113 lines
3.1 KiB
C
113 lines
3.1 KiB
C
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/* LibTomMath, multiple-precision integer library -- Tom St Denis
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*
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* LibTomMath is library that provides for multiple-precision
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* integer arithmetic as well as number theoretic functionality.
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*
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* The library is 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, tomstdenis@iahu.ca, http://libtommath.iahu.ca
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*/
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#include <tommath.h>
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/* fast squaring
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*
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* This is the comba method where the columns of the product are computed first
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* then the carries are computed. This has the effect of making a very simple
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* inner loop that is executed the most
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*
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* W2 represents the outer products and W the inner.
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*
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* A further optimizations is made because the inner products are of the form
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* "A * B * 2". The *2 part does not need to be computed until the end which is
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* good because 64-bit shifts are slow!
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*
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*
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*/
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int
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fast_s_mp_sqr (mp_int * a, mp_int * b)
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{
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int olduse, newused, res, ix, pa;
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mp_word W2[512], W[512];
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pa = a->used;
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newused = pa + pa + 1;
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if (b->alloc < newused) {
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if ((res = mp_grow (b, newused)) != MP_OKAY) {
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return res;
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}
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}
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/* zero temp buffer (columns)
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* Note that there are two buffers. Since squaring requires
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* a outter and inner product and the inner product requires
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* computing a product and doubling it (a relatively expensive
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* op to perform n^2 times if you don't have to) the inner and
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* outer products are computed in different buffers. This way
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* the inner product can be doubled using n doublings instead of
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* n^2
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*/
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memset (W, 0, newused * sizeof (mp_word));
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memset (W2, 0, newused * sizeof (mp_word));
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/* This computes the inner product. To simplify the inner N^2 loop
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* the multiplication by two is done afterwards in the N loop.
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*/
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for (ix = 0; ix < pa; ix++) {
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/* compute the outer product */
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W2[ix + ix] += ((mp_word) a->dp[ix]) * ((mp_word) a->dp[ix]);
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{
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register mp_digit tmpx, *tmpy;
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register mp_word *_W;
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register int iy;
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/* copy of left side */
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tmpx = a->dp[ix];
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/* alias for right side */
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tmpy = a->dp + (ix + 1);
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/* the column to store the result in */
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_W = W + (ix + ix + 1);
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/* inner products */
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for (iy = ix + 1; iy < pa; iy++) {
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*_W++ += ((mp_word) tmpx) * ((mp_word) * tmpy++);
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}
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}
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}
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/* setup dest */
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olduse = b->used;
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b->used = newused;
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/* double first value, since the inner products are half of what they should be */
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W[0] += W[0] + W2[0];
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/* now compute digits */
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for (ix = 1; ix < newused; ix++) {
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/* double/add next digit */
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W[ix] += W[ix] + W2[ix];
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W[ix] = W[ix] + (W[ix - 1] >> ((mp_word) DIGIT_BIT));
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b->dp[ix - 1] = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
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}
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b->dp[(newused) - 1] = (mp_digit) (W[(newused) - 1] & ((mp_word) MP_MASK));
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/* clear high */
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for (; ix < olduse; ix++) {
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b->dp[ix] = 0;
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}
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/* fix the sign (since we no longer make a fresh temp) */
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b->sign = MP_ZPOS;
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mp_clamp (b);
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return MP_OKAY;
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}
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