Chris@16: //  Copyright John Maddock 2008.
Chris@16: //  Use, modification and distribution are subject to the
Chris@16: //  Boost Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: //
Chris@16: // Wrapper that works with mpfr_class defined in gmpfrxx.h
Chris@16: // See http://math.berkeley.edu/~wilken/code/gmpfrxx/
Chris@16: // Also requires the gmp and mpfr libraries.
Chris@16: //
Chris@16: 
Chris@16: #ifndef BOOST_MATH_E_FLOAT_BINDINGS_HPP
Chris@16: #define BOOST_MATH_E_FLOAT_BINDINGS_HPP
Chris@16: 
Chris@16: #include <boost/config.hpp>
Chris@16: 
Chris@16: 
Chris@16: #include <e_float/e_float.h>
Chris@16: #include <functions/functions.h>
Chris@16: 
Chris@16: #include <boost/math/tools/precision.hpp>
Chris@16: #include <boost/math/tools/real_cast.hpp>
Chris@16: #include <boost/math/policies/policy.hpp>
Chris@16: #include <boost/math/distributions/fwd.hpp>
Chris@16: #include <boost/math/special_functions/math_fwd.hpp>
Chris@16: #include <boost/math/special_functions/fpclassify.hpp>
Chris@16: #include <boost/math/bindings/detail/big_digamma.hpp>
Chris@16: #include <boost/math/bindings/detail/big_lanczos.hpp>
Chris@16: #include <boost/lexical_cast.hpp>
Chris@16: 
Chris@16: 
Chris@16: namespace boost{ namespace math{ namespace ef{
Chris@16: 
Chris@16: class e_float
Chris@16: {
Chris@16: public:
Chris@16:    // Constructors:
Chris@16:    e_float() {}
Chris@16:    e_float(const ::e_float& c) : m_value(c){}
Chris@16:    e_float(char c)
Chris@16:    {
Chris@16:       m_value = ::e_float(c);
Chris@16:    }
Chris@16: #ifndef BOOST_NO_INTRINSIC_WCHAR_T
Chris@16:    e_float(wchar_t c)
Chris@16:    {
Chris@16:       m_value = ::e_float(c);
Chris@16:    }
Chris@16: #endif
Chris@16:    e_float(unsigned char c)
Chris@16:    {
Chris@16:       m_value = ::e_float(c);
Chris@16:    }
Chris@16:    e_float(signed char c)
Chris@16:    {
Chris@16:       m_value = ::e_float(c);
Chris@16:    }
Chris@16:    e_float(unsigned short c)
Chris@16:    {
Chris@16:       m_value = ::e_float(c);
Chris@16:    }
Chris@16:    e_float(short c)
Chris@16:    {
Chris@16:       m_value = ::e_float(c);
Chris@16:    }
Chris@16:    e_float(unsigned int c)
Chris@16:    {
Chris@16:       m_value = ::e_float(c);
Chris@16:    }
Chris@16:    e_float(int c)
Chris@16:    {
Chris@16:       m_value = ::e_float(c);
Chris@16:    }
Chris@16:    e_float(unsigned long c)
Chris@16:    {
Chris@16:       m_value = ::e_float((UINT64)c);
Chris@16:    }
Chris@16:    e_float(long c)
Chris@16:    {
Chris@16:       m_value = ::e_float((INT64)c);
Chris@16:    }
Chris@16: #ifdef BOOST_HAS_LONG_LONG
Chris@16:    e_float(boost::ulong_long_type c)
Chris@16:    {
Chris@16:       m_value = ::e_float(c);
Chris@16:    }
Chris@16:    e_float(boost::long_long_type c)
Chris@16:    {
Chris@16:       m_value = ::e_float(c);
Chris@16:    }
Chris@16: #endif
Chris@16:    e_float(float c)
Chris@16:    {
Chris@16:       assign_large_real(c);
Chris@16:    }
Chris@16:    e_float(double c)
Chris@16:    {
Chris@16:       assign_large_real(c);
Chris@16:    }
Chris@16:    e_float(long double c)
Chris@16:    {
Chris@16:       assign_large_real(c);
Chris@16:    }
Chris@16: 
Chris@16:    // Assignment:
Chris@16:    e_float& operator=(char c) { m_value = ::e_float(c); return *this; }
Chris@16:    e_float& operator=(unsigned char c) { m_value = ::e_float(c); return *this; }
Chris@16:    e_float& operator=(signed char c) { m_value = ::e_float(c); return *this; }
Chris@16: #ifndef BOOST_NO_INTRINSIC_WCHAR_T
