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[PATCH] libgmp: new module
|
From: |
Paul Eggert |
|
Subject: |
[PATCH] libgmp: new module |
|
Date: |
Mon, 6 Jul 2020 19:03:33 -0700 |
The idea is to let programs simply include <gmp.h>, and
so long as they live within the mini-gmp subset they need
not worry about whether the GMP libraries are installed.
* MODULES.html.sh: Mention it.
* config/srclist.txt: Mention files copied from GMP source.
* config/srclistvars.sh (GMP): New var.
* lib/mini-gmp-gnulib.c, m4/libgmp.m4, modules/libgmp:
* modules/libgmp-tests, tests/test-libgmp.c: New files.
* lib/mini-gmp.c, lib/mini-gmp.h: New files, copied from GMP.
---
ChangeLog | 13 +
MODULES.html.sh | 9 +
config/srclist.txt | 3 +
config/srclistvars.sh | 1 +
lib/mini-gmp-gnulib.c | 37 +
lib/mini-gmp.c | 4615 +++++++++++++++++++++++++++++++++++++++++
lib/mini-gmp.h | 308 +++
m4/libgmp.m4 | 44 +
modules/libgmp | 42 +
modules/libgmp-tests | 12 +
tests/test-libgmp.c | 24 +
11 files changed, 5108 insertions(+)
create mode 100644 lib/mini-gmp-gnulib.c
create mode 100644 lib/mini-gmp.c
create mode 100644 lib/mini-gmp.h
create mode 100644 m4/libgmp.m4
create mode 100644 modules/libgmp
create mode 100644 modules/libgmp-tests
create mode 100644 tests/test-libgmp.c
diff --git a/ChangeLog b/ChangeLog
index 4f2cab222..a82bd45be 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,16 @@
+2020-07-06 Paul Eggert <eggert@cs.ucla.edu>
+
+ libgmp: new module
+ The idea is to let programs simply include <gmp.h>, and
+ so long as they live within the mini-gmp subset they need
+ not worry about whether the GMP libraries are installed.
+ * MODULES.html.sh: Mention it.
+ * config/srclist.txt: Mention files copied from GMP source.
+ * config/srclistvars.sh (GMP): New var.
+ * lib/mini-gmp-gnulib.c, m4/libgmp.m4, modules/libgmp:
+ * modules/libgmp-tests, tests/test-libgmp.c: New files.
+ * lib/mini-gmp.c, lib/mini-gmp.h: New files, copied from GMP.
+
2020-07-05 Bruno Haible <bruno@clisp.org>
mkancesdirs: Trim module dependencies.
diff --git a/MODULES.html.sh b/MODULES.html.sh
index dea543d73..43a6dba4a 100755
--- a/MODULES.html.sh
+++ b/MODULES.html.sh
@@ -2372,6 +2372,15 @@ func_all_modules ()
func_module limits-h
func_end_table
+ element="Support for GNU multiple precision arithmetic"
+ func_section_wrap gmp
+ func_wrap H2
+ func_echo "$element"
+
+ func_begin_table
+ func_module libgmp
+ func_end_table
+
element="Support for sharing code with the GNU C Library"
func_section_wrap glibc
func_wrap H2
diff --git a/config/srclist.txt b/config/srclist.txt
index 16a799cc6..1ff511be1 100644
--- a/config/srclist.txt
+++ b/config/srclist.txt
@@ -17,6 +17,9 @@ $TEXINFOTEX texinfo.tex build-aux
strip-trailing-space
# we generate INSTALL from this via a rule in doc/Makefile.
$AUTOCONF doc/install.texi doc
+$GMP mini-gmp/mini-gmp.c lib
+$GMP mini-gmp/mini-gmp.h lib
+
$GNUSTANDARDS maintain.texi doc strip-trailing-space
$GNUSTANDARDS standards.texi doc strip-trailing-space
$GNUSTANDARDS make-stds.texi doc
diff --git a/config/srclistvars.sh b/config/srclistvars.sh
index ce3163759..72cf05189 100755
--- a/config/srclistvars.sh
+++ b/config/srclistvars.sh
@@ -27,6 +27,7 @@ esac
# Default to sibling (of parent) directories.
: ${AUTOCONF=../autoconf}
: ${AUTOMAKE=../automake}
+: ${GMP=../gmp}
: ${GNUCONFIG=../config}
: ${GNULIBSRC=../gnulib}
: ${GNUORG=../gnuorg}
diff --git a/lib/mini-gmp-gnulib.c b/lib/mini-gmp-gnulib.c
new file mode 100644
index 000000000..5019be5d5
--- /dev/null
+++ b/lib/mini-gmp-gnulib.c
@@ -0,0 +1,37 @@
+/* Tailor mini-gmp.c for Gnulib-using applications.
