3 ms·

I feel like a lot of discussion is on floating point accuracy and artifacts and most of it misses the point completely. It doesn't help there are IEEE standard

I feel like a lot of discussion is on floating point accuracy and artifacts and most of it misses the point completely. It doesn't help there are IEEE standards for fp calculations which are also very misunderstood. The point of these standards is to provide reproducibility and repeatability so that different types of software running on different machines or with different compilers provide same results. The goal of floating point never was to provide precise representation or calculation and in fact it is not possible to provide in general with floating point. The goal was to make it easy and relatively fast to perform real world calculations. You understand your calculator gives approximate results except for very special cases, so why would you bicker over some digits that are very far to the right of your result. It is actually much worse with calculators because they tend to employ very different calculation engines and very different precision. You can actually identify a particular model or model family of calculator by running couple calculations and finding what kind of artifacts are present in the results, exactly. Yet nobody will tell you calculators are useless as I frequently hear about floating point. I work with Java and there seems to be this movement recently where developers use arbitrary precision arithmetic to do any sort of calculation on anything without actual idea of when this is needed. Supposedly flating point is broken and cannot be trusted. Sigh...

T-hawk 6y ago
You bicker over the digits far to the right because there tends to be ways for those inaccuracies to propagate up into your significant figures. That doesn't happen from typing a few arithmetic operations into a handheld calculator. It does in a computational environment that might be looping over and summing a million or a billion elements and applying more operations to them. It became too easy and fast to use floats for real world calculations, overstressing and exposing their inadequacies. Of course, the right solution is to use the right tool for the job: algorithms that either use a better structure than a 64-bit float, or are smartly designed enough to avoid their inadequacies. But how many developers have both enough insight and enough development time to do that? Everything is a compromise; fixed-point decimal representation is one that works for many applications.
mehrdadn 6y ago
There's a huge difference between mathematical calculations having round-off error and computations that are not mathematical calculations exhibiting something akin to round-off error anyway. It's like giving someone a $10k check and seeing them get $9,999.99, and then getting irritated when people try to investigate what happened because it's only a penny to you. It's kind of missing the point that the error logically shouldn't be there in this situation.

T-hawk 6y ago

You bicker over the digits far to the right because there tends to be ways for those inaccuracies to propagate up into your significant figures. That doesn't happen from typing a few arithmetic operations into a handheld calculator. It does in a computational environment that might be looping over and summing a million or a billion elements and applying more operations to them. It became too easy and fast to use floats for real world calculations, overstressing and exposing their inadequacies. Of course, the right solution is to use the right tool for the job: algorithms that either use a better structure than a 64-bit float, or are smartly designed enough to avoid their inadequacies. But how many developers have both enough insight and enough development time to do that? Everything is a compromise; fixed-point decimal representation is one that works for many applications.

mehrdadn 6y ago

There's a huge difference between mathematical calculations having round-off error and computations that are not mathematical calculations exhibiting something akin to round-off error anyway. It's like giving someone a $10k check and seeing them get $9,999.99, and then getting irritated when people try to investigate what happened because it's only a penny to you. It's kind of missing the point that the error logically shouldn't be there in this situation.