Find value of y mod (2 raised to power x)

Given two positive integer x and y. we have to find the value of y mod 2x. That is remainder when y is divided by 2x.
Examples:

Input : x = 3, y = 14
Output : 6
Explanation : 14 % 23 =  14 % 8 = 6.

Input : x = 4, y = 14
Output : 14
Explanation : 14 % 24 =  14 % 16 = 14.

To solve this question we can use pow() and modulo operator and can easily find the remainder.
But there are some points we should care about:



  • For higher value of x such that 2x is greater than long long int range, we can not obtain proper result.
  • Whenever y < 2x the remainder will always be y. So, in that case we can restrict ourselves to calculate value of 2x as: 
    y < 2x
log y < x
// means if log y is less than x, then 
// we can print y as remainder.
  • The maximum value of 2x for which we can store 2x in a variable is 263. This means for x > 63, y is always going to be smaller than 2x and in that case remainder of y mod 2x is y itself.

keeping in mind the above points we can approach this problem as :

if (log y < x)
    return y;
else if (x  < 63)
    return y;
else 
    return (y % (pow(2, x)))

Note: As python is limit free we can directly use mod and pow() function

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ Program to find the 
// value of y mod 2^x
#include <bits/stdc++.h>
using namespace std;
  
// function to calculate y mod 2^x
long long int yMod(long long int y,
                    long long int x)
{
    // case 1 when y < 2^x
    if (log2(y) < x)
        return y;
  
    // case 2 when 2^x is out of 
    // range means again y < 2^x
    if (x > 63)
        return y;
  
    // if y > 2^x
    return (y % (1 << x));
}
  
// driver program
int main()
{
    long long int y = 12345;
    long long int x = 11;    
    cout << yMod(y, x);    
    return 0;
}

chevron_right






                        filter_none









Python














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















# Program to find the value  


# of y mod 2 ^ x function to  


# return y mod 2 ^ x 


def yMod(y, x) :      


    return (y % pow(2, x))    


       


# Driver code 


y = 12345


x = 11


print(yMod(y, x)) 



















                        chevron_right







                        filter_none









Java














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















// Java Program to find  


// the value of y mod 2^x 


import java.io.*; 


  


class GFG 


{ 


    // function to calculate 


    // y mod 2^x 


    static long yMod(long y,     


                     long x) 


    { 


        // case 1 when y < 2^x 


        if ((Math.log(y) /  


             Math.log(2)) < x) 


            return y; 


      


        // case 2 when 2^x is  


        // out of range means  


        // again y < 2^x 


        if (x > 63) 


            return y; 


      


        // if y > 2^x 


        return (y % (1 << (int)x)); 


    } 


      


    // Driver Code 


    public static void main(String args[]) 


    { 


        long y = 12345; 


        long x = 11;  


        System.out.print(yMod(y, x));  


    } 


} 


  


// This code is contributed by  


// Manish Shaw(manishshaw1) 



















                        chevron_right







                        filter_none









C#














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















// C# Program to find the  


// value of y mod 2^x 


using System; 


  


class GFG 


{ 


    // function to calculate 


    // y mod 2^x 


    static long yMod(long y,  


                     long x) 


    { 


        // case 1 when y < 2^x 


        if (Math.Log(y, 2) < x) 


            return y; 


      


        // case 2 when 2^x is  


        // out of range means  


        // again y < 2^x 


        if (x > 63) 


            return y; 


      


        // if y > 2^x 


        return (y % (1 << (int)x)); 


    } 


      


    // Driver Code 


    static void Main() 


    { 


        long y = 12345; 


        long x = 11;  


        Console.Write(yMod(y, x));  


    } 


} 


  


// This code is contributed by  


// Manish Shaw(manishshaw1) 



















                        chevron_right







                        filter_none









PHP














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















<?php 


// PHP Program to find the  


// value of y mod 2^x 


  


// function to  


// calculate y mod 2^x 


function yMod($y, $x) 


{ 


    // case 1 when y < 2^x 


    if ((log($y) / log(2)) < $x) 


        return $y; 


  


    // case 2 when 2^x is 


    // out of range means  


    // again y < 2^x 


    if ($x > 63) 


        return $y; 


  


    // if y > 2^x 


    return ($y % (1 << $x)); 


} 


  


// Driver Code 


$y = 12345; 


$x = 11;  


echo (yMod($y, $x));  


  


// This code is contributed by  


// Manish Shaw(manishshaw1) 


?> 



















                        chevron_right







                        filter_none










Output:


57



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



          
          
          
          

            

    

        My Personal Notes
        arrow_drop_up
    

    

        
        

            
            
        

    


Recommended Posts:
Shivam.Pradhan
Discovering ways to develop a plane for soaring career goals
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on  the "Improve Article" button below.


Improved By :  manishshaw1