为什么我的float被截断？ [英] Why is my float being truncated?

问题描述

在 27.8675309 IEEE754.htmlrel =nofollow> IEEE 754 Converter 将我输入的值更改为 27.86753 。同样，当解析一个具有相同值的字符串时，Java会丢弃最后两位数字。

  Float.parseFloat（27.8675309） //结果是浮点值为27.86753 
  

我不确定Decimal representation IEEE转换器实际上是（这是一个浮动？），但我希望它给了我可能最大的数字：

1. 是浮动值


2. 不超过我输入的原始值
   




我希望Java能在也就是说，我希望上面的代码行可以返回一个等于 27.8675308 的float值，或者是一个更接近我的原始输入的更大的float值只是下降小数位。我在这里错过了什么？

解决方案





如果你看27.8675309（27.867530822753906作为双精度）的二进制表示：



  01000001110111101111000010110100 
  
 
 $ b 
下一个最高值是：
 
 pre $ code > 01000001110111101111000010110101 
  

产生27.867533（27.86753273010254为双倍），而下一个最低值为： p>



  01000001110111101111000010110011 
  



< （27.867528915405273为双倍）

浮点数中没有足够的位浮点代表中间的任何值，所以你的价值是十进制舍入到27.867530




Entering a value such as 27.8675309 into the "Decimal representation" field of the IEEE 754 Converter changes the value I entered to 27.86753. Likewise, Java drops the last two digits when a parse a string with the same value.

Float.parseFloat("27.8675309") // Results in a float value of 27.86753

I am not sure what the "Decimal representation" of the IEEE converter actually is (is it a float?) but I would expect it to give me the biggest number possible that:

1. Is a float value
2. Does not exceed the original value I entered

I would expect Java to behave in a similar fashion, that is, I would expect the line of code above to return a float value equal to 27.8675308 or an even larger float value that is closer to my original input instead of just dropping decimal places. What am I missing here?

解决方案

This is as expected.

If you look at the binary representation of 27.8675309 (27.867530822753906 as a double):

01000001110111101111000010110100

the next highest value is:

01000001110111101111000010110101

which yields 27.867533 (27.86753273010254 as a double), and the next lowest value is:

01000001110111101111000010110011

which yields 27.867529 (27.867528915405273 as a double)

There simply aren't enough bits in the mantissa of a Float to represent any value in between, so your value is rounded down in decimal to 27.867530

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