OBJ)
+
 AC_CHECK_HEADERS(valgrind/valgrind.h)
 
 AC_CHECK_MEMBERS([struct unipair.unicode], [], [], [[#include <linux/kd.h>]])
@@ -5450,6 +5464,7 @@ AS_ECHO(["  Does Emacs use -lXaw3d?                                 ${HAVE_XAW3D
   Does Emacs use -lxft?                                   ${HAVE_XFT}
   Does Emacs use -lsystemd?                               ${HAVE_LIBSYSTEMD}
   Does Emacs use -ljansson?                               ${HAVE_JSON}
+  Does Emacs use -lgmp?                                   ${HAVE_GMP}
   Does Emacs directly use zlib?                           ${HAVE_ZLIB}
   Does Emacs have dynamic modules support?                ${HAVE_MODULES}
   Does Emacs use toolkit scroll bars?                     ${USE_TOOLKIT_SCROLL_BARS}
diff --git a/src/Makefile.in b/src/Makefile.in
index c3bcc503492..05d24acef6c 100644
--- a/src/Makefile.in
+++ b/src/Makefile.in
@@ -322,6 +322,9 @@ INTERVALS_H = dispextern.h intervals.h composite.h
 
 GETLOADAVG_LIBS = @GETLOADAVG_LIBS@
 
+GMP_LIB = @GMP_LIB@
+GMP_OBJ = @GMP_OBJ@
+
 RUN_TEMACS = ./temacs
 
 # Whether builds should contain details. '--no-build-details' or empty.
@@ -403,7 +406,7 @@ base_obj = dispnew.o frame.o scroll.o xdisp.o menu.o $(XMENU_OBJ) window.o \
         thread.o systhread.o \
         $(if $(HYBRID_MALLOC),sheap.o) \
         $(MSDOS_OBJ) $(MSDOS_X_OBJ) $(NS_OBJ) $(CYGWIN_OBJ) $(FONT_OBJ) \
-        $(W32_OBJ) $(WINDOW_SYSTEM_OBJ) $(XGSELOBJ) $(JSON_OBJ)
+        $(W32_OBJ) $(WINDOW_SYSTEM_OBJ) $(XGSELOBJ) $(JSON_OBJ) $(GMP_OBJ)
 obj = $(base_obj) $(NS_OBJC_OBJ)
 
 ## Object files used on some machine or other.
@@ -501,7 +504,7 @@ LIBES = $(LIBS) $(W32_LIBS) $(LIBS_GNUSTEP) $(LIBX_BASE) $(LIBIMAGE) \
    $(FREETYPE_LIBS) $(FONTCONFIG_LIBS) $(LIBOTF_LIBS) $(M17N_FLT_LIBS) \
    $(LIBGNUTLS_LIBS) $(LIB_PTHREAD) $(GETADDRINFO_A_LIBS) $(LCMS2_LIBS) \
    $(NOTIFY_LIBS) $(LIB_MATH) $(LIBZ) $(LIBMODULES) $(LIBSYSTEMD_LIBS) \
-   $(JSON_LIBS)
+   $(JSON_LIBS) $(GMP_LIB)
 
 ## FORCE it so that admin/unidata can decide whether these files
 ## are up-to-date.  Although since charprop depends on bootstrap-emacs,
diff --git a/src/mini-gmp.c b/src/mini-gmp.c
new file mode 100644
index 00000000000..c0d5b879a83
--- /dev/null
+++ b/src/mini-gmp.c
@@ -0,0 +1,4452 @@
+/* mini-gmp, a minimalistic implementation of a GNU GMP subset.
+
+   Contributed to the GNU project by Niels Möller
+
+Copyright 1991-1997, 1999-2018 Free Software Foundation, Inc.
+
+This file is part of the GNU MP Library.
+
+The GNU MP Library is free software; you can redistribute it and/or modify
+it under the terms of either:
+
+  * 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.
+
+or
+
+  * the GNU General Public License as published by the Free Software
+    Foundation; either version 2 of the License, or (at your option) any
+    later version.
+
+or both in parallel, as here.
+
+The GNU MP 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 General Public License
+for more details.
+
+You should have received copies of the GNU General Public License and the
+GNU Lesser General Public License along with the GNU MP Library.  If not,
+see https://www.gnu.org/licenses/.  */
+
+/* NOTE: All functions in this file which are not declared in
+   mini-gmp.h are internal, and are not intended to be compatible
+   neither with GMP nor with future versions of mini-gmp. */
+
+/* Much of the material copied from GMP files, including: gmp-impl.h,
+   longlong.h, mpn/generic/add_n.c, mpn/generic/addmul_1.c,
+   mpn/generic/lshift.c, mpn/generic/mul_1.c,
+   mpn/generic/mul_basecase.c, mpn/generic/rshift.c,
+   mpn/generic/sbpi1_div_qr.c, mpn/generic/sub_n.c,
+   mpn/generic/submul_1.c. */
+
+#include <assert.h>
+#include <ctype.h>
+#include <limits.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+#include "mini-gmp.h"
+
+#if !defined(MINI_GMP_DONT_USE_FLOAT_H)
+#include <float.h>
+#endif
+
+
+/* Macros */
+#define GMP_LIMB_BITS (sizeof(mp_limb_t) * CHAR_BIT)
+
+#define GMP_LIMB_MAX (~ (mp_limb_t) 0)
+#define GMP_LIMB_HIGHBIT ((mp_limb_t) 1 << (GMP_LIMB_BITS - 1))
+
+#define GMP_HLIMB_BIT ((mp_limb_t) 1 << (GMP_LIMB_BITS / 2))
+#define GMP_LLIMB_MASK (GMP_HLIMB_BIT - 1)
+
+#define GMP_ULONG_BITS (sizeof(unsigned long) * CHAR_BIT)
+#define GMP_ULONG_HIGHBIT ((unsigned long) 1 << (GMP_ULONG_BITS - 1))
+
+#define GMP_ABS(x) ((x) >= 0 ? (x) : -(x))
+#define GMP_NEG_CAST(T,x) (-((T)((x) + 1) - 1))
+
+#define GMP_MIN(a, b) ((a) < (b) ? (a) : (b))
+#define GMP_MAX(a, b) ((a) > (b) ? (a) : (b))
+
+#define GMP_CMP(a,b) (((a) > (b)) - ((a) < (b)))
+
+#if defined(DBL_MANT_DIG) && FLT_RADIX == 2
+#define GMP_DBL_MANT_BITS DBL_MANT_DIG
+#else
+#define GMP_DBL_MANT_BITS (53)
+#endif
+
+/* Return non-zero if xp,xsize and yp,ysize overlap.
+   If xp+xsize<=yp there's no overlap, or if yp+ysize<=xp there's no
+   overlap.  If both these are false, there's an overlap. */
+#define GMP_MPN_OVERLAP_P(xp, xsize, yp, ysize)                         \
+  ((xp) + (xsize) > (yp) && (yp) + (ysize) > (xp))
+
+#define gmp_assert_nocarry(x) do { \
+    mp_limb_t __cy = (x);          \
+    assert (__cy == 0);            \
+  } while (0)
+
+#define gmp_clz(count, x) do {                                          \
+    mp_limb_t __clz_x = (x);                                            \
+    unsigned __clz_c;                                                   \
+    for (__clz_c = 0;                                                   \
+         (__clz_x & ((mp_limb_t) 0xff << (GMP_LIMB_BITS - 8))) == 0;    \
+         __clz_c += 8)                                                  \
+      __clz_x <<= 8;                                                    \
+    for (; (__clz_x & GMP_LIMB_HIGHBIT) == 0; __clz_c++)                \
+      __clz_x <<= 1;                                                    \
+    (count) = __clz_c;                                                  \
+  } while (0)
+
+#define gmp_ctz(count, x) do {                                          \
+    mp_limb_t __ctz_x = (x);                                            \
+    unsigned __ctz_c = 0;                                               \
+    gmp_clz (__ctz_c, __ctz_x & - __ctz_x);                             \
+    (count) = GMP_LIMB_BITS - 1 - __ctz_c;                              \
+  } while (0)
+
+#define gmp_add_ssaaaa(sh, sl, ah, al, bh, bl) \
+  do {                                                                  \
+    mp_limb_t __x;                                                      \
+    __x = (al) + (bl);                                                  \
+    (sh) = (ah) + (bh) + (__x < (al));                                  \
+    (sl) = __x;                                                         \
+  } while (0)
+
+#define gmp_sub_ddmmss(sh, sl, ah, al, bh, bl) \
+  do {                                                                  \
+    mp_limb_t __x;                                                      \
+    __x = (al) - (bl);                                                  \
+    (sh) = (ah) - (bh) - ((al) < (bl));                                 \
+    (sl) = __x;                                                         \
+  } while (0)
+
+#define gmp_umul_ppmm(w1, w0, u, v)                                     \
+  do {                                                                  \
+    mp_limb_t __x0, __x1, __x2, __x3;                                   \
+    unsigned __ul, __vl, __uh, __vh;                                    \
+    mp_limb_t __u = (u), __v = (v);                                     \
+                                                                        \
+    __ul = __u & GMP_LLIMB_MASK;                                        \
+    __uh = __u >> (GMP_LIMB_BITS / 2);                                  \
+    __vl = __v & GMP_LLIMB_MASK;                                        \
+    __vh = __v >> (GMP_LIMB_BITS / 2);                                  \
+                                                                        \
+    __x0 = (mp_limb_t) __ul * __vl;                                     \
+    __x1 = (mp_limb_t) __ul * __vh;                                     \
+    __x2 = (mp_limb_t) __uh * __vl;                                     \
+    __x3 = (mp_limb_t) __uh * __vh;                                     \
+                                                                        \
+    __x1 += __x0 >> (GMP_LIMB_BITS / 2);/* this can't give carry */     \
+    __x1 += __x2;               /* but this indeed can */               \
+    if (__x1 < __x2)            /* did we get it? */                    \
+      __x3 += GMP_HLIMB_BIT;    /* yes, add it in the proper pos. */    \
+                                                                        \
+    (w1) = __x3 + (__x1 >> (GMP_LIMB_BITS / 2));                        \
+    (w0) = (__x1 << (GMP_LIMB_BITS / 2)) + (__x0 & GMP_LLIMB_MASK);     \
+  } while (0)
+
+#define gmp_udiv_qrnnd_preinv(q, r, nh, nl, d, di)                      \
+  do {                                                                  \
+    mp_limb_t _qh, _ql, _r, _mask;                                      \
+    gmp_umul_ppmm (_qh, _ql, (nh), (di));                               \
+    gmp_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 (_r >= (d))                                                      \
+      {                                                                 \
+        _r -= (d);                                                      \
+        _qh++;                                                          \
+      }                                                                 \
+                                                                        \
+    (r) = _r;                                                           \
+    (q) = _qh;                                                          \
+  } while (0)
+
+#define gmp_udiv_qr_3by2(q, r1, r0, n2, n1, n0, d1, d0, dinv)           \
+  do {                                                                  \
+    mp_limb_t _q0, _t1, _t0, _mask;                                     \
+    gmp_umul_ppmm ((q), _q0, (n2), (dinv));                             \
+    gmp_add_ssaaaa ((q), _q0, (q), _q0, (n2), (n1));                    \
+                                                                        \
+    /* Compute the two most significant limbs of n - q'd */             \
+    (r1) = (n1) - (d1) * (q);                                           \
+    gmp_sub_ddmmss ((r1), (r0), (r1), (n0), (d1), (d0));                \
+    gmp_umul_ppmm (_t1, _t0, (d0), (q));                                \
+    gmp_sub_ddmmss ((r1), (r0), (r1), (r0), _t1, _t0);                  \
+    (q)++;                                                              \
+                                                                        \
+    /* Conditionally adjust q and the remainders */                     \
+    _mask = - (mp_limb_t) ((r1) >= _q0);                                \
+    (q) += _mask;                                                       \
+    gmp_add_ssaaaa ((r1), (r0), (r1), (r0), _mask & (d1), _mask & (d0)); \
+    if ((r1) >= (d1))                                                   \
+      {                                                                 \
+        if ((r1) > (d1) || (r0) >= (d0))                                \
+          {                                                             \
+            (q)++;                                                      \
+            gmp_sub_ddmmss ((r1), (r0), (r1), (r0), (d1), (d0));        \
+          }                                                             \
+      }                                                                 \
+  } while (0)
+
+/* Swap macros. */
+#define MP_LIMB_T_SWAP(x, y)                                            \
+  do {                                                                  \
+    mp_limb_t __mp_limb_t_swap__tmp = (x);                              \
+    (x) = (y);                                                          \
+    (y) = __mp_limb_t_swap__tmp;                                        \
+  } while (0)
+#define MP_SIZE_T_SWAP(x, y)                                            \
+  do {                                                                  \
+    mp_size_t __mp_size_t_swap__tmp = (x);                              \
+    (x) = (y);                                                          \
+    (y) = __mp_size_t_swap__tmp;                                        \
+  } while (0)
+#define MP_BITCNT_T_SWAP(x,y)                   \
+  do {                                          \
+    mp_bitcnt_t __mp_bitcnt_t_swap__tmp = (x);  \
+    (x) = (y);                                  \
+    (y) = __mp_bitcnt_t_swap__tmp;              \
+  } while (0)
+#define MP_PTR_SWAP(x, y)                                               \
+  do {                                                                  \
+    mp_ptr __mp_ptr_swap__tmp = (x);                                    \
+    (x) = (y);                                                          \
+    (y) = __mp_ptr_swap__tmp;                                           \
+  } while (0)
+#define MP_SRCPTR_SWAP(x, y)                                            \
+  do {                                                                  \
+    mp_srcptr __mp_srcptr_swap__tmp = (x);                              \
+    (x) = (y);                                                          \
+    (y) = __mp_srcptr_swap__tmp;                                        \
+  } while (0)
+
+#define MPN_PTR_SWAP(xp,xs, yp,ys)                                      \
+  do {                                                                  \
+    MP_PTR_SWAP (xp, yp);                                               \
+    MP_SIZE_T_SWAP (xs, ys);                                            \
+  } while(0)
+#define MPN_SRCPTR_SWAP(xp,xs, yp,ys)                                   \
+  do {                                                                  \
+    MP_SRCPTR_SWAP (xp, yp);                                            \
+    MP_SIZE_T_SWAP (xs, ys);                                            \
+  } while(0)
+
+#define MPZ_PTR_SWAP(x, y)                                              \
+  do {                                                                  \
+    mpz_ptr __mpz_ptr_swap__tmp = (x);                                  \
+    (x) = (y);                                                          \
+    (y) = __mpz_ptr_swap__tmp;                                          \
+  } while (0)
+#define MPZ_SRCPTR_SWAP(x, y)                                           \
+  do {                                                                  \
+    mpz_srcptr __mpz_srcptr_swap__tmp = (x);                            \
+    (x) = (y);                                                          \
+    (y) = __mpz_srcptr_swap__tmp;                                       \
+  } while (0)
+
+const int mp_bits_per_limb = GMP_LIMB_BITS;
+
+
+/* Memory allocation and other helper functions. */
+static void
+gmp_die (const char *msg)
+{
+  fprintf (stderr, "%s\n", msg);
+  abort();
+}
+
+static void *
+gmp_default_alloc (size_t size)
+{
+  void *p;
+
+  assert (size > 0);
+
+  p = malloc (size);
+  if (!p)
+    gmp_die("gmp_default_alloc: Virtual memory exhausted.");
+
+  return p;
+}
+
+static void *
+gmp_default_realloc (void *old, size_t old_size, size_t new_size)
+{
+  void * p;
+
+  p = realloc (old, new_size);
+
+  if (!p)
+    gmp_die("gmp_default_realloc: Virtual memory exhausted.");
