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

   1 /* -*-c-*-
   2  *
   3  * $Id: gf-arith.c,v 1.4 2004/04/08 01:36:15 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 /*----- Header files ------------------------------------------------------*/
  31
  32 #include "gf.h"
  33
  34 /*----- Macros ------------------------------------------------------------*/
  35
  36 #define MAX(x, y) ((x) >= (y) ? (x) : (y))
  37
  38 /*----- Main code ---------------------------------------------------------*/
  39
  40 /* --- @gf_add@ --- *
  41  *
  42  * Arguments:   @mp *d@ = destination
  43  *              @mp *a, *b@ = sources
  44  *
  45  * Returns:     Result, @a@ added to @b@.
  46  */
  47
  48 mp *gf_add(mp *d, mp *a, mp *b)
  49 {
  50   MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)), (a->f | b->f) & MP_BURN);
  51   gfx_add(d->v, d->vl, a->v, a->vl, b->v, b->vl);
  52   d->f = (a->f | b->f) & MP_BURN;
  53   MP_SHRINK(d);
  54   return (d);
  55 }
  56
  57 /* --- @gf_mul@ --- *
  58  *
  59  * Arguments:   @mp *d@ = destination
  60  *              @mp *a, *b@ = sources
  61  *
  62  * Returns:     Result, @a@ multiplied by @b@.
  63  */
  64
  65 mp *gf_mul(mp *d, mp *a, mp *b)
  66 {
  67   a = MP_COPY(a);
  68   b = MP_COPY(b);
  69
  70   if (MP_LEN(a) <= MPK_THRESH || MP_LEN(b) <= GFK_THRESH) {
  71     MP_DEST(d, MP_LEN(a) + MP_LEN(b), a->f | b->f | MP_UNDEF);
  72     gfx_mul(d->v, d->vl, a->v, a->vl, b->v, b->vl);
  73   } else {
  74     size_t m = MAX(MP_LEN(a), MP_LEN(b));
  75     mpw *s;
  76     MP_DEST(d, 2 * m, a->f | b->f | MP_UNDEF);
  77     s = mpalloc(d->a, 3 * m);
  78     gfx_kmul(d->v, d->vl, a->v, a->vl, b->v, b->vl, s, s + 3 * m);
  79     mpfree(d->a, s);
  80   }
  81
  82   d->f = (a->f | b->f) & MP_BURN;
  83   MP_SHRINK(d);
  84   MP_DROP(a);
  85   MP_DROP(b);
  86   return (d);
  87 }
  88
  89 /* --- @gf_sqr@ --- *
  90  *
  91  * Arguments:   @mp *d@ = destination
  92  *              @mp *a@ = source
  93  *
  94  * Returns:     Result, @a@ squared.
  95  */
  96
  97 mp *gf_sqr(mp *d, mp *a)
  98 {
  99   MP_COPY(a);
 100   MP_DEST(d, 2 * MP_LEN(a), a->f & MP_BURN);
 101   gfx_sqr(d->v, d->vl, a->v, a->vl);
 102   d->f = a->f & MP_BURN;
 103   MP_SHRINK(d);
 104   MP_DROP(a);
 105   return (d);
 106 }
 107
 108 /* --- @gf_div@ --- *
 109  *
 110  * Arguments:   @mp **qq, **rr@ = destination, quotient and remainder
 111  *              @mp *a, *b@ = sources
 112  *
 113  * Use:         Calculates the quotient and remainder when @a@ is divided by
 114  *              @b@.  The destinations @*qq@ and @*rr@ must be distinct.
 115  *              Either of @qq@ or @rr@ may be null to indicate that the
 116  *              result is irrelevant.  (Discarding both results is silly.)
 117  *              There is a performance advantage if @a == *rr@.
 118  */
 119
 120 void gf_div(mp **qq, mp **rr, mp *a, mp *b)
 121  {
 122   mp *r = rr ? *rr : MP_NEW;
 123   mp *q = qq ? *qq : MP_NEW;
 124
 125   /* --- Set the remainder up right --- */
 126
 127   b = MP_COPY(b);
 128   a = MP_COPY(a);
 129   if (r)
 130     MP_DROP(r);
 131   r = a;
 132   MP_DEST(r, MP_LEN(b) + 2, a->f | b->f);
 133
 134   /* --- Fix up the quotient too --- */
 135
 136   r = MP_COPY(r);
 137   MP_DEST(q, MP_LEN(r), r->f | MP_UNDEF);
 138   MP_DROP(r);
 139
 140   /* --- Perform the calculation --- */
 141
 142   gfx_div(q->v, q->vl, r->v, r->vl, b->v, b->vl);
 143
 144   /* --- Sort out the sign of the results --- *
 145    *
 146    * If the signs of the arguments differ, and the remainder is nonzero, I
 147    * must add one to the absolute value of the quotient and subtract the
 148    * remainder from @b@.
 149    */
 150
 151   q->f = (r->f | b->f) & MP_BURN;
 152   r->f = (r->f | b->f) & MP_BURN;
 153
 154   /* --- Store the return values --- */
 155
 156   MP_DROP(b);
 157
 158   if (!qq)
 159     MP_DROP(q);
 160   else {
 161     MP_SHRINK(q);
 162     *qq = q;
 163   }
 164
 165   if (!rr)
 166     MP_DROP(r);
 167   else {
 168     MP_SHRINK(r);
 169     *rr = r;
 170   }
 171 }
 172
 173 /* --- @gf_irreduciblep@ --- *
 174  *
 175  * Arguments:   @mp *f@ = a polynomial
 176  *
 177  * Returns:     Nonzero if the polynomial is irreducible; otherwise zero.
