Question

Can anyone explain to me why this program:

for(float i = -1; i < 1; i += .1F)
    Console.WriteLine(i);

Outputs this:

-1

-0.9

-0.8

-0.6999999

-0.5999999

-0.4999999

-0.3999999

-0.2999999

-0.1999999

-0.99999993

7.450581E-08

0.1000001

0.2000001

0.3000001

0.4000001

0.5000001

0.6000001

0.7000001

0.8000001

0.9000002

Where is the rounding error coming from??

Answer 1

I’m sure this question must have been asked in some form before but I can’t find it anywhere quickly. 🙂

The answer comes down to the way that floating point numbers are represented. You can go into the technical detail via wikipedia but it is simply put that a decimal number doesn’t necessarily have an exact floating point representation…

The way floating point numbers (base 2 floating point anyway like doubles and floats) work [0]is by adding up powers of 1/2 to get to what you want. So 0.5 is just 1/2. 0.75 is 1/2+1/4 and so on.

the problem comes that you can never represent 0.1 in this binary system without an unending stream of increasingly smaller powers of 2 so the best a computer can do is store a number that is very close to but not quite 0.1.

Usually you don’t notice these differences but they are there and sometimes you can make them manifest themselves. There are a lot of ways to deal with these issues and which one you use is very much dependant on what you are actually doing with it.

[0] in the slightly handwavey close enough kind of way