From fd479439dd172e3206d04a37a76434adda029f53 Mon Sep 17 00:00:00 2001
From: yboucher <yann.boucher@etu.utc.fr>
Date: Fri, 11 Jun 2021 15:09:55 +0200
Subject: [PATCH] 100x performance increase with Griffeath!

---
 configurations/Griffeath/large_random.json    |    9 +
 configurations/Griffeath/spins.json           |    9 +
 include/alphabet.hpp                          |    2 +-
 include/gridview.hpp                          |    4 +-
 include/mathexpr.hpp                          |   49 +-
 include/state.hpp                             |    2 +-
 .../nonisotropictransition.hpp                |    5 +-
 .../transition_rules/totalistictransition.hpp |   67 +-
 patterns/Griffeath/Spin.json                  | 2148 +++++++++++++++++
 src/alphabet.cpp                              |    2 +-
 src/automaton.cpp                             |   11 +-
 src/gridview.cpp                              |   43 +-
 src/mathexpr.cpp                              |  132 +-
 .../mooreNeighborhoodRule.cpp                 |   39 +-
 src/simulation.cpp                            |    6 +
 .../nonisotropictransition.cpp                |    7 +-
 src/transition_rules/totalistictransition.cpp |   38 +-
 tests/totalistictransition_test.cpp           |    4 +-
 18 files changed, 2469 insertions(+), 108 deletions(-)
 create mode 100644 configurations/Griffeath/large_random.json
 create mode 100644 configurations/Griffeath/spins.json
 create mode 100644 patterns/Griffeath/Spin.json

diff --git a/configurations/Griffeath/large_random.json b/configurations/Griffeath/large_random.json
new file mode 100644
index 0000000..b75243a
--- /dev/null
+++ b/configurations/Griffeath/large_random.json
@@ -0,0 +1,9 @@
+{
+    "data": "x = 300, y = 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+    "height": 300,
+    "left": 0,
+    "model": "griffeath",
+    "title": "Big Random",
+    "top": 0,
+    "width": 300
+}
diff --git a/configurations/Griffeath/spins.json b/configurations/Griffeath/spins.json
new file mode 100644
index 0000000..b772b35
--- /dev/null
+++ b/configurations/Griffeath/spins.json
@@ -0,0 +1,9 @@
+{
+    "data": "x = 1000, y = 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+    "height": 1000,
+    "left": 0,
+    "model": "griffeath",
+    "title": "Spins",
+    "top": 0,
+    "width": 1000
+}
diff --git a/include/alphabet.hpp b/include/alphabet.hpp
index 5245491..5d6d6f1 100644
--- a/include/alphabet.hpp
+++ b/include/alphabet.hpp
@@ -55,7 +55,7 @@ public:
     void newEtat(const state& s);
 
     //! Renvoie l'état en fonction de son identifiant
-    state getState(unsigned int it) const;
+    const state& getState(unsigned int it) const;
 
     //! Affecte l'identifiant d'état à un état
     void setState(unsigned int i, const state& s);
diff --git a/include/gridview.hpp b/include/gridview.hpp
index 7779c0b..a43036d 100644
--- a/include/gridview.hpp
+++ b/include/gridview.hpp
@@ -159,7 +159,7 @@ private:
     void click_on(Coord coord);
     void update_current_mouse_pos(Coord coord);
 
-    const QPixmap &grid_pixmap() const;
+    const QImage &grid_image() const;
 
 private slots:
     void handle_rubberband(QRect, QPointF, QPointF);
@@ -173,8 +173,8 @@ private:
     QGraphicsScene* m_scene;
     detail::Graphics_view_zoom* m_zoom;
     History m_undo_history;
+    std::vector<uint32_t> m_image_data;
     QImage m_grid_image;
-    QPixmap m_grid_pixmap;
     QLabel* m_mouse_pos_label;
     Grid m_grid;
     Coord m_last_mouse_pos;
diff --git a/include/mathexpr.hpp b/include/mathexpr.hpp
index eca65c6..940e152 100644
--- a/include/mathexpr.hpp
+++ b/include/mathexpr.hpp
@@ -13,6 +13,27 @@ Ce fichier contient une fonction permettant d'exécuter une expression mathémat
 
 #include <map>
 #include <exception>
+#include <vector>
+#include <climits>
+
+namespace detail
+{
+struct rpl_token_t
+{
+    enum : uint8_t
+    {
+        LITERAL,
+        VARIABLE,
+        OP
+    } type;
+    union
+    {
+        int8_t value;
+        uint8_t var_alphabet_idx;
+        char op;
+    };
+};
+}
 
 //! \brief Exception lancée lors de l'évaluation d'une expression mathématique.
 class MathExprException : public std::exception
@@ -29,11 +50,37 @@ private:
     std::string m_what;
 };
 
+//! \brief Représente une expression mathématique parsée et mise en cache.
+class MathExpr
+{
+public:
+    //! \brief Initialise l'expression à partir d'une chaîne.
+    MathExpr(const std::string& expr = "0");
+
+    //! \brief Retourne une évaluation de l'expression mathématique.
+    int eval() const;
+
+    //! \brief Permet de spécifier la valeur d'une variable.
+    //! La constance symbolise ici l'immutabilité de l'expression mathématique en elle-même, pas son contexte d'évaluation.
+    void set_var(char var, int val) const
+    {
+        if (var < 'a' || var > 'z')
+            throw MathExprException("Invalid variable name");
+        variable_map[var - 'a'] = val;
+    }
+
+private:
+    std::vector<detail::rpl_token_t> rpl_stack;
+    mutable std::array<int8_t, 26> variable_map;
+    bool is_constant; // true if the expression contains no variables
+    int cached_result;
+};
+
 //! Evalue une expression mathématique selon une liste de variables fournies, et retourne un entier.
 //! Les opérateurs supportés sont les parenthèses, +, -, *, /, %.
 //! \param expr L'expression mathématique, en tant que std::string
 //! \param variables un std::map associant à chaque nom de variable une valeur entière
 //! \returns La valeur de résultat de l'expression mathématique évaluée.
-int eval_math(const std::string& expr, const std::map<std::string, int>& variables = {});
+int eval_math(const std::string& expr, const std::map<char, int> &variables = {});
 
