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https://github.com/stdlib-js/math-base-special-fast-alpha-max-plus-beta-min

Compute the hypotenuse using the alpha max plus beta min algorithm.
https://github.com/stdlib-js/math-base-special-fast-alpha-max-plus-beta-min

alpha-max-plus-beta-min euclid euclidean fast fastmath geometry hypot hypotenuse javascript math mathematics node node-js nodejs pythagoras pythagorean-theorem stdlib triangle trig trigonometry

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Compute the hypotenuse using the alpha max plus beta min algorithm.

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README 

        



  

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# Alpha Max Plus Beta Min



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



> Compute the [hypotenuse][hypotenuse] using the [alpha max plus beta min algorithm][alpha-max-plus-beta-min].



## Installation



```bash

npm install @stdlib/math-base-special-fast-alpha-max-plus-beta-min

```



Alternatively,



-   To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).

-   If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).

-   For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).



The [branches.md][branches-url] 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



```javascript

var ampbm = require( '@stdlib/math-base-special-fast-alpha-max-plus-beta-min' );

```



#### ampbm( x, y )



Computes the [hypotenuse][hypotenuse] using the [alpha max plus beta min algorithm][alpha-max-plus-beta-min].



```javascript

var h = ampbm( -5.0, 12.0 );

// returns ~13.5

```



#### ampbm.factory( alpha, beta, \[nonnegative\[, ints]] )



Returns a function for computing the [hypotenuse][hypotenuse] using coefficients `alpha` and `beta`.



```javascript

var hypot = ampbm.factory( 1.0, 0.5 );



var h = hypot( -5.0, 12.0 );

// returns 14.5

```



If the returned function should only expect nonnegative arguments, set the `nonnegative` argument to `true`.



```javascript

var hypot = ampbm.factory( 1.0, 0.5, true );



var h = hypot( 5.0, 12.0 );

// returns 14.5

```



If the returned function should only expect signed 32-bit integers, set the `ints` argument to `true`.



```javascript

var hypot = ampbm.factory( 1.0, 0.5, false, true );



var h = hypot( -5.0, 12.0 );

// returns 14

```



If the returned function should only expect unsigned 32-bit integer valued arguments, set the `nonnegative` and `ints` arguments to `true`.



```javascript

var hypot = ampbm.factory( 1.0, 0.5, true, true );



var h = hypot( 5.0, 12.0 );

// returns 14

```



## Notes



-   The algorithm computes only an **approximation**. For precise results, use [`hypot`][@stdlib/math/base/special/hypot].



## Examples



```javascript

var randu = require( '@stdlib/random-base-randu' );

var round = require( '@stdlib/math-base-special-round' );

var ampbm = require( '@stdlib/math-base-special-fast-alpha-max-plus-beta-min' );



var x;

var y;

var h;

var i;



for ( i = 0; i < 100; i++ ) {

    x = round( randu()*100.0 ) - 50.0;

    y = round( randu()*100.0 ) - 50.0;

    h = ampbm( x, y );

    console.log( 'hypot(%d,%d) = %d', x, y, h );

}

```



* * *



## C APIs



### Usage



```c

#include "stdlib/math/base/special/fast/alpha_max_plus_beta_min.h"

```



#### stdlib_base_fast_ampbm( x, y )



Computes the hypotenuse using the alpha max plus beta min algorithm.



```c

double h = stdlib_base_fast_ampbm( -5.0, 12.0 );

// returns ~13.5

```



### Examples



```c

#include "stdlib/math/base/special/fast/alpha_max_plus_beta_min.h"

#include 



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_fast_ampbm( x[ i ], x[ i + 1 ] );

        printf( "ampbm(%lf, %lf) = %lf\n", x[ i ], x[ i + 1 ], y );

    }

}

```



## References



-   Lyons, Richard G. 2011. _Understanding Digital Signal Processing, 3rd Edition_. Prentice Hall.



* * *



## See Also



-   [`@stdlib/math-base/special/hypot`][@stdlib/math/base/special/hypot]: compute the hypotenuse avoiding overflow and underflow.



* * *



## 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 © 2016-2025. The Stdlib [Authors][stdlib-authors].



[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-special-fast-alpha-max-plus-beta-min.svg

[npm-url]: https://npmjs.org/package/@stdlib/math-base-special-fast-alpha-max-plus-beta-min



[test-image]: https://github.com/stdlib-js/math-base-special-fast-alpha-max-plus-beta-min/actions/workflows/test.yml/badge.svg?branch=main

[test-url]: https://github.com/stdlib-js/math-base-special-fast-alpha-max-plus-beta-min/actions/workflows/test.yml?query=branch:main



[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-special-fast-alpha-max-plus-beta-min/main.svg

[coverage-url]: https://codecov.io/github/stdlib-js/math-base-special-fast-alpha-max-plus-beta-min?branch=main



[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg

[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im



[stdlib]: https://github.com/stdlib-js/stdlib



[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors



[umd]: https://github.com/umdjs/umd

[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules



[deno-url]: https://github.com/stdlib-js/math-base-special-fast-alpha-max-plus-beta-min/tree/deno

[deno-readme]: https://github.com/stdlib-js/math-base-special-fast-alpha-max-plus-beta-min/blob/deno/README.md

[umd-url]: https://github.com/stdlib-js/math-base-special-fast-alpha-max-plus-beta-min/tree/umd

[umd-readme]: https://github.com/stdlib-js/math-base-special-fast-alpha-max-plus-beta-min/blob/umd/README.md

[esm-url]: https://github.com/stdlib-js/math-base-special-fast-alpha-max-plus-beta-min/tree/esm

[esm-readme]: https://github.com/stdlib-js/math-base-special-fast-alpha-max-plus-beta-min/blob/esm/README.md

[branches-url]: https://github.com/stdlib-js/math-base-special-fast-alpha-max-plus-beta-min/blob/main/branches.md



[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-special-fast-alpha-max-plus-beta-min/main/LICENSE



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



[alpha-max-plus-beta-min]: https://en.wikipedia.org/wiki/Alpha_max_plus_beta_min_algorithm



[@stdlib/math/base/special/hypot]: https://github.com/stdlib-js/math-base-special-hypot