## File: bn_mp_karatsuba_mul.c

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libtommath 1.1.0-3
 `123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171` ``````#include "tommath_private.h" #ifdef BN_MP_KARATSUBA_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 */ /* c = |a| * |b| using Karatsuba Multiplication using * three half size multiplications * * Let B represent the radix [e.g. 2**DIGIT_BIT] and * let n represent half of the number of digits in * the min(a,b) * * a = a1 * B**n + a0 * b = b1 * B**n + b0 * * Then, a * b => a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0 * * Note that a1b1 and a0b0 are used twice and only need to be * computed once. So in total three half size (half # of * digit) multiplications are performed, a0b0, a1b1 and * (a1+b1)(a0+b0) * * Note that a multiplication of half the digits requires * 1/4th the number of single precision multiplications so in * total after one call 25% of the single precision multiplications * are saved. Note also that the call to mp_mul can end up back * in this function if the a0, a1, b0, or b1 are above the threshold. * This is known as divide-and-conquer and leads to the famous * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than * the standard O(N**2) that the baseline/comba methods use. * Generally though the overhead of this method doesn't pay off * until a certain size (N ~ 80) is reached. */ int mp_karatsuba_mul(const mp_int *a, const mp_int *b, mp_int *c) { mp_int x0, x1, y0, y1, t1, x0y0, x1y1; int B, err; /* default the return code to an error */ err = MP_MEM; /* min # of digits */ B = MIN(a->used, b->used); /* now divide in two */ B = B >> 1; /* init copy all the temps */ if (mp_init_size(&x0, B) != MP_OKAY) goto LBL_ERR; if (mp_init_size(&x1, a->used - B) != MP_OKAY) goto X0; if (mp_init_size(&y0, B) != MP_OKAY) goto X1; if (mp_init_size(&y1, b->used - B) != MP_OKAY) goto Y0; /* init temps */ if (mp_init_size(&t1, B * 2) != MP_OKAY) goto Y1; if (mp_init_size(&x0y0, B * 2) != MP_OKAY) goto T1; if (mp_init_size(&x1y1, B * 2) != MP_OKAY) goto X0Y0; /* now shift the digits */ x0.used = y0.used = B; x1.used = a->used - B; y1.used = b->used - B; { int x; mp_digit *tmpa, *tmpb, *tmpx, *tmpy; /* we copy the digits directly instead of using higher level functions * since we also need to shift the digits */ tmpa = a->dp; tmpb = b->dp; tmpx = x0.dp; tmpy = y0.dp; for (x = 0; x < B; x++) { *tmpx++ = *tmpa++; *tmpy++ = *tmpb++; } tmpx = x1.dp; for (x = B; x < a->used; x++) { *tmpx++ = *tmpa++; } tmpy = y1.dp; for (x = B; x < b->used; x++) { *tmpy++ = *tmpb++; } } /* only need to clamp the lower words since by definition the * upper words x1/y1 must have a known number of digits */ mp_clamp(&x0); mp_clamp(&y0); /* now calc the products x0y0 and x1y1 */ /* after this x0 is no longer required, free temp [x0==t2]! */ if (mp_mul(&x0, &y0, &x0y0) != MP_OKAY) goto X1Y1; /* x0y0 = x0*y0 */ if (mp_mul(&x1, &y1, &x1y1) != MP_OKAY) goto X1Y1; /* x1y1 = x1*y1 */ /* now calc x1+x0 and y1+y0 */ if (s_mp_add(&x1, &x0, &t1) != MP_OKAY) goto X1Y1; /* t1 = x1 - x0 */ if (s_mp_add(&y1, &y0, &x0) != MP_OKAY) goto X1Y1; /* t2 = y1 - y0 */ if (mp_mul(&t1, &x0, &t1) != MP_OKAY) goto X1Y1; /* t1 = (x1 + x0) * (y1 + y0) */ /* add x0y0 */ if (mp_add(&x0y0, &x1y1, &x0) != MP_OKAY) goto X1Y1; /* t2 = x0y0 + x1y1 */ if (s_mp_sub(&t1, &x0, &t1) != MP_OKAY) goto X1Y1; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */ /* shift by B */ if (mp_lshd(&t1, B) != MP_OKAY) goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))< master, tag: v1.1.0 */ /* git commit: 08549ad6bc8b0cede0b357a9c341c5c6473a9c55 */ /* commit time: 2019-01-28 20:32:32 +0100 */ ``````