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

   1 /* -*-c-*-
   2  *
   3  * $Id$
   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 /*----- Header files ------------------------------------------------------*/
  31
  32 #include <assert.h>
  33 #include <stdio.h>
  34
  35 #include "mpx.h"
  36 #include "karatsuba.h"
  37
  38 /*----- Tweakables --------------------------------------------------------*/
  39
  40 #ifdef TEST_RIG
  41 #  undef MPK_THRESH
  42 #  define MPK_THRESH 4                  /* Smallest possible correct value */
  43 #endif
  44
  45 /*----- Main code ---------------------------------------------------------*/
  46
  47 /* --- @mpx_kmul@ --- *
  48  *
  49  * Arguments:   @mpw *dv, *dvl@ = pointer to destination buffer
  50  *              @const mpw *av, *avl@ = pointer to first argument
  51  *              @const mpw *bv, *bvl@ = pointer to second argument
  52  *              @mpw *sv, *svl@ = pointer to scratch workspace
  53  *
  54  * Returns:     ---
  55  *
  56  * Use:         Multiplies two multiprecision integers using Karatsuba's
  57  *              algorithm.  This is rather faster than traditional long
  58  *              multiplication (e.g., @mpx_umul@) on large numbers, although
  59  *              more expensive on small ones.
  60  *
  61  *              The destination must be three times as large as the larger
  62  *              argument.  The scratch space must be five times as large as
  63  *              the larger argument.
  64  */
  65
  66 void mpx_kmul(mpw *dv, mpw *dvl,
  67               const mpw *av, const mpw *avl,
  68               const mpw *bv, const mpw *bvl,
  69               mpw *sv, mpw *svl)
  70 {
  71   const mpw *avm, *bvm;
  72   size_t m;
  73
  74   /* --- Dispose of easy cases to @mpx_umul@ --- *
  75    *
  76    * Karatsuba is only a win on large numbers, because of all the
  77    * recursiveness and bookkeeping.  The recursive calls make a quick check
  78    * to see whether to bottom out to @mpx_umul@ which should help quite a
  79    * lot, but sometimes the only way to know is to make sure...
  80    */
  81
  82   MPX_SHRINK(av, avl);
  83   MPX_SHRINK(bv, bvl);
  84
  85   if (avl - av <= MPK_THRESH || bvl - bv <= MPK_THRESH) {
  86     mpx_umul(dv, dvl, av, avl, bv, bvl);
  87     return;
  88   }
  89
  90   /* --- How the algorithm works --- *
  91    *
  92    * Let %$A = xb + y$% and %$B = ub + v$%.  Then, simply by expanding,
  93    * %$AB = x u b^2 + b(x v + y u) + y v$%.  That's not helped any, because
  94    * I've got four multiplications, each four times easier than the one I
  95    * started with.  However, note that I can rewrite the coefficient of %$b$%
  96    * as %$xv + yu = (x + y)(u + v) - xu - yv$%.  The terms %$xu$% and %$yv$%
  97    * I've already calculated, and that leaves only one more multiplication to
  98    * do.  So now I have three multiplications, each four times easier, and
  99    * that's a win.
 100    */
 101
 102   /* --- First things --- *
 103    *
 104    * Sort out where to break the factors in half.  I'll choose the midpoint
 105    * of the larger one, since this minimizes the amount of work I have to do
 106    * most effectively.
