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/* See LICENSE file for copyright and license details. */
#include "internals.h"
void
zmul(z_t a, z_t b, z_t c)
{
/*
* Karatsuba algorithm
*
* Basically, this is how you were toughed to multiply large numbers
* by hand in school: 4010⋅3020 = (4000 + 10)(3000 + 20) =
= 40⋅30⋅10⁴ + (40⋅20 + 30⋅10)⋅10² + 10⋅20, but the middle is
* optimised to only one multiplication:
* 40⋅20 + 30⋅10 = (40 + 10)(30 + 20) − 40⋅30 − 10⋅20.
*/
size_t m, m2;
z_t z0, z1, z2, b_high, b_low, c_high, c_low;
int b_sign, c_sign;
b_sign = zsignum(b);
c_sign = zsignum(c);
if (!b_sign || !c_sign) {
SET_SIGNUM(a, 0);
return;
}
m = zbits(b);
m2 = b == c ? m : zbits(c);
if (m + m2 <= BITS_PER_CHAR) {
/* zsetu(a, b->chars[0] * c->chars[0]); { */
ENSURE_SIZE(a, 1);
a->used = 1;
a->chars[0] = b->chars[0] * c->chars[0];
/* } */
SET_SIGNUM(a, b_sign * c_sign);
return;
}
SET_SIGNUM(b, 1);
SET_SIGNUM(c, 1);
m = MAX(m, m2);
m2 = m >> 1;
zinit(z0);
zinit(z1);
zinit(z2);
zinit(b_high);
zinit(b_low);
zinit(c_high);
zinit(c_low);
zsplit(b_high, b_low, b, m2);
zsplit(c_high, c_low, c, m2);
#if 1
zmul(z0, b_low, c_low);
zmul(z2, b_high, c_high);
zadd(b_low, b_low, b_high);
zadd(c_low, c_low, c_high);
zmul(z1, b_low, c_low);
zsub(z1, z1, z0);
zsub(z1, z1, z2);
zlsh(z1, z1, m2);
m2 <<= 1;
zlsh(z2, z2, m2);
zadd(a, z2, z1);
zadd(a, a, z0);
#else
zmul(z0, b_low, c_low);
zmul(z2, b_high, c_high);
zsub(b_low, b_high, b_low);
zsub(c_low, c_high, c_low);
zmul(z1, b_low, c_low);
zlsh(z0, z0, m2 + 1);
zlsh(z1, z1, m2);
zlsh(a, z2, m2);
m2 <<= 1;
zlsh(z2, z2, m2);
zadd(z2, z2, a);
zsub(a, z2, z1);
zadd(a, a, z0);
#endif
zfree(z0);
zfree(z1);
zfree(z2);
zfree(b_high);
zfree(b_low);
zfree(c_high);
zfree(c_low);
SET_SIGNUM(b, b_sign);
SET_SIGNUM(c, c_sign);
SET_SIGNUM(a, b_sign * c_sign);
}
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