Chris@16:    e_float& operator=(wchar_t c) { m_value = ::e_float(c); return *this; }
Chris@16: #endif
Chris@16:    e_float& operator=(short c) { m_value = ::e_float(c); return *this; }
Chris@16:    e_float& operator=(unsigned short c) { m_value = ::e_float(c); return *this; }
Chris@16:    e_float& operator=(int c) { m_value = ::e_float(c); return *this; }
Chris@16:    e_float& operator=(unsigned int c) { m_value = ::e_float(c); return *this; }
Chris@16:    e_float& operator=(long c) { m_value = ::e_float((INT64)c); return *this; }
Chris@16:    e_float& operator=(unsigned long c) { m_value = ::e_float((UINT64)c); return *this; }
Chris@16: #ifdef BOOST_HAS_LONG_LONG
Chris@16:    e_float& operator=(boost::long_long_type c) { m_value = ::e_float(c); return *this; }
Chris@16:    e_float& operator=(boost::ulong_long_type c) { m_value = ::e_float(c); return *this; }
Chris@16: #endif
Chris@16:    e_float& operator=(float c) { assign_large_real(c); return *this; }
Chris@16:    e_float& operator=(double c) { assign_large_real(c); return *this; }
Chris@16:    e_float& operator=(long double c) { assign_large_real(c); return *this; }
Chris@16: 
Chris@16:    // Access:
Chris@16:    ::e_float& value(){ return m_value; }
Chris@16:    ::e_float const& value()const{ return m_value; }
Chris@16: 
Chris@16:    // Member arithmetic:
Chris@16:    e_float& operator+=(const e_float& other)
Chris@16:    { m_value += other.value(); return *this; }
Chris@16:    e_float& operator-=(const e_float& other)
Chris@16:    { m_value -= other.value(); return *this; }
Chris@16:    e_float& operator*=(const e_float& other)
Chris@16:    { m_value *= other.value(); return *this; }
Chris@16:    e_float& operator/=(const e_float& other)
Chris@16:    { m_value /= other.value(); return *this; }
Chris@16:    e_float operator-()const
Chris@16:    { return -m_value; }
Chris@16:    e_float const& operator+()const
Chris@16:    { return *this; }
Chris@16: 
Chris@16: private:
Chris@16:    ::e_float m_value;
Chris@16: 
Chris@16:    template <class V>
Chris@16:    void assign_large_real(const V& a)
Chris@16:    {
Chris@16:       using std::frexp;
Chris@16:       using std::ldexp;
Chris@16:       using std::floor;
Chris@16:       if (a == 0) {
Chris@16:          m_value = ::ef::zero();
Chris@16:          return;
Chris@16:       }
Chris@16: 
Chris@16:       if (a == 1) {
Chris@16:          m_value = ::ef::one();
Chris@16:          return;
Chris@16:       }
Chris@16: 
Chris@16:       if ((boost::math::isinf)(a))
Chris@16:       {
Chris@16:          m_value = a > 0 ? m_value.my_value_inf() : -m_value.my_value_inf();
Chris@16:          return;
Chris@16:       }
Chris@16:       if((boost::math::isnan)(a))
Chris@16:       {
Chris@16:          m_value = m_value.my_value_nan();
Chris@16:          return;
Chris@16:       }
Chris@16: 
Chris@16:       int e;
Chris@16:       long double f, term;
Chris@16:       ::e_float t;
Chris@16:       m_value = ::ef::zero();
Chris@16: 
Chris@16:       f = frexp(a, &e);
Chris@16: 
Chris@16:       ::e_float shift = ::ef::pow2(30);
Chris@16: 
Chris@16:       while(f)
Chris@16:       {
Chris@16:          // extract 30 bits from f:
Chris@16:          f = ldexp(f, 30);
Chris@16:          term = floor(f);
Chris@16:          e -= 30;
Chris@16:          m_value *= shift;
Chris@16:          m_value += ::e_float(static_cast<INT64>(term));
Chris@16:          f -= term;
Chris@16:       }
Chris@16:       m_value *= ::ef::pow2(e);
Chris@16:    }
Chris@16: };
Chris@16: 
Chris@16: 
Chris@16: // Non-member arithmetic:
