std::numeric_limits::epsilon (3) Linux Manual Page

std::numeric_limits<T>::epsilon – std::numeric_limits<T>::epsilon

Synopsis

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.

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 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

Example

Demonstrates the use of machine epsilon to compare floating-point values for equality
// Run this code

#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";
}

Output:

  d1=0.20000000000000001110
  d2=0.19999999999999998335
  d1 != d2
  d1 almost equals d2

See also

nextafter
nextafterf
nextafterl
nexttoward
nexttowardf
nexttowardl next representable floating point value towards the given value
            (function)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)
(C++11)