/*****************************
* Copyright Henry Minsky (hqm@alum.mit.edu) 1991-2009
*
* This software library is licensed under terms of the GNU GENERAL
* PUBLIC LICENSE
*
* RSCODE is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* RSCODE is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with Rscode. If not, see .
* Commercial licensing is available under a separate license, please
* contact author for details.
*
* Source code is available at http://rscode.sourceforge.net
*
*
* Multiplication and Arithmetic on Galois Field GF(256)
*
* From Mee, Daniel, "Magnetic Recording, Volume III", Ch. 5 by Patel.
*
*
******************************/
#include
#include
#include "ecc.h"
/* This is one of 14 irreducible polynomials
* of degree 8 and cycle length 255. (Ch 5, pp. 275, Magnetic Recording)
* The high order 1 bit is implicit */
/* x^8 + x^4 + x^3 + x^2 + 1 */
#define PPOLY 0x1D
const int gexp[512] = {
1, 2, 4, 8, 16, 32, 64, 128, 29, 58, 116, 232, 205, 135, 19, 38,
76, 152, 45, 90, 180, 117, 234, 201, 143, 3, 6, 12, 24, 48, 96, 192,
157, 39, 78, 156, 37, 74, 148, 53, 106, 212, 181, 119, 238, 193, 159, 35,
70, 140, 5, 10, 20, 40, 80, 160, 93, 186, 105, 210, 185, 111, 222, 161,
95, 190, 97, 194, 153, 47, 94, 188, 101, 202, 137, 15, 30, 60, 120, 240,
253, 231, 211, 187, 107, 214, 177, 127, 254, 225, 223, 163, 91, 182, 113, 226,
217, 175, 67, 134, 17, 34, 68, 136, 13, 26, 52, 104, 208, 189, 103, 206,
129, 31, 62, 124, 248, 237, 199, 147, 59, 118, 236, 197, 151, 51, 102, 204,
133, 23, 46, 92, 184, 109, 218, 169, 79, 158, 33, 66, 132, 21, 42, 84,
168, 77, 154, 41, 82, 164, 85, 170, 73, 146, 57, 114, 228, 213, 183, 115,
230, 209, 191, 99, 198, 145, 63, 126, 252, 229, 215, 179, 123, 246, 241, 255,
227, 219, 171, 75, 150, 49, 98, 196, 149, 55, 110, 220, 165, 87, 174, 65,
130, 25, 50, 100, 200, 141, 7, 14, 28, 56, 112, 224, 221, 167, 83, 166,
81, 162, 89, 178, 121, 242, 249, 239, 195, 155, 43, 86, 172, 69, 138, 9,
18, 36, 72, 144, 61, 122, 244, 245, 247, 243, 251, 235, 203, 139, 11, 22,
44, 88, 176, 125, 250, 233, 207, 131, 27, 54, 108, 216, 173, 71, 142, 1,
2, 4, 8, 16, 32, 64, 128, 29, 58, 116, 232, 205, 135, 19, 38, 76,
152, 45, 90, 180, 117, 234, 201, 143, 3, 6, 12, 24, 48, 96, 192, 157,
39, 78, 156, 37, 74, 148, 53, 106, 212, 181, 119, 238, 193, 159, 35, 70,
140, 5, 10, 20, 40, 80, 160, 93, 186, 105, 210, 185, 111, 222, 161, 95,
190, 97, 194, 153, 47, 94, 188, 101, 202, 137, 15, 30, 60, 120, 240, 253,
231, 211, 187, 107, 214, 177, 127, 254, 225, 223, 163, 91, 182, 113, 226, 217,
175, 67, 134, 17, 34, 68, 136, 13, 26, 52, 104, 208, 189, 103, 206, 129,
31, 62, 124, 248, 237, 199, 147, 59, 118, 236, 197, 151, 51, 102, 204, 133,
