npm package: @stdlib/math-base-special-log1mexp
Description: Evaluate the natural logarithm of 1-exp(-|x|).
Author: The Stdlib Authors
Latest version: 0.2.4

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# log1mexp

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

> Evaluates the [natural logarithm][@stdlib/math/base/special/ln] of `1-exp(-|x|)`.

<section class="installation">

## Installation

```bash
npm install @stdlib/math-base-special-log1mexp
```

</section>

<section class="usage">

## Usage

```javascript
var log1mexp = require( '@stdlib/math-base-special-log1mexp' );
```

#### log1mexp( x )

Evaluates the [natural logarithm][@stdlib/math/base/special/ln] of `1-exp(-|x|)`.

```javascript
var y = log1mexp( 0.0 );
// returns -Infinity

y = log1mexp( 5.0 );
// returns ~-0.00676

y = log1mexp( 10.0 );
// returns ~-0.00005

y = log1mexp( -10.0 );
// returns ~-0.00005

y = log1mexp( NaN );
// returns NaN
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

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

```javascript
var incrspace = require( '@stdlib/array-base-incrspace' );
var log1mexp = require( '@stdlib/math-base-special-log1mexp' );

var x = incrspace( -10.0, 10.0, 0.01 );

var i;
for ( i = 0; i < x.length; i++ ) {
    console.log( 'x: %d, f(x): %d', x[ i ], log1mexp( x[ i ] ) );
}
```

</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/log1mexp.h"
```

#### stdlib_base_log1mexp( x )

Evaluates the [natural logarithm][@stdlib/math/base/special/ln] of `1-exp(-|x|)`.

```c
double out = stdlib_base_log1mexp( 10.0 );
// returns ~-0.00005

out = stdlib_base_log1mexp( 5.0 );
// returns ~-0.00676
```

The function accepts the following arguments:

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

```c
double stdlib_base_log1mexp( const double 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/log1mexp.h"
#include <stdlib.h>
#include <stdio.h>

int main( void ) {
    double x;
    double v;
    int i;

    for ( i = 0; i < 100; i++ ) {
        x = ( ( (double)rand() / (double)RAND_MAX ) * 20.0 ) - 10.0;
        v = stdlib_base_log1mexp( x );
        printf( "x: %lf, f(x): %lf\n", x, v );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<!-- 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/exp`][@stdlib/math/base/special/exp]</span><span class="delimiter">: </span><span class="description">natural exponential function.</span>
-   <span class="package-name">[`@stdlib/math-base/special/ln`][@stdlib/math/base/special/ln]</span><span class="delimiter">: </span><span class="description">evaluate the natural logarithm of a double-precision floating-point number.</span>
-   <span class="package-name">[`@stdlib/math-base/special/log1p`][@stdlib/math/base/special/log1p]</span><span class="delimiter">: </span><span class="description">evaluate the natural logarithm of 1+x.</span>
-   <span class="package-name">[`@stdlib/math-base/special/log1pexp`][@stdlib/math/base/special/log1pexp]</span><span class="delimiter">: </span><span class="description">evaluate the natural logarithm of 1+exp(x).</span>

</section>

<!-- /.related -->

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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].

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---

## License

See [LICENSE][stdlib-license].


## Copyright

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

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<!-- <related-links> -->

[@stdlib/math/base/special/exp]: https://www.npmjs.com/package/@stdlib/math-base-special-exp

[@stdlib/math/base/special/ln]: https://www.npmjs.com/package/@stdlib/math-base-special-ln

[@stdlib/math/base/special/log1p]: https://www.npmjs.com/package/@stdlib/math-base-special-log1p

[@stdlib/math/base/special/log1pexp]: https://www.npmjs.com/package/@stdlib/math-base-special-log1pexp

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