 #endif // MATHEXPR_HPP
diff --git a/include/state.hpp b/include/state.hpp
index b6f622e..1ac3333 100644
--- a/include/state.hpp
+++ b/include/state.hpp
@@ -26,7 +26,7 @@ public:
     state(stateColor c, const std::string& l = "sans nom"):color(c),label(l){}
 
     //! \brief Accesseur en lecture de la couleur
-    stateColor getColor() const { return color; }
+    const stateColor& getColor() const { return color; }
     //! \brief Accesseur en lecture du label
     std::string getStateLabel() const { return label; }
 
diff --git a/include/transition_rules/nonisotropictransition.hpp b/include/transition_rules/nonisotropictransition.hpp
index 313fd64..132b01b 100644
--- a/include/transition_rules/nonisotropictransition.hpp
+++ b/include/transition_rules/nonisotropictransition.hpp
@@ -4,6 +4,7 @@
 #include <exception>
 
 #include "transitionrule.hpp"
+#include "mathexpr.hpp"
 
 //! \brief Exception lancée lors de l'évaluation d'une règle totalistique.
 class NonIsotropicRuleException : public std::exception
@@ -40,10 +41,10 @@ private:
 
     bool m_initial_state_is_variable;
     // could use a union here, but it's a bit tricky as we'd have to call the correct destructor
-    std::string m_initial_variable;
+    char m_initial_variable;
     unsigned m_initial_state;
     std::vector<unsigned> m_constraints;
-    std::string m_result_state;
+    MathExpr m_result_state;
 };
 
 //! \brief Représente une règle de transition totalistique configurable textuellement.
diff --git a/include/transition_rules/totalistictransition.hpp b/include/transition_rules/totalistictransition.hpp
index 4b905eb..c9eb5ad 100644
--- a/include/transition_rules/totalistictransition.hpp
+++ b/include/transition_rules/totalistictransition.hpp
@@ -18,6 +18,7 @@ Cette classe représente une règle de transition totalistique configurable.
 #include "neighborhood.hpp"
 #include "mathexpr.hpp"
 #include "transitionrule.hpp"
+#include "constantes.hpp"
 
 //! \brief Exception lancée lors de l'évaluation d'une règle totalistique.
 class TotalisticRuleException : public std::exception
@@ -37,14 +38,26 @@ private:
 //! \brief Représente un intervalle [low;high] composé d'expressions mathématiques
 struct Interval
 {
-    std::string low, high;
+public:
+    Interval(const MathExpr& i_low = MathExpr("0"))
+    {
+        has_upper_bound = false;
+        low = i_low;
+
+    }
+    Interval(const MathExpr& i_low, const MathExpr& i_high)
+    {
+        has_upper_bound = true;
+        low = i_low;
+        high = i_high;
+    }
 
     //! Evalue l'intervalle pour vérifier si val est inclus dedans
     //! \returns true si inclus, false sinon
     bool contains(unsigned val) const
     {
-        unsigned low_v  =  eval_math(low , {});
-        unsigned high_v =  !high.empty() ? eval_math(high, {}) : std::numeric_limits<unsigned>::max();
+        unsigned low_v  =  low.eval();
+        unsigned high_v =  has_upper_bound ? high.eval() : std::numeric_limits<unsigned>::max();
 
         // sanity check
         if (low_v > high_v)
@@ -52,6 +65,10 @@ struct Interval
 
         return val >= low_v && val <= high_v;
     }
+
+private:
+    bool has_upper_bound;
+    MathExpr low, high;
 };
 
 //! \brief Représente une entrée de règle de transition totalistique configurable.
@@ -69,13 +86,51 @@ public:
     //! \returns true si accepté, false sinon.
     bool accept(unsigned initial_state, const Neighborhood& neighborhood, unsigned& next) const;
 
+private:
+    class Constraint
+    {
+        public:
+        Constraint(const MathExpr& e, const Interval& i)
+            : state(e), interval(i)
+        {
+            std::fill(cache_bitmap.begin(), cache_bitmap.end(), false);
+        }
+
+        // initial_variable == '\0' si il n'y a pas de variable initiale
+        bool valid(char initial_variable, unsigned initial_state, const Neighborhood& n) const
+        {
+            unsigned state_to_test;
+            // valeur d'état à tester déjà dans le cache
+            if (cache_bitmap[initial_state])
+            {
+                state_to_test = cache[initial_state];
+            }
+            else
+            {
+                cache_bitmap[initial_state] = true;
+                if (initial_variable != '\0')
+                    state.set_var(initial_variable, initial_state);
+                state_to_test = cache[initial_state] = state.eval();
+            }
+            return interval.contains(n.getNb(state_to_test));
+        }
+
+        private:
+        MathExpr state;
+        Interval interval;
+        mutable std::array<bool, MAX_ETATS> cache_bitmap;
+        mutable std::array<uint8_t, MAX_ETATS> cache;
+    };
+
 private:
     bool m_initial_state_is_variable;
     // could use a union here, but it's a bit tricky as we'd have to call the correct destructor
-    std::string m_initial_variable;
+    char m_initial_variable;
     unsigned m_initial_state;
-    std::map<std::string, Interval> m_constraints;
-    std::string m_result_state;
+    std::vector<Constraint> m_constraints;
+    MathExpr m_result_state;
+    mutable std::array<bool, MAX_ETATS> result_cache_bitmap;
+    mutable std::array<uint8_t, MAX_ETATS> result_cache;
 };
 
