203 lines
6.6 KiB
C
203 lines
6.6 KiB
C
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#include "tommath_private.h"
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#ifdef S_MP_MUL_TOOM_C
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/* LibTomMath, multiple-precision integer library -- Tom St Denis */
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/* SPDX-License-Identifier: Unlicense */
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/* multiplication using the Toom-Cook 3-way algorithm
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*
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* Much more complicated than Karatsuba but has a lower
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* asymptotic running time of O(N**1.464). This algorithm is
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* only particularly useful on VERY large inputs
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* (we're talking 1000s of digits here...).
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*/
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/*
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This file contains code from J. Arndt's book "Matters Computational"
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and the accompanying FXT-library with permission of the author.
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*/
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/*
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Setup from
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Chung, Jaewook, and M. Anwar Hasan. "Asymmetric squaring formulae."
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18th IEEE Symposium on Computer Arithmetic (ARITH'07). IEEE, 2007.
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The interpolation from above needed one temporary variable more
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than the interpolation here:
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Bodrato, Marco, and Alberto Zanoni. "What about Toom-Cook matrices optimality."
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Centro Vito Volterra Universita di Roma Tor Vergata (2006)
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*/
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mp_err s_mp_mul_toom(const mp_int *a, const mp_int *b, mp_int *c)
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{
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mp_int S1, S2, T1, a0, a1, a2, b0, b1, b2;
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int B;
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mp_err err;
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/* init temps */
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if ((err = mp_init_multi(&S1, &S2, &T1, NULL)) != MP_OKAY) {
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return err;
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}
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/* B */
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B = MP_MIN(a->used, b->used) / 3;
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/** a = a2 * x^2 + a1 * x + a0; */
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if ((err = mp_init_size(&a0, B)) != MP_OKAY) goto LBL_ERRa0;
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if ((err = mp_init_size(&a1, B)) != MP_OKAY) goto LBL_ERRa1;
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if ((err = mp_init_size(&a2, a->used - 2 * B)) != MP_OKAY) goto LBL_ERRa2;
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a0.used = a1.used = B;
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a2.used = a->used - 2 * B;
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s_mp_copy_digs(a0.dp, a->dp, a0.used);
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s_mp_copy_digs(a1.dp, a->dp + B, a1.used);
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s_mp_copy_digs(a2.dp, a->dp + 2 * B, a2.used);
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mp_clamp(&a0);
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mp_clamp(&a1);
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mp_clamp(&a2);
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/** b = b2 * x^2 + b1 * x + b0; */
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if ((err = mp_init_size(&b0, B)) != MP_OKAY) goto LBL_ERRb0;
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if ((err = mp_init_size(&b1, B)) != MP_OKAY) goto LBL_ERRb1;
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if ((err = mp_init_size(&b2, b->used - 2 * B)) != MP_OKAY) goto LBL_ERRb2;
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b0.used = b1.used = B;
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b2.used = b->used - 2 * B;
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s_mp_copy_digs(b0.dp, b->dp, b0.used);
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s_mp_copy_digs(b1.dp, b->dp + B, b1.used);
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s_mp_copy_digs(b2.dp, b->dp + 2 * B, b2.used);
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mp_clamp(&b0);
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mp_clamp(&b1);
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mp_clamp(&b2);
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/** \\ S1 = (a2+a1+a0) * (b2+b1+b0); */
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/** T1 = a2 + a1; */
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if ((err = mp_add(&a2, &a1, &T1)) != MP_OKAY) goto LBL_ERR;
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/** S2 = T1 + a0; */
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if ((err = mp_add(&T1, &a0, &S2)) != MP_OKAY) goto LBL_ERR;
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/** c = b2 + b1; */
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if ((err = mp_add(&b2, &b1, c)) != MP_OKAY) goto LBL_ERR;
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/** S1 = c + b0; */
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if ((err = mp_add(c, &b0, &S1)) != MP_OKAY) goto LBL_ERR;
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/** S1 = S1 * S2; */
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if ((err = mp_mul(&S1, &S2, &S1)) != MP_OKAY) goto LBL_ERR;
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/** \\S2 = (4*a2+2*a1+a0) * (4*b2+2*b1+b0); */
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/** T1 = T1 + a2; */
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if ((err = mp_add(&T1, &a2, &T1)) != MP_OKAY) goto LBL_ERR;
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/** T1 = T1 << 1; */
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if ((err = mp_mul_2(&T1, &T1)) != MP_OKAY) goto LBL_ERR;
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/** T1 = T1 + a0; */
