The modulo operation on negative numbers in Python

In python, modulo operator works like this.

>>> mod = n - math.floor(n/base) * base

so the result is (for your case):

mod = -5 - floor(-1.25) * 4
mod = -5 - (-2*4)
mod = 3

whereas other languages such as C, JAVA, JavaScript use truncation instead of floor.

>>> mod = n - int(n/base) * base

which results in:

mod = -5 - int(-1.25) * 4
mod = -5 - (-1*4)
mod = -1

If you need more information about rounding in python, read this.

Unlike C or C++, Python's modulo operator (%) always return a number having the same sign as the denominator (divisor). Your expression yields 3 because

(-5) / 4 = -1.25 --> floor(-1.25) = -2

(-5) % 4 = (-2 × 4 + 3) % 4 = 3.

It is chosen over the C behavior because a nonnegative result is often more useful. An example is to compute week days. If today is Tuesday (day #2), what is the week day N days before? In Python we can compute with

return (2 - N) % 7

but in C, if N ≥ 3, we get a negative number which is an invalid number, and we need to manually fix it up by adding 7:

int result = (2 - N) % 7;
return result < 0 ? result + 7 : result;

(See http://en.wikipedia.org/wiki/Modulo_operator for how the sign of result is determined for different languages.)

Here's an explanation from Guido van Rossum:

http://python-history.blogspot.com/2010/08/why-pythons-integer-division-floors.html

Essentially, it's so that a/b = q with remainder r preserves the relationships b*q + r = a and 0 <= r < b.