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++

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// 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;
}

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Python














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# 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)) 



















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Java














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// 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) 



















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C#














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// 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) 



















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PHP














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<?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) 


?> 



















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Output:


57



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



          
          
          
          

            

    

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