浮点加 - 给出奇怪的结果..！ [英] Floating point addition - giving strange result..!

问题描述

执行以下代码：

  public class FPoint {
 public static void main（String [] args ）{
 float f = 0.1f; 
 for（int i = 0; i <9; i ++）{
 f + = 0.1f; 
} 
 System.out.println（f）; 
 
 
 code $ 
 $ b $ p $显示以下输出：
 
 
 
  1.0000001  
 
 
 
但输出应该是 1.0000000 纠正我，如果我错了.. !! 
 
解决方案
 0.1与IEEE 754标准不是真正的0.1 
 $ b 
 0.1编码： 0 01111011 10011001100110011001101 （带浮点数） 
 
 
 
 
 0表示指数（= 123  - > 123  -  127 =  -4  （127是IEEE 754中的 bias>）
 
 
 10011001100110011001101尾数
 
 
 
 
 
要转换十进制数的尾数，我们有
 1.10011001100110011001101 * 2 ^  -4 （base2）[1.xxx隐含在IEEE 754中] 
 
 
 = 0.000110011001100110011001101（base2）
 
 = 1/2 ^ 4 + 1/2 ^ 5 + 1/2 ^ 8 + 1 / 2 ^ 9 + 1/2 ^ 12 + 1/2 ^ 13 + 1/2 ^ 16 + 1/2 ^ 17 + 1/2 ^ 20 + 1/2 ^ 21 + 1/2 ^ 24 + 1/2 ^ 25 + 1/2 ^ 27（base10）
 
 
 = 1/16 + 1/32 + 1/256 + 1/512 + 1/4096 + 1/8192 + 1/65536 + 1/131072 ...（base10）
 
 
 
 =  0.10000000149011612 （base10）
 
When executing the following code:
public class FPoint {
    public static void main(String[] args) {
        float f = 0.1f;
        for(int i = 0; i<9; i++) {
            f += 0.1f;
        }
        System.out.println(f);
    }
}
The following output is displayed:

1.0000001

But output should be 1.0000000, right? Correct me if I'm wrong..!!
解决方案
0.1 is not really "0.1" with IEEE 754 Standard.

0.1 is coded : 0 01111011 10011001100110011001101 (with float number)


0 is the sign (= positive)
01111011 the exponent (= 123 -> 123 - 127 = -4 (127 is the bias in IEEE 754))
10011001100110011001101 the mantissa


To convert the mantissa in decimal number we have 
1.10011001100110011001101*2^-4(base2) [the 1.xxx is implicit in IEEE 754]

= 0.000110011001100110011001101(base2)

= 1/2^4 + 1/2^5 + 1/2^8 + 1/2^9 + 1/2^12 + 1/2^13 + 1/2^16 + 1/2^17 + 1/2^20 + 1/2^21 + 1/2^24 + 1/2^25 + 1/2^27 (base10)

=  1/16 + 1/32 + 1/256 + 1/512 + 1/4096 + 1/8192 + 1/65536 + 1/131072 ...(base10)

= 0.10000000149011612(base10)

                        
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