|
|
|
@ -16,7 +16,7 @@
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
|
|
SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t *a, const uint64_t * SECP256K1_RESTRICT b) {
|
|
|
|
|
__int128 c, d;
|
|
|
|
|
uint128_t c, d;
|
|
|
|
|
uint64_t t3, t4, tx, u0;
|
|
|
|
|
uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
|
|
|
|
|
const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
|
|
|
|
@ -38,13 +38,13 @@ SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t
|
|
|
|
|
* Note that [x 0 0 0 0 0] = [x*R].
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
d = (__int128)a0 * b[3]
|
|
|
|
|
+ (__int128)a1 * b[2]
|
|
|
|
|
+ (__int128)a2 * b[1]
|
|
|
|
|
+ (__int128)a3 * b[0];
|
|
|
|
|
d = (uint128_t)a0 * b[3]
|
|
|
|
|
+ (uint128_t)a1 * b[2]
|
|
|
|
|
+ (uint128_t)a2 * b[1]
|
|
|
|
|
+ (uint128_t)a3 * b[0];
|
|
|
|
|
VERIFY_BITS(d, 114);
|
|
|
|
|
/* [d 0 0 0] = [p3 0 0 0] */
|
|
|
|
|
c = (__int128)a4 * b[4];
|
|
|
|
|
c = (uint128_t)a4 * b[4];
|
|
|
|
|
VERIFY_BITS(c, 112);
|
|
|
|
|
/* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
|
|
|
|
|
d += (c & M) * R; c >>= 52;
|
|
|
|
@ -56,11 +56,11 @@ SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t
|
|
|
|
|
VERIFY_BITS(d, 63);
|
|
|
|
|
/* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
|
|
|
|
|
|
|
|
|
|
d += (__int128)a0 * b[4]
|
|
|
|
|
+ (__int128)a1 * b[3]
|
|
|
|
|
+ (__int128)a2 * b[2]
|
|
|
|
|
+ (__int128)a3 * b[1]
|
|
|
|
|
+ (__int128)a4 * b[0];
|
|
|
|
|
d += (uint128_t)a0 * b[4]
|
|
|
|
|
+ (uint128_t)a1 * b[3]
|
|
|
|
|
+ (uint128_t)a2 * b[2]
|
|
|
|
|
+ (uint128_t)a3 * b[1]
|
|
|
|
|
+ (uint128_t)a4 * b[0];
|
|
|
|
|
VERIFY_BITS(d, 115);
|
|
|
|
|
/* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
|
|
|
|
|
d += c * R;
|
|
|
|
@ -75,13 +75,13 @@ SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t
|
|
|
|
|
VERIFY_BITS(t4, 48);
|
|
|
|
|
/* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
|
|
|
|
|
|
|
|
|
|
c = (__int128)a0 * b[0];
|
|
|
|
|
c = (uint128_t)a0 * b[0];
|
|
|
|
|
VERIFY_BITS(c, 112);
|
|
|
|
|
/* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
|
|
|
|
|
d += (__int128)a1 * b[4]
|
|
|
|
|
+ (__int128)a2 * b[3]
|
|
|
|
|
+ (__int128)a3 * b[2]
|
|
|
|
|
+ (__int128)a4 * b[1];
|
|
|
|
|
d += (uint128_t)a1 * b[4]
|
|
|
|
|
+ (uint128_t)a2 * b[3]
|
|
|
|
|
+ (uint128_t)a3 * b[2]
|
|
|
|
|
+ (uint128_t)a4 * b[1];
|
|
|
|
|
VERIFY_BITS(d, 115);
|
|
|
|
|
/* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
