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1.1 root 1: /* Previous - rs.c
2:
3: This file is distributed under the GNU Public License, version 2 or at
4: your option any later version. Read the file gpl.txt for details.
5:
6: NeXT magento-optical drive controller uses cross interleaved Reed-Solomon-Codes
7: for error correction. This implementation has been written by Olivier Galibert.
8: The original code was adapted to work with Previous.
9:
10: */
11:
12: #include <string.h>
13:
14: #include "main.h"
15: #include "rs.h"
16:
17:
18: /* Reed-Solomon(36,32) in GF(2**8), generator polynomial (x-1)*(x-2)*(x-4)*(x-8)
19: GF's polynom is the usual 11d
20: */
21:
22: /* Partial remainders, e.g. t_rem[i] = (i*x^4) % ((x-1)*(x-2)*(x-4)*(x-8)) */
23: const Uint32 t_rem[256] = {
24: 0x00000000, 0x0f367840, 0x1e6cf080, 0x115a88c0, 0x3cd8fd1d, 0x33ee855d, 0x22b40d9d, 0x2d8275dd,
25: 0x78ade73a, 0x779b9f7a, 0x66c117ba, 0x69f76ffa, 0x44751a27, 0x4b436267, 0x5a19eaa7, 0x552f92e7,
26: 0xf047d374, 0xff71ab34, 0xee2b23f4, 0xe11d5bb4, 0xcc9f2e69, 0xc3a95629, 0xd2f3dee9, 0xddc5a6a9,
27: 0x88ea344e, 0x87dc4c0e, 0x9686c4ce, 0x99b0bc8e, 0xb432c953, 0xbb04b113, 0xaa5e39d3, 0xa5684193,
28: 0xfd8ebbe8, 0xf2b8c3a8, 0xe3e24b68, 0xecd43328, 0xc15646f5, 0xce603eb5, 0xdf3ab675, 0xd00cce35,
29: 0x85235cd2, 0x8a152492, 0x9b4fac52, 0x9479d412, 0xb9fba1cf, 0xb6cdd98f, 0xa797514f, 0xa8a1290f,
30: 0x0dc9689c, 0x02ff10dc, 0x13a5981c, 0x1c93e05c, 0x31119581, 0x3e27edc1, 0x2f7d6501, 0x204b1d41,
31: 0x75648fa6, 0x7a52f7e6, 0x6b087f26, 0x643e0766, 0x49bc72bb, 0x468a0afb, 0x57d0823b, 0x58e6fa7b,
32: 0xe7016bcd, 0xe837138d, 0xf96d9b4d, 0xf65be30d, 0xdbd996d0, 0xd4efee90, 0xc5b56650, 0xca831e10,
33: 0x9fac8cf7, 0x909af4b7, 0x81c07c77, 0x8ef60437, 0xa37471ea, 0xac4209aa, 0xbd18816a, 0xb22ef92a,
34: 0x1746b8b9, 0x1870c0f9, 0x092a4839, 0x061c3079, 0x2b9e45a4, 0x24a83de4, 0x35f2b524, 0x3ac4cd64,
35: 0x6feb5f83, 0x60dd27c3, 0x7187af03, 0x7eb1d743, 0x5333a29e, 0x5c05dade, 0x4d5f521e, 0x42692a5e,
36: 0x1a8fd025, 0x15b9a865, 0x04e320a5, 0x0bd558e5, 0x26572d38, 0x29615578, 0x383bddb8, 0x370da5f8,
37: 0x6222371f, 0x6d144f5f, 0x7c4ec79f, 0x7378bfdf, 0x5efaca02, 0x51ccb242, 0x40963a82, 0x4fa042c2,
38: 0xeac80351, 0xe5fe7b11, 0xf4a4f3d1, 0xfb928b91, 0xd610fe4c, 0xd926860c, 0xc87c0ecc, 0xc74a768c,
39: 0x9265e46b, 0x9d539c2b, 0x8c0914eb, 0x833f6cab, 0xaebd1976, 0xa18b6136, 0xb0d1e9f6, 0xbfe791b6,
