Fast exact integer divisions using floating-point operations (ARM edition)

In my latest post, I explained how you could accelerate 32-bit integer divisions by transforming them into 64-bit floating-point divisions. Indeed, 64-bit floating-point numbers can represent accurately all 32-bit integers on most processors.

It is a strange result: Intel processors seem to do a lot better with floating-point divisions than integer divisions.

Recall the numbers that I got for the throughput of division operations:

64-bit integer division 25 cycles
32-bit integer division (compile-time constant) 2+ cycles
32-bit integer division 8 cycles
32-bit integer division via 64-bit float 4 cycles

I decided to run the same test on a 64-bit ARM processor (AMD A1100):

64-bit integer division 7 ns
32-bit integer division (compile-time constant) 2 ns
32-bit integer division 6 ns
32-bit integer division via 64-bit float 18 ns

These numbers are rough, my benchmark is naive (see code). Still, on this particular ARM processor, 64-bit floating-point divisions are not faster (in throughput) than 32-bit integer divisions. So ARM processors differ from Intel x64 processors quite a bit in this respect.

Published by

Daniel Lemire

A computer science professor at the University of Quebec (TELUQ).

4 thoughts on “Fast exact integer divisions using floating-point operations (ARM edition)”

  1. One important note, about UDIV/SDIV instruction on arm64 form ARMv8 ISA: ” The divide instructions do not generate a trap upon division by zero, but write zero to the destination register.”

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  2. Can you check the same on 16 bit integers and 32 bit floats? Maybe the arm processor divisor is not fast, say go through a lot of uops to get the results, but the 32 bit float is more probable to be fast.
    Another caveat is that in SKX you are pushed more for a division less algorithm as you have only a double pumped 256b divisor for a 512b vector. Still no integer divisor so it’s much more fast than scalar int.

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  3. This is nice. Note that if you need signed (floor) integer division this way, you can set the FP control register to round toward -inf (_mm_setcsr(_MM_ROUND_TOWARD_ZERO), or fesetround for portability).

    Reply

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