java-在控制台中输出时的浮点精度 [英] java - float precision when output in console

问题描述

float x = 0.98123452f;
System.out.println(x); //it prints out 0.9812345

float x = 0.98123453f;
System.out.println(x); //it prints out 0.98123455

我不知道为什么第二个输出是0.98123455而不是0.9812345.浮点数的精度不是7个十进制数字吗?

I have no idea why the second one's output is 0.98123455 instead of 0.9812345. Isn't the precision of float is 7 decimal digits?

推荐答案

0.98123453 

是32位(符号，exp，尾数):

is 32 bits of (sign, exp, mantissa):

0 01111110 11110110011001000110000

这是:

0.9812345504760742

以双精度显示，并转换回浮点十进制表示形式:

in double precision, and cast back to float decimal representation:

 0.98123455

分配给单精度(浮点数)的位数为32，而双精度则为64位.进一步请注意，经常建议BigDecimal将您的数字存储为字符串，而不是以IEEE754格式存储.当需要对数字进行操作且精度更高时，它将进行转换.这太慢了.

The number of bits allocated to a single precision (float) is 32, and 64 bits for double precision. Further note that BigDecimal that is frequently suggested will store your number as a string, and not in IEEE754 format. It will do a conversion when it needs to act on the number, and while it has a better precision, it is awfully slow.

编辑.为了弄清为什么打印0.98123455的原因，我们需要观察到它是数字0.98123453的最接近的单精度表示形式:

EDIT. To clarify why it prints 0.98123455, we need to observe that it is the closest single precision representation of the number 0.98123453:

00111111011110110011001000101111 = 0.9812345  (sp) = 0.9812344908714294 (dp)
00111111011110110011001000110000 = 0.98123455 (sp) = 0.9812345504760742 (dp)
00111111011110110011001000110001 = 0.9812346  (sp) = 0.981234610080719  (dp)

_{sp =单精度，dp =双精度}

该列表是围绕数字的[-1，+ 1]二进制范围的，您可以看到0.98123453最接近尾数的10000后缀，而0.98123452最接近01111后缀.

The listing is for the [-1,+1] binary range around the number, and you can see that 0.98123453 is closest to the 10000 suffix of the mantissa, while 0.98123452 is closest to the 01111 suffix.

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