Rick Teachey Rick Teachey - 3 months ago 7
Python Question

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

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.

This being the case, I would have expected the following line to take an inordinate amount of time, because in order to determine whether 1 quadrillion is in the range, a quadrillion values would have to be generated:

1000000000000000 in range(1000000000000001)


Furthermore: it seems that no matter how many zeroes I add on, the calculation more or less takes the same amount of time (basically instantaneous).

I have also tried things like this, but the calculation is still almost instant:

1000000000000000000000 in range(0,1000000000000000000001,10) # count by tens


If I try to implement my own range function, the result is not so nice!!

def my_crappy_range(N):
i = 0
while i < N:
yield i
i += 1
return


What is the
range()
object doing under the hood that makes it so fast?




EDIT: This has turned out to be a much more nuanced topic than I anticipated - there seems to be a bit of history behind the optimization of
range()
.

Martijn Pieters' answer was chosen for its completeness, but also see abarnert's first answer for a good discussion of what it means for
range
to be a full-fledged sequence in Python 3, and some information/warning regarding potential inconsistency for
__contains__
function optimization across Python implementations. abarnert's other answer goes into some more detail and provides links for those interested in the history behind the optimization in Python 3 (and lack of optimization of
xrange
in Python 2). Answers by poke and by wim provide the relevant C source code and explanations for those who are interested.

Answer

The Python 3 range() object doesn't produce numbers immediately; it is a smart sequence object that produces numbers on demand. All it contains is your start, stop and step values, then as you iterate over the object the next integer is calculated each iteration.

The object also implements the object.__contains__ hook, and calculates if your number is part of its range. Calculating is a O(1) constant time operation. There is never a need to scan through all possible integers in the range.

From the range() object documentation:

The advantage of the range type over a regular list or tuple is that a range object will always take the same (small) amount of memory, no matter the size of the range it represents (as it only stores the start, stop and step values, calculating individual items and subranges as needed).

So at a minimum, your range() object would do:

class my_range(object):
    def __init__(self, start, stop=None, step=1):
        if stop is None:
            start, stop = 0, start
        self.start, self.stop, self.step = start, stop, step
        if step < 0:
            lo, hi = stop, start
        else:
            lo, hi = start, stop
        self.length = ((hi - lo - 1) // abs(step)) + 1

    def __iter__(self):
        current = self.start
        if self.step < 0:
            while current > self.stop:
                yield current
                current += self.step
        else:
            while current < self.stop:
                yield current
                current += self.step

    def __len__(self):
        return self.length

    def __getitem__(self, i):
        if 0 <= i < self.length:
            return self.start + i * self.step
        raise IndexError('Index out of range: {}'.format(i))

    def __contains__(self, num):
        if self.step < 0:
            if not (self.stop < num <= self.start):
                return False
        else:
            if not (self.start <= num < self.stop):
                return False
        return (num - self.start) % self.step == 0

This is still missing several things that a real range() supports (such as the .index() or .count() methods, hashing, equality testing, or slicing), but should give you an idea.

I also simplified the __contains__ implementation to only focus on integer tests; if you give a real range() object a non-integer value (including subclasses of int), a slow scan is initiated to see if there is a match, just as if you use a containment test against a list of all the contained values. This was done to continue to support other numeric types that just happen to support equality testing with integers but are not expected to support integer arithmetic as well. See the original Python issue that implemented the containment test.