+
+  return p;
+}
+
+static void
+gmp_default_free (void *p, size_t size)
+{
+  free (p);
+}
+
+static void * (*gmp_allocate_func) (size_t) = gmp_default_alloc;
+static void * (*gmp_reallocate_func) (void *, size_t, size_t) = gmp_default_realloc;
+static void (*gmp_free_func) (void *, size_t) = gmp_default_free;
+
+void
+mp_get_memory_functions (void *(**alloc_func) (size_t),
+                         void *(**realloc_func) (void *, size_t, size_t),
+                         void (**free_func) (void *, size_t))
+{
+  if (alloc_func)
+    *alloc_func = gmp_allocate_func;
+
+  if (realloc_func)
+    *realloc_func = gmp_reallocate_func;
+
+  if (free_func)
+    *free_func = gmp_free_func;
+}
+
+void
+mp_set_memory_functions (void *(*alloc_func) (size_t),
+                         void *(*realloc_func) (void *, size_t, size_t),
+                         void (*free_func) (void *, size_t))
+{
+  if (!alloc_func)
+    alloc_func = gmp_default_alloc;
+  if (!realloc_func)
+    realloc_func = gmp_default_realloc;
+  if (!free_func)
+    free_func = gmp_default_free;
+
+  gmp_allocate_func = alloc_func;
+  gmp_reallocate_func = realloc_func;
+  gmp_free_func = free_func;
+}
+
+#define gmp_xalloc(size) ((*gmp_allocate_func)((size)))
+#define gmp_free(p) ((*gmp_free_func) ((p), 0))
+
+static mp_ptr
+gmp_xalloc_limbs (mp_size_t size)
+{
+  return (mp_ptr) gmp_xalloc (size * sizeof (mp_limb_t));
+}
+
+static mp_ptr
+gmp_xrealloc_limbs (mp_ptr old, mp_size_t size)
+{
+  assert (size > 0);
+  return (mp_ptr) (*gmp_reallocate_func) (old, 0, size * sizeof (mp_limb_t));
+}
+
+
+/* MPN interface */
+
+void
+mpn_copyi (mp_ptr d, mp_srcptr s, mp_size_t n)
+{
+  mp_size_t i;
+  for (i = 0; i < n; i++)
+    d[i] = s[i];
+}
+
+void
+mpn_copyd (mp_ptr d, mp_srcptr s, mp_size_t n)
+{
+  while (--n >= 0)
+    d[n] = s[n];
+}
+
+int
+mpn_cmp (mp_srcptr ap, mp_srcptr bp, mp_size_t n)
+{
+  while (--n >= 0)
+    {
+      if (ap[n] != bp[n])
+        return ap[n] > bp[n] ? 1 : -1;
+    }
+  return 0;
+}
+
+static int
+mpn_cmp4 (mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
+{
+  if (an != bn)
+    return an < bn ? -1 : 1;
+  else
+    return mpn_cmp (ap, bp, an);
+}
+
+static mp_size_t
+mpn_normalized_size (mp_srcptr xp, mp_size_t n)
+{
+  while (n > 0 && xp[n-1] == 0)
+    --n;
+  return n;
+}
+
+int
+mpn_zero_p(mp_srcptr rp, mp_size_t n)
+{
+  return mpn_normalized_size (rp, n) == 0;
+}
+
+void
+mpn_zero (mp_ptr rp, mp_size_t n)
+{
+  while (--n >= 0)
+    rp[n] = 0;
+}
+
+mp_limb_t
+mpn_add_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b)
+{
+  mp_size_t i;
+
+  assert (n > 0);
+  i = 0;
+  do
+    {
+      mp_limb_t r = ap[i] + b;
+      /* Carry out */
+      b = (r < b);
+      rp[i] = r;
+    }
+  while (++i < n);
+
+  return b;
+}
+
+mp_limb_t
+mpn_add_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
+{
+  mp_size_t i;
+  mp_limb_t cy;
+
+  for (i = 0, cy = 0; i < n; i++)
+    {
+      mp_limb_t a, b, r;
+      a = ap[i]; b = bp[i];
+      r = a + cy;
+      cy = (r < cy);
+      r += b;
+      cy += (r < b);
+      rp[i] = r;
+    }
+  return cy;
+}
+
+mp_limb_t
+mpn_add (mp_ptr rp, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
+{
+  mp_limb_t cy;
+
+  assert (an >= bn);
+
+  cy = mpn_add_n (rp, ap, bp, bn);
+  if (an > bn)
+    cy = mpn_add_1 (rp + bn, ap + bn, an - bn, cy);
+  return cy;
+}
+
+mp_limb_t
+mpn_sub_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b)
+{
+  mp_size_t i;
+
+  assert (n > 0);
+
+  i = 0;
+  do
+    {
+      mp_limb_t a = ap[i];
+      /* Carry out */
+      mp_limb_t cy = a < b;
+      rp[i] = a - b;
+      b = cy;
+    }
+  while (++i < n);
+
+  return b;
+}
+
+mp_limb_t
+mpn_sub_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
+{
+  mp_size_t i;
+  mp_limb_t cy;
+
+  for (i = 0, cy = 0; i < n; i++)
+    {
+      mp_limb_t a, b;
+      a = ap[i]; b = bp[i];
+      b += cy;
+      cy = (b < cy);
+      cy += (a < b);
+      rp[i] = a - b;
+    }
+  return cy;
+}
+
+mp_limb_t
+mpn_sub (mp_ptr rp, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
+{
+  mp_limb_t cy;
+
+  assert (an >= bn);
+
+  cy = mpn_sub_n (rp, ap, bp, bn);
+  if (an > bn)
+    cy = mpn_sub_1 (rp + bn, ap + bn, an - bn, cy);
+  return cy;
+}
+
+mp_limb_t
+mpn_mul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl)
+{
+  mp_limb_t ul, cl, hpl, lpl;
+
+  assert (n >= 1);
+
+  cl = 0;
+  do
+    {
+      ul = *up++;
+      gmp_umul_ppmm (hpl, lpl, ul, vl);
+
+      lpl += cl;
+      cl = (lpl < cl) + hpl;
+
+      *rp++ = lpl;
+    }
+  while (--n != 0);
+
+  return cl;
+}
+
+mp_limb_t
+mpn_addmul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl)
+{
+  mp_limb_t ul, cl, hpl, lpl, rl;
+
+  assert (n >= 1);
+
+  cl = 0;
+  do
+    {
+      ul = *up++;
+      gmp_umul_ppmm (hpl, lpl, ul, vl);
+
+      lpl += cl;
+      cl = (lpl < cl) + hpl;
+
+      rl = *rp;
+      lpl = rl + lpl;
+      cl += lpl < rl;
+      *rp++ = lpl;
+    }
+  while (--n != 0);
+
+  return cl;
+}
+
+mp_limb_t
+mpn_submul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl)
+{
+  mp_limb_t ul, cl, hpl, lpl, rl;
+
+  assert (n >= 1);
+
+  cl = 0;
+  do
+    {
+      ul = *up++;
+      gmp_umul_ppmm (hpl, lpl, ul, vl);
+
+      lpl += cl;
+      cl = (lpl < cl) + hpl;
+
+      rl = *rp;
+      lpl = rl - lpl;
+      cl += lpl > rl;
+      *rp++ = lpl;
+    }
+  while (--n != 0);
+
+  return cl;
+}
+
+mp_limb_t
+mpn_mul (mp_ptr rp, mp_srcptr up, mp_size_t un, mp_srcptr vp, mp_size_t vn)
+{
+  assert (un >= vn);
+  assert (vn >= 1);
+  assert (!GMP_MPN_OVERLAP_P(rp, un + vn, up, un));
+  assert (!GMP_MPN_OVERLAP_P(rp, un + vn, vp, vn));
+
+  /* We first multiply by the low order limb. This result can be
+     stored, not added, to rp. We also avoid a loop for zeroing this
+     way. */
+
+  rp[un] = mpn_mul_1 (rp, up, un, vp[0]);
+
+  /* Now accumulate the product of up[] and the next higher limb from
+     vp[]. */
+
+  while (--vn >= 1)
+    {
+      rp += 1, vp += 1;
+      rp[un] = mpn_addmul_1 (rp, up, un, vp[0]);
+    }
+  return rp[un];
+}
+
+void
+mpn_mul_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
+{
+  mpn_mul (rp, ap, n, bp, n);
+}
+
+void
+mpn_sqr (mp_ptr rp, mp_srcptr ap, mp_size_t n)
+{
+  mpn_mul (rp, ap, n, ap, n);
+}
+
+mp_limb_t
+mpn_lshift (mp_ptr rp, mp_srcptr up, mp_size_t n, unsigned int cnt)
+{
+  mp_limb_t high_limb, low_limb;
+  unsigned int tnc;
+  mp_limb_t retval;
+
+  assert (n >= 1);
+  assert (cnt >= 1);
+  assert (cnt < GMP_LIMB_BITS);
+
+  up += n;
+  rp += n;
+
+  tnc = GMP_LIMB_BITS - cnt;
+  low_limb = *--up;
+  retval = low_limb >> tnc;
+  high_limb = (low_limb << cnt);
+
+  while (--n != 0)
+    {
+      low_limb = *--up;
+      *--rp = high_limb | (low_limb >> tnc);
+      high_limb = (low_limb << cnt);
+    }
+  *--rp = high_limb;
+
+  return retval;
+}
+
+mp_limb_t
+mpn_rshift (mp_ptr rp, mp_srcptr up, mp_size_t n, unsigned int cnt)
+{
+  mp_limb_t high_limb, low_limb;
+  unsigned int tnc;
+  mp_limb_t retval;
+
+  assert (n >= 1);
+  assert (cnt >= 1);
+  assert (cnt < GMP_LIMB_BITS);
+
+  tnc = GMP_LIMB_BITS - cnt;
+  high_limb = *up++;
+  retval = (high_limb << tnc);
+  low_limb = high_limb >> cnt;
+
+  while (--n != 0)
+    {
+      high_limb = *up++;
+      *rp++ = low_limb | (high_limb << tnc);
+      low_limb = high_limb >> cnt;
+    }
+  *rp = low_limb;
+
+  return retval;
+}
+
+static mp_bitcnt_t
+mpn_common_scan (mp_limb_t limb, mp_size_t i, mp_srcptr up, mp_size_t un,
+                 mp_limb_t ux)
+{
+  unsigned cnt;
+
+  assert (ux == 0 || ux == GMP_LIMB_MAX);
+  assert (0 <= i && i <= un );
+
+  while (limb == 0)
+    {
+      i++;
+      if (i == un)
+        return (ux == 0 ? ~(mp_bitcnt_t) 0 : un * GMP_LIMB_BITS);
+      limb = ux ^ up[i];
+    }
+  gmp_ctz (cnt, limb);
+  return (mp_bitcnt_t) i * GMP_LIMB_BITS + cnt;
+}
+
+mp_bitcnt_t
+mpn_scan1 (mp_srcptr ptr, mp_bitcnt_t bit)
+{
+  mp_size_t i;
+  i = bit / GMP_LIMB_BITS;
+
+  return mpn_common_scan ( ptr[i] & (GMP_LIMB_MAX << (bit % GMP_LIMB_BITS)),
+                          i, ptr, i, 0);
+}
+
+mp_bitcnt_t
+mpn_scan0 (mp_srcptr ptr, mp_bitcnt_t bit)
+{
+  mp_size_t i;
+  i = bit / GMP_LIMB_BITS;
+
+  return mpn_common_scan (~ptr[i] & (GMP_LIMB_MAX << (bit % GMP_LIMB_BITS)),
+                          i, ptr, i, GMP_LIMB_MAX);
+}
+
+void
+mpn_com (mp_ptr rp, mp_srcptr up, mp_size_t n)
+{
+  while (--n >= 0)
+    *rp++ = ~ *up++;
+}
+
+mp_limb_t
+mpn_neg (mp_ptr rp, mp_srcptr up, mp_size_t n)
+{
+  while (*up == 0)
+    {
+      *rp = 0;
+      if (!--n)
+        return 0;
+      ++up; ++rp;
+    }
+  *rp = - *up;
+  mpn_com (++rp, ++up, --n);
+  return 1;
+}
+
+
+/* MPN division interface. */
+
+/* The 3/2 inverse is defined as
+
+     m = floor( (B^3-1) / (B u1 + u0)) - B
+*/
+mp_limb_t
+mpn_invert_3by2 (mp_limb_t u1, mp_limb_t u0)
+{
+  mp_limb_t r, p, m, ql;
+  unsigned ul, uh, qh;
+
+  assert (u1 >= GMP_LIMB_HIGHBIT);
+
+  /* For notation, let b denote the half-limb base, so that B = b^2.
+     Split u1 = b uh + ul. */
+  ul = u1 & GMP_LLIMB_MASK;
+  uh = u1 >> (GMP_LIMB_BITS / 2);
+
+  /* Approximation of the high half of quotient. Differs from the 2/1
+     inverse of the half limb uh, since we have already subtracted
+     u0. */
+  qh = ~u1 / uh;
+
+  /* Adjust to get a half-limb 3/2 inverse, i.e., we want
+
+     qh' = floor( (b^3 - 1) / u) - b = floor ((b^3 - b u - 1) / u
+         = floor( (b (~u) + b-1) / u),
+
+     and the remainder
+
+     r = b (~u) + b-1 - qh (b uh + ul)
+       = b (~u - qh uh) + b-1 - qh ul
+
+     Subtraction of qh ul may underflow, which implies adjustments.
+     But by normalization, 2 u >= B > qh ul, so we need to adjust by
+     at most 2.
+  */
+
+  r = ((~u1 - (mp_limb_t) qh * uh) << (GMP_LIMB_BITS / 2)) | GMP_LLIMB_MASK;
+
+  p = (mp_limb_t) qh * ul;
+  /* Adjustment steps taken from udiv_qrnnd_c */
+  if (r < p)
+    {
+      qh--;
+      r += u1;
+      if (r >= u1) /* i.e. we didn't get carry when adding to r */
+        if (r < p)
+          {
+            qh--;
+            r += u1;
+          }
+    }
+  r -= p;
+
+  /* Low half of the quotient is
+
+       ql = floor ( (b r + b-1) / u1).
+
+     This is a 3/2 division (on half-limbs), for which qh is a
+     suitable inverse. */
+
+  p = (r >> (GMP_LIMB_BITS / 2)) * qh + r;
+  /* Unlike full-limb 3/2, we can add 1 without overflow. For this to
+     work, it is essential that ql is a full mp_limb_t. */
+  ql = (p >> (GMP_LIMB_BITS / 2)) + 1;
+
+  /* By the 3/2 trick, we don't need the high half limb. */
+  r = (r << (GMP_LIMB_BITS / 2)) + GMP_LLIMB_MASK - ql * u1;
+
+  if (r >= (p << (GMP_LIMB_BITS / 2)))
+    {
+      ql--;
+      r += u1;
+    }
+  m = ((mp_limb_t) qh << (GMP_LIMB_BITS / 2)) + ql;
+  if (r >= u1)
+    {
+      m++;
+      r -= u1;
+    }
+
+  /* Now m is the 2/1 invers of u1. If u0 > 0, adjust it to become a
+     3/2 inverse. */
+  if (u0 > 0)
+    {
+      mp_limb_t th, tl;
+      r = ~r;
+      r += u0;
+      if (r < u0)
+        {
+          m--;
+          if (r >= u1)
+            {
+              m--;
+              r -= u1;
+            }
+          r -= u1;
+        }
+      gmp_umul_ppmm (th, tl, u0, m);
+      r += th;
+      if (r < th)
+        {
+          m--;
+          m -= ((r > u1) | ((r == u1) & (tl > u0)));
+        }
+    }
+
+  return m;
+}
+
+struct gmp_div_inverse
+{
+  /* Normalization shift count. */
+  unsigned shift;
+  /* Normalized divisor (d0 unused for mpn_div_qr_1) */
+  mp_limb_t d1, d0;
+  /* Inverse, for 2/1 or 3/2. */
+  mp_limb_t di;
+};
+
+static void
+mpn_div_qr_1_invert (struct gmp_div_inverse *inv, mp_limb_t d)
+{
+  unsigned shift;
+
+  assert (d > 0);
+  gmp_clz (shift, d);
+  inv->shift = shift;
+  inv->d1 = d << shift;
+  inv->di = mpn_invert_limb (inv->d1);
+}
+
+static void
+mpn_div_qr_2_invert (struct gmp_div_inverse *inv,
+                     mp_limb_t d1, mp_limb_t d0)
+{
+  unsigned shift;
+
+  assert (d1 > 0);
+  gmp_clz (shift, d1);
+  inv->shift = shift;
+  if (shift > 0)
+    {
+      d1 = (d1 << shift) | (d0 >> (GMP_LIMB_BITS - shift));
+      d0 <<= shift;
+    }
+  inv->d1 = d1;
+  inv->d0 = d0;
+  inv->di = mpn_invert_3by2 (d1, d0);
+}
+
+static void
+mpn_div_qr_invert (struct gmp_div_inverse *inv,
+                   mp_srcptr dp, mp_size_t dn)
+{
+  assert (dn > 0);
+
+  if (dn == 1)
+    mpn_div_qr_1_invert (inv, dp[0]);
+  else if (dn == 2)
+    mpn_div_qr_2_invert (inv, dp[1], dp[0]);
+  else
+    {
+      unsigned shift;
+      mp_limb_t d1, d0;
+
+      d1 = dp[dn-1];
+      d0 = dp[dn-2];
+      assert (d1 > 0);
+      gmp_clz (shift, d1);
+      inv->shift = shift;
+      if (shift > 0)
+        {
+          d1 = (d1 << shift) | (d0 >> (GMP_LIMB_BITS - shift));
+          d0 = (d0 << shift) | (dp[dn-3] >> (GMP_LIMB_BITS - shift));
+        }
+      inv->d1 = d1;
+      inv->d0 = d0;
+      inv->di = mpn_invert_3by2 (d1, d0);
+    }
+}
+
+/* Not matching current public gmp interface, rather corresponding to
+   the sbpi1_div_* functions. */
+static mp_limb_t
+mpn_div_qr_1_preinv (mp_ptr qp, mp_srcptr np, mp_size_t nn,
+                     const struct gmp_div_inverse *inv)
+{
+  mp_limb_t d, di;
+  mp_limb_t r;
+  mp_ptr tp = NULL;
+
+  if (inv->shift > 0)
+    {
+      /* Shift, reusing qp area if possible. In-place shift if qp == np. */
+      tp = qp ? qp : gmp_xalloc_limbs (nn);
+      r = mpn_lshift (tp, np, nn, inv->shift);
+      np = tp;
+    }
+  else
+    r = 0;
+
+  d = inv->d1;
+  di = inv->di;
+  while (--nn >= 0)
+    {
+      mp_limb_t q;
+
+      gmp_udiv_qrnnd_preinv (q, r, r, np[nn], d, di);
+      if (qp)
+        qp[nn] = q;
+    }
+  if ((inv->shift > 0) && (tp != qp))
+    gmp_free (tp);
+
+  return r >> inv->shift;
+}
+
+static mp_limb_t
+mpn_div_qr_1 (mp_ptr qp, mp_srcptr np, mp_size_t nn, mp_limb_t d)
+{
+  assert (d > 0);
+
+  /* Special case for powers of two. */
+  if ((d & (d-1)) == 0)
+    {
+      mp_limb_t r = np[0] & (d-1);
+      if (qp)
+        {
+          if (d <= 1)
+            mpn_copyi (qp, np, nn);
+          else
+            {
+              unsigned shift;
+              gmp_ctz (shift, d);
+              mpn_rshift (qp, np, nn, shift);
+            }
+        }
+      return r;
+    }
+  else
+    {
+      struct gmp_div_inverse inv;
+      mpn_div_qr_1_invert (&inv, d);
+      return mpn_div_qr_1_preinv (qp, np, nn, &inv);
+    }
+}
+
+static void
+mpn_div_qr_2_preinv (mp_ptr qp, mp_ptr np, mp_size_t nn,
+                     const struct gmp_div_inverse *inv)
+{
+  unsigned shift;
+  mp_size_t i;
+  mp_limb_t d1, d0, di, r1, r0;
+
+  assert (nn >= 2);
+  shift = inv->shift;
+  d1 = inv->d1;
+  d0 = inv->d0;
+  di = inv->di;
+
+  if (shift > 0)
+    r1 = mpn_lshift (np, np, nn, shift);
+  else
+    r1 = 0;
+
+  r0 = np[nn - 1];
+
+  i = nn - 2;
+  do
+    {
+      mp_limb_t n0, q;
+      n0 = np[i];
+      gmp_udiv_qr_3by2 (q, r1, r0, r1, r0, n0, d1, d0, di);
+
+      if (qp)
+        qp[i] = q;
+    }
+  while (--i >= 0);
+
+  if (shift > 0)
+    {
+      assert ((r0 << (GMP_LIMB_BITS - shift)) == 0);
+      r0 = (r0 >> shift) | (r1 << (GMP_LIMB_BITS - shift));
+      r1 >>= shift;
+    }
+
+  np[1] = r1;
+  np[0] = r0;
+}
+
+static void
+mpn_div_qr_pi1 (mp_ptr qp,
+                mp_ptr np, mp_size_t nn, mp_limb_t n1,
+                mp_srcptr dp, mp_size_t dn,
+                mp_limb_t dinv)
+{
+  mp_size_t i;
+
+  mp_limb_t d1, d0;
+  mp_limb_t cy, cy1;
+  mp_limb_t q;
+
+  assert (dn > 2);
+  assert (nn >= dn);
+
+  d1 = dp[dn - 1];
+  d0 = dp[dn - 2];
+
+  assert ((d1 & GMP_LIMB_HIGHBIT) != 0);
+  /* Iteration variable is the index of the q limb.
