-From da4e4f5db6561923ad239aa653660250aaeb5873 Mon Sep 17 00:00:00 2001
-From: Steven Barth <cyrus@openwrt.org>
-Date: Mon, 6 Oct 2014 07:26:13 +0200
-Subject: [PATCH 2/2] build: allow building with mini-gmp instead of gmp
-
-This introduces --without-libgmp which includes mini-gmp into nft
-(adding ~30k) but avoids linking libgmp which is >400k.
-
-This is useful for embedded distributions not using gmp otherwise.
-
-Note: currently --without-libgmp must be used with --disable-debug.
-
-Signed-off-by: Steven Barth <cyrus@openwrt.org>
----
- configure.ac | 14 +-
- include/bignum.h | 17 +
- include/expression.h | 2 +-
- include/gmputil.h | 2 +-
- include/mini-gmp.h | 294 ++++
- include/utils.h | 4 +-
- src/Makefile.in | 5 +
- src/datatype.c | 4 +-
- src/erec.c | 4 +-
- src/evaluate.c | 8 +-
- src/gmputil.c | 1 -
- src/mini-gmp-printf.c | 62 +
- src/mini-gmp.c | 4386 +++++++++++++++++++++++++++++++++++++++++++++++++
- 13 files changed, 4790 insertions(+), 13 deletions(-)
- create mode 100644 include/bignum.h
- create mode 100644 include/mini-gmp.h
- create mode 100644 src/mini-gmp-printf.c
- create mode 100644 src/mini-gmp.c
-
---- a/configure.ac
-+++ b/configure.ac
-@@ -72,8 +72,19 @@ AM_CONDITIONAL([BUILD_PDF], [test "$DBLA
- PKG_CHECK_MODULES([LIBMNL], [libmnl >= 1.0.3])
- PKG_CHECK_MODULES([LIBNFTNL], [libnftnl >= 1.0.2])
-
--AC_CHECK_LIB([gmp], [__gmpz_init], ,
-- AC_MSG_ERROR([No suitable version of libgmp found]))
-+AC_ARG_WITH([libgmp], [AS_HELP_STRING([--without-libgmp],
-+ [Disable libgmp support (use builtin mini-gmp)])], [],
-+ [with_libgmp=yes])
-+AS_IF([test "x$with_libgmp" != xno], [
-+AC_CHECK_LIB([gmp],[__gmpz_init], , AC_MSG_ERROR([No suitable version of libgmp found]))
-+AC_DEFINE([HAVE_LIBGMP], [1], [])
-+])
-+AM_CONDITIONAL([BUILD_MINIGMP], [test "x$with_libgmp" == xno])
-+
-+
-+AS_IF([test "x$with_libgmp" != xyes -a "x$CONFIG_DEBUG" = xy], [
-+AC_MSG_ERROR([--without-libgmp MUST be used with --disable-debug])
-+])
-
- AC_ARG_WITH([cli], [AS_HELP_STRING([--without-cli],
- [disable interactive CLI (libreadline support)])],
---- /dev/null
-+++ b/include/bignum.h
-@@ -0,0 +1,17 @@
-+#ifndef NFTABLES_BIGNUM_H
-+#define NFTABLES_BIGNUM_H
-+
-+#ifdef HAVE_LIBGMP
-+#include <gmp.h>
-+
-+#else
-+
-+#include <mini-gmp.h>
-+#include <stdio.h>
-+#include <stdarg.h>
-+
-+int gmp_printf(const char *format, const mpz_t value);
-+
-+#endif
-+
-+#endif /* NFTABLES_BIGNUM_H */
---- a/include/expression.h
-+++ b/include/expression.h
-@@ -2,7 +2,7 @@
- #define NFTABLES_EXPRESSION_H
-
- #include <stdbool.h>
--#include <gmp.h>
-+#include <bignum.h>
- #include <linux/netfilter/nf_tables.h>
-
- #include <nftables.h>
---- a/include/gmputil.h
-+++ b/include/gmputil.h
-@@ -1,7 +1,7 @@
- #ifndef NFTABLES_GMPUTIL_H
- #define NFTABLES_GMPUTIL_H
-
--#include <gmp.h>
-+#include <bignum.h>
- #include <asm/byteorder.h>
-
- enum mpz_word_order {
---- /dev/null
-+++ b/include/mini-gmp.h
-@@ -0,0 +1,294 @@
-+/* mini-gmp, a minimalistic implementation of a GNU GMP subset.
-+
-+Copyright 2011-2014 Free Software Foundation, Inc.
-+
-+This file is part of the GNU MP Library.
-+
-+The GNU MP Library is free software; you can redistribute it and/or modify
-+it under the terms of either:
-+
-+ * the GNU Lesser General Public License as published by the Free
-+ Software Foundation; either version 3 of the License, or (at your
-+ option) any later version.
-+
-+or
-+
-+ * the GNU General Public License as published by the Free Software
-+ Foundation; either version 2 of the License, or (at your option) any
-+ later version.
-+
-+or both in parallel, as here.
-+
-+The GNU MP Library is distributed in the hope that it will be useful, but
-+WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-+or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
-+for more details.
-+
-+You should have received copies of the GNU General Public License and the
-+GNU Lesser General Public License along with the GNU MP Library. If not,
-+see https://www.gnu.org/licenses/. */
-+
-+/* About mini-gmp: This is a minimal implementation of a subset of the
-+ GMP interface. It is intended for inclusion into applications which
-+ have modest bignums needs, as a fallback when the real GMP library
-+ is not installed.
-+
-+ This file defines the public interface. */
-+
-+#ifndef __MINI_GMP_H__
-+#define __MINI_GMP_H__
-+
-+/* For size_t */
-+#include <stddef.h>
-+
-+#if defined (__cplusplus)
-+extern "C" {
-+#endif
-+
-+void mp_set_memory_functions (void *(*) (size_t),
-+ void *(*) (void *, size_t, size_t),
-+ void (*) (void *, size_t));
-+
-+void mp_get_memory_functions (void *(**) (size_t),
-+ void *(**) (void *, size_t, size_t),
-+ void (**) (void *, size_t));
-+
-+typedef unsigned long mp_limb_t;
-+typedef long mp_size_t;
-+typedef unsigned long mp_bitcnt_t;
-+
-+typedef mp_limb_t *mp_ptr;
-+typedef const mp_limb_t *mp_srcptr;
-+
-+typedef struct
-+{
-+ int _mp_alloc; /* Number of *limbs* allocated and pointed
-+ to by the _mp_d field. */
-+ int _mp_size; /* abs(_mp_size) is the number of limbs the
-+ last field points to. If _mp_size is
-+ negative this is a negative number. */
-+ mp_limb_t *_mp_d; /* Pointer to the limbs. */
-+} __mpz_struct;
-+
-+typedef __mpz_struct mpz_t[1];
-+
-+typedef __mpz_struct *mpz_ptr;
-+typedef const __mpz_struct *mpz_srcptr;
-+
-+extern const int mp_bits_per_limb;
-+
-+void mpn_copyi (mp_ptr, mp_srcptr, mp_size_t);
-+void mpn_copyd (mp_ptr, mp_srcptr, mp_size_t);
-+void mpn_zero (mp_ptr, mp_size_t);
-+
-+int mpn_cmp (mp_srcptr, mp_srcptr, mp_size_t);
-+
-+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);
-+
-+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_bin_uiui (mpz_t, unsigned long, unsigned long);
-+
-+int mpz_probab_prime_p (const mpz_t, int);
-+
-+int mpz_tstbit (const mpz_t, mp_bitcnt_t);
-+void mpz_setbit (mpz_t, mp_bitcnt_t);
-+void mpz_clrbit (mpz_t, mp_bitcnt_t);
-+void mpz_combit (mpz_t, mp_bitcnt_t);
-+
-+void mpz_com (mpz_t, const mpz_t);
-+void mpz_and (mpz_t, const mpz_t, const mpz_t);
-+void mpz_ior (mpz_t, const mpz_t, const mpz_t);
-+void mpz_xor (mpz_t, const mpz_t, const mpz_t);
-+
-+mp_bitcnt_t mpz_popcount (const mpz_t);
-+mp_bitcnt_t mpz_hamdist (const mpz_t, const mpz_t);
-+mp_bitcnt_t mpz_scan0 (const mpz_t, mp_bitcnt_t);
-+mp_bitcnt_t mpz_scan1 (const mpz_t, mp_bitcnt_t);
-+
-+int mpz_fits_slong_p (const mpz_t);
-+int mpz_fits_ulong_p (const mpz_t);
-+long int mpz_get_si (const mpz_t);
-+unsigned long int mpz_get_ui (const mpz_t);
-+double mpz_get_d (const mpz_t);
-+size_t mpz_size (const mpz_t);
-+mp_limb_t mpz_getlimbn (const mpz_t, mp_size_t);
-+
-+void mpz_realloc2 (mpz_t, mp_bitcnt_t);
-+mp_srcptr mpz_limbs_read (mpz_srcptr);
-+mp_ptr mpz_limbs_modify (mpz_t, mp_size_t);
-+mp_ptr mpz_limbs_write (mpz_t, mp_size_t);
-+void mpz_limbs_finish (mpz_t, mp_size_t);
-+mpz_srcptr mpz_roinit_n (mpz_t, mp_srcptr, mp_size_t);
-+
-+#define MPZ_ROINIT_N(xp, xs) {{0, (xs),(xp) }}
-+
-+void mpz_set_si (mpz_t, signed long int);
-+void mpz_set_ui (mpz_t, unsigned long int);
-+void mpz_set (mpz_t, const mpz_t);
-+void mpz_set_d (mpz_t, double);
-+
-+void mpz_init_set_si (mpz_t, signed long int);
-+void mpz_init_set_ui (mpz_t, unsigned long int);
-+void mpz_init_set (mpz_t, const mpz_t);
-+void mpz_init_set_d (mpz_t, double);
-+
-+size_t mpz_sizeinbase (const mpz_t, int);
-+char *mpz_get_str (char *, int, const mpz_t);
-+int mpz_set_str (mpz_t, const char *, int);
-+int mpz_init_set_str (mpz_t, const char *, int);
-+
-+/* This long list taken from gmp.h. */
-+/* For reference, "defined(EOF)" cannot be used here. In g++ 2.95.4,
-+ <iostream> defines EOF but not FILE. */
-+#if defined (FILE) \
-+ || defined (H_STDIO) \
-+ || defined (_H_STDIO) /* AIX */ \
-+ || defined (_STDIO_H) /* glibc, Sun, SCO */ \
-+ || defined (_STDIO_H_) /* BSD, OSF */ \
-+ || defined (__STDIO_H) /* Borland */ \
-+ || defined (__STDIO_H__) /* IRIX */ \
-+ || defined (_STDIO_INCLUDED) /* HPUX */ \
-+ || defined (__dj_include_stdio_h_) /* DJGPP */ \
-+ || defined (_FILE_DEFINED) /* Microsoft */ \
-+ || defined (__STDIO__) /* Apple MPW MrC */ \
-+ || defined (_MSL_STDIO_H) /* Metrowerks */ \
-+ || defined (_STDIO_H_INCLUDED) /* QNX4 */ \
-+ || defined (_ISO_STDIO_ISO_H) /* Sun C++ */ \
-+ || defined (__STDIO_LOADED) /* VMS */
-+size_t mpz_out_str (FILE *, int, const mpz_t);
-+#endif
-+
-+void mpz_import (mpz_t, size_t, int, size_t, int, size_t, const void *);
-+void *mpz_export (void *, size_t *, int, size_t, int, size_t, const mpz_t);
-+
-+#if defined (__cplusplus)
-+}
-+#endif
-+#endif /* __MINI_GMP_H__ */
---- a/include/utils.h
-+++ b/include/utils.h
-@@ -9,14 +9,14 @@
- #include <unistd.h>
- #include <assert.h>
- #include <list.h>
--#include <gmp.h>
-+#include <bignum.h>
-
- #define BITS_PER_BYTE 8
-
- #ifdef DEBUG
- #define pr_debug(fmt, arg...) gmp_printf(fmt, ##arg)
- #else
--#define pr_debug(fmt, arg...) ({ if (false) gmp_printf(fmt, ##arg); 0; })
-+#define pr_debug(fmt, arg...)
- #endif
-
- #define __fmtstring(x, y) __attribute__((format(printf, x, y)))
---- a/src/datatype.c
-+++ b/src/datatype.c
-@@ -275,11 +275,9 @@ static struct error_record *integer_type
- struct expr **res)
- {
- mpz_t v;
-- int len;
-
- mpz_init(v);
-- if (gmp_sscanf(sym->identifier, "%Zu%n", v, &len) != 1 ||
-- (int)strlen(sym->identifier) != len) {
-+ if (mpz_set_str(v, sym->identifier, 0)) {
- mpz_clear(v);
- return error(&sym->location, "Could not parse %s",
- sym->dtype->desc);
---- a/src/erec.c
-+++ b/src/erec.c
-@@ -44,6 +44,7 @@ static void erec_destroy(struct error_re
- xfree(erec);
- }
-
-+__attribute__((format(printf, 3, 0)))
- struct error_record *erec_vcreate(enum error_record_types type,
- const struct location *loc,
- const char *fmt, va_list ap)
-@@ -55,10 +56,11 @@ struct error_record *erec_vcreate(enum e
- erec->num_locations = 0;
- erec_add_location(erec, loc);
-
-- gmp_vasprintf(&erec->msg, fmt, ap);
-+ if (vasprintf(&erec->msg, fmt, ap)) {}
- return erec;
- }
-
-+__attribute__((format(printf, 3, 4)))
- struct error_record *erec_create(enum error_record_types type,
- const struct location *loc,
- const char *fmt, ...)
---- a/src/evaluate.c
-+++ b/src/evaluate.c
-@@ -232,9 +232,13 @@ static int expr_evaluate_value(struct ev
- case TYPE_INTEGER:
- mpz_init_bitmask(mask, ctx->ectx.len);
- if (mpz_cmp((*expr)->value, mask) > 0) {
-+ char *valstr = mpz_get_str(NULL, 10, (*expr)->value);
-+ char *rangestr = mpz_get_str(NULL, 10, mask);
- expr_error(ctx->msgs, *expr,
-- "Value %Zu exceeds valid range 0-%Zu",
-- (*expr)->value, mask);
-+ "Value %s exceeds valid range 0-%s",
-+ valstr, rangestr);
-+ free(valstr);
-+ free(rangestr);
- mpz_clear(mask);
- return -1;
- }
---- a/src/gmputil.c
-+++ b/src/gmputil.c
-@@ -14,7 +14,6 @@
- #include <stdio.h>
- #include <unistd.h>
- #include <string.h>
--#include <gmp.h>
-
- #include <nftables.h>
- #include <datatype.h>
---- /dev/null
-+++ b/src/mini-gmp-printf.c
-@@ -0,0 +1,63 @@
-+#include <stdarg.h>
-+#include <stdbool.h>
-+#include <stdio.h>
-+#include <stdlib.h>
-+#include <bignum.h>
-+
-+// nftables mostly uses gmp_printf as below so we build a minimalistic
-+// version to avoid the awkwardness of wrapping printf.
