maths: add Luhn algorithm for credit card number validation

- Implements luhn_check(card_number) using the mod-10 checksum
- Handles double-and-subtract-9 step for values > 9
- Type hints on all parameters and return values
- Doctests for valid Visa number, invalid numbers, edge cases
- Raises ValueError for non-digit input
- Wikipedia reference included

Author: Akibuzzaman Akib

maths/luhn_algorithm.py

@@ -0,0 +1,79 @@
+"""
+Luhn Algorithm — credit card number validation.
+
+The Luhn algorithm (also known as the "modulus 10" or "mod 10" algorithm) is a
+simple checksum formula used to validate identification numbers such as credit
+card numbers, IMEI numbers, and Canadian Social Insurance Numbers.
+
+Algorithm:
+  1. From the rightmost digit (the check digit) and moving left, double the
+     value of every second digit.
+  2. If the result of doubling is greater than 9, subtract 9.
+  3. Sum all the digits (the undoubled ones and the doubled/adjusted ones).
+  4. If the total modulo 10 is 0, then the number is valid.
+
+References:
+  - https://en.wikipedia.org/wiki/Luhn_algorithm
+"""
+
+
+def luhn_check(card_number: str) -> bool:
+    """Validate a credit card number (given as a digit string) using the Luhn
+    algorithm.
+
+    :param card_number: A string containing only digit characters representing
+                        the card number to validate.
+    :raises ValueError: If *card_number* contains any non-digit characters.
+    :return: ``True`` if the number is valid according to the Luhn algorithm,
+             ``False`` otherwise.
+
+    Examples:
+    >>> luhn_check("4532015112830366")  # valid Visa
+    True
+    >>> luhn_check("4532015112830367")  # invalid — check digit off by one
+    False
+    >>> luhn_check("1234567890123456")  # invalid
+    False
+    >>> luhn_check("79927398713")  # canonical Luhn-valid test number
+    True
+    >>> luhn_check("79927398714")  # invalid
+    False
+    >>> luhn_check("0")  # single zero is valid (trivially)
+    True
+    >>> luhn_check("abc123")
+    Traceback (most recent call last):
+        ...
+    ValueError: luhn_check() only accepts strings of digits
+    >>> luhn_check("4111 1111 1111 1111")
+    Traceback (most recent call last):
+        ...
+    ValueError: luhn_check() only accepts strings of digits
+    """
+    if not card_number.isdigit():
+        raise ValueError("luhn_check() only accepts strings of digits")
+
+    digits = [int(d) for d in card_number]
+    # Double every second digit from the right (index from end: 1, 3, 5, …)
+    for i in range(len(digits) - 2, -1, -2):
+        digits[i] *= 2
+        if digits[i] > 9:
+            digits[i] -= 9
+
+    return sum(digits) % 10 == 0
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    test_numbers = [
+        ("4532015112830366", True),
+        ("4532015112830367", False),
+        ("79927398713", True),
+        ("1234567890123456", False),
+    ]
+    for number, expected in test_numbers:
+        result = luhn_check(number)
+        status = "✓" if result == expected else "✗"
+        print(f"{status} luhn_check({number!r}) = {result}")