tpl_ca_block_rule.H

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/*
                          Aleph_w
 
  Data structures & Algorithms
  version 2.0.0b
  https://github.com/lrleon/Aleph-w
 
  This file is part of Aleph-w library
 
  Copyright (c) 2002-2026 Leandro Rabindranath Leon
 
  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  copies of the Software, and to permit persons to whom the Software is
  furnished to do so, subject to the following conditions:
 
  The above copyright notice and this permission notice shall be included in all
  copies or substantial portions of the Software.
 
  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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*/
 
#ifndef TPL_CA_BLOCK_RULE_H
#define TPL_CA_BLOCK_RULE_H
 
#include <array>
#include <concepts>
#include <cstddef>
#include <type_traits>
#include <utility>
 
namespace Aleph {
namespace CA {
 
template <typename State>
using Block_2x2 = std::array<State, 4>;
 
template <typename R, typename State>
concept Block_Rule_2x2 = requires(const R &r, Block_2x2<State> b) {
  { r(b) } -> std::convertible_to<Block_2x2<State>>;
};
 
namespace ca_block_rule_detail {
 
template <typename State>
[[nodiscard]] inline constexpr State invert(const State &s) noexcept
{
  if constexpr (std::is_same_v<State, bool>)
    return not s;
  else if constexpr (std::is_integral_v<State>)
    return s == State{0} ? State{1} : State{0};
  else
    return s == State{} ? State{1} : State{};
}
 
template <typename State>
[[nodiscard]] inline constexpr std::size_t popcount(const Block_2x2<State> &b) noexcept
{
  std::size_t n = 0;
  for (const auto &v : b)
    if (v != State{})
      ++n;
  return n;
}
 
}  // namespace ca_block_rule_detail
 
// =======================================================================
// Critters
// =======================================================================
 
class Critters_Rule
{
public:
  template <typename State>
  [[nodiscard]] constexpr Block_2x2<State> operator()(const Block_2x2<State> &in) const noexcept
  {
    using namespace ca_block_rule_detail;
    if (popcount(in) == 2)
      return in;
    // Invert each cell, then rotate 180°: NW ↔ SE, NE ↔ SW.
    Block_2x2<State> out{};
    out[0] = invert(in[3]);
    out[1] = invert(in[2]);
    out[2] = invert(in[1]);
    out[3] = invert(in[0]);
    return out;
  }
};
 
// =======================================================================
// Billiard Ball Machine (BBM)
// =======================================================================
 
class BBM_Rule
{
public:
  template <typename State>
  [[nodiscard]] constexpr Block_2x2<State> operator()(const Block_2x2<State> &in) const noexcept
  {
    using namespace ca_block_rule_detail;
    const std::size_t n = popcount(in);
 
    if (n == 1)
      {
        // Ball moves to the diagonally-opposite corner.
        Block_2x2<State> out{};
        out[0] = in[3];
        out[1] = in[2];
        out[2] = in[1];
        out[3] = in[0];
        return out;
      }
    if (n == 2)
      {
        // Diagonal swap only on the two "head-on" patterns.
        const bool main_diag
          = (in[0] != State{}) and (in[3] != State{}) and (in[1] == State{}) and (in[2] == State{});
        const bool anti_diag
          = (in[1] != State{}) and (in[2] != State{}) and (in[0] == State{}) and (in[3] == State{});
        if (main_diag or anti_diag)
          {
            Block_2x2<State> out{};
            out[0] = in[3];
            out[1] = in[2];
            out[2] = in[1];
            out[3] = in[0];
            return out;
          }
      }
    return in;
  }
};
 
// =======================================================================
// Toffoli–Margolus lattice gas
// =======================================================================
 
class TM_Gas_Rule
{
public:
  template <typename State>
  [[nodiscard]] constexpr Block_2x2<State> operator()(const Block_2x2<State> &in) const noexcept
  {
    using namespace ca_block_rule_detail;
    const std::size_t n = popcount(in);
 
    if (n == 1 or n == 3)
      {
        // Horizontal swap: NW ↔ NE, SW ↔ SE.
        Block_2x2<State> out{};
        out[0] = in[1];
        out[1] = in[0];
        out[2] = in[3];
        out[3] = in[2];
        return out;
      }
    if (n == 2)
      {
        const bool top_row
          = (in[0] != State{}) and (in[1] != State{}) and (in[2] == State{}) and (in[3] == State{});
        const bool bottom_row
          = (in[2] != State{}) and (in[3] != State{}) and (in[0] == State{}) and (in[1] == State{});
        if (top_row or bottom_row)
          {
            // Vertical swap: top row ↔ bottom row.
            Block_2x2<State> out{};
            out[0] = in[2];
            out[1] = in[3];
            out[2] = in[0];
            out[3] = in[1];
            return out;
          }
 
        const bool left_col
          = (in[0] != State{}) and (in[2] != State{}) and (in[1] == State{}) and (in[3] == State{});
        const bool right_col
          = (in[1] != State{}) and (in[3] != State{}) and (in[0] == State{}) and (in[2] == State{});
        if (left_col or right_col)
          {
            // Horizontal swap: left column ↔ right column.
            Block_2x2<State> out{};
            out[0] = in[1];
            out[1] = in[0];
            out[2] = in[3];
            out[3] = in[2];
            return out;
          }
 
        const bool main_diag
          = (in[0] != State{}) and (in[3] != State{}) and (in[1] == State{}) and (in[2] == State{});
        const bool anti_diag
          = (in[1] != State{}) and (in[2] != State{}) and (in[0] == State{}) and (in[3] == State{});
        if (main_diag or anti_diag)
          {
            // Diagonal swap.
            Block_2x2<State> out{};
            out[0] = in[3];
            out[1] = in[2];
            out[2] = in[1];
            out[3] = in[0];
            return out;
          }
      }
    return in;
  }
};
 
// =======================================================================
// Cell_Rule_As_Block_Rule
// =======================================================================
 
template <typename Cell_Rule>
class Cell_Rule_As_Block_Rule
{
  Cell_Rule cell_;
 
public:
  constexpr explicit Cell_Rule_As_Block_Rule(Cell_Rule cr) : cell_(std::move(cr)) {}
 
  template <typename State>
  [[nodiscard]] constexpr Block_2x2<State> operator()(const Block_2x2<State> &in) const
  {
    Block_2x2<State> out{};
    for (std::size_t i = 0; i < 4; ++i)
      out[i] = cell_(in[i]);
    return out;
  }
};
 
}  // namespace CA
}  // namespace Aleph
 
#endif  // TPL_CA_BLOCK_RULE_H