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Problem in comparing Floating point numbers and how to compare them correctly?
  • Difficulty Level : Hard
  • Last Updated : 11 Jun, 2021

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

 

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);
}
Output: 
a is : 0.99999999999999988898
b is : 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 ponumbers correctly
 
def compareFloatNum(a, b):
     
    # Correct method to compare
    # floating-ponumbers
    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
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.
 

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