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+From da4e4f5db6561923ad239aa653660250aaeb5873 Mon Sep 17 00:00:00 2001
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+From: Steven Barth <[email protected]>
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+Date: Mon, 6 Oct 2014 07:26:13 +0200
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+Subject: [PATCH 2/2] build: allow building with mini-gmp instead of gmp
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+
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+This introduces --without-libgmp which includes mini-gmp into nft
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+(adding ~30k) but avoids linking libgmp which is >400k.
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+
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+This is useful for embedded distributions not using gmp otherwise.
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+
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+Note: currently --without-libgmp must be used with --disable-debug.
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+
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+Signed-off-by: Steven Barth <[email protected]>
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+---
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+ configure.ac | 14 +-
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+ include/bignum.h | 17 +
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+ include/expression.h | 2 +-
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+ include/gmputil.h | 2 +-
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+ include/mini-gmp.h | 294 ++++
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+ include/utils.h | 4 +-
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+ src/Makefile.in | 5 +
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+ src/datatype.c | 4 +-
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+ src/erec.c | 4 +-
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+ src/evaluate.c | 8 +-
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+ src/gmputil.c | 1 -
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+ src/mini-gmp-printf.c | 62 +
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+ src/mini-gmp.c | 4386 +++++++++++++++++++++++++++++++++++++++++++++++++
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+ 13 files changed, 4790 insertions(+), 13 deletions(-)
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+ create mode 100644 include/bignum.h
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+ create mode 100644 include/mini-gmp.h
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+ create mode 100644 src/mini-gmp-printf.c
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+ create mode 100644 src/mini-gmp.c
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+
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+--- a/configure.ac
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++++ b/configure.ac
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+@@ -68,8 +68,18 @@ AC_CHECK_LIB([mnl], [mnl_socket_open], ,
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+ AC_CHECK_LIB([nftnl], [nft_rule_alloc], ,
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+ AC_MSG_ERROR([No suitable version of libnftnl found]))
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+
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+-AC_CHECK_LIB([gmp], [__gmpz_init], ,
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+- AC_MSG_ERROR([No suitable version of libgmp found]))
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++AC_ARG_WITH([libgmp], [AS_HELP_STRING([--without-libgmp],
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++ [Disable libgmp support (use builtin mini-gmp)])], [],
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++ [with_libgmp=yes])
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++AS_IF([test "x$with_libgmp" != xno], [
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++AC_CHECK_LIB([gmp],[__gmpz_init], , AC_MSG_ERROR([No suitable version of libgmp found]))
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++])
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++AC_SUBST(with_libgmp)
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++
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++
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++AS_IF([test "x$with_libgmp" != xyes -a "x$CONFIG_DEBUG" = xy], [
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++AC_MSG_ERROR([--without-libgmp MUST be used with --disable-debug])
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++])
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+
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+
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+ AC_ARG_WITH([libreadline], [AS_HELP_STRING([--without-libreadline],
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+--- /dev/null
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++++ b/include/bignum.h
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+@@ -0,0 +1,17 @@
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++#ifndef NFTABLES_BIGNUM_H
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++#define NFTABLES_BIGNUM_H
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++
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++#ifdef HAVE_LIBGMP
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++#include <gmp.h>
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++
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++#else
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++
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++#include <mini-gmp.h>
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++#include <stdio.h>
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++#include <stdarg.h>
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++
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++int gmp_printf(const char *format, const mpz_t value);
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++
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++#endif
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++
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++#endif /* NFTABLES_BIGNUM_H */
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+--- a/include/expression.h
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++++ b/include/expression.h
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+@@ -2,7 +2,7 @@
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+ #define NFTABLES_EXPRESSION_H
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+
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+ #include <stdbool.h>
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+-#include <gmp.h>
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++#include <bignum.h>
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+ #include <linux/netfilter/nf_tables.h>
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+
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+ #include <nftables.h>
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+--- a/include/gmputil.h
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++++ b/include/gmputil.h
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+@@ -1,7 +1,7 @@
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+ #ifndef NFTABLES_GMPUTIL_H
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+ #define NFTABLES_GMPUTIL_H
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+
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+-#include <gmp.h>
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++#include <bignum.h>
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+ #include <asm/byteorder.h>
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+
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+ enum mpz_word_order {
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+--- /dev/null
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++++ b/include/mini-gmp.h
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+@@ -0,0 +1,294 @@
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++/* mini-gmp, a minimalistic implementation of a GNU GMP subset.
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++
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++Copyright 2011-2014 Free Software Foundation, Inc.
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++
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++This file is part of the GNU MP Library.
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++
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++The GNU MP Library is free software; you can redistribute it and/or modify
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++it under the terms of either:
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++
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++ * the GNU Lesser General Public License as published by the Free
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++ Software Foundation; either version 3 of the License, or (at your
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++ option) any later version.
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++
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++or
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++
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++ * the GNU General Public License as published by the Free Software
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++ Foundation; either version 2 of the License, or (at your option) any
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++ later version.
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++
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++or both in parallel, as here.
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++
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++The GNU MP Library is distributed in the hope that it will be useful, but
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++WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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++or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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++for more details.
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++
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++You should have received copies of the GNU General Public License and the
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++GNU Lesser General Public License along with the GNU MP Library. If not,
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++see https://www.gnu.org/licenses/. */
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++
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++/* About mini-gmp: This is a minimal implementation of a subset of the
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++ GMP interface. It is intended for inclusion into applications which
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++ have modest bignums needs, as a fallback when the real GMP library
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++ is not installed.
