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

   1 /* -*-c-*-
   2  *
   3  * Basic arithmetic on binary polynomials
   4  *
   5  * (c) 2004 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 "gf.h"
  31
  32 /*----- Macros ------------------------------------------------------------*/
  33
  34 #define MAX(x, y) ((x) >= (y) ? (x) : (y))
  35
  36 /*----- Main code ---------------------------------------------------------*/
  37
  38 /* --- @gf_add@ --- *
  39  *
  40  * Arguments:   @mp *d@ = destination
  41  *              @mp *a, *b@ = sources
  42  *
  43  * Returns:     Result, @a@ added to @b@.
  44  */
  45
  46 mp *gf_add(mp *d, mp *a, mp *b)
  47 {
  48   MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)), (a->f | b->f) & MP_BURN);
  49   gfx_add(d->v, d->vl, a->v, a->vl, b->v, b->vl);
  50   d->f = (a->f | b->f) & MP_BURN;
  51   MP_SHRINK(d);
  52   return (d);
  53 }
  54
  55 /* --- @gf_mul@ --- *
  56  *
  57  * Arguments:   @mp *d@ = destination
  58  *              @mp *a, *b@ = sources
  59  *
  60  * Returns:     Result, @a@ multiplied by @b@.
  61  */
  62
  63 mp *gf_mul(mp *d, mp *a, mp *b)
  64 {
  65   a = MP_COPY(a);
  66   b = MP_COPY(b);
  67
  68   if (MP_LEN(a) <= MPK_THRESH || MP_LEN(b) <= GFK_THRESH) {
  69     MP_DEST(d, MP_LEN(a) + MP_LEN(b), a->f | b->f | MP_UNDEF);
  70     gfx_mul(d->v, d->vl, a->v, a->vl, b->v, b->vl);
  71   } else {
  72     size_t m = MAX(MP_LEN(a), MP_LEN(b));
  73     mpw *s;
  74     MP_DEST(d, 2 * m, a->f | b->f | MP_UNDEF);
  75     s = mpalloc(d->a, 3 * m);
  76     gfx_kmul(d->v, d->vl, a->v, a->vl, b->v, b->vl, s, s + 3 * m);
  77     mpfree(d->a, s);
  78   }
  79
  80   d->f = (a->f | b->f) & MP_BURN;
  81   MP_SHRINK(d);
  82   MP_DROP(a);
  83   MP_DROP(b);
  84   return (d);
  85 }
  86
  87 /* --- @gf_sqr@ --- *
  88  *
  89  * Arguments:   @mp *d@ = destination
  90  *              @mp *a@ = source
  91  *
  92  * Returns:     Result, @a@ squared.
  93  */
  94
  95 mp *gf_sqr(mp *d, mp *a)
  96 {
  97   MP_COPY(a);
  98   MP_DEST(d, 2 * MP_LEN(a), a->f & MP_BURN);
  99   gfx_sqr(d->v, d->vl, a->v, a->vl);
 100   d->f = a->f & MP_BURN;
 101   MP_SHRINK(d);
 102   MP_DROP(a);
 103   return (d);
 104 }
 105
 106 /* --- @gf_div@ --- *
 107  *
 108  * Arguments:   @mp **qq, **rr@ = destination, quotient and remainder
 109  *              @mp *a, *b@ = sources
 110  *
 111  * Use:         Calculates the quotient and remainder when @a@ is divided by
 112  *              @b@.  The destinations @*qq@ and @*rr@ must be distinct.
 113  *              Either of @qq@ or @rr@ may be null to indicate that the
 114  *              result is irrelevant.  (Discarding both results is silly.)
 115  *              There is a performance advantage if @a == *rr@.
 116  */
 117
 118 void gf_div(mp **qq, mp **rr, mp *a, mp *b)
 119  {
 120   mp *r = rr ? *rr : MP_NEW;
 121   mp *q = qq ? *qq : MP_NEW;
 122
 123   /* --- Set the remainder up right --- */
 124
 125   b = MP_COPY(b);
 126   a = MP_COPY(a);
 127   if (r)
 128     MP_DROP(r);
 129   r = a;
 130   MP_DEST(r, MP_LEN(b) + 2, a->f | b->f);
 131
 132   /* --- Fix up the quotient too --- */
 133
 134   r = MP_COPY(r);
 135   MP_DEST(q, MP_LEN(r), r->f | MP_UNDEF);
 136   MP_DROP(r);
 137
 138   /* --- Perform the calculation --- */
 139
 140   gfx_div(q->v, q->vl, r->v, r->vl, b->v, b->vl);
 141
 142   /* --- Sort out the sign of the results --- *
 143    *
 144    * If the signs of the arguments differ, and the remainder is nonzero, I
 145    * must add one to the absolute value of the quotient and subtract the
 146    * remainder from @b@.
 147    */
 148
 149   q->f = (r->f | b->f) & MP_BURN;
 150   r->f = (r->f | b->f) & MP_BURN;
 151
 152   /* --- Store the return values --- */
 153
 154   MP_DROP(b);
 155
 156   if (!qq)
 157     MP_DROP(q);
 158   else {
 159     MP_SHRINK(q);
 160     *qq = q;
 161   }
 162
 163   if (!rr)
 164     MP_DROP(r);
 165   else {
 166     MP_SHRINK(r);
 167     *rr = r;
 168   }
 169 }
 170
 171 /* --- @gf_irreduciblep@ --- *
 172  *
 173  * Arguments:   @mp *f@ = a polynomial
 174  *
 175  * Returns:     Nonzero if the polynomial is irreducible; otherwise zero.
