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secp256k1/src/field_5x52_impl.h

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/***********************************************************************
* Copyright (c) 2013, 2014 Pieter Wuille *
* Distributed under the MIT software license, see the accompanying *
* file COPYING or https://www.opensource.org/licenses/mit-license.php.*
***********************************************************************/
#ifndef SECP256K1_FIELD_REPR_IMPL_H
#define SECP256K1_FIELD_REPR_IMPL_H
#include "checkmem.h"
#include "util.h"
#include "field.h"
#include "modinv64_impl.h"
#if defined(USE_ASM_X86_64)
#include "field_5x52_asm_impl.h"
#else
#include "field_5x52_int128_impl.h"
#endif
/** Implements arithmetic modulo FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F,
* represented as 5 uint64_t's in base 2^52, least significant first. Note that the limbs are allowed to
* contain >52 bits each.
*
* Each field element has a 'magnitude' associated with it. Internally, a magnitude M means:
* - 2*M*(2^48-1) is the max (inclusive) of the most significant limb
* - 2*M*(2^52-1) is the max (inclusive) of the remaining limbs
*
* Operations have different rules for propagating magnitude to their outputs. If an operation takes a
* magnitude M as a parameter, that means the magnitude of input field elements can be at most M (inclusive).
*
* Each field element also has a 'normalized' flag. A field element is normalized if its magnitude is either
* 0 or 1, and its value is already reduced modulo the order of the field.
*/
#ifdef VERIFY
static void secp256k1_fe_verify(const secp256k1_fe *a) {
const uint64_t *d = a->n;
int m = a->normalized ? 1 : 2 * a->magnitude, r = 1;
/* secp256k1 'p' value defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */
r &= (d[0] <= 0xFFFFFFFFFFFFFULL * m);
r &= (d[1] <= 0xFFFFFFFFFFFFFULL * m);
r &= (d[2] <= 0xFFFFFFFFFFFFFULL * m);
r &= (d[3] <= 0xFFFFFFFFFFFFFULL * m);
r &= (d[4] <= 0x0FFFFFFFFFFFFULL * m);
r &= (a->magnitude >= 0);
r &= (a->magnitude <= 2048);
if (a->normalized) {
r &= (a->magnitude <= 1);
if (r && (d[4] == 0x0FFFFFFFFFFFFULL) && ((d[3] & d[2] & d[1]) == 0xFFFFFFFFFFFFFULL)) {
r &= (d[0] < 0xFFFFEFFFFFC2FULL);
}
}
VERIFY_CHECK(r == 1);
}
#endif
static void secp256k1_fe_get_bounds(secp256k1_fe *r, int m) {
VERIFY_CHECK(m >= 0);
VERIFY_CHECK(m <= 2048);
r->n[0] = 0xFFFFFFFFFFFFFULL * 2 * m;
r->n[1] = 0xFFFFFFFFFFFFFULL * 2 * m;
r->n[2] = 0xFFFFFFFFFFFFFULL * 2 * m;
r->n[3] = 0xFFFFFFFFFFFFFULL * 2 * m;
r->n[4] = 0x0FFFFFFFFFFFFULL * 2 * m;
#ifdef VERIFY
r->magnitude = m;
r->normalized = (m == 0);
secp256k1_fe_verify(r);
#endif
}
static void secp256k1_fe_normalize(secp256k1_fe *r) {
uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
/* Reduce t4 at the start so there will be at most a single carry from the first pass */
uint64_t m;
uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
/* The first pass ensures the magnitude is 1, ... */
t0 += x * 0x1000003D1ULL;
t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1;
t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2;
t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3;
/* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
VERIFY_CHECK(t4 >> 49 == 0);
/* At most a single final reduction is needed; check if the value is >= the field characteristic */
x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL)
& (t0 >= 0xFFFFEFFFFFC2FULL));
/* Apply the final reduction (for constant-time behaviour, we do it always) */
t0 += x * 0x1000003D1ULL;
t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
