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:
C++
#include <bits/stdc++.h>
using namespace std;
#define CHARBIT 8
unsigned int getAbs(int n)
{
int const mask = n >> (sizeof(int) * CHARBIT - 1);
return ((n + mask) ^ mask);
}
int main()
{
int n = -6;
cout << "Absolute value of " << n << " is " << getAbs(n);
return 0;
}
|
C
#include <stdio.h>
#define CHAR_BIT 8
unsigned int getAbs(int n)
{
int const mask = n >> (sizeof(int) * CHAR_BIT - 1);
return ((n + mask) ^ mask);
}
int main()
{
int n = -6;
printf("Absolute value of %d is %u", n, getAbs(n));
getchar();
return 0;
}
|
Java
import java.io.*;
class GFG {
static final int CHAR_BIT = 8;
static final int SIZE_INT = 8;
static int getAbs(int n)
{
int mask = n >> (SIZE_INT * CHAR_BIT - 1);
return ((n + mask) ^ mask);
}
public static void main(String[] args)
{
int n = -6;
System.out.print("Absolute value of " + n + " is " + getAbs(n));
}
}
|
Python3
CHARBIT = 8;
SIZE_INT = 8;
def getAbs(n):
mask = n >> (SIZE_INT * CHARBIT - 1);
return ((n + mask) ^ mask);
n = -6;
print("Absolute value of",n,"is",getAbs(n));
|
C#
using System;
class GFG {
static int CHAR_BIT = 8;
static int SIZE_INT = 8;
static int getAbs(int n)
{
int mask = n >> (SIZE_INT * CHAR_BIT - 1);
return ((n + mask) ^ mask);
}
static void Main()
{
int n = -6;
Console.Write("Absolute value of " + n + " is " + getAbs(n));
}
}
|
PHP
<?php
$CHARBIT = 8;
$SIZE_INT = 8;
function getAbs($n)
{
global $SIZE_INT, $CHARBIT;
$mask = $n >> ($SIZE_INT * $CHARBIT - 1);
return (($n + $mask) ^ $mask);
}
$n = -6;
echo "Absolute value of " . $n .
" is " . getAbs($n);
?>
|
Javascript
<script>
var CHAR_BIT = 8;
var SIZE_INT = 8;
function getAbs(n)
{
var mask = n >> (SIZE_INT * CHAR_BIT - 1);
return ((n + mask) ^ mask);
}
var n = -6;
document.write("Absolute value of " + n + " is " + getAbs(n));
</script>
|
Output
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:
C++
#include <bits/stdc++.h>
using namespace std;
unsigned int getAbs(int n)
{
int const mask = n >> (sizeof(int) * CHAR_BIT - 1);
return ((n ^ mask) - mask);
}
int main()
{
int n = -6;
cout << "Absolute value of " << n << " is " << getAbs(n);
return 0;
}
|
C
#include <stdio.h>
#include <limits.h> //to include CHAR_BIT
unsigned int getAbs(int n)
{
int const mask = n >> (sizeof(int) * CHAR_BIT - 1);
return ((n ^ mask) - mask);
}
int main()
{
int n = -6;
printf("Absolute value of %d is %d\n", n, getAbs(n));
return 0;
}
|
Java
import java.io.*;
class GFG {
static final int CHAR_BIT = 8;
static final int SIZE_INT = 8;
static int getAbs(int n)
{
int mask = n >> (SIZE_INT * CHAR_BIT - 1);
return ((n ^ mask) - mask);
}
public static void main(String[] args)
{
int n = -6;
System.out.print("Absolute value of " + n + " is " + getAbs(n));
}
}
|
Python3
import os
import sys
def getAbs(n):
mask = n >> (sys.getsizeof(int()) * os.sysconf('SC_CHAR_BIT') - 1)
return ((n ^ mask) - mask)
n = -6
print("The absolute value of", n, "is", getAbs(n))
|
C#
using System;
public class GFG {
static int CHAR_BIT = 8;
static int SIZE_INT = 8;
static int getAbs(int n)
{
int mask = n >> (SIZE_INT * CHAR_BIT - 1);
return ((n + mask) ^ mask);
}
}
|
Javascript
function getAbs(n)
{
const mask = n >> (256 * 8 - 1);
return ((n ^ mask) - mask);
}
var n = -6;
console.log("Absolute value of %d is %d", n, getAbs(n));
|
Output
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