+
+ Copyright 2018-2020 Free Software Foundation, Inc.
+
+ This program is free software: you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation; either version 3 of the License, or
+ (at your option) any later version.
+
+ This program 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 a copy of the GNU General Public License
+ along with this program. If not, see <https://www.gnu.org/licenses/>. */
+
+#include <config.h>
+
+#include <stddef.h>
+#include <stdio.h>
+
+#include "mini-gmp.h"
+
+/* Pacify GCC -Wsuggest-attribute=const, malloc, pure. */
+#if 4 < __GNUC__ + (6 <= __GNUC_MINOR__)
+# pragma GCC diagnostic ignored "-Wsuggest-attribute=const"
+# pragma GCC diagnostic ignored "-Wsuggest-attribute=malloc"
+# pragma GCC diagnostic ignored "-Wsuggest-attribute=pure"
+#endif
+
+/* Pacify GCC -Wunused-variable for variables used only in 'assert' calls. */
+#if defined NDEBUG && 4 < __GNUC__ + (6 <= __GNUC_MINOR__)
+# pragma GCC diagnostic ignored "-Wunused-variable"
+#endif
+
+#include "mini-gmp.c"
diff --git a/lib/mini-gmp.c b/lib/mini-gmp.c
new file mode 100644
index 000000000..a7b719098
--- /dev/null
+++ b/lib/mini-gmp.c
@@ -0,0 +1,4615 @@
+/* mini-gmp, a minimalistic implementation of a GNU GMP subset.
+
+ Contributed to the GNU project by Niels Möller
+
+Copyright 1991-1997, 1999-2020 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) ~ (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 = 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; \
+ } 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 { \
+ 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); \
+ \
+ __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 unused_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 unused_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_alloc(size) ((*gmp_allocate_func)((size)))
+#define gmp_free(p, size) ((*gmp_free_func) ((p), (size)))
+#define gmp_realloc(ptr, old_size, size) ((*gmp_reallocate_func)(ptr,
old_size, size))
+
+static mp_ptr
+gmp_alloc_limbs (mp_size_t size)
+{
+ return (mp_ptr) gmp_alloc (size * sizeof (mp_limb_t));
+}
+
+static mp_ptr
+gmp_realloc_limbs (mp_ptr old, mp_size_t old_size, mp_size_t size)
+{
+ assert (size > 0);
+ return (mp_ptr) gmp_realloc (old, old_size * sizeof (mp_limb_t), size *
sizeof (mp_limb_t));
+}
+
+static void
+gmp_free_limbs (mp_ptr old, mp_size_t size)
+{
+ gmp_free (old, 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, m;
+
+ {
+ mp_limb_t p, ql;
+ unsigned ul, uh, qh;
+
+ /* 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 ^ GMP_LIMB_MAX) / 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 >= (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;
+ 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;
+ mp_size_t tn = 0;
+
+ if (inv->shift > 0)
+ {
+ /* Shift, reusing qp area if possible. In-place shift if qp == np. */
+ tp = qp;
+ if (!tp)
+ {
+ tn = nn;
+ tp = gmp_alloc_limbs (tn);
+ }
+ 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 (tn)
+ gmp_free_limbs (tp, tn);
+
+ return r >> inv->shift;
+}
+
+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_MAX >> (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_alloc_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_limbs (tp, dn);
+}
+
+
+/* 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_MAX >> (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 = GMP_LIMB_MAX & 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_alloc_limbs (rn);
+}
+
+void
+mpz_clear (mpz_t r)
+{
+ if (r->_mp_alloc)
+ gmp_free_limbs (r->_mp_d, r->_mp_alloc);
+}
+
+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_realloc_limbs (r->_mp_d, r->_mp_alloc, size);
+ else
+ r->_mp_d = gmp_alloc_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) */
+ 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;
+ 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;
+ 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;
+}
+
+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)
+{
+ return mpz_cmp_si (u, LONG_MAX) <= 0 && mpz_cmp_si (u, LONG_MIN) >= 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
