feat: add math/base/special/fast/alpha-max-plus-beta-minf

lib/node_modules/@stdlib/math/base/special/fast/alpha-max-plus-beta-minf/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2025 The Stdlib Authors.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+   http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+
+-->
+
+# Alpha Max Plus Beta Minf
+
+> Compute the [hypotenuse][hypotenuse] of a single-precision floating point number using the [alpha max plus beta min algorithm][alpha-max-plus-beta-min].
+
+<!-- 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="usage">
+
+## Usage
+
+```javascript
+var ampbmf = require( '@stdlib/math/base/special/fast/alpha-max-plus-beta-minf' );
+```
+
+#### ampbmf( x, y )
+
+Computes the [hypotenuse][hypotenuse] of a single-precision floating point number using the [alpha max plus beta min algorithm][alpha-max-plus-beta-min].
+
+```javascript
+var h = ampbmf( -5.0, 12.0 );
+// returns ~13.5
+```
+
+#### ampbmf.factory( alpha, beta, \[nonnegative\[, ints]] )
+
+Returns a function for computing the [hypotenuse][hypotenuse] using coefficients `alpha` and `beta`.
+
+```javascript
+var hypotf = ampbmf.factory( 1.0, 0.5 );
+
+var h = hypotf( -5.0, 12.0 );
+// returns 14.5
+```
+
+If the returned function should only expect nonnegative arguments, set the `nonnegative` argument to `true`.
+
+```javascript
+var hypotf = ampbmf.factory( 1.0, 0.5, true );
+
+var h = hypotf( 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 hypotf = ampbmf.factory( 1.0, 0.5, false, true );
+
+var h = hypotf( -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 hypotf = ampbmf.factory( 1.0, 0.5, true, true );
+
+var h = hypotf( 5.0, 12.0 );
+// returns 14
+```
+
+</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 algorithm computes only an **approximation**. For precise results, use [`hypot`][@stdlib/math/base/special/hypot].
+
+</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 ampbmf = require( '@stdlib/math/base/special/fast/alpha-max-plus-beta-minf' );
+
+var opts = {
+    'dtype': 'float32'
+};
+var x = discreteUniform( 100, -50, 50, opts );
+var y = discreteUniform( 100, -50, 50, opts );
+
+logEachMap( 'hypotf(%f,%f) = %0.4f', x, y, ampbmf );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- C interface documentation. -->
+
+* * *
+
+<section class="c">
+
+## C APIs
+
+<!-- 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 -->
+
+<!-- C usage documentation. -->
+
+<section class="usage">
+
+### Usage
+
+```c
+#include "stdlib/math/base/special/fast/alpha_max_plus_beta_minf.h"
+```
+
+#### stdlib_base_fast_ampbmf( x, y )
+
+Computes the hypotenuse of a single-precision floating point number using the alpha max plus beta min algorithm.
+
+```c
+float h = stdlib_base_fast_ampbmf( -5.0f, 12.0f );
+// returns ~13.5
+```
+
+</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/fast/alpha_max_plus_beta_minf.h"
+#include <stdio.h>
+
+int main( void ) {
+    const float x[] = { 3.0f, 4.0f, 5.0f, 12.0f };
+
+    float y;
+    int i;
+    for ( i = 0; i < 4; i += 2 ) {
+        y = stdlib_base_fast_ampbmf( x[ i ], x[ i + 1 ] );
+        printf( "ampbmf(%f, %f) = %f\n", x[ i ], x[ i + 1 ], y );
+    }
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="references">
+
+## References
+
+-   Lyons, Richard G. 2011. _Understanding Digital Signal Processing, 3rd Edition_. Prentice Hall.
+
+</section>
+
+<!-- /.references -->
+
+<!-- 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/special/hypot`][@stdlib/math/base/special/hypot]</span><span class="delimiter">: </span><span class="description">compute the hypotenuse avoiding overflow and underflow.</span>
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[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/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/hypot
+
+<!-- <related-links> -->
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->