| // Copyright John Maddock 2005-2006. |
| // 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) |
| |
| #ifndef BOOST_MATH_TOOLS_PRECISION_INCLUDED |
| #define BOOST_MATH_TOOLS_PRECISION_INCLUDED |
| |
| #ifdef _MSC_VER |
| #pragma once |
| #endif |
| |
| #include <boost/limits.hpp> |
| #include <boost/assert.hpp> |
| #include <boost/static_assert.hpp> |
| #include <boost/mpl/int.hpp> |
| #include <boost/mpl/bool.hpp> |
| #include <boost/mpl/if.hpp> |
| #include <boost/math/policies/policy.hpp> |
| |
| #include <iostream> |
| #include <iomanip> |
| // These two are for LDBL_MAN_DIG: |
| #include <limits.h> |
| #include <math.h> |
| |
| namespace boost{ namespace math |
| { |
| namespace tools |
| { |
| // If T is not specialized, the functions digits, max_value and min_value, |
| // all get synthesised automatically from std::numeric_limits. |
| // However, if numeric_limits is not specialised for type RealType, |
| // for example with NTL::RR type, then you will get a compiler error |
| // when code tries to use these functions, unless you explicitly specialise them. |
| |
| // For example if the precision of RealType varies at runtime, |
| // then numeric_limits support may not be appropriate, |
| // see boost/math/tools/ntl.hpp for examples like |
| // template <> NTL::RR max_value<NTL::RR> ... |
| // See Conceptual Requirements for Real Number Types. |
| |
| template <class T> |
| inline int digits(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(T)) |
| { |
| #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS |
| BOOST_STATIC_ASSERT( ::std::numeric_limits<T>::is_specialized); |
| #else |
| BOOST_ASSERT(::std::numeric_limits<T>::is_specialized); |
| #endif |
| return std::numeric_limits<T>::digits; |
| } |
| |
| template <class T> |
| inline T max_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE(T)) |
| { |
| #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS |
| BOOST_STATIC_ASSERT( ::std::numeric_limits<T>::is_specialized); |
| #else |
| BOOST_ASSERT(::std::numeric_limits<T>::is_specialized); |
| #endif |
| return (std::numeric_limits<T>::max)(); |
| } // Also used as a finite 'infinite' value for - and +infinity, for example: |
| // -max_value<double> = -1.79769e+308, max_value<double> = 1.79769e+308. |
| |
| template <class T> |
| inline T min_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE(T)) |
| { |
| #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS |
| BOOST_STATIC_ASSERT( ::std::numeric_limits<T>::is_specialized); |
| #else |
| BOOST_ASSERT(::std::numeric_limits<T>::is_specialized); |
| #endif |
| return (std::numeric_limits<T>::min)(); |
| } |
| |
| namespace detail{ |
| // |
| // Logarithmic limits come next, note that although |
| // we can compute these from the log of the max value |
| // that is not in general thread safe (if we cache the value) |
| // so it's better to specialise these: |
| // |
| // For type float first: |
| // |
| template <class T> |
| inline T log_max_value(const mpl::int_<128>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T)) |
| { |
| return 88.0f; |
| } |
| |
| template <class T> |
| inline T log_min_value(const mpl::int_<128>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T)) |
| { |
| return -87.0f; |
| } |
| // |
| // Now double: |
| // |
| template <class T> |
| inline T log_max_value(const mpl::int_<1024>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T)) |
| { |
| return 709.0; |
| } |
| |
| template <class T> |
| inline T log_min_value(const mpl::int_<1024>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T)) |
| { |
| return -708.0; |
| } |
| // |
| // 80 and 128-bit long doubles: |
| // |
| template <class T> |
| inline T log_max_value(const mpl::int_<16384>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T)) |
| { |
| return 11356.0L; |
| } |
| |
| template <class T> |
| inline T log_min_value(const mpl::int_<16384>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T)) |
| { |
| return -11355.0L; |
| } |
| |
| template <class T> |
| inline T log_max_value(const mpl::int_<0>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T)) |
| { |
| #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS |
| BOOST_STATIC_ASSERT( ::std::numeric_limits<T>::is_specialized); |
| #else |
| BOOST_ASSERT(::std::numeric_limits<T>::is_specialized); |
| #endif |
| BOOST_MATH_STD_USING |
| static const T val = log((std::numeric_limits<T>::max)()); |
| return val; |
| } |
| |
| template <class T> |
| inline T log_min_value(const mpl::int_<0>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T)) |
| { |
| #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS |
| BOOST_STATIC_ASSERT( ::std::numeric_limits<T>::is_specialized); |
| #else |
| BOOST_ASSERT(::std::numeric_limits<T>::is_specialized); |
| #endif |
| BOOST_MATH_STD_USING |
| static const T val = log((std::numeric_limits<T>::max)()); |
| return val; |
| } |
| |
| template <class T> |
| inline T epsilon(const mpl::true_& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T)) |
| { |
| return std::numeric_limits<T>::epsilon(); |
| } |
| |
| #if (defined(macintosh) || defined(__APPLE__) || defined(__APPLE_CC__)) && ((LDBL_MANT_DIG == 106) || (__LDBL_MANT_DIG__ == 106)) |
