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Thanks for pointing this exmple out. Now, I'm also confident that graphics are doable in integer arithmetic. Anybody any ideas where IEEE-754 is mandatory to a

by madez 9y ago

Thanks for pointing this exmple out. Now, I'm also confident that graphics are doable in integer arithmetic. Anybody any ideas where IEEE-754 is mandatory to achieve acceptable performance in individual computing workloads?

dathinab 9y ago
I do not think IEEE-754 is mandatory for any work load, it is just that using fixedpoint arithmetic, especially if mapped onto of a number of common integer types tends to be more complex to implement then simply using float. With fixed point you have to be much more aware about e.g. the min-max-range of values and the precision needed, potentially changing them between different computation steps. If you have any complex math algorithm you should also look into this aspects with float for error calculation etc. So maybe using fixed-point would not be so bad there, but for a lot of "just get it done" tasks people want to just have a float and not bother about it. If you have a way to quickly translate math specific programs using floats + little amounts of meta data into math specific programs using fixed-point arithmetic including error analysis/correction* you probably would get ride of >90% of float requirements, through you would "still" have all that legacy software ;=) [*] If I remember correctly someone did that for Neural Networks using tensorflow, but I don't remember the details
deleted 9y ago
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stephencanon 9y ago
Floating-point is (almost) never necessary to achieve acceptable performance in one specific compute workload. The value of IEEE 754 floating-point is that it makes it much, much easier to write correct numerically stable programs, because the arithmetic has a scale-invariant rounding error model (assuming no over-/underflow), and the results in the case of over/underflow are fully defined, so no unpleasant surprises like UB for integers. For (almost) any one fixed algorithm with specified input scaling and known error tolerance, you can choose an appropriate fixed-point format and come within a reasonable constant of floating-point performance on generic hardware, and exceed it on special-purpose hardware. The real value of floating-point is in writing libraries that deliver good performance and acceptable numeric results without any a priori knowledge of input data scaling. This is critical to allowing people to quickly re-use and repurpose all the existing numerical computing software for new problems, and allows engineering tools like Matlab to be useful to people who are not numerics experts.

by madez 9y ago

dathinab 9y ago

I do not think IEEE-754 is mandatory for any work load, it is just that using fixedpoint arithmetic, especially if mapped onto of a number of common integer types tends to be more complex to implement then simply using float. With fixed point you have to be much more aware about e.g. the min-max-range of values and the precision needed, potentially changing them between different computation steps. If you have any complex math algorithm you should also look into this aspects with float for error calculation etc. So maybe using fixed-point would not be so bad there, but for a lot of "just get it done" tasks people want to just have a float and not bother about it. If you have a way to quickly translate math specific programs using floats + little amounts of meta data into math specific programs using fixed-point arithmetic including error analysis/correction* you probably would get ride of >90% of float requirements, through you would "still" have all that legacy software ;=) [*] If I remember correctly someone did that for Neural Networks using tensorflow, but I don't remember the details

deleted 9y ago

[deleted]

stephencanon 9y ago

Floating-point is (almost) never necessary to achieve acceptable performance in one specific compute workload. The value of IEEE 754 floating-point is that it makes it much, much easier to write correct numerically stable programs, because the arithmetic has a scale-invariant rounding error model (assuming no over-/underflow), and the results in the case of over/underflow are fully defined, so no unpleasant surprises like UB for integers. For (almost) any one fixed algorithm with specified input scaling and known error tolerance, you can choose an appropriate fixed-point format and come within a reasonable constant of floating-point performance on generic hardware, and exceed it on special-purpose hardware. The real value of floating-point is in writing libraries that deliver good performance and acceptable numeric results without any a priori knowledge of input data scaling. This is critical to allowing people to quickly re-use and repurpose all the existing numerical computing software for new problems, and allows engineering tools like Matlab to be useful to people who are not numerics experts.