std::numeric_limits<T>::epsilon

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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。

[编辑] 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

[编辑] 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

[编辑] 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) [编辑]