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pythoncomparisonfloating-pointepsilon
thornate
thornate

Reputation: 5130

Value for epsilon in Python

Is there a standard value for (or method for obtaining) epsilon in Python? I need to compare floating point values and want to compare against the smallest possible difference.

In C++ there's a function provided numeric_limits::epsilon( ) which gives the epsilon value for any given data type. Is there an equivalent in Python?

Upvotes: 99

Views: 147753

Answers (5)

Rúben Dias
Rúben Dias

Reputation: 472

The following worked for me as well:

>>> import math
>>> math.ulp(1.0)
2.220446049250313e-16

Upvotes: 9

s.ouchene
s.ouchene

Reputation: 1869

If you cannot find a function to do that, remember that the algorithm to calculate the machine epsilon is very easy (you can test with your favourite programming language).E.g, for python:

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

In my case, I got:

The machine epsilon is: 2.220446049250313e-16

Upvotes: 23

Jonathan H
Jonathan H

Reputation: 7933

Surprised nobody mentioned this here; I think many people would use numpy.finfo( type(variable) ).eps instead. Or .resolution if it is to assess precision.

Note that finfo is only for floating point types, and that it also works with Python's own float type (i.e. not restricted to numpy's types). The equivalent for integer types is iinfo, though it does not contain precision information (because, well, why would it?).

Upvotes: 12

Ergwun
Ergwun

Reputation: 12968

As strcat posted, there is sys.float_info.epsilon.

But don't forget the pitfalls of using it as an absolute error margin for floating point comparisons. E.g. for large numbers, rounding error could exceed epsilon.

If you think you need a refresher, the standard reference is David Goldberg's What Every Computer Scientist Should Know About Floating-Point Arithmetic, or for a simpler review you can check out The Floating Point Guide.

Upvotes: 40

strcat
strcat

Reputation: 5612

The information is available in sys.float_info, which corresponds to float.h in C99.

>>> import sys
>>> sys.float_info.epsilon
2.220446049250313e-16

Upvotes: 166

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