# evalrational
> Compile a module for evaluating a [rational function][@stdlib/math/base/tools/evalrational].
## Usage
```javascript
var compile = require( '@stdlib/math/base/tools/evalrational-compile' );
```
#### compile( P, Q )
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
```
In the example above, the output `string` would correspond to the following module:
```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))); // eslint-disable-line max-len
s2 = -1.0 + (x * (-2.0 + (x * -3.0))); // eslint-disable-line max-len
} else {
x = 1.0 / x;
s1 = 1.0 + (x * (2.0 + (x * 3.0))); // eslint-disable-line max-len
s2 = -3.0 + (x * (-2.0 + (x * -1.0))); // eslint-disable-line max-len
}
return s1 / s2;
}
// EXPORTS //
module.exports = evalrational;
```
The coefficients should be ordered in **ascending** degree, thus matching summation notation.
## Notes
- 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' );
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 module for evaluating a rational function:
str = compile( P, Q );
console.log( str );
```
[@stdlib/math/base/tools/evalrational]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/tools/evalrational