### view libtommath/bn_s_mp_karatsuba_mul.c @ 1785:9026f976eee8

fuzz: work around fuzz_connect_remote() limitations
author Matt Johnston Sun, 06 Dec 2020 21:27:25 +0800 1051e4eea25a
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```#include "tommath_private.h"
#ifdef BN_S_MP_KARATSUBA_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis */

/* c = |a| * |b| using Karatsuba Multiplication using
* three half size multiplications
*
* Let B represent the radix [e.g. 2**MP_DIGIT_BIT] and
* let n represent half of the number of digits in
* the min(a,b)
*
* a = a1 * B**n + a0
* b = b1 * B**n + b0
*
* Then, a * b =>
a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0
*
* Note that a1b1 and a0b0 are used twice and only need to be
* computed once.  So in total three half size (half # of
* digit) multiplications are performed, a0b0, a1b1 and
* (a1+b1)(a0+b0)
*
* Note that a multiplication of half the digits requires
* 1/4th the number of single precision multiplications so in
* total after one call 25% of the single precision multiplications
* are saved.  Note also that the call to mp_mul can end up back
* in this function if the a0, a1, b0, or b1 are above the threshold.
* This is known as divide-and-conquer and leads to the famous
* O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than
* the standard O(N**2) that the baseline/comba methods use.
* Generally though the overhead of this method doesn't pay off
* until a certain size (N ~ 80) is reached.
*/
mp_err s_mp_karatsuba_mul(const mp_int *a, const mp_int *b, mp_int *c)
{
mp_int  x0, x1, y0, y1, t1, x0y0, x1y1;
int     B;
mp_err  err = MP_MEM; /* default the return code to an error */

/* min # of digits */
B = MP_MIN(a->used, b->used);

/* now divide in two */
B = B >> 1;

/* init copy all the temps */
if (mp_init_size(&x0, B) != MP_OKAY) {
goto LBL_ERR;
}
if (mp_init_size(&x1, a->used - B) != MP_OKAY) {
goto X0;
}
if (mp_init_size(&y0, B) != MP_OKAY) {
goto X1;
}
if (mp_init_size(&y1, b->used - B) != MP_OKAY) {
goto Y0;
}

/* init temps */
if (mp_init_size(&t1, B * 2) != MP_OKAY) {
goto Y1;
}
if (mp_init_size(&x0y0, B * 2) != MP_OKAY) {
goto T1;
}
if (mp_init_size(&x1y1, B * 2) != MP_OKAY) {
goto X0Y0;
}

/* now shift the digits */
x0.used = y0.used = B;
x1.used = a->used - B;
y1.used = b->used - B;

{
int x;
mp_digit *tmpa, *tmpb, *tmpx, *tmpy;

/* we copy the digits directly instead of using higher level functions
* since we also need to shift the digits
*/
tmpa = a->dp;
tmpb = b->dp;

tmpx = x0.dp;
tmpy = y0.dp;
for (x = 0; x < B; x++) {
*tmpx++ = *tmpa++;
*tmpy++ = *tmpb++;
}

tmpx = x1.dp;
for (x = B; x < a->used; x++) {
*tmpx++ = *tmpa++;
}

tmpy = y1.dp;
for (x = B; x < b->used; x++) {
*tmpy++ = *tmpb++;
}
}

/* only need to clamp the lower words since by definition the
* upper words x1/y1 must have a known number of digits
*/
mp_clamp(&x0);
mp_clamp(&y0);

/* now calc the products x0y0 and x1y1 */
/* after this x0 is no longer required, free temp [x0==t2]! */
if (mp_mul(&x0, &y0, &x0y0) != MP_OKAY) {
goto X1Y1;          /* x0y0 = x0*y0 */
}
if (mp_mul(&x1, &y1, &x1y1) != MP_OKAY) {
goto X1Y1;          /* x1y1 = x1*y1 */
}

/* now calc x1+x0 and y1+y0 */
if (s_mp_add(&x1, &x0, &t1) != MP_OKAY) {
goto X1Y1;          /* t1 = x1 - x0 */
}
if (s_mp_add(&y1, &y0, &x0) != MP_OKAY) {
goto X1Y1;          /* t2 = y1 - y0 */
}
if (mp_mul(&t1, &x0, &t1) != MP_OKAY) {
goto X1Y1;          /* t1 = (x1 + x0) * (y1 + y0) */
}

/* add x0y0 */
if (mp_add(&x0y0, &x1y1, &x0) != MP_OKAY) {
goto X1Y1;          /* t2 = x0y0 + x1y1 */
}
if (s_mp_sub(&t1, &x0, &t1) != MP_OKAY) {
goto X1Y1;          /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */
}

/* shift by B */
if (mp_lshd(&t1, B) != MP_OKAY) {
goto X1Y1;          /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
}
if (mp_lshd(&x1y1, B * 2) != MP_OKAY) {
goto X1Y1;          /* x1y1 = x1y1 << 2*B */
}

if (mp_add(&x0y0, &t1, &t1) != MP_OKAY) {
goto X1Y1;          /* t1 = x0y0 + t1 */
}
if (mp_add(&t1, &x1y1, c) != MP_OKAY) {
goto X1Y1;          /* t1 = x0y0 + t1 + x1y1 */
}

/* Algorithm succeeded set the return code to MP_OKAY */
err = MP_OKAY;

X1Y1:
mp_clear(&x1y1);
X0Y0:
mp_clear(&x0y0);
T1:
mp_clear(&t1);
Y1:
mp_clear(&y1);
Y0:
mp_clear(&y0);
X1:
mp_clear(&x1);
X0:
mp_clear(&x0);
LBL_ERR:
return err;
}
#endif
```