std::numeric_limits<T>::epsilon

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.

#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

std::numeric_limits<T>::epsilon

Return value

Example

See also