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_too... * 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_too... 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.