Why is “1000000000000000 in range(1000000000000001)” so fast in Python 3?

Question

It is my understanding that the range() function, which is actually an object type in Python 3, generates its contents on the fly, similar to a generator.

Answer 1

If you're wondering why this optimization was added to range.__contains__, and why it wasn't added to xrange.__contains__ in 2.7:

First, as Ashwini Chaudhary discovered, issue 1766304 was opened explicitly to optimize [x]range.__contains__. A patch for this was accepted and checked in for 3.2, but not backported to 2.7 because "xrange has behaved like this for such a long time that I don't see what it buys us to commit the patch this late." (2.7 was nearly out at that point.)

Meanwhile:

Originally, xrange was a not-quite-sequence object. As the 3.1 docs say:

Range objects have very little behavior: they only support indexing, iteration, and the len function.

This wasn't quite true; an xrange object actually supported a few other things that come automatically with indexing and len,^* including __contains__ (via linear search). But nobody thought it was worth making them full sequences at the time.

Then, as part of implementing the Abstract Base Classes PEP, it was important to figure out which builtin types should be marked as implementing which ABCs, and xrange/range claimed to implement collections.Sequence, even though it still only handled the same "very little behavior". Nobody noticed that problem until issue 9213. The patch for that issue not only added index and count to 3.2's range, it also re-worked the optimized __contains__ (which shares the same math with index, and is directly used by count).^** This change went in for 3.2 as well, and was not backported to 2.x, because "it's a bugfix that adds new methods". (At this point, 2.7 was already past rc status.)

So, there were two chances to get this optimization backported to 2.7, but they were both rejected.

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_{* In fact, you even get iteration for free with indexing alone, but in 2.3 xrange objects got a custom iterator.}

_{** The first version actually reimplemented it, and got the details wrong—e.g., it would give you MyIntSubclass(2) in range(5) == False. But Daniel Stutzbach's updated version of the patch restored most of the previous code, including the fallback to the generic, slow _PySequence_IterSearch that pre-3.2 range.__contains__ was implicitly using when the optimization doesn't apply.}