Chris@16: inline e_float operator+(const e_float& a, const e_float& b)
Chris@16: {
Chris@16:    e_float result(a);
Chris@16:    result += b;
Chris@16:    return result;
Chris@16: }
Chris@16: inline e_float operator-(const e_float& a, const e_float& b)
Chris@16: {
Chris@16:    e_float result(a);
Chris@16:    result -= b;
Chris@16:    return result;
Chris@16: }
Chris@16: inline e_float operator*(const e_float& a, const e_float& b)
Chris@16: {
Chris@16:    e_float result(a);
Chris@16:    result *= b;
Chris@16:    return result;
Chris@16: }
Chris@16: inline e_float operator/(const e_float& a, const e_float& b)
Chris@16: {
Chris@16:    e_float result(a);
Chris@16:    result /= b;
Chris@16:    return result;
Chris@16: }
Chris@16: 
Chris@16: // Comparison:
Chris@16: inline bool operator == (const e_float& a, const e_float& b)
Chris@16: { return a.value() == b.value() ? true : false; }
Chris@16: inline bool operator != (const e_float& a, const e_float& b)
Chris@16: { return a.value() != b.value() ? true : false;}
Chris@16: inline bool operator < (const e_float& a, const e_float& b)
Chris@16: { return a.value() < b.value() ? true : false; }
Chris@16: inline bool operator <= (const e_float& a, const e_float& b)
Chris@16: { return a.value() <= b.value() ? true : false; }
Chris@16: inline bool operator > (const e_float& a, const e_float& b)
Chris@16: { return a.value() > b.value() ? true : false; }
Chris@16: inline bool operator >= (const e_float& a, const e_float& b)
Chris@16: { return a.value() >= b.value() ? true : false; }
Chris@16: 
Chris@16: std::istream& operator >> (std::istream& is, e_float& f)
Chris@16: {
Chris@16:    return is >> f.value();
Chris@16: }
Chris@16: 
Chris@16: std::ostream& operator << (std::ostream& os, const e_float& f)
Chris@16: {
Chris@16:    return os << f.value();
Chris@16: }
Chris@16: 
Chris@16: inline e_float fabs(const e_float& v)
Chris@16: {
Chris@16:    return ::ef::fabs(v.value());
Chris@16: }
Chris@16: 
Chris@16: inline e_float abs(const e_float& v)
Chris@16: {
Chris@16:    return ::ef::fabs(v.value());
Chris@16: }
Chris@16: 
Chris@16: inline e_float floor(const e_float& v)
Chris@16: {
Chris@16:    return ::ef::floor(v.value());
Chris@16: }
Chris@16: 
Chris@16: inline e_float ceil(const e_float& v)
Chris@16: {
Chris@16:    return ::ef::ceil(v.value());
Chris@16: }
Chris@16: 
Chris@16: inline e_float pow(const e_float& v, const e_float& w)
Chris@16: {
Chris@16:    return ::ef::pow(v.value(), w.value());
Chris@16: }
Chris@16: 
Chris@16: inline e_float pow(const e_float& v, int i)
Chris@16: {
Chris@16:    return ::ef::pow(v.value(), ::e_float(i));
Chris@16: }
Chris@16: 
Chris@16: inline e_float exp(const e_float& v)
Chris@16: {
Chris@16:    return ::ef::exp(v.value());
Chris@16: }
Chris@16: 
Chris@16: inline e_float log(const e_float& v)
Chris@16: {
Chris@16:    return ::ef::log(v.value());
Chris@16: }
Chris@16: 
Chris@16: inline e_float sqrt(const e_float& v)
Chris@16: {
Chris@16:    return ::ef::sqrt(v.value());
Chris@16: }
Chris@16: 
Chris@16: inline e_float sin(const e_float& v)
Chris@16: {
Chris@16:    return ::ef::sin(v.value());
Chris@16: }
Chris@16: 
Chris@16: inline e_float cos(const e_float& v)
Chris@16: {
Chris@16:    return ::ef::cos(v.value());
Chris@16: }
Chris@16: 
Chris@16: inline e_float tan(const e_float& v)
Chris@16: {
Chris@16:    return ::ef::tan(v.value());
Chris@16: }
Chris@16: 
Chris@16: inline e_float acos(const e_float& v)
Chris@16: {
Chris@16:    return ::ef::acos(v.value());
Chris@16: }
Chris@16: 
