mathjs/lib/function/arithmetic/xgcd.js

module.exports = function (math) {
  var util = require('../../util/index.js'),

      isNumber = util.number.isNumber,
      isInteger = util.number.isInteger;

  /**
   * Calculate the extended greatest common divisor for two values.
   *
   *     xgcd(a, b)
   *
   * @param {Number} a       An integer number
   * @param {Number} b       An integer number
   * @return {Array}         An array containing 3 integers [div, m, n]
   *                         where div = gcd(a, b) and a*m + b*n = div
   *
   * @see http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm
   */
  math.xgcd = function xgcd(a, b) {
    if (arguments.length == 2) {
      // two arguments
      if (isNumber(a) && isNumber(b)) {
        if (!isInteger(a) || !isInteger(b)) {
          throw new Error('Parameters in function xgcd must be integer numbers');
        }

        if(b == 0) {
          return [a, 1, 0];
        }

        var tmp = xgcd(b, a % b),
            div = tmp[0],
            x = tmp[1],
            y = tmp[2];

        return [div, y, x - y * Math.floor(a / b)];
      }

      throw new util.error.UnsupportedTypeError('xgcd', a, b);
    }

    // zero or one argument
    throw new SyntaxError('Function xgcd expects two arguments');
  };
};