feat: add math/base/special/factoriallnf

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stdlib-js · Planeshifter · Aug 7, 2025 · Aug 6, 2025 · Aug 7, 2025 · Aug 7, 2025
commit d8227b0efd00eb00b8de9f321debc8351f414e0a
diff --git a/lib/node_modules/@stdlib/math/base/special/factoriallnf/README.md b/lib/node_modules/@stdlib/math/base/special/factoriallnf/README.md
@@ -0,0 +1,257 @@
+<!--
+
+@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.
+
+-->
+
+# factoriallnf
+
+> Natural logarithm of the [factorial][factorial-function] of a single-precision floating-point number.
+
+<section class="intro">
+
+The natural logarithm of the factorial function may be expressed
+
+<!-- <equation class="equation" label="eq:factorialln_function" align="center" raw="f(n)=\ln (n!)" alt="Equation of the natural logarithm of the factorial."> -->
+
+```math
+f(n)=\ln (n!)
+```
+
+<!-- </equation> -->
+
+The [factorial function][factorial-function] may be defined as the product
+
+<!-- <equation class="equation" label="eq:factorial_function" align="center" raw="n! = \prod_{k=1}^n k" alt="Factorial function definition"> -->
+
+```math
+n! = \prod_{k=1}^n k
+```
+
+<!-- </equation> -->
+
+or according to the recurrence relation
+
+<!-- <equation class="equation" label="eq:factorial_recurrence_relation" align="center" raw="n! = \begin{cases}1 & \textrm{if } n = 0,\\(n-1)! \times n & \textrm{if } n > 1\end{cases}" alt="Factorial function recurrence relation"> -->
+
+```math
+n! = \begin{cases}1 & \textrm{if } n = 0,\\(n-1)! \times n & \textrm{if } n > 1\end{cases}
+```
+
+<!-- </equation> -->
+
+Following the convention for an [empty product][empty-product], in all definitions,
+
+<!-- <equation class="equation" label="eq:zero_factorial" align="center" raw="0! = 1" alt="Zero factorial"> -->
+
+```math
+0! = 1
+```
+
+<!-- </equation> -->
+
+The [Gamma][gamma-function] function extends the [factorial function][factorial-function] for non-integer values.
+
+<!-- <equation class="equation" label="eq:factorial_function_and_gamma" align="center" raw="n! = \Gamma(n+1)" alt="Factorial function extension via the Gamma function"> -->
+
+```math
+n! = \Gamma(n+1)
+```
+
+<!-- </equation> -->
+
+The [factorial][factorial-function] of a **negative** integer is not defined.
+
+Evaluating the natural logarithm of [factorial function][factorial-function] is useful as the [factorial function][factorial-function] can overflow for large `n`. Thus, `factoriallnf( n )` is generally preferred to `lnf( n! )`.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var factoriallnf = require( '@stdlib/math/base/special/factoriallnf' );
+```
+
+#### factoriallnf( x )
+
+Evaluates the natural logarithm of the [factorial][factorial-function] of a single-precision floating-point number. For input values other than negative integers, the function returns `ln( x! ) = ln( Γ(x+1) )`, where `Γ` is the [Gamma][gamma-function] function. For negative integers, the function returns `NaN`.
+
+```javascript
+var v = factoriallnf( 3.0 );
+// returns ~1.792
+
+v = factoriallnf( 2.4 );
+// returns ~1.092
+
+v = factoriallnf( -1.0 );
+// returns NaN
+
+v = factoriallnf( -1.5 );
+// returns ~1.266
+```
+
+If provided `NaN`, the function returns `NaN`.
+
+```javascript
+var v = factoriallnf( NaN );
+// returns NaN
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var uniform = require( '@stdlib/random/array/uniform' );
+var logEachMap = require( '@stdlib/console/log-each-map' );
+var factoriallnf = require( '@stdlib/math/base/special/factoriallnf' );
+
+var opts = {
+    'dtype': 'float32'
+};
+var x = uniform( 100, -10.0, 50.0, opts );
+
+logEachMap( 'factoriallnf(%0.4f) = %0.4f', x, factoriallnf );
+```
+
+</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/factoriallnf.h"
+```
+
+#### stdlib_base_factoriallnf( x )
+
+Evaluates the natural logarithm of the [factorial][factorial-function] of a single-precision floating-point number. For input values other than negative integers, the function returns `ln( x! ) = ln( Γ(x+1) )`, where `Γ` is the [Gamma][gamma-function] function. For negative integers, the function returns `NaN`.
+
+```c
+float out = stdlib_base_factoriallnf( 3.0f );
+// returns ~1.792f
+
+out = stdlib_base_factoriallnf( -1.5f );
+// returns ~1.266f
+```
+
+The function accepts the following arguments:
+
+-   **x**: `[in] float` input value.
+
+```c
+float stdlib_base_factoriallnf( const float x );
+```
+
+</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/factoriallnf.h"
+#include <stdio.h>
+
+int main( void ) {
+    const float x[] = { 2.0f, 3.0f, 5.0f, 8.0f };
+
+    float y;
+    int i;
+    for ( i = 0; i < 4; i++ ) {
+        y = stdlib_base_factoriallnf( x[ i ] );
+        printf( "factoriallnf(%f) = %f\n", x[ i ], y );
+    }
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</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">
+
+[gamma-function]: https://en.wikipedia.org/wiki/Gamma_Function
+
+[factorial-function]: https://en.wikipedia.org/wiki/Factorial
+
+[empty-product]: https://en.wikipedia.org/wiki/Empty_product
+
+<!-- <related-links> -->
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->
diff --git a/lib/node_modules/@stdlib/math/base/special/factoriallnf/benchmark/benchmark.js b/lib/node_modules/@stdlib/math/base/special/factoriallnf/benchmark/benchmark.js
@@ -0,0 +1,79 @@
+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var floorf = require( '@stdlib/math/base/special/floorf' );
+var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
+var pkg = require( './../package.json' ).name;
+var factoriallnf = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg+'::integers', function benchmark( b ) {
+	var x;
+	var y;
+	var i;
+
+	x = uniform( 100, 1.0, 35.0, {
+		'dtype': 'float32'
+	});
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = factoriallnf( floorf( x[ i%x.length ] ) );
+		if ( isnanf( y ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnanf( y ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
+
+bench( pkg+'::decimals', function benchmark( b ) {
+	var x;
+	var y;
+	var i;
+
+	x = uniform( 100, 1.0, 35.0, {
+		'dtype': 'float32'
+	});
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = factoriallnf( x[ i%x.length ] );
+		if ( isnanf( y ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnanf( y ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});