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++
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++ This file defines the public interface. */
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++
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++#ifndef __MINI_GMP_H__
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++#define __MINI_GMP_H__
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++
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++/* For size_t */
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++#include <stddef.h>
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++
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++#if defined (__cplusplus)
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++extern "C" {
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++#endif
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++
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++void mp_set_memory_functions (void *(*) (size_t),
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++ void *(*) (void *, size_t, size_t),
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++ void (*) (void *, size_t));
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++
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++void mp_get_memory_functions (void *(**) (size_t),
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++ void *(**) (void *, size_t, size_t),
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++ void (**) (void *, size_t));
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++
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++typedef unsigned long mp_limb_t;
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++typedef long mp_size_t;
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++typedef unsigned long mp_bitcnt_t;
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++
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++typedef mp_limb_t *mp_ptr;
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++typedef const mp_limb_t *mp_srcptr;
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++
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++typedef struct
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++{
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++ int _mp_alloc; /* Number of *limbs* allocated and pointed
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++ to by the _mp_d field. */
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++ int _mp_size; /* abs(_mp_size) is the number of limbs the
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++ last field points to. If _mp_size is
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++ negative this is a negative number. */
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++ mp_limb_t *_mp_d; /* Pointer to the limbs. */
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++} __mpz_struct;
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++
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++typedef __mpz_struct mpz_t[1];
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++
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++typedef __mpz_struct *mpz_ptr;
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++typedef const __mpz_struct *mpz_srcptr;
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++
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++extern const int mp_bits_per_limb;
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++
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++void mpn_copyi (mp_ptr, mp_srcptr, mp_size_t);
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++void mpn_copyd (mp_ptr, mp_srcptr, mp_size_t);
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++void mpn_zero (mp_ptr, mp_size_t);
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++
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++int mpn_cmp (mp_srcptr, mp_srcptr, mp_size_t);
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++
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++mp_limb_t mpn_add_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
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++mp_limb_t mpn_add_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
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++mp_limb_t mpn_add (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t);
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++
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++mp_limb_t mpn_sub_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
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++mp_limb_t mpn_sub_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
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++mp_limb_t mpn_sub (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t);
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++
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++mp_limb_t mpn_mul_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
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++mp_limb_t mpn_addmul_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
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++mp_limb_t mpn_submul_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
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++
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++mp_limb_t mpn_mul (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t);
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++void mpn_mul_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
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++void mpn_sqr (mp_ptr, mp_srcptr, mp_size_t);
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++int mpn_perfect_square_p (mp_srcptr, mp_size_t);
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++mp_size_t mpn_sqrtrem (mp_ptr, mp_ptr, mp_srcptr, mp_size_t);
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++