+   *
+   * We divide <n1, np[dn-1+i], np[dn-2+i], np[dn-3+i],..., np[i]>
+   * by            <d1,          d0,        dp[dn-3],  ..., dp[0] >
+   */
+
+  i = nn - dn;
+  do
+    {
+      mp_limb_t n0 = np[dn-1+i];
+
+      if (n1 == d1 && n0 == d0)
+        {
+          q = GMP_LIMB_MAX;
+          mpn_submul_1 (np+i, dp, dn, q);
+          n1 = np[dn-1+i];      /* update n1, last loop's value will now be invalid */
+        }
+      else
+        {
+          gmp_udiv_qr_3by2 (q, n1, n0, n1, n0, np[dn-2+i], d1, d0, dinv);
+
+          cy = mpn_submul_1 (np + i, dp, dn-2, q);
+
+          cy1 = n0 < cy;
+          n0 = n0 - cy;
+          cy = n1 < cy1;
+          n1 = n1 - cy1;
+          np[dn-2+i] = n0;
+
+          if (cy != 0)
+            {
+              n1 += d1 + mpn_add_n (np + i, np + i, dp, dn - 1);
+              q--;
+            }
+        }
+
+      if (qp)
+        qp[i] = q;
+    }
+  while (--i >= 0);
+
+  np[dn - 1] = n1;
+}
+
+static void
+mpn_div_qr_preinv (mp_ptr qp, mp_ptr np, mp_size_t nn,
+                   mp_srcptr dp, mp_size_t dn,
+                   const struct gmp_div_inverse *inv)
+{
+  assert (dn > 0);
+  assert (nn >= dn);
+
+  if (dn == 1)
+    np[0] = mpn_div_qr_1_preinv (qp, np, nn, inv);
+  else if (dn == 2)
+    mpn_div_qr_2_preinv (qp, np, nn, inv);
+  else
+    {
+      mp_limb_t nh;
+      unsigned shift;
+
+      assert (inv->d1 == dp[dn-1]);
+      assert (inv->d0 == dp[dn-2]);
+      assert ((inv->d1 & GMP_LIMB_HIGHBIT) != 0);
+
+      shift = inv->shift;
+      if (shift > 0)
+        nh = mpn_lshift (np, np, nn, shift);
+      else
+        nh = 0;
+
+      mpn_div_qr_pi1 (qp, np, nn, nh, dp, dn, inv->di);
+
+      if (shift > 0)
+        gmp_assert_nocarry (mpn_rshift (np, np, dn, shift));
+    }
+}
+
+static void
+mpn_div_qr (mp_ptr qp, mp_ptr np, mp_size_t nn, mp_srcptr dp, mp_size_t dn)
+{
+  struct gmp_div_inverse inv;
+  mp_ptr tp = NULL;
+
+  assert (dn > 0);
+  assert (nn >= dn);
+
+  mpn_div_qr_invert (&inv, dp, dn);
+  if (dn > 2 && inv.shift > 0)
+    {
+      tp = gmp_xalloc_limbs (dn);
+      gmp_assert_nocarry (mpn_lshift (tp, dp, dn, inv.shift));
+      dp = tp;
+    }
+  mpn_div_qr_preinv (qp, np, nn, dp, dn, &inv);
+  if (tp)
+    gmp_free (tp);
+}
+
+
+/* MPN base conversion. */
+static unsigned
+mpn_base_power_of_two_p (unsigned b)
+{
+  switch (b)
+    {
+    case 2: return 1;
+    case 4: return 2;
+    case 8: return 3;
+    case 16: return 4;
+    case 32: return 5;
+    case 64: return 6;
+    case 128: return 7;
+    case 256: return 8;
+    default: return 0;
+    }
+}
+
+struct mpn_base_info
+{
+  /* bb is the largest power of the base which fits in one limb, and
+     exp is the corresponding exponent. */
+  unsigned exp;
+  mp_limb_t bb;
+};
+
+static void
+mpn_get_base_info (struct mpn_base_info *info, mp_limb_t b)
+{
+  mp_limb_t m;
+  mp_limb_t p;
+  unsigned exp;
+
+  m = GMP_LIMB_MAX / b;
+  for (exp = 1, p = b; p <= m; exp++)
+    p *= b;
+
+  info->exp = exp;
+  info->bb = p;
+}
+
+static mp_bitcnt_t
+mpn_limb_size_in_base_2 (mp_limb_t u)
+{
+  unsigned shift;
+
+  assert (u > 0);
+  gmp_clz (shift, u);
+  return GMP_LIMB_BITS - shift;
+}
+
+static size_t
+mpn_get_str_bits (unsigned char *sp, unsigned bits, mp_srcptr up, mp_size_t un)
+{
+  unsigned char mask;
+  size_t sn, j;
+  mp_size_t i;
+  unsigned shift;
+
+  sn = ((un - 1) * GMP_LIMB_BITS + mpn_limb_size_in_base_2 (up[un-1])
+        + bits - 1) / bits;
+
+  mask = (1U << bits) - 1;
+
+  for (i = 0, j = sn, shift = 0; j-- > 0;)
+    {
+      unsigned char digit = up[i] >> shift;
+
+      shift += bits;
+
+      if (shift >= GMP_LIMB_BITS && ++i < un)
+        {
+          shift -= GMP_LIMB_BITS;
+          digit |= up[i] << (bits - shift);
+        }
+      sp[j] = digit & mask;
+    }
+  return sn;
+}
+
+/* We generate digits from the least significant end, and reverse at
+   the end. */
+static size_t
+mpn_limb_get_str (unsigned char *sp, mp_limb_t w,
+                  const struct gmp_div_inverse *binv)
+{
+  mp_size_t i;
+  for (i = 0; w > 0; i++)
+    {
+      mp_limb_t h, l, r;
+
+      h = w >> (GMP_LIMB_BITS - binv->shift);
+      l = w << binv->shift;
+
+      gmp_udiv_qrnnd_preinv (w, r, h, l, binv->d1, binv->di);
+      assert ( (r << (GMP_LIMB_BITS - binv->shift)) == 0);
+      r >>= binv->shift;
+
+      sp[i] = r;
+    }
+  return i;
+}
+
+static size_t
+mpn_get_str_other (unsigned char *sp,
+                   int base, const struct mpn_base_info *info,
+                   mp_ptr up, mp_size_t un)
+{
+  struct gmp_div_inverse binv;
+  size_t sn;
+  size_t i;
+
+  mpn_div_qr_1_invert (&binv, base);
+
+  sn = 0;
+
+  if (un > 1)
+    {
+      struct gmp_div_inverse bbinv;
+      mpn_div_qr_1_invert (&bbinv, info->bb);
+
+      do
+        {
+          mp_limb_t w;
+          size_t done;
+          w = mpn_div_qr_1_preinv (up, up, un, &bbinv);
+          un -= (up[un-1] == 0);
+          done = mpn_limb_get_str (sp + sn, w, &binv);
+
+          for (sn += done; done < info->exp; done++)
+            sp[sn++] = 0;
+        }
+      while (un > 1);
+    }
+  sn += mpn_limb_get_str (sp + sn, up[0], &binv);
+
+  /* Reverse order */
+  for (i = 0; 2*i + 1 < sn; i++)
+    {
+      unsigned char t = sp[i];
+      sp[i] = sp[sn - i - 1];
+      sp[sn - i - 1] = t;
+    }
+
+  return sn;
+}
+
+size_t
+mpn_get_str (unsigned char *sp, int base, mp_ptr up, mp_size_t un)
+{
+  unsigned bits;
+
+  assert (un > 0);
+  assert (up[un-1] > 0);
+
+  bits = mpn_base_power_of_two_p (base);
+  if (bits)
+    return mpn_get_str_bits (sp, bits, up, un);
+  else
+    {
+      struct mpn_base_info info;
+
+      mpn_get_base_info (&info, base);
+      return mpn_get_str_other (sp, base, &info, up, un);
+    }
+}
+
+static mp_size_t
+mpn_set_str_bits (mp_ptr rp, const unsigned char *sp, size_t sn,
+                  unsigned bits)
+{
+  mp_size_t rn;
+  size_t j;
+  unsigned shift;
+
+  for (j = sn, rn = 0, shift = 0; j-- > 0; )
+    {
+      if (shift == 0)
+        {
+          rp[rn++] = sp[j];
+          shift += bits;
+        }
+      else
+        {
+          rp[rn-1] |= (mp_limb_t) sp[j] << shift;
+          shift += bits;
+          if (shift >= GMP_LIMB_BITS)
+            {
+              shift -= GMP_LIMB_BITS;
+              if (shift > 0)
+                rp[rn++] = (mp_limb_t) sp[j] >> (bits - shift);
+            }
+        }
+    }
+  rn = mpn_normalized_size (rp, rn);
+  return rn;
+}
+
+/* Result is usually normalized, except for all-zero input, in which
+   case a single zero limb is written at *RP, and 1 is returned. */
+static mp_size_t
+mpn_set_str_other (mp_ptr rp, const unsigned char *sp, size_t sn,
+                   mp_limb_t b, const struct mpn_base_info *info)
+{
+  mp_size_t rn;
+  mp_limb_t w;
+  unsigned k;
+  size_t j;
+
+  assert (sn > 0);
+
+  k = 1 + (sn - 1) % info->exp;
+
+  j = 0;
+  w = sp[j++];
+  while (--k != 0)
+    w = w * b + sp[j++];
+
+  rp[0] = w;
+
+  for (rn = 1; j < sn;)
+    {
+      mp_limb_t cy;
+
+      w = sp[j++];
+      for (k = 1; k < info->exp; k++)
+        w = w * b + sp[j++];
+
+      cy = mpn_mul_1 (rp, rp, rn, info->bb);
+      cy += mpn_add_1 (rp, rp, rn, w);
+      if (cy > 0)
+        rp[rn++] = cy;
+    }
+  assert (j == sn);
+
+  return rn;
+}
+
+mp_size_t
+mpn_set_str (mp_ptr rp, const unsigned char *sp, size_t sn, int base)
+{
+  unsigned bits;
+
+  if (sn == 0)
+    return 0;
+
+  bits = mpn_base_power_of_two_p (base);
+  if (bits)
+    return mpn_set_str_bits (rp, sp, sn, bits);
+  else
+    {
+      struct mpn_base_info info;
+
+      mpn_get_base_info (&info, base);
+      return mpn_set_str_other (rp, sp, sn, base, &info);
+    }
+}
+
+
+/* MPZ interface */
+void
+mpz_init (mpz_t r)
+{
+  static const mp_limb_t dummy_limb = 0xc1a0;
+
+  r->_mp_alloc = 0;
+  r->_mp_size = 0;
+  r->_mp_d = (mp_ptr) &dummy_limb;
+}
+
+/* The utility of this function is a bit limited, since many functions
+   assigns the result variable using mpz_swap. */
+void
+mpz_init2 (mpz_t r, mp_bitcnt_t bits)
+{
+  mp_size_t rn;
+
+  bits -= (bits != 0);          /* Round down, except if 0 */
+  rn = 1 + bits / GMP_LIMB_BITS;
+
+  r->_mp_alloc = rn;
+  r->_mp_size = 0;
+  r->_mp_d = gmp_xalloc_limbs (rn);
+}
+
+void
+mpz_clear (mpz_t r)
+{
+  if (r->_mp_alloc)
+    gmp_free (r->_mp_d);
+}
+
+static mp_ptr
+mpz_realloc (mpz_t r, mp_size_t size)
+{
+  size = GMP_MAX (size, 1);
+
+  if (r->_mp_alloc)
+    r->_mp_d = gmp_xrealloc_limbs (r->_mp_d, size);
+  else
+    r->_mp_d = gmp_xalloc_limbs (size);
+  r->_mp_alloc = size;
+
+  if (GMP_ABS (r->_mp_size) > size)
+    r->_mp_size = 0;
+
+  return r->_mp_d;
+}
+
+/* Realloc for an mpz_t WHAT if it has less than NEEDED limbs.  */
+#define MPZ_REALLOC(z,n) ((n) > (z)->_mp_alloc                  \
+                          ? mpz_realloc(z,n)                    \
+                          : (z)->_mp_d)
+
+/* MPZ assignment and basic conversions. */
+void
+mpz_set_si (mpz_t r, signed long int x)
+{
+  if (x >= 0)
+    mpz_set_ui (r, x);
+  else /* (x < 0) */
+    {
+      r->_mp_size = -1;
+      MPZ_REALLOC (r, 1)[0] = GMP_NEG_CAST (unsigned long int, x);
+    }
+}
+
+void
+mpz_set_ui (mpz_t r, unsigned long int x)
+{
+  if (x > 0)
+    {
+      r->_mp_size = 1;
+      MPZ_REALLOC (r, 1)[0] = x;
+    }
+  else
+    r->_mp_size = 0;
+}
+
+void
+mpz_set (mpz_t r, const mpz_t x)
+{
+  /* Allow the NOP r == x */
+  if (r != x)
+    {
+      mp_size_t n;
+      mp_ptr rp;
+
+      n = GMP_ABS (x->_mp_size);
+      rp = MPZ_REALLOC (r, n);
+
+      mpn_copyi (rp, x->_mp_d, n);
+      r->_mp_size = x->_mp_size;
+    }
+}
+
+void
+mpz_init_set_si (mpz_t r, signed long int x)
+{
+  mpz_init (r);
+  mpz_set_si (r, x);
+}
+
+void
+mpz_init_set_ui (mpz_t r, unsigned long int x)
+{
+  mpz_init (r);
+  mpz_set_ui (r, x);
+}
+
+void
+mpz_init_set (mpz_t r, const mpz_t x)
+{
+  mpz_init (r);
+  mpz_set (r, x);
+}
+
+int
+mpz_fits_slong_p (const mpz_t u)
+{
+  mp_size_t us = u->_mp_size;
+
+  if (us == 1)
+    return u->_mp_d[0] < GMP_LIMB_HIGHBIT;
+  else if (us == -1)
+    return u->_mp_d[0] <= GMP_LIMB_HIGHBIT;
+  else
+    return (us == 0);
+}
+
+int
+mpz_fits_ulong_p (const mpz_t u)
+{
+  mp_size_t us = u->_mp_size;
+
+  return (us == (us > 0));
+}
+
+long int
+mpz_get_si (const mpz_t u)
+{
+  if (u->_mp_size < 0)
+    /* This expression is necessary to properly handle 0x80000000 */
+    return -1 - (long) ((u->_mp_d[0] - 1) & ~GMP_LIMB_HIGHBIT);
+  else
+    return (long) (mpz_get_ui (u) & ~GMP_LIMB_HIGHBIT);
+}
+
+unsigned long int
+mpz_get_ui (const mpz_t u)
+{
+  return u->_mp_size == 0 ? 0 : u->_mp_d[0];
+}
+
+size_t
+mpz_size (const mpz_t u)
+{
+  return GMP_ABS (u->_mp_size);
+}
+
+mp_limb_t
+mpz_getlimbn (const mpz_t u, mp_size_t n)
+{
+  if (n >= 0 && n < GMP_ABS (u->_mp_size))
+    return u->_mp_d[n];
+  else
+    return 0;
+}
+
+void
+mpz_realloc2 (mpz_t x, mp_bitcnt_t n)
+{
+  mpz_realloc (x, 1 + (n - (n != 0)) / GMP_LIMB_BITS);
+}
+
+mp_srcptr
+mpz_limbs_read (mpz_srcptr x)
+{
+  return x->_mp_d;
+}
+
+mp_ptr
+mpz_limbs_modify (mpz_t x, mp_size_t n)
+{
+  assert (n > 0);
+  return MPZ_REALLOC (x, n);
+}
+
+mp_ptr
+mpz_limbs_write (mpz_t x, mp_size_t n)
+{
+  return mpz_limbs_modify (x, n);
+}
+
+void
+mpz_limbs_finish (mpz_t x, mp_size_t xs)
+{
+  mp_size_t xn;
+  xn = mpn_normalized_size (x->_mp_d, GMP_ABS (xs));
+  x->_mp_size = xs < 0 ? -xn : xn;
+}
+
+static mpz_srcptr
+mpz_roinit_normal_n (mpz_t x, mp_srcptr xp, mp_size_t xs)
+{
+  x->_mp_alloc = 0;
+  x->_mp_d = (mp_ptr) xp;
+  x->_mp_size = xs;
+  return x;
+}
+
+mpz_srcptr
+mpz_roinit_n (mpz_t x, mp_srcptr xp, mp_size_t xs)
+{
+  mpz_roinit_normal_n (x, xp, xs);
+  mpz_limbs_finish (x, xs);
+  return x;
+}
+
+
+/* Conversions and comparison to double. */
+void
+mpz_set_d (mpz_t r, double x)
+{
+  int sign;
+  mp_ptr rp;
+  mp_size_t rn, i;
+  double B;
+  double Bi;
+  mp_limb_t f;
+
+  /* x != x is true when x is a NaN, and x == x * 0.5 is true when x is
+     zero or infinity. */
+  if (x != x || x == x * 0.5)
+    {
+      r->_mp_size = 0;
+      return;
+    }
+
+  sign = x < 0.0 ;
+  if (sign)
+    x = - x;
+
+  if (x < 1.0)
+    {
+      r->_mp_size = 0;
+      return;
+    }
+  B = 2.0 * (double) GMP_LIMB_HIGHBIT;
+  Bi = 1.0 / B;
+  for (rn = 1; x >= B; rn++)
+    x *= Bi;
+
+  rp = MPZ_REALLOC (r, rn);
+
+  f = (mp_limb_t) x;
+  x -= f;
+  assert (x < 1.0);
+  i = rn-1;
+  rp[i] = f;
+  while (--i >= 0)
+    {
+      x = B * x;
+      f = (mp_limb_t) x;
+      x -= f;
+      assert (x < 1.0);
+      rp[i] = f;
+    }
+
+  r->_mp_size = sign ? - rn : rn;
+}
+
+void
+mpz_init_set_d (mpz_t r, double x)
+{
+  mpz_init (r);
+  mpz_set_d (r, x);
+}
+
+double
+mpz_get_d (const mpz_t u)
+{
+  int m;
+  mp_limb_t l;
+  mp_size_t un;
+  double x;
+  double B = 2.0 * (double) GMP_LIMB_HIGHBIT;
+
+  un = GMP_ABS (u->_mp_size);
+
+  if (un == 0)
+    return 0.0;
+
+  l = u->_mp_d[--un];
+  gmp_clz (m, l);
