# Kernel Tangent
> Compute the [tangent][tangent] of a number on `[-π/4, π/4]`.
## Usage
```javascript
var kernelTan = require( '@stdlib/math/base/special/kernel-tan' );
```
#### kernelTan( x, y, k )
Computes the [tangent][tangent] of a `number` on `[-π/4, π/4]`. 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`).
```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
```
## Notes
- As components of a [double-double number][double-double-arithmetic], the two [double-precision floating-point numbers][ieee754] `x` and `y` must satisfy
where `ulp` stands for [units in the last place][ulp].
## Examples
```javascript
var linspace = require( '@stdlib/array/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 ) );
}
```
[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
