std::numeric_limits::epsilon(3)

NAME
std::numeric_limits::epsilon - std::numeric_limits::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 (C++20) 0
   char16_t (C++11) 0
   char32_t (C++11) 0
   short 0
   unsigned short 0
   int 0
   unsigned int 0
   long 0
   unsigned long 0
   long long (C++11) 0
   unsigned long long(C++11) 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::fabs(x-y) <= std::numeric_limits<T>::epsilon() * std::fabs(x+y) * ulp
         // unless the result is subnormal
         || std::fabs(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
   (C++11) (function)
   (C++11)
   (C++11)
   (C++11)
   (C++11)
   (C++11)