/* If t4 didn't carry to bit 48 already, then it should have after any final reduction */
VERIFY_CHECK(t4 >> 48 == x);
/* Mask off the possible multiple of 2^256 from the final reduction */
t4 &= 0x0FFFFFFFFFFFFULL;
r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 1;
secp256k1_fe_verify(r);
#endif
}
static void secp256k1_fe_normalize_weak(secp256k1_fe *r) {
uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
/* Reduce t4 at the start so there will be at most a single carry from the first pass */
uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
/* The first pass ensures the magnitude is 1, ... */
t0 += x * 0x1000003D1ULL;
t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
/* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
VERIFY_CHECK(t4 >> 49 == 0);
r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
#ifdef VERIFY
r->magnitude = 1;
secp256k1_fe_verify(r);
#endif
}
static void secp256k1_fe_normalize_var(secp256k1_fe *r) {
uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
/* Reduce t4 at the start so there will be at most a single carry from the first pass */
uint64_t m;
uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
/* The first pass ensures the magnitude is 1, ... */
t0 += x * 0x1000003D1ULL;
t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1;
t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2;
t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3;
/* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
VERIFY_CHECK(t4 >> 49 == 0);
/* At most a single final reduction is needed; check if the value is >= the field characteristic */
x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL)
& (t0 >= 0xFFFFEFFFFFC2FULL));
if (x) {
t0 += 0x1000003D1ULL;
t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
/* If t4 didn't carry to bit 48 already, then it should have after any final reduction */
VERIFY_CHECK(t4 >> 48 == x);
/* Mask off the possible multiple of 2^256 from the final reduction */
t4 &= 0x0FFFFFFFFFFFFULL;
}
r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 1;
secp256k1_fe_verify(r);
#endif
}
static int secp256k1_fe_normalizes_to_zero(const secp256k1_fe *r) {
uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
/* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
uint64_t z0, z1;
/* Reduce t4 at the start so there will be at most a single carry from the first pass */
uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
/* The first pass ensures the magnitude is 1, ... */
t0 += x * 0x1000003D1ULL;
t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; z0 = t0; z1 = t0 ^ 0x1000003D0ULL;
t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1;
t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2;
t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3;
z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL;
/* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
VERIFY_CHECK(t4 >> 49 == 0);
return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL);
}
static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r) {
uint64_t t0, t1, t2, t3, t4;
uint64_t z0, z1;
uint64_t x;
t0 = r->n[0];
t4 = r->n[4];
/* Reduce t4 at the start so there will be at most a single carry from the first pass */
x = t4 >> 48;
/* The first pass ensures the magnitude is 1, ... */
t0 += x * 0x1000003D1ULL;
/* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
z0 = t0 & 0xFFFFFFFFFFFFFULL;
z1 = z0 ^ 0x1000003D0ULL;
/* Fast return path should catch the majority of cases */
if ((z0 != 0ULL) & (z1 != 0xFFFFFFFFFFFFFULL)) {
return 0;
}
t1 = r->n[1];
t2 = r->n[2];
t3 = r->n[3];
