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 // This file is part of the ACTS project.
 //
 // Copyright (C) 2016 CERN for the benefit of the ACTS project
 //
 // This Source Code Form is subject to the terms of the Mozilla Public
 // License, v. 2.0. If a copy of the MPL was not distributed with this
 // file, You can obtain one at https://mozilla.org/MPL/2.0/.
 
 #pragma once
 
 #include <algorithm>
 #include <array>
 #include <cassert>
 #include <limits>
 #include <sstream>
 #include <string>
 
 namespace Acts {
 /// @brief An orthogonal range in an arbitrary number of dimensions
 ///
 /// By combining a number one-dimensional ranges we can (under the assumption
 /// that our axes are orthogonal) construct an orthogonal range of values. In
 /// other words, a hyperrectangular volume in space.
 ///
 /// @tparam Dims The number of dimensions in our range
 /// @tparam Type The scalar type of our ranges
 /// @tparam Vector The vector type used to define coordinates
 template <std::size_t Dims, typename Type,
           template <typename, std::size_t> typename Vector = std::array>
 class RangeXD {
  private:
   // @TODO: Replace with std::span or boost::span once available
   template <typename, std::size_t>
   struct SingleElementContainer {
     Type* element;
 
     Type& operator[](std::size_t i) {
       (void)i;
       assert(i == 0);
 
       return *element;
     }
   };
 
  public:
   RangeXD() {
     for (std::size_t i = 0; i < Dims; ++i) {
       min(i) = std::numeric_limits<Type>::lowest();
       max(i) = std::numeric_limits<Type>::max();
     }
   }
 
   /// @brief Construct a range from a pair of minimum and maximum values
   /// @param minima The minimum values of the range
   /// @param maxima The maximum values of the range
   RangeXD(Vector<Type, Dims> minima, Vector<Type, Dims> maxima)
       : m_minima(minima), m_maxima(maxima) {}
 
   /// @brief Construct a range from a pair of single minimum and maximum values
   /// @note Only available for one-dimensional ranges
   /// @param minimum The minimum value of the range
   /// @param maximum The maximum value of the range
   RangeXD(Type minimum, Type maximum)
     requires(Dims == 1)
       : m_minima({minimum}), m_maxima({maximum}) {}
 
   /// @brief Construct a range from a pair of minimum and maximum values
   /// @note Only available for one-dimensional ranges
   /// @param p The pair of minimum and maximum values
   RangeXD(const std::pair<Type, Type>& p)
     requires(Dims == 1)
       : m_minima({p.first}), m_maxima({p.second}) {}
 
   /// @brief Determine whether this range is degenerate
   ///
   /// A degenerate multi-dimensional range has no volume and cannot contain
   /// any values. This is the case if any of its dimensions are degenerate.
   ///
   /// @return true The range is degenerate
   /// @return false The range is not degenerate
   bool degenerate() const {
     for (std::size_t i = 0; i < Dims; ++i) {
       if (min(i) >= max(i)) {
         return true;
       }
     }
     return false;
   }
 
   /// @brief Determine whether the range contains a certain point
   ///
   /// This is true if and only if the range contains the point in all of its
   /// dimensions.
   ///
   /// @param v The coordinate to check for membership in the range
   ///
   /// @return true The coordinate is inside the range
   /// @return false The coordinate is outside the range
   template <template <typename, std::size_t> typename coordinate_t = std::array>
   bool contains(const coordinate_t<Type, Dims>& v) const {
     for (std::size_t i = 0; i < Dims; ++i) {
       if (!(min(i) <= v[i] && v[i] < max(i))) {
         return false;
       }
     }
 
     return true;
   }
 
   /// @brief Access one of the dimensional ranges of the volume
   ///
   /// @param i The index of the dimension to access
   /// @return A reference to the dimension contained in this range
   RangeXD<1, Type, SingleElementContainer> operator[](const std::size_t& i) {
     return RangeXD<1, Type, SingleElementContainer>{{&min(i)}, {&max(i)}};
   }
 