40: 0xd302d687, 0xdc34aec7, 0xcd6e2607, 0xc2585e47, 0xefda2b9a, 0xe0ec53da, 0xf1b6db1a, 0xfe80a35a,
41: 0xabaf31bd, 0xa49949fd, 0xb5c3c13d, 0xbaf5b97d, 0x9777cca0, 0x9841b4e0, 0x891b3c20, 0x862d4460,
42: 0x234505f3, 0x2c737db3, 0x3d29f573, 0x321f8d33, 0x1f9df8ee, 0x10ab80ae, 0x01f1086e, 0x0ec7702e,
43: 0x5be8e2c9, 0x54de9a89, 0x45841249, 0x4ab26a09, 0x67301fd4, 0x68066794, 0x795cef54, 0x766a9714,
44: 0x2e8c6d6f, 0x21ba152f, 0x30e09def, 0x3fd6e5af, 0x12549072, 0x1d62e832, 0x0c3860f2, 0x030e18b2,
45: 0x56218a55, 0x5917f215, 0x484d7ad5, 0x477b0295, 0x6af97748, 0x65cf0f08, 0x749587c8, 0x7ba3ff88,
46: 0xdecbbe1b, 0xd1fdc65b, 0xc0a74e9b, 0xcf9136db, 0xe2134306, 0xed253b46, 0xfc7fb386, 0xf349cbc6,
47: 0xa6665921, 0xa9502161, 0xb80aa9a1, 0xb73cd1e1, 0x9abea43c, 0x9588dc7c, 0x84d254bc, 0x8be42cfc,
48: 0x3403bd4a, 0x3b35c50a, 0x2a6f4dca, 0x2559358a, 0x08db4057, 0x07ed3817, 0x16b7b0d7, 0x1981c897,
49: 0x4cae5a70, 0x43982230, 0x52c2aaf0, 0x5df4d2b0, 0x7076a76d, 0x7f40df2d, 0x6e1a57ed, 0x612c2fad,
50: 0xc4446e3e, 0xcb72167e, 0xda289ebe, 0xd51ee6fe, 0xf89c9323, 0xf7aaeb63, 0xe6f063a3, 0xe9c61be3,
51: 0xbce98904, 0xb3dff144, 0xa2857984, 0xadb301c4, 0x80317419, 0x8f070c59, 0x9e5d8499, 0x916bfcd9,
52: 0xc98d06a2, 0xc6bb7ee2, 0xd7e1f622, 0xd8d78e62, 0xf555fbbf, 0xfa6383ff, 0xeb390b3f, 0xe40f737f,
53: 0xb120e198, 0xbe1699d8, 0xaf4c1118, 0xa07a6958, 0x8df81c85, 0x82ce64c5, 0x9394ec05, 0x9ca29445,
54: 0x39cad5d6, 0x36fcad96, 0x27a62556, 0x28905d16, 0x051228cb, 0x0a24508b, 0x1b7ed84b, 0x1448a00b,
55: 0x416732ec, 0x4e514aac, 0x5f0bc26c, 0x503dba2c, 0x7dbfcff1, 0x7289b7b1, 0x63d33f71, 0x6ce54731,
56: };
57:
58: const Uint8 t_exp[768] = {
59: 0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80, 0x1d, 0x3a, 0x74, 0xe8, 0xcd, 0x87, 0x13, 0x26,
60: 0x4c, 0x98, 0x2d, 0x5a, 0xb4, 0x75, 0xea, 0xc9, 0x8f, 0x03, 0x06, 0x0c, 0x18, 0x30, 0x60, 0xc0,
61: 0x9d, 0x27, 0x4e, 0x9c, 0x25, 0x4a, 0x94, 0x35, 0x6a, 0xd4, 0xb5, 0x77, 0xee, 0xc1, 0x9f, 0x23,
62: 0x46, 0x8c, 0x05, 0x0a, 0x14, 0x28, 0x50, 0xa0, 0x5d, 0xba, 0x69, 0xd2, 0xb9, 0x6f, 0xde, 0xa1,
63: 0x5f, 0xbe, 0x61, 0xc2, 0x99, 0x2f, 0x5e, 0xbc, 0x65, 0xca, 0x89, 0x0f, 0x1e, 0x3c, 0x78, 0xf0,
64: 0xfd, 0xe7, 0xd3, 0xbb, 0x6b, 0xd6, 0xb1, 0x7f, 0xfe, 0xe1, 0xdf, 0xa3, 0x5b, 0xb6, 0x71, 0xe2,
65: 0xd9, 0xaf, 0x43, 0x86, 0x11, 0x22, 0x44, 0x88, 0x0d, 0x1a, 0x34, 0x68, 0xd0, 0xbd, 0x67, 0xce,
