named-numbers.hpp

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#pragma once    // Source encoding: UTF-8 with BOM (π is a lowercase Greek "pi").

#include <cppx-core/language/syntax/macro-use.hpp>
#include <cppx-core/language/types/Truth.hpp>                   // cppx::Truth

#include <c/math.hpp>
#include <limits>           // std::numeric_limits

namespace cppx
{
    CPPX_USE_STD( numeric_limits );

#ifdef M_PI
    const auto e                = M_E;              // e              2.71828182845904523536
    const auto log2e            = M_LOG2E;          // log2(e)        1.44269504088896340736
    const auto log10e           = M_LOG10E;         // log10(e)       0.434294481903251827651
    const auto ln2              = M_LN2;            // ln(2)          0.693147180559945309417
    const auto ln10             = M_LN10;           // ln(10)         2.30258509299404568402
    const auto pi               = M_PI;             // pi             3.14159265358979323846
                                                    // pi/2 M_PI_2    1.57079632679489661923
                                                    // pi/4 M_PI_4    0.785398163397448309616
                                                    // 1/pi M_1_PI    0.318309886183790671538
                                                    // 2/pi M_2_PI    0.636619772367581343076
    const auto inv_sqrt_pi      = M_2_SQRTPI/2;     // 2/sqrt(pi)     1.12837916709551257390
    const auto sqrt2            = M_SQRT2;          // sqrt(2)        1.41421356237309504880
    const auto inv_sqrt2        = M_SQRT1_2;        // 1/sqrt(2)      0.707106781186547524401
#else
    const auto e                = 2.71828182845904523536;
    const auto log2e            = 1.44269504088896340736;
    const auto log10e           = 0.434294481903251827651;
    const auto ln2              = 0.693147180559945309417;
    const auto ln10             = 2.30258509299404568402;
    const auto pi               = 3.14159265358979323846;
                                    //1.57079632679489661923
                                    //0.785398163397448309616
                                    //0.318309886183790671538
                                    //0.636619772367581343076
    const auto inv_sqrt_pi      = 1.12837916709551257390;
    const auto sqrt2            = 1.41421356237309504880;
    const auto inv_sqrt2        = 0.707106781186547524401;
#endif
    template< class Number = double >
    constexpr Truth has_nan_        = numeric_limits<Number>::has_quiet_NaN;

    constexpr Truth has_nan         = has_nan_<double>;

    template< class Number >
    constexpr auto nan_()
        -> Number
    { return numeric_limits<Number>::quiet_NaN(); }

    constexpr inline auto nan()
        -> double
    { return nan_<double>(); }

    template< class Number = double >
    constexpr Truth has_infinity_   = numeric_limits<double>::has_infinity;

    constexpr Truth has_infinity    = has_infinity_<double>;

    template< class Number >
    constexpr auto infinity_()
        -> Number
    { return numeric_limits<Number>::infinity(); }

    constexpr inline auto infinity()
        -> double
    { return infinity_<double>(); }

    namespace calc
    {
        CPPX_USE_CPPX(
            e, log2e, log10e, ln2, ln10, pi, inv_sqrt_pi, sqrt2, inv_sqrt2,
            has_nan_, has_nan, nan_, nan, has_infinity_, has_infinity, infinity_, infinity
            );
    }  // namespace calc

}  // namespace cppx