git.distorted.org.uk Git - u/mdw/catacomb/blob - gf-arith.c

   1 /* -*-c-*-
   2  *
   3  * $Id: gf-arith.c,v 1.3 2004/03/27 17:54:11 mdw Exp $
   4  *
   5  * Basic arithmetic on binary polynomials
   6  *
   7  * (c) 2004 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: gf-arith.c,v $
  33  * Revision 1.3  2004/03/27 17:54:11  mdw
  34  * Standard curves and curve checking.
  35  *
  36  * Revision 1.2  2004/03/21 22:52:06  mdw
  37  * Merge and close elliptic curve branch.
  38  *
  39  * Revision 1.1.2.1  2004/03/21 22:39:46  mdw
  40  * Elliptic curves on binary fields work.
  41  *
  42  */
  43
  44 /*----- Header files ------------------------------------------------------*/
  45
  46 #include "gf.h"
  47
  48 /*----- Macros ------------------------------------------------------------*/
  49
  50 #define MAX(x, y) ((x) >= (y) ? (x) : (y))
  51
  52 /*----- Main code ---------------------------------------------------------*/
  53
  54 /* --- @gf_add@ --- *
  55  *
  56  * Arguments:   @mp *d@ = destination
  57  *              @mp *a, *b@ = sources
  58  *
  59  * Returns:     Result, @a@ added to @b@.
  60  */
  61
  62 mp *gf_add(mp *d, mp *a, mp *b)
  63 {
  64   MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)), (a->f | b->f) & MP_BURN);
  65   gfx_add(d->v, d->vl, a->v, a->vl, b->v, b->vl);
  66   d->f = (a->f | b->f) & MP_BURN;
  67   MP_SHRINK(d);
  68   return (d);
  69 }
  70
  71 /* --- @gf_mul@ --- *
  72  *
  73  * Arguments:   @mp *d@ = destination
  74  *              @mp *a, *b@ = sources
  75  *
  76  * Returns:     Result, @a@ multiplied by @b@.
  77  */
  78
  79 mp *gf_mul(mp *d, mp *a, mp *b)
  80 {
  81   a = MP_COPY(a);
  82   b = MP_COPY(b);
  83
  84   if (MP_LEN(a) <= MPK_THRESH || MP_LEN(b) <= GFK_THRESH) {
  85     MP_DEST(d, MP_LEN(a) + MP_LEN(b), a->f | b->f | MP_UNDEF);
  86     gfx_mul(d->v, d->vl, a->v, a->vl, b->v, b->vl);
  87   } else {
  88     size_t m = MAX(MP_LEN(a), MP_LEN(b));
  89     mpw *s;
  90     MP_DEST(d, 2 * m, a->f | b->f | MP_UNDEF);
  91     s = mpalloc(d->a, 3 * m);
  92     gfx_kmul(d->v, d->vl, a->v, a->vl, b->v, b->vl, s, s + 3 * m);
  93     mpfree(d->a, s);
  94   }
  95
  96   d->f = (a->f | b->f) & MP_BURN;
  97   MP_SHRINK(d);
  98   MP_DROP(a);
  99   MP_DROP(b);
 100   return (d);
 101 }
 102
 103 /* --- @gf_sqr@ --- *
 104  *
 105  * Arguments:   @mp *d@ = destination
 106  *              @mp *a@ = source
 107  *
 108  * Returns:     Result, @a@ squared.
 109  */
 110
 111 mp *gf_sqr(mp *d, mp *a)
 112 {
 113   MP_COPY(a);
 114   MP_DEST(d, 2 * MP_LEN(a), a->f & MP_BURN);
 115   gfx_sqr(d->v, d->vl, a->v, a->vl);
 116   d->f = a->f & MP_BURN;
 117   MP_SHRINK(d);
 118   MP_DROP(a);
 119   return (d);
 120 }
 121
 122 /* --- @gf_div@ --- *
 123  *
 124  * Arguments:   @mp **qq, **rr@ = destination, quotient and remainder
 125  *              @mp *a, *b@ = sources
 126  *
 127  * Use:         Calculates the quotient and remainder when @a@ is divided by
 128  *              @b@.  The destinations @*qq@ and @*rr@ must be distinct.
 129  *              Either of @qq@ or @rr@ may be null to indicate that the
 130  *              result is irrelevant.  (Discarding both results is silly.)
 131  *              There is a performance advantage if @a == *rr@.
 132  */
 133
 134 void gf_div(mp **qq, mp **rr, mp *a, mp *b)
 135  {
 136   mp *r = rr ? *rr : MP_NEW;
 137   mp *q = qq ? *qq : MP_NEW;
 138
 139   /* --- Set the remainder up right --- */
 140
 141   b = MP_COPY(b);
 142   a = MP_COPY(a);
 143   if (r)
 144     MP_DROP(r);
 145   r = a;
 146   MP_DEST(r, MP_LEN(b) + 2, a->f | b->f);
 147
 148   /* --- Fix up the quotient too --- */
 149
 150   r = MP_COPY(r);
 151   MP_DEST(q, MP_LEN(r), r->f | MP_UNDEF);
 152   MP_DROP(r);
 153
 154   /* --- Perform the calculation --- */
 155
 156   gfx_div(q->v, q->vl, r->v, r->vl, b->v, b->vl);
 157
 158   /* --- Sort out the sign of the results --- *
 159    *
 160    * If the signs of the arguments differ, and the remainder is nonzero, I
 161    * must add one to the absolute value of the quotient and subtract the
 162    * remainder from @b@.