66: 0x81, 0x1f, 0x3e, 0x7c, 0xf8, 0xed, 0xc7, 0x93, 0x3b, 0x76, 0xec, 0xc5, 0x97, 0x33, 0x66, 0xcc,
67: 0x85, 0x17, 0x2e, 0x5c, 0xb8, 0x6d, 0xda, 0xa9, 0x4f, 0x9e, 0x21, 0x42, 0x84, 0x15, 0x2a, 0x54,
68: 0xa8, 0x4d, 0x9a, 0x29, 0x52, 0xa4, 0x55, 0xaa, 0x49, 0x92, 0x39, 0x72, 0xe4, 0xd5, 0xb7, 0x73,
69: 0xe6, 0xd1, 0xbf, 0x63, 0xc6, 0x91, 0x3f, 0x7e, 0xfc, 0xe5, 0xd7, 0xb3, 0x7b, 0xf6, 0xf1, 0xff,
70: 0xe3, 0xdb, 0xab, 0x4b, 0x96, 0x31, 0x62, 0xc4, 0x95, 0x37, 0x6e, 0xdc, 0xa5, 0x57, 0xae, 0x41,
71: 0x82, 0x19, 0x32, 0x64, 0xc8, 0x8d, 0x07, 0x0e, 0x1c, 0x38, 0x70, 0xe0, 0xdd, 0xa7, 0x53, 0xa6,
72: 0x51, 0xa2, 0x59, 0xb2, 0x79, 0xf2, 0xf9, 0xef, 0xc3, 0x9b, 0x2b, 0x56, 0xac, 0x45, 0x8a, 0x09,
73: 0x12, 0x24, 0x48, 0x90, 0x3d, 0x7a, 0xf4, 0xf5, 0xf7, 0xf3, 0xfb, 0xeb, 0xcb, 0x8b, 0x0b, 0x16,
74: 0x2c, 0x58, 0xb0, 0x7d, 0xfa, 0xe9, 0xcf, 0x83, 0x1b, 0x36, 0x6c, 0xd8, 0xad, 0x47, 0x8e, 0x01,
75: 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80, 0x1d, 0x3a, 0x74, 0xe8, 0xcd, 0x87, 0x13, 0x26, 0x4c,
76: 0x98, 0x2d, 0x5a, 0xb4, 0x75, 0xea, 0xc9, 0x8f, 0x03, 0x06, 0x0c, 0x18, 0x30, 0x60, 0xc0, 0x9d,
77: 0x27, 0x4e, 0x9c, 0x25, 0x4a, 0x94, 0x35, 0x6a, 0xd4, 0xb5, 0x77, 0xee, 0xc1, 0x9f, 0x23, 0x46,
78: 0x8c, 0x05, 0x0a, 0x14, 0x28, 0x50, 0xa0, 0x5d, 0xba, 0x69, 0xd2, 0xb9, 0x6f, 0xde, 0xa1, 0x5f,
79: 0xbe, 0x61, 0xc2, 0x99, 0x2f, 0x5e, 0xbc, 0x65, 0xca, 0x89, 0x0f, 0x1e, 0x3c, 0x78, 0xf0, 0xfd,
80: 0xe7, 0xd3, 0xbb, 0x6b, 0xd6, 0xb1, 0x7f, 0xfe, 0xe1, 0xdf, 0xa3, 0x5b, 0xb6, 0x71, 0xe2, 0xd9,
81: 0xaf, 0x43, 0x86, 0x11, 0x22, 0x44, 0x88, 0x0d, 0x1a, 0x34, 0x68, 0xd0, 0xbd, 0x67, 0xce, 0x81,
82: 0x1f, 0x3e, 0x7c, 0xf8, 0xed, 0xc7, 0x93, 0x3b, 0x76, 0xec, 0xc5, 0x97, 0x33, 0x66, 0xcc, 0x85,
83: 0x17, 0x2e, 0x5c, 0xb8, 0x6d, 0xda, 0xa9, 0x4f, 0x9e, 0x21, 0x42, 0x84, 0x15, 0x2a, 0x54, 0xa8,
84: 0x4d, 0x9a, 0x29, 0x52, 0xa4, 0x55, 0xaa, 0x49, 0x92, 0x39, 0x72, 0xe4, 0xd5, 0xb7, 0x73, 0xe6,
85: 0xd1, 0xbf, 0x63, 0xc6, 0x91, 0x3f, 0x7e, 0xfc, 0xe5, 0xd7, 0xb3, 0x7b, 0xf6, 0xf1, 0xff, 0xe3,
86: 0xdb, 0xab, 0x4b, 0x96, 0x31, 0x62, 0xc4, 0x95, 0x37, 0x6e, 0xdc, 0xa5, 0x57, 0xae, 0x41, 0x82,
87: 0x19, 0x32, 0x64, 0xc8, 0x8d, 0x07, 0x0e, 0x1c, 0x38, 0x70, 0xe0, 0xdd, 0xa7, 0x53, 0xa6, 0x51,
88: 0xa2, 0x59, 0xb2, 0x79, 0xf2, 0xf9, 0xef, 0xc3, 0x9b, 0x2b, 0x56, 0xac, 0x45, 0x8a, 0x09, 0x12,
89: 0x24, 0x48, 0x90, 0x3d, 0x7a, 0xf4, 0xf5, 0xf7, 0xf3, 0xfb, 0xeb, 0xcb, 0x8b, 0x0b, 0x16, 0x2c,