+  m = m + GMP_DBL_MANT_BITS - GMP_LIMB_BITS;
+  if (m < 0)
+    l &= GMP_LIMB_MAX << -m;
+
+  for (x = l; --un >= 0;)
+    {
+      x = B*x;
+      if (m > 0) {
+        l = u->_mp_d[un];
+        m -= GMP_LIMB_BITS;
+        if (m < 0)
+          l &= GMP_LIMB_MAX << -m;
+        x += l;
+      }
+    }
+
+  if (u->_mp_size < 0)
+    x = -x;
+
+  return x;
+}
+
+int
+mpz_cmpabs_d (const mpz_t x, double d)
+{
+  mp_size_t xn;
+  double B, Bi;
+  mp_size_t i;
+
+  xn = x->_mp_size;
+  d = GMP_ABS (d);
+
+  if (xn != 0)
+    {
+      xn = GMP_ABS (xn);
+
+      B = 2.0 * (double) GMP_LIMB_HIGHBIT;
+      Bi = 1.0 / B;
+
+      /* Scale d so it can be compared with the top limb. */
+      for (i = 1; i < xn; i++)
+        d *= Bi;
+
+      if (d >= B)
+        return -1;
+
+      /* Compare floor(d) to top limb, subtract and cancel when equal. */
+      for (i = xn; i-- > 0;)
+        {
+          mp_limb_t f, xl;
+
+          f = (mp_limb_t) d;
+          xl = x->_mp_d[i];
+          if (xl > f)
+            return 1;
+          else if (xl < f)
+            return -1;
+          d = B * (d - f);
+        }
+    }
+  return - (d > 0.0);
+}
+
+int
+mpz_cmp_d (const mpz_t x, double d)
+{
+  if (x->_mp_size < 0)
+    {
+      if (d >= 0.0)
+        return -1;
+      else
+        return -mpz_cmpabs_d (x, d);
+    }
+  else
+    {
+      if (d < 0.0)
+        return 1;
+      else
+        return mpz_cmpabs_d (x, d);
+    }
+}
+
+
+/* MPZ comparisons and the like. */
+int
+mpz_sgn (const mpz_t u)
+{
+  return GMP_CMP (u->_mp_size, 0);
+}
+
+int
+mpz_cmp_si (const mpz_t u, long v)
+{
+  mp_size_t usize = u->_mp_size;
+
+  if (usize < -1)
+    return -1;
+  else if (v >= 0)
+    return mpz_cmp_ui (u, v);
+  else if (usize >= 0)
+    return 1;
+  else /* usize == -1 */
+    return GMP_CMP (GMP_NEG_CAST (mp_limb_t, v), u->_mp_d[0]);
+}
+
+int
+mpz_cmp_ui (const mpz_t u, unsigned long v)
+{
+  mp_size_t usize = u->_mp_size;
+
+  if (usize > 1)
+    return 1;
+  else if (usize < 0)
+    return -1;
+  else
+    return GMP_CMP (mpz_get_ui (u), v);
+}
+
+int
+mpz_cmp (const mpz_t a, const mpz_t b)
+{
+  mp_size_t asize = a->_mp_size;
+  mp_size_t bsize = b->_mp_size;
+
+  if (asize != bsize)
+    return (asize < bsize) ? -1 : 1;
+  else if (asize >= 0)
+    return mpn_cmp (a->_mp_d, b->_mp_d, asize);
+  else
+    return mpn_cmp (b->_mp_d, a->_mp_d, -asize);
+}
+
+int
+mpz_cmpabs_ui (const mpz_t u, unsigned long v)
+{
+  if (GMP_ABS (u->_mp_size) > 1)
+    return 1;
+  else
+    return GMP_CMP (mpz_get_ui (u), v);
+}
+
+int
+mpz_cmpabs (const mpz_t u, const mpz_t v)
+{
+  return mpn_cmp4 (u->_mp_d, GMP_ABS (u->_mp_size),
+                   v->_mp_d, GMP_ABS (v->_mp_size));
+}
+
+void
+mpz_abs (mpz_t r, const mpz_t u)
+{
+  mpz_set (r, u);
+  r->_mp_size = GMP_ABS (r->_mp_size);
+}
+
+void
+mpz_neg (mpz_t r, const mpz_t u)
+{
+  mpz_set (r, u);
+  r->_mp_size = -r->_mp_size;
+}
+
+void
+mpz_swap (mpz_t u, mpz_t v)
+{
+  MP_SIZE_T_SWAP (u->_mp_size, v->_mp_size);
+  MP_SIZE_T_SWAP (u->_mp_alloc, v->_mp_alloc);
+  MP_PTR_SWAP (u->_mp_d, v->_mp_d);
+}
+
+
+/* MPZ addition and subtraction */
+
+/* Adds to the absolute value. Returns new size, but doesn't store it. */
+static mp_size_t
+mpz_abs_add_ui (mpz_t r, const mpz_t a, unsigned long b)
+{
+  mp_size_t an;
+  mp_ptr rp;
+  mp_limb_t cy;
+
+  an = GMP_ABS (a->_mp_size);
+  if (an == 0)
+    {
+      MPZ_REALLOC (r, 1)[0] = b;
+      return b > 0;
+    }
+
+  rp = MPZ_REALLOC (r, an + 1);
+
+  cy = mpn_add_1 (rp, a->_mp_d, an, b);
+  rp[an] = cy;
+  an += cy;
+
+  return an;
+}
+
+/* Subtract from the absolute value. Returns new size, (or -1 on underflow),
+   but doesn't store it. */
+static mp_size_t
+mpz_abs_sub_ui (mpz_t r, const mpz_t a, unsigned long b)
+{
+  mp_size_t an = GMP_ABS (a->_mp_size);
+  mp_ptr rp;
+
+  if (an == 0)
+    {
+      MPZ_REALLOC (r, 1)[0] = b;
+      return -(b > 0);
+    }
+  rp = MPZ_REALLOC (r, an);
+  if (an == 1 && a->_mp_d[0] < b)
+    {
+      rp[0] = b - a->_mp_d[0];
+      return -1;
+    }
+  else
+    {
+      gmp_assert_nocarry (mpn_sub_1 (rp, a->_mp_d, an, b));
+      return mpn_normalized_size (rp, an);
+    }
+}
+
+void
+mpz_add_ui (mpz_t r, const mpz_t a, unsigned long b)
+{
+  if (a->_mp_size >= 0)
+    r->_mp_size = mpz_abs_add_ui (r, a, b);
+  else
+    r->_mp_size = -mpz_abs_sub_ui (r, a, b);
+}
+
+void
+mpz_sub_ui (mpz_t r, const mpz_t a, unsigned long b)
+{
+  if (a->_mp_size < 0)
+    r->_mp_size = -mpz_abs_add_ui (r, a, b);
+  else
+    r->_mp_size = mpz_abs_sub_ui (r, a, b);
+}
+
+void
+mpz_ui_sub (mpz_t r, unsigned long a, const mpz_t b)
+{
+  if (b->_mp_size < 0)
+    r->_mp_size = mpz_abs_add_ui (r, b, a);
+  else
+    r->_mp_size = -mpz_abs_sub_ui (r, b, a);
+}
+
+static mp_size_t
+mpz_abs_add (mpz_t r, const mpz_t a, const mpz_t b)
+{
+  mp_size_t an = GMP_ABS (a->_mp_size);
+  mp_size_t bn = GMP_ABS (b->_mp_size);
+  mp_ptr rp;
+  mp_limb_t cy;
+
+  if (an < bn)
+    {
+      MPZ_SRCPTR_SWAP (a, b);
+      MP_SIZE_T_SWAP (an, bn);
+    }
+
+  rp = MPZ_REALLOC (r, an + 1);
+  cy = mpn_add (rp, a->_mp_d, an, b->_mp_d, bn);
+
+  rp[an] = cy;
+
+  return an + cy;
+}
+
+static mp_size_t
+mpz_abs_sub (mpz_t r, const mpz_t a, const mpz_t b)
+{
+  mp_size_t an = GMP_ABS (a->_mp_size);
+  mp_size_t bn = GMP_ABS (b->_mp_size);
+  int cmp;
+  mp_ptr rp;
+
+  cmp = mpn_cmp4 (a->_mp_d, an, b->_mp_d, bn);
+  if (cmp > 0)
+    {
+      rp = MPZ_REALLOC (r, an);
+      gmp_assert_nocarry (mpn_sub (rp, a->_mp_d, an, b->_mp_d, bn));
+      return mpn_normalized_size (rp, an);
+    }
+  else if (cmp < 0)
+    {
+      rp = MPZ_REALLOC (r, bn);
+      gmp_assert_nocarry (mpn_sub (rp, b->_mp_d, bn, a->_mp_d, an));
+      return -mpn_normalized_size (rp, bn);
+    }
+  else
+    return 0;
+}
+
+void
+mpz_add (mpz_t r, const mpz_t a, const mpz_t b)
+{
+  mp_size_t rn;
+
+  if ( (a->_mp_size ^ b->_mp_size) >= 0)
+    rn = mpz_abs_add (r, a, b);
+  else
+    rn = mpz_abs_sub (r, a, b);
+
+  r->_mp_size = a->_mp_size >= 0 ? rn : - rn;
+}
+
+void
+mpz_sub (mpz_t r, const mpz_t a, const mpz_t b)
+{
+  mp_size_t rn;
+
+  if ( (a->_mp_size ^ b->_mp_size) >= 0)
+    rn = mpz_abs_sub (r, a, b);
+  else
+    rn = mpz_abs_add (r, a, b);
+
+  r->_mp_size = a->_mp_size >= 0 ? rn : - rn;
+}
+
+
+/* MPZ multiplication */
+void
+mpz_mul_si (mpz_t r, const mpz_t u, long int v)
+{
+  if (v < 0)
+    {
+      mpz_mul_ui (r, u, GMP_NEG_CAST (unsigned long int, v));
+      mpz_neg (r, r);
+    }
+  else
+    mpz_mul_ui (r, u, (unsigned long int) v);
+}
+
+void
+mpz_mul_ui (mpz_t r, const mpz_t u, unsigned long int v)
+{
+  mp_size_t un, us;
+  mp_ptr tp;
+  mp_limb_t cy;
+
+  us = u->_mp_size;
+
+  if (us == 0 || v == 0)
+    {
+      r->_mp_size = 0;
+      return;
+    }
+
+  un = GMP_ABS (us);
+
+  tp = MPZ_REALLOC (r, un + 1);
+  cy = mpn_mul_1 (tp, u->_mp_d, un, v);
+  tp[un] = cy;
+
+  un += (cy > 0);
+  r->_mp_size = (us < 0) ? - un : un;
+}
+
+void
+mpz_mul (mpz_t r, const mpz_t u, const mpz_t v)
+{
+  int sign;
+  mp_size_t un, vn, rn;
+  mpz_t t;
+  mp_ptr tp;
+
+  un = u->_mp_size;
+  vn = v->_mp_size;
+
+  if (un == 0 || vn == 0)
+    {
+      r->_mp_size = 0;
+      return;
+    }
+
+  sign = (un ^ vn) < 0;
+
+  un = GMP_ABS (un);
+  vn = GMP_ABS (vn);
+
+  mpz_init2 (t, (un + vn) * GMP_LIMB_BITS);
+
+  tp = t->_mp_d;
+  if (un >= vn)
+    mpn_mul (tp, u->_mp_d, un, v->_mp_d, vn);
+  else
+    mpn_mul (tp, v->_mp_d, vn, u->_mp_d, un);
+
+  rn = un + vn;
+  rn -= tp[rn-1] == 0;
+
+  t->_mp_size = sign ? - rn : rn;
+  mpz_swap (r, t);
+  mpz_clear (t);
+}
+
+void
+mpz_mul_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t bits)
+{
+  mp_size_t un, rn;
+  mp_size_t limbs;
+  unsigned shift;
+  mp_ptr rp;
+
+  un = GMP_ABS (u->_mp_size);
+  if (un == 0)
+    {
+      r->_mp_size = 0;
+      return;
+    }
+
+  limbs = bits / GMP_LIMB_BITS;
+  shift = bits % GMP_LIMB_BITS;
+
+  rn = un + limbs + (shift > 0);
+  rp = MPZ_REALLOC (r, rn);
+  if (shift > 0)
+    {
+      mp_limb_t cy = mpn_lshift (rp + limbs, u->_mp_d, un, shift);
+      rp[rn-1] = cy;
+      rn -= (cy == 0);
+    }
+  else
+    mpn_copyd (rp + limbs, u->_mp_d, un);
+
+  mpn_zero (rp, limbs);
+
+  r->_mp_size = (u->_mp_size < 0) ? - rn : rn;
+}
+
+void
+mpz_addmul_ui (mpz_t r, const mpz_t u, unsigned long int v)
+{
+  mpz_t t;
+  mpz_init (t);
+  mpz_mul_ui (t, u, v);
+  mpz_add (r, r, t);
+  mpz_clear (t);
+}
+
+void
+mpz_submul_ui (mpz_t r, const mpz_t u, unsigned long int v)
+{
+  mpz_t t;
+  mpz_init (t);
+  mpz_mul_ui (t, u, v);
+  mpz_sub (r, r, t);
+  mpz_clear (t);
+}
+
+void
+mpz_addmul (mpz_t r, const mpz_t u, const mpz_t v)
+{
+  mpz_t t;
+  mpz_init (t);
+  mpz_mul (t, u, v);
+  mpz_add (r, r, t);
+  mpz_clear (t);
+}
+
+void
+mpz_submul (mpz_t r, const mpz_t u, const mpz_t v)
+{
+  mpz_t t;
+  mpz_init (t);
+  mpz_mul (t, u, v);
+  mpz_sub (r, r, t);
+  mpz_clear (t);
+}
+
+
+/* MPZ division */
+enum mpz_div_round_mode { GMP_DIV_FLOOR, GMP_DIV_CEIL, GMP_DIV_TRUNC };
+
+/* Allows q or r to be zero. Returns 1 iff remainder is non-zero. */
+static int
+mpz_div_qr (mpz_t q, mpz_t r,
+            const mpz_t n, const mpz_t d, enum mpz_div_round_mode mode)
+{
+  mp_size_t ns, ds, nn, dn, qs;
+  ns = n->_mp_size;
+  ds = d->_mp_size;
+
+  if (ds == 0)
+    gmp_die("mpz_div_qr: Divide by zero.");
+
+  if (ns == 0)
+    {
+      if (q)
+        q->_mp_size = 0;
+      if (r)
+        r->_mp_size = 0;
+      return 0;
+    }
+
+  nn = GMP_ABS (ns);
+  dn = GMP_ABS (ds);
+
+  qs = ds ^ ns;
+
+  if (nn < dn)
+    {
+      if (mode == GMP_DIV_CEIL && qs >= 0)
+        {
+          /* q = 1, r = n - d */
+          if (r)
+            mpz_sub (r, n, d);
+          if (q)
+            mpz_set_ui (q, 1);
+        }
+      else if (mode == GMP_DIV_FLOOR && qs < 0)
+        {
+          /* q = -1, r = n + d */
+          if (r)
+            mpz_add (r, n, d);
+          if (q)
+            mpz_set_si (q, -1);
+        }
+      else
+        {
+          /* q = 0, r = d */
+          if (r)
+            mpz_set (r, n);
+          if (q)
+            q->_mp_size = 0;
+        }
+      return 1;
+    }
+  else
+    {
+      mp_ptr np, qp;
+      mp_size_t qn, rn;
+      mpz_t tq, tr;
+
+      mpz_init_set (tr, n);
+      np = tr->_mp_d;
+
+      qn = nn - dn + 1;
+
+      if (q)
+        {
+          mpz_init2 (tq, qn * GMP_LIMB_BITS);
+          qp = tq->_mp_d;
+        }
+      else
+        qp = NULL;
+
+      mpn_div_qr (qp, np, nn, d->_mp_d, dn);
+
+      if (qp)
+        {
+          qn -= (qp[qn-1] == 0);
+
+          tq->_mp_size = qs < 0 ? -qn : qn;
+        }
+      rn = mpn_normalized_size (np, dn);
+      tr->_mp_size = ns < 0 ? - rn : rn;
+
+      if (mode == GMP_DIV_FLOOR && qs < 0 && rn != 0)
+        {
+          if (q)
+            mpz_sub_ui (tq, tq, 1);
+          if (r)
+            mpz_add (tr, tr, d);
+        }
+      else if (mode == GMP_DIV_CEIL && qs >= 0 && rn != 0)
+        {
+          if (q)
+            mpz_add_ui (tq, tq, 1);
+          if (r)
+            mpz_sub (tr, tr, d);
+        }
+
+      if (q)
+        {
+          mpz_swap (tq, q);
+          mpz_clear (tq);
+        }
+      if (r)
+        mpz_swap (tr, r);
+
+      mpz_clear (tr);
+
+      return rn != 0;
+    }
+}
+
+void
+mpz_cdiv_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d)
+{
+  mpz_div_qr (q, r, n, d, GMP_DIV_CEIL);
+}
+
+void
+mpz_fdiv_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d)
+{
+  mpz_div_qr (q, r, n, d, GMP_DIV_FLOOR);
+}
+
+void
+mpz_tdiv_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d)
+{
+  mpz_div_qr (q, r, n, d, GMP_DIV_TRUNC);
+}
+
+void
+mpz_cdiv_q (mpz_t q, const mpz_t n, const mpz_t d)
+{
+  mpz_div_qr (q, NULL, n, d, GMP_DIV_CEIL);
+}
+
+void
+mpz_fdiv_q (mpz_t q, const mpz_t n, const mpz_t d)
+{
+  mpz_div_qr (q, NULL, n, d, GMP_DIV_FLOOR);
+}
+
+void
+mpz_tdiv_q (mpz_t q, const mpz_t n, const mpz_t d)
+{
+  mpz_div_qr (q, NULL, n, d, GMP_DIV_TRUNC);
+}
+
+void
+mpz_cdiv_r (mpz_t r, const mpz_t n, const mpz_t d)
+{
+  mpz_div_qr (NULL, r, n, d, GMP_DIV_CEIL);
+}
+
+void
+mpz_fdiv_r (mpz_t r, const mpz_t n, const mpz_t d)
+{
+  mpz_div_qr (NULL, r, n, d, GMP_DIV_FLOOR);
+}
+
+void
+mpz_tdiv_r (mpz_t r, const mpz_t n, const mpz_t d)
+{
+  mpz_div_qr (NULL, r, n, d, GMP_DIV_TRUNC);
+}
+
+void
+mpz_mod (mpz_t r, const mpz_t n, const mpz_t d)
+{
+  mpz_div_qr (NULL, r, n, d, d->_mp_size >= 0 ? GMP_DIV_FLOOR : GMP_DIV_CEIL);
+}
+
+static void
+mpz_div_q_2exp (mpz_t q, const mpz_t u, mp_bitcnt_t bit_index,
+                enum mpz_div_round_mode mode)
+{
+  mp_size_t un, qn;
+  mp_size_t limb_cnt;
+  mp_ptr qp;
+  int adjust;
+
+  un = u->_mp_size;
+  if (un == 0)
+    {
+      q->_mp_size = 0;
+      return;
+    }
+  limb_cnt = bit_index / GMP_LIMB_BITS;
+  qn = GMP_ABS (un) - limb_cnt;
+  bit_index %= GMP_LIMB_BITS;
+
+  if (mode == ((un > 0) ? GMP_DIV_CEIL : GMP_DIV_FLOOR)) /* un != 0 here. */
