// test nthRoots
var assert = require('assert');
var math = require('../../../index');
var complex = math.complex;
var nthRoots = math.nthRoots;

describe('nthRoots', function() {
  it('should return an array of Complex roots', function() {
    var roots = nthRoots(complex("-1"), 6);
    var roots1 = [
      complex({r: 1, phi: Math.PI/6}),
      complex(0, 1),
      complex({r: 1, phi: (5 * Math.PI)/6}),
      complex({r: 1, phi: (7 * Math.PI)/6}),
      complex(0, -1),
      complex({r: 1, phi: (11 * Math.PI)/6})
    ];

    roots.forEach(function (value, index, array) {
      assert.deepEqual(value, roots1[index]);
    });
  });

  it('should return the correct answer for Complex values', function() {
    var roots = nthRoots(complex(3, 4), 2);
    var roots1 = [
      { re: 2, im: 1 },
      { re: -2.0000000000000004, im: -0.9999999999999999}
    ];
    roots.forEach(function (value, index, array) {
      assert.deepEqual(value, roots1[index]);
    });
  });

  var twos = [
    complex(2, 0),
    complex(0, 2),
    complex(-2, 0),
    complex(0, -2),
  ];
  it('should return pure roots without artifacts', function() {
    var roots = nthRoots(complex("16"), 4);

    roots.forEach(function (value, index, array) {
      assert.deepEqual(value, twos[index]);
    });
  });

  it('should return roots for numeric arguments', function() {
    var roots = nthRoots(16, 4);

    roots.forEach(function (value, index, array) {
      assert.deepEqual(value, twos[index]);
    });
  });

  it('should return roots for string arguments', function() {
    var roots = nthRoots("16", 4);

    roots.forEach(function (value, index, array) {
      assert.deepEqual(value, twos[index]);
    });
  });

  it('should return zero exactly once', function() {
    var roots2 = nthRoots(0);
    var roots4 = nthRoots(0, 4);
    var roots8 = nthRoots(0, 8);
    assert.deepEqual(roots2, [complex(0)]);
    assert.deepEqual(roots4, [complex(0)]);
    assert.deepEqual(roots8, [complex(0)]);
  });

});