Chris@16: inline e_float asin(const e_float& v)
Chris@16: {
Chris@16:    return ::ef::asin(v.value());
Chris@16: }
Chris@16: 
Chris@16: inline e_float atan(const e_float& v)
Chris@16: {
Chris@16:    return ::ef::atan(v.value());
Chris@16: }
Chris@16: 
Chris@16: inline e_float atan2(const e_float& v, const e_float& u)
Chris@16: {
Chris@16:    return ::ef::atan2(v.value(), u.value());
Chris@16: }
Chris@16: 
Chris@16: inline e_float ldexp(const e_float& v, int e)
Chris@16: {
Chris@16:    return v.value() * ::ef::pow2(e);
Chris@16: }
Chris@16: 
Chris@16: inline e_float frexp(const e_float& v, int* expon)
Chris@16: {
Chris@16:    double d;
Chris@16:    INT64 i;
Chris@16:    v.value().extract_parts(d, i);
Chris@16:    *expon = static_cast<int>(i);
Chris@16:    return v.value() * ::ef::pow2(-i);
Chris@16: }
Chris@16: 
Chris@16: inline e_float sinh (const e_float& x)
Chris@16: {
Chris@16:    return ::ef::sinh(x.value());
Chris@16: }
Chris@16: 
Chris@16: inline e_float cosh (const e_float& x)
Chris@16: {
Chris@16:    return ::ef::cosh(x.value());
Chris@16: }
Chris@16: 
Chris@16: inline e_float tanh (const e_float& x)
Chris@16: {
Chris@16:    return ::ef::tanh(x.value());
Chris@16: }
Chris@16: 
Chris@16: inline e_float asinh (const e_float& x)
Chris@16: {
Chris@16:    return ::ef::asinh(x.value());
Chris@16: }
Chris@16: 
Chris@16: inline e_float acosh (const e_float& x)
Chris@16: {
Chris@16:    return ::ef::acosh(x.value());
Chris@16: }
Chris@16: 
Chris@16: inline e_float atanh (const e_float& x)
Chris@16: {
Chris@16:    return ::ef::atanh(x.value());
Chris@16: }
Chris@16: 
Chris@16: e_float fmod(const e_float& v1, const e_float& v2)
Chris@16: {
Chris@16:    e_float n;
Chris@16:    if(v1 < 0)
Chris@16:       n = ceil(v1 / v2);
Chris@16:    else
Chris@16:       n = floor(v1 / v2);
Chris@16:    return v1 - n * v2;
Chris@16: }
Chris@16: 
Chris@16: } namespace detail{
Chris@16: 
Chris@16: template <>
Chris@16: inline int fpclassify_imp< boost::math::ef::e_float> BOOST_NO_MACRO_EXPAND(boost::math::ef::e_float x, const generic_tag<true>&)
Chris@16: {
Chris@16:    if(x.value().isnan())
Chris@16:       return FP_NAN;
Chris@16:    if(x.value().isinf())
Chris@16:       return FP_INFINITE;
Chris@16:    if(x == 0)
Chris@16:       return FP_ZERO;
Chris@16:    return FP_NORMAL;
Chris@16: }
Chris@16: 
Chris@16: } namespace ef{
Chris@16: 
Chris@16: template <class Policy>
Chris@16: inline int itrunc(const e_float& v, const Policy& pol)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING
Chris@16:    e_float r = boost::math::trunc(v, pol);
Chris@16:    if(fabs(r) > (std::numeric_limits<int>::max)())
Chris@16:       return static_cast<int>(policies::raise_rounding_error("boost::math::itrunc<%1%>(%1%)", 0, 0, v, pol));
Chris@16:    return static_cast<int>(r.value().extract_int64());
Chris@16: }
Chris@16: 
Chris@16: template <class Policy>
Chris@16: inline long ltrunc(const e_float& v, const Policy& pol)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING
Chris@16:    e_float r = boost::math::trunc(v, pol);
Chris@16:    if(fabs(r) > (std::numeric_limits<long>::max)())
Chris@16:       return static_cast<long>(policies::raise_rounding_error("boost::math::ltrunc<%1%>(%1%)", 0, 0L, v, pol));
Chris@16:    return static_cast<long>(r.value().extract_int64());
Chris@16: }
Chris@16: 
Chris@16: #ifdef BOOST_HAS_LONG_LONG
Chris@16: template <class Policy>
Chris@16: inline boost::long_long_type lltrunc(const e_float& v, const Policy& pol)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING
