# Floating point numbers

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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SteamKing
Staff Emeritus
Homework Helper
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.

Mark44
Mentor
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.

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.

Mark44
Mentor
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

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.

Mark44
Mentor
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.

pbuk
Gold Member
... I'm supposed to find a min floating point...
Why are we dealing with homework in this forum?

• jim mcnamara
Mark44
Mentor
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.