410 lines
14 KiB
Plaintext
410 lines
14 KiB
Plaintext
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// Copyright John Maddock 2005-2006.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_MATH_TOOLS_PRECISION_INCLUDED
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#define BOOST_MATH_TOOLS_PRECISION_INCLUDED
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#ifdef _MSC_VER
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#pragma once
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#endif
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#include <boost/limits.hpp>
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#include <boost/assert.hpp>
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#include <boost/static_assert.hpp>
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#include <boost/mpl/int.hpp>
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#include <boost/mpl/bool.hpp>
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#include <boost/mpl/if.hpp>
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#include <boost/math/policies/policy.hpp>
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// These two are for LDBL_MAN_DIG:
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#include <limits.h>
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#include <math.h>
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namespace boost{ namespace math
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{
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namespace tools
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{
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// If T is not specialized, the functions digits, max_value and min_value,
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// all get synthesised automatically from std::numeric_limits.
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// However, if numeric_limits is not specialised for type RealType,
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// for example with NTL::RR type, then you will get a compiler error
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// when code tries to use these functions, unless you explicitly specialise them.
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// For example if the precision of RealType varies at runtime,
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// then numeric_limits support may not be appropriate,
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// see boost/math/tools/ntl.hpp for examples like
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// template <> NTL::RR max_value<NTL::RR> ...
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// See Conceptual Requirements for Real Number Types.
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template <class T>
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inline BOOST_MATH_CONSTEXPR int digits(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(T)) BOOST_NOEXCEPT
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{
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#ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
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BOOST_STATIC_ASSERT( ::std::numeric_limits<T>::is_specialized);
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BOOST_STATIC_ASSERT( ::std::numeric_limits<T>::radix == 2 || ::std::numeric_limits<T>::radix == 10);
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#else
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BOOST_ASSERT(::std::numeric_limits<T>::is_specialized);
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BOOST_ASSERT(::std::numeric_limits<T>::radix == 2 || ::std::numeric_limits<T>::radix == 10);
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#endif
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return std::numeric_limits<T>::radix == 2
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? std::numeric_limits<T>::digits
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: ((std::numeric_limits<T>::digits + 1) * 1000L) / 301L;
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}
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template <class T>
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inline BOOST_MATH_CONSTEXPR T max_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE(T)) BOOST_MATH_NOEXCEPT(T)
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{
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#ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
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BOOST_STATIC_ASSERT( ::std::numeric_limits<T>::is_specialized);
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#else
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BOOST_ASSERT(::std::numeric_limits<T>::is_specialized);
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#endif
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return (std::numeric_limits<T>::max)();
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} // Also used as a finite 'infinite' value for - and +infinity, for example:
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// -max_value<double> = -1.79769e+308, max_value<double> = 1.79769e+308.
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template <class T>
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inline BOOST_MATH_CONSTEXPR T min_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE(T)) BOOST_MATH_NOEXCEPT(T)
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{
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#ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
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BOOST_STATIC_ASSERT( ::std::numeric_limits<T>::is_specialized);
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#else
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BOOST_ASSERT(::std::numeric_limits<T>::is_specialized);
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#endif
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return (std::numeric_limits<T>::min)();
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}
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namespace detail{
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//
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// Logarithmic limits come next, note that although
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// we can compute these from the log of the max value
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// that is not in general thread safe (if we cache the value)
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// so it's better to specialise these:
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//
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// For type float first:
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//
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template <class T>
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inline BOOST_MATH_CONSTEXPR T log_max_value(const mpl::int_<128>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T)) BOOST_MATH_NOEXCEPT(T)
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{
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return 88.0f;
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}
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template <class T>
