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std::numeric_limits::epsilon

STD：：数字[医]限制：：Epsilon

static T epsilon(​(until C++11)
static constexpr T epsilon(​(since C++11)

返回机器epsilon，即1.0和下一个可由浮点类型表示的值。T.只有在下列情况下才有意义std::numeric_limits<T>::is_integer==false...

返回值

Tstd::numeric_limits::epsilon()
/* non-specialized */T(
boolfalse
char​0​
signed char​0​
unsigned char​0​
wchar_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​
floatFLT_EPSILON
doubleDBL_EPSILON
long doubleLDBL_EPSILON

例外

(none)(until C++11)
noexcept specification: noexcept(since C++11)

例

演示如何使用机器epsilon比较浮点值是否相等。

二次

#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
 
    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";
}

二次

产出：

二次

d1 != d2
d1 almost equals d2

二次

另见

nextafternexttoward (C++11)(C++11)next representable floating point value towards the given value (function)

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在CreativeCommonsAttribution下授权-ShareAlike未移植许可v3.0。

http：//en.cppreference.com/w/cpp/type/NUMERIC[医]极限/epsilon

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