Re: [julia-users] Re: John L. Gustafson's UNUMs

Speaking of going out on a limb: are you aware of Mark Kikgard's work on GPU accelerated path rendering? http://www.slideshare.net/mobile/Mark_Kilgard/gtc-2014-nvidia-path-rendering There is obvious *thematic* overlap, with the promise of faster, more accurate 2D graphics using LESS power. Rend

Re: [julia-users] Re: John L. Gustafson's UNUMs

Actually, Jason, the book went through intense peer review repeatedly for over a year before it hit the shelves. Horst Simon, the series editor, vetted the manuscript and made sure William Kahan saw it as well. Kahan, the guy behind the IEEE 754 Standard for floats and a Turing Award recipient,

Re: [julia-users] Re: John L. Gustafson's UNUMs

The chapter "Permission to Guess" explains how to "round" unums. The "guess" function replaces an inexact unum with an exact one, either the one closest to the midpoint if there is at least one more bit of fraction precision available, or one of the endpoints if the ULP size is already as small

[julia-users] Re: John L. Gustafson's UNUMs

Zenna, If unums are used without the ubox method and some of the other techniques described in the book (like tightest-possible evaluation in the *g*-layer for a well-defined set of functions), they will indeed fall prey to two of the main problems of interval arithmetic: the dependency problem

[julia-users] Re: John L. Gustafson's UNUMs

What IEEE 754 did with "negative zero" is a half-baked attempt to represent inexactness. Consider, for example, that the square root of negative zero is defined to be negative zero. Unums have the same representation of zero as floats in that the sign bit can be 0 or 1, but the sign bit is ignor

[julia-users] Re: John L. Gustafson's UNUMs

I just now learned about this discussion and I see quite a few messages I need to reply to. I am very excited about a Julia version of unum arithmetic, and it does seem like the ideal language for it. Alan Edelman, Deepak Vinchhi, and Viral Shah proposed to create it with funding from A*STAR in

Re: [julia-users] Re: John L. Gustafson's UNUMs

How about moving the discussion here: https://github.com/tbreloff/Unums.jl/issues/2 On Thu, Jul 30, 2015 at 1:09 PM, Jeffrey Sarnoff wrote: > +1 for "grain of salt" > > > On Saturday, July 25, 2015 at 9:11:54 AM UTC-4, Job van der Zwan wrote: >> >> So I came across the concept of UNUMs on the Po

[julia-users] Re: John L. Gustafson's UNUMs

+1 for "grain of salt" On Saturday, July 25, 2015 at 9:11:54 AM UTC-4, Job van der Zwan wrote: > > So I came across the concept of UNUMs on the Pony language mailing list > this > morning. I hadn't heard of them before, and a qu

Re: [julia-users] Re: John L. Gustafson's UNUMs

On Wednesday, July 29, 2015 at 5:31:12 PM UTC-4, Stefan Karpinski wrote: > > The most compelling part of the proposal to me was the claim of > associativity, which I suppose comes along with the variable precision > since you can actually drop trailing bits that you can't get right. > I bought a

Re: [julia-users] Re: John L. Gustafson's UNUMs

My comment was only relating to ordinary floating point, I still don't really understand unums. On Thursday, 30 July 2015 14:47:20 UTC+1, Tom Breloff wrote: > > Simon: if I understand what you're suggesting, you'd like to add a > "rounding direction" flag whenever the ubit is set that would indi

Re: [julia-users] Re: John L. Gustafson's UNUMs

Simon: if I understand what you're suggesting, you'd like to add a "rounding direction" flag whenever the ubit is set that would indicate which direction you *would* round if you wanted to? I like this idea, as it allows you to throw away the implicit open interval in favor of a rounded exact valu

[julia-users] Re: John L. Gustafson's UNUMs

On Wednesday, 29 July 2015 22:07:45 UTC+1, Steven G. Johnson wrote: > > And I don't see a clear practical use-case for an inexact bit per value, > as opposed to a single inexact flag for a whole set of computations (as in > IEEE). > Probably not quite what others had in mind, but an instruction-

Re: [julia-users] Re: John L. Gustafson's UNUMs

On Wed, Jul 29, 2015 at 4:59 PM, Zenna Tavares wrote: > As a result of these properties, unums can be closed under arithmetic > operations and won't hide your errors due to approximation. I'm glad to hear this because this was that part that made me question the whole thing. I guess the fact th

[julia-users] Re: John L. Gustafson's UNUMs

On Wednesday, July 29, 2015 at 4:59:02 PM UTC-4, Zenna Tavares wrote: > > I read the book (well, somewhere between a skim and a proper read). It's > not formal but it is clear and the ideas are concise. > I actually think it's a pretty good example of how to explain an idea > without unnecessary

[julia-users] Re: John L. Gustafson's UNUMs

I read the book (well, somewhere between a skim and a proper read). It's not formal but it is clear and the ideas are concise. I actually think it's a pretty good example of how to explain an idea without unnecessary jargon. As for unums themselves, I am mostly convinced of his arguments on unu

[julia-users] Re: John L. Gustafson's UNUMs

On Sunday, July 26, 2015 at 7:51:51 AM UTC-4, Job van der Zwan wrote: > > So on an impulse I got the ebook, and even for a physics dropout like me > it's surprisingly engaging and accessible! There's some stuff in there that > isn't mentioned in the online slides that might clarify the idea bet

[julia-users] Re: John L. Gustafson's UNUMs

So on an impulse I got the ebook, and even for a physics dropout like me it's surprisingly engaging and accessible! There's some stuff in there that isn't mentioned in the online slides that might clarify the idea better. For example, floats already have a way to represent the largest represent

[julia-users] Re: John L. Gustafson's UNUMs

On Sunday, July 26, 2015 at 4:06:05 AM UTC-4, Job van der Zwan wrote: > > On Sunday, 26 July 2015 05:00:44 UTC+3, Scott Jones wrote: > >> There also doesn't seem to be any representation of -0.0, which from what >> I've read, is important to represent negative underflows. >> > > Apparently, his

[julia-users] Re: John L. Gustafson's UNUMs

On Sunday, 26 July 2015 05:00:44 UTC+3, Scott Jones wrote: > There also doesn't seem to be any representation of -0.0, which from what > I've read, is important to represent negative underflows. > Apparently, his format doesn't have underflow, or overflow. I'm still trying to wrap my head aroun

[julia-users] Re: John L. Gustafson's UNUMs

This seems interesting, I'd like to know what David Sanders (https://github.com/dpsanders) thinks of the math (I missed his talk at JuliaCon, I'm waiting for the video, but the description made it sound relevant). There also doesn't seem to be any representation of -0.0, which from what I've r

[julia-users] Re: John L. Gustafson's UNUMs

On Saturday, 25 July 2015 23:34:45 UTC+3, Simon Byrne wrote: > > Some HN discussion here: > https://news.ycombinator.com/item?id=9943589 > Oh, hadn't seen that. The linked presentation is also more recent! I found the "slidecast" version of it, where he presents the slides in podcast form.

[julia-users] Re: John L. Gustafson's UNUMs

Some HN discussion here: https://news.ycombinator.com/item?id=9943589 I'd be keen to know more but he hasn't really published any details other than his book . Based on the free preview, it looks like a bit of a diatrib

[julia-users] Re: John L. Gustafson's UNUMs

How cool! I don't know much about this matter, but this looks very exciting! Julia seems to be a good fit to prototype this! Am Samstag, 25. Juli 2015 15:11:54 UTC+2 schrieb Job van der Zwan: > > So I came across the concept of UNUMs on the Pony language mailing list >