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Unum Computing: An Energy Efficient and Massively Parallel Approach to Numerics

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Re: Unum Computing: An Energy Efficient and Massively Parallel Approach to Numerics

#11

Post by [deleted] »

stephencanon wrote: post #6
bmh100 wrote: post #4

Earlier quoted context omitted.

I am not sure that I understand what you're saying. Given a charitable reading of the presentation, the author seems to be saying that his standard explicitly specifies range of values, as opposed to the IEEE Float. It did not seem like he was saying that he could explicitly represent an infinite amount of exact, distinct values using a finite number of bits. Low level data structures are not my area of expertise, so…

Under that reading, he's saying nothing: just represent the interval [-inf, inf] as "0" and call it a day. So assuming that he's saying anything at all, he's at least being imprecise, and the actually claim should be something like "represent any dyadic interval using a finite number of bits".

[deleted]

Re: Unum Computing: An Energy Efficient and Massively Parallel Approach to Numerics

#12

Post by [deleted] »

dnautics wrote: post #3
stephencanon wrote: post #2

> Complete representation of all real numbers using a finite number of bits He's 1/3 of the way to three impossible things before breakfast by slide 15.

All real numbers are representable, but not necessarily to arbitrary precision. You should really read the book. A lot of the atomic operations seem cumbersome, because the unum doesn't have a fixed size representation, but you just get over that when you remember that the real problem is shuttling data over buses. More compute transistors is not a problem.

[deleted]

Re: Unum Computing: An Energy Efficient and Massively Parallel Approach to Numerics

#13

Post by yoklov »

cossatot wrote: post #9

Are there architectural or other challenges to building processors for this? How compatible are unums with modern processors? Would LAPACK et al have to be re-written?

My understanding is that it's not compatible with modern processors, and new hardware would be required to efficiently execute it.

It seems to be a superset of floating point (and fixed point?) though, so maybe LAPACK could still work? I may be misreading or misunderstanding this however.

Re: Unum Computing: An Energy Efficient and Massively Parallel Approach to Numerics

#14

Post by simonbyrne »

Are there any more details on unums available online (i.e. without purchasing his book)? The presentation is quite heavy on promotion, but a bit sparse on details.

I also note that he dedicates a page on his website to "Gustafson's law". http://johngustafson.net/glaw.html

Re: Unum Computing: An Energy Efficient and Massively Parallel Approach to Numerics

#15

Post by trsohmers »

simonbyrne wrote: post #14

Are there any more details on unums available online (i.e. without purchasing his book)? The presentation is quite heavy on promotion, but a bit sparse on details. I also note that he dedicates a page on his website to "Gustafson's law". http://johngustafson.net/glaw.html

If you are not in HPC, you may not have heard about Gustafson's law, but it is a legit and important thing... His 1988 paper is still a very worthy read (And winner of the first Gordon Bell award for showing a 1000x speedup, which was previously thought impossible)

Re: Unum Computing: An Energy Efficient and Massively Parallel Approach to Numerics

#16

Post by simonbyrne »

trsohmers wrote: post #15
simonbyrne wrote: post #14

Are there any more details on unums available online (i.e. without purchasing his book)? The presentation is quite heavy on promotion, but a bit sparse on details. I also note that he dedicates a page on his website to "Gustafson's law". http://johngustafson.net/glaw.html

If you are not in HPC, you may not have heard about Gustafson's law, but it is a legit and important thing... His 1988 paper is still a very worthy read (And winner of the first Gordon Bell award for showing a 1000x speedup, which was previously thought impossible)

Fair enough: a pity he doesn't explain what it is though.

Re: Unum Computing: An Energy Efficient and Massively Parallel Approach to Numerics

#17

Post by Lawtonfogle »

yoklov wrote: post #7
stephencanon wrote: post #5

Earlier quoted context omitted.

No. The set of "representable" (i.e. computable) numbers is countable (because the set of programs is countable), so in fact almost all real numbers cannot be represented.

I got the impression that the unum explicitly modeled a range of values, so I'm not sure that applies. Not an expert here though.

Regardless if it is representing number, ranges, or a mix of both, there are still 2^n maximum possible representations for n bits. Perhaps you could create a mix of numbers and ranges equal to (2^n)-2 and then add one range that is from the lowest number represented to negative infinity and add another that does the same for positives. But I can do that system with -, 0, +, NAN. See, I just represented all numbers. It isn't as useful, but boy are there savings on storage, cost, and computation time.

Unums shouldn't be seen as better than ints, longs, floats, or doubles anymore than a double is seen as better than an int. They have different uses and strengths, and there are problems where none are a good choice. Perhaps unums are the best choice for some problems. Perhaps they are clearly and significantly better in some areas. But they should be thought of as an alternative to the existing formats and not a superior replacement.

Re: Unum Computing: An Energy Efficient and Massively Parallel Approach to Numerics

#18

Post by trsohmers »

cossatot wrote: post #9

Are there architectural or other challenges to building processors for this? How compatible are unums with modern processors? Would LAPACK et al have to be re-written?

It requires additional complexity than what is in modern FPUs, but it arguably more efficient when actually operating due to being able to have the same accuracy while using fewer bits.

Most people don't realize that it is the data movement that is most expensive thing in a processor... It takes 100 picojoules to do a double precision (64 bit) floating point operation, but a humongous 4200 picojoules to actually move the 64 bits from DRAM to your registers. The really crazy thing is that around 60% of that power used to move the data is wasted in the processor itself, in the logic powering the hardware cache hierarchy. My startup (http://rexcomputing.com) is solving this with our new processor, and are working with John Gustafson in experimenting with unum for future generations of our chip.

Re: Unum Computing: An Energy Efficient and Massively Parallel Approach to Numerics

#19

Post by yoklov »

The big issue I see with these is that the number of bits is dependent on the stored value. It's also not a power of two. This has a lot of problematic consequences. Indexing into a list of them wouldn't be constant time, for example. You'd need to unpack them (into fixed size unums?) first.

That said, information here is sparse and I'm not an expert on numerical computing (although I do graphics at work and know some about the subject).

Re: Unum Computing: An Energy Efficient and Massively Parallel Approach to Numerics

#20

Post by trsohmers »

simonbyrne wrote: post #16
trsohmers wrote: post #15

Earlier quoted context omitted.

If you are not in HPC, you may not have heard about Gustafson's law, but it is a legit and important thing... His 1988 paper is still a very worthy read (And winner of the first Gordon Bell award for showing a 1000x speedup, which was previously thought impossible)

Fair enough: a pity he doesn't explain what it is though.

Wikipedia is your friend... https://en.wikipedia.org/wiki/Gustafson%27s_law

Would be happy to explain it further, but about to get on a flight.

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