Update embedded mini-gmp to version 6.2.0 (#9396)

2 files changed, 1159 insertions, 692 deletions

diff --git a/lib/gmp/mini-gmp.c b/lib/gmp/mini-gmp.c
index f3b43fbe8..e2e686123 100644
--- a/lib/gmp/mini-gmp.c
+++ b/lib/gmp/mini-gmp.c
@@ -2,9 +2,7 @@
 
    Contributed to the GNU project by Niels Möller
 
-Copyright 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1999, 2000, 2001,
-2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013
-Free Software Foundation, Inc.
+Copyright 1991-1997, 1999-2019 Free Software Foundation, Inc.
 
 This file is part of the GNU MP Library.
 
@@ -41,11 +39,15 @@ along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.  */
 
 #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_MAX ((mp_limb_t) ~ (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))
@@ -60,18 +62,34 @@ along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.  */
 #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;		   \
+    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;							\
+    unsigned __clz_c = 0;						\
+    int LOCAL_SHIFT_BITS = 8;						\
+    if (GMP_LIMB_BITS > LOCAL_SHIFT_BITS)				\
+      for (;								\
+	   (__clz_x & ((mp_limb_t) 0xff << (GMP_LIMB_BITS - 8))) == 0;	\
+	   __clz_c += 8)						\
+	{ __clz_x <<= LOCAL_SHIFT_BITS;	}				\
     for (; (__clz_x & GMP_LIMB_HIGHBIT) == 0; __clz_c++)		\
       __clz_x <<= 1;							\
     (count) = __clz_c;							\
@@ -102,27 +120,42 @@ along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.  */
 
 #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);					\
+    int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS;				\
+    if (sizeof(unsigned int) * CHAR_BIT >= 2 * GMP_LIMB_BITS)		\
+      {									\
+	unsigned int __ww = (unsigned int) (u) * (v);			\
+	w0 = (mp_limb_t) __ww;						\
+	w1 = (mp_limb_t) (__ww >> LOCAL_GMP_LIMB_BITS);			\
+      }									\
+    else if (GMP_ULONG_BITS >= 2 * GMP_LIMB_BITS)			\
+      {									\
+	unsigned long int __ww = (unsigned long int) (u) * (v);		\
+	w0 = (mp_limb_t) __ww;						\
+	w1 = (mp_limb_t) (__ww >> LOCAL_GMP_LIMB_BITS);			\
+      }									\
+    else {								\
+      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);					\
+      __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;					\
+      __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. */	\
+      __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);	\
+      (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)			\
@@ -222,11 +255,13 @@ along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.  */
   } while (0)
 #define MPZ_SRCPTR_SWAP(x, y)						\
   do {									\
-    mpz_srcptr __mpz_srcptr_swap__tmp = (x);			\
+    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
@@ -251,20 +286,20 @@ gmp_default_alloc (size_t size)
 }
 
 static void *
-gmp_default_realloc (void *old, size_t old_size, size_t new_size)
+gmp_default_realloc (void *old, size_t unused_old_size, size_t new_size)
 {
-  mp_ptr p;
+  void * p;
 
   p = realloc (old, new_size);
 
   if (!p)
-    gmp_die("gmp_default_realoc: Virtual memory exhausted.");
+    gmp_die("gmp_default_realloc: Virtual memory exhausted.");
 
   return p;
 }
 
 static void
-gmp_default_free (void *p, size_t size)
+gmp_default_free (void *p, size_t unused_size)
 {
   free (p);
 }
@@ -311,14 +346,14 @@ mp_set_memory_functions (void *(*alloc_func) (size_t),
 static mp_ptr
 gmp_xalloc_limbs (mp_size_t size)
 {
-  return gmp_xalloc (size * sizeof (mp_limb_t));
+  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 (*gmp_reallocate_func) (old, 0, size * sizeof (mp_limb_t));
+  return (mp_ptr) (*gmp_reallocate_func) (old, 0, size * sizeof (mp_limb_t));
 }
 
 
@@ -335,19 +370,17 @@ mpn_copyi (mp_ptr d, mp_srcptr s, mp_size_t n)
 void
 mpn_copyd (mp_ptr d, mp_srcptr s, mp_size_t n)
 {
-  while (n-- > 0)
+  while (--n >= 0)
     d[n] = s[n];
 }
 
 int
 mpn_cmp (mp_srcptr ap, mp_srcptr bp, mp_size_t n)
 {
-  for (; n > 0; n--)
+  while (--n >= 0)
     {
-      if (ap[n-1] < bp[n-1])
-	return -1;
-      else if (ap[n-1] > bp[n-1])
-	return 1;
+      if (ap[n] != bp[n])
+	return ap[n] > bp[n] ? 1 : -1;
     }
   return 0;
 }
@@ -355,10 +388,8 @@ mpn_cmp (mp_srcptr ap, mp_srcptr bp, mp_size_t n)
 static int
 mpn_cmp4 (mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
 {
-  if (an > bn)
-    return 1;
-  else if (an < bn)
-    return -1;
+  if (an != bn)
+    return an < bn ? -1 : 1;
   else
     return mpn_cmp (ap, bp, an);
 }
@@ -366,12 +397,23 @@ mpn_cmp4 (mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
 static mp_size_t
 mpn_normalized_size (mp_srcptr xp, mp_size_t n)
 {
-  for (; n > 0 && xp[n-1] == 0; n--)
-    ;
+  while (n > 0 && xp[n-1] == 0)
+    --n;
   return n;
 }
 
-#define mpn_zero_p(xp, n) (mpn_normalized_size ((xp), (n)) == 0)
+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)
@@ -379,14 +421,16 @@ mpn_add_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b)
   mp_size_t i;
 
   assert (n > 0);
-
-  for (i = 0; i < n; i++)
+  i = 0;
+  do
     {
       mp_limb_t r = ap[i] + b;
       /* Carry out */
       b = (r < b);
       rp[i] = r;
     }
+  while (++i < n);
+
   return b;
 }
 
@@ -429,14 +473,17 @@ mpn_sub_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b)
 
   assert (n > 0);
 
-  for (i = 0; i < n; i++)
+  i = 0;
+  do
     {
       mp_limb_t a = ap[i];
       /* Carry out */
-      mp_limb_t cy = a < b;;
+      mp_limb_t cy = a < b;
       rp[i] = a - b;
       b = cy;
     }
+  while (++i < n);
+
   return b;
 }
 
@@ -551,23 +598,24 @@ 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]);
-  rp += 1, vp += 1, vn -= 1;
 
   /* Now accumulate the product of up[] and the next higher limb from
      vp[]. */
 
-  while (vn >= 1)
+  while (--vn >= 1)
     {
+      rp += 1, vp += 1;
       rp[un] = mpn_addmul_1 (rp, up, un, vp[0]);
-      rp += 1, vp += 1, vn -= 1;
     }
-  return rp[un - 1];
+  return rp[un];
 }
 
 void
@@ -587,7 +635,6 @@ 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_size_t i;
   mp_limb_t retval;
 
   assert (n >= 1);
@@ -602,7 +649,7 @@ mpn_lshift (mp_ptr rp, mp_srcptr up, mp_size_t n, unsigned int cnt)
   retval = low_limb >> tnc;
   high_limb = (low_limb << cnt);
 
-  for (i = n - 1; i != 0; i--)
+  while (--n != 0)
     {
       low_limb = *--up;
       *--rp = high_limb | (low_limb >> tnc);
@@ -618,7 +665,6 @@ 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_size_t i;
   mp_limb_t retval;
 
   assert (n >= 1);
@@ -630,7 +676,7 @@ mpn_rshift (mp_ptr rp, mp_srcptr up, mp_size_t n, unsigned int cnt)
   retval = (high_limb << tnc);
   low_limb = high_limb >> cnt;
 
-  for (i = n - 1; i != 0; i--)
+  while (--n != 0)
     {
       high_limb = *up++;
       *rp++ = low_limb | (high_limb << tnc);
@@ -641,60 +687,156 @@ mpn_rshift (mp_ptr rp, mp_srcptr up, mp_size_t n, unsigned int cnt)
   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;
-  unsigned ul, uh;
-  unsigned ql, qh;
+  mp_limb_t r, m;
 
-  /* First, do a 2/1 inverse. */
-  /* The inverse m is defined as floor( (B^2 - 1 - u1)/u1 ), so that 0 <
-   * B^2 - (B + m) u1 <= u1 */
-  assert (u1 >= GMP_LIMB_HIGHBIT);
+  {
+    mp_limb_t p, ql;
+    unsigned ul, uh, qh;
 
-  ul = u1 & GMP_LLIMB_MASK;
-  uh = u1 >> (GMP_LIMB_BITS / 2);
+    /* 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);
 
-  qh = ~u1 / uh;
-  r = ((~u1 - (mp_limb_t) qh * uh) << (GMP_LIMB_BITS / 2)) | GMP_LLIMB_MASK;
+    /* 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 ^ GMP_LIMB_MAX) / uh;
 
-  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;
+    /* Adjust to get a half-limb 3/2 inverse, i.e., we want
 
