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Minor optimizations to _scalar_inverse to save 4M 

- Precalculate x^5 and use for "01010" patterns during accumulation. (net -2M)
- Further use of x^5 to allow shorter addition chain (net -2M)
This commit is contained in:
Peter Dettman 2017-04-18 11:43:56 +07:00
parent 119949232a
commit cf12fa13cb
1 changed files with 56 additions and 70 deletions
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124
src/scalar_impl.h
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@ -66,76 +66,70 @@ static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar
#else #else
secp256k1_scalar *t; secp256k1_scalar *t;
int i; int i;
/* First compute x ^ (2^N - 1) for some values of N. */ /* First compute xN as x ^ (2^N - 1) for some values of N,
secp256k1_scalar x2, x3, x4, x6, x7, x8, x15, x30, x60, x120, x127; * and uM as x ^ M for some values of M. */
secp256k1_scalar x2, x3, x6, x8, x14, x28, x56, x112, x126;
secp256k1_scalar u2, u5;
secp256k1_scalar_sqr(&x2, x); secp256k1_scalar_sqr(&u2, x);
secp256k1_scalar_mul(&x2, &x2, x); secp256k1_scalar_mul(&x2, &u2, x);
secp256k1_scalar_mul(&u5, &u2, &x2);
secp256k1_scalar_mul(&x3, &u5, &u2);
secp256k1_scalar_sqr(&x3, &x2); secp256k1_scalar_sqr(&x6, &x3);
secp256k1_scalar_mul(&x3, &x3, x); for (i = 0; i < 2; i++) {
secp256k1_scalar_sqr(&x4, &x3);
secp256k1_scalar_mul(&x4, &x4, x);
secp256k1_scalar_sqr(&x6, &x4);
secp256k1_scalar_sqr(&x6, &x6); secp256k1_scalar_sqr(&x6, &x6);
secp256k1_scalar_mul(&x6, &x6, &x2);
secp256k1_scalar_sqr(&x7, &x6);
secp256k1_scalar_mul(&x7, &x7, x);
secp256k1_scalar_sqr(&x8, &x7);
secp256k1_scalar_mul(&x8, &x8, x);
secp256k1_scalar_sqr(&x15, &x8);
for (i = 0; i < 6; i++) {
secp256k1_scalar_sqr(&x15, &x15);
} }
secp256k1_scalar_mul(&x15, &x15, &x7); secp256k1_scalar_mul(&x6, &x6, &x3);
secp256k1_scalar_sqr(&x30, &x15); secp256k1_scalar_sqr(&x8, &x6);
for (i = 0; i < 14; i++) { secp256k1_scalar_sqr(&x8, &x8);
secp256k1_scalar_sqr(&x30, &x30); secp256k1_scalar_mul(&x8, &x8, &x2);
secp256k1_scalar_sqr(&x14, &x8);
for (i = 0; i < 5; i++) {
secp256k1_scalar_sqr(&x14, &x14);
} }
secp256k1_scalar_mul(&x30, &x30, &x15); secp256k1_scalar_mul(&x14, &x14, &x6);
secp256k1_scalar_sqr(&x60, &x30); secp256k1_scalar_sqr(&x28, &x14);
for (i = 0; i < 29; i++) { for (i = 0; i < 13; i++) {
secp256k1_scalar_sqr(&x60, &x60); secp256k1_scalar_sqr(&x28, &x28);
} }
secp256k1_scalar_mul(&x60, &x60, &x30); secp256k1_scalar_mul(&x28, &x28, &x14);
secp256k1_scalar_sqr(&x120, &x60); secp256k1_scalar_sqr(&x56, &x28);
for (i = 0; i < 59; i++) { for (i = 0; i < 27; i++) {
secp256k1_scalar_sqr(&x120, &x120); secp256k1_scalar_sqr(&x56, &x56);
} }
secp256k1_scalar_mul(&x120, &x120, &x60); secp256k1_scalar_mul(&x56, &x56, &x28);
secp256k1_scalar_sqr(&x127, &x120); secp256k1_scalar_sqr(&x112, &x56);
for (i = 0; i < 6; i++) { for (i = 0; i < 55; i++) {
secp256k1_scalar_sqr(&x127, &x127); secp256k1_scalar_sqr(&x112, &x112);
} }
secp256k1_scalar_mul(&x127, &x127, &x7); secp256k1_scalar_mul(&x112, &x112, &x56);
/* Then accumulate the final result (t starts at x127). */ secp256k1_scalar_sqr(&x126, &x112);
t = &x127; for (i = 0; i < 13; i++) {
