Comments on Motion 10v2 (elementary functions)
(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.
(2) I assume hypot is expected to avoid intermediate overflow, so
that no accidental widening to unbounded should occur when the
result is representable but one of the squares is not.
(3) rootn and powr need a note explaining that (like pown in table 1)
these are families of one-argument interval functions indexed by
one or two integers.
(4) sin2 -- same comment as (1) above with respect to range, this time
for bound 1/Pi.
(Somebody asked whether the desired function was not really sin3,
i.e. (sin(x)-x)/x^3 -- but the issue would remain since 1/6 is
also not an FP number in either binary or decimal. So perhaps
intervallers would prefer 3*(sin(x)-x)/x^3 as a primitive?)
Michel.
---Sent: 2009-11-04 21:18:52 UTC