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after-rounding tinyness detection and directed rounding
- To: stds-754 <stds-754@xxxxxxxxxxxxxxxxx>
- Subject: after-rounding tinyness detection and directed rounding
- From: Michel Hack (1-914-784-7648) <hack@xxxxxxxxxxxxxx>
- Date: Monday 15 Oct 2007 at 11:21 a.m. EDT (2007-10-15 15:21 GMT)
The returned result when rounding a positive tiny-before-rounding value
in roundTowardPositive is Nmin, regardless of how small the true value is.
The rounded result appears to have a full count of bits, but most or all
of them are meaningless. That's ok, we asked for a bound and got one.
The result is not wrong.
Nevertheless, the information that the true value is very small is lost.
The before-rounding method would return the same result, but would also
indicate that the true result was tiny.
Mike Cowlishaw pointed out that the pactical difference between the two
methods is small, affecting just a narrow band of true results between
Nmin-Dmin/2 and Nmin -- but that is only for round-to-nearest. Here the
affected range is ALL positive values less than Nmin (even less than Dmin).
Michel.
Sent: 2007-10-15 15:33:25 UTC