tpl_ca_rule_test.cc

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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
 
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# include <array>
# include <cstdint>
# include <span>
# include <stdexcept>
# include <utility>
# include <vector>
 
# include <gtest/gtest.h>
 
# include <ca-traits.H>
# include <tpl_ca_concepts.H>
# include <tpl_ca_storage.H>
# include <tpl_ca_lattice.H>
# include <tpl_ca_neighborhood.H>
# include <tpl_ca_rule.H>
 
using namespace Aleph;
using namespace Aleph::CA;
 
namespace
{
  template <typename Rule, typename Boundary>
  Lattice<Dense_Cell_Storage<int, 2>, Boundary>
  step_2d(const Lattice<Dense_Cell_Storage<int, 2>, Boundary> & cur,
          const Rule & rule)
  {
    Lattice<Dense_Cell_Storage<int, 2>, Boundary> nxt(cur.extents());
    Moore<2, 1> nh;
    std::array<int, Moore<2, 1>::size_v> buf { };
    for (ca_index_t i = 0; i < static_cast<ca_index_t>(cur.size(0)); ++i)
      for (ca_index_t j = 0; j < static_cast<ca_index_t>(cur.size(1)); ++j)
        {
          gather_neighbors(nh, cur, Coord_Vec<2>{ i, j },
                           std::span<int>(buf.data(), buf.size()));
          nxt.set({ i, j },
                  rule(cur.at({ i, j }),
                       Neighbor_View<int>(buf.data(), buf.size())));
        }
    return nxt;
  }
 
  template <typename Rule, typename Boundary>
  Lattice<Dense_Cell_Storage<int, 1>, Boundary>
  step_1d(const Lattice<Dense_Cell_Storage<int, 1>, Boundary> & cur,
          const Rule & rule)
  {
    Lattice<Dense_Cell_Storage<int, 1>, Boundary> nxt(cur.extents());
    Custom_Neighborhood<1, 2> nh(std::array<Offset_Vec<1>, 2>{ Offset_Vec<1>{ -1 },
                                                               Offset_Vec<1>{  1 } });
    std::array<int, 2> buf { };
    for (ca_index_t i = 0; i < static_cast<ca_index_t>(cur.size(0)); ++i)
      {
        gather_neighbors(nh, cur, Coord_Vec<1>{ i },
                         std::span<int>(buf.data(), buf.size()));
        nxt.set({ i },
                rule(cur.at({ i }),
                     Neighbor_View<int>(buf.data(), buf.size())));
      }
    return nxt;
  }
 
  template <typename Boundary>
  Lattice<Dense_Cell_Storage<int, 2>, Boundary>
  make_grid(std::array<ca_size_t, 2> ext, const std::vector<int> & data)
  {
    Lattice<Dense_Cell_Storage<int, 2>, Boundary> lat(ext);
    for (ca_size_t i = 0; i < ext[0]; ++i)
      for (ca_size_t j = 0; j < ext[1]; ++j)
        lat.set({ static_cast<ca_index_t>(i),
                  static_cast<ca_index_t>(j) },
                data[i * ext[1] + j]);
    return lat;
  }
 
  template <typename B1, typename B2>
  bool same(const Lattice<Dense_Cell_Storage<int, 2>, B1> & a,
            const Lattice<Dense_Cell_Storage<int, 2>, B2> & b)
  {
    if (a.size(0) != b.size(0) or a.size(1) != b.size(1))
      return false;
    for (ca_index_t i = 0; i < static_cast<ca_index_t>(a.size(0)); ++i)
      for (ca_index_t j = 0; j < static_cast<ca_index_t>(a.size(1)); ++j)
        if (a.at({ i, j }) != b.at({ i, j }))
          return false;
    return true;
  }
}
 
// ---------------------------------------------------------------------------
// Game of Life — canonical patterns.
// ---------------------------------------------------------------------------
 
TEST(CAGameOfLife, BlockIsStill)
{
  // 4x4 grid, 2x2 block at rows/cols [1..2].
  auto lat = make_grid<OpenBoundary>(
    { 4, 4 },
    { 0, 0, 0, 0,
      0, 1, 1, 0,
      0, 1, 1, 0,
      0, 0, 0, 0 });
  auto rule = make_game_of_life_rule();
  for (int t = 0; t < 5; ++t)
    {
      auto nxt = step_2d(lat, rule);
      ASSERT_TRUE(same(lat, nxt)) << "Block must be stationary at t=" << t;
      lat = std::move(nxt);
    }
}
 
