852 lines
26 KiB
C++
852 lines
26 KiB
C++
/*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*
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* Copyright 2012-2016 Danny Robson <danny@nerdcruft.net>
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*/
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#ifndef __UTIL_COORDS_OPS
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#define __UTIL_COORDS_OPS
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#include "./fwd.hpp"
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#include "../debug.hpp"
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#include "../maths.hpp"
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#include "../preprocessor.hpp"
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#include "../types/bits.hpp"
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#include <cmath>
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#include <cstdlib>
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namespace util {
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///////////////////////////////////////////////////////////////////////
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// operation traits
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namespace coord {
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template <
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template <size_t,typename> class A,
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template <size_t,typename> class B
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>
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struct result { };
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//-------------------------------------------------------------------------
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template <> struct result<colour,colour> { template <size_t S, typename T> using type = colour<S,T>; };
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template <> struct result<extent,extent> { template <size_t S, typename T> using type = extent<S,T>; };
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template <> struct result<extent,vector> { template <size_t S, typename T> using type = extent<S,T>; };
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template <> struct result<point,extent> { template <size_t S, typename T> using type = point <S,T>; };
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template <> struct result<point,vector> { template <size_t S, typename T> using type = point <S,T>; };
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template <> struct result<vector,point> { template <size_t S, typename T> using type = point <S,T>; };
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template <> struct result<vector,vector> { template <size_t S, typename T> using type = vector<S,T>; };
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template <
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template <size_t,typename> class A,
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template <size_t,typename> class B
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>
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using result_t = typename result<A,B>::type;
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//---------------------------------------------------------------------
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template <template <size_t,typename> class K>
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struct has_norm : public std::false_type { };
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template <> struct has_norm<vector> : public std::true_type { };
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template <template <size_t,typename> class K>
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constexpr auto has_norm_v = has_norm<K>::value;
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//---------------------------------------------------------------------
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template <template <size_t,typename> class K>
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struct has_scalar_op : public std::false_type { };
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template <> struct has_scalar_op<colour> : public std::true_type { };
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template <> struct has_scalar_op<extent> : public std::true_type { };
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template <> struct has_scalar_op<point> : public std::true_type { };
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template <> struct has_scalar_op<vector> : public std::true_type { };
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template <template <size_t,typename> class K>
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constexpr auto has_scalar_op_v = has_scalar_op<K>::value;
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}
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template <class> struct is_coord : std::false_type { };
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template <size_t S, typename T> struct is_coord<point<S,T>> : std::true_type { };
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template <size_t S, typename T> struct is_coord<extent<S,T>> : std::true_type { };
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template <size_t S, typename T> struct is_coord<vector<S,T>> : std::true_type { };
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template <size_t S, typename T> struct is_coord<colour<S,T>> : std::true_type { };
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template <class K>
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constexpr bool
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is_coord_v = is_coord<K>::value;
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///////////////////////////////////////////////////////////////////////////
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// vector operators
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#define ELEMENT_OP(OP) \
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template < \
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size_t S, \
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typename T, \
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typename U, \
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template <size_t,typename> class A, \
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template <size_t,typename> class B, \
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typename = std::enable_if_t< \
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is_coord_v<A<S,T>> && is_coord_v<B<S,U>>, \
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void \
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> \
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> \
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constexpr \
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auto \
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operator OP (A<S,T> a, B<S,U> b) \
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{ \
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typename coord::result<A,B>::template type< \
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S,std::common_type_t<T,U> \
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> out {}; \
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for (size_t i = 0; i < S; ++i) \
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out[i] = a[i] OP b[i]; \
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return out; \
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} \
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\
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template < \
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size_t S, \
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typename T, \
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typename U, \
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template <size_t,typename> class A, \
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template <size_t,typename> class B, \
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typename = std::enable_if_t< \
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is_coord_v<A<S,T>> && \
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is_coord_v<B<S,U>> && \
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std::is_same< \
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std::common_type_t<T,U>, T \
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>::value, \
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void \
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> \
