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

   1 /* -*-c-*-
   2  *
   3  * $Id: mpx-ksqr.c,v 1.3 2000/06/17 11:42:54 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 1.3  2000/06/17 11:42:54  mdw
  34  * Moved the Karatsuba macros into a separate file for better sharing.
  35  * Fixed some comments.  Use an improved technique so that all the
  36  * operations are squarings.
  37  *
  38  * Revision 1.2  1999/12/13 15:35:01  mdw
  39  * Simplify and improve.
  40  *
  41  * Revision 1.1  1999/12/11 10:57:43  mdw
  42  * Karatsuba squaring algorithm.
  43  *
  44  */
  45
  46 /*----- Header files ------------------------------------------------------*/
  47
  48 #include <assert.h>
  49 #include <stdio.h>
  50
  51 #include "mpx.h"
  52 #include "mpx-kmac.h"
  53
  54 /*----- Tweakables --------------------------------------------------------*/
  55
  56 #ifdef TEST_RIG
  57 #  undef KARATSUBA_CUTOFF
  58 #  define KARATSUBA_CUTOFF 2
  59 #endif
  60
  61 /*----- Main code ---------------------------------------------------------*/
  62
  63 /* --- @mpx_ksqr@ --- *
  64  *
  65  * Arguments:   @mpw *dv, *dvl@ = pointer to destination buffer
  66  *              @const mpw *av, *avl@ = pointer to first argument
  67  *              @mpw *sv, *svl@ = pointer to scratch workspace
  68  *
  69  * Returns:     ---
  70  *
  71  * Use:         Squares a multiprecision integers using something similar to
  72  *              Karatsuba's multiplication algorithm.  This is rather faster
  73  *              than traditional long multiplication (e.g., @mpx_umul@) on
  74  *              large numbers, although more expensive on small ones, and
  75  *              rather simpler than full-blown Karatsuba multiplication.
  76  *
  77  *              The destination must be twice as large as the argument.  The
  78  *              scratch space must be twice as large as the argument, plus
  79  *              the magic number @KARATSUBA_SLOP@.
  80  */
  81
  82 void mpx_ksqr(mpw *dv, mpw *dvl,
  83               const mpw *av, const mpw *avl,
  84               mpw *sv, mpw *svl)
  85 {
  86   const mpw *avm;
  87   size_t m;
  88
  89   /* --- Dispose of easy cases to @mpx_usqr@ --- *
  90    *
  91    * Karatsuba is only a win on large numbers, because of all the
  92    * recursiveness and bookkeeping.  The recursive calls make a quick check
  93    * to see whether to bottom out to @mpx_usqr@ which should help quite a
  94    * lot, but sometimes the only way to know is to make sure...
  95    */
  96
  97   MPX_SHRINK(av, avl);
  98
  99   if (avl - av <= KARATSUBA_CUTOFF) {
 100     mpx_usqr(dv, dvl, av, avl);
 101     return;
 102   }
 103
 104   /* --- How the algorithm works --- *
 105    *
 106    * The identity for squaring is known to all schoolchildren.
 107    * Let %$A = xb + y$%.  Then %$A^2 = x^2 b^2 + 2 x y b + y^2$%.  Now,
 108    * %$(x + y)^2 - x^2 - y^2 = 2 x y$%, which means I only need to do three
 109    * squarings.
 110    */
 111
 112   /* --- First things --- *
 113    *
 114    * Sort out where to break the factor in half.
