[SciPy-dev] Bessel functions from Boost

Charles R Harris charlesr.harris@gmail....
Mon Feb 9 10:28:42 CST 2009


On Mon, Feb 9, 2009 at 3:26 AM, Pauli Virtanen <pav@iki.fi> wrote:

> Mon, 09 Feb 2009 01:20:11 -0800, Ondrej Certik wrote:
> [clip]
> > Right. For double precision I think mpmath is not so fast. Fredrik, is
> > it difficult to make mpmath fast even for double precision?
> >
> > Last time I asked:
> >
> > http://groups.google.com/group/mpmath/browse_thread/thread/
> bca53c3382945c34/<http://groups.google.com/group/mpmath/browse_thread/thread/%0Abca53c3382945c34/>
> >
> > you replied:
> >
> > "
> > SciPy already provides a truckload of machine precision special
> > functions, with excellent (fast and robust) implementations. It'd be
> > hard to top that.
> > "
> >
> > But apparently, maybe mpmath can be useful.
>
> I'd say that mpmath faces the same robustness and testing issues as Scipy
> with regard to special functions. (In addition, since it's written in
> Python, I'd assume it also faces additional performance issues.)
>
> Also, algorithms that work well in arbitrary precision might not work for
> limited precision, due to loss of precision or under/overflows in
> intermediate steps. Looking at the Bessel function implementations in
> mpmath/functions.py, I'd say that at least besselj and besseli would face
> overflow issues for large arguments if they were working in double
> precision. This kind of issues are actually the most difficult to get
> right.
>
> To clarify: Definitely I think that mpmath is great work, and I'm happy
> to see people working on it, including improvements to its special
> function library.
>
> But at the present, I think the path of least resistance for Scipy is to
> continue using, testing, and improving existing implementations of
> special function codes, written in C or F77, directly for limited
> precision.
>

Here are some references for both testing and implementations:
http://math.nist.gov/mcsd/Reports/2001/nesf/ . I found Cody's book(s) a good
reference back in the day.

I wonder if anything happened with this proposal:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.44.7298 ? Note the
references to Cody which are to works with both implementations and tests. I
think Cody was responsible for specfun, have there been problems with that
package?

Chuck
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