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767 lines
19 KiB
C++
767 lines
19 KiB
C++
// Boost.Geometry (aka GGL, Generic Geometry Library)
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// Copyright (c) 2007-2015 Barend Gehrels, Amsterdam, the Netherlands.
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// Copyright (c) 2008-2015 Bruno Lalande, Paris, France.
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// Copyright (c) 2009-2015 Mateusz Loskot, London, UK.
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// This file was modified by Oracle on 2014, 2015.
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// Modifications copyright (c) 2014-2015, Oracle and/or its affiliates.
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// Contributed and/or modified by Menelaos Karavelas, on behalf of Oracle
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// Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle
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// Parts of Boost.Geometry are redesigned from Geodan's Geographic Library
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// (geolib/GGL), copyright (c) 1995-2010 Geodan, Amsterdam, the Netherlands.
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// Use, modification and distribution is subject to the Boost Software License,
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// Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_GEOMETRY_UTIL_MATH_HPP
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#define BOOST_GEOMETRY_UTIL_MATH_HPP
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#include <cmath>
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#include <limits>
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#include <boost/core/ignore_unused.hpp>
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#include <boost/math/constants/constants.hpp>
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#include <boost/math/special_functions/fpclassify.hpp>
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//#include <boost/math/special_functions/round.hpp>
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#include <boost/numeric/conversion/cast.hpp>
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#include <boost/type_traits/is_fundamental.hpp>
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#include <boost/type_traits/is_integral.hpp>
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#include <boost/geometry/core/cs.hpp>
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#include <boost/geometry/util/select_most_precise.hpp>
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namespace boost { namespace geometry
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{
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namespace math
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{
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#ifndef DOXYGEN_NO_DETAIL
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namespace detail
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{
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template <typename T>
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inline T const& greatest(T const& v1, T const& v2)
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{
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return (std::max)(v1, v2);
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}
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template <typename T>
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inline T const& greatest(T const& v1, T const& v2, T const& v3)
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{
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return (std::max)(greatest(v1, v2), v3);
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}
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template <typename T>
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inline T const& greatest(T const& v1, T const& v2, T const& v3, T const& v4)
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{
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return (std::max)(greatest(v1, v2, v3), v4);
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}
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template <typename T>
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inline T const& greatest(T const& v1, T const& v2, T const& v3, T const& v4, T const& v5)
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{
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return (std::max)(greatest(v1, v2, v3, v4), v5);
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}
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template <typename T,
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bool IsFloatingPoint = boost::is_floating_point<T>::value>
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struct abs
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{
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static inline T apply(T const& value)
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{
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T const zero = T();
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return value < zero ? -value : value;
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}
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};
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template <typename T>
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struct abs<T, true>
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{
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static inline T apply(T const& value)
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{
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using ::fabs;
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using std::fabs; // for long double
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return fabs(value);
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}
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};
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struct equals_default_policy
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{
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template <typename T>
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static inline T apply(T const& a, T const& b)
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{
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// See http://www.parashift.com/c++-faq-lite/newbie.html#faq-29.17
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return greatest(abs<T>::apply(a), abs<T>::apply(b), T(1));
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}
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};
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template <typename T,
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bool IsFloatingPoint = boost::is_floating_point<T>::value>
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struct equals_factor_policy
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{
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equals_factor_policy()
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: factor(1) {}
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explicit equals_factor_policy(T const& v)
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: factor(greatest(abs<T>::apply(v), T(1)))
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{}
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equals_factor_policy(T const& v0, T const& v1, T const& v2, T const& v3)
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: factor(greatest(abs<T>::apply(v0), abs<T>::apply(v1),
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abs<T>::apply(v2), abs<T>::apply(v3),
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T(1)))
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{}
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T const& apply(T const&, T const&) const
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{
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return factor;
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}
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T factor;
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};
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template <typename T>
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struct equals_factor_policy<T, false>
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{
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equals_factor_policy() {}
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explicit equals_factor_policy(T const&) {}
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equals_factor_policy(T const& , T const& , T const& , T const& ) {}
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static inline T apply(T const&, T const&)
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{
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return T(1);
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}
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};
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template <typename Type,
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bool IsFloatingPoint = boost::is_floating_point<Type>::value>
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struct equals
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{
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template <typename Policy>
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static inline bool apply(Type const& a, Type const& b, Policy const&)
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{
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return a == b;
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}
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};
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template <typename Type>
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struct equals<Type, true>
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{
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template <typename Policy>
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static inline bool apply(Type const& a, Type const& b, Policy const& policy)
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{
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boost::ignore_unused(policy);
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if (a == b)
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{
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return true;
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}
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if (boost::math::isfinite(a) && boost::math::isfinite(b))
