The modulo operation on negative numbers in Python

Question

I\'ve found some strange behaviour in Python regarding negative numbers:

>>> -5 % 4
3

Could anyone explain what\'s going on?

Answer 1

As pointed out, Python modulo makes a well-reasoned exception to the conventions of other languages.

This gives negative numbers a seamless behavior, especially when used in combination with the // integer-divide operator, as % modulo often is (as in math.divmod):

for n in range(-8,8):
    print n, n//4, n%4

Produces:

 -8 -2 0
 -7 -2 1
 -6 -2 2
 -5 -2 3

 -4 -1 0
 -3 -1 1
 -2 -1 2
 -1 -1 3

  0  0 0
  1  0 1
  2  0 2
  3  0 3

  4  1 0
  5  1 1
  6  1 2
  7  1 3

• Python % always outputs zero or positive*
• Python // always rounds toward negative infinity

_{* ... as long as the right operand is positive. On the other hand 11 % -10 == -9}