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if ((err = mp_add(&T1, &a0, &T1)) != MP_OKAY) goto LBL_ERR;
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/** c = c + b2; */
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if ((err = mp_add(c, &b2, c)) != MP_OKAY) goto LBL_ERR;
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/** c = c << 1; */
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if ((err = mp_mul_2(c, c)) != MP_OKAY) goto LBL_ERR;
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/** c = c + b0; */
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if ((err = mp_add(c, &b0, c)) != MP_OKAY) goto LBL_ERR;
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/** S2 = T1 * c; */
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if ((err = mp_mul(&T1, c, &S2)) != MP_OKAY) goto LBL_ERR;
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/** \\S3 = (a2-a1+a0) * (b2-b1+b0); */
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/** a1 = a2 - a1; */
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if ((err = mp_sub(&a2, &a1, &a1)) != MP_OKAY) goto LBL_ERR;
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/** a1 = a1 + a0; */
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if ((err = mp_add(&a1, &a0, &a1)) != MP_OKAY) goto LBL_ERR;
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/** b1 = b2 - b1; */
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if ((err = mp_sub(&b2, &b1, &b1)) != MP_OKAY) goto LBL_ERR;
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/** b1 = b1 + b0; */
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if ((err = mp_add(&b1, &b0, &b1)) != MP_OKAY) goto LBL_ERR;
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/** a1 = a1 * b1; */
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if ((err = mp_mul(&a1, &b1, &a1)) != MP_OKAY) goto LBL_ERR;
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/** b1 = a2 * b2; */
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if ((err = mp_mul(&a2, &b2, &b1)) != MP_OKAY) goto LBL_ERR;
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/** \\S2 = (S2 - S3)/3; */
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/** S2 = S2 - a1; */
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if ((err = mp_sub(&S2, &a1, &S2)) != MP_OKAY) goto LBL_ERR;
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/** S2 = S2 / 3; \\ this is an exact division */
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if ((err = s_mp_div_3(&S2, &S2, NULL)) != MP_OKAY) goto LBL_ERR;
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/** a1 = S1 - a1; */
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if ((err = mp_sub(&S1, &a1, &a1)) != MP_OKAY) goto LBL_ERR;
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/** a1 = a1 >> 1; */
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if ((err = mp_div_2(&a1, &a1)) != MP_OKAY) goto LBL_ERR;
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/** a0 = a0 * b0; */
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if ((err = mp_mul(&a0, &b0, &a0)) != MP_OKAY) goto LBL_ERR;
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/** S1 = S1 - a0; */
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if ((err = mp_sub(&S1, &a0, &S1)) != MP_OKAY) goto LBL_ERR;
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/** S2 = S2 - S1; */
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if ((err = mp_sub(&S2, &S1, &S2)) != MP_OKAY) goto LBL_ERR;
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/** S2 = S2 >> 1; */
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if ((err = mp_div_2(&S2, &S2)) != MP_OKAY) goto LBL_ERR;
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/** S1 = S1 - a1; */
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if ((err = mp_sub(&S1, &a1, &S1)) != MP_OKAY) goto LBL_ERR;
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/** S1 = S1 - b1; */
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if ((err = mp_sub(&S1, &b1, &S1)) != MP_OKAY) goto LBL_ERR;
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/** T1 = b1 << 1; */
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if ((err = mp_mul_2(&b1, &T1)) != MP_OKAY) goto LBL_ERR;
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/** S2 = S2 - T1; */
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if ((err = mp_sub(&S2, &T1, &S2)) != MP_OKAY) goto LBL_ERR;
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/** a1 = a1 - S2; */
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if ((err = mp_sub(&a1, &S2, &a1)) != MP_OKAY) goto LBL_ERR;
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/** P = b1*x^4+ S2*x^3+ S1*x^2+ a1*x + a0; */
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if ((err = mp_lshd(&b1, 4 * B)) != MP_OKAY) goto LBL_ERR;
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if ((err = mp_lshd(&S2, 3 * B)) != MP_OKAY) goto LBL_ERR;
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if ((err = mp_add(&b1, &S2, &b1)) != MP_OKAY) goto LBL_ERR;
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if ((err = mp_lshd(&S1, 2 * B)) != MP_OKAY) goto LBL_ERR;
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if ((err = mp_add(&b1, &S1, &b1)) != MP_OKAY) goto LBL_ERR;
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if ((err = mp_lshd(&a1, 1 * B)) != MP_OKAY) goto LBL_ERR;
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if ((err = mp_add(&b1, &a1, &b1)) != MP_OKAY) goto LBL_ERR;
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if ((err = mp_add(&b1, &a0, c)) != MP_OKAY) goto LBL_ERR;
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/** a * b - P */
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LBL_ERR:
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mp_clear(&b2);
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LBL_ERRb2:
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mp_clear(&b1);
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LBL_ERRb1:
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mp_clear(&b0);
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LBL_ERRb0:
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mp_clear(&a2);
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LBL_ERRa2:
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mp_clear(&a1);
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LBL_ERRa1:
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mp_clear(&a0);
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LBL_ERRa0:
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mp_clear_multi(&S1, &S2, &T1, NULL);
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return err;
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}
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#endif
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