90: 0x58, 0xb0, 0x7d, 0xfa, 0xe9, 0xcf, 0x83, 0x1b, 0x36, 0x6c, 0xd8, 0xad, 0x47, 0x8e, 0x01, 0x02,
91: 0x04, 0x08, 0x10, 0x20, 0x40, 0x80, 0x1d, 0x3a, 0x74, 0xe8, 0xcd, 0x87, 0x13, 0x26, 0x4c, 0x98,
92: 0x2d, 0x5a, 0xb4, 0x75, 0xea, 0xc9, 0x8f, 0x03, 0x06, 0x0c, 0x18, 0x30, 0x60, 0xc0, 0x9d, 0x27,
93: 0x4e, 0x9c, 0x25, 0x4a, 0x94, 0x35, 0x6a, 0xd4, 0xb5, 0x77, 0xee, 0xc1, 0x9f, 0x23, 0x46, 0x8c,
94: 0x05, 0x0a, 0x14, 0x28, 0x50, 0xa0, 0x5d, 0xba, 0x69, 0xd2, 0xb9, 0x6f, 0xde, 0xa1, 0x5f, 0xbe,
95: 0x61, 0xc2, 0x99, 0x2f, 0x5e, 0xbc, 0x65, 0xca, 0x89, 0x0f, 0x1e, 0x3c, 0x78, 0xf0, 0xfd, 0xe7,
96: 0xd3, 0xbb, 0x6b, 0xd6, 0xb1, 0x7f, 0xfe, 0xe1, 0xdf, 0xa3, 0x5b, 0xb6, 0x71, 0xe2, 0xd9, 0xaf,
97: 0x43, 0x86, 0x11, 0x22, 0x44, 0x88, 0x0d, 0x1a, 0x34, 0x68, 0xd0, 0xbd, 0x67, 0xce, 0x81, 0x1f,
98: 0x3e, 0x7c, 0xf8, 0xed, 0xc7, 0x93, 0x3b, 0x76, 0xec, 0xc5, 0x97, 0x33, 0x66, 0xcc, 0x85, 0x17,
99: 0x2e, 0x5c, 0xb8, 0x6d, 0xda, 0xa9, 0x4f, 0x9e, 0x21, 0x42, 0x84, 0x15, 0x2a, 0x54, 0xa8, 0x4d,
100: 0x9a, 0x29, 0x52, 0xa4, 0x55, 0xaa, 0x49, 0x92, 0x39, 0x72, 0xe4, 0xd5, 0xb7, 0x73, 0xe6, 0xd1,
101: 0xbf, 0x63, 0xc6, 0x91, 0x3f, 0x7e, 0xfc, 0xe5, 0xd7, 0xb3, 0x7b, 0xf6, 0xf1, 0xff, 0xe3, 0xdb,
102: 0xab, 0x4b, 0x96, 0x31, 0x62, 0xc4, 0x95, 0x37, 0x6e, 0xdc, 0xa5, 0x57, 0xae, 0x41, 0x82, 0x19,
103: 0x32, 0x64, 0xc8, 0x8d, 0x07, 0x0e, 0x1c, 0x38, 0x70, 0xe0, 0xdd, 0xa7, 0x53, 0xa6, 0x51, 0xa2,
104: 0x59, 0xb2, 0x79, 0xf2, 0xf9, 0xef, 0xc3, 0x9b, 0x2b, 0x56, 0xac, 0x45, 0x8a, 0x09, 0x12, 0x24,
105: 0x48, 0x90, 0x3d, 0x7a, 0xf4, 0xf5, 0xf7, 0xf3, 0xfb, 0xeb, 0xcb, 0x8b, 0x0b, 0x16, 0x2c, 0x58,
106: 0xb0, 0x7d, 0xfa, 0xe9, 0xcf, 0x83, 0x1b, 0x36, 0x6c, 0xd8, 0xad, 0x47, 0x8e, 0x01, 0x02, 0x04,
107: };
108:
109: const Uint8 t_log[256] = {
110: 0x00, 0x00, 0x01, 0x19, 0x02, 0x32, 0x1a, 0xc6, 0x03, 0xdf, 0x33, 0xee, 0x1b, 0x68, 0xc7, 0x4b,
111: 0x04, 0x64, 0xe0, 0x0e, 0x34, 0x8d, 0xef, 0x81, 0x1c, 0xc1, 0x69, 0xf8, 0xc8, 0x08, 0x4c, 0x71,
112: 0x05, 0x8a, 0x65, 0x2f, 0xe1, 0x24, 0x0f, 0x21, 0x35, 0x93, 0x8e, 0xda, 0xf0, 0x12, 0x82, 0x45,
113: 0x1d, 0xb5, 0xc2, 0x7d, 0x6a, 0x27, 0xf9, 0xb9, 0xc9, 0x9a, 0x09, 0x78, 0x4d, 0xe4, 0x72, 0xa6,
114: 0x06, 0xbf, 0x8b, 0x62, 0x66, 0xdd, 0x30, 0xfd, 0xe2, 0x98, 0x25, 0xb3, 0x10, 0x91, 0x22, 0x88,
115: 0x36, 0xd0, 0x94, 0xce, 0x8f, 0x96, 0xdb, 0xbd, 0xf1, 0xd2, 0x13, 0x5c, 0x83, 0x38, 0x46, 0x40,
