Oh, just another note.

There are people who have made their whole careers on devising
asymptotically fast algorithms
which have never been implemented, or (if they have been implemented)
are not fast because
their overly-simplified analysis does not fit the currently available
computer efficiency profile.
Indeed, their analysis may not fit any past profile of computers, and
their algorithms were never
practical.

Note, for example, that memory access is far more expensive than
arithmetic, and that
many computers now can multiply or add in comparable time; and they
have several multipliers. Etc.

RJF

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