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# log1pexp

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

<section class="usage">

## Usage

```javascript
var log1pexp = require( '@stdlib/math/base/special/log1pexp' );
```

#### log1pexp( x )

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

```javascript
var y = log1pexp( -10.0 );
// returns ~0.000045

y = log1pexp( 0.0 );
// returns ~0.693147

y = log1pexp( 5.0 );
// returns ~5.006715

y = log1pexp( 34.0 );
// returns 34.0

y = log1pexp( NaN );
// returns NaN
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

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

```javascript
var incrspace = require( '@stdlib/array/base/incrspace' );
var log1pexp = require( '@stdlib/math/base/special/log1pexp' );

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 ], log1pexp( 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/log1pexp.h"
```

#### stdlib_base_log1pexp( x )

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

```c
double out = stdlib_base_log1pexp( 5.0 );
// returns ~5.006715

out = stdlib_base_log1pexp( 34.0 );
// returns 34.0
```

The function accepts the following arguments:

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

```c
double stdlib_base_log1pexp( 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/log1pexp.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_log1pexp( 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/log1mexp`][@stdlib/math/base/special/log1mexp]</span><span class="delimiter">: </span><span class="description">evaluate the natural logarithm of 1-exp(-\|x\|).</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>

</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">

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

[@stdlib/math/base/special/exp]: https://github.com/stdlib-js/math/tree/main/base/special/exp

[@stdlib/math/base/special/ln]: https://github.com/stdlib-js/math/tree/main/base/special/ln

[@stdlib/math/base/special/log1mexp]: https://github.com/stdlib-js/math/tree/main/base/special/log1mexp

[@stdlib/math/base/special/log1p]: https://github.com/stdlib-js/math/tree/main/base/special/log1p

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

</section>

<!-- /.links -->
