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Compute modulus division by a power-of-2-number

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  • Difficulty Level : Medium
  • Last Updated : 13 Jul, 2022
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Compute n modulo d without division(/) and modulo(%) operators, where d is a power of 2 number. 

Input: 6 4
Output: 2 
Explanation: As 6%4 = 2

Input: 12 8
Output: 4
Explanation: As 12%8 = 4

Input: 10 2
Output: 0
Explanation:As 10%2 = 0

Let ith bit from right is set in d. For getting n modulus d, we just need to return 0 to i-1 (from right) bits of n as they are and other bits as 0.
For example if n = 6 (00..110) and d = 4(00..100). Last set bit in d is at position 3 (from right side). So we need to return last two bits of n as they are and other bits as 0, i.e., 00..010. 
Now doing it is so easy, guess it….
Yes, you have guessing it right. See the below program. 
 

C++




#include<iostream>
using namespace std;
// This function will return n % d.
// d must be one of: 1, 2, 4, 8, 16, 32, … 
unsigned int getModulo(unsigned int n, 
                       unsigned int d)
{
  return ( n & (d - 1) );
}         
  
// Driver Code
int main()
{
  unsigned int n = 6;
  
  // d must be a power of 2
  unsigned int d = 4; 
  cout<< n <<" modulo "<<d <<" is "<< getModulo(n, d);
  
  getchar();
  return 0;
}     
  
// this code is contributed by shivanisinghss2110


C




#include<stdio.h>
  
// This function will return n % d.
// d must be one of: 1, 2, 4, 8, 16, 32, … 
unsigned int getModulo(unsigned int n, 
                       unsigned int d)
{
return ( n & (d - 1) );
}         
  
// Driver Code
int main()
{
unsigned int n = 6;
  
// d must be a power of 2
unsigned int d = 4; 
printf("%u modulo %u is %u", n, d, getModulo(n, d));
  
getchar();
return 0;
}     


Java




// Java code for Compute modulus division by 
// a power-of-2-number
class GFG {
      
    // This function will return n % d.
    // d must be one of: 1, 2, 4, 8, 16, 32,
    static int getModulo(int n, int d)
    {
        return ( n & (d-1) );
    }     
      
    // Driver Code
    public static void main(String[] args)
    {
        int n = 6;
          
        /*d must be a power of 2*/
        int d = 4
          
        System.out.println(n+" modulo " + d + 
                    " is " + getModulo(n, d));
    }
  
// This code is contributed 
// by Smitha Dinesh Semwal.


Python3




# Python code to demonstrate
# modulus division by power of 2
  
  
# This function will
# return n % d.
# d must be one of:
# 1, 2, 4, 8, 16, 32, … 
def getModulo(n, d):
  
    return ( n & (d-1) )
           
# Driver program to
# test above function 
n = 6
  
#d must be a power of 2
d = 4 
print(n,"modulo",d,"is",
      getModulo(n, d))
  
# This code is contributed by 
# Smitha Dinesh Semwal


C#




// C# code for Compute modulus
// division by a power-of-2-number
using System;
  
class GFG {
      
// This function will return n % d.
// d must be one of: 1, 2, 4, 8, 16, 32, … 
static uint getModulo( uint n, uint d)
{
return ( n & (d-1) );
}     
  
// Driver code
static public void Main () 
   {
    uint n = 6;
    uint d = 4; /*d must be a power of 2*/
  
    Console.WriteLine( n + " modulo " + d + 
                " is " + getModulo(n, d));
      
    }
}
// This code is contributed by vt_m.


PHP




<?php
// This function will return n % d.
// d must be one of: 1, 2, 4, 8, 16, 32, … 
function getModulo($n, $d)
{
return ( $n & ($d - 1) );
}     
  
// Driver Code
$n = 6;
  
// d must be a power of 2
$d = 4; 
echo $n ," modulo"," ", $d, " is "
         " ",getModulo($n, $d);
      
// This code is contributed by vt_m.
?>


Javascript




<script>
// This function will return n % d.
// d must be one of: 1, 2, 4, 8, 16, 32, … 
function getModulo(n,d) 
{
    return ( n & (d - 1) );
}         
    
// Driver Code
 n = 6;
 d = 4; 
   
document.write(n  +" modulo "+ d + " is "+ getModulo(n, d));
  
  // This code is contributed by simranarora5sos
</script>


Output

6 modulo 4 is 2

Time Complexity: O(1)

As we are doing single operation which takes constant time.

Auxiliary Space: O(1)

As constant extra space is used.

 

References: 
http://graphics.stanford.edu/~seander/bithacks.html#ModulusDivisionEasy
Please write comments if you find any bug in the above program/algorithm or other ways to solve the same problem. 
 

 


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