# Python math.ulp() – Least Significant Bit

Contents

## Python math.ulp()

math.ulp(x) function returns the least significant bit of the float value x.

## Syntax

The syntax to call ulp() function is

``math.ulp(x)``

where

math.ulp() function is new in Python version 3.9.

## Examples

### 1. Least significant bit of a float value

In the following program, we find the least significant bit of float x=3.1415.

Python Program

``````import math

x = 3.1415
result = math.ulp(x)
print('ulp(x) :', result)``````
Run Code Copy

Output

``ulp(x) : 4.440892098500626e-16``

### 2. Least significant bit of a negative float value

In the following program, we find the least significant bit of negative float x=-3.1415. If x is negative value, then math.ulp() returns ulp(-x).

Python Program

``````import math

x = -3.1415
result = math.ulp(x)
print('ulp(x) :', result)``````
Run Code Copy

Output

``ulp(x) : 4.440892098500626e-16``

### 3. Least significant bit of infinity

In the following program, we find the least significant bit of x=infinity. math.ulp() returns infinity.

Python Program

``````import math

x = math.inf
result = math.ulp(x)
print('ulp(x) :', result)``````
Run Code Copy

Output

``ulp(x) : inf``

### 4. Least significant bit of nan

In the following program, we find the least significant bit of x=NaN. math.ulp() returns nan.

Python Program

``````import math

x = math.nan
result = math.ulp(x)
print('ulp(x) :', result)``````
Run Code Copy

Output

``ulp(x) : nan``

### 5. Least significant bit of 0

In the following program, we find the least significant bit of float x=0. math.ulp() returns smallest positive denormalised representable float.

Python Program

``````import math

x = 0
result = math.ulp(x)
print('ulp(x) :', result)``````
Run Code Copy

Output

``ulp(x) : 5e-324``

## Summary

In this Python Math tutorial, we learned the syntax of, and examples for math.trunc() function.

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