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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 (C++20) 0 char16_t (C++11) 0 char32_t (C++11) 0 short 0 unsigned short 0 int 0 unsigned int 0 long 0 unsigned long 0 long long (C++11) 0 unsigned long long(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 <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::fabs(x-y) <= std::numeric_limits<T>::epsilon() * std::fabs(x+y) * ulp // unless the result is subnormal || std::fabs(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 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 2022.07.31 std::numeri...ts::epsilon(3)
NAME | Synopsis | Return value | Example | Output: | See also
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