1027 lines
20 KiB
C
1027 lines
20 KiB
C
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/*
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* RabbitSign - Tools for signing TI graphing calculator software
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* Copyright (C) 2009 Benjamin Moody
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*
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* This program is free software; you can redistribute it and/or
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* modify it under the terms of the GNU General Public License as
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* published by the Free Software Foundation; either version 3 of the
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* License, or (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifdef HAVE_CONFIG_H
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# include <config.h>
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#endif
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#include <stdio.h>
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#include <stdarg.h>
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#ifdef HAVE_STDLIB_H
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# include <stdlib.h>
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#endif
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#ifdef HAVE_ASSERT_H
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# include <assert.h>
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#else
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# define assert(xxx) if (!(xxx)) { \
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fprintf(stderr, "mpz: assertion \"%s\" failed\n", #xxx); \
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abort(); \
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}
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#endif
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#include "mpz.h"
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/*
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* This file contains multiple-precision arithmetic functions. These
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* are equivalent to the corresponding GMP functions in the ways they
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* are used by RabbitSign.
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*
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* HOWEVER, they are not by any means complete. They do not meet the
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* specifications of the GMP functions; for the sake of portability
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* and compactness they are vastly less efficient; and they may even
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* have bugs.
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*/
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/*
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#define DBG(args...) if (1) \
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do { \
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gmp_fprintf(stderr, "mpz: " args); \
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fputc('\n', stderr); \
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} while (0)
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*/
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#define IDX(nnn, iii) (nnn)->m[iii]
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/* \
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(*(__extension__ ({ \
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int _ii = (iii); \
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const struct _mpz* _nn = (nnn); \
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assert(_nn->size <= _nn->size_alloc); \
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assert(_ii >= 0); \
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assert(((unsigned) _ii) < (_nn->size)); \
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&(_nn->m[_ii]); })))
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*/
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static void* xrealloc(p, n)
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void* p;
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size_t n;
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{
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void* res;
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if (n <= 0)
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n = 1;
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if (p)
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res = realloc(p, n);
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else
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res = malloc(n);