-  /* Do a 3/2 division (with half limb size) */
-  p = (r >> (GMP_LIMB_BITS / 2)) * qh + r;
-  ql = (p >> (GMP_LIMB_BITS / 2)) + 1;
+       qh' = floor( (b^3 - 1) / u) - b = floor ((b^3 - b u - 1) / u
+	   = floor( (b (~u) + b-1) / u),
 
-  /* By the 3/2 method, we don't need the high half limb. */
-  r = (r << (GMP_LIMB_BITS / 2)) + GMP_LLIMB_MASK - ql * u1;
+       and the remainder
 
-  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;
-    }
+       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 >= (GMP_LIMB_MAX & (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 inverse of u1. If u0 > 0, adjust it to become a
+     3/2 inverse. */
   if (u0 > 0)
     {
       mp_limb_t th, tl;
@@ -715,8 +857,7 @@ mpn_invert_3by2 (mp_limb_t u1, mp_limb_t u0)
       if (r < th)
 	{
 	  m--;
-	  if (r > u1 || (r == u1 && tl > u0))
-	    m--;
+	  m -= ((r > u1) | ((r == u1) & (tl > u0)));
 	}
     }
 
@@ -807,7 +948,8 @@ mpn_div_qr_1_preinv (mp_ptr qp, mp_srcptr np, mp_size_t nn,
 
   if (inv->shift > 0)
     {
-      tp = gmp_xalloc_limbs (nn);
+      /* 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;
     }
@@ -816,7 +958,7 @@ mpn_div_qr_1_preinv (mp_ptr qp, mp_srcptr np, mp_size_t nn,
 
   d = inv->d1;
   di = inv->di;
-  while (nn-- > 0)
+  while (--nn >= 0)
     {
       mp_limb_t q;
 
@@ -824,44 +966,19 @@ mpn_div_qr_1_preinv (mp_ptr qp, mp_srcptr np, mp_size_t nn,
       if (qp)
 	qp[nn] = q;
     }
-  if (inv->shift > 0)
+  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 > 1 && (d & (d-1)) == 0)
-    {
-      unsigned shift;
-      mp_limb_t r = np[0] & (d-1);
-      gmp_ctz (shift, d);
-      if (qp)
-	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 rp, mp_srcptr np, mp_size_t nn,
+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;
-  mp_ptr tp;
 
   assert (nn >= 2);
   shift = inv->shift;
@@ -870,17 +987,14 @@ mpn_div_qr_2_preinv (mp_ptr qp, mp_ptr rp, mp_srcptr np, mp_size_t nn,
   di = inv->di;
 
   if (shift > 0)
-    {
-      tp = gmp_xalloc_limbs (nn);
-      r1 = mpn_lshift (tp, np, nn, shift);
-      np = tp;
-    }
+    r1 = mpn_lshift (np, np, nn, shift);
   else
     r1 = 0;
 
   r0 = np[nn - 1];
 
-  for (i = nn - 2; i >= 0; i--)
+  i = nn - 2;
+  do
     {
       mp_limb_t n0, q;
       n0 = np[i];
@@ -889,32 +1003,18 @@ mpn_div_qr_2_preinv (mp_ptr qp, mp_ptr rp, mp_srcptr np, mp_size_t nn,
       if (qp)
 	qp[i] = q;
     }
+  while (--i >= 0);
 
   if (shift > 0)
     {
-      assert ((r0 << (GMP_LIMB_BITS - shift)) == 0);
+      assert ((r0 & (GMP_LIMB_MAX >> (GMP_LIMB_BITS - shift))) == 0);
       r0 = (r0 >> shift) | (r1 << (GMP_LIMB_BITS - shift));
       r1 >>= shift;
-
-      gmp_free (tp);
     }
 
-  rp[1] = r1;
-  rp[0] = r0;
-}
-
-#if 0
-static void
-mpn_div_qr_2 (mp_ptr qp, mp_ptr rp, mp_srcptr np, mp_size_t nn,
-	      mp_limb_t d1, mp_limb_t d0)
-{
-  struct gmp_div_inverse inv;
-  assert (nn >= 2);
-
-  mpn_div_qr_2_invert (&inv, d1, d0);
-  mpn_div_qr_2_preinv (qp, rp, np, nn, &inv);
+  np[1] = r1;
+  np[0] = r0;
 }
-#endif
 
 static void
 mpn_div_qr_pi1 (mp_ptr qp,
@@ -941,7 +1041,8 @@ mpn_div_qr_pi1 (mp_ptr qp,
    * by            <d1,          d0,        dp[dn-3],  ..., dp[0] >
    */
 
-  for (i = nn - dn; i >= 0; i--)
+  i = nn - dn;
+  do
     {
       mp_limb_t n0 = np[dn-1+i];
 
@@ -973,6 +1074,7 @@ mpn_div_qr_pi1 (mp_ptr qp,
       if (qp)
 	qp[i] = q;
     }
+  while (--i >= 0);
 
   np[dn - 1] = n1;
 }
@@ -988,7 +1090,7 @@ mpn_div_qr_preinv (mp_ptr qp, mp_ptr np, mp_size_t nn,
   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, np, nn, inv);
+    mpn_div_qr_2_preinv (qp, np, nn, inv);
   else
     {
       mp_limb_t nh;
@@ -1090,7 +1192,7 @@ 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;
-  int shift;
+  unsigned shift;
 
   sn = ((un - 1) * GMP_LIMB_BITS + mpn_limb_size_in_base_2 (up[un-1])
 	+ bits - 1) / bits;
@@ -1128,7 +1230,7 @@ mpn_limb_get_str (unsigned char *sp, mp_limb_t w,
       l = w << binv->shift;
 
       gmp_udiv_qrnnd_preinv (w, r, h, l, binv->d1, binv->di);
-      assert ( (r << (GMP_LIMB_BITS - binv->shift)) == 0);
+      assert ((r & (GMP_LIMB_MAX >> (GMP_LIMB_BITS - binv->shift))) == 0);
       r >>= binv->shift;
 
       sp[i] = r;
@@ -1231,26 +1333,29 @@ mpn_set_str_bits (mp_ptr rp, const unsigned char *sp, size_t sn,
   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 first;
   unsigned k;
   size_t j;
 
-  first = 1 + (sn - 1) % info->exp;
+  assert (sn > 0);
+
+  k = 1 + (sn - 1) % info->exp;
 
   j = 0;
   w = sp[j++];
-  for (k = 1; k < first; k++)
+  while (--k != 0)
     w = w * b + sp[j++];
 
   rp[0] = w;
 
-  for (rn = (w > 0); j < sn;)
+  for (rn = 1; j < sn;)
     {
       mp_limb_t cy;
 
@@ -1293,13 +1398,15 @@ mpn_set_str (mp_ptr rp, const unsigned char *sp, size_t sn, int base)
 void
 mpz_init (mpz_t r)
 {
-  r->_mp_alloc = 1;
+  static const mp_limb_t dummy_limb = GMP_LIMB_MAX & 0xc1a0;
+
+  r->_mp_alloc = 0;
   r->_mp_size = 0;
-  r->_mp_d = gmp_xalloc_limbs (1);
+  r->_mp_d = (mp_ptr) &dummy_limb;
 }
 
 /* The utility of this function is a bit limited, since many functions
-   assings the result variable using mpz_swap. */
+   assigns the result variable using mpz_swap. */
 void
 mpz_init2 (mpz_t r, mp_bitcnt_t bits)
 {
@@ -1316,15 +1423,19 @@ mpz_init2 (mpz_t r, mp_bitcnt_t bits)
 void
 mpz_clear (mpz_t r)
 {
-  gmp_free (r->_mp_d);
+  if (r->_mp_alloc)
+    gmp_free (r->_mp_d);
 }
 
-static void *
+static mp_ptr
 mpz_realloc (mpz_t r, mp_size_t size)
 {
   size = GMP_MAX (size, 1);
 
-  r->_mp_d = gmp_xrealloc_limbs (r->_mp_d, size);
+  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)
@@ -1345,9 +1456,15 @@ mpz_set_si (mpz_t r, signed long int x)
   if (x >= 0)
     mpz_set_ui (r, x);
   else /* (x < 0) */
+    if (GMP_LIMB_BITS < GMP_ULONG_BITS)
+      {
+	mpz_set_ui (r, GMP_NEG_CAST (unsigned long int, x));
+	mpz_neg (r, r);
+      }
+  else
     {
       r->_mp_size = -1;
-      r->_mp_d[0] = GMP_NEG_CAST (unsigned long int, x);
+      MPZ_REALLOC (r, 1)[0] = GMP_NEG_CAST (unsigned long int, x);
     }
 }
 
