64/32-bit division on a processor with 32/16-bit division

algorithm optimization division
Thomas O picture Thomas O · Jan 23, 2011 · Viewed 14.1k times · Source

My processor, a small 16-bit microcontroller with no FPU and integer math only has 16/16 division and 32/16 division which both take 18 cycles. At the moment I'm using a very slow software routine (~7,500 cycles) to do 64/32 division. Is there any way to use these division engines to calculate a 64/32 division? Similar to how I'm already using the 16x16 multiplier and adder to calculate 32x32 multiplies? I'm using C but can work with any general explanation on how it can be done... I'm hoping to target <200 cycles (if it's at all possible.)

Answer

payne picture payne · Jan 23, 2011

See "Hacker's Delight", multiword division (pages 140-145).

The basic concept (going back to Knuth) is to think of your problem in base-65536 terms. Then you have a 4 digit by 2 digit division problem, with 2/1 digit division as a primitive.

The C code is here: https://github.com/hcs0/Hackers-Delight/blob/master/divmnu.c.txt

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