1557 lines
43 KiB
C++
1557 lines
43 KiB
C++
/*
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* This Source Code Form is subject to the terms of the Mozilla Public
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* License, v. 2.0. If a copy of the MPL was not distributed with this
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* file, You can obtain one at http://mozilla.org/MPL/2.0/.
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*
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* Copyright 2012-2017 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 "traits.hpp"
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// we specifically rely on vector<bool> to compute a few logical operations
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#include "../vector.hpp"
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#include "../tuple/value.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 <algorithm>
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#include <cmath>
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#include <cstdlib>
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#include <iterator>
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#include <functional>
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namespace util {
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/// returns the data at a templated index in a coordinate.
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///
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/// specifically required for structured bindings support.
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///
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/// \tparam I index of the requested data
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/// \tparam S dimensionality of the coordinate
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/// \tparam T underlying data type of the coordinate
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/// \tparam K coordinate data type to operate on
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template <
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std::size_t I,
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typename K,
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typename = std::enable_if_t<
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is_coord_v<K>, void
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>
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>
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const auto&
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get (const K &k)
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{
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static_assert (I < K::elements);
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return k[I];
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};
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/// returns the data at a templated index in a coordinate.
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///
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/// specifically required for structured bindings support.
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///
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/// \tparam I index of the requested data
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/// \tparam S dimensionality of the coordinate
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/// \tparam T underlying data type of the coordinate
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/// \tparam K coordinate data type to operate on
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template <
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std::size_t I,
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typename K,
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typename = std::enable_if_t<
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is_coord_v<K> && I < K::elements, void
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>
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>
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auto &
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get (K &k)
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{
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static_assert (I < K::elements);
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return k[I];
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};
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///////////////////////////////////////////////////////////////////////////
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// a templated functor that exposes arithmetic and assignment maths
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// functions for vector-vector or vector-scalar operations.
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//
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// we implement the operations this way because it (somewhat) simplifies
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// ambiguity resolution in the various operators we need to provide.
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// eg, operator+(vec,vec) vs operator+(vec,int).
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//
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// it used to be directly implemented with a series of templated free
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// functions when we could restrict the arguments more easily with quite
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// specific template template parameters. but the introduction of
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// coordinate types that do not expose size or type information as template
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// parameters we can't rely on this mechanism anymore.
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template <typename, typename, typename=void>
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struct assignment {};
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//-------------------------------------------------------------------------
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template <typename CoordA, typename CoordB>
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struct assignment<
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CoordA,
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CoordB,
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std::enable_if_t<
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is_coord_v<CoordA> &&
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is_coord_v<CoordB> &&
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arity_v<CoordA> == arity_v<CoordB> &&
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std::is_same_v<
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typename CoordA::value_type,
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std::common_type_t<
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typename CoordA::value_type,
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typename CoordB::value_type
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>
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>
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,
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void
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>
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> {
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template <typename OperationT>
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static constexpr CoordA&
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eval (OperationT &&op, CoordA &a, const CoordB &b)
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{
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for (std::size_t i = 0; i < CoordA::elements; ++i)
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a[i] = op (a[i], b[i]);
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return a;
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}
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};
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//-------------------------------------------------------------------------
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// vector-scalar operations
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template <
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typename CoordT,
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typename ScalarT
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>
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struct assignment<
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CoordT,
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ScalarT,
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std::enable_if_t<
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is_coord_v<CoordT> &&
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!is_coord_v<ScalarT> &&
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has_scalar_op_v<CoordT> &&
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std::is_same_v<
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typename CoordT::value_type,
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std::common_type_t<
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typename CoordT::value_type,
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ScalarT
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>
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>
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,
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void
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>
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> {
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// we allow scalar types which can be naturally promoted to the vector's
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// value_type
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template <typename OperationT>
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static constexpr CoordT&
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eval (OperationT &&op, CoordT &coord, const ScalarT scalar)
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{
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for (size_t i = 0; i < CoordT::elements; ++i)
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coord[i] = op (coord[i], scalar);
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return coord;
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}
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};
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///////////////////////////////////////////////////////////////////////////
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/// create a coord from supplied arguments, optionally specifying the
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/// underlying type.
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///
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/// much like experimental::make_array we use a void type to signal we
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/// need to deduce the underlying type.
