ecma130ab.c (xorriso-1.5.2) | : | ecma130ab.c (xorriso-1.5.4) | ||
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skipping to change at line 77 | skipping to change at line 77 | |||

The P-parity bytes of each column get reunited as LSB and MSB of two words. | The P-parity bytes of each column get reunited as LSB and MSB of two words. | |||

word1 gets written to positions 1032 to 1074, word0 to 1075 to 1117. | word1 gets written to positions 1032 to 1074, word0 to 1075 to 1117. | |||

The Q-parity bytes of each diagonal get reunited too. word1 goes to 1118 | The Q-parity bytes of each diagonal get reunited too. word1 goes to 1118 | |||

to 1143, word0 to 1144 to 1169. | to 1143, word0 to 1144 to 1169. | |||

>>> I do not read this swap of word1 and word0 from ECMA-130 Annex A. | >>> I do not read this swap of word1 and word0 from ECMA-130 Annex A. | |||

>>> But the new output matches the old output only if it is done that way. | >>> But the new output matches the old output only if it is done that way. | |||

>>> See correctness reservation below. | >>> See correctness reservation below. | |||

Algebra on Galois fields is the same as on Rational Numbers. | Algebra on Galois fields is the same as on Rational Numbers. | |||

But arithmetics is defined by operations on polynomials rather than the | But arithmetics on its polynomials differ from usual integer arithmetics | |||

usual integer arithmetics on binary numbers. | on binary numbers. | |||

Addition and subtraction are identical with the binary exor operator. | Addition and subtraction are identical with the binary exor operator. | |||

Multiplication and division would demand polynomial division, e.g. by the | Multiplication and division would demand polynomial division, e.g. by the | |||

euclidian algorithm. The computing path over logarithms and powers follows | euclidean algorithm. The computing path over logarithms and powers follows | |||

algebra and reduces the arithmetic task to table lookups, additions | algebra and reduces the arithmetic task to table lookups, additions | |||

modulo 255, and exor operations. Note that the logarithms are natural | modulo 255, and exor operations. Note that the logarithms are natural | |||

numbers, not polynomials. They get added or subtracted by the usual addition | numbers, not polynomials. They get added or subtracted by the usual addition | |||

(not by exor) and their polynomial power depends on their value modulo 255. | (not by exor) and their polynomial power depends on their value modulo 255. | |||

Needed are a logarithm table and a power table (or inverse logarithm table) | Needed are a logarithm table and a power table (or inverse logarithm table) | |||

for Galois Field GF(2^8) which will serve to perform the peculiar | for Galois Field GF(2^8) which will serve to perform the peculiar | |||

multiplication and division operation of Galois fields. | multiplication and division operation of Galois fields. | |||

The power table is simply an enumeration of x^n accorting to | The power table is simply an enumeration of x^n accorting to | |||

End of changes. 2 change blocks. | ||||

3 lines changed or deleted | | 3 lines changed or added |