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std::numeric_limits::epsilon

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std::numeric_limits
 
static T epsilon()
(hasta C++11)
static constexpr T epsilon()
(desde C++11)
Devuelve el epsilon de la máquina, es decir, la diferencia entre 1.0 y el siguiente valor representable por la T tipo de punto flotante. Esto sólo tiene sentido si std::numeric_limits<T>::is_integer == false .
Original:
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.
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Contenido

[editar] Valor de retorno

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

[editar] Excepciones

noexcept specification:  
noexcept
  (desde C++11)

[editar] Ejemplo

Muestra el uso simplista de epsilon de la máquina para comparar valores de punto flotante .
Original:
Demonstrates the simplistic use of machine epsilon to compare floating-point values.
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#include <cmath>
#include <limits>
#include <iomanip>
#include <iostream>
#include <type_traits>
 
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 larger value
    // and multiplied by the desired precision in ULPs (units in the last place)
    return std::abs(x-y) <=   std::numeric_limits<T>::epsilon()
                            * std::max(std::abs(x), std::abs(y))
                            * ulp;
}
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

[editar] Ver también

(C++11)
(C++11)
siguiente valor representable en coma flotante a un valor dado
Original:
next representable floating point value towards the given value
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(función) [edit]