for (i = 0; i < 2; i++) { /* 0 */ secp256k1_scalar_sqr(&x126, &x126);
}
secp256k1_scalar_mul(&x126, &x126, &x14);
/* Then accumulate the final result (t starts at x126). */
t = &x126;
for (i = 0; i < 3; i++) {
secp256k1_scalar_sqr(t, t); secp256k1_scalar_sqr(t, t);
} }
secp256k1_scalar_mul(t, t, x); /* 1 */ secp256k1_scalar_mul(t, t, &u5); /* 101 */
for (i = 0; i < 4; i++) { /* 0 */ for (i = 0; i < 4; i++) { /* 0 */
secp256k1_scalar_sqr(t, t); secp256k1_scalar_sqr(t, t);
} }
secp256k1_scalar_mul(t, t, &x3); /* 111 */ secp256k1_scalar_mul(t, t, &x3); /* 111 */
for (i = 0; i < 2; i++) { /* 0 */ for (i = 0; i < 4; i++) { /* 0 */
secp256k1_scalar_sqr(t, t); secp256k1_scalar_sqr(t, t);
} }
secp256k1_scalar_mul(t, t, x); /* 1 */ secp256k1_scalar_mul(t, t, &u5); /* 101 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 2; i++) { /* 0 */ for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t); secp256k1_scalar_sqr(t, t);
} }
@ -160,34 +154,26 @@ static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar
secp256k1_scalar_sqr(t, t); secp256k1_scalar_sqr(t, t);
} }
secp256k1_scalar_mul(t, t, &x2); /* 11 */ secp256k1_scalar_mul(t, t, &x2); /* 11 */
for (i = 0; i < 2; i++) { /* 0 */ for (i = 0; i < 4; i++) { /* 0 */
secp256k1_scalar_sqr(t, t); secp256k1_scalar_sqr(t, t);
} }
secp256k1_scalar_mul(t, t, x); /* 1 */ secp256k1_scalar_mul(t, t, &u5); /* 101 */
for (i = 0; i < 2; i++) { /* 0 */ for (i = 0; i < 4; i++) { /* 0 */
secp256k1_scalar_sqr(t, t); secp256k1_scalar_sqr(t, t);
} }
secp256k1_scalar_mul(t, t, x); /* 1 */ secp256k1_scalar_mul(t, t, &x3); /* 111 */
for (i = 0; i < 5; i++) { /* 0 */ for (i = 0; i < 3; i++) {
secp256k1_scalar_sqr(t, t); secp256k1_scalar_sqr(t, t);
} }
secp256k1_scalar_mul(t, t, &x4); /* 1111 */ secp256k1_scalar_mul(t, t, &u5); /* 101 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 3; i++) { /* 00 */ for (i = 0; i < 3; i++) { /* 00 */
secp256k1_scalar_sqr(t, t); secp256k1_scalar_sqr(t, t);
} }
secp256k1_scalar_mul(t, t, x); /* 1 */ secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 4; i++) { /* 000 */ for (i = 0; i < 6; i++) { /* 000 */
secp256k1_scalar_sqr(t, t); secp256k1_scalar_sqr(t, t);
} }
secp256k1_scalar_mul(t, t, x); /* 1 */ secp256k1_scalar_mul(t, t, &u5); /* 101 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 10; i++) { /* 0000000 */ for (i = 0; i < 10; i++) { /* 0000000 */
secp256k1_scalar_sqr(t, t); secp256k1_scalar_sqr(t, t);
} }
@ -212,14 +198,14 @@ static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar
secp256k1_scalar_sqr(t, t); secp256k1_scalar_sqr(t, t);
} }
secp256k1_scalar_mul(t, t, x); /* 1 */ secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 5; i++) { /* 0 */ for (i = 0; i < 4; i++) { /* 0 */
secp256k1_scalar_sqr(t, t); secp256k1_scalar_sqr(t, t);
} }
secp256k1_scalar_mul(t, t, &x4); /* 1111 */ secp256k1_scalar_mul(t, t, &x3); /* 111 */
for (i = 0; i < 2; i++) { /* 0 */ for (i = 0; i < 3; i++) {
secp256k1_scalar_sqr(t, t); secp256k1_scalar_sqr(t, t);
} }
secp256k1_scalar_mul(t, t, x); /* 1 */ secp256k1_scalar_mul(t, t, &u5); /* 101 */
for (i = 0; i < 5; i++) { /* 000 */ for (i = 0; i < 5; i++) { /* 000 */
secp256k1_scalar_sqr(t, t); secp256k1_scalar_sqr(t, t);
} }