Open In App

Problem in comparing Floating point numbers and how to compare them correctly?

Improve
Improve
Improve
Like Article
Like
Save Article
Save
Share
Report issue
Report

In this article, we will see what is the problem in comparing floating-point numbers and we will discuss the correct way to compare two floating-point numbers. 
What is the problem in comparing Floating-Point Numbers usually?
Let us first compare two floating-point numbers with the help of relational operator (==).
Example: Using “==” for comparison
 

CPP




// C++ program to compare
// floating point numbers
 
#include <bits/stdc++.h>
using namespace std;
 
void compareFloatNum(double a, double b)
{
    if (a == b) {
        cout << "The numbers are equal"
             << endl;
    }
    else {
        cout << "The numbers are not equal"
             << endl;
    }
}
 
// Driver code
int main()
{
    double a = (0.3 * 3) + 0.1;
    double b = 1;
    compareFloatNum(a, b);
}


Java




// Java program to compare
// floating point numbers
class GFG
{
 
    static void compareFloatNum(double a, double b)
    {
        if (a == b)
        {
            System.out.print("The numbers are equal" + "\n");
        }
        else
        {
            System.out.print("The numbers are not equal" + "\n");
        }
    }
 
    // Driver code
    public static void main(String[] args)
    {
        double a = (0.3 * 3) + 0.1;
        double b = 1;
        compareFloatNum(a, b);
    }
}
 
// This code is contributed by 29AjayKumar


Python




# Python program to compare
# floating point numbers
def compareFloatNum(a, b):
    if (a == b):
        print("The numbers are equal")
 
    else:
        print("The numbers are not equal")
 
# Driver code
 
a = (0.3 * 3) + 0.1
b = 1
compareFloatNum(a, b)
 
# This code is contributed by mohit kumar 29


C#




// C# program to compare
// floating point numbers
using System;
 
class GFG
{
 
    static void comparefloatNum(double a, double b)
    {
        if (a == b)
        {
            Console.Write("The numbers are equal" + "\n");
        }
        else
        {
            Console.Write("The numbers are not equal" + "\n");
        }
    }
 
    // Driver code
    public static void Main(String[] args)
    {
        double a = (0.3 * 3) + 0.1;
        double b = 1;
        comparefloatNum(a, b);
    }
}
 
// This code is contributed by PrinciRaj1992


Javascript




<script>
 
function compareFloatNum(a,b)
{
    if (a == b)
        {
            document.write("The numbers are equal" + "<br>");
        }
        else
        {
            document.write("The numbers are not equal" + "<br>");
        }
}
 
let a = (0.3 * 3) + 0.1;
 let b = 1;
 compareFloatNum(a, b);
 
 
// This code is contributed by patel2127
 
</script>


Output: 

The numbers are not equal

 

Time complexity of this program is O(1), as it only performs a comparison between two floating point numbers.

The space complexity is also O(1), as the program uses only a constant amount of memory for storing the two floating point numbers and a few local variables used for the comparison.

Why does this problem occur?
In the case of floating-point numbers, the relational operator (==) does not produce correct output, this is due to the internal precision errors in rounding up floating-point numbers.
In the above example, we can see the inaccuracy in comparing two floating-point numbers using “==” operator. The two numbers ‘a’ and ‘b’ are equal ( as (0.3 * 3) + 0.1 = 1 ) but the program results in an incorrect output.
Let’s take a closer look at the numbers in the next snippet.
 

CPP




// C++ program to compare
// floating point numbers
 
#include <bits/stdc++.h>
using namespace std;
 
void printFloatNum(double a, double b)
{
    // To print decimal numbers up to 20 digits
    cout << setprecision(20);
 
    cout << "a is : " << a << endl;
    cout << "b is : " << b << endl;
}
 
// Driver code
int main()
{
    double a = (0.3 * 3) + 0.1;
    double b = 1;
    printFloatNum(a, b);
}


Python3




# Python 3 program to compare
# floating point numbers
def printFloatNum(a,  b):
 
    # To print decimal numbers up to 20 digits
    print("a is : %.20f" %a)
    print("b is : %.20f" %b)
 
# Driver code
if __name__ == "__main__":
 
    a = (0.3 * 3) + 0.1
    b = 1
    printFloatNum(a, b)
 
    # This code is contributed by ukasp.


Javascript




// JavaScript program to compare floating point numbers
 
function printFloatNum(a, b) {
    // To print decimal numbers up to 20 digits
    console.log(`a is : ${a.toFixed(20)}`);
    console.log(`b is : ${b.toFixed(20)}`);
}
 
