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# std::numeric_limits::epsilon

From cppreference.com
< cpp‎ | types‎ | numeric limits

static T epsilon(); |  | (until C++11)
static constexpr T epsilon(); |  | (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.

### [edit] Return value

`T` | std::numeric_limits<T>::epsilon()
/* non-specialized */ | `T();`
bool | false
char | ​0​
signed char | ​0​
unsigned char | ​0​
wchar_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

### [edit] Exceptions

(none) | (until C++11)
`noexcept` specification: noexcept | (since C++11)

### [edit] Example

Demonstrates the simplistic use of machine epsilon to compare floating-point values (this approach doesn't work for the subnormal values, for which the epsilon is meaningless)

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 larger value
        // 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;
    }
    int main()
    {
        double d1 = 0.2;
        double d2 = 1 / std::sqrt(5) / std::sqrt(5);

        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 != d2
    d1 almost equals d2

### [edit] See also

nextafter nexttoward (C++11)(C++11) | next representable floating point value towards the given value (function) [edit]

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Category:

- unconditionally noexcept