Skip to content
Related Articles

Related Articles

Improve Article
How to perform modulo with negative values in Python?
  • Last Updated : 17 May, 2020

Taking modulo of a negative number is a bit more complex mathematics which is done behind the program of Python. If we don’t understand the mathematics behind the modulo of negative number than it will become a huge blender.
 

Mathematics behind the negative modulo :

Let’s Consider an example, where we want to find the -5mod4 i.e. -5%4. You all must be wondering that the answer will be according to the below rule – 

-5/4 = 1.25 
and
math.floor(-1.25) = -2

But this is not the anser we get, when we’ll run the above code we’ll get the answer as 3. This is because Python’s modulo operator (%) always return a number having the same sign as the denominator. What happens behind the scene is that Python applies the distribute law of Modulo operator which is – 

(a+b)mod n = [(a mod n)+(b mod n)]mod n

To apply this math Python break the given statement as – 



-5%4 = (-2*4 + 3) % 4 = 3

This was done so that the (-2*4)%4 will give the answer as 0 (as we are always getting a multiple of divisor as our first number) and the overall result will be 3. Let’s see more examples for better understanding.

Examples:

-3 % 7 = ( -1*7 + 4 ) % 7 = 4 
-5 % 2 = (-3*2 + 1) % 2 = 1

Example #1 : 
In this example we can see that by using this mathematics, we are able to perform and understand the negative modulo.
 




# Using negative modulo
res1 = -5 % 4
res2 = ((-2*4) + 3) % 4
  
print(res1)
print(res2)

Output :

3
3

Example #2 :
 




# Using negative modulo
res1 = -3 % 7
res2 = - 12 % 4
  
print(res1)
print(res2)

Output :

4
0

 Attention geek! Strengthen your foundations with the Python Programming Foundation Course and learn the basics.  

To begin with, your interview preparations Enhance your Data Structures concepts with the Python DS Course. And to begin with your Machine Learning Journey, join the Machine Learning – Basic Level Course




My Personal Notes arrow_drop_up
Recommended Articles
Page :