@@ -1357,7 +1474,16 @@ mpz_set_ui (mpz_t r, unsigned long int x)
   if (x > 0)
     {
       r->_mp_size = 1;
-      r->_mp_d[0] = x;
+      MPZ_REALLOC (r, 1)[0] = x;
+      if (GMP_LIMB_BITS < GMP_ULONG_BITS)
+	{
+	  int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS;
+	  while (x >>= LOCAL_GMP_LIMB_BITS)
+	    {
+	      ++ r->_mp_size;
+	      MPZ_REALLOC (r, r->_mp_size)[r->_mp_size - 1] = x;
+	    }
+	}
     }
   else
     r->_mp_size = 0;
@@ -1404,16 +1530,20 @@ mpz_init_set (mpz_t r, const mpz_t x)
 int
 mpz_fits_slong_p (const mpz_t u)
 {
-  mp_size_t us = u->_mp_size;
+  return (LONG_MAX + LONG_MIN == 0 || mpz_cmp_ui (u, LONG_MAX) <= 0) &&
+    mpz_cmpabs_ui (u, GMP_NEG_CAST (unsigned long int, LONG_MIN)) <= 0;
+}
 
-  if (us == 0)
-    return 1;
-  else 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 0;
+static int
+mpn_absfits_ulong_p (mp_srcptr up, mp_size_t un)
+{
+  int ulongsize = GMP_ULONG_BITS / GMP_LIMB_BITS;
+  mp_limb_t ulongrem = 0;
+
+  if (GMP_ULONG_BITS % GMP_LIMB_BITS != 0)
+    ulongrem = (mp_limb_t) (ULONG_MAX >> GMP_LIMB_BITS * ulongsize) + 1;
+
+  return un <= ulongsize || (up[ulongsize] < ulongrem && un == ulongsize + 1);
 }
 
 int
@@ -1421,25 +1551,36 @@ mpz_fits_ulong_p (const mpz_t u)
 {
   mp_size_t us = u->_mp_size;
 
-  return us == 0 || us == 1;
+  return us >= 0 && mpn_absfits_ulong_p (u->_mp_d, us);
 }
 
 long int
 mpz_get_si (const mpz_t u)
 {
-  mp_size_t us = u->_mp_size;
+  unsigned long r = mpz_get_ui (u);
+  unsigned long c = -LONG_MAX - LONG_MIN;
 
-  if (us > 0)
-    return (long) (u->_mp_d[0] & ~GMP_LIMB_HIGHBIT);
-  else if (us < 0)
-    return (long) (- u->_mp_d[0] | GMP_LIMB_HIGHBIT);
+  if (u->_mp_size < 0)
+    /* This expression is necessary to properly handle -LONG_MIN */
+    return -(long) c - (long) ((r - c) & LONG_MAX);
   else
-    return 0;
+    return (long) (r & LONG_MAX);
 }
 
 unsigned long int
 mpz_get_ui (const mpz_t u)
 {
+  if (GMP_LIMB_BITS < GMP_ULONG_BITS)
+    {
+      int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS;
+      unsigned long r = 0;
+      mp_size_t n = GMP_ABS (u->_mp_size);
+      n = GMP_MIN (n, 1 + (mp_size_t) (GMP_ULONG_BITS - 1) / GMP_LIMB_BITS);
+      while (--n >= 0)
+	r = (r << LOCAL_GMP_LIMB_BITS) + u->_mp_d[n];
+      return r;
+    }
+
   return u->_mp_size == 0 ? 0 : u->_mp_d[0];
 }
 
@@ -1458,6 +1599,56 @@ mpz_getlimbn (const mpz_t u, mp_size_t n)
     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
@@ -1472,26 +1663,22 @@ mpz_set_d (mpz_t r, double x)
 
   /* x != x is true when x is a NaN, and x == x * 0.5 is true when x is
      zero or infinity. */
-  if (x == 0.0 || x != x || x == x * 0.5)
+  if (x != x || x == x * 0.5)
     {
       r->_mp_size = 0;
       return;
     }
 
-  if (x < 0.0)
-    {
-      x = - x;
-      sign = 1;
-    }
-  else
-    sign = 0;
+  sign = x < 0.0 ;
+  if (sign)
+    x = - x;
 
   if (x < 1.0)
     {
       r->_mp_size = 0;
       return;
     }
-  B = 2.0 * (double) GMP_LIMB_HIGHBIT;
+  B = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1);
   Bi = 1.0 / B;
   for (rn = 1; x >= B; rn++)
     x *= Bi;
@@ -1501,8 +1688,9 @@ mpz_set_d (mpz_t r, double x)
   f = (mp_limb_t) x;
   x -= f;
   assert (x < 1.0);
-  rp[rn-1] = f;
-  for (i = rn-1; i-- > 0; )
+  i = rn-1;
+  rp[i] = f;
+  while (--i >= 0)
     {
       x = B * x;
       f = (mp_limb_t) x;
@@ -1524,18 +1712,34 @@ mpz_init_set_d (mpz_t r, double 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;
+  double B = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1);
 
   un = GMP_ABS (u->_mp_size);
 
   if (un == 0)
     return 0.0;
 
-  x = u->_mp_d[--un];
-  while (un > 0)
-    x = B*x + u->_mp_d[--un];
+  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;
@@ -1557,7 +1761,7 @@ mpz_cmpabs_d (const mpz_t x, double d)
     {
       xn = GMP_ABS (xn);
 
-      B = 2.0 * (double) GMP_LIMB_HIGHBIT;
+      B = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1);
       Bi = 1.0 / B;
 
       /* Scale d so it can be compared with the top limb. */
@@ -1608,14 +1812,7 @@ mpz_cmp_d (const mpz_t x, double d)
 int
 mpz_sgn (const mpz_t u)
 {
-  mp_size_t usize = u->_mp_size;
-
-  if (usize > 0)
-    return 1;
-  else if (usize < 0)
-    return -1;
-  else
-    return 0;
+  return GMP_CMP (u->_mp_size, 0);
 }
 
 int
@@ -1623,21 +1820,12 @@ 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)
+  if (v >= 0)
     return mpz_cmp_ui (u, v);
   else if (usize >= 0)
     return 1;
-  else /* usize == -1 */
-    {
-      mp_limb_t ul = u->_mp_d[0];
-      if ((mp_limb_t)GMP_NEG_CAST (unsigned long int, v) < ul)
-	return -1;
-      else if ( (mp_limb_t)GMP_NEG_CAST (unsigned long int, v) > ul)
-	return 1;
-    }
-  return 0;
+  else
+    return - mpz_cmpabs_ui (u, GMP_NEG_CAST (unsigned long int, v));
 }
 
 int
@@ -1645,19 +1833,10 @@ 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)
+  if (usize < 0)
     return -1;
   else
-    {
-      mp_limb_t ul = (usize > 0) ? u->_mp_d[0] : 0;
-      if (ul > v)
-	return 1;
-      else if (ul < v)
-	return -1;
-    }
-  return 0;
+    return mpz_cmpabs_ui (u, v);
 }
 
 int
@@ -1666,35 +1845,26 @@ 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 1;
-  else if (asize < bsize)
-    return -1;
-  else if (asize > 0)
+  if (asize != bsize)
+    return (asize < bsize) ? -1 : 1;
+  else if (asize >= 0)
     return mpn_cmp (a->_mp_d, b->_mp_d, asize);
-  else if (asize < 0)
-    return -mpn_cmp (a->_mp_d, b->_mp_d, -asize);
   else
-    return 0;
+    return mpn_cmp (b->_mp_d, a->_mp_d, -asize);
 }
 
 int
 mpz_cmpabs_ui (const mpz_t u, unsigned long v)
 {
   mp_size_t un = GMP_ABS (u->_mp_size);
-  mp_limb_t ul;
 
-  if (un > 1)
+  if (! mpn_absfits_ulong_p (u->_mp_d, un))
     return 1;
-
-  ul = (un == 1) ? u->_mp_d[0] : 0;
-
-  if (ul > v)
-    return 1;
-  else if (ul < v)
-    return -1;
   else
-    return 0;
+    {
+      unsigned long uu = mpz_get_ui (u);
+      return GMP_CMP(uu, v);
+    }
 }
 
 int
@@ -1707,18 +1877,14 @@ mpz_cmpabs (const mpz_t u, const mpz_t v)
 void
 mpz_abs (mpz_t r, const mpz_t u)
 {
-  if (r != u)
-    mpz_set (r, u);
-
+  mpz_set (r, u);
   r->_mp_size = GMP_ABS (r->_mp_size);
 }
 
 void
 mpz_neg (mpz_t r, const mpz_t u)
 {
-  if (r != u)
-    mpz_set (r, u);
-
+  mpz_set (r, u);
   r->_mp_size = -r->_mp_size;
 }
 
@@ -1733,80 +1899,28 @@ mpz_swap (mpz_t u, mpz_t v)
 
 /* 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)
-    {
-      r->_mp_d[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 > 0);
-
-  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 = MPZ_REALLOC (r, an);
-
-  if (an == 0)
-    {
-      rp[0] = b;
-      return -(b > 0);
-    }
-  else 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);
+  mpz_t bb;
+  mpz_init_set_ui (bb, b);
+  mpz_add (r, a, bb);
+  mpz_clear (bb);
 }
 
 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);
+  mpz_ui_sub (r, b, a);
+  mpz_neg (r, r);
 }
 
 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);
+  mpz_neg (r, b);
+  mpz_add_ui (r, r, a);
 }
 
 static mp_size_t
@@ -1814,20 +1928,21 @@ 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_size_t rn;
   mp_ptr rp;
   mp_limb_t cy;
 
