'use strict';

var deepMap = require('../../utils/collection/deepMap');
var constants = require('../../utils/bignumber/constants');

function factory (type, config, load, typed) {
  var gamma = load(require('./gamma'));
  var latex = require('../../utils/latex');

  /**
   * Compute the factorial of a value
   *
   * Factorial only supports an integer value as argument.
   * For matrices, the function is evaluated element wise.
   *
   * Syntax:
   *
   *    math.factorial(n)
   *
   * Examples:
   *
   *    math.factorial(5);    // returns 120
   *    math.factorial(3);    // returns 6
   *
   * See also:
   *
   *    combinations, gamma, permutations
   *
   * @param {number | BigNumber | Array | Matrix} n   An integer number
   * @return {number | BigNumber | Array | Matrix}    The factorial of `n`
   */
  var factorial = typed('factorial', {
    'number': function (n) {
      if (n === Number.POSITIVE_INFINITY) {
       return Math.sqrt(2 * Math.PI);
      }

      return gamma(n + 1);
    },

    'BigNumber': function (n) {
      if (!n.isFinite() && !n.isNegative()) {
        return constants.tau(type.BigNumber).sqrt();
      }

      return gamma(n.plus(1));
    },

    'Array | Matrix': function (n) {
      return deepMap(n, factorial);
    }
  });

  factorial.toTex = '\\left(${args[0]}\\right)' + latex.operators['factorial'];

  return factorial;
}

exports.name = 'factorial';
exports.factory = factory;