Re: More on trits & tetrits... (long) - compromises
IEEE took a few shortcuts to make 754 more implementable. One is that as I've mentioned before the separate concepts of Overflow and Infinity were merged into a single value (for each sign), when it would be more correct to keep them separate. Another that several others have implied is that Underflow and Zero were merged into the single value zero (for each sign), when it would be more correct to keep them separate (eg, make the smallest subnormal mean Underflow). Another mentioned previously is the lack of a signless Infinity. So it was inevitable that zero would be signed and that some operations and functions (IEEE or not) would care about its sign, while others don't. Treating zero as signed also matches keeping negation simple (just flipping the sign bit).
An issue we need to deal with is to what extent 1788 can use 754 semantics. I expect most implementations in the next decade to have to use 754 hardware, and to be vastly slower if any of the fundamental semantics differ. Many users outside this group may be reluctant to adopt it if it differs or is slower. So its success likely depends on compromise. On the other hand, if any of the semantics are incompatible or if it is only feasible with brand new hardware, then a number of 754 compromises and shortcuts could be cleaned up.
- Ian McIntosh IBM Canada Lab Compiler Back End Support and Development
Vincent Lefevre ---04/29/2010 03:00:55 AM---On 2010-04-28 12:01:43 -0400, Michel Hack wrote: > That would be a very different arithmetic. Yes,
From: |
Vincent Lefevre <vincent@xxxxxxxxxx> |
To: |
Ian McIntosh/Toronto/IBM@IBMCA |
Date: |
04/29/2010 03:00 AM |
Subject: |
Re: More on trits & tetrits... (long) |
On 2010-04-28 12:01:43 -0400, Michel Hack wrote:
> That would be a very different arithmetic. Yes, 1788 is defined over
> the Reals, but 754 is defined over the Affine Extended Reals, which is
> also why it has signed zeros as well as signed infinities.
From a rigorous mathematical point of view, it isn't: there are no
signed zeros in the affinely extended reals.
http://mathworld.wolfram.com/AffinelyExtendedRealNumbers.html
If x is zero, one has f(-x) = f(x) in the affinely extended reals, but
in IEEE 754 arithmetic, this is wrong, even if all the operations are
exact.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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