Edge Cases

Division by zero

Since division by zero is not defined, we should handle the case, where the user calls the division function with 0 as divisor. Both implemented division algorithms would be stuck in the while loop if 0 is passed as the second argument and thus block further commands from being executed. We obviously do not want this to happen.

In general, there are two ways to deal with "forbidden" values. The first one is to raise an error, just like the build-in division operators, which raises a ZeroDivisionError and halts the program. This is realized by adding an if-condition at the beginning of the algorithm:

def div_err(a, b):
    if b == 0:
        raise ZeroDivisionError
    ...

Sometimes, however, we want the program to continue even after encountering forbidden values. In this case, we can make the algorithm return something, which is recognizable as invalid. This way, the user can be informed about forbidden values through the outputs. One possible choice of such invalid object is the None object and can be used like

def div_none(a, b):
    if b == 0:
        return None
    ...

Negative input

While implementing multiplication and division algorithms, the problems were only analyzed using non-negative integers. Inputs of negative integers may therefore lead to undefined behaviors. Again, we can raise an exception when this happens or utilise an invalid object. The following listings show both cases on the multiplication algorithm:

def mul_err(a, b):
    if a < 0 or b < 0:
        raise ValueError
    ...

def mul_none(a, b):
    if a < 0 or b < 0:
        return None
    ...

These lines can be directly added to division algorithms to deal with negative inputs.

Floating-point input

Just like in the case of negative input values, floating-point numbers as inputs may also lead to undefined behaviors. Although the same input guards can be applied to deal with floating-point numbers, a more sensible way would be to convert the input values to integer using int function before executing the algorithms.