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{
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// If a is INF and b is e.g. 0, the expression below returns true
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// but the values are obviously not equal, hence the condition
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return abs<Type>::apply(a - b)
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<= std::numeric_limits<Type>::epsilon() * policy.apply(a, b);
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}
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else
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{
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return a == b;
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}
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}
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};
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template <typename T1, typename T2, typename Policy>
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inline bool equals_by_policy(T1 const& a, T2 const& b, Policy const& policy)
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{
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return detail::equals
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<
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typename select_most_precise<T1, T2>::type
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>::apply(a, b, policy);
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}
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template <typename Type,
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bool IsFloatingPoint = boost::is_floating_point<Type>::value>
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struct smaller
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{
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static inline bool apply(Type const& a, Type const& b)
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{
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return a < b;
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}
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};
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template <typename Type>
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struct smaller<Type, true>
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{
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static inline bool apply(Type const& a, Type const& b)
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{
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if (!(a < b)) // a >= b
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{
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return false;
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}
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return ! equals<Type, true>::apply(b, a, equals_default_policy());
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}
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};
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template <typename Type,
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bool IsFloatingPoint = boost::is_floating_point<Type>::value>
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struct smaller_or_equals
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{
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static inline bool apply(Type const& a, Type const& b)
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{
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return a <= b;
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}
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};
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template <typename Type>
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struct smaller_or_equals<Type, true>
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{
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static inline bool apply(Type const& a, Type const& b)
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{
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if (a <= b)
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{
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return true;
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}
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return equals<Type, true>::apply(a, b, equals_default_policy());
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}
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};
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template <typename Type,
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bool IsFloatingPoint = boost::is_floating_point<Type>::value>
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struct equals_with_epsilon
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: public equals<Type, IsFloatingPoint>
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{};
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template
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<
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typename T,
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bool IsFundemantal = boost::is_fundamental<T>::value /* false */
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>
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struct square_root
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{
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typedef T return_type;
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static inline T apply(T const& value)
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{
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// for non-fundamental number types assume that sqrt is
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// defined either:
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// 1) at T's scope, or
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// 2) at global scope, or
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// 3) in namespace std
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using ::sqrt;
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using std::sqrt;
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return sqrt(value);
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}
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};
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template <typename FundamentalFP>
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struct square_root_for_fundamental_fp
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{
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typedef FundamentalFP return_type;
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static inline FundamentalFP apply(FundamentalFP const& value)
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{
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#ifdef BOOST_GEOMETRY_SQRT_CHECK_FINITENESS
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// This is a workaround for some 32-bit platforms.
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// For some of those platforms it has been reported that
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// std::sqrt(nan) and/or std::sqrt(-nan) returns a finite value.
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// For those platforms we need to define the macro
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// BOOST_GEOMETRY_SQRT_CHECK_FINITENESS so that the argument
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// to std::sqrt is checked appropriately before passed to std::sqrt
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if (boost::math::isfinite(value))
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{
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return std::sqrt(value);
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}
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else if (boost::math::isinf(value) && value < 0)
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{
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return -std::numeric_limits<FundamentalFP>::quiet_NaN();
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}
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return value;
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#else
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// for fundamental floating point numbers use std::sqrt
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return std::sqrt(value);
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#endif // BOOST_GEOMETRY_SQRT_CHECK_FINITENESS
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}
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};
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template <>
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struct square_root<float, true>
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: square_root_for_fundamental_fp<float>
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{
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};
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template <>
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struct square_root<double, true>
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: square_root_for_fundamental_fp<double>
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{
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};
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template <>
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struct square_root<long double, true>
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: square_root_for_fundamental_fp<long double>
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{
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};
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template <typename T>
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struct square_root<T, true>
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{
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typedef double return_type;
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static inline double apply(T const& value)
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{
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// for all other fundamental number types use also std::sqrt
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//
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// Note: in C++98 the only other possibility is double;
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// in C++11 there are also overloads for integral types;
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// this specialization works for those as well.
