浮点文字与浮点变量的奇怪编译器行为 [英] Strange compiler behavior with float literals vs float variables

问题描述

我注意到C＃编译器对float舍入/截断有一个有趣的行为。即，当float文字超出保证的可表示范围（7个十进制数字）时，a）将float结果显式转换为float（从语义上讲是不必要的操作），b）将中间计算结果存储在局部变量中都会改变输出。例如：

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);
    }
}

输出为：

205
204
205
205
205

在计算机上的JITted调试版本中，b的计算方式如下：

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 

而d计算为

          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 

最后，我的问题：为什么输出的第二行与第四行不同吗？那多余的fmul会带来不同吗？还要注意，如果删除或什至减少了浮点数f的最后一个数字（已经无法表示），则所有内容都会落在原处。

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".

推荐答案

您的问题可以简化为询问为什么这两个结果不同：

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);

如果您查看.NET Reflector中的代码，您会发现上面的代码实际上被编译为如果是以下代码：

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);

不能始终精确地计算浮点数。 2.05 * 100f 的结果不完全等于205，但由于舍入误差而略少。当此中间结果转换为整数时，将被截断。作为浮点数存储时，将四舍五入为最接近的可表示形式。这两种舍入方法给出不同的结果。

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.

关于您在撰写本文时对我的答案的评论：

Regarding your comment to my answer when you write this:

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

计算完全在编译器中完成。上面的代码等效于此：

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

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

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