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

   1 /* -*-c-*-
   2  *
   3  * $Id: mpx-ksqr.c,v 1.7 2002/10/09 00:36:03 mdw Exp $
   4  *
   5  * Karatsuba-based squaring 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-ksqr.c,v $
  33  * Revision 1.7  2002/10/09 00:36:03  mdw
  34  * Fix bounds on workspace for Karatsuba operations.
  35  *
  36  * Revision 1.6  2000/10/08 15:48:35  mdw
  37  * Rename Karatsuba constants now that we have @gfx_kmul@ too.
  38  *
  39  * Revision 1.5  2000/10/08 12:11:01  mdw
  40  * Use @mpx_ueq@ instead of @MPX_UCMP@.
  41  *
  42  * Revision 1.4  2000/07/29 17:04:02  mdw
  43  * Remove useless header `mpscan.h'.
  44  *
  45  * Revision 1.3  2000/06/17 11:42:54  mdw
  46  * Moved the Karatsuba macros into a separate file for better sharing.
  47  * Fixed some comments.  Use an improved technique so that all the
  48  * operations are squarings.
  49  *
  50  * Revision 1.2  1999/12/13 15:35:01  mdw
  51  * Simplify and improve.
  52  *
  53  * Revision 1.1  1999/12/11 10:57:43  mdw
  54  * Karatsuba squaring algorithm.
  55  *
  56  */
  57
  58 /*----- Header files ------------------------------------------------------*/
  59
  60 #include <assert.h>
  61 #include <stdio.h>
  62
  63 #include "mpx.h"
  64 #include "karatsuba.h"
  65
  66 /*----- Tweakables --------------------------------------------------------*/
  67
  68 #ifdef TEST_RIG
  69 #  undef MPK_THRESH
  70 #  define MPK_THRESH 4
  71 #endif
  72
  73 /*----- Main code ---------------------------------------------------------*/
  74
  75 /* --- @mpx_ksqr@ --- *
  76  *
  77  * Arguments:   @mpw *dv, *dvl@ = pointer to destination buffer
  78  *              @const mpw *av, *avl@ = pointer to first argument
  79  *              @mpw *sv, *svl@ = pointer to scratch workspace
  80  *
  81  * Returns:     ---
  82  *
  83  * Use:         Squares a multiprecision integers using something similar to
  84  *              Karatsuba's multiplication algorithm.  This is rather faster
  85  *              than traditional long multiplication (e.g., @mpx_umul@) on
  86  *              large numbers, although more expensive on small ones, and
  87  *              rather simpler than full-blown Karatsuba multiplication.
  88  *
  89  *              The destination must be three times as large as the larger
  90  *              argument.  The scratch space must be five times as large as
  91  *              the larger argument.
  92  */
  93
  94 void mpx_ksqr(mpw *dv, mpw *dvl,
  95               const mpw *av, const mpw *avl,
  96               mpw *sv, mpw *svl)
  97 {
  98   const mpw *avm;
  99   size_t m;
 100
 101   /* --- Dispose of easy cases to @mpx_usqr@ --- *
 102    *
 103    * Karatsuba is only a win on large numbers, because of all the
 104    * recursiveness and bookkeeping.  The recursive calls make a quick check
 105    * to see whether to bottom out to @mpx_usqr@ which should help quite a
 106    * lot, but sometimes the only way to know is to make sure...
 107    */
 108
 109   MPX_SHRINK(av, avl);
 110
 111   if (avl - av <= MPK_THRESH) {
 112     mpx_usqr(dv, dvl, av, avl);
 113     return;
 114   }
 115
 116   /* --- How the algorithm works --- *
 117    *
 118    * The identity for squaring is known to all schoolchildren.
 119    * Let %$A = xb + y$%.  Then %$A^2 = x^2 b^2 + 2 x y b + y^2$%.  Now,
 120    * %$(x + y)^2 - x^2 - y^2 = 2 x y$%, which means I only need to do three
 121    * squarings.
 122    */
 123
 124   /* --- First things --- *
 125    *
 126    * Sort out where to break the factor in half.
