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I want to learn more about numerical algorithms that use mixed-precision computational models (where instead of everything being 32/64 bit floating points, we can do lower precision calculations at lower costs).

Does anyone know of good articles/books on this? All I can find are various haphazard fpga-implementation articles on google scholar.

Thanks!

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  • $\begingroup$ I feel like you may want to go to StackOVerflow for this question. $\endgroup$ – Harry Gindi Jan 29 '10 at 11:43
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Check also arithmetic filters, eg in http://dx.doi.org/10.1016/S0166-218X(00)00231-6.

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I wonder whether this approach is worthwhile on modern hardware. There's not as much difference between integer, float, and double operations as there used to be.

One way it may matter, however, is saving space. With smaller data types, you can fit more numbers at a time into cache, and that may give you a speed up. The time savings doesn't come from arithmetic operations but from faster access to the data if you can avoid a cache miss.

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Jonathan Shewchuk's adaptive-precision floating-point arithmetic might be relevant. Mixed-precision computation is exactly what it does, but I believe it really implements the dual of what you're asking, since it's accuracy-driven, not cost-driven.

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