479 lines
17 KiB
Plaintext
479 lines
17 KiB
Plaintext
// Copyright John Maddock 2006.
|
|
// Use, modification and distribution are subject to the
|
|
// Boost Software License, Version 1.0. (See accompanying file
|
|
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
|
|
|
|
// Test real concept.
|
|
|
|
// real_concept is an archetype for User defined Real types.
|
|
|
|
// This file defines the features, constructors, operators, functions...
|
|
// that are essential to use mathematical and statistical functions.
|
|
// The template typename "RealType" is used where this type
|
|
// (as well as the normal built-in types, float, double & long double)
|
|
// can be used.
|
|
// That this is the minimum set is confirmed by use as a type
|
|
// in tests of all functions & distributions, for example:
|
|
// test_spots(0.F); & test_spots(0.); for float and double, but also
|
|
// test_spots(boost::math::concepts::real_concept(0.));
|
|
// NTL quad_float type is an example of a type meeting the requirements,
|
|
// but note minor additions are needed - see ntl.diff and documentation
|
|
// "Using With NTL - a High-Precision Floating-Point Library".
|
|
|
|
#ifndef BOOST_MATH_REAL_CONCEPT_HPP
|
|
#define BOOST_MATH_REAL_CONCEPT_HPP
|
|
|
|
#include <boost/config.hpp>
|
|
#include <boost/limits.hpp>
|
|
#include <boost/math/special_functions/round.hpp>
|
|
#include <boost/math/special_functions/trunc.hpp>
|
|
#include <boost/math/special_functions/modf.hpp>
|
|
#include <boost/math/tools/big_constant.hpp>
|
|
#include <boost/math/tools/precision.hpp>
|
|
#include <boost/math/policies/policy.hpp>
|
|
#if defined(__SGI_STL_PORT)
|
|
# include <boost/math/tools/real_cast.hpp>
|
|
#endif
|
|
#include <ostream>
|
|
#include <istream>
|
|
#include <boost/config/no_tr1/cmath.hpp>
|
|
#include <math.h> // fmodl
|
|
|
|
#if defined(__SGI_STL_PORT) || defined(_RWSTD_VER) || defined(__LIBCOMO__)
|
|
# include <cstdio>
|
|
#endif
|
|
|
|
namespace boost{ namespace math{
|
|
|
|
namespace concepts
|
|
{
|
|
|
|
#ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
|
|
typedef double real_concept_base_type;
|
|
#else
|
|
typedef long double real_concept_base_type;
|
|
#endif
|
|
|
|
class real_concept
|
|
{
|
|
public:
|
|
// Constructors:
|
|
real_concept() : m_value(0){}
|
|
real_concept(char c) : m_value(c){}
|
|
#ifndef BOOST_NO_INTRINSIC_WCHAR_T
|
|
real_concept(wchar_t c) : m_value(c){}
|
|
#endif
|
|
real_concept(unsigned char c) : m_value(c){}
|
|
real_concept(signed char c) : m_value(c){}
|
|
real_concept(unsigned short c) : m_value(c){}
|
|
real_concept(short c) : m_value(c){}
|
|
real_concept(unsigned int c) : m_value(c){}
|
|
real_concept(int c) : m_value(c){}
|
|
real_concept(unsigned long c) : m_value(c){}
|
|
real_concept(long c) : m_value(c){}
|
|
#if defined(__DECCXX) || defined(__SUNPRO_CC)
|
|
real_concept(unsigned long long c) : m_value(static_cast<real_concept_base_type>(c)){}
|
|
real_concept(long long c) : m_value(static_cast<real_concept_base_type>(c)){}
|
|
#elif defined(BOOST_HAS_LONG_LONG)
|
|
real_concept(boost::ulong_long_type c) : m_value(static_cast<real_concept_base_type>(c)){}
|
|
real_concept(boost::long_long_type c) : m_value(static_cast<real_concept_base_type>(c)){}
|
|
#elif defined(BOOST_HAS_MS_INT64)
|
|
real_concept(unsigned __int64 c) : m_value(static_cast<real_concept_base_type>(c)){}
|
|
real_concept(__int64 c) : m_value(static_cast<real_concept_base_type>(c)){}
|
|
#endif
|
|
real_concept(float c) : m_value(c){}
|
|
real_concept(double c) : m_value(c){}
|
|
real_concept(long double c) : m_value(c){}
|
|
#ifdef BOOST_MATH_USE_FLOAT128
|
|
real_concept(BOOST_MATH_FLOAT128_TYPE c) : m_value(c){}
|
|
#endif
|
|
|
|
// Assignment:
|
|
real_concept& operator=(char c) { m_value = c; return *this; }