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++mp_limb_t mpn_lshift (mp_ptr, mp_srcptr, mp_size_t, unsigned int);
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++mp_limb_t mpn_rshift (mp_ptr, mp_srcptr, mp_size_t, unsigned int);
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++
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++mp_bitcnt_t mpn_scan0 (mp_srcptr, mp_bitcnt_t);
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++mp_bitcnt_t mpn_scan1 (mp_srcptr, mp_bitcnt_t);
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++
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++mp_bitcnt_t mpn_popcount (mp_srcptr, mp_size_t);
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++
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++mp_limb_t mpn_invert_3by2 (mp_limb_t, mp_limb_t);
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++#define mpn_invert_limb(x) mpn_invert_3by2 ((x), 0)
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++
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++size_t mpn_get_str (unsigned char *, int, mp_ptr, mp_size_t);
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++mp_size_t mpn_set_str (mp_ptr, const unsigned char *, size_t, int);
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++
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++void mpz_init (mpz_t);
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++void mpz_init2 (mpz_t, mp_bitcnt_t);
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++void mpz_clear (mpz_t);
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++
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++#define mpz_odd_p(z) (((z)->_mp_size != 0) & (int) (z)->_mp_d[0])
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++#define mpz_even_p(z) (! mpz_odd_p (z))
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++
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++int mpz_sgn (const mpz_t);
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++int mpz_cmp_si (const mpz_t, long);
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++int mpz_cmp_ui (const mpz_t, unsigned long);
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++int mpz_cmp (const mpz_t, const mpz_t);
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++int mpz_cmpabs_ui (const mpz_t, unsigned long);
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++int mpz_cmpabs (const mpz_t, const mpz_t);
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++int mpz_cmp_d (const mpz_t, double);
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++int mpz_cmpabs_d (const mpz_t, double);
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++
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++void mpz_abs (mpz_t, const mpz_t);
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++void mpz_neg (mpz_t, const mpz_t);
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++void mpz_swap (mpz_t, mpz_t);
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++
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++void mpz_add_ui (mpz_t, const mpz_t, unsigned long);
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++void mpz_add (mpz_t, const mpz_t, const mpz_t);
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++void mpz_sub_ui (mpz_t, const mpz_t, unsigned long);
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++void mpz_ui_sub (mpz_t, unsigned long, const mpz_t);
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++void mpz_sub (mpz_t, const mpz_t, const mpz_t);
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++
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++void mpz_mul_si (mpz_t, const mpz_t, long int);
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++void mpz_mul_ui (mpz_t, const mpz_t, unsigned long int);
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++void mpz_mul (mpz_t, const mpz_t, const mpz_t);
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++void mpz_mul_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
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++void mpz_addmul_ui (mpz_t, const mpz_t, unsigned long int);
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++void mpz_addmul (mpz_t, const mpz_t, const mpz_t);
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++void mpz_submul_ui (mpz_t, const mpz_t, unsigned long int);
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++void mpz_submul (mpz_t, const mpz_t, const mpz_t);
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++
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++void mpz_cdiv_qr (mpz_t, mpz_t, const mpz_t, const mpz_t);
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++void mpz_fdiv_qr (mpz_t, mpz_t, const mpz_t, const mpz_t);
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++void mpz_tdiv_qr (mpz_t, mpz_t, const mpz_t, const mpz_t);
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++void mpz_cdiv_q (mpz_t, const mpz_t, const mpz_t);
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++void mpz_fdiv_q (mpz_t, const mpz_t, const mpz_t);
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++void mpz_tdiv_q (mpz_t, const mpz_t, const mpz_t);
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++void mpz_cdiv_r (mpz_t, const mpz_t, const mpz_t);
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++void mpz_fdiv_r (mpz_t, const mpz_t, const mpz_t);
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++void mpz_tdiv_r (mpz_t, const mpz_t, const mpz_t);
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++
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++void mpz_cdiv_q_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
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++void mpz_fdiv_q_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
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++void mpz_tdiv_q_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
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++void mpz_cdiv_r_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