-+// This requires rewriting other occurences of gmp_printf or
-+// variants which are rare (only 1 so far).
-+// Also we exclude pr_debug here since this is a rathole
-+// and if debugging is desired then libgmp can be used.
-+
-+int gmp_printf(const char *f, const mpz_t value)
-+{
-+ int n = 0;
-+ while (*f) {
-+ if (*f != '%') {
-+ if (fputc(*f, stdout) != *f)
-+ return -1;
-+
-+ ++n;
-+ } else {
-+ unsigned long prec = 0;
-+ int base;
-+ size_t len;
-+ char *str;
-+ bool ok;
-+
-+ if (*++f == '.')
-+ prec = strtoul(++f, (char**)&f, 10);
-+
-+ if (*f++ != 'Z')
-+ return -1;
-+
-+ if (*f == 'u')
-+ base = 10;
-+ else if (*f == 'x')
-+ base = 16;
-+ else
-+ return -1;
-+
-+ len = mpz_sizeinbase(value, base);
-+ while (prec-- > len) {
-+ if (fputc('0', stdout) != '0')
-+ return -1;
-+
-+ ++n;
-+ }
-+
-+ str = mpz_get_str(NULL, base, value);
-+ ok = str && fwrite(str, 1, len, stdout) == len;
-+ free(str);
-+
-+ if (!ok)
-+ return -1;
-+
-+ n += len;
-+ }
-+ ++f;
-+ }
-+ return n;
-+}
---- /dev/null
-+++ b/src/mini-gmp.c
-@@ -0,0 +1,4386 @@
-+/* mini-gmp, a minimalistic implementation of a GNU GMP subset.
-+
-+ Contributed to the GNU project by Niels Möller
-+
-+Copyright 1991-1997, 1999-2014 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"
-+
-+\f
-+/* Macros */
-+#define GMP_LIMB_BITS (sizeof(mp_limb_t) * CHAR_BIT)
-+
-+#define GMP_LIMB_MAX (~ (mp_limb_t) 0)
-+#define GMP_LIMB_HIGHBIT ((mp_limb_t) 1 << (GMP_LIMB_BITS - 1))
-+
-+#define GMP_HLIMB_BIT ((mp_limb_t) 1 << (GMP_LIMB_BITS / 2))
-+#define GMP_LLIMB_MASK (GMP_HLIMB_BIT - 1)
-+
-+#define GMP_ULONG_BITS (sizeof(unsigned long) * CHAR_BIT)
-+#define GMP_ULONG_HIGHBIT ((unsigned long) 1 << (GMP_ULONG_BITS - 1))
-+
-+#define GMP_ABS(x) ((x) >= 0 ? (x) : -(x))
-+#define GMP_NEG_CAST(T,x) (-((T)((x) + 1) - 1))
-+
-+#define GMP_MIN(a, b) ((a) < (b) ? (a) : (b))
-+#define GMP_MAX(a, b) ((a) > (b) ? (a) : (b))
-+
-+#define gmp_assert_nocarry(x) do { \
-+ mp_limb_t __cy = x; \
-+ assert (__cy == 0); \
-+ } while (0)
-+
-+#define gmp_clz(count, x) do { \
-+ mp_limb_t __clz_x = (x); \
-+ unsigned __clz_c; \
-+ for (__clz_c = 0; \
-+ (__clz_x & ((mp_limb_t) 0xff << (GMP_LIMB_BITS - 8))) == 0; \
-+ __clz_c += 8) \
-+ __clz_x <<= 8; \
-+ for (; (__clz_x & GMP_LIMB_HIGHBIT) == 0; __clz_c++) \
-+ __clz_x <<= 1; \
-+ (count) = __clz_c; \
-+ } while (0)
-+
-+#define gmp_ctz(count, x) do { \
-+ mp_limb_t __ctz_x = (x); \
-+ unsigned __ctz_c = 0; \
-+ gmp_clz (__ctz_c, __ctz_x & - __ctz_x); \
-+ (count) = GMP_LIMB_BITS - 1 - __ctz_c; \
-+ } while (0)
-+
-+#define gmp_add_ssaaaa(sh, sl, ah, al, bh, bl) \
-+ do { \
-+ mp_limb_t __x; \
-+ __x = (al) + (bl); \
-+ (sh) = (ah) + (bh) + (__x < (al)); \
-+ (sl) = __x; \
-+ } while (0)
-+
-+#define gmp_sub_ddmmss(sh, sl, ah, al, bh, bl) \
-+ do { \
-+ mp_limb_t __x; \
-+ __x = (al) - (bl); \
-+ (sh) = (ah) - (bh) - ((al) < (bl)); \
-+ (sl) = __x; \
-+ } while (0)
-+
-+#define gmp_umul_ppmm(w1, w0, u, v) \
-+ do { \
-+ mp_limb_t __x0, __x1, __x2, __x3; \
-+ unsigned __ul, __vl, __uh, __vh; \
-+ mp_limb_t __u = (u), __v = (v); \
-+ \
-+ __ul = __u & GMP_LLIMB_MASK; \
-+ __uh = __u >> (GMP_LIMB_BITS / 2); \
-+ __vl = __v & GMP_LLIMB_MASK; \
-+ __vh = __v >> (GMP_LIMB_BITS / 2); \
-+ \
-+ __x0 = (mp_limb_t) __ul * __vl; \
-+ __x1 = (mp_limb_t) __ul * __vh; \
-+ __x2 = (mp_limb_t) __uh * __vl; \
-+ __x3 = (mp_limb_t) __uh * __vh; \
-+ \
-+ __x1 += __x0 >> (GMP_LIMB_BITS / 2);/* this can't give carry */ \
-+ __x1 += __x2; /* but this indeed can */ \
-+ if (__x1 < __x2) /* did we get it? */ \
-+ __x3 += GMP_HLIMB_BIT; /* yes, add it in the proper pos. */ \
-+ \
-+ (w1) = __x3 + (__x1 >> (GMP_LIMB_BITS / 2)); \
-+ (w0) = (__x1 << (GMP_LIMB_BITS / 2)) + (__x0 & GMP_LLIMB_MASK); \
-+ } while (0)
-+
-+#define gmp_udiv_qrnnd_preinv(q, r, nh, nl, d, di) \
-+ do { \
-+ mp_limb_t _qh, _ql, _r, _mask; \
-+ gmp_umul_ppmm (_qh, _ql, (nh), (di)); \
-+ gmp_add_ssaaaa (_qh, _ql, _qh, _ql, (nh) + 1, (nl)); \
-+ _r = (nl) - _qh * (d); \
-+ _mask = -(mp_limb_t) (_r > _ql); /* both > and >= are OK */ \
-+ _qh += _mask; \
-+ _r += _mask & (d); \
-+ if (_r >= (d)) \
-+ { \
-+ _r -= (d); \
-+ _qh++; \
-+ } \
-+ \
-+ (r) = _r; \
-+ (q) = _qh; \
-+ } while (0)
-+
-+#define gmp_udiv_qr_3by2(q, r1, r0, n2, n1, n0, d1, d0, dinv) \
-+ do { \
-+ mp_limb_t _q0, _t1, _t0, _mask; \
-+ gmp_umul_ppmm ((q), _q0, (n2), (dinv)); \
-+ gmp_add_ssaaaa ((q), _q0, (q), _q0, (n2), (n1)); \
-+ \
-+ /* Compute the two most significant limbs of n - q'd */ \
-+ (r1) = (n1) - (d1) * (q); \
-+ gmp_sub_ddmmss ((r1), (r0), (r1), (n0), (d1), (d0)); \
-+ gmp_umul_ppmm (_t1, _t0, (d0), (q)); \
-+ gmp_sub_ddmmss ((r1), (r0), (r1), (r0), _t1, _t0); \
-+ (q)++; \
-+ \
-+ /* Conditionally adjust q and the remainders */ \
-+ _mask = - (mp_limb_t) ((r1) >= _q0); \
-+ (q) += _mask; \
-+ gmp_add_ssaaaa ((r1), (r0), (r1), (r0), _mask & (d1), _mask & (d0)); \
-+ if ((r1) >= (d1)) \
-+ { \
-+ if ((r1) > (d1) || (r0) >= (d0)) \
-+ { \
-+ (q)++; \
-+ gmp_sub_ddmmss ((r1), (r0), (r1), (r0), (d1), (d0)); \
-+ } \
-+ } \
-+ } while (0)
-+
-+/* Swap macros. */
-+#define MP_LIMB_T_SWAP(x, y) \
-+ do { \
-+ mp_limb_t __mp_limb_t_swap__tmp = (x); \
-+ (x) = (y); \
-+ (y) = __mp_limb_t_swap__tmp; \
-+ } while (0)
-+#define MP_SIZE_T_SWAP(x, y) \
-+ do { \
-+ mp_size_t __mp_size_t_swap__tmp = (x); \
-+ (x) = (y); \
-+ (y) = __mp_size_t_swap__tmp; \
-+ } while (0)
-+#define MP_BITCNT_T_SWAP(x,y) \
-+ do { \
-+ mp_bitcnt_t __mp_bitcnt_t_swap__tmp = (x); \
-+ (x) = (y); \
-+ (y) = __mp_bitcnt_t_swap__tmp; \
-+ } while (0)
-+#define MP_PTR_SWAP(x, y) \
-+ do { \
-+ mp_ptr __mp_ptr_swap__tmp = (x); \
-+ (x) = (y); \
-+ (y) = __mp_ptr_swap__tmp; \
-+ } while (0)
-+#define MP_SRCPTR_SWAP(x, y) \
-+ do { \
-+ mp_srcptr __mp_srcptr_swap__tmp = (x); \
-+ (x) = (y); \
-+ (y) = __mp_srcptr_swap__tmp; \
-+ } while (0)
-+
-+#define MPN_PTR_SWAP(xp,xs, yp,ys) \
-+ do { \
-+ MP_PTR_SWAP (xp, yp); \
-+ MP_SIZE_T_SWAP (xs, ys); \
-+ } while(0)
-+#define MPN_SRCPTR_SWAP(xp,xs, yp,ys) \
-+ do { \
-+ MP_SRCPTR_SWAP (xp, yp); \
-+ MP_SIZE_T_SWAP (xs, ys); \
-+ } while(0)
-+
-+#define MPZ_PTR_SWAP(x, y) \
-+ do { \
-+ mpz_ptr __mpz_ptr_swap__tmp = (x); \
-+ (x) = (y); \
-+ (y) = __mpz_ptr_swap__tmp; \
-+ } while (0)
-+#define MPZ_SRCPTR_SWAP(x, y) \
-+ do { \
-+ mpz_srcptr __mpz_srcptr_swap__tmp = (x); \
-+ (x) = (y); \
-+ (y) = __mpz_srcptr_swap__tmp; \
-+ } while (0)
-+
-+const int mp_bits_per_limb = GMP_LIMB_BITS;
-+
-+\f
-+/* Memory allocation and other helper functions. */
-+static void
-+gmp_die (const char *msg)
-+{
-+ fprintf (stderr, "%s\n", msg);
-+ abort();
-+}
-+
-+static void *
-+gmp_default_alloc (size_t size)
-+{
-+ void *p;
-+
-+ assert (size > 0);
-+
-+ p = malloc (size);
-+ if (!p)
-+ gmp_die("gmp_default_alloc: Virtual memory exhausted.");
-+
-+ return p;
-+}
-+
-+static void *
-+gmp_default_realloc (void *old, size_t old_size, size_t new_size)
-+{
-+ mp_ptr p;
-+
-+ p = realloc (old, new_size);
-+
-+ if (!p)
-+ gmp_die("gmp_default_realoc: Virtual memory exhausted.");
-+
-+ return p;
-+}
-+
-+static void
-+gmp_default_free (void *p, size_t size)
-+{
-+ free (p);
-+}
-+
-+static void * (*gmp_allocate_func) (size_t) = gmp_default_alloc;
-+static void * (*gmp_reallocate_func) (void *, size_t, size_t) = gmp_default_realloc;
-+static void (*gmp_free_func) (void *, size_t) = gmp_default_free;
-+
-+void
-+mp_get_memory_functions (void *(**alloc_func) (size_t),
-+ void *(**realloc_func) (void *, size_t, size_t),
-+ void (**free_func) (void *, size_t))
-+{
-+ if (alloc_func)
-+ *alloc_func = gmp_allocate_func;
-+
-+ if (realloc_func)
-+ *realloc_func = gmp_reallocate_func;
-+
-+ if (free_func)
-+ *free_func = gmp_free_func;
-+}
-+
-+void
-+mp_set_memory_functions (void *(*alloc_func) (size_t),
-+ void *(*realloc_func) (void *, size_t, size_t),
-+ void (*free_func) (void *, size_t))
-+{
-+ if (!alloc_func)
-+ alloc_func = gmp_default_alloc;
-+ if (!realloc_func)
-+ realloc_func = gmp_default_realloc;
-+ if (!free_func)
-+ free_func = gmp_default_free;
-+
-+ gmp_allocate_func = alloc_func;
-+ gmp_reallocate_func = realloc_func;
-+ gmp_free_func = free_func;
-+}
-+
-+#define gmp_xalloc(size) ((*gmp_allocate_func)((size)))
-+#define gmp_free(p) ((*gmp_free_func) ((p), 0))
-+
-+static mp_ptr
-+gmp_xalloc_limbs (mp_size_t size)
-+{
-+ return gmp_xalloc (size * sizeof (mp_limb_t));
-+}
-+
-+static mp_ptr
-+gmp_xrealloc_limbs (mp_ptr old, mp_size_t size)
-+{
-+ assert (size > 0);
-+ return (*gmp_reallocate_func) (old, 0, size * sizeof (mp_limb_t));
-+}
-+
-+\f
-+/* 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)
-+{
-+ for (; n > 0 && xp[n-1] == 0; n--)
-+ ;
-+ return n;
-+}
-+
-+#define mpn_zero_p(xp, n) (mpn_normalized_size ((xp), (n)) == 0)
-+
-+void
-+mpn_zero (mp_ptr rp, mp_size_t n)
-+{
-+ mp_size_t i;
-+
-+ for (i = 0; i < n; i++)
-+ rp[i] = 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);
-+
-+ /* We first multiply by the low order limb. This result can be
-+ stored, not added, to rp. We also avoid a loop for zeroing this
-+ way. */
-+
-+ rp[un] = mpn_mul_1 (rp, up, un, vp[0]);
-+ rp += 1, vp += 1, vn -= 1;
-+
-+ /* Now accumulate the product of up[] and the next higher limb from
-+ vp[]. */
-+
-+ while (vn >= 1)
-+ {
-+ rp[un] = mpn_addmul_1 (rp, up, un, vp[0]);
