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

About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

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.

Community

---

Copyright

Copyright © 2016-2024. The Stdlib Authors.

Changelog

0.2.3 (2024-07-27)

<section class="commits">

Commits

<details>

• d04dcbd - docs: remove private annotations in C comments (by Philipp Burckhardt)

</details> </section> <!-- /.commits --> <section class="contributors">

Contributors

A total of 1 person contributed to this release. Thank you to this contributor:

• Philipp Burckhardt

</section> <!-- /.contributors --> </section> <!-- /.release --> <section class="release" id="v0.2.2">