git.distorted.org.uk Git - u/mdw/catacomb/blob - mpx-kmul.c

   1 /* -*-c-*-
   2  *
   3  * $Id: mpx-kmul.c,v 1.8 2002/10/09 00:36:03 mdw Exp $
   4  *
   5  * Karatsuba's multiplication algorithm
   6  *
   7  * (c) 1999 Straylight/Edgeware
   8  */
   9
  10 /*----- Licensing notice --------------------------------------------------*
  11  *
  12  * This file is part of Catacomb.
  13  *
  14  * Catacomb is free software; you can redistribute it and/or modify
  15  * it under the terms of the GNU Library General Public License as
  16  * published by the Free Software Foundation; either version 2 of the
  17  * License, or (at your option) any later version.
  18  *
  19  * Catacomb is distributed in the hope that it will be useful,
  20  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  21  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  22  * GNU Library General Public License for more details.
  23  *
  24  * You should have received a copy of the GNU Library General Public
  25  * License along with Catacomb; if not, write to the Free
  26  * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
  27  * MA 02111-1307, USA.
  28  */
  29
  30 /*----- Revision history --------------------------------------------------*
  31  *
  32  * $Log: mpx-kmul.c,v $
  33  * Revision 1.8  2002/10/09 00:36:03  mdw
  34  * Fix bounds on workspace for Karatsuba operations.
  35  *
  36  * Revision 1.7  2000/10/08 15:48:35  mdw
  37  * Rename Karatsuba constants now that we have @gfx_kmul@ too.
  38  *
  39  * Revision 1.6  2000/10/08 12:11:01  mdw
  40  * Use @mpx_ueq@ instead of @MPX_UCMP@.
  41  *
  42  * Revision 1.5  2000/07/29 17:04:02  mdw
  43  * Remove useless header `mpscan.h'.
  44  *
  45  * Revision 1.4  2000/06/17 11:42:11  mdw
  46  * Moved the Karatsuba macros into a separate file for better sharing.
  47  * Fixed some comments.
  48  *
  49  * Revision 1.3  1999/12/13 15:35:01  mdw
  50  * Simplify and improve.
  51  *
  52  * Revision 1.2  1999/12/11 10:58:02  mdw
  53  * Remove tweakable comments.
  54  *
  55  * Revision 1.1  1999/12/10 23:23:51  mdw
  56  * Karatsuba-Ofman multiplication algorithm.
  57  *
  58  */
  59
  60 /*----- Header files ------------------------------------------------------*/
  61
  62 #include <assert.h>
  63 #include <stdio.h>
  64
  65 #include "mpx.h"
  66 #include "karatsuba.h"
  67
  68 /*----- Tweakables --------------------------------------------------------*/
  69
  70 #ifdef TEST_RIG
  71 #  undef MPK_THRESH
  72 #  define MPK_THRESH 4                  /* Smallest possible correct value */
  73 #endif
  74
  75 /*----- Main code ---------------------------------------------------------*/
  76
  77 /* --- @mpx_kmul@ --- *
  78  *
  79  * Arguments:   @mpw *dv, *dvl@ = pointer to destination buffer
  80  *              @const mpw *av, *avl@ = pointer to first argument
  81  *              @const mpw *bv, *bvl@ = pointer to second argument
  82  *              @mpw *sv, *svl@ = pointer to scratch workspace
  83  *
  84  * Returns:     ---
  85  *
  86  * Use:         Multiplies two multiprecision integers using Karatsuba's
  87  *              algorithm.  This is rather faster than traditional long
  88  *              multiplication (e.g., @mpx_umul@) on large numbers, although
  89  *              more expensive on small ones.
  90  *
  91  *              The destination must be three times as large as the larger
  92  *              argument.  The scratch space must be five times as large as
  93  *              the larger argument.
  94  */
  95
  96 void mpx_kmul(mpw *dv, mpw *dvl,
  97               const mpw *av, const mpw *avl,
  98               const mpw *bv, const mpw *bvl,
  99               mpw *sv, mpw *svl)
 100 {
 101   const mpw *avm, *bvm;
 102   size_t m;
 103
 104   /* --- Dispose of easy cases to @mpx_umul@ --- *
 105    *
 106    * Karatsuba is only a win on large numbers, because of all the
 107    * recursiveness and bookkeeping.  The recursive calls make a quick check
 108    * to see whether to bottom out to @mpx_umul@ which should help quite a
 109    * lot, but sometimes the only way to know is to make sure...
 110    */
 111
 112   MPX_SHRINK(av, avl);
 113   MPX_SHRINK(bv, bvl);
 114
 115   if (avl - av <= MPK_THRESH || bvl - bv <= MPK_THRESH) {
 116     mpx_umul(dv, dvl, av, avl, bv, bvl);
 117     return;
 118   }
 119
 120   /* --- How the algorithm works --- *
 121    *
 122    * Let %$A = xb + y$% and %$B = ub + v$%.  Then, simply by expanding,
 123    * %$AB = x u b^2 + b(x v + y u) + y v$%.  That's not helped any, because
 124    * I've got four multiplications, each four times easier than the one I
 125    * started with.  However, note that I can rewrite the coefficient of %$b$%
 126    * as %$xv + yu = (x + y)(u + v) - xu - yv$%.  The terms %$xu$% and %$yv$%
 127    * I've already calculated, and that leaves only one more multiplication to
 128    * do.  So now I have three multiplications, each four times easier, and
 129    * that's a win.
 130    */
 131
 132   /* --- First things --- *
 133    *
 134    * Sort out where to break the factors in half.  I'll choose the midpoint
 135    * of the larger one, since this minimizes the amount of work I have to do
 136    * most effectively.
