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

   1 /* -*-c-*-
   2  *
   3  * Karatsuba's multiplication algorithm on binary polynomials
   4  *
   5  * (c) 2000 Straylight/Edgeware
   6  */
   7
   8 /*----- Licensing notice --------------------------------------------------*
   9  *
  10  * This file is part of Catacomb.
  11  *
  12  * Catacomb is free software; you can redistribute it and/or modify
  13  * it under the terms of the GNU Library General Public License as
  14  * published by the Free Software Foundation; either version 2 of the
  15  * License, or (at your option) any later version.
  16  *
  17  * Catacomb is distributed in the hope that it will be useful,
  18  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  19  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  20  * GNU Library General Public License for more details.
  21  *
  22  * You should have received a copy of the GNU Library General Public
  23  * License along with Catacomb; if not, write to the Free
  24  * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
  25  * MA 02111-1307, USA.
  26  */
  27
  28 /*----- Header files ------------------------------------------------------*/
  29
  30 #include <assert.h>
  31 #include <stdio.h>
  32
  33 #include "gfx.h"
  34 #include "karatsuba.h"
  35
  36 /*----- Tweakables --------------------------------------------------------*/
  37
  38 #ifdef TEST_RIG
  39 #  undef GFK_THRESH
  40 #  define GFK_THRESH 1
  41 #endif
  42
  43 /*----- Main code ---------------------------------------------------------*/
  44
  45 /* --- @gfx_kmul@ --- *
  46  *
  47  * Arguments:   @mpw *dv, *dvl@ = pointer to destination buffer
  48  *              @const mpw *av, *avl@ = pointer to first argument
  49  *              @const mpw *bv, *bvl@ = pointer to second argument
  50  *              @mpw *sv, *svl@ = pointer to scratch workspace
  51  *
  52  * Returns:     ---
  53  *
  54  * Use:         Multiplies two binary polynomials using Karatsuba's
  55  *              algorithm.  This is rather faster than traditional long
  56  *              multiplication (e.g., @gfx_umul@) on polynomials with large
  57  *              degree, although more expensive on small ones.
  58  *
  59  *              The destination must be twice as large as the larger
  60  *              argument.  The scratch space must be twice as large as the
  61  *              larger argument.
  62  */
  63
  64 void gfx_kmul(mpw *dv, mpw *dvl,
  65               const mpw *av, const mpw *avl,
  66               const mpw *bv, const mpw *bvl,
  67               mpw *sv, mpw *svl)
  68 {
  69   const mpw *avm, *bvm;
  70   size_t m;
  71
  72   /* --- Dispose of easy cases to @mpx_umul@ --- *
  73    *
  74    * Karatsuba is only a win on large numbers, because of all the
  75    * recursiveness and bookkeeping.  The recursive calls make a quick check
  76    * to see whether to bottom out to @gfx_umul@ which should help quite a
  77    * lot, but sometimes the only way to know is to make sure...
  78    */
  79
  80   MPX_SHRINK(av, avl);
  81   MPX_SHRINK(bv, bvl);
  82
  83   if (avl - av <= GFK_THRESH || bvl - bv <= GFK_THRESH) {
  84     gfx_mul(dv, dvl, av, avl, bv, bvl);
  85     return;
  86   }
  87
  88   /* --- How the algorithm works --- *
  89    *
  90    * Let %$A = xb + y$% and %$B = ub + v$%.  Then, simply by expanding,
  91    * %$AB = x u b^2 + b(x v + y u) + y v$%.  That's not helped any, because
  92    * I've got four multiplications, each four times easier than the one I
  93    * started with.  However, note that I can rewrite the coefficient of %$b$%
  94    * as %$xv + yu = (x + y)(u + v) - xu - yv$%.  The terms %$xu$% and %$yv$%
  95    * I've already calculated, and that leaves only one more multiplication to
  96    * do.  So now I have three multiplications, each four times easier, and
  97    * that's a win.
  98    */
  99
 100   /* --- First things --- *
 101    *
 102    * Sort out where to break the factors in half.  I'll choose the midpoint
 103    * of the larger one, since this minimizes the amount of work I have to do
 104    * most effectively.
