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Epsilon Difference

Compute the relative difference of two real numbers in units of double-precision floating-point epsilon.

Installation

npm install @stdlib/math-base-utils-float64-epsilon-difference

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

var epsdiff = require( '@stdlib/math-base-utils-float64-epsilon-difference' );

epsdiff( x, y[, scale] )

Computes the relative difference of two real numbers in units of double-precision floating-point epsilon.

var d = epsdiff( 12.15, 12.149999999999999 ); // => ~0.658ε
// returns ~0.658

The following scale functions are supported:

• max-abs: maximum absolute value of x and y (default).
• max: maximum value of x and y.
• min-abs: minimum absolute value of x and y.
• min: minimum value of x and y.
• mean-abs: arithmetic mean of the absolute values of x and y.
• mean: arithmetic mean of x and y.
• x: x (noncommutative).
• y: y (noncommutative).

By default, the function scales the absolute difference by dividing the absolute difference by the maximum absolute value of x and y. To scale by a different function, specify a scale function name.

var d = epsdiff( 2.4341309458983933, 2.4341309458633909, 'mean-abs' ); // => ~64761.5ε => ~1.438e-11
// returns ~64761.5

To use a custom scale function, provide a function which accepts two numeric arguments x and y.

function scale( x, y ) {
    // Return the minimum value:
    return ( x > y ) ? y : x;
}

var d = epsdiff( 1.0000000000000002, 1.0000000000000100, scale ); // => ~44ε
// returns ~44

Notes

• If computing the relative difference in units of epsilon will result in overflow, the function returns the maximum double-precision floating-point number.

  var d = epsdiff( 1.0e304, 1.0, 'min' ); // => ~1.798e308ε => 1.0e304/ε overflows
  // returns ~1.798e308

• If the absolute difference of x and y is 0, the relative difference is always 0.

  var d = epsdiff( 0.0, 0.0 );
  // returns 0.0
  
  d = epsdiff( 3.14, 3.14 );
  // returns 0.0

• If x = y = +infinity or x = y = -infinity, the function returns NaN.

  var PINF = require( '@stdlib/constants-float64-pinf' );
  var NINF = require( '@stdlib/constants-float64-ninf' );
  
  var d = epsdiff( PINF, PINF );
  // returns NaN
  
  d = epsdiff( NINF, NINF );
  // returns NaN

• If x = -y = +infinity or -x = y = +infinity, the relative difference is +infinity.

  var PINF = require( '@stdlib/constants-float64-pinf' );
  var NINF = require( '@stdlib/constants-float64-ninf' );
  
  var d = epsdiff( PINF, NINF );
  // returns Infinity
  
  d = epsdiff( NINF, PINF );
  // returns Infinity

• If a scale function returns 0, the function returns NaN.

  var d = epsdiff( -1.0, 1.0, 'mean' ); // => |2/0|
  // returns NaN

Examples

var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var epsdiff = require( '@stdlib/math-base-utils-float64-epsilon-difference' );

var sign;
var x;
var y;
var d;
var i;

for ( i = 0; i < 100; i++ ) {
    x = randu();
    sign = ( randu() > 0.5 ) ? 1.0 : -1.0;
    y = x + ( sign*EPS*i );
    d = epsdiff( x, y );
    console.log( 'x = %d. y = %d. d = %dε.', x, y, d );
}

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See Also

• @stdlib/math-base/utils/absolute-difference: compute the absolute difference of two real numbers.
• @stdlib/math-base/utils/relative-difference: compute the relative difference of two real numbers.

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Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.