| template <> |
| inline long double epsilon<long double>(const mpl::true_& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(long double)) |
| { |
| // numeric_limits on Darwin tells lies here. |
| // This static assert fails for some unknown reason, so |
| // disabled for now... |
| // BOOST_STATIC_ASSERT(std::numeric_limits<long double>::digits == 106); |
| return 2.4651903288156618919116517665087e-32L; |
| } |
| #endif |
| |
| template <class T> |
| inline T epsilon(const mpl::false_& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T)) |
| { |
| BOOST_MATH_STD_USING // for ADL of std names |
| static const T eps = ldexp(static_cast<T>(1), 1-policies::digits<T, policies::policy<> >()); |
| return eps; |
| } |
| |
| } // namespace detail |
| |
| template <class T> |
| inline T log_max_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE(T)) |
| { |
| #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS |
| typedef typename mpl::if_c< |
| std::numeric_limits<T>::max_exponent == 128 |
| || std::numeric_limits<T>::max_exponent == 1024 |
| || std::numeric_limits<T>::max_exponent == 16384, |
| mpl::int_<std::numeric_limits<T>::max_exponent>, |
| mpl::int_<0> |
| >::type tag_type; |
| BOOST_STATIC_ASSERT( ::std::numeric_limits<T>::is_specialized); |
| return detail::log_max_value<T>(tag_type()); |
| #else |
| BOOST_ASSERT(::std::numeric_limits<T>::is_specialized); |
| BOOST_MATH_STD_USING |
| static const T val = log((std::numeric_limits<T>::max)()); |
| return val; |
| #endif |
| } |
| |
| template <class T> |
| inline T log_min_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE(T)) |
| { |
| #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS |
| typedef typename mpl::if_c< |
| std::numeric_limits<T>::max_exponent == 128 |
| || std::numeric_limits<T>::max_exponent == 1024 |
| || std::numeric_limits<T>::max_exponent == 16384, |
| mpl::int_<std::numeric_limits<T>::max_exponent>, |
| mpl::int_<0> |
| >::type tag_type; |
| |
| BOOST_STATIC_ASSERT( ::std::numeric_limits<T>::is_specialized); |
| return detail::log_min_value<T>(tag_type()); |
| #else |
| BOOST_ASSERT(::std::numeric_limits<T>::is_specialized); |
| BOOST_MATH_STD_USING |
| static const T val = log((std::numeric_limits<T>::min)()); |
| return val; |
| #endif |
| } |
| |
| template <class T> |
| inline T epsilon(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(T)) |
| { |
| #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS |
| return detail::epsilon<T>(mpl::bool_< ::std::numeric_limits<T>::is_specialized>()); |
| #else |
| return ::std::numeric_limits<T>::is_specialized ? |
| detail::epsilon<T>(mpl::true_()) : |
| detail::epsilon<T>(mpl::false_()); |
| #endif |
| } |
| |
| namespace detail{ |
| |
| template <class T> |
| inline T root_epsilon_imp(const mpl::int_<24>&) |
| { |
| return static_cast<T>(0.00034526698300124390839884978618400831996329879769945L); |
| } |
| |
| template <class T> |
| inline T root_epsilon_imp(const T*, const mpl::int_<53>&) |
| { |
| return static_cast<T>(0.1490116119384765625e-7L); |
| } |
| |
| template <class T> |
| inline T root_epsilon_imp(const T*, const mpl::int_<64>&) |
| { |
| return static_cast<T>(0.32927225399135962333569506281281311031656150598474e-9L); |
| } |
| |
| template <class T> |
| inline T root_epsilon_imp(const T*, const mpl::int_<113>&) |
| { |
| return static_cast<T>(0.1387778780781445675529539585113525390625e-16L); |
| } |
| |
| template <class T, class Tag> |
| inline T root_epsilon_imp(const T*, const Tag&) |
| { |
| BOOST_MATH_STD_USING |
| static const T r_eps = sqrt(tools::epsilon<T>()); |
| return r_eps; |
| } |
| |
| template <class T> |
| inline T forth_root_epsilon_imp(const T*, const mpl::int_<24>&) |
| { |
| return static_cast<T>(0.018581361171917516667460937040007436176452688944747L); |
| } |
| |
| template <class T> |
| inline T forth_root_epsilon_imp(const T*, const mpl::int_<53>&) |
| { |
| return static_cast<T>(0.0001220703125L); |
| } |
| |
| template <class T> |
| inline T forth_root_epsilon_imp(const T*, const mpl::int_<64>&) |
| { |
| return static_cast<T>(0.18145860519450699870567321328132261891067079047605e-4L); |
| } |
| |
| template <class T> |
| inline T forth_root_epsilon_imp(const T*, const mpl::int_<113>&) |
| { |
| return static_cast<T>(0.37252902984619140625e-8L); |
| } |
| |
| template <class T, class Tag> |
| inline T forth_root_epsilon_imp(const T*, const Tag&) |
| { |
| BOOST_MATH_STD_USING |
| static const T r_eps = sqrt(sqrt(tools::epsilon<T>())); |
| return r_eps; |
| } |
| |
| } |
| |
| template <class T> |
| inline T root_epsilon() |
| { |
| typedef mpl::int_<std::numeric_limits<T>::digits> tag_type; |
| return detail::root_epsilon_imp(static_cast<T const*>(0), tag_type()); |
| } |
| |
| template <class T> |
| inline T forth_root_epsilon() |
| { |
| typedef mpl::int_<std::numeric_limits<T>::digits> tag_type; |
| return detail::forth_root_epsilon_imp(static_cast<T const*>(0), tag_type()); |
| } |
| |
| } // namespace tools |
| } // namespace math |
| } // namespace boost |
| |
| #endif // BOOST_MATH_TOOLS_PRECISION_INCLUDED |
| |