mathjs/test/utils/bignumber/nearlyEqual.test.js

Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser and offers an integrated solution to work with numbers, big numbers, complex numbers, units, and matrices.

var assert = require('assert');
var BigNumber = require('decimal.js');
var nearlyEqual = require('../../../lib/utils/bignumber/nearlyEqual');

describe('nearlyEqual', function () {

  it('should test whether two BigNumbers are nearly equal', function () {
    var epsilon = 1e-2;
    assert.equal(nearlyEqual(new BigNumber(1), new BigNumber(0.9), epsilon), false);
    assert.equal(nearlyEqual(new BigNumber(1), new BigNumber(0.95), epsilon), false);
    assert.equal(nearlyEqual(new BigNumber(1), new BigNumber(0.98), epsilon), false);
    assert.equal(nearlyEqual(new BigNumber(1), new BigNumber(0.99), epsilon), true);
    assert.equal(nearlyEqual(new BigNumber(1), new BigNumber(0.991), epsilon), true);
    assert.equal(nearlyEqual(new BigNumber(1), new BigNumber(1.1), epsilon), false);
    assert.equal(nearlyEqual(new BigNumber(1), new BigNumber(1.05), epsilon), false);
    assert.equal(nearlyEqual(new BigNumber(1), new BigNumber(1.02), epsilon), false);
    assert.equal(nearlyEqual(new BigNumber(1), new BigNumber(1.01), epsilon), true);
    assert.equal(nearlyEqual(new BigNumber(1), new BigNumber(1), epsilon), true);

    // smaller epsilon
    var epsilon2 = 1e-4;
    assert.equal(nearlyEqual(new BigNumber(1), new BigNumber(0.99), epsilon2), false);
    assert.equal(nearlyEqual(new BigNumber(1), new BigNumber(0.999), epsilon2), false);
    assert.equal(nearlyEqual(new BigNumber(1), new BigNumber(0.9999), epsilon2), true);
  });

  it('should test whether a positive and negative number are nearly equal', function () {
    var epsilon = 1e-3;
    assert.equal(nearlyEqual(new BigNumber( 1.2), new BigNumber( 1.2), epsilon), true);
    assert.equal(nearlyEqual(new BigNumber( 1.2), new BigNumber(-1.2), epsilon), false);
    assert.equal(nearlyEqual(new BigNumber(-1.2), new BigNumber( 1.2), epsilon), false);
    assert.equal(nearlyEqual(new BigNumber(-1.2), new BigNumber(-1.2), epsilon), true);
  });

  it('should test whether two large numbers are nearly equal', function () {
    var epsilon = 1e-2;
    assert.equal(nearlyEqual(new BigNumber('1e500'), new BigNumber('0.90e500'), epsilon), false);
    assert.equal(nearlyEqual(new BigNumber('1e500'), new BigNumber('0.95e500'), epsilon), false);
    assert.equal(nearlyEqual(new BigNumber('1e500'), new BigNumber('0.98e500'), epsilon), false);
    assert.equal(nearlyEqual(new BigNumber('1e500'), new BigNumber('0.99e500'), epsilon), true);
  });

  it('should test whether two small numbers are nearly equal (always true)', function () {
    var epsilon = 1e-2;
    assert.equal(nearlyEqual(new BigNumber('1e-200'), new BigNumber('0.99e-200'), epsilon), true);
    assert.equal(nearlyEqual(new BigNumber('1e-200'), new BigNumber('10e-200'), epsilon), false);
  });

  it('should compare with zero', function () {
    var epsilon = 1e-3;
    assert.equal(nearlyEqual(new BigNumber(0), new BigNumber(0), epsilon), true);
    assert.equal(nearlyEqual(new BigNumber(0), new BigNumber(-0), epsilon), true);
    assert.equal(nearlyEqual(new BigNumber(0), new BigNumber(1.2), epsilon), false);
    assert.equal(nearlyEqual(new BigNumber(0), new BigNumber(1e30), epsilon), false);
    assert.equal(nearlyEqual(new BigNumber(0), new BigNumber(1e-30), epsilon), false);
  });

  it('should compare with Infinity', function () {
    var epsilon = 1e-3;

    assert.equal(nearlyEqual(new BigNumber(1.2), new BigNumber(Infinity), epsilon), false);
    assert.equal(nearlyEqual(new BigNumber(Infinity), new BigNumber(1.2), epsilon), false);
    assert.equal(nearlyEqual(new BigNumber(Infinity), new BigNumber(Infinity), epsilon), true);
    assert.equal(nearlyEqual(new BigNumber(Infinity), new BigNumber(-Infinity), epsilon), false);
    assert.equal(nearlyEqual(new BigNumber(-Infinity), new BigNumber(Infinity), epsilon), false);
    assert.equal(nearlyEqual(new BigNumber(-Infinity), new BigNumber(-Infinity), epsilon), true);
  });

  it('should compare with NaN', function () {
    var epsilon = 1e-3;
    assert.equal(nearlyEqual(new BigNumber(1.2), new BigNumber(NaN), epsilon), false);
    assert.equal(nearlyEqual(new BigNumber(NaN), new BigNumber(1.2), epsilon), false);
    assert.equal(nearlyEqual(new BigNumber(NaN), new BigNumber(NaN), epsilon), false);
  });

  it('should do exact comparison when epsilon is null or undefined', function () {
    assert.equal(nearlyEqual(new BigNumber(1.2), new BigNumber(1.2)), true);
    assert.equal(nearlyEqual(new BigNumber(1.2), new BigNumber(1.2), null), true);

    assert.equal(nearlyEqual(new BigNumber(1.2).plus(1e-18), new BigNumber(1.2)), false);
    assert.equal(nearlyEqual(new BigNumber(1.2).plus(1e-18), new BigNumber(1.2), null), false);
  });

});