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https://github.com/stdlib-js/math-base-tools-evalrational-compile-c

Compile a C function for evaluating a rational function.
https://github.com/stdlib-js/math-base-tools-evalrational-compile-c

c compile eval evalp evaluate horner javascript math mathematics native node node-js nodejs polynomial ratio rational stdlib

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Compile a C function for evaluating a rational function.

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README 

        



  

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# evalrational



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



> Compile a C function for evaluating a [rational function][@stdlib/math/base/tools/evalrational].



## Installation



```bash

npm install @stdlib/math-base-tools-evalrational-compile-c

```



## Usage



```javascript

var compile = require( '@stdlib/math-base-tools-evalrational-compile-c' );

```



#### compile( P, Q )



Compiles a C function for evaluating a [rational function][@stdlib/math/base/tools/evalrational] having coefficients `P` and `Q`.



```javascript

var P = [ 3.0, 2.0, 1.0 ];

var Q = [ -1.0, -2.0, -3.0 ];



var str = compile( P, Q );

// returns 

```



The function supports the following `options`:



-   **dtype**: input argument floating-point data type (e.g., `double` or `float`). Default: `'double'`.

-   **name**: function name. Default: `'evalpoly'`.



In the example above, the output string would correspond to the following function:



```c

/**

* Evaluates a rational function (i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\)).

*

* ## Notes

*

* -   Coefficients should be sorted in ascending degree.

* -   The implementation uses [Horner's rule][horners-method] for efficient computation.

*

* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method

*

* @param x    value at which to evaluate the rational function

* @returns    evaluated rational function

*/

static double evalrational( const double x ) {

    double ax;

    double ix;

    double s1;

    double s2;

    if ( x == 0.0 ) {

        return -3.0;

    }

    if ( x < 0.0 ) {

        ax = -x;

    } else {

        ax = x;

    }

    if ( ax <= 1.0 ) {

        s1 = 3.0 + (x * (2.0 + (x * 1.0)));

        s2 = -1.0 + (x * (-2.0 + (x * -3.0)));

    } else {

        ix = 1.0 / x;

        s1 = 1.0 + (ix * (2.0 + (ix * 3.0)));

        s2 = -3.0 + (ix * (-2.0 + (ix * -1.0)));

    }

    return s1 / s2;

}

```



To generate a function having a custom name and supporting single-precision floating-point numbers, provide the corresponding options.



```javascript

var P = [ 3.0, 2.0, 1.0 ];

var Q = [ -1.0, -2.0, -3.0 ];



var opts = {

    'dtype': 'float',

    'name': 'rational123'

};

var str = compile( P, Q, opts );

// returns 

```



For the previous example, the output string would correspond to the following function:



```c

/**

* Evaluates a rational function (i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\)).

*

* ## Notes

*

* -   Coefficients should be sorted in ascending degree.

* -   The implementation uses [Horner's rule][horners-method] for efficient computation.

*

* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method

*

* @param x    value at which to evaluate the rational function

* @returns    evaluated rational function

*/

static float rational123( const float x ) {

    float ax;

    float ix;

    float s1;

    float s2;

    if ( x == 0.0f ) {

        return -3.0f;

    }

    if ( x < 0.0f ) {

        ax = -x;

    } else {

        ax = x;

    }

    if ( ax <= 1.0f ) {

        s1 = 3.0f + (x * (2.0f + (x * 1.0f)));

        s2 = -1.0f + (x * (-2.0f + (x * -3.0f)));

    } else {

        ix = 1.0f / x;

        s1 = 1.0f + (ix * (2.0f + (ix * 3.0f)));

        s2 = -3.0f + (ix * (-2.0f + (ix * -1.0f)));

    }

    return s1 / s2;

}

```



## Notes



-   The coefficients should be ordered in **ascending** degree, thus matching summation notation.

-   The function is intended for **non-browser** environments for the purpose of generating module files.



## Examples



```javascript

var randu = require( '@stdlib/random-base-randu' );

var round = require( '@stdlib/math-base-special-round' );

var Float64Array = require( '@stdlib/array-float64' );

var compile = require( '@stdlib/math-base-tools-evalrational-compile-c' );



var sign;

var str;

var P;

var Q;

var i;



// Create two arrays of random coefficients...

P = new Float64Array( 10 );

Q = new Float64Array( 10 );

for ( i = 0; i < P.length; i++ ) {

    if ( randu() < 0.5 ) {

        sign = -1.0;

    } else {

        sign = 1.0;

    }

    P[ i ] = sign * round( randu()*100.0 );

    Q[ i ] = sign * round( randu()*100.0 );

}



// Compile a function for evaluating a rational function:

str = compile( P, Q );

console.log( str );

```



* * *



## 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 © 2016-2024. The Stdlib [Authors][stdlib-authors].



[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-tools-evalrational-compile-c.svg

[npm-url]: https://npmjs.org/package/@stdlib/math-base-tools-evalrational-compile-c



[test-image]: https://github.com/stdlib-js/math-base-tools-evalrational-compile-c/actions/workflows/test.yml/badge.svg?branch=main

[test-url]: https://github.com/stdlib-js/math-base-tools-evalrational-compile-c/actions/workflows/test.yml?query=branch:main



[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-tools-evalrational-compile-c/main.svg

[coverage-url]: https://codecov.io/github/stdlib-js/math-base-tools-evalrational-compile-c?branch=main



[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg

[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im



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



[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors



[@stdlib/math/base/tools/evalrational]: https://github.com/stdlib-js/math-base-tools-evalrational