test(maths): add doctests and pytest for Sieve of Atkin

Author: idrisibrahimerten

maths/sieve_of_atkin.py

@@ -2,6 +2,37 @@
 
 
 def sieve_of_atkin(limit: int) -> List[int]:
+    """
+    Compute all prime numbers up to the given limit using the Sieve of Atkin.
+
+    Parameters
+    ----------
+    limit : int
+        Upper bound of primes to generate (inclusive).
+
+    Returns
+    -------
+    List[int]
+        A list of prime numbers <= limit.
+
+    Raises
+    ------
+    ValueError
+        If limit is not an integer or is less than 2.
+
+    References
+    ----------
+    https://en.wikipedia.org/wiki/Sieve_of_Atkin
+
+    Examples
+    --------
+    >>> sieve_of_atkin(10)
+    [2, 3, 5, 7]
+    >>> sieve_of_atkin(1)
+    Traceback (most recent call last):
+    ...
+    ValueError: limit must be an integer >= 2
+    """
     if not isinstance(limit, int) or limit < 2:
         raise ValueError("limit must be an integer >= 2")
 

maths/test_sieve_of_atkin.py

@@ -0,0 +1,10 @@
+# tests/test_sieve_of_atkin.py
+import pytest
+from maths.sieve_of_atkin import sieve_of_atkin
+
+def test_small_primes():
+    assert sieve_of_atkin(10) == [2, 3, 5, 7]
+
+def test_invalid_limit():
+    with pytest.raises(ValueError):
+        sieve_of_atkin(1)