c - float 错误

Question

#include <stdio.h>
int main()
{
    int n;
    while ( scanf( "%d", &n ) != EOF ) {
        double sum = 0,k;
        if( n > 5000000 || n<=0 )   //the judgment of the arrange
            break;
        for ( int i = 1; i <= n; i++ ) {
            k = (double) 1 / i;
            sum += k;
        }
        /*
        for ( int i = n; i > 0; i-- ) {
            k = 1 / (double)i;
            sum += k;
        }
        */
        printf("%.12lf\n", sum);
    }
    return 0;
}

为什么在不同的循环中我得到不同的答案。有 float 错误吗？当我输入 5000000总和是16.002164235299但是当我使用 for (符号部分)的另一个循环时，我得到了总和 16.002164235300 .

Answer 1

因为 floating point math is not associative :

即(a + b) + c 不一定等于 a + (b + c)