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#define MAKE_COORD(KLASS) \
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template < \
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typename _T = void, \
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typename ...Args \
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> \
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constexpr auto \
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make_##KLASS (Args &&...args) \
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{ \
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using T = std::conditional_t< \
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std::is_void_v<_T>, \
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std::common_type_t<Args...>, \
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_T \
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>; \
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\
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return KLASS<sizeof...(Args),T> { \
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std::forward<Args> (args)... \
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}; \
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}
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MAKE_COORD(extent)
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MAKE_COORD(point)
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MAKE_COORD(vector)
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#undef MAKE_COORD
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template <
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template <std::size_t,typename> class K,
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typename ...Args
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>
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constexpr auto
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make_coord (Args &&...args)
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{
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using T = std::common_type_t<Args...>;
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return K<sizeof...(Args),T> { std::forward<Args> (args)... };
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}
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///////////////////////////////////////////////////////////////////////////
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template <typename ValueA, typename ValueB, typename=void>
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struct arithmetic {};
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//-------------------------------------------------------------------------
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template <typename CoordA, typename CoordB>
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struct arithmetic<
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CoordA,
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CoordB,
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std::enable_if_t<
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is_coord_v<CoordA> &&
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is_coord_v<CoordB> &&
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arity_v<CoordA> == arity_v<CoordB> &&
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has_result_v<CoordA,CoordB>
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,
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void
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>
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> {
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template <typename OperationT>
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static constexpr auto
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eval (OperationT &&op, const CoordA &a, const CoordB &b)
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{
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using common_t = std::common_type_t<
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typename CoordA::value_type,
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typename CoordB::value_type
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>;
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revalue_t<result_t<CoordA,CoordB>,common_t> out {};
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for (size_t i = 0; i < CoordA::elements; ++i)
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out[i] = op (a[i], b[i]);
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return out;
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}
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};
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//-------------------------------------------------------------------------
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template <typename CoordT, typename ScalarT>
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struct arithmetic<
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CoordT,
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ScalarT,
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std::enable_if_t<
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is_coord_v<CoordT> && std::is_arithmetic_v<ScalarT> && has_scalar_op_v<CoordT>,
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void
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>
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> {
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template <typename OperationT>
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static constexpr auto
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eval (OperationT &&op, const CoordT &coord, const ScalarT &scalar)
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{
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using common_t = std::common_type_t<typename CoordT::value_type, ScalarT>;
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revalue_t<CoordT,common_t> out {};
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for (size_t i = 0; i < CoordT::elements; ++i)
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out[i] = op (coord[i], scalar);
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return out;
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}
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};
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//-------------------------------------------------------------------------
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template <typename ScalarT, typename CoordT>
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struct arithmetic<
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ScalarT,
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CoordT,
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std::enable_if_t<
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is_coord_v<CoordT> && std::is_arithmetic_v<ScalarT> && has_scalar_op_v<CoordT>,
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void
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>
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> {
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template <typename OperationT>
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static constexpr auto
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eval (OperationT &&op, const ScalarT &scalar, const CoordT &coord)
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{
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using common_t = std::common_type_t<typename CoordT::value_type, ScalarT>;
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revalue_t<CoordT,common_t> out {};
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for (size_t i = 0; i < CoordT::elements; ++i)
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out[i] = op (scalar, coord[i]);
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return out;
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}
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};
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///////////////////////////////////////////////////////////////////////////
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template <
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typename A,
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typename B,
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typename = std::enable_if_t<
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(is_coord_v<std::decay_t<A>> || is_coord_v<std::decay_t<B>>) &&
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(is_coord_v<std::decay_t<A>> || std::is_arithmetic_v<std::decay_t<A>>) &&
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(is_coord_v<std::decay_t<B>> || std::is_arithmetic_v<std::decay_t<B>>)
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>
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>
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constexpr auto
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operator+ (A &&a, B &&b)
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{
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return arithmetic<std::decay_t<A>, std::decay_t<B>>::template eval (std::plus{}, a, b);
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}
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template <
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typename A,
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typename B,
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typename = std::enable_if_t<
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(is_coord_v<std::decay_t<A>> || is_coord_v<std::decay_t<B>>) &&
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(is_coord_v<std::decay_t<A>> || std::is_arithmetic_v<std::decay_t<A>>) &&
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(is_coord_v<std::decay_t<B>> || std::is_arithmetic_v<std::decay_t<B>>)
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>
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>
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constexpr auto
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operator- (A &&a, B &&b)
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{
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return arithmetic<std::decay_t<A>, std::decay_t<B>>::template eval (std::minus{}, a, b);
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}
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template <
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typename A,
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typename B,
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typename = std::enable_if_t<
