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by corysama
1707 days ago
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At least as far as int32 vs float32 goes, surprisingly float is easier to make fast in the hardware. This is because floats are composed of multiple sections that can be processed in parallel whereas all of the bits of and integer addition, for example, have a serial dependency. |
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While floating point numbers can be cleanly split into a mantissa and exponent, adding floats requires shifting the exponent, which can be an expensive operation. Each portion of a floating point arithmetic operation is also implemented with integer arithmetic, which limits the performance spread. Many floating point operations require significantly fewer bits though, which can lead to major speedups.
On the integer side, the serial carry dependence mean ripple-carry adders are usually a bummer, but there a ton of carry-lookahead variants that can lessen the performance impact of that dependency. If you have several integer additions at once, you can use a carry-save variant to only pay that serial cost once all of the additions are done. Finally, if you are willing to significantly change your integer encoding, there are tools like redundant number systems[0] that allow you to move around the traditional trade-offs for arithmetic circuits including completely removing the serial dependency on carries. That said, if you require rescaling your fixed-point numbers during the computation, the fixed-point implementation will require more integer operations than floating-point operations.
All of this is also quite dependent on the overall architecture of the chip too, since the number of integer units vs float units and how data is moved around can have a way bigger impact on performance than how each arithmetic operation is implemented.
[0] http://lux.dmcs.pl/csII/ca2_RedundantNS.pdf