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inline BOOST_MATH_CONSTEXPR T log_min_value(const mpl::int_<128>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T)) BOOST_MATH_NOEXCEPT(T)
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{
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return -87.0f;
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}
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//
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// Now double:
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//
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template <class T>
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inline BOOST_MATH_CONSTEXPR T log_max_value(const mpl::int_<1024>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T)) BOOST_MATH_NOEXCEPT(T)
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{
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return 709.0;
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}
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template <class T>
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inline BOOST_MATH_CONSTEXPR T log_min_value(const mpl::int_<1024>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T)) BOOST_MATH_NOEXCEPT(T)
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{
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return -708.0;
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}
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//
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// 80 and 128-bit long doubles:
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//
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template <class T>
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inline BOOST_MATH_CONSTEXPR T log_max_value(const mpl::int_<16384>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T)) BOOST_MATH_NOEXCEPT(T)
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{
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return 11356.0L;
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}
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template <class T>
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inline BOOST_MATH_CONSTEXPR T log_min_value(const mpl::int_<16384>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T)) BOOST_MATH_NOEXCEPT(T)
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{
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return -11355.0L;
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}
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template <class T>
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inline T log_max_value(const mpl::int_<0>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T))
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{
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BOOST_MATH_STD_USING
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#ifdef __SUNPRO_CC
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static const T m = boost::math::tools::max_value<T>();
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static const T val = log(m);
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#else
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static const T val = log(boost::math::tools::max_value<T>());
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#endif
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return val;
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}
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template <class T>
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inline T log_min_value(const mpl::int_<0>& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T))
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{
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BOOST_MATH_STD_USING
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#ifdef __SUNPRO_CC
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static const T m = boost::math::tools::min_value<T>();
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static const T val = log(m);
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#else
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static const T val = log(boost::math::tools::min_value<T>());
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#endif
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return val;
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}
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template <class T>
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inline BOOST_MATH_CONSTEXPR T epsilon(const mpl::true_& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T)) BOOST_MATH_NOEXCEPT(T)
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{
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return std::numeric_limits<T>::epsilon();
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}
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#if defined(__GNUC__) && ((LDBL_MANT_DIG == 106) || (__LDBL_MANT_DIG__ == 106))
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template <>
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inline BOOST_MATH_CONSTEXPR long double epsilon<long double>(const mpl::true_& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(long double)) BOOST_MATH_NOEXCEPT(long double)
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{
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// numeric_limits on Darwin (and elsewhere) tells lies here:
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// the issue is that long double on a few platforms is
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// really a "double double" which has a non-contiguous
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// mantissa: 53 bits followed by an unspecified number of
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// zero bits, followed by 53 more bits. Thus the apparent
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// precision of the type varies depending where it's been.
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// Set epsilon to the value that a 106 bit fixed mantissa
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// type would have, as that will give us sensible behaviour everywhere.
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//
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// This static assert fails for some unknown reason, so
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// disabled for now...
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// BOOST_STATIC_ASSERT(std::numeric_limits<long double>::digits == 106);
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return 2.4651903288156618919116517665087e-32L;
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}
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#endif
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template <class T>
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inline T epsilon(const mpl::false_& BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE(T))
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{
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// Note: don't cache result as precision may vary at runtime:
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BOOST_MATH_STD_USING // for ADL of std names
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return ldexp(static_cast<T>(1), 1-policies::digits<T, policies::policy<> >());
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}
