mathjs/src/function/relational/compare.js

'use strict'

import { nearlyEqual as bigNearlyEqual } from '../../utils/bignumber/nearlyEqual'
import { nearlyEqual } from '../../utils/number'

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

  const algorithm03 = load(require('../../type/matrix/utils/algorithm03'))
  const algorithm05 = load(require('../../type/matrix/utils/algorithm05'))
  const algorithm12 = load(require('../../type/matrix/utils/algorithm12'))
  const algorithm13 = load(require('../../type/matrix/utils/algorithm13'))
  const algorithm14 = load(require('../../type/matrix/utils/algorithm14'))

  /**
   * Compare two values. Returns 1 when x > y, -1 when x < y, and 0 when x == y.
   *
   * x and y are considered equal when the relative difference between x and y
   * is smaller than the configured epsilon. The function cannot be used to
   * compare values smaller than approximately 2.22e-16.
   *
   * For matrices, the function is evaluated element wise.
   * Strings are compared by their numerical value.
   *
   * Syntax:
   *
   *    math.compare(x, y)
   *
   * Examples:
   *
   *    math.compare(6, 1)           // returns 1
   *    math.compare(2, 3)           // returns -1
   *    math.compare(7, 7)           // returns 0
   *    math.compare('10', '2')      // returns 1
   *    math.compare('1000', '1e3')  // returns 0
   *
   *    const a = math.unit('5 cm')
   *    const b = math.unit('40 mm')
   *    math.compare(a, b)           // returns 1
   *
   *    math.compare(2, [1, 2, 3])   // returns [1, 0, -1]
   *
   * See also:
   *
   *    equal, unequal, smaller, smallerEq, larger, largerEq, compareNatural, compareText
   *
   * @param  {number | BigNumber | Fraction | Unit | string | Array | Matrix} x First value to compare
   * @param  {number | BigNumber | Fraction | Unit | string | Array | Matrix} y Second value to compare
   * @return {number | BigNumber | Fraction | Array | Matrix} Returns the result of the comparison:
   *                                                          1 when x > y, -1 when x < y, and 0 when x == y.
   */
  const compare = typed('compare', {

    'boolean, boolean': function (x, y) {
      return x === y ? 0 : (x > y ? 1 : -1)
    },

    'number, number': function (x, y) {
      return (x === y || nearlyEqual(x, y, config.epsilon))
        ? 0
        : (x > y ? 1 : -1)
    },

    'BigNumber, BigNumber': function (x, y) {
      return (x.eq(y) || bigNearlyEqual(x, y, config.epsilon))
        ? new type.BigNumber(0)
        : new type.BigNumber(x.cmp(y))
    },

    'Fraction, Fraction': function (x, y) {
      return new type.Fraction(x.compare(y))
    },

    'Complex, Complex': function () {
      throw new TypeError('No ordering relation is defined for complex numbers')
    },

    'Unit, Unit': function (x, y) {
      if (!x.equalBase(y)) {
        throw new Error('Cannot compare units with different base')
      }
      return compare(x.value, y.value)
    },

    'SparseMatrix, SparseMatrix': function (x, y) {
      return algorithm05(x, y, compare)
    },

    'SparseMatrix, DenseMatrix': function (x, y) {
      return algorithm03(y, x, compare, true)
    },

    'DenseMatrix, SparseMatrix': function (x, y) {
      return algorithm03(x, y, compare, false)
    },

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

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

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

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

    'SparseMatrix, any': function (x, y) {
      return algorithm12(x, y, compare, false)
    },

    'DenseMatrix, any': function (x, y) {
      return algorithm14(x, y, compare, false)
    },

    'any, SparseMatrix': function (x, y) {
      return algorithm12(y, x, compare, true)
    },

    'any, DenseMatrix': function (x, y) {
      return algorithm14(y, x, compare, true)
    },

    'Array, any': function (x, y) {
      // use matrix implementation
      return algorithm14(matrix(x), y, compare, false).valueOf()
    },

    'any, Array': function (x, y) {
      // use matrix implementation
      return algorithm14(matrix(y), x, compare, true).valueOf()
    }
  })

  compare.toTex = undefined // use default template

  return compare
}

export const name = 'compare'