Chris@16:    e_float r = boost::math::trunc(v, pol);
Chris@16:    if(fabs(r) > (std::numeric_limits<boost::long_long_type>::max)())
Chris@16:       return static_cast<boost::long_long_type>(policies::raise_rounding_error("boost::math::lltrunc<%1%>(%1%)", 0, v, 0LL, pol).value().extract_int64());
Chris@16:    return static_cast<boost::long_long_type>(r.value().extract_int64());
Chris@16: }
Chris@16: #endif
Chris@16: 
Chris@16: template <class Policy>
Chris@16: inline int iround(const e_float& v, const Policy& pol)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING
Chris@16:    e_float r = boost::math::round(v, pol);
Chris@16:    if(fabs(r) > (std::numeric_limits<int>::max)())
Chris@16:       return static_cast<int>(policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, 0, pol).value().extract_int64());
Chris@16:    return static_cast<int>(r.value().extract_int64());
Chris@16: }
Chris@16: 
Chris@16: template <class Policy>
Chris@16: inline long lround(const e_float& v, const Policy& pol)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING
Chris@16:    e_float r = boost::math::round(v, pol);
Chris@16:    if(fabs(r) > (std::numeric_limits<long>::max)())
Chris@16:       return static_cast<long int>(policies::raise_rounding_error("boost::math::lround<%1%>(%1%)", 0, v, 0L, pol).value().extract_int64());
Chris@16:    return static_cast<long int>(r.value().extract_int64());
Chris@16: }
Chris@16: 
Chris@16: #ifdef BOOST_HAS_LONG_LONG
Chris@16: template <class Policy>
Chris@16: inline boost::long_long_type llround(const e_float& v, const Policy& pol)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING
Chris@16:    e_float r = boost::math::round(v, pol);
Chris@16:    if(fabs(r) > (std::numeric_limits<boost::long_long_type>::max)())
Chris@16:       return static_cast<boost::long_long_type>(policies::raise_rounding_error("boost::math::llround<%1%>(%1%)", 0, v, 0LL, pol).value().extract_int64());
Chris@16:    return static_cast<boost::long_long_type>(r.value().extract_int64());
Chris@16: }
Chris@16: #endif
Chris@16: 
Chris@16: }}}
Chris@16: 
Chris@16: namespace std{
Chris@16: 
Chris@16:    template<>
Chris@16:    class numeric_limits< ::boost::math::ef::e_float> : public numeric_limits< ::e_float>
Chris@16:    {
Chris@16:    public:
Chris@16:       static const ::boost::math::ef::e_float (min) (void)
Chris@16:       {
Chris@16:          return (numeric_limits< ::e_float>::min)();
Chris@16:       }
Chris@16:       static const ::boost::math::ef::e_float (max) (void)
Chris@16:       {
Chris@16:          return (numeric_limits< ::e_float>::max)();
Chris@16:       }
Chris@16:       static const ::boost::math::ef::e_float epsilon (void)
Chris@16:       {
Chris@16:          return (numeric_limits< ::e_float>::epsilon)();
Chris@16:       }
Chris@16:       static const ::boost::math::ef::e_float round_error(void)
Chris@16:       {
Chris@16:          return (numeric_limits< ::e_float>::round_error)();
Chris@16:       }
Chris@16:       static const ::boost::math::ef::e_float infinity (void)
Chris@16:       {
Chris@16:          return (numeric_limits< ::e_float>::infinity)();
Chris@16:       }
Chris@16:       static const ::boost::math::ef::e_float quiet_NaN (void)
Chris@16:       {
Chris@16:          return (numeric_limits< ::e_float>::quiet_NaN)();
Chris@16:       }
Chris@16:       //
Chris@16:       // e_float's supplied digits member is wrong 
Chris@16:       // - it should be same the same as digits 10
Chris@16:       // - given that radix is 10.
