#include <algorithm>#include <cmath>#include <cstddef>#include <iomanip>#include <iostream>#include <limits>#include <type_traits> template<class T>std::enable_if_t<notstd::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;}}

x = 0x1.3333333333333p-2y = 0x1.3333333333334p-2x != yx equals y within 1 ulps