Question

I have noticed an interesting behavior with float rounding / truncation by the C# compiler. Namely, when a float literal is beyond the guaranteed representable range (7 decimal digits), then a) explicitly casting a float result to float (a semantically unnecessary operation) and b) storing intermediate calculation results in a local variable both change the output. An example:

using System;

class Program
{
    static void Main()
    {
        float f = 2.0499999f;
        var a = f * 100f;
        var b = (int) (f * 100f);
        var c = (int) (float) (f * 100f);
        var d = (int) a;
        var e = (int) (float) a;
        Console.WriteLine(a);
        Console.WriteLine(b);
        Console.WriteLine(c);
        Console.WriteLine(d);
        Console.WriteLine(e);
    }
}

The output is:

205
204
205
205
205

In the JITted debug build on my computer, b is calculated as follows:

          var b = (int) (f * 100f);
0000005a  fld         dword ptr [ebp-3Ch] 
0000005d  fmul        dword ptr ds:[035E1648h] 
00000063  fstp        qword ptr [ebp-5Ch] 
00000066  movsd       xmm0,mmword ptr [ebp-5Ch] 
0000006b  cvttsd2si   eax,xmm0 
0000006f  mov         dword ptr [ebp-44h],eax 

whereas d is calculated as

          var d = (int) a;
00000096  fld         dword ptr [ebp-40h] 
00000099  fstp        qword ptr [ebp-5Ch] 
0000009c  movsd       xmm0,mmword ptr [ebp-5Ch] 
000000a1  cvttsd2si   eax,xmm0 
000000a5  mov         dword ptr [ebp-4Ch],eax 

Finally, my question: why is the second line of the output different from the fourth? Does that extra fmul make such a difference? Also note that if the last (already unrepresentable) digit from the float f is removed or even reduced, everything “falls in place”.

Answer 1

Your question can be simplified to asking why these two results are different:

float f = 2.0499999f;
var a = f * 100f;
var b = (int)(f * 100f);
var d = (int)a;
Console.WriteLine(b);
Console.WriteLine(d);

If you look at the code in .NET Reflector you can see that the above code is actually compiled as if it were the following code:

float f = 2.05f;
float a = f * 100f;
int b = (int) (f * 100f);
int d = (int) a;
Console.WriteLine(b);
Console.WriteLine(d);

Floating point calculations cannot always be made exactly. The result of 2.05 * 100f is not exactly equal to 205, but just a little less due to rounding errors. When this intermediate result is converted to an integer is truncated. When stored as a float it is rounded to the nearest representable form. These two methods of rounding give different results.

---

Regarding your comment to my answer when you write this:

Console.WriteLine((int) (2.0499999f * 100f));
Console.WriteLine((int)(float)(2.0499999f * 100f));

The calculations are done entirely in the compiler. The above code is equivalent to this:

Console.WriteLine(204);
Console.WriteLine(205);