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

Re:Unum Computing: An Energy Efficient and Massively Paralle... by Lawtonfogle on Friday July 24, 2015 @04:34PM (#9945002)

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.

[ Parent | on HN ]

Re:Unum Computing: An Energy Efficient and Massively Paralle... by dnautics on Friday July 24, 2015 @05:03PM (#9945181)

Sure, you can claim that but it doesn't mean squat unless your underlying circuits correctly process operations (*,+,/etc) on the representation in a way that is faithful to your claim.

In the book he talks about a simple unum with values -inf, less than -2, -2, between -2 ... -1, -1, between -1 ... 0, 0, 0...1, 1, 1...2, 2, > 2, and inf, also intervals like 0...2, -2...0 etc 1...inf, emerge when you intentionally use less precision.

This is a mathematically closed system that represents all real numbers and is even useful!

[ Parent | on HN ]