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

   1 /* -*-c-*-
   2  *
   3  * $Id: gfx-kmul.c,v 1.3 2004/03/27 17:54:11 mdw Exp $
   4  *
   5  * Karatsuba's multiplication algorithm on binary polynomials
   6  *
   7  * (c) 2000 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: gfx-kmul.c,v $
  33  * Revision 1.3  2004/03/27 17:54:11  mdw
  34  * Standard curves and curve checking.
  35  *
  36  * Revision 1.2  2002/10/09 00:36:03  mdw
  37  * Fix bounds on workspace for Karatsuba operations.
  38  *
  39  * Revision 1.1  2000/10/08 15:49:37  mdw
  40  * First glimmerings of binary polynomial arithmetic.
  41  *
  42  */
  43
  44 /*----- Header files ------------------------------------------------------*/
  45
  46 #include <assert.h>
  47 #include <stdio.h>
  48
  49 #include "gfx.h"
  50 #include "karatsuba.h"
  51
  52 /*----- Tweakables --------------------------------------------------------*/
  53
  54 #ifdef TEST_RIG
  55 #  undef GFK_THRESH
  56 #  define GFK_THRESH 1
  57 #endif
  58
  59 /*----- Main code ---------------------------------------------------------*/
  60
  61 /* --- @gfx_kmul@ --- *
  62  *
  63  * Arguments:   @mpw *dv, *dvl@ = pointer to destination buffer
  64  *              @const mpw *av, *avl@ = pointer to first argument
  65  *              @const mpw *bv, *bvl@ = pointer to second argument
  66  *              @mpw *sv, *svl@ = pointer to scratch workspace
  67  *
  68  * Returns:     ---
  69  *
  70  * Use:         Multiplies two binary polynomials using Karatsuba's
  71  *              algorithm.  This is rather faster than traditional long
  72  *              multiplication (e.g., @gfx_umul@) on polynomials with large
  73  *              degree, although more expensive on small ones.
  74  *
  75  *              The destination must be twice as large as the larger
  76  *              argument.  The scratch space must be twice as large as the
  77  *              larger argument.
  78  */
  79
  80 void gfx_kmul(mpw *dv, mpw *dvl,
  81               const mpw *av, const mpw *avl,
  82               const mpw *bv, const mpw *bvl,
  83               mpw *sv, mpw *svl)
  84 {
  85   const mpw *avm, *bvm;
  86   size_t m;
  87
  88   /* --- Dispose of easy cases to @mpx_umul@ --- *
  89    *
  90    * Karatsuba is only a win on large numbers, because of all the
  91    * recursiveness and bookkeeping.  The recursive calls make a quick check
  92    * to see whether to bottom out to @gfx_umul@ which should help quite a
  93    * lot, but sometimes the only way to know is to make sure...
  94    */
  95
  96   MPX_SHRINK(av, avl);
  97   MPX_SHRINK(bv, bvl);
  98
  99   if (avl - av <= GFK_THRESH || bvl - bv <= GFK_THRESH) {
 100     gfx_mul(dv, dvl, av, avl, bv, bvl);
 101     return;
 102   }
 103
 104   /* --- How the algorithm works --- *
 105    *
 106    * Let %$A = xb + y$% and %$B = ub + v$%.  Then, simply by expanding,
 107    * %$AB = x u b^2 + b(x v + y u) + y v$%.  That's not helped any, because
 108    * I've got four multiplications, each four times easier than the one I
 109    * started with.  However, note that I can rewrite the coefficient of %$b$%
 110    * as %$xv + yu = (x + y)(u + v) - xu - yv$%.  The terms %$xu$% and %$yv$%
 111    * I've already calculated, and that leaves only one more multiplication to
 112    * do.  So now I have three multiplications, each four times easier, and
 113    * that's a win.
 114    */
 115
 116   /* --- First things --- *
 117    *
 118    * Sort out where to break the factors in half.  I'll choose the midpoint
 119    * of the larger one, since this minimizes the amount of work I have to do
 120    * most effectively.
