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