Intel
®
81341 and 81342 I/O Processors
December 2007
Developer’s Manual
Order Number: 315037-002US
495
Application DMA Unit—Intel
®
81341 and 81342
The blocks for gflog (Galois Field Multiply) and gfilog (Galois Field Divide) are the Galois
Field Logarithm and Inverse Logarithm transformations respectively. These
transformations for 8-bit words are provided in
, with the upper
nibble used to index the rows, and the lower nibble used to index the columns. These
are based on the primitive polynomial listed in
Equation 15.Galois Field Primitive Polynomial (0x11D)
X
8
+ X
4
+ X
3
+ X
2
+ 1
Figure 60. Galois Field Logarithm Transformation Table
Figure 61. Galois Field Inverse Logarithm Transformation table
0
1
2
3
4
5
6
7
8
9
a
b
c
d
e
f
0
--
00
01
19
02
32
1a
c6
03
df
33
ee
1b
68
c7
4b
1
04
64
e0
0e
34
8d
ef
81
1c
c1
69
f8
c8
08
4c
71
2
05
8a
65
2f
e1
24
0f
21
35
93
8e
da
f0
12
82
45
3
1d
b5
c2
7d
6a
27
f9
b9
c9
9a
09
78
4d
e4
72
a6
4
06
bf
8b
62
66
dd
30
fd
e2
98
25
b3
10
91
22
88
5
36
d0
94
ce
8f
96
db
bd
f1
d2
13
5c
83
38
46
40
6
1e
42
b6
a3
c3
48
7e
6e
6b
3a
28
54
fa
85
ba
3d
7
ca
5e
9b
9f
0a
15
79
2b
4e
d4
e5
ac
73
f3
a7
57
8
07
70
c0
f7
8c
80
63
0d
67
4a
de
ed
31
c5
fe
18
9
e3
a5
99
77
26
b8
b4
7c
11
44
92
d9
23
20
89
2e
a
37
3f
d1
5b
95
bc
cf
cd
90
87
97
b2
dc
fc
be
61
b
f2
56
d3
ab
14
2a
5d
9e
84
3c
39
53
47
6d
41
a2
c
1f
2d
43
d8
b7
7b
a4
76
c4
17
49
ec
7f
0c
6f
f6
d
6c
a1
3b
52
29
9d
55
aa
fb
60
86
b1
bb
cc
3e
5a
e
cb
59
5f
b0
9c
a9
a0
51
0b
f5
16
eb
7a
75
2c
d7
f
4f
ae
d5
e9
e6
e7
ad
e8
74
d6
f4
ea
a8
50
58
af
x
Table of gflog(2^8): gflog(xy)
gflog(xy)
y
0
1
2
3
4
5
6
7
8
9
a
b
c
d
e
f
0
01
02
04
08
10
20
40
80
1d
3a
74
e8
cd
87
13
26
1
4c
98
2d
5a
b4
75
ea
c9
8f
03
06
0c
18
30
60
c0
2
9d
27
4e
9c
25
4a
94
35
6a
d4
b5
77
ee
c1
9f
23
3
46
8c
05
0a
14
28
50
a0
5d
ba
69
d2
b9
6f
de
a1
4
5f
be
61
c2
99
2f
5e
bc
65
ca
89
0f
1e
3c
78
f0
5
fd
e7
d3
bb
6b
d6
b1
7f
fe
e1
df
a3
5b
b6
71
e2
6
d9
af
43
86
11
22
44
88
0d
1a
34
68
d0
bd
67
ce
7
81
1f
3e
7c
f8
ed
c7
93
3b
76
ec
c5
97
33
66
cc
8
85
17
2e
5c
b8
6d
da
a9
4f
9e
21
42
84
15
2a
54
9
a8
4d
9a
29
52
a4
55
aa
49
92
39
72
e4
d5
b7
73
a
e6
d1
bf
63
c6
91
3f
7e
fc
e5
d7
b3
7b
f6
f1
ff
b
e3
db
ab
4b
96
31
62
c4
95
37
6e
dc
a5
57
ae
41
c
82
19
32
64
c8
8d
07
0e
1c
38
70
e0
dd
a7
53
a6
d
51
a2
59
b2
79
f2
f9
ef
c3
9b
2b
56
ac
45
8a
09
e
12
24
48
90
3d
7a
f4
f5
f7
f3
fb
eb
cb
8b
0b
16
f
2c
58
b0
7d
fa
e9
cf
83
1b
36
6c
d8
ad
47
8e
--
x
Table of gfilog(2^8): gfilog(xy)
gfilog(xy)
y