# std::numeric_limits<T>::epsilon

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< cpp‎ | types‎ | numeric limits

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

nextafternextafterfnextafterlnexttowardnexttowardfnexttowardl (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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