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

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

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// 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);
}

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Java

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// 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

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Python

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# 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

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C#

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// 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

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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.

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// 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);
}

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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++

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// 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);
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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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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