Chris@16:       //
Chris@16:       static const int digits = digits10;
Chris@16:    };
Chris@16: 
Chris@16: } // namespace std
Chris@16: 
Chris@16: namespace boost{ namespace math{
Chris@16: 
Chris@16: namespace policies{
Chris@16: 
Chris@16: template <class Policy>
Chris@16: struct precision< ::boost::math::ef::e_float, Policy>
Chris@16: {
Chris@16:    typedef typename Policy::precision_type precision_type;
Chris@16:    typedef digits2<((::std::numeric_limits< ::boost::math::ef::e_float>::digits10 + 1) * 1000L) / 301L> digits_2;
Chris@16:    typedef typename mpl::if_c<
Chris@16:       ((digits_2::value <= precision_type::value) 
Chris@16:       || (Policy::precision_type::value <= 0)),
Chris@16:       // Default case, full precision for RealType:
Chris@16:       digits_2,
Chris@16:       // User customised precision:
Chris@16:       precision_type
Chris@16:    >::type type;
Chris@16: };
Chris@16: 
Chris@16: }
Chris@16: 
Chris@16: namespace tools{
Chris@16: 
Chris@16: template <>
Chris@16: inline int digits< ::boost::math::ef::e_float>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC( ::boost::math::ef::e_float))
Chris@16: {
Chris@16:    return ((::std::numeric_limits< ::boost::math::ef::e_float>::digits10 + 1) * 1000L) / 301L;
Chris@16: }
Chris@16: 
Chris@16: template <>
Chris@16: inline  ::boost::math::ef::e_float root_epsilon< ::boost::math::ef::e_float>()
Chris@16: {
Chris@16:    return detail::root_epsilon_imp(static_cast< ::boost::math::ef::e_float const*>(0), mpl::int_<0>());
Chris@16: }
Chris@16: 
Chris@16: template <>
Chris@16: inline  ::boost::math::ef::e_float forth_root_epsilon< ::boost::math::ef::e_float>()
Chris@16: {
Chris@16:    return detail::forth_root_epsilon_imp(static_cast< ::boost::math::ef::e_float const*>(0), mpl::int_<0>());
Chris@16: }
Chris@16: 
Chris@16: }
Chris@16: 
Chris@16: namespace lanczos{
Chris@16: 
Chris@16: template<class Policy>
Chris@16: struct lanczos<boost::math::ef::e_float, Policy>
Chris@16: {
Chris@16:    typedef typename mpl::if_c<
Chris@16:       std::numeric_limits< ::e_float>::digits10 < 22,
Chris@16:       lanczos13UDT,
Chris@16:       typename mpl::if_c<
Chris@16:          std::numeric_limits< ::e_float>::digits10 < 36,
Chris@16:          lanczos22UDT,
Chris@16:          typename mpl::if_c<
Chris@16:             std::numeric_limits< ::e_float>::digits10 < 50,
Chris@16:             lanczos31UDT,
Chris@16:             typename mpl::if_c<
Chris@16:                std::numeric_limits< ::e_float>::digits10 < 110,
Chris@16:                lanczos61UDT,
Chris@16:                undefined_lanczos
Chris@16:             >::type
Chris@16:          >::type
Chris@16:       >::type
Chris@16:    >::type type;
Chris@16: };
Chris@16: 
Chris@16: } // namespace lanczos
Chris@16: 
Chris@16: template <class Policy>
Chris@16: inline boost::math::ef::e_float skewness(const extreme_value_distribution<boost::math::ef::e_float, Policy>& /*dist*/)
Chris@16: {
Chris@16:    //
Chris@16:    // This is 12 * sqrt(6) * zeta(3) / pi^3:
Chris@16:    // See http://mathworld.wolfram.com/ExtremeValueDistribution.html
Chris@16:    //
Chris@16:    return boost::lexical_cast<boost::math::ef::e_float>("1.1395470994046486574927930193898461120875997958366");
Chris@16: }
Chris@16: 
Chris@16: template <class Policy>
Chris@16: inline boost::math::ef::e_float skewness(const rayleigh_distribution<boost::math::ef::e_float, Policy>& /*dist*/)
Chris@16: {
Chris@16:   // using namespace boost::math::constants;
Chris@16:   return boost::lexical_cast<boost::math::ef::e_float>("0.63111065781893713819189935154422777984404221106391");
Chris@16:   // Computed using NTL at 150 bit, about 50 decimal digits.
Chris@16:   // return 2 * root_pi<RealType>() * pi_minus_three<RealType>() / pow23_four_minus_pi<RealType>();
Chris@16: }
Chris@16: 
Chris@16: template <class Policy>
Chris@16: inline boost::math::ef::e_float kurtosis(const rayleigh_distribution<boost::math::ef::e_float, Policy>& /*dist*/)
Chris@16: {
Chris@16:   // using namespace boost::math::constants;
Chris@16:   return boost::lexical_cast<boost::math::ef::e_float>("3.2450893006876380628486604106197544154170667057995");
Chris@16:   // Computed using NTL at 150 bit, about 50 decimal digits.
Chris@16:   // return 3 - (6 * pi<RealType>() * pi<RealType>() - 24 * pi<RealType>() + 16) /
Chris@16:   // (four_minus_pi<RealType>() * four_minus_pi<RealType>());
Chris@16: }
Chris@16: 
Chris@16: template <class Policy>
Chris@16: inline boost::math::ef::e_float kurtosis_excess(const rayleigh_distribution<boost::math::ef::e_float, Policy>& /*dist*/)
Chris@16: {
Chris@16:   //using namespace boost::math::constants;
Chris@16:   // Computed using NTL at 150 bit, about 50 decimal digits.
