## Floating point addition is not associative

February 28th, 2014

A lot of people don’t seem to know this….and they should. When working with floating point arithmetic, it is not necessarily true that a+(b+c) = (a+b)+c. Here is a demo using MATLAB

>> x=0.1+(0.2+0.3);
>> y=(0.1+0.2)+0.3;
>> % are they equal?
>> x==y

ans =
0

>> % lets look
>> sprintf('%.17f',x)
ans =
0.59999999999999998

>> sprintf('%.17f',y)
ans =
0.60000000000000009

These results have nothing to do with the fact that I am using MATLAB. Here’s the same thing in Python

>>> x=(0.1+0.2)+0.3
>>> y=0.1+(0.2+0.3)
>>> x==y
False
>>> print('%.17f' %x)
0.60000000000000009
>>> print('%.17f' %y)
0.59999999999999998

If this upsets you, or if you don’t understand why, I suggest you read the following

Does anyone else out there have suggestions for similar resources on this topic?