About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

factoriallnf

Natural logarithm of the factorial of a single-precision floating-point number.

The natural logarithm of the factorial function may be expressed

$$f(n)=\ln (n!)$$

The factorial function may be defined as the product

$$n! = \prod_{k=1}^n k$$

or according to the recurrence relation

$$n! = \begin{cases}1 & \textrm{if } n = 0,\\(n-1)! \times n & \textrm{if } n > 1\end{cases}$$

Following the convention for an empty product, in all definitions,

$$0! = 1$$

The Gamma function extends the factorial function for non-integer values.

$$n! = \Gamma(n+1)$$

The factorial of a negative integer is not defined.

Evaluating the natural logarithm of factorial function is useful as the factorial function can overflow for large n. Thus, factoriallnf( n ) is generally preferred to lnf( n! ).

Installation

npm install @stdlib/math-base-special-factoriallnf

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md 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

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

factoriallnf( x )

Evaluates the natural logarithm of the factorial 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 function. For negative integers, the function returns NaN.

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.

var v = factoriallnf( NaN );
// returns NaN

Examples

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 );

---

C APIs

Usage

#include "stdlib/math/base/special/factoriallnf.h"

stdlib_base_factoriallnf( x )

Evaluates the natural logarithm of the factorial 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 function. For negative integers, the function returns NaN.

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.

float stdlib_base_factoriallnf( const float x );

Examples

#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 );
    }
}

---

Notice

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

Community

---

License

See LICENSE.

Copyright

Copyright © 2016-2025. The Stdlib Authors.