 176  */
 177
 178 int gf_irreduciblep(mp *f)
 179 {
 180   unsigned long m;
 181   mp *u = MP_TWO;
 182   mp *v = MP_NEW;
 183
 184   if (MP_ZEROP(f))
 185     return (0);
 186   else if (MP_LEN(f) == 1) {
 187     if (f->v[0] < 2) return (0);
 188     if (f->v[0] < 4) return (1);
 189   }
 190   m = (mp_bits(f) - 1)/2;
 191   while (m) {
 192     u = gf_sqr(u, u);
 193     gf_div(0, &u, u, f);
 194     v = gf_add(v, u, MP_TWO);
 195     gf_gcd(&v, 0, 0, v, f);
 196     if (!MP_EQ(v, MP_ONE)) break;
 197     m--;
 198   }
 199   MP_DROP(u);
 200   MP_DROP(v);
 201   return (!m);
 202 }
 203
 204 /*----- Test rig ----------------------------------------------------------*/
 205
 206 #ifdef TEST_RIG
 207
 208 static int verify(const char *op, mp *expect, mp *result, mp *a, mp *b)
 209 {
 210   if (!MP_EQ(expect, result)) {
 211     fprintf(stderr, "\n*** %s failed", op);
 212     fputs("\n*** a      = ", stderr); mp_writefile(a, stderr, 16);
 213     fputs("\n*** b      = ", stderr); mp_writefile(b, stderr, 16);
 214     fputs("\n*** result = ", stderr); mp_writefile(result, stderr, 16);
 215     fputs("\n*** expect = ", stderr); mp_writefile(expect, stderr, 16);
 216     fputc('\n', stderr);
 217     return (0);
 218   }
 219   return (1);
 220 }
 221
 222 #define RIG(name, op)                                                   \
 223   static int t##name(dstr *v)                                           \
 224   {                                                                     \
 225     mp *a = *(mp **)v[0].buf;                                           \
 226     mp *b = *(mp **)v[1].buf;                                           \
 227     mp *r = *(mp **)v[2].buf;                                           \
 228     mp *c = op(MP_NEW, a, b);                                           \
 229     int ok = verify(#name, r, c, a, b);                                 \
 230     mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r);                     \
 231     assert(mparena_count(MPARENA_GLOBAL) == 0);                         \
 232     return (ok);                                                        \
 233   }
 234
 235 RIG(add, gf_add)
 236 RIG(mul, gf_mul)
 237 RIG(exp, gf_exp)
 238
 239 #undef RIG
 240
 241 static int tsqr(dstr *v)
 242 {
 243   mp *a = *(mp **)v[0].buf;
 244   mp *r = *(mp **)v[1].buf;
 245   mp *c = MP_NEW;
 246   int ok = 1;
 247   c = gf_sqr(MP_NEW, a);
 248   ok &= verify("sqr", r, c, a, MP_ZERO);
 249   mp_drop(a); mp_drop(r); mp_drop(c);
 250   assert(mparena_count(MPARENA_GLOBAL) == 0);
 251   return (ok);
 252 }
 253
 254 static int tdiv(dstr *v)
 255 {
 256   mp *a = *(mp **)v[0].buf;
 257   mp *b = *(mp **)v[1].buf;
 258   mp *q = *(mp **)v[2].buf;
 259   mp *r = *(mp **)v[3].buf;
 260   mp *c = MP_NEW, *d = MP_NEW;
 261   int ok = 1;
 262   gf_div(&c, &d, a, b);
 263   ok &= verify("div(quotient)", q, c, a, b);
 264   ok &= verify("div(remainder)", r, d, a, b);
 265   mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(d); mp_drop(r); mp_drop(q);
 266   assert(mparena_count(MPARENA_GLOBAL) == 0);
 267   return (ok);
 268 }
 269
 270 static int tirred(dstr *v)
 271 {
 272   mp *a = *(mp **)v[0].buf;
 273   int r = *(int *)v[1].buf;
 274   int c = gf_irreduciblep(a);
 275   int ok = 1;
 276   if (r != c) {
 277     ok = 0;
 278     fprintf(stderr, "\n*** irred failed");
 279     fputs("\n*** a      = ", stderr); mp_writefile(a, stderr, 16);
 280     fprintf(stderr, "\n*** r      = %d\n", r);
 281     fprintf(stderr, "*** c      = %d\n", c);
 282   }
 283   mp_drop(a);
 284   assert(mparena_count(MPARENA_GLOBAL) == 0);
 285   return (ok);
 286 }
 287
 288 static test_chunk tests[] = {
 289   { "add", tadd, { &type_mp, &type_mp, &type_mp, 0 } },
 290   { "mul", tmul, { &type_mp, &type_mp, &type_mp, 0 } },
 291   { "sqr", tsqr, { &type_mp, &type_mp, 0 } },
 292   { "div", tdiv, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
 293   { "exp", texp, { &type_mp, &type_mp, &type_mp, 0 } },
 294   { "irred", tirred, { &type_mp, &type_int, 0 } },
 295   { 0, 0, { 0 } },
 296 };
 297
 298 int main(int argc, char *argv[])
 299 {
 300   sub_init();
 301   test_run(argc, argv, tests, SRCDIR "/t/gf");
 302   return (0);
 303 }
 304
 305 #endif
 306
 307 /*----- That's all, folks -------------------------------------------------*/