C++ program to find Machine Epsilon

Machine Epsilon is the smallest number of EPS (epsilon) such that 1 + EPS not equal to 1. Machine Epsilon is a machine-dependent floating point value that provides an upper bound on relative error due to rounding in floating point arithmetic. Mathematically, for each floating point type, it is equivalent to the difference between 1.0 and the smallest representable value that is greater than 1.0.

In C, machine epsilon is specified in the standard header with the names FLT_EPSILON, DBL_EPSILON, and LDBL_EPSILON. Those three macros give the machine epsilon for the float, double, and long double types, respectively.

In C++, similar macros are available in the standard header. The preferred way in C++ is to use std::numeric_limits::epsilon( ) – specified in the standard header .

In Java, it is referred to as ULP (unit in last place). You can find it by using the java.lang.Math package and the Math.ulp() method.

In Python3, the information is available in sys.float_info, which corresponds to float.h in C99.
This is c++ equivalent of std::numeric_limits::epsilon( ).
>>> import sys
>>> sys.float_info.epsilon

CPP

// C++ program to find machine epsilon
#include<iostream>
#include <cfloat>
using namespace std;

// Function for Machine Epsilon with an
// initial value provided as EPS.
void machineEpsilon(float EPS)
{
    // taking a floating type variable
    float prev_epsilon;

    // run until condition satisfy
    while ((1+EPS) != 1)
    {
        // copying value of epsilon into previous epsilon
        prev_epsilon = EPS;

        // dividing epsilon by 2
        EPS /=2;
    }

    // print output of the program
    cout << "Machine Epsilon is : " << prev_epsilon << endl;
}

// Driver Code
int main()
{
    // calling function which calculate machine epsilon
    // with initial value provided as 0.5
    machineEpsilon(0.5);

    return 0;
}

Java

// Java program to find machine epsilon

import java.util.*;

class Count{

    // Function for Machine Epsilon with an
    // initial value provided as EPS.

    public static void machineEpsilon(double EPS)
    {
        // taking a floating type variable
        double prev_epsilon = 0.0;

        // run until condition satisfy
        while ((1+EPS) != 1)
        {
            // copying value of epsilon
            // into previous epsilon
            prev_epsilon = EPS;

            // dividing epsilon by 2
            EPS /=2;
        }

        // print output of the program
        System.out.print( "Machine Epsilon is : "
                         + prev_epsilon);
    }

    public static void main(String[] args)
    {
        // calling function which
        // calculate machine epsilon
        // with initial value provided as 0.5
        machineEpsilon(0.5);

    }
}

// This code is contributed by rishabh_jain

Python3

# Python program to find machine epsilon

# Function for Machine Epsilon with an
# initial value provided as EPS.
def machineEpsilon(EPS):

    # taking a floating type variable
    # run until condition satisfy
    while ((1+EPS) != 1):

        # copying value of epsilon
        # into previous epsilon
        prev_epsilon = EPS

        # dividing epsilon by 2
        EPS = EPS / 2

    # print output of the program
    print( "Machine Epsilon is : " ,
            prev_epsilon )

# Driven code
# calling function which
# calculate machine epsilon
# with initial value provided as 0.5
machineEpsilon(0.5);

# This code is contributed by
# "rishabh_jain".

Output:

Machine Epsilon is : 1.19209e-07

Note that the above result varies from machine to machine.