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

1. Due to optimization, it is very easy to compare given integers just with min and max range.
2. The reason that range() function is so fast in Python3 is that here we use mathematical reasoning for the bounds, rather than a direct iteration of the range object.
3. So for explaining the logic here:
   • Check whether the number is between the start and stop.
   • Check whether the step precision value doesn't go over our number.

4. Take an example, 997 is in range(4, 1000, 3) because:

   4 <= 997 < 1000, and (997 - 4) % 3 == 0.