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++void mpz_fdiv_r_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
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++void mpz_tdiv_r_2exp (mpz_t, const mpz_t, mp_bitcnt_t);
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++
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++void mpz_mod (mpz_t, const mpz_t, const mpz_t);
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++
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++void mpz_divexact (mpz_t, const mpz_t, const mpz_t);
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++
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++int mpz_divisible_p (const mpz_t, const mpz_t);
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++int mpz_congruent_p (const mpz_t, const mpz_t, const mpz_t);
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++
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++unsigned long mpz_cdiv_qr_ui (mpz_t, mpz_t, const mpz_t, unsigned long);
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++unsigned long mpz_fdiv_qr_ui (mpz_t, mpz_t, const mpz_t, unsigned long);
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++unsigned long mpz_tdiv_qr_ui (mpz_t, mpz_t, const mpz_t, unsigned long);
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++unsigned long mpz_cdiv_q_ui (mpz_t, const mpz_t, unsigned long);
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++unsigned long mpz_fdiv_q_ui (mpz_t, const mpz_t, unsigned long);
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++unsigned long mpz_tdiv_q_ui (mpz_t, const mpz_t, unsigned long);
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++unsigned long mpz_cdiv_r_ui (mpz_t, const mpz_t, unsigned long);
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++unsigned long mpz_fdiv_r_ui (mpz_t, const mpz_t, unsigned long);
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++unsigned long mpz_tdiv_r_ui (mpz_t, const mpz_t, unsigned long);
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++unsigned long mpz_cdiv_ui (const mpz_t, unsigned long);
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++unsigned long mpz_fdiv_ui (const mpz_t, unsigned long);
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++unsigned long mpz_tdiv_ui (const mpz_t, unsigned long);
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++
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++unsigned long mpz_mod_ui (mpz_t, const mpz_t, unsigned long);
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++
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++void mpz_divexact_ui (mpz_t, const mpz_t, unsigned long);
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++
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++int mpz_divisible_ui_p (const mpz_t, unsigned long);
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++
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++unsigned long mpz_gcd_ui (mpz_t, const mpz_t, unsigned long);
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++void mpz_gcd (mpz_t, const mpz_t, const mpz_t);
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++void mpz_gcdext (mpz_t, mpz_t, mpz_t, const mpz_t, const mpz_t);
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++void mpz_lcm_ui (mpz_t, const mpz_t, unsigned long);
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++void mpz_lcm (mpz_t, const mpz_t, const mpz_t);
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++int mpz_invert (mpz_t, const mpz_t, const mpz_t);
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++
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++void mpz_sqrtrem (mpz_t, mpz_t, const mpz_t);
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++void mpz_sqrt (mpz_t, const mpz_t);
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++int mpz_perfect_square_p (const mpz_t);
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++
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++void mpz_pow_ui (mpz_t, const mpz_t, unsigned long);
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++void mpz_ui_pow_ui (mpz_t, unsigned long, unsigned long);
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++void mpz_powm (mpz_t, const mpz_t, const mpz_t, const mpz_t);
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++void mpz_powm_ui (mpz_t, const mpz_t, unsigned long, const mpz_t);
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++
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++void mpz_rootrem (mpz_t, mpz_t, const mpz_t, unsigned long);
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++int mpz_root (mpz_t, const mpz_t, unsigned long);
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++
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++void mpz_fac_ui (mpz_t, unsigned long);
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++void mpz_bin_uiui (mpz_t, unsigned long, unsigned long);
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++
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++int mpz_probab_prime_p (const mpz_t, int);
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++
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++int mpz_tstbit (const mpz_t, mp_bitcnt_t);
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++void mpz_setbit (mpz_t, mp_bitcnt_t);
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++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/Makefile.in
|
|
|
++++ b/src/Makefile.in
|
|
|
+@@ -31,3 +31,8 @@ nft-extra-clean-files += parser.c parser
|
|
|
+
|
|
|
+ nft-obj += scanner.o
|
|
|
+ nft-extra-clean-files += scanner.c scanner.h
|
|
|
++
|
|
|
++ifneq (@with_libgmp@,yes)
|
|
|
++nft-obj += mini-gmp.o
|
|
|
++nft-obj += mini-gmp-printf.o
|
|
|
++endif
|
|
|
+--- a/src/datatype.c
|
|
|
++++ b/src/datatype.c
|
|
|
+@@ -252,11 +252,9 @@ 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);
|
|
|
+ if (sym->dtype != &integer_type)
|
|
|
+ return NULL;
|
|
|
+--- a/src/erec.c