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> \
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auto& \
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operator PASTE(OP,=) (A<S,T>& a, B<S,U> b) \
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{ \
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for (size_t i = 0; i < S; ++i) \
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a[i] PASTE(OP,=) b[i]; \
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return a; \
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}
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ELEMENT_OP(+)
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ELEMENT_OP(-)
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ELEMENT_OP(*)
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ELEMENT_OP(/)
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ELEMENT_OP(%)
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#undef ELEMENT_OP
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///////////////////////////////////////////////////////////////////////////
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// scalar operators
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#define SCALAR_OP(OP) \
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template < \
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size_t S, \
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typename T, \
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typename U, \
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template <size_t,typename> class K, \
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typename = std::enable_if_t< \
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coord::has_scalar_op_v<K>, void \
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> \
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> \
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constexpr \
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auto \
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operator OP (U u, K<S,T> k) \
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{ \
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K<S,std::common_type_t<T,U>> out{}; \
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\
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for (size_t i = 0; i < S; ++i) \
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out[i] = u OP k[i]; \
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return out; \
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} \
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\
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template < \
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size_t S, \
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typename T, \
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typename U, \
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template <size_t,typename> class K, \
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typename = std::enable_if_t< \
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coord::has_scalar_op_v<K>,void \
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> \
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> \
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constexpr \
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auto \
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operator OP (K<S,T> k, U u) \
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{ \
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K<S,std::common_type_t<T,U>> out {}; \
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\
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for (size_t i = 0; i < S; ++i) \
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out[i] = k[i] OP u; \
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return out; \
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}
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SCALAR_OP(+)
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SCALAR_OP(-)
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SCALAR_OP(*)
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SCALAR_OP(/)
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SCALAR_OP(%)
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#undef SCALAR_OP
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//-------------------------------------------------------------------------
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// scalar assignment operators.
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//
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// we must check the operands/results do not need casting to store in the
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// destination type to avoid silent errors accumulating.
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#define SCALAR_OP(OP) \
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template < \
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size_t S, \
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typename T, \
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typename U, \
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template <size_t,typename> class K, \
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typename = std::enable_if_t< \
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is_coord<K<S,T>>::value && \
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std::is_arithmetic<T>::value && \
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std::is_arithmetic<U>::value, \
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void \
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> \
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> \
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std::enable_if_t< \
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std::is_same< \
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T, \
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std::common_type_t<T,U> \
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>::value, \
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K<S,T> \
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>& \
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operator OP (K<S,T> &k, U u) \
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{ \
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for (size_t i = 0; i < S; ++i) \
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k[i] OP u; \
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\
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return k; \
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}
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SCALAR_OP(+=)
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SCALAR_OP(-=)
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SCALAR_OP(*=)
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SCALAR_OP(/=)
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SCALAR_OP(%=)
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#undef SCALAR_OP
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///////////////////////////////////////////////////////////////////////////
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// unary operators
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#define UNARY_OP(OP) \
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template < \
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size_t S, \
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typename T, \
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template <size_t,typename> class K, \
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typename = std::enable_if_t< \
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is_coord_v<K<S,T>>, void \
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> \
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> \
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constexpr \
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auto \
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operator OP (K<S,T> k) \
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{ \
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K<S,decltype(OP std::declval<T> ())> out{}; \
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\
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for (size_t i = 0; i < S; ++i) \
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out[i] = OP k[i]; \
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\
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return out; \
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}
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UNARY_OP(!)
