His slides claim that happens in 32 and 64 bits. He'll have to answer how he got that result -- it DOES seem incredibly unlikely.
http://web.stanford.edu/class/ee380/Abstracts/170201-slides.pdf He does have a neural network and FFT in the video (not mentioned in the slides) -- it's actually most of the video, showing off a Julia implementation (the Julia language is made to allow alternate numbering systems, so many of its built-in and library functions will work with any type of number you've defined). Personally, I'm very impressed with his past work, but it's taking me a lot of mental effort to figure out this one. It does seem strictly superior to his original unum design, and faster than unum2 (nobody ever did build a fast implementation of that; most of the work was done on VERY incomplete implementations). -Wm Raul Miller <[email protected]> wrote: > My guess, looking at those numbers, but not mustering enough interest > to plow through the video, is that by IEEE-754, he meant 32 bit > IEEE-754, but J uses 64 bit IEEE-754. > > I'm having trouble mustering up interest because while focusing on > specific cases is useful for working with simple algorithms, for > something like this you really need to be considering much larger > fields of values. And I'm not going to see anything like that in this > video. > > -- > Raul > > > On Thu, Feb 9, 2017 at 10:51 AM, Raul Miller <[email protected]> > wrote: > > Does this answer your question? > > > > a=.3.2e7 1 _1 8.0e7 > > b=. 4.0e7 1 _1 _1.6e7 > > a +/ .* b > > 2 > > (a +/ .* b) - 2 > > 0 > > mm=: +/@(*"1 _) > > a mm b > > 2 > > (a mm b) - 2 > > 0 > > > > Thanks, > > > > -- > > Raul > > > > On Thu, Feb 9, 2017 at 10:44 AM, William Tanksley, Jr > > <[email protected]> wrote: > >> I'd be curious about whether J is automatically using one of the matrix > >> multiplication algorithms that avoid the problem. > >> > >> On Thu, Feb 9, 2017 at 7:26 AM Skip Cave <[email protected]> > wrote: > >> > >>> I posted the results Brian & Robert got from Gustafson's matrix > multiply > >>> example in J and APL to the Unum Computing forum on Google Groups > >>> <https://groups.google.com/forum/#!forum/unum-computing>. Gustafson > >>> occasionally posts on that group. We'll see what he says. > >>> > >>> Skip Cave > >>> Cave Consulting LLC > >>> ---------------------------------------------------------------------- > >>> For information about J forums see http://www.jsoftware.com/forums.htm > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