-+ rp += 1, vp += 1, vn -= 1;
-+ }
-+ return rp[un - 1];
-+}
-+
-+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_size_t i;
-+ 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);
-+
-+ for (i = n; --i != 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_size_t i;
-+ 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;
-+
-+ for (i = n; --i != 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);
-+}
-+
-+\f
-+/* MPN division interface. */
-+mp_limb_t
-+mpn_invert_3by2 (mp_limb_t u1, mp_limb_t u0)
-+{
-+ mp_limb_t r, p, m;
-+ unsigned ul, uh;
-+ unsigned ql, qh;
-+
-+ /* First, do a 2/1 inverse. */
-+ /* The inverse m is defined as floor( (B^2 - 1 - u1)/u1 ), so that 0 <
-+ * B^2 - (B + m) u1 <= u1 */
-+ assert (u1 >= GMP_LIMB_HIGHBIT);
-+
-+ ul = u1 & GMP_LLIMB_MASK;
-+ uh = u1 >> (GMP_LIMB_BITS / 2);
-+
-+ qh = ~u1 / uh;
-+ r = ((~u1 - (mp_limb_t) qh * uh) << (GMP_LIMB_BITS / 2)) | GMP_LLIMB_MASK;
-+
-+ 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;
-+
-+ /* Do a 3/2 division (with half limb size) */
-+ p = (r >> (GMP_LIMB_BITS / 2)) * qh + r;
-+ ql = (p >> (GMP_LIMB_BITS / 2)) + 1;
-+
-+ /* By the 3/2 method, we don't need the high half limb. */
-+ r = (r << (GMP_LIMB_BITS / 2)) + GMP_LLIMB_MASK - ql * u1;
-+
-+ if (r >= (p << (GMP_LIMB_BITS / 2)))
-+ {
-+ ql--;
-+ r += u1;
-+ }
-+ m = ((mp_limb_t) qh << (GMP_LIMB_BITS / 2)) + ql;
-+ if (r >= u1)
-+ {
-+ m++;
-+ r -= u1;
-+ }
-+
-+ if (u0 > 0)
-+ {
-+ mp_limb_t th, tl;
-+ r = ~r;
-+ r += u0;
-+ if (r < u0)
-+ {
-+ m--;
-+ if (r >= u1)
-+ {
-+ m--;
-+ r -= u1;
-+ }
-+ r -= u1;
-+ }
-+ gmp_umul_ppmm (th, tl, u0, m);
-+ r += th;
-+ if (r < th)
-+ {
-+ m--;
-+ m -= ((r > u1) | ((r == u1) & (tl > u0)));
-+ }
-+ }
-+
-+ return m;
-+}
-+
-+struct gmp_div_inverse
-+{
-+ /* Normalization shift count. */
-+ unsigned shift;
-+ /* Normalized divisor (d0 unused for mpn_div_qr_1) */
-+ mp_limb_t d1, d0;
-+ /* Inverse, for 2/1 or 3/2. */
-+ mp_limb_t di;
-+};
-+
-+static void
-+mpn_div_qr_1_invert (struct gmp_div_inverse *inv, mp_limb_t d)
-+{
-+ unsigned shift;
-+
-+ assert (d > 0);
-+ gmp_clz (shift, d);
-+ inv->shift = shift;
-+ inv->d1 = d << shift;
-+ inv->di = mpn_invert_limb (inv->d1);
-+}
-+
-+static void
-+mpn_div_qr_2_invert (struct gmp_div_inverse *inv,
-+ mp_limb_t d1, mp_limb_t d0)
-+{
-+ unsigned shift;
-+
-+ assert (d1 > 0);
-+ gmp_clz (shift, d1);
-+ inv->shift = shift;
-+ if (shift > 0)
-+ {
-+ d1 = (d1 << shift) | (d0 >> (GMP_LIMB_BITS - shift));
-+ d0 <<= shift;
-+ }
-+ inv->d1 = d1;
-+ inv->d0 = d0;
-+ inv->di = mpn_invert_3by2 (d1, d0);
-+}
-+
-+static void
-+mpn_div_qr_invert (struct gmp_div_inverse *inv,
-+ mp_srcptr dp, mp_size_t dn)
-+{
-+ assert (dn > 0);
-+
-+ if (dn == 1)
-+ mpn_div_qr_1_invert (inv, dp[0]);
-+ else if (dn == 2)
-+ mpn_div_qr_2_invert (inv, dp[1], dp[0]);
-+ else
-+ {
-+ unsigned shift;
-+ mp_limb_t d1, d0;
-+
-+ d1 = dp[dn-1];
-+ d0 = dp[dn-2];
-+ assert (d1 > 0);
-+ gmp_clz (shift, d1);
-+ inv->shift = shift;
-+ if (shift > 0)
-+ {
-+ d1 = (d1 << shift) | (d0 >> (GMP_LIMB_BITS - shift));
-+ d0 = (d0 << shift) | (dp[dn-3] >> (GMP_LIMB_BITS - shift));
-+ }
-+ inv->d1 = d1;
-+ inv->d0 = d0;
-+ inv->di = mpn_invert_3by2 (d1, d0);
-+ }
-+}
-+
-+/* Not matching current public gmp interface, rather corresponding to
-+ the sbpi1_div_* functions. */
-+static mp_limb_t
-+mpn_div_qr_1_preinv (mp_ptr qp, mp_srcptr np, mp_size_t nn,
-+ const struct gmp_div_inverse *inv)
-+{
-+ mp_limb_t d, di;
-+ mp_limb_t r;
-+ mp_ptr tp = NULL;
-+
-+ if (inv->shift > 0)
-+ {
-+ tp = gmp_xalloc_limbs (nn);
-+ r = mpn_lshift (tp, np, nn, inv->shift);
-+ np = tp;
-+ }
-+ else
-+ r = 0;
-+
-+ d = inv->d1;
-+ di = inv->di;
-+ while (nn-- > 0)
-+ {
-+ mp_limb_t q;
-+
-+ gmp_udiv_qrnnd_preinv (q, r, r, np[nn], d, di);
-+ if (qp)
-+ qp[nn] = q;
-+ }
-+ if (inv->shift > 0)
-+ gmp_free (tp);
-+
-+ return r >> inv->shift;
-+}
-+
-+static mp_limb_t
-+mpn_div_qr_1 (mp_ptr qp, mp_srcptr np, mp_size_t nn, mp_limb_t d)
-+{
-+ assert (d > 0);
-+
-+ /* Special case for powers of two. */
-+ if ((d & (d-1)) == 0)
-+ {
-+ mp_limb_t r = np[0] & (d-1);
-+ if (qp)
-+ {
-+ if (d <= 1)
-+ mpn_copyi (qp, np, nn);
-+ else
-+ {
-+ unsigned shift;
-+ gmp_ctz (shift, d);
-+ mpn_rshift (qp, np, nn, shift);
-+ }
-+ }
-+ return r;
-+ }
-+ else
-+ {
-+ struct gmp_div_inverse inv;
-+ mpn_div_qr_1_invert (&inv, d);
-+ return mpn_div_qr_1_preinv (qp, np, nn, &inv);
-+ }
-+}
-+
-+static void
-+mpn_div_qr_2_preinv (mp_ptr qp, mp_ptr rp, mp_srcptr np, mp_size_t nn,
-+ const struct gmp_div_inverse *inv)
-+{
-+ unsigned shift;
-+ mp_size_t i;
-+ mp_limb_t d1, d0, di, r1, r0;
-+ mp_ptr tp;
-+
-+ assert (nn >= 2);
-+ shift = inv->shift;
-+ d1 = inv->d1;
-+ d0 = inv->d0;
-+ di = inv->di;
-+
-+ if (shift > 0)
-+ {
-+ tp = gmp_xalloc_limbs (nn);
-+ r1 = mpn_lshift (tp, np, nn, shift);
-+ np = tp;
-+ }
-+ else
-+ r1 = 0;
-+
-+ r0 = np[nn - 1];
-+
-+ i = nn - 2;
-+ do
-+ {
-+ mp_limb_t n0, q;
-+ n0 = np[i];
-+ gmp_udiv_qr_3by2 (q, r1, r0, r1, r0, n0, d1, d0, di);
-+
-+ if (qp)
-+ qp[i] = q;
-+ }
-+ while (--i >= 0);
-+
-+ if (shift > 0)
-+ {
-+ assert ((r0 << (GMP_LIMB_BITS - shift)) == 0);
-+ r0 = (r0 >> shift) | (r1 << (GMP_LIMB_BITS - shift));
-+ r1 >>= shift;
-+
-+ gmp_free (tp);
-+ }
-+
-+ rp[1] = r1;
-+ rp[0] = r0;
-+}
-+
-+#if 0
-+static void
-+mpn_div_qr_2 (mp_ptr qp, mp_ptr rp, mp_srcptr np, mp_size_t nn,
-+ mp_limb_t d1, mp_limb_t d0)
-+{
-+ struct gmp_div_inverse inv;
-+ assert (nn >= 2);
-+
-+ mpn_div_qr_2_invert (&inv, d1, d0);
-+ mpn_div_qr_2_preinv (qp, rp, np, nn, &inv);
-+}
-+#endif
-+
-+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, np, nn, inv);
-+ else
-+ {
-+ mp_limb_t nh;
-+ unsigned shift;
-+
-+ assert (inv->d1 == dp[dn-1]);
-+ assert (inv->d0 == dp[dn-2]);
-+ assert ((inv->d1 & GMP_LIMB_HIGHBIT) != 0);
-+
-+ shift = inv->shift;
-+ if (shift > 0)
-+ nh = mpn_lshift (np, np, nn, shift);
-+ else
-+ nh = 0;
-+
-+ mpn_div_qr_pi1 (qp, np, nn, nh, dp, dn, inv->di);
-+
-+ if (shift > 0)
-+ gmp_assert_nocarry (mpn_rshift (np, np, dn, shift));
-+ }
-+}
-+
-+static void
-+mpn_div_qr (mp_ptr qp, mp_ptr np, mp_size_t nn, mp_srcptr dp, mp_size_t dn)
-+{
-+ struct gmp_div_inverse inv;
-+ mp_ptr tp = NULL;
-+
-+ assert (dn > 0);
-+ assert (nn >= dn);
-+
-+ mpn_div_qr_invert (&inv, dp, dn);
-+ if (dn > 2 && inv.shift > 0)
-+ {
-+ tp = gmp_xalloc_limbs (dn);
-+ gmp_assert_nocarry (mpn_lshift (tp, dp, dn, inv.shift));
-+ dp = tp;
-+ }
-+ mpn_div_qr_preinv (qp, np, nn, dp, dn, &inv);
-+ if (tp)
-+ gmp_free (tp);
-+}
-+
-+\f
-+/* 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;
-+ int shift;
-+
-+ sn = ((un - 1) * GMP_LIMB_BITS + mpn_limb_size_in_base_2 (up[un-1])
-+ + bits - 1) / bits;
-+
-+ mask = (1U << bits) - 1;
-+
-+ for (i = 0, j = sn, shift = 0; j-- > 0;)
-+ {
-+ unsigned char digit = up[i] >> shift;
-+
-+ shift += bits;
-+
-+ if (shift >= GMP_LIMB_BITS && ++i < un)
-+ {
-+ shift -= GMP_LIMB_BITS;
-+ digit |= up[i] << (bits - shift);
-+ }
-+ sp[j] = digit & mask;
-+ }
-+ return sn;
-+}
-+
-+/* We generate digits from the least significant end, and reverse at
-+ the end. */
-+static size_t
-+mpn_limb_get_str (unsigned char *sp, mp_limb_t w,
-+ const struct gmp_div_inverse *binv)
-+{
-+ mp_size_t i;
-+ for (i = 0; w > 0; i++)
-+ {
-+ mp_limb_t h, l, r;
-+
-+ h = w >> (GMP_LIMB_BITS - binv->shift);
-+ l = w << binv->shift;
-+
-+ gmp_udiv_qrnnd_preinv (w, r, h, l, binv->d1, binv->di);
-+ assert ( (r << (GMP_LIMB_BITS - binv->shift)) == 0);
-+ r >>= binv->shift;
-+
-+ sp[i] = r;
-+ }
-+ return i;
-+}
-+
-+static size_t
-+mpn_get_str_other (unsigned char *sp,
-+ int base, const struct mpn_base_info *info,
-+ mp_ptr up, mp_size_t un)
-+{
-+ struct gmp_div_inverse binv;
-+ size_t sn;
-+ size_t i;
-+
-+ mpn_div_qr_1_invert (&binv, base);
-+
-+ sn = 0;
-+
-+ if (un > 1)
-+ {
-+ struct gmp_div_inverse bbinv;
-+ mpn_div_qr_1_invert (&bbinv, info->bb);
-+
-+ do
-+ {
-+ mp_limb_t w;
-+ size_t done;
-+ w = mpn_div_qr_1_preinv (up, up, un, &bbinv);
-+ un -= (up[un-1] == 0);
-+ done = mpn_limb_get_str (sp + sn, w, &binv);
-+
-+ for (sn += done; done < info->exp; done++)
-+ sp[sn++] = 0;
-+ }
-+ while (un > 1);
-+ }
-+ sn += mpn_limb_get_str (sp + sn, up[0], &binv);
-+
-+ /* Reverse order */
-+ for (i = 0; 2*i + 1 < sn; i++)
-+ {
-+ unsigned char t = sp[i];
-+ sp[i] = sp[sn - i - 1];
-+ sp[sn - i - 1] = t;
-+ }
-+
-+ return sn;
-+}
-+
-+size_t
-+mpn_get_str (unsigned char *sp, int base, mp_ptr up, mp_size_t un)
-+{
-+ unsigned bits;
-+
-+ assert (un > 0);
-+ assert (up[un-1] > 0);
-+
-+ bits = mpn_base_power_of_two_p (base);
-+ if (bits)
-+ return mpn_get_str_bits (sp, bits, up, un);
-+ else
-+ {
-+ struct mpn_base_info info;
-+
-+ mpn_get_base_info (&info, base);
-+ return mpn_get_str_other (sp, base, &info, up, un);
-+ }
-+}
-+
-+static mp_size_t
-+mpn_set_str_bits (mp_ptr rp, const unsigned char *sp, size_t sn,
-+ unsigned bits)
-+{
-+ mp_size_t rn;
-+ size_t j;
-+ unsigned shift;
-+
-+ for (j = sn, rn = 0, shift = 0; j-- > 0; )
-+ {
-+ if (shift == 0)
-+ {
-+ rp[rn++] = sp[j];
-+ shift += bits;
-+ }
-+ else
-+ {
-+ rp[rn-1] |= (mp_limb_t) sp[j] << shift;
-+ shift += bits;
-+ if (shift >= GMP_LIMB_BITS)
-+ {
-+ shift -= GMP_LIMB_BITS;
-+ if (shift > 0)
-+ rp[rn++] = (mp_limb_t) sp[j] >> (bits - shift);
-+ }
-+ }