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if (!res) {
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fprintf(stderr,"mpz: out of memory (need %lu bytes)\n",
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(unsigned long) n);
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abort();
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}
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return res;
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}
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static inline void allocate_mpz(x)
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mpz_t x;
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{
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if (x->size_alloc < x->size) {
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x->size_alloc = x->size;
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x->m = (limb_t*) xrealloc(x->m, x->size_alloc * sizeof(limb_t));
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}
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}
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static inline void zero_mpz(x)
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mpz_t x;
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{
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size_t i;
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for (i = 0; i < x->size; i++)
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IDX(x, i) = 0;
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}
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static inline void copyref_mpz(dest, src)
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mpz_t dest;
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const mpz_t src;
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{
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dest->size = src->size;
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dest->size_alloc = src->size_alloc;
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dest->m = src->m;
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dest->sign = src->sign;
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}
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static inline void reduce_mpz(x)
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mpz_t x;
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{
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while (x->size > 0 && IDX(x, (x->size) - 1) == 0)
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x->size--;
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}
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/**************** Init / Clear ****************/
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void mpz_init(x)
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mpz_t x;
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{
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x->size = 0;
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x->size_alloc = 0;
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x->m = (limb_t*)0;
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x->sign = 1;
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}
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void mpz_clear(x)
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mpz_t x;
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{
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if (x->m)
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free(x->m);
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mpz_init(x);
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}
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/**************** Setting ****************/
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void mpz_set(dest, src)
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mpz_t dest;
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const mpz_t src;
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{
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size_t i;
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dest->size = src->size;
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allocate_mpz(dest);
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dest->sign = src->sign;
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for (i = 0; i < src->size; i++)
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IDX(dest, i) = IDX(src, i);
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}
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void mpz_set_ui(dest, a)
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mpz_t dest;
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unsigned int a;
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{
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if (a) {
