70 lines
1.9 KiB
JavaScript
70 lines
1.9 KiB
JavaScript
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const EXP_TABLE = new Uint8Array(512)
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const LOG_TABLE = new Uint8Array(256)
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/**
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* Precompute the log and anti-log tables for faster computation later
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*
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* For each possible value in the galois field 2^8, we will pre-compute
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* the logarithm and anti-logarithm (exponential) of this value
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*
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* ref {@link https://en.wikiversity.org/wiki/Reed%E2%80%93Solomon_codes_for_coders#Introduction_to_mathematical_fields}
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*/
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;(function initTables () {
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let x = 1
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for (let i = 0; i < 255; i++) {
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EXP_TABLE[i] = x
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LOG_TABLE[x] = i
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x <<= 1 // multiply by 2
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// The QR code specification says to use byte-wise modulo 100011101 arithmetic.
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// This means that when a number is 256 or larger, it should be XORed with 0x11D.
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if (x & 0x100) { // similar to x >= 256, but a lot faster (because 0x100 == 256)
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x ^= 0x11D
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}
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}
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// Optimization: double the size of the anti-log table so that we don't need to mod 255 to
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// stay inside the bounds (because we will mainly use this table for the multiplication of
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// two GF numbers, no more).
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// @see {@link mul}
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for (let i = 255; i < 512; i++) {
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EXP_TABLE[i] = EXP_TABLE[i - 255]
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}
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}())
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/**
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* Returns log value of n inside Galois Field
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*
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* @param {Number} n
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* @return {Number}
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*/
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exports.log = function log (n) {
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if (n < 1) throw new Error('log(' + n + ')')
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return LOG_TABLE[n]
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}
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/**
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* Returns anti-log value of n inside Galois Field
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*
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* @param {Number} n
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* @return {Number}
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*/
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exports.exp = function exp (n) {
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return EXP_TABLE[n]
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}
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/**
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* Multiplies two number inside Galois Field
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*
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* @param {Number} x
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* @param {Number} y
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* @return {Number}
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*/
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exports.mul = function mul (x, y) {
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if (x === 0 || y === 0) return 0
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// should be EXP_TABLE[(LOG_TABLE[x] + LOG_TABLE[y]) % 255] if EXP_TABLE wasn't oversized
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// @see {@link initTables}
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return EXP_TABLE[LOG_TABLE[x] + LOG_TABLE[y]]
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}
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