-  rn = GMP_MAX (an, bn);
-  rp = MPZ_REALLOC (r, rn + 1);
-  if (an >= bn)
-    cy = mpn_add (rp, a->_mp_d, an, b->_mp_d, bn);
-  else
-    cy = mpn_add (rp, b->_mp_d, bn, a->_mp_d, an);
+  if (an < bn)
+    {
+      MPZ_SRCPTR_SWAP (a, b);
+      MP_SIZE_T_SWAP (an, bn);
+    }
 
-  rp[rn] = cy;
+  rp = MPZ_REALLOC (r, an + 1);
+  cy = mpn_add (rp, a->_mp_d, an, b->_mp_d, bn);
 
-  return rn + (cy > 0);
+  rp[an] = cy;
+
+  return an + cy;
 }
 
 static mp_size_t
@@ -1892,37 +2007,17 @@ mpz_mul_si (mpz_t r, const mpz_t u, long int v)
       mpz_neg (r, r);
     }
   else
-    mpz_mul_ui (r, u, (unsigned long int) v);
+    mpz_mul_ui (r, u, v);
 }
 
 void
 mpz_mul_ui (mpz_t r, const mpz_t u, unsigned long int v)
 {
-  mp_size_t un;
-  mpz_t t;
-  mp_ptr tp;
-  mp_limb_t cy;
-
-  un = GMP_ABS (u->_mp_size);
-
-  if (un == 0 || v == 0)
-    {
-      r->_mp_size = 0;
-      return;
-    }
-
-  mpz_init2 (t, (un + 1) * GMP_LIMB_BITS);
-
-  tp = t->_mp_d;
-  cy = mpn_mul_1 (tp, u->_mp_d, un, v);
-  tp[un] = cy;
-
-  t->_mp_size = un + (cy > 0);
-  if (u->_mp_size < 0)
-    t->_mp_size = - t->_mp_size;
-
-  mpz_swap (r, t);
-  mpz_clear (t);
+  mpz_t vv;
+  mpz_init_set_ui (vv, v);
+  mpz_mul (r, u, vv);
+  mpz_clear (vv);
+  return;
 }
 
 void
@@ -1933,8 +2028,8 @@ mpz_mul (mpz_t r, const mpz_t u, const mpz_t v)
   mpz_t t;
   mp_ptr tp;
 
-  un = GMP_ABS (u->_mp_size);
-  vn = GMP_ABS (v->_mp_size);
+  un = u->_mp_size;
+  vn = v->_mp_size;
 
   if (un == 0 || vn == 0)
     {
@@ -1942,7 +2037,10 @@ mpz_mul (mpz_t r, const mpz_t u, const mpz_t v)
       return;
     }
 
-  sign = (u->_mp_size ^ v->_mp_size) < 0;
+  sign = (un ^ vn) < 0;
+
+  un = GMP_ABS (un);
+  vn = GMP_ABS (vn);
 
   mpz_init2 (t, (un + vn) * GMP_LIMB_BITS);
 
@@ -1989,12 +2087,51 @@ mpz_mul_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t bits)
   else
     mpn_copyd (rp + limbs, u->_mp_d, un);
 
-  while (limbs > 0)
-    rp[--limbs] = 0;
+  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_set_ui (t, v);
+  mpz_mul (t, u, t);
+  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_set_ui (t, v);
+  mpz_mul (t, u, t);
+  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 };
@@ -2059,8 +2196,7 @@ mpz_div_qr (mpz_t q, mpz_t r,
       mp_size_t qn, rn;
       mpz_t tq, tr;
 
-      mpz_init (tr);
-      mpz_set (tr, n);
+      mpz_init_set (tr, n);
       np = tr->_mp_d;
 
       qn = nn - dn + 1;
@@ -2170,10 +2306,7 @@ mpz_tdiv_r (mpz_t r, const mpz_t n, const mpz_t d)
 void
 mpz_mod (mpz_t r, const mpz_t n, const mpz_t d)
 {
-  if (d->_mp_size >= 0)
-    mpz_div_qr (NULL, r, n, d, GMP_DIV_FLOOR);
-  else
-    mpz_div_qr (NULL, r, n, d, GMP_DIV_CEIL);
+  mpz_div_qr (NULL, r, n, d, d->_mp_size >= 0 ? GMP_DIV_FLOOR : GMP_DIV_CEIL);
 }
 
 static void
@@ -2183,7 +2316,7 @@ mpz_div_q_2exp (mpz_t q, const mpz_t u, mp_bitcnt_t bit_index,
   mp_size_t un, qn;
   mp_size_t limb_cnt;
   mp_ptr qp;
-  mp_limb_t adjust;
+  int adjust;
 
   un = u->_mp_size;
   if (un == 0)
@@ -2207,7 +2340,6 @@ mpz_div_q_2exp (mpz_t q, const mpz_t u, mp_bitcnt_t bit_index,
 
   if (qn <= 0)
     qn = 0;
-
   else
     {
       qp = MPZ_REALLOC (q, qn);
@@ -2225,7 +2357,8 @@ mpz_div_q_2exp (mpz_t q, const mpz_t u, mp_bitcnt_t bit_index,
 
   q->_mp_size = qn;
 
-  mpz_add_ui (q, q, adjust);
+  if (adjust)
+    mpz_add_ui (q, q, 1);
   if (un < 0)
     mpz_neg (q, q);
 }
@@ -2260,16 +2393,9 @@ mpz_div_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t bit_index,
 	{
 	  /* Have to negate and sign extend. */
 	  mp_size_t i;
-	  mp_limb_t cy;
 
-	  for (cy = 1, i = 0; i < un; i++)
-	    {
-	      mp_limb_t s = ~u->_mp_d[i] + cy;
-	      cy = s < cy;
-	      rp[i] = s;
-	    }
-	  assert (cy == 0);
-	  for (; i < rn - 1; 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;
@@ -2294,23 +2420,13 @@ mpz_div_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t bit_index,
       if (mode == ((us > 0) ? GMP_DIV_CEIL : GMP_DIV_FLOOR)) /* us != 0 here. */
 	{
 	  /* If r != 0, compute 2^{bit_count} - r. */
-	  mp_size_t i;
-
-	  for (i = 0; i < rn && rp[i] == 0; i++)
-	    ;
-	  if (i < rn)
-	    {
-	      /* r > 0, need to flip sign. */
-	      rp[i] = ~rp[i] + 1;
-	      for (i++; i < rn; i++)
-		rp[i] = ~rp[i];
+	  mpn_neg (rp, rp, rn);
 
-	      rp[rn-1] &= mask;
+	  rp[rn-1] &= mask;
 
-	      /* us is not used for anything else, so we can modify it
-		 here to indicate flipped sign. */
-	      us = -us;
-	    }
+	  /* 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);
@@ -2365,60 +2481,42 @@ mpz_divisible_p (const mpz_t n, const mpz_t d)
   return mpz_div_qr (NULL, NULL, n, d, GMP_DIV_TRUNC) == 0;
 }
 
-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)
+int
+mpz_congruent_p (const mpz_t a, const mpz_t b, const mpz_t m)
 {
-  mp_size_t ns, qn;
-  mp_ptr qp;
-  mp_limb_t rl;
-  mp_size_t rs;
+  mpz_t t;
+  int res;
 
-  ns = n->_mp_size;
-  if (ns == 0)
-    {
-      if (q)
-	q->_mp_size = 0;
-      if (r)
-	r->_mp_size = 0;
-      return 0;
-    }
+  /* a == b (mod 0) iff a == b */
+  if (mpz_sgn (m) == 0)
+    return (mpz_cmp (a, b) == 0);
 
-  qn = GMP_ABS (ns);
-  if (q)
-    qp = MPZ_REALLOC (q, qn);
-  else
-    qp = NULL;
+  mpz_init (t);
+  mpz_sub (t, a, b);
+  res = mpz_divisible_p (t, m);
+  mpz_clear (t);
 
-  rl = mpn_div_qr_1 (qp, n->_mp_d, qn, d);
-  assert (rl < d);
+  return res;
+}
 
-  rs = rl > 0;
-  rs = (ns < 0) ? -rs : rs;
+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)
+{
+  unsigned long ret;
+  mpz_t rr, dd;
 
-  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;
-    }
+  mpz_init (rr);
+  mpz_init_set_ui (dd, d);
+  mpz_div_qr (q, rr, n, dd, mode);
+  mpz_clear (dd);
+  ret = mpz_get_ui (rr);
 
   if (r)
-    {
-      r->_mp_d[0] = rl;
-      r->_mp_size = rs;
-    }
-  if (q)
-    {
-      qn -= (qp[qn-1] == 0);
-      assert (qn == 0 || qp[qn-1] > 0);
+    mpz_swap (r, rr);
+  mpz_clear (rr);
 