+    /* Note: Below, the final indexing at limb_cnt is valid because at
+       that point we have qn > 0. */
+    adjust = (qn <= 0
+              || !mpn_zero_p (u->_mp_d, limb_cnt)
+              || (u->_mp_d[limb_cnt]
+                  & (((mp_limb_t) 1 << bit_index) - 1)));
+  else
+    adjust = 0;
+
+  if (qn <= 0)
+    qn = 0;
+  else
+    {
+      qp = MPZ_REALLOC (q, qn);
+
+      if (bit_index != 0)
+        {
+          mpn_rshift (qp, u->_mp_d + limb_cnt, qn, bit_index);
+          qn -= qp[qn - 1] == 0;
+        }
+      else
+        {
+          mpn_copyi (qp, u->_mp_d + limb_cnt, qn);
+        }
+    }
+
+  q->_mp_size = qn;
+
+  if (adjust)
+    mpz_add_ui (q, q, 1);
+  if (un < 0)
+    mpz_neg (q, q);
+}
+
+static void
+mpz_div_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t bit_index,
+                enum mpz_div_round_mode mode)
+{
+  mp_size_t us, un, rn;
+  mp_ptr rp;
+  mp_limb_t mask;
+
+  us = u->_mp_size;
+  if (us == 0 || bit_index == 0)
+    {
+      r->_mp_size = 0;
+      return;
+    }
+  rn = (bit_index + GMP_LIMB_BITS - 1) / GMP_LIMB_BITS;
+  assert (rn > 0);
+
+  rp = MPZ_REALLOC (r, rn);
+  un = GMP_ABS (us);
+
+  mask = GMP_LIMB_MAX >> (rn * GMP_LIMB_BITS - bit_index);
+
+  if (rn > un)
+    {
+      /* Quotient (with truncation) is zero, and remainder is
+         non-zero */
+      if (mode == ((us > 0) ? GMP_DIV_CEIL : GMP_DIV_FLOOR)) /* us != 0 here. */
+        {
+          /* Have to negate and sign extend. */
+          mp_size_t i;
+
+          gmp_assert_nocarry (! mpn_neg (rp, u->_mp_d, un));
+          for (i = un; i < rn - 1; i++)
+            rp[i] = GMP_LIMB_MAX;
+
+          rp[rn-1] = mask;
+          us = -us;
+        }
+      else
+        {
+          /* Just copy */
+          if (r != u)
+            mpn_copyi (rp, u->_mp_d, un);
+
+          rn = un;
+        }
+    }
+  else
+    {
+      if (r != u)
+        mpn_copyi (rp, u->_mp_d, rn - 1);
+
+      rp[rn-1] = u->_mp_d[rn-1] & mask;
+
+      if (mode == ((us > 0) ? GMP_DIV_CEIL : GMP_DIV_FLOOR)) /* us != 0 here. */
+        {
+          /* If r != 0, compute 2^{bit_count} - r. */
+          mpn_neg (rp, rp, rn);
+
+          rp[rn-1] &= mask;
+
+          /* us is not used for anything else, so we can modify it
+             here to indicate flipped sign. */
+          us = -us;
+        }
+    }
+  rn = mpn_normalized_size (rp, rn);
+  r->_mp_size = us < 0 ? -rn : rn;
+}
+
+void
+mpz_cdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
+{
+  mpz_div_q_2exp (r, u, cnt, GMP_DIV_CEIL);
+}
+
+void
+mpz_fdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
+{
+  mpz_div_q_2exp (r, u, cnt, GMP_DIV_FLOOR);
+}
+
+void
+mpz_tdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
+{
+  mpz_div_q_2exp (r, u, cnt, GMP_DIV_TRUNC);
+}
+
+void
+mpz_cdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
+{
+  mpz_div_r_2exp (r, u, cnt, GMP_DIV_CEIL);
+}
+
+void
+mpz_fdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
+{
+  mpz_div_r_2exp (r, u, cnt, GMP_DIV_FLOOR);
+}
+
+void
+mpz_tdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
+{
+  mpz_div_r_2exp (r, u, cnt, GMP_DIV_TRUNC);
+}
+
+void
+mpz_divexact (mpz_t q, const mpz_t n, const mpz_t d)
+{
+  gmp_assert_nocarry (mpz_div_qr (q, NULL, n, d, GMP_DIV_TRUNC));
+}
+
+int
+mpz_divisible_p (const mpz_t n, const mpz_t d)
+{
+  return mpz_div_qr (NULL, NULL, n, d, GMP_DIV_TRUNC) == 0;
+}
+
+int
+mpz_congruent_p (const mpz_t a, const mpz_t b, const mpz_t m)
+{
+  mpz_t t;
+  int res;
+
+  /* a == b (mod 0) iff a == b */
+  if (mpz_sgn (m) == 0)
+    return (mpz_cmp (a, b) == 0);
+
+  mpz_init (t);
+  mpz_sub (t, a, b);
+  res = mpz_divisible_p (t, m);
+  mpz_clear (t);
+
+  return res;
+}
+
+static unsigned long
+mpz_div_qr_ui (mpz_t q, mpz_t r,
+               const mpz_t n, unsigned long d, enum mpz_div_round_mode mode)
+{
+  mp_size_t ns, qn;
+  mp_ptr qp;
+  mp_limb_t rl;
+  mp_size_t rs;
+
+  ns = n->_mp_size;
+  if (ns == 0)
+    {
+      if (q)
+        q->_mp_size = 0;
+      if (r)
+        r->_mp_size = 0;
+      return 0;
+    }
+
+  qn = GMP_ABS (ns);
+  if (q)
+    qp = MPZ_REALLOC (q, qn);
+  else
+    qp = NULL;
+
+  rl = mpn_div_qr_1 (qp, n->_mp_d, qn, d);
+  assert (rl < d);
+
+  rs = rl > 0;
+  rs = (ns < 0) ? -rs : rs;
+
+  if (rl > 0 && ( (mode == GMP_DIV_FLOOR && ns < 0)
+                  || (mode == GMP_DIV_CEIL && ns >= 0)))
+    {
+      if (q)
+        gmp_assert_nocarry (mpn_add_1 (qp, qp, qn, 1));
+      rl = d - rl;
+      rs = -rs;
+    }
+
+  if (r)
+    {
+      MPZ_REALLOC (r, 1)[0] = rl;
+      r->_mp_size = rs;
+    }
+  if (q)
+    {
+      qn -= (qp[qn-1] == 0);
+      assert (qn == 0 || qp[qn-1] > 0);
+
+      q->_mp_size = (ns < 0) ? - qn : qn;
+    }
+
+  return rl;
+}
+
+unsigned long
+mpz_cdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d)
+{
+  return mpz_div_qr_ui (q, r, n, d, GMP_DIV_CEIL);
+}
+
+unsigned long
+mpz_fdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d)
+{
+  return mpz_div_qr_ui (q, r, n, d, GMP_DIV_FLOOR);
+}
+
+unsigned long
+mpz_tdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d)
+{
+  return mpz_div_qr_ui (q, r, n, d, GMP_DIV_TRUNC);
+}
+
+unsigned long
+mpz_cdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d)
+{
+  return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_CEIL);
+}
+
+unsigned long
+mpz_fdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d)
+{
+  return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_FLOOR);
+}
+
+unsigned long
+mpz_tdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d)
+{
+  return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_TRUNC);
+}
+
+unsigned long
+mpz_cdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d)
+{
+  return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_CEIL);
+}
+unsigned long
+mpz_fdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d)
+{
+  return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_FLOOR);
+}
+unsigned long
+mpz_tdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d)
+{
+  return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_TRUNC);
+}
+
+unsigned long
+mpz_cdiv_ui (const mpz_t n, unsigned long d)
+{
+  return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_CEIL);
+}
+
+unsigned long
+mpz_fdiv_ui (const mpz_t n, unsigned long d)
+{
+  return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_FLOOR);
+}
+
+unsigned long
+mpz_tdiv_ui (const mpz_t n, unsigned long d)
+{
+  return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_TRUNC);
+}
+
+unsigned long
+mpz_mod_ui (mpz_t r, const mpz_t n, unsigned long d)
+{
+  return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_FLOOR);
+}
+
+void
+mpz_divexact_ui (mpz_t q, const mpz_t n, unsigned long d)
+{
+  gmp_assert_nocarry (mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_TRUNC));
+}
+
+int
+mpz_divisible_ui_p (const mpz_t n, unsigned long d)
+{
+  return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_TRUNC) == 0;
+}
+
+
+/* GCD */
+static mp_limb_t
+mpn_gcd_11 (mp_limb_t u, mp_limb_t v)
+{
+  unsigned shift;
+
+  assert ( (u | v) > 0);
+
+  if (u == 0)
+    return v;
+  else if (v == 0)
+    return u;
+
+  gmp_ctz (shift, u | v);
+
+  u >>= shift;
+  v >>= shift;
+
+  if ( (u & 1) == 0)
+    MP_LIMB_T_SWAP (u, v);
+
+  while ( (v & 1) == 0)
+    v >>= 1;
+
+  while (u != v)
+    {
+      if (u > v)
+        {
+          u -= v;
+          do
+            u >>= 1;
+          while ( (u & 1) == 0);
+        }
+      else
+        {
+          v -= u;
+          do
+            v >>= 1;
+          while ( (v & 1) == 0);
+        }
+    }
+  return u << shift;
+}
+
+unsigned long
+mpz_gcd_ui (mpz_t g, const mpz_t u, unsigned long v)
+{
+  mp_size_t un;
+
+  if (v == 0)
+    {
+      if (g)
+        mpz_abs (g, u);
+    }
+  else
+    {
+      un = GMP_ABS (u->_mp_size);
+      if (un != 0)
+        v = mpn_gcd_11 (mpn_div_qr_1 (NULL, u->_mp_d, un, v), v);
+
+      if (g)
+        mpz_set_ui (g, v);
+    }
+
+  return v;
+}
+
+static mp_bitcnt_t
+mpz_make_odd (mpz_t r)
+{
+  mp_bitcnt_t shift;
+
+  assert (r->_mp_size > 0);
+  /* Count trailing zeros, equivalent to mpn_scan1, because we know that there is a 1 */
+  shift = mpn_common_scan (r->_mp_d[0], 0, r->_mp_d, 0, 0);
+  mpz_tdiv_q_2exp (r, r, shift);
+
+  return shift;
+}
+
+void
+mpz_gcd (mpz_t g, const mpz_t u, const mpz_t v)
+{
+  mpz_t tu, tv;
+  mp_bitcnt_t uz, vz, gz;
+
+  if (u->_mp_size == 0)
+    {
+      mpz_abs (g, v);
+      return;
+    }
+  if (v->_mp_size == 0)
+    {
+      mpz_abs (g, u);
+      return;
+    }
+
+  mpz_init (tu);
+  mpz_init (tv);
+
+  mpz_abs (tu, u);
+  uz = mpz_make_odd (tu);
+  mpz_abs (tv, v);
+  vz = mpz_make_odd (tv);
+  gz = GMP_MIN (uz, vz);
+
+  if (tu->_mp_size < tv->_mp_size)
+    mpz_swap (tu, tv);
+
+  mpz_tdiv_r (tu, tu, tv);
+  if (tu->_mp_size == 0)
+    {
+      mpz_swap (g, tv);
+    }
+  else
+    for (;;)
+      {
+        int c;
+
+        mpz_make_odd (tu);
+        c = mpz_cmp (tu, tv);
+        if (c == 0)
+          {
+            mpz_swap (g, tu);
+            break;
+          }
+        if (c < 0)
+          mpz_swap (tu, tv);
+
+        if (tv->_mp_size == 1)
+          {
+            mp_limb_t vl = tv->_mp_d[0];
+            mp_limb_t ul = mpz_tdiv_ui (tu, vl);
+            mpz_set_ui (g, mpn_gcd_11 (ul, vl));
+            break;
+          }
+        mpz_sub (tu, tu, tv);
+      }
+  mpz_clear (tu);
+  mpz_clear (tv);
+  mpz_mul_2exp (g, g, gz);
+}
+
+void
+mpz_gcdext (mpz_t g, mpz_t s, mpz_t t, const mpz_t u, const mpz_t v)
+{
+  mpz_t tu, tv, s0, s1, t0, t1;
+  mp_bitcnt_t uz, vz, gz;
+  mp_bitcnt_t power;
+
+  if (u->_mp_size == 0)
+    {
+      /* g = 0 u + sgn(v) v */
+      signed long sign = mpz_sgn (v);
+      mpz_abs (g, v);
+      if (s)
+        mpz_set_ui (s, 0);
+      if (t)
+        mpz_set_si (t, sign);
+      return;
+    }
+
+  if (v->_mp_size == 0)
+    {
+      /* g = sgn(u) u + 0 v */
+      signed long sign = mpz_sgn (u);
+      mpz_abs (g, u);
+      if (s)
+        mpz_set_si (s, sign);
+      if (t)
+        mpz_set_ui (t, 0);
+      return;
+    }
+
+  mpz_init (tu);
+  mpz_init (tv);
+  mpz_init (s0);
+  mpz_init (s1);
+  mpz_init (t0);
+  mpz_init (t1);
+
+  mpz_abs (tu, u);
+  uz = mpz_make_odd (tu);
+  mpz_abs (tv, v);
+  vz = mpz_make_odd (tv);
+  gz = GMP_MIN (uz, vz);
+
+  uz -= gz;
+  vz -= gz;
+
+  /* Cofactors corresponding to odd gcd. gz handled later. */
+  if (tu->_mp_size < tv->_mp_size)
+    {
+      mpz_swap (tu, tv);
+      MPZ_SRCPTR_SWAP (u, v);
+      MPZ_PTR_SWAP (s, t);
+      MP_BITCNT_T_SWAP (uz, vz);
+    }
+
+  /* Maintain
+   *
+   * u = t0 tu + t1 tv
+   * v = s0 tu + s1 tv
+   *
+   * where u and v denote the inputs with common factors of two
+   * eliminated, and det (s0, t0; s1, t1) = 2^p. Then
+   *
+   * 2^p tu =  s1 u - t1 v
+   * 2^p tv = -s0 u + t0 v
+   */
+
+  /* After initial division, tu = q tv + tu', we have
+   *
+   * u = 2^uz (tu' + q tv)
+   * v = 2^vz tv
+   *
+   * or
+   *
+   * t0 = 2^uz, t1 = 2^uz q
+   * s0 = 0,    s1 = 2^vz
+   */
+
+  mpz_setbit (t0, uz);
+  mpz_tdiv_qr (t1, tu, tu, tv);
+  mpz_mul_2exp (t1, t1, uz);
+
+  mpz_setbit (s1, vz);
+  power = uz + vz;
+
+  if (tu->_mp_size > 0)
+    {
+      mp_bitcnt_t shift;
+      shift = mpz_make_odd (tu);
+      mpz_mul_2exp (t0, t0, shift);
+      mpz_mul_2exp (s0, s0, shift);
+      power += shift;
+
+      for (;;)
+        {
+          int c;
+          c = mpz_cmp (tu, tv);
+          if (c == 0)
+            break;
+
+          if (c < 0)
+            {
+              /* tv = tv' + tu
+               *
+               * u = t0 tu + t1 (tv' + tu) = (t0 + t1) tu + t1 tv'
+               * v = s0 tu + s1 (tv' + tu) = (s0 + s1) tu + s1 tv' */
+
+              mpz_sub (tv, tv, tu);
+              mpz_add (t0, t0, t1);
+              mpz_add (s0, s0, s1);
+
+              shift = mpz_make_odd (tv);
+              mpz_mul_2exp (t1, t1, shift);
+              mpz_mul_2exp (s1, s1, shift);
+            }
+          else
+            {
+              mpz_sub (tu, tu, tv);
+              mpz_add (t1, t0, t1);
+              mpz_add (s1, s0, s1);
+
+              shift = mpz_make_odd (tu);
+              mpz_mul_2exp (t0, t0, shift);
+              mpz_mul_2exp (s0, s0, shift);
+            }
+          power += shift;
+        }
+    }
+
+  /* Now tv = odd part of gcd, and -s0 and t0 are corresponding
+     cofactors. */
+
+  mpz_mul_2exp (tv, tv, gz);
+  mpz_neg (s0, s0);
+
+  /* 2^p g = s0 u + t0 v. Eliminate one factor of two at a time. To
+     adjust cofactors, we need u / g and v / g */
+
+  mpz_divexact (s1, v, tv);
+  mpz_abs (s1, s1);
+  mpz_divexact (t1, u, tv);
+  mpz_abs (t1, t1);
+
+  while (power-- > 0)
+    {
+      /* s0 u + t0 v = (s0 - v/g) u - (t0 + u/g) v */
+      if (mpz_odd_p (s0) || mpz_odd_p (t0))
+        {
+          mpz_sub (s0, s0, s1);
+          mpz_add (t0, t0, t1);
+        }