t4 &= 0x0FFFFFFFFFFFFULL;
t1 += (t0 >> 52);
t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1;
t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2;
t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3;
z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL;
/* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
VERIFY_CHECK(t4 >> 49 == 0);
return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL);
}
SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) {
VERIFY_CHECK(0 <= a && a <= 0x7FFF);
r->n[0] = a;
r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
#ifdef VERIFY
r->magnitude = (a != 0);
r->normalized = 1;
secp256k1_fe_verify(r);
#endif
}
SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) {
const uint64_t *t = a->n;
#ifdef VERIFY
VERIFY_CHECK(a->normalized);
secp256k1_fe_verify(a);
#endif
return (t[0] | t[1] | t[2] | t[3] | t[4]) == 0;
}
SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) {
#ifdef VERIFY
VERIFY_CHECK(a->normalized);
secp256k1_fe_verify(a);
#endif
return a->n[0] & 1;
}
SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) {
int i;
#ifdef VERIFY
a->magnitude = 0;
a->normalized = 1;
#endif
for (i=0; i<5; i++) {
a->n[i] = 0;
}
}
static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
int i;
#ifdef VERIFY
VERIFY_CHECK(a->normalized);
VERIFY_CHECK(b->normalized);
secp256k1_fe_verify(a);
secp256k1_fe_verify(b);
#endif
for (i = 4; i >= 0; i--) {
if (a->n[i] > b->n[i]) {
return 1;
}
if (a->n[i] < b->n[i]) {
return -1;
}
}
return 0;
}
static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) {
int ret;
r->n[0] = (uint64_t)a[31]
| ((uint64_t)a[30] << 8)
| ((uint64_t)a[29] << 16)
| ((uint64_t)a[28] << 24)
| ((uint64_t)a[27] << 32)
| ((uint64_t)a[26] << 40)
| ((uint64_t)(a[25] & 0xF) << 48);
r->n[1] = (uint64_t)((a[25] >> 4) & 0xF)
| ((uint64_t)a[24] << 4)
| ((uint64_t)a[23] << 12)
| ((uint64_t)a[22] << 20)
| ((uint64_t)a[21] << 28)
| ((uint64_t)a[20] << 36)
| ((uint64_t)a[19] << 44);
r->n[2] = (uint64_t)a[18]
| ((uint64_t)a[17] << 8)
| ((uint64_t)a[16] << 16)
| ((uint64_t)a[15] << 24)
| ((uint64_t)a[14] << 32)
| ((uint64_t)a[13] << 40)
| ((uint64_t)(a[12] & 0xF) << 48);
r->n[3] = (uint64_t)((a[12] >> 4) & 0xF)
| ((uint64_t)a[11] << 4)
| ((uint64_t)a[10] << 12)
| ((uint64_t)a[9] << 20)
| ((uint64_t)a[8] << 28)
| ((uint64_t)a[7] << 36)
| ((uint64_t)a[6] << 44);
r->n[4] = (uint64_t)a[5]
| ((uint64_t)a[4] << 8)
| ((uint64_t)a[3] << 16)
| ((uint64_t)a[2] << 24)
| ((uint64_t)a[1] << 32)
| ((uint64_t)a[0] << 40);
ret = !((r->n[4] == 0x0FFFFFFFFFFFFULL) & ((r->n[3] & r->n[2] & r->n[1]) == 0xFFFFFFFFFFFFFULL) & (r->n[0] >= 0xFFFFEFFFFFC2FULL));
#ifdef VERIFY
r->magnitude = 1;
if (ret) {
r->normalized = 1;
secp256k1_fe_verify(r);
} else {
r->normalized = 0;
}
#endif
return ret;
}
/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) {
#ifdef VERIFY
VERIFY_CHECK(a->normalized);
secp256k1_fe_verify(a);
#endif
r[0] = (a->n[4] >> 40) & 0xFF;
r[1] = (a->n[4] >> 32) & 0xFF;
r[2] = (a->n[4] >> 24) & 0xFF;
r[3] = (a->n[4] >> 16) & 0xFF;
r[4] = (a->n[4] >> 8) & 0xFF;
r[5] = a->n[4] & 0xFF;
r[6] = (a->n[3] >> 44) & 0xFF;
r[7] = (a->n[3] >> 36) & 0xFF;
r[8] = (a->n[3] >> 28) & 0xFF;
r[9] = (a->n[3] >> 20) & 0xFF;
r[10] = (a->n[3] >> 12) & 0xFF;
r[11] = (a->n[3] >> 4) & 0xFF;
r[12] = ((a->n[2] >> 48) & 0xF) | ((a->n[3] & 0xF) << 4);
r[13] = (a->n[2] >> 40) & 0xFF;
r[14] = (a->n[2] >> 32) & 0xFF;
r[15] = (a->n[2] >> 24) & 0xFF;
r[16] = (a->n[2] >> 16) & 0xFF;
r[17] = (a->n[2] >> 8) & 0xFF;
r[18] = a->n[2] & 0xFF;
r[19] = (a->n[1] >> 44) & 0xFF;
r[20] = (a->n[1] >> 36) & 0xFF;
r[21] = (a->n[1] >> 28) & 0xFF;
