fastgl.hpp

//*******************************************
//   Copyright (C) 2014 by Ignace Bogaert   *
//*******************************************

// This software package is based on the paper
//    I. Bogaert, "Iteration-Free Computation of Gauss-Legendre Quadrature Nodes and Weights",
//    to be published in the SIAM Journal of Scientific Computing.

// The main features of this software are:
// - Speed: due to the simple formulas and the O(1) complexity computation of individual Gauss-Legendre 
//   quadrature nodes and weights. This makes it compatible with parallel computing paradigms.
// - Accuracy: the error on the nodes and weights is within a few ulps (see the paper for details).

// Disclaimer:
// THIS SOFTWARE IS PROVIDED "AS IS" AND ANY EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED 
// WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR 
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, 
// BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
// HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR 
// OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

#ifndef FASTGL_H
#define FASTGL_H

#include <stddef.h>
#include <cmath>

// Functions for fastgl in double precision
namespace fastgl {
	// A struct for containing a Node-Weight pair
	struct QuadPair {
		double theta, weight;
		
		// A function for getting the node in x-space
		double x() {return cos(theta);}
		
		// A constructor
		QuadPair(double t, double w) : theta(t), weight(w) {}
		QuadPair() {}
	};
	
	// Function for getting Gauss-Legendre nodes & weights
	// Theta values of the zeros are in [0,pi], and monotonically increasing. 
	// The index of the zero k should always be in [1,n].
	// Compute a node-weight pair:
	QuadPair GLPair(size_t n, size_t k);
}








#endif