std::numeric_limits<T>::epsilon
From cppreference.com
< cpp | types | numeric limits
static T epsilon()throw(); | (until C++11) | |
staticconstexpr 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.
[edit]Return value
T | std::numeric_limits<T>::epsilon() |
| /* non-specialized */ | T() |
| bool | false |
| char | 0 |
| signedchar | 0 |
| unsignedchar | 0 |
| wchar_t | 0 |
| char8_t(since C++20) | 0 |
| char16_t(since C++11) | 0 |
| char32_t(since C++11) | 0 |
| short | 0 |
| unsignedshort | 0 |
| int | 0 |
| unsignedint | 0 |
| long | 0 |
| unsignedlong | 0 |
| longlong(since C++11) | 0 |
| unsignedlonglong(since C++11) | 0 |
| float | FLT_EPSILON |
| double | DBL_EPSILON |
| longdouble | LDBL_EPSILON |
[edit]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`.constint 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.returnstd::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
[edit]See also
(C++11)(C++11)(C++11)(C++11)(C++11)(C++11) | next representable floating-point value towards the given value (function) |