r[22] = (a->n[1] >> 20) & 0xFF;
r[23] = (a->n[1] >> 12) & 0xFF;
r[24] = (a->n[1] >> 4) & 0xFF;
r[25] = ((a->n[0] >> 48) & 0xF) | ((a->n[1] & 0xF) << 4);
r[26] = (a->n[0] >> 40) & 0xFF;
r[27] = (a->n[0] >> 32) & 0xFF;
r[28] = (a->n[0] >> 24) & 0xFF;
r[29] = (a->n[0] >> 16) & 0xFF;
r[30] = (a->n[0] >> 8) & 0xFF;
r[31] = a->n[0] & 0xFF;
}
SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) {
#ifdef VERIFY
VERIFY_CHECK(a->magnitude <= m);
secp256k1_fe_verify(a);
VERIFY_CHECK(0xFFFFEFFFFFC2FULL * 2 * (m + 1) >= 0xFFFFFFFFFFFFFULL * 2 * m);
VERIFY_CHECK(0xFFFFFFFFFFFFFULL * 2 * (m + 1) >= 0xFFFFFFFFFFFFFULL * 2 * m);
VERIFY_CHECK(0x0FFFFFFFFFFFFULL * 2 * (m + 1) >= 0x0FFFFFFFFFFFFULL * 2 * m);
#endif
r->n[0] = 0xFFFFEFFFFFC2FULL * 2 * (m + 1) - a->n[0];
r->n[1] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[1];
r->n[2] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[2];
r->n[3] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[3];
r->n[4] = 0x0FFFFFFFFFFFFULL * 2 * (m + 1) - a->n[4];
#ifdef VERIFY
r->magnitude = m + 1;
r->normalized = 0;
secp256k1_fe_verify(r);
#endif
}
SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) {
r->n[0] *= a;
r->n[1] *= a;
r->n[2] *= a;
r->n[3] *= a;
r->n[4] *= a;
#ifdef VERIFY
r->magnitude *= a;
r->normalized = 0;
secp256k1_fe_verify(r);
#endif
}
SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) {
#ifdef VERIFY
secp256k1_fe_verify(a);
#endif
r->n[0] += a->n[0];
r->n[1] += a->n[1];
r->n[2] += a->n[2];
r->n[3] += a->n[3];
r->n[4] += a->n[4];
#ifdef VERIFY
r->magnitude += a->magnitude;
r->normalized = 0;
secp256k1_fe_verify(r);
#endif
}
static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
#ifdef VERIFY
VERIFY_CHECK(a->magnitude <= 8);
VERIFY_CHECK(b->magnitude <= 8);
secp256k1_fe_verify(a);
secp256k1_fe_verify(b);
VERIFY_CHECK(r != b);
VERIFY_CHECK(a != b);
#endif
secp256k1_fe_mul_inner(r->n, a->n, b->n);
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 0;
secp256k1_fe_verify(r);
#endif
}
static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
#ifdef VERIFY
VERIFY_CHECK(a->magnitude <= 8);
secp256k1_fe_verify(a);
#endif
secp256k1_fe_sqr_inner(r->n, a->n);
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 0;
secp256k1_fe_verify(r);
#endif
}
static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
uint64_t mask0, mask1;
SECP256K1_CHECKMEM_CHECK_VERIFY(r->n, sizeof(r->n));
mask0 = flag + ~((uint64_t)0);
mask1 = ~mask0;
r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
#ifdef VERIFY
if (flag) {
r->magnitude = a->magnitude;
r->normalized = a->normalized;
}
#endif
}
static SECP256K1_INLINE void secp256k1_fe_half(secp256k1_fe *r) {
uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
uint64_t one = (uint64_t)1;
uint64_t mask = -(t0 & one) >> 12;
#ifdef VERIFY
secp256k1_fe_verify(r);
VERIFY_CHECK(r->magnitude < 32);
#endif
/* Bounds analysis (over the rationals).
*
* Let m = r->magnitude
* C = 0xFFFFFFFFFFFFFULL * 2
* D = 0x0FFFFFFFFFFFFULL * 2
*
* Initial bounds: t0..t3 <= C * m
* t4 <= D * m
*/
t0 += 0xFFFFEFFFFFC2FULL & mask;
t1 += mask;
t2 += mask;
t3 += mask;
t4 += mask >> 4;
VERIFY_CHECK((t0 & one) == 0);
/* t0..t3: added <= C/2
* t4: added <= D/2
*
* Current bounds: t0..t3 <= C * (m + 1/2)
* t4 <= D * (m + 1/2)
*/
r->n[0] = (t0 >> 1) + ((t1 & one) << 51);
r->n[1] = (t1 >> 1) + ((t2 & one) << 51);
r->n[2] = (t2 >> 1) + ((t3 & one) << 51);
r->n[3] = (t3 >> 1) + ((t4 & one) << 51);
r->n[4] = (t4 >> 1);
/* t0..t3: shifted right and added <= C/4 + 1/2
* t4: shifted right
*
* Current bounds: t0..t3 <= C * (m/2 + 1/2)
* t4 <= D * (m/2 + 1/4)
*/