|
|
real_concept& operator=(unsigned char c) { m_value = c; return *this; }
|
|
real_concept& operator=(signed char c) { m_value = c; return *this; }
|
|
#ifndef BOOST_NO_INTRINSIC_WCHAR_T
|
|
real_concept& operator=(wchar_t c) { m_value = c; return *this; }
|
|
#endif
|
|
real_concept& operator=(short c) { m_value = c; return *this; }
|
|
real_concept& operator=(unsigned short c) { m_value = c; return *this; }
|
|
real_concept& operator=(int c) { m_value = c; return *this; }
|
|
real_concept& operator=(unsigned int c) { m_value = c; return *this; }
|
|
real_concept& operator=(long c) { m_value = c; return *this; }
|
|
real_concept& operator=(unsigned long c) { m_value = c; return *this; }
|
|
#ifdef BOOST_HAS_LONG_LONG
|
|
real_concept& operator=(boost::long_long_type c) { m_value = static_cast<real_concept_base_type>(c); return *this; }
|
|
real_concept& operator=(boost::ulong_long_type c) { m_value = static_cast<real_concept_base_type>(c); return *this; }
|
|
#endif
|
|
real_concept& operator=(float c) { m_value = c; return *this; }
|
|
real_concept& operator=(double c) { m_value = c; return *this; }
|
|
real_concept& operator=(long double c) { m_value = c; return *this; }
|
|
|
|
// Access:
|
|
real_concept_base_type value()const{ return m_value; }
|
|
|
|
// Member arithmetic:
|
|
real_concept& operator+=(const real_concept& other)
|
|
{ m_value += other.value(); return *this; }
|
|
real_concept& operator-=(const real_concept& other)
|
|
{ m_value -= other.value(); return *this; }
|
|
real_concept& operator*=(const real_concept& other)
|
|
{ m_value *= other.value(); return *this; }
|
|
real_concept& operator/=(const real_concept& other)
|
|
{ m_value /= other.value(); return *this; }
|
|
real_concept operator-()const
|
|
{ return -m_value; }
|
|
real_concept const& operator+()const
|
|
{ return *this; }
|
|
real_concept& operator++()
|
|
{ ++m_value; return *this; }
|
|
real_concept& operator--()
|
|
{ --m_value; return *this; }
|
|
|
|
private:
|
|
real_concept_base_type m_value;
|
|
};
|
|
|
|
// Non-member arithmetic:
|
|
inline real_concept operator+(const real_concept& a, const real_concept& b)
|
|
{
|
|
real_concept result(a);
|
|
result += b;
|
|
return result;
|
|
}
|
|
inline real_concept operator-(const real_concept& a, const real_concept& b)
|
|
{
|
|
real_concept result(a);
|
|
result -= b;
|
|
return result;
|
|
}
|
|
inline real_concept operator*(const real_concept& a, const real_concept& b)
|
|
{
|
|
real_concept result(a);
|
|
result *= b;
|
|
return result;
|
|
}
|
|
inline real_concept operator/(const real_concept& a, const real_concept& b)
|
|
{
|
|
real_concept result(a);
|
|
result /= b;
|
|
return result;
|
|
}
|
|
|
|
// Comparison:
|
|
inline bool operator == (const real_concept& a, const real_concept& b)
|
|
{ return a.value() == b.value(); }
|
|
inline bool operator != (const real_concept& a, const real_concept& b)
|
|
{ return a.value() != b.value();}
|
|
inline bool operator < (const real_concept& a, const real_concept& b)
|
|
{ return a.value() < b.value(); }
|
|
inline bool operator <= (const real_concept& a, const real_concept& b)
|
|
{ return a.value() <= b.value(); }
|
|
inline bool operator > (const real_concept& a, const real_concept& b)
|
|
{ return a.value() > b.value(); }
|
|
inline bool operator >= (const real_concept& a, const real_concept& b)
|
|
{ return a.value() >= b.value(); }
|
|
|
|
// Non-member functions:
|
|
inline real_concept acos(real_concept a)
|
|
{ return std::acos(a.value()); }
|
|
inline real_concept cos(real_concept a)
|
|
{ return std::cos(a.value()); }
|
|
inline real_concept asin(real_concept a)
|
|
{ return std::asin(a.value()); }
|
|
inline real_concept atan(real_concept a)
|
|
{ return std::atan(a.value()); }
|
|
