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Subject: Re: [boost] Review request: extended complex number library
From: Neal Becker (ndbecker2_at_[hidden])
Date: 2012-03-06 07:28:20

Matthieu Schaller wrote:

> 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
> (
> 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
> 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

Seems quite interesting. One issue I have though, as a user of gcc/libstdc++, I
see that the versions of many std::complex operations seem to be optimized in
terms of gcc builtins. For example:

  inline float
  __complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); }

  inline double
  __complex_abs(__complex__ double __z) { return __builtin_cabs(__z); }

So if I switched to boost::complex, I'd loose these optimizations.

Is it useful to have an imaginary library that complements std::complex, rather
than replaces it?

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