Raul wrote:
>Or, since the leading zero is irrelevant (and was
>not an official part of the original algorithm):
> #:
I considered this approach, but I concluded it evades the spirit of the
algorithm.
Ethiopian multiplication is an approach used by humans to multiply
inconveniently large numbers. As such, its "implementation" should be
realizable by a human.
A human (incapable of multiplying inconveniently large numbers) is
incapable of calculating #: (of similarly inconveniently large numbers).
Or, put another way, <....@-:^:a: is the way a human would calculate #: .
> emul=: p.&2@([ * |....@#:@])
We can trim 3 words from this:
p.&2@(* |....@#:)
I'm impressed by p.&2 . I had come up with #: (as I mentioned), but
couldn't find a way to "exclude the zeros" without filtering, using # .
I had tried #. , being obviously related, but of course that doesn't
work.
I believe that p.&2 is in the spirit of the challenge. Considered one
way, it's "evaluate a polynomial at 2"; at first blush, this does not
appear to be an operation a multiplication-shortcutter could realize.
However, drilling deeper, we realize "evaluating a polynomial at 2" is
precisely steps 3-5 but expresses it concisely. Which is the goal.
-Dan
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