inline real_concept atan2(real_concept a, real_concept b)
|
|
{ return std::atan2(a.value(), b.value()); }
|
|
inline real_concept ceil(real_concept a)
|
|
{ return std::ceil(a.value()); }
|
|
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
|
|
// I've seen std::fmod(long double) crash on some platforms
|
|
// so use fmodl instead:
|
|
#ifdef _WIN32_WCE
|
|
//
|
|
// Ugly workaround for macro fmodl:
|
|
//
|
|
inline long double call_fmodl(long double a, long double b)
|
|
{ return fmodl(a, b); }
|
|
inline real_concept fmod(real_concept a, real_concept b)
|
|
{ return call_fmodl(a.value(), b.value()); }
|
|
#else
|
|
inline real_concept fmod(real_concept a, real_concept b)
|
|
{ return fmodl(a.value(), b.value()); }
|
|
#endif
|
|
#endif
|
|
inline real_concept cosh(real_concept a)
|
|
{ return std::cosh(a.value()); }
|
|
inline real_concept exp(real_concept a)
|
|
{ return std::exp(a.value()); }
|
|
inline real_concept fabs(real_concept a)
|
|
{ return std::fabs(a.value()); }
|
|
inline real_concept abs(real_concept a)
|
|
{ return std::abs(a.value()); }
|
|
inline real_concept floor(real_concept a)
|
|
{ return std::floor(a.value()); }
|
|
inline real_concept modf(real_concept a, real_concept* ipart)
|
|
{
|
|
#ifdef __MINGW32__
|
|
real_concept_base_type ip;
|
|
real_concept_base_type result = boost::math::modf(a.value(), &ip);
|
|
*ipart = ip;
|
|
return result;
|
|
#else
|
|
real_concept_base_type ip;
|
|
real_concept_base_type result = std::modf(a.value(), &ip);
|
|
*ipart = ip;
|
|
return result;
|
|
#endif
|
|
}
|
|
inline real_concept frexp(real_concept a, int* expon)
|
|
{ return std::frexp(a.value(), expon); }
|
|
inline real_concept ldexp(real_concept a, int expon)
|
|
{ return std::ldexp(a.value(), expon); }
|
|
inline real_concept log(real_concept a)
|
|
{ return std::log(a.value()); }
|
|
inline real_concept log10(real_concept a)
|
|
{ return std::log10(a.value()); }
|
|
inline real_concept tan(real_concept a)
|
|
{ return std::tan(a.value()); }
|
|
inline real_concept pow(real_concept a, real_concept b)
|
|
{ return std::pow(a.value(), b.value()); }
|
|
#if !defined(__SUNPRO_CC)
|
|
inline real_concept pow(real_concept a, int b)
|
|
{ return std::pow(a.value(), b); }
|
|
#else
|
|
inline real_concept pow(real_concept a, int b)
|
|
{ return std::pow(a.value(), static_cast<real_concept_base_type>(b)); }
|
|
#endif
|
|
inline real_concept sin(real_concept a)
|
|
{ return std::sin(a.value()); }
|
|
inline real_concept sinh(real_concept a)
|
|
{ return std::sinh(a.value()); }
|
|
inline real_concept sqrt(real_concept a)
|
|
{ return std::sqrt(a.value()); }
|
|
inline real_concept tanh(real_concept a)
|
|
{ return std::tanh(a.value()); }
|
|
|
|
//
|
|
// Conversion and truncation routines:
|
|
//
|
|
template <class Policy>
|
|
inline int iround(const concepts::real_concept& v, const Policy& pol)
|
|
{ return boost::math::iround(v.value(), pol); }
|
|
inline int iround(const concepts::real_concept& v)
|
|
{ return boost::math::iround(v.value(), policies::policy<>()); }
|
|
template <class Policy>
|
|
inline long lround(const concepts::real_concept& v, const Policy& pol)
|
|
{ return boost::math::lround(v.value(), pol); }
|
|
inline long lround(const concepts::real_concept& v)
|
|
{ return boost::math::lround(v.value(), policies::policy<>()); }
|
|
|
|
#ifdef BOOST_HAS_LONG_LONG
|
|
template <class Policy>
|
|
inline boost::long_long_type llround(const concepts::real_concept& v, const Policy& pol)
|
|
{ return boost::math::llround(v.value(), pol); }
|
|
inline boost::long_long_type llround(const concepts::real_concept& v)
|
|
{ return boost::math::llround(v.value(), policies::policy<>()); }
|
|
#endif
|
|
|
|
template <class Policy>
|
|
inline int itrunc(const concepts::real_concept& v, const Policy& pol)