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UNARY_OP(~)
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UNARY_OP(+)
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UNARY_OP(-)
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#undef UNARY_OP
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///////////////////////////////////////////////////////////////////////////
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// logic operators
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/// elementwise equality operator
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template <
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size_t S,
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typename T,
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template <size_t,typename> class K,
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typename = std::enable_if_t<
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is_coord_v<K<S,T>>, void
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>
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>
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constexpr
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bool
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operator== (const K<S,T> a, const K<S,T> b)
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{
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bool (*predicate)(const T&, const T&) = almost_equal;
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return std::equal (std::cbegin (a),
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std::cend (a),
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std::cbegin (b),
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predicate);
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}
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///------------------------------------------------------------------------
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/// elementwise inquality operator
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template <
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size_t S,
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typename T,
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template <size_t,typename> class K,
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typename = std::enable_if_t<
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is_coord_v<K<S,T>>, void
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>
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>
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constexpr
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bool
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operator!= (K<S,T> a, K<S,T> 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 <
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size_t S,
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typename T,
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template <size_t,typename> class K,
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typename = std::enable_if_t<
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is_coord_v<K<S,T>>, void
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>
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>
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constexpr
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bool
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almost_zero (const K<S,T> &k)
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{
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return std::all_of (
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std::cbegin (k),
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std::cend (k),
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[] (T t) { return almost_equal (t); }
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);
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}
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///////////////////////////////////////////////////////////////////////////
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// special operators
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/// point-point subtraction giving a vector difference
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template <
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size_t S,
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typename T,
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typename U
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>
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constexpr
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vector<S,std::common_type_t<T,U>>
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operator- (point<S,T> a, point<S,U> b)
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{
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vector<S,std::common_type_t<T,U>> out {};
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for (size_t i = 0; i < S; ++i)
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out[i] = a[i] - b[i];
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return out;
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}
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//-------------------------------------------------------------------------
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template <
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size_t S,
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typename T,
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typename U,
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typename = std::enable_if_t<
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std::is_arithmetic<T>::value && std::is_arithmetic<U>::value,
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void
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>
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>
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constexpr
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vector<S,std::common_type_t<T,U>>
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operator- (U u, point<S,T> p)
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{
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return point<S,U> {u} - p;
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}
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///////////////////////////////////////////////////////////////////////////
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template <
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size_t S,
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typename T
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>
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constexpr
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T
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dot (const T (&a)[S], const T (&b)[S])
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{
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T sum = 0;
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for (size_t i = 0; i < S; ++i)
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sum += a[i] * b[i];
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return sum;
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}
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//-------------------------------------------------------------------------
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template <
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size_t S,
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typename T,
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template <size_t,typename> class A,
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template <size_t,typename> class B,
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typename = std::enable_if_t<
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is_coord_v<A<S,T>> && is_coord_v<B<S,T>>, void
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>
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>
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constexpr
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T
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dot (A<S,T> a, B<S,T> b)
