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cppreference std::numeric_limits

The numeric_limits class template provides a standardized way to query various properties of arithmetic types (e.g. the largest possible value for type int is std::numeric_limits<int>::max()).

NOTE: 1、trait consistent interface abstraction

Implementations may provide specializations of std::numeric_limits for implementation-specific types: e.g. GCC provides std::numeric_limits<__int128>. Non-standard libraries may add specializations for library-provided types, e.g. OpenEXR provides std::numeric_limits<half> for a 16-bit floating-point type.

NOTE:

1、上述描述的是extend std library，C++是允许通过添加specialization来进行extend的

cppreference std::numeric_limits<T>::epsilon

static T epsilon() throw(); // (until C++11)
static constexpr 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.

NOTE:

1、仅仅对float point number才有用

Example

Demonstrates the use of machine epsilon to compare floating-point values for equality

NOTE:

1、这是非常好的例子

#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::fabs(x - y) <= std::numeric_limits<T>::epsilon() * std::fabs(x + y) * ulp
    // unless the result is subnormal
                    || std::fabs(x - y) < std::numeric_limits<T>::min();
}

int main()
{
    double d1 = 0.2;
    double d2 = 1 / std::sqrt(5) / std::sqrt(5);
    std::cout << std::fixed << std::setprecision(20) << "d1=" << d1 << "\nd2=" << d2 << '\n';

    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";
}
// g++ test.cpp --std=c++11

NOTE:

1、上述例子涉及了如下内容:

a、ULPs (units in the last place)

b、subnormal

这些是理解上述例子的关键