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

   1 /* -*-c-*-
   2  *
   3  * $Id$
   4  *
   5  * Euclidian algorithm 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 /*----- Main code ---------------------------------------------------------*/
  35
  36 /* --- @gf_gcd@ --- *
  37  *
  38  * Arguments:   @mp **gcd, **xx, **yy@ = where to write the results
  39  *              @mp *a, *b@ = sources (must be nonzero)
  40  *
  41  *
  42  * Returns:     ---
  43  *
  44  * Use:         Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that
  45  *              @ax + by = gcd(a, b)@.  This is useful for computing modular
  46  *              inverses.
  47  */
  48
  49 void gf_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b)
  50 {
  51   mp *x = MP_ONE, *X = MP_ZERO;
  52   mp *y = MP_ZERO, *Y = MP_ONE;
  53   mp *u, *v;
  54   mp *q = MP_NEW;
  55   unsigned f = 0;
  56
  57 #define f_swap 1u
  58 #define f_ext 2u
  59
  60   /* --- Sort out some initial flags --- */
  61
  62   if (xx || yy)
  63     f |= f_ext;
  64
  65   /* --- Ensure that @a@ is larger than @b@ --- *
  66    *
  67    * If they're the same length we don't care which order they're in, so this
  68    * unsigned comparison is fine.
  69    */
  70
  71   if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
  72     { mp *t = a; a = b; b = t; }
  73     f |= f_swap;
  74   }
  75
  76   /* --- Check for zeroness --- */
  77
  78   if (MP_EQ(b, MP_ZERO)) {
  79
  80     /* --- Store %$|a|$% as the GCD --- */
  81
  82     if (gcd) {
  83       if (*gcd) MP_DROP(*gcd);
  84       a = MP_COPY(a);
  85       *gcd = a;
  86     }
  87
  88     /* --- Store %$1$% and %$0$% in the appropriate bins --- */
  89
  90     if (f & f_ext) {
  91       if (f & f_swap) {
  92         mp **t = xx; xx = yy; yy = t;
  93       }
  94       if (xx) {
  95         if (*xx) MP_DROP(*xx);
  96         if (MP_EQ(a, MP_ZERO))
  97           *xx = MP_ZERO;
  98         else
  99           *xx = MP_ONE;
 100       }
 101       if (yy) {
 102         if (*yy) MP_DROP(*yy);
 103         *yy = MP_ZERO;
 104       }
 105     }
 106     return;
 107   }
 108
 109   /* --- Main extended Euclidean algorithm --- */
 110
 111   u = MP_COPY(a);
 112   v = MP_COPY(b);
 113
 114   while (!MP_ZEROP(v)) {
 115     mp *t;
 116     gf_div(&q, &u, u, v);
 117     if (f & f_ext) {
 118       t = gf_mul(MP_NEW, X, q);
 119       t = gf_add(t, t, x);
 120       MP_DROP(x); x = X; X = t;
 121       t = gf_mul(MP_NEW, Y, q);
 122       t = gf_add(t, t, y);
 123       MP_DROP(y); y = Y; Y = t;
 124     }
 125     t = u; u = v; v = t;
 126   }
 127
 128   MP_DROP(q);
 129   if (!gcd)
 130     MP_DROP(u);
 131   else {
 132     if (*gcd) MP_DROP(*gcd);
 133     u->f &= ~MP_NEG;
 134     *gcd = u;
 135   }
 136
 137   /* --- Perform a little normalization --- */
 138
 139   if (f & f_ext) {
 140
 141     /* --- If @a@ and @b@ got swapped, swap the coefficients back --- */
 142
 143     if (f & f_swap) {
 144       mp *t = x; x = y; y = t;
 145       t = a; a = b; b = t;
 146     }
 147
 148     /* --- Store the results --- */
 149
 150     if (!xx)
 151       MP_DROP(x);
 152     else {
 153       if (*xx) MP_DROP(*xx);
 154       *xx = x;
 155     }
 156
 157     if (!yy)
 158       MP_DROP(y);
 159     else {
 160       if (*yy) MP_DROP(*yy);
 161       *yy = y;
 162     }
 163   }
 164
 165   MP_DROP(v);
 166   MP_DROP(X); MP_DROP(Y);
 167 }
 168
 169 /* -- @gf_modinv@ --- *
 170  *
 171  * Arguments:   @mp *d@ = destination
 172  *              @mp *x@ = argument
 173  *              @mp *p@ = modulus
 174  *
 175  * Returns:     The inverse %$x^{-1} \bmod p$%.
