c++ - Is floating-point addition and multiplication associative?

Question

I had a problem when I was adding three floating point values and comparing them to 1.

cout << ((0.7 + 0.2 + 0.1)==1)<<endl;     //output is 0
cout << ((0.7 + 0.1 + 0.2)==1)<<endl;     //output is 1

Why would these values come out different?

Answer 1

Floating point addition is not necessarily associative. If you change the order in which you add things up, this can change the result.

The standard paper on the subject is What Every Computer Scientist Should Know about Floating Point Arithmetic. It gives the following example:

Another grey area concerns the interpretation of parentheses. Due to roundoff errors, the associative laws of algebra do not necessarily hold for floating-point numbers. For example, the expression (x+y)+z has a totally different answer than x+(y+z) when x = 1e30, y = -1e30 and z = 1 (it is 1 in the former case, 0 in the latter).