116: 0x1e, 0x42, 0xb6, 0xa3, 0xc3, 0x48, 0x7e, 0x6e, 0x6b, 0x3a, 0x28, 0x54, 0xfa, 0x85, 0xba, 0x3d,
117: 0xca, 0x5e, 0x9b, 0x9f, 0x0a, 0x15, 0x79, 0x2b, 0x4e, 0xd4, 0xe5, 0xac, 0x73, 0xf3, 0xa7, 0x57,
118: 0x07, 0x70, 0xc0, 0xf7, 0x8c, 0x80, 0x63, 0x0d, 0x67, 0x4a, 0xde, 0xed, 0x31, 0xc5, 0xfe, 0x18,
119: 0xe3, 0xa5, 0x99, 0x77, 0x26, 0xb8, 0xb4, 0x7c, 0x11, 0x44, 0x92, 0xd9, 0x23, 0x20, 0x89, 0x2e,
120: 0x37, 0x3f, 0xd1, 0x5b, 0x95, 0xbc, 0xcf, 0xcd, 0x90, 0x87, 0x97, 0xb2, 0xdc, 0xfc, 0xbe, 0x61,
121: 0xf2, 0x56, 0xd3, 0xab, 0x14, 0x2a, 0x5d, 0x9e, 0x84, 0x3c, 0x39, 0x53, 0x47, 0x6d, 0x41, 0xa2,
122: 0x1f, 0x2d, 0x43, 0xd8, 0xb7, 0x7b, 0xa4, 0x76, 0xc4, 0x17, 0x49, 0xec, 0x7f, 0x0c, 0x6f, 0xf6,
123: 0x6c, 0xa1, 0x3b, 0x52, 0x29, 0x9d, 0x55, 0xaa, 0xfb, 0x60, 0x86, 0xb1, 0xbb, 0xcc, 0x3e, 0x5a,
124: 0xcb, 0x59, 0x5f, 0xb0, 0x9c, 0xa9, 0xa0, 0x51, 0x0b, 0xf5, 0x16, 0xeb, 0x7a, 0x75, 0x2c, 0xd7,
125: 0x4f, 0xae, 0xd5, 0xe9, 0xe6, 0xe7, 0xad, 0xe8, 0x74, 0xd6, 0xf4, 0xea, 0xa8, 0x50, 0x58, 0xaf,
126: };
127:
128: Uint32 ecc_block(const Uint8 *s, int ss)
129: {
130: int i;
131: Uint32 r = (s[0] << 24) | (s[ss] << 16) | (s[2*ss] << 8) | s[3*ss];
132:
133: s += 4*ss;
134: for(i=4; i<36; i++) {
135: r = t_rem[r >> 24] ^ (r << 8);
136: if(i < 32) {
137: r ^= *s;
138: s += ss;
139: }
140: }
141: return r;
142: }
143:
144: void rs_encode_string(Uint8 *sector, int off, int step)
145: {
146: Uint32 ecc = ecc_block(sector+off, step);
147: sector[off+32*step] = ecc >> 24;
148: sector[off+33*step] = ecc >> 16;
149: sector[off+34*step] = ecc >> 8;
150: sector[off+35*step] = ecc;
151: }
152:
153: int rs_decode_string(Uint8 *sector, int off, int step)
154: {
155: int i;
156: Uint32 ecc = ecc_block(sector+off, step);
157: Uint32 ref_ecc =
158: (sector[off+32*step] << 24) |
159: (sector[off+33*step] << 16) |
160: (sector[off+34*step] << 8) |
161: sector[off+35*step];
162: if(ref_ecc == ecc)
163: return 0;
164:
165: // Syndrome polynomial
166: // syn[i] = value of the codebook polynom at 2**(i-1)
167: Uint8 syn[5];
168: memset(syn, 0, 5);
169: syn[0] = 1;
170: for(i=0; i<36; i++) {
171: Uint8 v = sector[off+step*(35-i)];
172: if(v) {
173: syn[1] ^= v;
174: int lv = t_log[v];
175: syn[2] ^= t_exp[lv+i];
176: syn[3] ^= t_exp[lv+2*i];
177: syn[4] ^= t_exp[lv+3*i];
178: }
179: }
180:
181: // Berlekamp-Massey
182:
183: Uint8 sigma[5];
184: Uint8 omega[5];
185: Uint8 tau[5];
