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346 lines
11 KiB
346 lines
11 KiB
// Copyright (c) 2013 Pieter Wuille
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// Distributed under the MIT/X11 software license, see the accompanying
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// file COPYING or http://www.opensource.org/licenses/mit-license.php.
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#ifndef _SECP256K1_NUM_REPR_IMPL_H_
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#define _SECP256K1_NUM_REPR_IMPL_H_
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#include <assert.h>
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#include <string.h>
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#include <stdlib.h>
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#include <gmp.h>
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#include "num.h"
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#ifdef VERIFY
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void static secp256k1_num_sanity(const secp256k1_num_t *a) {
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assert(a->limbs == 1 || (a->limbs > 1 && a->data[a->limbs-1] != 0));
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}
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#else
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#define secp256k1_num_sanity(a) do { } while(0)
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#endif
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void static secp256k1_num_init(secp256k1_num_t *r) {
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r->neg = 0;
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r->limbs = 1;
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r->data[0] = 0;
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}
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void static secp256k1_num_free(secp256k1_num_t *r) {
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}
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void static secp256k1_num_copy(secp256k1_num_t *r, const secp256k1_num_t *a) {
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*r = *a;
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}
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int static secp256k1_num_bits(const secp256k1_num_t *a) {
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int ret=(a->limbs-1)*GMP_NUMB_BITS;
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mp_limb_t x=a->data[a->limbs-1];
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while (x) {
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x >>= 1;
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ret++;
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}
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return ret;
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}
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void static secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num_t *a) {
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unsigned char tmp[65];
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int len = 0;
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if (a->limbs>1 || a->data[0] != 0) {
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len = mpn_get_str(tmp, 256, (mp_limb_t*)a->data, a->limbs);
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}
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int shift = 0;
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while (shift < len && tmp[shift] == 0) shift++;
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assert(len-shift <= rlen);
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memset(r, 0, rlen - len + shift);
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if (len > shift)
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memcpy(r + rlen - len + shift, tmp + shift, len - shift);
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}
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void static secp256k1_num_set_bin(secp256k1_num_t *r, const unsigned char *a, unsigned int alen) {
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assert(alen > 0);
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assert(alen <= 64);
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int len = mpn_set_str(r->data, a, alen, 256);
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assert(len <= NUM_LIMBS*2);
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r->limbs = len;
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r->neg = 0;
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while (r->limbs > 1 && r->data[r->limbs-1]==0) r->limbs--;
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}
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void static secp256k1_num_set_int(secp256k1_num_t *r, int a) {
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r->limbs = 1;
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r->neg = (a < 0);
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r->data[0] = (a < 0) ? -a : a;
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}
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void static secp256k1_num_add_abs(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
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mp_limb_t c = mpn_add(r->data, a->data, a->limbs, b->data, b->limbs);
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r->limbs = a->limbs;
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if (c != 0) {
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assert(r->limbs < 2*NUM_LIMBS);
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r->data[r->limbs++] = c;
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}
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}
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void static secp256k1_num_sub_abs(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
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mp_limb_t c = mpn_sub(r->data, a->data, a->limbs, b->data, b->limbs);
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assert(c == 0);
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r->limbs = a->limbs;
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while (r->limbs > 1 && r->data[r->limbs-1]==0) r->limbs--;
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}
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void static secp256k1_num_mod(secp256k1_num_t *r, const secp256k1_num_t *m) {
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secp256k1_num_sanity(r);
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secp256k1_num_sanity(m);
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if (r->limbs >= m->limbs) {
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mp_limb_t t[2*NUM_LIMBS];
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mpn_tdiv_qr(t, r->data, 0, r->data, r->limbs, m->data, m->limbs);
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r->limbs = m->limbs;
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while (r->limbs > 1 && r->data[r->limbs-1]==0) r->limbs--;
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}
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if (r->neg && (r->limbs > 1 || r->data[0] != 0)) {
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secp256k1_num_sub_abs(r, m, r);
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r->neg = 0;
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}
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}
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void static secp256k1_num_mod_inverse(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *m) {
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secp256k1_num_sanity(a);
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secp256k1_num_sanity(m);
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// mpn_gcdext computes: (G,S) = gcdext(U,V), where
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// * G = gcd(U,V)
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// * G = U*S + V*T
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// * U has equal or more limbs than V, and V has no padding
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// If we set U to be (a padded version of) a, and V = m:
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// G = a*S + m*T
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// G = a*S mod m
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// Assuming G=1:
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// S = 1/a mod m