-      q->_mp_size = (ns < 0) ? - qn : qn;
-    }
-
-  return rl;
+  return ret;
 }
 
 unsigned long
@@ -2557,53 +2655,31 @@ mpn_gcd_11 (mp_limb_t u, mp_limb_t v)
 unsigned long
 mpz_gcd_ui (mpz_t g, const mpz_t u, unsigned long v)
 {
-  mp_size_t un;
+  mpz_t t;
+  mpz_init_set_ui(t, v);
+  mpz_gcd (t, u, t);
+  if (v > 0)
+    v = mpz_get_ui (t);
 
-  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_swap (t, g);
 
-      if (g)
-	mpz_set_ui (g, v);
-    }
+  mpz_clear (t);
 
   return v;
 }
 
 static mp_bitcnt_t
-mpz_make_odd (mpz_t r, const mpz_t u)
+mpz_make_odd (mpz_t r)
 {
-  mp_size_t un, rn, i;
-  mp_ptr rp;
-  unsigned shift;
-
-  un = GMP_ABS (u->_mp_size);
-  assert (un > 0);
-
-  for (i = 0; u->_mp_d[i] == 0; i++)
-    ;
+  mp_bitcnt_t shift;
 
-  gmp_ctz (shift, u->_mp_d[i]);
+  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);
 
-  rn = un - i;
-  rp = MPZ_REALLOC (r, rn);
-  if (shift > 0)
-    {
-      mpn_rshift (rp, u->_mp_d + i, rn, shift);
-      rn -= (rp[rn-1] == 0);
-    }
-  else
-    mpn_copyi (rp, u->_mp_d + i, rn);
-
-  r->_mp_size = rn;
-  return i * GMP_LIMB_BITS + shift;
+  return shift;
 }
 
 void
@@ -2626,8 +2702,10 @@ mpz_gcd (mpz_t g, const mpz_t u, const mpz_t v)
   mpz_init (tu);
   mpz_init (tv);
 
-  uz = mpz_make_odd (tu, u);
-  vz = mpz_make_odd (tv, v);
+  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)
@@ -2643,7 +2721,7 @@ mpz_gcd (mpz_t g, const mpz_t u, const mpz_t v)
       {
 	int c;
 
-	mpz_make_odd (tu, tu);
+	mpz_make_odd (tu);
 	c = mpz_cmp (tu, tv);
 	if (c == 0)
 	  {
@@ -2680,7 +2758,7 @@ mpz_gcdext (mpz_t g, mpz_t s, mpz_t t, const mpz_t u, const mpz_t v)
       signed long sign = mpz_sgn (v);
       mpz_abs (g, v);
       if (s)
-	mpz_set_ui (s, 0);
+	s->_mp_size = 0;
       if (t)
 	mpz_set_si (t, sign);
       return;
@@ -2694,7 +2772,7 @@ mpz_gcdext (mpz_t g, mpz_t s, mpz_t t, const mpz_t u, const mpz_t v)
       if (s)
 	mpz_set_si (s, sign);
       if (t)
-	mpz_set_ui (t, 0);
+	t->_mp_size = 0;
       return;
     }
 
@@ -2705,8 +2783,10 @@ mpz_gcdext (mpz_t g, mpz_t s, mpz_t t, const mpz_t u, const mpz_t v)
   mpz_init (t0);
   mpz_init (t1);
 
-  uz = mpz_make_odd (tu, u);
-  vz = mpz_make_odd (tv, v);
+  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;
@@ -2754,7 +2834,7 @@ mpz_gcdext (mpz_t g, mpz_t s, mpz_t t, const mpz_t u, const mpz_t v)
   if (tu->_mp_size > 0)
     {
       mp_bitcnt_t shift;
-      shift = mpz_make_odd (tu, tu);
+      shift = mpz_make_odd (tu);
       mpz_mul_2exp (t0, t0, shift);
       mpz_mul_2exp (s0, s0, shift);
       power += shift;
@@ -2777,7 +2857,7 @@ mpz_gcdext (mpz_t g, mpz_t s, mpz_t t, const mpz_t u, const mpz_t v)
 	      mpz_add (t0, t0, t1);
 	      mpz_add (s0, s0, s1);
 
-	      shift = mpz_make_odd (tv, tv);
+	      shift = mpz_make_odd (tv);
 	      mpz_mul_2exp (t1, t1, shift);
 	      mpz_mul_2exp (s1, s1, shift);
 	    }
@@ -2787,7 +2867,7 @@ mpz_gcdext (mpz_t g, mpz_t s, mpz_t t, const mpz_t u, const mpz_t v)
 	      mpz_add (t1, t0, t1);
 	      mpz_add (s1, s0, s1);
 
-	      shift = mpz_make_odd (tu, tu);
+	      shift = mpz_make_odd (tu);
 	      mpz_mul_2exp (t0, t0, shift);
 	      mpz_mul_2exp (s0, s0, shift);
 	    }
@@ -2817,8 +2897,9 @@ mpz_gcdext (mpz_t g, mpz_t s, mpz_t t, const mpz_t u, const mpz_t v)
 	  mpz_sub (s0, s0, s1);
 	  mpz_add (t0, t0, t1);
 	}
-      mpz_divexact_ui (s0, s0, 2);
-      mpz_divexact_ui (t0, t0, 2);
+      assert (mpz_even_p (t0) && mpz_even_p (s0));
+      mpz_tdiv_q_2exp (s0, s0, 1);
+      mpz_tdiv_q_2exp (t0, t0, 1);
     }
 
   /* Arrange so that |s| < |u| / 2g */
@@ -2925,12 +3006,16 @@ mpz_pow_ui (mpz_t r, const mpz_t b, unsigned long e)
   mpz_t tr;
   mpz_init_set_ui (tr, 1);
 
-  for (bit = GMP_ULONG_HIGHBIT; bit > 0; bit >>= 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);
 }
@@ -2939,6 +3024,7 @@ void
 mpz_ui_pow_ui (mpz_t r, unsigned long blimb, unsigned long e)
 {
   mpz_t b;
+
   mpz_init_set_ui (b, blimb);
   mpz_pow_ui (r, b, e);
   mpz_clear (b);
@@ -2986,7 +3072,7 @@ mpz_powm (mpz_t r, const mpz_t b, const mpz_t e, const mpz_t m)
   if (e->_mp_size < 0)
     {
       if (!mpz_invert (base, b, m))
-	gmp_die ("mpz_powm: Negative exponent and non-invertibe base.");
+	gmp_die ("mpz_powm: Negative exponent and non-invertible base.");
     }
   else
     {
@@ -3013,12 +3099,13 @@ mpz_powm (mpz_t r, const mpz_t b, const mpz_t e, const mpz_t m)
     }
   mpz_init_set_ui (tr, 1);
 
-  while (en-- > 0)
+  while (--en >= 0)
     {
       mp_limb_t w = e->_mp_d[en];
       mp_limb_t bit;
 
-      for (bit = GMP_LIMB_HIGHBIT; bit > 0; bit >>= 1)
+      bit = GMP_LIMB_HIGHBIT;
+      do
 	{
 	  mpz_mul (tr, tr, tr);
 	  if (w & bit)
@@ -3028,7 +3115,9 @@ mpz_powm (mpz_t r, const mpz_t b, const mpz_t e, const mpz_t m)
 	      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 */
@@ -3050,6 +3139,7 @@ void
 mpz_powm_ui (mpz_t r, const mpz_t b, unsigned long elimb, const mpz_t m)
 {
   mpz_t e;
+
   mpz_init_set_ui (e, elimb);
   mpz_powm (r, b, e, m);
   mpz_clear (e);
@@ -3063,20 +3153,21 @@ mpz_rootrem (mpz_t x, mpz_t r, const mpz_t y, unsigned long z)
   mpz_t t, u;
 
   sgn = y->_mp_size < 0;
-  if (sgn && (z & 1) == 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) {
-    mpz_set (x, y);
+    if (x)
+      mpz_set (x, y);
     if (r)
       r->_mp_size = 0;
     return;
   }
 
-  mpz_init (t);
   mpz_init (u);
+  mpz_init (t);
   mpz_setbit (t, mpz_sizeinbase (y, 2) / z + 1);
 
   if (z == 2) /* simplify sqrt loop: z-1 == 1 */
@@ -3109,7 +3200,8 @@ mpz_rootrem (mpz_t x, mpz_t r, const mpz_t y, unsigned long z)
     mpz_pow_ui (t, u, z);
     mpz_sub (r, y, t);
   }
-  mpz_swap (x, u);
+  if (x)
+    mpz_swap (x, u);
   mpz_clear (u);
   mpz_clear (t);
 }
@@ -3141,19 +3233,69 @@ 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)
 {
-  if (n < 2) {
-    mpz_set_ui (x, 1);
-    return;
-  }
-  mpz_set_ui (x, n);
-  for (;--n > 1;)
-    mpz_mul_ui (x, x, n);
+  mpz_mfac_uiui (x, n, 1);
 }
 
 void
@@ -3161,25 +3303,299 @@ mpz_bin_uiui (mpz_t r, unsigned long n, unsigned long k)
 {
   mpz_t t;
 