+      mpz_divexact_ui (s0, s0, 2);
+      mpz_divexact_ui (t0, t0, 2);
+    }
+
+  /* Arrange so that |s| < |u| / 2g */
+  mpz_add (s1, s0, s1);
+  if (mpz_cmpabs (s0, s1) > 0)
+    {
+      mpz_swap (s0, s1);
+      mpz_sub (t0, t0, t1);
+    }
+  if (u->_mp_size < 0)
+    mpz_neg (s0, s0);
+  if (v->_mp_size < 0)
+    mpz_neg (t0, t0);
+
+  mpz_swap (g, tv);
+  if (s)
+    mpz_swap (s, s0);
+  if (t)
+    mpz_swap (t, t0);
+
+  mpz_clear (tu);
+  mpz_clear (tv);
+  mpz_clear (s0);
+  mpz_clear (s1);
+  mpz_clear (t0);
+  mpz_clear (t1);
+}
+
+void
+mpz_lcm (mpz_t r, const mpz_t u, const mpz_t v)
+{
+  mpz_t g;
+
+  if (u->_mp_size == 0 || v->_mp_size == 0)
+    {
+      r->_mp_size = 0;
+      return;
+    }
+
+  mpz_init (g);
+
+  mpz_gcd (g, u, v);
+  mpz_divexact (g, u, g);
+  mpz_mul (r, g, v);
+
+  mpz_clear (g);
+  mpz_abs (r, r);
+}
+
+void
+mpz_lcm_ui (mpz_t r, const mpz_t u, unsigned long v)
+{
+  if (v == 0 || u->_mp_size == 0)
+    {
+      r->_mp_size = 0;
+      return;
+    }
+
+  v /= mpz_gcd_ui (NULL, u, v);
+  mpz_mul_ui (r, u, v);
+
+  mpz_abs (r, r);
+}
+
+int
+mpz_invert (mpz_t r, const mpz_t u, const mpz_t m)
+{
+  mpz_t g, tr;
+  int invertible;
+
+  if (u->_mp_size == 0 || mpz_cmpabs_ui (m, 1) <= 0)
+    return 0;
+
+  mpz_init (g);
+  mpz_init (tr);
+
+  mpz_gcdext (g, tr, NULL, u, m);
+  invertible = (mpz_cmp_ui (g, 1) == 0);
+
+  if (invertible)
+    {
+      if (tr->_mp_size < 0)
+        {
+          if (m->_mp_size >= 0)
+            mpz_add (tr, tr, m);
+          else
+            mpz_sub (tr, tr, m);
+        }
+      mpz_swap (r, tr);
+    }
+
+  mpz_clear (g);
+  mpz_clear (tr);
+  return invertible;
+}
+
+
+/* Higher level operations (sqrt, pow and root) */
+
+void
+mpz_pow_ui (mpz_t r, const mpz_t b, unsigned long e)
+{
+  unsigned long bit;
+  mpz_t tr;
+  mpz_init_set_ui (tr, 1);
+
+  bit = GMP_ULONG_HIGHBIT;
+  do
+    {
+      mpz_mul (tr, tr, tr);
+      if (e & bit)
+        mpz_mul (tr, tr, b);
+      bit >>= 1;
+    }
+  while (bit > 0);
+
+  mpz_swap (r, tr);
+  mpz_clear (tr);
+}
+
+void
+mpz_ui_pow_ui (mpz_t r, unsigned long blimb, unsigned long e)
+{
+  mpz_t b;
+  mpz_pow_ui (r, mpz_roinit_normal_n (b, &blimb, blimb != 0), e);
+}
+
+void
+mpz_powm (mpz_t r, const mpz_t b, const mpz_t e, const mpz_t m)
+{
+  mpz_t tr;
+  mpz_t base;
+  mp_size_t en, mn;
+  mp_srcptr mp;
+  struct gmp_div_inverse minv;
+  unsigned shift;
+  mp_ptr tp = NULL;
+
+  en = GMP_ABS (e->_mp_size);
+  mn = GMP_ABS (m->_mp_size);
+  if (mn == 0)
+    gmp_die ("mpz_powm: Zero modulo.");
+
+  if (en == 0)
+    {
+      mpz_set_ui (r, 1);
+      return;
+    }
+
+  mp = m->_mp_d;
+  mpn_div_qr_invert (&minv, mp, mn);
+  shift = minv.shift;
+
+  if (shift > 0)
+    {
+      /* To avoid shifts, we do all our reductions, except the final
+         one, using a *normalized* m. */
+      minv.shift = 0;
+
+      tp = gmp_xalloc_limbs (mn);
+      gmp_assert_nocarry (mpn_lshift (tp, mp, mn, shift));
+      mp = tp;
+    }
+
+  mpz_init (base);
+
+  if (e->_mp_size < 0)
+    {
+      if (!mpz_invert (base, b, m))
+        gmp_die ("mpz_powm: Negative exponent and non-invertible base.");
+    }
+  else
+    {
+      mp_size_t bn;
+      mpz_abs (base, b);
+
+      bn = base->_mp_size;
+      if (bn >= mn)
+        {
+          mpn_div_qr_preinv (NULL, base->_mp_d, base->_mp_size, mp, mn, &minv);
+          bn = mn;
+        }
+
+      /* We have reduced the absolute value. Now take care of the
+         sign. Note that we get zero represented non-canonically as
+         m. */
+      if (b->_mp_size < 0)
+        {
+          mp_ptr bp = MPZ_REALLOC (base, mn);
+          gmp_assert_nocarry (mpn_sub (bp, mp, mn, bp, bn));
+          bn = mn;
+        }
+      base->_mp_size = mpn_normalized_size (base->_mp_d, bn);
+    }
+  mpz_init_set_ui (tr, 1);
+
+  while (--en >= 0)
+    {
+      mp_limb_t w = e->_mp_d[en];
+      mp_limb_t bit;
+
+      bit = GMP_LIMB_HIGHBIT;
+      do
+        {
+          mpz_mul (tr, tr, tr);
+          if (w & bit)
+            mpz_mul (tr, tr, base);
+          if (tr->_mp_size > mn)
+            {
+              mpn_div_qr_preinv (NULL, tr->_mp_d, tr->_mp_size, mp, mn, &minv);
+              tr->_mp_size = mpn_normalized_size (tr->_mp_d, mn);
+            }
+          bit >>= 1;
+        }
+      while (bit > 0);
+    }
+
+  /* Final reduction */
+  if (tr->_mp_size >= mn)
+    {
+      minv.shift = shift;
+      mpn_div_qr_preinv (NULL, tr->_mp_d, tr->_mp_size, mp, mn, &minv);
+      tr->_mp_size = mpn_normalized_size (tr->_mp_d, mn);
+    }
+  if (tp)
+    gmp_free (tp);
+
+  mpz_swap (r, tr);
+  mpz_clear (tr);
+  mpz_clear (base);
+}
+
+void
+mpz_powm_ui (mpz_t r, const mpz_t b, unsigned long elimb, const mpz_t m)
+{
+  mpz_t e;
+  mpz_powm (r, b, mpz_roinit_normal_n (e, &elimb, elimb != 0), m);
+}
+
+/* x=trunc(y^(1/z)), r=y-x^z */
+void
+mpz_rootrem (mpz_t x, mpz_t r, const mpz_t y, unsigned long z)
+{
+  int sgn;
+  mpz_t t, u;
+
+  sgn = y->_mp_size < 0;
+  if ((~z & sgn) != 0)
+    gmp_die ("mpz_rootrem: Negative argument, with even root.");
+  if (z == 0)
+    gmp_die ("mpz_rootrem: Zeroth root.");
+
+  if (mpz_cmpabs_ui (y, 1) <= 0) {
+    if (x)
+      mpz_set (x, y);
+    if (r)
+      r->_mp_size = 0;
+    return;
+  }
+
+  mpz_init (u);
+  mpz_init (t);
+  mpz_setbit (t, mpz_sizeinbase (y, 2) / z + 1);
+
+  if (z == 2) /* simplify sqrt loop: z-1 == 1 */
+    do {
+      mpz_swap (u, t);                  /* u = x */
+      mpz_tdiv_q (t, y, u);             /* t = y/x */
+      mpz_add (t, t, u);                /* t = y/x + x */
+      mpz_tdiv_q_2exp (t, t, 1);        /* x'= (y/x + x)/2 */
+    } while (mpz_cmpabs (t, u) < 0);    /* |x'| < |x| */
+  else /* z != 2 */ {
+    mpz_t v;
+
+    mpz_init (v);
+    if (sgn)
+      mpz_neg (t, t);
+
+    do {
+      mpz_swap (u, t);                  /* u = x */
+      mpz_pow_ui (t, u, z - 1);         /* t = x^(z-1) */
+      mpz_tdiv_q (t, y, t);             /* t = y/x^(z-1) */
+      mpz_mul_ui (v, u, z - 1);         /* v = x*(z-1) */
+      mpz_add (t, t, v);                /* t = y/x^(z-1) + x*(z-1) */
+      mpz_tdiv_q_ui (t, t, z);          /* x'=(y/x^(z-1) + x*(z-1))/z */
+    } while (mpz_cmpabs (t, u) < 0);    /* |x'| < |x| */
+
+    mpz_clear (v);
+  }
+
+  if (r) {
+    mpz_pow_ui (t, u, z);
+    mpz_sub (r, y, t);
+  }
+  if (x)
+    mpz_swap (x, u);
+  mpz_clear (u);
+  mpz_clear (t);
+}
+
+int
+mpz_root (mpz_t x, const mpz_t y, unsigned long z)
+{
+  int res;
+  mpz_t r;
+
+  mpz_init (r);
+  mpz_rootrem (x, r, y, z);
+  res = r->_mp_size == 0;
+  mpz_clear (r);
+
+  return res;
+}
+
+/* Compute s = floor(sqrt(u)) and r = u - s^2. Allows r == NULL */
+void
+mpz_sqrtrem (mpz_t s, mpz_t r, const mpz_t u)
+{
+  mpz_rootrem (s, r, u, 2);
+}
+
+void
+mpz_sqrt (mpz_t s, const mpz_t u)
+{
+  mpz_rootrem (s, NULL, u, 2);
+}
+
+int
+mpz_perfect_square_p (const mpz_t u)
+{
+  if (u->_mp_size <= 0)
+    return (u->_mp_size == 0);
+  else
+    return mpz_root (NULL, u, 2);
+}
+
+int
+mpn_perfect_square_p (mp_srcptr p, mp_size_t n)
+{
+  mpz_t t;
+
+  assert (n > 0);
+  assert (p [n-1] != 0);
+  return mpz_root (NULL, mpz_roinit_normal_n (t, p, n), 2);
+}
+
+mp_size_t
+mpn_sqrtrem (mp_ptr sp, mp_ptr rp, mp_srcptr p, mp_size_t n)
+{
+  mpz_t s, r, u;
+  mp_size_t res;
+
+  assert (n > 0);
+  assert (p [n-1] != 0);
+
+  mpz_init (r);
+  mpz_init (s);
+  mpz_rootrem (s, r, mpz_roinit_normal_n (u, p, n), 2);
+
+  assert (s->_mp_size == (n+1)/2);
+  mpn_copyd (sp, s->_mp_d, s->_mp_size);
+  mpz_clear (s);
+  res = r->_mp_size;
+  if (rp)
+    mpn_copyd (rp, r->_mp_d, res);
+  mpz_clear (r);
+  return res;
+}
+
+/* Combinatorics */
+
+void
+mpz_mfac_uiui (mpz_t x, unsigned long n, unsigned long m)
+{
+  mpz_set_ui (x, n + (n == 0));
+  if (m + 1 < 2) return;
+  while (n > m + 1)
+    mpz_mul_ui (x, x, n -= m);
+}
+
+void
+mpz_2fac_ui (mpz_t x, unsigned long n)
+{
+  mpz_mfac_uiui (x, n, 2);
+}
+
+void
+mpz_fac_ui (mpz_t x, unsigned long n)
+{
+  mpz_mfac_uiui (x, n, 1);
+}
+
+void
+mpz_bin_uiui (mpz_t r, unsigned long n, unsigned long k)
+{
+  mpz_t t;
+
+  mpz_set_ui (r, k <= n);
+
+  if (k > (n >> 1))
+    k = (k <= n) ? n - k : 0;
+
+  mpz_init (t);
+  mpz_fac_ui (t, k);
+
+  for (; k > 0; --k)
+      mpz_mul_ui (r, r, n--);
+
+  mpz_divexact (r, r, t);
+  mpz_clear (t);
+}
+
+
+/* Primality testing */
+static int
+gmp_millerrabin (const mpz_t n, const mpz_t nm1, mpz_t y,
+                 const mpz_t q, mp_bitcnt_t k)
+{
+  assert (k > 0);
+
+  /* Caller must initialize y to the base. */
+  mpz_powm (y, y, q, n);
+
+  if (mpz_cmp_ui (y, 1) == 0 || mpz_cmp (y, nm1) == 0)
+    return 1;
+
+  while (--k > 0)
+    {
+      mpz_powm_ui (y, y, 2, n);
+      if (mpz_cmp (y, nm1) == 0)
+        return 1;
+      /* y == 1 means that the previous y was a non-trivial square root
+         of 1 (mod n). y == 0 means that n is a power of the base.
+         In either case, n is not prime. */
+      if (mpz_cmp_ui (y, 1) <= 0)
+        return 0;
+    }
+  return 0;
+}
+
+/* This product is 0xc0cfd797, and fits in 32 bits. */
+#define GMP_PRIME_PRODUCT \
+  (3UL*5UL*7UL*11UL*13UL*17UL*19UL*23UL*29UL)
+
+/* Bit (p+1)/2 is set, for each odd prime <= 61 */
+#define GMP_PRIME_MASK 0xc96996dcUL
+
+int
+mpz_probab_prime_p (const mpz_t n, int reps)
+{
+  mpz_t nm1;
+  mpz_t q;
+  mpz_t y;
+  mp_bitcnt_t k;
+  int is_prime;
+  int j;
+
+  /* Note that we use the absolute value of n only, for compatibility
+     with the real GMP. */
+  if (mpz_even_p (n))
+    return (mpz_cmpabs_ui (n, 2) == 0) ? 2 : 0;
+
+  /* Above test excludes n == 0 */
+  assert (n->_mp_size != 0);
+
+  if (mpz_cmpabs_ui (n, 64) < 0)
+    return (GMP_PRIME_MASK >> (n->_mp_d[0] >> 1)) & 2;
+
+  if (mpz_gcd_ui (NULL, n, GMP_PRIME_PRODUCT) != 1)
+    return 0;
+
+  /* All prime factors are >= 31. */
+  if (mpz_cmpabs_ui (n, 31*31) < 0)
+    return 2;
+
+  /* Use Miller-Rabin, with a deterministic sequence of bases, a[j] =
+     j^2 + j + 41 using Euler's polynomial. We potentially stop early,
+     if a[j] >= n - 1. Since n >= 31*31, this can happen only if reps >
+     30 (a[30] == 971 > 31*31 == 961). */
+
+  mpz_init (nm1);
+  mpz_init (q);
+  mpz_init (y);
+
+  /* Find q and k, where q is odd and n = 1 + 2**k * q.  */
+  nm1->_mp_size = mpz_abs_sub_ui (nm1, n, 1);
+  k = mpz_scan1 (nm1, 0);
+  mpz_tdiv_q_2exp (q, nm1, k);
+
+  for (j = 0, is_prime = 1; is_prime & (j < reps); j++)
+    {
+      mpz_set_ui (y, (unsigned long) j*j+j+41);
+      if (mpz_cmp (y, nm1) >= 0)
+        {
+          /* Don't try any further bases. This "early" break does not affect
+             the result for any reasonable reps value (<=5000 was tested) */
+          assert (j >= 30);
+          break;
+        }
+      is_prime = gmp_millerrabin (n, nm1, y, q, k);
+    }
+  mpz_clear (nm1);
+  mpz_clear (q);
+  mpz_clear (y);
+
+  return is_prime;
+}
+
+
+/* Logical operations and bit manipulation. */
+
+/* Numbers are treated as if represented in two's complement (and
+   infinitely sign extended). For a negative values we get the two's
+   complement from -x = ~x + 1, where ~ is bitwise complement.
+   Negation transforms
+
+     xxxx10...0
+
+   into
+
+     yyyy10...0
+
+   where yyyy is the bitwise complement of xxxx. So least significant
+   bits, up to and including the first one bit, are unchanged, and
+   the more significant bits are all complemented.
+
+   To change a bit from zero to one in a negative number, subtract the
+   corresponding power of two from the absolute value. This can never
+   underflow. To change a bit from one to zero, add the corresponding
+   power of two, and this might overflow. E.g., if x = -001111, the
+   two's complement is 110001. Clearing the least significant bit, we
+   get two's complement 110000, and -010000. */
+
+int
+mpz_tstbit (const mpz_t d, mp_bitcnt_t bit_index)
+{
+  mp_size_t limb_index;
+  unsigned shift;
+  mp_size_t ds;
+  mp_size_t dn;
+  mp_limb_t w;
+  int bit;
+
+  ds = d->_mp_size;
+  dn = GMP_ABS (ds);
+  limb_index = bit_index / GMP_LIMB_BITS;
+  if (limb_index >= dn)
+    return ds < 0;
+
+  shift = bit_index % GMP_LIMB_BITS;
+  w = d->_mp_d[limb_index];
+  bit = (w >> shift) & 1;
+
+  if (ds < 0)
+    {
+      /* d < 0. Check if any of the bits below is set: If so, our bit
+         must be complemented. */
+      if (shift > 0 && (w << (GMP_LIMB_BITS - shift)) > 0)
+        return bit ^ 1;
+      while (--limb_index >= 0)
+        if (d->_mp_d[limb_index] > 0)
+          return bit ^ 1;
+    }
+  return bit;
+}
+
+static void
+mpz_abs_add_bit (mpz_t d, mp_bitcnt_t bit_index)
+{
+  mp_size_t dn, limb_index;
+  mp_limb_t bit;
+  mp_ptr dp;
+
+  dn = GMP_ABS (d->_mp_size);
+
+  limb_index = bit_index / GMP_LIMB_BITS;
+  bit = (mp_limb_t) 1 << (bit_index % GMP_LIMB_BITS);
+
+  if (limb_index >= dn)
+    {
+      mp_size_t i;
+      /* The bit should be set outside of the end of the number.