 137    */
 138
 139   if (avl - av > bvl - bv) {
 140     m = (avl - av + 1) >> 1;
 141     avm = av + m;
 142     if (bvl - bv > m)
 143       bvm = bv + m;
 144     else
 145       bvm = bvl;
 146   } else {
 147     m = (bvl - bv + 1) >> 1;
 148     bvm = bv + m;
 149     if (avl - av > m)
 150       avm = av + m;
 151     else
 152       avm = avl;
 153   }
 154
 155   /* --- Sort out the middle term --- */
 156
 157   {
 158     mpw *bsv = sv + m + 1, *ssv = bsv + m + 1;
 159     mpw *rdv = dv + m, *rdvl = rdv + 2 * (m + 2);
 160
 161     assert(rdvl < dvl);
 162     assert(ssv < svl);
 163     UADD2(sv, bsv, av, avm, avm, avl);
 164     UADD2(bsv, ssv, bv, bvm, bvm, bvl);
 165     if (m > MPK_THRESH)
 166       mpx_kmul(rdv, rdvl, sv, bsv, bsv, ssv, ssv, svl);
 167     else
 168       mpx_umul(rdv, rdvl, sv, bsv, bsv, ssv);
 169   }
 170
 171   /* --- Sort out the other two terms --- */
 172
 173   {
 174     mpw *svm = sv + m, *svn = svm + m, *ssv = svn + 4;
 175     mpw *tdv = dv + m;
 176     mpw *rdv = tdv + m;
 177
 178     if (avl == avm || bvl == bvm)
 179       MPX_ZERO(rdv + m + 1, dvl);
 180     else {
 181       if (m > MPK_THRESH)
 182         mpx_kmul(sv, ssv, avm, avl, bvm, bvl, ssv, svl);
 183       else
 184         mpx_umul(sv, ssv, avm, avl, bvm, bvl);
 185       MPX_COPY(rdv + m + 1, dvl, svm + 1, svn);
 186       UADD(rdv, sv, svm + 1);
 187       USUB(tdv, sv, svn);
 188     }
 189
 190     if (m > MPK_THRESH)
 191       mpx_kmul(sv, ssv, av, avm, bv, bvm, ssv, svl);
 192     else
 193       mpx_umul(sv, ssv, av, avm, bv, bvm);
 194     MPX_COPY(dv, tdv, sv, svm);
 195     USUB(tdv, sv, svn);
 196     UADD(tdv, svm, svn);
 197   }
 198 }
 199
 200 /*----- Test rig ----------------------------------------------------------*/
 201
 202 #ifdef TEST_RIG
 203
 204 #include <mLib/alloc.h>
 205 #include <mLib/testrig.h>
 206
 207 #define ALLOC(v, vl, sz) do {                                           \
 208   size_t _sz = (sz);                                                    \
 209   mpw *_vv = xmalloc(MPWS(_sz));                                        \
 210   mpw *_vvl = _vv + _sz;                                                \
 211   (v) = _vv;                                                            \
 212   (vl) = _vvl;                                                          \
 213 } while (0)
 214
 215 #define LOAD(v, vl, d) do {                                             \
 216   const dstr *_d = (d);                                                 \
 217   mpw *_v, *_vl;                                                        \
 218   ALLOC(_v, _vl, MPW_RQ(_d->len));                                      \
 219   mpx_loadb(_v, _vl, _d->buf, _d->len);                                 \
 220   (v) = _v;                                                             \
 221   (vl) = _vl;                                                           \
 222 } while (0)
 223
 224 #define MAX(x, y) ((x) > (y) ? (x) : (y))
 225
 226 static void dumpmp(const char *msg, const mpw *v, const mpw *vl)
 227 {
 228   fputs(msg, stderr);
 229   MPX_SHRINK(v, vl);
 230   while (v < vl)
 231     fprintf(stderr, " %08lx", (unsigned long)*--vl);
 232   fputc('\n', stderr);
 233 }
 234
 235 static int umul(dstr *v)
 236 {
 237   mpw *a, *al;
 238   mpw *b, *bl;
 239   mpw *c, *cl;
 240   mpw *d, *dl;
 241   mpw *s, *sl;
 242   size_t m;
 243   int ok = 1;
 244
 245   LOAD(a, al, &v[0]);
 246   LOAD(b, bl, &v[1]);
 247   LOAD(c, cl, &v[2]);
 248   m = MAX(al - a, bl - b) + 1;
 249   ALLOC(d, dl, 3 * m);
 250   ALLOC(s, sl, 5 * m);
 251
 252   mpx_kmul(d, dl, a, al, b, bl, s, sl);
 253   if (!mpx_ueq(d, dl, c, cl)) {
 254     fprintf(stderr, "\n*** umul failed\n");
 255     dumpmp("       a", a, al);
 256     dumpmp("       b", b, bl);
 257     dumpmp("expected", c, cl);
 258     dumpmp("  result", d, dl);
 259     ok = 0;
 260   }
 261
 262   free(a); free(b); free(c); free(d); free(s);
 263   return (ok);
 264 }
 265
 266 static test_chunk defs[] = {
 267   { "umul", umul, { &type_hex, &type_hex, &type_hex, 0 } },
 268   { 0, 0, { 0 } }
 269 };
 270
 271 int main(int argc, char *argv[])
 272 {
 273   test_run(argc, argv, defs, SRCDIR"/tests/mpx");
 274   return (0);
 275 }
 276
 277 #endif
 278
 279 /*----- That's all, folks -------------------------------------------------*/