var assert = require('assert'),
    math = require('../../../index')(),
    approx = require('../../../tools/approx'),
    pi = math.pi,
    complex = math.complex,
    matrix = math.matrix,
    unit = math.unit,
    atan = math.atan,
    tan = math.tan;

describe('atan', function() {
  it('should return the arctan of a boolean', function () {
    approx.equal(atan(true), 0.25 * pi);
    approx.equal(atan(false), 0);
  });

  it('should return the arctan of a number', function() {
    approx.equal(atan(-1) / pi, -0.25);
    approx.equal(atan(-0.5) / pi, -0.147583617650433);
    approx.equal(atan(0) / pi, 0);
    approx.equal(atan(0.5) / pi, 0.147583617650433);
    approx.equal(atan(1) / pi, 0.25);
  });
  
  it('should be the inverse function of tan', function() {
    approx.equal(atan(tan(-1)), -1);
    approx.equal(atan(tan(0)), 0);
    approx.equal(atan(tan(0.1)), 0.1);
    approx.equal(atan(tan(0.5)), 0.5);
    approx.equal(atan(tan(2)), -1.14159265358979);
  });

  it('should return the arctan of a complex number', function() {
    var re = 1.409921049596575,
        im = 0.229072682968539;
    approx.deepEqual(atan(complex('2+3i')), complex(re, im));
    approx.deepEqual(atan(complex('2-3i')), complex(re, -im));
    approx.deepEqual(atan(complex('-2+3i')), complex(-re, im));
    approx.deepEqual(atan(complex('-2-3i')), complex(-re, -im));
    approx.deepEqual(atan(complex('i')), complex(NaN, NaN)); // TODO: should return NaN + Infi instead
    approx.deepEqual(atan(complex('1')), complex(0.785398163397448, 0));
    approx.deepEqual(atan(complex('1+i')), complex(1.017221967897851, 0.402359478108525));
  });

  it('should throw an error if called with a unit', function() {
    assert.throws(function () {atan(unit('45deg'))});
    assert.throws(function () {atan(unit('5 celsius'))});
  });

  it('should throw an error if called with a string', function() {
    assert.throws(function () {atan('string')});
  });

  it('should calculate the arctan element-wise for arrays and matrices', function() {
    // matrix, array, range
    var atan123 = [0.785398163397448, 1.107148717794090, 1.249045772398254];
    approx.deepEqual(atan([1,2,3]), atan123);
    approx.deepEqual(atan(matrix([1,2,3])), matrix(atan123));
  });

});