+mpz_fits_ulong_p (const mpz_t u)
+{
+ mp_size_t us = u->_mp_size;
+
+ return us >= 0 && mpn_absfits_ulong_p (u->_mp_d, us);
+}
+
+int
+mpz_fits_sint_p (const mpz_t u)
+{
+ return mpz_cmp_si (u, INT_MAX) <= 0 && mpz_cmp_si (u, INT_MIN) >= 0;
+}
+
+int
+mpz_fits_uint_p (const mpz_t u)
+{
+ return u->_mp_size >= 0 && mpz_cmpabs_ui (u, UINT_MAX) <= 0;
+}
+
+int
+mpz_fits_sshort_p (const mpz_t u)
+{
+ return mpz_cmp_si (u, SHRT_MAX) <= 0 && mpz_cmp_si (u, SHRT_MIN) >= 0;
+}
+
+int
+mpz_fits_ushort_p (const mpz_t u)
+{
+ return u->_mp_size >= 0 && mpz_cmpabs_ui (u, USHRT_MAX) <= 0;
+}
+
+long int
+mpz_get_si (const mpz_t u)
+{
+ unsigned long r = mpz_get_ui (u);
+ unsigned long c = -LONG_MAX - LONG_MIN;
+
+ if (u->_mp_size < 0)
+ /* This expression is necessary to properly handle -LONG_MIN */
+ return -(long) c - (long) ((r - c) & LONG_MAX);
+ else
+ 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];
+}
+
+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 = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1);
+ 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 = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1);
+
+ 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 = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1);
+ 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 (v >= 0)
+ return mpz_cmp_ui (u, v);
+ else if (usize >= 0)
+ return 1;
+ else
+ return - mpz_cmpabs_ui (u, GMP_NEG_CAST (unsigned long int, v));
+}
+
+int
+mpz_cmp_ui (const mpz_t u, unsigned long v)
+{
+ mp_size_t usize = u->_mp_size;
+
+ if (usize < 0)
+ return -1;
+ else
+ return mpz_cmpabs_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)
+{
+ mp_size_t un = GMP_ABS (u->_mp_size);
+
+ if (! mpn_absfits_ulong_p (u->_mp_d, un))
+ return 1;
+ else
+ {
+ unsigned long uu = mpz_get_ui (u);
+ return GMP_CMP(uu, 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 */
+
+
+void
+mpz_add_ui (mpz_t r, const mpz_t a, unsigned long 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)
+{
+ mpz_ui_sub (r, b, a);
+ mpz_neg (r, r);
+}
+
+void
+mpz_ui_sub (mpz_t r, unsigned long a, const mpz_t b)
+{
+ mpz_neg (r, b);
+ mpz_add_ui (r, r, 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, v);
+}
+
+void
+mpz_mul_ui (mpz_t r, const mpz_t u, unsigned long int v)
+{
+ mpz_t vv;
+ mpz_init_set_ui (vv, v);
+ mpz_mul (r, u, vv);
+ mpz_clear (vv);
+ return;
+}
+
+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_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 };
+
+/* 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)
+{
+ unsigned long ret;
+ mpz_t rr, dd;
+
+ 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)
+ mpz_swap (r, rr);
+ mpz_clear (rr);
+
+ return ret;
+}
+
+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)
+{
+ mpz_t t;
+ mpz_init_set_ui(t, v);
+ mpz_gcd (t, u, t);
+ if (v > 0)
+ v = mpz_get_ui (t);
+
+ if (g)
+ mpz_swap (t, g);
+
+ mpz_clear (t);
+
+ 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)
+ s->_mp_size = 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)
+ t->_mp_size = 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);
+ }
+ 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 */
+ 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_init_set_ui (b, blimb);
+ mpz_pow_ui (r, b, e);
+ mpz_clear (b);
+}
+
+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_alloc_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_limbs (tp, mn);
+
+ 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_init_set_ui (e, elimb);
+ mpz_powm (r, b, e, m);
+ mpz_clear (e);
+}
+
+/* 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 */
+
+/* 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;
+
+ for (;;)
+ {
+ a >>= c;
+ /* (2/b) = -1 if b = 3 or 5 mod 8 */
+ bit ^= c & (b ^ (b >> 1));
+ if (a < b)
+ {
+ if (a == 0)
+ return bit & 1 ? -1 : 1;
+ bit ^= a & b;
+ a = b - a;
+ b -= a;
+ }
+ else
+ {
+ a -= b;
+ assert (a != 0);
+ }
+
+ gmp_ctz(c, a);
+ ++c;
+ }
+}
+
+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 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 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 && (mp_limb_t) (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_add_ui (r, u, 1);