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return square_root_for_fundamental_fp
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<
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double
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>::apply(boost::numeric_cast<double>(value));
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}
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};
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template
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<
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typename T,
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bool IsFundemantal = boost::is_fundamental<T>::value /* false */
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>
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struct modulo
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{
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typedef T return_type;
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static inline T apply(T const& value1, T const& value2)
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{
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// for non-fundamental number types assume that a free
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// function mod() is defined either:
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// 1) at T's scope, or
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// 2) at global scope
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return mod(value1, value2);
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}
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};
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template
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<
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typename Fundamental,
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bool IsIntegral = boost::is_integral<Fundamental>::value
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>
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struct modulo_for_fundamental
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{
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typedef Fundamental return_type;
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static inline Fundamental apply(Fundamental const& value1,
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Fundamental const& value2)
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{
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return value1 % value2;
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}
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};
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// specialization for floating-point numbers
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template <typename Fundamental>
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struct modulo_for_fundamental<Fundamental, false>
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{
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typedef Fundamental return_type;
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static inline Fundamental apply(Fundamental const& value1,
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Fundamental const& value2)
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{
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return std::fmod(value1, value2);
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}
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};
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// specialization for fundamental number type
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template <typename Fundamental>
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struct modulo<Fundamental, true>
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: modulo_for_fundamental<Fundamental>
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{};
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/*!
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\brief Short constructs to enable partial specialization for PI, 2*PI
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and PI/2, currently not possible in Math.
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*/
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template <typename T>
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struct define_pi
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{
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static inline T apply()
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{
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// Default calls Boost.Math
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return boost::math::constants::pi<T>();
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}
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};
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template <typename T>
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struct define_two_pi
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{
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static inline T apply()
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{
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// Default calls Boost.Math
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return boost::math::constants::two_pi<T>();
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}
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};
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template <typename T>
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struct define_half_pi
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{
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static inline T apply()
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{
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// Default calls Boost.Math
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return boost::math::constants::half_pi<T>();
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}
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};
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template <typename T>
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struct relaxed_epsilon
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{
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static inline T apply(const T& factor)
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{
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return factor * std::numeric_limits<T>::epsilon();
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}
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};
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// This must be consistent with math::equals.
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// By default math::equals() scales the error by epsilon using the greater of
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// compared values but here is only one value, though it should work the same way.
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// (a-a) <= max(a, a) * EPS -> 0 <= a*EPS
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// (a+da-a) <= max(a+da, a) * EPS -> da <= (a+da)*EPS
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template <typename T, bool IsFloat = boost::is_floating_point<T>::value>
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struct scaled_epsilon
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{
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static inline T apply(T const& val)
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{
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return (std::max)(abs<T>::apply(val), T(1))
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* std::numeric_limits<T>::epsilon();
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}
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};
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template <typename T>
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struct scaled_epsilon<T, false>
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{
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static inline T apply(T const&)
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{
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return T(0);
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}
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};
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// ItoF ItoI FtoF
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template <typename Result, typename Source,
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bool ResultIsInteger = std::numeric_limits<Result>::is_integer,
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bool SourceIsInteger = std::numeric_limits<Source>::is_integer>
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struct rounding_cast
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{
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static inline Result apply(Source const& v)
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{
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return boost::numeric_cast<Result>(v);
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}
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};
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// TtoT
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template <typename Source, bool ResultIsInteger, bool SourceIsInteger>
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struct rounding_cast<Source, Source, ResultIsInteger, SourceIsInteger>
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{
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static inline Source apply(Source const& v)
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{
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return v;
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}
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};
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// FtoI
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template <typename Result, typename Source>
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struct rounding_cast<Result, Source, true, false>
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{
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static inline Result apply(Source const& v)
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{
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return boost::numeric_cast<Result>(v < Source(0) ?