+         We have to increase the size of the number. */
+      dp = MPZ_REALLOC (d, limb_index + 1);
+
+      dp[limb_index] = bit;
+      for (i = dn; i < limb_index; i++)
+        dp[i] = 0;
+      dn = limb_index + 1;
+    }
+  else
+    {
+      mp_limb_t cy;
+
+      dp = d->_mp_d;
+
+      cy = mpn_add_1 (dp + limb_index, dp + limb_index, dn - limb_index, bit);
+      if (cy > 0)
+        {
+          dp = MPZ_REALLOC (d, dn + 1);
+          dp[dn++] = cy;
+        }
+    }
+
+  d->_mp_size = (d->_mp_size < 0) ? - dn : dn;
+}
+
+static void
+mpz_abs_sub_bit (mpz_t d, mp_bitcnt_t bit_index)
+{
+  mp_size_t dn, limb_index;
+  mp_ptr dp;
+  mp_limb_t bit;
+
+  dn = GMP_ABS (d->_mp_size);
+  dp = d->_mp_d;
+
+  limb_index = bit_index / GMP_LIMB_BITS;
+  bit = (mp_limb_t) 1 << (bit_index % GMP_LIMB_BITS);
+
+  assert (limb_index < dn);
+
+  gmp_assert_nocarry (mpn_sub_1 (dp + limb_index, dp + limb_index,
+                                 dn - limb_index, bit));
+  dn = mpn_normalized_size (dp, dn);
+  d->_mp_size = (d->_mp_size < 0) ? - dn : dn;
+}
+
+void
+mpz_setbit (mpz_t d, mp_bitcnt_t bit_index)
+{
+  if (!mpz_tstbit (d, bit_index))
+    {
+      if (d->_mp_size >= 0)
+        mpz_abs_add_bit (d, bit_index);
+      else
+        mpz_abs_sub_bit (d, bit_index);
+    }
+}
+
+void
+mpz_clrbit (mpz_t d, mp_bitcnt_t bit_index)
+{
+  if (mpz_tstbit (d, bit_index))
+    {
+      if (d->_mp_size >= 0)
+        mpz_abs_sub_bit (d, bit_index);
+      else
+        mpz_abs_add_bit (d, bit_index);
+    }
+}
+
+void
+mpz_combit (mpz_t d, mp_bitcnt_t bit_index)
+{
+  if (mpz_tstbit (d, bit_index) ^ (d->_mp_size < 0))
+    mpz_abs_sub_bit (d, bit_index);
+  else
+    mpz_abs_add_bit (d, bit_index);
+}
+
+void
+mpz_com (mpz_t r, const mpz_t u)
+{
+  mpz_neg (r, u);
+  mpz_sub_ui (r, r, 1);
+}
+
+void
+mpz_and (mpz_t r, const mpz_t u, const mpz_t v)
+{
+  mp_size_t un, vn, rn, i;
+  mp_ptr up, vp, rp;
+
+  mp_limb_t ux, vx, rx;
+  mp_limb_t uc, vc, rc;
+  mp_limb_t ul, vl, rl;
+
+  un = GMP_ABS (u->_mp_size);
+  vn = GMP_ABS (v->_mp_size);
+  if (un < vn)
+    {
+      MPZ_SRCPTR_SWAP (u, v);
+      MP_SIZE_T_SWAP (un, vn);
+    }
+  if (vn == 0)
+    {
+      r->_mp_size = 0;
+      return;
+    }
+
+  uc = u->_mp_size < 0;
+  vc = v->_mp_size < 0;
+  rc = uc & vc;
+
+  ux = -uc;
+  vx = -vc;
+  rx = -rc;
+
+  /* If the smaller input is positive, higher limbs don't matter. */
+  rn = vx ? un : vn;
+
+  rp = MPZ_REALLOC (r, rn + (mp_size_t) rc);
+
+  up = u->_mp_d;
+  vp = v->_mp_d;
+
+  i = 0;
+  do
+    {
+      ul = (up[i] ^ ux) + uc;
+      uc = ul < uc;
+
+      vl = (vp[i] ^ vx) + vc;
+      vc = vl < vc;
+
+      rl = ( (ul & vl) ^ rx) + rc;
+      rc = rl < rc;
+      rp[i] = rl;
+    }
+  while (++i < vn);
+  assert (vc == 0);
+
+  for (; i < rn; i++)
+    {
+      ul = (up[i] ^ ux) + uc;
+      uc = ul < uc;
+
+      rl = ( (ul & vx) ^ rx) + rc;
+      rc = rl < rc;
+      rp[i] = rl;
+    }
+  if (rc)
+    rp[rn++] = rc;
+  else
+    rn = mpn_normalized_size (rp, rn);
+
+  r->_mp_size = rx ? -rn : rn;
+}
+
+void
+mpz_ior (mpz_t r, const mpz_t u, const mpz_t v)
+{
+  mp_size_t un, vn, rn, i;
+  mp_ptr up, vp, rp;
+
+  mp_limb_t ux, vx, rx;
+  mp_limb_t uc, vc, rc;
+  mp_limb_t ul, vl, rl;
+
+  un = GMP_ABS (u->_mp_size);
+  vn = GMP_ABS (v->_mp_size);
+  if (un < vn)
+    {
+      MPZ_SRCPTR_SWAP (u, v);
+      MP_SIZE_T_SWAP (un, vn);
+    }
+  if (vn == 0)
+    {
+      mpz_set (r, u);
+      return;
+    }
+
+  uc = u->_mp_size < 0;
+  vc = v->_mp_size < 0;
+  rc = uc | vc;
+
+  ux = -uc;
+  vx = -vc;
+  rx = -rc;
+
+  /* If the smaller input is negative, by sign extension higher limbs
+     don't matter. */
+  rn = vx ? vn : un;
+
+  rp = MPZ_REALLOC (r, rn + (mp_size_t) rc);
+
+  up = u->_mp_d;
+  vp = v->_mp_d;
+
+  i = 0;
+  do
+    {
+      ul = (up[i] ^ ux) + uc;
+      uc = ul < uc;
+
+      vl = (vp[i] ^ vx) + vc;
+      vc = vl < vc;
+
+      rl = ( (ul | vl) ^ rx) + rc;
+      rc = rl < rc;
+      rp[i] = rl;
+    }
+  while (++i < vn);
+  assert (vc == 0);
+
+  for (; i < rn; i++)
+    {
+      ul = (up[i] ^ ux) + uc;
+      uc = ul < uc;
+
+      rl = ( (ul | vx) ^ rx) + rc;
+      rc = rl < rc;
+      rp[i] = rl;
+    }
+  if (rc)
+    rp[rn++] = rc;
+  else
+    rn = mpn_normalized_size (rp, rn);
+
+  r->_mp_size = rx ? -rn : rn;
+}
+
+void
+mpz_xor (mpz_t r, const mpz_t u, const mpz_t v)
+{
+  mp_size_t un, vn, i;
+  mp_ptr up, vp, rp;
+
+  mp_limb_t ux, vx, rx;
+  mp_limb_t uc, vc, rc;
+  mp_limb_t ul, vl, rl;
+
+  un = GMP_ABS (u->_mp_size);
+  vn = GMP_ABS (v->_mp_size);
+  if (un < vn)
+    {
+      MPZ_SRCPTR_SWAP (u, v);
+      MP_SIZE_T_SWAP (un, vn);
+    }
+  if (vn == 0)
+    {
+      mpz_set (r, u);
+      return;
+    }
+
+  uc = u->_mp_size < 0;
+  vc = v->_mp_size < 0;
+  rc = uc ^ vc;
+
+  ux = -uc;
+  vx = -vc;
+  rx = -rc;
+
+  rp = MPZ_REALLOC (r, un + (mp_size_t) rc);
+
+  up = u->_mp_d;
+  vp = v->_mp_d;
+
+  i = 0;
+  do
+    {
+      ul = (up[i] ^ ux) + uc;
+      uc = ul < uc;
+
+      vl = (vp[i] ^ vx) + vc;
+      vc = vl < vc;
+
+      rl = (ul ^ vl ^ rx) + rc;
+      rc = rl < rc;
+      rp[i] = rl;
+    }
+  while (++i < vn);
+  assert (vc == 0);
+
+  for (; i < un; i++)
+    {
+      ul = (up[i] ^ ux) + uc;
+      uc = ul < uc;
+
+      rl = (ul ^ ux) + rc;
+      rc = rl < rc;
+      rp[i] = rl;
+    }
+  if (rc)
+    rp[un++] = rc;
+  else
+    un = mpn_normalized_size (rp, un);
+
+  r->_mp_size = rx ? -un : un;
+}
+
+static unsigned
+gmp_popcount_limb (mp_limb_t x)
+{
+  unsigned c;
+
+  /* Do 16 bits at a time, to avoid limb-sized constants. */
+  for (c = 0; x > 0; x >>= 16)
+    {
+      unsigned w = x - ((x >> 1) & 0x5555);
+      w = ((w >> 2) & 0x3333) + (w & 0x3333);
+      w =  (w >> 4) + w;
+      w = ((w >> 8) & 0x000f) + (w & 0x000f);
+      c += w;
+    }
+  return c;
+}
+
+mp_bitcnt_t
+mpn_popcount (mp_srcptr p, mp_size_t n)
+{
+  mp_size_t i;
+  mp_bitcnt_t c;
+
+  for (c = 0, i = 0; i < n; i++)
+    c += gmp_popcount_limb (p[i]);
+
+  return c;
+}
+
+mp_bitcnt_t
+mpz_popcount (const mpz_t u)
+{
+  mp_size_t un;
+
+  un = u->_mp_size;
+
+  if (un < 0)
+    return ~(mp_bitcnt_t) 0;
+
+  return mpn_popcount (u->_mp_d, un);
+}
+
+mp_bitcnt_t
+mpz_hamdist (const mpz_t u, const mpz_t v)
+{
+  mp_size_t un, vn, i;
+  mp_limb_t uc, vc, ul, vl, comp;
+  mp_srcptr up, vp;
+  mp_bitcnt_t c;
+
+  un = u->_mp_size;
+  vn = v->_mp_size;
+
+  if ( (un ^ vn) < 0)
+    return ~(mp_bitcnt_t) 0;
+
+  comp = - (uc = vc = (un < 0));
+  if (uc)
+    {
+      assert (vn < 0);
+      un = -un;
+      vn = -vn;
+    }
+
+  up = u->_mp_d;
+  vp = v->_mp_d;
+
+  if (un < vn)
+    MPN_SRCPTR_SWAP (up, un, vp, vn);
+
+  for (i = 0, c = 0; i < vn; i++)
+    {
+      ul = (up[i] ^ comp) + uc;
+      uc = ul < uc;
+
+      vl = (vp[i] ^ comp) + vc;
+      vc = vl < vc;
+
+      c += gmp_popcount_limb (ul ^ vl);
+    }
+  assert (vc == 0);
+
+  for (; i < un; i++)
+    {
+      ul = (up[i] ^ comp) + uc;
+      uc = ul < uc;
+
+      c += gmp_popcount_limb (ul ^ comp);
+    }
+
+  return c;
+}
+
+mp_bitcnt_t
+mpz_scan1 (const mpz_t u, mp_bitcnt_t starting_bit)
+{
+  mp_ptr up;
+  mp_size_t us, un, i;
+  mp_limb_t limb, ux;
+
+  us = u->_mp_size;
+  un = GMP_ABS (us);
+  i = starting_bit / GMP_LIMB_BITS;
+
+  /* Past the end there's no 1 bits for u>=0, or an immediate 1 bit
+     for u<0. Notice this test picks up any u==0 too. */
+  if (i >= un)
+    return (us >= 0 ? ~(mp_bitcnt_t) 0 : starting_bit);
+
+  up = u->_mp_d;
+  ux = 0;
+  limb = up[i];
+
+  if (starting_bit != 0)
+    {
+      if (us < 0)
+        {
+          ux = mpn_zero_p (up, i);
+          limb = ~ limb + ux;
+          ux = - (mp_limb_t) (limb >= ux);
+        }
+
+      /* Mask to 0 all bits before starting_bit, thus ignoring them. */
+      limb &= (GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS));
+    }
+
+  return mpn_common_scan (limb, i, up, un, ux);
+}
+
+mp_bitcnt_t
+mpz_scan0 (const mpz_t u, mp_bitcnt_t starting_bit)
+{
+  mp_ptr up;
+  mp_size_t us, un, i;
+  mp_limb_t limb, ux;
+
+  us = u->_mp_size;
+  ux = - (mp_limb_t) (us >= 0);
+  un = GMP_ABS (us);
+  i = starting_bit / GMP_LIMB_BITS;
+
+  /* When past end, there's an immediate 0 bit for u>=0, or no 0 bits for
+     u<0.  Notice this test picks up all cases of u==0 too. */
+  if (i >= un)
+    return (ux ? starting_bit : ~(mp_bitcnt_t) 0);
+
+  up = u->_mp_d;
+  limb = up[i] ^ ux;
+
+  if (ux == 0)
+    limb -= mpn_zero_p (up, i); /* limb = ~(~limb + zero_p) */
+
+  /* Mask all bits before starting_bit, thus ignoring them. */
+  limb &= (GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS));
+
+  return mpn_common_scan (limb, i, up, un, ux);
+}
+
+
+/* MPZ base conversion. */
+
+size_t
+mpz_sizeinbase (const mpz_t u, int base)
+{
+  mp_size_t un;
+  mp_srcptr up;
+  mp_ptr tp;
+  mp_bitcnt_t bits;
+  struct gmp_div_inverse bi;
+  size_t ndigits;
+
+  assert (base >= 2);
+  assert (base <= 62);
+
+  un = GMP_ABS (u->_mp_size);
+  if (un == 0)
+    return 1;
+
+  up = u->_mp_d;
+
+  bits = (un - 1) * GMP_LIMB_BITS + mpn_limb_size_in_base_2 (up[un-1]);
+  switch (base)
+    {
+    case 2:
+      return bits;
+    case 4:
+      return (bits + 1) / 2;
+    case 8:
+      return (bits + 2) / 3;
+    case 16:
+      return (bits + 3) / 4;
+    case 32:
+      return (bits + 4) / 5;
+      /* FIXME: Do something more clever for the common case of base
+         10. */
+    }
+
+  tp = gmp_xalloc_limbs (un);
+  mpn_copyi (tp, up, un);
+  mpn_div_qr_1_invert (&bi, base);
+
+  ndigits = 0;
+  do
+    {
+      ndigits++;
+      mpn_div_qr_1_preinv (tp, tp, un, &bi);
+      un -= (tp[un-1] == 0);
+    }
+  while (un > 0);
+
+  gmp_free (tp);
+  return ndigits;
+}
+
+char *
+mpz_get_str (char *sp, int base, const mpz_t u)
+{
+  unsigned bits;
+  const char *digits;
+  mp_size_t un;
+  size_t i, sn;
+
+  digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz";
+  if (base > 1)
+    {
+      if (base <= 36)
+        digits = "0123456789abcdefghijklmnopqrstuvwxyz";
+      else if (base > 62)
+        return NULL;
+    }
+  else if (base >= -1)
+    base = 10;
+  else
+    {
+      base = -base;
+      if (base > 36)
+        return NULL;
+    }
+
+  sn = 1 + mpz_sizeinbase (u, base);
+  if (!sp)
+    sp = (char *) gmp_xalloc (1 + sn);
+
+  un = GMP_ABS (u->_mp_size);
+
+  if (un == 0)
+    {
+      sp[0] = '0';
+      sp[1] = '\0';
+      return sp;
+    }
+
+  i = 0;
+
+  if (u->_mp_size < 0)
+    sp[i++] = '-';
+
+  bits = mpn_base_power_of_two_p (base);
+
+  if (bits)
+    /* Not modified in this case. */
+    sn = i + mpn_get_str_bits ((unsigned char *) sp + i, bits, u->_mp_d, un);
+  else
+    {
+      struct mpn_base_info info;
+      mp_ptr tp;
+
+      mpn_get_base_info (&info, base);
+      tp = gmp_xalloc_limbs (un);
+      mpn_copyi (tp, u->_mp_d, un);
+
+      sn = i + mpn_get_str_other ((unsigned char *) sp + i, base, &info, tp, un);
+      gmp_free (tp);
+    }
+
+  for (; i < sn; i++)
+    sp[i] = digits[(unsigned char) sp[i]];
+
+  sp[sn] = '\0';
+  return sp;
+}
+
+int
+mpz_set_str (mpz_t r, const char *sp, int base)
+{
+  unsigned bits, value_of_a;
+  mp_size_t rn, alloc;
+  mp_ptr rp;
+  size_t dn;
+  int sign;
+  unsigned char *dp;
+
+  assert (base == 0 || (base >= 2 && base <= 62));
+
+  while (isspace( (unsigned char) *sp))
+    sp++;
+
+  sign = (*sp == '-');
+  sp += sign;
+
+  if (base == 0)
+    {
+      if (sp[0] == '0')
+        {
+          if (sp[1] == 'x' || sp[1] == 'X')
+            {
+              base = 16;
+              sp += 2;
+            }
+          else if (sp[1] == 'b' || sp[1] == 'B')
+            {
+              base = 2;
+              sp += 2;
+            }
+          else
+            base = 8;
+        }
+      else
+        base = 10;
+    }
+
+  if (!*sp)
+    {
+      r->_mp_size = 0;
+      return -1;
+    }
+  dp = (unsigned char *) gmp_xalloc (strlen (sp));
+
+  value_of_a = (base > 36) ? 36 : 10;
+  for (dn = 0; *sp; sp++)
+    {
+      unsigned digit;
+
+      if (isspace ((unsigned char) *sp))
+        continue;
+      else if (*sp >= '0' && *sp <= '9')
+        digit = *sp - '0';
+      else if (*sp >= 'a' && *sp <= 'z')
+        digit = *sp - 'a' + value_of_a;
+      else if (*sp >= 'A' && *sp <= 'Z')
+        digit = *sp - 'A' + 10;
+      else
+        digit = base; /* fail */
+
+      if (digit >= (unsigned) base)
+        {
+          gmp_free (dp);
+          r->_mp_size = 0;
+          return -1;
+        }
+
+      dp[dn++] = digit;
+    }
+
+  if (!dn)
+    {
+      gmp_free (dp);
+      r->_mp_size = 0;
+      return -1;
+    }
+  bits = mpn_base_power_of_two_p (base);
+
+  if (bits > 0)
+    {
+      alloc = (dn * bits + GMP_LIMB_BITS - 1) / GMP_LIMB_BITS;
+      rp = MPZ_REALLOC (r, alloc);
+      rn = mpn_set_str_bits (rp, dp, dn, bits);
+    }
+  else
+    {
+      struct mpn_base_info info;
+      mpn_get_base_info (&info, base);
+      alloc = (dn + info.exp - 1) / info.exp;
+      rp = MPZ_REALLOC (r, alloc);
+      rn = mpn_set_str_other (rp, dp, dn, base, &info);
+      /* Normalization, needed for all-zero input. */
+      assert (rn > 0);
+      rn -= rp[rn-1] == 0;
+    }
+  assert (rn <= alloc);
+  gmp_free (dp);
+
+  r->_mp_size = sign ? - rn : rn;
+
+  return 0;
+}
+
+int
+mpz_init_set_str (mpz_t r, const char *sp, int base)
+{
+  mpz_init (r);
+  return mpz_set_str (r, sp, base);
+}
+
+size_t
+mpz_out_str (FILE *stream, int base, const mpz_t x)
+{
+  char *str;
+  size_t len;
+
+  str = mpz_get_str (NULL, base, x);
+  len = strlen (str);
+  len = fwrite (str, 1, len, stream);
+  gmp_free (str);
+  return len;
+}
+
+
+static int
+gmp_detect_endian (void)
+{
+  static const int i = 2;
+  const unsigned char *p = (const unsigned char *) &i;
+  return 1 - *p;
+}
+
+/* Import and export. Does not support nails. */
+void
+mpz_import (mpz_t r, size_t count, int order, size_t size, int endian,
+            size_t nails, const void *src)
+{
+  const unsigned char *p;
+  ptrdiff_t word_step;
+  mp_ptr rp;
+  mp_size_t rn;
+
+  /* The current (partial) limb. */
+  mp_limb_t limb;
+  /* The number of bytes already copied to this limb (starting from
+     the low end). */
+  size_t bytes;
+  /* The index where the limb should be stored, when completed. */
+  mp_size_t i;
+
+  if (nails != 0)
+    gmp_die ("mpz_import: Nails not supported.");
+
+  assert (order == 1 || order == -1);
+  assert (endian >= -1 && endian <= 1);
+
+  if (endian == 0)
+    endian = gmp_detect_endian ();
+
+  p = (unsigned char *) src;
+
+  word_step = (order != endian) ? 2 * size : 0;
+
+  /* Process bytes from the least significant end, so point p at the
+     least significant word. */
+  if (order == 1)
+    {
+      p += size * (count - 1);
+      word_step = - word_step;
+    }
+
+  /* And at least significant byte of that word. */
+  if (endian == 1)
+    p += (size - 1);
+
+  rn = (size * count + sizeof(mp_limb_t) - 1) / sizeof(mp_limb_t);
+  rp = MPZ_REALLOC (r, rn);
+
+  for (limb = 0, bytes = 0, i = 0; count > 0; count--, p += word_step)
+    {
+      size_t j;
+      for (j = 0; j < size; j++, p -= (ptrdiff_t) endian)
+        {
+          limb |= (mp_limb_t) *p << (bytes++ * CHAR_BIT);
+          if (bytes == sizeof(mp_limb_t))
+            {
+              rp[i++] = limb;
+              bytes = 0;
+              limb = 0;
+            }
+        }
+    }
+  assert (i + (bytes > 0) == rn);
+  if (limb != 0)
+    rp[i++] = limb;
+  else
+    i = mpn_normalized_size (rp, i);
+
+  r->_mp_size = i;
+}
+
+void *
+mpz_export (void *r, size_t *countp, int order, size_t size, int endian,
+            size_t nails, const mpz_t u)
+{
+  size_t count;
+  mp_size_t un;
+
+  if (nails != 0)
+    gmp_die ("mpz_import: Nails not supported.");
+
+  assert (order == 1 || order == -1);
+  assert (endian >= -1 && endian <= 1);
+  assert (size > 0 || u->_mp_size == 0);
+
+  un = u->_mp_size;
+  count = 0;
+  if (un != 0)
+    {
+      size_t k;
+      unsigned char *p;
+      ptrdiff_t word_step;
+      /* The current (partial) limb. */
+      mp_limb_t limb;
+      /* The number of bytes left to to in this limb. */
+      size_t bytes;
+      /* The index where the limb was read. */
+      mp_size_t i;
+
+      un = GMP_ABS (un);
+
+      /* Count bytes in top limb. */
+      limb = u->_mp_d[un-1];
+      assert (limb != 0);
+
+      k = 0;
+      do {
+        k++; limb >>= CHAR_BIT;
+      } while (limb != 0);
+
+      count = (k + (un-1) * sizeof (mp_limb_t) + size - 1) / size;
+
+      if (!r)
+        r = gmp_xalloc (count * size);
+
+      if (endian == 0)
+        endian = gmp_detect_endian ();
+
+      p = (unsigned char *) r;
+
+      word_step = (order != endian) ? 2 * size : 0;
+
+      /* Process bytes from the least significant end, so point p at the
+         least significant word. */
+      if (order == 1)
+        {
+          p += size * (count - 1);
+          word_step = - word_step;
+        }
+
+      /* And at least significant byte of that word. */
+      if (endian == 1)
+        p += (size - 1);
+
+      for (bytes = 0, i = 0, k = 0; k < count; k++, p += word_step)
+        {
+          size_t j;
+          for (j = 0; j < size; j++, p -= (ptrdiff_t) endian)
+            {
+              if (bytes == 0)
+                {
+                  if (i < un)
+                    limb = u->_mp_d[i++];
+                  bytes = sizeof (mp_limb_t);
+                }
+              *p = limb;
+              limb >>= CHAR_BIT;
+              bytes--;
+            }
+        }
+      assert (i == un);
+      assert (k == count);
+    }
+
+  if (countp)
+    *countp = count;
+
+  return r;
+}
diff --git a/src/mini-gmp.h b/src/mini-gmp.h
new file mode 100644
index 00000000000..27e0c0671a2
--- /dev/null
+++ b/src/mini-gmp.h
@@ -0,0 +1,300 @@
+/* mini-gmp, a minimalistic implementation of a GNU GMP subset.