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assert(m->limbs <= NUM_LIMBS);
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assert(m->data[m->limbs-1] != 0);
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mp_limb_t g[NUM_LIMBS+1];
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mp_limb_t u[NUM_LIMBS+1];
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mp_limb_t v[NUM_LIMBS+1];
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for (int i=0; i < m->limbs; i++) {
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u[i] = (i < a->limbs) ? a->data[i] : 0;
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v[i] = m->data[i];
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}
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mp_size_t sn = NUM_LIMBS+1;
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mp_size_t gn = mpn_gcdext(g, r->data, &sn, u, m->limbs, v, m->limbs);
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assert(gn == 1);
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assert(g[0] == 1);
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r->neg = a->neg ^ m->neg;
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if (sn < 0) {
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mpn_sub(r->data, m->data, m->limbs, r->data, -sn);
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r->limbs = m->limbs;
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while (r->limbs > 1 && r->data[r->limbs-1]==0) r->limbs--;
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} else {
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r->limbs = sn;
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}
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}
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int static secp256k1_num_is_zero(const secp256k1_num_t *a) {
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return (a->limbs == 1 && a->data[0] == 0);
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}
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int static secp256k1_num_is_odd(const secp256k1_num_t *a) {
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return a->data[0] & 1;
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}
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int static secp256k1_num_is_neg(const secp256k1_num_t *a) {
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return (a->limbs > 1 || a->data[0] != 0) && a->neg;
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}
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int static secp256k1_num_cmp(const secp256k1_num_t *a, const secp256k1_num_t *b) {
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if (a->limbs > b->limbs) return 1;
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if (a->limbs < b->limbs) return -1;
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return mpn_cmp(a->data, b->data, a->limbs);
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}
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void static secp256k1_num_subadd(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b, int bneg) {
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if (!(b->neg ^ bneg ^ a->neg)) { // a and b have the same sign
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r->neg = a->neg;
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if (a->limbs >= b->limbs) {
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secp256k1_num_add_abs(r, a, b);
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} else {
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secp256k1_num_add_abs(r, b, a);
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}
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} else {
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if (secp256k1_num_cmp(a, b) > 0) {
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r->neg = a->neg;
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secp256k1_num_sub_abs(r, a, b);
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} else {
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r->neg = b->neg ^ bneg;
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secp256k1_num_sub_abs(r, b, a);
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}
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}
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}
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void static secp256k1_num_add(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
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secp256k1_num_sanity(a);
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secp256k1_num_sanity(b);
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secp256k1_num_subadd(r, a, b, 0);
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}
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void static secp256k1_num_sub(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
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secp256k1_num_sanity(a);
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secp256k1_num_sanity(b);
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secp256k1_num_subadd(r, a, b, 1);
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}
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void static secp256k1_num_mul(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
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secp256k1_num_sanity(a);
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secp256k1_num_sanity(b);
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mp_limb_t tmp[2*NUM_LIMBS+1];
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assert(a->limbs + b->limbs <= 2*NUM_LIMBS+1);
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if ((a->limbs==1 && a->data[0]==0) || (b->limbs==1 && b->data[0]==0)) {
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r->limbs = 1;
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r->neg = 0;
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r->data[0] = 0;
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return;
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}
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if (a->limbs >= b->limbs)
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mpn_mul(tmp, a->data, a->limbs, b->data, b->limbs);
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else
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mpn_mul(tmp, b->data, b->limbs, a->data, a->limbs);
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r->limbs = a->limbs + b->limbs;
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if (r->limbs > 1 && tmp[r->limbs - 1]==0) r->limbs--;
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assert(r->limbs <= 2*NUM_LIMBS);
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mpn_copyi(r->data, tmp, r->limbs);
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r->neg = a->neg ^ b->neg;
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}
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void static secp256k1_num_div(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
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secp256k1_num_sanity(a);
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secp256k1_num_sanity(b);
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if (b->limbs > a->limbs) {
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r->limbs = 1;
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r->data[0] = 0;
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r->neg = 0;
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return;
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}
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mp_limb_t quo[2*NUM_LIMBS+1];
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mp_limb_t rem[2*NUM_LIMBS+1];
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mpn_tdiv_qr(quo, rem, 0, a->data, a->limbs, b->data, b->limbs);
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mpn_copyi(r->data, quo, a->limbs - b->limbs + 1);
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r->limbs = a->limbs - b->limbs + 1;
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while (r->limbs > 1 && r->data[r->limbs - 1]==0) r->limbs--;
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r->neg = a->neg ^ b->neg;
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}
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void static secp256k1_num_mod_mul(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b, const secp256k1_num_t *m) {
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secp256k1_num_mul(r, a, b);