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(is_coord_v<std::decay_t<A>> || is_coord_v<std::decay_t<B>>) &&
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(is_coord_v<std::decay_t<A>> || std::is_arithmetic_v<std::decay_t<A>>) &&
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(is_coord_v<std::decay_t<B>> || std::is_arithmetic_v<std::decay_t<B>>)
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>
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>
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constexpr auto
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operator* (A &&a, B &&b)
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{
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return arithmetic<
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std::decay_t<A>,
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std::decay_t<B>
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>::template eval (std::multiplies{}, a, b);
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}
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template <
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typename A,
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typename B,
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typename = std::enable_if_t<
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(is_coord_v<std::decay_t<A>> || is_coord_v<std::decay_t<B>>) &&
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(is_coord_v<std::decay_t<A>> || std::is_arithmetic_v<std::decay_t<A>>) &&
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(is_coord_v<std::decay_t<B>> || std::is_arithmetic_v<std::decay_t<B>>)
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>
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>
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constexpr auto
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operator/ (A &&a, B &&b)
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{
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return arithmetic<std::decay_t<A>, std::decay_t<B>>::template eval (std::divides{}, a, b);
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}
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//-------------------------------------------------------------------------
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template <
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typename A,
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typename B,
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typename = std::enable_if_t<
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(is_coord_v<std::decay_t<A>> || is_coord_v<std::decay_t<B>>) &&
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(is_coord_v<std::decay_t<A>> || std::is_arithmetic_v<std::decay_t<A>>) &&
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(is_coord_v<std::decay_t<B>> || std::is_arithmetic_v<std::decay_t<B>>)
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>
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>
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constexpr auto
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operator += (A &&a, B &&b)
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{
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return assignment<
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std::decay_t<A>,
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std::decay_t<B>
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>::eval (std::plus{}, a, b);
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}
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template <
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typename A,
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typename B,
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typename = std::enable_if_t<
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(is_coord_v<std::decay_t<A>> || is_coord_v<std::decay_t<B>>) &&
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(is_coord_v<std::decay_t<A>> || std::is_arithmetic_v<std::decay_t<A>>) &&
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(is_coord_v<std::decay_t<B>> || std::is_arithmetic_v<std::decay_t<B>>)
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>
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>
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constexpr auto
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operator -= (A &&a, B &&b)
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{
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return assignment<
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std::decay_t<A>,
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std::decay_t<B>
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>::eval (std::minus{}, a, b);
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}
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template <
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typename A,
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typename B,
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typename = std::enable_if_t<
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(is_coord_v<std::decay_t<A>> || is_coord_v<std::decay_t<B>>) &&
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(is_coord_v<std::decay_t<A>> || std::is_arithmetic_v<std::decay_t<A>>) &&
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(is_coord_v<std::decay_t<B>> || std::is_arithmetic_v<std::decay_t<B>>)
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>
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>
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constexpr auto
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operator *= (A &&a, B &&b)
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{
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return assignment<
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std::decay_t<A>,
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std::decay_t<B>
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>::eval (std::multiplies{}, a, b);
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}
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template <
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typename A,
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typename B,
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typename = std::enable_if_t<
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(is_coord_v<std::decay_t<A>> || is_coord_v<std::decay_t<B>>) &&
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(is_coord_v<std::decay_t<A>> || std::is_arithmetic_v<std::decay_t<A>>) &&
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(is_coord_v<std::decay_t<B>> || std::is_arithmetic_v<std::decay_t<B>>)
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>
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>
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constexpr auto
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operator /= (A &&a, B &&b)
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{
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return assignment<
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std::decay_t<A>,
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std::decay_t<B>
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>::eval (std::divides{}, a, b);
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}
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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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typename K, \
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typename = std::enable_if_t< \
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is_coord_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 k) \
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{ \
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using value_type = decltype( \
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OP std::declval<typename K::value_type> () \
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); \
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\
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revalue_t<K,value_type> out {}; \
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\
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for (std::size_t i = 0; i < K::elements; ++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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|
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#undef UNARY_OP
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|
|
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///////////////////////////////////////////////////////////////////////////
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namespace detail {
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/// invoke a function elementwise to the arguments elementwise.
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///
|
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/// \tparam ArgsT a tuple containing the (coord) arguments for the func
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template <
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typename RetT,
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typename FuncT,
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typename ArgsT,
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std::size_t ...Indices
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>
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constexpr auto
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apply (const std::index_sequence<Indices...>,
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FuncT &&func,
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ArgsT args) noexcept
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|
{
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using part_t = std::tuple_element_t<0,ArgsT>;
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using value_t = typename part_t::value_type;
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return RetT {
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std::apply (
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func,
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::util::tuple::value::map (
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static_cast<
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const value_t& (&)(const part_t&)
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|
> (
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get<Indices,RetT>
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), args
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)
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|
)...