+
+Copyright 2011-2015, 2017 Free Software Foundation, Inc.
+
+This file is part of the GNU MP Library.
+
+The GNU MP Library is free software; you can redistribute it and/or modify
+it under the terms of either:
+
+  * 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.
+
+or
+
+  * the GNU General Public License as published by the Free Software
+    Foundation; either version 2 of the License, or (at your option) any
+    later version.
+
+or both in parallel, as here.
+
+The GNU MP 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 General Public License
+for more details.
+
+You should have received copies of the GNU General Public License and the
+GNU Lesser General Public License along with the GNU MP Library.  If not,
+see https://www.gnu.org/licenses/.  */
+
+/* About mini-gmp: This is a minimal implementation of a subset of the
+   GMP interface. It is intended for inclusion into applications which
+   have modest bignums needs, as a fallback when the real GMP library
+   is not installed.
+
+   This file defines the public interface. */
+
+#ifndef __MINI_GMP_H__
+#define __MINI_GMP_H__
+
+/* For size_t */
+#include <stddef.h>
+
+#if defined (__cplusplus)
+extern "C" {
+#endif
+
+void mp_set_memory_functions (void *(*) (size_t),
+                              void *(*) (void *, size_t, size_t),
+                              void (*) (void *, size_t));
+
+void mp_get_memory_functions (void *(**) (size_t),
+                              void *(**) (void *, size_t, size_t),
+                              void (**) (void *, size_t));
+
+typedef unsigned long mp_limb_t;
+typedef long mp_size_t;
+typedef unsigned long mp_bitcnt_t;
+
+typedef mp_limb_t *mp_ptr;
+typedef const mp_limb_t *mp_srcptr;
+
+typedef struct
+{
+  int _mp_alloc;                /* Number of *limbs* allocated and pointed
+                                   to by the _mp_d field.  */
+  int _mp_size;                 /* abs(_mp_size) is the number of limbs the
+                                   last field points to.  If _mp_size is
+                                   negative this is a negative number.  */
+  mp_limb_t *_mp_d;             /* Pointer to the limbs.  */
+} __mpz_struct;
+
+typedef __mpz_struct mpz_t[1];
+
+typedef __mpz_struct *mpz_ptr;
+typedef const __mpz_struct *mpz_srcptr;
+
+extern const int mp_bits_per_limb;
+
+void mpn_copyi (mp_ptr, mp_srcptr, mp_size_t);
+void mpn_copyd (mp_ptr, mp_srcptr, mp_size_t);
+void mpn_zero (mp_ptr, mp_size_t);
+
+int mpn_cmp (mp_srcptr, mp_srcptr, mp_size_t);
+int mpn_zero_p (mp_srcptr, mp_size_t);
+
+mp_limb_t mpn_add_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
+mp_limb_t mpn_add_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
+mp_limb_t mpn_add (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t);
+
+mp_limb_t mpn_sub_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
+mp_limb_t mpn_sub_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
+mp_limb_t mpn_sub (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t);
+
+mp_limb_t mpn_mul_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
+mp_limb_t mpn_addmul_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
+mp_limb_t mpn_submul_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
+
+mp_limb_t mpn_mul (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t);
+void mpn_mul_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
+void mpn_sqr (mp_ptr, mp_srcptr, mp_size_t);
+int mpn_perfect_square_p (mp_srcptr, mp_size_t);
+mp_size_t mpn_sqrtrem (mp_ptr, mp_ptr, mp_srcptr, mp_size_t);
+
+mp_limb_t mpn_lshift (mp_ptr, mp_srcptr, mp_size_t, unsigned int);
+mp_limb_t mpn_rshift (mp_ptr, mp_srcptr, mp_size_t, unsigned int);
+
+mp_bitcnt_t mpn_scan0 (mp_srcptr, mp_bitcnt_t);
+mp_bitcnt_t mpn_scan1 (mp_srcptr, mp_bitcnt_t);
+
+void mpn_com (mp_ptr, mp_srcptr, mp_size_t);
+mp_limb_t mpn_neg (mp_ptr, mp_srcptr, mp_size_t);
+
+mp_bitcnt_t mpn_popcount (mp_srcptr, mp_size_t);
+
+mp_limb_t mpn_invert_3by2 (mp_limb_t, mp_limb_t);
+#define mpn_invert_limb(x) mpn_invert_3by2 ((x), 0)
+
+size_t mpn_get_str (unsigned char *, int, mp_ptr, mp_size_t);
+mp_size_t mpn_set_str (mp_ptr, const unsigned char *, size_t, int);
+
+void mpz_init (mpz_t);
+void mpz_init2 (mpz_t, mp_bitcnt_t);
+void mpz_clear (mpz_t);
+
+#define mpz_odd_p(z)   (((z)->_mp_size != 0) & (int) (z)->_mp_d[0])
+#define mpz_even_p(z)  (! mpz_odd_p (z))
+
+int mpz_sgn (const mpz_t);
+int mpz_cmp_si (const mpz_t, long);
+int mpz_cmp_ui (const mpz_t, unsigned long);
+int mpz_cmp (const mpz_t, const mpz_t);
+int mpz_cmpabs_ui (const mpz_t, unsigned long);
+int mpz_cmpabs (const mpz_t, const mpz_t);
+int mpz_cmp_d (const mpz_t, double);
+int mpz_cmpabs_d (const mpz_t, double);
+
+void mpz_abs (mpz_t, const mpz_t);
+void mpz_neg (mpz_t, const mpz_t);
+void mpz_swap (mpz_t, mpz_t);
+
+void mpz_add_ui (mpz_t, const mpz_t, unsigned long);
+void mpz_add (mpz_t, const mpz_t, const mpz_t);
+void mpz_sub_ui (mpz_t, const mpz_t, unsigned long);
+void mpz_ui_sub (mpz_t, unsigned long, const mpz_t);
+void mpz_sub (mpz_t, const mpz_t, const mpz_t);
+
+void mpz_mul_si (mpz_t, const mpz_t, long int);
+void mpz_mul_ui (mpz_t, const mpz_t, unsigned long int);
+void mpz_mul (mpz_t, const mpz_t, const mpz_t);
+void mpz_mul_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
+void mpz_addmul_ui (mpz_t, const mpz_t, unsigned long int);
+void mpz_addmul (mpz_t, const mpz_t, const mpz_t);
+void mpz_submul_ui (mpz_t, const mpz_t, unsigned long int);
+void mpz_submul (mpz_t, const mpz_t, const mpz_t);
+
+void mpz_cdiv_qr (mpz_t, mpz_t, const mpz_t, const mpz_t);
+void mpz_fdiv_qr (mpz_t, mpz_t, const mpz_t, const mpz_t);
+void mpz_tdiv_qr (mpz_t, mpz_t, const mpz_t, const mpz_t);
+void mpz_cdiv_q (mpz_t, const mpz_t, const mpz_t);
+void mpz_fdiv_q (mpz_t, const mpz_t, const mpz_t);
+void mpz_tdiv_q (mpz_t, const mpz_t, const mpz_t);
+void mpz_cdiv_r (mpz_t, const mpz_t, const mpz_t);
+void mpz_fdiv_r (mpz_t, const mpz_t, const mpz_t);
+void mpz_tdiv_r (mpz_t, const mpz_t, const mpz_t);
+
+void mpz_cdiv_q_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
+void mpz_fdiv_q_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
+void mpz_tdiv_q_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
+void mpz_cdiv_r_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
+void mpz_fdiv_r_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
+void mpz_tdiv_r_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
+
+void mpz_mod (mpz_t, const mpz_t, const mpz_t);
+
+void mpz_divexact (mpz_t, const mpz_t, const mpz_t);
+
+int mpz_divisible_p (const mpz_t, const mpz_t);
+int mpz_congruent_p (const mpz_t, const mpz_t, const mpz_t);
+
+unsigned long mpz_cdiv_qr_ui (mpz_t, mpz_t, const mpz_t, unsigned long);
+unsigned long mpz_fdiv_qr_ui (mpz_t, mpz_t, const mpz_t, unsigned long);
+unsigned long mpz_tdiv_qr_ui (mpz_t, mpz_t, const mpz_t, unsigned long);
+unsigned long mpz_cdiv_q_ui (mpz_t, const mpz_t, unsigned long);
+unsigned long mpz_fdiv_q_ui (mpz_t, const mpz_t, unsigned long);
+unsigned long mpz_tdiv_q_ui (mpz_t, const mpz_t, unsigned long);
+unsigned long mpz_cdiv_r_ui (mpz_t, const mpz_t, unsigned long);
+unsigned long mpz_fdiv_r_ui (mpz_t, const mpz_t, unsigned long);
+unsigned long mpz_tdiv_r_ui (mpz_t, const mpz_t, unsigned long);
+unsigned long mpz_cdiv_ui (const mpz_t, unsigned long);
+unsigned long mpz_fdiv_ui (const mpz_t, unsigned long);
+unsigned long mpz_tdiv_ui (const mpz_t, unsigned long);
+
+unsigned long mpz_mod_ui (mpz_t, const mpz_t, unsigned long);
+
+void mpz_divexact_ui (mpz_t, const mpz_t, unsigned long);
+
+int mpz_divisible_ui_p (const mpz_t, unsigned long);
+
+unsigned long mpz_gcd_ui (mpz_t, const mpz_t, unsigned long);
+void mpz_gcd (mpz_t, const mpz_t, const mpz_t);
+void mpz_gcdext (mpz_t, mpz_t, mpz_t, const mpz_t, const mpz_t);
+void mpz_lcm_ui (mpz_t, const mpz_t, unsigned long);
+void mpz_lcm (mpz_t, const mpz_t, const mpz_t);
+int mpz_invert (mpz_t, const mpz_t, const mpz_t);
+
+void mpz_sqrtrem (mpz_t, mpz_t, const mpz_t);
+void mpz_sqrt (mpz_t, const mpz_t);
+int mpz_perfect_square_p (const mpz_t);
+
+void mpz_pow_ui (mpz_t, const mpz_t, unsigned long);
+void mpz_ui_pow_ui (mpz_t, unsigned long, unsigned long);
+void mpz_powm (mpz_t, const mpz_t, const mpz_t, const mpz_t);
+void mpz_powm_ui (mpz_t, const mpz_t, unsigned long, const mpz_t);
+
+void mpz_rootrem (mpz_t, mpz_t, const mpz_t, unsigned long);
+int mpz_root (mpz_t, const mpz_t, unsigned long);
+
+void mpz_fac_ui (mpz_t, unsigned long);
+void mpz_2fac_ui (mpz_t, unsigned long);
+void mpz_mfac_uiui (mpz_t, unsigned long, unsigned long);
+void mpz_bin_uiui (mpz_t, unsigned long, unsigned long);
+
+int mpz_probab_prime_p (const mpz_t, int);
+
+int mpz_tstbit (const mpz_t, mp_bitcnt_t);
+void mpz_setbit (mpz_t, mp_bitcnt_t);
+void mpz_clrbit (mpz_t, mp_bitcnt_t);
+void mpz_combit (mpz_t, mp_bitcnt_t);
+
+void mpz_com (mpz_t, const mpz_t);
+void mpz_and (mpz_t, const mpz_t, const mpz_t);
+void mpz_ior (mpz_t, const mpz_t, const mpz_t);
+void mpz_xor (mpz_t, const mpz_t, const mpz_t);
+
+mp_bitcnt_t mpz_popcount (const mpz_t);
+mp_bitcnt_t mpz_hamdist (const mpz_t, const mpz_t);
+mp_bitcnt_t mpz_scan0 (const mpz_t, mp_bitcnt_t);
+mp_bitcnt_t mpz_scan1 (const mpz_t, mp_bitcnt_t);
+
+int mpz_fits_slong_p (const mpz_t);
+int mpz_fits_ulong_p (const mpz_t);
+long int mpz_get_si (const mpz_t);
+unsigned long int mpz_get_ui (const mpz_t);
+double mpz_get_d (const mpz_t);
+size_t mpz_size (const mpz_t);
+mp_limb_t mpz_getlimbn (const mpz_t, mp_size_t);
+
+void mpz_realloc2 (mpz_t, mp_bitcnt_t);
+mp_srcptr mpz_limbs_read (mpz_srcptr);
+mp_ptr mpz_limbs_modify (mpz_t, mp_size_t);
+mp_ptr mpz_limbs_write (mpz_t, mp_size_t);
+void mpz_limbs_finish (mpz_t, mp_size_t);
+mpz_srcptr mpz_roinit_n (mpz_t, mp_srcptr, mp_size_t);
+
+#define MPZ_ROINIT_N(xp, xs) {{0, (xs),(xp) }}
+
+void mpz_set_si (mpz_t, signed long int);
+void mpz_set_ui (mpz_t, unsigned long int);
+void mpz_set (mpz_t, const mpz_t);
+void mpz_set_d (mpz_t, double);
+
+void mpz_init_set_si (mpz_t, signed long int);
+void mpz_init_set_ui (mpz_t, unsigned long int);
+void mpz_init_set (mpz_t, const mpz_t);
+void mpz_init_set_d (mpz_t, double);
+
+size_t mpz_sizeinbase (const mpz_t, int);
+char *mpz_get_str (char *, int, const mpz_t);
+int mpz_set_str (mpz_t, const char *, int);
+int mpz_init_set_str (mpz_t, const char *, int);
+
+/* This long list taken from gmp.h. */
+/* For reference, "defined(EOF)" cannot be used here.  In g++ 2.95.4,
+   <iostream> defines EOF but not FILE.  */
+#if defined (FILE)                                              \
+  || defined (H_STDIO)                                          \
+  || defined (_H_STDIO)               /* AIX */                 \
+  || defined (_STDIO_H)               /* glibc, Sun, SCO */     \
+  || defined (_STDIO_H_)              /* BSD, OSF */            \
+  || defined (__STDIO_H)              /* Borland */             \
+  || defined (__STDIO_H__)            /* IRIX */                \
+  || defined (_STDIO_INCLUDED)        /* HPUX */                \
+  || defined (__dj_include_stdio_h_)  /* DJGPP */               \
+  || defined (_FILE_DEFINED)          /* Microsoft */           \
+  || defined (__STDIO__)              /* Apple MPW MrC */       \
+  || defined (_MSL_STDIO_H)           /* Metrowerks */          \
+  || defined (_STDIO_H_INCLUDED)      /* QNX4 */                \
+  || defined (_ISO_STDIO_ISO_H)       /* Sun C++ */             \
+  || defined (__STDIO_LOADED)         /* VMS */
+size_t mpz_out_str (FILE *, int, const mpz_t);
+#endif
+
+void mpz_import (mpz_t, size_t, int, size_t, int, size_t, const void *);
+void *mpz_export (void *, size_t *, int, size_t, int, size_t, const mpz_t);
+
+#if defined (__cplusplus)
+}
+#endif
+#endif /* __MINI_GMP_H__ */