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Compute the integer absolute value (abs) without branching

  • Difficulty Level : Hard
  • Last Updated : 10 Aug, 2021

We need not to do anything if a number is positive. We want to change only negative numbers. Since negative numbers are stored in 2’s complement form, to get the absolute value of a negative number we have to toggle bits of the number and add 1 to the result.
For example -2 in a 8 bit system is stored as follows 1 1 1 1 1 1 1 0 where leftmost bit is the sign bit. To get the absolute value of a negative number, we have to toggle all bits and add 1 to the toggled number i.e, 0 0 0 0 0 0 0 1 + 1 will give the absolute value of 1 1 1 1 1 1 1 0. Also remember, we need to do these operations only if the number is negative (sign bit is set).
Method 1 
1) Set the mask as right shift of integer by 31 (assuming integers are stored using 32 bits). 
 

 mask = n>>31 

2) For negative numbers, above step sets mask as 1 1 1 1 1 1 1 1 and 0 0 0 0 0 0 0 0 for positive numbers. Add the mask to the given number. 
 

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 mask + n 

3) XOR of mask +n and mask gives the absolute value. 
 



 (mask + n)^mask 

Implementation: 

C++




#include <bits/stdc++.h>
using namespace std;
#define CHARBIT 8
 
/* This function will return absolute value of n*/
unsigned int getAbs(int n)
{
    int const mask = n >> (sizeof(int) * CHARBIT - 1);
    return ((n + mask) ^ mask);
}
 
/* Driver program to test above function */
int main()
{
    int n = -6;
    cout << "Absolute value of " << n << " is " << getAbs(n);
    return 0;
}
 
// This code is contributed by rathbhupendra

C




#include <stdio.h>
#define CHAR_BIT 8
 
/* This function will return absolute value of n*/
unsigned int getAbs(int n)
{
    int const mask = n >> (sizeof(int) * CHAR_BIT - 1);
    return ((n + mask) ^ mask);
}
 
/* Driver program to test above function */
int main()
{
    int n = -6;
    printf("Absolute value of %d is %u", n, getAbs(n));
 
    getchar();
    return 0;
}

Java




// Java implementation of above approach
class GFG {
 
    static final int CHAR_BIT = 8;
    static final int SIZE_INT = 8;
 
    /* This function will return absolute value of n*/
    static int getAbs(int n)
    {
        int mask = n >> (SIZE_INT * CHAR_BIT - 1);
        return ((n + mask) ^ mask);
    }
 
    /* Driver code */
    public static void main(String[] args)
    {
        int n = -6;
        System.out.print("Absolute value of " + n + " is " + getAbs(n));
    }
}
 
// This code is contributed by Rajput-Ji

Python3




# Python3 implementation of above approach
CHARBIT = 8;
SIZE_INT = 8;
 
# This function will return
# absolute value of n
def getAbs(n):
    mask = n >> (SIZE_INT * CHARBIT - 1);
    return ((n + mask) ^ mask);
 
# Driver Code
n = -6;
print("Absolute value of",n,"is",getAbs(n));
 
# This code is contributed by mits

C#




// C# implementation of above approach
using System;
 
class GFG {
 
    static int CHAR_BIT = 8;
    static int SIZE_INT = 8;
 
    /* This function will return absolute value of n*/
    static int getAbs(int n)
    {
        int mask = n >> (SIZE_INT * CHAR_BIT - 1);
        return ((n + mask) ^ mask);
    }
 
    /* Driver code */
    static void Main()
    {
        int n = -6;
        Console.Write("Absolute value of " + n + " is " + getAbs(n));
    }
}
 
// This code is contributed by mits

PHP




<?php
// PHP implementation of above approach
$CHARBIT = 8;
$SIZE_INT = 8;
 
// This function will return
// absolute value of n
function getAbs($n)
{
    global $SIZE_INT, $CHARBIT;
    $mask = $n >> ($SIZE_INT * $CHARBIT - 1);
    return (($n + $mask) ^ $mask);
}
 
// Driver Code
$n = -6;
echo "Absolute value of " . $n .
            " is " . getAbs($n);
 
// This code is contributed by mits
?>

Javascript




<script>
// javascript implementation of above approach   
var CHAR_BIT = 8;
var SIZE_INT = 8;
 
    /* This function will return absolute value of n */
    function getAbs(n)
    {
        var mask = n >> (SIZE_INT * CHAR_BIT - 1);
        return ((n + mask) ^ mask);
    }
 
    /* Driver code */
        var n = -6;
        document.write("Absolute value of " + n + " is " + getAbs(n));
 
// This code is contributed by shikhasingrajput
</script>

Output: 
 

Absolute value of -6 is 6

Method 2: 
1) Set the mask as right shift of integer by 31 (assuming integers are stored using 32 bits). 
 

 mask = n>>31 

2) XOR the mask with number 
 

 mask ^ n 

3) Subtract mask from result of step 2 and return the result. 
 

 (mask^n) - mask 

Implementation: 

c




/* This function will return absolute value of n*/
unsigned int getAbs(int n)
{
    int const mask = n >> (sizeof(int) * CHAR_BIT - 1);
    return ((n ^ mask) - mask);
}

On machines where branching is expensive, the above expression can be faster than the obvious approach, r = (v < 0) ? -(unsigned)v : v, even though the number of operations is the same.
Please see this for more details about the above two methods.
Please write comments if you find any of the above explanations/algorithms incorrect, or a better ways to solve the same problem.
References: 
http://graphics.stanford.edu/~seander/bithacks.html#IntegerAbs
 




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