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   1 /* -*-c-*-
   2  *
   3  * $Id: mpx-ksqr.c,v 1.5 2000/10/08 12:11:01 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 1.5  2000/10/08 12:11:01  mdw
  34  * Use @mpx_ueq@ instead of @MPX_UCMP@.
  35  *
  36  * Revision 1.4  2000/07/29 17:04:02  mdw
  37  * Remove useless header `mpscan.h'.
  38  *
  39  * Revision 1.3  2000/06/17 11:42:54  mdw
  40  * Moved the Karatsuba macros into a separate file for better sharing.
  41  * Fixed some comments.  Use an improved technique so that all the
  42  * operations are squarings.
  43  *
  44  * Revision 1.2  1999/12/13 15:35:01  mdw
  45  * Simplify and improve.
  46  *
  47  * Revision 1.1  1999/12/11 10:57:43  mdw
  48  * Karatsuba squaring algorithm.
  49  *
  50  */
  51
  52 /*----- Header files ------------------------------------------------------*/
  53
  54 #include <assert.h>
  55 #include <stdio.h>
  56
  57 #include "mpx.h"
  58 #include "mpx-kmac.h"
  59
  60 /*----- Tweakables --------------------------------------------------------*/
  61
  62 #ifdef TEST_RIG
  63 #  undef KARATSUBA_CUTOFF
  64 #  define KARATSUBA_CUTOFF 2
  65 #endif
  66
  67 /*----- Main code ---------------------------------------------------------*/
  68
  69 /* --- @mpx_ksqr@ --- *
  70  *
  71  * Arguments:   @mpw *dv, *dvl@ = pointer to destination buffer
  72  *              @const mpw *av, *avl@ = pointer to first argument
  73  *              @mpw *sv, *svl@ = pointer to scratch workspace
  74  *
  75  * Returns:     ---
  76  *
  77  * Use:         Squares a multiprecision integers using something similar to
  78  *              Karatsuba's multiplication algorithm.  This is rather faster
  79  *              than traditional long multiplication (e.g., @mpx_umul@) on
  80  *              large numbers, although more expensive on small ones, and
  81  *              rather simpler than full-blown Karatsuba multiplication.
  82  *
  83  *              The destination must be twice as large as the argument.  The
  84  *              scratch space must be twice as large as the argument, plus
  85  *              the magic number @KARATSUBA_SLOP@.
  86  */
  87
  88 void mpx_ksqr(mpw *dv, mpw *dvl,
  89               const mpw *av, const mpw *avl,
  90               mpw *sv, mpw *svl)
  91 {
  92   const mpw *avm;
  93   size_t m;
  94
  95   /* --- Dispose of easy cases to @mpx_usqr@ --- *
  96    *
  97    * Karatsuba is only a win on large numbers, because of all the
  98    * recursiveness and bookkeeping.  The recursive calls make a quick check
  99    * to see whether to bottom out to @mpx_usqr@ which should help quite a
 100    * lot, but sometimes the only way to know is to make sure...
 101    */
 102
 103   MPX_SHRINK(av, avl);
 104
 105   if (avl - av <= KARATSUBA_CUTOFF) {
 106     mpx_usqr(dv, dvl, av, avl);
 107     return;
 108   }
 109
 110   /* --- How the algorithm works --- *
 111    *
 112    * The identity for squaring is known to all schoolchildren.
 113    * Let %$A = xb + y$%.  Then %$A^2 = x^2 b^2 + 2 x y b + y^2$%.  Now,
 114    * %$(x + y)^2 - x^2 - y^2 = 2 x y$%, which means I only need to do three
 115    * squarings.
 116    */
 117
 118   /* --- First things --- *
 119    *
 120    * Sort out where to break the factor in half.
