Re: complex number policy for beast

[Tim Janik <timj gtk org>]

On Sat, 4 Nov 2006, Tim Janik wrote:

> - C++ source files can use BseComplex but may opt to include <complex>
>   and use that. (they have to convert back-and-forth between std::complex
>   and BseComplex for API though).

after reading some more C++ headers, i have to add that using C++ complex 
numbers can not be recommended from an accuracy point of view, from
/usr/include/c++/3.4/complex:

  // 26.2.5/13
  // XXX: This is a grammar school implementation.
  template<typename _Tp>
    template<typename _Up>
    complex<_Tp>&
    complex<_Tp>::operator*=(const complex<_Up>& __z)
    {
      const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag();
      _M_imag = _M_real * __z.imag() + _M_imag * __z.real();
      _M_real = __r;
      return *this;
    }

this has many cancellation/etc problems, described e.g. in Numerical Recipes
and is usually worked around by in math packages, or e.g. the _Cdiv() from the
C9x specification.
also our bse_complex_div() from bsemath.[hc]* has none of these problems
(similar things hold for our other complex number functions), so if accuracy
matters at all, we better use BseComplex over std::complex<double>.

---
ciaoTJ