+ mpz_neg (r, r);
+}
+
+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. */
+ int LOCAL_SHIFT_BITS = 16;
+ for (c = 0; x > 0;)
+ {
+ unsigned w = x - ((x >> 1) & 0x5555);
+ w = ((w >> 2) & 0x3333) + (w & 0x3333);
+ 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
+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, tn;
+ 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_alloc_limbs (un);
+ mpn_copyi (tp, up, un);
+ mpn_div_qr_1_invert (&bi, base);
+
+ tn = un;
+ ndigits = 0;
+ do
+ {
+ ndigits++;
+ mpn_div_qr_1_preinv (tp, tp, tn, &bi);
+ tn -= (tp[tn-1] == 0);
+ }
+ while (tn > 0);
+
+ gmp_free_limbs (tp, un);
+ 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, osn;
+
+ 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)
+ {
+ osn = 1 + sn;
+ sp = (char *) gmp_alloc (osn);
+ }
+ else
+ osn = 0;
+ un = GMP_ABS (u->_mp_size);
+
+ if (un == 0)
+ {
+ sp[0] = '0';
+ sn = 1;
+ goto ret;
+ }
+
+ 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_alloc_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_limbs (tp, un);
+ }
+
+ for (; i < sn; i++)
+ sp[i] = digits[(unsigned char) sp[i]];
+
+ret:
+ sp[sn] = '\0';
+ if (osn && osn != sn + 1)
+ sp = gmp_realloc(sp, osn, sn + 1);
+ 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, sn;
+ 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;
+ }
+ sn = strlen(sp);
+ dp = (unsigned char *) gmp_alloc (sn);
+
+ 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, sn);
+ r->_mp_size = 0;
+ return -1;
+ }
+
+ dp[dn++] = digit;
+ }
+
+ if (!dn)
+ {
+ gmp_free (dp, sn);
+ 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, sn);
+
+ 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, n;
+
+ str = mpz_get_str (NULL, base, x);
+ len = strlen (str);
+ n = fwrite (str, 1, len, stream);
+ gmp_free (str, len + 1);
+ return n;
+}
+
+
+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 do 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 = (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; */
+
+ count = (k + (un-1) * sizeof (mp_limb_t) + size - 1) / size;
+
+ if (!r)
+ r = gmp_alloc (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 (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;
+
+ return r;
+}
diff --git a/lib/mini-gmp.h b/lib/mini-gmp.h
new file mode 100644
index 000000000..ef64823d4
--- /dev/null
+++ b/lib/mini-gmp.h
@@ -0,0 +1,308 @@
+/* mini-gmp, a minimalistic implementation of a GNU GMP subset.
+
+Copyright 2011-2015, 2017, 2019 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));
+
+#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;
+
+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);
+int mpz_fits_sint_p (const mpz_t);
+int mpz_fits_uint_p (const mpz_t);
+int mpz_fits_sshort_p (const mpz_t);
+int mpz_fits_ushort_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__ */
diff --git a/m4/libgmp.m4 b/m4/libgmp.m4
new file mode 100644
index 000000000..b569bb734
--- /dev/null
+++ b/m4/libgmp.m4
@@ -0,0 +1,44 @@
+# Configure the GMP library or a replacement.
+
+dnl Copyright 2020 Free Software Foundation, Inc.
+dnl This file is free software; the Free Software Foundation
+dnl gives unlimited permission to copy and/or distribute it,
+dnl with or without modifications, as long as this notice is preserved.
+
+AC_DEFUN([gl_LIBGMP],
+[
+ AC_ARG_WITH([libgmp],
+ [AS_HELP_STRING([--without-libgmp],
+ [do not use the GNU Multiple Precision (GMP) library;
+ this is the default on systems lacking libgmp.])])
+
+ AC_CHECK_HEADERS_ONCE([gmp.h])
+ GMP_H=gmp.h
+ LIB_GMP=
+
+ case $with_libgmp in
+ no) ;;
+ yes) GMP_H= LIB_GMP=-lgmp;;
+ *) if test "$ac_cv_header_gmp_h" = yes; then
+ gl_saved_LIBS=$LIBS
+ AC_SEARCH_LIBS([__gmpz_roinit_n], [gmp])
+ LIBS=$gl_saved_LIBS
+ case $ac_cv_search___gmpz_roinit_n in
+ 'none needed')
+ GMP_H=;;
+ -*)
+ GMP_H= LIB_GMP=$ac_cv_search___gmpz_roinit_n;;
+ esac
+ fi;;
+ esac
+
+ if test -z "$GMP_H"; then
+ AC_DEFINE([HAVE_GMP], 1,
+ [Define to 1 if you have the GMP library instead of just the
+ mini-gmp replacement.])