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|
};
|
|
}
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
// invokes a function elementwise using elementwise parameters from the
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// supplied arguments.
|
|
//
|
|
// equivalent to this pseduocode:
|
|
// for (int i: indices (ReturnT))
|
|
// res[i] = func (args[i]...);
|
|
// return res;
|
|
//
|
|
// forwards the arguments as a tuple to a helper function that has access
|
|
// to indices as a template parameter.
|
|
template <
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typename ReturnT,
|
|
typename FuncT,
|
|
typename ...ArgT,
|
|
typename = std::enable_if_t<
|
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// return type and arguments must be coordinates
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|
(is_coord_v<ReturnT> && ... && is_coord_v<std::decay_t<ArgT>>) &&
|
|
// all types must be the same arity
|
|
((ReturnT::elements == std::decay_t<ArgT>::elements) && ...) &&
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|
// all the arguments must be the same type
|
|
(std::is_same_v<
|
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std::tuple_element_t<0,std::tuple<std::decay_t<ArgT>...>>,
|
|
std::decay_t<ArgT>
|
|
> && ...),
|
|
void
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>,
|
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typename Indices = std::make_index_sequence<ReturnT::elements>
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|
>
|
|
constexpr auto
|
|
invoke (FuncT &&func, ArgT &&...args) noexcept
|
|
{
|
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return detail::apply<ReturnT> (
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Indices{},
|
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std::forward<FuncT> (func),
|
|
std::tuple (std::forward<ArgT> (args)...)
|
|
);
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
// logic operators
|
|
namespace detail {
|
|
template <
|
|
typename K,
|
|
typename FuncT,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K>, void
|
|
>,
|
|
std::size_t ...Indices
|
|
>
|
|
constexpr auto
|
|
compare (FuncT &&func, std::index_sequence<Indices...>, const K a, const K b)
|
|
{
|
|
return vector<K::elements,bool> {
|
|
std::invoke (func, a[Indices], b[Indices])...
|
|
};
|
|
}
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <
|
|
typename K,
|
|
typename FuncT,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K>, void
|
|
>,
|
|
typename Indices = std::make_index_sequence<K::elements>
|
|
>
|
|
constexpr auto
|
|
compare (const K a, const K b, FuncT &&func)
|
|
{
|
|
return detail::compare (std::forward<FuncT> (func), Indices{}, a, b);
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K>, void
|
|
>
|
|
>
|
|
constexpr auto
|
|
compare (const K a, const K b)
|
|
{
|
|
return compare (a, b, std::equal_to<typename K::value_type> {});
|
|
}
|
|
|
|
|
|
/// elementwise equality operator
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K>, void
|
|
>
|
|
>
|
|
constexpr bool
|
|
operator== (const K a, const K b)
|
|
{
|
|
return all (compare (a, b, std::equal_to<typename K::value_type> {}));
|
|
}
|
|
|
|
///------------------------------------------------------------------------
|
|
/// elementwise inquality operator
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K>, void
|
|
>
|
|
>
|
|
constexpr bool
|
|
operator!= (const K a, const K b)
|
|
{
|
|
return any (compare (a, b, std::not_equal_to<typename K::value_type> {}));
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K>, void
|
|
>
|
|
>
|
|
constexpr
|
|
bool
|
|
almost_zero (const K &k)
|
|
{
|
|
return std::all_of (
|
|
std::cbegin (k),
|
|
std::cend (k),
|
|
[] (auto t) { return almost_zero (t); }
|
|
);
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
// special operators
|
|
|
|
/// point-point subtraction giving a vector difference
|
|
template <
|
|
std::size_t S,
|
|
typename T,
|
|
typename U
|
|
>
|
|
constexpr
|
|
vector<S,std::common_type_t<T,U>>
|
|
operator- (point<S,T> a, point<S,U> b)
|
|
{
|
|
vector<S,std::common_type_t<T,U>> out {};
|
|
for (std::size_t i = 0; i < S; ++i)
|
|
out[i] = a[i] - b[i];
|
|
return out;
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <
|
|
std::size_t S,
|
|
typename T,
|
|
typename U,
|
|
typename = std::enable_if_t<
|
|
std::is_arithmetic<T>::value && std::is_arithmetic<U>::value,
|
|
void
|
|
>
|
|
>
|
|
constexpr
|
|
vector<S,std::common_type_t<T,U>>
|
|
operator- (U u, point<S,T> p)
|
|
{
|
|
return point<S,U> {u} - p;
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
template <
|
|
std::size_t S,
|
|
typename T
|
|
>
|
|
constexpr
|
|
T
|
|
dot (const T (&a)[S], const T (&b)[S])
|
|
{
|
|
T sum = 0;
|
|
for (std::size_t i = 0; i < S; ++i)
|
|
sum += a[i] * b[i];
|
|
return sum;
|
|
}
|
|
|
|
|
|
