C / C ++：1.00000 <= 1.0f =假

问题描述：

有人可以解释为什么1.000000

Can someone explain why 1.000000 <= 1.0f is false?

代码：

#include <iostream>
#include <stdio.h>

using namespace std;

int main(int argc, char **argv)
{
    float step = 1.0f / 10;
    float t;

    for(t = 0; t <= 1.0f; t += step)
    {
        printf("t = %f\n", t);
        cout << "t = " << t << "\n";
        cout << "(t <= 1.0f) = " << (t <= 1.0f) << "\n";
    }

    printf("t = %f\n", t );
    cout << "t = " << t << "\n";
    cout << "(t <= 1.0f) = " << (t <= 1.0f) << "\n";
    cout << "\n(1.000000 <= 1.0f) = " << (1.000000 <= 1.0f) << "\n";
}

结果：

t = 0.000000
t = 0
(t <= 1.0f) = 1
t = 0.100000
t = 0.1
(t <= 1.0f) = 1
t = 0.200000
t = 0.2
(t <= 1.0f) = 1
t = 0.300000
t = 0.3
(t <= 1.0f) = 1
t = 0.400000
t = 0.4
(t <= 1.0f) = 1
t = 0.500000
t = 0.5
(t <= 1.0f) = 1
t = 0.600000
t = 0.6
(t <= 1.0f) = 1
t = 0.700000
t = 0.7
(t <= 1.0f) = 1
t = 0.800000
t = 0.8
(t <= 1.0f) = 1
t = 0.900000
t = 0.9
(t <= 1.0f) = 1
t = 1.000000
t = 1
(t <= 1.0f) = 0

(1.000000 <= 1.0f) = 1

答

正如在注释中正确指出的， t 的值实际上并不是你在 1.00000

As correctly pointed out in the comments, the value of t is not actually the same 1.00000 that you are defining in the line below.

使用 std :: setprecision（20）以更高的精度打印t将显示其实际值： 1.0000001192092895508 。

Printing t with higher precision with std::setprecision(20) will reveal its actual value: 1.0000001192092895508.

避免这类问题的常见方法是不与 1 ，但是使用 1 + epsilon ，其中epsilon是一个非常小的数字，也许是一个或两个大于您的浮点精度。

The common way to avoid these kinds of issues is to compare not with 1, but with 1 + epsilon, where epsilon is a very small number, that is maybe one or two magnitudes greater than your floating point precision.

所以你可以写你的for循环条件为

So you would write your for loop condition as

for(t = 0; t <= 1.000001f; t += step)

$ b

Note that in your case, epsilon should be atleast ten times greater than the maximum possible floating point error, as the float is added ten times.

如Muepe和Alain所指出的， t！= 1.0f的原因$ c>是 1/10 无法用二进制浮点数精确表示。

As pointed out by Muepe and Alain, the reason for t != 1.0f is that 1/10 can not be precisely represented in binary floating point numbers.

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