Unum Computing: An Energy Efficient and Massively Parallel Approach to Numerics
1–10 of 58 posts
Re: Unum Computing: An Energy Efficient and Massively Parallel Approach to Numerics
#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.
Re: Unum Computing: An Energy Efficient and Massively Parallel Approach to Numerics
#3> 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.
Re: Unum Computing: An Energy Efficient and Massively Parallel Approach to Numerics
#4> 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.
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 did I misunderstand what he was saying or what you are saying?
Re: Unum Computing: An Energy Efficient and Massively Parallel Approach to Numerics
#5> 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.
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.
Re: Unum Computing: An Energy Efficient and Massively Parallel Approach to Numerics
#6> 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.
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".
Re: Unum Computing: An Energy Efficient and Massively Parallel Approach to Numerics
#7Earlier quoted context omitted.
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.
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.
Re: Unum Computing: An Energy Efficient and Massively Parallel Approach to Numerics
#8> 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.
If I had a number system of -100, 0, and 100, could I claim all real numbers are represented, just not to arbitrary precision? With n bits, there are 2^n possible representations max. If you can say all real numbers are represented for n around 30, or 60, or even 1,000,000, then can't you say the same for n equal to 1 or 2?
Now I think we can say some representations are better than others (at least for certain applications). It may even be possible that some representation with a given n can be better in all cases than a representation with a larger n. So an n equals 1 system will obviously be terrible compared to many systems with n around 30 or 60. But I'm not really concerned with that point, just the claim of being able to represent all real numbers.
Re: Unum Computing: An Energy Efficient and Massively Parallel Approach to Numerics
#9Are 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?
Re: Unum Computing: An Energy Efficient and Massively Parallel Approach to Numerics
#10Earlier 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.
That's fine, but then you're representing dyadic intervals, not real numbers. Simple question: what's unum[sqrt(2)]?