 //! \brief Représente une règle de transition totalistique configurable textuellement.
diff --git a/patterns/Griffeath/Spin.json b/patterns/Griffeath/Spin.json
new file mode 100644
index 0000000..d6c0453
--- /dev/null
+++ b/patterns/Griffeath/Spin.json
@@ -0,0 +1,2148 @@
+{
+    "author": "JM",
+    "cells": [
+        {
+            "state": 1,
+            "x": 1,
+            "y": 0
+        },
+        {
+            "state": 1,
+            "x": 2,
+            "y": 0
+        },
+        {
+            "state": 1,
+            "x": 3,
+            "y": 0
+        },
+        {
+            "state": 1,
+            "x": 4,
+            "y": 0
+        },
+        {
+            "state": 2,
+            "x": 5,
+            "y": 0
+        },
+        {
+            "state": 2,
+            "x": 6,
+            "y": 0
+        },
+        {
+            "state": 2,
+            "x": 7,
+            "y": 0
+        },
+        {
+            "state": 2,
+            "x": 8,
+            "y": 0
+        },
+        {
+            "state": 2,
+            "x": 9,
+            "y": 0
+        },
+        {
+            "state": 2,
+            "x": 10,
+            "y": 0
+        },
+        {
+            "state": 3,
+            "x": 11,
+            "y": 0
+        },
+        {
+            "state": 3,
+            "x": 12,
+            "y": 0
+        },
+        {
+            "state": 3,
+            "x": 13,
+            "y": 0
+        },
+        {
+            "state": 3,
+            "x": 14,
+            "y": 0
+        },
+        {
+            "state": 3,
+            "x": 15,
+            "y": 0
+        },
+        {
+            "state": 2,
+            "x": 16,
+            "y": 0
+        },
+        {
+            "state": 2,
+            "x": 17,
+            "y": 0
+        },
+        {
+            "state": 2,
+            "x": 18,
+            "y": 0
+        },
+        {
+            "state": 2,
+            "x": 19,
+            "y": 0
+        },
+        {
+            "state": 2,
+            "x": 20,
+            "y": 0
+        },
+        {
+            "state": 2,
+            "x": 21,
+            "y": 0
+        },
+        {
+            "state": 1,
+            "x": 22,
+            "y": 0
+        },
+        {
+            "state": 1,
+            "x": 23,
+            "y": 0
+        },
+        {
+            "state": 1,
+            "x": 24,
+            "y": 0
+        },
+        {
+            "state": 1,
+            "x": 1,
+            "y": 1
+        },
+        {
+            "state": 1,
+            "x": 2,
+            "y": 1
+        },
+        {
+            "state": 1,
+            "x": 3,
+            "y": 1
+        },
+        {
+            "state": 2,
+            "x": 4,
+            "y": 1
+        },
+        {
+            "state": 2,
+            "x": 5,
+            "y": 1
+        },
+        {
+            "state": 2,
+            "x": 6,
+            "y": 1
+        },
+        {
+            "state": 2,
+            "x": 7,
+            "y": 1
+        },
+        {
+            "state": 2,
+            "x": 8,
+            "y": 1
+        },
+        {
+            "state": 3,
+            "x": 9,
+            "y": 1
+        },
+        {
+            "state": 3,
+            "x": 10,
+            "y": 1
+        },
+        {
+            "state": 3,
+            "x": 11,
+            "y": 1
+        },
+        {
+            "state": 3,
+            "x": 12,
+            "y": 1
+        },
+        {
+            "state": 3,
+            "x": 13,
+            "y": 1
+        },
+        {
+            "state": 3,
+            "x": 14,
+            "y": 1
+        },
+        {
+            "state": 3,
+            "x": 15,
+            "y": 1
+        },
+        {
+            "state": 3,
+            "x": 16,
+            "y": 1
+        },
+        {
+            "state": 3,
+            "x": 17,
+            "y": 1
+        },
+        {
+            "state": 2,
+            "x": 18,
+            "y": 1
+        },
+        {
+            "state": 2,
+            "x": 19,
+            "y": 1
+        },
+        {
+            "state": 2,
+            "x": 20,
+            "y": 1
+        },
+        {
+            "state": 2,
+            "x": 21,
+            "y": 1
+        },
+        {
+            "state": 2,
+            "x": 22,
+            "y": 1
+        },
+        {
+            "state": 2,
+            "x": 23,
+            "y": 1
+        },
+        {
+            "state": 1,
+            "x": 24,
+            "y": 1
+        },
+        {
+            "state": 1,
+            "x": 0,
+            "y": 2
+        },
+        {
+            "state": 1,
+            "x": 1,
+            "y": 2
+        },
+        {
+            "state": 1,
+            "x": 2,
+            "y": 2
+        },
+        {
+            "state": 2,
+            "x": 3,
+            "y": 2
+        },
+        {
+            "state": 2,
+            "x": 4,
+            "y": 2
+        },
+        {
+            "state": 2,
+            "x": 5,
+            "y": 2
+        },
+        {
+            "state": 2,
+            "x": 6,
+            "y": 2
+        },
+        {
+            "state": 3,
+            "x": 7,
+            "y": 2
+        },
+        {
+            "state": 3,
+            "x": 8,
+            "y": 2
+        },
+        {
+            "state": 3,
+            "x": 9,
+            "y": 2
+        },
+        {
+            "state": 3,
+            "x": 10,
+            "y": 2
+        },
+        {
+            "state": 3,
+            "x": 11,
+            "y": 2
+        },
+        {
+            "state": 3,
+            "x": 12,
+            "y": 2
+        },
+        {
+            "state": 3,
+            "x": 14,
+            "y": 2
+        },
+        {
+            "state": 3,
+            "x": 15,
+            "y": 2
+        },
+        {
+            "state": 3,
+            "x": 16,
+            "y": 2
+        },
+        {
+            "state": 3,
+            "x": 17,
+            "y": 2
+        },
+        {
+            "state": 3,
+            "x": 18,
+            "y": 2
+        },
+        {
+            "state": 3,
+            "x": 19,
+            "y": 2
+        },
+        {
+            "state": 2,
+            "x": 20,
+            "y": 2
+        },
+        {
+            "state": 2,
+            "x": 21,
+            "y": 2
+        },
+        {
+            "state": 2,
+            "x": 22,
+            "y": 2
+        },
+        {
+            "state": 2,
+            "x": 23,
+            "y": 2
+        },
+        {
+            "state": 2,
+            "x": 24,
+            "y": 2
+        },
+        {
+            "state": 1,
+            "x": 0,
+            "y": 3
+        },
+        {
+            "state": 1,
+            "x": 1,
+            "y": 3
+        },
+        {
+            "state": 1,
+            "x": 2,
+            "y": 3
+        },
+        {
+            "state": 2,
+            "x": 3,
+            "y": 3
+        },
+        {
+            "state": 2,
+            "x": 4,
+            "y": 3
+        },
+        {
+            "state": 2,
+            "x": 5,
+            "y": 3
+        },
+        {
+            "state": 3,
+            "x": 6,
+            "y": 3
+        },
+        {
+            "state": 3,
+            "x": 7,
+            "y": 3
+        },
+        {
+            "state": 3,
+            "x": 8,
+            "y": 3
+        },
+        {
+            "state": 3,
+            "x": 9,
+            "y": 3
+        },
+        {
+            "state": 3,
+            "x": 10,
+            "y": 3
+        },
+        {
+            "state": 3,
+            "x": 16,
+            "y": 3
+        },
+        {
+            "state": 3,
+            "x": 17,
+            "y": 3
+        },
+        {
+            "state": 3,
+            "x": 18,
+            "y": 3
+        },
+        {
+            "state": 3,
+            "x": 19,
+            "y": 3
+        },
+        {
+            "state": 3,
+            "x": 20,
+            "y": 3
+        },
+        {
+            "state": 3,
+            "x": 21,
+            "y": 3
+        },
+        {
+            "state": 2,
+            "x": 22,
+            "y": 3
+        },
+        {
+            "state": 2,
+            "x": 23,
+            "y": 3
+        },
+        {
+            "state": 2,
+            "x": 24,
+            "y": 3
+        },
+        {
+            "state": 1,
+            "x": 0,
+            "y": 4
+        },
+        {
+            "state": 1,
+            "x": 1,
+            "y": 4
+        },
+        {
+            "state": 2,
+            "x": 2,
+            "y": 4
+        },
+        {
+            "state": 2,
+            "x": 3,
+            "y": 4
+        },
+        {
+            "state": 2,
+            "x": 4,
+            "y": 4
+        },
+        {
+            "state": 3,
+            "x": 5,
+            "y": 4
+        },
+        {
+            "state": 3,
+            "x": 6,
+            "y": 4
+        },
+        {
+            "state": 3,
+            "x": 7,
+            "y": 4
+        },
+        {
+            "state": 3,
+            "x": 8,
+            "y": 4
+        },
+        {
