Python math.ulp() Method

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The Python math.ulp() method is used to calculate the "unit in the last place" (ULP) of a floating-point number. The ULP represents the difference between the given floating-point number and the next larger floating-point number of the same precision.

For example, if "x" is represented in binary floating-point format, the ulp(x) method returns the smallest positive floating-point number that, when added to "x", produces a different floating-point number.

This smallest positive difference is often referred to as the "unit in the last place", indicating the minimum increment by which a floating-point number can change in its least significant digit.

Syntax

Following is the basic syntax of the Python math.ulp() method −

math.ulp(x)

Parameters

This method accepts a numeric value representing the floating-point number as a parameter for which you want to calculate the ulp.

Return Value

The method returns a float, which represents the distance between x and the next larger representable floating-point number.

Example 1

In the following example, we are calculating the least significant bit of the floating-point number "1.0" using the math.ulp() method −

import math
result = math.ulp(1.0)
print("The result obtained is:",result)         

Output

The output obtained is as follows −

The result obtained is: 2.220446049250313e-16

Example 2

Here, we are calculating the least significant bit of the negative floating-point number "-2.5" −

import math
result = math.ulp(-2.5)
print("The result obtained is:",result)     

Output

Following is the output of the above code −

The result obtained is: 4.440892098500626e-16

Example 3

Now, we calculate the least significant bit of the floating-point number "0.0" using the math.ulp() method −

import math
result = math.ulp(0.0)
print("The result obtained is:",result)  

Output

We get the output as shown below −

The result obtained is: 5e-324

Example 4

In this example, we use a variable "x" to store the floating-point number "3.14159". We then calculate the least significant bit of "x" −

import math
x = 3.14159
result = math.ulp(x)
print("The result obtained is:",result) 

Output

The result produced is as shown below −

The result obtained is: 4.440892098500626e-16