mathjs/lib/function/probability/factorial.js

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

      collection = require('../../type/collection.js'),

      isNumber = util.number.isNumber,
      isBoolean = util.boolean.isBoolean,
      isInteger = util.number.isInteger,
      isCollection = collection.isCollection;

  /**
   * Compute the factorial of a value
   *
   *     x!
   *     factorial(x)
   *
   * Factorial only supports an integer value as argument.
   * For matrices, the function is evaluated element wise.
   *
   * @Param {Number | Array | Matrix} x
   * @return {Number | Array | Matrix} res
   */
  math.factorial = function factorial (x) {
    if (arguments.length != 1) {
      throw new util.error.ArgumentsError('factorial', arguments.length, 1);
    }

    if (isNumber(x)) {
      if (!isInteger(x) || x < 0) {
        throw new TypeError('Positive integer value expected in function factorial');
      }

      var value = x,
          res = value;
      value--;
      while (value > 1) {
        res *= value;
        value--;
      }

      if (res == 0) {
        res = 1;        // 0! is per definition 1
      }

      return res;
    }

    if (isBoolean(x)) {
      return 1; // factorial(1) = 1, factorial(0) = 1
    }

    if (isCollection(x)) {
      return collection.deepMap(x, factorial);
    }

    if (x.valueOf() !== x) {
      // fallback on the objects primitive value
      return factorial(x.valueOf());
    }

    throw new util.error.UnsupportedTypeError('factorial', x);
  };
};