Thanks. I had a go at optimising your routine (I hope that's ok), by calculating initial upper and lower bounds. This gives a smaller range to search. This improves the performance, but as it stands my sqrt10.a is still a little bit faster in general and smaller (no tables).

Here's the performance of my optimised version of your routine in red:

Your procedure is amazing and I'm going to steal it for my project, if you don't mind

No problem, go for it!

After briefly struggling with the nuts and bolts, I have tentatively concluded that Bruce's subroutine is the likely destination for my attempts to "integerize" MJM's subroutine. The probability of me being able to out-golf Bruce is low enough to steer me toward spending my increasingly limited attention elsewhere, after congratulating everyone for an entertaining and informative thread. Cheers!

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Got a kilobyte lying fallow in your 65xx's memory map? Sprinkle some VTL02C on it and see how it grows on you!

Mike B. (about me) (learning how to github)