 163    */
 164
 165   q->f = (r->f | b->f) & MP_BURN;
 166   r->f = (r->f | b->f) & MP_BURN;
 167
 168   /* --- Store the return values --- */
 169
 170   MP_DROP(b);
 171
 172   if (!qq)
 173     MP_DROP(q);
 174   else {
 175     MP_SHRINK(q);
 176     *qq = q;
 177   }
 178
 179   if (!rr)
 180     MP_DROP(r);
 181   else {
 182     MP_SHRINK(r);
 183     *rr = r;
 184   }
 185 }
 186
 187 /* --- @gf_irreduciblep@ --- *
 188  *
 189  * Arguments:   @mp *f@ = a polynomial
 190  *
 191  * Returns:     Nonzero if the polynomial is irreducible; otherwise zero.
 192  */
 193
 194 int gf_irreduciblep(mp *f)
 195 {
 196   unsigned long m = mp_bits(f) - 1;
 197   mp *u = MP_TWO;
 198   mp *v = MP_NEW;
 199
 200   m /= 2;
 201   while (m) {
 202     u = gf_sqr(u, u);
 203     gf_div(0, &u, u, f);
 204     v = gf_add(v, u, MP_TWO);
 205     gf_gcd(&v, 0, 0, v, f);
 206     if (!MP_EQ(v, MP_ONE)) break;
 207     m--;
 208   }
 209   MP_DROP(u);
 210   MP_DROP(v);
 211   return (!m);
 212 }
 213
 214 /*----- Test rig ----------------------------------------------------------*/
 215
 216 #ifdef TEST_RIG
 217
 218 static int verify(const char *op, mp *expect, mp *result, mp *a, mp *b)
 219 {
 220   if (!MP_EQ(expect, result)) {
 221     fprintf(stderr, "\n*** %s failed", op);
 222     fputs("\n*** a      = ", stderr); mp_writefile(a, stderr, 16);
 223     fputs("\n*** b      = ", stderr); mp_writefile(b, stderr, 16);
 224     fputs("\n*** result = ", stderr); mp_writefile(result, stderr, 16);
 225     fputs("\n*** expect = ", stderr); mp_writefile(expect, stderr, 16);
 226     fputc('\n', stderr);
 227     return (0);
 228   }
 229   return (1);
 230 }
 231
 232 #define RIG(name, op)                                                   \
 233   static int t##name(dstr *v)                                           \
 234   {                                                                     \
 235     mp *a = *(mp **)v[0].buf;                                           \
 236     mp *b = *(mp **)v[1].buf;                                           \
 237     mp *r = *(mp **)v[2].buf;                                           \
 238     mp *c = op(MP_NEW, a, b);                                           \
 239     int ok = verify(#name, r, c, a, b);                                 \
 240     mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r);                     \
 241     assert(mparena_count(MPARENA_GLOBAL) == 0);                         \
 242     return (ok);                                                        \
 243   }
 244
 245 RIG(add, gf_add)
 246 RIG(mul, gf_mul)
 247
 248 #undef RIG
 249
 250 static int tsqr(dstr *v)
 251 {
 252   mp *a = *(mp **)v[0].buf;
 253   mp *r = *(mp **)v[1].buf;
 254   mp *c = MP_NEW;
 255   int ok = 1;
 256   c = gf_sqr(MP_NEW, a);
 257   ok &= verify("sqr", r, c, a, MP_ZERO);
 258   mp_drop(a); mp_drop(r); mp_drop(c);
 259   assert(mparena_count(MPARENA_GLOBAL) == 0);
 260   return (ok);
 261 }
 262
 263 static int tdiv(dstr *v)
 264 {
 265   mp *a = *(mp **)v[0].buf;
 266   mp *b = *(mp **)v[1].buf;
 267   mp *q = *(mp **)v[2].buf;
 268   mp *r = *(mp **)v[3].buf;
 269   mp *c = MP_NEW, *d = MP_NEW;
 270   int ok = 1;
 271   gf_div(&c, &d, a, b);
 272   ok &= verify("div(quotient)", q, c, a, b);
 273   ok &= verify("div(remainder)", r, d, a, b);
 274   mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(d); mp_drop(r); mp_drop(q);
 275   assert(mparena_count(MPARENA_GLOBAL) == 0);
 276   return (ok);
 277 }
 278
 279 static int tirred(dstr *v)
 280 {
 281   mp *a = *(mp **)v[0].buf;
 282   int r = *(int *)v[1].buf;
 283   int c = gf_irreduciblep(a);
 284   int ok = 1;
 285   if (r != c) {
 286     ok = 0;
 287     fprintf(stderr, "\n*** irred failed");
 288     fputs("\n*** a      = ", stderr); mp_writefile(a, stderr, 16);
 289     fprintf(stderr, "\n*** r      = %d\n", r);
 290     fprintf(stderr, "*** c      = %d\n", c);
 291   }
 292   mp_drop(a);
 293   assert(mparena_count(MPARENA_GLOBAL) == 0);
 294   return (ok);
 295 }
 296
 297 static test_chunk tests[] = {
 298   { "add", tadd, { &type_mp, &type_mp, &type_mp, 0 } },
 299   { "mul", tmul, { &type_mp, &type_mp, &type_mp, 0 } },
 300   { "sqr", tsqr, { &type_mp, &type_mp, 0 } },
 301   { "div", tdiv, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
 302   { "irred", tirred, { &type_mp, &type_int, 0 } },
 303   { 0, 0, { 0 } },
 304 };
 305
 306 int main(int argc, char *argv[])
 307 {
 308   sub_init();
 309   test_run(argc, argv, tests, SRCDIR "/tests/gf");
 310   return (0);
 311 }
 312
 313 #endif
 314
 315 /*----- That's all, folks -------------------------------------------------*/