What would be the first problem you address with this made hardware?
On Friday, July 31, 2015 at 3:39:01 PM UTC-4, John Gustafson wrote: > > I discuss this in the book; there have to be strict bounds on how long a > computation remains in the *g*-layer (fused) or people would dump their > entire calculation in there. I think i got most of the fused operations > that make sense, and I pointed out some that do not make sense. It is key > that you should have a finite and predictable bound on the memory > requirement of the *g*-layer where scratch work is done. It cannot be > regarded as unlimited, or limited only by available system memory. For > every fused operation, I can predict how many bits will be needed to return > a correct answer, which means there is hope for a hardware implementation > someday. > > On Thursday, July 30, 2015 at 3:44:26 PM UTC-7, Stefan Karpinski wrote: >> >> Fused polynomials do seem like a good idea (again, can be done for >> intervals too), but what is the end game of this approach? Is there some >> set of primitives that are sufficient to express all computations you might >> want to do in a way that doesn't lose accuracy too rapidly to be useful? It >> seems like the reductio ad absurdum is producing a fused version of your >> entire program that cleverly produces a correct interval. >> >> On Thu, Jul 30, 2015 at 5:20 PM, Jason Merrill <[email protected]> wrote: >> >>> On Thursday, July 30, 2015 at 4:22:34 PM UTC-4, Job van der Zwan wrote: >>>> >>>> On Thursday, 30 July 2015 21:54:39 UTC+2, Jason Merrill wrote: >>>> >>>>> <Analysis of examples in the book> >>>>> >>>> >>>> Thanks for correcting me! The open/closed element becomes pretty >>>> crucial later on though, when he claims on page 225 that: >>>> >>>> a general approach for evaluating polynomials with interval arguments >>>>> without any information loss is presented here for the first time. >>>>> >>>> >>>> Two pages later he gives the general scheme for it (see attached >>>> picture - it was too much of a pain to extract that text with proper >>>> formatting. This is ok under fair use right?). >>>> >>>> Do you have any thoughts on that? >>>> >>> >>> The fused polynomial evaluation seems pretty brilliant to me. He later >>> goes on to suggest having a fused product ratio, which should largely allow >>> eliminating the dependency problem from evaluating rational functions. You >>> can get an awful lot done with rational functions. >>> >>> >>> <https://lh3.googleusercontent.com/-f-sYnCMJFpQ/VbqE8zbN5AI/AAAAAAAAHOk/cNTnxAUAyoU/s1600/polynomial.png>I >>> >>> actually think keeping track of open vs. closed intervals sounds like a >>> pretty good idea. It might also be worth doing for other kinds of interval >>> arithmetic, and I don't see any major reason that that would be impossible. >>> I didn't meant to say that open vs closed intervals doesn't matter--I just >>> meant that it doesn't seem to be the "secret sauce" in any of the challenge >>> problems in Chapter 14. To me, the fused operations are the secret sauce in >>> terms of precision, and the variable length representation *might be* the >>> secret sauce for performance, but I can't really comment on that. >>> >> >>
