npm package: @stdlib/math-base-special-hypot
Description: Compute the hypotenuse avoiding overflow and underflow.
Author: The Stdlib Authors
Latest version: 0.2.4

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# hypot

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Compute the [hypotenuse][hypotenuse] avoiding overflow and underflow.

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

```bash
npm install @stdlib/math-base-special-hypot
```

</section>

<section class="usage">

## Usage

```javascript
var hypot = require( '@stdlib/math-base-special-hypot' );
```

#### hypot( x, y )

Computes the [hypotenuse][hypotenuse] avoiding overflow and underflow.

```javascript
var h = hypot( -5.0, 12.0 );
// returns 13.0

h = hypot( -0.0, -0.0 );
// returns +0.0
```

If either argument is `NaN` and the other argument is not `+-Infinity`, the function returns `NaN`.

```javascript
var h = hypot( NaN, 12.0 );
// returns NaN

h = hypot( 5.0, NaN );
// returns NaN
```

</section>

<!-- /.usage -->

<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

## Notes

-   The textbook approach to calculating the hypotenuse is subject to overflow and underflow. For example, for a sufficiently large `x` and/or `y`, computing the hypotenuse will overflow.

    ```javascript
    var sqrt = require( '@stdlib/math-base-special-sqrt' );

    var x2 = 1.0e154 * 1.0e154;
    // returns 1.0e308

    var h = sqrt( x2 + x2 );
    // returns Infinity
    ```

    Similarly, for sufficiently small `x` and/or `y`, computing the hypotenuse will underflow.

    ```javascript
    var sqrt = require( '@stdlib/math-base-special-sqrt' );

    var x2 = 1.0e-200 * 1.0e-200;
    // returns 0.0

    var h = sqrt( x2 + x2 );
    // returns 0.0
    ```

    This implementation uses a numerically stable algorithm which avoids overflow and underflow.

    ```javascript
    var h = hypot( 1.0e154, 1.0e154 );
    // returns ~1.4142e+154

    h = hypot( 1.0e-200, 1.0e-200 );
    // returns ~1.4142e-200
    ```

</section>

<!-- /.notes -->

<!-- Package usage examples. -->

<section class="examples">

## Examples

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

```javascript
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var hypot = require( '@stdlib/math-base-special-hypot' );

var opts = {
    'dtype': 'float64'
};
var x = discreteUniform( 100, -50, 50, opts );
var y = discreteUniform( 100, -50, 50, opts );

logEachMap( 'h(%d,%d) = %0.4f', x, y, hypot );
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

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<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/math/base/special/hypot.h"
```

#### stdlib_base_hypot( x, y )

Computes the hypotenuse avoiding overflow and underflow.

```c
double h = stdlib_base_hypot( 5.0, 12.0 );
// returns 13.0
```

The function accepts the following arguments:

-   **x**: `[in] double` input value.
-   **y**: `[in] double` input value.

```c
double stdlib_base_hypot( const double x, const double y );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/math/base/special/hypot.h"
#include <stdio.h>

int main( void ) {
    const double x[] = { 3.0, 4.0, 5.0, 12.0 };

    double y;
    int i;
    for ( i = 0; i < 4; i += 2 ) {
        y = stdlib_base_hypot( x[ i ], x[ i+1 ] );
        printf( "hypot(%lf, %lf) = %lf\n", x[ i ], x[ i+1 ], y );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

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</section>

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<section class="related">

</section>

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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

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

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

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[umd]: https://github.com/umdjs/umd
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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-special-hypot/main/LICENSE

[hypotenuse]: https://en.wikipedia.org/wiki/Pythagorean_theorem

</section>

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