npm package: @stdlib/math-base-special-kernel-log1p
Description: Evaluate a correction term for double-precision base-2 and base-10 logarithms when 1+f is in [√2/2, √2].
Author: The Stdlib Authors
Latest version: 0.0.3

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# kernelLog1p

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

> Evaluate a correction term for double-precision base-2 and base-10 logarithms when `1+f` is in `[√2/2, √2]`.

<section class="installation">

## Installation

```bash
npm install @stdlib/math-base-special-kernel-log1p
```

</section>

<section class="usage">

## Usage

```javascript
var kernelLog1p = require( '@stdlib/math-base-special-kernel-log1p' );
```

#### kernelLog1p( f )

Evaluates a correction term for double-precision base-2 and base-10 logarithms when `1+f` is in `[√2/2, √2]`.

```javascript
var v = kernelLog1p( 1.0 );
// returns ~0.1931

v = kernelLog1p( 1.4142135623730951 );
// returns ~0.4672

v = kernelLog1p( NaN );
// returns NaN
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   This function is a helper function for computing logarithms in base `e`. Argument reduction and adding the final term of the polynomial must be done by the caller for increased accuracy when different bases are used. For reference, see [`@stdlib/math-base/special/log2`][@stdlib/math/base/special/log2] and [`@stdlib/math/base/special/log10`][@stdlib/math/base/special/log10].

</section>

<!-- /.notes -->

<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 sqrt = require( '@stdlib/math-base-special-sqrt' );
var kernelLog1p = require( '@stdlib/math-base-special-kernel-log1p' );

var opts = {
    'dtype': 'float64'
};
var x = uniform( 100, sqrt( 2.0 ) / 2.0, sqrt( 2.0 ), opts );

logEachMap( 'kernelLog1p(%0.4f) = %0.4f', x, kernelLog1p );
```

</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/kernel_log1p.h"
```

#### stdlib_base_kernel_log1p( f )

Evaluates a correction term for double-precision base-2 and base-10 logarithms when `1+f` is in `[√2/2, √2]`.

```c
double out = stdlib_base_kernel_log1p( 1.0 );
// returns ~0.1931

out = stdlib_base_kernel_log1p( 1.4142135623730951 );
// returns ~0.4672
```

The function accepts the following arguments:

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

```c
double stdlib_base_kernel_log1p( const double f );
```

</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/kernel_log1p.h"
#include <stdio.h>

int main( void ) {
    const double x[] = { 0.7071, 0.7856, 0.8642, 0.9428, 1.0213, 1.0999, 1.1785, 1.2570, 1.3356, 1.4142 };

    double out;
    int i;
    for ( i = 0; i < 10; i++ ) {
        out = stdlib_base_kernel_log1p( x[ i ] );
        printf ( "x[ i ]: %lf, out: %lf\n", x[ i ], out );
    }
}
```

</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/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="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].

#### Community

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---

## Copyright

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

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[@stdlib/math/base/special/log2]: https://www.npmjs.com/package/@stdlib/math-base-special-log2

[@stdlib/math/base/special/log10]: https://www.npmjs.com/package/@stdlib/math-base-special-log10

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

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</section>

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