template <
|
|
std::size_t S,
|
|
typename T,
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K> && std::is_same_v<typename K::value_type, T> && K::elements == S,
|
|
void
|
|
>
|
|
>
|
|
constexpr
|
|
T
|
|
dot (const T (&a)[S], K k)
|
|
{
|
|
return dot (a, k.data);
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <
|
|
typename A,
|
|
typename B,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<A> && is_coord_v<B>, void
|
|
>
|
|
>
|
|
constexpr auto
|
|
dot (A a, B b)
|
|
{
|
|
return dot (a.data, b.data);
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <
|
|
typename K,
|
|
typename T,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K> && std::is_same_v<T,typename K::value_type>, void
|
|
>
|
|
>
|
|
constexpr auto
|
|
dot (K a, const T (&b)[K::elements])
|
|
{
|
|
return dot (a.data, b);
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K>, void
|
|
>
|
|
>
|
|
constexpr auto
|
|
dot (const typename K::value_type (&a)[K::elements], K b)
|
|
{
|
|
return dot (a, b.data);
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<has_norm_v<K>,void>
|
|
>
|
|
constexpr
|
|
auto
|
|
norm2 (const K &k)
|
|
{
|
|
return dot (k, k);
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
has_norm_v<K>,
|
|
void
|
|
>
|
|
>
|
|
constexpr
|
|
auto
|
|
norm (const K &k)
|
|
{
|
|
return std::sqrt (norm2 (k));
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
has_norm_v<K>,
|
|
void
|
|
>
|
|
>
|
|
constexpr
|
|
auto
|
|
normalised (const K &k)
|
|
{
|
|
CHECK_NEZ (norm (k));
|
|
return k / norm (k);
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
has_norm_v<K>,
|
|
void
|
|
>
|
|
>
|
|
constexpr
|
|
bool
|
|
is_normalised (const K &k)
|
|
{
|
|
using value_type = typename K::value_type;
|
|
constexpr auto hi = value_type (1.00001);
|
|
constexpr auto lo = value_type (0.99999);
|
|
|
|
const auto n2 = norm2 (k);
|
|
return n2 < hi && n2 > lo;
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K>, void
|
|
>
|
|
>
|
|
constexpr
|
|
K
|
|
abs (K k)
|
|
{
|
|
for (auto &v: k)
|
|
v = std::abs (v);
|
|
return k;
|
|
}
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
template <
|
|
typename BaseT,
|
|
typename = std::enable_if_t<is_coord_v<BaseT>>
|
|
>
|
|
constexpr
|
|
auto
|
|
pow (BaseT k, float p)
|
|
{
|
|
for (auto &v: k)
|
|
v = std::pow (v, p);
|
|
return k;
|
|
}
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
// root of sum of squares
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K>, void
|
|
>
|
|
>
|
|
constexpr typename K::value_type
|
|
hypot (K k)
|
|
{
|
|
return std::sqrt (sum (k * k));
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
template <
|
|
typename K,
|
|
typename T,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K> && std::is_same_v<T, typename K::value_type>, void
|
|
>
|
|
>
|
|
constexpr auto
|
|
mod (K k, T t)
|
|
{
|
|
std::transform (
|
|
std::cbegin (k),
|
|
std::cend (k),
|
|
std::begin (k),
|
|
[t] (auto v) { return mod (v, t);
|
|
});
|
|
|
|
return k;
|
|
}
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
// trigonometric functions
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<is_coord_v<K>,void>
|
|
>
|
|
constexpr auto
|
|
sin (K k)
|
|
{
|
|
std::transform (
|
|
std::cbegin (k),
|
|
std::cend (k),
|
|
std::begin (k),
|
|
[] (auto v) { return std::sin (v); }
|
|
);
|
|
|
|
return k;
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<is_coord_v<K>,void>
|
|
>
|
|
constexpr auto
|
|
cos (K 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 <
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K>, void
|
|
>,
|
|
typename ...Args
|
|
>
|
|
constexpr auto
|
|
min (K a, K b, Args &&...args)
|
|
{
|
|
// the varargs must be the same types as the first two arguments
|
|
static_assert ((
|
|
... && std::is_same_v<
|
|
K,
|
|
std::decay_t<Args>
|
|
>
|
|
));
|
|
|
|
K out {};
|
|
for (std::size_t i = 0; i < K::elements; ++i)
|
|
out[i] = min (a[i], b[i], args[i]...);
|
|
return out;
|
|
}
|
|
|
|
|
|
///------------------------------------------------------------------------
|
|
// /return a coord type containing the max element at each offset
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K>, void
|
|
>,
|
|
typename ...Args
|
|
>
|
|
constexpr auto
|
|
max (K a, K b, Args &&...args)
|
|
{
|
|
static_assert ((
|
|
... && std::is_same_v<
|
|
K,
|
|
std::decay_t<Args>
|
|
>
|
|
));
|
|
|
|
K out {};
|
|
for (std::size_t i = 0; i < K::elements; ++i)
|
|
out[i] = max (a[i], b[i], args[i]...);
|
|
return out;
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
/// returns a coordinate type where each element has been clamped to the
|
|
/// range [lo,hi].
|
|
///
|
|
/// we specifically do not allow different coordinate types for val, lo,
|
|
/// and hi because the min and max calls are ill definied for varying
|
|
/// types (not because varying types would not be useful).
