Re: [Boost-users] Spherical Bessel function (nu, x as real) implementation

Subject: Re: [Boost-users] Spherical Bessel function (nu, x as real) implementation
From: John Maddock (jz.maddock_at_[hidden])
Date: 2016-02-26 06:47:25

> 1)
> Does you use this reference to compute Spherical Bessel Functions for 
> real argument?
>
> Accurate recursive generation of spherical Bessel and Neumann 
> functions for a large range of indices
> E. Gillman <http://scitation.aip.org/content/contributor/AU0510272>^1 
> and H. R. Fiebig 
> <http://scitation.aip.org/search?value1=H.+R.+Fiebig&option1=author&option912=resultCategory&value912=ResearchPublicationContent>Comput. 
> Phys. 2, 62(1988); http://dx.doi.org/10.1063/1.168296
>
They're implemented in terms of the regular (non-spherical) functions - 
please see the documentation for full details.

> 2) is there a way to speed up the computation of j_nu(x) if one wants 
> 10 digits accuracy for instance?

Yes, by way of an experiment suggest you define:

BOOST_MATH_PROMOTE_DOUBLE_POLICY=false
BOOST_MATH_DIGITS10_POLICY=10

at the start of the compilation unit (or on the command line).  The 
second one will make only a small difference to speed, the first can 
make as much as a 2x difference on Linux x64.

HTH, John.