Re: [boost] boost.math

Subject: Re: [boost] boost.math
From: John Maddock (john_at_[hidden])
Date: 2009-10-28 08:56:59

> i need to implement the computation of huges series. These series are
> made of floats, and thus the error propagates.
> The problem is that the main constrain is the execution time, thus i
> must use the more "native" type possible.
> Is boost.math offer a solution to minimize this error? Which type of
> float (float, double, any structure?) must i use?

It depends why the error is creeping in:

* Computing with double is usually as fast as with float (the only exception 
occurs where SSE optimizations can parrelellise the code).
* You could use either NTL::RR or MPFR to obtain high precision arithmetic - 
Boost.Math contains wrappers for these that make them look "just like a 
built in type" plus the glue and traits classes required to work well with 
the rest of Boost.Math, but performance will be many many times slower than 
a native type.  See 
http://www.boost.org/doc/libs/1_40_0/libs/math/doc/sf_and_dist/html/math_toolkit/using_udt.html
* You could try computing the series using Kahan's summation algorithm 
http://www.boost.org/doc/libs/1_40_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html 
but the advantage gained is usually minimal except possibly in some special 
cases.

Ultimately before you do any of the above, what you need to decide, is why 
is the error occurring?  Once you know what it is about the arithmetic 
involved that generates the error then you can start to do something about 
it.  One trick I sometimes use if I can't spot anything obvious right away 
is to write some debugging code that computes the result at two different 
precisions - set it to break when the results start to drift apart, and with 
luck you can then spot what's causing the problem.

HTH, John.