 176  *
 177  * Use:         Computes a modular inverse, the catch being that the
 178  *              arguments and results are binary polynomials.  An assertion
 179  *              fails if %$p$% has no inverse.
 180  */
 181
 182 mp *gf_modinv(mp *d, mp *x, mp *p)
 183 {
 184   mp *g = MP_NEW;
 185   gf_gcd(&g, 0, &d, p, x);
 186   assert(MP_EQ(g, MP_ONE));
 187   mp_drop(g);
 188   return (d);
 189 }
 190
 191 /*----- Test rig ----------------------------------------------------------*/
 192
 193 #ifdef TEST_RIG
 194
 195 static int gcd(dstr *v)
 196 {
 197   int ok = 1;
 198   mp *a = *(mp **)v[0].buf;
 199   mp *b = *(mp **)v[1].buf;
 200   mp *g = *(mp **)v[2].buf;
 201   mp *x = *(mp **)v[3].buf;
 202   mp *y = *(mp **)v[4].buf;
 203
 204   mp *gg = MP_NEW, *xx = MP_NEW, *yy = MP_NEW;
 205   gf_gcd(&gg, &xx, &yy, a, b);
 206   if (!MP_EQ(x, xx)) {
 207     fputs("\n*** gf_gcd(x) failed", stderr);
 208     fputs("\na      = ", stderr); mp_writefile(a, stderr, 16);
 209     fputs("\nb      = ", stderr); mp_writefile(b, stderr, 16);
 210     fputs("\nexpect = ", stderr); mp_writefile(x, stderr, 16);
 211     fputs("\nresult = ", stderr); mp_writefile(xx, stderr, 16);
 212     fputc('\n', stderr);
 213     ok = 0;
 214   }
 215   if (!MP_EQ(y, yy)) {
 216     fputs("\n*** gf_gcd(y) failed", stderr);
 217     fputs("\na      = ", stderr); mp_writefile(a, stderr, 16);
 218     fputs("\nb      = ", stderr); mp_writefile(b, stderr, 16);
 219     fputs("\nexpect = ", stderr); mp_writefile(y, stderr, 16);
 220     fputs("\nresult = ", stderr); mp_writefile(yy, stderr, 16);
 221     fputc('\n', stderr);
 222     ok = 0;
 223   }
 224
 225   if (!ok) {
 226     mp *ax = gf_mul(MP_NEW, a, xx);
 227     mp *by = gf_mul(MP_NEW, b, yy);
 228     ax = gf_add(ax, ax, by);
 229     if (MP_EQ(ax, gg))
 230       fputs("\n*** (Alternative result found.)\n", stderr);
 231     MP_DROP(ax);
 232     MP_DROP(by);
 233   }
 234
 235   if (!MP_EQ(g, gg)) {
 236     fputs("\n*** gf_gcd(gcd) failed", stderr);
 237     fputs("\na      = ", stderr); mp_writefile(a, stderr, 16);
 238     fputs("\nb      = ", stderr); mp_writefile(b, stderr, 16);
 239     fputs("\nexpect = ", stderr); mp_writefile(g, stderr, 16);
 240     fputs("\nresult = ", stderr); mp_writefile(gg, stderr, 16);
 241     fputc('\n', stderr);
 242     ok = 0;
 243   }
 244   MP_DROP(a); MP_DROP(b); MP_DROP(g); MP_DROP(x); MP_DROP(y);
 245   MP_DROP(gg); MP_DROP(xx); MP_DROP(yy);
 246   assert(mparena_count(MPARENA_GLOBAL) == 0);
 247   return (ok);
 248 }
 249
 250 static test_chunk tests[] = {
 251   { "gcd", gcd, { &type_mp, &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
 252   { 0, 0, { 0 } }
 253 };
 254
 255 int main(int argc, char *argv[])
 256 {
 257   sub_init();
 258   test_run(argc, argv, tests, SRCDIR "/tests/gf");
 259   return (0);
 260 }
 261
 262 #endif
 263
 264 /*----- That's all, folks -------------------------------------------------*/