-  if (k > n) {
-    r->_mp_size = 0;
-    return;
-  }
-  mpz_fac_ui (r, n);
+  mpz_set_ui (r, k <= n);
+
+  if (k > (n >> 1))
+    k = (k <= n) ? n - k : 0;
+
   mpz_init (t);
   mpz_fac_ui (t, k);
-  mpz_divexact (r, r, t);
-  mpz_fac_ui (t, n - k);
+
+  for (; k > 0; --k)
+    mpz_mul_ui (r, r, n--);
+
   mpz_divexact (r, r, t);
   mpz_clear (t);
 }
 
 
+/* Primality testing */
+
+/* Computes Kronecker (a/b) with odd b, a!=0 and GCD(a,b) = 1 */
+/* Adapted from JACOBI_BASE_METHOD==4 in mpn/generic/jacbase.c */
+static int
+gmp_jacobi_coprime (mp_limb_t a, mp_limb_t b)
+{
+  int c, bit = 0;
+
+  assert (b & 1);
+  assert (a != 0);
+  /* assert (mpn_gcd_11 (a, b) == 1); */
+
+  /* Below, we represent a and b shifted right so that the least
+     significant one bit is implicit. */
+  b >>= 1;
+
+  gmp_ctz(c, a);
+  a >>= 1;
+
+  do
+    {
+      a >>= c;
+      /* (2/b) = -1 if b = 3 or 5 mod 8 */
+      bit ^= c & (b ^ (b >> 1));
+      if (a < b)
+	{
+	  bit ^= a & b;
+	  a = b - a;
+	  b -= a;
+	}
+      else
+	{
+	  a -= b;
+	  assert (a != 0);
+	}
+
+      gmp_ctz(c, a);
+      ++c;
+    }
+  while (b > 0);
+
+  return bit & 1 ? -1 : 1;
+}
+
+static void
+gmp_lucas_step_k_2k (mpz_t V, mpz_t Qk, const mpz_t n)
+{
+  mpz_mod (Qk, Qk, n);
+  /* V_{2k} <- V_k ^ 2 - 2Q^k */
+  mpz_mul (V, V, V);
+  mpz_submul_ui (V, Qk, 2);
+  mpz_tdiv_r (V, V, n);
+  /* Q^{2k} = (Q^k)^2 */
+  mpz_mul (Qk, Qk, Qk);
+}
+
+/* Computes V_k, Q^k (mod n) for the Lucas' sequence */
+/* with P=1, Q=Q; k = (n>>b0)|1. */
+/* Requires an odd n > 4; b0 > 0; -2*Q must not overflow a long */
+/* Returns (U_k == 0) and sets V=V_k and Qk=Q^k. */
+static int
+gmp_lucas_mod (mpz_t V, mpz_t Qk, long Q,
+	       mp_bitcnt_t b0, const mpz_t n)
+{
+  mp_bitcnt_t bs;
+  mpz_t U;
+  int res;
+
+  assert (b0 > 0);
+  assert (Q <= - (LONG_MIN / 2));
+  assert (Q >= - (LONG_MAX / 2));
+  assert (mpz_cmp_ui (n, 4) > 0);
+  assert (mpz_odd_p (n));
+
+  mpz_init_set_ui (U, 1); /* U1 = 1 */
+  mpz_set_ui (V, 1); /* V1 = 1 */
+  mpz_set_si (Qk, Q);
+
+  for (bs = mpz_sizeinbase (n, 2) - 1; --bs >= b0;)
+    {
+      /* U_{2k} <- U_k * V_k */
+      mpz_mul (U, U, V);
+      /* V_{2k} <- V_k ^ 2 - 2Q^k */
+      /* Q^{2k} = (Q^k)^2 */
+      gmp_lucas_step_k_2k (V, Qk, n);
+
+      /* A step k->k+1 is performed if the bit in $n$ is 1	*/
+      /* mpz_tstbit(n,bs) or the the bit is 0 in $n$ but	*/
+      /* should be 1 in $n+1$ (bs == b0)			*/
+      if (b0 == bs || mpz_tstbit (n, bs))
+	{
+	  /* Q^{k+1} <- Q^k * Q */
+	  mpz_mul_si (Qk, Qk, Q);
+	  /* U_{k+1} <- (U_k + V_k) / 2 */
+	  mpz_swap (U, V); /* Keep in V the old value of U_k */
+	  mpz_add (U, U, V);
+	  /* We have to compute U/2, so we need an even value, */
+	  /* equivalent (mod n) */
+	  if (mpz_odd_p (U))
+	    mpz_add (U, U, n);
+	  mpz_tdiv_q_2exp (U, U, 1);
+	  /* V_{k+1} <-(D*U_k + V_k) / 2 =
+			U_{k+1} + (D-1)/2*U_k = U_{k+1} - 2Q*U_k */
+	  mpz_mul_si (V, V, -2*Q);
+	  mpz_add (V, U, V);
+	  mpz_tdiv_r (V, V, n);
+	}
+      mpz_tdiv_r (U, U, n);
+    }
+
+  res = U->_mp_size == 0;
+  mpz_clear (U);
+  return res;
+}
+
+/* Performs strong Lucas' test on x, with parameters suggested */
+/* for the BPSW test. Qk is only passed to recycle a variable. */
+/* Requires GCD (x,6) = 1.*/
+static int
+gmp_stronglucas (const mpz_t x, mpz_t Qk)
+{
+  mp_bitcnt_t b0;
+  mpz_t V, n;
+  mp_limb_t maxD, D; /* The absolute value is stored. */
+  long Q;
+  mp_limb_t tl;
+
+  /* Test on the absolute value. */
+  mpz_roinit_normal_n (n, x->_mp_d, GMP_ABS (x->_mp_size));
+
+  assert (mpz_odd_p (n));
+  /* assert (mpz_gcd_ui (NULL, n, 6) == 1); */
+  if (mpz_root (Qk, n, 2))
+    return 0; /* A square is composite. */
+
+  /* Check Ds up to square root (in case, n is prime)
+     or avoid overflows */
+  maxD = (Qk->_mp_size == 1) ? Qk->_mp_d [0] - 1 : GMP_LIMB_MAX;
+
+  D = 3;
+  /* Search a D such that (D/n) = -1 in the sequence 5,-7,9,-11,.. */
+  /* For those Ds we have (D/n) = (n/|D|) */
+  do
+    {
+      if (D >= maxD)
+	return 1 + (D != GMP_LIMB_MAX); /* (1 + ! ~ D) */
+      D += 2;
+      tl = mpz_tdiv_ui (n, D);
+      if (tl == 0)
+	return 0;
+    }
+  while (gmp_jacobi_coprime (tl, D) == 1);
+
+  mpz_init (V);
+
+  /* n-(D/n) = n+1 = d*2^{b0}, with d = (n>>b0) | 1 */
+  b0 = mpz_scan0 (n, 0);
+
+  /* D= P^2 - 4Q; P = 1; Q = (1-D)/4 */
+  Q = (D & 2) ? (long) (D >> 2) + 1 : -(long) (D >> 2);
+
+  if (! gmp_lucas_mod (V, Qk, Q, b0, n))	/* If Ud != 0 */
+    while (V->_mp_size != 0 && --b0 != 0)	/* while Vk != 0 */
+      /* V <- V ^ 2 - 2Q^k */
+      /* Q^{2k} = (Q^k)^2 */
+      gmp_lucas_step_k_2k (V, Qk, n);
+
+  mpz_clear (V);
+  return (b0 != 0);
+}
+
+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;
+
+  mpz_init (nm1);
+  mpz_init (q);
+
+  /* Find q and k, where q is odd and n = 1 + 2**k * q.  */
+  mpz_abs (nm1, n);
+  nm1->_mp_d[0] -= 1;
+  k = mpz_scan1 (nm1, 0);
+  mpz_tdiv_q_2exp (q, nm1, k);
+
+  /* BPSW test */
+  mpz_init_set_ui (y, 2);
+  is_prime = gmp_millerrabin (n, nm1, y, q, k) && gmp_stronglucas (n, y);
+  reps -= 24; /* skip the first 24 repetitions */
+
+  /* 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). */
+
+  for (j = 0; 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 complementt.
+   complement from -x = ~x + 1, where ~ is bitwise complement.
    Negation transforms
 
      xxxx10...0
@@ -3223,9 +3639,9 @@ mpz_tstbit (const mpz_t d, mp_bitcnt_t bit_index)
     {
       /* 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)
+      if (shift > 0 && (mp_limb_t) (w << (GMP_LIMB_BITS - shift)) > 0)
 	return bit ^ 1;
-      while (limb_index-- > 0)
+      while (--limb_index >= 0)
 	if (d->_mp_d[limb_index] > 0)
 	  return bit ^ 1;
     }
@@ -3290,7 +3706,7 @@ mpz_abs_sub_bit (mpz_t d, mp_bitcnt_t bit_index)
 
   gmp_assert_nocarry (mpn_sub_1 (dp + limb_index, dp + limb_index,
 				 dn - limb_index, bit));
-  dn -= (dp[dn-1] == 0);
+  dn = mpn_normalized_size (dp, dn);
   d->_mp_size = (d->_mp_size < 0) ? - dn : dn;
 }
 
