static T epsilon(); | (until C++11) | |
static constexpr T epsilon(); | (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 |
char16_t | 0 |
char32_t | 0 |
short | 0 |
unsigned short | 0 |
int | 0 |
unsigned int | 0 |
long | 0 |
unsigned long | 0 |
long long | 0 |
unsigned long long | 0 |
float | FLT_EPSILON |
double | DBL_EPSILON |
long double | LDBL_EPSILON |
Exceptions
| (none) | (until C++11) |
noexcept specification: noexcept | (since C++11) |
Example
Demonstrates the use of machine epsilon to compare floating-point values for equality.
#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::abs(x-y) < std::numeric_limits<T>::epsilon() * std::abs(x+y) * ulp
// unless the result is subnormal
|| std::abs(x-y) < std::numeric_limits<T>::min();
}
int main()
{
double d1 = 0.2;
double d2 = 1 / std::sqrt(5) / std::sqrt(5);
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 != d2 d1 almost equals d2
See also
| (C++11)(C++11) | next representable floating point value towards the given value (function) |
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