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dest->size = 1;
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allocate_mpz(dest);
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IDX(dest, 0) = a;
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}
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else
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dest->size = 0;
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dest->sign = 1;
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}
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unsigned int mpz_get_ui(a)
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const mpz_t a;
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{
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return IDX(a, 0);
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}
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static void mpz_swap(a, b)
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mpz_t a;
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mpz_t b;
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{
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mpz_t temp;
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copyref_mpz(temp, a);
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copyref_mpz(a, b);
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copyref_mpz(b, temp);
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}
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/**************** Import / Export ****************/
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void mpz_import(dest, count, order, size, endian, nails, op)
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mpz_t dest;
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size_t count;
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int order; /* must be -1 (little endian structure) */
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int size; /* must be 1 (bytes) */
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int endian; /* must be 0 (native endian words, doesn't matter for bytes) */
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size_t nails; /* must be 0 (no nails) */
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const void* op;
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{
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size_t i, j;
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assert(order == -1);
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assert(size == 1);
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assert(endian == 0);
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assert(nails == 0);
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dest->size = (count + LIMB_BYTES - 1) / LIMB_BYTES;
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allocate_mpz(dest);
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dest->sign = 1;
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for (i = 0; i < dest->size; i++) {
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IDX(dest, i) = 0;
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for (j = 0; j < LIMB_BYTES && ((i * LIMB_BYTES) + j) < count; j++) {
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IDX(dest, i) |= ((unsigned char*)op)[(i * LIMB_BYTES) + j] << 8 * j;
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}
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}
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}
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void mpz_export(dest, count, order, size, endian, nails, op)
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void* dest;
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size_t* count;
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int order; /* must be -1 (little endian structure) */
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int size; /* must be 1 (bytes) */
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int endian; /* must be 0 (native endian words, doesn't matter for bytes) */
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size_t nails; /* must be 0 (no nails) */
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const mpz_t op;
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{
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size_t i, j;
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assert(order == -1);
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assert(size == 1);
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assert(endian == 0);
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assert(nails == 0);
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for (i = 0; i < op->size; i++) {
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for (j = 0; j < LIMB_BYTES; j++) {
