有人可以向我解释为什么float x = 0.1 * 7不会导致x == 0.7为真？ [英] Can someone explain to me why float x = 0.1 * 7 does not result in x == 0.7 to be true?

问题描述

编辑：这里有很多不满的成员，因为这个问题在网站上有一个副本。在我的辩护中，我试图寻找答案，也许我正在使用较差的搜索关键字，但是我找不到一个直接，明确的答案，这个具体的代码示例。没有一个人知道有一个从那里 ** 2009 ** ，然后将链接到这里。

这是一个编码的例子：

  #include< iostream> 
使用namespace std; 
 
 int main（）{
 float x = 0.1 * 7; 
 if（x == 0.7）
 cout<< 真实。\\\
; 
 else 
 cout<< FALSE。\\\
; 
 
返回0; 
} 
  

这会导致FALSE。但是，当我输出x，它确实输出为0.7。解释？

806-3568 / ncg_goldberg.htmlrel =nofollow>每个计算机科学家应该知道什么是浮点运算。首先， code> 0.1 是 double 类型的字面值。在IEEE 754双精度中，最接近0.1的值是：

  0.1000000000000000055511151231257827021181583404541015625 
 如果你乘以7，IEE 754单精度中最接近的可表示值（因为你将它存储在 
  0.699999988079071044921875 
  
正如你所看到的，它几乎是0.7，但并不完全。然后将它转换为 double 作比较，最后比较以下两个值：
 
 
  0.699999988079071044921875 == 0.6999999999999999555910790149937383830547332763671875 
  
当然计算结果为 false 。
 
EDIT:  There are a lot of disgruntled members here because this question had a duplicate on the site.  In my defense, I tried searching for the answer FIRST, and maybe I was using poor searching keywords, but I could not find a direct, clear answer to this specific code example.  Little did I know there was one out there from **2009** that would then be linked to from here.

Here's a coded example:
#include <iostream>
using namespace std;

int main() {
    float x = 0.1 * 7;
    if (x == 0.7)
        cout << "TRUE. \n";
    else
        cout << "FALSE. \n";

    return 0;
}
This results in FALSE.  However, when I output x, it does indeed output as 0.7.  Explanation?
解决方案
Please read What Every Computer Scientist Should Know About Floating-Point Arithmetic.

First of all, 0.1 is a literal of type double. The closest representable value to 0.1 in IEEE 754 double-precision is:
0.1000000000000000055511151231257827021181583404541015625
If you multiply that by 7, the closest representable value in IEE 754 single-precision (since you're storing it in a float) is:
0.699999988079071044921875
Which, as you can see, is almost 0.7, but not quite. This then gets converted to a double for the comparison, and you end up comparing the following two values:
0.699999988079071044921875 == 0.6999999999999999555910790149937383830547332763671875
Which of course evaluates to false.

                        
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