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Merge bitcoin#452: Minor optimizations to _scalar_inverse to save 4M
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465159c Further shorten the addition chain for scalar inversion. (Brian Smith)
cf12fa1 Minor optimizations to _scalar_inverse to save 4M (Peter Dettman)

Tree-SHA512: b03ae53bd48435f8ef8a89ba3b45f9a35f3f3c6cfba7deb6820ab2146205656d198e4317a4cb98a986f434df244ae735313d303d0ce5a5c40519d37621238957
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@sipa
sipa committed Apr 26, 2017
2 parents 4cc8f52 + 465159c commit cbc20b8
Showing 1 changed file with 67 additions and 104 deletions.
171 changes: 67 additions & 104 deletions src/scalar_impl.h
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Original file line number Diff line number Diff line change
Expand Up @@ -66,88 +66,79 @@ 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, u9, u11, u13;

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_mul(&u9, &x3, &u2);
secp256k1_scalar_mul(&u11, &u9, &u2);
secp256k1_scalar_mul(&u13, &u11, &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, &u13);
secp256k1_scalar_sqr(&x6, &x6);
secp256k1_scalar_mul(&x6, &x6, &x2);

secp256k1_scalar_sqr(&x7, &x6);
secp256k1_scalar_mul(&x7, &x7, x);
secp256k1_scalar_mul(&x6, &x6, &u11);

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 */
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 < 4; i++) { /* 0 */
secp256k1_scalar_mul(t, t, &u5); /* 101 */
for (i = 0; i < 5; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x3); /* 111 */
for (i = 0; i < 3; i++) { /* 0 */
secp256k1_scalar_mul(t, t, &u11); /* 1011 */
for (i = 0; i < 4; i++) {
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x2); /* 11 */
secp256k1_scalar_mul(t, t, &u11); /* 1011 */
for (i = 0; i < 4; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
Expand All @@ -156,38 +147,26 @@ static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x3); /* 111 */
for (i = 0; i < 4; i++) { /* 00 */
for (i = 0; i < 6; i++) { /* 00 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x2); /* 11 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_mul(t, t, &u13); /* 1101 */
for (i = 0; i < 4; i++) { /* 0 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 2; i++) { /* 0 */
secp256k1_scalar_mul(t, t, &u5); /* 101 */
for (i = 0; i < 3; i++) {
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 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x4); /* 1111 */
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 */
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 */
secp256k1_scalar_mul(t, t, &u9); /* 1001 */
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 @@ -200,50 +179,34 @@ static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x8); /* 11111111 */
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 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 3; i++) { /* 00 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 5; 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, &u9); /* 1001 */
for (i = 0; i < 6; i++) { /* 00 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 5; i++) { /* 000 */
secp256k1_scalar_mul(t, t, &u11); /* 1011 */
for (i = 0; i < 4; i++) {
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x2); /* 11 */
for (i = 0; i < 4; i++) { /* 00 */
secp256k1_scalar_mul(t, t, &u13); /* 1101 */
for (i = 0; i < 5; i++) {
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x2); /* 11 */
for (i = 0; i < 2; i++) { /* 0 */
for (i = 0; i < 6; i++) { /* 00 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
for (i = 0; i < 8; i++) { /* 000000 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x2); /* 11 */
for (i = 0; i < 3; i++) { /* 0 */
secp256k1_scalar_mul(t, t, &u13); /* 1101 */
for (i = 0; i < 10; i++) { /* 000000 */
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, &x2); /* 11 */
for (i = 0; i < 3; i++) { /* 00 */
secp256k1_scalar_mul(t, t, &u13); /* 1101 */
for (i = 0; i < 4; i++) {
secp256k1_scalar_sqr(t, t);
}
secp256k1_scalar_mul(t, t, x); /* 1 */
secp256k1_scalar_mul(t, t, &u9); /* 1001 */
for (i = 0; i < 6; i++) { /* 00000 */
secp256k1_scalar_sqr(t, t);
}
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