[PATCH] Adding fixed-order Gauss-Legendre integration routines

Rhys Ulerich rhys.ulerich@gmail.com
Mon Jun 22 14:00:00 GMT 2009

> The routines include precomputed full double precision points and
> weights for n = 2, ..., 512, and 1024 Gauss points.  If the user selects
> any other number, the necessary points and weights are computed
> on the fly and remain quite good.

A quick comment from Pavel about the numerical precision in the
patch's coefficients...

> ... fixed tables included in [the patch] are way beyond full double precision.
> Full double precision is about 1e-16, fixed tables are of 1e-25.
> This doesn't hurt the double calculations and allows future extensions
> e.g. for 'long double' and multi-precision libraries (like gmp or mpfr).
> Tables generated on the fly are of 1e-10, which is pretty much the
> maximum precision we can get using double to calculate weights.
> So, on-the-fly tables are of full double precision, fixed have much
> higher precision.

- Rhys

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