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)