+            "state": 3,
+            "x": 18,
+            "y": 4
+        },
+        {
+            "state": 3,
+            "x": 19,
+            "y": 4
+        },
+        {
+            "state": 3,
+            "x": 20,
+            "y": 4
+        },
+        {
+            "state": 3,
+            "x": 21,
+            "y": 4
+        },
+        {
+            "state": 3,
+            "x": 22,
+            "y": 4
+        },
+        {
+            "state": 2,
+            "x": 23,
+            "y": 4
+        },
+        {
+            "state": 2,
+            "x": 24,
+            "y": 4
+        },
+        {
+            "state": 1,
+            "x": 0,
+            "y": 5
+        },
+        {
+            "state": 1,
+            "x": 1,
+            "y": 5
+        },
+        {
+            "state": 2,
+            "x": 2,
+            "y": 5
+        },
+        {
+            "state": 2,
+            "x": 3,
+            "y": 5
+        },
+        {
+            "state": 2,
+            "x": 4,
+            "y": 5
+        },
+        {
+            "state": 3,
+            "x": 5,
+            "y": 5
+        },
+        {
+            "state": 3,
+            "x": 6,
+            "y": 5
+        },
+        {
+            "state": 3,
+            "x": 7,
+            "y": 5
+        },
+        {
+            "state": 1,
+            "x": 13,
+            "y": 5
+        },
+        {
+            "state": 3,
+            "x": 20,
+            "y": 5
+        },
+        {
+            "state": 3,
+            "x": 21,
+            "y": 5
+        },
+        {
+            "state": 3,
+            "x": 22,
+            "y": 5
+        },
+        {
+            "state": 3,
+            "x": 23,
+            "y": 5
+        },
+        {
+            "state": 2,
+            "x": 24,
+            "y": 5
+        },
+        {
+            "state": 1,
+            "x": 0,
+            "y": 6
+        },
+        {
+            "state": 2,
+            "x": 1,
+            "y": 6
+        },
+        {
+            "state": 2,
+            "x": 2,
+            "y": 6
+        },
+        {
+            "state": 2,
+            "x": 3,
+            "y": 6
+        },
+        {
+            "state": 3,
+            "x": 4,
+            "y": 6
+        },
+        {
+            "state": 3,
+            "x": 5,
+            "y": 6
+        },
+        {
+            "state": 3,
+            "x": 6,
+            "y": 6
+        },
+        {
+            "state": 1,
+            "x": 11,
+            "y": 6
+        },
+        {
+            "state": 1,
+            "x": 12,
+            "y": 6
+        },
+        {
+            "state": 1,
+            "x": 13,
+            "y": 6
+        },
+        {
+            "state": 1,
+            "x": 14,
+            "y": 6
+        },
+        {
+            "state": 1,
+            "x": 15,
+            "y": 6
+        },
+        {
+            "state": 3,
+            "x": 21,
+            "y": 6
+        },
+        {
+            "state": 3,
+            "x": 22,
+            "y": 6
+        },
+        {
+            "state": 3,
+            "x": 23,
+            "y": 6
+        },
+        {
+            "state": 2,
+            "x": 24,
+            "y": 6
+        },
+        {
+            "state": 1,
+            "x": 0,
+            "y": 7
+        },
+        {
+            "state": 2,
+            "x": 1,
+            "y": 7
+        },
+        {
+            "state": 2,
+            "x": 2,
+            "y": 7
+        },
+        {
+            "state": 2,
+            "x": 3,
+            "y": 7
+        },
+        {
+            "state": 3,
+            "x": 4,
+            "y": 7
+        },
+        {
+            "state": 3,
+            "x": 5,
+            "y": 7
+        },
+        {
+            "state": 3,
+            "x": 6,
+            "y": 7
+        },
+        {
+            "state": 1,
+            "x": 10,
+            "y": 7
+        },
+        {
+            "state": 1,
+            "x": 11,
+            "y": 7
+        },
+        {
+            "state": 1,
+            "x": 12,
+            "y": 7
+        },
+        {
+            "state": 1,
+            "x": 13,
+            "y": 7
+        },
+        {
+            "state": 1,
+            "x": 14,
+            "y": 7
+        },
+        {
+            "state": 1,
+            "x": 15,
+            "y": 7
+        },
+        {
+            "state": 1,
+            "x": 16,
+            "y": 7
+        },
+        {
+            "state": 1,
+            "x": 17,
+            "y": 7
+        },
+        {
+            "state": 3,
+            "x": 22,
+            "y": 7
+        },
+        {
+            "state": 3,
+            "x": 23,
+            "y": 7
+        },
+        {
+            "state": 3,
+            "x": 24,
+            "y": 7
+        },
+        {
+            "state": 2,
+            "x": 0,
+            "y": 8
+        },
+        {
+            "state": 2,
+            "x": 1,
+            "y": 8
+        },
+        {
+            "state": 2,
+            "x": 2,
+            "y": 8
+        },
+        {
+            "state": 3,
+            "x": 3,
+            "y": 8
+        },
+        {
+            "state": 3,
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+            "x": 18,
+            "y": 19
+        },
+        {
+            "state": 3,
+            "x": 22,
+            "y": 19
+        },
+        {
+            "state": 3,
+            "x": 23,
+            "y": 19
+        },
+        {
+            "state": 3,
+            "x": 24,
+            "y": 19
+        },
+        {
+            "state": 1,
+            "x": 2,
+            "y": 20
+        },
+        {
+            "state": 1,
+            "x": 3,
+            "y": 20
+        },
+        {
+            "state": 1,
+            "x": 4,
+            "y": 20
+        },
+        {
+            "state": 1,
+            "x": 5,
+            "y": 20
+        },
+        {
+            "state": 1,
+            "x": 6,
+            "y": 20
+        },
+        {
+            "state": 1,
+            "x": 7,
+            "y": 20
+        },
+        {
+            "state": 2,
+            "x": 8,
+            "y": 20
+        },
+        {
+            "state": 2,
+            "x": 9,
+            "y": 20
+        },
+        {
+            "state": 2,
+            "x": 10,
+            "y": 20
+        },
+        {
+            "state": 2,
+            "x": 11,
+            "y": 20
+        },
+        {
+            "state": 2,
+            "x": 12,
+            "y": 20
+        },
+        {
+            "state": 1,
+            "x": 13,
+            "y": 20
+        },
+        {
+            "state": 1,
+            "x": 14,
+            "y": 20
+        },
+        {
+            "state": 1,
+            "x": 15,
+            "y": 20
+        },
+        {
+            "state": 1,
+            "x": 16,
+            "y": 20
+        },
+        {
+            "state": 1,
+            "x": 17,
+            "y": 20
+        },
+        {
+            "state": 3,
+            "x": 21,
+            "y": 20
+        },
+        {
+            "state": 3,
+            "x": 22,
+            "y": 20
+        },
+        {
+            "state": 3,
+            "x": 23,
+            "y": 20
+        },
+        {
+            "state": 2,
+            "x": 24,
+            "y": 20
+        },
+        {
+            "state": 1,
+            "x": 4,
+            "y": 21
+        },
+        {
+            "state": 1,
+            "x": 5,
+            "y": 21
+        },
+        {
+            "state": 1,
+            "x": 6,
+            "y": 21
+        },
+        {
+            "state": 1,
+            "x": 7,
+            "y": 21
+        },
+        {
+            "state": 1,
+            "x": 8,
+            "y": 21
+        },
+        {
+            "state": 1,
+            "x": 9,
+            "y": 21
+        },
+        {
+            "state": 2,
+            "x": 10,
+            "y": 21
+        },
+        {
+            "state": 1,
+            "x": 11,
+            "y": 21
+        },
+        {
+            "state": 1,
+            "x": 12,
+            "y": 21
+        },
+        {
+            "state": 1,
+            "x": 13,
+            "y": 21
+        },
+        {
+            "state": 1,
+            "x": 14,
+            "y": 21
+        },
+        {
+            "state": 1,
+            "x": 15,
+            "y": 21
+        },
+        {
+            "state": 1,
+            "x": 16,
+            "y": 21
+        },
+        {
+            "state": 3,
+            "x": 21,
+            "y": 21
+        },
+        {
+            "state": 3,
+            "x": 22,
+            "y": 21
+        },
+        {
+            "state": 3,
+            "x": 23,
+            "y": 21
+        },
+        {
+            "state": 2,
+            "x": 24,
+            "y": 21
+        }
+    ],
+    "date": "ven. juin 11 2021",
+    "desc": "",
+    "title": "Spin"
+}
diff --git a/src/alphabet.cpp b/src/alphabet.cpp
index 610f022..edff000 100644
--- a/src/alphabet.cpp
+++ b/src/alphabet.cpp
@@ -14,7 +14,7 @@ void Alphabet::newEtat(const state& s){ // Définition de la méthode de créati
     etats.push_back(s);
 }
 
