mathjs/test/function/trigonometry/acoth.test.js

var assert = require('assert'),
    error = require('../../../lib/error/index'),
    math = require('../../../index'),
    approx = require('../../../tools/approx'),
    pi = math.pi,
    acoth = math.acoth,
    coth = math.coth,
    complex = math.complex,
    matrix = math.matrix,
    unit = math.unit,
    bigmath = math.create({number: 'bignumber', precision: 20}),
    biggermath = math.create({precision: 21}),
    acothBig = bigmath.acoth,
    Big = bigmath.bignumber;

describe('acoth', function() {
  it('should return the hyperbolic arccot of a boolean', function () {
    assert.equal(acoth(true), Infinity);
    approx.deepEqual(acoth(false), complex(0, pi / 2));
    //assert.ok(isNaN(acoth(false)));
  });

  it('should return the hyperbolic arccot of null', function () {
    approx.deepEqual(acoth(null), complex(0, pi / 2));
    //assert.ok(isNaN(acoth(null)));
  });

  it('should return the hyperbolic arccot of a number', function() {
    approx.deepEqual(acoth(0), complex(0, pi / 2));
    approx.deepEqual(acoth(0.5), complex(0.5493061443340548, -1.5707963267949));
    //assert.ok(isNaN(acoth(0)));
    //assert.ok(isNaN(acoth(0.5)));

    approx.equal(acoth(-2), -0.54930614433405484569762261846);
    assert.equal(acoth(-1), -Infinity);
    assert.equal(acoth(1), Infinity);
    approx.equal(acoth(2), 0.54930614433405484569762261846);
    assert.equal(acoth(Infinity), 0);
  });

  it('should return the hyperbolic arccot of a bignumber', function() {
    var arg2 = Big(-2);
    var arg3 = Big(-1);
    assert.deepEqual(acothBig(Big(-Infinity)), Big(0));
    assert.deepEqual(acothBig(arg2), Big('-0.5493061443340548457'));
    assert.deepEqual(acothBig(arg3), Big(-Infinity));
    assert.deepEqual(acothBig(Big(1)), Big(Infinity));
    assert.deepEqual(acothBig(Big(2)), Big('0.5493061443340548457'));
    assert.deepEqual(acothBig(Big(Infinity)), Big(0));

    //Make sure arg was not changed
    assert.deepEqual(arg2, Big(-2));
    assert.deepEqual(arg3, Big(-1));
  });

  it('should be the inverse function of hyperbolic cot', function() {
    approx.equal(acoth(coth(-2)), -2);
    approx.equal(acoth(coth(-1)), -1);
    approx.equal(acoth(coth(0)), 0);
    approx.equal(acoth(coth(1)), 1);
    approx.equal(acoth(coth(2)), 2);
  });

  it('should be the inverse function of bignumber coth', function() {
    assert.deepEqual(acothBig(bigmath.coth(Big(-1))), Big(-1));
    assert.deepEqual(acothBig(bigmath.coth(Big(0))), Big(0));
    assert.deepEqual(acothBig(bigmath.coth(Big(1))), Big(1));

    /* Pass in more digits to pi. */
    assert.deepEqual(acothBig(biggermath.coth(Big(-2))), Big(-2));
    assert.deepEqual(acothBig(biggermath.coth(Big(2))), Big(2));
  });

  it('should throw an error if the bignumber result is complex', function() {
    assert.throws(function () {
      acoth(Big(-0.5));
    }, /acoth() has complex values for |x| < 1./);
    assert.throws(function () {
      acoth(Big(0.5));
    }, /acoth() has complex values for |x| < 1./);
    assert.throws(function () {
      acoth(Big(0));
    }, /acoth() has complex values for |x| < 1./);
  });

  it('should return the arccoth of a complex number', function() {
    approx.deepEqual(acoth(complex('2+3i')), complex(0.1469466662255, -0.2318238045004));
    approx.deepEqual(acoth(complex('2-3i')), complex(0.1469466662255, 0.2318238045004));
    approx.deepEqual(acoth(complex('-2+3i')), complex(-0.1469466662255, -0.2318238045004));
    approx.deepEqual(acoth(complex('-2-3i')), complex(-0.1469466662255, 0.2318238045004));
    approx.deepEqual(acoth(complex('1+i')), complex(0.4023594781085251, -0.55357435889705));
    approx.deepEqual(acoth(complex('i')), complex(0, -pi / 4));
    assert.deepEqual(acoth(complex('1')), complex(Infinity, 0));
    approx.deepEqual(acoth(complex('0.5')), complex(0.5493061443340548, -1.5707963267949));
    approx.deepEqual(acoth(complex('0')), complex(0, pi / 2));
  });

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

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

  it('should calculate the arccot element-wise for arrays and matrices', function() {
    var acoth123 = [Infinity, 0.54930614433405, 0.34657359027997];
    approx.deepEqual(acoth([1,2,3]), acoth123);
    approx.deepEqual(acoth(matrix([1,2,3])), matrix(acoth123));
  });

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

  it('should LaTeX acoth', function () {
    var expression = math.parse('acoth(2)');
    assert.equal(expression.toTex(), '\\coth^{-1}\\left({2}\\right)');
  });

});