Python Finding Epsilon & Smallest Floating Point - Python

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SUMMARY

The discussion focuses on determining the machine epsilon and the smallest floating point number in Python, specifically in version 3.4.2. The machine epsilon is confirmed to be 2.220446049250313e-16, accessible via the sys.float_info.epsilon attribute. The smallest positive normalized float is identified as 2.2250738585072014e-308, found using sys.float_info.min. It is clarified that machine epsilon and the smallest floating point number serve different purposes in floating point arithmetic.

PREREQUISITES
  • Understanding of floating point representation in computing
  • Familiarity with Python programming language
  • Knowledge of the IEEE 754 standard for floating point arithmetic
  • Basic understanding of the sys module in Python
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  • Explore the sys.float_info documentation in Python
  • Learn about the IEEE 754 standard and its implications on floating point calculations
  • Investigate how to implement routines to test machine epsilon in Python
  • Research the differences between machine epsilon and the smallest positive normalized float
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Programmers, data scientists, and software engineers who require precise floating point calculations in Python, as well as students studying numerical methods and computer science concepts.

BubblesAreUs
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I'm finding it difficult to find the exact value of epsilon on python? Moreover, I am also supposed to find the smallest floating point number as well.

Wikipedia tells me that the machine epsilon is 2−52 ≈ 2.22e-16 for 64-bit
IEEE 754 - 2008? Is this the exact value on Python?

Outside of that, I'm not sure where to start.
 
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BubblesAreUs said:
I'm finding it difficult to find the exact value of epsilon on python? Moreover, I am also supposed to find the smallest floating point number as well.

Wikipedia tells me that the machine epsilon is 2−52 ≈ 2.22e-16 for 64-bit
IEEE 754 - 2008? Is this the exact value on Python?

Outside of that, I'm not sure where to start.
Programmers have written routines to test for the machine epsilon using various programming languages. You could probably do a Google search and find either a routine or a description of one to use in Python.
 
BubblesAreUs said:
I'm finding it difficult to find the exact value of epsilon on python? Moreover, I am also supposed to find the smallest floating point number as well.

Wikipedia tells me that the machine epsilon is 2−52 ≈ 2.22e-16 for 64-bit
IEEE 754 - 2008? Is this the exact value on Python?

Outside of that, I'm not sure where to start.
In Python v3.4.2, epsilon is 2.220446049250313e-16. The float_info member of the sys module contains this information.
 
Mark44 said:
In Python v3.4.2, epsilon is 2.220446049250313e-16. The float_info member of the sys module contains this information.
I just tried out sys. and got the following:

>>> sys.float_info.epsilon
2.220446049250313e-16
>>> sys.float_info.min
2.2250738585072014e-308

I am looking for the smallest floating point number. Oddly, I was expecting the smallest floating point number to be greater than machin epsilon.

PS: Will try that out as well SteamKing.
 
BubblesAreUs said:
I am looking for the smallest floating point number. Oddly, I was expecting the smallest floating point number to be greater than machin epsilon.
Machine epsilon and the smallest floating point number are different things.
From the Python docs:
epsilon - difference between 1 and the least value greater than 1 that is representable as a float
min - minimum positive normalized float
 
Mark44 said:
Machine epsilon and the smallest floating point number are different things.
From the Python docs:
epsilon - difference between 1 and the least value greater than 1 that is representable as a float
min - minimum positive normalized float
Oh that makes sense. Now what I even more puzzling is that I'm supposed to find a min floating point such that, it plus 1 should not return 1. Interestingly, the output I am getting when adding min float and 1 is 1.
 
BubblesAreUs said:
Oh that makes sense. Now what I even more puzzling is that I'm supposed to find a min floating point such that, it plus 1 should not return 1. Interestingly, the output I am getting when adding min float and 1 is 1.
That's really not that surprising. The smallest positive number that you can add to 1, and still get 1, is machine epsilon, which is many orders of magnitude larger than min.
 
BubblesAreUs said:
... I'm supposed to find a min floating point...
Why are we dealing with homework in this forum?
 
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MrAnchovy said:
Why are we dealing with homework in this forum?
Good point.
@BubblesAreUs, this should have been posted in the Homework & Coursework section, under Engineering & Computer Science. For future posts of this nature, please put them in that forum section.
 

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