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((unsigned char*)dest)[(i * LIMB_BYTES) + j] = IDX(op, i) >> 8 * j;
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}
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}
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*count = op->size * LIMB_BYTES;
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}
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/**************** Comparison ****************/
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int mpz_sgn(a)
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const mpz_t a;
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{
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size_t i = a->size;
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while (i > 0 && IDX(a, i - 1) == 0)
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i--;
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if (i == 0)
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return 0;
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else
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return a->sign;
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}
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static int mpz_cmpabs(a, b)
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const mpz_t a;
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const mpz_t b;
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{
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size_t sa = a->size;
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size_t sb = b->size;
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while (sa > 0 && IDX(a, sa - 1) == 0)
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sa--;
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while (sb > 0 && IDX(b, sb - 1) == 0)
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sb--;
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if (sa > sb)
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return 1;
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else if (sb > sa)
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return -1;
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while (sa > 0) {
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if (IDX(a, sa - 1) > IDX(b, sa - 1))
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return 1;
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else if (IDX(a, sa - 1) < IDX(b, sa - 1))
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return -1;
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sa--;
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}
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return 0;
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}
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int mpz_cmp(a, b)
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const mpz_t a;
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const mpz_t b;
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{
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size_t sa = a->size;
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size_t sb = b->size;
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while (sa > 0 && IDX(a, sa - 1) == 0)
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sa--;
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while (sb > 0 && IDX(b, sb - 1) == 0)
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sb--;
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if (sa == 0 && sb == 0)
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return 0;
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else if (sa == 0)
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return -(b->sign);
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else if (sb == 0)
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return a->sign;
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else if (a->sign != b->sign)
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return a->sign;
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return a->sign * mpz_cmpabs(a, b);
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}
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int mpz_cmp_ui(a, b)
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const mpz_t a;
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unsigned int b;
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{
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size_t sa = a->size;
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while (sa > 0 && IDX(a, sa - 1) == 0)
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sa--;
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if (sa == 0 && b == 0)
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return 0;
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if (sa == 1 && a->sign == 1) {
