mathjs/src/function/arithmetic/log1p.js

Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser with support for symbolic computation, comes with a large set of built-in functions and constants, and offers an integrated solution to work with dif

import { factory } from '../../utils/factory'
import { deepMap } from '../../utils/collection'
import { log1p as _log1p } from '../../utils/number'

const name = 'log1p'
const dependencies = ['typed', 'config', 'divideScalar', 'log', 'Complex']

export const createLog1p = /* #__PURE__ */ factory(name, dependencies, ({ typed, config, divideScalar, log, Complex }) => {
  /**
   * Calculate the logarithm of a `value+1`.
   *
   * For matrices, the function is evaluated element wise.
   *
   * Syntax:
   *
   *    math.log1p(x)
   *    math.log1p(x, base)
   *
   * Examples:
   *
   *    math.log1p(2.5)                 // returns 1.252762968495368
   *    math.exp(math.log1p(1.4))       // returns 2.4
   *
   *    math.pow(10, 4)                 // returns 10000
   *    math.log1p(9999, 10)            // returns 4
   *    math.log1p(9999) / math.log(10) // returns 4
   *
   * See also:
   *
   *    exp, log, log2, log10
   *
   * @param {number | BigNumber | Complex | Array | Matrix} x
   *            Value for which to calculate the logarithm of `x+1`.
   * @param {number | BigNumber | Complex} [base=e]
   *            Optional base for the logarithm. If not provided, the natural
   *            logarithm of `x+1` is calculated.
   * @return {number | BigNumber | Complex | Array | Matrix}
   *            Returns the logarithm of `x+1`
   */
  const log1p = typed(name, {
    number: function (x) {
      if (x >= -1 || config.predictable) {
        return _log1p(x)
      } else {
        // negative value -> complex value computation
        return _log1pComplex(new Complex(x, 0))
      }
    },

    Complex: _log1pComplex,

    BigNumber: function (x) {
      const y = x.plus(1)
      if (!y.isNegative() || config.predictable) {
        return y.ln()
      } else {
        // downgrade to number, return Complex valued result
        return _log1pComplex(new Complex(x.toNumber(), 0))
      }
    },

    'Array | Matrix': function (x) {
      return deepMap(x, log1p)
    },

    'any, any': function (x, base) {
      // calculate logarithm for a specified base, log1p(x, base)
      return divideScalar(log1p(x), log(base))
    }
  })

  /**
   * Calculate the natural logarithm of a complex number + 1
   * @param {Complex} x
   * @returns {Complex}
   * @private
   */
  function _log1pComplex (x) {
    const xRe1p = x.re + 1
    return new Complex(
      Math.log(Math.sqrt(xRe1p * xRe1p + x.im * x.im)),
      Math.atan2(x.im, xRe1p)
    )
  }

  return log1p
})