 121    */
 122
 123   m = (avl - av + 1) >> 1;
 124   avm = av + m;
 125
 126   assert(((void)"Destination too small for Karatsuba square",
 127           dvl - dv >= 4 * m));
 128   assert(((void)"Not enough workspace for Karatsuba square",
 129           svl - sv >= 4 * m));
 130
 131   /* --- Sort out everything --- */
 132
 133   {
 134     mpw *svm = sv + m, *svn = svm + m, *ssv = svn + 4;
 135     mpw *tdv = dv + m;
 136     mpw *rdv = tdv + m;
 137
 138     UADD2(sv, svm, av, avm, avm, avl);
 139     if (m > KARATSUBA_CUTOFF)
 140       mpx_ksqr(tdv, rdv + m + 4, sv, svm + 1, ssv, svl);
 141     else
 142       mpx_usqr(tdv, rdv + m + 4, sv, svm + 1);
 143
 144     if (m > KARATSUBA_CUTOFF)
 145       mpx_ksqr(sv, ssv, avm, avl, ssv, svl);
 146     else
 147       mpx_usqr(sv, ssv, avm, avl);
 148     MPX_COPY(rdv + m + 1, dvl, svm + 1, svn);
 149     UADD(rdv, sv, svm + 1);
 150     USUB(tdv, sv, svn);
 151
 152     if (m > KARATSUBA_CUTOFF)
 153       mpx_ksqr(sv, ssv, av, avm, ssv, svl);
 154     else
 155       mpx_usqr(sv, ssv, av, avm);
 156     MPX_COPY(dv, tdv, sv, svm);
 157     UADD(tdv, svm, svn);
 158     USUB(tdv, sv, svn);
 159   }
 160 }
 161
 162 /*----- Test rig ----------------------------------------------------------*/
 163
 164 #ifdef TEST_RIG
 165
 166 #include <mLib/alloc.h>
 167 #include <mLib/testrig.h>
 168
 169 #define ALLOC(v, vl, sz) do {                                           \
 170   size_t _sz = (sz);                                                    \
 171   mpw *_vv = xmalloc(MPWS(_sz));                                        \
 172   mpw *_vvl = _vv + _sz;                                                \
 173   (v) = _vv;                                                            \
 174   (vl) = _vvl;                                                          \
 175 } while (0)
 176
 177 #define LOAD(v, vl, d) do {                                             \
 178   const dstr *_d = (d);                                                 \
 179   mpw *_v, *_vl;                                                        \
 180   ALLOC(_v, _vl, MPW_RQ(_d->len));                                      \
 181   mpx_loadb(_v, _vl, _d->buf, _d->len);                                 \
 182   (v) = _v;                                                             \
 183   (vl) = _vl;                                                           \
 184 } while (0)
 185
 186 #define MAX(x, y) ((x) > (y) ? (x) : (y))
 187
 188 static void dumpmp(const char *msg, const mpw *v, const mpw *vl)
 189 {
 190   fputs(msg, stderr);
 191   MPX_SHRINK(v, vl);
 192   while (v < vl)
 193     fprintf(stderr, " %08lx", (unsigned long)*--vl);
 194   fputc('\n', stderr);
 195 }
 196
 197 static int usqr(dstr *v)
 198 {
 199   mpw *a, *al;
 200   mpw *c, *cl;
 201   mpw *d, *dl;
 202   mpw *s, *sl;
 203   size_t m;
 204   int ok = 1;
 205
 206   LOAD(a, al, &v[0]);
 207   LOAD(c, cl, &v[1]);
 208   m = al - a + 1;
 209   ALLOC(d, dl, 2 * m);
 210   ALLOC(s, sl, 2 * m + 32);
 211
 212   mpx_ksqr(d, dl, a, al, s, sl);
 213   if (!mpx_ueq(d, dl, c, cl)) {
 214     fprintf(stderr, "\n*** usqr failed\n");
 215     dumpmp("       a", a, al);
 216     dumpmp("expected", c, cl);
 217     dumpmp("  result", d, dl);
 218     ok = 0;
 219   }
 220
 221   free(a); free(c); free(d); free(s);
 222   return (ok);
 223 }
 224
 225 static test_chunk defs[] = {
 226   { "usqr", usqr, { &type_hex, &type_hex, 0 } },
 227   { 0, 0, { 0 } }
 228 };
 229
 230 int main(int argc, char *argv[])
 231 {
 232   test_run(argc, argv, defs, SRCDIR"/tests/mpx");
 233   return (0);
 234 }
 235
 236 #endif
 237
 238 /*----- That's all, folks -------------------------------------------------*/