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v - Source(0.5) :
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v + Source(0.5));
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}
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};
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} // namespace detail
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#endif
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template <typename T>
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inline T pi() { return detail::define_pi<T>::apply(); }
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template <typename T>
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inline T two_pi() { return detail::define_two_pi<T>::apply(); }
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template <typename T>
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inline T half_pi() { return detail::define_half_pi<T>::apply(); }
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template <typename T>
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inline T relaxed_epsilon(T const& factor)
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{
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return detail::relaxed_epsilon<T>::apply(factor);
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}
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template <typename T>
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inline T scaled_epsilon(T const& value)
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{
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return detail::scaled_epsilon<T>::apply(value);
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}
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// Maybe replace this by boost equals or boost ublas numeric equals or so
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/*!
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\brief returns true if both arguments are equal.
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\ingroup utility
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\param a first argument
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\param b second argument
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\return true if a == b
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\note If both a and b are of an integral type, comparison is done by ==.
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If one of the types is floating point, comparison is done by abs and
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comparing with epsilon. If one of the types is non-fundamental, it might
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be a high-precision number and comparison is done using the == operator
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of that class.
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*/
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template <typename T1, typename T2>
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inline bool equals(T1 const& a, T2 const& b)
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{
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return detail::equals
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<
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typename select_most_precise<T1, T2>::type
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>::apply(a, b, detail::equals_default_policy());
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}
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template <typename T1, typename T2>
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inline bool equals_with_epsilon(T1 const& a, T2 const& b)
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{
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return detail::equals_with_epsilon
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<
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typename select_most_precise<T1, T2>::type
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>::apply(a, b, detail::equals_default_policy());
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}
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template <typename T1, typename T2>
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inline bool smaller(T1 const& a, T2 const& b)
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{
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return detail::smaller
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<
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typename select_most_precise<T1, T2>::type
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>::apply(a, b);
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}
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template <typename T1, typename T2>
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inline bool larger(T1 const& a, T2 const& b)
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{
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return detail::smaller
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<
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typename select_most_precise<T1, T2>::type
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>::apply(b, a);
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}
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template <typename T1, typename T2>
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inline bool smaller_or_equals(T1 const& a, T2 const& b)
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{
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return detail::smaller_or_equals
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<
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typename select_most_precise<T1, T2>::type
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>::apply(a, b);
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}
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template <typename T1, typename T2>
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inline bool larger_or_equals(T1 const& a, T2 const& b)
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|
{
|
|
return detail::smaller_or_equals
|
|
<
|
|
typename select_most_precise<T1, T2>::type
|
|
>::apply(b, a);
|
|
}
|
|
|
|
|
|
template <typename T>
|
|
inline T d2r()
|
|
{
|
|
static T const conversion_coefficient = geometry::math::pi<T>() / T(180.0);
|
|
return conversion_coefficient;
|
|
}
|
|
|
|
template <typename T>
|
|
inline T r2d()
|
|
{
|
|
static T const conversion_coefficient = T(180.0) / geometry::math::pi<T>();
|
|
return conversion_coefficient;
|
|
}
|
|
|
|
|
|
#ifndef DOXYGEN_NO_DETAIL
|
|
namespace detail {
|
|
|
|
template <typename DegreeOrRadian>
|
|
struct as_radian
|
|
{
|
|
template <typename T>
|
|
static inline T apply(T const& value)
|
|
{
|
|
return value;
|
|
}
|
|
};
|
|
|
|
template <>
|
|
struct as_radian<degree>
|
|
{
|
|
template <typename T>
|
|
static inline T apply(T const& value)
|
|
{
|
|
return value * d2r<T>();
|
|
}
|
|
};
|
|
|
|
template <typename DegreeOrRadian>
|
|
struct from_radian
|
|
{
|
|
template <typename T>
|
|
static inline T apply(T const& value)
|
|
{
|
|
return value;
|
|
}
|
|
};
|
|
|
|
template <>
|
|
struct from_radian<degree>
|
|
{
|
|
template <typename T>
|
|
static inline T apply(T const& value)
|
|
{
|
|
return value * r2d<T>();
|
|
}
|
|
};
|
|
|
|
} // namespace detail
|
|
#endif
|
|
|
|
template <typename DegreeOrRadian, typename T>
|
|
inline T as_radian(T const& value)
|
|
{
|
|
return detail::as_radian<DegreeOrRadian>::apply(value);
|
|
}
|
|
|
|
template <typename DegreeOrRadian, typename T>
|
|
inline T from_radian(T const& value)
|
|
{
|
|
return detail::from_radian<DegreeOrRadian>::apply(value);
|
|
}
|
|
|
|
|
|
/*!
