浮动小于FLT_MIN。为什么FLT_TRUE_MIN？ [英] floats smaller than FLT_MIN. why FLT_TRUE_MIN?

问题描述

为了试图看看在下溢的情况下会发生什么，我发现我可以使浮点数比FLT_MIN小得多。我在OS 10.9上使用xcode 5.1。语言方言是gnu99。

  #include< stdio.h> 
 #include< stdlib.h> 
 #include< float.h> 
 
 int main（int argc，const char * argv []）
 {
 float underflow = FLT_MIN * 0.0000004; 
 $ b printf（Float min是％f或％e.\\\
下流是％f或％e \ nMin float exp是％d.\\\
，FLT_MIN，FLT_MIN，下溢，下溢，FLT_MIN_10_EXP）; 
 
返回0; 
 
 
 
 
 
 $ p $浮动最小值是0.000000或1.175494e -38。
下溢是0.000000或4.203895e-45 
 
最小浮动exp是-37。  
 
 
 
 
有没有更有效的方法来证明数据类型的限制？
 
为什么FLT_MIN实际上不是最小的浮点值？我应该使用其他常量吗？输入之前的问题后，我发现FLT_TRUE_MIN。这个数字是什么？       2个可能性使得低于最低限度：
 
 
 
  float 范围：
 
典型的 float 数字有2个范围：从 FLT_MAX 下降到<$ c $的全精度（正常范围） c> FLT_MIN 和第二个范围，精度从 FLT_MIN 下降到 FLT_TRUE_MIN 。这个第二个范围，称为subnormal通常提供大约10 ^ -7更多的范围。
 $ b 
 
 
  FLT_TRUE_MIN 是最小正浮点数
 
 $ FLT_MIN 是最小正规浮点数点的数量
 
 
  FLT_MIN_10_EXP 是最小的负整数，使得10次上升到该范围内
 
  C11dr§5.2.4.2.2 
 
 
 
 <一般而言 0<数学运算如下： double 。
 
 
 
  printf（） float 传递给 double 。 C允许代码进行优化，使得传递给 printf（）的值可以是<$ c $的 double 乘积c> FLT_MIN * 0.0000004 。
  float underflow = FLT_MIN * 0.0000004; 
 printf（％e \\\
，下溢）; 
  
如果输出为 4.701976e-45 而不是 4.203895e-45 ，情况就是这样。
 
 
 
 
 
 
 
 
 
请注意subnormal。对于低于正常（或反常规）数字的令人信服的理由在于以下问题。
  float a， b; 
 ... //以某种方式设置a和b。 
 
 //是否等于2？ 
 if（a == b）foo（）; 
 if（（a  -  b）== 0）foo（）; 
  
如果没有低于正常的数字，那么在 FLT_MIN 将会有一个非零的数学差异，远远低于 FLT_MIN ，结果会变成 0.0 。 
 $ b $ p 
如果子数目不正确，每对不同的 float  s的区别可以用< $ C> 0.0 。 ** 
 
 
 
 **除 +0.0，-0.0 外。签名的零有自己的特点。
 
In an attempt to see what would happen in the case of a float underflow I found that I could make float numbers much smaller than FLT_MIN. I'm using xcode 5.1 on OS 10.9. The language dialect is gnu99.
#include <stdio.h>
#include <stdlib.h>
#include <float.h>

int main(int argc, const char * argv[])
{
    float underflow = FLT_MIN * 0.0000004;

    printf("Float min is %f or %e.\nUnderflow is %f or %e\nMin float exp is %d.\n", FLT_MIN, FLT_MIN, underflow, underflow, FLT_MIN_10_EXP);

    return 0;
}
Prints:

Float min is 0.000000 or 1.175494e-38.

Underflow is 0.000000 or 4.203895e-45

Min float exp is -37.  

Is there a more effective method of demonstrating the limits of data types?
Why is FLT_MIN not actually the smallest float value? Are there other constants that I'm supposed to be using? After typing the previous question I found FLT_TRUE_MIN. What is this number?

解决方案
2 possibilities to get "below minimum":

float range: 

Typical float numbers have 2 ranges: full precision (normal range) from FLT_MAX down to FLT_MIN and a 2nd range with reducing precision from FLT_MIN down to FLT_TRUE_MIN.  This 2nd range, called "subnormal" typically provides about 10^-7 more range.

  
FLT_TRUE_MIN is the "minimum positive floating-point number"
  
  
FLT_MIN is the "minimum normalized positive floating-point number"  
  
  
FLT_MIN_10_EXP is the "minimum negative integer such that 10 raised to that power is in the range of normalized floating-point numbers"
  
  
C11dr §5.2.4.2.2
In general 0 < FLT_TRUE_MIN <= FLT_MIN <= 10^FLT_MIN_10_EXP <= 10^-37
Math performed as double.

printf() coverts each float passed to it to a double.  C allows code to optimize such that the value passed to printf() may be the double product of FLT_MIN * 0.0000004.
float underflow = FLT_MIN * 0.0000004;
printf("%e\n", underflow);
Had the output been 4.701976e-45 rather than 4.203895e-45, this would have been the case.




Note on "subnormal".  A compelling reason for subnormal (or denormal) numbers lies in the following problem.
float a,b;
... // somehow a and b are set.

// Are the 2 below equivalent?
if (a == b) foo();
if ((a - b) == 0) foo();
Without subnormal numbers, 2 nearly the same value numbers near FLT_MIN would have a non-zero mathematical difference much below FLT_MIN and the result would round to 0.0.  

With subnormal numbers, the difference of every pair of different floats is representable by something other than 0.0.  **

** Except +0.0, -0.0.  Signed zeros have their own peculiarities.

                        
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