Question

Been looking through other answers and I still don’t understand the modulo for negative numbers in python

For example the answer by df

x == (x/y)*y + (x%y)

so it makes sense that (-2)%5 = -2 – (-2/5)*5 = 3

Doesn’t this (-2 – (-2/5)*5) =0 or am I just crazy?
Modulus operation with negatives values – weird thing?

Same with this
negative numbers modulo in python
Where did he get -2 from?

Lastly if the sign is dependent on the dividend why don’t negative dividends have the same output as their positive counterparts?

For instance the output of

print([8%5,-8%5,4%5,-4%5])

is

[3, 2, 4, 1]

Answer 1

In Python, modulo is calculated according to two rules:

• (a // b) * b + (a % b) == a, and
• a % b has the same sign as b.

Combine this with the fact that integer division rounds down (towards −∞), and the resulting behavior is explained.

If you do -8 // 5, you get -1.6 rounded down, which is -2. Multiply that by 5 and you get -10; 2 is the number that you’d have to add to that to get -8. Therefore, -8 % 5 is 2.