|
|
\brief Calculates the haversine of an angle
|
|
\ingroup utility
|
|
\note See http://en.wikipedia.org/wiki/Haversine_formula
|
|
haversin(alpha) = sin2(alpha/2)
|
|
*/
|
|
template <typename T>
|
|
inline T hav(T const& theta)
|
|
{
|
|
T const half = T(0.5);
|
|
T const sn = sin(half * theta);
|
|
return sn * sn;
|
|
}
|
|
|
|
/*!
|
|
\brief Short utility to return the square
|
|
\ingroup utility
|
|
\param value Value to calculate the square from
|
|
\return The squared value
|
|
*/
|
|
template <typename T>
|
|
inline T sqr(T const& value)
|
|
{
|
|
return value * value;
|
|
}
|
|
|
|
/*!
|
|
\brief Short utility to return the square root
|
|
\ingroup utility
|
|
\param value Value to calculate the square root from
|
|
\return The square root value
|
|
*/
|
|
template <typename T>
|
|
inline typename detail::square_root<T>::return_type
|
|
sqrt(T const& value)
|
|
{
|
|
return detail::square_root
|
|
<
|
|
T, boost::is_fundamental<T>::value
|
|
>::apply(value);
|
|
}
|
|
|
|
/*!
|
|
\brief Short utility to return the modulo of two values
|
|
\ingroup utility
|
|
\param value1 First value
|
|
\param value2 Second value
|
|
\return The result of the modulo operation on the (ordered) pair
|
|
(value1, value2)
|
|
*/
|
|
template <typename T>
|
|
inline typename detail::modulo<T>::return_type
|
|
mod(T const& value1, T const& value2)
|
|
{
|
|
return detail::modulo
|
|
<
|
|
T, boost::is_fundamental<T>::value
|
|
>::apply(value1, value2);
|
|
}
|
|
|
|
/*!
|
|
\brief Short utility to workaround gcc/clang problem that abs is converting to integer
|
|
and that older versions of MSVC does not support abs of long long...
|
|
\ingroup utility
|
|
*/
|
|
template<typename T>
|
|
inline T abs(T const& value)
|
|
{
|
|
return detail::abs<T>::apply(value);
|
|
}
|
|
|
|
/*!
|
|
\brief Short utility to calculate the sign of a number: -1 (negative), 0 (zero), 1 (positive)
|
|
\ingroup utility
|
|
*/
|
|
template <typename T>
|
|
inline int sign(T const& value)
|
|
{
|
|
T const zero = T();
|
|
return value > zero ? 1 : value < zero ? -1 : 0;
|
|
}
|
|
|
|
/*!
|
|
\brief Short utility to cast a value possibly rounding it to the nearest
|
|
integral value.
|
|
\ingroup utility
|
|
\note If the source T is NOT an integral type and Result is an integral type
|
|
the value is rounded towards the closest integral value. Otherwise it's
|
|
casted without rounding.
|
|
*/
|
|
template <typename Result, typename T>
|
|
inline Result rounding_cast(T const& v)
|
|
{
|
|
return detail::rounding_cast<Result, T>::apply(v);
|
|
}
|
|
|
|
} // namespace math
|
|
|
|
|
|
}} // namespace boost::geometry
|
|
|
|
#endif // BOOST_GEOMETRY_UTIL_MATH_HPP
|