186: Uint8 gamma[5];
187: int d;
188: int b;
189:
190: memset(sigma, 0, 5);
191: memset(omega, 0, 5);
192: memset(tau, 0, 5);
193: memset(gamma, 0, 5);
194: sigma[0] = 1;
195: omega[0] = 1;
196: tau[0] = 1;
197: d = 0;
198: b = 0;
199:
200: int l;
201: for(l=1; l<5; l++) {
202: // 1- Determine the l-order coefficient syn*sigma
203: Uint8 delta = 0;
204: for(i=0; i<=l; i++)
205: if(sigma[i] && syn[l-i])
206: delta ^= t_exp[t_log[sigma[i]] + t_log[syn[l-i]]];
207:
208: // 2- Select update method a/b
209: int limit = (l+1)/2;
210: int exact = l & 1;
211: if(!delta || d > limit || (d == limit && exact && !b)) {
212: // 2.1- Method a
213: // b and d unchanged
214: // tau and gamma multiplied by x
215: // sigma = sigma - delta * tau
216: // omega = omega - delta * gamma
217:
218: for(i=0; i<l; i++) {
219: tau[l-i] = tau[l-i-1];
220: gamma[l-i] = gamma[l-i-1];
221: }
222: tau[0] = gamma[0] = 0;
223:
224: if(delta) {
225: Uint8 ldelta = t_log[delta];
226: for(i=1; i<=l; i++) {
227: if(tau[i])
228: sigma[i] ^= t_exp[t_log[tau [i]] + ldelta];
229: if(gamma[i])
230: omega[i] ^= t_exp[t_log[gamma[i]] + ldelta];
231: }
232: }
233: } else {
234: // 2.2- Method b
235: d = l-d;
236: b = !b;
237: // tau(n+1) = sigma(n) / delta
238: // gamma(n+1) = omega(n) / delta
239: // sigma(n+1) = sigma(n) - delta*x*tau(n)
240: // omega(n+1) = omega(n) - delta*x*gamma(n)
241: Uint8 ldelta = t_log[delta];
242: Uint8 ildelta = ldelta ^ 255;
243: for(i=l; i>0; i--) {
244: if(tau[i-1])
245: sigma[i] = sigma[i] ^ t_exp[t_log[tau [i-1]] + ldelta];
246:
247: if(gamma[i-1])
248: omega[i] = omega[i] ^ t_exp[t_log[gamma[i-1]] + ldelta];
249:
250: if(sigma[i-1])
251: tau[i-1] = t_exp[t_log[sigma[i-1]] + ildelta];
252: else
253: tau[i-1] = 0x00;
254:
255: if(omega[i-1])
256: gamma[i-1] = t_exp[t_log[omega[i-1]] + ildelta];
257: else
258: gamma[i-1] = 0x00;
259: }
260: }
261: }
262:
263: // Find the roots of sigma to get the error positions (they're the inverses of 2**position)
264: // Compute the error(s)
265:
266: if(sigma[3] || sigma[4]) {
267: // Should not happen
268: return -1;
269: }
270:
271: if(sigma[2] && sigma[0]) {
272: int epos1, epos2;
273: Uint8 ls1 = t_log[sigma[1]];
274: Uint8 ls2 = t_log[sigma[2]];
275: for(epos1 = 0; epos1 < 256; epos1++) {
276: Uint8 res = sigma[0];
277: if(sigma[1])
278: res ^= t_exp[255-epos1+ls1];
279: res ^= t_exp[2*(255-epos1)+ls2];
280: if(!res)
