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1 | /* -*-apcalc-*- |
2 | * |
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3 | * $Id: gfx.cal,v 1.3 2004/04/08 01:36:15 mdw Exp $ |
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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 | |
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30 | /*----- Object types ------------------------------------------------------*/ |
31 | |
32 | obj gf { x }; |
33 | |
34 | /*----- Static variables --------------------------------------------------*/ |
35 | |
36 | static obj gf example_gf_object; |
37 | |
38 | /*----- Main code ---------------------------------------------------------*/ |
39 | |
40 | dummy = config("lib_debug", -1); |
41 | |
42 | define gf(x) |
43 | { |
44 | local obj gf g; |
45 | g.x = x; |
46 | return (g); |
47 | } |
48 | |
49 | define gfint(x) |
50 | { |
51 | if (istype(x, example_gf_object)) |
52 | return (x.x); |
53 | else |
54 | return (x); |
55 | } |
56 | |
57 | define gf_add(x, y) = gf(xor(gfint(x), gfint(y))); |
58 | define gf_sub(x, y) = gf(xor(gfint(x), gfint(y))); |
59 | define gf_neg(x) = x; |
60 | |
61 | define gf_mul(x, y) |
62 | { |
63 | local a = gfint(x), b = gfint(y), z = 0, i, bits = highbit(a); |
64 | for (i = 0; i <= bits; i++) { |
65 | if (bit(a, i)) |
66 | z = xor(z, b << i); |
67 | } |
68 | return gf(z); |
69 | } |
70 | |
71 | define gfx_div(rx, dx) |
72 | { |
73 | local r = gfint(rx), d = gfint(dx), i; |
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74 | local q = 0, dbits, rbits; |
75 | dbits = highbit(d); |
76 | rbits = highbit(r); |
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77 | for (i = rbits - dbits; i >= 0; i--) { |
78 | if (bit(r, i + dbits)) { |
79 | r = xor(r, d << i); |
80 | q |= (1 << i); |
81 | } |
82 | } |
83 | return list(q, r); |
84 | } |
85 | |
86 | define gf_div(x, y) |
87 | { |
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88 | local l; |
89 | l = gfx_div(x, y); |
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90 | return gf(l[[0]]); |
91 | } |
92 | |
93 | define gf_mod(x, y) |
94 | { |
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95 | local l; |
96 | l = gfx_div(x, y); |
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97 | return gf(l[[1]]); |
98 | } |
99 | |
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100 | define gf_inv(a, b) |
101 | { |
102 | local g, x, y, X, Y, u, v, t, q, r; |
103 | x = gf(1); X = gf(0); |
104 | y = gf(0); Y = gf(1); |
105 | |
106 | if (b == gf(0)) { g = a; } else if (a == gf(0)) { g = b; } |
107 | else { |
108 | while (b != gf(0)) { |
109 | q = gf_div(b, a); r = gf_mod(b, a); |
110 | t = X * q + x; x = X; X = t; |
111 | t = Y * q + y; y = Y; Y = t; |
112 | b = a; a = r; |
113 | } |
114 | g = a; |
115 | } |
116 | if (g != gf(1)) quit "not coprime in gf_inv"; |
117 | return Y; |
118 | } |
119 | |
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120 | /*----- That's all, folks -------------------------------------------------*/ |