evalrational

Usage

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

compile( P, Q )

Compiles a C function for evaluating a rational function having coefficients P and Q.

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., double or float). Default: 'double'.
• name: function name. Default: 'evalpoly'.

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

/**
* 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.

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 <string>

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

/**
* 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;
}