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if (IDX(a, 0) > b)
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return 1;
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else if (IDX(a, 0) < b)
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return -1;
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else
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return 0;
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}
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return (a->sign);
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}
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/**************** Addition / Subtraction ****************/
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static void mpz_addabs(dest, a, b)
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mpz_t dest; /* != a, b */
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const mpz_t a;
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const mpz_t b;
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{
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size_t i;
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double_limb_t carry = 0;
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if (a->size > b->size)
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dest->size = a->size + 1;
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else
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dest->size = b->size + 1;
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allocate_mpz(dest);
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assert(dest != a);
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assert(dest != b);
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for (i = 0; i < a->size && i < b->size; i++) {
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carry += IDX(a, i);
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carry += IDX(b, i);
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IDX(dest, i) = carry & LIMB_MASK;
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carry >>= LIMB_BITS;
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}
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for (; i < a->size; i++) {
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carry += IDX(a, i);
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IDX(dest, i) = carry & LIMB_MASK;
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carry >>= LIMB_BITS;
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}
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for (; i < b->size; i++) {
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carry += IDX(b, i);
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IDX(dest, i) = carry & LIMB_MASK;
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carry >>= LIMB_BITS;
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}
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IDX(dest, i) = carry;
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}
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static void mpz_subabs(dest, a, b)
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mpz_t dest; /* != b */
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const mpz_t a;
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const mpz_t b; /* must be <= a */
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{
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size_t i;
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signed_double_limb_t carry = 0;
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dest->size = a->size;
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allocate_mpz(dest);
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assert(dest != b);
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for (i = 0; i < a->size && i < b->size; i++) {
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carry += IDX(a, i);
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carry -= IDX(b, i);
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IDX(dest, i) = carry & LIMB_MASK;
|
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carry >>= LIMB_BITS;
|
||
|
}
|
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|
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for (; i < a->size; i++) {
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carry += IDX(a, i);
|
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IDX(dest, i) = carry & LIMB_MASK;
|
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carry >>= LIMB_BITS;
|
||
|
}
|
||
|
|
||
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assert(carry == 0);
|
||
|
}
|
||
|
|
||
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void mpz_add(dest, a, b)
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mpz_t dest;
|
||
|
const mpz_t a;
|
||
|
const mpz_t b;
|
||
|
