# std::numeric_limits<T>::epsilon

< cpp‎ | types‎ | numeric limits

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 (C++20) | ​0​
char16_t (C++11) | ​0​
char32_t (C++11) | ​0​
short | ​0​
unsigned short | ​0​
int | ​0​
unsigned int | ​0​
long | ​0​
unsigned long | ​0​
long long (C++11) | ​0​
unsigned long long(C++11) | ​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

    #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

nextafter nextafterf nextafterl nexttoward nexttowardf nexttowardl (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)