230 – Addition isn’t commutative

When working with floating-point numbers keep in mind that addition isn’t associative. That is, in a chain of additions, the order in which you do them is important.

As an example, consider the following addition that produces the correct result:

eps = 10**-16
print(eps + eps + 1)
# 1.0000000000000002

The addition above evaluates from left to right, so eps + eps + 1 is the same as (eps + eps) + 1. However, if you add parenthesis on the right, the result changes and becomes wrong:

print(eps + (eps + 1))
# 1.0

You should be mindful of this when writing code that works with floating-point numbers, especially in sensitive contexts.

Further reading:

• Precision of Python floats, https://mathspp.com/blog/til/precision-of-python-floats