What determines the sign of m % n for integers?

Question

The modulo in Python is confusing.

In Python, % operator is calculating the remainder:

>>> 9 % 5
4

However:

Answer 1

In integers, you can't always pick such a quotient that quotient * divisor == dividend. If the product does not equal the dividend, one always has to make a choice, whether to make it slightly less than the dividend, or slightly greater than the dividend. The sum of the product with the remainder makes the dividend, that's what the remainder is. In any case, the dividends and products have to be close, meaning the absolute value of the remainder has to be less than that of the divisor.

When the divisor is positive, the products increase as the quotients increase; when the divisor is negative, the products decrease as the quotients increase. In the first case, the products go from the below, in the second case, the products go from the above. In Python, in both cases the next quotient is only taken when the dividend reaches the next possible product, going the same way the products go. Before that, only the remainder changes to accommodate for the next dividend, again always going in the same direction as the dividends change, without a break at zero. This rule is universal in Python, it holds always.

That is not the reason why this choice had been made, but that gives the idea what happens (i. e. why the results are what they are, and which results to expect).