   /// @brief Access one of the dimensional ranges of the volume
   ///
   /// @param i The index of the dimension to access
   /// @return A reference to the dimension contained in this range
   RangeXD<1, Type> operator[](const std::size_t& i) const {
     return RangeXD<1, Type>{{min(i)}, {max(i)}};
   }
 
   /// @brief Assignment operator
   ///
   /// Copy the right-hand range into the left-hand range, which means setting
   /// the minimum and maximum to equal the minimum and maximum of the
   /// right-hand side.
   ///
   /// @param o The range of values to copy
   ///
   /// @return This range
   template <template <typename, std::size_t> typename V>
   RangeXD& operator=(const RangeXD<Dims, Type, V>& o) {
     for (std::size_t i = 0; i < Dims; ++i) {
       min(i) = o.min(i);
       max(i) = o.max(i);
     }
 
     return *this;
   }
 
   /// @brief Determine whether two ranges are equal
   ///
   /// Two n-dimensional ranges are equal if and only if they are equal in each
   /// of their n dimensions.
   ///
   /// @param o The other range to check for equality
   ///
   /// @return true The ranges are equal
   /// @return false The ranges are not equal
   bool operator==(const RangeXD<Dims, Type, Vector>& o) const {
     for (std::size_t i = 0; i < Dims; ++i) {
       if (!(min(i) == o.min(i) && max(i) == o.max(i))) {
         return false;
       }
     }
 
     return true;
   }
 
   /// @brief Determine whether one range is a subset of another range
   ///
   /// One range is a subset of another range if and only if all points
   /// contained within the first set are also contained within the second set.
   /// Alternatively, this is equivalent to each of the first range's
   /// one-dimensional ranges being a subset of the second range's equivalent
   /// one-dimensional range.
   ///
   /// @param o The other range to compare to
   ///
   /// @return true The first range is a subset of the second range
   /// @return false The first range is not a subset of the second range
   bool operator<=(const RangeXD<Dims, Type, Vector>& o) const {
     for (std::size_t i = 0; i < Dims; ++i) {
       if (!(min(i) >= o.min(i) && max(i) <= o.max(i))) {
         return false;
       }
     }
 
     return true;
   }
 
   /// @brief Determine whether one range is a superset of another range
   ///
   /// One range is a superset of another range if and only if all points
   /// contained within the second range are also contained within the first
   /// range. Alternatively, this is equivalent to each of the one-dimensional
   /// ranges in the first range being a superset of the corresponding
   /// one-dimensional range in the second range.
   ///
   /// @param o The other range to compare to
   ///
   /// @return true The left-hand range is a superset of the right-hand range
   /// @return false The left-hand range is not a superset of the right-hand
   /// range
   bool operator>=(const RangeXD<Dims, Type, Vector>& o) const {
     for (std::size_t i = 0; i < Dims; ++i) {
       if (!(min(i) <= o.min(i) && max(i) >= o.max(i))) {
         return false;
       }
     }
 
     return true;
   }
 
   /// @brief Compute the intersection of this range with another range
   ///
   /// The intersection of one orthogonal range with another orthogonal range
   /// is in itself an orthogonal range. This operation is commutative. This
   /// intersection between two n-dimensional ranges is defined simply as the
   /// intersection in each dimension of the two ranges.
   ///
   /// @param o The orthogonal range to compute the intersection with
   ///
   /// @return The intersection between the ranges
   RangeXD<Dims, Type, Vector> operator&(
       const RangeXD<Dims, Type, Vector>& o) const {
     RangeXD<Dims, Type> res;
 
     for (std::size_t i = 0; i < Dims; ++i) {
       res.min(i) = std::max(min(i), o.min(i));
       res.max(i) = std::min(max(i), o.max(i));
     }
 
     return res;
   }
 
   /// @brief Update the range to the intersection with another range
   ///
   /// This is the assignment version of the operator& method, meaning that it
   /// updates the object on which it is called rather than producing a new
   /// range.
   ///
   /// @param o The range to compute the intersection with
   ///
   /// @return This object
   RangeXD<Dims, Type, Vector>& operator&=(
       const RangeXD<Dims, Type, Vector>& o) {
     for (std::size_t i = 0; i < Dims; ++i) {
       min(i) = std::max(min(i), o.min(i));
       max(i) = std::min(max(i), o.max(i));
     }
 
