1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
|
/*
* Galois field maths.
*
* Copyright (c) 2006-2008 Miru Limited.
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library 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
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
#if !defined (__PGM_IMPL_FRAMEWORK_H_INSIDE__) && !defined (PGM_COMPILATION)
# error "Only <framework.h> can be included directly."
#endif
#ifndef __PGM_IMPL_GALOIS_H__
#define __PGM_IMPL_GALOIS_H__
#include <pgm/types.h>
PGM_BEGIN_DECLS
/* 8 bit wide galois field integer: GF(2⁸) */
#ifdef _MSC_VER
typedef uint8_t pgm_gf8_t;
#else
typedef uint8_t __attribute__((__may_alias__)) pgm_gf8_t;
#endif
/* E denotes the encoding symbol length in bytes.
* S denotes the symbol size in units of m-bit elements. When m = 8,
* then S and E are equal.
*/
#define PGM_GF_ELEMENT_BYTES sizeof(pgm_gf8_t)
/* m defines the length of the elements in the finite field, in bits.
* m belongs to {2..16}.
*/
#define PGM_GF_ELEMENT_BITS ( 8 * PGM_GF_ELEMENT_BYTES )
/* q defines the number of elements in the finite field.
*/
#define PGM_GF_NO_ELEMENTS ( 1 << PGM_GF_ELEMENT_BITS )
#define PGM_GF_MAX ( PGM_GF_NO_ELEMENTS - 1 )
extern const pgm_gf8_t pgm_gflog[PGM_GF_NO_ELEMENTS];
extern const pgm_gf8_t pgm_gfantilog[PGM_GF_NO_ELEMENTS];
#ifdef CONFIG_GALOIS_MUL_LUT
extern const pgm_gf8_t pgm_gftable[PGM_GF_NO_ELEMENTS * PGM_GF_NO_ELEMENTS];
#endif
/* In a finite field with characteristic 2, addition and subtraction are
* identical, and are accomplished using the XOR operator.
*/
static inline
pgm_gf8_t
pgm_gfadd (
pgm_gf8_t a,
pgm_gf8_t b
)
{
return a ^ b;
}
static inline
pgm_gf8_t
pgm_gfadd_equals (
pgm_gf8_t a,
pgm_gf8_t b
)
{
return a ^= b;
}
static inline
pgm_gf8_t
pgm_gfsub (
pgm_gf8_t a,
pgm_gf8_t b
)
{
return pgm_gfadd (a, b);
}
static inline
pgm_gf8_t
pgm_gfsub_equals (
pgm_gf8_t a,
pgm_gf8_t b
)
{
return pgm_gfadd_equals (a, b);
}
static inline
pgm_gf8_t
pgm_gfmul (
pgm_gf8_t a,
pgm_gf8_t b
)
{
if (PGM_UNLIKELY( !(a && b) )) {
return 0;
}
#ifdef CONFIG_GALOIS_MUL_LUT
return pgm_gftable[ (uint16_t)a << 8 | (uint16_t)b ];
#else
unsigned sum = pgm_gflog[ a ] + pgm_gflog[ b ];
return sum >= PGM_GF_MAX ? pgm_gfantilog[ sum - PGM_GF_MAX ] : pgm_gfantilog[ sum ];
#endif
}
static inline
pgm_gf8_t
pgm_gfdiv (
pgm_gf8_t a,
pgm_gf8_t b
)
{
#if defined(__STDC_VERSION__) && (__STDC_VERSION__ >= 199901L)
/* C99 version */
if (PGM_UNLIKELY( !a )) {
return 0;
}
const int sum = pgm_gflog[ a ] - pgm_gflog[ b ];
return sum < 0 ? pgm_gfantilog[ sum + PGM_GF_MAX ] : pgm_gfantilog[ sum ];
#else
/* C89 version */
const int sum = pgm_gflog[ a ] - pgm_gflog[ b ];
if (PGM_UNLIKELY( !a )) {
return 0;
}
return sum < 0 ? pgm_gfantilog[ sum + PGM_GF_MAX ] : pgm_gfantilog[ sum ];
#endif
}
PGM_END_DECLS
#endif /* __PGM_IMPL_GALOIS_H__ */
|