 107    */
 108
 109   if (avl - av > bvl - bv) {
 110     m = (avl - av + 1) >> 1;
 111     avm = av + m;
 112     if (bvl - bv > m)
 113       bvm = bv + m;
 114     else
 115       bvm = bvl;
 116   } else {
 117     m = (bvl - bv + 1) >> 1;
 118     bvm = bv + m;
 119     if (avl - av > m)
 120       avm = av + m;
 121     else
 122       avm = avl;
 123   }
 124
 125   /* --- Sort out the middle term --- */
 126
 127   {
 128     mpw *bsv = sv + m + 1, *ssv = bsv + m + 1;
 129     mpw *rdv = dv + m, *rdvl = rdv + 2 * (m + 2);
 130
 131     assert(rdvl <= dvl);
 132     assert(ssv <= svl);
 133     UADD2(sv, bsv, av, avm, avm, avl);
 134     UADD2(bsv, ssv, bv, bvm, bvm, bvl);
 135     if (m > MPK_THRESH)
 136       mpx_kmul(rdv, rdvl, sv, bsv, bsv, ssv, ssv, svl);
 137     else
 138       mpx_umul(rdv, rdvl, sv, bsv, bsv, ssv);
 139   }
 140
 141   /* --- Sort out the other two terms --- */
 142
 143   {
 144     mpw *svm = sv + m, *svn = svm + m, *ssv = svn + 4;
 145     mpw *tdv = dv + m;
 146     mpw *rdv = tdv + m;
 147
 148     if (avl == avm || bvl == bvm)
 149       MPX_ZERO(rdv + m + 1, dvl);
 150     else {
 151       if (m > MPK_THRESH)
 152         mpx_kmul(sv, ssv, avm, avl, bvm, bvl, ssv, svl);
 153       else
 154         mpx_umul(sv, ssv, avm, avl, bvm, bvl);
 155       MPX_COPY(rdv + m + 1, dvl, svm + 1, svn);
 156       UADD(rdv, sv, svm + 1);
 157       USUB(tdv, sv, svn);
 158     }
 159
 160     if (m > MPK_THRESH)
 161       mpx_kmul(sv, ssv, av, avm, bv, bvm, ssv, svl);
 162     else
 163       mpx_umul(sv, ssv, av, avm, bv, bvm);
 164     MPX_COPY(dv, tdv, sv, svm);
 165     USUB(tdv, sv, svn);
 166     UADD(tdv, svm, svn);
 167   }
 168 }
 169
 170 /*----- Test rig ----------------------------------------------------------*/
 171
 172 #ifdef TEST_RIG
 173
 174 #include <mLib/alloc.h>
 175 #include <mLib/testrig.h>
 176
 177 #define ALLOC(v, vl, sz) do {                                           \
 178   size_t _sz = (sz);                                                    \
 179   mpw *_vv = xmalloc(MPWS(_sz));                                        \
 180   mpw *_vvl = _vv + _sz;                                                \
 181   (v) = _vv;                                                            \
 182   (vl) = _vvl;                                                          \
 183 } while (0)
 184
 185 #define LOAD(v, vl, d) do {                                             \
 186   const dstr *_d = (d);                                                 \
 187   mpw *_v, *_vl;                                                        \
 188   ALLOC(_v, _vl, MPW_RQ(_d->len));                                      \
 189   mpx_loadb(_v, _vl, _d->buf, _d->len);                                 \
 190   (v) = _v;                                                             \
 191   (vl) = _vl;                                                           \
 192 } while (0)
 193
 194 #define MAX(x, y) ((x) > (y) ? (x) : (y))
 195
 196 static void dumpmp(const char *msg, const mpw *v, const mpw *vl)
 197 {
 198   fputs(msg, stderr);
 199   MPX_SHRINK(v, vl);
 200   while (v < vl)
 201     fprintf(stderr, " %08lx", (unsigned long)*--vl);
 202   fputc('\n', stderr);
 203 }
 204
 205 static int umul(dstr *v)
 206 {
 207   mpw *a, *al;
 208   mpw *b, *bl;
 209   mpw *c, *cl;
 210   mpw *d, *dl;
 211   mpw *s, *sl;
 212   size_t m;
 213   int ok = 1;
 214
 215   LOAD(a, al, &v[0]);
 216   LOAD(b, bl, &v[1]);
 217   LOAD(c, cl, &v[2]);
 218   m = MAX(al - a, bl - b) + 1;
 219   ALLOC(d, dl, 3 * m);
 220   ALLOC(s, sl, 5 * m);
 221
 222   mpx_kmul(d, dl, a, al, b, bl, s, sl);
 223   if (!mpx_ueq(d, dl, c, cl)) {
 224     fprintf(stderr, "\n*** umul failed\n");
 225     dumpmp("       a", a, al);
 226     dumpmp("       b", b, bl);
 227     dumpmp("expected", c, cl);
 228     dumpmp("  result", d, dl);
 229     ok = 0;
 230   }
 231
 232   xfree(a); xfree(b); xfree(c); xfree(d); xfree(s);
 233   return (ok);
 234 }
 235
 236 static test_chunk defs[] = {
 237   { "umul", umul, { &type_hex, &type_hex, &type_hex, 0 } },
 238   { 0, 0, { 0 } }
 239 };
 240
 241 int main(int argc, char *argv[])
 242 {
 243   test_run(argc, argv, defs, SRCDIR"/tests/mpx");
 244   return (0);
 245 }
 246
 247 #endif
 248
 249 /*----- That's all, folks -------------------------------------------------*/