CantorEdge.hpp

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// This file is part of the Acts project.
//
// Copyright (C) 2022 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 http://mozilla.org/MPL/2.0/.

#pragma once

#include <cmath>
#include <cstdint>

namespace Acts::detail {

template <typename T>
class CantorEdge {
  T m_value;

 public:
  CantorEdge(T x, T y, bool sort = true) {
    if ((x > y) and sort) {
      std::swap(x, y);
    }
    m_value = y + ((x + y) * (x + y + 1)) / 2;
  }

  std::pair<T, T> inverse() const {
    auto f = [](T w) -> T { return (w * (w + 1)) / 2; };
    auto q = [](T w) -> T {
      return std::floor((std::sqrt(8 * w + 1) - 1) / 2);
    };

    auto y = m_value - f(q(m_value));
    auto x = q(m_value) - y;

    return {x, y};
  }

  T value() const { return m_value; }
};

template <typename T>
bool operator==(const CantorEdge<T> &a, const CantorEdge<T> &b) {
  return a.value() == b.value();
}

template <typename T>
bool operator<(const CantorEdge<T> &a, const CantorEdge<T> &b) {
  return a.value() < b.value();
}

}  // namespace Acts::detail