-state Alphabet::getState(unsigned int it) const{ // Définition de la méthode de récupération d'un état en fonction de son identifiant
+const state &Alphabet::getState(unsigned int it) const{ // Définition de la méthode de récupération d'un état en fonction de son identifiant
     if (it < etats.size())
     {
         return etats[it];
diff --git a/src/automaton.cpp b/src/automaton.cpp
index 77b933e..7046a6e 100644
--- a/src/automaton.cpp
+++ b/src/automaton.cpp
@@ -59,9 +59,14 @@ void Automaton::runOnce() {
     // On s'assure d'avoir une stratégie de frontière de réseau à jour
     grid.set_boundary_policy(border_policy);
     Grid tempGrid(grid);
-    for(int i=0; i<static_cast<int>(grid.get_col()); ++i) {
-        for(int j=0; j<static_cast<int>(grid.get_rows()); ++j) {
-             tempGrid.set_cell({i, j}, transitionRule->getState(grid.get_state({i,j}),neighbourhoodRule->getNeighborhood(grid, {i, j}))%alphabet.taille());
+    for(int i=0; i<static_cast<int>(grid.get_rows()); ++i) {
+        for(int j=0; j<static_cast<int>(grid.get_col()); ++j) {
+            unsigned prev = grid.get_state({j,i});
+            unsigned next = transitionRule->getState(prev,neighbourhoodRule->getNeighborhood(grid, {j, i}));
+            if (next >= alphabet.taille()) // embrace the magic of branch prediction
+                next %= alphabet.taille();
+            if (prev != next)
+                tempGrid.set_cell({j, i}, next);
         }
     }
     grid = tempGrid;
diff --git a/src/gridview.cpp b/src/gridview.cpp
index 5f6d37c..b24a52e 100644
--- a/src/gridview.cpp
+++ b/src/gridview.cpp
@@ -247,7 +247,8 @@ void GridGraphicsView::drawBackground(QPainter *painter, const QRectF &rect)
 {
     QGraphicsView::drawBackground(painter, rect);
 