     return *this;
   }
 
   /// @brief Determine whether this range intersects another
   ///
   /// Two n-dimensional ranges intersect if and only if they intersect in
   /// every one of their n dimensions. Otherwise, they are disjoint.
   ///
   /// @param r The other range to check
   ///
   /// @return true The ranges intersect
   /// @return false The ranges do not intersect
   bool operator&&(const RangeXD<Dims, Type, Vector>& r) const {
     for (std::size_t i = 0; i < Dims; ++i) {
       if (!(min(i) < r.max(i) && r.min(i) < max(i))) {
         return false;
       }
     }
 
     return true;
   }
 
   /// @brief Represent the range as a string
   ///
   /// This method produces a helpful string that can be used to debug the
   /// range if needed. Not really designed to be used in production code.
   ///
   /// @return A string representing the range
   std::string toString(void) const {
     std::stringstream s;
 
     for (std::size_t i = 0; i < Dims; ++i) {
       s << min(i) << " <= v[" << i << "] <= " << max(i);
       if (i != Dims - 1) {
         s << ", ";
       }
     }
 
     return s.str();
   }
 
   /// @brief Shrink a range by increasing the minimum value
   ///
   /// Shrink the range by increasing the minimum value. If the given value is
   /// smaller than the current minimum (in other words, if the proposed new
   /// range would be larger than the current range), this is a no-op.
   ///
   /// @param i The index of the dimension to shrink
   /// @param v The proposed new minimum for the range
   void shrinkMin(std::size_t i, const Type& v) { min(i) = std::max(min(i), v); }
 
   /// @brief Shrink a range by decreasing the maximum value
   ///
   /// Shrink the range by decreasing the maximum value. If the given value is
   /// larger than the current maximum (in other words, if the proposed new
   /// range would be larger than the current range), this is a no-op.
   ///
   /// @param i The index of the dimension to shrink
   /// @param v The proposed new maximum for the range
   void shrinkMax(std::size_t i, const Type& v) { max(i) = std::min(max(i), v); }
 
   /// @brief Shrink a range on both ends
   ///
   /// Shrink a range by increasing the minimum value as well as decreasing the
   /// maximum value. If either of the values are already smaller or larger
   /// (respectively) than the proposed values, then that particular boundary
   /// of the interval is not shrunk.
   ///
   /// @note After this operation, the range is always equal to or smaller than
   /// [min, max].
   ///
   /// @param i The index of the dimension to shrink
   /// @param min The proposed new minimum for the range
   /// @param max The proposed new maximum for the range
   void shrink(std::size_t i, const Type& min, const Type& max) {
     shrinkMin(i, min);
     shrinkMax(i, max);
   }
 
   /// @brief Expand a range by decreasing the minimum value
   ///
   /// Expand the range by decreasing the minimum value. If the given value is
   /// larger than the current minimum (in other words, if the proposed new
   /// range would be smaller than the current range), this is a no-op.
   ///
   /// @param i The index of the dimension to expand
   /// @param v The proposed new minimum for the range
   void expandMin(std::size_t i, const Type& v) { min(i) = std::min(min(i), v); }
 
   /// @brief Expand a range by increasing the maximum value
   ///
   /// Expand the range by increasing the maximum value. If the given value is
   /// smaller than the current maximum (in other words, if the proposed new
   /// range would be smaller than the current range), this is a no-op.
   ///
   /// @param i The index of the dimension to expand
   /// @param v The proposed new maximum for the range
   void expandMax(std::size_t i, const Type& v) { max(i) = std::max(max(i), v); }
 
   /// @brief Expand a range on both ends
   ///
   /// Expand a range by decreasing the minimum value as well as increasing the
   /// maximum value. If either of the values are already larger or smaller
   /// (respectively) than the proposed values, then that particular boundary
   /// of the interval is not expanded.
   ///
   /// @note After this operation, the range is always equal to or larger than
   /// [min, max].
   ///
   /// @param i The index of the dimension to expand
   /// @param min The proposed new minimum for the range
   /// @param max The proposed new maximum for the range
   void expand(std::size_t i, const Type& min, const Type& max) {
     expandMin(i, min);
     expandMax(i, max);
   }
 
