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Rewrite mul/sqr for 32bit/64bit

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- interleave calculation of the lower and upper partial product ranges, and reduction
- less registers needed, more opportunities for parallel ops
This commit is contained in:
Peter Dettman
2014-10-27 22:10:26 +07:00
committed by Pieter Wuille
parent 027eb9c610
commit 5dd421bab5
2 changed files with 348 additions and 331 deletions
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183
src/field_5x52_int128_impl.h
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@@ -8,98 +8,109 @@
#include <stdint.h>
SECP256K1_INLINE static void secp256k1_fe_mul_inner(const uint64_t *a, const uint64_t *b, uint64_t *r) {
__int128 c = (__int128)a[0] * b[0];
uint64_t t0 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 0FFFFFFFFFFFFFE0
c = c + (__int128)a[0] * b[1] +
(__int128)a[1] * b[0];
uint64_t t1 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 20000000000000BF
c = c + (__int128)a[0] * b[2] +
(__int128)a[1] * b[1] +
(__int128)a[2] * b[0];
uint64_t t2 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 30000000000001A0
c = c + (__int128)a[0] * b[3] +
(__int128)a[1] * b[2] +
(__int128)a[2] * b[1] +
(__int128)a[3] * b[0];
uint64_t t3 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 4000000000000280
c = c + (__int128)a[0] * b[4] +
(__int128)a[1] * b[3] +
(__int128)a[2] * b[2] +
(__int128)a[3] * b[1] +
(__int128)a[4] * b[0];
uint64_t t4 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 320000000000037E
c = c + (__int128)a[1] * b[4] +
(__int128)a[2] * b[3] +
(__int128)a[3] * b[2] +
(__int128)a[4] * b[1];
uint64_t t5 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 22000000000002BE
c = c + (__int128)a[2] * b[4] +
(__int128)a[3] * b[3] +
(__int128)a[4] * b[2];
uint64_t t6 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 12000000000001DE
c = c + (__int128)a[3] * b[4] +
(__int128)a[4] * b[3];
uint64_t t7 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 02000000000000FE
c = c + (__int128)a[4] * b[4];
uint64_t t8 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 001000000000001E
uint64_t t9 = c;
c = t0 + (__int128)t5 * 0x1000003D10ULL;
t0 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 0000001000003D10
c = c + t1 + (__int128)t6 * 0x1000003D10ULL;
t1 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 0000001000003D10
c = c + t2 + (__int128)t7 * 0x1000003D10ULL;
r[2] = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 0000001000003D10
c = c + t3 + (__int128)t8 * 0x1000003D10ULL;
r[3] = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 0000001000003D10
c = c + t4 + (__int128)t9 * 0x1000003D10ULL;
r[4] = c & 0x0FFFFFFFFFFFFULL; c = c >> 48; // c max 000001000003D110
c = t0 + (__int128)c * 0x1000003D1ULL;
r[0] = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 1000008
r[1] = t1 + c;
const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
__int128 c, d;
d = (__int128)a[0] * b[3]
+ (__int128)a[1] * b[2]
+ (__int128)a[2] * b[1]
+ (__int128)a[3] * b[0];
c = (__int128)a[4] * b[4];
d += (c & M) * R; c >>= 52;
uint64_t t3 = d & M; d >>= 52;
d += (__int128)a[0] * b[4]
+ (__int128)a[1] * b[3]
+ (__int128)a[2] * b[2]
+ (__int128)a[3] * b[1]
+ (__int128)a[4] * b[0];
d += c * R;
uint64_t t4 = d & M; d >>= 52;
uint64_t tx = (t4 >> 48); t4 &= (M >> 4);
c = (__int128)a[0] * b[0];
d += (__int128)a[1] * b[4]
+ (__int128)a[2] * b[3]
+ (__int128)a[3] * b[2]
+ (__int128)a[4] * b[1];