@@ -3330,8 +3746,8 @@ mpz_combit (mpz_t d, mp_bitcnt_t bit_index)
 void
 mpz_com (mpz_t r, const mpz_t u)
 {
-  mpz_neg (r, u);
-  mpz_sub_ui (r, r, 1);
+  mpz_add_ui (r, u, 1);
+  mpz_neg (r, r);
 }
 
 void
@@ -3368,12 +3784,13 @@ mpz_and (mpz_t r, const mpz_t u, const mpz_t v)
   /* If the smaller input is positive, higher limbs don't matter. */
   rn = vx ? un : vn;
 
-  rp = MPZ_REALLOC (r, rn + rc);
+  rp = MPZ_REALLOC (r, rn + (mp_size_t) rc);
 
   up = u->_mp_d;
   vp = v->_mp_d;
 
-  for (i = 0; i < vn; i++)
+  i = 0;
+  do
     {
       ul = (up[i] ^ ux) + uc;
       uc = ul < uc;
@@ -3385,6 +3802,7 @@ mpz_and (mpz_t r, const mpz_t u, const mpz_t v)
       rc = rl < rc;
       rp[i] = rl;
     }
+  while (++i < vn);
   assert (vc == 0);
 
   for (; i < rn; i++)
@@ -3439,12 +3857,13 @@ mpz_ior (mpz_t r, const mpz_t u, const mpz_t v)
      don't matter. */
   rn = vx ? vn : un;
 
-  rp = MPZ_REALLOC (r, rn + rc);
+  rp = MPZ_REALLOC (r, rn + (mp_size_t) rc);
 
   up = u->_mp_d;
   vp = v->_mp_d;
 
-  for (i = 0; i < vn; i++)
+  i = 0;
+  do
     {
       ul = (up[i] ^ ux) + uc;
       uc = ul < uc;
@@ -3456,6 +3875,7 @@ mpz_ior (mpz_t r, const mpz_t u, const mpz_t v)
       rc = rl < rc;
       rp[i] = rl;
     }
+  while (++i < vn);
   assert (vc == 0);
 
   for (; i < rn; i++)
@@ -3506,12 +3926,13 @@ mpz_xor (mpz_t r, const mpz_t u, const mpz_t v)
   vx = -vc;
   rx = -rc;
 
-  rp = MPZ_REALLOC (r, un + rc);
+  rp = MPZ_REALLOC (r, un + (mp_size_t) rc);
 
   up = u->_mp_d;
   vp = v->_mp_d;
 
-  for (i = 0; i < vn; i++)
+  i = 0;
+  do
     {
       ul = (up[i] ^ ux) + uc;
       uc = ul < uc;
@@ -3523,6 +3944,7 @@ mpz_xor (mpz_t r, const mpz_t u, const mpz_t v)
       rc = rl < rc;
       rp[i] = rl;
     }
+  while (++i < vn);
   assert (vc == 0);
 
   for (; i < un; i++)
@@ -3548,32 +3970,45 @@ 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)
+  int LOCAL_SHIFT_BITS = 16;
+  for (c = 0; x > 0;)
     {
-      unsigned w = ((x >> 1) & 0x5555) + (x & 0x5555);
+      unsigned w = x - ((x >> 1) & 0x5555);
       w = ((w >> 2) & 0x3333) + (w & 0x3333);
-      w = ((w >> 4) & 0x0f0f) + (w & 0x0f0f);
-      w = (w >> 8) + (w & 0x00ff);
+      w =  (w >> 4) + w;
+      w = ((w >> 8) & 0x000f) + (w & 0x000f);
       c += w;
+      if (GMP_LIMB_BITS > LOCAL_SHIFT_BITS)
+	x >>= LOCAL_SHIFT_BITS;
+      else
+	x = 0;
     }
   return c;
 }
 
 mp_bitcnt_t
-mpz_popcount (const mpz_t u)
+mpn_popcount (mp_srcptr p, mp_size_t n)
 {
-  mp_size_t un, i;
+  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;
 
-  for (c = 0, i = 0; i < un; i++)
-    c += gmp_popcount_limb (u->_mp_d[i]);
-
-  return c;
+  return mpn_popcount (u->_mp_d, un);
 }
 
 mp_bitcnt_t
@@ -3590,16 +4025,13 @@ mpz_hamdist (const mpz_t u, const mpz_t v)
   if ( (un ^ vn) < 0)
     return ~(mp_bitcnt_t) 0;
 
-  if (un < 0)
+  comp = - (uc = vc = (un < 0));
+  if (uc)
     {
       assert (vn < 0);
       un = -un;
       vn = -vn;
-      uc = vc = 1;
-      comp = - (mp_limb_t) 1;
     }
-  else
-    uc = vc = comp = 0;
 
   up = u->_mp_d;
   vp = v->_mp_d;
@@ -3635,10 +4067,8 @@ 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, uc;
-  unsigned cnt;
+  mp_limb_t limb, ux;
 
-  up = u->_mp_d;
   us = u->_mp_size;
   un = GMP_ABS (us);
   i = starting_bit / GMP_LIMB_BITS;
@@ -3648,36 +4078,24 @@ mpz_scan1 (const mpz_t u, mp_bitcnt_t starting_bit)
   if (i >= un)
     return (us >= 0 ? ~(mp_bitcnt_t) 0 : starting_bit);
 
-  if (us < 0)
-    {
-      ux = GMP_LIMB_MAX;
-      uc = mpn_zero_p (up, i);
-    }
-  else
-    ux = uc = 0;
-
-  limb = (ux ^ up[i]) + uc;
-  uc = limb < uc;
-
-  /* Mask to 0 all bits before starting_bit, thus ignoring them. */
-  limb &= (GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS));
+  up = u->_mp_d;
+  ux = 0;
+  limb = up[i];
 
-  while (limb == 0)
+  if (starting_bit != 0)
     {
-      i++;
-      if (i == un)
+      if (us < 0)
 	{
-	  assert (uc == 0);
-	  /* For the u > 0 case, this can happen only for the first
-	     masked limb. For the u < 0 case, it happens when the
-	     highest limbs of the absolute value are all ones. */
-	  return (us >= 0 ? ~(mp_bitcnt_t) 0 : un * GMP_LIMB_BITS);
+	  ux = mpn_zero_p (up, i);
+	  limb = ~ limb + ux;
+	  ux = - (mp_limb_t) (limb >= ux);
 	}
-      limb = (ux ^ up[i]) + uc;
-      uc = limb < uc;
+
+      /* Mask to 0 all bits before starting_bit, thus ignoring them. */
+      limb &= GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS);
     }
-  gmp_ctz (cnt, limb);
-  return (mp_bitcnt_t) i * GMP_LIMB_BITS + cnt;
+
+  return mpn_common_scan (limb, i, up, un, ux);
 }
 
 mp_bitcnt_t
@@ -3685,46 +4103,28 @@ 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, uc;
-  unsigned cnt;
+  mp_limb_t limb, ux;
 
-  up = u->_mp_d;
   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 (us >= 0 ? starting_bit : ~(mp_bitcnt_t) 0);
+    return (ux ? starting_bit : ~(mp_bitcnt_t) 0);
 
-  if (us < 0)
-    {
-      ux = GMP_LIMB_MAX;
-      uc = mpn_zero_p (up, i);
-    }
-  else
-    ux = uc = 0;
+  up = u->_mp_d;
+  limb = up[i] ^ ux;
 
-  limb = (ux ^ up[i]) + uc;
-  uc = limb < uc;
+  if (ux == 0)
+    limb -= mpn_zero_p (up, i); /* limb = ~(~limb + zero_p) */
 
-  /* Mask to 1 all bits before starting_bit, thus ignoring them. */
-  limb |= ((mp_limb_t) 1 << (starting_bit % GMP_LIMB_BITS)) - 1;
+  /* Mask all bits before starting_bit, thus ignoring them. */
+  limb &= GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS);
 
-  while (limb == GMP_LIMB_MAX)
-    {
-      i++;
-      if (i == un)
-	{
-	  assert (uc == 0);
-	  return (us >= 0 ? un * GMP_LIMB_BITS : ~(mp_bitcnt_t) 0);
-	}
-      limb = (ux ^ up[i]) + uc;
-      uc = limb < uc;
-    }
-  gmp_ctz (cnt, ~limb);
-  return (mp_bitcnt_t) i * GMP_LIMB_BITS + cnt;
+  return mpn_common_scan (limb, i, up, un, ux);
 }
 
 
@@ -3741,7 +4141,7 @@ mpz_sizeinbase (const mpz_t u, int base)
   size_t ndigits;
 
   assert (base >= 2);
-  assert (base <= 36);
+  assert (base <= 62);
 
   un = GMP_ABS (u->_mp_size);
   if (un == 0)
@@ -3770,11 +4170,15 @@ mpz_sizeinbase (const mpz_t u, int base)
   mpn_copyi (tp, up, un);
   mpn_div_qr_1_invert (&bi, base);
 
-  for (ndigits = 0; un > 0; ndigits++)
+  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;
 }
@@ -3787,23 +4191,26 @@ mpz_get_str (char *sp, int base, const mpz_t u)
   mp_size_t un;
   size_t i, sn;
 
