mathjs/test/unit-tests/function/trigonometry/acoth.test.js

import assert from 'assert'
import math from '../../../../src/defaultInstance.js'
import approx from '../../../../tools/approx.js'
const pi = math.pi
const acoth = math.acoth
const coth = math.coth
const complex = math.complex
const matrix = math.matrix
const unit = math.unit
const bigmath = math.create({ number: 'BigNumber', precision: 20 })
const biggermath = math.create({ precision: 21 })
const predmath = math.create({ predictable: true })
const acothBig = bigmath.acoth
const Big = bigmath.bignumber

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

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

  it('should return the hyperbolic arccot of a number when predictable:true', function () {
    assert.strictEqual(typeof predmath.acoth(0.5), 'number')
    assert(isNaN(predmath.acoth(0.5)))
  })

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

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

    // out of range
    assert.ok(acothBig(Big(-0.5)).isNaN())
    assert.ok(acothBig(Big(0.5)).isNaN())
  })

  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.deepStrictEqual(acothBig(bigmath.coth(Big(-1))), Big(-1))
    assert.deepStrictEqual(acothBig(bigmath.coth(Big(0))), Big(0))
    assert.deepStrictEqual(acothBig(bigmath.coth(Big(1))), Big(1))

    /* Pass in more digits to pi. */
    assert.deepStrictEqual(acothBig(biggermath.coth(Big(-2))), Big('-2.0000000000000000001'))
    assert.deepStrictEqual(acothBig(biggermath.coth(Big(2))), Big('2.0000000000000000001'))
  })

  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.deepStrictEqual(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 () {
    const 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() }, /TypeError: Too few arguments/)
    assert.throws(function () { acoth(1, 2) }, /TypeError: Too many arguments/)
  })

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