git.distorted.org.uk Git - u/mdw/catacomb/blob - calc/gfx.cal

   1 /* -*-apcalc-*-
   2  *
   3  * $Id: gfx.cal,v 1.1.4.1 2004/03/21 22:39:46 mdw Exp $
   4  *
   5  * Testbed for %$\gf{2}$% poltnomial arithmetic
   6  *
   7  * (c) 2000 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: gfx.cal,v $
  33  * Revision 1.1.4.1  2004/03/21 22:39:46  mdw
  34  * Elliptic curves on binary fields work.
  35  *
  36  * Revision 1.1  2000/10/08 16:01:37  mdw
  37  * Prototypes of various bits of code.
  38  *
  39  */
  40
  41 /*----- Object types ------------------------------------------------------*/
  42
  43 obj gf { x };
  44
  45 /*----- Static variables --------------------------------------------------*/
  46
  47 static obj gf example_gf_object;
  48
  49 /*----- Main code ---------------------------------------------------------*/
  50
  51 dummy = config("lib_debug", -1);
  52
  53 define gf(x)
  54 {
  55   local obj gf g;
  56   g.x = x;
  57   return (g);
  58 }
  59
  60 define gfint(x)
  61 {
  62   if (istype(x, example_gf_object))
  63     return (x.x);
  64   else
  65     return (x);
  66 }
  67
  68 define gf_add(x, y) = gf(xor(gfint(x), gfint(y)));
  69 define gf_sub(x, y) = gf(xor(gfint(x), gfint(y)));
  70 define gf_neg(x) = x;
  71
  72 define gf_mul(x, y)
  73 {
  74   local a = gfint(x), b = gfint(y), z = 0, i, bits = highbit(a);
  75   for (i = 0; i <= bits; i++) {
  76     if (bit(a, i))
  77       z = xor(z, b << i);
  78   }
  79   return gf(z);
  80 }
  81
  82 define gfx_div(rx, dx)
  83 {
  84   local r = gfint(rx), d = gfint(dx), i;
  85   local q = 0, dbits, rbits;
  86   dbits = highbit(d);
  87   rbits = highbit(r);
  88   for (i = rbits - dbits; i >= 0; i--) {
  89     if (bit(r, i + dbits)) {
  90       r = xor(r, d << i);
  91       q |= (1 << i);
  92     }
  93   }
  94   return list(q, r);
  95 }
  96
  97 define gf_div(x, y)
  98 {
  99   local l;
 100   l = gfx_div(x, y);
 101   return gf(l[[0]]);
 102 }
 103
 104 define gf_mod(x, y)
 105 {
 106   local l;
 107   l = gfx_div(x, y);
 108   return gf(l[[1]]);
 109 }
 110
 111 define gf_inv(a, b)
 112 {
 113   local g, x, y, X, Y, u, v, t, q, r;
 114   x = gf(1); X = gf(0);
 115   y = gf(0); Y = gf(1);
 116
 117   if (b == gf(0)) { g = a; } else if (a == gf(0)) { g = b; }
 118   else {
 119     while (b != gf(0)) {
 120       q = gf_div(b, a); r = gf_mod(b, a);
 121       t = X * q + x; x = X; X = t;
 122       t = Y * q + y; y = Y; Y = t;
 123       b = a; a = r;
 124     }
 125     g = a;
 126   }
 127   if (g != gf(1)) quit "not coprime in gf_inv";
 128   return Y;
 129 }
 130
 131 /*----- That's all, folks -------------------------------------------------*/