std::numeric_limits<T>::epsilon (3) - Linux Manuals

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

NAME

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