mathjs/src/function/trigonometry/atanh.js

'use strict'

const deepMap = require('../../utils/collection/deepMap')

function factory (type, config, load, typed) {
  /**
   * Calculate the hyperbolic arctangent of a value,
   * defined as `atanh(x) = ln((1 + x)/(1 - x)) / 2`.
   *
   * For matrices, the function is evaluated element wise.
   *
   * Syntax:
   *
   *    math.atanh(x)
   *
   * Examples:
   *
   *    math.atanh(0.5)       // returns 0.5493061443340549
   *
   * See also:
   *
   *    acosh, asinh
   *
   * @param {number | Complex | Array | Matrix} x  Function input
   * @return {number | Complex | Array | Matrix} Hyperbolic arctangent of x
   */
  const atanh = typed('atanh', {
    'number': function (x) {
      if ((x <= 1 && x >= -1) || config.predictable) {
        return _atanh(x)
      }
      return new type.Complex(x, 0).atanh()
    },

    'Complex': function (x) {
      return x.atanh()
    },

    'BigNumber': function (x) {
      return x.atanh()
    },

    'Array | Matrix': function (x) {
      // deep map collection, skip zeros since atanh(0) = 0
      return deepMap(x, atanh, true)
    }
  })

  atanh.toTex = { 1: `\\tanh^{-1}\\left(\${args[0]}\\right)` }

  return atanh
}

/**
 * Calculate the hyperbolic arctangent of a number
 * @param {number} x
 * @return {number}
 * @private
 */
const _atanh = Math.atanh || function (x) {
  return Math.log((1 + x) / (1 - x)) / 2
}

exports.name = 'atanh'
exports.factory = factory