@stdlib/math-base-tools-evalrational-compile-c/lib/templates/loop.c.txt

Compile a C function for evaluating a rational function.

static const {{dtype}} {{FNAME}}_COEFFICIENTS_P = {
{{P}}
};
static const {{dtype}} {{FNAME}}_COEFFICIENTS_Q = {
{{Q}}
};

/**
* 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
* @return     evaluated rational function
*/
static {{dtype}} {{fname}}( const {{dtype}} x ) {
	{{dtype}} s1;
	{{dtype}} s2;
	{{dtype}} ax;
	{{dtype}} ix;
	int i;

	if ( x == 0.0{{dtype_suffix}} ) {
		return {{ratio}};
	}
	if ( x < 0.0{{dtype_suffix}} ) {
		ax = -x;
	} else {
		ax = x;
	}
	if ( ax <= 1.0{{dtype_suffix}} ) {
		s1 = {{FNAME}}_COEFFICIENTS_P[ {{num_coefficients}} ];
		s2 = {{FNAME}}_COEFFICIENTS_Q[ {{num_coefficients}} ];
		for ( i = {{num_coefficients}}-1; i >= 0; i-- ) {
			s1 *= x;
			s2 *= x;
			s1 += {{FNAME}}_COEFFICIENTS_P[ i ];
			s2 += {{FNAME}}_COEFFICIENTS_Q[ i ];
		}
	} else {
		ix = 1.0{{dtype_suffix}} / x; // use inverse to avoid overflow
		s1 = {{FNAME}}_COEFFICIENTS_P[ 0 ];
		s2 = {{FNAME}}_COEFFICIENTS_Q[ 0 ];
		for ( i = 1; i <= {{num_coefficients}}; i++ ) {
			s1 *= ix;
			s2 *= ix;
			s1 += {{FNAME}}_COEFFICIENTS_P[ i ];
			s2 += {{FNAME}}_COEFFICIENTS_Q[ i ];
		}
	}
	return s1 / s2;
}