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K>, void
|
|
>
|
|
>
|
|
constexpr auto
|
|
clamp (K k, K lo, K hi)
|
|
{
|
|
assert (all (lo <= hi));
|
|
return max (min (k, hi), lo);
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K>, void
|
|
>
|
|
>
|
|
constexpr auto
|
|
clamp (K k, typename K::value_type lo, K hi)
|
|
{
|
|
return clamp (k, K {lo}, hi);
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K>, void
|
|
>
|
|
>
|
|
constexpr auto
|
|
clamp (K k, K lo, typename K::value_type hi)
|
|
{
|
|
return clamp (k, lo, K {hi});
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K>, void
|
|
>
|
|
>
|
|
constexpr auto
|
|
clamp (K k, typename K::value_type lo, typename K::value_type hi)
|
|
{
|
|
return clamp (k, K {lo}, K {hi});
|
|
}
|
|
|
|
|
|
///------------------------------------------------------------------------
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K>, void
|
|
>
|
|
>
|
|
constexpr auto
|
|
min (const K &k)
|
|
{
|
|
return *std::min_element (std::cbegin (k), std::cend (k));
|
|
}
|
|
|
|
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K>, void
|
|
>
|
|
>
|
|
constexpr auto
|
|
max (const K &k)
|
|
{
|
|
return *std::max_element (std::cbegin (k), std::cend (k));
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K>, void
|
|
>
|
|
>
|
|
constexpr auto
|
|
sum (const K &k)
|
|
{
|
|
// DO NOT USE util::sum(begin, end) from maths.hpp
|
|
//
|
|
// It would be nice to use kahan summation from maths.hpp but speed
|
|
// and simplicity is more important for these fixed sized
|
|
// coordinates. Infinities tend to crop up using these classes and
|
|
// they cause a few headaches in the kahan code.
|
|
//
|
|
// So, if the user wants kahan summation they can request it
|
|
// explicitly.
|
|
|
|
return std::accumulate (std::cbegin (k), std::cend (k), typename K::value_type{0});
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<is_coord_v<K>>
|
|
>
|
|
auto
|
|
product (K const& k)
|
|
{
|
|
typename K::value_type accum = 1;
|
|
for (auto i: k)
|
|
accum *= i;
|
|
return accum;
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
#define VECTOR_OP(OP) \
|
|
template < \
|
|
typename A, \
|
|
typename B, \
|
|
typename = std::enable_if_t< \
|
|
is_coord_v<A> && \
|
|
is_coord_v<B> && \
|
|
A::elements == B::elements && \
|
|
std::is_same_v< \
|
|
typename A::value_type, \
|
|
typename B::value_type \
|
|
>, \
|
|
void \
|
|
> \
|
|
> \
|
|
constexpr auto \
|
|
operator OP (const A a, const B b) \
|
|
{ \
|
|
vector<A::elements,bool> out {}; \
|
|
for (std::size_t i = 0; i < A::elements; ++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 < \
|
|
typename K, \
|
|
typename U, \
|
|
typename = std::enable_if_t< \
|
|
is_coord_v<K> && \
|
|
std::is_arithmetic_v<U>, \
|
|
void \
|
|
> \
|
|
> \
|
|
constexpr auto \
|
|
operator OP (const K &k, const U u) \
|
|
{ \
|
|
vector<K::elements,bool> out {}; \
|
|
for (std::size_t i = 0; i < K::elements; ++i) \
|
|
out[i] = k[i] OP u; \
|
|
return out; \
|
|
} \
|
|
\
|
|
template < \
|
|
typename K, \
|
|
typename U, \
|
|
typename = std::enable_if_t< \
|
|
is_coord_v<K> && \
|
|
std::is_arithmetic_v<U>, \
|
|
void \
|
|
> \
|
|
> \
|
|
constexpr auto \
|
|
operator OP (const U u, const K &k) \
|
|
{ \
|
|
vector<K::elements,bool> out {}; \
|
|
for (std::size_t i = 0; i < K::elements; ++i) \
|
|
out[i] = u OP k[i]; \
|
|
return out; \
|
|
}
|
|
|
|
SCALAR_OP(<)
|
|
SCALAR_OP(>)
|
|
SCALAR_OP(<=)
|
|
SCALAR_OP(>=)
|
|
SCALAR_OP(==)
|
|
SCALAR_OP(&&)
|
|
SCALAR_OP(||)
|
|
|
|
#undef SCALAR_OP
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
namespace detail {
|
|
template <
|
|
std::size_t S,
|
|
template <std::size_t,typename> class K,
|
|
std::size_t ...I,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K<S,bool>>,
|
|
void
|
|
>
|
|
>
|
|
constexpr bool
|
|
any (const K<S,bool> k, std::index_sequence<I...>)
|
|
{
|
|
return (k[I] || ...);
|
|
}
|
|
};
|
|
|
|
|
|
///---------------------------------------------------------------------------
|
|
/// returns true if any element is true.
