std::numeric_limits::epsilon - cppreference.com (original) (raw)

| 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.

[edit] Return value

[edit] Example

Demonstrates the use of machine epsilon to compare floating-point values for equality:

#include #include #include #include #include #include #include   template std::enable_if_t<not std::numeric_limits::is_integer, bool> equal_within_ulps(T x, T y, std::size_t n) { // Since epsilon() is the gap size (ULP, unit in the last place) // of floating-point numbers in interval [1, 2), we can scale it to // the gap size in interval [2^e, 2^{e+1}), where e is the exponent // of x and y.   // If x and y have different gap sizes (which means they have // different exponents), we take the smaller one. Taking the bigger // one is also reasonable, I guess. const T m = std::min(std::fabs(x), std::fabs(y));   // Subnormal numbers have fixed exponent, which is min_exponent - 1. const int exp = m < std::numeric_limits::min() ? std::numeric_limits::min_exponent - 1 : std::ilogb(m);   // We consider x and y equal if the difference between them is // within n ULPs. return std::fabs(x - y) <= n * std::ldexp(std::numeric_limits::epsilon(), exp); }   int main() { double x = 0.3; double y = 0.1 + 0.2; std::cout << std::hexfloat; std::cout << "x = " << x << '\n'; std::cout << "y = " << y << '\n'; std::cout << (x == y ? "x == y" : "x != y") << '\n'; for (std::size_t n = 0; n <= 10; ++n) if (equal_within_ulps(x, y, n)) { std::cout << "x equals y within " << n << " ulps" << '\n'; break; } }

Output:

x = 0x1.3333333333333p-2 y = 0x1.3333333333334p-2 x != y x equals y within 1 ulps

[edit] See also