Epsilon in Python

1. What is Epsilon in Python
2. Calculate Epsilon in Python
3. Use the sys Module to Find Epsilon in Python
4. Use the Numpy Module to Find Epsilon in Python
5. Conclusion

While solving integral calculus and mathematical domains, we often use epsilon as the smallest possible value. In this article, we will discuss how we can calculate the value of epsilon in Python.

What is Epsilon in Python

Epsilon doesn’t have any special meaning in Python. It is not a keyword, and you can use the term epsilon to define variable names.

In Python, the semantic meaning of epsilon has been derived from its mathematical meaning. Thus, we can define epsilon as the smallest possible positive floating-point number.

In other words, epsilon is a number such that 1+epsilon is the next floating-point number after 1 in Python. You can also define epsilon as the maximum possible error while representing a floating-point number in Python.

Having learned the meaning of epsilon, let us now calculate the value of epsilon in Python using different approaches.

Calculate Epsilon in Python

As epsilon is the smallest possible floating-point value such that 1+epsilon is greater than 1, we will try to find the smallest value for epsilon such that 1+epsilon>1. For this, we will initialize a variable epsilon with the value 1.0.

After that, we will keep dividing epsilon by 2 until 1+epsilon is greater than 1 in a while loop. Once we find that the sum of 1 and the current value of epsilon is not greater than 1, we will exit the while loop.

After that, we will multiply the current value of epsilon by 2 so that the sum of epsilon and 1 becomes greater than 1. In this way, we can find the value of epsilon in Python, as shown below.

epsilon = 1.0
while epsilon + 1 > 1:
    epsilon = epsilon / 2
epsilon = epsilon * 2
print("The value of epsilon is:", epsilon)

Output:

The value of epsilon is: 2.220446049250313e-16

Instead of manually calculating the value of epsilon in Python, we can use built-in methods as discussed in the following sections.

Use the sys Module to Find Epsilon in Python

Python provides us with the sys module to perform various operations on the system using Python programs.

Using the sys module, we can also find the value of epsilon in Python. For this, we will use the float_info attribute of the sys module.

The float_info object in the sys module contains definitions of various floating-point constants and limits. You can observe this in the following example.

import sys

print(sys.float_info)

Output:

sys.float_info(max=1.7976931348623157e+308, max_exp=1024, max_10_exp=308, min=2.2250738585072014e-308, min_exp=-1021, min_10_exp=-307, dig=15, mant_dig=53, epsilon=2.220446049250313e-16, radix=2, rounds=1)

In the output above, you can observe that the constant epsilon is also present in the float_info object. Hence, we can obtain the value of epsilon using the sys.float_info object in Python as follows.

import sys

epsilon = sys.float_info.epsilon
print("The value of epsilon is:", epsilon)

Output:

The value of epsilon is: 2.220446049250313e-16

Use the Numpy Module to Find Epsilon in Python

Instead of using the sys module, we can also use the numpy module to find the value of epsilon in Python. For this, we will use the finfo() method.

The finfo() method is also used to obtain the floating-point constants and limits. It takes the literal float as an input argument and returns an object of type numpy.finfo.

We can use the eps attribute of the object to find the value of epsilon in Python as follows.

import numpy

epsilon = numpy.finfo("float").eps
print("The value of epsilon is:", epsilon)

Output:

The value of epsilon is: 2.220446049250313e-16

Conclusion

This article has discussed various approaches to finding epsilon’s value in Python. For this, we have first calculated the value of epsilon by writing a program from scratch.

Later, we also used the sys module and the numpy module to find the value of epsilon in Python.

We hope you enjoyed reading this article. Stay tuned for more informative articles.