Re: the "set paradigm" is harmful
Michel & all
---- Michel Hack <hack@xxxxxxxxxxxxxx> wrote:
> For bounded intervals, conversion from InfSup to MidRad is typically
> less lossy (i.e. less blowup) -- typically a bit more than half an
> ulp, but not more than one ulp. However, a strictly positive interval
> could end up having a zero endpoint: when Inf is much smaller than Sup,
> and both positive, we would get Mid = Rad = ceil((Inf+Sup)/2). This
> could change the dynamics in a significant way down the road.
>
> I think back-and-forth conversion would be stable after one round.
I think that isn't so. Using 4-digit decimal floating point I got
0.9997-+ 0.0003100
-> [0.9993, 1.001]
-> 1.000-+0.0008500
-> [0.9991, 1.001]
-> 1.000-+0.0009500
-> [ 0.9990, 1.001]
-> 1.000-+0.001000
after which it settles down. This used the (arbitrary) policy that when there are two equally good midpoints, you choose the smaller.
I may have slipped up on the arithmetic, of course.
John