-+ }
-+ rn = mpn_normalized_size (rp, rn);
-+ return rn;
-+}
-+
-+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;
-+
-+ k = 1 + (sn - 1) % info->exp;
-+
-+ j = 0;
-+ w = sp[j++];
-+ for (; --k > 0; )
-+ w = w * b + sp[j++];
-+
-+ rp[0] = w;
-+
-+ for (rn = (w > 0); 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);
-+ }
-+}
-+
-+\f
-+/* MPZ interface */
-+void
-+mpz_init (mpz_t r)
-+{
-+ r->_mp_alloc = 1;
-+ r->_mp_size = 0;
-+ r->_mp_d = gmp_xalloc_limbs (1);
-+}
-+
-+/* The utility of this function is a bit limited, since many functions
-+ assigns the result variable using mpz_swap. */
-+void
-+mpz_init2 (mpz_t r, mp_bitcnt_t bits)
-+{
-+ mp_size_t rn;
-+
-+ bits -= (bits != 0); /* Round down, except if 0 */
-+ rn = 1 + bits / GMP_LIMB_BITS;
-+
-+ r->_mp_alloc = rn;
-+ r->_mp_size = 0;
-+ r->_mp_d = gmp_xalloc_limbs (rn);
-+}
-+
-+void
-+mpz_clear (mpz_t r)
-+{
-+ gmp_free (r->_mp_d);
-+}
-+
-+static void *
-+mpz_realloc (mpz_t r, mp_size_t size)
-+{
-+ size = GMP_MAX (size, 1);
-+
-+ r->_mp_d = gmp_xrealloc_limbs (r->_mp_d, 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)
-+\f
-+/* MPZ assignment and basic conversions. */
-+void
-+mpz_set_si (mpz_t r, signed long int x)
-+{
-+ if (x >= 0)
-+ mpz_set_ui (r, x);
-+ else /* (x < 0) */
-+ {
-+ r->_mp_size = -1;
-+ r->_mp_d[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;
-+ r->_mp_d[0] = x;
-+ }
-+ else
-+ r->_mp_size = 0;
-+}
-+
-+void
-+mpz_set (mpz_t r, const mpz_t x)
-+{
-+ /* Allow the NOP r == x */
-+ if (r != x)
-+ {
-+ mp_size_t n;
-+ mp_ptr rp;
-+
-+ n = GMP_ABS (x->_mp_size);
-+ rp = MPZ_REALLOC (r, n);
-+
-+ mpn_copyi (rp, x->_mp_d, n);
-+ r->_mp_size = x->_mp_size;
-+ }
-+}
-+
-+void
-+mpz_init_set_si (mpz_t r, signed long int x)
-+{
-+ mpz_init (r);
-+ mpz_set_si (r, x);
-+}
-+
-+void
-+mpz_init_set_ui (mpz_t r, unsigned long int x)
-+{
-+ mpz_init (r);
-+ mpz_set_ui (r, x);
-+}
-+
-+void
-+mpz_init_set (mpz_t r, const mpz_t x)
-+{
-+ mpz_init (r);
-+ mpz_set (r, x);
-+}
-+
-+int
-+mpz_fits_slong_p (const mpz_t u)
-+{
-+ mp_size_t us = u->_mp_size;
-+
-+ if (us == 0)
-+ return 1;
-+ else if (us == 1)
-+ return u->_mp_d[0] < GMP_LIMB_HIGHBIT;
-+ else if (us == -1)
-+ return u->_mp_d[0] <= GMP_LIMB_HIGHBIT;
-+ else
-+ return 0;
-+}
-+
-+int
-+mpz_fits_ulong_p (const mpz_t u)
-+{
-+ mp_size_t us = u->_mp_size;
-+
-+ return (us == (us > 0));
-+}
-+
-+long int
-+mpz_get_si (const mpz_t u)
-+{
-+ mp_size_t us = u->_mp_size;
-+
-+ if (us > 0)
-+ return (long) (u->_mp_d[0] & ~GMP_LIMB_HIGHBIT);
-+ else if (us < 0)
-+ return (long) (- u->_mp_d[0] | GMP_LIMB_HIGHBIT);
-+ else
-+ return 0;
-+}
-+
-+unsigned long int
-+mpz_get_ui (const mpz_t u)
-+{
-+ return u->_mp_size == 0 ? 0 : u->_mp_d[0];
-+}
-+
-+size_t
-+mpz_size (const mpz_t u)
-+{
-+ return GMP_ABS (u->_mp_size);
-+}
-+
-+mp_limb_t
-+mpz_getlimbn (const mpz_t u, mp_size_t n)
-+{
-+ if (n >= 0 && n < GMP_ABS (u->_mp_size))
-+ return u->_mp_d[n];
-+ else
-+ return 0;
-+}
-+
-+void
-+mpz_realloc2 (mpz_t x, mp_bitcnt_t n)
-+{
-+ mpz_realloc (x, 1 + (n - (n != 0)) / GMP_LIMB_BITS);
-+}
-+
-+mp_srcptr
-+mpz_limbs_read (mpz_srcptr x)
-+{
-+ return x->_mp_d;;
-+}
-+
-+mp_ptr
-+mpz_limbs_modify (mpz_t x, mp_size_t n)
-+{
-+ assert (n > 0);
-+ return MPZ_REALLOC (x, n);
-+}
-+
-+mp_ptr
-+mpz_limbs_write (mpz_t x, mp_size_t n)
-+{
-+ return mpz_limbs_modify (x, n);
-+}
-+
-+void
-+mpz_limbs_finish (mpz_t x, mp_size_t xs)
-+{
-+ mp_size_t xn;
-+ xn = mpn_normalized_size (x->_mp_d, GMP_ABS (xs));
-+ x->_mp_size = xs < 0 ? -xn : xn;
-+}
-+
-+mpz_srcptr
-+mpz_roinit_n (mpz_t x, mp_srcptr xp, mp_size_t xs)
-+{
-+ x->_mp_alloc = 0;
-+ x->_mp_d = (mp_ptr) xp;
-+ mpz_limbs_finish (x, xs);
-+ return x;
-+}
-+
-+\f
-+/* Conversions and comparison to double. */
-+void
-+mpz_set_d (mpz_t r, double x)
-+{
-+ int sign;
-+ mp_ptr rp;
-+ mp_size_t rn, i;
-+ double B;
-+ double Bi;
-+ mp_limb_t f;
-+
-+ /* x != x is true when x is a NaN, and x == x * 0.5 is true when x is
-+ zero or infinity. */
-+ if (x != x || x == x * 0.5)
-+ {
-+ r->_mp_size = 0;
-+ return;
-+ }
-+
-+ sign = x < 0.0 ;
-+ if (sign)
-+ x = - x;
-+
-+ if (x < 1.0)
-+ {
-+ r->_mp_size = 0;
-+ return;
-+ }
-+ B = 2.0 * (double) GMP_LIMB_HIGHBIT;
-+ Bi = 1.0 / B;
-+ for (rn = 1; x >= B; rn++)
-+ x *= Bi;
-+
-+ rp = MPZ_REALLOC (r, rn);
-+
-+ f = (mp_limb_t) x;
-+ x -= f;
-+ assert (x < 1.0);
-+ i = rn-1;
-+ rp[i] = f;
-+ while (--i >= 0)
-+ {
-+ x = B * x;
-+ f = (mp_limb_t) x;
-+ x -= f;
-+ assert (x < 1.0);
-+ rp[i] = f;
-+ }
-+
-+ r->_mp_size = sign ? - rn : rn;
-+}
-+
-+void
-+mpz_init_set_d (mpz_t r, double x)
-+{
-+ mpz_init (r);
-+ mpz_set_d (r, x);
-+}
-+
-+double
-+mpz_get_d (const mpz_t u)
-+{
-+ mp_size_t un;
-+ double x;
-+ double B = 2.0 * (double) GMP_LIMB_HIGHBIT;
-+
-+ un = GMP_ABS (u->_mp_size);
-+
-+ if (un == 0)
-+ return 0.0;
-+
-+ x = u->_mp_d[--un];
-+ while (un > 0)
-+ x = B*x + u->_mp_d[--un];
-+
-+ if (u->_mp_size < 0)
-+ x = -x;
-+
-+ return x;
-+}
-+
-+int
-+mpz_cmpabs_d (const mpz_t x, double d)
-+{
-+ mp_size_t xn;
-+ double B, Bi;
-+ mp_size_t i;
-+
-+ xn = x->_mp_size;
-+ d = GMP_ABS (d);
-+
-+ if (xn != 0)
-+ {
-+ xn = GMP_ABS (xn);
-+
-+ B = 2.0 * (double) GMP_LIMB_HIGHBIT;
-+ Bi = 1.0 / B;
-+
-+ /* Scale d so it can be compared with the top limb. */
-+ for (i = 1; i < xn; i++)
-+ d *= Bi;
-+
-+ if (d >= B)
-+ return -1;
-+
-+ /* Compare floor(d) to top limb, subtract and cancel when equal. */
-+ for (i = xn; i-- > 0;)
-+ {
-+ mp_limb_t f, xl;
-+
-+ f = (mp_limb_t) d;
-+ xl = x->_mp_d[i];
-+ if (xl > f)
-+ return 1;
-+ else if (xl < f)
-+ return -1;
-+ d = B * (d - f);
-+ }
-+ }
-+ return - (d > 0.0);
-+}
-+
-+int
-+mpz_cmp_d (const mpz_t x, double d)
-+{
-+ if (x->_mp_size < 0)
-+ {
-+ if (d >= 0.0)
-+ return -1;
-+ else
-+ return -mpz_cmpabs_d (x, d);
-+ }
-+ else
-+ {
-+ if (d < 0.0)
-+ return 1;
-+ else
-+ return mpz_cmpabs_d (x, d);
-+ }
-+}
-+
-+\f
-+/* MPZ comparisons and the like. */
-+int
-+mpz_sgn (const mpz_t u)
-+{
-+ mp_size_t usize = u->_mp_size;
-+
-+ return (usize > 0) - (usize < 0);
-+}
-+
-+int
-+mpz_cmp_si (const mpz_t u, long v)
-+{
-+ mp_size_t usize = u->_mp_size;
-+
-+ if (usize < -1)
-+ return -1;
-+ else if (v >= 0)
-+ return mpz_cmp_ui (u, v);
-+ else if (usize >= 0)
-+ return 1;
-+ else /* usize == -1 */
-+ {
-+ mp_limb_t ul = u->_mp_d[0];
-+ if ((mp_limb_t)GMP_NEG_CAST (unsigned long int, v) < ul)
-+ return -1;
-+ else
-+ return (mp_limb_t)GMP_NEG_CAST (unsigned long int, v) > ul;
-+ }
-+}
-+
-+int
-+mpz_cmp_ui (const mpz_t u, unsigned long v)
-+{
-+ mp_size_t usize = u->_mp_size;
-+
-+ if (usize > 1)
-+ return 1;
-+ else if (usize < 0)
-+ return -1;
-+ else
-+ {
-+ mp_limb_t ul = (usize > 0) ? u->_mp_d[0] : 0;
-+ return (ul > v) - (ul < 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);
-+ mp_limb_t ul;
-+
-+ if (un > 1)
-+ return 1;
-+
-+ ul = (un == 1) ? u->_mp_d[0] : 0;
-+
-+ return (ul > v) - (ul < 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)
-+{
-+ if (r != u)
-+ mpz_set (r, u);
-+
-+ r->_mp_size = GMP_ABS (r->_mp_size);
-+}
-+
-+void
-+mpz_neg (mpz_t r, const mpz_t u)
-+{
-+ if (r != u)
-+ mpz_set (r, u);
-+
-+ 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);
-+}
-+
-+\f
-+/* MPZ addition and subtraction */
-+
-+/* Adds to the absolute value. Returns new size, but doesn't store it. */
-+static mp_size_t
-+mpz_abs_add_ui (mpz_t r, const mpz_t a, unsigned long b)
-+{
-+ mp_size_t an;
-+ mp_ptr rp;
-+ mp_limb_t cy;
-+
-+ an = GMP_ABS (a->_mp_size);
-+ if (an == 0)
-+ {
-+ r->_mp_d[0] = b;
-+ return b > 0;
-+ }
-+
-+ rp = MPZ_REALLOC (r, an + 1);
-+
-+ cy = mpn_add_1 (rp, a->_mp_d, an, b);
-+ rp[an] = cy;
-+ an += cy;
-+
-+ return an;
-+}
-+
-+/* Subtract from the absolute value. Returns new size, (or -1 on underflow),
-+ but doesn't store it. */
-+static mp_size_t
-+mpz_abs_sub_ui (mpz_t r, const mpz_t a, unsigned long b)
-+{
-+ mp_size_t an = GMP_ABS (a->_mp_size);
-+ mp_ptr rp = MPZ_REALLOC (r, an);
-+
-+ if (an == 0)
-+ {
-+ rp[0] = b;
-+ return -(b > 0);
-+ }
-+ else if (an == 1 && a->_mp_d[0] < b)
-+ {
-+ rp[0] = b - a->_mp_d[0];
-+ return -1;
-+ }
-+ else
-+ {
-+ gmp_assert_nocarry (mpn_sub_1 (rp, a->_mp_d, an, b));
-+ return mpn_normalized_size (rp, an);
-+ }
-+}
-+
-+void
-+mpz_add_ui (mpz_t r, const mpz_t a, unsigned long b)
-+{
-+ if (a->_mp_size >= 0)
-+ r->_mp_size = mpz_abs_add_ui (r, a, b);
-+ else
-+ r->_mp_size = -mpz_abs_sub_ui (r, a, b);
-+}
-+
-+void
-+mpz_sub_ui (mpz_t r, const mpz_t a, unsigned long b)
-+{
-+ if (a->_mp_size < 0)
-+ r->_mp_size = -mpz_abs_add_ui (r, a, b);
-+ else
-+ r->_mp_size = mpz_abs_sub_ui (r, a, b);
-+}
-+
-+void
-+mpz_ui_sub (mpz_t r, unsigned long a, const mpz_t b)
-+{
-+ if (b->_mp_size < 0)
-+ r->_mp_size = mpz_abs_add_ui (r, b, a);
-+ else
-+ r->_mp_size = -mpz_abs_sub_ui (r, b, a);
-+}
-+
-+static mp_size_t
-+mpz_abs_add (mpz_t r, const mpz_t a, const mpz_t b)
-+{
-+ mp_size_t an = GMP_ABS (a->_mp_size);
-+ mp_size_t bn = GMP_ABS (b->_mp_size);
-+ mp_ptr rp;
-+ mp_limb_t cy;
-+
-+ if (an < bn)
-+ {
-+ MPZ_SRCPTR_SWAP (a, b);
-+ MP_SIZE_T_SWAP (an, bn);
-+ }
-+
-+ rp = MPZ_REALLOC (r, an + 1);
-+ cy = mpn_add (rp, a->_mp_d, an, b->_mp_d, bn);
-+
-+ rp[an] = cy;
-+
-+ return an + cy;
-+}
-+
-+static mp_size_t
-+mpz_abs_sub (mpz_t r, const mpz_t a, const mpz_t b)
