std::numeric_limits<T>::epsilon

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std::numeric_limits
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numeric_limits::epsilon
Helper types
 
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

(C++11)(C++11) (C++11)(C++11)(C++11)(C++11)
 next representable floating point value towards the given value
(function)
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