master-server/deps/libtommath/s_mp_sqr_toom.c
2023-12-11 20:30:44 -05:00

134 lines
4.3 KiB
C

#include "tommath_private.h"
#ifdef S_MP_SQR_TOOM_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_sqr_toom(const mp_int *a, mp_int *b)
{
mp_int S0, a0, a1, a2;
int B;
mp_err err;
/* 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 LBL_ERRa0;
if ((err = mp_init_size(&a1, B)) != MP_OKAY) goto LBL_ERRa1;
if ((err = mp_init_size(&a2, a->used - (2 * B))) != MP_OKAY) goto LBL_ERRa2;
a0.used = a1.used = B;
a2.used = a->used - 2 * B;
s_mp_copy_digs(a0.dp, a->dp, a0.used);
s_mp_copy_digs(a1.dp, a->dp + B, a1.used);
s_mp_copy_digs(a2.dp, a->dp + 2 * B, a2.used);
mp_clamp(&a0);
mp_clamp(&a1);
mp_clamp(&a2);
/** S0 = a0^2; */
if ((err = mp_sqr(&a0, &S0)) != MP_OKAY) goto LBL_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 LBL_ERR;
/** \\S2 = S1 - a1; */
/** b = a0 - a1; */
if ((err = mp_sub(&a0, &a1, b)) != MP_OKAY) goto LBL_ERR;
/** \\S1 = S1 + a1; */
/** a0 = a0 + a1; */
if ((err = mp_add(&a0, &a1, &a0)) != MP_OKAY) goto LBL_ERR;
/** \\S1 = S1^2; */
/** a0 = a0^2; */
if ((err = mp_sqr(&a0, &a0)) != MP_OKAY) goto LBL_ERR;
/** \\S2 = S2^2; */
/** b = b^2; */
if ((err = mp_sqr(b, b)) != MP_OKAY) goto LBL_ERR;
/** \\ S3 = 2 * a1 * a2 */
/** \\S3 = a1 * a2; */
/** a1 = a1 * a2; */
if ((err = mp_mul(&a1, &a2, &a1)) != MP_OKAY) goto LBL_ERR;
/** \\S3 = S3 << 1; */
/** a1 = a1 << 1; */
if ((err = mp_mul_2(&a1, &a1)) != MP_OKAY) goto LBL_ERR;
/** \\S4 = a2^2; */
/** a2 = a2^2; */
if ((err = mp_sqr(&a2, &a2)) != MP_OKAY) goto LBL_ERR;
/** \\ tmp = (S1 + S2)/2 */
/** \\tmp = S1 + S2; */
/** b = a0 + b; */
if ((err = mp_add(&a0, b, b)) != MP_OKAY) goto LBL_ERR;
/** \\tmp = tmp >> 1; */
/** b = b >> 1; */
if ((err = mp_div_2(b, b)) != MP_OKAY) goto LBL_ERR;
/** \\ S1 = S1 - tmp - S3 */
/** \\S1 = S1 - tmp; */
/** a0 = a0 - b; */
if ((err = mp_sub(&a0, b, &a0)) != MP_OKAY) goto LBL_ERR;
/** \\S1 = S1 - S3; */
/** a0 = a0 - a1; */
if ((err = mp_sub(&a0, &a1, &a0)) != MP_OKAY) goto LBL_ERR;
/** \\S2 = tmp - S4 -S0 */
/** \\S2 = tmp - S4; */
/** b = b - a2; */
if ((err = mp_sub(b, &a2, b)) != MP_OKAY) goto LBL_ERR;
/** \\S2 = S2 - S0; */
/** b = b - S0; */
if ((err = mp_sub(b, &S0, b)) != MP_OKAY) goto LBL_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 LBL_ERR;
if ((err = mp_lshd(&a1, 3 * B)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_lshd(b, 2 * B)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_lshd(&a0, 1 * B)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(&a2, &a1, &a2)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(&a2, b, b)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(b, &a0, b)) != MP_OKAY) goto LBL_ERR;
if ((err = mp_add(b, &S0, b)) != MP_OKAY) goto LBL_ERR;
/** a^2 - P */
LBL_ERR:
mp_clear(&a2);
LBL_ERRa2:
mp_clear(&a1);
LBL_ERRa1:
mp_clear(&a0);
LBL_ERRa0:
mp_clear(&S0);
return err;
}
#endif