 178  */
 179
 180 int gf_irreduciblep(mp *f)
 181 {
 182   unsigned long m = mp_bits(f) - 1;
 183   mp *u = MP_TWO;
 184   mp *v = MP_NEW;
 185
 186   m /= 2;
 187   while (m) {
 188     u = gf_sqr(u, u);
 189     gf_div(0, &u, u, f);
 190     v = gf_add(v, u, MP_TWO);
 191     gf_gcd(&v, 0, 0, v, f);
 192     if (!MP_EQ(v, MP_ONE)) break;
 193     m--;
 194   }
 195   MP_DROP(u);
 196   MP_DROP(v);
 197   return (!m);
 198 }
 199
 200 /*----- Test rig ----------------------------------------------------------*/
 201
 202 #ifdef TEST_RIG
 203
 204 static int verify(const char *op, mp *expect, mp *result, mp *a, mp *b)
 205 {
 206   if (!MP_EQ(expect, result)) {
 207     fprintf(stderr, "\n*** %s failed", op);
 208     fputs("\n*** a      = ", stderr); mp_writefile(a, stderr, 16);
 209     fputs("\n*** b      = ", stderr); mp_writefile(b, stderr, 16);
 210     fputs("\n*** result = ", stderr); mp_writefile(result, stderr, 16);
 211     fputs("\n*** expect = ", stderr); mp_writefile(expect, stderr, 16);
 212     fputc('\n', stderr);
 213     return (0);
 214   }
 215   return (1);
 216 }
 217
 218 #define RIG(name, op)                                                   \
 219   static int t##name(dstr *v)                                           \
 220   {                                                                     \
 221     mp *a = *(mp **)v[0].buf;                                           \
 222     mp *b = *(mp **)v[1].buf;                                           \
 223     mp *r = *(mp **)v[2].buf;                                           \
 224     mp *c = op(MP_NEW, a, b);                                           \
 225     int ok = verify(#name, r, c, a, b);                                 \
 226     mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r);                     \
 227     assert(mparena_count(MPARENA_GLOBAL) == 0);                         \
 228     return (ok);                                                        \
 229   }
 230
 231 RIG(add, gf_add)
 232 RIG(mul, gf_mul)
 233
 234 #undef RIG
 235
 236 static int tsqr(dstr *v)
 237 {
 238   mp *a = *(mp **)v[0].buf;
 239   mp *r = *(mp **)v[1].buf;
 240   mp *c = MP_NEW;
 241   int ok = 1;
 242   c = gf_sqr(MP_NEW, a);
 243   ok &= verify("sqr", r, c, a, MP_ZERO);
 244   mp_drop(a); mp_drop(r); mp_drop(c);
 245   assert(mparena_count(MPARENA_GLOBAL) == 0);
 246   return (ok);
 247 }
 248
 249 static int tdiv(dstr *v)
 250 {
 251   mp *a = *(mp **)v[0].buf;
 252   mp *b = *(mp **)v[1].buf;
 253   mp *q = *(mp **)v[2].buf;
 254   mp *r = *(mp **)v[3].buf;
 255   mp *c = MP_NEW, *d = MP_NEW;
 256   int ok = 1;
 257   gf_div(&c, &d, a, b);
 258   ok &= verify("div(quotient)", q, c, a, b);
 259   ok &= verify("div(remainder)", r, d, a, b);
 260   mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(d); mp_drop(r); mp_drop(q);
 261   assert(mparena_count(MPARENA_GLOBAL) == 0);
 262   return (ok);
 263 }
 264
 265 static int tirred(dstr *v)
 266 {
 267   mp *a = *(mp **)v[0].buf;
 268   int r = *(int *)v[1].buf;
 269   int c = gf_irreduciblep(a);
 270   int ok = 1;
 271   if (r != c) {
 272     ok = 0;
 273     fprintf(stderr, "\n*** irred failed");
 274     fputs("\n*** a      = ", stderr); mp_writefile(a, stderr, 16);
 275     fprintf(stderr, "\n*** r      = %d\n", r);
 276     fprintf(stderr, "*** c      = %d\n", c);
 277   }
 278   mp_drop(a);
 279   assert(mparena_count(MPARENA_GLOBAL) == 0);
 280   return (ok);
 281 }
 282
 283 static test_chunk tests[] = {
 284   { "add", tadd, { &type_mp, &type_mp, &type_mp, 0 } },
 285   { "mul", tmul, { &type_mp, &type_mp, &type_mp, 0 } },
 286   { "sqr", tsqr, { &type_mp, &type_mp, 0 } },
 287   { "div", tdiv, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
 288   { "irred", tirred, { &type_mp, &type_int, 0 } },
 289   { 0, 0, { 0 } },
 290 };
 291
 292 int main(int argc, char *argv[])
 293 {
 294   sub_init();
 295   test_run(argc, argv, tests, SRCDIR "/tests/gf");
 296   return (0);
 297 }
 298
 299 #endif
 300
 301 /*----- That's all, folks -------------------------------------------------*/