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RE: new domain for atan() in Aug 8 draft.
Peter Markstein wrote:
So, the last three sentences of Annex D, which are now in green, should
be restored to Black to be in accord with the motion which we passed.
In other words, the correctly rounded domain excludes +-Inf for certain
rounding modes (away from zero, and nearest for binary32 and decimal64).
I suppose we could compute reasonably tight finite bounds. I think that
something like (-1/1ulp, +1/1ulp) would do, since 1 < pi/2 < 2 < 10.
This suggests [-2^24+1, +2^24-1] for Binary32, and [-1e16+1, +1e16-1]
for Decimal64. In that case |atan()| would not exceed pi/2-1ulp, and
rounding would have two legitimate results to choose from. (It is
possible that the +-1 is not needed, e.g. [-2^24, +2^24] may work: at
the edge, |atan()| would exceed pi/2-1ulp, but by too little to matter.)
This is based on tan(pi/2-eps) = 1/eps - (1 + eps/3 + ...).
Michel.
Sent: 2006-08-14 00:33:13 UTC