TEST(CAGameOfLife, BlinkerOscillatesPeriod2)
{
  // 5x5 grid, horizontal blinker at row 2, cols 1..3.
  auto horiz = make_grid<OpenBoundary>(
    { 5, 5 },
    { 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0,
      0, 1, 1, 1, 0,
      0, 0, 0, 0, 0,
      0, 0, 0, 0, 0 });
  auto vert = make_grid<OpenBoundary>(
    { 5, 5 },
    { 0, 0, 0, 0, 0,
      0, 0, 1, 0, 0,
      0, 0, 1, 0, 0,
      0, 0, 1, 0, 0,
      0, 0, 0, 0, 0 });
  auto rule = make_game_of_life_rule();
 
  auto t1 = step_2d(horiz, rule);
  EXPECT_TRUE(same(t1, vert));
  auto t2 = step_2d(t1, rule);
  EXPECT_TRUE(same(t2, horiz));
  auto t3 = step_2d(t2, rule);
  EXPECT_TRUE(same(t3, vert));
}
 
TEST(CAGameOfLife, GliderMovesByOneOneEveryFourSteps)
{
  // 8x8 toroidal so the glider can travel without falling off the edge.
  auto lat = make_grid<ToroidalBoundary>(
    { 8, 8 },
    { 0, 1, 0, 0, 0, 0, 0, 0,
      0, 0, 1, 0, 0, 0, 0, 0,
      1, 1, 1, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0 });
  // After 4 steps a glider translates by (1, 1).
  auto expected = make_grid<ToroidalBoundary>(
    { 8, 8 },
    { 0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 1, 0, 0, 0, 0, 0,
      0, 0, 0, 1, 0, 0, 0, 0,
      0, 1, 1, 1, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0,
      0, 0, 0, 0, 0, 0, 0, 0 });
 
  auto rule = make_game_of_life_rule();
  for (int t = 0; t < 4; ++t)
    lat = step_2d(lat, rule);
  EXPECT_TRUE(same(lat, expected)) << "Glider must shift by (1,1) in 4 steps";
}
 
// ---------------------------------------------------------------------------
// Wolfram elementary rules — spot-checked outputs.
// ---------------------------------------------------------------------------
 
namespace
{
  int wolfram_next(std::uint8_t r, int l, int s, int rg)
  {
    const std::size_t idx = (l << 2) | (s << 1) | rg;
    return (r >> idx) & 1;
  }
}
 
TEST(CAWolfram1D, AllRulesMatchReferenceFor10Patterns)
{
  // For every elementary rule and every 3-bit pattern, the precomputed
  // table built by `make_wolfram_elementary_rule` must produce the
  // same next-state as the textbook formula.
  for (int r = 0; r < 256; ++r)
    {
      auto rule = make_wolfram_elementary_rule(static_cast<std::uint8_t>(r));
      for (int l = 0; l < 2; ++l)
        for (int s = 0; s < 2; ++s)
          for (int rg = 0; rg < 2; ++rg)
            {
              std::array<int, 2> nb { l, rg };
              const int got = rule(s, Neighbor_View<int>(nb.data(), 2));
              const int want = wolfram_next(static_cast<std::uint8_t>(r),
                                            l, s, rg);
              ASSERT_EQ(got, want)
                << "rule=" << r << " (l,s,r)=(" << l << "," << s << ","
                << rg << ")";
            }
    }
}
 
TEST(CAWolfram1D, Rule90StepFromCenterImpulse)
{
  // Rule 90 from a single 1 at the centre produces the Sierpinski pattern.
  // After one step, only the cells adjacent to the impulse become 1.
  auto lat = make_grid<OpenBoundary>(
    { 1, 7 },
    { 0, 0, 0, 1, 0, 0, 0 });
  auto rule = make_wolfram_elementary_rule(90);
  // Adapt 1D step using the 2D infrastructure with size(0)=1:
  // we just iterate j over the single row.
  Lattice<Dense_Cell_Storage<int, 1>, OpenBoundary> row({ 7 });
  for (ca_index_t j = 0; j < 7; ++j) row.set({ j }, lat.at({ 0, j }));
 
  auto nxt = step_1d(row, rule);
  // Expected after rule 90 from impulse at index 3:
  // (l,s,r)=(0,0,0)→0, (0,0,1)→1, (0,1,0)→0, (1,0,0)→1, others → 0
  // Centred impulse at j=3:
  // j=2: l=0,s=0,r=1 → 1
  // j=3: l=0,s=1,r=0 → 0
  // j=4: l=1,s=0,r=0 → 1
  // others stay 0.
  EXPECT_EQ(nxt.at({ 0 }), 0);
  EXPECT_EQ(nxt.at({ 1 }), 0);
  EXPECT_EQ(nxt.at({ 2 }), 1);
  EXPECT_EQ(nxt.at({ 3 }), 0);
  EXPECT_EQ(nxt.at({ 4 }), 1);
  EXPECT_EQ(nxt.at({ 5 }), 0);
  EXPECT_EQ(nxt.at({ 6 }), 0);
}
 