23, 46, 92, 184, 109, 218, 169, 79, 158, 33, 66, 132, 21, 42, 84, 168,
77, 154, 41, 82, 164, 85, 170, 73, 146, 57, 114, 228, 213, 183, 115, 230,
209, 191, 99, 198, 145, 63, 126, 252, 229, 215, 179, 123, 246, 241, 255, 227,
219, 171, 75, 150, 49, 98, 196, 149, 55, 110, 220, 165, 87, 174, 65, 130,
25, 50, 100, 200, 141, 7, 14, 28, 56, 112, 224, 221, 167, 83, 166, 81,
162, 89, 178, 121, 242, 249, 239, 195, 155, 43, 86, 172, 69, 138, 9, 18,
36, 72, 144, 61, 122, 244, 245, 247, 243, 251, 235, 203, 139, 11, 22, 44,
88, 176, 125, 250, 233, 207, 131, 27, 54, 108, 216, 173, 71, 142, 1, 0,
};
const int glog[256] = {
0, 0, 1, 25, 2, 50, 26, 198, 3, 223, 51, 238, 27, 104, 199, 75,
4, 100, 224, 14, 52, 141, 239, 129, 28, 193, 105, 248, 200, 8, 76, 113,
5, 138, 101, 47, 225, 36, 15, 33, 53, 147, 142, 218, 240, 18, 130, 69,
29, 181, 194, 125, 106, 39, 249, 185, 201, 154, 9, 120, 77, 228, 114, 166,
6, 191, 139, 98, 102, 221, 48, 253, 226, 152, 37, 179, 16, 145, 34, 136,
54, 208, 148, 206, 143, 150, 219, 189, 241, 210, 19, 92, 131, 56, 70, 64,
30, 66, 182, 163, 195, 72, 126, 110, 107, 58, 40, 84, 250, 133, 186, 61,
202, 94, 155, 159, 10, 21, 121, 43, 78, 212, 229, 172, 115, 243, 167, 87,
7, 112, 192, 247, 140, 128, 99, 13, 103, 74, 222, 237, 49, 197, 254, 24,
227, 165, 153, 119, 38, 184, 180, 124, 17, 68, 146, 217, 35, 32, 137, 46,
55, 63, 209, 91, 149, 188, 207, 205, 144, 135, 151, 178, 220, 252, 190, 97,
242, 86, 211, 171, 20, 42, 93, 158, 132, 60, 57, 83, 71, 109, 65, 162,
31, 45, 67, 216, 183, 123, 164, 118, 196, 23, 73, 236, 127, 12, 111, 246,
108, 161, 59, 82, 41, 157, 85, 170, 251, 96, 134, 177, 187, 204, 62, 90,
203, 89, 95, 176, 156, 169, 160, 81, 11, 245, 22, 235, 122, 117, 44, 215,
79, 174, 213, 233, 230, 231, 173, 232, 116, 214, 244, 234, 168, 80, 88, 175,
};
//static void init_exp_table (void);
void
init_galois_tables (void)
{
/* initialize the table of powers of alpha */
//init_exp_table();
}
#ifdef NEVER
static void
init_exp_table (void)
{
int i, z;
int pinit,p1,p2,p3,p4,p5,p6,p7,p8;
pinit = p2 = p3 = p4 = p5 = p6 = p7 = p8 = 0;
p1 = 1;
gexp[0] = 1;
gexp[255] = gexp[0];
glog[0] = 0; /* shouldn't log[0] be an error? */
for (i = 1; i < 256; i++) {
pinit = p8;
p8 = p7;
p7 = p6;
p6 = p5;
p5 = p4 ^ pinit;
p4 = p3 ^ pinit;
p3 = p2 ^ pinit;
p2 = p1;
p1 = pinit;
gexp[i] = p1 + p2*2 + p3*4 + p4*8 + p5*16 + p6*32 + p7*64 + p8*128;
gexp[i+255] = gexp[i];
}
for (i = 1; i < 256; i++) {
for (z = 0; z < 256; z++) {
if (gexp[z] == i) {
glog[i] = z;
break;
}
}
}
}
#endif
/* multiplication using logarithms */
int gmult(int a, int b)
{
int i,j;
if (a==0 || b == 0) return (0);
i = glog[a];
j = glog[b];
return (gexp[i+j]);
}
int ginv (int elt)
{
return (gexp[255-glog[elt]]);
}