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Re: Comments on Motion 10v2 (elementary functions)



P1788

On 4 Nov 2009, at 20:53, Michel Hack wrote:
(1)  The range for asin and acos is shown as bounded inclusively by
     mathematical Pi/2, and that for atan (and atan2) as bounded but
     excluding those endpoints.  Yet in most FP formats Pi/2 is not
     an FP number, so what does that mean?  Is the endpoint of a
     result maximally PI/2 (Math Pi/2 rounded down), or can it be
     Pi/2 rounded up?

     This issue becomes acute when converting an interval to one
     using a wider base format, because at that point new FP numbers
     come into existence that should be included (or excluded) from
     the interval.  Given general containment rules I suppose the
     range should be defined by outward rounding.

This is one reason why I think the functions like sinPi(x)=sin(Pi*x) (see IEEE 754-2008 table 9.1 of recommended functions) have a lot going for them in the interval context.

John