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.

This article is contributed by **Sahil Rajput**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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