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/**********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
#ifndef _SECP256K1_NUM_REPR_IMPL_H_
#define _SECP256K1_NUM_REPR_IMPL_H_
#include <string.h>
#include <stdlib.h>
#include <gmp.h>
#include "util.h"
#include "num.h"
#ifdef VERIFY
static void secp256k1_num_sanity(const secp256k1_num_t *a) {
VERIFY_CHECK(a->limbs == 1 || (a->limbs > 1 && a->data[a->limbs-1] != 0));
}
#else
#define secp256k1_num_sanity(a) do { } while(0)
#endif
static void secp256k1_num_copy(secp256k1_num_t *r, const secp256k1_num_t *a) {
*r = *a;
}
static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num_t *a) {
unsigned char tmp[65];
int len = 0;
if (a->limbs>1 || a->data[0] != 0) {
len = mpn_get_str(tmp, 256, (mp_limb_t*)a->data, a->limbs);
}
int shift = 0;
while (shift < len && tmp[shift] == 0) shift++;
VERIFY_CHECK(len-shift <= (int)rlen);
memset(r, 0, rlen - len + shift);
if (len > shift) {
memcpy(r + rlen - len + shift, tmp + shift, len - shift);
}
memset(tmp, 0, sizeof(tmp));
}
static void secp256k1_num_set_bin(secp256k1_num_t *r, const unsigned char *a, unsigned int alen) {
VERIFY_CHECK(alen > 0);
VERIFY_CHECK(alen <= 64);
int len = mpn_set_str(r->data, a, alen, 256);
if (len == 0) {
r->data[0] = 0;
len = 1;
}
VERIFY_CHECK(len <= NUM_LIMBS*2);
r->limbs = len;
r->neg = 0;
while (r->limbs > 1 && r->data[r->limbs-1]==0) r->limbs--;
}
static void secp256k1_num_add_abs(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
mp_limb_t c = mpn_add(r->data, a->data, a->limbs, b->data, b->limbs);
r->limbs = a->limbs;
if (c != 0) {
VERIFY_CHECK(r->limbs < 2*NUM_LIMBS);
r->data[r->limbs++] = c;
}
}
static void secp256k1_num_sub_abs(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
mp_limb_t c = mpn_sub(r->data, a->data, a->limbs, b->data, b->limbs);
VERIFY_CHECK(c == 0);
r->limbs = a->limbs;
while (r->limbs > 1 && r->data[r->limbs-1]==0) r->limbs--;
}
static void secp256k1_num_mod(secp256k1_num_t *r, const secp256k1_num_t *m) {
secp256k1_num_sanity(r);
secp256k1_num_sanity(m);
if (r->limbs >= m->limbs) {
mp_limb_t t[2*NUM_LIMBS];
mpn_tdiv_qr(t, r->data, 0, r->data, r->limbs, m->data, m->limbs);
memset(t, 0, sizeof(t));
r->limbs = m->limbs;
while (r->limbs > 1 && r->data[r->limbs-1]==0) r->limbs--;
}
if (r->neg && (r->limbs > 1 || r->data[0] != 0)) {
secp256k1_num_sub_abs(r, m, r);
r->neg = 0;
}
}
static void secp256k1_num_mod_inverse(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *m) {
secp256k1_num_sanity(a);
secp256k1_num_sanity(m);
/** mpn_gcdext computes: (G,S) = gcdext(U,V), where
* * G = gcd(U,V)
* * G = U*S + V*T
* * U has equal or more limbs than V, and V has no padding
* If we set U to be (a padded version of) a, and V = m:
* G = a*S + m*T
* G = a*S mod m
* Assuming G=1:
* S = 1/a mod m
*/
VERIFY_CHECK(m->limbs <= NUM_LIMBS);
VERIFY_CHECK(m->data[m->limbs-1] != 0);
mp_limb_t g[NUM_LIMBS+1];
mp_limb_t u[NUM_LIMBS+1];
mp_limb_t v[NUM_LIMBS+1];
for (int i=0; i < m->limbs; i++) {
u[i] = (i < a->limbs) ? a->data[i] : 0;
v[i] = m->data[i];
}
mp_size_t sn = NUM_LIMBS+1;
mp_size_t gn = mpn_gcdext(g, r->data, &sn, u, m->limbs, v, m->limbs);
