feat(maths): add function to perform calculation (#6602)

* feat(maths): add function to perform calculation
- Add single function to calculate sum of two positive numbers
  using bitwise operator

* docs: add wikipedia url as explanation

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Co-authored-by: Caeden Perelli-Harris <[email protected]>

* Update sum_of_two_positive_numbers_bitwise.py

* Update sum_of_two_positive_numbers_bitwise.py

* Update sum_of_two_positive_numbers_bitwise.py

---------

Co-authored-by: Okza Pradhana <[email protected]>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Tianyi Zheng <[email protected]>
Co-authored-by: Caeden Perelli-Harris <[email protected]>

Author: 5 people

Diff for: maths/sum_of_two_positive_numbers_bitwise.py

@@ -0,0 +1,55 @@
+"""
+Calculates the sum of two non-negative integers using bitwise operators
+Wikipedia explanation: https://en.wikipedia.org/wiki/Binary_number
+"""
+
+
+def bitwise_addition_recursive(number: int, other_number: int) -> int:
+    """
+    >>> bitwise_addition_recursive(4, 5)
+    9
+    >>> bitwise_addition_recursive(8, 9)
+    17
+    >>> bitwise_addition_recursive(0, 4)
+    4
+    >>> bitwise_addition_recursive(4.5, 9)
+    Traceback (most recent call last):
+        ...
+    TypeError: Both arguments MUST be integers!
+    >>> bitwise_addition_recursive('4', 9)
+    Traceback (most recent call last):
+        ...
+    TypeError: Both arguments MUST be integers!
+    >>> bitwise_addition_recursive('4.5', 9)
+    Traceback (most recent call last):
+        ...
+    TypeError: Both arguments MUST be integers!
+    >>> bitwise_addition_recursive(-1, 9)
+    Traceback (most recent call last):
+        ...
+    ValueError: Both arguments MUST be non-negative!
+    >>> bitwise_addition_recursive(1, -9)
+    Traceback (most recent call last):
+        ...
+    ValueError: Both arguments MUST be non-negative!
+    """
+
+    if not isinstance(number, int) or not isinstance(other_number, int):
+        raise TypeError("Both arguments MUST be integers!")
+
+    if number < 0 or other_number < 0:
+        raise ValueError("Both arguments MUST be non-negative!")
+
+    bitwise_sum = number ^ other_number
+    carry = number & other_number
+
+    if carry == 0:
+        return bitwise_sum
+
+    return bitwise_addition_recursive(bitwise_sum, carry << 1)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()