-+{
-+ mp_size_t an = GMP_ABS (a->_mp_size);
-+ mp_size_t bn = GMP_ABS (b->_mp_size);
-+ int cmp;
-+ mp_ptr rp;
-+
-+ cmp = mpn_cmp4 (a->_mp_d, an, b->_mp_d, bn);
-+ if (cmp > 0)
-+ {
-+ rp = MPZ_REALLOC (r, an);
-+ gmp_assert_nocarry (mpn_sub (rp, a->_mp_d, an, b->_mp_d, bn));
-+ return mpn_normalized_size (rp, an);
-+ }
-+ else if (cmp < 0)
-+ {
-+ rp = MPZ_REALLOC (r, bn);
-+ gmp_assert_nocarry (mpn_sub (rp, b->_mp_d, bn, a->_mp_d, an));
-+ return -mpn_normalized_size (rp, bn);
-+ }
-+ else
-+ return 0;
-+}
-+
-+void
-+mpz_add (mpz_t r, const mpz_t a, const mpz_t b)
-+{
-+ mp_size_t rn;
-+
-+ if ( (a->_mp_size ^ b->_mp_size) >= 0)
-+ rn = mpz_abs_add (r, a, b);
-+ else
-+ rn = mpz_abs_sub (r, a, b);
-+
-+ r->_mp_size = a->_mp_size >= 0 ? rn : - rn;
-+}
-+
-+void
-+mpz_sub (mpz_t r, const mpz_t a, const mpz_t b)
-+{
-+ mp_size_t rn;
-+
-+ if ( (a->_mp_size ^ b->_mp_size) >= 0)
-+ rn = mpz_abs_sub (r, a, b);
-+ else
-+ rn = mpz_abs_add (r, a, b);
-+
-+ r->_mp_size = a->_mp_size >= 0 ? rn : - rn;
-+}
-+
-+\f
-+/* MPZ multiplication */
-+void
-+mpz_mul_si (mpz_t r, const mpz_t u, long int v)
-+{
-+ if (v < 0)
-+ {
-+ mpz_mul_ui (r, u, GMP_NEG_CAST (unsigned long int, v));
-+ mpz_neg (r, r);
-+ }
-+ else
-+ mpz_mul_ui (r, u, (unsigned long int) v);
-+}
-+
-+void
-+mpz_mul_ui (mpz_t r, const mpz_t u, unsigned long int v)
-+{
-+ mp_size_t un, us;
-+ mp_ptr tp;
-+ mp_limb_t cy;
-+
-+ us = u->_mp_size;
-+
-+ if (us == 0 || v == 0)
-+ {
-+ r->_mp_size = 0;
-+ return;
-+ }
-+
-+ un = GMP_ABS (us);
-+
-+ tp = MPZ_REALLOC (r, un + 1);
-+ cy = mpn_mul_1 (tp, u->_mp_d, un, v);
-+ tp[un] = cy;
-+
-+ un += (cy > 0);
-+ r->_mp_size = (us < 0) ? - un : un;
-+}
-+
-+void
-+mpz_mul (mpz_t r, const mpz_t u, const mpz_t v)
-+{
-+ int sign;
-+ mp_size_t un, vn, rn;
-+ mpz_t t;
-+ mp_ptr tp;
-+
-+ un = u->_mp_size;
-+ vn = v->_mp_size;
-+
-+ if (un == 0 || vn == 0)
-+ {
-+ r->_mp_size = 0;
-+ return;
-+ }
-+
-+ sign = (un ^ vn) < 0;
-+
-+ un = GMP_ABS (un);
-+ vn = GMP_ABS (vn);
-+
-+ mpz_init2 (t, (un + vn) * GMP_LIMB_BITS);
-+
-+ tp = t->_mp_d;
-+ if (un >= vn)
-+ mpn_mul (tp, u->_mp_d, un, v->_mp_d, vn);
-+ else
-+ mpn_mul (tp, v->_mp_d, vn, u->_mp_d, un);
-+
-+ rn = un + vn;
-+ rn -= tp[rn-1] == 0;
-+
-+ t->_mp_size = sign ? - rn : rn;
-+ mpz_swap (r, t);
-+ mpz_clear (t);
-+}
-+
-+void
-+mpz_mul_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t bits)
-+{
-+ mp_size_t un, rn;
-+ mp_size_t limbs;
-+ unsigned shift;
-+ mp_ptr rp;
-+
-+ un = GMP_ABS (u->_mp_size);
-+ if (un == 0)
-+ {
-+ r->_mp_size = 0;
-+ return;
-+ }
-+
-+ limbs = bits / GMP_LIMB_BITS;
-+ shift = bits % GMP_LIMB_BITS;
-+
-+ rn = un + limbs + (shift > 0);
-+ rp = MPZ_REALLOC (r, rn);
-+ if (shift > 0)
-+ {
-+ mp_limb_t cy = mpn_lshift (rp + limbs, u->_mp_d, un, shift);
-+ rp[rn-1] = cy;
-+ rn -= (cy == 0);
-+ }
-+ else
-+ mpn_copyd (rp + limbs, u->_mp_d, un);
-+
-+ while (limbs > 0)
-+ rp[--limbs] = 0;
-+
-+ r->_mp_size = (u->_mp_size < 0) ? - rn : rn;
-+}
-+
-+void
-+mpz_addmul_ui (mpz_t r, const mpz_t u, unsigned long int v)
-+{
-+ mpz_t t;
-+ mpz_init (t);
-+ mpz_mul_ui (t, u, v);
-+ mpz_add (r, r, t);
-+ mpz_clear (t);
-+}
-+
-+void
-+mpz_submul_ui (mpz_t r, const mpz_t u, unsigned long int v)
-+{
-+ mpz_t t;
-+ mpz_init (t);
-+ mpz_mul_ui (t, u, v);
-+ mpz_sub (r, r, t);
-+ mpz_clear (t);
-+}
-+
-+void
-+mpz_addmul (mpz_t r, const mpz_t u, const mpz_t v)
-+{
-+ mpz_t t;
-+ mpz_init (t);
-+ mpz_mul (t, u, v);
-+ mpz_add (r, r, t);
-+ mpz_clear (t);
-+}
-+
-+void
-+mpz_submul (mpz_t r, const mpz_t u, const mpz_t v)
-+{
-+ mpz_t t;
-+ mpz_init (t);
-+ mpz_mul (t, u, v);
-+ mpz_sub (r, r, t);
-+ mpz_clear (t);
-+}
-+
-+\f
-+/* 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;
-+ mp_limb_t cy;
-+
-+ for (cy = 1, i = 0; i < un; i++)
-+ {
-+ mp_limb_t s = ~u->_mp_d[i] + cy;
-+ cy = s < cy;
-+ rp[i] = s;
-+ }
-+ assert (cy == 0);
-+ for (; i < rn - 1; i++)
-+ 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. */
-+ mp_size_t i;
-+
-+ for (i = 0; i < rn && rp[i] == 0; i++)
-+ ;
-+ if (i < rn)
-+ {
-+ /* r > 0, need to flip sign. */
-+ rp[i] = ~rp[i] + 1;
-+ while (++i < rn)
-+ rp[i] = ~rp[i];
-+
-+ rp[rn-1] &= mask;
-+
-+ /* us is not used for anything else, so we can modify it
-+ here to indicate flipped sign. */
-+ us = -us;
-+ }
-+ }
-+ }
-+ rn = mpn_normalized_size (rp, rn);
-+ r->_mp_size = us < 0 ? -rn : rn;
-+}
-+
-+void
-+mpz_cdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
-+{
-+ mpz_div_q_2exp (r, u, cnt, GMP_DIV_CEIL);
-+}
-+
-+void
-+mpz_fdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
-+{
-+ mpz_div_q_2exp (r, u, cnt, GMP_DIV_FLOOR);
-+}
-+
-+void
-+mpz_tdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
-+{
-+ mpz_div_q_2exp (r, u, cnt, GMP_DIV_TRUNC);
-+}
-+
-+void
-+mpz_cdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
-+{
-+ mpz_div_r_2exp (r, u, cnt, GMP_DIV_CEIL);
-+}
-+
-+void
-+mpz_fdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
-+{
-+ mpz_div_r_2exp (r, u, cnt, GMP_DIV_FLOOR);
-+}
-+
-+void
-+mpz_tdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
-+{
-+ mpz_div_r_2exp (r, u, cnt, GMP_DIV_TRUNC);
-+}
-+
-+void
-+mpz_divexact (mpz_t q, const mpz_t n, const mpz_t d)
-+{
-+ gmp_assert_nocarry (mpz_div_qr (q, NULL, n, d, GMP_DIV_TRUNC));
-+}
-+
-+int
-+mpz_divisible_p (const mpz_t n, const mpz_t d)
-+{
-+ return mpz_div_qr (NULL, NULL, n, d, GMP_DIV_TRUNC) == 0;
-+}
-+
-+int
-+mpz_congruent_p (const mpz_t a, const mpz_t b, const mpz_t m)
-+{
-+ mpz_t t;
-+ int res;
-+
-+ /* a == b (mod 0) iff a == b */
-+ if (mpz_sgn (m) == 0)
-+ return (mpz_cmp (a, b) == 0);
-+
-+ mpz_init (t);
-+ mpz_sub (t, a, b);
-+ res = mpz_divisible_p (t, m);
-+ mpz_clear (t);
-+
-+ return res;
-+}
-+
-+static unsigned long
-+mpz_div_qr_ui (mpz_t q, mpz_t r,
-+ const mpz_t n, unsigned long d, enum mpz_div_round_mode mode)
-+{
-+ mp_size_t ns, qn;
-+ mp_ptr qp;
-+ mp_limb_t rl;
-+ mp_size_t rs;
-+
-+ ns = n->_mp_size;
-+ if (ns == 0)
-+ {
-+ if (q)
-+ q->_mp_size = 0;
-+ if (r)
-+ r->_mp_size = 0;
-+ return 0;
-+ }
-+
-+ qn = GMP_ABS (ns);
-+ if (q)
-+ qp = MPZ_REALLOC (q, qn);
-+ else
-+ qp = NULL;
-+
-+ rl = mpn_div_qr_1 (qp, n->_mp_d, qn, d);
-+ assert (rl < d);
-+
-+ rs = rl > 0;
-+ rs = (ns < 0) ? -rs : rs;
-+
-+ if (rl > 0 && ( (mode == GMP_DIV_FLOOR && ns < 0)
-+ || (mode == GMP_DIV_CEIL && ns >= 0)))
-+ {
-+ if (q)
-+ gmp_assert_nocarry (mpn_add_1 (qp, qp, qn, 1));
-+ rl = d - rl;
-+ rs = -rs;
-+ }
-+
-+ if (r)
-+ {
-+ r->_mp_d[0] = rl;
-+ r->_mp_size = rs;
-+ }
-+ if (q)
-+ {
-+ qn -= (qp[qn-1] == 0);
-+ assert (qn == 0 || qp[qn-1] > 0);
-+
-+ q->_mp_size = (ns < 0) ? - qn : qn;
-+ }
-+
-+ return rl;
-+}
-+
-+unsigned long
-+mpz_cdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d)
-+{
-+ return mpz_div_qr_ui (q, r, n, d, GMP_DIV_CEIL);
-+}
-+
-+unsigned long
-+mpz_fdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d)
-+{
-+ return mpz_div_qr_ui (q, r, n, d, GMP_DIV_FLOOR);
-+}
-+
-+unsigned long
-+mpz_tdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d)
-+{
-+ return mpz_div_qr_ui (q, r, n, d, GMP_DIV_TRUNC);
-+}
-+
-+unsigned long
-+mpz_cdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d)
-+{
-+ return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_CEIL);
-+}
-+
-+unsigned long
-+mpz_fdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d)
-+{
-+ return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_FLOOR);
-+}
-+
-+unsigned long
-+mpz_tdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d)
-+{
-+ return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_TRUNC);
-+}
-+
-+unsigned long
-+mpz_cdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d)
-+{
-+ return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_CEIL);
-+}
-+unsigned long
-+mpz_fdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d)
-+{
-+ return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_FLOOR);
-+}
-+unsigned long
-+mpz_tdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d)
-+{
-+ return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_TRUNC);
-+}
-+
-+unsigned long
-+mpz_cdiv_ui (const mpz_t n, unsigned long d)
-+{
-+ return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_CEIL);
-+}
-+
-+unsigned long
-+mpz_fdiv_ui (const mpz_t n, unsigned long d)
-+{
-+ return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_FLOOR);
-+}
-+
-+unsigned long
-+mpz_tdiv_ui (const mpz_t n, unsigned long d)
-+{
-+ return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_TRUNC);
-+}
-+
-+unsigned long
-+mpz_mod_ui (mpz_t r, const mpz_t n, unsigned long d)
-+{
-+ return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_FLOOR);
-+}
-+
-+void
-+mpz_divexact_ui (mpz_t q, const mpz_t n, unsigned long d)
-+{
-+ gmp_assert_nocarry (mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_TRUNC));
-+}
-+
-+int
-+mpz_divisible_ui_p (const mpz_t n, unsigned long d)
-+{
-+ return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_TRUNC) == 0;
-+}
-+
-+\f
-+/* GCD */
-+static mp_limb_t
-+mpn_gcd_11 (mp_limb_t u, mp_limb_t v)
-+{
-+ unsigned shift;
-+
-+ assert ( (u | v) > 0);
-+
-+ if (u == 0)
-+ return v;
-+ else if (v == 0)
-+ return u;
-+
-+ gmp_ctz (shift, u | v);
-+
-+ u >>= shift;
-+ v >>= shift;
-+
-+ if ( (u & 1) == 0)
-+ MP_LIMB_T_SWAP (u, v);
-+
