node-qrcode-lite/lib/core/polynomial.js

var Buffer = require('../utils/buffer')
var GF = require('./galois-field')

/**
 * Multiplies two polynomials inside Galois Field
 *
 * @param  {Buffer} p1 Polynomial
 * @param  {Buffer} p2 Polynomial
 * @return {Buffer}    Product of p1 and p2
 */
exports.mul = function mul (p1, p2) {
  var coeff = new Buffer(p1.length + p2.length - 1)
  coeff.fill(0)

  for (var i = 0; i < p1.length; i++) {
    for (var j = 0; j < p2.length; j++) {
      coeff[i + j] ^= GF.mul(p1[i], p2[j])
    }
  }

  return coeff
}

/**
 * Calculate the remainder of polynomials division
 *
 * @param  {Buffer} divident Polynomial
 * @param  {Buffer} divisor  Polynomial
 * @return {Buffer}          Remainder
 */
exports.mod = function mod (divident, divisor) {
  var result = new Buffer(divident)

  while ((result.length - divisor.length) >= 0) {
    var coeff = result[0]

    for (var i = 0; i < divisor.length; i++) {
      result[i] ^= GF.mul(divisor[i], coeff)
    }

    // remove all zeros from buffer head
    var offset = 0
    while (offset < result.length && result[offset] === 0) offset++
    result = result.slice(offset)
  }

  return result
}

/**
 * Generate an irreducible generator polynomial of specified degree
 * (used by Reed-Solomon encoder)
 *
 * @param  {Number} degree Degree of the generator polynomial
 * @return {Buffer}        Buffer containing polynomial coefficients
 */
exports.generateECPolynomial = function generateECPolynomial (degree) {
  var poly = new Buffer([1])
  for (var i = 0; i < degree; i++) {
    poly = exports.mul(poly, [1, GF.exp(i)])
  }

  return poly
}