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From: John Phillips (phillips_at_[hidden])
Date: 2007-04-25 11:29:56

Matthias Schabel wrote:
> Here are some questions you might want to answer in your review:
> • What is your evaluation of the design?

   A very good design. Choices of when to use classes, member functions
and free functions are well reasoned and well documented. Use flows
sensibly from the structure of the library.

> • What is your evaluation of the implementation?

   Quite good, though I have a few nits to pick.
   Many of the special functions are implemented as rational
approximations. I'm curious whether polynomial approximations were also
tested. I know that in most cases it takes a higher degree polynomial
approximation to reach similar accuracy, so the total operation count
can benefit from rational approximations, however, not all operations
are created equal. In most common modern architectures a divide takes
about 10 times as long as a multiply or add. So, it may not be a savings
to replace 5 multiply/adds with 1 divide. Other factors such as
processor pipelining make this a difficult question to answer without
timing tests, so testing is needed to find the best mix. Unfortunately,
I don't currently have the time to run the tests myself. Since this is a
detail that is hidden from the user, later testing could lead to a
change in the implementation without causing an issue.
   I'm also curious about the source for the coefficients in these
expansions. I've looked at a couple using the Maple provided routines
for producing minimax approximations and gotten somewhat different
results. Rational coefficients via minimax is a known area where though
errors are common (the problem is usually ill-posed in a formal sense),
those errors almost always cancel out. Thus I doubt this will cause any
problem for the quality of the approximation, but I am curious.
   In general, I'm pleased to see the level of attention given to
numeric issues and the reasonable solutions provided.

> • What is your evaluation of the documentation?

   Again, my only issues are nits.
   The documentation is huge and thorough. It almost forms a framework
for a couple of texts. There are some minor editing issues, but so far I
have only found one relatively major one (in the PDF, at least). In the
introduction you give a list of the included special functions that is
very much shorter than the real list.
   Otherwise, it is readable, informative and reasonably complete.

> • What is your evaluation of the potential usefulness of the library?

   Inferior solutions to this set of problems are currently in wide use
in the computational science community. Given time for people to find
out about and adopt these, I would expect wide use in this community. I
don't feel qualified to talk about use in the business world.

> • Did you try to use the library? With what compiler? Did you
> have any problems?

   I used it with gcc 4.0.1 for a few small examples. I'd love to
combine it with the accumulators library for an example implementation
of the Kolmogorov-Smirnov test, but I haven't had time, yet.

> • How much effort did you put into your evaluation? A glance? A
> quick reading? In-depth study?

   About 4 hours with the docs, 3 hours looking at the details of the
numerics and an hour with code. It's worthy of far more time. I just
don't have the time, yet. I plan to continue looking and hopefully run
some timing tests, soon.

> • Are you knowledgeable about the problem domain?

   I'm reasonably knowledgeable. My academic work involves simulations,
statistical analyzes and some special functions. I have also taught
computational science courses.

> And finally, every review should answer this question:
> • Do you think the library should be accepted as a Boost library?

   Yes. I do. The authors deserve high praise for producing one of the
best facilities of this kind available. People spend a lot of money to
license far worse software.

                        John Phillips

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