-+ while ( (v & 1) == 0)
-+ v >>= 1;
-+
-+ while (u != v)
-+ {
-+ if (u > v)
-+ {
-+ u -= v;
-+ do
-+ u >>= 1;
-+ while ( (u & 1) == 0);
-+ }
-+ else
-+ {
-+ v -= u;
-+ do
-+ v >>= 1;
-+ while ( (v & 1) == 0);
-+ }
-+ }
-+ return u << shift;
-+}
-+
-+unsigned long
-+mpz_gcd_ui (mpz_t g, const mpz_t u, unsigned long v)
-+{
-+ mp_size_t un;
-+
-+ if (v == 0)
-+ {
-+ if (g)
-+ mpz_abs (g, u);
-+ }
-+ else
-+ {
-+ un = GMP_ABS (u->_mp_size);
-+ if (un != 0)
-+ v = mpn_gcd_11 (mpn_div_qr_1 (NULL, u->_mp_d, un, v), v);
-+
-+ if (g)
-+ mpz_set_ui (g, v);
-+ }
-+
-+ return v;
-+}
-+
-+static mp_bitcnt_t
-+mpz_make_odd (mpz_t r)
-+{
-+ mp_bitcnt_t shift;
-+
-+ assert (r->_mp_size > 0);
-+ /* Count trailing zeros, equivalent to mpn_scan1, because we know that there is a 1 */
-+ shift = mpn_common_scan (r->_mp_d[0], 0, r->_mp_d, 0, 0);
-+ mpz_tdiv_q_2exp (r, r, shift);
-+
-+ return shift;
-+}
-+
-+void
-+mpz_gcd (mpz_t g, const mpz_t u, const mpz_t v)
-+{
-+ mpz_t tu, tv;
-+ mp_bitcnt_t uz, vz, gz;
-+
-+ if (u->_mp_size == 0)
-+ {
-+ mpz_abs (g, v);
-+ return;
-+ }
-+ if (v->_mp_size == 0)
-+ {
-+ mpz_abs (g, u);
-+ return;
-+ }
-+
-+ mpz_init (tu);
-+ mpz_init (tv);
-+
-+ mpz_abs (tu, u);
-+ uz = mpz_make_odd (tu);
-+ mpz_abs (tv, v);
-+ vz = mpz_make_odd (tv);
-+ gz = GMP_MIN (uz, vz);
-+
-+ if (tu->_mp_size < tv->_mp_size)
-+ mpz_swap (tu, tv);
-+
-+ mpz_tdiv_r (tu, tu, tv);
-+ if (tu->_mp_size == 0)
-+ {
-+ mpz_swap (g, tv);
-+ }
-+ else
-+ for (;;)
-+ {
-+ int c;
-+
-+ mpz_make_odd (tu);
-+ c = mpz_cmp (tu, tv);
-+ if (c == 0)
-+ {
-+ mpz_swap (g, tu);
-+ break;
-+ }
-+ if (c < 0)
-+ mpz_swap (tu, tv);
-+
-+ if (tv->_mp_size == 1)
-+ {
-+ mp_limb_t vl = tv->_mp_d[0];
-+ mp_limb_t ul = mpz_tdiv_ui (tu, vl);
-+ mpz_set_ui (g, mpn_gcd_11 (ul, vl));
-+ break;
-+ }
-+ mpz_sub (tu, tu, tv);
-+ }
-+ mpz_clear (tu);
-+ mpz_clear (tv);
-+ mpz_mul_2exp (g, g, gz);
-+}
-+
-+void
-+mpz_gcdext (mpz_t g, mpz_t s, mpz_t t, const mpz_t u, const mpz_t v)
-+{
-+ mpz_t tu, tv, s0, s1, t0, t1;
-+ mp_bitcnt_t uz, vz, gz;
-+ mp_bitcnt_t power;
-+
-+ if (u->_mp_size == 0)
-+ {
-+ /* g = 0 u + sgn(v) v */
-+ signed long sign = mpz_sgn (v);
-+ mpz_abs (g, v);
-+ if (s)
-+ mpz_set_ui (s, 0);
-+ if (t)
-+ mpz_set_si (t, sign);
-+ return;
-+ }
-+
-+ if (v->_mp_size == 0)
-+ {
-+ /* g = sgn(u) u + 0 v */
-+ signed long sign = mpz_sgn (u);
-+ mpz_abs (g, u);
-+ if (s)
-+ mpz_set_si (s, sign);
-+ if (t)
-+ mpz_set_ui (t, 0);
-+ return;
-+ }
-+
-+ mpz_init (tu);
-+ mpz_init (tv);
-+ mpz_init (s0);
-+ mpz_init (s1);
-+ mpz_init (t0);
-+ mpz_init (t1);
-+
-+ mpz_abs (tu, u);
-+ uz = mpz_make_odd (tu);
-+ mpz_abs (tv, v);
-+ vz = mpz_make_odd (tv);
-+ gz = GMP_MIN (uz, vz);
-+
-+ uz -= gz;
-+ vz -= gz;
-+
-+ /* Cofactors corresponding to odd gcd. gz handled later. */
-+ if (tu->_mp_size < tv->_mp_size)
-+ {
-+ mpz_swap (tu, tv);
-+ MPZ_SRCPTR_SWAP (u, v);
-+ MPZ_PTR_SWAP (s, t);
-+ MP_BITCNT_T_SWAP (uz, vz);
-+ }
-+
-+ /* Maintain
-+ *
-+ * u = t0 tu + t1 tv
-+ * v = s0 tu + s1 tv
-+ *
-+ * where u and v denote the inputs with common factors of two
-+ * eliminated, and det (s0, t0; s1, t1) = 2^p. Then
-+ *
-+ * 2^p tu = s1 u - t1 v
-+ * 2^p tv = -s0 u + t0 v
-+ */
-+
-+ /* After initial division, tu = q tv + tu', we have
-+ *
-+ * u = 2^uz (tu' + q tv)
-+ * v = 2^vz tv
-+ *
-+ * or
-+ *
-+ * t0 = 2^uz, t1 = 2^uz q
-+ * s0 = 0, s1 = 2^vz
-+ */
-+
-+ mpz_setbit (t0, uz);
-+ mpz_tdiv_qr (t1, tu, tu, tv);
-+ mpz_mul_2exp (t1, t1, uz);
-+
-+ mpz_setbit (s1, vz);
-+ power = uz + vz;
-+
-+ if (tu->_mp_size > 0)
-+ {
-+ mp_bitcnt_t shift;
-+ shift = mpz_make_odd (tu);
-+ mpz_mul_2exp (t0, t0, shift);
-+ mpz_mul_2exp (s0, s0, shift);
-+ power += shift;
-+
-+ for (;;)
-+ {
-+ int c;
-+ c = mpz_cmp (tu, tv);
-+ if (c == 0)
-+ break;
-+
-+ if (c < 0)
-+ {
-+ /* tv = tv' + tu
-+ *
-+ * u = t0 tu + t1 (tv' + tu) = (t0 + t1) tu + t1 tv'
-+ * v = s0 tu + s1 (tv' + tu) = (s0 + s1) tu + s1 tv' */
-+
-+ mpz_sub (tv, tv, tu);
-+ mpz_add (t0, t0, t1);
-+ mpz_add (s0, s0, s1);
-+
-+ shift = mpz_make_odd (tv);
-+ mpz_mul_2exp (t1, t1, shift);
-+ mpz_mul_2exp (s1, s1, shift);
-+ }
-+ else
-+ {
-+ mpz_sub (tu, tu, tv);
-+ mpz_add (t1, t0, t1);
-+ mpz_add (s1, s0, s1);
-+
-+ shift = mpz_make_odd (tu);
-+ mpz_mul_2exp (t0, t0, shift);
-+ mpz_mul_2exp (s0, s0, shift);
-+ }
-+ power += shift;
-+ }
-+ }
-+
-+ /* Now tv = odd part of gcd, and -s0 and t0 are corresponding
-+ cofactors. */
-+
-+ mpz_mul_2exp (tv, tv, gz);
-+ mpz_neg (s0, s0);
-+
-+ /* 2^p g = s0 u + t0 v. Eliminate one factor of two at a time. To
-+ adjust cofactors, we need u / g and v / g */
-+
-+ mpz_divexact (s1, v, tv);
-+ mpz_abs (s1, s1);
-+ mpz_divexact (t1, u, tv);
-+ mpz_abs (t1, t1);
-+
-+ while (power-- > 0)
-+ {
-+ /* s0 u + t0 v = (s0 - v/g) u - (t0 + u/g) v */
-+ if (mpz_odd_p (s0) || mpz_odd_p (t0))
-+ {
-+ mpz_sub (s0, s0, s1);
-+ mpz_add (t0, t0, t1);
-+ }
-+ mpz_divexact_ui (s0, s0, 2);
-+ mpz_divexact_ui (t0, t0, 2);
-+ }
-+
-+ /* Arrange so that |s| < |u| / 2g */
-+ mpz_add (s1, s0, s1);
-+ if (mpz_cmpabs (s0, s1) > 0)
-+ {
-+ mpz_swap (s0, s1);
-+ mpz_sub (t0, t0, t1);
-+ }
-+ if (u->_mp_size < 0)
-+ mpz_neg (s0, s0);
-+ if (v->_mp_size < 0)
-+ mpz_neg (t0, t0);
-+
-+ mpz_swap (g, tv);
-+ if (s)
-+ mpz_swap (s, s0);
-+ if (t)
-+ mpz_swap (t, t0);
-+
-+ mpz_clear (tu);
-+ mpz_clear (tv);
-+ mpz_clear (s0);
-+ mpz_clear (s1);
-+ mpz_clear (t0);
-+ mpz_clear (t1);
-+}
-+
-+void
-+mpz_lcm (mpz_t r, const mpz_t u, const mpz_t v)
-+{
-+ mpz_t g;
-+
-+ if (u->_mp_size == 0 || v->_mp_size == 0)
-+ {
-+ r->_mp_size = 0;
-+ return;
-+ }
-+
-+ mpz_init (g);
-+
-+ mpz_gcd (g, u, v);
-+ mpz_divexact (g, u, g);
-+ mpz_mul (r, g, v);
-+
-+ mpz_clear (g);
-+ mpz_abs (r, r);
-+}
-+
-+void
-+mpz_lcm_ui (mpz_t r, const mpz_t u, unsigned long v)
-+{
-+ if (v == 0 || u->_mp_size == 0)
-+ {
-+ r->_mp_size = 0;
-+ return;
-+ }
-+
-+ v /= mpz_gcd_ui (NULL, u, v);
-+ mpz_mul_ui (r, u, v);
-+
-+ mpz_abs (r, r);
-+}
-+
-+int
-+mpz_invert (mpz_t r, const mpz_t u, const mpz_t m)
-+{
-+ mpz_t g, tr;
-+ int invertible;
-+
-+ if (u->_mp_size == 0 || mpz_cmpabs_ui (m, 1) <= 0)
-+ return 0;
-+
-+ mpz_init (g);
-+ mpz_init (tr);
-+
-+ mpz_gcdext (g, tr, NULL, u, m);
-+ invertible = (mpz_cmp_ui (g, 1) == 0);
-+
-+ if (invertible)
-+ {
-+ if (tr->_mp_size < 0)
-+ {
-+ if (m->_mp_size >= 0)
-+ mpz_add (tr, tr, m);
-+ else
-+ mpz_sub (tr, tr, m);
-+ }
-+ mpz_swap (r, tr);
-+ }
-+
-+ mpz_clear (g);
-+ mpz_clear (tr);
-+ return invertible;
-+}
-+
-+\f
-+/* 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_xalloc_limbs (mn);
-+ gmp_assert_nocarry (mpn_lshift (tp, mp, mn, shift));
-+ mp = tp;
-+ }
-+
-+ mpz_init (base);
-+
-+ if (e->_mp_size < 0)
-+ {
-+ if (!mpz_invert (base, b, m))
-+ gmp_die ("mpz_powm: Negative exponent and non-invertible base.");
-+ }
-+ else
-+ {
-+ mp_size_t bn;
-+ mpz_abs (base, b);
-+
-+ bn = base->_mp_size;
-+ if (bn >= mn)
-+ {
-+ mpn_div_qr_preinv (NULL, base->_mp_d, base->_mp_size, mp, mn, &minv);
-+ bn = mn;
-+ }
-+
-+ /* We have reduced the absolute value. Now take care of the
-+ sign. Note that we get zero represented non-canonically as
-+ m. */
-+ if (b->_mp_size < 0)
-+ {
-+ mp_ptr bp = MPZ_REALLOC (base, mn);
-+ gmp_assert_nocarry (mpn_sub (bp, mp, mn, bp, bn));
-+ bn = mn;
-+ }
-+ base->_mp_size = mpn_normalized_size (base->_mp_d, bn);
-+ }
-+ mpz_init_set_ui (tr, 1);
-+
-+ while (en-- > 0)
-+ {
-+ mp_limb_t w = e->_mp_d[en];
-+ mp_limb_t bit;
-+
-+ bit = GMP_LIMB_HIGHBIT;
-+ do
-+ {
-+ mpz_mul (tr, tr, tr);
-+ if (w & bit)
-+ mpz_mul (tr, tr, base);
-+ if (tr->_mp_size > mn)
-+ {
-+ mpn_div_qr_preinv (NULL, tr->_mp_d, tr->_mp_size, mp, mn, &minv);
-+ tr->_mp_size = mpn_normalized_size (tr->_mp_d, mn);
-+ }
-+ bit >>= 1;
-+ }
-+ while (bit > 0);
-+ }
-+
-+ /* Final reduction */
-+ if (tr->_mp_size >= mn)
-+ {
-+ minv.shift = shift;
-+ mpn_div_qr_preinv (NULL, tr->_mp_d, tr->_mp_size, mp, mn, &minv);
-+ tr->_mp_size = mpn_normalized_size (tr->_mp_d, mn);
-+ }
-+ if (tp)
-+ gmp_free (tp);
-+
-+ mpz_swap (r, tr);
-+ mpz_clear (tr);
-+ mpz_clear (base);
-+}
-+
-+void
-+mpz_powm_ui (mpz_t r, const mpz_t b, unsigned long elimb, const mpz_t m)
-+{
-+ mpz_t e;
-+ mpz_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);
-+ {
-+ mp_bitcnt_t tb;
-+ tb = mpz_sizeinbase (y, 2) / z + 1;
-+ mpz_init2 (t, tb);
-+ mpz_setbit (t, tb);
-+ }
-+
-+ 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_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_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;
-+}
-+\f
-+/* Combinatorics */
-+
-+void
-+mpz_fac_ui (mpz_t x, unsigned long n)
-+{
-+ mpz_set_ui (x, n + (n == 0));
-+ for (;n > 2;)
-+ mpz_mul_ui (x, x, --n);
-+}
-+
-+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);
-+}
-+
-+\f
-+/* Primality testing */
-+static int
-+gmp_millerrabin (const mpz_t n, const mpz_t nm1, mpz_t y,
-+ const mpz_t q, mp_bitcnt_t k)
-+{
-+ assert (k > 0);
-+
-+ /* Caller must initialize y to the base. */
-+ mpz_powm (y, y, q, n);
-+
-+ if (mpz_cmp_ui (y, 1) == 0 || mpz_cmp (y, nm1) == 0)
-+ return 1;
-+
-+ while (--k > 0)
-+ {
-+ mpz_powm_ui (y, y, 2, n);
-+ if (mpz_cmp (y, nm1) == 0)
-+ return 1;
-+ /* y == 1 means that the previous y was a non-trivial square root
-+ of 1 (mod n). y == 0 means that n is a power of the base.
