RE: [boost] Formal Review for Interval Library- getting intervalsof constants

From: Paul A. Bristow (boost_at_[hidden])
Date: 2002-09-07 05:13:20

The drawback of this is that in practice you only need sparse handful of
intervals for significands numeric_limits<>::digits
= 23, 24, 32, 53, 64, 80, 106, 112, 128 perhaps.
So a switch, and perhaps some default, as Sylvain Pion suggested is quite
adequate.

Paul

> -----Original Message-----
> From: boost-bounces_at_[hidden]
> [mailto:boost-bounces_at_[hidden]]On Behalf Of Herve Bronnimann
> Sent: Friday, September 06, 2002 11:11 PM
> To: boost_at_[hidden]
> Subject: Re: [boost] Formal Review for Interval Library- getting
> intervalsof constants
>
>
> On Fri, Sep 06, 2002 at 03:39:57PM -0400, Sylvain Pion wrote:
> > The naive approach (which I guess is what you had in mind) is
> to use a RUN-TIME
> > algorithm, and make it dump enough precision in decimal (e.g.
> Maple), and just
> > use this.
> > But this DOES NOT work : it is not reliable enough given the precise
> > constraints that I have given.
> > Read again my quote of the C++ standard from [2.13.3.1].
> > The key remark in this paragraph is that if the decimal scaled
> value is NOT
> > representable (which is what you highly probably get with the
> naive approach),
> > then the necessary rounding which is done by the compiler at
> compile-time is
> > implementation-defined.  So, as I want to be sure of the
> correct FP values that
> > I get, I need to fall back on a decimal value which is EXACTLY
> representable
> > in the compiler's FP format (which I can know via
> numeric_limits::digits and
> > radix).  Which is what led me to my proposal : testing in a
> compile-time switch
> > (several ?: ) using numeric_limits::digits (and this method
> should also switch
> > on radix to be complete).
>
> 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... ?
> --
> Herve'
>
>
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