   /// @brief Set the minimum value
   ///
   /// Override the minimum value of the range, regardless of what was already
   /// set.
   ///
   /// @note If you want to shrink or expand the range, use the shrink and
   /// expand methods.
   ///
   /// @param i The index of the dimension to set
   /// @param v The value to use as the new minimum
   void setMin(std::size_t i, const Type& v) { min(i) = v; }
 
   /// @brief Set the maximum value
   ///
   /// Override the maximum value of the range, regardless of what was already
   /// set.
   ///
   /// @note If you want to shrink or expand the range, use the shrink and
   /// expand methods.
   ///
   /// @param i The index of the dimension to set
   /// @param v The value to use as the new maximum
   void setMax(std::size_t i, const Type& v) { max(i) = v; }
 
   /// @brief Set the minimum and maximum value
   ///
   /// Override both the minimum and maximum value of the range, regardless of
   /// what they were set to.
   ///
   /// @note If you want to shrink or expand the range, use the shrink and
   /// expand methods.
   ///
   /// @note After this operation, the range should be exactly equal to [min,
   /// max]
   ///
   /// @param i The index of the dimension to set
   /// @param min The new minimum value of the range
   /// @param max The new maximum value of the range
   void set(std::size_t i, const Type& min, const Type& max) {
     setMin(i, min);
     setMax(i, max);
   }
 
   /// @brief Return the minimum value of the range @p i (inclusive)
   /// @param i The index of the dimension to access
   Type& min(std::size_t i) { return m_minima[i]; }
 
   /// @brief Return the maximum value of the range @p i (inclusive)
   /// @param i The index of the dimension to access
   Type& max(std::size_t i) { return m_maxima[i]; }
 
   /// @brief Return the minimum value of the range @p i (inclusive)
   /// @param i The index of the dimension to access
   Type min(std::size_t i) const { return m_minima[i]; }
 
   /// @brief Return the maximum value of the range @p i (inclusive)
   /// @param i The index of the dimension to access
   Type max(std::size_t i) const { return m_maxima[i]; }
 
   /// Methods for manipulating a range of dimension 1
   /// @{
 
   /// @brief Expand a range by decreasing the minimum value
   ///
   /// Expand the range by decreasing the minimum value. If the given value is
   /// larger than the current minimum (in other words, if the proposed new
   /// range would be smaller than the current range), this is a no-op.
   ///
   /// @param v The proposed new minimum for the range
   void expandMin(const Type& v)
     requires(Dims == 1)
   {
     min() = std::min(min(), v);
   }
 
   /// @brief Expand a range by increasing the maximum value
   ///
   /// Expand the range by increasing the maximum value. If the given value is
   /// smaller than the current maximum (in other words, if the proposed new
   /// range would be smaller than the current range), this is a no-op.
   ///
   /// @param v The proposed new maximum for the range
   void expandMax(const Type& v)
     requires(Dims == 1)
   {
     max() = std::max(max(), v);
   }
 
   /// @brief Expand a range on both ends
   ///
   /// Expand a range by decreasing the minimum value as well as increasing the
   /// maximum value. If either of the values are already larger or smaller
   /// (respectively) than the proposed values, then that particular boundary
   /// of the interval is not expanded.
   ///
   /// @note After this operation, the range is always equal to or larger than
   /// [min, max].
   ///
   /// @param min The proposed new minimum for the range
   /// @param max The proposed new maximum for the range
   void expand(const Type& min, const Type& max)
     requires(Dims == 1)
   {
     expandMin(min);
     expandMax(max);
   }
 
   /// @brief Shrink a range by increasing the minimum value
   ///
   /// Shrink the range by increasing the minimum value. If the given value is
   /// smaller than the current minimum (in other words, if the proposed new
   /// range would be larger than the current range), this is a no-op.
   ///
   /// @param v The proposed new minimum for the range
   void shrinkMin(const Type& v)
     requires(Dims == 1)
   {
     min() = std::max(min(), v);
   }
 