VERIFY_CHECK(gn == 1);
VERIFY_CHECK(g[0] == 1);
r->neg = a->neg ^ m->neg;
if (sn < 0) {
mpn_sub(r->data, m->data, m->limbs, r->data, -sn);
r->limbs = m->limbs;
while (r->limbs > 1 && r->data[r->limbs-1]==0) r->limbs--;
} else {
r->limbs = sn;
}
memset(g, 0, sizeof(g));
memset(u, 0, sizeof(u));
memset(v, 0, sizeof(v));
}
static int secp256k1_num_is_zero(const secp256k1_num_t *a) {
return (a->limbs == 1 && a->data[0] == 0);
}
static int secp256k1_num_is_neg(const secp256k1_num_t *a) {
return (a->limbs > 1 || a->data[0] != 0) && a->neg;
}
static int secp256k1_num_cmp(const secp256k1_num_t *a, const secp256k1_num_t *b) {
if (a->limbs > b->limbs) return 1;
if (a->limbs < b->limbs) return -1;
return mpn_cmp(a->data, b->data, a->limbs);
}
static int secp256k1_num_eq(const secp256k1_num_t *a, const secp256k1_num_t *b) {
if (a->limbs > b->limbs) return 0;
if (a->limbs < b->limbs) return 0;
if ((a->neg && !secp256k1_num_is_zero(a)) != (b->neg && !secp256k1_num_is_zero(b))) return 0;
return mpn_cmp(a->data, b->data, a->limbs) == 0;
}
static void secp256k1_num_subadd(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b, int bneg) {
if (!(b->neg ^ bneg ^ a->neg)) { /* a and b have the same sign */
r->neg = a->neg;
if (a->limbs >= b->limbs) {
secp256k1_num_add_abs(r, a, b);
} else {
secp256k1_num_add_abs(r, b, a);
}
} else {
if (secp256k1_num_cmp(a, b) > 0) {
r->neg = a->neg;
secp256k1_num_sub_abs(r, a, b);
} else {
r->neg = b->neg ^ bneg;
secp256k1_num_sub_abs(r, b, a);
}
}
}
static void secp256k1_num_add(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
secp256k1_num_sanity(a);
secp256k1_num_sanity(b);
secp256k1_num_subadd(r, a, b, 0);
}
static void secp256k1_num_sub(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
secp256k1_num_sanity(a);
secp256k1_num_sanity(b);
secp256k1_num_subadd(r, a, b, 1);
}
static void secp256k1_num_mul(secp256k1_num_t *r, const secp256k1_num_t *a, const secp256k1_num_t *b) {
secp256k1_num_sanity(a);
secp256k1_num_sanity(b);
mp_limb_t tmp[2*NUM_LIMBS+1];
VERIFY_CHECK(a->limbs + b->limbs <= 2*NUM_LIMBS+1);
if ((a->limbs==1 && a->data[0]==0) || (b->limbs==1 && b->data[0]==0)) {
r->limbs = 1;
r->neg = 0;
r->data[0] = 0;
return;
}
if (a->limbs >= b->limbs)
mpn_mul(tmp, a->data, a->limbs, b->data, b->limbs);
else
mpn_mul(tmp, b->data, b->limbs, a->data, a->limbs);
r->limbs = a->limbs + b->limbs;
if (r->limbs > 1 && tmp[r->limbs - 1]==0) r->limbs--;
VERIFY_CHECK(r->limbs <= 2*NUM_LIMBS);
mpn_copyi(r->data, tmp, r->limbs);
r->neg = a->neg ^ b->neg;
memset(tmp, 0, sizeof(tmp));
}
static void secp256k1_num_shift(secp256k1_num_t *r, int bits) {
if (bits % GMP_NUMB_BITS) {
// Shift within limbs.
mpn_rshift(r->data, r->data, r->limbs, bits % GMP_NUMB_BITS);
}
if (bits >= GMP_NUMB_BITS) {
// Shift full limbs.
for (int i = 0; i < r->limbs; i++) {
int index = i + (bits / GMP_NUMB_BITS);
if (index < r->limbs && index < 2*NUM_LIMBS) {
r->data[i] = r->data[index];
} else {
r->data[i] = 0;
}
}
}
while (r->limbs>1 && r->data[r->limbs-1]==0) r->limbs--;
}
static void secp256k1_num_negate(secp256k1_num_t *r) {
r->neg ^= 1;
}
#endif
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