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{
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return dot<S,T> (a.data, b.data);
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}
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//-------------------------------------------------------------------------
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template <
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size_t S,
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typename T,
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template <size_t,typename> class K,
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typename = std::enable_if_t<
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is_coord_v<K<S,T>>, void
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>
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>
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constexpr
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T
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dot (K<S,T> a, const T (&b)[S])
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{
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return dot<S,T> (a.data, b);
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}
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//-------------------------------------------------------------------------
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template <
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size_t S,
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typename T,
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template <size_t,typename> class K,
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typename = std::enable_if_t<
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is_coord_v<K<S,T>>, void
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>
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>
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constexpr
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T
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dot (const T (&a)[S], K<S,T> b)
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{
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return dot<S,T> (a, b.data);
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}
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///////////////////////////////////////////////////////////////////////////
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template <
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size_t S,
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typename T,
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template <size_t,typename> class K,
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typename = std::enable_if_t<coord::has_norm_v<K>,void>
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>
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constexpr
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T
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norm2 (const K<S,T> &k)
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{
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T sum = T{0};
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for (auto &t: k)
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sum += t * t;
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return sum;
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}
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//-------------------------------------------------------------------------
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template <
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size_t S,
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typename T,
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template <size_t,typename> class K,
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typename = std::enable_if_t<
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coord::has_norm_v<K>,
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void
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>
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>
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constexpr
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T
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norm (const K<S,T> &k)
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{
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return std::sqrt (norm2 (k));
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}
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//-------------------------------------------------------------------------
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template <
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size_t S,
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typename T,
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template <size_t,typename> class K,
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typename = std::enable_if_t<
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coord::has_norm_v<K>,
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void
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>
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>
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constexpr
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K<S,T>
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normalised (const K<S,T> &k)
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{
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auto n = norm (k);
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CHECK_NEZ (n);
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return k / n;
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}
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//-------------------------------------------------------------------------
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template <
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size_t S,
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typename T,
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template <size_t,typename> class K,
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typename = std::enable_if_t<
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coord::has_norm_v<K>,
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void
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>
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>
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constexpr
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bool
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is_normalised (const K<S,T> &k)
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{
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return almost_equal (norm2 (k), T{1});
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}
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///////////////////////////////////////////////////////////////////////////
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template <
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size_t S,
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typename T,
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template <size_t,typename> class K,
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typename = std::enable_if_t<
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is_coord_v<K<S,T>>, void
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>
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>
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constexpr
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K<S,T>
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abs (K<S,T> k)
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{
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for (auto &v: k)
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v = std::abs (v);
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return k;
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}
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///////////////////////////////////////////////////////////////////////////
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template <
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size_t S,
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typename T,
