Kernel Tangent

Compute the tangent of a number on [-π/4, π/4].

Usage

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

kernelTan( x, y, k )

Computes the tangent of a number on [-π/4, π/4]. For increased accuracy, the number for which the tangent should be evaluated can be supplied as a double-double number (i.e., a non-evaluated sum of two double-precision floating-point numbers x and y).

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.

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

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

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, the two double-precision floating-point numbers x and y must satisfy
where ulp stands for units in the last place.

Examples

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 ) );
}