|
|
|
++++ b/src/erec.c
|
|
|
+@@ -43,6 +43,7 @@ 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)
|
|
|
+@@ -54,10 +55,11 @@ 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
|
|
|
+@@ -228,9 +228,13 @@ 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"
|
|
|
++
|
|
|
++
|
|
|
++/* 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;
|
|
|
++
|
|
|
++
|
|
|
++/* 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));
|
|
|
++}
|
|
|
++
|
|
|
++
|
|
|
++/* 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);
|
|
|
++}
|
|
|
++
|
|
|
++
|
|
|
++/* 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);
|
|
|
++}
|
|
|
++
|
|
|
++
|
|
|
++/* 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);
|
|
|
++ }
|
|
|
++}
|
|
|
++
|
|
|
++
|
|
|
++/* 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)
|
|
|
++
|
|
|
++/* 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;
|
|
|
++}
|
|
|
++
|
|
|
++
|
|
|
++/* 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);
|
|
|
++ }
|
|
|
++}
|
|
|
++
|
|
|
++
|
|
|
++/* 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);
|
|
|
++}
|
|
|
++
|
|
|
++
|
|
|
++/* 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;
|
|
|
++}
|
|
|
++
|
|
|
++
|
|
|
++/* 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);
|
|
|
++}
|
|
|
++
|
|
|
++
|
|
|
++/* 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;
|
|
|
++}
|
|
|
++
|
|
|
++
|
|
|
++/* GCD */
|
|
|
++static mp_limb_t
|
|
|
++mpn_gcd_11 (mp_limb_t u, mp_limb_t v)
|
|
|
++{
|
|
|
++ unsigned shift;
|
|
|
++
|
|
|
++ assert ( (u | v) > 0);
|
|
|
++
|
|
|
++ if (u == 0)
|
|
|
++ return v;
|
|
|
++ else if (v == 0)
|
|
|
++ return u;
|
|
|
++
|
|
|
++ gmp_ctz (shift, u | v);
|
|
|
++
|
|
|
++ u >>= shift;
|
|
|
++ v >>= shift;
|
|
|
++
|
|
|
++ if ( (u & 1) == 0)
|
|
|
++ MP_LIMB_T_SWAP (u, v);
|
|
|
++
|
|
|
++ while ( (v & 1) == 0)
|
|
|
++ v >>= 1;
|
|
|
++
|
|
|
++ while (u != v)
|
|
|
++ {
|
|
|
++ if (u > v)
|
|
|
++ {
|
|
|
++ u -= v;
|
|
|
++ do
|
|
|
++ u >>= 1;
|
|
|
++ while ( (u & 1) == 0);
|
|
|
++ }
|
|
|
++ else
|
|
|
++ {
|
|
|
++ v -= u;
|
|
|
++ do
|
|
|
++ v >>= 1;
|
|
|
++ while ( (v & 1) == 0);
|
|
|
++ }
|
|
|
++ }
|
|
|
++ return u << shift;
|
|
|
++}
|
|
|
++
|
|
|
++unsigned long
|
|
|
++mpz_gcd_ui (mpz_t g, const mpz_t u, unsigned long v)
|
|
|
++{
|
|
|
++ mp_size_t un;
|
|
|
++
|
|
|
++ if (v == 0)
|
|
|
++ {
|
|
|
++ if (g)
|
|
|
++ mpz_abs (g, u);
|
|
|
++ }
|
|
|
++ else
|
|
|
++ {
|
|
|
++ un = GMP_ABS (u->_mp_size);
|
|
|
++ if (un != 0)
|
|
|
++ v = mpn_gcd_11 (mpn_div_qr_1 (NULL, u->_mp_d, un, v), v);
|
|
|
++
|
|
|
++ if (g)
|
|
|
++ mpz_set_ui (g, v);
|
|
|
++ }
|
|
|
++
|
|
|
++ return v;
|
|
|
++}
|
|
|
++
|
|
|
++static mp_bitcnt_t
|
|
|
++mpz_make_odd (mpz_t r)
|
|
|
++{
|
|
|
++ mp_bitcnt_t shift;
|
|
|
++
|
|
|
++ assert (r->_mp_size > 0);
|
|
|
++ /* Count trailing zeros, equivalent to mpn_scan1, because we know that there is a 1 */
|
|
|
++ shift = mpn_common_scan (r->_mp_d[0], 0, r->_mp_d, 0, 0);
|
|
|
++ mpz_tdiv_q_2exp (r, r, shift);
|
|
|
++
|
|
|
++ return shift;
|
|
|
++}
|
|
|
++
|
|
|
++void
|
|
|
++mpz_gcd (mpz_t g, const mpz_t u, const mpz_t v)
|
|
|
++{
|
|
|
++ mpz_t tu, tv;
|
|
|
++ mp_bitcnt_t uz, vz, gz;
|
|
|
++
|
|
|
++ if (u->_mp_size == 0)
|
|
|
++ {
|
|
|
++ mpz_abs (g, v);
|
|
|
++ return;
|
|
|
++ }
|
|
|
++ if (v->_mp_size == 0)
|
|
|
++ {
|
|
|
++ mpz_abs (g, u);
|
|
|
++ return;
|
|
|
++ }
|
|
|
++
|
|
|
++ mpz_init (tu);
|
|
|
++ mpz_init (tv);
|
|
|
++
|
|
|
++ mpz_abs (tu, u);
|
|
|
++ uz = mpz_make_odd (tu);
|
|
|
++ mpz_abs (tv, v);
|
|
|
++ vz = mpz_make_odd (tv);
|
|
|
++ gz = GMP_MIN (uz, vz);
|
|
|
++
|
|
|
++ if (tu->_mp_size < tv->_mp_size)
|
|
|
++ mpz_swap (tu, tv);
|
|
|
++
|
|
|
++ mpz_tdiv_r (tu, tu, tv);
|
|
|
++ if (tu->_mp_size == 0)
|
|
|
++ {
|
|
|
++ mpz_swap (g, tv);
|
|
|
++ }
|
|
|
++ else
|
|
|
++ for (;;)
|
|
|
++ {
|
|
|
++ int c;
|
|
|
++
|
|
|
++ mpz_make_odd (tu);
|
|
|
++ c = mpz_cmp (tu, tv);
|
|
|
++ if (c == 0)
|
|
|
++ {
|
|
|
++ mpz_swap (g, tu);
|
|
|
++ break;
|
|
|
++ }
|
|
|
++ if (c < 0)
|
|
|
++ mpz_swap (tu, tv);
|
|
|
++
|
|
|
++ if (tv->_mp_size == 1)
|
|
|
++ {
|
|
|
++ mp_limb_t vl = tv->_mp_d[0];
|
|
|
++ mp_limb_t ul = mpz_tdiv_ui (tu, vl);
|
|
|
++ mpz_set_ui (g, mpn_gcd_11 (ul, vl));
|
|
|
++ break;
|
|
|
++ }
|
|
|
++ mpz_sub (tu, tu, tv);
|
|
|
++ }
|
|
|
++ mpz_clear (tu);
|
|
|
++ mpz_clear (tv);
|
|
|
++ mpz_mul_2exp (g, g, gz);
|
|
|
++}
|
|
|
++
|
|
|
++void
|
|
|
++mpz_gcdext (mpz_t g, mpz_t s, mpz_t t, const mpz_t u, const mpz_t v)
|
|
|
++{
|
|
|
++ mpz_t tu, tv, s0, s1, t0, t1;
|
|
|
++ mp_bitcnt_t uz, vz, gz;
|
|
|
++ mp_bitcnt_t power;
|
|
|
++
|
|
|
++ if (u->_mp_size == 0)
|
|
|
++ {
|
|
|
++ /* g = 0 u + sgn(v) v */
|
|
|
++ signed long sign = mpz_sgn (v);
|
|
|
++ mpz_abs (g, v);
|
|
|
++ if (s)
|
|
|
++ mpz_set_ui (s, 0);
|
|
|
++ if (t)
|
|
|
++ mpz_set_si (t, sign);
|
|
|
++ return;
|
|
|
++ }
|
|
|
++
|
|
|
++ if (v->_mp_size == 0)
|
|
|
++ {
|
|
|
++ /* g = sgn(u) u + 0 v */
|
|
|
++ signed long sign = mpz_sgn (u);
|
|
|
++ mpz_abs (g, u);
|
|
|
++ if (s)
|
|
|
++ mpz_set_si (s, sign);
|
|
|
++ if (t)
|
|
|
++ mpz_set_ui (t, 0);
|
|
|
++ return;
|
|
|
++ }
|
|
|
++
|
|
|
++ mpz_init (tu);
|
|
|
++ mpz_init (tv);
|
|
|
++ mpz_init (s0);
|
|
|
++ mpz_init (s1);
|
|
|
++ mpz_init (t0);
|
|
|
++ mpz_init (t1);
|
|
|
++
|
|
|
++ mpz_abs (tu, u);
|
|
|
++ uz = mpz_make_odd (tu);
|
|
|
++ mpz_abs (tv, v);
|
|
|
++ vz = mpz_make_odd (tv);
|
|
|
++ gz = GMP_MIN (uz, vz);
|
|
|
++
|
|
|
++ uz -= gz;
|
|
|
++ vz -= gz;
|
|
|
++
|
|
|
++ /* Cofactors corresponding to odd gcd. gz handled later. */
|
|
|
++ if (tu->_mp_size < tv->_mp_size)
|
|
|
++ {
|
|
|
++ mpz_swap (tu, tv);
|
|
|
++ MPZ_SRCPTR_SWAP (u, v);
|
|
|
++ MPZ_PTR_SWAP (s, t);
|
|
|
++ MP_BITCNT_T_SWAP (uz, vz);
|
|
|
++ }
|
|
|
++
|
|
|
++ /* Maintain
|
|
|
++ *
|
|
|
++ * u = t0 tu + t1 tv
|
|
|
++ * v = s0 tu + s1 tv
|
|
|
++ *
|
|
|
++ * where u and v denote the inputs with common factors of two
