c＃浮点循环，意外的结果 [英] c# floating point for loop, unexpected results

问题描述

任何人都可以向我解释为什么这个程序：

pre $ for（float i = -1; i <1; i + = .1F）
Console.WriteLine（i）;


输出：

-1

<-0> -0.9

<-0> -0

-0.6999999

-0.5999999

-0.4999999

- 0.3999999

-0.2999999

-0.1999999

-0.99999993
$ b $ 7.450581E-08
$ b $ 0.1000001


$ b
$ b $ 0.3000001

0.4000001

0.5000001 $ b $ 0.6000001

0.7000001

0.8000001

0.9000002

解决方案

我确定这个问题一定是以某种形式问过的，但是我无法快速找到它。 ：）

答案归结为浮点数的表示方式。您可以通过维基百科进入技术细节，但简单地说，十进制数不会必然有一个精确的浮点数表示...

浮点数（基2浮点数，无论如何双打和浮点数）工作[0]的方式是加权1/2来达到你想要的。所以0.5只是1/2。 0.75是1/2 + 1/4等等。

问题出现了，在这个二进制系统中，你永远不能代表0.1 2所以最好的电脑可以做的是存储一个非常接近，但不是0.1的数字。通常你不会注意到这些差异，但他们在那里，有时候你可以让自己表现出来。有很多方法来处理这些问题，你使用哪一个是非常依赖于你实际上在做什么。

[0]在稍微handwavey接近足够的方式

Can anyone explain to me why this program:

for(float i = -1; i < 1; i += .1F)
    Console.WriteLine(i);

Outputs this:

-1

-0.9

-0.8

-0.6999999

-0.5999999

-0.4999999

-0.3999999

-0.2999999

-0.1999999

-0.99999993

7.450581E-08

0.1000001

0.2000001

0.3000001

0.4000001

0.5000001

0.6000001

0.7000001

0.8000001

0.9000002

Where is the rounding error coming from??

解决方案

I'm sure this question must have been asked in some form before but I can't find it anywhere quickly. :)

The answer comes down to the way that floating point numbers are represented. You can go into the technical detail via wikipedia but it is simply put that a decimal number doesn't necessarily have an exact floating point representation...

The way floating point numbers (base 2 floating point anyway like doubles and floats) work [0]is by adding up powers of 1/2 to get to what you want. So 0.5 is just 1/2. 0.75 is 1/2+1/4 and so on.

the problem comes that you can never represent 0.1 in this binary system without an unending stream of increasingly smaller powers of 2 so the best a computer can do is store a number that is very close to but not quite 0.1.

Usually you don't notice these differences but they are there and sometimes you can make them manifest themselves. There are a lot of ways to deal with these issues and which one you use is very much dependant on what you are actually doing with it.

[0] in the slightly handwavey close enough kind of way

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