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static T epsilon() throw();
(until C++11)
static constexpr T epsilon() noexcept;
(since C++11)

Returns the machine epsilon, that is, the difference between 1.0 and the next value representable by the floating-point type T. It is only meaningful if std::numeric_limits<T>::is_integer == false.

[edit] Return value

T std::numeric_limits<T>::epsilon()
/* non-specialized */ T()
bool false
char 0
signed char 0
unsigned char 0
wchar_t 0
char8_t (since C++20) 0
char16_t (since C++11) 0
char32_t (since C++11) 0
short 0
unsigned short 0
int 0
unsigned int 0
long 0
unsigned long 0
long long (since C++11) 0
unsigned long long(since C++11) 0
long double LDBL_EPSILON

[edit] Example

Demonstrates the use of machine epsilon to compare floating-point values for equality:

#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';


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

[edit] See also

next representable floating-point value towards the given value
(function) [edit]