|
|
|
++ * eliminated, and det (s0, t0; s1, t1) = 2^p. Then
|
|
|
++ *
|
|
|
++ * 2^p tu = s1 u - t1 v
|
|
|
++ * 2^p tv = -s0 u + t0 v
|
|
|
++ */
|
|
|
++
|
|
|
++ /* After initial division, tu = q tv + tu', we have
|
|
|
++ *
|
|
|
++ * u = 2^uz (tu' + q tv)
|
|
|
++ * v = 2^vz tv
|
|
|
++ *
|
|
|
++ * or
|
|
|
++ *
|
|
|
++ * t0 = 2^uz, t1 = 2^uz q
|
|
|
++ * s0 = 0, s1 = 2^vz
|
|
|
++ */
|
|
|
++
|
|
|
++ mpz_setbit (t0, uz);
|
|
|
++ mpz_tdiv_qr (t1, tu, tu, tv);
|
|
|
++ mpz_mul_2exp (t1, t1, uz);
|
|
|
++
|
|
|
++ mpz_setbit (s1, vz);
|
|
|
++ power = uz + vz;
|
|
|
++
|
|
|
++ if (tu->_mp_size > 0)
|
|
|
++ {
|
|
|
++ mp_bitcnt_t shift;
|
|
|
++ shift = mpz_make_odd (tu);
|
|
|
++ mpz_mul_2exp (t0, t0, shift);
|
|
|
++ mpz_mul_2exp (s0, s0, shift);
|
|
|
++ power += shift;
|
|
|
++
|
|
|
++ for (;;)
|
|
|
++ {
|
|
|
++ int c;
|
|
|
++ c = mpz_cmp (tu, tv);
|
|
|
++ if (c == 0)
|
|
|
++ break;
|
|
|
++
|
|
|
++ if (c < 0)
|
|
|
++ {
|
|
|
++ /* tv = tv' + tu
|
|
|
++ *
|
|
|
++ * u = t0 tu + t1 (tv' + tu) = (t0 + t1) tu + t1 tv'
|
|
|
++ * v = s0 tu + s1 (tv' + tu) = (s0 + s1) tu + s1 tv' */
|
|
|
++
|
|
|
++ mpz_sub (tv, tv, tu);
|
|
|
++ mpz_add (t0, t0, t1);
|
|
|
++ mpz_add (s0, s0, s1);
|
|
|
++
|
|
|
++ shift = mpz_make_odd (tv);
|
|
|
++ mpz_mul_2exp (t1, t1, shift);
|
|
|
++ mpz_mul_2exp (s1, s1, shift);
|
|
|
++ }
|
|
|
++ else
|
|
|
++ {
|
|
|
++ mpz_sub (tu, tu, tv);
|
|
|
++ mpz_add (t1, t0, t1);
|
|
|
++ mpz_add (s1, s0, s1);
|
|
|
++
|
|
|
++ shift = mpz_make_odd (tu);
|
|
|
++ mpz_mul_2exp (t0, t0, shift);
|
|
|
++ mpz_mul_2exp (s0, s0, shift);
|
|
|
++ }
|
|
|
++ power += shift;
|
|
|
++ }
|
|
|
++ }
|
|
|
++
|
|
|
++ /* Now tv = odd part of gcd, and -s0 and t0 are corresponding
|
|
|
++ cofactors. */
|
|
|
++
|
|
|
++ mpz_mul_2exp (tv, tv, gz);
|
|
|
++ mpz_neg (s0, s0);
|
|
|
++
|
|
|
++ /* 2^p g = s0 u + t0 v. Eliminate one factor of two at a time. To
|
|
|
++ adjust cofactors, we need u / g and v / g */
|
|
|
++
|
|
|
++ mpz_divexact (s1, v, tv);
|
|
|
++ mpz_abs (s1, s1);
|
|
|
++ mpz_divexact (t1, u, tv);
|
|
|
++ mpz_abs (t1, t1);
|
|
|
++
|
|
|
++ while (power-- > 0)
|
|
|
++ {
|
|
|
++ /* s0 u + t0 v = (s0 - v/g) u - (t0 + u/g) v */
|
|
|
++ if (mpz_odd_p (s0) || mpz_odd_p (t0))
|
|
|
++ {
|
|
|
++ mpz_sub (s0, s0, s1);
|
|
|
++ mpz_add (t0, t0, t1);
|
|
|
++ }
|
|
|
++ mpz_divexact_ui (s0, s0, 2);
|
|
|
++ mpz_divexact_ui (t0, t0, 2);
|
|
|
++ }
|
|
|
++
|
|
|
++ /* Arrange so that |s| < |u| / 2g */
|
|
|
++ mpz_add (s1, s0, s1);
|
|
|
++ if (mpz_cmpabs (s0, s1) > 0)
|
|
|
++ {
|
|
|
++ mpz_swap (s0, s1);
|
|
|
++ mpz_sub (t0, t0, t1);
|
|
|
++ }
|
|
|
++ if (u->_mp_size < 0)
|
|
|
++ mpz_neg (s0, s0);
|
|
|
++ if (v->_mp_size < 0)
|
|
|
++ mpz_neg (t0, t0);
|
|
|
++
|
|
|
++ mpz_swap (g, tv);
|
|
|
++ if (s)
|
|
|
++ mpz_swap (s, s0);
|
|
|
++ if (t)
|
|
|
++ mpz_swap (t, t0);
|
|
|
++
|
|
|
++ mpz_clear (tu);
|
|
|
++ mpz_clear (tv);
|
|
|
++ mpz_clear (s0);
|
|
|
++ mpz_clear (s1);
|
|
|
++ mpz_clear (t0);
|
|
|
++ mpz_clear (t1);
|
|
|
++}
|
|
|
++
|
|
|
++void
|
|
|
++mpz_lcm (mpz_t r, const mpz_t u, const mpz_t v)
|
|
|
++{
|
|
|
++ mpz_t g;
|
|
|
++
|
|
|
++ if (u->_mp_size == 0 || v->_mp_size == 0)
|
|
|
++ {
|
|
|
++ r->_mp_size = 0;
|
|
|
++ return;
|
|
|
++ }
|
|
|
++
|
|
|
++ mpz_init (g);
|
|
|
++
|
|
|
++ mpz_gcd (g, u, v);
|
|
|
++ mpz_divexact (g, u, g);
|
|
|
++ mpz_mul (r, g, v);
|
|
|
++
|
|
|
++ mpz_clear (g);
|
|
|
++ mpz_abs (r, r);
|
|
|
++}
|
|
|
++
|
|
|
++void
|
|
|
++mpz_lcm_ui (mpz_t r, const mpz_t u, unsigned long v)
|
|
|
++{
|
|
|
++ if (v == 0 || u->_mp_size == 0)
|
|
|
++ {
|
|
|
++ r->_mp_size = 0;
|
|
|
++ return;
|
|
|
++ }
|
|
|
++
|
|
|
++ v /= mpz_gcd_ui (NULL, u, v);
|
|
|
++ mpz_mul_ui (r, u, v);
|
|
|
++
|
|
|
++ mpz_abs (r, r);
|
|
|
++}
|
|
|
++
|
|
|
++int
|
|
|
++mpz_invert (mpz_t r, const mpz_t u, const mpz_t m)
|
|
|
++{
|
|
|
++ mpz_t g, tr;
|
|
|
++ int invertible;
|
|
|
++
|
|
|
++ if (u->_mp_size == 0 || mpz_cmpabs_ui (m, 1) <= 0)
|
|
|
++ return 0;
|
|
|
++
|
|
|
++ mpz_init (g);
|
|
|
++ mpz_init (tr);
|
|
|
++
|
|
|
++ mpz_gcdext (g, tr, NULL, u, m);
|
|
|
++ invertible = (mpz_cmp_ui (g, 1) == 0);
|
|
|
++
|
|
|
++ if (invertible)
|
|
|
++ {
|
|
|
++ if (tr->_mp_size < 0)
|
|
|
++ {
|
|
|
++ if (m->_mp_size >= 0)
|
|
|
++ mpz_add (tr, tr, m);
|
|
|
++ else
|
|
|
++ mpz_sub (tr, tr, m);
|
|
|
++ }
|
|
|
++ mpz_swap (r, tr);
|
|
|
++ }
|
|
|
++
|
|
|
++ mpz_clear (g);
|
|
|
++ mpz_clear (tr);
|
|
|
++ return invertible;
|
|
|
++}
|
|
|
++
|
|
|
++
|
|
|
++/* Higher level operations (sqrt, pow and root) */
|
|
|
++
|
|
|
++void
|
|
|
++mpz_pow_ui (mpz_t r, const mpz_t b, unsigned long e)
|
|
|
++{
|
|
|
++ unsigned long bit;
|
|
|
++ mpz_t tr;
|
|
|
++ mpz_init_set_ui (tr, 1);
|
|
|
++
|
|
|
++ bit = GMP_ULONG_HIGHBIT;
|
|
|
++ do
|
|
|
++ {
|
|
|
++ mpz_mul (tr, tr, tr);
|
|
|
++ if (e & bit)
|
|
|
++ mpz_mul (tr, tr, b);
|
|
|
++ bit >>= 1;
|
|
|
++ }
|
|
|
++ while (bit > 0);
|
|
|
++
|
|
|
++ mpz_swap (r, tr);
|
|
|
++ mpz_clear (tr);
|
|
|
++}
|
|
|
++
|
|
|
++void
|
|
|
++mpz_ui_pow_ui (mpz_t r, unsigned long blimb, unsigned long e)
|
|
|
++{
|
|
|
++ mpz_t b;
|
|
|
++ mpz_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;
|
|
|
++}
|
|
|
++
|
|
|
++/* 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);
|
|
|
++}
|
|
|
++
|
|
|
++
|
|
|
++/* Primality testing */
|
|
|
++static int
|
|
|
++gmp_millerrabin (const mpz_t n, const mpz_t nm1, mpz_t y,
|
|
|
++ const mpz_t q, mp_bitcnt_t k)
|
|
|
++{
|
|
|
++ assert (k > 0);
|
|
|
++
|
|
|
++ /* Caller must initialize y to the base. */
|
|
|
++ mpz_powm (y, y, q, n);
|
|
|
++
|
|
|
++ if (mpz_cmp_ui (y, 1) == 0 || mpz_cmp (y, nm1) == 0)
|
|
|
++ return 1;
|
|
|
++
|
|
|
++ while (--k > 0)
|
|
|
++ {
|
|
|
++ mpz_powm_ui (y, y, 2, n);
|
|
|
++ if (mpz_cmp (y, nm1) == 0)
|
|
|
++ return 1;
|
|
|
++ /* y == 1 means that the previous y was a non-trivial square root
|
|
|
++ of 1 (mod n). y == 0 means that n is a power of the base.