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secp256k1_num_mod(r, m);
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}
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int static secp256k1_num_shift(secp256k1_num_t *r, int bits) {
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assert(bits <= GMP_NUMB_BITS);
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mp_limb_t ret = mpn_rshift(r->data, r->data, r->limbs, bits);
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if (r->limbs>1 && r->data[r->limbs-1]==0) r->limbs--;
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ret >>= (GMP_NUMB_BITS - bits);
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return ret;
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}
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int static secp256k1_num_get_bit(const secp256k1_num_t *a, int pos) {
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return (a->limbs*GMP_NUMB_BITS > pos) && ((a->data[pos/GMP_NUMB_BITS] >> (pos % GMP_NUMB_BITS)) & 1);
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}
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void static secp256k1_num_inc(secp256k1_num_t *r) {
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mp_limb_t ret = mpn_add_1(r->data, r->data, r->limbs, (mp_limb_t)1);
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if (ret) {
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assert(r->limbs < 2*NUM_LIMBS);
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r->data[r->limbs++] = ret;
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}
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}
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void static secp256k1_num_set_hex(secp256k1_num_t *r, const char *a, int alen) {
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static const unsigned char cvt[256] = {
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0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
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0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
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0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
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0, 1, 2, 3, 4, 5, 6,7,8,9,0,0,0,0,0,0,
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0,10,11,12,13,14,15,0,0,0,0,0,0,0,0,0,
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0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
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0,10,11,12,13,14,15,0,0,0,0,0,0,0,0,0,
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0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
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0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
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0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
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0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
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0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
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0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
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0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
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0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
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0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0
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};
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unsigned char num[257] = {};
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for (int i=0; i<alen; i++) {
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num[i] = cvt[a[i]];
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}
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r->limbs = mpn_set_str(r->data, num, alen, 16);
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while (r->limbs > 1 && r->data[r->limbs-1] == 0) r->limbs--;
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}
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void static secp256k1_num_get_hex(char *r, int rlen, const secp256k1_num_t *a) {
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static const unsigned char cvt[16] = {'0', '1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B', 'C', 'D', 'E', 'F'};
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unsigned char *tmp = malloc(257);
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mp_size_t len = mpn_get_str(tmp, 16, (mp_limb_t*)a->data, a->limbs);
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assert(len <= rlen);
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for (int i=0; i<len; i++) {
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assert(rlen-len+i >= 0);
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assert(rlen-len+i < rlen);
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assert(tmp[i] >= 0);
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assert(tmp[i] < 16);
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r[rlen-len+i] = cvt[tmp[i]];
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}
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for (int i=0; i<rlen-len; i++) {
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assert(i >= 0);
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assert(i < rlen);
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r[i] = cvt[0];
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}
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free(tmp);
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}
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void static secp256k1_num_split(secp256k1_num_t *rl, secp256k1_num_t *rh, const secp256k1_num_t *a, int bits) {
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assert(bits > 0);
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rh->neg = a->neg;
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if (bits >= a->limbs * GMP_NUMB_BITS) {
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*rl = *a;
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rh->limbs = 1;
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rh->data[0] = 0;
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return;
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}
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rl->limbs = 0;
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rl->neg = a->neg;
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int left = bits;
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while (left >= GMP_NUMB_BITS) {
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rl->data[rl->limbs] = a->data[rl->limbs];
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rl->limbs++;
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left -= GMP_NUMB_BITS;
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}
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if (left == 0) {
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mpn_copyi(rh->data, a->data + rl->limbs, a->limbs - rl->limbs);
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rh->limbs = a->limbs - rl->limbs;
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} else {
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mpn_rshift(rh->data, a->data + rl->limbs, a->limbs - rl->limbs, left);
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rh->limbs = a->limbs - rl->limbs;
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while (rh->limbs>1 && rh->data[rh->limbs-1]==0) rh->limbs--;
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}
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if (left > 0) {
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rl->data[rl->limbs] = a->data[rl->limbs] & ((((mp_limb_t)1) << left) - 1);
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rl->limbs++;
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}
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while (rl->limbs>1 && rl->data[rl->limbs-1]==0) rl->limbs--;
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}
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void static secp256k1_num_negate(secp256k1_num_t *r) {
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r->neg ^= 1;
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}
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#endif
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