168 lines
4.7 KiB
C
168 lines
4.7 KiB
C
#include <tommath.h>
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#ifdef BN_MP_KARATSUBA_MUL_C
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/* LibTomMath, multiple-precision integer library -- Tom St Denis
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*
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* LibTomMath is a library that provides multiple-precision
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* integer arithmetic as well as number theoretic functionality.
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*
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* The library was designed directly after the MPI library by
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* Michael Fromberger but has been written from scratch with
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* additional optimizations in place.
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*
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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tstdenis82@gmail.com, http://libtom.org
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*/
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/* c = |a| * |b| using Karatsuba Multiplication using
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* three half size multiplications
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*
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* Let B represent the radix [e.g. 2**DIGIT_BIT] and
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* let n represent half of the number of digits in
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* the min(a,b)
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*
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* a = a1 * B**n + a0
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* b = b1 * B**n + b0
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*
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* Then, a * b =>
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a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0
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*
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* Note that a1b1 and a0b0 are used twice and only need to be
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* computed once. So in total three half size (half # of
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* digit) multiplications are performed, a0b0, a1b1 and
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* (a1+b1)(a0+b0)
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*
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* Note that a multiplication of half the digits requires
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* 1/4th the number of single precision multiplications so in
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* total after one call 25% of the single precision multiplications
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* are saved. Note also that the call to mp_mul can end up back
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* in this function if the a0, a1, b0, or b1 are above the threshold.
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* This is known as divide-and-conquer and leads to the famous
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* O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than
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* the standard O(N**2) that the baseline/comba methods use.
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* Generally though the overhead of this method doesn't pay off
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* until a certain size (N ~ 80) is reached.
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*/
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int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c)
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{
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mp_int x0, x1, y0, y1, t1, x0y0, x1y1;
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int B, err;
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/* default the return code to an error */
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err = MP_MEM;
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/* min # of digits */
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B = MIN (a->used, b->used);
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/* now divide in two */
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B = B >> 1;
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/* init copy all the temps */
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if (mp_init_size (&x0, B) != MP_OKAY)
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goto ERR;
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if (mp_init_size (&x1, a->used - B) != MP_OKAY)
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goto X0;
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if (mp_init_size (&y0, B) != MP_OKAY)
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goto X1;
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if (mp_init_size (&y1, b->used - B) != MP_OKAY)
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goto Y0;
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/* init temps */
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if (mp_init_size (&t1, B * 2) != MP_OKAY)
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goto Y1;
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if (mp_init_size (&x0y0, B * 2) != MP_OKAY)
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goto T1;
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if (mp_init_size (&x1y1, B * 2) != MP_OKAY)
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goto X0Y0;
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/* now shift the digits */
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x0.used = y0.used = B;
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x1.used = a->used - B;
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y1.used = b->used - B;
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{
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register int x;
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register mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
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/* we copy the digits directly instead of using higher level functions
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* since we also need to shift the digits
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*/
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tmpa = a->dp;
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tmpb = b->dp;
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tmpx = x0.dp;
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tmpy = y0.dp;
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for (x = 0; x < B; x++) {
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*tmpx++ = *tmpa++;
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*tmpy++ = *tmpb++;
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}
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tmpx = x1.dp;
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for (x = B; x < a->used; x++) {
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*tmpx++ = *tmpa++;
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}
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tmpy = y1.dp;
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for (x = B; x < b->used; x++) {
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*tmpy++ = *tmpb++;
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}
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}
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/* only need to clamp the lower words since by definition the
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* upper words x1/y1 must have a known number of digits
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*/
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mp_clamp (&x0);
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mp_clamp (&y0);
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/* now calc the products x0y0 and x1y1 */
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/* after this x0 is no longer required, free temp [x0==t2]! */
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if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY)
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goto X1Y1; /* x0y0 = x0*y0 */
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if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY)
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goto X1Y1; /* x1y1 = x1*y1 */
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/* now calc x1+x0 and y1+y0 */
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if (s_mp_add (&x1, &x0, &t1) != MP_OKAY)
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goto X1Y1; /* t1 = x1 - x0 */
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if (s_mp_add (&y1, &y0, &x0) != MP_OKAY)
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goto X1Y1; /* t2 = y1 - y0 */
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if (mp_mul (&t1, &x0, &t1) != MP_OKAY)
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goto X1Y1; /* t1 = (x1 + x0) * (y1 + y0) */
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/* add x0y0 */
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if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY)
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goto X1Y1; /* t2 = x0y0 + x1y1 */
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if (s_mp_sub (&t1, &x0, &t1) != MP_OKAY)
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goto X1Y1; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */
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/* shift by B */
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if (mp_lshd (&t1, B) != MP_OKAY)
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goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
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if (mp_lshd (&x1y1, B * 2) != MP_OKAY)
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goto X1Y1; /* x1y1 = x1y1 << 2*B */
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if (mp_add (&x0y0, &t1, &t1) != MP_OKAY)
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goto X1Y1; /* t1 = x0y0 + t1 */
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if (mp_add (&t1, &x1y1, c) != MP_OKAY)
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goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */
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/* Algorithm succeeded set the return code to MP_OKAY */
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err = MP_OKAY;
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X1Y1:mp_clear (&x1y1);
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X0Y0:mp_clear (&x0y0);
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T1:mp_clear (&t1);
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Y1:mp_clear (&y1);
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Y0:mp_clear (&y0);
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X1:mp_clear (&x1);
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X0:mp_clear (&x0);
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ERR:
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return err;
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}
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#endif
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/* $Source$ */
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/* $Revision$ */
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/* $Date$ */
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