Fast computation of Gauss-Legendre Quadrature Points and Weights

FASTGL is a FORTRAN90 library which carries out the fast computation of the K-th value and weight of an N-point Gauss-Legendre quadrature rule, by Ignace Bogaert.


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


FASTGL is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

LEGENDRE_RULE, a FORTRAN90 program which computes a Gauss-Legendre quadrature rule.

QUADMOM, a FORTRAN90 library which computes a Gaussian quadrature rule for a weight function rho(x) based on the Golub-Welsch procedure that only requires knowledge of the moments of rho(x).

QUADRULE, a FORTRAN90 library which contains information about quadrature rules, both as tabulated values, and as computational procedures.

TOMS655, a FORTRAN90 library which computes the weights for interpolatory quadrature rules; this library is commonly called IQPACK, by Sylvan Elhay and Jaroslav Kautsky.


  1. Ignace Bogaert,
    Iteration-free computation of Gauss-Legendre quadrature nodes and weights,
    SIAM Journal on Scientific Computing,
    Volume 36, Number 3, 2014, pages A1008-1026.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the FORTRAN90 source codes.

Last revised on 05 January 2016.