|
|
|
++ In either case, n is not prime. */
|
|
|
++ if (mpz_cmp_ui (y, 1) <= 0)
|
|
|
++ return 0;
|
|
|
++ }
|
|
|
++ return 0;
|
|
|
++}
|
|
|
++
|
|
|
++/* This product is 0xc0cfd797, and fits in 32 bits. */
|
|
|
++#define GMP_PRIME_PRODUCT \
|
|
|
++ (3UL*5UL*7UL*11UL*13UL*17UL*19UL*23UL*29UL)
|
|
|
++
|
|
|
++/* Bit (p+1)/2 is set, for each odd prime <= 61 */
|
|
|
++#define GMP_PRIME_MASK 0xc96996dcUL
|
|
|
++
|
|
|
++int
|
|
|
++mpz_probab_prime_p (const mpz_t n, int reps)
|
|
|
++{
|
|
|
++ mpz_t nm1;
|
|
|
++ mpz_t q;
|
|
|
++ mpz_t y;
|
|
|
++ mp_bitcnt_t k;
|
|
|
++ int is_prime;
|
|
|
++ int j;
|
|
|
++
|
|
|
++ /* Note that we use the absolute value of n only, for compatibility
|
|
|
++ with the real GMP. */
|
|
|
++ if (mpz_even_p (n))
|
|
|
++ return (mpz_cmpabs_ui (n, 2) == 0) ? 2 : 0;
|
|
|
++
|
|
|
++ /* Above test excludes n == 0 */
|
|
|
++ assert (n->_mp_size != 0);
|
|
|
++
|
|
|
++ if (mpz_cmpabs_ui (n, 64) < 0)
|
|
|
++ return (GMP_PRIME_MASK >> (n->_mp_d[0] >> 1)) & 2;
|
|
|
++
|
|
|
++ if (mpz_gcd_ui (NULL, n, GMP_PRIME_PRODUCT) != 1)
|
|
|
++ return 0;
|
|
|
++
|
|
|
++ /* All prime factors are >= 31. */
|
|
|
++ if (mpz_cmpabs_ui (n, 31*31) < 0)
|
|
|
++ return 2;
|
|
|
++
|
|
|
++ /* Use Miller-Rabin, with a deterministic sequence of bases, a[j] =
|
|
|
++ j^2 + j + 41 using Euler's polynomial. We potentially stop early,
|
|
|
++ if a[j] >= n - 1. Since n >= 31*31, this can happen only if reps >
|
|
|
++ 30 (a[30] == 971 > 31*31 == 961). */
|
|
|
++
|
|
|
++ mpz_init (nm1);
|
|
|
++ mpz_init (q);
|
|
|
++ mpz_init (y);
|
|
|
++
|
|
|
++ /* Find q and k, where q is odd and n = 1 + 2**k * q. */
|
|
|
++ nm1->_mp_size = mpz_abs_sub_ui (nm1, n, 1);
|
|
|
++ k = mpz_scan1 (nm1, 0);
|
|
|
++ mpz_tdiv_q_2exp (q, nm1, k);
|
|
|
++
|
|
|
++ for (j = 0, is_prime = 1; is_prime & (j < reps); j++)
|
|
|
++ {
|
|
|
++ mpz_set_ui (y, (unsigned long) j*j+j+41);
|
|
|
++ if (mpz_cmp (y, nm1) >= 0)
|
|
|
++ {
|
|
|
++ /* Don't try any further bases. This "early" break does not affect
|
|
|
++ the result for any reasonable reps value (<=5000 was tested) */
|
|
|
++ assert (j >= 30);
|
|
|
++ break;
|
|
|
++ }
|
|
|
++ is_prime = gmp_millerrabin (n, nm1, y, q, k);
|
|
|
++ }
|
|
|
++ mpz_clear (nm1);
|
|
|
++ mpz_clear (q);
|
|
|
++ mpz_clear (y);
|
|
|
++
|
|
|
++ return is_prime;
|
|
|
++}
|
|
|
++
|
|
|
++
|
|
|
++/* Logical operations and bit manipulation. */
|
|
|
++
|
|
|
++/* Numbers are treated as if represented in two's complement (and
|
|
|
++ infinitely sign extended). For a negative values we get the two's
|
|
|
++ complement from -x = ~x + 1, where ~ is bitwise complement.
|
|
|
++ Negation transforms
|
|
|
++
|
|
|
++ xxxx10...0
|
|
|
++
|
|
|
++ into
|
|
|
++
|
|
|
++ yyyy10...0
|
|
|
++
|
|
|
++ where yyyy is the bitwise complement of xxxx. So least significant
|
|
|
++ bits, up to and including the first one bit, are unchanged, and
|
|
|
++ the more significant bits are all complemented.
|
|
|
++
|
|
|
++ To change a bit from zero to one in a negative number, subtract the
|
|
|
++ corresponding power of two from the absolute value. This can never
|
|
|
++ underflow. To change a bit from one to zero, add the corresponding
|
|
|
++ power of two, and this might overflow. E.g., if x = -001111, the
|
|
|
++ two's complement is 110001. Clearing the least significant bit, we
|
|
|
++ get two's complement 110000, and -010000. */
|
|
|
++
|
|
|
++int
|
|
|
++mpz_tstbit (const mpz_t d, mp_bitcnt_t bit_index)
|
|
|
++{
|
|
|
++ mp_size_t limb_index;
|
|
|
++ unsigned shift;
|
|
|
++ mp_size_t ds;
|
|
|
++ mp_size_t dn;
|
|
|
++ mp_limb_t w;
|
|
|
++ int bit;
|
|
|
++
|
|
|
++ ds = d->_mp_size;
|
|
|
++ dn = GMP_ABS (ds);
|
|
|
++ limb_index = bit_index / GMP_LIMB_BITS;
|
|
|
++ if (limb_index >= dn)
|
|
|
++ return ds < 0;
|
|
|
++
|
|
|
++ shift = bit_index % GMP_LIMB_BITS;
|
|
|
++ w = d->_mp_d[limb_index];
|
|
|
++ bit = (w >> shift) & 1;
|
|
|
++
|
|
|
++ if (ds < 0)
|
|
|
++ {
|
|
|
++ /* d < 0. Check if any of the bits below is set: If so, our bit
|
|
|
++ must be complemented. */
|
|
|
++ if (shift > 0 && (w << (GMP_LIMB_BITS - shift)) > 0)
|
|
|
++ return bit ^ 1;
|
|
|
++ while (limb_index-- > 0)
|
|
|
++ if (d->_mp_d[limb_index] > 0)
|
|
|
++ return bit ^ 1;
|
|
|
++ }
|
|
|
++ return bit;
|
|
|
++}
|
|
|
++
|
|
|
++static void
|
|
|
++mpz_abs_add_bit (mpz_t d, mp_bitcnt_t bit_index)
|
|
|
++{
|
|
|
++ mp_size_t dn, limb_index;
|
|
|
++ mp_limb_t bit;
|
|
|
++ mp_ptr dp;
|
|
|
++
|
|
|
++ dn = GMP_ABS (d->_mp_size);
|
|
|
++
|
|
|
++ limb_index = bit_index / GMP_LIMB_BITS;
|
|
|
++ bit = (mp_limb_t) 1 << (bit_index % GMP_LIMB_BITS);
|
|
|
++
|
|
|
++ if (limb_index >= dn)
|
|
|
++ {
|
|
|
++ mp_size_t i;
|
|
|
++ /* The bit should be set outside of the end of the number.
