Read CPython's longobject.c: How Python Integers Work

Arbitrary Precision Integers

Python integers are not fixed-width C `long` values. CPython stores them as `PyLongObject` with a digit array in base 2^30, defined in `longobject.c` and `longintrepr.h`.

Digit Limbs and Small-Int Cache

Each limb is a `digit` (typically `uint32`) but only 30 bits are used so multiplication of two digits never overflows a 64-bit intermediate. A number like 2^60 splits into limbs `[0, 1]` because 2^60 = 1 * 2^30 + 0.

CPython also caches integers from -5 to 256:

• `x = 5; y = 5; x is y` prints `True` because both names point at the same cached object
• Values outside the cache allocate a fresh `PyLongObject`

For example, 1234567890123 requires multiple 30-bit limbs when stored in little-endian order.

```c typedef struct { PyObject_HEAD ssize_t ob_size; digit ob_digit[1]; } PyLongObject; ```

Design Notes

Arbitrary precision is not free: every large integer operation allocates and may carry across limbs. Profile hot loops that accidentally promote small ints to big ints when values exceed the machine word.

For This Exercise

This exercise asks you to model `PyLongObject` layout in C. You will implement limb splitting for a 64-bit input and document the small-integer cache range that explains Python's identity quirks.