TEST(CAWolfram1D, LookupRuleRejectsBadArityAndStateRange)
{
  auto rule = make_wolfram_elementary_rule(90);
  std::array<int, 1> short_nb { 0 };
  EXPECT_THROW((void) rule(0, Neighbor_View<int>(short_nb.data(),
                                                 short_nb.size())),
               std::length_error);
 
  std::array<int, 2> nb { 0, 1 };
  EXPECT_THROW((void) rule(2, Neighbor_View<int>(nb.data(), nb.size())),
               std::domain_error);
 
  std::array<int, 2> bad_nb { 0, -1 };
  EXPECT_THROW((void) rule(0, Neighbor_View<int>(bad_nb.data(),
                                                 bad_nb.size())),
               std::domain_error);
}
 
TEST(CAWolfram1D, Rule30FirstFiveStepsFromImpulse)
{
  // Lattice large enough to avoid hitting OpenBoundary in 5 steps.
  Lattice<Dense_Cell_Storage<int, 1>, OpenBoundary> row({ 21 });
  row.set({ 10 }, 1);  // central impulse
  auto rule = make_wolfram_elementary_rule(30);
 
  // Reference rows (rule 30 is the canonical Wolfram example).
  // Source: Wolfram MathWorld "Rule 30".
  std::vector<std::vector<int>> expected = {
    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, // t=0
    { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 }, // t=1
    { 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 }, // t=2
    { 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0 }, // t=3
    { 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 }, // t=4
    { 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0 }, // t=5
  };
 
  for (std::size_t t = 0; t < expected.size(); ++t)
    {
      for (ca_index_t j = 0; j < 21; ++j)
        ASSERT_EQ(row.at({ j }), expected[t][j])
          << "rule 30 t=" << t << " j=" << j;
      row = step_1d(row, rule);
    }
}
 
// ---------------------------------------------------------------------------
// Composite_Rule
// ---------------------------------------------------------------------------
 
TEST(CACompositeRule, AppliesRulesInSequence)
{
  // Build two rules over a tiny state machine. Rule A: x -> x + 1.
  // Rule B: x -> x * 2. Composite(A, B): x -> 2(x+1).
  struct Add_One {
    int operator()(int x, Neighbor_View<int>) const { return x + 1; }
  };
  struct Times_Two {
    int operator()(int x, Neighbor_View<int>) const { return x * 2; }
  };
  Composite_Rule<Add_One, Times_Two> r{ Add_One{}, Times_Two{} };
  std::array<int, 0> nb { };
  EXPECT_EQ(r(3, Neighbor_View<int>(nb.data(), 0)), 8);
  EXPECT_EQ(r(0, Neighbor_View<int>(nb.data(), 0)), 2);
}
 
// ---------------------------------------------------------------------------
// Totalistic_Rule
// ---------------------------------------------------------------------------
 
TEST(CATotalisticRule, SumsCellAndNeighbours)
{
  // Identity-on-sum: f(s) = s. The rule then returns
  //   current + sum(neighbours) for any state type.
  auto identity = [](int s) { return s; };
  Totalistic_Rule<decltype(identity)> r(identity);
  std::array<int, 4> nb { 1, 2, 3, 4 };
  EXPECT_EQ(r(10, Neighbor_View<int>(nb.data(), 4)), 20);
}
 
// ---------------------------------------------------------------------------
// Outer_Totalistic_Rule with a non-bool state type.
// ---------------------------------------------------------------------------
 
TEST(CAOuterTotalisticRule, AliveCountIgnoresMagnitude)
{
  // F: returns the number of non-zero neighbours regardless of `current`.
  auto f = [](int /*current*/, std::size_t alive) -> int
  { return static_cast<int>(alive); };
  Outer_Totalistic_Rule<decltype(f)> r(f);
 
  std::array<int, 5> nb { 0, 7, 0, -3, 0 };
  EXPECT_EQ(r(99, Neighbor_View<int>(nb.data(), 5)), 2);
}