std::numeri...ts::epsilon(3) C++ Standard Libary std::numeri...ts::epsilon(3) NAME std::numeric_limits::epsilon - std::numeric_limits::epsilon Synopsis 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 (since C++20) 0 char16_t (since C++11) 0 char32_t (since C++11) 0 short 0 unsigned short 0 int 0 unsigned int 0 long 0 unsigned long 0 long long (since C++11) 0 unsigned long long(since C++11) 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 <algorithm> #include <cmath> #include <cstddef> #include <iomanip> #include <iostream> #include <limits> #include <type_traits> template <class T> std::enable_if_t<not std::numeric_limits<T>::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<T>::min() ? std::numeric_limits<T>::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<T>::ep- silon(), 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 See also nextafter nextafterf nextafterl nexttoward nexttowardf nexttowardl next representable floating-point value towards the given value (C++11) (function) (C++11) (C++11) (C++11) (C++11) (C++11) http://cppreference.com 2024.06.10 std::numeri...ts::epsilon(3)
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