mathjs/src/function/arithmetic/pow.js

'use strict'

const isInteger = require('../../utils/number').isInteger
const size = require('../../utils/array').size

function factory (type, config, load, typed) {
  const latex = require('../../utils/latex')
  const identity = load(require('../matrix/identity'))
  const multiply = load(require('./multiply'))
  const matrix = load(require('../../type/matrix/function/matrix'))
  const fraction = load(require('../../type/fraction/function/fraction'))
  const number = load(require('../../type/number'))

  /**
   * Calculates the power of x to y, `x ^ y`.
   * Matrix exponentiation is supported for square matrices `x`, and positive
   * integer exponents `y`.
   *
   * For cubic roots of negative numbers, the function returns the principal
   * root by default. In order to let the function return the real root,
   * math.js can be configured with `math.config({predictable: true})`.
   * To retrieve all cubic roots of a value, use `math.cbrt(x, true)`.
   *
   * Syntax:
   *
   *    math.pow(x, y)
   *
   * Examples:
   *
   *    math.pow(2, 3)               // returns number 8
   *
   *    const a = math.complex(2, 3)
   *    math.pow(a, 2)                // returns Complex -5 + 12i
   *
   *    const b = [[1, 2], [4, 3]]
   *    math.pow(b, 2)               // returns Array [[9, 8], [16, 17]]
   *
   * See also:
   *
   *    multiply, sqrt, cbrt, nthRoot
   *
   * @param  {number | BigNumber | Complex | Unit | Array | Matrix} x  The base
   * @param  {number | BigNumber | Complex} y                          The exponent
   * @return {number | BigNumber | Complex | Array | Matrix} The value of `x` to the power `y`
   */
  const pow = typed('pow', {
    'number, number': _pow,

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

    'BigNumber, BigNumber': function (x, y) {
      if (y.isInteger() || x >= 0 || config.predictable) {
        return x.pow(y)
      } else {
        return new type.Complex(x.toNumber(), 0).pow(y.toNumber(), 0)
      }
    },

    'Fraction, Fraction': function (x, y) {
      if (y.d !== 1) {
        if (config.predictable) {
          throw new Error('Function pow does not support non-integer exponents for fractions.')
        } else {
          return _pow(x.valueOf(), y.valueOf())
        }
      } else {
        return x.pow(y)
      }
    },

    'Array, number': _powArray,

    'Array, BigNumber': function (x, y) {
      return _powArray(x, y.toNumber())
    },

    'Matrix, number': _powMatrix,

    'Matrix, BigNumber': function (x, y) {
      return _powMatrix(x, y.toNumber())
    },

    'Unit, number | BigNumber': function (x, y) {
      return x.pow(y)
    }

  })

  /**
   * Calculates the power of x to y, x^y, for two numbers.
   * @param {number} x
   * @param {number} y
   * @return {number | Complex} res
   * @private
   */
  function _pow (x, y) {
    // Alternatively could define a 'realmode' config option or something, but
    // 'predictable' will work for now
    if (config.predictable && !isInteger(y) && x < 0) {
      // Check to see if y can be represented as a fraction
      try {
        const yFrac = fraction(y)
        const yNum = number(yFrac)
        if (y === yNum || Math.abs((y - yNum) / y) < 1e-14) {
          if (yFrac.d % 2 === 1) {
            return (yFrac.n % 2 === 0 ? 1 : -1) * Math.pow(-x, y)
          }
        }
      } catch (ex) {
        // fraction() throws an error if y is Infinity, etc.
      }

      // Unable to express y as a fraction, so continue on
    }

    // x^Infinity === 0 if -1 < x < 1
    // A real number 0 is returned instead of complex(0)
    if ((x * x < 1 && y === Infinity) ||
        (x * x > 1 && y === -Infinity)) {
      return 0
    }

    // **for predictable mode** x^Infinity === NaN if x < -1
    // N.B. this behavour is different from `Math.pow` which gives
    // (-2)^Infinity === Infinity
    if (config.predictable &&
        ((x < -1 && y === Infinity) ||
         (x > -1 && x < 0 && y === -Infinity))) {
      return NaN
    }

    if (isInteger(y) || x >= 0 || config.predictable) {
      return Math.pow(x, y)
    } else {
      return new type.Complex(x, 0).pow(y, 0)
    }
  }

  /**
   * Calculate the power of a 2d array
   * @param {Array} x     must be a 2 dimensional, square matrix
   * @param {number} y    a positive, integer value
   * @returns {Array}
   * @private
   */
  function _powArray (x, y) {
    if (!isInteger(y) || y < 0) {
      throw new TypeError('For A^b, b must be a positive integer (value is ' + y + ')')
    }
    // verify that A is a 2 dimensional square matrix
    const s = size(x)
    if (s.length !== 2) {
      throw new Error('For A^b, A must be 2 dimensional (A has ' + s.length + ' dimensions)')
    }
    if (s[0] !== s[1]) {
      throw new Error('For A^b, A must be square (size is ' + s[0] + 'x' + s[1] + ')')
    }

    let res = identity(s[0]).valueOf()
    let px = x
    while (y >= 1) {
      if ((y & 1) === 1) {
        res = multiply(px, res)
      }
      y >>= 1
      px = multiply(px, px)
    }
    return res
  }

  /**
   * Calculate the power of a 2d matrix
   * @param {Matrix} x     must be a 2 dimensional, square matrix
   * @param {number} y    a positive, integer value
   * @returns {Matrix}
   * @private
   */
  function _powMatrix (x, y) {
    return matrix(_powArray(x.valueOf(), y))
  }

  pow.toTex = {
    2: `\\left(\${args[0]}\\right)${latex.operators['pow']}{\${args[1]}}`
  }

  return pow
}

exports.name = 'pow'
exports.factory = factory