uint64_t u0 = d & M; d >>= 52;
u0 = (u0 << 4) | tx;
c += (__int128)u0 * (R >> 4);
uint64_t t0 = c & M; c >>= 52;
c += (__int128)a[0] * b[1]
+ (__int128)a[1] * b[0];
d += (__int128)a[2] * b[4]
+ (__int128)a[3] * b[3]
+ (__int128)a[4] * b[2];
c += (d & M) * R; d >>= 52;
uint64_t t1 = c & M; c >>= 52;
c += (__int128)a[0] * b[2]
+ (__int128)a[1] * b[1]
+ (__int128)a[2] * b[0];
d += (__int128)a[3] * b[4]
+ (__int128)a[4] * b[3];
c += (d & M) * R; d >>= 52;
r[0] = t0;
r[1] = t1;
r[2] = c & M; c >>= 52;
c += d * R + t3;;
r[3] = c & M; c >>= 52;
c += t4;
r[4] = c;
}
SECP256K1_INLINE static void secp256k1_fe_sqr_inner(const uint64_t *a, uint64_t *r) {
__int128 c = (__int128)a[0] * a[0];
uint64_t t0 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 0FFFFFFFFFFFFFE0
c = c + (__int128)(a[0]*2) * a[1];
uint64_t t1 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 20000000000000BF
c = c + (__int128)(a[0]*2) * a[2] +
(__int128)a[1] * a[1];
uint64_t t2 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 30000000000001A0
c = c + (__int128)(a[0]*2) * a[3] +
(__int128)(a[1]*2) * a[2];
uint64_t t3 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 4000000000000280
c = c + (__int128)(a[0]*2) * a[4] +
(__int128)(a[1]*2) * a[3] +
(__int128)a[2] * a[2];
uint64_t t4 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 320000000000037E
c = c + (__int128)(a[1]*2) * a[4] +
(__int128)(a[2]*2) * a[3];
uint64_t t5 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 22000000000002BE
c = c + (__int128)(a[2]*2) * a[4] +
(__int128)a[3] * a[3];
uint64_t t6 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 12000000000001DE
c = c + (__int128)(a[3]*2) * a[4];
uint64_t t7 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 02000000000000FE
c = c + (__int128)a[4] * a[4];
uint64_t t8 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 001000000000001E
uint64_t t9 = c;
c = t0 + (__int128)t5 * 0x1000003D10ULL;
t0 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 0000001000003D10
c = c + t1 + (__int128)t6 * 0x1000003D10ULL;
t1 = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 0000001000003D10
c = c + t2 + (__int128)t7 * 0x1000003D10ULL;
r[2] = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 0000001000003D10
c = c + t3 + (__int128)t8 * 0x1000003D10ULL;
r[3] = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 0000001000003D10
c = c + t4 + (__int128)t9 * 0x1000003D10ULL;
r[4] = c & 0x0FFFFFFFFFFFFULL; c = c >> 48; // c max 000001000003D110
c = t0 + (__int128)c * 0x1000003D1ULL;
r[0] = c & 0xFFFFFFFFFFFFFULL; c = c >> 52; // c max 1000008
r[1] = t1 + c;
const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
__int128 c, d;
uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
d = (__int128)(a0*2) * a3
+ (__int128)(a1*2) * a2;
c = (__int128)a4 * a4;
d += (c & M) * R; c >>= 52;
uint64_t t3 = d & M; d >>= 52;
a4 *= 2;
d += (__int128)a0 * a4
+ (__int128)(a1*2) * a3
+ (__int128)a2 * a2;
d += c * R;
uint64_t t4 = d & M; d >>= 52;
uint64_t tx = (t4 >> 48); t4 &= (M >> 4);
c = (__int128)a0 * a0;
d += (__int128)a1 * a4
+ (__int128)(a2*2) * a3;
uint64_t u0 = d & M; d >>= 52;
u0 = (u0 << 4) | tx;
c += (__int128)u0 * (R >> 4);
r[0] = c & M; c >>= 52;
a0 *= 2;
c += (__int128)a0 * a1;
d += (__int128)a2 * a4
+ (__int128)a3 * a3;
c += (d & M) * R; d >>= 52;
r[1] = c & M; c >>= 52;
c += (__int128)a0 * a2
+ (__int128)a1 * a1;
d += (__int128)a3 * a4;
c += (d & M) * R; d >>= 52;
r[2] = c & M; c >>= 52;
c += d * R + t3;;
r[3] = c & M; c >>= 52;
c += t4;
r[4] = c;
}
#endif