|
|
///
|
|
/// this function must be suitable for use in static_assert, so it must remain
|
|
/// constexpr.
|
|
///
|
|
/// we would ideally use std::any_of, but it is not constexpr.
|
|
/// we would ideally use range-for, but cbegin is not constexpr.
|
|
/// so... moar templates.
|
|
template <
|
|
std::size_t S,
|
|
template <std::size_t,typename> class K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K<S,bool>>, void
|
|
>,
|
|
typename Indices = std::make_index_sequence<S>
|
|
>
|
|
constexpr
|
|
bool
|
|
any (const K<S,bool> k)
|
|
{
|
|
return detail::any (k, Indices{});
|
|
}
|
|
|
|
|
|
///------------------------------------------------------------------------
|
|
/// returns true if the value is true.
|
|
///
|
|
/// provided so that templates may operate with the same calls for vectors
|
|
/// and scalars. eg, any (t >= 0 && t <= 1) should work for arbitrary
|
|
/// types.
|
|
constexpr
|
|
bool any (const bool val)
|
|
{
|
|
return val;
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
namespace detail {
|
|
template <
|
|
std::size_t S,
|
|
template <std::size_t,typename> class K,
|
|
std::size_t ...I,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K<S,bool>>,
|
|
void
|
|
>
|
|
>
|
|
constexpr bool
|
|
all (const K<S,bool> k, std::index_sequence<I...>)
|
|
{
|
|
return (k[I] && ...);
|
|
}
|
|
}
|
|
|
|
//-------------------------------------------------------------------------
|
|
/// returns true if all elements are true.
|
|
///
|
|
/// this function must be suitable for use in static_assert, so it must be
|
|
/// constexpr.
|
|
///
|
|
/// we would ideally use std::all_of, but it is not constexpr.
|
|
/// we would ideally use range-for, but cbegin is not constexpr.
|
|
/// so... moar templates.
|
|
template <
|
|
std::size_t S,
|
|
template <std::size_t,typename> class K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K<S,bool>>, void
|
|
>,
|
|
typename Indices = std::make_index_sequence<S>
|
|
>
|
|
constexpr
|
|
bool
|
|
all (const K<S,bool> k)
|
|
{
|
|
return detail::all (k, Indices {});
|
|
}
|
|
|
|
|
|
///------------------------------------------------------------------------
|
|
/// returns true if the value is true.
|
|
///
|
|
/// provided so that templates may operate with the same calls for vectors
|
|
/// and scalars. eg, all (t >= 0 && t <= 1) should work for either type.
|
|
constexpr bool
|
|
all (bool val)
|
|
{
|
|
return val;
|
|
}
|
|
|
|
|
|
///------------------------------------------------------------------------
|
|
/// returns an instance of K elementwise using a when s is true, and b
|
|
/// otherwise. ie, k[i] = s[i] ? a[i] : b[i];
|
|
///
|
|
/// corresponds to the function `select' from OpenCL.
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K>, void
|
|
>
|
|
>
|
|
constexpr auto
|
|
select (vector<K::elements,bool> s, K a, K b)
|
|
{
|
|
K k {};
|
|
for (std::size_t i = 0; i < K::elements; ++i)
|
|
k[i] = s[i] ? a[i] : b[i];
|
|
return k;
|
|
}
|
|
|
|
|
|
template <
|
|
size_t S,
|
|
typename T,
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K> && !is_coord_v<T>
|
|
>
|
|
>
|
|
constexpr auto
|
|
select (vector<S,bool> s, K a, T b)
|
|
{
|
|
return select (s, a, K {b});
|
|
}
|
|
|
|
|
|
template <
|
|
size_t S,
|
|
typename T,
|
|
typename = std::enable_if_t<!is_coord_v<T>>
|
|
>
|
|
constexpr auto
|
|
select (vector<S,bool> s, T a, T b)
|
|
{
|
|
return select (s, vector<S,T> {a}, vector<S,T> {b});
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
// return the componentwise floor of the coordinate type
|
|
//
|
|
// don't use std::floor, it's _really_ slow in comparison.
|
|
//
|
|
// ideally we'd use SIMD or other more useful instructions here.
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K> && std::is_floating_point_v<typename K::value_type>
|
|
>
|
|
>
|
|
constexpr auto
|
|
floor (const K &k)
|
|
{
|
|
K out {};
|
|
std::transform (
|
|
std::cbegin (k),
|
|
std::cend (k),
|
|
std::begin (out),
|
|
[] (auto i) {
|
|
return i >= 0 ? static_cast<intmax_t> (i) : static_cast<intmax_t> (i) - 1;
|
|
}
|
|
);
|
|
|
|
return out;
|
|
}
|
|
|
|
|
|
///------------------------------------------------------------------------
|
|
/// Return the fractional part of a real value.
|
|
///
|
|
/// This is an extraodinarily naive implementation. We avoid doing
|
|
/// explicit casts here in the hope that floor and sub is more efficient
|
|
/// (ie, keeps floats as floats in registers).
