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From: brianjparker_at_[hidden]
Date: 20011023 22:07:16
 In boost_at_y..., helmut.zeisel_at_a... wrote:
>  In boost_at_y..., brianjparker_at_h... wrote:
> >  In boost_at_y..., Daryle Walker <darylew_at_m...> wrote:
>
> I uploaded a first version of the rational approximation:
>
>
http://groups.yahoo.com/group/boost/files/big_int/farey_20011022.zip
I have only had a quick look through the documentation and
implementation for now and give my initial comments below I will
test it more fully at a later date.
> The prototype is
>
> template<class Int, class Float>
> boost::rational<Int> farey(const Float& v, const Int& lim);
>
> > >
> > > Maybe we should have both.
> >
> > Yes, that is my conclusion as well.
>
> This would be no problem for me  I would appreciate
> to have different options.
>
> > It may be possible to overload
> > the function based on the error term type double or float for
> > relative error and integer for max. denominator, although this
may
> be
> > too fragile and separate function names may be better.
>
> Do not try to be too clever.
> Since there are different options for rational approximation,
> it will be difficult to find a single interface
> for all of them.
>
> I chose the name "farey" to point out
> that it is just one algorithm
> and not the only solution for rational approximation.
>
> > An advantage of the relative error approach is that a default
small
> > value close to the epsilon of the floating point representation
> could
> > be specified, so that the error argument could be ignored in many
> > cases.
>
> If you just want to control the relative error,
> there is a simple rule how to specify the max. denominator.
> You can find it in my preliminary documentation.
Yes, good point. It may still be a good idea to provide both
interfaces as a convenience.
> Observe that the return type is rational<Int>,
> so we need one way to secify the integer type to be used.
> Specifying it by the type of the second parameter
> is IMHO the most convenient solution.
It may be better to pass in the rational as a nonconst reference,
also I think the name should be more suggestive of its purpose,
perhaps something like (better names could be found)
template<class Int, class Float>
void rational_approximation_farey(boost::rational<Int>& r, const
Float& v, const Int& lim);
template<class Int, class Float>
void rational_approximation_farey2(boost::rational<Int>& r, const
Float& v, double error);
>
> > Also, as was pointed out in a previous posting, the Netlib code
> needs
> > to have two defines updated for IEEE754 floating point I will
look
> > into this in the future.
> >
>
> IMHO updating for IEEE754 is not enough 
> the algorithm should also work for some future
> high precision floating point type.
You mean a userdefined extended floating point type?
> A better solution would be to choose these
> values from std::numeric_limits.
Agreed.
> I fear, however, that this will not be possible
> without deeper understanding of the algorithm used there,
> and this (thanks to the gotos) will not be possible
> without a look into the book referenced there.
>
> Helmut
Your code looks like it would be a useful addition to Boost, IMO.
,Brian Parker.
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