gl_fast_rule, a Fortran90 code 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 information on this web page is distributed under the MIT license.


gl_fast_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and codes:


legendre_rule, a Fortran90 code which computes a Gauss-Legendre quadrature rule.

quadmom, a Fortran90 code 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).

quad_rule, a Fortran90 code which defines 1-dimensional quadrature rules.

toms655, a Fortran90 code which computes the weights for interpolatory quadrature rules; this code 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:

Last revised on 22 June 2020.