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Re: [PATCH] Adding fixed-order Gauss-Legendre integration routines
- From: Rhys Ulerich <rhys dot ulerich at gmail dot com>
- To: gsl-discuss at sourceware dot org
- Date: Mon, 22 Jun 2009 09:00:12 -0500
- Subject: Re: [PATCH] Adding fixed-order Gauss-Legendre integration routines
- References: <4a00655d0906211327x742b7224of110fa0621fbbad9@mail.gmail.com> <4a00655d0906211331y127e5693uda4805cf347561b3@mail.gmail.com>
> 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