-+ In either case, n is not prime. */
-+ if (mpz_cmp_ui (y, 1) <= 0)
-+ return 0;
-+ }
-+ return 0;
-+}
-+
-+/* This product is 0xc0cfd797, and fits in 32 bits. */
-+#define GMP_PRIME_PRODUCT \
-+ (3UL*5UL*7UL*11UL*13UL*17UL*19UL*23UL*29UL)
-+
-+/* Bit (p+1)/2 is set, for each odd prime <= 61 */
-+#define GMP_PRIME_MASK 0xc96996dcUL
-+
-+int
-+mpz_probab_prime_p (const mpz_t n, int reps)
-+{
-+ mpz_t nm1;
-+ mpz_t q;
-+ mpz_t y;
-+ mp_bitcnt_t k;
-+ int is_prime;
-+ int j;
-+
-+ /* Note that we use the absolute value of n only, for compatibility
-+ with the real GMP. */
-+ if (mpz_even_p (n))
-+ return (mpz_cmpabs_ui (n, 2) == 0) ? 2 : 0;
-+
-+ /* Above test excludes n == 0 */
-+ assert (n->_mp_size != 0);
-+
-+ if (mpz_cmpabs_ui (n, 64) < 0)
-+ return (GMP_PRIME_MASK >> (n->_mp_d[0] >> 1)) & 2;
-+
-+ if (mpz_gcd_ui (NULL, n, GMP_PRIME_PRODUCT) != 1)
-+ return 0;
-+
-+ /* All prime factors are >= 31. */
-+ if (mpz_cmpabs_ui (n, 31*31) < 0)
-+ return 2;
-+
-+ /* Use Miller-Rabin, with a deterministic sequence of bases, a[j] =
-+ j^2 + j + 41 using Euler's polynomial. We potentially stop early,
-+ if a[j] >= n - 1. Since n >= 31*31, this can happen only if reps >
-+ 30 (a[30] == 971 > 31*31 == 961). */
-+
-+ mpz_init (nm1);
-+ mpz_init (q);
-+ mpz_init (y);
-+
-+ /* Find q and k, where q is odd and n = 1 + 2**k * q. */
-+ nm1->_mp_size = mpz_abs_sub_ui (nm1, n, 1);
-+ k = mpz_scan1 (nm1, 0);
-+ mpz_tdiv_q_2exp (q, nm1, k);
-+
-+ for (j = 0, is_prime = 1; is_prime & (j < reps); j++)
-+ {
-+ mpz_set_ui (y, (unsigned long) j*j+j+41);
-+ if (mpz_cmp (y, nm1) >= 0)
-+ {
-+ /* Don't try any further bases. This "early" break does not affect
-+ the result for any reasonable reps value (<=5000 was tested) */
-+ assert (j >= 30);
-+ break;
-+ }
-+ is_prime = gmp_millerrabin (n, nm1, y, q, k);
-+ }
-+ mpz_clear (nm1);
-+ mpz_clear (q);
-+ mpz_clear (y);
-+
-+ return is_prime;
-+}
-+
-+\f
-+/* Logical operations and bit manipulation. */
-+
-+/* Numbers are treated as if represented in two's complement (and
-+ infinitely sign extended). For a negative values we get the two's
-+ complement from -x = ~x + 1, where ~ is bitwise complement.
-+ Negation transforms
-+
-+ xxxx10...0
-+
-+ into
-+
-+ yyyy10...0
-+
-+ where yyyy is the bitwise complement of xxxx. So least significant
-+ bits, up to and including the first one bit, are unchanged, and
-+ the more significant bits are all complemented.
-+
-+ To change a bit from zero to one in a negative number, subtract the
-+ corresponding power of two from the absolute value. This can never
-+ underflow. To change a bit from one to zero, add the corresponding
-+ power of two, and this might overflow. E.g., if x = -001111, the
-+ two's complement is 110001. Clearing the least significant bit, we
-+ get two's complement 110000, and -010000. */
-+
-+int
-+mpz_tstbit (const mpz_t d, mp_bitcnt_t bit_index)
-+{
-+ mp_size_t limb_index;
-+ unsigned shift;
-+ mp_size_t ds;
-+ mp_size_t dn;
-+ mp_limb_t w;
-+ int bit;
-+
-+ ds = d->_mp_size;
-+ dn = GMP_ABS (ds);
-+ limb_index = bit_index / GMP_LIMB_BITS;
-+ if (limb_index >= dn)
-+ return ds < 0;
-+
-+ shift = bit_index % GMP_LIMB_BITS;
-+ w = d->_mp_d[limb_index];
-+ bit = (w >> shift) & 1;
-+
-+ if (ds < 0)
-+ {
-+ /* d < 0. Check if any of the bits below is set: If so, our bit
-+ must be complemented. */
-+ if (shift > 0 && (w << (GMP_LIMB_BITS - shift)) > 0)
-+ return bit ^ 1;
-+ while (limb_index-- > 0)
-+ if (d->_mp_d[limb_index] > 0)
-+ return bit ^ 1;
-+ }
-+ return bit;
-+}
-+
-+static void
-+mpz_abs_add_bit (mpz_t d, mp_bitcnt_t bit_index)
-+{
-+ mp_size_t dn, limb_index;
-+ mp_limb_t bit;
-+ mp_ptr dp;
-+
-+ dn = GMP_ABS (d->_mp_size);
-+
-+ limb_index = bit_index / GMP_LIMB_BITS;
-+ bit = (mp_limb_t) 1 << (bit_index % GMP_LIMB_BITS);
-+
-+ if (limb_index >= dn)
-+ {
-+ mp_size_t i;
-+ /* The bit should be set outside of the end of the number.
-+ We have to increase the size of the number. */
-+ dp = MPZ_REALLOC (d, limb_index + 1);
-+
-+ dp[limb_index] = bit;
-+ for (i = dn; i < limb_index; i++)
-+ dp[i] = 0;
-+ dn = limb_index + 1;
-+ }
-+ else
-+ {
-+ mp_limb_t cy;
-+
-+ dp = d->_mp_d;
-+
-+ cy = mpn_add_1 (dp + limb_index, dp + limb_index, dn - limb_index, bit);
-+ if (cy > 0)
-+ {
-+ dp = MPZ_REALLOC (d, dn + 1);
-+ dp[dn++] = cy;
-+ }
-+ }
-+
-+ d->_mp_size = (d->_mp_size < 0) ? - dn : dn;
-+}
-+
-+static void
-+mpz_abs_sub_bit (mpz_t d, mp_bitcnt_t bit_index)
-+{
-+ mp_size_t dn, limb_index;
-+ mp_ptr dp;
-+ mp_limb_t bit;
-+
-+ dn = GMP_ABS (d->_mp_size);
-+ dp = d->_mp_d;
-+
-+ limb_index = bit_index / GMP_LIMB_BITS;
-+ bit = (mp_limb_t) 1 << (bit_index % GMP_LIMB_BITS);
-+
-+ assert (limb_index < dn);
-+
-+ gmp_assert_nocarry (mpn_sub_1 (dp + limb_index, dp + limb_index,
-+ dn - limb_index, bit));
-+ dn = mpn_normalized_size (dp, dn);
-+ d->_mp_size = (d->_mp_size < 0) ? - dn : dn;
-+}
-+
-+void
-+mpz_setbit (mpz_t d, mp_bitcnt_t bit_index)
-+{
-+ if (!mpz_tstbit (d, bit_index))
-+ {
-+ if (d->_mp_size >= 0)
-+ mpz_abs_add_bit (d, bit_index);
-+ else
-+ mpz_abs_sub_bit (d, bit_index);
-+ }
-+}
-+
-+void
-+mpz_clrbit (mpz_t d, mp_bitcnt_t bit_index)
-+{
-+ if (mpz_tstbit (d, bit_index))
-+ {
-+ if (d->_mp_size >= 0)
-+ mpz_abs_sub_bit (d, bit_index);
-+ else
-+ mpz_abs_add_bit (d, bit_index);
-+ }
-+}
-+
-+void
-+mpz_combit (mpz_t d, mp_bitcnt_t bit_index)
-+{
-+ if (mpz_tstbit (d, bit_index) ^ (d->_mp_size < 0))
-+ mpz_abs_sub_bit (d, bit_index);
-+ else
-+ mpz_abs_add_bit (d, bit_index);
-+}
-+
-+void
-+mpz_com (mpz_t r, const mpz_t u)
-+{
-+ mpz_neg (r, u);
-+ mpz_sub_ui (r, r, 1);
-+}
-+
-+void
-+mpz_and (mpz_t r, const mpz_t u, const mpz_t v)
-+{
-+ mp_size_t un, vn, rn, i;
-+ mp_ptr up, vp, rp;
-+
-+ mp_limb_t ux, vx, rx;
-+ mp_limb_t uc, vc, rc;
-+ mp_limb_t ul, vl, rl;
-+
-+ un = GMP_ABS (u->_mp_size);
-+ vn = GMP_ABS (v->_mp_size);
-+ if (un < vn)
-+ {
-+ MPZ_SRCPTR_SWAP (u, v);
-+ MP_SIZE_T_SWAP (un, vn);
-+ }
-+ if (vn == 0)
-+ {
-+ r->_mp_size = 0;
-+ return;
-+ }
-+
-+ uc = u->_mp_size < 0;
-+ vc = v->_mp_size < 0;
-+ rc = uc & vc;
-+
-+ ux = -uc;
-+ vx = -vc;
-+ rx = -rc;
-+
-+ /* If the smaller input is positive, higher limbs don't matter. */
-+ rn = vx ? un : vn;
-+
-+ rp = MPZ_REALLOC (r, rn + 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 + 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 + rc);
-+
-+ up = u->_mp_d;
-+ vp = v->_mp_d;
-+
-+ i = 0;
-+ do
-+ {
-+ ul = (up[i] ^ ux) + uc;
-+ uc = ul < uc;
-+
-+ vl = (vp[i] ^ vx) + vc;
-+ vc = vl < vc;
-+
-+ rl = (ul ^ vl ^ rx) + rc;
-+ rc = rl < rc;
-+ rp[i] = rl;
-+ }
-+ while (++i < vn);
-+ assert (vc == 0);
-+
-+ for (; i < un; i++)
-+ {
-+ ul = (up[i] ^ ux) + uc;
-+ uc = ul < uc;
-+
-+ rl = (ul ^ ux) + rc;
-+ rc = rl < rc;
-+ rp[i] = rl;
-+ }
-+ if (rc)
-+ rp[un++] = rc;
-+ else
-+ un = mpn_normalized_size (rp, un);
-+
-+ r->_mp_size = rx ? -un : un;
-+}
-+
-+static unsigned
-+gmp_popcount_limb (mp_limb_t x)
-+{
-+ unsigned c;
-+
-+ /* Do 16 bits at a time, to avoid limb-sized constants. */
-+ for (c = 0; x > 0; x >>= 16)
-+ {
-+ unsigned w = ((x >> 1) & 0x5555) + (x & 0x5555);
-+ w = ((w >> 2) & 0x3333) + (w & 0x3333);
-+ w = ((w >> 4) & 0x0f0f) + (w & 0x0f0f);
-+ w = (w >> 8) + (w & 0x00ff);
-+ c += w;
-+ }
-+ return c;
-+}
-+
-+mp_bitcnt_t
-+mpn_popcount (mp_srcptr p, mp_size_t n)
-+{
-+ mp_size_t i;
-+ mp_bitcnt_t c;
-+
-+ for (c = 0, i = 0; i < n; i++)
-+ c += gmp_popcount_limb (p[i]);
-+
-+ return c;
-+}
-+
-+mp_bitcnt_t
-+mpz_popcount (const mpz_t u)
-+{
-+ mp_size_t un;
-+
-+ un = u->_mp_size;
-+
-+ if (un < 0)
-+ return ~(mp_bitcnt_t) 0;
-+
-+ return mpn_popcount (u->_mp_d, un);
-+}
-+
-+mp_bitcnt_t
-+mpz_hamdist (const mpz_t u, const mpz_t v)
-+{
-+ mp_size_t un, vn, i;
-+ mp_limb_t uc, vc, ul, vl, comp;
-+ mp_srcptr up, vp;
-+ mp_bitcnt_t c;
-+
-+ un = u->_mp_size;
-+ vn = v->_mp_size;
-+
-+ if ( (un ^ vn) < 0)
-+ return ~(mp_bitcnt_t) 0;
-+
-+ comp = - (uc = vc = (un < 0));
-+ if (uc)
-+ {
-+ assert (vn < 0);
-+ un = -un;
-+ vn = -vn;
-+ }
-+
-+ up = u->_mp_d;
-+ vp = v->_mp_d;
-+
-+ if (un < vn)
-+ MPN_SRCPTR_SWAP (up, un, vp, vn);
-+
-+ for (i = 0, c = 0; i < vn; i++)
-+ {
-+ ul = (up[i] ^ comp) + uc;
-+ uc = ul < uc;
-+
-+ vl = (vp[i] ^ comp) + vc;
-+ vc = vl < vc;
-+
-+ c += gmp_popcount_limb (ul ^ vl);
-+ }
-+ assert (vc == 0);
-+
-+ for (; i < un; i++)
-+ {
-+ ul = (up[i] ^ comp) + uc;
-+ uc = ul < uc;
-+
-+ c += gmp_popcount_limb (ul ^ comp);
-+ }
-+
-+ return c;
-+}
-+
-+mp_bitcnt_t
-+mpz_scan1 (const mpz_t u, mp_bitcnt_t starting_bit)
-+{
-+ mp_ptr up;
-+ mp_size_t us, un, i;
-+ mp_limb_t limb, ux;
-+
-+ us = u->_mp_size;
-+ un = GMP_ABS (us);
-+ i = starting_bit / GMP_LIMB_BITS;
-+
-+ /* Past the end there's no 1 bits for u>=0, or an immediate 1 bit
-+ for u<0. Notice this test picks up any u==0 too. */
-+ if (i >= un)
-+ return (us >= 0 ? ~(mp_bitcnt_t) 0 : starting_bit);
-+
-+ up = u->_mp_d;
-+ ux = 0;
-+ limb = up[i];
-+
-+ if (starting_bit != 0)
-+ {
-+ if (us < 0)
-+ {
-+ ux = mpn_zero_p (up, i);
-+ limb = ~ limb + ux;