 105    */
 106
 107   if (avl - av > bvl - bv) {
 108     m = (avl - av + 1) >> 1;
 109     avm = av + m;
 110     if (bvl - bv > m)
 111       bvm = bv + m;
 112     else
 113       bvm = bvl;
 114   } else {
 115     m = (bvl - bv + 1) >> 1;
 116     bvm = bv + m;
 117     if (avl - av > m)
 118       avm = av + m;
 119     else
 120       avm = avl;
 121   }
 122
 123   /* --- Sort out the middle term --- */
 124
 125   {
 126     mpw *bsv = sv + m, *ssv = bsv + m;
 127     mpw *rdv = dv + m, *rdvl = rdv + 2 * m;
 128
 129     assert(rdvl <= dvl);
 130     assert(ssv <= svl);
 131     UXOR2(sv, bsv, av, avm, avm, avl);
 132     UXOR2(bsv, ssv, bv, bvm, bvm, bvl);
 133     if (m > GFK_THRESH)
 134       gfx_kmul(rdv, rdvl, sv, bsv, bsv, ssv, ssv, svl);
 135     else
 136       gfx_mul(rdv, rdvl, sv, bsv, bsv, ssv);
 137   }
 138
 139   /* --- Sort out the other two terms --- */
 140
 141   {
 142     mpw *svm = sv + m, *ssv = svm + m;
 143     mpw *tdv = dv + m;
 144     mpw *rdv = tdv + m;
 145
 146     if (avl == avm || bvl == bvm)
 147       MPX_ZERO(rdv + m, dvl);
 148     else {
 149       if (m > GFK_THRESH)
 150         gfx_kmul(sv, ssv, avm, avl, bvm, bvl, ssv, svl);
 151       else
 152         gfx_mul(sv, ssv, avm, avl, bvm, bvl);
 153       MPX_COPY(rdv + m, dvl, svm, ssv);
 154       UXOR(rdv, sv, svm);
 155       UXOR(tdv, sv, ssv);
 156     }
 157
 158     if (m > GFK_THRESH)
 159       gfx_kmul(sv, ssv, av, avm, bv, bvm, ssv, svl);
 160     else
 161       gfx_mul(sv, ssv, av, avm, bv, bvm);
 162     MPX_COPY(dv, tdv, sv, svm);
 163     UXOR(tdv, sv, ssv);
 164     UXOR(tdv, svm, ssv);
 165   }
 166 }
 167
 168 /*----- Test rig ----------------------------------------------------------*/
 169
 170 #ifdef TEST_RIG
 171
 172 #include <mLib/alloc.h>
 173 #include <mLib/testrig.h>
 174
 175 #define ALLOC(v, vl, sz) do {                                           \
 176   size_t _sz = (sz);                                                    \
 177   mpw *_vv = xmalloc(MPWS(_sz));                                        \
 178   mpw *_vvl = _vv + _sz;                                                \
 179   (v) = _vv;                                                            \
 180   (vl) = _vvl;                                                          \
 181 } while (0)
 182
 183 #define LOAD(v, vl, d) do {                                             \
 184   const dstr *_d = (d);                                                 \
 185   mpw *_v, *_vl;                                                        \
 186   ALLOC(_v, _vl, MPW_RQ(_d->len));                                      \
 187   mpx_loadb(_v, _vl, _d->buf, _d->len);                                 \
 188   (v) = _v;                                                             \
 189   (vl) = _vl;                                                           \
 190 } while (0)
 191
 192 #define MAX(x, y) ((x) > (y) ? (x) : (y))
 193
 194 static void dumpmp(const char *msg, const mpw *v, const mpw *vl)
 195 {
 196   fputs(msg, stderr);
 197   MPX_SHRINK(v, vl);
 198   while (v < vl)
 199     fprintf(stderr, " %08lx", (unsigned long)*--vl);
 200   fputc('\n', stderr);
 201 }
 202
 203 static int mul(dstr *v)
 204 {
 205   mpw *a, *al;
 206   mpw *b, *bl;
 207   mpw *c, *cl;
 208   mpw *d, *dl;
 209   mpw *s, *sl;
 210   size_t m;
 211   int ok = 1;
 212
 213   LOAD(a, al, &v[0]);
 214   LOAD(b, bl, &v[1]);
 215   LOAD(c, cl, &v[2]);
 216   m = MAX(al - a, bl - b) + 1;
 217   ALLOC(d, dl, 2 * m);
 218   ALLOC(s, sl, 2 * m);
 219
 220   gfx_kmul(d, dl, a, al, b, bl, s, sl);
 221   if (!mpx_ueq(d, dl, c, cl)) {
 222     fprintf(stderr, "\n*** mul failed\n");
 223     dumpmp("       a", a, al);
 224     dumpmp("       b", b, bl);
 225     dumpmp("expected", c, cl);
 226     dumpmp("  result", d, dl);
 227     ok = 0;
 228   }
 229
 230   xfree(a); xfree(b); xfree(c); xfree(d); xfree(s);
 231   return (ok);
 232 }
 233
 234 static test_chunk defs[] = {
 235   { "mul", mul, { &type_hex, &type_hex, &type_hex, 0 } },
 236   { 0, 0, { 0 } }
 237 };
 238
 239 int main(int argc, char *argv[])
 240 {
 241   test_run(argc, argv, defs, SRCDIR"/t/gfx");
 242   return (0);
 243 }
 244
 245 #endif
 246
 247 /*----- That's all, folks -------------------------------------------------*/