C++ 参考手册

std::numeric_limits<T>::epsilon

static T epsilon() throw();
 (C++11 前)
static constexpr T epsilon() noexcept;
 (C++11 起)

返回机器 epsilon ，即 1.0 与浮点类型 T 的下个可表示值的差。它仅若 std::numeric_limits<T>::is_integer == false 才有意义。

返回值

 
T std::numeric_limits<T>::epsilon()
/* non-specialized */ T()
bool false
char ​0​
signed char ​0​
unsigned char ​0​
wchar_t ​0​
char8_t ​0​
char16_t ​0​
char32_t ​0​
short ​0​
unsigned short ​0​
int ​0​
unsigned int ​0​
long ​0​
unsigned long ​0​
long long ​0​
unsigned long long ​0​
float FLT_EPSILON
double DBL_EPSILON
long double LDBL_EPSILON

示例

演示用机器 epsilon 比较浮点值是否相等

运行此代码
#include <cmath>
#include <limits>
#include <iomanip>
#include <iostream>
#include <type_traits>
#include <algorithm>
 
template<class T>
typename std::enable_if<!std::numeric_limits<T>::is_integer, bool>::type
    almost_equal(T x, T y, int ulp)
{
    // the machine epsilon has to be scaled to the magnitude of the values used
    // and multiplied by the desired precision in ULPs (units in the last place)
    return std::abs(x-y) <= std::numeric_limits<T>::epsilon() * std::abs(x+y) * ulp
        // unless the result is subnormal
        || std::abs(x-y) < std::numeric_limits<T>::min();
}
 
int main()
{
    double d1 = 0.2;
    double d2 = 1 / std::sqrt(5) / std::sqrt(5);
    std::cout << std::fixed << std::setprecision(20) 
        << "d1=" << d1 << "\nd2=" << d2 << '\n';
 
    if(d1 == d2)
        std::cout << "d1 == d2\n";
    else
        std::cout << "d1 != d2\n";
 
    if(almost_equal(d1, d2, 2))
        std::cout << "d1 almost equals d2\n";
    else
        std::cout << "d1 does not almost equal d2\n";
}

输出： 

d1=0.20000000000000001110
d2=0.19999999999999998335
d1 != d2
d1 almost equals d2

参阅

(C++11)(C++11) (C++11)(C++11)(C++11)(C++11)
 趋向给定值的下个可表示浮点值
(函数)