-+ ux = - (mp_limb_t) (limb >= ux);
-+ }
-+
-+ /* Mask to 0 all bits before starting_bit, thus ignoring them. */
-+ limb &= (GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS));
-+ }
-+
-+ return mpn_common_scan (limb, i, up, un, ux);
-+}
-+
-+mp_bitcnt_t
-+mpz_scan0 (const mpz_t u, mp_bitcnt_t starting_bit)
-+{
-+ mp_ptr up;
-+ mp_size_t us, un, i;
-+ mp_limb_t limb, ux;
-+
-+ us = u->_mp_size;
-+ ux = - (mp_limb_t) (us >= 0);
-+ un = GMP_ABS (us);
-+ i = starting_bit / GMP_LIMB_BITS;
-+
-+ /* When past end, there's an immediate 0 bit for u>=0, or no 0 bits for
-+ u<0. Notice this test picks up all cases of u==0 too. */
-+ if (i >= un)
-+ return (ux ? starting_bit : ~(mp_bitcnt_t) 0);
-+
-+ up = u->_mp_d;
-+ limb = up[i] ^ ux;
-+
-+ if (ux == 0)
-+ limb -= mpn_zero_p (up, i); /* limb = ~(~limb + zero_p) */
-+
-+ /* Mask all bits before starting_bit, thus ignoring them. */
-+ limb &= (GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS));
-+
-+ return mpn_common_scan (limb, i, up, un, ux);
-+}
-+
-+\f
-+/* MPZ base conversion. */
-+
-+size_t
-+mpz_sizeinbase (const mpz_t u, int base)
-+{
-+ mp_size_t un;
-+ mp_srcptr up;
-+ mp_ptr tp;
-+ mp_bitcnt_t bits;
-+ struct gmp_div_inverse bi;
-+ size_t ndigits;
-+
-+ assert (base >= 2);
-+ assert (base <= 36);
-+
-+ un = GMP_ABS (u->_mp_size);
-+ if (un == 0)
-+ return 1;
-+
-+ up = u->_mp_d;
-+
-+ bits = (un - 1) * GMP_LIMB_BITS + mpn_limb_size_in_base_2 (up[un-1]);
-+ switch (base)
-+ {
-+ case 2:
-+ return bits;
-+ case 4:
-+ return (bits + 1) / 2;
-+ case 8:
-+ return (bits + 2) / 3;
-+ case 16:
-+ return (bits + 3) / 4;
-+ case 32:
-+ return (bits + 4) / 5;
-+ /* FIXME: Do something more clever for the common case of base
-+ 10. */
-+ }
-+
-+ tp = gmp_xalloc_limbs (un);
-+ mpn_copyi (tp, up, un);
-+ mpn_div_qr_1_invert (&bi, base);
-+
-+ ndigits = 0;
-+ do
-+ {
-+ ndigits++;
-+ mpn_div_qr_1_preinv (tp, tp, un, &bi);
-+ un -= (tp[un-1] == 0);
-+ }
-+ while (un > 0);
-+
-+ gmp_free (tp);
-+ return ndigits;
-+}
-+
-+char *
-+mpz_get_str (char *sp, int base, const mpz_t u)
-+{
-+ unsigned bits;
-+ const char *digits;
-+ mp_size_t un;
-+ size_t i, sn;
-+
-+ if (base >= 0)
-+ {
-+ digits = "0123456789abcdefghijklmnopqrstuvwxyz";
-+ }
-+ else
-+ {
-+ base = -base;
-+ digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
-+ }
-+ if (base <= 1)
-+ base = 10;
-+ if (base > 36)
-+ return NULL;
-+
-+ sn = 1 + mpz_sizeinbase (u, base);
-+ if (!sp)
-+ sp = gmp_xalloc (1 + sn);
-+
-+ un = GMP_ABS (u->_mp_size);
-+
-+ if (un == 0)
-+ {
-+ sp[0] = '0';
-+ sp[1] = '\0';
-+ return sp;
-+ }
-+
-+ i = 0;
-+
-+ if (u->_mp_size < 0)
-+ sp[i++] = '-';
-+
-+ bits = mpn_base_power_of_two_p (base);
-+
-+ if (bits)
-+ /* Not modified in this case. */
-+ sn = i + mpn_get_str_bits ((unsigned char *) sp + i, bits, u->_mp_d, un);
-+ else
-+ {
-+ struct mpn_base_info info;
-+ mp_ptr tp;
-+
-+ mpn_get_base_info (&info, base);
-+ tp = gmp_xalloc_limbs (un);
-+ mpn_copyi (tp, u->_mp_d, un);
-+
-+ sn = i + mpn_get_str_other ((unsigned char *) sp + i, base, &info, tp, un);
-+ gmp_free (tp);
-+ }
-+
-+ for (; i < sn; i++)
-+ sp[i] = digits[(unsigned char) sp[i]];
-+
-+ sp[sn] = '\0';
-+ return sp;
-+}
-+
-+int
-+mpz_set_str (mpz_t r, const char *sp, int base)
-+{
-+ unsigned bits;
-+ mp_size_t rn, alloc;
-+ mp_ptr rp;
-+ size_t sn;
-+ int sign;
-+ unsigned char *dp;
-+
-+ assert (base == 0 || (base >= 2 && base <= 36));
-+
-+ while (isspace( (unsigned char) *sp))
-+ sp++;
-+
-+ sign = (*sp == '-');
-+ sp += sign;
-+
-+ if (base == 0)
-+ {
-+ if (*sp == '0')
-+ {
-+ sp++;
-+ if (*sp == 'x' || *sp == 'X')
-+ {
-+ base = 16;
-+ sp++;
-+ }
-+ else if (*sp == 'b' || *sp == 'B')
-+ {
-+ base = 2;
-+ sp++;
-+ }
-+ else
-+ base = 8;
-+ }
-+ else
-+ base = 10;
-+ }
-+
-+ sn = strlen (sp);
-+ dp = gmp_xalloc (sn + (sn == 0));
-+
-+ for (sn = 0; *sp; sp++)
-+ {
-+ unsigned digit;
-+
-+ if (isspace ((unsigned char) *sp))
-+ continue;
-+ if (*sp >= '0' && *sp <= '9')
-+ digit = *sp - '0';
-+ else if (*sp >= 'a' && *sp <= 'z')
-+ digit = *sp - 'a' + 10;
-+ else if (*sp >= 'A' && *sp <= 'Z')
-+ digit = *sp - 'A' + 10;
-+ else
-+ digit = base; /* fail */
-+
-+ if (digit >= base)
-+ {
-+ gmp_free (dp);
-+ r->_mp_size = 0;
-+ return -1;
-+ }
-+
-+ dp[sn++] = digit;
-+ }
-+
-+ bits = mpn_base_power_of_two_p (base);
-+
-+ if (bits > 0)
-+ {
-+ alloc = (sn * bits + GMP_LIMB_BITS - 1) / GMP_LIMB_BITS;
-+ rp = MPZ_REALLOC (r, alloc);
-+ rn = mpn_set_str_bits (rp, dp, sn, bits);
-+ }
-+ else
-+ {
-+ struct mpn_base_info info;
-+ mpn_get_base_info (&info, base);
-+ alloc = (sn + info.exp - 1) / info.exp;
-+ rp = MPZ_REALLOC (r, alloc);
-+ rn = mpn_set_str_other (rp, dp, sn, base, &info);
-+ }
-+ assert (rn <= alloc);
-+ gmp_free (dp);
-+
-+ r->_mp_size = sign ? - rn : rn;
-+
-+ return 0;
-+}
-+
-+int
-+mpz_init_set_str (mpz_t r, const char *sp, int base)
-+{
-+ mpz_init (r);
-+ return mpz_set_str (r, sp, base);
-+}
-+
-+size_t
-+mpz_out_str (FILE *stream, int base, const mpz_t x)
-+{
-+ char *str;
-+ size_t len;
-+
-+ str = mpz_get_str (NULL, base, x);
-+ len = strlen (str);
-+ len = fwrite (str, 1, len, stream);
-+ gmp_free (str);
-+ return len;
-+}
-+
-+\f
-+static int
-+gmp_detect_endian (void)
-+{
-+ static const int i = 2;
-+ const unsigned char *p = (const unsigned char *) &i;
-+ return 1 - *p;
-+}
-+
-+/* Import and export. Does not support nails. */
-+void
-+mpz_import (mpz_t r, size_t count, int order, size_t size, int endian,
-+ size_t nails, const void *src)
-+{
-+ const unsigned char *p;
-+ ptrdiff_t word_step;
-+ mp_ptr rp;
-+ mp_size_t rn;
-+
-+ /* The current (partial) limb. */
-+ mp_limb_t limb;
-+ /* The number of bytes already copied to this limb (starting from
-+ the low end). */
-+ size_t bytes;
-+ /* The index where the limb should be stored, when completed. */
-+ mp_size_t i;
-+
-+ if (nails != 0)
-+ gmp_die ("mpz_import: Nails not supported.");
-+
-+ assert (order == 1 || order == -1);
-+ assert (endian >= -1 && endian <= 1);
-+
-+ if (endian == 0)
-+ endian = gmp_detect_endian ();
-+
-+ p = (unsigned char *) src;
-+
-+ word_step = (order != endian) ? 2 * size : 0;
-+
-+ /* Process bytes from the least significant end, so point p at the
-+ least significant word. */
-+ if (order == 1)
-+ {
-+ p += size * (count - 1);
-+ word_step = - word_step;
-+ }
-+
-+ /* And at least significant byte of that word. */
-+ if (endian == 1)
-+ p += (size - 1);
-+
-+ rn = (size * count + sizeof(mp_limb_t) - 1) / sizeof(mp_limb_t);
-+ rp = MPZ_REALLOC (r, rn);
-+
-+ for (limb = 0, bytes = 0, i = 0; count > 0; count--, p += word_step)
-+ {
-+ size_t j;
-+ for (j = 0; j < size; j++, p -= (ptrdiff_t) endian)
-+ {
-+ limb |= (mp_limb_t) *p << (bytes++ * CHAR_BIT);
-+ if (bytes == sizeof(mp_limb_t))
-+ {
-+ rp[i++] = limb;
-+ bytes = 0;
-+ limb = 0;
-+ }
-+ }
-+ }
-+ assert (i + (bytes > 0) == rn);
-+ if (limb != 0)
-+ rp[i++] = limb;
-+ else
-+ i = mpn_normalized_size (rp, i);
-+
-+ r->_mp_size = i;
-+}
-+
-+void *
-+mpz_export (void *r, size_t *countp, int order, size_t size, int endian,
-+ size_t nails, const mpz_t u)
-+{
-+ size_t count;
-+ mp_size_t un;
-+
-+ if (nails != 0)
-+ gmp_die ("mpz_import: Nails not supported.");
-+
-+ assert (order == 1 || order == -1);
-+ assert (endian >= -1 && endian <= 1);
-+ assert (size > 0 || u->_mp_size == 0);
-+
-+ un = u->_mp_size;
-+ count = 0;
-+ if (un != 0)
-+ {
-+ size_t k;
-+ unsigned char *p;
-+ ptrdiff_t word_step;
-+ /* The current (partial) limb. */
-+ mp_limb_t limb;
-+ /* The number of bytes left to to in this limb. */
-+ size_t bytes;
-+ /* The index where the limb was read. */
-+ mp_size_t i;
-+
-+ un = GMP_ABS (un);
-+
-+ /* Count bytes in top limb. */
-+ limb = u->_mp_d[un-1];
-+ assert (limb != 0);
-+
-+ k = 0;
-+ do {
-+ k++; limb >>= CHAR_BIT;
-+ } while (limb != 0);
-+
-+ count = (k + (un-1) * sizeof (mp_limb_t) + size - 1) / size;
-+
-+ if (!r)
-+ r = gmp_xalloc (count * size);
-+
-+ if (endian == 0)
-+ endian = gmp_detect_endian ();
-+
-+ p = (unsigned char *) r;
-+
-+ word_step = (order != endian) ? 2 * size : 0;
-+
-+ /* Process bytes from the least significant end, so point p at the
-+ least significant word. */
-+ if (order == 1)
-+ {
-+ p += size * (count - 1);
-+ word_step = - word_step;
-+ }
-+
-+ /* And at least significant byte of that word. */
-+ if (endian == 1)
-+ p += (size - 1);
-+
-+ for (bytes = 0, i = 0, k = 0; k < count; k++, p += word_step)
-+ {
-+ size_t j;
-+ for (j = 0; j < size; j++, p -= (ptrdiff_t) endian)
-+ {
-+ if (bytes == 0)
-+ {
-+ if (i < un)
-+ limb = u->_mp_d[i++];
-+ bytes = sizeof (mp_limb_t);
-+ }
-+ *p = limb;
-+ limb >>= CHAR_BIT;
-+ bytes--;
-+ }
-+ }
-+ assert (i == un);
-+ assert (k == count);
-+ }
-+
-+ if (countp)
-+ *countp = count;
-+
-+ return r;
-+}
---- a/src/Makefile.am
-+++ b/src/Makefile.am
-@@ -48,4 +48,8 @@ if BUILD_CLI
- nft_SOURCES += cli.c
- endif
-
-+if BUILD_MINIGMP
-+nft_SOURCES += mini-gmp.c mini-gmp-printf.c
-+endif
-+
- nft_LDADD = ${LIBMNL_LIBS} ${LIBNFTNL_LIBS}
projects / openwrt / staging / chunkeey.git / commitdiff