Edit
kc3-lang/libtommath/bn_mp_toom_mul.c
Steffen Jaeckel
- bn_mp_toom_mul.c
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#include "tommath_private.h" #ifdef BN_MP_TOOM_MUL_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision * integer arithmetic as well as number theoretic functionality. * * The library was designed directly after the MPI library by * Michael Fromberger but has been written from scratch with * additional optimizations in place. * * SPDX-License-Identifier: Unlicense */ /* multiplication using the Toom-Cook 3-way algorithm * * Much more complicated than Karatsuba but has a lower * asymptotic running time of O(N**1.464). This algorithm is * only particularly useful on VERY large inputs * (we're talking 1000s of digits here...). */ int mp_toom_mul(const mp_int *a, const mp_int *b, mp_int *c) { mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2; int res, B; /* init temps */ if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &b0, &b1, &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) { return res; } /* B */ B = MIN(a->used, b->used) / 3; /* a = a2 * B**2 + a1 * B + a0 */ if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_copy(a, &a1)) != MP_OKAY) { goto LBL_ERR; } mp_rshd(&a1, B); if ((res = mp_mod_2d(&a1, DIGIT_BIT * B, &a1)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_copy(a, &a2)) != MP_OKAY) { goto LBL_ERR; } mp_rshd(&a2, B*2); /* b = b2 * B**2 + b1 * B + b0 */ if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_copy(b, &b1)) != MP_OKAY) { goto LBL_ERR; } mp_rshd(&b1, B); (void)mp_mod_2d(&b1, DIGIT_BIT * B, &b1); if ((res = mp_copy(b, &b2)) != MP_OKAY) { goto LBL_ERR; } mp_rshd(&b2, B*2); /* w0 = a0*b0 */ if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) { goto LBL_ERR; } /* w4 = a2 * b2 */ if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) { goto LBL_ERR; } /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */ if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) { goto LBL_ERR; } /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */ if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) { goto LBL_ERR; } /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */ if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) { goto LBL_ERR; } /* now solve the matrix 0 0 0 0 1 1 2 4 8 16 1 1 1 1 1 16 8 4 2 1 1 0 0 0 0 using 12 subtractions, 4 shifts, 2 small divisions and 1 small multiplication */ /* r1 - r4 */ if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) { goto LBL_ERR; } /* r3 - r0 */ if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) { goto LBL_ERR; } /* r1/2 */ if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) { goto LBL_ERR; } /* r3/2 */ if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) { goto LBL_ERR; } /* r2 - r0 - r4 */ if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) { goto LBL_ERR; } /* r1 - r2 */ if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) { goto LBL_ERR; } /* r3 - r2 */ if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) { goto LBL_ERR; } /* r1 - 8r0 */ if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) { goto LBL_ERR; } /* r3 - 8r4 */ if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) { goto LBL_ERR; } /* 3r2 - r1 - r3 */ if ((res = mp_mul_d(&w2, 3uL, &w2)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) { goto LBL_ERR; } /* r1 - r2 */ if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) { goto LBL_ERR; } /* r3 - r2 */ if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) { goto LBL_ERR; } /* r1/3 */ if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) { goto LBL_ERR; } /* r3/3 */ if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) { goto LBL_ERR; } /* at this point shift W[n] by B*n */ if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) { goto LBL_ERR; } if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) { goto LBL_ERR; } LBL_ERR: mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &b0, &b1, &b2, &tmp1, &tmp2, NULL); return res; } #endif /* ref: $Format:%D$ */ /* git commit: $Format:%H$ */ /* commit time: $Format:%ai$ */