 121    */
 122
 123   if (avl - av > bvl - bv) {
 124     m = (avl - av + 1) >> 1;
 125     avm = av + m;
 126     if (bvl - bv > m)
 127       bvm = bv + m;
 128     else
 129       bvm = bvl;
 130   } else {
 131     m = (bvl - bv + 1) >> 1;
 132     bvm = bv + m;
 133     if (avl - av > m)
 134       avm = av + m;
 135     else
 136       avm = avl;
 137   }
 138
 139   /* --- Sort out the middle term --- */
 140
 141   {
 142     mpw *bsv = sv + m, *ssv = bsv + m;
 143     mpw *rdv = dv + m, *rdvl = rdv + 2 * m;
 144
 145     assert(rdvl <= dvl);
 146     assert(ssv <= svl);
 147     UXOR2(sv, bsv, av, avm, avm, avl);
 148     UXOR2(bsv, ssv, bv, bvm, bvm, bvl);
 149     if (m > GFK_THRESH)
 150       gfx_kmul(rdv, rdvl, sv, bsv, bsv, ssv, ssv, svl);
 151     else
 152       gfx_mul(rdv, rdvl, sv, bsv, bsv, ssv);
 153   }
 154
 155   /* --- Sort out the other two terms --- */
 156
 157   {
 158     mpw *svm = sv + m, *ssv = svm + m;
 159     mpw *tdv = dv + m;
 160     mpw *rdv = tdv + m;
 161
 162     if (avl == avm || bvl == bvm)
 163       MPX_ZERO(rdv + m, dvl);
 164     else {
 165       if (m > GFK_THRESH)
 166         gfx_kmul(sv, ssv, avm, avl, bvm, bvl, ssv, svl);
 167       else
 168         gfx_mul(sv, ssv, avm, avl, bvm, bvl);
 169       MPX_COPY(rdv + m, dvl, svm, ssv);
 170       UXOR(rdv, sv, svm);
 171       UXOR(tdv, sv, ssv);
 172     }
 173
 174     if (m > GFK_THRESH)
 175       gfx_kmul(sv, ssv, av, avm, bv, bvm, ssv, svl);
 176     else
 177       gfx_mul(sv, ssv, av, avm, bv, bvm);
 178     MPX_COPY(dv, tdv, sv, svm);
 179     UXOR(tdv, sv, ssv);
 180     UXOR(tdv, svm, ssv);
 181   }
 182 }
 183
 184 /*----- Test rig ----------------------------------------------------------*/
 185
 186 #ifdef TEST_RIG
 187
 188 #include <mLib/alloc.h>
 189 #include <mLib/testrig.h>
 190
 191 #define ALLOC(v, vl, sz) do {                                           \
 192   size_t _sz = (sz);                                                    \
 193   mpw *_vv = xmalloc(MPWS(_sz));                                        \
 194   mpw *_vvl = _vv + _sz;                                                \
 195   (v) = _vv;                                                            \
 196   (vl) = _vvl;                                                          \
 197 } while (0)
 198
 199 #define LOAD(v, vl, d) do {                                             \
 200   const dstr *_d = (d);                                                 \
 201   mpw *_v, *_vl;                                                        \
 202   ALLOC(_v, _vl, MPW_RQ(_d->len));                                      \
 203   mpx_loadb(_v, _vl, _d->buf, _d->len);                                 \
 204   (v) = _v;                                                             \
 205   (vl) = _vl;                                                           \
 206 } while (0)
 207
 208 #define MAX(x, y) ((x) > (y) ? (x) : (y))
 209
 210 static void dumpmp(const char *msg, const mpw *v, const mpw *vl)
 211 {
 212   fputs(msg, stderr);
 213   MPX_SHRINK(v, vl);
 214   while (v < vl)
 215     fprintf(stderr, " %08lx", (unsigned long)*--vl);
 216   fputc('\n', stderr);
 217 }
 218
 219 static int mul(dstr *v)
 220 {
 221   mpw *a, *al;
 222   mpw *b, *bl;
 223   mpw *c, *cl;
 224   mpw *d, *dl;
 225   mpw *s, *sl;
 226   size_t m;
 227   int ok = 1;
 228
 229   LOAD(a, al, &v[0]);
 230   LOAD(b, bl, &v[1]);
 231   LOAD(c, cl, &v[2]);
 232   m = MAX(al - a, bl - b) + 1;
 233   ALLOC(d, dl, 2 * m);
 234   ALLOC(s, sl, 2 * m);
 235
 236   gfx_kmul(d, dl, a, al, b, bl, s, sl);
 237   if (!mpx_ueq(d, dl, c, cl)) {
 238     fprintf(stderr, "\n*** mul failed\n");
 239     dumpmp("       a", a, al);
 240     dumpmp("       b", b, bl);
 241     dumpmp("expected", c, cl);
 242     dumpmp("  result", d, dl);
 243     ok = 0;
 244   }
 245
 246   free(a); free(b); free(c); free(d); free(s);
 247   return (ok);
 248 }
 249
 250 static test_chunk defs[] = {
 251   { "mul", mul, { &type_hex, &type_hex, &type_hex, 0 } },
 252   { 0, 0, { 0 } }
 253 };
 254
 255 int main(int argc, char *argv[])
 256 {
 257   test_run(argc, argv, defs, SRCDIR"/tests/gfx");
 258   return (0);
 259 }
 260
 261 #endif
 262
 263 /*----- That's all, folks -------------------------------------------------*/