-    painter->drawPixmap(0, 0, m_gridview.grid_pixmap());
+    //painter->drawPixmap(0, 0, m_gridview.grid_image());
+    painter->drawImage(0, 0, m_gridview.grid_image());
 }
 
 // Algorithme de Bresenham pour tracer une ligne entre les deux points et dessiner sur ces items
@@ -448,17 +449,31 @@ void GridView::load_grid(const Grid &grid)
     m_width = grid.get_col();
     m_grid = grid;
 
-    m_grid_image = QImage(m_width, m_height, QImage::Format_ARGB32);
-    for (int i = 0; i < (int)m_width; ++i)
+    m_image_data.resize(m_width*m_height);
+    for (int i = 0; i < (int)m_height; ++i)
     {
-        for (int j = 0; j < (int)m_height; ++j)
+        for (int j = 0; j < (int)m_width; ++j)
         {
-            QColor color = stateColor_to_QColor(m_alph.getState(grid.get_state(Coord{i, j}) % m_alph.taille()).getColor());
-            m_grid_image.setPixelColor(i, j, color);
-            m_grid.set_cell(Coord{i, j}, grid.get_state(Coord{i, j}) % m_alph.taille());
+            unsigned state_id = grid.get_state(Coord{j, i});
+            if (state_id < m_alph.taille())
+            {
+                const auto& state_color = m_alph.getState(state_id).getColor();
+                m_image_data[i * m_width + j] = 0xff000000 | ((uint32_t)state_color.getRed() << 16)
+                                                | ((uint32_t)state_color.getGreen() << 8)
+                                                | ((uint32_t)state_color.getBlue() << 0);
+            }
+            else
+            {
+                const auto& state_color = m_alph.getState(state_id % m_alph.taille()).getColor();
+                m_image_data[i * m_width + j] = 0xff000000 | ((uint32_t)state_color.getRed() << 16)
+                                                | ((uint32_t)state_color.getGreen() << 8)
+                                                | ((uint32_t)state_color.getBlue() << 0);
+                m_grid.set_cell(Coord{j, i}, state_id % m_alph.taille());
+            }
         }
     }
-    m_grid_pixmap.convertFromImage(m_grid_image);
+
+    m_grid_image = QImage((const uchar*)m_image_data.data(), m_width, m_height, QImage::Format_ARGB32);
     m_scene->setSceneRect(QRectF(0, 0, m_width, m_height));
     m_drag_drop_handler->setRect(QRectF(0, 0, m_width, m_height));
     update_current_mouse_pos(m_last_mouse_pos);
@@ -467,14 +482,16 @@ void GridView::load_grid(const Grid &grid)
 void GridView::set_cell_state(Coord pos, unsigned state)
 {
     state %= m_alph.taille();
-    QColor color = stateColor_to_QColor(m_alph.getState(state).getColor());
-    m_grid_image.setPixelColor(pos.x, pos.y, color);
+    auto state_color = m_alph.getState(state).getColor();
+    m_image_data[pos.y * m_width + pos.x] = 0xff000000 | ((uint32_t)state_color.getRed() << 16)
+                                            | ((uint32_t)state_color.getGreen() << 8)
+                                            | ((uint32_t)state_color.getBlue() << 0);
     m_grid.set_cell(pos, state);
 }
 
 void GridView::update_gridview()
 {
-    m_grid_pixmap.convertFromImage(m_grid_image);
+    m_grid_image = QImage((const uchar*)m_image_data.data(), m_width, m_height, QImage::Format_ARGB32);
     m_scene->update();
 }
 
@@ -583,9 +600,9 @@ void GridView::paste_structure_at(Coord origin, const Structure &s)
     update_gridview();
 }
 
-const QPixmap &GridView::grid_pixmap() const
+const QImage &GridView::grid_image() const
 {
-    return m_grid_pixmap;
+    return m_grid_image;
 }
 
 void GridView::handle_rubberband(QRect rubberBandRect, QPointF fromScenePoint, QPointF toScenePoint)
diff --git a/src/mathexpr.cpp b/src/mathexpr.cpp
index 5c9a008..9fb8905 100644
--- a/src/mathexpr.cpp
+++ b/src/mathexpr.cpp
@@ -17,19 +17,7 @@ Ce fichier contient une fonction permettant d'exécuter une expression mathémat
 #include <algorithm>
 #include <cctype>
 
-struct rpl_token_t
-{
-    enum
-    {
-        LITERAL,
-        OP
-    } type;
-    union
-    {
-        int value;
-        char op;
-    };
-};
+    using detail::rpl_token_t;
 
 //! Priorité de l'opérateur
 static int precedence(char op)
@@ -45,9 +33,6 @@ static int precedence(char op)
 //! Evalue une opération binaire entre x et y, dénotée par op.
 static int eval_int_binop(char op, int x, int y)
 {
-    if ((op == '/' || op == '%') && y == 0)
-        throw MathExprException("Divsion by zero error");
-
     switch (op)
     {
         case '+':
@@ -57,49 +42,60 @@ static int eval_int_binop(char op, int x, int y)
         case '*':
             return x*y;
         case '/':
+            if (y == 0)
+                throw MathExprException("Divsion by zero error");
             return x/y;
         case '%':
+            if (y == 0)
+                throw MathExprException("Divsion by zero error");
             return x%y;
         default:
             throw MathExprException("Unknown operator");
     }
 }
 