281: break;
282: }
283: if(epos1 > 35)
284: return -1;
285:
286: // sigma = c.(x-1/r1)(x-1/r2) = c.x*x - c*x*(1/r1+1/r2) + c/(r1*r2)
287:
288: // s0 = s2/(r1*r2) -> r1*r2*s0 = s2 -> r1 = s2 / (r1*s0)
289: // -> r2 = sigma[2]/(r1*sigma[0])
290: epos2 = ls2 - epos1 - t_log[sigma[0]];
291: if(epos2 < 0)
292: epos2 += 255;
293: if(epos2 > 35)
294: return -1;
295:
296: Uint8 err1 = omega[0];
297: if(omega[1])
298: err1 ^= t_exp[t_log[omega[1]] + 255 - epos1];
299: if(omega[2])
300: err1 ^= t_exp[t_log[omega[2]] + 2*(255 - epos1)];
301: err1 = t_log[err1] + epos1;
302: Uint8 div = t_log[1 ^ t_exp[255 + epos2 - epos1]];
303: err1 = t_exp[255 + err1 - div];
304:
305: Uint8 err2 = omega[0];
306: if(omega[1])
307: err2 ^= t_exp[t_log[omega[1]] + 255 - epos2];
308: if(omega[2])
309: err2 ^= t_exp[t_log[omega[2]] + 2*(255 - epos2)];
310: err2 = t_log[err2] + epos2;
311: div = t_log[1 ^ t_exp[255 + epos1 - epos2]];
312: err2 = t_exp[255 + err2 - div];
313:
314: sector[off + step*(35-epos1)] ^= err1;
315: sector[off + step*(35-epos2)] ^= err2;
316: return 2;
317:
318: } else if(sigma[1] && sigma[0]) {
319: // sigma = c.(x-1/r1) -> r1=sigma[1]/sigma[0]
320: int epos = t_log[sigma[1]] - t_log[sigma[0]];
321:
322: if(epos > 35)
323: return -1;
324:
325: Uint8 err = sigma[1]^omega[1];
326: sector[off + step*(35-epos)] ^= err;
327: return 1;
328:
329: } else {
330: // Should not happen
331: return -1;
332: }
333: }
334:
335: void rs_encode(Uint8 *sector)
336: {
337: int i;
338: /* Create encoded sector structure */
339: for(i=31; i>0; i--)
340: memmove(sector+36*i, sector+32*i, 32);
341: /* Encode columns */
342: for(i=0; i<32; i++)
343: rs_encode_string(sector, i, 36);
344: /* Encode rows */
345: for(i=0; i<36; i++)
346: rs_encode_string(sector, 36*i, 1);
347: }
348:
349: int rs_decode(Uint8 *sector)
350: {
351: int i,e;
352: int ecount = 0;
353: /* Decode rows */
354: for(i=0; i<36; i++) {
355: e = rs_decode_string(sector, 36*i, 1);
356: if(e!=-1) {
357: ecount += e;
358: }
359: }
360: /* Decode columns */
361: for(i=0; i<32; i++) {
362: e = rs_decode_string(sector, i, 36);
363: if(e==-1) {
364: return -1; /* Uncorrectable */
365: } else {
366: ecount += e;
367: }
368: }
369: /* Build decoded sector structure */
370: for(i=1; i<32; i++)
371: memmove(sector+i*32, sector+i*36, 32);
372:
373: return ecount;
374: }
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