mathjs/src/function/arithmetic/gcd.js

'use strict'

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

function factory (type, config, load, typed) {
  const matrix = load(require('../../type/matrix/function/matrix'))

  const algorithm01 = load(require('../../type/matrix/utils/algorithm01'))
  const algorithm04 = load(require('../../type/matrix/utils/algorithm04'))
  const algorithm10 = load(require('../../type/matrix/utils/algorithm10'))
  const algorithm13 = load(require('../../type/matrix/utils/algorithm13'))
  const algorithm14 = load(require('../../type/matrix/utils/algorithm14'))

  /**
   * Calculate the greatest common divisor for two or more values or arrays.
   *
   * For matrices, the function is evaluated element wise.
   *
   * Syntax:
   *
   *    math.gcd(a, b)
   *    math.gcd(a, b, c, ...)
   *
   * Examples:
   *
   *    math.gcd(8, 12)              // returns 4
   *    math.gcd(-4, 6)              // returns 2
   *    math.gcd(25, 15, -10)        // returns 5
   *
   *    math.gcd([8, -4], [12, 6])   // returns [4, 2]
   *
   * See also:
   *
   *    lcm, xgcd
   *
   * @param {... number | BigNumber | Fraction | Array | Matrix} args  Two or more integer numbers
   * @return {number | BigNumber | Fraction | Array | Matrix}                           The greatest common divisor
   */
  const gcd = typed('gcd', {

    'number, number': _gcd,

    'BigNumber, BigNumber': _gcdBigNumber,

    'Fraction, Fraction': function (x, y) {
      return x.gcd(y)
    },

    'SparseMatrix, SparseMatrix': function (x, y) {
      return algorithm04(x, y, gcd)
    },

    'SparseMatrix, DenseMatrix': function (x, y) {
      return algorithm01(y, x, gcd, true)
    },

    'DenseMatrix, SparseMatrix': function (x, y) {
      return algorithm01(x, y, gcd, false)
    },

    'DenseMatrix, DenseMatrix': function (x, y) {
      return algorithm13(x, y, gcd)
    },

    'Array, Array': function (x, y) {
      // use matrix implementation
      return gcd(matrix(x), matrix(y)).valueOf()
    },

    'Array, Matrix': function (x, y) {
      // use matrix implementation
      return gcd(matrix(x), y)
    },

    'Matrix, Array': function (x, y) {
      // use matrix implementation
      return gcd(x, matrix(y))
    },

    'SparseMatrix, number | BigNumber': function (x, y) {
      return algorithm10(x, y, gcd, false)
    },

    'DenseMatrix, number | BigNumber': function (x, y) {
      return algorithm14(x, y, gcd, false)
    },

    'number | BigNumber, SparseMatrix': function (x, y) {
      return algorithm10(y, x, gcd, true)
    },

    'number | BigNumber, DenseMatrix': function (x, y) {
      return algorithm14(y, x, gcd, true)
    },

    'Array, number | BigNumber': function (x, y) {
      // use matrix implementation
      return algorithm14(matrix(x), y, gcd, false).valueOf()
    },

    'number | BigNumber, Array': function (x, y) {
      // use matrix implementation
      return algorithm14(matrix(y), x, gcd, true).valueOf()
    },

    // TODO: need a smarter notation here
    'Array | Matrix | number | BigNumber, Array | Matrix | number | BigNumber, ...Array | Matrix | number | BigNumber': function (a, b, args) {
      let res = gcd(a, b)
      for (let i = 0; i < args.length; i++) {
        res = gcd(res, args[i])
      }
      return res
    }
  })

  gcd.toTex = `\\gcd\\left(\${args}\\right)`

  return gcd

  /**
   * Calculate gcd for BigNumbers
   * @param {BigNumber} a
   * @param {BigNumber} b
   * @returns {BigNumber} Returns greatest common denominator of a and b
   * @private
   */
  function _gcdBigNumber (a, b) {
    if (!a.isInt() || !b.isInt()) {
      throw new Error('Parameters in function gcd must be integer numbers')
    }

    // https://en.wikipedia.org/wiki/Euclidean_algorithm
    const zero = new type.BigNumber(0)
    while (!b.isZero()) {
      const r = a.mod(b)
      a = b
      b = r
    }
    return a.lt(zero) ? a.neg() : a
  }
}

/**
 * Calculate gcd for numbers
 * @param {number} a
 * @param {number} b
 * @returns {number} Returns the greatest common denominator of a and b
 * @private
 */
function _gcd (a, b) {
  if (!isInteger(a) || !isInteger(b)) {
    throw new Error('Parameters in function gcd must be integer numbers')
  }

  // https://en.wikipedia.org/wiki/Euclidean_algorithm
  let r
  while (b !== 0) {
    r = a % b
    a = b
    b = r
  }
  return (a < 0) ? -a : a
}

exports.name = 'gcd'
exports.factory = factory