Chris@16:   return boost::lexical_cast<boost::math::ef::e_float>("0.2450893006876380628486604106197544154170667057995");
Chris@16:   // return -(6 * pi<RealType>() * pi<RealType>() - 24 * pi<RealType>() + 16) /
Chris@16:   //   (four_minus_pi<RealType>() * four_minus_pi<RealType>());
Chris@16: } // kurtosis
Chris@16: 
Chris@16: namespace detail{
Chris@16: 
Chris@16: //
Chris@16: // Version of Digamma accurate to ~100 decimal digits.
Chris@16: //
Chris@16: template <class Policy>
Chris@16: boost::math::ef::e_float digamma_imp(boost::math::ef::e_float x, const mpl::int_<0>* , const Policy& pol)
Chris@16: {
Chris@16:    //
Chris@16:    // This handles reflection of negative arguments, and all our
Chris@16:    // eboost::math::ef::e_floator handling, then forwards to the T-specific approximation.
Chris@16:    //
Chris@16:    BOOST_MATH_STD_USING // ADL of std functions.
Chris@16: 
Chris@16:    boost::math::ef::e_float result = 0;
Chris@16:    //
Chris@16:    // Check for negative arguments and use reflection:
Chris@16:    //
Chris@16:    if(x < 0)
Chris@16:    {
Chris@16:       // Reflect:
Chris@16:       x = 1 - x;
Chris@16:       // Argument reduction for tan:
Chris@16:       boost::math::ef::e_float remainder = x - floor(x);
Chris@16:       // Shift to negative if > 0.5:
Chris@16:       if(remainder > 0.5)
Chris@16:       {
Chris@16:          remainder -= 1;
Chris@16:       }
Chris@16:       //
Chris@16:       // check for evaluation at a negative pole:
Chris@16:       //
Chris@16:       if(remainder == 0)
Chris@16:       {
Chris@16:          return policies::raise_pole_error<boost::math::ef::e_float>("boost::math::digamma<%1%>(%1%)", 0, (1-x), pol);
Chris@16:       }
Chris@16:       result = constants::pi<boost::math::ef::e_float>() / tan(constants::pi<boost::math::ef::e_float>() * remainder);
Chris@16:    }
Chris@16:    result += big_digamma(x);
Chris@16:    return result;
Chris@16: }
Chris@16: boost::math::ef::e_float bessel_i0(boost::math::ef::e_float x)
Chris@16: {
Chris@16:     static const boost::math::ef::e_float P1[] = {
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-2.2335582639474375249e+15"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-5.5050369673018427753e+14"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-3.2940087627407749166e+13"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-8.4925101247114157499e+11"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-1.1912746104985237192e+10"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-1.0313066708737980747e+08"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-5.9545626019847898221e+05"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-2.4125195876041896775e+03"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-7.0935347449210549190e+00"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-1.5453977791786851041e-02"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-2.5172644670688975051e-05"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-3.0517226450451067446e-08"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-2.6843448573468483278e-11"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-1.5982226675653184646e-14"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-5.2487866627945699800e-18"),
Chris@16:     };
Chris@16:     static const boost::math::ef::e_float Q1[] = {
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-2.2335582639474375245e+15"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("7.8858692566751002988e+12"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-1.2207067397808979846e+10"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("1.0377081058062166144e+07"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-4.8527560179962773045e+03"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("1.0"),
Chris@16:     };
Chris@16:     static const boost::math::ef::e_float P2[] = {
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-2.2210262233306573296e-04"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("1.3067392038106924055e-02"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-4.4700805721174453923e-01"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("5.5674518371240761397e+00"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-2.3517945679239481621e+01"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("3.1611322818701131207e+01"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-9.6090021968656180000e+00"),
Chris@16:     };
Chris@16:     static const boost::math::ef::e_float Q2[] = {
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-5.5194330231005480228e-04"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("3.2547697594819615062e-02"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-1.1151759188741312645e+00"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("1.3982595353892851542e+01"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-6.0228002066743340583e+01"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("8.5539563258012929600e+01"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("-3.1446690275135491500e+01"),
Chris@16:         boost::lexical_cast<boost::math::ef::e_float>("1.0"),
Chris@16:     };
Chris@16:     boost::math::ef::e_float value, factor, r;
Chris@16: 
Chris@16:     BOOST_MATH_STD_USING
Chris@16:     using namespace boost::math::tools;
Chris@16: 
Chris@16:     if (x < 0)
Chris@16:     {
