npm package: @stdlib/math-base-tools-evalrational-compile
Description: Compile a module for evaluating a rational function.
Author: The Stdlib Authors
Latest version: 0.3.1

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# evalrational

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

<section class="intro">

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/math-base-tools-evalrational-compile
```

</section>

<section class="usage">

## Usage

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

#### compile( P, Q\[, options] )

Compiles a module string containing an exported function which evaluates 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 <string>
```

The function supports the following `options`:

-   **dtype**: input argument floating-point data type (e.g., `float64` or `float32`). Default: `'float64'`.

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

<!-- eslint-disable no-unused-expressions -->

```javascript
'use strict';

// MAIN //

/**
* 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
*
* @private
* @param {number} x - value at which to evaluate the rational function
* @returns {number} evaluated rational function
*/
function evalrational( x ) {
    var ax;
    var s1;
    var 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 {
        x = 1.0 / x;
        s1 = 1.0 + (x * (2.0 + (x * 3.0)));
        s2 = -3.0 + (x * (-2.0 + (x * -1.0)));
    }
    return s1 / s2;
}


// EXPORTS //

module.exports = evalrational;
```

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

By default, the function assumes double-precision floating-point arithmetic. To emulate single-precision floating-point arithmetic, set the `dtype` option to `'float32'`.

```javascript
var P = [ 3.0, 2.0, 1.0 ];
var Q = [ -1.0, -2.0, -3.0 ];

var str = compile( P, Q, {
    'dtype': 'float32'
});
// returns <string>
```

In the previous example, the output string would correspond to the following module:

<!-- eslint-disable no-unused-expressions -->

```javascript
'use strict';

// MODULES //

var float64ToFloat32 = require( '@stdlib/number-float64-base-to-float32' );


// MAIN //

/**
* 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
*
* @private
* @param {number} x - value at which to evaluate the rational function
* @returns {number} evaluated rational function
*/
function evalrational( x ) {
    var ax;
    var s1;
    var s2;
    if ( x === 0.0 ) {
        return -3.0;
    }
    if ( x < 0.0 ) {
        ax = -x;
    } else {
        ax = x;
    }
    if ( ax <= 1.0 ) {
        s1 = float64ToFloat32(3.0 + float64ToFloat32(x * float64ToFloat32(2.0 + float64ToFloat32(x * 1.0)))); // eslint-disable-line max-len
        s2 = float64ToFloat32(-1.0 + float64ToFloat32(x * float64ToFloat32(-2.0 + float64ToFloat32(x * -3.0)))); // eslint-disable-line max-len
    } else {
        x = float64ToFloat32( 1.0 / x );
        s1 = float64ToFloat32(1.0 + float64ToFloat32(x * float64ToFloat32(2.0 + float64ToFloat32(x * 3.0)))); // eslint-disable-line max-len
        s2 = float64ToFloat32(-3.0 + float64ToFloat32(x * float64ToFloat32(-2.0 + float64ToFloat32(x * -1.0)))); // eslint-disable-line max-len
    }
    return float64ToFloat32( s1 / s2 );
}


// EXPORTS //

module.exports = evalrational;
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

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

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var compile = require( '@stdlib/math-base-tools-evalrational-compile' );

// Create arrays of random coefficients:
var P = discreteUniform( 10, -100, 100 );
var Q = discreteUniform( 10, -100, 100 );

// Compile a module for evaluating a rational function:
var str = compile( P, Q );
console.log( str );
```

</section>

<!-- /.examples -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## 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

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

<!-- /.stdlib -->

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