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

   1 /* -*-c-*-
   2  *
   3  * $Id$
   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 /*----- 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
  43 #endif
  44
  45 /*----- Main code ---------------------------------------------------------*/
  46
  47 /* --- @mpx_ksqr@ --- *
  48  *
  49  * Arguments:   @mpw *dv, *dvl@ = pointer to destination buffer
  50  *              @const mpw *av, *avl@ = pointer to first argument
  51  *              @mpw *sv, *svl@ = pointer to scratch workspace
  52  *
  53  * Returns:     ---
  54  *
  55  * Use:         Squares a multiprecision integers using something similar to
  56  *              Karatsuba's multiplication algorithm.  This is rather faster
  57  *              than traditional long multiplication (e.g., @mpx_umul@) on
  58  *              large numbers, although more expensive on small ones, and
  59  *              rather simpler than full-blown Karatsuba multiplication.
  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_ksqr(mpw *dv, mpw *dvl,
  67               const mpw *av, const mpw *avl,
  68               mpw *sv, mpw *svl)
  69 {
  70   const mpw *avm;
  71   size_t m;
  72
  73   /* --- Dispose of easy cases to @mpx_usqr@ --- *
  74    *
  75    * Karatsuba is only a win on large numbers, because of all the
  76    * recursiveness and bookkeeping.  The recursive calls make a quick check
  77    * to see whether to bottom out to @mpx_usqr@ which should help quite a
  78    * lot, but sometimes the only way to know is to make sure...
  79    */
  80
  81   MPX_SHRINK(av, avl);
  82
  83   if (avl - av <= MPK_THRESH) {
  84     mpx_usqr(dv, dvl, av, avl);
  85     return;
  86   }
  87
  88   /* --- How the algorithm works --- *
  89    *
  90    * The identity for squaring is known to all schoolchildren.
  91    * Let %$A = xb + y$%.  Then %$A^2 = x^2 b^2 + 2 x y b + y^2$%.  Now,
  92    * %$(x + y)^2 - x^2 - y^2 = 2 x y$%, which means I only need to do three
  93    * squarings.
  94    */
  95
  96   /* --- First things --- *
  97    *
  98    * Sort out where to break the factor in half.
  99    */
 100
 101   m = (avl - av + 1) >> 1;
 102   avm = av + m;
 103
 104   /* --- Sort out everything --- */
 105
 106   {
 107     mpw *svm = sv + m, *svn = svm + m, *ssv = svn + 4;
 108     mpw *tdv = dv + m;
 109     mpw *rdv = tdv + m;
 110
 111     assert(rdv + m + 4 < dvl);
 112     assert(ssv < svl);
 113     UADD2(sv, svm, av, avm, avm, avl);
 114     if (m > MPK_THRESH)
 115       mpx_ksqr(tdv, rdv + m + 4, sv, svm + 1, ssv, svl);
 116     else
 117       mpx_usqr(tdv, rdv + m + 4, sv, svm + 1);
 118
 119     if (m > MPK_THRESH)
 120       mpx_ksqr(sv, ssv, avm, avl, ssv, svl);
 121     else
 122       mpx_usqr(sv, ssv, avm, avl);
 123     MPX_COPY(rdv + m + 1, dvl, svm + 1, svn);
 124     UADD(rdv, sv, svm + 1);
 125     USUB(tdv, sv, svn);
 126
 127     if (m > MPK_THRESH)
 128       mpx_ksqr(sv, ssv, av, avm, ssv, svl);
 129     else
 130       mpx_usqr(sv, ssv, av, avm);
 131     MPX_COPY(dv, tdv, sv, svm);
 132     UADD(tdv, svm, svn);
 133     USUB(tdv, sv, svn);
 134   }
 135 }
 136
 137 /*----- Test rig ----------------------------------------------------------*/
 138
 139 #ifdef TEST_RIG
 140
 141 #include <mLib/alloc.h>
 142 #include <mLib/testrig.h>
 143
 144 #define ALLOC(v, vl, sz) do {                                           \
 145   size_t _sz = (sz);                                                    \
 146   mpw *_vv = xmalloc(MPWS(_sz));                                        \
 147   mpw *_vvl = _vv + _sz;                                                \
 148   (v) = _vv;                                                            \
 149   (vl) = _vvl;                                                          \
 150 } while (0)
 151
 152 #define LOAD(v, vl, d) do {                                             \
 153   const dstr *_d = (d);                                                 \
 154   mpw *_v, *_vl;                                                        \
 155   ALLOC(_v, _vl, MPW_RQ(_d->len));                                      \
 156   mpx_loadb(_v, _vl, _d->buf, _d->len);                                 \
 157   (v) = _v;                                                             \
 158   (vl) = _vl;                                                           \
 159 } while (0)
 160
 161 #define MAX(x, y) ((x) > (y) ? (x) : (y))
 162
 163 static void dumpmp(const char *msg, const mpw *v, const mpw *vl)
 164 {
 165   fputs(msg, stderr);
 166   MPX_SHRINK(v, vl);
 167   while (v < vl)
 168     fprintf(stderr, " %08lx", (unsigned long)*--vl);
 169   fputc('\n', stderr);
 170 }
 171
 172 static int usqr(dstr *v)
 173 {
 174   mpw *a, *al;
 175   mpw *c, *cl;
 176   mpw *d, *dl;
 177   mpw *s, *sl;
 178   size_t m;
 179   int ok = 1;
 180
 181   LOAD(a, al, &v[0]);
 182   LOAD(c, cl, &v[1]);
 183   m = al - a + 1;
 184   ALLOC(d, dl, 3 * m);
 185   ALLOC(s, sl, 5 * m);
 186
 187   mpx_ksqr(d, dl, a, al, s, sl);
 188   if (!mpx_ueq(d, dl, c, cl)) {
 189     fprintf(stderr, "\n*** usqr failed\n");
 190     dumpmp("       a", a, al);
 191     dumpmp("expected", c, cl);
 192     dumpmp("  result", d, dl);
 193     ok = 0;
 194   }
 195
 196   xfree(a); xfree(c); xfree(d); xfree(s);
 197   return (ok);
 198 }
 199
 200 static test_chunk defs[] = {
 201   { "usqr", usqr, { &type_hex, &type_hex, 0 } },
 202   { 0, 0, { 0 } }
 203 };
 204
 205 int main(int argc, char *argv[])
 206 {
 207   test_run(argc, argv, defs, SRCDIR"/tests/mpx");
 208   return (0);
 209 }
 210
 211 #endif
 212
 213 /*----- That's all, folks -------------------------------------------------*/