math-evalrational/lib/factory.js

Evaluates a rational function.

/* jshint evil:true */
'use strict';

// EVAL RATIONAL FACTORY //

/**
* FUNCTION: factory( P, Q )
*	Returns a function for evaluating a rational function.
*
* @param {Number[]|Int8Array|Uint8Array|Uint8ClampedArray|Int16Array|Uint16Array|Int32Array|Uint32Array|Float32Array|Float64Array} P - numerator polynomial coefficients sorted in ascending degree
* @param {Number[]|Int8Array|Uint8Array|Uint8ClampedArray|Int16Array|Uint16Array|Int32Array|Uint32Array|Float32Array|Float64Array} Q - denominator polynomial coefficients sorted in ascending degree
* @returns {Function} function for evaluating a rational function
*/
function factory( P, Q ) {
	var f;
	var r;
	var n;
	var m;
	var i;

	// Code generation. Start with the function definition...
	f = 'return function evalrational(x){';

	// Create the function body...
	n = P.length;

	// Declare variables...
	f += 'var ax,s1,s2;';

	// If no coefficients, the function always returns NaN...
	if ( n === 0 ) {
		f += 'return NaN;';
	}
	// If P and Q have different lengths, the function always returns NaN...
	else if ( n !== Q.length ) {
		f += 'return NaN;';
	}
	// If P and Q have only one coefficient, the function always returns the ratio of the first coefficients...
	else if ( n === 1 ) {
		r = P[ 0 ] / Q[ 0 ];
		f += 'return ' + r + ';';
	}
	// If more than one coefficient, apply Horner's method to both the numerator and denominator...
	else {
		// If `x == 0`, return the ratio of the first coefficients...
		r = P[ 0 ] / Q[ 0 ];
		f += 'if(x===0){return ' + r + ';}';

		// Compute the absolute value of `x`...
		f += 'if(x<0){ax=-x;}else{ax=x;}';

		// If `abs(x) <= 1`, evaluate the numerator and denominator of the rational function using Horner's method...
		f += 'if(ax<=1){';
		f += 's1 = ' + P[ 0 ];
		m = n - 1;
		for ( i = 1; i < n; i++ ) {
			f += '+x*';
			if ( i < m ) {
				f += '(';
			}
			f += P[ i ];
		}
		// Close all the parentheses...
		for ( i = 0; i < m-1; i++ ) {
			f += ')';
		}
		f += ';';
		f += 's2 = ' + Q[ 0 ];
		m = n - 1;
		for ( i = 1; i < n; i++ ) {
			f += '+x*';
			if ( i < m ) {
				f += '(';
			}
			f += Q[ i ];
		}
		// Close all the parentheses...
		for ( i = 0; i < m-1; i++ ) {
			f += ')';
		}
		f += ';';

		// Close the if statement...
		f += '}else{';

		// If `abs(x) > 1`, evaluate the numerator and denominator via the inverse to avoid overflow...
		f += 'x = 1/x;';
		m = n - 1;
		f += 's1 = ' + P[ m ];
		for ( i = m - 1; i >= 0; i-- ) {
			f += '+x*';
			if ( i > 0 ) {
				f += '(';
			}
			f += P[ i ];
		}
		// Close all the parentheses...
		for ( i = 0; i < m-1; i++ ) {
			f += ')';
		}
		f += ';';

		m = n - 1;
		f += 's2 = ' + Q[ m ];
		for ( i = m - 1; i >= 0; i-- ) {
			f += '+x*';
			if ( i > 0 ) {
				f += '(';
			}
			f += Q[ i ];
		}
		// Close all the parentheses...
		for ( i = 0; i < m-1; i++ ) {
			f += ')';
		}
		f += ';';

		// Close the else statement...
		f += '}';

		// Return the ratio of the two sums...
		f += 'return s1/s2;';
	}
	// Close the function:
	f += '}';

	// Create the function in the global scope:
	return ( new Function( f ) )();

	/**
	* returns
	*	function evalrational( x ) {
	*		var ax, s1, s2;
	*		if ( x === 0 ) {
	*			return P[0] / Q[0];
	*		}
	*		if ( x < 0 ) {
	*			ax = -x;
	*		} else {
	*			ax = x;
	*		}
	*		if ( ax <= 1 ) {
	*			s1 = P[0]+x*(P[1]+x*(P[2]+x*(P[3]+...+x*(P[n-2]+x*P[n-1]))));
	*			s2 = Q[0]+x*(Q[1]+x*(Q[2]+x*(Q[3]+...+x*(Q[n-2]+x*Q[n-1]))));
	*		} else {
	*			x = 1/x;
	*			s1 = P[n-1]+x*(P[n-2]+x*(P[n-3]+x*(P[n-4]+...+x*(P[1]+x*P[0]))));
	*			s2 = Q[n-1]+x*(Q[n-2]+x*(Q[n-3]+x*(Q[n-4]+...+x*(Q[1]+x*Q[0]))));
	*		}
	*		return s1 / s2;
	*	}
	*/
} // end FUNCTION factory()


// EXPORTS //

module.exports = factory;