{
|
||
|
mpz_t temp;
|
||
|
mpz_init(temp);
|
||
|
|
||
|
if (a->sign == b->sign) {
|
||
|
temp->sign = a->sign;
|
||
|
mpz_addabs(temp, a, b);
|
||
|
}
|
||
|
else if (mpz_cmpabs(a, b) > 0) {
|
||
|
temp->sign = a->sign;
|
||
|
mpz_subabs(temp, a, b);
|
||
|
}
|
||
|
else {
|
||
|
temp->sign = b->sign;
|
||
|
mpz_subabs(temp, b, a);
|
||
|
}
|
||
|
|
||
|
reduce_mpz(temp);
|
||
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mpz_clear(dest);
|
||
|
copyref_mpz(dest, temp);
|
||
|
}
|
||
|
|
||
|
void mpz_sub(dest, a, b)
|
||
|
mpz_t dest;
|
||
|
const mpz_t a;
|
||
|
const mpz_t b;
|
||
|
{
|
||
|
mpz_t temp;
|
||
|
mpz_init(temp);
|
||
|
|
||
|
if (a->sign != b->sign) {
|
||
|
temp->sign = a->sign;
|
||
|
mpz_addabs(temp, a, b);
|
||
|
}
|
||
|
else if (mpz_cmpabs(a, b) > 0) {
|
||
|
temp->sign = a->sign;
|
||
|
mpz_subabs(temp, a, b);
|
||
|
}
|
||
|
else {
|
||
|
temp->sign = -(b->sign);
|
||
|
mpz_subabs(temp, b, a);
|
||
|
}
|
||
|
|
||
|
reduce_mpz(temp);
|
||
|
mpz_clear(dest);
|
||
|
copyref_mpz(dest, temp);
|
||
|
}
|
||
|
|
||
|
void mpz_add_ui(dest, a, b)
|
||
|
mpz_t dest;
|
||
|
const mpz_t a;
|
||
|
unsigned int b;
|
||
|
{
|
||
|
size_t i;
|
||
|
mpz_t temp;
|
||
|
mpz_init(temp);
|
||
|
|
||
|
temp->size = a->size + 1;
|
||
|
temp->sign = a->sign;
|
||
|
allocate_mpz(temp);
|
||
|
|
||
|
for (i = 0; i < a->size; i++) {
|
||
|
IDX(temp, i) = IDX(a, i) + b;
|
||
|
b = (IDX(temp, i) < IDX(a, i)) ? 1 : 0;
|
||
|
}
|
||
|
IDX(temp, i) = b;
|
||
|
|
||
|
reduce_mpz(temp);
|
||
|
mpz_clear(dest);
|
||
|
copyref_mpz(dest, temp);
|
||
|
}
|
||
|
|
||
|
void mpz_sub_ui(dest, a, b)
|
||
|
mpz_t dest;
|
||
|
const mpz_t a;
|
||
|
unsigned int b;
|
||
|
{
|
||
|
size_t i;
|
||
|
mpz_t temp;
|
||
|
mpz_init(temp);
|
||
|
|
||
|
temp->size = a->size;
|
||
|
temp->sign = a->sign;
|
||
|
allocate_mpz(temp);
|
||
|
|
||
|
for (i = 0; i < a->size; i++) {
|
||
|
IDX(temp, i) = IDX(a, i) - b;
|
||
|
b = (IDX(temp, i) > IDX(a, i)) ? 1 : 0;
|
||
|
}
|
||
|
assert(b == 0);
|
||
|
|
||
|
reduce_mpz(temp);
|
||
|
mpz_clear(dest);
|
||
|
copyref_mpz(dest, temp);
|
||
|
}
|
||
|
|
||
|
/**************** Multiplication ****************/
|
||
|
|
||
|
void mpz_mul(dest, a, b)
|
||
|
mpz_t dest;
|
||
|
const mpz_t a;
|
||
|
const mpz_t b;
|
||
|
{
|
||
|
double_limb_t carry = 0, newcarry;
|
||
|
size_t i, j, k;
|
||
|
mpz_t temp;
|
||
|
mpz_init(temp);
|
||
|
|
||
|
temp->size = a->size + b->size;
|
||
|
temp->sign = a->sign * b->sign;
|
||
|
allocate_mpz(temp);
|
||
|
zero_mpz(temp);
|
||
|
|
||
|
for (i = 0; i < a->size; i++) {
|
||
|
for (j = 0; j < b->size; j++) {
|
||
|
carry = IDX(a, i);
|
||
|
carry *= IDX(b, j);
|
||
|
for (k = i + j; k < temp->size && carry; k++) {
|
||
|
newcarry = carry + IDX(temp, k);
|
||
|
if (newcarry < carry) {
|
||
|
IDX(temp, k) = newcarry & LIMB_MASK;
|
||
|
carry = (newcarry >> LIMB_BITS) + LIMB_MASK + 1;
|
||
|
}
|
||
|
else {
|
||
|
IDX(temp, k) = newcarry & LIMB_MASK;
|
||
|
carry = (newcarry >> LIMB_BITS);
|
||
|
}
|
||
|
}
|
||
|
assert(carry == 0);
|
||
|
}
|
||
|
}
|
||
|
|
||
|
reduce_mpz(temp);
|
||
|
mpz_clear(dest);
|
||
|
copyref_mpz(dest, temp);
|
||
|
}
|
||
|
|
||
|
void mpz_mul_ui(dest, a, b)
|
||
|
mpz_t dest;
|
||
|
const mpz_t a;
|
||
|
unsigned int b; /* must be fairly small */
|
||
|
{
|
||
|
double_limb_t carry = 0;
|
||
|
size_t i;
|
||
|
mpz_t temp;
|
||
|
mpz_init(temp);
|
||
|
|
||
|
temp->size = a->size + 1;
|
||
|
temp->sign = a->sign;
|
||
|
allocate_mpz(temp);
|
||
|
|
||
|
for (i = 0; i < a->size; i++) {
|
||
|
carry += (double_limb_t) IDX(a, i) * b;
|
||
|
IDX(temp, i) = carry & LIMB_MASK;
|
||
|
carry >>= LIMB_BITS;
|
||
|
}
|
||
|
IDX(temp, i) = carry & LIMB_MASK;
|
||
|
|
||
|
reduce_mpz(temp);
|
||
|
mpz_clear(dest);
|
||
|
copyref_mpz(dest, temp);
|
||
|
}
|
||
|
|
||
|
/**************** Division ****************/
|
||
|
|
||
|
void mpz_fdiv_q_2exp(dest, a, b)
|
||
|
mpz_t dest;
|
||
|
const mpz_t a;
|
||
|
unsigned int b; /* must be <= LIMB_BITS */
|
||
|
{
|
||
|
size_t i;
|
||
|
mpz_t temp;
|
||
|
mpz_init(temp);
|
||
|
|
||
|
assert(b <= LIMB_BITS);
|
||
|
|
||
|
temp->size = a->size;
|
||
|
temp->sign = a->sign;
|
||
|
allocate_mpz(temp);
|
||
|
|
||
|
if (a->size > 0) {
|
||
|
for (i = 0; i < (a->size - 1); i++) {
|
||
|
IDX(temp, i) = (((IDX(a, i) >> b) | (IDX(a, i + 1) << (LIMB_BITS - b)))
|
||
|
& LIMB_MASK);
|
||
|
}
|
||
|
IDX(temp, a->size - 1) = IDX(a, a->size - 1) >> b;
|
||
|
}
|
||
|
|
||
|
reduce_mpz(temp);
|
||
|
mpz_clear(dest);
|
||
|
copyref_mpz(dest, temp);
|
||
|
}
|
||
|
|
||
|
/**************** Division / Modulus ****************/
|
||
|
|
||
|
static void mpz_setbit(dest, n)
|
||
|
mpz_t dest;
|
||
|
unsigned int n;
|
||
|
{
|
||
|
size_t i, j;
|
||
|
|
||
|
i = n / LIMB_BITS + 1;
|
||
|
|
||
|
if (dest->size < i) {
|
||
|
j = dest->size;
|
||
|
dest->size = i;
|
||
|
allocate_mpz(dest);
|
||
|
while (j < i) {
