Re: Sun's interval library
Baker Kearfott wrote:
> I had earlier interpreted "correctly rounded" to mean to the greatest
> floating point number less than, the nearest floating point number,
> or the smallest floating point number greater than, depending on the
> rounding mode. Actually, IEEE 754-2008 uses the term to mean simply
> "less than the exact result" in the case of downward rounding, etc.
> 754-2008 only requires the "nearest" such floating point number for
> the basic operations, and for binary to decimal and decimal to binary
> conversions, but allows the language to define the "quantum" for
> rounding for the recommended elementary functions.
Sorry, there are two confusions here.
(1) "Correctly rounded" means that the result is the ONE AND ONLY result
that corresponds to the applicable rounding direction.
(2) "Quantum" only applies to Decimal formats, and only affects the
representation, NOT the value. It is also only relevant for exact
results; inexact results always use the smallest possible quantum
in order to deliver as much precision as the format allows.
The "quantum" of a BFP datum is always 1 ulp, and the precision is
always full except for subnormals, which all have the same quantum,
namely the smallest subnormal value.
Michel.
---Sent: 2013-07-01 14:22:33 UTC