std::numeric_limits::epsilon
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                    < cpp | types | numeric limits
                    
                                                            
                    | 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.
| Contents | 
[edit] 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 | 
[edit] Exceptions
| (none) | (until C++11) | 
| noexcept specification:   noexcept | (since C++11) | 
[edit] 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::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
[edit] See also
| (C++11)(C++11) | next representable floating point value towards the given value (function) | 


