Python Numpy MAChine Epsilon

python numpy machine epsilon

An easier way to get the machine epsilon for a given float type is to use np.finfo():

print(np.finfo(float).eps)
# 2.22044604925e-16

print(np.finfo(np.float32).eps)
# 1.19209e-07

Machine Epsilon in Python

Floating point numbers have a certain precision, to a few decimal places in scientific notation. The larger the number, the larger the least significant digit in that representation, and thus the larger the "epsilon" that could contribute to that number.

Thus, the epsilon is relative to the number it is added to, which is in fact stated in the documentation you cited: "... such that 1.0 + eps != 1.0". If the "reference" number is smaller by, e.g. one order of magnitude, then eps is smaller, too.

If that was not the case, you could not calculate at all with numbers smaller than eps (2.2e-16 in my case).

Value for epsilon in Python

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

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

Machine epsilon with Numba

You can use np.finfo(np.float64).eps in Numba njit functions. This works well with Numba 0.54.1. See the following code:

@nb.njit('float64()')
def test():
    return np.finfo(np.float64).eps
test() # Returns 2.220446049250313e-16

Declaring a constant is also fine. In both cases Numba generate a good assembly code that directly return the (precomputed) constant.

Is Python's epsilon value correct?

I think that what you you are seeing is how Python's float type handles rounding when it runs out of precision. The Wikipedia text you quoted describing epsilon appears to leave this part out.

In your example, 1 + delta gets rounded up to 1 + epsilon. Even though a float can specify the differences between delta and epsilon, it cannot represent the difference between 1 + delta and 1 + epsilon. As you have noticed (with your delta2 test), the largest number that gets rounded down to 1 rather than up to 1 + epsilon appears to be 1 + epsilon/2.

So, a correct definition of what epsilon means in Python might be:

epsilon is the smallest positive floating point number such that (1 + epsilon) - 1 equals epsilon.

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