[std-interval] list of functions for intervals

[first.i.last at comcast.net]

 -------------- Original message ----------------------
From: Sylvain Pion <Sylvain.Pion at sophia.inria.fr>
> Dear all,
> 
> We have been thinking about the list of floating-point functions
> which we could propose an interval version for.
> More precisely, we have looked at the current list of floating-point
> functions from the latest draft of C++0x

[...] 

> What do you think of these lists ?
> Is something important excluded ?
> Is there anything that should be excluded ?
> 
> Note that existing implementations do not necessarily offer all
> proposed functions, so any comment on the implementation
> difficulty (for interval<float>, interval<double> and
> interval<long double>) would be appreciated.

Attached is a file containing comments on the issues you raised and suggested specifications for many of the functions at issue.  Having studied this issue in great detail, implemented all of the <cmath> functions, and designed implementations of the c99 functions I can assure you that the implementation of the interval versions of the <cmath> functions, including disjoint results, is quite reasonable.

Using typical elementary functions as a benchmark (trig, hyperbolics, and exponentials) all but two of the c99 functions require similar or lesser implementation effort.  We are still studying the recalcitrant pair of functions, beta() and ellint_1(), with an eye to efficient and robust implementation.

The attached document is a summary aimed at raising issues and identifying areas meriting additional discussion rather than a comprehensive specification with endless detail but no rationale.  Therefore readers who are only concerned with concrete suggestions should not read it.

-- Lee Winter
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