.NET rounding error in ToString("f2")

Question

Hello I have this code in C#:

float n = 2.99499989f;
MessageBox.Show("n = " + n.ToString("f2", CultureInfo.InvariantCulture));

And this code in C++:

float n = 2.99499989f;
printf("n = %.2f", n);

First one outputs 3.00.
Second one outputs 2.99.

I have no clue why this is happening.

Update:

I also tried Objective-C NSLog and the output is 2.99.

I needed to fix it fast so I used following method:

float n = 2.99499989f;
float round = (float)Math.Round(n, 2);
MessageBox.Show("round = " + round.ToString(CultureInfo.InvariantCulture));

This code shows 2.99, but computes round in double precision. I can't find Math.RoundF.

Answer 1

First one rounds the number incorrectly.

Second one only selects two digits after comma, I guess.

Maybe some floating-point-precission issues? 2.9949... in fact rounds to more than 2.995?

Answer 2

Isn't that due to the fact that a 'float' isn't 'that' precise ?

Check this out, when you use a decimal:

        // float
        Console.WriteLine (2.99499989f.ToString ("f2"));
        // The above line outputs 3.00

        // decimal
        Console.WriteLine (2.99499989M.ToString ("f2"));
        // The above line outputs 2.99

Perhaps float can't represent 2.99499989 or whatever as 2.99.
Look also what happens when you do this:

// float
Console.WriteLine (2.98499f.ToString ("f2"));
// The above line outputs 2.99

Answer 3

The number 2.99499989f can't be presented exactly in IEEE754. Apparently printf and ToString handle this situation differently.

Answer 4

The float precision is 2^{-23} or about 0,0000001192 (relative error). Look, 2.995-2.99499989 = 0,00000011. Relative error is 3,6*10^{-8}.

If some compiler reads all digits of the 2.99499989f constant then the result is number greater than 2.995. But if another compiler reads only 2.994999 (because the precision is less than 2^{-23} and last digits are unimportant) then the result is number less than 2.995

Answer 5

Using BitConverter.GetBytes and printing out the actual bytes produced shows that this is not a compiler difference - in both cases, the actual float value stored is 0x403FAE14, which this handy calculator tells me is the exact value

2.99499988555908203125

The difference therefore must lie in differing behaviours of printf and ToString. More than that I cannot immediately say.