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std::numeric_limits<T>:: epsilon

From cppreference.net
C++
Utilities library
Type support
std::numeric_limits
Static constants
(C++11)
Static member functions
(C++11)
numeric_limits::epsilon
Helper types
static T epsilon ( ) throw ( ) ;
(C++11まで)
static constexpr T epsilon ( ) noexcept ;
(C++11以降)

マシンイプシロン、すなわち浮動小数点型 T で表現可能な 1.0 と次の値との差を返す。 std:: numeric_limits < T > :: is_integer == false の場合にのみ意味を持つ。

戻り値

T std:: numeric_limits < T > :: epsilon ( )
/* 特殊化されていない場合 */ T ( )
bool false
char ​ 0 ​
signed char ​ 0 ​
unsigned char ​ 0 ​
wchar_t ​ 0 ​
char8_t (C++20以降) ​ 0 ​
char16_t (C++11以降) ​ 0 ​
char32_t (C++11以降) ​ 0 ​
short ​ 0 ​
unsigned short ​ 0 ​
int ​ 0 ​
unsigned int ​ 0 ​
long ​ 0 ​
unsigned long ​ 0 ​
long long (C++11以降) ​ 0 ​
unsigned long long (C++11以降) ​ 0 ​
float FLT_EPSILON
double DBL_EPSILON
long double LDBL_EPSILON

例

浮動小数点値の等価性比較における機械イプシロンの使用例を示します：

このコードを実行 
#include <algorithm>
#include <cmath>
#include <cstddef>
#include <iomanip>
#include <iostream>
#include <limits>
#include <type_traits>
template <class T>
std::enable_if_t<not std::numeric_limits<T>::is_integer, bool>
equal_within_ulps(T x, T y, std::size_t n)
{
    // Since `epsilon()` is the gap size (ULP, unit in the last place)
    // of floating-point numbers in interval [1, 2), we can scale it to
    // the gap size in interval [2^e, 2^{e+1}), where `e` is the exponent
    // of `x` and `y`.
    // If `x` and `y` have different gap sizes (which means they have
    // different exponents), we take the smaller one. Taking the bigger
    // one is also reasonable, I guess.
    const T m = std::min(std::fabs(x), std::fabs(y));
    // Subnormal numbers have fixed exponent, which is `min_exponent - 1`.
    const int exp = m < std::numeric_limits<T>::min()
                  ? std::numeric_limits<T>::min_exponent - 1
                  : std::ilogb(m);
    // We consider `x` and `y` equal if the difference between them is
    // within `n` ULPs.
    return std::fabs(x - y) <= n * std::ldexp(std::numeric_limits<T>::epsilon(), exp);
}
int main()
{
    double x = 0.3;
    double y = 0.1 + 0.2;
    std::cout << std::hexfloat;
    std::cout << "x = " << x << '\n';
    std::cout << "y = " << y << '\n';
    std::cout << (x == y ? "x == y" : "x != y") << '\n';
    for (std::size_t n = 0; n <= 10; ++n)
        if (equal_within_ulps(x, y, n))
        {
            std::cout << "x equals y within " << n << " ulps" << '\n';
            break;
        }
}

出力： 

x = 0x1.3333333333333p-2
y = 0x1.3333333333334p-2
x != y
x equals y within 1 ulps

関連項目

(C++11) (C++11) (C++11) (C++11) (C++11) (C++11)
指定された値に向かう次の表現可能な浮動小数点値
(関数)