A toy implementation of Knuth's up-arrow notation

up_arrow.py

#!/usr/bin/env python3

import pytest


def up_n(arrows, a, b):
    """Return a ↑(arrows times) b."""

    if arrows == 1:
        return a ** b
      
    n = a
    for _ in range(b - 1):
        n = up_n(arrows - 1, a, n)
    return n


@pytest.mark.parametrize("a,b,expected", [(2, 3, 8), (3, 2, 9)])
def test_up_1(a, b, expected):
    """This is just a ** b. It's pretty much a given."""

    assert up_n(1, a, b) == expected


JFC = 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@pytest.mark.parametrize(
    "a,b,expected",
    [
        (2, 2, 4),
        (2, 3, 16),
        (2, 4, 65536),
        # The numbers start to grow very quickly.
        (2, 5, JFC),
        (3, 2, 27),
        (3, 3, 7_625_597_484_987),
    ],
)
def test_up_2(a, b, expected):
    """These numbers grow a lot faster than exponentiation."""

    assert up_n(2, a, b) == expected


@pytest.mark.parametrize("a,b,expected", [(2, 2, 4), (2, 3, 65536), (3, 2, 7_625_597_484_987)])
def test_up_3(a, b, expected):
    """I only have 16GB of RAM, so can't test 2↑↑↑4 or 3↑↑↑3."""

    assert up_n(3, a, b) == expected