|
|
|
|
|
u0 = d & M; d >>= 52;
|
|
|
|
@ -92,7 +92,7 @@ SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t
|
|
|
|
|
u0 = (u0 << 4) | tx;
|
|
|
|
|
VERIFY_BITS(u0, 56);
|
|
|
|
|
/* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
|
|
|
|
|
c += (__int128)u0 * (R >> 4);
|
|
|
|
|
c += (uint128_t)u0 * (R >> 4);
|
|
|
|
|
VERIFY_BITS(c, 115);
|
|
|
|
|
/* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
|
|
|
|
|
r[0] = c & M; c >>= 52;
|
|
|
|
@ -100,13 +100,13 @@ SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t
|
|
|
|
|
VERIFY_BITS(c, 61);
|
|
|
|
|
/* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
|
|
|
|
|
|
|
|
|
|
c += (__int128)a0 * b[1]
|
|
|
|
|
+ (__int128)a1 * b[0];
|
|
|
|
|
c += (uint128_t)a0 * b[1]
|
|
|
|
|
+ (uint128_t)a1 * b[0];
|
|
|
|
|
VERIFY_BITS(c, 114);
|
|
|
|
|
/* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
|
|
|
|
|
d += (__int128)a2 * b[4]
|
|
|
|
|
+ (__int128)a3 * b[3]
|
|
|
|
|
+ (__int128)a4 * b[2];
|
|
|
|
|
d += (uint128_t)a2 * b[4]
|
|
|
|
|
+ (uint128_t)a3 * b[3]
|
|
|
|
|
+ (uint128_t)a4 * b[2];
|
|
|
|
|
VERIFY_BITS(d, 114);
|
|
|
|
|
/* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
|
|
|
|
|
c += (d & M) * R; d >>= 52;
|
|
|
|
@ -118,13 +118,13 @@ SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t
|
|
|
|
|
VERIFY_BITS(c, 63);
|
|
|
|
|
/* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
|
|
|
|
|
|
|
|
|
|
c += (__int128)a0 * b[2]
|
|
|
|
|
+ (__int128)a1 * b[1]
|
|
|
|
|
+ (__int128)a2 * b[0];
|
|
|
|
|
c += (uint128_t)a0 * b[2]
|
|
|
|
|
+ (uint128_t)a1 * b[1]
|
|
|
|
|
+ (uint128_t)a2 * b[0];
|
|
|
|
|
VERIFY_BITS(c, 114);
|
|
|
|
|
/* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
|
|
|
|
|
d += (__int128)a3 * b[4]
|
|
|
|
|
+ (__int128)a4 * b[3];
|
|
|
|
|
d += (uint128_t)a3 * b[4]
|
|
|
|
|
+ (uint128_t)a4 * b[3];
|
|
|
|
|
VERIFY_BITS(d, 114);
|
|
|
|
|
/* [d 0 0 t4 t3 c t1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
|
|
|
|
|
c += (d & M) * R; d >>= 52;
|
|
|
|
@ -153,7 +153,7 @@ SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t *a) {
|
|
|
|
|
__int128 c, d;
|
|
|
|
|
uint128_t c, d;
|
|
|
|
|
uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
|
|
|
|
|
int64_t t3, t4, tx, u0;
|
|
|
|
|
const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
|
|
|
|
@ -169,11 +169,11 @@ SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t
|
|
|
|
|
* Note that [x 0 0 0 0 0] = [x*R].
