npm package: @stdlib/math-base-special-kernel-tan
Description: Compute the tangent of a double-precision floating-point number on [-π/4, π/4].
Author: The Stdlib Authors
Latest version: 0.2.4

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# kernelTan

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

> Compute the [tangent][tangent] of a double-precision floating-point number on `[-π/4, π/4]`.

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### kernelTan( x, y, k )

Computes the [tangent][tangent] of a double-precision floating-point number on `[-π/4, π/4]`.

```javascript
var out = kernelTan( 3.141592653589793/4.0, 0.0, 1 );
// returns ~1.0

out = kernelTan( 3.141592653589793/6.0, 0.0, 1 );
// returns ~0.577

out = kernelTan( 0.664, 5.288e-17, 1 );
// returns ~0.783
```

If `k = 1`, the function returns `tan(x+y)`. To return the negative inverse `-1/tan(x+y)`, set `k = -1`.

```javascript
var out = kernelTan( 3.141592653589793/4.0, 0.0, -1 );
// returns ~-1.0
```

If either `x` or `y` is `NaN`, the function returns `NaN`.

```javascript
var out = kernelTan( NaN, 0.0, 1 );
// returns NaN

out = kernelTan( 3.0, NaN, 1 );
// returns NaN

out = kernelTan( NaN, NaN, 1 );
// returns NaN
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   For increased accuracy, the number for which the [tangent][tangent] should be evaluated can be supplied as a [double-double number][double-double-arithmetic] (i.e., a non-evaluated sum of two [double-precision floating-point numbers][ieee754] `x` and `y`).

-   As components of a [double-double number][double-double-arithmetic], the two [double-precision floating-point numbers][ieee754] `x` and `y` must satisfy

    <!-- <equation class="equation" label="eq:double_double_inequality" align="center" raw="|y| \leq \frac{1}{2} \operatorname{ulp}(x)" alt="Inequality for the two components of a double-double number."> -->

    <div class="equation" align="center" data-raw-text="|y| \leq \frac{1}{2} \operatorname{ulp}(x)" data-equation="eq:double_double_inequality">
        <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/kernel-tan/docs/img/equation_double_double_inequality.svg" alt="Inequality for the two components of a double-double number.">
        <br>
    </div>

    <!-- </equation> -->

    where `ulp` stands for [units in the last place][ulp].

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var linspace = require( '@stdlib/array-base-linspace' );
var binomial = require( '@stdlib/random-base-binomial' ).factory;
var PI = require( '@stdlib/constants-float64-pi' );
var kernelTan = require( '@stdlib/math-base-special-kernel-tan' );

var x = linspace( -PI/4.0, PI/4.0, 100 );
var rbinom = binomial( 1, 0.5 );

var descr;
var i;
var k;

for ( i = 0; i < x.length; i++ ) {
    k = rbinom();
    descr = ( k === 1 ) ? 'tan(%d) = %d' : '-1/tan(%d) = %d';
    console.log( descr, x[ i ], kernelTan( x[ i ], 0.0, k ) );
}
```

</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_tan.h"
```

#### stdlib_base_kernel_tan( x, y, k )

Computes the [tangent][tangent] of a double-precision floating-point number on `[-π/4, π/4]`.

```c
double out = stdlib_base_kernel_tan( 3.141592653589793/4.0, 0.0, 1 );
// returns ~1.0

out = stdlib_base_kernel_tan( 3.141592653589793/6.0, 0.0, 1 );
// returns ~0.577
```

The function accepts the following arguments:

-   **x**: `[in] double` input value (in radians, assumed to be bounded by `~pi/4` in magnitude).
-   **y**: `[in] double` tail of `x`.
-   **k**: `[in] int32_t` indicates whether `tan(x+y)` (if `k = 1`) or `-1/tan(x+y)` (if `k = -1`) is returned.

```c
double stdlib_base_kernel_tan( const double x, const double y, const int32_t k );
```

</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">

### Notes

-   For increased accuracy, the number for which the [tangent][tangent] should be evaluated can be supplied as a [double-double number][double-double-arithmetic] (i.e., a non-evaluated sum of two [double-precision floating-point numbers][ieee754] `x` and `y`).

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/math/base/special/kernel_tan.h"
#include <stdio.h>

int main( void ) {
    const double x[] = { -0.7853981633974483, -0.6108652381980153, -0.4363323129985824, -0.26179938779914946, -0.08726646259971649, 0.08726646259971649, 0.26179938779914935, 0.43633231299858233, 0.6108652381980153, 0.7853981633974483 };

    double out;
    int i;
    for ( i = 0; i < 10; i++ ) {
        out = stdlib_base_kernel_tan( x[ i ], 0.0, 1 );
        printf( "tan(%lf) = %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/kernel-cos`][@stdlib/math/base/special/kernel-cos]</span><span class="delimiter">: </span><span class="description">compute the cosine of a double-precision floating-point number on \[-π/4, π/4].</span>
-   <span class="package-name">[`@stdlib/math-base/special/kernel-sin`][@stdlib/math/base/special/kernel-sin]</span><span class="delimiter">: </span><span class="description">compute the sine of a double-precision floating-point number on \[-π/4, π/4].</span>
-   <span class="package-name">[`@stdlib/math-base/special/tan`][@stdlib/math/base/special/tan]</span><span class="delimiter">: </span><span class="description">evaluate the tangent of a number.</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

[![Chat][chat-image]][chat-url]

---

## Copyright

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

</section>

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[stdlib]: https://github.com/stdlib-js/stdlib

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[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

[deno-url]: https://github.com/stdlib-js/math-base-special-kernel-tan/tree/deno
[deno-readme]: https://github.com/stdlib-js/math-base-special-kernel-tan/blob/deno/README.md
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[branches-url]: https://github.com/stdlib-js/math-base-special-kernel-tan/blob/main/branches.md

[tangent]: https://en.wikipedia.org/wiki/Tangent

[double-double-arithmetic]: https://en.wikipedia.org/wiki/Quadruple-precision_floating-point_format#Double-double_arithmetic

[ieee754]: https://en.wikipedia.org/wiki/IEEE_floating_point

[ulp]: https://en.wikipedia.org/wiki/Unit_in_the_last_place

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

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

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

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

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

</section>

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