Re: Bare decorations (was ...level 2 datums) - level 2 versus level 3
Ian McIntosh wrote, partially agreeing with Nate Hayes' claim that
there is "NO way" to discuss level 2 without reference to level 3:
> It also shows that you NEED to know some of the Level 3 details to
> determine parts of the Level 2 abstract data type (eg, that Infinities
> cannot have payloads - IF 754 had used different exponent field values
> for NaNs versus Infinities, then Infinities could have had payloads).
Not so. I have no difficulty at all understanding Level 2 on its own
terms, including determining the cardinality of its support set.
Just recently I had offered a DIFFERENT level 3 way to represent
infinities with payloads that did not disturb the exponent range,
but instead reduced the payload field by one bit. In fact, 754-2008
has already reduced the NaN payload by one bit, since the bit that
distinguishes QNaN from SNaN *must* now be the high-order bit of
the trailing-significand field (unlike 754-1985 where it could be
any distinction).
If payloads are not part of level 2, we remain with one NaN, two
Infinities (+ vs -), 2*(1+emax-emin)*2**(precision-1) Normals, two
zeros (+ vs -) and 2*(2**(precision-1)-1) subnormals.
No need for any reference to level 3.
BFP happens to represent these one-for-one at level 3 (except for NaN
payloads), whereas DFP has a fair amount of redundancy, even semantically,
as quantum selection within a cohort is considered to be a level-3 issue.
Not all semantic distinctions are thus reflected at level 2; indeed, to
the surprise of many, the QNaN vs SNaN distinction is considered to be
a level-3 distinction in 754-2008. (The significance of Q vs S is most
crucial in the definiion of comparison operators. Leaving this out from
Level 2 could have been a left-over from the 1985 situation where the
distinction between QNaN and SNaN was perhaps less solid -- I would have
preferred to include it. The exclusion of DFP cohorts from Level 2 is
justified because it permits Level 2 to be radix-independent.)
Michel.
---Sent: 2010-10-26 15:42:09 UTC