/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* Fast (comba) multiplier
*
* This is the fast column-array [comba] multiplier. It is designed to compute
* the columns of the product first then handle the carries afterwards. This
* has the effect of making the nested loops that compute the columns very
* simple and schedulable on super-scalar processors.
*
* This has been modified to produce a variable number of digits of output so
* if say only a half-product is required you don't have to compute the upper half
* (a feature required for fast Barrett reduction).
*
* Based on Algorithm 14.12 on pp.595 of HAC.
*
*/
int
fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
{
int olduse, res, pa, ix;
mp_word W[512];
/* grow the destination as required */
if (c->alloc < digs) {
if ((res = mp_grow (c, digs)) != MP_OKAY) {
return res;
}
}
/* clear temp buf (the columns) */
memset (W, 0, sizeof (mp_word) * digs);
/* calculate the columns */
pa = a->used;
for (ix = 0; ix < pa; ix++) {
/* this multiplier has been modified to allow you to control how many digits
* of output are produced. So at most we want to make upto "digs" digits
* of output.
*
* this adds products to distinct columns (at ix+iy) of W
* note that each step through the loop is not dependent on
* the previous which means the compiler can easily unroll
* the loop without scheduling problems
*/
{
register mp_digit tmpx, *tmpy;
register mp_word *_W;
register int iy, pb;
/* alias for the the word on the left e.g. A[ix] * A[iy] */
tmpx = a->dp[ix];
/* alias for the right side */
tmpy = b->dp;
/* alias for the columns, each step through the loop adds a new
term to each column
*/
_W = W + ix;
/* the number of digits is limited by their placement. E.g.
we avoid multiplying digits that will end up above the # of
digits of precision requested
*/
pb = MIN (b->used, digs - ix);
for (iy = 0; iy < pb; iy++) {
*_W++ += ((mp_word) tmpx) * ((mp_word) * tmpy++);
}
}
}
/* setup dest */
olduse = c->used;
c->used = digs;
{
register mp_digit *tmpc;
/* At this point W[] contains the sums of each column. To get the
* correct result we must take the extra bits from each column and
* carry them down
*
* Note that while this adds extra code to the multiplier it saves time
* since the carry propagation is removed from the above nested loop.
* This has the effect of reducing the work from N*(N+N*c)==N^2 + c*N^2 to
* N^2 + N*c where c is the cost of the shifting. On very small numbers
* this is slower but on most cryptographic size numbers it is faster.
*/
tmpc = c->dp;
for (ix = 1; ix < digs; ix++) {
W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT));
*tmpc++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
}
*tmpc++ = (mp_digit) (W[digs - 1] & ((mp_word) MP_MASK));
/* clear unused */
for (; ix < olduse; ix++) {
*tmpc++ = 0;
}
}
mp_clamp (c);
return MP_OKAY;
}
