浮点运算是太可靠 [英] Floating point arithmetic is too reliable

问题描述

据我了解，在现代计算机系统进行浮点运算并不总是与实数运算是一致的。我想图谋小C＃程序来证明这一点。例如：

 静态无效的主要（字串[] args）
 {
双X = 0，Y = 0; 
 
 X + = 20013.8; 
 X + = 20012.7; 
 
 Y + = 10016.4; 
 Y + = 30010.1; 
 
 Console.WriteLine（结果：+ X ++ Y ++（X == Y））; 
 Console.Write（按任意键继续。）; Console.ReadKey（真）; 
} 
  

然而，在这种情况下， X 和是到底是相等的。

是否有可能对我来说，证明浮动使用类似的复杂程序浮点运算的不一致，并没有使用任何真正疯狂的数字？我想，如果可能的话，避免去比超出小数点少数地方更数学上正确的值。

解决方案

 双X =（0.1 * 3）/ 3; 
 Console.WriteLine（X：{0}，X）; //输出X：0.1
 Console.WriteLine（X == 0.1：{0}中，x == 0.1）; //输出×== 0.1：假
  

备注：在此基础上不作假设浮点运算是在.NET中不可靠的。

I understand that floating point arithmetic as performed in modern computer systems is not always consistent with real arithmetic. I am trying to contrive a small C# program to demonstrate this. eg:

static void Main(string[] args)
    {
        double x = 0, y = 0;

        x += 20013.8;
        x += 20012.7;

        y += 10016.4;
        y += 30010.1;

        Console.WriteLine("Result: "+ x + " " + y + " " + (x==y));
        Console.Write("Press any key to continue . . . "); Console.ReadKey(true);
    }

However, in this case, x and y are equal in the end.

Is it possible for me to demonstrate the inconsistency of floating point arithmetic using a program of similar complexity, and without using any really crazy numbers? I would like, if possible, to avoid mathematically correct values that go more than a few places beyond the decimal point.

解决方案

double x = (0.1 * 3) / 3;
Console.WriteLine("x: {0}", x); // prints "x: 0.1"
Console.WriteLine("x == 0.1: {0}", x == 0.1); // prints "x == 0.1: False"

Remark: based on this don't make the assumption that floating point arithmetic is unreliable in .NET.

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