There is a hint of how he claims that 64-bit IEEE-754 is wrong,
on his penultimate slide:
"IEEE floats require 80-bit precision to get it right."
I think 80-bits is the default precision used by gcc. If so,
then Gustafson's claim is correct. Now, it would have
been nice if he had clarified that on slide 0...
Bob
On 2017-02-09 12:34 PM, William Tanksley, Jr wrote:
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
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Robert Bernecky
Snake Island Research Inc
18 Fifth Street
Ward's Island
Toronto, Ontario M5J 2B9
[email protected]
tel: +1 416 203 0854
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