mathjs/lib/function/trigonometry/asinh.js

'use strict';

var deepMap = require('../../utils/collection/deepMap');
var acoshAsinhAsechAcsch = require('../../utils/bignumber/acoshAsinhAsechAcsch');

function factory (type, config, load, typed) {
  var complexAsin = typed.find(load(require('./asin')), ['Complex']);

  /**
   * Calculate the hyperbolic arcsine of a value,
   * defined as `asinh(x) = ln(x + sqrt(x^2 + 1))`.
   *
   * For matrices, the function is evaluated element wise.
   *
   * Syntax:
   *
   *    math.asinh(x)
   *
   * Examples:
   *
   *    math.asinh(0.5);       // returns 0.48121182505960347
   *
   * See also:
   *
   *    acosh, atanh
   *
   * @param {number | Complex | Array | Matrix} x  Function input
   * @return {number | Complex | Array | Matrix} Hyperbolic arcsine of x
   */
  var asinh = typed('asinh', {
    'number': function (x) {
      return Math.log(Math.sqrt(x*x + 1) + x);
    },

    'Complex': function (x) {
      // asinh(z) = (-asin((z.im, -z.re)).im, asin((z.im, -z.re)).re)
      var temp = x.im;
      x.im = -x.re;
      x.re = temp;

      var res = complexAsin(x);

      // restore original values
      x.re = -x.im;
      x.im = temp;

      temp = res.re;
      res.re = -res.im;
      res.im = temp;

      return res;
    },

    'BigNumber': function (x) {
      return acoshAsinhAsechAcsch(x, type.BigNumber, true, false);
    },

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

  asinh.toTex = '\\sinh^{-1}\\left(${args[0]}\\right)';

  return asinh;
}

exports.name = 'asinh';
exports.factory = factory;