std::numeric_limits<T>::epsilon
From cppreference.com
< 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 (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 <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
| (C++11)(C++11) (C++11)(C++11)(C++11)(C++11) |
next representable floating point value towards the given value (function) |