var assert = require('assert'),
    error = require('../../../lib/error/index'),
    math = require('../../../index')(),
    approx = require('../../../tools/approx'),
    pi = math.pi,
    complex = math.complex,
    matrix = math.matrix,
    unit = math.unit,
    asin = math.asin,
    sin = math.sin;

describe('asin', function() {
  it('should return the arcsin of a boolean', function () {
    approx.equal(asin(true), 0.5 * pi);
    approx.equal(asin(false), 0);
  });

  it('should return the arcsin of a number', function() {
    approx.equal(asin(-1) / pi, -0.5);
    approx.equal(asin(-0.5) / pi, -1/6);
    approx.equal(asin(0) / pi, 0);
    approx.equal(asin(0.5) / pi, 1/6);
    approx.equal(asin(1) / pi, 0.5);
  });

  it('should return the arcsin of a bignumber (downgrades to number)', function() {
    approx.equal(asin(math.bignumber(-1)), -pi / 2);
  });

  it('should be the inverse function of sin', function() {
    approx.equal(asin(sin(-1)), -1);
    approx.equal(asin(sin(0)), 0);
    approx.equal(asin(sin(0.1)), 0.1);
    approx.equal(asin(sin(0.5)), 0.5);
    approx.equal(asin(sin(2)), 1.14159265358979);
  });

  it('should return the arcsin of a complex number', function() {
    var re = 0.570652784321099;
    var im = 1.983387029916536;
    approx.deepEqual(asin(complex('2+3i')), complex(re, im));
    approx.deepEqual(asin(complex('2-3i')), complex(re, -im));
    approx.deepEqual(asin(complex('-2+3i')), complex(-re, im));
    approx.deepEqual(asin(complex('-2-3i')), complex(-re, -im));
    approx.deepEqual(asin(complex('i')), complex(0, 0.881373587019543));
    approx.deepEqual(asin(complex('1')), complex(1.57079632679490, 0));
    approx.deepEqual(asin(complex('1+i')), complex(0.666239432492515, 1.061275061905036));
  });

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

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

  it('should calculate the arcsin element-wise for arrays and matrices', function() {
    // note: the results of asin(2) and asin(3) differs in octave
    // the next tests are verified with mathematica
    var asin123 = [
      1.57079632679490,
      complex(1.57079632679490, -1.31695789692482),
      complex(1.57079632679490, -1.76274717403909)];
    approx.deepEqual(asin([1,2,3]), asin123);
    approx.deepEqual(asin(matrix([1,2,3])), matrix(asin123));
  });

  it('should throw an error in case of invalid number of arguments', function() {
    assert.throws(function () {asin()}, error.ArgumentsError);
    assert.throws(function () {asin(1, 2)}, error.ArgumentsError);
  });

});