Compute the integer absolute value (abs) without branching

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.  

 mask + n 

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

 (mask + n)^mask 

Implementation: 

#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 

#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 implementation of above approach import java.io.*; 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 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# implementation of above approach using System; class GFG {  static int CHAR_BIT = 8;  static int SIZE_INT = 4;  /* 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 

// 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;  console.log("Absolute value of " + n + " is " + getAbs(n)); // This code is contributed by shikhasingrajput 

<?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 ?> 

Absolute value of -6 is 6 

Time Complexity: O(1)
Auxiliary Space: O(1)

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: 

#include <bits/stdc++.h> using namespace std; /* 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;  cout << "Absolute value of " << n << " is " << getAbs(n);  return 0; } // This code is contributed by phalasi. 

#include <stdio.h> #include <limits.h> //to include CHAR_BIT /* 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 %d\n", n, getAbs(n));  return 0; } 

// Java implementation of above approach import java.io.*; 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 code_hunt. 

import os import sys # This function will return absolute value of n def getAbs(n): mask = n >> (sys.getsizeof(int()) * os.sysconf('SC_CHAR_BIT') - 1) return ((n ^ mask) - mask) # Driver code n = -6 print("The absolute value of", n, "is", getAbs(n)) # This code is contributed by phalasi. 

// C# implementation of above approach using System; public class GFG {  static int CHAR_BIT = 8;  static int SIZE_INT = 4;    /* 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);  } } // This code is contributed by Rajput-Ji 

// JavaScript code to implement the approach /* This function will return absolute value of n*/ function getAbs(n) {  // note: the size of int is 256 bytes  // and the size of char is 8 bytes  const mask = n >> (256 * 8 - 1);  return ((n ^ mask) - mask); } /* Driver program to test above function */ var n = -6; console.log("Absolute value of %d is %d", n, getAbs(n)); // this code is contributed by phasing17. 

Absolute value of -6 is 6 

Time Complexity: O(1)
Auxiliary Space: O(1)

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