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template <size_t,typename> class K,
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typename = std::enable_if_t<
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is_coord_v<K<S,T>>, void
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>
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>
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constexpr
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K<S,T>
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pow (K<S,T> k)
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{
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for (auto &v: k)
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v = pow (v);
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return k;
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}
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///////////////////////////////////////////////////////////////////////////
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// root of sum of squares
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template <
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size_t S,
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typename T,
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template <size_t,typename> class K,
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typename = std::enable_if_t<
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is_coord_v<K<S,T>>, void
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>
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>
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constexpr
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T
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hypot (K<S,T> k)
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{
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return std::sqrt (sum (k * k));
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}
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|
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///////////////////////////////////////////////////////////////////////////
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template <
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size_t S,
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typename T,
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template <size_t,typename> class K,
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typename = std::enable_if_t<
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is_coord_v<K<S,T>>, void
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>
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>
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constexpr
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K<S,T>
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mod (K<S,T> k, T t)
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{
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std::transform (
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std::cbegin (k),
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|
std::cend (k),
|
|
std::begin (k),
|
|
[t] (auto v) { return mod (v, t);
|
|
});
|
|
return k;
|
|
}
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
// trigonometric functions
|
|
template <
|
|
size_t S,
|
|
typename T,
|
|
template <size_t,typename> class K,
|
|
typename = std::enable_if_t<is_coord_v<K<S,T>>,void>
|
|
>
|
|
constexpr
|
|
K<S,T>
|
|
sin (K<S,T> k)
|
|
{
|
|
std::transform (
|
|
std::cbegin (k),
|
|
std::cend (k),
|
|
std::begin (k),
|
|
[] (auto v) { return std::sin (v); }
|
|
);
|
|
|
|
return k;
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <
|
|
size_t S,
|
|
typename T,
|
|
template <size_t,typename> class K,
|
|
typename = std::enable_if_t<is_coord_v<K<S,T>>,void>
|
|
>
|
|
constexpr
|
|
K<S,T>
|
|
cos (K<S,T> k)
|
|
{
|
|
std::transform (
|
|
std::cbegin (k),
|
|
std::cend (k),
|
|
std::begin (k),
|
|
[] (auto v) { return std::cos (v); }
|
|
);
|
|
|
|
return k;
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
// logical element operators
|
|
|
|
/// return a coord type containing the max element at each offset
|
|
template <
|
|
size_t S,
|
|
typename T,
|
|
template <size_t,typename> class K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K<S,T>>, void
|
|
>
|
|
>
|
|
constexpr
|
|
K<S,T>
|
|
min (K<S,T> a, K<S,T> b)
|
|
{
|
|
K<S,T> out {};
|
|
for (size_t i = 0; i < S; ++i)
|
|
out[i] = min (a[i], b[i]);
|
|
return out;
|
|
}
|
|
|
|
|
|
///------------------------------------------------------------------------
|
|
// /return a coord type containing the max element at each offset
|
|
template <
|
|
size_t S,
|
|
typename T,
|
|
template <size_t,typename> class K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K<S,T>>, void
|
|
>
|
|
>
|
|
constexpr
|
|
K<S,T>
|
|
max (K<S,T> a, K<S,T> b)
|
|
{
|
|
K<S,T> out {};
|
|
for (size_t i = 0; i < S; ++i)
|
|
out[i] = max (a[i], b[i]);
|
|
return out;
|
|
}
|
|
|
|
|
|
///------------------------------------------------------------------------
|
|
template <
|
|
size_t S,
|
|
typename T,
|
|
template<size_t,typename> class K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K<S,T>>, void
|
|
>
|
|
>
|
|
constexpr
|
|
T
|
|
min (const K<S,T> k)
|
|
{
|
|
return *std::min_element (std::cbegin (k), std::cend (k));
|
|
}
|
|
|
|
|
|
template <
|
|
size_t S,
|
|
typename T,
|
|
template<size_t,typename> class K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K<S,T>>, void
|
|
>
|
|
>
|
|
constexpr
|
|
T
|
|
max (const K<S,T> k)
|
|
{
|
|
return *std::max_element (std::cbegin (k), std::cend (k));
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
template <
|
|
size_t S,
|
|
typename T,
|
|
template <size_t,typename> class K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K<S,T>>, void
|
|
>
|
|
>
|
|
constexpr
|
|
T
|
|
sum (const K<S,T> k)
|
|
{
|
|
return sum (std::cbegin (k), std::cend (k));
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
#define VECTOR_OP(OP) \
|
|
template < \
|
|
size_t S, \
|
|
typename T, \
|
|
typename U, \
|
|
template <size_t,typename> class A, \
|
|
template <size_t,typename> class B, \
|
|
typename = std::enable_if_t< \
|
|
is_coord_v<A<S,T>> && is_coord_v<B<S,U>>, void \
|
|
> \
|
|
> \
|
|
constexpr \
|
|
vector<S,bool> \
|
|
operator OP (const A<S,T> a, const B<S,U> b) \
|
|
{ \
|
|
vector<S,bool> out {}; \
|
|
for (size_t i = 0; i < S; ++i) \
|
|
out[i] = a[i] OP b[i]; \
|
|
return out; \
|
|
}
|
|
|
|
VECTOR_OP(<)
|
|
VECTOR_OP(>)
|
|
VECTOR_OP(<=)
|
|
VECTOR_OP(>=)
|
|
VECTOR_OP(&&)
|
|
VECTOR_OP(||)
|
|
|
|
#undef VECTOR_OP
|
|
|
|
|
|
#define SCALAR_OP(OP) \
|
|
template < \
|
|
size_t S, \
|
|
typename T, \
|
|
typename U, \
|
|
template <size_t,typename> class K, \
|
|
typename = std::enable_if_t< \
|
|
is_coord_v<K<S,T>>, void \
|
|
> \
|
|
> \
|
|
constexpr \
|
|
vector<S,bool> \
|
|
operator OP (const K<S,T> k, const U u) \
|
|
{ \
|
|
vector<S,bool> out {}; \
|
|
for (size_t i = 0; i < S; ++i) \
|
|
out[i] = k[i] OP u; \
|
|
return out; \
|
|
}
|
|
|
|
SCALAR_OP(<)
|
|
SCALAR_OP(>)
|
|
SCALAR_OP(<=)
|
|
SCALAR_OP(>=)
|
|
SCALAR_OP(&&)
|
|
SCALAR_OP(||)
|
|
|
|
#undef SCALAR_OP
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <
|
|
size_t S,
|
|
template <size_t,typename> class K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K<S,bool>>, void
|
|
>
|
|
>
|
|
constexpr
|
|
bool
|
|
any (const K<S,bool> k)
|
|
{
|
|
return std::any_of (std::cbegin (k),
|
|
std::cend (k),
|
|
identity<bool>);
|
|
}
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <
|
|
size_t S,
|
|
template <size_t,typename> class K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K<S,bool>>, void
|
|
>
|
|
>
|
|
constexpr
|
|
bool
|
|
all (const K<S,bool> k)
|
|
{
|
|
return std::all_of (std::cbegin (k),
|
|
std::cend (k),
|
|
identity<bool>);
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
template <
|
|
size_t S,
|
|
typename T,
|
|
template<size_t,typename> class K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K<S,T>> && std::is_floating_point<T>::value, void
|
|
>
|
|
>
|
|
constexpr
|
|
K<S,T>
|
|
floor (const K<S,T> k)
|
|
{
|
|
T (*floor_func)(T) = std::floor;
|
|
|
|
K<S,T> out {};
|
|
std::transform (std::cbegin (k),
|
|
std::cend (k),
|
|
std::begin (out),
|
|
floor_func);
|
|
return out;
|
|
}
|
|
}
|
|
|
|
#endif
|