Is the iteration protocol used when indexing a range object?

Question

Since the range object produces values on demand, does it mean that anytime a range is indexed, the iteration protocol is invoked up to that index?

What I mean is when:

>>> R = range(1,11)
>>> print(R[5])
6

Since R[5] isn't stored in memory, is it calculated every time by creating a new iterator? If not, how is it possible to index a range object?

Answer 1

No iterator is created here, and no iteration occurs. The range object is implemented such that Python computes the value of R[5] on-demand in constant time.¹

If the index i is not negative, the computation boils down to:

i * step + start

So in the case of your code R[5], this would be 5*1 + 1 which is 6.

If the index i is negative, the length of R is added to i first, and then the value is computed as before:

(i + len(R)) * step + start

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Python-internals

When you write R[5], this Python syntax is eventually translated into a call to PyObject_GetItem, which inspects the object R to see how it should proceed to find the item at index 5.

PyObject_GetItem first checks the tp_as_mapping slot of the range type. This is not null; it holds a reference to a struct called range_as_mapping. PyObject_GetItem then checks to see what is in the mp_subscript field of this struct:

static PyMappingMethods range_as_mapping = {
        (lenfunc)range_length,       /* mp_length */
        (binaryfunc)range_subscript, /* mp_subscript */
        (objobjargproc)0,            /* mp_ass_subscript */
};

As you can see in the snippet above, it finds the range_subscript function occupying the mp_subscript field.²

Now range_subscript inspects the arguments it was passed (R and 5) to decide if a single index or a slice was requested. The integer 5 means that just a single index is needed and so the function delegates the computation of the value to compute_range_item. This function performs the computation to return the integer 6 as outlined in the first part of this answer.

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¹ I have assumed you are using CPython: other Python implementations may implement the range object differently.

² If you were to call len(R), you can see the internal function in mp_length that is called to compute the length of R (cf. Why is "1000000000000000 in range(1000000000000001)" so fast in Python 3?).