Re: [boost] Formal Review for Interval Library- getting intervals of constants

From: Sylvain Pion (pion_at_[hidden])
Date: 2002-09-06 17:56:13

On Fri, Sep 06, 2002 at 06:11:25PM -0400, Herve Bronnimann wrote:
> Just occured to me: If you want to take advantage of compile-time,
> template arguments of the form <unsigned int> would work, and
> specializations for various ints would give you the desired rounding.
> 
> Example (the constants are bogus, but you'll get my point):
> 
>      template <unsigned int decimal_precision>
>      struct interval_pi {
>        static const double lower = 3; // default version
>        static const double upper = 4;
>      };
>      
>      #define BOOST_INTERVAL_SPECIALIZE_PI_CONSTANT(n, l, u) \
>        template <> struct interval_pi<n> { \
>          static const double lower = l;  \
>          static const double upper = u;  \
>        }
>      
>      BOOST_INTERVAL_SPECIALIZE_PI_CONSTANT(1,  3.1          , 3.2          );
>      BOOST_INTERVAL_SPECIALIZE_PI_CONSTANT(2,  3.14         , 3.15         );
>      BOOST_INTERVAL_SPECIALIZE_PI_CONSTANT(3,  3.141        , 3.142        );
>      BOOST_INTERVAL_SPECIALIZE_PI_CONSTANT(4,  3.1415       , 3.1416       );
>      BOOST_INTERVAL_SPECIALIZE_PI_CONSTANT(5,  3.14159      , 3.14160      );
>      BOOST_INTERVAL_SPECIALIZE_PI_CONSTANT(6,  3.1415926    , 3.1415927    );
>      BOOST_INTERVAL_SPECIALIZE_PI_CONSTANT(7,  3.14159265   , 3.14159266   );
>      BOOST_INTERVAL_SPECIALIZE_PI_CONSTANT(8,  3.141592653  , 3.141592654  );
>      BOOST_INTERVAL_SPECIALIZE_PI_CONSTANT(9,  3.1415926535 , 3.1415926536 );
> 
>      std::cout << interval_pi<7>::lower << std::endl;
> 
> You can go on to provide all the (precomputed) precisions ever needed by
> users. It's a little less flexible than switches ( ? : ) but it's
> perhaps more readable... ?

Doesn't work.

You miss the point of where the problem is, and Gaby as well it seems.

My problem is not to generate compile-time constants alone, nor to generate
correct constants alone.  I want _both_, and _this_ is harder.

The fact is that the standard (always this good ol' 2.13.3.1) says that, since
the (decimal) numbers that you use are not representable (*), then the compiler
will have the choice between the two representable numbers enclosing it, and
can pick either one.  Hence it can pick the one I don't want.  So it doesn't
work.

Go read again my proposed solution (going through representable numbers) once
you've understood the problem.  And then try to finally propose me the working
nicer solution of my dreams :)

-- 
Sylvain
(*) 3.1 is NOT representable in binary, whatever value "digits" has, since it
    has infinite representation in base 2.
    Same for most, if not all the ones you use above.