|
|
{ return boost::math::itrunc(v.value(), pol); }
|
|
inline int itrunc(const concepts::real_concept& v)
|
|
{ return boost::math::itrunc(v.value(), policies::policy<>()); }
|
|
template <class Policy>
|
|
inline long ltrunc(const concepts::real_concept& v, const Policy& pol)
|
|
{ return boost::math::ltrunc(v.value(), pol); }
|
|
inline long ltrunc(const concepts::real_concept& v)
|
|
{ return boost::math::ltrunc(v.value(), policies::policy<>()); }
|
|
|
|
#ifdef BOOST_HAS_LONG_LONG
|
|
template <class Policy>
|
|
inline boost::long_long_type lltrunc(const concepts::real_concept& v, const Policy& pol)
|
|
{ return boost::math::lltrunc(v.value(), pol); }
|
|
inline boost::long_long_type lltrunc(const concepts::real_concept& v)
|
|
{ return boost::math::lltrunc(v.value(), policies::policy<>()); }
|
|
#endif
|
|
|
|
// Streaming:
|
|
template <class charT, class traits>
|
|
inline std::basic_ostream<charT, traits>& operator<<(std::basic_ostream<charT, traits>& os, const real_concept& a)
|
|
{
|
|
return os << a.value();
|
|
}
|
|
template <class charT, class traits>
|
|
inline std::basic_istream<charT, traits>& operator>>(std::basic_istream<charT, traits>& is, real_concept& a)
|
|
{
|
|
#if defined(BOOST_MSVC) && defined(__SGI_STL_PORT)
|
|
//
|
|
// STLPort 5.1.4 has a problem reading long doubles from strings,
|
|
// see http://sourceforge.net/tracker/index.php?func=detail&aid=1811043&group_id=146814&atid=766244
|
|
//
|
|
double v;
|
|
is >> v;
|
|
a = v;
|
|
return is;
|
|
#elif defined(__SGI_STL_PORT) || defined(_RWSTD_VER) || defined(__LIBCOMO__) || defined(_LIBCPP_VERSION)
|
|
std::string s;
|
|
real_concept_base_type d;
|
|
is >> s;
|
|
std::sscanf(s.c_str(), "%Lf", &d);
|
|
a = d;
|
|
return is;
|
|
#else
|
|
real_concept_base_type v;
|
|
is >> v;
|
|
a = v;
|
|
return is;
|
|
#endif
|
|
}
|
|
|
|
} // namespace concepts
|
|
|
|
namespace tools
|
|
{
|
|
|
|
template <>
|
|
inline concepts::real_concept make_big_value<concepts::real_concept>(boost::math::tools::largest_float val, const char* , mpl::false_ const&, mpl::false_ const&)
|
|
{
|
|
return val; // Can't use lexical_cast here, sometimes it fails....
|
|
}
|
|
|
|
template <>
|
|
inline concepts::real_concept max_value<concepts::real_concept>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::real_concept))
|
|
{
|
|
return max_value<concepts::real_concept_base_type>();
|
|
}
|
|
|
|
template <>
|
|
inline concepts::real_concept min_value<concepts::real_concept>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::real_concept))
|
|
{
|
|
return min_value<concepts::real_concept_base_type>();
|
|
}
|
|
|
|
template <>
|
|
inline concepts::real_concept log_max_value<concepts::real_concept>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::real_concept))
|
|
{
|
|
return log_max_value<concepts::real_concept_base_type>();
|
|
}
|
|
|
|
template <>
|
|
inline concepts::real_concept log_min_value<concepts::real_concept>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::real_concept))
|
|
{
|
|
return log_min_value<concepts::real_concept_base_type>();
|
|
}
|
|
|
|
template <>
|
|
inline concepts::real_concept epsilon<concepts::real_concept>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::real_concept))
|
|
{
|
|
#ifdef __SUNPRO_CC
|
|
return std::numeric_limits<concepts::real_concept_base_type>::epsilon();
|
|
#else
|
|
return tools::epsilon<concepts::real_concept_base_type>();
|
|
#endif
|
|
}
|
|
|
|
template <>
|
|
inline BOOST_MATH_CONSTEXPR int digits<concepts::real_concept>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::real_concept)) BOOST_NOEXCEPT
|
|
{
|
|
// Assume number of significand bits is same as real_concept_base_type,
|
|
// unless std::numeric_limits<T>::is_specialized to provide digits.