 127    */
 128
 129   m = (avl - av + 1) >> 1;
 130   avm = av + m;
 131
 132   /* --- Sort out everything --- */
 133
 134   {
 135     mpw *svm = sv + m, *svn = svm + m, *ssv = svn + 4;
 136     mpw *tdv = dv + m;
 137     mpw *rdv = tdv + m;
 138
 139     assert(rdv + m + 4 < dvl);
 140     assert(ssv < svl);
 141     UADD2(sv, svm, av, avm, avm, avl);
 142     if (m > MPK_THRESH)
 143       mpx_ksqr(tdv, rdv + m + 4, sv, svm + 1, ssv, svl);
 144     else
 145       mpx_usqr(tdv, rdv + m + 4, sv, svm + 1);
 146
 147     if (m > MPK_THRESH)
 148       mpx_ksqr(sv, ssv, avm, avl, ssv, svl);
 149     else
 150       mpx_usqr(sv, ssv, avm, avl);
 151     MPX_COPY(rdv + m + 1, dvl, svm + 1, svn);
 152     UADD(rdv, sv, svm + 1);
 153     USUB(tdv, sv, svn);
 154
 155     if (m > MPK_THRESH)
 156       mpx_ksqr(sv, ssv, av, avm, ssv, svl);
 157     else
 158       mpx_usqr(sv, ssv, av, avm);
 159     MPX_COPY(dv, tdv, sv, svm);
 160     UADD(tdv, svm, svn);
 161     USUB(tdv, sv, svn);
 162   }
 163 }
 164
 165 /*----- Test rig ----------------------------------------------------------*/
 166
 167 #ifdef TEST_RIG
 168
 169 #include <mLib/alloc.h>
 170 #include <mLib/testrig.h>
 171
 172 #define ALLOC(v, vl, sz) do {                                           \
 173   size_t _sz = (sz);                                                    \
 174   mpw *_vv = xmalloc(MPWS(_sz));                                        \
 175   mpw *_vvl = _vv + _sz;                                                \
 176   (v) = _vv;                                                            \
 177   (vl) = _vvl;                                                          \
 178 } while (0)
 179
 180 #define LOAD(v, vl, d) do {                                             \
 181   const dstr *_d = (d);                                                 \
 182   mpw *_v, *_vl;                                                        \
 183   ALLOC(_v, _vl, MPW_RQ(_d->len));                                      \
 184   mpx_loadb(_v, _vl, _d->buf, _d->len);                                 \
 185   (v) = _v;                                                             \
 186   (vl) = _vl;                                                           \
 187 } while (0)
 188
 189 #define MAX(x, y) ((x) > (y) ? (x) : (y))
 190
 191 static void dumpmp(const char *msg, const mpw *v, const mpw *vl)
 192 {
 193   fputs(msg, stderr);
 194   MPX_SHRINK(v, vl);
 195   while (v < vl)
 196     fprintf(stderr, " %08lx", (unsigned long)*--vl);
 197   fputc('\n', stderr);
 198 }
 199
 200 static int usqr(dstr *v)
 201 {
 202   mpw *a, *al;
 203   mpw *c, *cl;
 204   mpw *d, *dl;
 205   mpw *s, *sl;
 206   size_t m;
 207   int ok = 1;
 208
 209   LOAD(a, al, &v[0]);
 210   LOAD(c, cl, &v[1]);
 211   m = al - a + 1;
 212   ALLOC(d, dl, 3 * m);
 213   ALLOC(s, sl, 5 * m);
 214
 215   mpx_ksqr(d, dl, a, al, s, sl);
 216   if (!mpx_ueq(d, dl, c, cl)) {
 217     fprintf(stderr, "\n*** usqr failed\n");
 218     dumpmp("       a", a, al);
 219     dumpmp("expected", c, cl);
 220     dumpmp("  result", d, dl);
 221     ok = 0;
 222   }
 223
 224   free(a); free(c); free(d); free(s);
 225   return (ok);
 226 }
 227
 228 static test_chunk defs[] = {
 229   { "usqr", usqr, { &type_hex, &type_hex, 0 } },
 230   { 0, 0, { 0 } }
 231 };
 232
 233 int main(int argc, char *argv[])
 234 {
 235   test_run(argc, argv, defs, SRCDIR"/tests/mpx");
 236   return (0);
 237 }
 238
 239 #endif
 240
 241 /*----- That's all, folks -------------------------------------------------*/