var FORTPI = Math.PI/4;
var srat = require('../common/srat');
var HALF_PI = Math.PI/2;
var MAX_ITER = 20;
exports.init = function() {
  var sphi = Math.sin(this.lat0);
  var cphi = Math.cos(this.lat0);
  cphi *= cphi;
  this.rc = Math.sqrt(1 - this.es) / (1 - this.es * sphi * sphi);
  this.C = Math.sqrt(1 + this.es * cphi * cphi / (1 - this.es));
  this.phic0 = Math.asin(sphi / this.C);
  this.ratexp = 0.5 * this.C * this.e;
  this.K = Math.tan(0.5 * this.phic0 + FORTPI) / (Math.pow(Math.tan(0.5 * this.lat0 + FORTPI), this.C) * srat(this.e * sphi, this.ratexp));
};

exports.forward = function(p) {
  var lon = p.x;
  var lat = p.y;

  p.y = 2 * Math.atan(this.K * Math.pow(Math.tan(0.5 * lat + FORTPI), this.C) * srat(this.e * Math.sin(lat), this.ratexp)) - HALF_PI;
  p.x = this.C * lon;
  return p;
};

exports.inverse = function(p) {
  var DEL_TOL = 1e-14;
  var lon = p.x / this.C;
  var lat = p.y;
  var num = Math.pow(Math.tan(0.5 * lat + FORTPI) / this.K, 1 / this.C);
  for (var i = MAX_ITER; i > 0; --i) {
    lat = 2 * Math.atan(num * srat(this.e * Math.sin(p.y), - 0.5 * this.e)) - HALF_PI;
    if (Math.abs(lat - p.y) < DEL_TOL) {
      break;
    }
    p.y = lat;
  }
  /* convergence failed */
  if (!i) {
    return null;
  }
  p.x = lon;
  p.y = lat;
  return p;
};
exports.names = ["gauss"];