浮点比较给出了不同的结果 [英] Float comparison gives different results

问题描述

 ＃include  
 h取代; 
 int main（）{
 float a = 0.9; 
 if（a <0.9）
 printf（hi）; //这将是答案
 else 
 printf（bye）; 
返回0; 
 
 
 
 
 
 $ p如果我们将0.9更改为0.8，则会打印其他语句： p> 
 
 
  #include< stdio.h> 
 int main（）{
 float a = 0.8; 
 if（a <0.8）
 printf（hi）; 
 else 
 printf（bye）; //这将是答案
 return 0; 
 
 
 
 
 
 $ b 
那么为什么当我们改变一个数字时这个输出会改变呢？
解决方案
您必须知道浮点是如何工作的。 
 
 
浮点通过使用2的幂数，每个数字用来表示 2 ^ -x ，其中X是第n位数字。
 
 
例如， 0.011 （二进制）将是 2 ^ -2 + 2 ^ -3 ，这是 0.25 + 0.125 = 0.375  
 
 
 
现在尝试表示 0.9 。你有麻烦了，因为没有二的力量来代表它。在32位和可能的64位机器中表示的值将给出略小于0.9的结果，而对于0.8而言，结果是精确的，并且可以由2的幂来表示。
 b 
 $ b 
你可以通过打开 python 提示来试试。尝试输入一些数字，最后以 ... 99999999 结尾。
 
Look at the following two codes, and tell me the reason why answers vary a lot.
#include<stdio.h>
int main() {
    float a = 0.9;
    if(a<0.9)
        printf("hi"); // This will be the answer
    else
        printf("bye");
    return 0;
}
And if we change 0.9 to 0.8, then else's statement is printed:
#include<stdio.h>
int main() {
    float a = 0.8;
    if(a<0.8)
        printf("hi");
    else
        printf("bye");//this will be the answer
    return 0;
}
So why this output changes when we just change a single digit?
解决方案
You have to know how floating points works.

Floating points are represented by using powers of two, each digit is used to represent 2^-x where X is the n-th digit.

For example, 0.011 (binary) would be 2^-2 + 2^-3, which is 0.25 + 0.125 = 0.375

Now try to represent 0.9. You are in trouble, since no power of two to represent it. The value this is represented in 32-bits and probably 64-bits machines will give a result slightly smaller than 0.9, whereas for 0.8 the result is precise and representable by powers of two.

You can try this out by opening a python prompt. Try and type a few numbers, eventually one will end with ...99999999.

                        
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