-  if (base >= 0)
+  digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz";
+  if (base > 1)
     {
-      digits = "0123456789abcdefghijklmnopqrstuvwxyz";
+      if (base <= 36)
+	digits = "0123456789abcdefghijklmnopqrstuvwxyz";
+      else if (base > 62)
+	return NULL;
     }
+  else if (base >= -1)
+    base = 10;
   else
     {
       base = -base;
-      digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
+      if (base > 36)
+	return NULL;
     }
-  if (base <= 1)
-    base = 10;
-  if (base > 36)
-    return NULL;
 
   sn = 1 + mpz_sizeinbase (u, base);
   if (!sp)
-    sp = gmp_xalloc (1 + sn);
+    sp = (char *) gmp_xalloc (1 + sn);
 
   un = GMP_ABS (u->_mp_size);
 
@@ -3847,41 +4254,34 @@ mpz_get_str (char *sp, int base, const mpz_t u)
 int
 mpz_set_str (mpz_t r, const char *sp, int base)
 {
-  unsigned bits;
+  unsigned bits, value_of_a;
   mp_size_t rn, alloc;
   mp_ptr rp;
-  size_t sn;
   size_t dn;
   int sign;
   unsigned char *dp;
 
-  assert (base == 0 || (base >= 2 && base <= 36));
+  assert (base == 0 || (base >= 2 && base <= 62));
 
   while (isspace( (unsigned char) *sp))
     sp++;
 
-  if (*sp == '-')
-    {
-      sign = 1;
-      sp++;
-    }
-  else
-    sign = 0;
+  sign = (*sp == '-');
+  sp += sign;
 
   if (base == 0)
     {
-      if (*sp == '0')
+      if (sp[0] == '0')
 	{
-	  sp++;
-	  if (*sp == 'x' || *sp == 'X')
+	  if (sp[1] == 'x' || sp[1] == 'X')
 	    {
 	      base = 16;
-	      sp++;
+	      sp += 2;
 	    }
-	  else if (*sp == 'b' || *sp == 'B')
+	  else if (sp[1] == 'b' || sp[1] == 'B')
 	    {
 	      base = 2;
-	      sp++;
+	      sp += 2;
 	    }
 	  else
 	    base = 8;
@@ -3890,25 +4290,30 @@ mpz_set_str (mpz_t r, const char *sp, int base)
 	base = 10;
     }
 
-  sn = strlen (sp);
-  dp = gmp_xalloc (sn + (sn == 0));
+  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;
-      if (*sp >= '0' && *sp <= '9')
+      else if (*sp >= '0' && *sp <= '9')
 	digit = *sp - '0';
       else if (*sp >= 'a' && *sp <= 'z')
-	digit = *sp - 'a' + 10;
+	digit = *sp - 'a' + value_of_a;
       else if (*sp >= 'A' && *sp <= 'Z')
 	digit = *sp - 'A' + 10;
       else
 	digit = base; /* fail */
 
-      if (digit >= base)
+      if (digit >= (unsigned) base)
 	{
 	  gmp_free (dp);
 	  r->_mp_size = 0;
@@ -3918,11 +4323,17 @@ mpz_set_str (mpz_t r, const char *sp, int base)
       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 = (sn * bits + GMP_LIMB_BITS - 1) / GMP_LIMB_BITS;
+      alloc = (dn * bits + GMP_LIMB_BITS - 1) / GMP_LIMB_BITS;
       rp = MPZ_REALLOC (r, alloc);
       rn = mpn_set_str_bits (rp, dp, dn, bits);
     }
@@ -3930,9 +4341,12 @@ mpz_set_str (mpz_t r, const char *sp, int base)
     {
       struct mpn_base_info info;
       mpn_get_base_info (&info, base);
-      alloc = (sn + info.exp - 1) / info.exp;
+      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);
@@ -3966,14 +4380,9 @@ mpz_out_str (FILE *stream, int base, const mpz_t x)
 static int
 gmp_detect_endian (void)
 {
-  static const int i = 1;
+  static const int i = 2;
   const unsigned char *p = (const unsigned char *) &i;
-  if (*p == 1)
-    /* Little endian */
-    return -1;
-  else
-    /* Big endian */
-    return 1;
+  return 1 - *p;
 }
 
 /* Import and export. Does not support nails. */
@@ -4036,29 +4445,22 @@ mpz_import (mpz_t r, size_t count, int order, size_t size, int endian,
 	    }
 	}
     }
-  if (bytes > 0)
+  assert (i + (bytes > 0) == rn);
+  if (limb != 0)
     rp[i++] = limb;
-  assert (i == rn);
+  else
+    i = mpn_normalized_size (rp, i);
 
-  r->_mp_size = 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)
 {
-  unsigned char *p;
-  ptrdiff_t word_step;
-  size_t count, k;
+  size_t count;
   mp_size_t un;
 
-  /* 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;
-
   if (nails != 0)
     gmp_die ("mpz_import: Nails not supported.");
 
@@ -4066,62 +4468,90 @@ mpz_export (void *r, size_t *countp, int order, size_t size, int endian,
   assert (endian >= -1 && endian <= 1);
   assert (size > 0 || u->_mp_size == 0);
 
-  un = GMP_ABS (u->_mp_size);
-  if (un == 0)
-    {
-      if (countp)
-	*countp = 0;
-      return r;
-    }
+  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;
 
-  /* Count bytes in top limb. */
-  for (limb = u->_mp_d[un-1], k = 0; limb > 0; k++, limb >>= CHAR_BIT)
-    ;
+      un = GMP_ABS (un);
 
-  assert (k > 0);
+      /* Count bytes in top limb. */
+      limb = u->_mp_d[un-1];
+      assert (limb != 0);
 
-  count = (k + (un-1) * sizeof (mp_limb_t) + size - 1) / size;
+      k = (GMP_LIMB_BITS <= CHAR_BIT);
+      if (!k)
+	{
+	  do {
+	    int LOCAL_CHAR_BIT = CHAR_BIT;
+	    k++; limb >>= LOCAL_CHAR_BIT;
+	  } while (limb != 0);
+	}
+      /* else limb = 0; */
 
-  if (!r)
-    r = gmp_xalloc (count * size);
+      count = (k + (un-1) * sizeof (mp_limb_t) + size - 1) / size;
 
-  if (endian == 0)
-    endian = gmp_detect_endian ();
+      if (!r)
+	r = gmp_xalloc (count * size);
 
-  p = (unsigned char *) r;
+      if (endian == 0)
+	endian = gmp_detect_endian ();
 
-  word_step = (order != endian) ? 2 * size : 0;
+      p = (unsigned char *) r;
 
-  /* 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;
-    }
+      word_step = (order != endian) ? 2 * size : 0;
 
-  /* And at least significant byte of that word. */
-  if (endian == 1)
-    p += (size - 1);
+      /* 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;
+	}
 
-  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);
+      /* 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 (sizeof (mp_limb_t) == 1)
+		{
+		  if (i < un)
+		    *p = u->_mp_d[i++];
+		  else
+		    *p = 0;
+		}
+	      else
+		{
+		  int LOCAL_CHAR_BIT = CHAR_BIT;
+		  if (bytes == 0)
+		    {
+		      if (i < un)
+			limb = u->_mp_d[i++];
+		      bytes = sizeof (mp_limb_t);
+		    }
+		  *p = limb;
+		  limb >>= LOCAL_CHAR_BIT;
+		  bytes--;
+		}
+	    }
+	}
+      assert (i == un);
+      assert (k == count);
+    }
 
   if (countp)
     *countp = count;
diff --git a/lib/gmp/mini-gmp.h b/lib/gmp/mini-gmp.h
index 8c94ca2ed..45ec808c1 100644
--- a/lib/gmp/mini-gmp.h
+++ b/lib/gmp/mini-gmp.h
@@ -1,6 +1,6 @@
 /* mini-gmp, a minimalistic implementation of a GNU GMP subset.
 
-Copyright 2011, 2012, 2013 Free Software Foundation, Inc.
+Copyright 2011-2015, 2017, 2019 Free Software Foundation, Inc.
 
 This file is part of the GNU MP Library.
 
@@ -42,7 +42,11 @@ void mp_get_memory_functions (void *(**) (size_t),
 			      void *(**) (void *, size_t, size_t),
 			      void (**) (void *, size_t));
 
-typedef unsigned long mp_limb_t;
+#ifndef MINI_GMP_LIMB_TYPE
+#define MINI_GMP_LIMB_TYPE long
+#endif
+
+typedef unsigned MINI_GMP_LIMB_TYPE mp_limb_t;
 typedef long mp_size_t;
 typedef unsigned long mp_bitcnt_t;
 
@@ -64,10 +68,14 @@ 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);
@@ -84,10 +92,20 @@ 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)
 
@@ -124,6 +142,10 @@ 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);
@@ -147,6 +169,7 @@ 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);
@@ -176,6 +199,7 @@ 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);
@@ -186,8 +210,12 @@ 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);
@@ -211,6 +239,15 @@ 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);