mathjs/test/function/trigonometry/asin.test.js

var assert = require('assert');
var error = require('../../../lib/error/index');
var math = require('../../../index');
var approx = require('../../../tools/approx');
var pi = math.pi;
var complex = math.complex;
var matrix = math.matrix;
var unit = math.unit;
var asin = math.asin;
var sin = math.sin;
var bigmath = math.create({number: 'bignumber', precision: 20});
var biggermath = math.create({precision: 21});
var predmath = math.create({predictable: true});
var asinBig = bigmath.asin;
var Big = bigmath.bignumber;

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

  it('should return the arcsin of null', function () {
    assert.equal(asin(null), 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);

    approx.deepEqual(asin(-2), complex('-1.57079632679490 + 1.31695789692482i'));
    approx.deepEqual(asin(2), complex('1.57079632679490 - 1.31695789692482i'));
  });

  it('should return the arccos of a number when predictable:true', function() {
    assert.equal(typeof predmath.asin(-2), 'number');
    assert(isNaN(predmath.asin(-2)));
  });

  it('should return the arcsin of a bignumber', function() {
    var arg1 = Big(-1);
    var arg2 = Big(-0.581);
    var arg3 = Big(-0.5);

    assert.deepEqual(asinBig(arg1), Big('-1.5707963267948966192'));
    assert.deepEqual(asinBig(arg2), Big('-0.6199567994522537004'));
    assert.deepEqual(asinBig(arg3), Big('-0.5235987755982988731'));
    assert.deepEqual(asinBig(Big(0)), Big(0));
    assert.deepEqual(asinBig(Big(0.5)), Big('0.5235987755982988731'));
    assert.deepEqual(asinBig(Big(0.581)), Big('0.6199567994522537004'));
    assert.deepEqual(asinBig(Big(1)), Big('1.5707963267948966192'));

    // Make sure args were not changed
    assert.deepEqual(arg1, Big(-1));
    assert.deepEqual(arg2, Big(-0.581));
    assert.deepEqual(arg3, Big(-0.5));

    // Hit Newton's method case
    bigmath.config({precision: 61});

    var arg4 = Big(0.00000001);
    assert.deepEqual(asinBig(arg4), Big('1.0000000000000000166666666666666674166666666666667113e-8'));
    assert.deepEqual(arg4, Big(0.00000001));
  });

  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 be the inverse function of bignumber sin', function() {
    // More Newton's method test cases
    assert.deepEqual(asinBig(bigmath.sin(Big(-2))), Big('-1.141592653589793238462643383279502884197169399375105820974945'));
    assert.deepEqual(asinBig(bigmath.sin(Big(-0.5))), Big(-0.5));
    assert.deepEqual(asinBig(bigmath.sin(Big(-0.1))), Big(-0.1));
    assert.deepEqual(asinBig(bigmath.sin(Big(0.1))), Big(0.1));
    assert.deepEqual(asinBig(bigmath.sin(Big(0.5))), Big(0.5));
    assert.deepEqual(asinBig(bigmath.sin(Big(2))), Big('1.141592653589793238462643383279502884197169399375105820974945'));

    // Full decimal Taylor test cases
    bigmath.config({precision: 20});
    assert.deepEqual(asinBig(bigmath.sin(Big(0))), Big(0));
    assert.deepEqual(asinBig(bigmath.sin(Big(0.1))), Big(0.1));
    assert.deepEqual(asinBig(bigmath.sin(Big(0.5))), Big(0.5));
    assert.deepEqual(asinBig(bigmath.sin(Big(2))), Big('1.1415926535897932385'));

    assert.deepEqual(asinBig(biggermath.sin(Big(-1))), Big('-1'));
  });

  it('should throw an error if the bignumber result is complex', function() {
    assert.throws(function () {
      asin(Big(1.1));
    }, /asin() only has non-complex values for |x| <= 1./);
    assert.throws(function () {
      asin(Big(-1.1));
    }, /asin() only has non-complex values for |x| <= 1./);
  });

  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()}, /TypeError: Too few arguments/);
    assert.throws(function () {asin(1, 2)}, /TypeError: Too many arguments/);
  });

  it('should LaTeX asin', function () {
    var expression = math.parse('asin(0.5)');
    assert.equal(expression.toTex(), '\\sin^{-1}\\left(0.5\\right)');
  });

});