kernelTan

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

Installation

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

Usage

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

kernelTan( x, y, k )

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

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

• 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).

• 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 ) );
}

C APIs

Usage

#include "stdlib/math/base/special/kernel_tan.h"

stdlib_base_kernel_tan( x, y, k)

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

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.

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

Notes

• 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).

Examples

#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 );
    }
}

See Also

• @stdlib/math-base/special/kernel-cos: compute the cosine of a double-precision floating-point number on [-π/4, π/4].
• @stdlib/math-base/special/kernel-sin: compute the sine of a double-precision floating-point number on [-π/4, π/4].
• @stdlib/math-base/special/tan: evaluate the tangent of a number.

Notice

This package is part of 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, see the main project repository.

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Copyright

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