不精确的浮法除法 [英] Inexact float division

问题描述

看到这个，我正在练习一些c编程:

I were practicing some c programming when I saw this:

#include <stdio.h>

int main (void){
printf("result %.50lf",(double)10.0/10000000.0);
return 0;
}

其结果是0.00000099999999999999995474811182588628625868561393872

And the result was 0.00000099999999999999995474811182588625868561393872

有人可以解释一下为什么会这样吗?

Can somebody explain me why happens this?

推荐答案

double的内部表示是二进制浮点编码，无法精确表示所有(或实际上大多数)十进制小数，出于同样的原因，例如1/3不能精确地用十进制表示，10.0/10000000.0不能精确地用二进制表示.

The internal representation of double is a binary floating-point encoding that cannot precisely represent all (or indeed most) decimal fractions, for the same reason for example 1/3 cannot be exactly represented in decimal, 10.0/10000000.0 cannot be exactly represented in binary.

此外，64位双精度二进制浮点的精度约为15个十进制有效数字，因此，尝试输出50个十进制小数总是以无关紧要的数字结尾.在两倍精度范围内的实际结果是0.000000999999999999999.

Moreover 64-bit double precision binary floating point has a precision of around 15 decimal significant figures so attempting to output 50 decimal places is always going to end up in irrelevant and meaningless digits. Your actual result within the precision of a double is 0.000000999999999999999.

另请参见:每个程序员应了解的有关浮点算法的信息

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