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

   1 /* -*-c-*-
   2  *
   3  * $Id: mpx-ksqr.c,v 1.2 1999/12/13 15:35:01 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 1.2  1999/12/13 15:35:01  mdw
  34  * Simplify and improve.
  35  *
  36  * Revision 1.1  1999/12/11 10:57:43  mdw
  37  * Karatsuba squaring algorithm.
  38  *
  39  */
  40
  41 /*----- Header files ------------------------------------------------------*/
  42
  43 #include <assert.h>
  44 #include <stdio.h>
  45
  46 #include "mpx.h"
  47
  48 /*----- Tweakables --------------------------------------------------------*/
  49
  50 #ifdef TEST_RIG
  51 #  undef KARATSUBA_CUTOFF
  52 #  define KARATSUBA_CUTOFF 2
  53 #endif
  54
  55 /*----- Addition macros ---------------------------------------------------*/
  56
  57 #define ULSL1(dv, av, avl) do {                                         \
  58   mpw *_dv = (dv);                                                      \
  59   const mpw *_av = (av), *_avl = (avl);                                 \
  60   mpw _c = 0;                                                           \
  61                                                                         \
  62   while (_av < _avl) {                                                  \
  63     mpw _x = *_av++;                                                    \
  64     *_dv++ = MPW(_c | (_x << 1));                                       \
  65     _c = MPW(_x >> (MPW_BITS - 1));                                     \
  66   }                                                                     \
  67   *_dv++ = _c;                                                          \
  68 } while (0)
  69
  70 #define UADD(dv, av, avl) do {                                          \
  71   mpw *_dv = (dv);                                                      \
  72   const mpw *_av = (av), *_avl = (avl);                                 \
  73   mpw _c = 0;                                                           \
  74                                                                         \
  75   while (_av < _avl) {                                                  \
  76     mpw _a, _b;                                                         \
  77     mpd _x;                                                             \
  78     _a = *_av++;                                                        \
  79     _b = *_dv;                                                          \
  80     _x = (mpd)_a + (mpd)_b + _c;                                        \
  81     *_dv++ = MPW(_x);                                                   \
  82     _c = _x >> MPW_BITS;                                                \
  83   }                                                                     \
  84   while (_c) {                                                          \
  85     mpd _x = (mpd)*_dv + (mpd)_c;                                       \
  86     *_dv++ = MPW(_x);                                                   \
  87     _c = _x >> MPW_BITS;                                                \
  88   }                                                                     \
  89 } while (0)
  90
  91 /*----- Main code ---------------------------------------------------------*/
  92
  93 /* --- @mpx_ksqr@ --- *
  94  *
  95  * Arguments:   @mpw *dv, *dvl@ = pointer to destination buffer
  96  *              @const mpw *av, *avl@ = pointer to first argument
  97  *              @mpw *sv, *svl@ = pointer to scratch workspace
  98  *
  99  * Returns:     ---
 100  *
 101  * Use:         Squares a multiprecision integers using something similar to
 102  *              Karatsuba's multiplication algorithm.  This is rather faster
 103  *              than traditional long multiplication (e.g., @mpx_umul@) on
 104  *              large numbers, although more expensive on small ones, and
 105  *              rather simpler than full-blown Karatsuba multiplication.
 106  *
 107  *              The destination must be twice as large as the argument.  The
 108  *              scratch space must be twice as large as the argument, plus
 109  *              the magic number @KARATSUBA_SLOP@.
 110  */
 111
 112 void mpx_ksqr(mpw *dv, mpw *dvl,
 113               const mpw *av, const mpw *avl,
 114               mpw *sv, mpw *svl)
 115 {
 116   const mpw *avm;
 117   size_t m;
 118
 119   /* --- Dispose of easy cases to @mpx_usqr@ --- *
 120    *
 121    * Karatsuba is only a win on large numbers, because of all the
 122    * recursiveness and bookkeeping.  The recursive calls make a quick check
 123    * to see whether to bottom out to @mpx_usqr@ which should help quite a
 124    * lot, but sometimes the only way to know is to make sure...
 125    */
 126
 127   MPX_SHRINK(av, avl);
 128
 129   if (avl - av <= KARATSUBA_CUTOFF) {
 130     mpx_usqr(dv, dvl, av, avl);
 131     return;
 132   }
 133
 134   /* --- How the algorithm works --- *
 135    *
 136    * Unlike Karatsuba's identity for multiplication which isn't particularly
 137    * obvious, the identity for multiplication is known to all schoolchildren.
 138    * Let %$A = xb + y$%.  Then %$A^2 = x^2 b^x + 2 x y b + y^2$%.  So now I
 139    * have three multiplications, each four times easier, and that's a win.
 140    */
 141
 142   /* --- First things --- *
 143    *
 144    * Sort out where to break the factor in half.
