# The multiplication and addition tables are derived from
# a Galois field order(2^3), from (0, 1, a, a^2, ... a^6)
# where a^3 = a + 1.
#
# multiply
#         0     1     a    a^2   a^3   a^4   a^5   a^6
# ------------------------------------------------------
#   0  |  0  |  0  |  0  |  0  |  0  |  0  |  0  |  0  |
#      |------------------------------------------------
#   1  |  0  |  1  |  a  | a^2 | a^3 | a^4 | a^5 | a^6 |
#      |------------------------------------------------
#   a  |  0  |  a  | a^2 | a^3 | a^4 | a^5 | a^6 |  1  |
#      |------------------------------------------------
#   a^2|  0  | a^2 | a^3 | a^4 | a^5 | a^6 |  1  |  a  |
#      |------------------------------------------------
#   a^3|  0  | a^3 | a^4 | a^5 | a^6 |  1  |  a  | a^2 |
#      |------------------------------------------------
#   a^4|  0  | a^4 | a^5 | a^6 |  1  |  a  | a^2 | a^3 |
#      |------------------------------------------------
#   a^5|  0  | a^5 | a^6 |  1  |  a  | a^2 | a^3 | a^4 |
#      |------------------------------------------------
#   a^6|  0  | a^6 |  1  |  a  | a^2 | a^3 | a^4 | a^5 |
#      |------------------------------------------------
# 
# add
# 
#         0     1     a    a^2   a^3   a^4   a^5   a^6
# ------------------------------------------------------
#   0  |  0  |  1  |  a  | a^2 | a^3 | a^4 | a^5 | a^6 |
#      |------------------------------------------------
#   1  |  1  |  0  | a^3 | a^6 |  a  | a^5 | a^4 | a^2 |
#      |------------------------------------------------
#   a  |  a  | a^3 |  0  | a^4 |  1  | a^2 | a^6 | a^5 |
#      |------------------------------------------------
#   a^2| a^2 | a^6 | a^4 |  0  | a^5 |  a  | a^3 |  1  |
#      |------------------------------------------------
#   a^3| a^3 |  a  |  1  | a^5 |  0  | a^6 | a^2 | a^4 |
#      |------------------------------------------------
#   a^4| a^4 | a^5 | a^2 |  a  | a^6 |  0  |  1  | a^3 |
#      |------------------------------------------------
#   a^5| a^5 | a^4 | a^6 | a^3 | a^2 |  1  |  0  |  a  |
#      |------------------------------------------------
#   a^6| a^6 | a^2 | a^5 |  1  | a^4 | a^3 |  a  |  0  |
#      |------------------------------------------------

BEGIN {
@Field8::mtable = (
           [0,  0,  0,  0,  0,  0,  0,  0],
           [0,  1,  2,  3,  4,  5,  6,  7],
           [0,  2,  3,  4,  5,  6,  7,  1],
           [0,  3,  4,  5,  6,  7,  1,  2],
           [0,  4,  5,  6,  7,  1,  2,  3],
           [0,  5,  6,  7,  1,  2,  3,  4],
           [0,  6,  7,  1,  2,  3,  4,  5],
           [0,  7,  1,  2,  3,  4,  5,  6]
           );

@Field8::atable = (
           [0,  1,  2,  3,  4,  5,  6,  7],
           [1,  0,  4,  7,  2,  6,  5,  3],
           [2,  4,  0,  5,  1,  3,  7,  6],
           [3,  7,  5,  0,  6,  2,  4,  1],
           [4,  2,  1,  6,  0,  7,  3,  5],
           [5,  6,  3,  2,  7,  0,  1,  4],
           [6,  5,  7,  4,  3,  1,  0,  2],
           [7,  3,  6,  1,  5,  4,  2,  0]
           );
}