+ fi
+
+ AC_SUBST([LIB_GMP])
+ AC_SUBST([GMP_H])
+ AM_CONDITIONAL([GL_GENERATE_GMP_H], [test -n "$GMP_H"])
+])
diff --git a/modules/libgmp b/modules/libgmp
new file mode 100644
index 000000000..b68671768
--- /dev/null
+++ b/modules/libgmp
@@ -0,0 +1,42 @@
+Description:
+GNU Multiple Precision Arithmetic library, or its mini-gmp substitute
+
+Files:
+lib/mini-gmp-gnulib.c
+lib/mini-gmp.c
+lib/mini-gmp.h
+m4/libgmp.m4
+
+Depends-on:
+
+configure.ac:
+gl_LIBGMP
+if test -n "$GMP_H"; then
+ AC_LIBOBJ([mini-gmp-gnulib])
+fi
+
+Makefile.am:
+BUILT_SOURCES += $(GMP_H)
+
+# Build gmp.h as a wrapper for mini-gmp.h when using mini-gmp.
+if GL_GENERATE_GMP_H
+gmp.h: $(top_builddir)/config.status
+ echo '#include "mini-gmp.h"' >$@-t
+ mv $@-t $@
+else
+gmp.h: $(top_builddir)/config.status
+ rm -f $@
+endif
+MOSTLYCLEANFILES += gmp.h gmp.h-t
+
+Include:
+<gmp.h>
+
+Link:
+$(LIB_GMP)
+
+License:
+LGPLv3+ or GPLv2+
+
+Maintainer:
+all
diff --git a/modules/libgmp-tests b/modules/libgmp-tests
new file mode 100644
index 000000000..50a18016c
--- /dev/null
+++ b/modules/libgmp-tests
@@ -0,0 +1,12 @@
+Files:
+tests/macros.h
+tests/test-libgmp.c
+
+Depends-on:
+
+configure.ac:
+
+Makefile.am:
+TESTS += test-libgmp
+check_PROGRAMS += test-libgmp
+test_libgmp_LDADD = $(LDADD) @LIB_GMP@
diff --git a/tests/test-libgmp.c b/tests/test-libgmp.c
new file mode 100644
index 000000000..af8e4d77b
--- /dev/null
+++ b/tests/test-libgmp.c
@@ -0,0 +1,24 @@
+#include <config.h>
+
+#include <gmp.h>
+
+#include "macros.h"
+
+int
+main ()
+{
+ /* A simple sanity check that 2 + 2 = 4. */
+ static mp_limb_t const twobody[] = { 2 };
+ static mpz_t const two = MPZ_ROINIT_N ((mp_limb_t *) twobody, 1);
+ ASSERT (mpz_fits_slong_p (two));
+ ASSERT (mpz_get_si (two) == 2);
+
+ mpz_t four;
+ mpz_init (four);
+ mpz_add (four, two, two);
+ ASSERT (mpz_fits_slong_p (four));
+ ASSERT (mpz_get_si (four) == 4);
+ mpz_clear (four);
+
+ return 0;
+}
--
2.25.4
- [PATCH] libgmp: new module,
Paul Eggert <=
- Re: [PATCH] libgmp: new module, Bruno Haible, 2020/07/12
- libgmp tests: Add some safety checks, Bruno Haible, 2020/07/12
- libgmp: link to the correct shared library, Bruno Haible, 2020/07/12
- Re: libgmp: link to the correct shared library, Paul Eggert, 2020/07/23
- Re: libgmp: link to the correct shared library, Bruno Haible, 2020/07/23
- Re: libgmp: link to the correct shared library, Paul Eggert, 2020/07/23
- Re: libgmp: link to the correct shared library, Bruno Haible, 2020/07/23
- Re: libgmp: link to the correct shared library, Paul Eggert, 2020/07/26
- Re: libgmp: link to the correct shared library, Paul Eggert, 2020/07/26
libgmp: Avoid warning when --without-libgmp is used, Bruno Haible, 2020/07/12