Chris@16:         x = -x;                         // even function
Chris@16:     }
Chris@16:     if (x == 0)
Chris@16:     {
Chris@16:         return static_cast<boost::math::ef::e_float>(1);
Chris@16:     }
Chris@16:     if (x <= 15)                        // x in (0, 15]
Chris@16:     {
Chris@16:         boost::math::ef::e_float y = x * x;
Chris@16:         value = evaluate_polynomial(P1, y) / evaluate_polynomial(Q1, y);
Chris@16:     }
Chris@16:     else                                // x in (15, \infty)
Chris@16:     {
Chris@16:         boost::math::ef::e_float y = 1 / x - boost::math::ef::e_float(1) / 15;
Chris@16:         r = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y);
Chris@16:         factor = exp(x) / sqrt(x);
Chris@16:         value = factor * r;
Chris@16:     }
Chris@16: 
Chris@16:     return value;
Chris@16: }
Chris@16: 
Chris@16: boost::math::ef::e_float bessel_i1(boost::math::ef::e_float x)
Chris@16: {
Chris@16:     static const boost::math::ef::e_float P1[] = {
Chris@16:         lexical_cast<boost::math::ef::e_float>("-1.4577180278143463643e+15"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("-1.7732037840791591320e+14"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("-6.9876779648010090070e+12"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("-1.3357437682275493024e+11"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("-1.4828267606612366099e+09"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("-1.0588550724769347106e+07"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("-5.1894091982308017540e+04"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("-1.8225946631657315931e+02"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("-4.7207090827310162436e-01"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("-9.1746443287817501309e-04"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("-1.3466829827635152875e-06"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("-1.4831904935994647675e-09"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("-1.1928788903603238754e-12"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("-6.5245515583151902910e-16"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("-1.9705291802535139930e-19"),
Chris@16:     };
Chris@16:     static const boost::math::ef::e_float Q1[] = {
Chris@16:         lexical_cast<boost::math::ef::e_float>("-2.9154360556286927285e+15"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("9.7887501377547640438e+12"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("-1.4386907088588283434e+10"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("1.1594225856856884006e+07"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("-5.1326864679904189920e+03"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("1.0"),
Chris@16:     };
Chris@16:     static const boost::math::ef::e_float P2[] = {
Chris@16:         lexical_cast<boost::math::ef::e_float>("1.4582087408985668208e-05"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("-8.9359825138577646443e-04"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("2.9204895411257790122e-02"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("-3.4198728018058047439e-01"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("1.3960118277609544334e+00"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("-1.9746376087200685843e+00"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("8.5591872901933459000e-01"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("-6.0437159056137599999e-02"),
Chris@16:     };
Chris@16:     static const boost::math::ef::e_float Q2[] = {
Chris@16:         lexical_cast<boost::math::ef::e_float>("3.7510433111922824643e-05"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("-2.2835624489492512649e-03"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("7.4212010813186530069e-02"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("-8.5017476463217924408e-01"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("3.2593714889036996297e+00"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("-3.8806586721556593450e+00"),
Chris@16:         lexical_cast<boost::math::ef::e_float>("1.0"),
Chris@16:     };
Chris@16:     boost::math::ef::e_float value, factor, r, w;
Chris@16: 
Chris@16:     BOOST_MATH_STD_USING
Chris@16:     using namespace boost::math::tools;
Chris@16: 
Chris@16:     w = abs(x);
Chris@16:     if (x == 0)
Chris@16:     {
Chris@16:         return static_cast<boost::math::ef::e_float>(0);
Chris@16:     }
Chris@16:     if (w <= 15)                        // w in (0, 15]
Chris@16:     {
Chris@16:         boost::math::ef::e_float y = x * x;
Chris@16:         r = evaluate_polynomial(P1, y) / evaluate_polynomial(Q1, y);
Chris@16:         factor = w;
Chris@16:         value = factor * r;
Chris@16:     }
Chris@16:     else                                // w in (15, \infty)
Chris@16:     {
Chris@16:         boost::math::ef::e_float y = 1 / w - boost::math::ef::e_float(1) / 15;
Chris@16:         r = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y);
Chris@16:         factor = exp(w) / sqrt(w);
Chris@16:         value = factor * r;
Chris@16:     }
Chris@16: 
Chris@16:     if (x < 0)
Chris@16:     {
Chris@16:         value *= -value;                 // odd function
Chris@16:     }
Chris@16:     return value;
Chris@16: }
Chris@16: 
Chris@16: } // namespace detail
Chris@16: 
Chris@16: }}
Chris@16: #endif // BOOST_MATH_E_FLOAT_BINDINGS_HPP
Chris@16: