Hi Paul,

you wrote:

>  > I've again tried to compile this with GCC 3.2.1. Here are the
diagnostics:
>  >
>  > In file included from test_circle_area.cpp:12:
>  > function_constants.hpp:83: uninitialized const `
>  >    boost::math::float_constants::pi
>  >
>  > The following workaround (applied to all constants) heals this
>  >
>  >   namespace float_constants
>  >   {
>  > #ifndef __GNUC__
>  >    constant< float, pi_tag > const pi;
>  > #else
>  >    constant< float, pi_tag > const pi = constant< float, pi_tag >();
>  > #endif
>  >   }
> 
>  This may be better for all platforms? I'll think about this.

Some more information: ICC 7.0 seems to accept both forms and Kylix none of
them (didn't analyze further) ;-(

>  > The preprocessor symbol __TIMESTAMP__ seems to be platform specific.
>  Agreed - but I personally find it useful so tend to use it. I should
bracket
>  with #ifdef MSVC ...
>  >
>  > Ok, back to my earlier question. If I understand you correctly, we
better
>  > should write
>  >
>  > return boost::math::constant< T, boost::math::pi_tag >() * radius *
radius;
>  >
>  > instead of something like
>  >
>  > return boost::math::constant< T >::pi() * radius * radius;
>  >
>  > in generic code? I'll have to think about this.
> 
>  It depends if Boosters decide to accept this fancy presentation of pi.
> 
>  If not, then going back to the macro (long double)
> 
>   #define PI 3.141592653589793238462643383279502884197L
> 
>  and using the compiler to convert to type T

As far as I understand long double is optional (in IEEE 754). This would
mean you'd have to provide the double constant, too.

>  template <typename T>
>  T circle_area(const T& radius)
>  {
>   // Usage example: circle_area<double>( 2.) // Explicit type double.
>   // or             circle_area(2.F) // Implicit type float.
>  return T(PI) * radius * radius;
>  }

Interesting option. I'll probably play with it one day.

>  *_probably yields_* the same end result
>  (as will the appropriate function of float pi(), double pi(), long double
pi()).

When these use the same (long double) constant internally?

>  But if you want the exactly representable value for interval arithmetic,
>  then I think the form
> 
>  return boost::math::constant< T, boost::math::pi_tag >() * radius *
radius;
> 
>  will always give the exact value for pi.
> 
>  (But, to confuse the matter further, is it not going to be more accurate,
if
>  less portable, to calculate PI * radius * radius using long double before
a
>  final rounding to type T?  So we are choosing portability over accuracy
here,
>  rightly in my view.  Anyone who wants maximum accuracy will have to do
their own
>  thing with the 40 decimal digit macro value for pi, and probably only
wants long
>  double type anyway.)

Thanks,

Joerg


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