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

   1 /* -*-c-*-
   2  *
   3  * Karatsuba-based squaring algorithm
   4  *
   5  * (c) 1999 Straylight/Edgeware
   6  */
   7
   8 /*----- Licensing notice --------------------------------------------------*
   9  *
  10  * This file is part of Catacomb.
  11  *
  12  * Catacomb is free software; you can redistribute it and/or modify
  13  * it under the terms of the GNU Library General Public License as
  14  * published by the Free Software Foundation; either version 2 of the
  15  * License, or (at your option) any later version.
  16  *
  17  * Catacomb is distributed in the hope that it will be useful,
  18  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  19  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  20  * GNU Library General Public License for more details.
  21  *
  22  * You should have received a copy of the GNU Library General Public
  23  * License along with Catacomb; if not, write to the Free
  24  * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
  25  * MA 02111-1307, USA.
  26  */
  27
  28 /*----- Header files ------------------------------------------------------*/
  29
  30 #include <assert.h>
  31 #include <stdio.h>
  32
  33 #include "mpx.h"
  34 #include "karatsuba.h"
  35
  36 /*----- Tweakables --------------------------------------------------------*/
  37
  38 #ifdef TEST_RIG
  39 #  undef MPK_THRESH
  40 #  define MPK_THRESH 4
  41 #endif
  42
  43 /*----- Main code ---------------------------------------------------------*/
  44
  45 /* --- @mpx_ksqr@ --- *
  46  *
  47  * Arguments:   @mpw *dv, *dvl@ = pointer to destination buffer
  48  *              @const mpw *av, *avl@ = pointer to first argument
  49  *              @mpw *sv, *svl@ = pointer to scratch workspace
  50  *
  51  * Returns:     ---
  52  *
  53  * Use:         Squares a multiprecision integers using something similar to
  54  *              Karatsuba's multiplication algorithm.  This is rather faster
  55  *              than traditional long multiplication (e.g., @mpx_umul@) on
  56  *              large numbers, although more expensive on small ones, and
  57  *              rather simpler than full-blown Karatsuba multiplication.
  58  *
  59  *              The destination must be three times as large as the larger
  60  *              argument.  The scratch space must be five times as large as
  61  *              the larger argument.
  62  */
  63
  64 void mpx_ksqr(mpw *dv, mpw *dvl,
  65               const mpw *av, const mpw *avl,
  66               mpw *sv, mpw *svl)
  67 {
  68   const mpw *avm;
  69   size_t m;
  70
  71   /* --- Dispose of easy cases to @mpx_usqr@ --- *
  72    *
  73    * Karatsuba is only a win on large numbers, because of all the
  74    * recursiveness and bookkeeping.  The recursive calls make a quick check
  75    * to see whether to bottom out to @mpx_usqr@ which should help quite a
  76    * lot, but sometimes the only way to know is to make sure...
  77    */
  78
  79   MPX_SHRINK(av, avl);
  80
  81   if (avl - av <= MPK_THRESH) {
  82     mpx_usqr(dv, dvl, av, avl);
  83     return;
  84   }
  85
  86   /* --- How the algorithm works --- *
  87    *
  88    * The identity for squaring is known to all schoolchildren.
  89    * Let %$A = xb + y$%.  Then %$A^2 = x^2 b^2 + 2 x y b + y^2$%.  Now,
  90    * %$(x + y)^2 - x^2 - y^2 = 2 x y$%, which means I only need to do three
  91    * squarings.
  92    */
  93
  94   /* --- First things --- *
  95    *
  96    * Sort out where to break the factor in half.