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
d = (__int128)(a0*2) * a3
|
|
|
|
|
+ (__int128)(a1*2) * a2;
|
|
|
|
|
d = (uint128_t)(a0*2) * a3
|
|
|
|
|
+ (uint128_t)(a1*2) * a2;
|
|
|
|
|
VERIFY_BITS(d, 114);
|
|
|
|
|
/* [d 0 0 0] = [p3 0 0 0] */
|
|
|
|
|
c = (__int128)a4 * a4;
|
|
|
|
|
c = (uint128_t)a4 * a4;
|
|
|
|
|
VERIFY_BITS(c, 112);
|
|
|
|
|
/* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
|
|
|
|
|
d += (c & M) * R; c >>= 52;
|
|
|
|
@ -186,9 +186,9 @@ SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t
|
|
|
|
|
/* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
|
|
|
|
|
|
|
|
|
|
a4 *= 2;
|
|
|
|
|
d += (__int128)a0 * a4
|
|
|
|
|
+ (__int128)(a1*2) * a3
|
|
|
|
|
+ (__int128)a2 * a2;
|
|
|
|
|
d += (uint128_t)a0 * a4
|
|
|
|
|
+ (uint128_t)(a1*2) * a3
|
|
|
|
|
+ (uint128_t)a2 * a2;
|
|
|
|
|
VERIFY_BITS(d, 115);
|
|
|
|
|
/* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
|
|
|
|
|
d += c * R;
|
|
|
|
@ -203,11 +203,11 @@ SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t
|
|
|
|
|
VERIFY_BITS(t4, 48);
|
|
|
|
|
/* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
|
|
|
|
|
|
|
|
|
|
c = (__int128)a0 * a0;
|
|
|
|
|
c = (uint128_t)a0 * a0;
|
|
|
|
|
VERIFY_BITS(c, 112);
|
|
|
|
|
/* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
|
|
|
|
|
d += (__int128)a1 * a4
|
|
|
|
|
+ (__int128)(a2*2) * a3;
|
|
|
|
|
d += (uint128_t)a1 * a4
|
|
|
|
|
+ (uint128_t)(a2*2) * a3;
|
|
|
|
|
VERIFY_BITS(d, 114);
|
|
|
|
|
/* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
|
|
|
|
|
u0 = d & M; d >>= 52;
|
|
|
|
@ -218,7 +218,7 @@ SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t
|
|
|
|
|
u0 = (u0 << 4) | tx;
|
|
|
|
|
VERIFY_BITS(u0, 56);
|
|
|
|
|
/* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
|
|
|
|
|
c += (__int128)u0 * (R >> 4);
|
|
|
|
|
c += (uint128_t)u0 * (R >> 4);
|
|
|
|
|
VERIFY_BITS(c, 113);
|
|
|
|
|
/* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
|
|
|
|
|
r[0] = c & M; c >>= 52;
|
|
|
|
@ -227,11 +227,11 @@ SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t
|
|
|
|
|
/* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
|
|
|
|
|
|
|
|
|
|
a0 *= 2;
|
|
|
|
|
c += (__int128)a0 * a1;
|
|
|
|
|
c += (uint128_t)a0 * a1;
|
|
|
|
|
VERIFY_BITS(c, 114);
|
|
|
|
|
/* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
|
|
|
|
|
d += (__int128)a2 * a4
|
|
|
|
|
+ (__int128)a3 * a3;
|
|
|
|
|
d += (uint128_t)a2 * a4
|
|
|
|
|
+ (uint128_t)a3 * a3;
|
|
|
|
|
VERIFY_BITS(d, 114);
|
|
|
|
|
/* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
|
|
|
|
|
c += (d & M) * R; d >>= 52;
|
|
|
|
@ -243,11 +243,11 @@ SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t
|
|
|
|
|
VERIFY_BITS(c, 63);
|
|
|
|
|
/* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
|
|
|
|
|
|
|
|
|
|
c += (__int128)a0 * a2
|
|
|
|
|
+ (__int128)a1 * a1;
|
|
|
|
|
c += (uint128_t)a0 * a2
|
|
|
|
|
+ (uint128_t)a1 * a1;
|
|
|
|
|
VERIFY_BITS(c, 114);
|
|
|
|
|
/* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
|
|
|
|
|
d += (__int128)a3 * a4;
|
|
|
|
|
d += (uint128_t)a3 * a4;
|
|
|
|
|
VERIFY_BITS(d, 114);
|
|
|
|
|
/* [d 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
|
|
|
|
|
c += (d & M) * R; d >>= 52;
|
|
|
|
|