|
||
|
IDX(dest, j) = 0;
|
||
|
j++;
|
||
|
}
|
||
|
}
|
||
|
|
||
|
IDX(dest, i - 1) |= (1 << (n % LIMB_BITS));
|
||
|
}
|
||
|
|
||
|
static void mpz_fdiv_qr(q, r, num, den)
|
||
|
mpz_t q;
|
||
|
mpz_t r;
|
||
|
const mpz_t num;
|
||
|
const mpz_t den;
|
||
|
{
|
||
|
size_t shiftct = 0;
|
||
|
size_t i;
|
||
|
mpz_t remainder;
|
||
|
mpz_t quotient;
|
||
|
mpz_t shifted; /* shifted = mod * 2^(shiftct) */
|
||
|
|
||
|
mpz_init(remainder);
|
||
|
mpz_init(shifted);
|
||
|
if (q) {
|
||
|
mpz_init(quotient);
|
||
|
quotient->sign = num->sign * den->sign;
|
||
|
}
|
||
|
|
||
|
shifted->size = num->size;
|
||
|
allocate_mpz(shifted);
|
||
|
|
||
|
mpz_set(remainder, num);
|
||
|
mpz_set(shifted, den);
|
||
|
|
||
|
reduce_mpz(shifted);
|
||
|
assert(shifted->size > 0);
|
||
|
|
||
|
while (mpz_cmpabs(remainder, shifted) > 0) {
|
||
|
shifted->size++;
|
||
|
allocate_mpz(shifted);
|
||
|
for (i = shifted->size - 1; i > 0; i--)
|
||
|
IDX(shifted, i) = IDX(shifted, i - 1);
|
||
|
IDX(shifted, 0) = 0;
|
||
|
shiftct += LIMB_BITS;
|
||
|
}
|
||
|
|
||
|
while (shiftct != 0) {
|
||
|
if (mpz_cmpabs(remainder, shifted) >= 0) {
|
||
|
mpz_subabs(remainder, remainder, shifted);
|
||
|
reduce_mpz(remainder);
|
||
|
if (q)
|
||
|
mpz_setbit(quotient, shiftct);
|
||
|
}
|
||
|
mpz_fdiv_q_2exp(shifted, shifted, 1);
|
||
|
shiftct--;
|
||
|
}
|
||
|
|
||
|
if (mpz_cmpabs(remainder, den) >= 0) {
|
||
|
mpz_subabs(remainder, remainder, den);
|
||
|
if (q)
|
||
|
mpz_setbit(quotient, 0);
|
||
|
}
|
||
|
|
||
|
if (mpz_sgn(remainder) == -1) {
|
||
|
mpz_add(remainder, remainder, den);
|
||
|
if (q)
|
||
|
mpz_sub_ui(quotient, quotient, 1);
|
||
|
}
|
||
|
|
||
|
mpz_clear(shifted);
|
||
|
reduce_mpz(remainder);
|
||
|
mpz_clear(r);
|
||
|
copyref_mpz(r, remainder);
|
||
|
|
||
|
if (q) {
|
||
|
reduce_mpz(quotient);
|
||
|
mpz_clear(q);
|
||
|
copyref_mpz(q, quotient);
|
||
|
}
|
||
|
}
|
||
|
|
||
|
void mpz_mod(dest, a, mod)
|
||
|
mpz_t dest;
|
||
|
const mpz_t a;
|
||
|
const mpz_t mod;
|
||
|
{
|
||
|
mpz_fdiv_qr(NULL, dest, a, mod);
|
||
|
}
|
||
|
|
||
|
/**************** Modular exponent ****************/
|
||
|
|
||
|
void mpz_powm(dest, base, exp, mod)
|
||
|
mpz_t dest;
|
||
|
const mpz_t base;
|
||
|
const mpz_t exp;
|
||
|
const mpz_t mod;
|
||
|
{
|
||
|
mpz_t exp_bits;
|
||
|
mpz_t base_power;
|
||
|
mpz_t temp;
|
||
|
mpz_init(exp_bits);
|
||
|
mpz_init(base_power);
|
||
|
mpz_init(temp);
|
||
|
|
||
|
mpz_set(exp_bits, exp);
|
||
|
mpz_set(base_power, base);
|
||
|
mpz_set_ui(temp, 1);
|
||
|
|
||
|
reduce_mpz(exp_bits);
|
||
|
assert(exp_bits->sign == 1 || exp_bits->size == 0);
|
||
|
|
||
|
while (exp_bits->size > 0) {
|
||
|
if (IDX(exp_bits, 0) & 1) {
|
||
|
mpz_mul(temp, temp, base_power);
|
||
|
mpz_mod(temp, temp, mod);
|
||
|
}
|
||
|
mpz_mul(base_power, base_power, base_power);
|
||
|
mpz_mod(base_power, base_power, mod);
|
||
|
mpz_fdiv_q_2exp(exp_bits, exp_bits, 1);
|
||
|
}
|
||
|
|
||
|
mpz_clear(exp_bits);
|
||
|
mpz_clear(base_power);
|
||
|
reduce_mpz(temp);
|
||
|
mpz_clear(dest);
|
||
|
copyref_mpz(dest, temp);
|
||
|
}
|
||
|
|
||
|
/**************** Legendre symbol ****************/
|
||
|
|
||
|
int mpz_legendre(a, p)
|
||
|
const mpz_t a;
|
||
|
const mpz_t p;
|
||
|
{
|
||
|
int x;
|
||
|
mpz_t exp;
|
||
|
mpz_t pow;
|
||
|
mpz_init(exp);
|
||
|
mpz_init(pow);
|
||
|
|
||
|
mpz_set(exp, p);
|
||
|
mpz_sub_ui(exp, exp, 1);
|
||
|
mpz_fdiv_q_2exp(exp, exp, 1);
|
||
|
mpz_powm(pow, a, exp, p);
|
||
|
|
||
|
if (pow->size == 1 && IDX(pow, 0) == 1)
|
||
|
x = 1;
|
||
|
else if (pow->size == 0)
|
||
|
x = 0;
|
||
|
else
|
||
|
x = -1;
|
||
|
|
||
|
mpz_clear(exp);
|
||
|
mpz_clear(pow);
|
||
|
|
||
|
return x;
|
||
|
}
|
||
|
|
||
|
/**************** GCD ****************/
|
||
|
|
||
|
static void mpz_gcdext_main(g, ai, bi, a, b)
|
||
|
mpz_t g;
|
||
|
mpz_t ai;
|
||
|
mpz_t bi;
|
||
|
const mpz_t a;
|
||
|
const mpz_t b;
|
||
|
{
|
||
|
mpz_t rem_last, rem_cur;
|
||
|
mpz_t ai_last, ai_cur;
|
||
|
mpz_t bi_last, bi_cur;
|
||
|
mpz_t q, temp;
|
||
|
|
||
|
mpz_init(rem_last);
|
||
|
mpz_init(rem_cur);
|
||
|
mpz_init(q);
|
||
|
|
||
|
mpz_set(rem_last, a);
|
||
|
mpz_set(rem_cur, b);
|
||
|
|
||
|
if (ai) {
|
||
|
mpz_init(ai_last);
|
||
|
mpz_init(ai_cur);
|
||
|
mpz_set_ui(ai_last, 1);
|
||
|
}
|
||
|
|
||
|
if (bi) {
|
||
|
mpz_init(bi_last);
|
||
|
mpz_init(bi_cur);
|
||
|
mpz_set_ui(bi_cur, 1);
|
||
|
}
|
||
|
|
||
|
assert(a->sign == 1 && a->size > 0);
|
||
|
assert(b->sign == 1 && b->size > 0);
|
||
|
|
||
|
while (1) {
|
||
|
mpz_fdiv_qr(q, rem_last, rem_last, rem_cur);
|
||
|
mpz_swap(rem_last, rem_cur);
|
||
|
if (!mpz_sgn(rem_cur))
|
||
|
break;
|
||
|
|
||
|
if (ai) {
|
||
|
mpz_init(temp);
|
||
|
mpz_mul(temp, q, ai_cur);
|
||
|
mpz_sub(temp, ai_last, temp);
|
||
|
mpz_clear(ai_last);
|
||
|
copyref_mpz(ai_last, ai_cur);
|
||
|
copyref_mpz(ai_cur, temp);
