[The Economist] Letting computers make mistakes - Page 4

That be some funny chit!

Bring on the error makers!

This concept has been around for a long time. I have read several like this in the news section before. Its a novel idea, but there are big problems with implementing it. There are some tasks, like in graphics, where a small number of errors is quite acceptable. One miss placed pixel every two or three frames in a game or a movie is not going to be perceptible to the average person. However, it is not easy to implement this in silicon effectively. At which stage in a pipeline do you allow error? How do you account for that error in other stages? How do you provide enough bandwidth or reduce latency to make the trade offs worth while? In most processors, the slowest part of the processing must be exactly accurate in order to preserve the integrity of the machine.

I know very little about micro processor design, a person who does could probably talk at much more length on it. It is for these reasons though, as I understand it, that this idea hasn't been implemented in modern microprocessors. I would wager the idea has been around for decades at least.

EDIT: I would also like to point out, that for CPUs at least, there isn't much room for an acceptable error design. The majority of processing time in nearly all applications is taken up by conditional branches, for several reasons; they make up the majority of operations in code, and the result of intermediate operations is often neccessary in order to make a decision in the conditional branch. There is a lot of waiting involved. Thanks to advance branch predition algorithms, and techniques like "Out of Order Processing" (OoO) this is mitigated quite a bit. There isn't much room for making mistakes if you can just process several likely branches of a conditional statement at the same time and save the value you need once the direction of the conditional branch has been figured out.

Graphics cards however, do not operate in this way (traditionally, they are becoming more flexible over time for GPGPU purposes). Since graphics cards operate almost entirely serially, with little conditional branches, acceptable error might work in these processors. Sense GPUs are moving into the heterogeneous and multipurpose space as time goes on though, I think it is unlikely that such a design will ever be implement by AMD or Nvidia.
Edited by mothergoose729 - 6/11/12 at 7:08pm

speak for yourself! my brain is perfect.

Now someone feel free to correct me if I'm wrong(haven't quite gotten my CMIS degree yet), but isn't that a software issue? I know that if you divide 4 by 6 in Common Lisp the computer will return 2/3(on the other hand, 4 divided by 6.0 will get the result you mentioned).

Fractions do not exist to computer hardware. Everything is an integer or float.

Its a limitation of any system that isn't base three. You can't represent 1/3 exactly in binary.

floating point number do technically evaluate to a rational though .

And again, not trying to be argumentative, just trying to learn, but how is it that Common Lisp evaluates integer division as fractions? It seems that what you are saying is certainly true at a basic level, but can be solved by software.

I think Duckie is talking about how numbers are stored in memory in binary/hex. The software likely approximates the value in memory based off the float precision.
Edited by Riou - 6/11/12 at 11:47pm

I'll have to look into that. But even if that is so, it kind of invalidates the case as an example of the computer's flaws in comparison to the human brain. Saying that a fraction can't be represented in binary math is like saying that the taste of cake can't be comprehended by a firing synapse.