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Minor optimizations to _scalar_inverse to save 4M
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- Precalculate x^5 and use for "01010" patterns during accumulation. (net -2M)
- Further use of x^5 to allow shorter addition chain (net -2M)
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@peterdettman
peterdettman committed Apr 18, 2017
1 parent 1199492 commit cf12fa1
Showing 1 changed file with 54 additions and 68 deletions.
122 changes: 54 additions & 68 deletions src/scalar_impl.h
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Original file line number Diff line number Diff line change
Expand Up @@ -66,76 +66,70 @@ static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar
#else
secp256k1_scalar *t;
int i;
/* First compute x ^ (2^N - 1) for some values of N. */
secp256k1_scalar x2, x3, x4, x6, x7, x8, x15, x30, x60, x120, x127;
/* First compute xN as x ^ (2^N - 1) for some values of N,
* 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_mul(&x2, &x2, x);
secp256k1_scalar_sqr(&u2, 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_mul(&x3, &x3, x);

secp256k1_scalar_sqr(&x4, &x3);
secp256k1_scalar_mul(&x4, &x4, x);

secp256k1_scalar_sqr(&x6, &x4);
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(&x6, &x3);
for (i = 0; i < 2; i++) {
secp256k1_scalar_sqr(&x6, &x6);
}
secp256k1_scalar_mul(&x6, &x6, &x3);

secp256k1_scalar_sqr(&x8, &x7);
secp256k1_scalar_mul(&x8, &x8, x);
secp256k1_scalar_sqr(&x8, &x6);
secp256k1_scalar_sqr(&x8, &x8);
secp256k1_scalar_mul(&x8, &x8, &x2);

secp256k1_scalar_sqr(&x15, &x8);
for (i = 0; i < 6; i++) {
secp256k1_scalar_sqr(&x15, &x15);
secp256k1_scalar_sqr(&x14, &x8);
for (i = 0; i < 5; i++) {
secp256k1_scalar_sqr(&x14, &x14);
}
secp256k1_scalar_mul(&x15, &x15, &x7);
secp256k1_scalar_mul(&x14, &x14, &x6);

secp256k1_scalar_sqr(&x30, &x15);
for (i = 0; i < 14; i++) {
secp256k1_scalar_sqr(&x30, &x30);
secp256k1_scalar_sqr(&x28, &x14);
for (i = 0; i < 13; i++) {
secp256k1_scalar_sqr(&x28, &x28);
}
secp256k1_scalar_mul(&x30, &x30, &x15);
secp256k1_scalar_mul(&x28, &x28, &x14);

secp256k1_scalar_sqr(&x60, &x30);
for (i = 0; i < 29; i++) {
secp256k1_scalar_sqr(&x60, &x60);
secp256k1_scalar_sqr(&x56, &x28);
for (i = 0; i < 27; i++) {
secp256k1_scalar_sqr(&x56, &x56);
}
secp256k1_scalar_mul(&x60, &x60, &x30);
secp256k1_scalar_mul(&x56, &x56, &x28);

secp256k1_scalar_sqr(&x120, &x60);
for (i = 0; i < 59; i++) {
secp256k1_scalar_sqr(&x120, &x120);
secp256k1_scalar_sqr(&x112, &x56);
for (i = 0; i < 55; i++) {
secp256k1_scalar_sqr(&x112, &x112);
}
secp256k1_scalar_mul(&x120, &x120, &x60);
secp256k1_scalar_mul(&x112, &x112, &x56);

secp256k1_scalar_sqr(&x127, &x120);
for (i = 0; i < 6; i++) {
secp256k1_scalar_sqr(&x127, &x127);
secp256k1_scalar_sqr(&x126, &x112);
for (i = 0; i < 13; i++) {
secp256k1_scalar_sqr(&x126, &x126);
}
secp256k1_scalar_mul(&x127, &x127, &x7);
secp256k1_scalar_mul(&x126, &x126, &x14);

/* Then accumulate the final result (t starts at x127). */
t = &x127;
for (i = 0; i < 2; i++) { /* 0 */
/* Then accumulate the final result (t starts at x126). */
t = &x126;
for (i = 0; i < 3; i++) {
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 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x3); /* 111 */
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 < 4; i++) { /* 0 */
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);
}
Expand All @@ -160,34 +154,26 @@ static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x2); /* 11 */
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 < 4; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 5; i++) { /* 0 */
secp256k1_scalar_mul(t, t, &u5); /* 101 */
for (i = 0; i < 4; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x4); /* 1111 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_mul(t, t, &x3); /* 111 */
for (i = 0; i < 3; i++) {
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
secp256k1_scalar_mul(t, t, &u5); /* 101 */
for (i = 0; i < 3; i++) { /* 00 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 4; i++) { /* 000 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 2; i++) { /* 0 */
for (i = 0; i < 6; i++) { /* 000 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
secp256k1_scalar_mul(t, t, &u5); /* 101 */
for (i = 0; i < 10; i++) { /* 0000000 */
secp256k1_scalar_sqr(t, t);
}
Expand All @@ -212,14 +198,14 @@ static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar
secp256k1_scalar_sqr(t, t);
}
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_mul(t, t, &x4); /* 1111 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_mul(t, t, &x3); /* 111 */
for (i = 0; i < 3; i++) {
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 */
secp256k1_scalar_sqr(t, t);
}
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