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Flaky: datatypes for real world quantities

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Re: Flaky: datatypes for real world quantities

#2

Post by weichi »

Hard to comment without seeing more concrete examples of his approach. But it makes me wonder whether processors are now so fast that, for a large class of numerical problems, the default should be to give up calculational speed in return for eliminating some of the trickiness involved with floating point.

Re: Flaky: datatypes for real world quantities

#7

Post by blackhole »

This is a terrible idea. This is a catastrophically bad idea. How do you compare numbers? How do you figure out that 2.2 is less than exp(65)? You have to represent these as numbers at some point in the calculation, and in order to do that, you're probably going to be using either floating point or fixed point, which means it's still trivially possible to construct an error case that suffers the exact same problems normal floating point numbers have. Observe:

    x=1
    for(i=0;i
You can't simplify this, so it will simply loop until it hits the datatype boundary, and then get rounded into oblivion, because the underlying floating point representation will break in the exact same way. The only way to get rid of this would be to use an arbitrary number of bits for precision, in which case... just use an arbitrary precision library instead! This is EXACTLY WHY WE HAVE THEM.

Most equations that aren't trivial cannot be simplified. This datatype would only be useful for spoon-fed high school math problems. Furthermore, it costs so much CPU to perform you might as well just use an arbitrary precision library, which will probably be faster and be just as effective at preventing edge cases.

https://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic

Re: Flaky: datatypes for real world quantities

#8

Post by eksith »

jamesaguilar wrote: post #5

Maybe it's just me, but saying that something in current use in billions of computers around the globe is . . . somewhat of a stretch of the word "obsolete."

In this case "obsolete" may be the relevant term as in Automobile coach builders, meet the Buggy Whip makers. The two did co-exist in the early 1900's so the alternative, "outmoded" didn't happen overnight. But it did eventually happen.

The numbers, in the billions, of course weren't there, but my guess is that the proportions are applicable.

Edit: After reading the article, I strongly disagree this approach is "better" in any sense of the word. More along the lines of using whale oil for the automobile instead of gasoline. Gasoline isn't perfect, but it works. Until we have something better (I.E. Electric), I'll stick to that.

Re: Flaky: datatypes for real world quantities

#9

Post by darkmighty »

Interesting take on floating point problem, but it seems as if writer isn't well versed on the centuries old solution of this problem, namely refinement calculations for lin algebra and more general iterated numerical methods for nonlinear systems -- and those are the places where the precision matters, where you are trying to calculate a figure with a given accuracy.

Note however, that solutions to many problems may in a sense 'non-analytic', there may be no finite set of elementary functions on a given rational number which yields the solution.

Also, iterative answers are usually the only viable way to reach solutions, they're usually much faster than the exact solution (or the floating point precision limited solution), and you can always control how good your solution is.

Observation: So in a sense what is practically used may indeed very close to the Kolmogorov complexity of the solutions - the representation as R=IterativeProblemSolve(Problem,ClosestSolution), where we publish the problem and the desired solution! (assumig we are efficiently describing the problem)

Re: Flaky: datatypes for real world quantities

#10

Post by GhotiFish »

floating point will never be obsolete, it is a log scale datatype, and log scale datatypes represent most natural values perfectly.

The only place where the shoe doesn't fit is where you need a minimum accuracy. In that case what you should be doing is using integers to represent your minimum quantifiable unit.

For example, you could represent currency in millicents to give you respectably accurate rounding. Not accurate enough? Microcents then. Now you don't have enough range? Good, you're thinking about your requirements now, floating point DEFINITELY wouldn't of worked.

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