#ifdef VERIFY
/* Therefore the output magnitude (M) has to be set such that:
* t0..t3: C * M >= C * (m/2 + 1/2)
* t4: D * M >= D * (m/2 + 1/4)
*
* It suffices for all limbs that, for any input magnitude m:
* M >= m/2 + 1/2
*
* and since we want the smallest such integer value for M:
* M == floor(m/2) + 1
*/
r->magnitude = (r->magnitude >> 1) + 1;
r->normalized = 0;
secp256k1_fe_verify(r);
#endif
}
static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) {
uint64_t mask0, mask1;
SECP256K1_CHECKMEM_CHECK_VERIFY(r->n, sizeof(r->n));
mask0 = flag + ~((uint64_t)0);
mask1 = ~mask0;
r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
}
static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
#ifdef VERIFY
VERIFY_CHECK(a->normalized);
#endif
r->n[0] = a->n[0] | a->n[1] << 52;
r->n[1] = a->n[1] >> 12 | a->n[2] << 40;
r->n[2] = a->n[2] >> 24 | a->n[3] << 28;
r->n[3] = a->n[3] >> 36 | a->n[4] << 16;
}
static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
r->n[0] = a->n[0] & 0xFFFFFFFFFFFFFULL;
r->n[1] = a->n[0] >> 52 | ((a->n[1] << 12) & 0xFFFFFFFFFFFFFULL);
r->n[2] = a->n[1] >> 40 | ((a->n[2] << 24) & 0xFFFFFFFFFFFFFULL);
r->n[3] = a->n[2] >> 28 | ((a->n[3] << 36) & 0xFFFFFFFFFFFFFULL);
r->n[4] = a->n[3] >> 16;
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 1;
secp256k1_fe_verify(r);
#endif
}
static void secp256k1_fe_from_signed62(secp256k1_fe *r, const secp256k1_modinv64_signed62 *a) {
const uint64_t M52 = UINT64_MAX >> 12;
const uint64_t a0 = a->v[0], a1 = a->v[1], a2 = a->v[2], a3 = a->v[3], a4 = a->v[4];
/* The output from secp256k1_modinv64{_var} should be normalized to range [0,modulus), and
* have limbs in [0,2^62). The modulus is < 2^256, so the top limb must be below 2^(256-62*4).
*/
VERIFY_CHECK(a0 >> 62 == 0);
VERIFY_CHECK(a1 >> 62 == 0);
VERIFY_CHECK(a2 >> 62 == 0);
VERIFY_CHECK(a3 >> 62 == 0);
VERIFY_CHECK(a4 >> 8 == 0);
r->n[0] = a0 & M52;
r->n[1] = (a0 >> 52 | a1 << 10) & M52;
r->n[2] = (a1 >> 42 | a2 << 20) & M52;
r->n[3] = (a2 >> 32 | a3 << 30) & M52;
r->n[4] = (a3 >> 22 | a4 << 40);
#ifdef VERIFY
r->magnitude = 1;
r->normalized = 1;
secp256k1_fe_verify(r);
#endif
}
static void secp256k1_fe_to_signed62(secp256k1_modinv64_signed62 *r, const secp256k1_fe *a) {
const uint64_t M62 = UINT64_MAX >> 2;
const uint64_t a0 = a->n[0], a1 = a->n[1], a2 = a->n[2], a3 = a->n[3], a4 = a->n[4];
#ifdef VERIFY
VERIFY_CHECK(a->normalized);
#endif
r->v[0] = (a0 | a1 << 52) & M62;
r->v[1] = (a1 >> 10 | a2 << 42) & M62;
r->v[2] = (a2 >> 20 | a3 << 32) & M62;
r->v[3] = (a3 >> 30 | a4 << 22) & M62;
r->v[4] = a4 >> 40;
}
static const secp256k1_modinv64_modinfo secp256k1_const_modinfo_fe = {
{{-0x1000003D1LL, 0, 0, 0, 256}},
0x27C7F6E22DDACACFLL
};
static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *x) {
secp256k1_fe tmp;
secp256k1_modinv64_signed62 s;
tmp = *x;
secp256k1_fe_normalize(&tmp);
secp256k1_fe_to_signed62(&s, &tmp);
secp256k1_modinv64(&s, &secp256k1_const_modinfo_fe);
secp256k1_fe_from_signed62(r, &s);
#ifdef VERIFY
VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == secp256k1_fe_normalizes_to_zero(&tmp));
#endif
}
static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *x) {
secp256k1_fe tmp;
secp256k1_modinv64_signed62 s;
tmp = *x;
secp256k1_fe_normalize_var(&tmp);
secp256k1_fe_to_signed62(&s, &tmp);
secp256k1_modinv64_var(&s, &secp256k1_const_modinfo_fe);
secp256k1_fe_from_signed62(r, &s);
#ifdef VERIFY
VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == secp256k1_fe_normalizes_to_zero(&tmp));
#endif
}
#endif /* SECP256K1_FIELD_REPR_IMPL_H */
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