+#define MAX_DATA_STACK_SIZE 256
 //! Evalue une expression RPL
-static int evaluate_rpl_input(const std::vector<rpl_token_t>& rpl_stack)
+static int evaluate_rpl_input(const std::vector<rpl_token_t>& rpl_stack, const std::array<int8_t, 26>& variable_map)
 {
-    std::vector<int> data_stack;
+    static std::array<int, MAX_DATA_STACK_SIZE> data_stack;
+    unsigned stack_len = 0;
 
     for (unsigned i = 0; i < rpl_stack.size(); ++i)
     {
+        if (stack_len+1 >= MAX_DATA_STACK_SIZE)
+            throw MathExprException("Internal error: Exceeded the maximum amount of RPL tokens");
+
         if (rpl_stack[i].type == rpl_token_t::LITERAL)
-            data_stack.push_back(rpl_stack[i].value);
+            data_stack[stack_len++] = rpl_stack[i].value;
+        else if (rpl_stack[i].type == rpl_token_t::VARIABLE)
+            data_stack[stack_len++] = variable_map[rpl_stack[i].var_alphabet_idx];
         else
         {
             int op = rpl_stack[i].op;
-            if (data_stack.size() <= 1)
+            if (stack_len <= 1)
                 throw MathExprException("Invalid math expression error");
 
-            int x = data_stack[data_stack.size()-2];
-            int y = data_stack[data_stack.size()-1];
+            int x = data_stack[stack_len-2];
+            int y = data_stack[stack_len-1];
             int result = eval_int_binop(op, x, y);
-            data_stack.pop_back();
-            data_stack[data_stack.size()-1] = result;
+            --stack_len;
+            data_stack[stack_len-1] = result;
 
         }
     }
 
-    if (data_stack.size() != 1)
+    if (stack_len != 1)
         throw MathExprException("Invalid math expression error");
 
     return data_stack[0];
 }
 
-int eval_math(const std::string &in_expr, const std::map<std::string, int> &variables)
+std::vector<rpl_token_t> parse_math(const std::string& in_expr)
 {
     std::string expr = in_expr;
     // remove whitespace out of the equation altogether
-    expr.erase(std::remove_if(expr.begin(), expr.end(), ::isspace), expr.end());   
+    expr.erase(std::remove_if(expr.begin(), expr.end(), ::isspace), expr.end());
 
     std::vector<rpl_token_t> rpl_stack;
     std::stack<char> op_stack;
@@ -130,19 +126,19 @@ int eval_math(const std::string &in_expr, const std::map<std::string, int> &vari
             case '/':
             case '%':
                 // binary operator
-            {
-                while  (!op_stack.empty() &&
-                        (op_stack.top() != '(') &&
-                        (precedence(op_stack.top()) > precedence(expr[idx])))
                 {
-                    rpl_token.type = rpl_token_t::OP;
-                    rpl_token.op = op_stack.top();
-                    rpl_stack.push_back(rpl_token);
-                    op_stack.pop();
+                    while  (!op_stack.empty() &&
+                           (op_stack.top() != '(') &&
+                           (precedence(op_stack.top()) > precedence(expr[idx])))
+                    {
+                        rpl_token.type = rpl_token_t::OP;
+                        rpl_token.op = op_stack.top();
+                        rpl_stack.push_back(rpl_token);
+                        op_stack.pop();
+                    }
+                    op_stack.push(expr[idx]);
+                    ++idx;
                 }
-                op_stack.push(expr[idx]);
-                ++idx;
-            }
                 break;
             case '(':
                 op_stack.push('(');
@@ -166,21 +162,16 @@ int eval_math(const std::string &in_expr, const std::map<std::string, int> &vari
                 break;
             default:
                 // assume it's a variable name then
-            {
-                std::string var_name;
-                while (isalnum(expr[idx]))
                 {
-                    var_name += expr[idx];
-                    ++idx;
-                }
+                    char var_name = expr[idx++];
+                    if (var_name < 'a' || var_name > 'z')
+                        throw MathExprException("Invalid variable name");
 
-                if (!variables.count(var_name))
-                    throw MathExprException("No such variable '" + var_name + "' found");
-                rpl_token.type = rpl_token_t::LITERAL;
-                rpl_token.value = variables.at(var_name);
-                rpl_stack.push_back(rpl_token);
-                break;
-            }
+                    rpl_token.type = rpl_token_t::VARIABLE;
+                    rpl_token.var_alphabet_idx = var_name - 'a';
+                    rpl_stack.push_back(rpl_token);
+                    break;
+                }
         }
     }
     // while there are remaining operators on the op stack
@@ -192,6 +183,43 @@ int eval_math(const std::string &in_expr, const std::map<std::string, int> &vari
         rpl_stack.push_back(rpl_token);
     }
 
+    return rpl_stack;
+}
+
+int eval_math(const std::string &in_expr, const std::map<char, int> &variables)
+{
+    auto rpl_stack = parse_math(in_expr);
+
+    std::array<int8_t, 26> variable_map;
+    for (const auto& pair : variables)
+    {
+        if (pair.second < 'a' || pair.second > 'z')
+            throw MathExprException("Invalid variable name");
+        variable_map[pair.first] = pair.second - 'a';
+    }
+    return evaluate_rpl_input(rpl_stack, variable_map);
+}
 
-    return evaluate_rpl_input(rpl_stack);
+MathExpr::MathExpr(const std::string &expr)
+{
+    is_constant = false;
+
+    rpl_stack = parse_math(expr);
+    // Constant expression, cache the result
+    if (std::find_if(expr.begin(), expr.end(), ::isalpha) == expr.end())
+    {
+        is_constant = true;
+        cached_result = evaluate_rpl_input(rpl_stack, variable_map);
+    }
+}
+
+int MathExpr::eval() const
+{
+    if (is_constant)
+        return cached_result;
+    else
+    {
+        int result = evaluate_rpl_input(rpl_stack, variable_map);
+        return result;
+    }
 }
diff --git a/src/neighborhood_rules/mooreNeighborhoodRule.cpp b/src/neighborhood_rules/mooreNeighborhoodRule.cpp
index c894c7a..ceec70c 100644
--- a/src/neighborhood_rules/mooreNeighborhoodRule.cpp
+++ b/src/neighborhood_rules/mooreNeighborhoodRule.cpp
@@ -18,16 +18,37 @@ Neighborhood mooreNeighborhoodRule::getNeighborhood(const Grid& grid, Coord pos)
         update_format();
 
