bpo-37000: Remove obsolete comment in _randbelow_with_getrandbits #95775
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In random._randbelow_with_getrandbits we are generating a random integer in [0,n). We do that by repeatedly drawing a random number, r, in [0,2**k) until we hit an r < n. That's a great strategy. It's not only very simple, but even with worst case input, we only need to draw 2 random numbers on average, before we hit the jackpot. However, the code is a bit overly cautious. When n is a power of 2, we ask `getrandbits` to sample from [0,2*n]. The code justifies that strange behaviour with a comment expressing fear of the special case n==1. That fear is unfounded: the obvious code works just fine for n==1. Fixing this not only makes the code simpler to understand, it also guarantees that the important special case of n being a power of two now has a guaranteed worst case runtime of only a single call to getrandbits; instead of an expected runtime of two calls with no worst case bound. Existing tests already cover this code and the special cases of interest. So we don't need any new tests. This minor performance bug was introduced in 0515661 as far as I can tell. But I can't really tell what the original author was thinking.
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Before Python 3.9, But there's a different issue now: as the failing tests show, while |
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Thanks for the quick review, @tim-one! You make a very good point. If you are interested, I have restored the original behaviour and included your reasoning to explain this seemingly unusual behaviour to the next person reading this code. If you think that might be useful, I can polish the description etc to make this merge-able? |
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See also previous discussion at #81181. |
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For efficiency, we'd like to use k = (n-1).bit_length() here, but before Python 3.9, `getrandbits()` did not accept 0 as an argument. That's why using `n-1` was a problem when `n` was 1. Now we are stuck with this version, because we want to reproduce results after explicitly setting a seed even between releases.
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@matthiasgoergens: Status check is done, and it's a failure ❌ . |
In
random._randbelow_with_getrandbitswe are generating a random integerin [0,n). We do that by repeatedly drawing a random number, r, in [0,2**k)
until we hit an r < n.
That's a great strategy. It's not only very simple, but even with worst
case input, we only need to draw 2 random numbers on average, before we
hit the jackpot.
However, the code is a bit overly cautious. When n is a power of 2, we
ask
getrandbitsto sample from [0,2*n]. The code justifies thatstrange behaviour with a comment expressing fear of the special case n==1.
That fear is unfounded: the obvious code works just fine for n==1.
Fixing this not only makes the code simpler to understand, it also
guarantees that the important special case of n being a power of two now
has a guaranteed worst case runtime of only a single call to
getrandbits; instead of an expected runtime of two calls with no worst
case bound.
Existing tests already cover this code and the special cases of
interest. So we don't need any new tests.
This minor performance bug was introduced in
0515661 as far as I can tell. But I
can't really tell what the original author was thinking.
Since this is a fairly trivial change, I did not create an issue. (But I am happy to create one, if you think it's better this way.)
I discovered this problem while working on https://discuss.python.org/t/random-choice-from-a-dict/17834
Automerge-Triggered-By: GH:rhettinger