   /// @brief Shrink a range by decreasing the maximum value
   ///
   /// Shrink the range by decreasing the maximum value. If the given value is
   /// larger than the current maximum (in other words, if the proposed new
   /// range would be larger than the current range), this is a no-op.
   ///
   /// @param v The proposed new maximum for the range
   void shrinkMax(const Type& v)
     requires(Dims == 1)
   {
     max() = std::min(max(), v);
   }
 
   /// @brief Shrink a range on both ends
   ///
   /// Shrink a range by increasing the minimum value as well as decreasing the
   /// maximum value. If either of the values are already smaller or larger
   /// (respectively) than the proposed values, then that particular boundary
   /// of the interval is not shrunk.
   ///
   /// @note After this operation, the range is always equal to or smaller than
   /// [min, max].
   ///
   /// @param min The proposed new minimum for the range
   /// @param max The proposed new maximum for the range
   void shrink(const Type& min, const Type& max)
     requires(Dims == 1)
   {
     shrinkMin(min);
     shrinkMax(max);
   }
 
   /// @brief Set the minimum value
   ///
   /// Override the minimum value of the range, regardless of what was already
   /// set.
   ///
   /// @note If you want to shrink or expand the range, use the shrink and
   /// expand methods.
   ///
   /// @param v The value to use as the new minimum
   void setMin(const Type& v)
     requires(Dims == 1)
   {
     min() = v;
   }
 
   /// @brief Set the maximum value
   ///
   /// Override the maximum value of the range, regardless of what was already
   /// set.
   ///
   /// @note If you want to shrink or expand the range, use the shrink and
   /// expand methods.
   ///
   /// @param v The value to use as the new maximum
   void setMax(const Type& v)
     requires(Dims == 1)
   {
     max() = v;
   }
 
   /// @brief Set the minimum and maximum value
   ///
   /// Override both the minimum and maximum value of the range, regardless of
   /// what they were set to.
   ///
   /// @note If you want to shrink or expand the range, use the shrink and
   /// expand methods.
   ///
   /// @note After this operation, the range should be exactly equal to [min,
   /// max]
   ///
   /// @param min The new minimum value of the range
   /// @param max The new maximum value of the range
   void set(const Type& min, const Type& max)
     requires(Dims == 1)
   {
     setMin(min);
     setMax(max);
   }
 
   /// @brief Return the minimum value of the range (inclusive)
   Type min() const
     requires(Dims == 1)
   {
     return min(0);
   }
 
   /// @brief Return the minimum value of the range (inclusive)
   Type& min()
     requires(Dims == 1)
   {
     return min(0);
   }
 
   /// @brief Return the maximum value of the range (inclusive)
   Type max() const
     requires(Dims == 1)
   {
     return max(0);
   }
 
   /// @brief Return the maximum value of the range (inclusive)
   Type& max()
     requires(Dims == 1)
   {
     return max(0);
   }
 
   /// @brief Compute the size of the range
   ///
   /// The size of a range is defined as the difference between the minimum and
   /// the maximum. For degenerate ranges, this is zero.
   ///
   /// @warning Due to the nature of numbers, the result of this function can be
   /// somewhat ambiguous. For natural numbers, you could argue that the range
   /// [n, n] has size 0 or size 1. In this case we say it has size 0. The
   /// uncountable nature of the reals means this doesn't matter for them, but
   /// this can be awkward when working with integers.
   ///
   /// @return The size of the range
   Type size() const
     requires(Dims == 1)
   {
     return std::max(static_cast<Type>(0), max() - min());
   }
 
   /// @brief Determine if the range contains a given value
   ///
   /// A value is inside a range if and only if it is greater than the minimum
   /// and smaller than the maximum.
   ///
   /// @param v The value to check
   ///
   /// @return true The value is inside the range
   /// @return false The value is not inside the range
   bool contains(const Type& v) const
     requires(Dims == 1)
   {
     return min() <= v && v < max();
   }
 
   /// @}
 
  private:
   Vector<Type, Dims> m_minima{};
   Vector<Type, Dims> m_maxima{};
 };
 
 template <typename Type,
           template <typename, std::size_t> typename Vector = std::array>
 using Range1D = RangeXD<1, Type, Vector>;
 
 }  // namespace Acts

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