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template <class T>
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struct log_limit_traits
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{
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typedef typename mpl::if_c<
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(std::numeric_limits<T>::radix == 2) &&
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(std::numeric_limits<T>::max_exponent == 128
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|| std::numeric_limits<T>::max_exponent == 1024
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|| std::numeric_limits<T>::max_exponent == 16384),
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mpl::int_<(std::numeric_limits<T>::max_exponent > INT_MAX ? INT_MAX : static_cast<int>(std::numeric_limits<T>::max_exponent))>,
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mpl::int_<0>
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>::type tag_type;
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BOOST_STATIC_CONSTANT(bool, value = tag_type::value ? true : false);
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BOOST_STATIC_ASSERT(::std::numeric_limits<T>::is_specialized || (value == 0));
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};
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template <class T, bool b> struct log_limit_noexcept_traits_imp : public log_limit_traits<T> {};
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template <class T> struct log_limit_noexcept_traits_imp<T, false> : public boost::integral_constant<bool, false> {};
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template <class T>
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struct log_limit_noexcept_traits : public log_limit_noexcept_traits_imp<T, BOOST_MATH_IS_FLOAT(T)> {};
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} // namespace detail
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#ifdef BOOST_MSVC
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#pragma warning(push)
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#pragma warning(disable:4309)
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#endif
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template <class T>
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inline BOOST_MATH_CONSTEXPR T log_max_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE(T)) BOOST_NOEXCEPT_IF(detail::log_limit_noexcept_traits<T>::value)
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{
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#ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
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return detail::log_max_value<T>(typename detail::log_limit_traits<T>::tag_type());
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#else
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BOOST_ASSERT(::std::numeric_limits<T>::is_specialized);
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BOOST_MATH_STD_USING
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static const T val = log((std::numeric_limits<T>::max)());
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return val;
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#endif
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}
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template <class T>
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inline BOOST_MATH_CONSTEXPR T log_min_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE(T)) BOOST_NOEXCEPT_IF(detail::log_limit_noexcept_traits<T>::value)
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{
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#ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
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return detail::log_min_value<T>(typename detail::log_limit_traits<T>::tag_type());
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#else
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BOOST_ASSERT(::std::numeric_limits<T>::is_specialized);
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BOOST_MATH_STD_USING
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static const T val = log((std::numeric_limits<T>::min)());
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return val;
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#endif
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}
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#ifdef BOOST_MSVC
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#pragma warning(pop)
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#endif
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template <class T>
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inline BOOST_MATH_CONSTEXPR T epsilon(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(T)) BOOST_MATH_NOEXCEPT(T)
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{
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#ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
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return detail::epsilon<T>(mpl::bool_< ::std::numeric_limits<T>::is_specialized>());
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#else
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return ::std::numeric_limits<T>::is_specialized ?
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detail::epsilon<T>(mpl::true_()) :
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detail::epsilon<T>(mpl::false_());
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#endif
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}
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namespace detail{
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template <class T>
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inline BOOST_MATH_CONSTEXPR T root_epsilon_imp(const mpl::int_<24>&) BOOST_MATH_NOEXCEPT(T)
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{
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return static_cast<T>(0.00034526698300124390839884978618400831996329879769945L);
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}
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template <class T>
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inline BOOST_MATH_CONSTEXPR T root_epsilon_imp(const T*, const mpl::int_<53>&) BOOST_MATH_NOEXCEPT(T)
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{
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return static_cast<T>(0.1490116119384765625e-7L);
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}
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template <class T>
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inline BOOST_MATH_CONSTEXPR T root_epsilon_imp(const T*, const mpl::int_<64>&) BOOST_MATH_NOEXCEPT(T)
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{
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return static_cast<T>(0.32927225399135962333569506281281311031656150598474e-9L);
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}
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template <class T>
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inline BOOST_MATH_CONSTEXPR T root_epsilon_imp(const T*, const mpl::int_<113>&) BOOST_MATH_NOEXCEPT(T)
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{
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return static_cast<T>(0.1387778780781445675529539585113525390625e-16L);
