Dynamically swapping between two algorithms

[MRAB]

On 2014-09-23 15:48, Steven D'Aprano wrote:
> I have a certain calculation which can be performed two radically different
> ways. With the first algorithm, let's call it SHORT, performance is very
> fast for small values of the argument, but terrible for large values. For
> the second algorithm, LARGE, performance is quite poor for small values,
> but excellent for large values.
>
> To add to the complexity, I perform this calculation repeatedly, in a loop:
>
> value = 1
> while True:
>      x = SHORT(value)  # Or should I use LARGE? Decisions, decisions...
>      process(x)
>      value += some_increment()
>      if condition: break
>
> Luckily, the value never gets smaller. So if I could somehow determine a
> cut-over point, CUTOFF, I might write my loop like this:
>
> value = 1
> while True:
>      f = SHORT if value < CUTOFF else LARGE
>      x = f(value)
>      process(x)
>      value += some_increment()
>      if condition: break
>
> alas, the CUTOVER point is likely to be machine-dependent. Take it as a
> given that inserting a fixed CUTOVER point into the source code (say,
> ``CUTOVER = 123456``) is not likely to be very effective, and dynamically
> calculating it at import time is impractical.
>
> *If* Python was a different language, I would spawn two threads, one using
> SHORT and the other using LARGE, then which ever completes first, I'd just
> kill the other. Alas, this won't work because (1) the GIL and (2) you
> cannot forcibly kill threads, only ask them to die and hope they listen.
>
> I am seeking other ideas for dynamically swapping between the two
> algorithms, based on runtime information. Any thoughts?
>
>
> (1) I can't tell in advance how many loops I will make.
>
> (2) Both SHORT and LARGE get slower as the size of their argument increases.
> This is unavoidable due to the nature of the problem.
>
> (3) SHORT starts off relatively speedy, significantly faster than LARGE for
> the first few tens of thousands of loops. I'm not talking about trivial
> micro-optimizations here, I'm talking about the difference between 0.1
> second for SHORT versus 10 seconds for LARGE.
>
> (4) But as the size of the argument increases, SHORT suffers catastrophic
> quadratic slowdown, while LARGE slows down only linearly. (Give or take.)
>
> (5) Consequently, by the time I reach a few million loops, the difference is
> now between (say) 5 minutes for LARGE versus 15 hours for SHORT.
>
> (6) There is no single algorithm which performs acceptably across the entire
> range of values I'm expecting to process in practice.
>
> (7) Leaving the choice up to the caller is not an option. I am the caller.
>
How about this:

Try both of them initially, and use the faster one until it takes
longer than the slower one did initially. Then try both of them again.
Repeat.