/** * 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}} ax; {{dtype}} ix; {{dtype}} s1; {{dtype}} s2; 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 = {{P_ASCENDING}}; s2 = {{Q_ASCENDING}}; } else { ix = 1.0{{dtype_suffix}} / x; s1 = {{P_DESCENDING}}; s2 = {{Q_DESCENDING}}; } return s1 / s2; }