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}
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template <class T, class Tag>
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inline T root_epsilon_imp(const T*, const Tag&)
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{
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BOOST_MATH_STD_USING
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static const T r_eps = sqrt(tools::epsilon<T>());
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return r_eps;
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}
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template <class T>
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inline T root_epsilon_imp(const T*, const mpl::int_<0>&)
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{
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BOOST_MATH_STD_USING
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return sqrt(tools::epsilon<T>());
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}
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template <class T>
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inline BOOST_MATH_CONSTEXPR T cbrt_epsilon_imp(const mpl::int_<24>&) BOOST_MATH_NOEXCEPT(T)
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{
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return static_cast<T>(0.0049215666011518482998719164346805794944150447839903L);
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}
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template <class T>
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inline BOOST_MATH_CONSTEXPR T cbrt_epsilon_imp(const T*, const mpl::int_<53>&) BOOST_MATH_NOEXCEPT(T)
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{
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return static_cast<T>(6.05545445239333906078989272793696693569753008995e-6L);
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}
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template <class T>
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inline BOOST_MATH_CONSTEXPR T cbrt_epsilon_imp(const T*, const mpl::int_<64>&) BOOST_MATH_NOEXCEPT(T)
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{
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return static_cast<T>(4.76837158203125e-7L);
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}
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template <class T>
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inline BOOST_MATH_CONSTEXPR T cbrt_epsilon_imp(const T*, const mpl::int_<113>&) BOOST_MATH_NOEXCEPT(T)
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{
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return static_cast<T>(5.7749313854154005630396773604745549542403508090496e-12L);
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}
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template <class T, class Tag>
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inline T cbrt_epsilon_imp(const T*, const Tag&)
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{
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BOOST_MATH_STD_USING;
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static const T cbrt_eps = pow(tools::epsilon<T>(), T(1) / 3);
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return cbrt_eps;
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}
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template <class T>
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inline T cbrt_epsilon_imp(const T*, const mpl::int_<0>&)
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||
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|
{
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||
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BOOST_MATH_STD_USING;
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return pow(tools::epsilon<T>(), T(1) / 3);
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}
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||
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template <class T>
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inline BOOST_MATH_CONSTEXPR T forth_root_epsilon_imp(const T*, const mpl::int_<24>&) BOOST_MATH_NOEXCEPT(T)
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||
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{
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||
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|
return static_cast<T>(0.018581361171917516667460937040007436176452688944747L);
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||
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|
}
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||
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|
|
||
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template <class T>
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||
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inline BOOST_MATH_CONSTEXPR T forth_root_epsilon_imp(const T*, const mpl::int_<53>&) BOOST_MATH_NOEXCEPT(T)
|
||
|
|
{
|
||
|
|
return static_cast<T>(0.0001220703125L);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class T>
|
||
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inline BOOST_MATH_CONSTEXPR T forth_root_epsilon_imp(const T*, const mpl::int_<64>&) BOOST_MATH_NOEXCEPT(T)
|
||
|
|
{
|
||
|
|
return static_cast<T>(0.18145860519450699870567321328132261891067079047605e-4L);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
inline BOOST_MATH_CONSTEXPR T forth_root_epsilon_imp(const T*, const mpl::int_<113>&) BOOST_MATH_NOEXCEPT(T)
|
||
|
|
{
|
||
|
|
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 forth_root_epsilon_imp(const T*, const mpl::int_<0>&)
|
||
|
|
{
|
||
|
|
BOOST_MATH_STD_USING
|
||
|
|
return sqrt(sqrt(tools::epsilon<T>()));
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
struct root_epsilon_traits
|
||
|
|
{
|
||
|
|
typedef mpl::int_< (::std::numeric_limits<T>::radix == 2) ? std::numeric_limits<T>::digits : 0> tag_type;
|
||
|
|
BOOST_STATIC_CONSTANT(bool, has_noexcept = (tag_type::value == 113) || (tag_type::value == 64) || (tag_type::value == 53) || (tag_type::value == 24));
|
||
|
|
};
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
inline BOOST_MATH_CONSTEXPR T root_epsilon() BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(T) && detail::root_epsilon_traits<T>::has_noexcept)
|
||
|
|
{
|
||
|
|
return detail::root_epsilon_imp(static_cast<T const*>(0), typename detail::root_epsilon_traits<T>::tag_type());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
inline BOOST_MATH_CONSTEXPR T cbrt_epsilon() BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(T) && detail::root_epsilon_traits<T>::has_noexcept)
|
||
|
|
{
|
||
|
|
return detail::cbrt_epsilon_imp(static_cast<T const*>(0), typename detail::root_epsilon_traits<T>::tag_type());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class T>
|
||
|
|
inline BOOST_MATH_CONSTEXPR T forth_root_epsilon() BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(T) && detail::root_epsilon_traits<T>::has_noexcept)
|
||
|
|
{
|
||
|
|
return detail::forth_root_epsilon_imp(static_cast<T const*>(0), typename detail::root_epsilon_traits<T>::tag_type());
|
||
|
|
}
|
||
|
|
|
||
|
|
} // namespace tools
|
||
|
|
} // namespace math
|
||
|
|
} // namespace boost
|
||
|
|
|
||
|
|
#endif // BOOST_MATH_TOOLS_PRECISION_INCLUDED
|
||
|
|
|