|
||
|
}
|
||
|
|
||
|
if (bi) {
|
||
|
mpz_init(temp);
|
||
|
mpz_mul(temp, q, bi_cur);
|
||
|
mpz_sub(temp, bi_last, temp);
|
||
|
mpz_clear(bi_last);
|
||
|
copyref_mpz(bi_last, bi_cur);
|
||
|
copyref_mpz(bi_cur, temp);
|
||
|
}
|
||
|
}
|
||
|
|
||
|
mpz_clear(g);
|
||
|
copyref_mpz(g, rem_last);
|
||
|
mpz_clear(rem_cur);
|
||
|
mpz_clear(q);
|
||
|
|
||
|
if (ai) {
|
||
|
mpz_clear(ai);
|
||
|
copyref_mpz(ai, ai_cur);
|
||
|
mpz_clear(ai_last);
|
||
|
}
|
||
|
if (bi) {
|
||
|
mpz_clear(bi);
|
||
|
copyref_mpz(bi, bi_cur);
|
||
|
mpz_clear(bi_last);
|
||
|
}
|
||
|
}
|
||
|
|
||
|
void mpz_gcdext(g, ai, bi, a, b)
|
||
|
mpz_t g;
|
||
|
mpz_t ai;
|
||
|
mpz_t bi;
|
||
|
const mpz_t a;
|
||
|
const mpz_t b;
|
||
|
{
|
||
|
if (mpz_cmpabs(a, b) > 0)
|
||
|
mpz_gcdext_main(g, ai, bi, a, b);
|
||
|
else
|
||
|
mpz_gcdext_main(g, bi, ai, b, a);
|
||
|
}
|
||
|
|
||
|
/**************** Output ****************/
|
||
|
|
||
|
#define PUTCH(bbb, sss, nnn, ccc) do { \
|
||
|
if ((sss) > 1) { \
|
||
|
*(bbb) = (ccc); \
|
||
|
(bbb)++; \
|
||
|
(sss)--; \
|
||
|
} \
|
||
|
(nnn)++; \
|
||
|
} while (0)
|
||
|
|
||
|
static int putnum(char** buf, size_t* size, unsigned long value,
|
||
|
unsigned int base)
|
||
|
{
|
||
|
unsigned long s;
|
||
|
unsigned int d;
|
||
|
int count = 0;
|
||
|
|
||
|
if (value == 0) {
|
||
|
PUTCH(*buf, *size, count, '0');
|
||
|
}
|
||
|
else {
|
||
|
s = value / base;
|
||
|
if (s)
|
||
|
count = putnum(buf, size, value / base, base);
|
||
|
d = value % base;
|
||
|
if (d < 10)
|
||
|
PUTCH(*buf, *size, count, d + '0');
|
||
|
else
|
||
|
PUTCH(*buf, *size, count, d + 'A' - 10);
|
||
|
}
|
||
|
|
||
|
return count;
|
||
|
}
|
||
|
|
||
|
/* Supported conversions:
|
||
|
%% %s %c %d %i %o %u %X %ld %li %lo %lu %lX %ZX
|
||
|
*/
|
||
|
|
||
|
int rs_vsnprintf(char* buf, size_t size, const char* fmt, va_list ap)
|
||
|
{
|
||
|
int count = 0;
|
||
|
int argtype, convtype;
|
||
|
const char* strval;
|
||
|
long longval;
|
||
|
struct _mpz *mpval;
|
||
|
limb_t v, d;
|
||
|
size_t i;
|
||
|
int j;
|
||
|
|
||
|
while (fmt[0]) {
|
||
|
if (fmt[0] != '%') {
|
||
|
PUTCH(buf, size, count, fmt[0]);
|
||
|
fmt++;
|
||
|
}
|
||
|
else if (fmt[1] == '%') {
|
||
|
PUTCH(buf, size, count, '%');
|
||
|
fmt += 2;
|
||
|
}
|
||
|
else {
|
||
|
if (fmt[1] == 'l' || fmt[1] == 'Z') {
|
||
|
argtype = fmt[1];
|
||
|
convtype = fmt[2];
|
||
|
fmt += 3;
|
||
|
}
|
||
|
else {
|
||
|
argtype = 0;
|
||
|
convtype = fmt[1];
|
||
|
fmt += 2;
|
||
|
}
|
||
|
|
||
|
if (!convtype)
|
||
|
break;
|
||
|
|
||
|
if (convtype == 's') {
|
||
|
/* string argument */
|
||
|
strval = va_arg(ap, const char *);
|
||
|
if (!strval)
|
||
|
strval = "(NULL)";
|
||
|
while (*strval) {
|
||
|
PUTCH(buf, size, count, *strval);
|
||
|
strval++;
|
||
|
}
|
||
|
}
|
||
|
else if (convtype == 'c' || convtype == 'd' || convtype == 'i'
|
||
|
|| convtype == 'u' || convtype == 'x' || convtype == 'X') {
|
||
|
if (argtype == 'Z') {
|
||
|
/* mpz argument -- always print in hexadecimal */
|
||
|
mpval = va_arg(ap, struct _mpz *);
|
||
|
|
||
|
if (mpval->sign < 0)
|
||
|
PUTCH(buf, size, count, '-');
|
||
|
|
||
|
v = IDX(mpval, mpval->size - 1);
|
||
|
count += putnum(&buf, &size, v, 16);
|
||
|
|
||
|
for (i = mpval->size - 1; i > 0; i--) {
|
||
|
v = IDX(mpval, i - 1);
|
||
|
for (j = LIMB_BITS - 4; j >= 0; j -= 4) {
|
||
|
d = ((v >> j) & 0x0f);
|
||
|
if (d < 10)
|
||
|
PUTCH(buf, size, count, d + '0');
|
||
|
else
|
||
|
PUTCH(buf, size, count, d + 'A' - 10);
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
else {
|
||
|
/* int or long argument */
|
||
|
if (argtype == 'l')
|
||
|
longval = va_arg(ap, long);
|
||
|
else
|
||
|
longval = va_arg(ap, int);
|
||
|
|
||
|
if (convtype == 'c') {
|
||
|
PUTCH(buf, size, count, (char) (unsigned char) longval);
|
||
|
}
|
||
|
else if (convtype == 'x' || convtype == 'X') {
|
||
|
count += putnum(&buf, &size, longval, 16);
|
||
|
}
|
||
|
else if (convtype == 'o') {
|
||
|
count += putnum(&buf, &size, longval, 8);
|
||
|
}
|
||
|
else if (convtype == 'u' || longval >= 0) {
|
||
|
count += putnum(&buf, &size, longval, 10);
|
||
|
}
|
||
|
else {
|
||
|
PUTCH(buf, size, count, '-');
|
||
|
count += putnum(&buf, &size, -longval, 10);
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
else {
|
||
|
fprintf(stderr, "*** ERROR: mpz: unsupported conversion '%%%c'",
|
||
|
convtype);
|
||
|
if (argtype)
|
||
|
PUTCH(buf, size, count, argtype);
|
||
|
PUTCH(buf, size, count, convtype);
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
|
||
|
if (size != 0)
|
||
|
*buf = 0;
|
||
|
|
||
|
return count;
|
||
|
}
|
||
|
|
||
|
int rs_snprintf(char* buf, size_t size, const char* fmt, ...)
|
||
|
{
|
||
|
va_list ap;
|
||
|
int count;
|
||
|
|
||
|
va_start(ap, fmt);
|
||
|
count = rs_vsnprintf(buf, size, fmt, ap);
|
||
|
va_end(ap);
|
||
|
|
||
|
return count;
|
||
|
}
|
||
|
|