+++ /dev/null
-/* -*-c-*-
- *
- * $Id$
- *
- * Karatsuba-based squaring algorithm
- *
- * (c) 1999 Straylight/Edgeware
- */
-
-/*----- Licensing notice --------------------------------------------------*
- *
- * This file is part of Catacomb.
- *
- * Catacomb is free software; you can redistribute it and/or modify
- * it under the terms of the GNU Library General Public License as
- * published by the Free Software Foundation; either version 2 of the
- * License, or (at your option) any later version.
- *
- * Catacomb is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU Library General Public License for more details.
- *
- * You should have received a copy of the GNU Library General Public
- * License along with Catacomb; if not, write to the Free
- * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- */
-
-/*----- Header files ------------------------------------------------------*/
-
-#include <assert.h>
-#include <stdio.h>
-
-#include "mpx.h"
-#include "karatsuba.h"
-
-/*----- Tweakables --------------------------------------------------------*/
-
-#ifdef TEST_RIG
-# undef MPK_THRESH
-# define MPK_THRESH 4
-#endif
-
-/*----- Main code ---------------------------------------------------------*/
-
-/* --- @mpx_ksqr@ --- *
- *
- * Arguments: @mpw *dv, *dvl@ = pointer to destination buffer
- * @const mpw *av, *avl@ = pointer to first argument
- * @mpw *sv, *svl@ = pointer to scratch workspace
- *
- * Returns: ---
- *
- * Use: Squares a multiprecision integers using something similar to
- * Karatsuba's multiplication algorithm. This is rather faster
- * than traditional long multiplication (e.g., @mpx_umul@) on
- * large numbers, although more expensive on small ones, and
- * rather simpler than full-blown Karatsuba multiplication.
- *
- * The destination must be three times as large as the larger
- * argument. The scratch space must be five times as large as
- * the larger argument.
- */
-
-void mpx_ksqr(mpw *dv, mpw *dvl,
- const mpw *av, const mpw *avl,
- mpw *sv, mpw *svl)
-{
- const mpw *avm;
- size_t m;
-
- /* --- Dispose of easy cases to @mpx_usqr@ --- *
- *
- * Karatsuba is only a win on large numbers, because of all the
- * recursiveness and bookkeeping. The recursive calls make a quick check
- * to see whether to bottom out to @mpx_usqr@ which should help quite a
- * lot, but sometimes the only way to know is to make sure...
- */
-
- MPX_SHRINK(av, avl);
-
- if (avl - av <= MPK_THRESH) {
- mpx_usqr(dv, dvl, av, avl);
- return;
- }
-
- /* --- How the algorithm works --- *
- *
- * The identity for squaring is known to all schoolchildren.
- * Let %$A = xb + y$%. Then %$A^2 = x^2 b^2 + 2 x y b + y^2$%. Now,
- * %$(x + y)^2 - x^2 - y^2 = 2 x y$%, which means I only need to do three
- * squarings.
- */
-
- /* --- First things --- *
- *
- * Sort out where to break the factor in half.
- */
-
- m = (avl - av + 1) >> 1;
- avm = av + m;
-
- /* --- Sort out everything --- */
-
- {
- mpw *svm = sv + m, *svn = svm + m, *ssv = svn + 4;
- mpw *tdv = dv + m;
- mpw *rdv = tdv + m;
-
- assert(rdv + m + 4 < dvl);
- assert(ssv < svl);
- UADD2(sv, svm, av, avm, avm, avl);
- if (m > MPK_THRESH)
- mpx_ksqr(tdv, rdv + m + 4, sv, svm + 1, ssv, svl);
- else
- mpx_usqr(tdv, rdv + m + 4, sv, svm + 1);
-
- if (m > MPK_THRESH)
- mpx_ksqr(sv, ssv, avm, avl, ssv, svl);
- else
- mpx_usqr(sv, ssv, avm, avl);
- MPX_COPY(rdv + m + 1, dvl, svm + 1, svn);
- UADD(rdv, sv, svm + 1);
- USUB(tdv, sv, svn);
-
- if (m > MPK_THRESH)
- mpx_ksqr(sv, ssv, av, avm, ssv, svl);
- else
- mpx_usqr(sv, ssv, av, avm);
- MPX_COPY(dv, tdv, sv, svm);
- UADD(tdv, svm, svn);
- USUB(tdv, sv, svn);
- }
-}
-
-/*----- Test rig ----------------------------------------------------------*/
-
-#ifdef TEST_RIG
-
-#include <mLib/alloc.h>
-#include <mLib/testrig.h>
-
-#define ALLOC(v, vl, sz) do { \
- size_t _sz = (sz); \
- mpw *_vv = xmalloc(MPWS(_sz)); \
- mpw *_vvl = _vv + _sz; \
- (v) = _vv; \
- (vl) = _vvl; \
-} while (0)
-
-#define LOAD(v, vl, d) do { \
- const dstr *_d = (d); \
- mpw *_v, *_vl; \
- ALLOC(_v, _vl, MPW_RQ(_d->len)); \
- mpx_loadb(_v, _vl, _d->buf, _d->len); \
- (v) = _v; \
- (vl) = _vl; \
-} while (0)
-
-#define MAX(x, y) ((x) > (y) ? (x) : (y))
-
-static void dumpmp(const char *msg, const mpw *v, const mpw *vl)
-{
- fputs(msg, stderr);
- MPX_SHRINK(v, vl);
- while (v < vl)
- fprintf(stderr, " %08lx", (unsigned long)*--vl);
- fputc('\n', stderr);
-}
-
-static int usqr(dstr *v)
-{
- mpw *a, *al;
- mpw *c, *cl;
- mpw *d, *dl;
- mpw *s, *sl;
- size_t m;
- int ok = 1;
-
- LOAD(a, al, &v[0]);
- LOAD(c, cl, &v[1]);
- m = al - a + 1;
- ALLOC(d, dl, 3 * m);
- ALLOC(s, sl, 5 * m);
-
- mpx_ksqr(d, dl, a, al, s, sl);
- if (!mpx_ueq(d, dl, c, cl)) {
- fprintf(stderr, "\n*** usqr failed\n");
- dumpmp(" a", a, al);
- dumpmp("expected", c, cl);
- dumpmp(" result", d, dl);
- ok = 0;
- }
-
- xfree(a); xfree(c); xfree(d); xfree(s);
- return (ok);
-}
-
-static test_chunk defs[] = {
- { "usqr", usqr, { &type_hex, &type_hex, 0 } },
- { 0, 0, { 0 } }
-};
-
-int main(int argc, char *argv[])
-{
- test_run(argc, argv, defs, SRCDIR"/tests/mpx");
- return (0);
-}
-
-#endif
-
-/*----- That's all, folks -------------------------------------------------*/
projects / u / mdw / catacomb / blobdiff