[boost] Review request: extended complex number library

Subject: [boost] Review request: extended complex number library
From: Matthieu Schaller (matthieu.schaller_at_[hidden])
Date: 2012-03-05 16:41:16

Dear all,

Following the comments from V. Escriba, I formally propose my complex 
number library for review.
The library is an extension of the std::complex class addressing two issues:
- The standard does not guaranty the behaviour of the complex class if 
instantiated with types other than float/double/long double.
- Some calculation where pure imaginary numbers (i.e. multiples of 
sqrt(-1)) appear are unnecessarily slowed down due to the lack of 
support for these numbers.
The code I submit contains two interleaved classes boost::complex and 
boost::imaginary which can be instantiated with any type T provided T 
overloads the usual arithmetic operators and some basic (real) 
mathematical functions depending on which complex function will be 
used.  It is thus an extended version of Thorsten Ottosen's n1869 
proposal 
(http://www.open-std.org/JTC1/SC22/WG21/docs/papers/2005/n1869.html)

Performance tests show some non-negligible speed-ups compared to 
std::complex for calculations where pure imaginary numbers are involved. 
A speed-up of 25% has been observed when solving the Schroedinger 
equation explicitly on a regular mesh and some comparable figures can be 
observed when computing the Mandelbrot set (the two examples snippets 
provided in the archive).
Furthermore, the functions (sin(), exp(), log(),...) involving 
boost::imaginary numbers are more precise than their equivalent using a 
std::complex with the real part set to 0.

The code and (doxygen) documentation is available in the repository 
http://code.google.com/p/cpp-imaginary-numbers/
A comprehensive zip archive can be found in the "download" and the code 
can also be checked-out via the SVN repository.
The archive contains the class header, two examples, a comprehensive 
precision test, a brute-force performance test and the documentation.

I'd be happy to answer any question from your side and to provide more 
detailed information if required.

Regards,

Matthieu
-- 
Matthieu Schaller
PhD student - Durham University