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Mon, 02 Oct 2023

Irish logarithm forward instead of backward

Yesterday I posted about the so-called “Irish logarithm”, Percy Ludgate's little algorithm for single-digit multiplication.

Hacker News user sksksfpuzhpx said:

There's a much simpler way to derive Ludgate's logarithms

and referred to Brian Coghlan's aticle “Percy Ludgate's Logarithmic indices”.

Whereas I was reverse-engineering Ludgate's tables with a sort of ad-hoc backtracking search, if you do it right you can do it it more easily with a simple greedy search.

Uh oh, I thought, I will want to write this up before I move on to the thing I planned to do next, which made it all the more likely that I never would get to the thing I had planned to do next. But Shreevatsa R. came to my rescue and wrote up the Coghlan thing at least as well as I could have myself. Definitely check it out.

Thank you, Shreevatsa!

[ Update 20231015: A different kind of all-integer logarithm: the discrete logarithm. ]

[ Update 20231020: Better explanation of the discrete logarithm. ]

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