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 <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>::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
See also
| (C++11)(C++11)(C++11)(C++11)(C++11)(C++11) |
next representable floating-point value towards the given value (function) |