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[DM16] Euclidean algorithm in stack

Posted: Wed Mar 25, 2020 12:23 pm
by IainGray
The Euclidean algorithm https://en.wikipedia.org/wiki/Euclidean_algorithm is an efficient method of finding the GCD (greatest common divisor) of two integers. It proceeds by finding successive remainders of the larger by the smaller and swapping the smaller with the remainder until the remainder equals zero, returning the divisor as the GCD.

The code
Screenshot 2020-03-24 at 11.35.21.png
Screenshot 2020-03-24 at 11.35.21.png (19.29 KiB) Viewed 92 times
was developed on an HP16C emulator and so works on the DM16 but will run on any DM calculator.

Line 4 LBL E for Euclid is the normal entry point after entering your two numbers, i.e. <number 1> ENTER <number 2> GSB E, the GCD is returned. The re-entrant loop at line 1 LBL F is only for non-zero remainders. Only stack variables x, y and LST X are used and no Registers.