Edge case conversions, exceptions to IEEE FPA
On (Tue, 11 Nov 2008 14:47:34 -0800) Van Snyder wrote:
> For an FP number not known to be exact, the closest
> to exact it can be is 1/2 ulp each way.
Not really. Pisot numbers are near-integers, and if
their value is such that 1 ulp = 1, the error bound
would be much smaller than .5 ulp. (But I note that
Van said "not known to be exact" as opposed to "known
to be inexact, with known error bounds".)
Of course, any serious treatment of Pisot numbers
would express them as the sum of two numbers, the
first of which known exact (or out of range for
this representation).
A more general case is the sum of a float known
to be exact and a much smaller inexact float.
(That one might not even known to be inexact,
as the perturbation might be zero.)
Michel.
Sent: 2008-11-12 14:29:45 UTC