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Rejig the bottom-level loops in internal_mul_* to use pointers instead

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of array indices. You'd hope that compilers could automatically turn
the one representation into the other if it was faster to do so, but
apparently not: even on gcc -O3, this source transformation gains over
15% performance.

[originally from svn r9105]
This commit is contained in:
Simon Tatham 2011-02-22 19:09:27 +00:00
parent 9d4005e5c1
commit 7957ca1153
1 changed files with 45 additions and 38 deletions
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83
sshbn.c
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@ -221,10 +221,8 @@ static int mul_compute_scratch(int len)
static void internal_mul(const BignumInt *a, const BignumInt *b, static void internal_mul(const BignumInt *a, const BignumInt *b,
BignumInt *c, int len, BignumInt *scratch) BignumInt *c, int len, BignumInt *scratch)
{ {
int i, j;
BignumDblInt t;
if (len > KARATSUBA_THRESHOLD) { if (len > KARATSUBA_THRESHOLD) {
int i;
/* /*
* Karatsuba divide-and-conquer algorithm. Cut each input in * Karatsuba divide-and-conquer algorithm. Cut each input in
@ -311,9 +309,9 @@ static void internal_mul(const BignumInt *a, const BignumInt *b,
* copied over. */ * copied over. */
scratch[0] = scratch[1] = scratch[midlen] = scratch[midlen+1] = 0; scratch[0] = scratch[1] = scratch[midlen] = scratch[midlen+1] = 0;
for (j = 0; j < toplen; j++) { for (i = 0; i < toplen; i++) {
scratch[midlen - toplen + j] = a[j]; /* a_1 */ scratch[midlen - toplen + i] = a[i]; /* a_1 */
scratch[2*midlen - toplen + j] = b[j]; /* b_1 */ scratch[2*midlen - toplen + i] = b[i]; /* b_1 */
} }
/* compute a_1 + a_0 */ /* compute a_1 + a_0 */
@ -355,8 +353,8 @@ static void internal_mul(const BignumInt *a, const BignumInt *b,
* product to obtain the middle one. * product to obtain the middle one.
*/ */
scratch[0] = scratch[1] = scratch[2] = scratch[3] = 0; scratch[0] = scratch[1] = scratch[2] = scratch[3] = 0;
for (j = 0; j < 2*toplen; j++) for (i = 0; i < 2*toplen; i++)
scratch[2*midlen - 2*toplen + j] = c[j]; scratch[2*midlen - 2*toplen + i] = c[i];
scratch[1] = internal_add(scratch+2, c + 2*toplen, scratch[1] = internal_add(scratch+2, c + 2*toplen,
scratch+2, 2*botlen); scratch+2, 2*botlen);
#ifdef KARA_DEBUG #ifdef KARA_DEBUG
@ -386,13 +384,13 @@ static void internal_mul(const BignumInt *a, const BignumInt *b,
carry = internal_add(c + 2*len - botlen - 2*midlen, carry = internal_add(c + 2*len - botlen - 2*midlen,
scratch + 2*midlen, scratch + 2*midlen,
c + 2*len - botlen - 2*midlen, 2*midlen); c + 2*len - botlen - 2*midlen, 2*midlen);
j = 2*len - botlen - 2*midlen - 1; i = 2*len - botlen - 2*midlen - 1;
while (carry) { while (carry) {
assert(j >= 0); assert(i >= 0);
carry += c[j]; carry += c[i];
c[j] = (BignumInt)carry; c[i] = (BignumInt)carry;
carry >>= BIGNUM_INT_BITS; carry >>= BIGNUM_INT_BITS;
j--; i--;
} }
#ifdef KARA_DEBUG #ifdef KARA_DEBUG
printf("ab = 0x"); printf("ab = 0x");
@ -403,23 +401,27 @@ static void internal_mul(const BignumInt *a, const BignumInt *b,
#endif #endif
} else { } else {
int i;
BignumInt carry;
BignumDblInt t;
const BignumInt *ap, *bp;
BignumInt *cp, *cps;
/* /*
* Multiply in the ordinary O(N^2) way. * Multiply in the ordinary O(N^2) way.
*/ */
for (j = 0; j < 2 * len; j++) for (i = 0; i < 2 * len; i++)
c[j] = 0; c[i] = 0;
for (i = len - 1; i >= 0; i--) { for (cps = c + 2*len, ap = a + len; ap-- > a; cps--) {
t = 0; carry = 0;
for (j = len - 1; j >= 0; j--) { for (cp = cps, bp = b + len; cp--, bp-- > b ;) {
t += MUL_WORD(a[i], (BignumDblInt) b[j]); t = (MUL_WORD(*ap, *bp) + carry) + *cp;
t += (BignumDblInt) c[i + j + 1]; *cp = (BignumInt) t;
c[i + j + 1] = (BignumInt) t; carry = t >> BIGNUM_INT_BITS;
t = t >> BIGNUM_INT_BITS;
} }
c[i] = (BignumInt) t; *cp = carry;
} }
} }
} }
@ -432,10 +434,8 @@ static void internal_mul(const BignumInt *a, const BignumInt *b,
static void internal_mul_low(const BignumInt *a, const BignumInt *b, static void internal_mul_low(const BignumInt *a, const BignumInt *b,
BignumInt *c, int len, BignumInt *scratch) BignumInt *c, int len, BignumInt *scratch)
{ {
int i, j;
BignumDblInt t;
if (len > KARATSUBA_THRESHOLD) { if (len > KARATSUBA_THRESHOLD) {
int i;
/* /*
* Karatsuba-aware version of internal_mul_low. As before, we * Karatsuba-aware version of internal_mul_low. As before, we
@ -492,8 +492,8 @@ static void internal_mul_low(const BignumInt *a, const BignumInt *b,
scratch + 2*len); scratch + 2*len);
/* Copy the bottom half of the big coefficient into place */ /* Copy the bottom half of the big coefficient into place */
for (j = 0; j < botlen; j++) for (i = 0; i < botlen; i++)
c[toplen + j] = scratch[2*toplen + botlen + j]; c[toplen + i] = scratch[2*toplen + botlen + i];
/* Add the two small coefficients, throwing away the returned carry */ /* Add the two small coefficients, throwing away the returned carry */
internal_add(scratch, scratch + toplen, scratch, toplen); internal_add(scratch, scratch + toplen, scratch, toplen);
@ -503,20 +503,27 @@ static void internal_mul_low(const BignumInt *a, const BignumInt *b,
c, toplen); c, toplen);
} else { } else {
int i;
BignumInt carry;
BignumDblInt t;
const BignumInt *ap, *bp;
BignumInt *cp, *cps;
for (j = 0; j < len; j++) /*
c[j] = 0; * Multiply in the ordinary O(N^2) way.
*/
for (i = len - 1; i >= 0; i--) { for (i = 0; i < len; i++)
t = 0; c[i] = 0;
for (j = len - 1; j >= len - i - 1; j--) {
t += MUL_WORD(a[i], (BignumDblInt) b[j]); for (cps = c + len, ap = a + len; ap-- > a; cps--) {
t += (BignumDblInt) c[i + j + 1 - len]; carry = 0;
c[i + j + 1 - len] = (BignumInt) t; for (cp = cps, bp = b + len; bp--, cp-- > c ;) {
t = t >> BIGNUM_INT_BITS; t = (MUL_WORD(*ap, *bp) + carry) + *cp;
*cp = (BignumInt) t;
carry = t >> BIGNUM_INT_BITS;
} }
} }
} }
} }