C++ program to find Machine Epsilon
Last Updated :
23 Jan, 2018
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
#include<iostream>
#include <cfloat>
using namespace std;
void machineEpsilon( float EPS)
{
float prev_epsilon;
while ((1+EPS) != 1)
{
prev_epsilon = EPS;
EPS /=2;
}
cout << "Machine Epsilon is : " << prev_epsilon << endl;
}
int main()
{
machineEpsilon(0.5);
return 0;
}
|
Java
import java.util.*;
class Count{
public static void machineEpsilon( double EPS)
{
double prev_epsilon = 0.0 ;
while (( 1 +EPS) != 1 )
{
prev_epsilon = EPS;
EPS /= 2 ;
}
System.out.print( "Machine Epsilon is : "
+ prev_epsilon);
}
public static void main(String[] args)
{
machineEpsilon( 0.5 );
}
}
|
Python3
def machineEpsilon(EPS):
while (( 1 + EPS) ! = 1 ):
prev_epsilon = EPS
EPS = EPS / 2
print ( "Machine Epsilon is : " ,
prev_epsilon )
machineEpsilon( 0.5 );
|
Output:
Machine Epsilon is : 1.19209e-07
Note that the above result varies from machine to machine.
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