 115    */
 116
 117   m = (avl - av + 1) >> 1;
 118   avm = av + m;
 119
 120   assert(((void)"Destination too small for Karatsuba square",
 121           dvl - dv >= 4 * m));
 122   assert(((void)"Not enough workspace for Karatsuba square",
 123           svl - sv >= 4 * m));
 124
 125   /* --- Sort out everything --- */
 126
 127   {
 128     mpw *svm = sv + m, *svn = svm + m, *ssv = svn + 4;
 129     mpw *tdv = dv + m;
 130     mpw *rdv = tdv + m;
 131
 132     UADD2(sv, svm, av, avm, avm, avl);
 133     if (m > KARATSUBA_CUTOFF)
 134       mpx_ksqr(tdv, rdv + m + 4, sv, svm + 1, ssv, svl);
 135     else
 136       mpx_usqr(tdv, rdv + m + 4, sv, svm + 1);
 137
 138     if (m > KARATSUBA_CUTOFF)
 139       mpx_ksqr(sv, ssv, avm, avl, ssv, svl);
 140     else
 141       mpx_usqr(sv, ssv, avm, avl);
 142     MPX_COPY(rdv + m + 1, dvl, svm + 1, svn);
 143     UADD(rdv, sv, svm + 1);
 144     USUB(tdv, sv, svn);
 145
 146     if (m > KARATSUBA_CUTOFF)
 147       mpx_ksqr(sv, ssv, av, avm, ssv, svl);
 148     else
 149       mpx_usqr(sv, ssv, av, avm);
 150     MPX_COPY(dv, tdv, sv, svm);
 151     UADD(tdv, svm, svn);
 152     USUB(tdv, sv, svn);
 153   }
 154 }
 155
 156 /*----- Test rig ----------------------------------------------------------*/
 157
 158 #ifdef TEST_RIG
 159
 160 #include <mLib/alloc.h>
 161 #include <mLib/testrig.h>
 162
 163 #include "mpscan.h"
 164
 165 #define ALLOC(v, vl, sz) do {                                           \
 166   size_t _sz = (sz);                                                    \
 167   mpw *_vv = xmalloc(MPWS(_sz));                                        \
 168   mpw *_vvl = _vv + _sz;                                                \
 169   (v) = _vv;                                                            \
 170   (vl) = _vvl;                                                          \
 171 } while (0)
 172
 173 #define LOAD(v, vl, d) do {                                             \
 174   const dstr *_d = (d);                                                 \
 175   mpw *_v, *_vl;                                                        \
 176   ALLOC(_v, _vl, MPW_RQ(_d->len));                                      \
 177   mpx_loadb(_v, _vl, _d->buf, _d->len);                                 \
 178   (v) = _v;                                                             \
 179   (vl) = _vl;                                                           \
 180 } while (0)
 181
 182 #define MAX(x, y) ((x) > (y) ? (x) : (y))
 183
 184 static void dumpmp(const char *msg, const mpw *v, const mpw *vl)
 185 {
 186   fputs(msg, stderr);
 187   MPX_SHRINK(v, vl);
 188   while (v < vl)
 189     fprintf(stderr, " %08lx", (unsigned long)*--vl);
 190   fputc('\n', stderr);
 191 }
 192
 193 static int usqr(dstr *v)
 194 {
 195   mpw *a, *al;
 196   mpw *c, *cl;
 197   mpw *d, *dl;
 198   mpw *s, *sl;
 199   size_t m;
 200   int ok = 1;
 201
 202   LOAD(a, al, &v[0]);
 203   LOAD(c, cl, &v[1]);
 204   m = al - a + 1;
 205   ALLOC(d, dl, 2 * m);
 206   ALLOC(s, sl, 2 * m + 32);
 207
 208   mpx_ksqr(d, dl, a, al, s, sl);
 209   if (MPX_UCMP(d, dl, !=, c, cl)) {
 210     fprintf(stderr, "\n*** usqr failed\n");
 211     dumpmp("       a", a, al);
 212     dumpmp("expected", c, cl);
 213     dumpmp("  result", d, dl);
 214     ok = 0;
 215   }
 216
 217   free(a); free(c); free(d); free(s);
 218   return (ok);
 219 }
 220
 221 static test_chunk defs[] = {
 222   { "usqr", usqr, { &type_hex, &type_hex, 0 } },
 223   { 0, 0, { 0 } }
 224 };
 225
 226 int main(int argc, char *argv[])
 227 {
 228   test_run(argc, argv, defs, SRCDIR"/tests/mpx");
 229   return (0);
 230 }
 231
 232 #endif
 233
 234 /*----- That's all, folks -------------------------------------------------*/