|
|
return tools::digits<concepts::real_concept_base_type>();
|
|
// Note that if numeric_limits real concept is NOT specialized to provide digits10
|
|
// (or max_digits10) then the default precision of 6 decimal digits will be used
|
|
// by Boost test (giving misleading error messages like
|
|
// "difference between {9.79796} and {9.79796} exceeds 5.42101e-19%"
|
|
// and by Boost lexical cast and serialization causing loss of accuracy.
|
|
}
|
|
|
|
} // namespace tools
|
|
/*
|
|
namespace policies {
|
|
namespace detail {
|
|
|
|
template <class T>
|
|
inline concepts::real_concept raise_rounding_error(
|
|
const char*,
|
|
const char*,
|
|
const T& val,
|
|
const concepts::real_concept&,
|
|
const ::boost::math::policies::rounding_error< ::boost::math::policies::errno_on_error>&) BOOST_MATH_NOEXCEPT(T)
|
|
{
|
|
errno = ERANGE;
|
|
// This may or may not do the right thing, but the user asked for the error
|
|
// to be silent so here we go anyway:
|
|
return val > 0 ? boost::math::tools::max_value<concepts::real_concept>() : -boost::math::tools::max_value<concepts::real_concept>();
|
|
}
|
|
|
|
}
|
|
}*/
|
|
|
|
#if defined(__SGI_STL_PORT) || defined(BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS)
|
|
//
|
|
// We shouldn't really need these type casts any more, but there are some
|
|
// STLport iostream bugs we work around by using them....
|
|
//
|
|
namespace tools
|
|
{
|
|
// real_cast converts from T to integer and narrower floating-point types.
|
|
|
|
// Convert from T to integer types.
|
|
|
|
template <>
|
|
inline unsigned int real_cast<unsigned int, concepts::real_concept>(concepts::real_concept r)
|
|
{
|
|
return static_cast<unsigned int>(r.value());
|
|
}
|
|
|
|
template <>
|
|
inline int real_cast<int, concepts::real_concept>(concepts::real_concept r)
|
|
{
|
|
return static_cast<int>(r.value());
|
|
}
|
|
|
|
template <>
|
|
inline long real_cast<long, concepts::real_concept>(concepts::real_concept r)
|
|
{
|
|
return static_cast<long>(r.value());
|
|
}
|
|
|
|
// Converts from T to narrower floating-point types, float, double & long double.
|
|
|
|
template <>
|
|
inline float real_cast<float, concepts::real_concept>(concepts::real_concept r)
|
|
{
|
|
return static_cast<float>(r.value());
|
|
}
|
|
template <>
|
|
inline double real_cast<double, concepts::real_concept>(concepts::real_concept r)
|
|
{
|
|
return static_cast<double>(r.value());
|
|
}
|
|
template <>
|
|
inline long double real_cast<long double, concepts::real_concept>(concepts::real_concept r)
|
|
{
|
|
return r.value();
|
|
}
|
|
|
|
} // STLPort
|
|
|
|
#endif
|
|
|
|
#if BOOST_WORKAROUND(BOOST_MSVC, <= 1310)
|
|
//
|
|
// For some strange reason ADL sometimes fails to find the
|
|
// correct overloads, unless we bring these declarations into scope:
|
|
//
|
|
using concepts::itrunc;
|
|
using concepts::iround;
|
|
|
|
#endif
|
|
|
|
} // namespace math
|
|
} // namespace boost
|
|
|
|
#endif // BOOST_MATH_REAL_CONCEPT_HPP
|
|
|
|
|