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Filename : galois-field.js
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const EXP_TABLE = new Uint8Array(512)
const LOG_TABLE = new Uint8Array(256)
/**
 * Precompute the log and anti-log tables for faster computation later
 *
 * For each possible value in the galois field 2^8, we will pre-compute
 * the logarithm and anti-logarithm (exponential) of this value
 *
 * ref {@link https://en.wikiversity.org/wiki/Reed%E2%80%93Solomon_codes_for_coders#Introduction_to_mathematical_fields}
 */
;(function initTables () {
  let x = 1
  for (let i = 0; i < 255; i++) {
    EXP_TABLE[i] = x
    LOG_TABLE[x] = i

    x <<= 1 // multiply by 2

    // The QR code specification says to use byte-wise modulo 100011101 arithmetic.
    // This means that when a number is 256 or larger, it should be XORed with 0x11D.
    if (x & 0x100) { // similar to x >= 256, but a lot faster (because 0x100 == 256)
      x ^= 0x11D
    }
  }

  // Optimization: double the size of the anti-log table so that we don't need to mod 255 to
  // stay inside the bounds (because we will mainly use this table for the multiplication of
  // two GF numbers, no more).
  // @see {@link mul}
  for (let i = 255; i < 512; i++) {
    EXP_TABLE[i] = EXP_TABLE[i - 255]
  }
}())

/**
 * Returns log value of n inside Galois Field
 *
 * @param  {Number} n
 * @return {Number}
 */
exports.log = function log (n) {
  if (n < 1) throw new Error('log(' + n + ')')
  return LOG_TABLE[n]
}

/**
 * Returns anti-log value of n inside Galois Field
 *
 * @param  {Number} n
 * @return {Number}
 */
exports.exp = function exp (n) {
  return EXP_TABLE[n]
}

/**
 * Multiplies two number inside Galois Field
 *
 * @param  {Number} x
 * @param  {Number} y
 * @return {Number}
 */
exports.mul = function mul (x, y) {
  if (x === 0 || y === 0) return 0

  // should be EXP_TABLE[(LOG_TABLE[x] + LOG_TABLE[y]) % 255] if EXP_TABLE wasn't oversized
  // @see {@link initTables}
  return EXP_TABLE[LOG_TABLE[x] + LOG_TABLE[y]]
}