 145    */
 146
 147   m = (avl - av + 1) >> 1;
 148   avm = av + m;
 149
 150   assert(((void)"Destination too small for Karatsuba square",
 151           dvl - dv >= 4 * m));
 152   assert(((void)"Not enough workspace for Karatsuba square",
 153           svl - sv >= 4 * m));
 154
 155   /* --- Sort out everything --- */
 156
 157   {
 158     mpw *svm = sv + m, *svn = svm + m, *ssv = svn + 4;
 159     mpw *tdv = dv + m;
 160     mpw *rdv = tdv + m;
 161
 162     /* --- The cross term in the middle needs a multiply --- *
 163      *
 164      * This isn't actually true, since %$x y = ((x + y)^2 - (x - y)^2)/4%.
 165      * But that's two squarings, versus one multiplication.
 166      */
 167
 168     if (m > KARATSUBA_CUTOFF)
 169       mpx_kmul(sv, ssv, av, avm, avm, avl, ssv, svl);
 170     else
 171       mpx_umul(sv, ssv, av, avm, avm, avl);
 172     ULSL1(tdv, sv, svn);
 173
 174     if (m > KARATSUBA_CUTOFF)
 175       mpx_ksqr(sv, ssv, avm, avl, ssv, svl);
 176     else
 177       mpx_usqr(sv, ssv, avm, avl);
 178     MPX_COPY(rdv + m + 1, dvl, svm + 1, svn);
 179     UADD(rdv, sv, svm + 1);
 180
 181     if (m > KARATSUBA_CUTOFF)
 182       mpx_ksqr(sv, ssv, av, avm, ssv, svl);
 183     else
 184       mpx_usqr(sv, ssv, av, avm);
 185     MPX_COPY(dv, tdv, sv, svm);
 186     UADD(tdv, svm, svn);
 187   }
 188 }
 189
 190 /*----- Test rig ----------------------------------------------------------*/
 191
 192 #ifdef TEST_RIG
 193
 194 #include <mLib/alloc.h>
 195 #include <mLib/testrig.h>
 196
 197 #include "mpscan.h"
 198
 199 #define ALLOC(v, vl, sz) do {                                           \
 200   size_t _sz = (sz);                                                    \
 201   mpw *_vv = xmalloc(MPWS(_sz));                                        \
 202   mpw *_vvl = _vv + _sz;                                                \
 203   (v) = _vv;                                                            \
 204   (vl) = _vvl;                                                          \
 205 } while (0)
 206
 207 #define LOAD(v, vl, d) do {                                             \
 208   const dstr *_d = (d);                                                 \
 209   mpw *_v, *_vl;                                                        \
 210   ALLOC(_v, _vl, MPW_RQ(_d->len));                                      \
 211   mpx_loadb(_v, _vl, _d->buf, _d->len);                                 \
 212   (v) = _v;                                                             \
 213   (vl) = _vl;                                                           \
 214 } while (0)
 215
 216 #define MAX(x, y) ((x) > (y) ? (x) : (y))
 217
 218 static void dumpmp(const char *msg, const mpw *v, const mpw *vl)
 219 {
 220   fputs(msg, stderr);
 221   MPX_SHRINK(v, vl);
 222   while (v < vl)
 223     fprintf(stderr, " %08lx", (unsigned long)*--vl);
 224   fputc('\n', stderr);
 225 }
 226
 227 static int usqr(dstr *v)
 228 {
 229   mpw *a, *al;
 230   mpw *c, *cl;
 231   mpw *d, *dl;
 232   mpw *s, *sl;
 233   size_t m;
 234   int ok = 1;
 235
 236   LOAD(a, al, &v[0]);
 237   LOAD(c, cl, &v[1]);
 238   m = al - a + 1;
 239   ALLOC(d, dl, 2 * m);
 240   ALLOC(s, sl, 2 * m + 32);
 241
 242   mpx_ksqr(d, dl, a, al, s, sl);
 243   if (MPX_UCMP(d, dl, !=, c, cl)) {
 244     fprintf(stderr, "\n*** usqr failed\n");
 245     dumpmp("       a", a, al);
 246     dumpmp("expected", c, cl);
 247     dumpmp("  result", d, dl);
 248     ok = 0;
 249   }
 250
 251   free(a); free(c); free(d); free(s);
 252   return (ok);
 253 }
 254
 255 static test_chunk defs[] = {
 256   { "usqr", usqr, { &type_hex, &type_hex, 0 } },
 257   { 0, 0, { 0 } }
 258 };
 259
 260 int main(int argc, char *argv[])
 261 {
 262   test_run(argc, argv, defs, SRCDIR"/tests/mpx");
 263   return (0);
 264 }
 265
 266 #endif
 267
 268 /*----- That's all, folks -------------------------------------------------*/