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K> &&
|
|
std::is_floating_point_v<
|
|
typename K::value_type
|
|
>
|
|
>
|
|
>
|
|
constexpr auto
|
|
frac (const K k)
|
|
{
|
|
return k - floor (k);
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////
|
|
/// shifts all elements `num' indices to the right, setting the left-most
|
|
/// `num' indices to the value `fill'.
|
|
///
|
|
/// num must be between 0 and S. when 0 it is equivalent to an ordinary
|
|
/// fill, when S it is equivalent to a noop.
|
|
template<
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K>, void
|
|
>
|
|
>
|
|
constexpr auto
|
|
rshift (const K k, const int num, const K fill)
|
|
{
|
|
CHECK_LIMIT (num, 0, int (K::elements));
|
|
|
|
K res {};
|
|
|
|
std::copy_n (std::cbegin (k), K::elements - num, std::begin (res) + num);
|
|
std::copy_n (std::cbegin (fill), num, std::begin (res));
|
|
|
|
return res;
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template<
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K>, void
|
|
>
|
|
>
|
|
constexpr auto
|
|
rshift (const K k, const int num, typename K::value_type fill)
|
|
{
|
|
return rshift (k, num, K {fill});
|
|
}
|
|
|
|
|
|
template <
|
|
typename K,
|
|
typename = std::enable_if_t<
|
|
is_coord_v<K>
|
|
>
|
|
>
|
|
constexpr auto
|
|
lshift (const K k, const int places, typename K::value_type fill)
|
|
{
|
|
K res {};
|
|
std::copy_n (std::cbegin (k) + places, K::elements - places, std::begin (res));
|
|
std::fill_n (std::begin (res) + K::elements - places, places, fill);
|
|
return res;
|
|
}
|
|
};
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////////
|
|
#include <tuple>
|
|
|
|
namespace std {
|
|
/// returns the dimensions of a coordinate type.
|
|
///
|
|
/// specifically required for structured bindings support.
|
|
///
|
|
/// \tparam S dimensions
|
|
/// \tparam T data type
|
|
/// \tparam K coordinate class
|
|
template <
|
|
std::size_t S,
|
|
typename T,
|
|
template <std::size_t,typename> typename K
|
|
>
|
|
class tuple_size<K<S,T>> : public std::enable_if_t<
|
|
::util::is_coord_v<K<S,T>>,
|
|
std::integral_constant<std::size_t, S>
|
|
> { };
|
|
|
|
|
|
/// indicates the type at a given index of a coordinate type
|
|
///
|
|
/// specifically required for structured bindings support.
|
|
///
|
|
/// \tparam I data index
|
|
/// \tparam S dimensionality of the coordinate
|
|
/// \tparam T data type for the coordinate
|
|
/// \tparam K the underlying coordinate class
|
|
template <
|
|
std::size_t I,
|
|
std::size_t S,
|
|
typename T,
|
|
template <std::size_t,typename> typename K
|
|
>
|
|
class tuple_element<I,K<S,T>> : public std::enable_if<
|
|
::util::is_coord_v<K<S,T>>,
|
|
T
|
|
> {};
|
|
}
|
|
|
|
|
|
///////////////////////////////////////////////////////////////////////////////
|
|
#include "../hash.hpp"
|
|
|
|
|
|
namespace std {
|
|
//-------------------------------------------------------------------------
|
|
template <
|
|
std::size_t S,
|
|
typename T,
|
|
template <std::size_t,typename> typename K
|
|
>
|
|
struct hash<K<S,T>> : enable_if<
|
|
::util::is_coord_v<K<S,T>>
|
|
> {
|
|
uint32_t operator() (K<S,T> k) const {
|
|
uint32_t v = 0xdeadbeef;
|
|
|
|
for (T t: k)
|
|
v = ::util::hash::mix (t, v);
|
|
|
|
return v;
|
|
}
|
|
};
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <
|
|
typename CoordT,
|
|
typename = std::enable_if_t<
|
|
::util::is_coord_v<CoordT>, void
|
|
>
|
|
>
|
|
auto cos (CoordT val)
|
|
{
|
|
return ::util::invoke<CoordT> (::util::cos<typename CoordT::value_type>, val);
|
|
}
|
|
|
|
|
|
//-------------------------------------------------------------------------
|
|
template <
|
|
typename CoordT,
|
|
typename = std::enable_if_t<
|
|
::util::is_coord_v<CoordT>, void
|
|
>
|
|
>
|
|
auto sin (CoordT val)
|
|
{
|
|
return ::util::invoke<CoordT> (::util::sin<typename CoordT::value_type>, val);
|
|
}
|
|
};
|
|
|
|
|
|
#endif
|