Re: Motion on interval flavors
On 2012-07-08 11:05:16 -0500, Nate Hayes wrote:
> On the other hand, with Kaucher/modal intervals realized in hardware, one
> can compute:
[...]
> As discussed in detail in Chapter 6 of
> http://grouper.ieee.org/groups/1788/Material/Hayes_Modal%20Intervals.pdf
> one can also compute the optimal bounds by reverse-engineering the modal
> interval arithmetic into primitive floating-point operations, i.e., the
> linearInt() function that appeared in an version of the Vienna Proposal.
> However, then one is stuck with a bunch of floating-point operations. But as
> I've mentioned many times before, this suffers from tremendous performance
> penalties due to the required if-then branching, which can flush the
> floating-point processor pipeline; not to mention the required changing of
> rounding mode directions etc. Also, these operations can not be performed on
> the SIMD registers of modern Intel and AMD computers, e.g.
P1788 will not be a hardware standard. Even if a part of the interval
arithmetic is implemented in hardware on some processors, whether or
not Kaucher/modal intervals are in the standard won't change anything
concerning their support in hardware.
For instance, IEEE 754 floating-point arithmetic is nowadays often
implemented in hardware (this includes cell phones and GPUs), except
for some embedded devices. But some parts of it is left to software:
subnormal support, and decimal arithmetic on most processors. Ditto
for complex arithmetic (not covered by IEEE 754, but by some other
standards like LIA and ISO C). A reason is that they are not really
useful (if not completely useless) in most common applications for
the average user. However many processors have vectorized operations,
though they are not covered by IEEE 754 / LIA / ISO C (for instance),
because they are useful in practice.
Now, what is the status of Kaucher/modal intervals in current
processors?
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Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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