npm package: @stdlib/math-base-utils-float64-epsilon-difference
Description: Compute the relative difference of two real numbers in units of double-precision floating-point epsilon.
Author: The Stdlib Authors
Latest version: 0.2.3

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# Epsilon Difference

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> Compute the [relative difference][@stdlib/math/base/utils/relative-difference] of two real numbers in units of [double-precision floating-point epsilon][@stdlib/constants/float64/eps].

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### epsdiff( x, y\[, scale] )

Computes the [relative difference][@stdlib/math/base/utils/relative-difference] of two real numbers in units of [double-precision floating-point epsilon][@stdlib/constants/float64/eps].

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

The following [`scale`][@stdlib/math/base/utils/relative-difference] functions are supported:

-   **max-abs**: maximum [absolute value][@stdlib/math/base/special/abs] of `x` and `y` (_default_).
-   **max**: maximum value of `x` and `y`.
-   **min-abs**: minimum [absolute value][@stdlib/math/base/special/abs] of `x` and `y`.
-   **min**: minimum value of `x` and `y`.
-   **mean-abs**: arithmetic mean of the [absolute values][@stdlib/math/base/special/abs] 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][@stdlib/math/base/utils/absolute-difference] by dividing the [absolute difference][@stdlib/math/base/utils/absolute-difference] by the maximum [absolute value][@stdlib/math/base/special/abs] of `x` and `y`. To scale by a different function, specify a scale function name.

```javascript
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`.

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

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

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If computing the [relative difference][@stdlib/math/base/utils/relative-difference] in units of [epsilon][@stdlib/constants/float64/eps] will result in overflow, the function returns the [maximum double-precision floating-point number][@stdlib/constants/float64/max].

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

-   If the [absolute difference][@stdlib/math/base/utils/absolute-difference] of `x` and `y` is `0`, the [relative difference][@stdlib/math/base/utils/relative-difference] is **always** `0`.

    ```javascript
    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`.

    ```javascript
    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][@stdlib/math/base/utils/relative-difference] is `+infinity`.

    ```javascript
    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`.

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

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
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 );
}
```

</section>

<!-- /.examples -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/math-base/utils/absolute-difference`][@stdlib/math/base/utils/absolute-difference]</span><span class="delimiter">: </span><span class="description">compute the absolute difference of two real numbers.</span>
-   <span class="package-name">[`@stdlib/math-base/utils/relative-difference`][@stdlib/math/base/utils/relative-difference]</span><span class="delimiter">: </span><span class="description">compute the relative difference of two real numbers.</span>

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].

#### Community

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

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<!-- <related-links> -->

[@stdlib/math/base/utils/absolute-difference]: https://www.npmjs.com/package/@stdlib/math-base-utils-absolute-difference

[@stdlib/math/base/utils/relative-difference]: https://www.npmjs.com/package/@stdlib/math-base-utils-relative-difference

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