#include "tommath_private.h"
#ifdef BN_S_MP_TOOM_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
/* SPDX-License-Identifier: Unlicense */
/* squaring using Toom-Cook 3-way algorithm */
/*
This file contains code from J. Arndt's book "Matters Computational"
and the accompanying FXT-library with permission of the author.
*/
/* squaring using Toom-Cook 3-way algorithm */
/*
Setup and interpolation from algorithm SQR_3 in
Chung, Jaewook, and M. Anwar Hasan. "Asymmetric squaring formulae."
18th IEEE Symposium on Computer Arithmetic (ARITH'07). IEEE, 2007.
*/
mp_err s_mp_toom_sqr(const mp_int *a, mp_int *b)
{
mp_int S0, a0, a1, a2;
mp_digit *tmpa, *tmpc;
mp_err err, B, count;
/* init temps */
if ((err = mp_init(&S0)) != MP_OKAY) {
return err;
}
/* B */
B = a->used / 3;
/** a = a2 * x^2 + a1 * x + a0; */
if ((err = mp_init_size(&a0, B)) != MP_OKAY) {
goto LTM_ERRa0;
}
a0.used = B;
if ((err = mp_init_size(&a1, B)) != MP_OKAY) {
goto LTM_ERRa1;
}
a1.used = B;
if ((err = mp_init_size(&a2, B + (a->used - (3 * B)))) != MP_OKAY) {
goto LTM_ERRa2;
}
tmpa = a->dp;
tmpc = a0.dp;
for (count = 0; count < B; count++) {
*tmpc++ = *tmpa++;
}
tmpc = a1.dp;
for (; count < (2 * B); count++) {
*tmpc++ = *tmpa++;
}
tmpc = a2.dp;
for (; count < a->used; count++) {
*tmpc++ = *tmpa++;
a2.used++;
}
mp_clamp(&a0);
mp_clamp(&a1);
/** S0 = a0^2; */
if ((err = mp_sqr(&a0, &S0)) != MP_OKAY) {
goto LTM_ERR;
}
/** \\S1 = (a2 + a1 + a0)^2 */
/** \\S2 = (a2 - a1 + a0)^2 */
/** \\S1 = a0 + a2; */
/** a0 = a0 + a2; */
if ((err = mp_add(&a0, &a2, &a0)) != MP_OKAY) {
goto LTM_ERR;
}
/** \\S2 = S1 - a1; */
/** b = a0 - a1; */
if ((err = mp_sub(&a0, &a1, b)) != MP_OKAY) {
goto LTM_ERR;
}
/** \\S1 = S1 + a1; */
/** a0 = a0 + a1; */
if ((err = mp_add(&a0, &a1, &a0)) != MP_OKAY) {
goto LTM_ERR;
}
/** \\S1 = S1^2; */
/** a0 = a0^2; */
if ((err = mp_sqr(&a0, &a0)) != MP_OKAY) {
goto LTM_ERR;
}
/** \\S2 = S2^2; */
/** b = b^2; */
if ((err = mp_sqr(b, b)) != MP_OKAY) {
goto LTM_ERR;
}
/** \\ S3 = 2 * a1 * a2 */
/** \\S3 = a1 * a2; */
/** a1 = a1 * a2; */
if ((err = mp_mul(&a1, &a2, &a1)) != MP_OKAY) {
goto LTM_ERR;
}
/** \\S3 = S3 << 1; */
/** a1 = a1 << 1; */
if ((err = mp_mul_2(&a1, &a1)) != MP_OKAY) {
goto LTM_ERR;
}
/** \\S4 = a2^2; */
/** a2 = a2^2; */
if ((err = mp_sqr(&a2, &a2)) != MP_OKAY) {
goto LTM_ERR;
}
/** \\ tmp = (S1 + S2)/2 */
/** \\tmp = S1 + S2; */
/** b = a0 + b; */
if ((err = mp_add(&a0, b, b)) != MP_OKAY) {
goto LTM_ERR;
}
/** \\tmp = tmp >> 1; */
/** b = b >> 1; */
if ((err = mp_div_2(b, b)) != MP_OKAY) {
goto LTM_ERR;
}
/** \\ S1 = S1 - tmp - S3 */
/** \\S1 = S1 - tmp; */
/** a0 = a0 - b; */
if ((err = mp_sub(&a0, b, &a0)) != MP_OKAY) {
goto LTM_ERR;
}
/** \\S1 = S1 - S3; */
/** a0 = a0 - a1; */
if ((err = mp_sub(&a0, &a1, &a0)) != MP_OKAY) {
goto LTM_ERR;
}
/** \\S2 = tmp - S4 -S0 */
/** \\S2 = tmp - S4; */
/** b = b - a2; */
if ((err = mp_sub(b, &a2, b)) != MP_OKAY) {
goto LTM_ERR;
}
/** \\S2 = S2 - S0; */
/** b = b - S0; */
if ((err = mp_sub(b, &S0, b)) != MP_OKAY) {
goto LTM_ERR;
}
/** \\P = S4*x^4 + S3*x^3 + S2*x^2 + S1*x + S0; */
/** P = a2*x^4 + a1*x^3 + b*x^2 + a0*x + S0; */
if ((err = mp_lshd(&a2, 4 * B)) != MP_OKAY) {
goto LTM_ERR;
}
if ((err = mp_lshd(&a1, 3 * B)) != MP_OKAY) {
goto LTM_ERR;
}
if ((err = mp_lshd(b, 2 * B)) != MP_OKAY) {
goto LTM_ERR;
}
if ((err = mp_lshd(&a0, 1 * B)) != MP_OKAY) {
goto LTM_ERR;
}
if ((err = mp_add(&a2, &a1, &a2)) != MP_OKAY) {
goto LTM_ERR;
}
if ((err = mp_add(&a2, b, b)) != MP_OKAY) {
goto LTM_ERR;
}
if ((err = mp_add(b, &a0, b)) != MP_OKAY) {
goto LTM_ERR;
}
if ((err = mp_add(b, &S0, b)) != MP_OKAY) {
goto LTM_ERR;
}
/** a^2 - P */
LTM_ERR:
mp_clear(&a2);
LTM_ERRa2:
mp_clear(&a1);
LTM_ERRa1:
mp_clear(&a0);
LTM_ERRa0:
mp_clear(&S0);
return err;
}
#endif