// Driver code
    let a = (0.3 * 3) + 0.1;
    let b = 1;
    printFloatNum(a, b);


Java




import java.util.*;
 
public class CompareFloatingPointNumbers {
    public static void printFloatNum(double a, double b) {
        // To print decimal numbers up to 20 digits
        System.out.println(String.format("a is : %.20f", a));
        System.out.println(String.format("b is : %.20f", b));
    }
 
    public static void main(String[] args) {
        double a = (0.3 * 3) + 0.1;
        double b = 1;
        printFloatNum(a, b);
    }
}


Output: 

a is : 0.99999999999999988898
b is : 1

 

Time complexity:
The program has a constant time complexity, as it only performs a fixed set of operations and does not depend on the input size. Therefore, the time complexity is O(1).

Space complexity:
The program uses a fixed amount of memory for the double variables a and b, as well as for the output printed to the console. Therefore, the space complexity is also O(1).

Now we can see the internal rounding error in floating-point numbers. Number ‘a’ is not correctly rounded up to 1, 
there is an internal error in rounding up, a very small error but makes a huge difference when we are comparing the numbers.
How to compare floating-point numbers correctly? 
If we do have to compare two floating-point numbers then rather than using “==” operator we will find the absolute difference between the numbers (which if were correctly represented, the difference would have been 0) and compare it with a very small number 1e-9 (i.e 10^-9, this number is very small) and if the difference is less than this number, we can safely say that the two floating-point numbers are equal.
Example: 
 

C++




// C++ program to compare
// floating point numbers correctly
 
#include <bits/stdc++.h>
using namespace std;
 
void compareFloatNum(double a, double b)
{
 
    // Correct method to compare
    // floating-point numbers
    if (abs(a - b) < 1e-9) {
        cout << "The numbers are equal "
             << endl;
    }
    else {
        cout << "The numbers are not equal "
             << endl;
    }
}
 
// Driver code
int main()
{
    double a = (0.3 * 3) + 0.1;
    double b = 1;
    compareFloatNum(a, b);
}


Java




// Java program to compare
// floating point numbers correctly
class GFG
{
 
static void compareFloatNum(double a, double b)
{
 
    // Correct method to compare
    // floating-point numbers
    if (Math.abs(a - b) < 1e-9)
    {
        System.out.print("The numbers are equal "
            +"\n");
    }
    else
    {
        System.out.print("The numbers are not equal "
            +"\n");
    }
}
 
// Driver code
public static void main(String[] args)
{
    double a = (0.3 * 3) + 0.1;
    double b = 1;
    compareFloatNum(a, b);
}
}
 
// This code is contributed by Rajput-Ji


Python3




# Python program to compare
# floating point numbers correctly
 
def compareFloatNum(a, b):
     
    # Correct method to compare
    # floating-point numbers
    if (abs(a - b) < 1e-9):
        print("The numbers are equal ");
    else:
        print("The numbers are not equal ");
     
# Driver code
if __name__ == '__main__':
    a = (0.3 * 3) + 0.1;
    b = 1;
    compareFloatNum(a, b);
 
# This code is contributed by PrinciRaj1992


C#




     
// C# program to compare
// floating point numbers correctly
using System;
 
class GFG
{
 
static void comparefloatNum(double a, double b)
{
 
    // Correct method to compare
    // floating-point numbers
    if (Math.Abs(a - b) < 1e-9)
    {
        Console.Write("The numbers are equal "
            +"\n");
    }
    else
    {
        Console.Write("The numbers are not equal "
            +"\n");
    }
}
 
// Driver code
public static void Main(String[] args)
{
    double a = (0.3 * 3) + 0.1;
    double b = 1;
    comparefloatNum(a, b);
}
}
 
// This code is contributed by 29AjayKumar


Javascript




<script>
// Javascript program to compare
// floating point numbers correctly
 
function compareFloatNum(a,b)
{
    // Correct method to compare
    // floating-point numbers
    if (Math.abs(a - b) < 1e-9)
    {
        document.write("The numbers are equal "
            +"<br>");
    }
    else
    {
        document.write("The numbers are not equal "
            +"<br>");
    }
}
 
// Driver code
let a = (0.3 * 3) + 0.1;
let b = 1;
compareFloatNum(a, b);
 
// This code is contributed by unknown2108
</script>


Output: 

The numbers are equal

 

This code results in the correct output, so whenever two floating point numbers are two be compared then rather than using “==” operator, we will use the above technique.
 



Last Updated : 03 May, 2023
Like Article
Save Article
Previous
Next
Share your thoughts in the comments
Similar Reads