|
|
|
++ We have to increase the size of the number. */
|
|
|
++ dp = MPZ_REALLOC (d, limb_index + 1);
|
|
|
++
|
|
|
++ dp[limb_index] = bit;
|
|
|
++ for (i = dn; i < limb_index; i++)
|
|
|
++ dp[i] = 0;
|
|
|
++ dn = limb_index + 1;
|
|
|
++ }
|
|
|
++ else
|
|
|
++ {
|
|
|
++ mp_limb_t cy;
|
|
|
++
|
|
|
++ dp = d->_mp_d;
|
|
|
++
|
|
|
++ cy = mpn_add_1 (dp + limb_index, dp + limb_index, dn - limb_index, bit);
|
|
|
++ if (cy > 0)
|
|
|
++ {
|
|
|
++ dp = MPZ_REALLOC (d, dn + 1);
|
|
|
++ dp[dn++] = cy;
|
|
|
++ }
|
|
|
++ }
|
|
|
++
|
|
|
++ d->_mp_size = (d->_mp_size < 0) ? - dn : dn;
|
|
|
++}
|
|
|
++
|
|
|
++static void
|
|
|
++mpz_abs_sub_bit (mpz_t d, mp_bitcnt_t bit_index)
|
|
|
++{
|
|
|
++ mp_size_t dn, limb_index;
|
|
|
++ mp_ptr dp;
|
|
|
++ mp_limb_t bit;
|
|
|
++
|
|
|
++ dn = GMP_ABS (d->_mp_size);
|
|
|
++ dp = d->_mp_d;
|
|
|
++
|
|
|
++ limb_index = bit_index / GMP_LIMB_BITS;
|
|
|
++ bit = (mp_limb_t) 1 << (bit_index % GMP_LIMB_BITS);
|
|
|
++
|
|
|
++ assert (limb_index < dn);
|
|
|
++
|
|
|
++ gmp_assert_nocarry (mpn_sub_1 (dp + limb_index, dp + limb_index,
|
|
|
++ dn - limb_index, bit));
|
|
|
++ dn = mpn_normalized_size (dp, dn);
|
|
|
++ d->_mp_size = (d->_mp_size < 0) ? - dn : dn;
|
|
|
++}
|
|
|
++
|
|
|
++void
|
|
|
++mpz_setbit (mpz_t d, mp_bitcnt_t bit_index)
|
|
|
++{
|
|
|
++ if (!mpz_tstbit (d, bit_index))
|
|
|
++ {
|
|
|
++ if (d->_mp_size >= 0)
|
|
|
++ mpz_abs_add_bit (d, bit_index);
|
|
|
++ else
|
|
|
++ mpz_abs_sub_bit (d, bit_index);
|
|
|
++ }
|
|
|
++}
|
|
|
++
|
|
|
++void
|
|
|
++mpz_clrbit (mpz_t d, mp_bitcnt_t bit_index)
|
|
|
++{
|
|
|
++ if (mpz_tstbit (d, bit_index))
|
|
|
++ {
|
|
|
++ if (d->_mp_size >= 0)
|
|
|
++ mpz_abs_sub_bit (d, bit_index);
|
|
|
++ else
|
|
|
++ mpz_abs_add_bit (d, bit_index);
|
|
|
++ }
|
|
|
++}
|
|
|
++
|
|
|
++void
|
|
|
++mpz_combit (mpz_t d, mp_bitcnt_t bit_index)
|
|
|
++{
|
|
|
++ if (mpz_tstbit (d, bit_index) ^ (d->_mp_size < 0))
|
|
|
++ mpz_abs_sub_bit (d, bit_index);
|
|
|
++ else
|
|
|
++ mpz_abs_add_bit (d, bit_index);
|
|
|
++}
|
|
|
++
|
|
|
++void
|
|
|
++mpz_com (mpz_t r, const mpz_t u)
|
|
|
++{
|
|
|
++ mpz_neg (r, u);
|
|
|
++ mpz_sub_ui (r, r, 1);
|
|
|
++}
|
|
|
++
|
|
|
++void
|
|
|
++mpz_and (mpz_t r, const mpz_t u, const mpz_t v)
|
|
|
++{
|
|
|
++ mp_size_t un, vn, rn, i;
|
|
|
++ mp_ptr up, vp, rp;
|
|
|
++
|
|
|
++ mp_limb_t ux, vx, rx;
|
|
|
++ mp_limb_t uc, vc, rc;
|
|
|
++ mp_limb_t ul, vl, rl;
|
|
|
++
|
|
|
++ un = GMP_ABS (u->_mp_size);
|
|
|
++ vn = GMP_ABS (v->_mp_size);
|
|
|
++ if (un < vn)
|
|
|
++ {
|
|
|
++ MPZ_SRCPTR_SWAP (u, v);
|
|
|
++ MP_SIZE_T_SWAP (un, vn);
|
|
|
++ }
|
|
|
++ if (vn == 0)
|
|
|
++ {
|
|
|
++ r->_mp_size = 0;
|
|
|
++ return;
|
|
|
++ }
|
|
|
++
|
|
|
++ uc = u->_mp_size < 0;
|
|
|
++ vc = v->_mp_size < 0;
|
|
|
++ rc = uc & vc;
|
|
|
++
|
|
|
++ ux = -uc;
|
|
|
++ vx = -vc;
|
|
|
++ rx = -rc;
|
|
|
++
|
|
|
++ /* If the smaller input is positive, higher limbs don't matter. */
|
|
|
++ rn = vx ? un : vn;
|
|
|
++
|
|
|
++ rp = MPZ_REALLOC (r, rn + 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);
|
|
|
++}
|
|
|
++
|
|
|
++
|
|
|
++/* 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;
|
|
|
++}
|
|
|
++
|
|
|
++
|
|
|
++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;
|
|
|
++}
|
Steven Barth