Re: Motion 10 -- elementary functions
>> ... my question about ranges with unrepresentable endpoints ...
Dan Zuras replied:
> Therefore, I would have to say that motion 10 IS addressing
> this problem as best it can in that correct containment is
> the correct answer in this case.
My problem is that I don't know how to interpret the specification
of the range of the point function whose interval hull is to be
used when computing the interval result.
Let PI be the closest floater not exceeding mathematical \pi.
For binary64 and a value near 1.5, one ulp is 2^-52.
Take atan(x), whose given range is (-\pi/2, +\pi/2), for an argument
x that exceeds tan(PI/2) -- i.e. an interval with values greater than
about 2^52, a quite moderate floater. Should the result then include
nextup(PI/2), or should it stay within the specified bounds and return
the equally valid -PI/2 which *is* within the specified bounds? After
all, the reflected just-out-of-bounds angle is just within bounds:
let PI/2 = \pi/2 - eps, with eps < ulp
the next floater after PI/2 is PI/2+ulp = \pi/2-eps+ulp
this reflects to PI/2+ulp-\pi = -(\pi/2 -(ulp-eps))
which is inside (-\pi/2, +\pi/2)
It is this ambiguity in the specification that I would like to
see cleared up.
Michel.
---Sent: 2009-12-01 00:21:02 UTC