  97    */
  98
  99   m = (avl - av + 1) >> 1;
 100   avm = av + m;
 101
 102   /* --- Sort out everything --- */
 103
 104   {
 105     mpw *svm = sv + m, *svn = svm + m, *ssv = svn + 4;
 106     mpw *tdv = dv + m;
 107     mpw *rdv = tdv + m;
 108
 109     assert(rdv + m + 4 < dvl);
 110     assert(ssv < svl);
 111     UADD2(sv, svm, av, avm, avm, avl);
 112     if (m > MPK_THRESH)
 113       mpx_ksqr(tdv, rdv + m + 4, sv, svm + 1, ssv, svl);
 114     else
 115       mpx_usqr(tdv, rdv + m + 4, sv, svm + 1);
 116
 117     if (m > MPK_THRESH)
 118       mpx_ksqr(sv, ssv, avm, avl, ssv, svl);
 119     else
 120       mpx_usqr(sv, ssv, avm, avl);
 121     MPX_COPY(rdv + m + 1, dvl, svm + 1, svn);
 122     UADD(rdv, sv, svm + 1);
 123     USUB(tdv, sv, svn);
 124
 125     if (m > MPK_THRESH)
 126       mpx_ksqr(sv, ssv, av, avm, ssv, svl);
 127     else
 128       mpx_usqr(sv, ssv, av, avm);
 129     MPX_COPY(dv, tdv, sv, svm);
 130     UADD(tdv, svm, svn);
 131     USUB(tdv, sv, svn);
 132   }
 133 }
 134
 135 /*----- Test rig ----------------------------------------------------------*/
 136
 137 #ifdef TEST_RIG
 138
 139 #include <mLib/alloc.h>
 140 #include <mLib/testrig.h>
 141
 142 #define ALLOC(v, vl, sz) do {                                           \
 143   size_t _sz = (sz);                                                    \
 144   mpw *_vv = xmalloc(MPWS(_sz));                                        \
 145   mpw *_vvl = _vv + _sz;                                                \
 146   (v) = _vv;                                                            \
 147   (vl) = _vvl;                                                          \
 148 } while (0)
 149
 150 #define LOAD(v, vl, d) do {                                             \
 151   const dstr *_d = (d);                                                 \
 152   mpw *_v, *_vl;                                                        \
 153   ALLOC(_v, _vl, MPW_RQ(_d->len));                                      \
 154   mpx_loadb(_v, _vl, _d->buf, _d->len);                                 \
 155   (v) = _v;                                                             \
 156   (vl) = _vl;                                                           \
 157 } while (0)
 158
 159 #define MAX(x, y) ((x) > (y) ? (x) : (y))
 160
 161 static void dumpmp(const char *msg, const mpw *v, const mpw *vl)
 162 {
 163   fputs(msg, stderr);
 164   MPX_SHRINK(v, vl);
 165   while (v < vl)
 166     fprintf(stderr, " %08lx", (unsigned long)*--vl);
 167   fputc('\n', stderr);
 168 }
 169
 170 static int usqr(dstr *v)
 171 {
 172   mpw *a, *al;
 173   mpw *c, *cl;
 174   mpw *d, *dl;
 175   mpw *s, *sl;
 176   size_t m;
 177   int ok = 1;
 178
 179   LOAD(a, al, &v[0]);
 180   LOAD(c, cl, &v[1]);
 181   m = al - a + 1;
 182   ALLOC(d, dl, 3 * m);
 183   ALLOC(s, sl, 5 * m);
 184
 185   mpx_ksqr(d, dl, a, al, s, sl);
 186   if (!mpx_ueq(d, dl, c, cl)) {
 187     fprintf(stderr, "\n*** usqr failed\n");
 188     dumpmp("       a", a, al);
 189     dumpmp("expected", c, cl);
 190     dumpmp("  result", d, dl);
 191     ok = 0;
 192   }
 193
 194   xfree(a); xfree(c); xfree(d); xfree(s);
 195   return (ok);
 196 }
 197
 198 static test_chunk defs[] = {
 199   { "usqr", usqr, { &type_hex, &type_hex, 0 } },
 200   { 0, 0, { 0 } }
 201 };
 202
 203 int main(int argc, char *argv[])
 204 {
 205   test_run(argc, argv, defs, SRCDIR"/t/mpx");
 206   return (0);
 207 }
 208
 209 #endif
 210
 211 /*----- That's all, folks -------------------------------------------------*/