     Neighborhood newNeighborhood;
-    // Coordonnées des voisins dans la grille
-    Coord gridCoord;
-    std::vector<Coord>::const_iterator it = format.positions.begin();
-    for (it = format.positions.begin() ; it != format.positions.end(); ++it) {
-        // Calcul des coordonnées du voisin sur la grille
-        gridCoord.x = pos.x + it->x;
-        gridCoord.y = pos.y + it->y;
-        // Ajout du nouveau voisin <Coordonnée_relative, état>
-        newNeighborhood.addNeighbor(*it , grid.get_state(gridCoord));
+
+    // fast path
+    if (radius.val == 1)
+    {
+        newNeighborhood.addNeighbor(pos + Coord{-1, -1}, grid.get_state(pos + Coord{-1, -1}));
+        newNeighborhood.addNeighbor(pos + Coord{0, -1}, grid.get_state(pos + Coord{0, -1}));
+        newNeighborhood.addNeighbor(pos + Coord{+1, -1}, grid.get_state(pos + Coord{+1, -1}));
+
+        newNeighborhood.addNeighbor(pos + Coord{-1, 0}, grid.get_state(pos + Coord{-1, 0}));
+        newNeighborhood.addNeighbor(pos + Coord{+1, 0}, grid.get_state(pos + Coord{+1, 0}));
+
+        newNeighborhood.addNeighbor(pos + Coord{-1, +1}, grid.get_state(pos + Coord{-1, +1}));
+        newNeighborhood.addNeighbor(pos + Coord{0, +1}, grid.get_state(pos + Coord{0, +1}));
+        newNeighborhood.addNeighbor(pos + Coord{+1, +1}, grid.get_state(pos + Coord{+1, +1}));
+
     }
+    else
+    {
+        // Coordonnées des voisins dans la grille
+        Coord gridCoord;
+        std::vector<Coord>::const_iterator it = format.positions.begin();
+        for (it = format.positions.begin() ; it != format.positions.end(); ++it) {
+            // Calcul des coordonnées du voisin sur la grille
+            gridCoord.x = pos.x + it->x;
+            gridCoord.y = pos.y + it->y;
+            // Ajout du nouveau voisin <Coordonnée_relative, état>
+            newNeighborhood.addNeighbor(*it , grid.get_state(gridCoord));
+        }
+    }
+
+
     return newNeighborhood;
 }
 
diff --git a/src/simulation.cpp b/src/simulation.cpp
index acc836b..04c06be 100644
--- a/src/simulation.cpp
+++ b/src/simulation.cpp
@@ -65,13 +65,19 @@ void Simulation::resize(size_t l,size_t c) {
     hist = History(hist.get_nbMax());
 }
 
+#include <QElapsedTimer>
 void Simulation::step() {
     if(!canRun) {
         return;
     }
     ++time;
     hist.pushGrid(automaton.getGrid());
+
+    QElapsedTimer t;
+    t.start();
     automaton.runOnce();
+    qDebug() << t.elapsed();
+
     automaton.getNeighborhoodRule()->update_generation(time);
     if(!period && startGrid == automaton.getGrid()) {
         period = time;
diff --git a/src/transition_rules/nonisotropictransition.cpp b/src/transition_rules/nonisotropictransition.cpp
index df35769..534bc14 100644
--- a/src/transition_rules/nonisotropictransition.cpp
+++ b/src/transition_rules/nonisotropictransition.cpp
@@ -45,7 +45,7 @@ NonIsotropicRuleEntry::NonIsotropicRuleEntry(string rule_string, bool vertical_s
     else
     {
         m_initial_state_is_variable = true;
-        m_initial_variable = comma_tokens[0];
+        m_initial_variable = comma_tokens[0][0];
     }
 
     for (size_t i = 1; i < comma_tokens.size(); ++i)
@@ -107,7 +107,10 @@ bool NonIsotropicRuleEntry::accept(unsigned initial_state, const Neighborhood &n
 
     if (entry_accepted)
     {
-        next = eval_math(m_result_state, {{m_initial_variable, initial_state}});
+        if (m_initial_state_is_variable)
+            m_result_state.set_var(m_initial_variable, initial_state);
+        next = m_result_state.eval();
+        //next = eval_math(m_result_state, {{m_initial_variable, initial_state}});
         return true;
     }
     else
diff --git a/src/transition_rules/totalistictransition.cpp b/src/transition_rules/totalistictransition.cpp
index 632ba4b..c3fa316 100644
--- a/src/transition_rules/totalistictransition.cpp
+++ b/src/transition_rules/totalistictransition.cpp
@@ -14,7 +14,7 @@ Cette classe représente une règle de transition totalistique configurable.
 #include <algorithm>
 #include <sstream>
 
-REGISTER_FACTORY_ENTRY(TransitionRule, TotalisticTransition, "Totalistic rulestring");
+    REGISTER_FACTORY_ENTRY(TransitionRule, TotalisticTransition, "Totalistic rulestring");
 
 static std::vector<std::string> split(std::string str, std::string token){
     std::vector<std::string>result;
@@ -37,12 +37,12 @@ static Interval read_interval( std::string str)
     // remove whitespace
     str.erase(std::remove_if(str.begin(), str.end(), ::isspace), str.end());
 
-    Interval interval = Interval{"0", ""}; // full interval by default
+    Interval interval = Interval{}; // full interval by default
 
     if (str.size() < 1)
         throw TotalisticRuleException("Invalid rule entry format");
     if (str == "*")
-        return Interval{"0", ""}; // lowest bound, no higher bound
+        return Interval{}; // lowest bound, no higher bound
     if (str[0] != '[' || str.back() != ']')
         throw TotalisticRuleException("Invalid rule entry format");
 
@@ -54,17 +54,16 @@ static Interval read_interval( std::string str)
     if (interval_split.size() == 1)
     {
         if (interval_split[0] == "*")
-            return Interval{"0", ""}; // lowest bound, no higher bound
+            return Interval{}; // lowest bound, no higher bound
         else
-            interval.low = interval.high = interval_split[0]; // single-point interval
+            interval = Interval{interval_split[0], interval_split[0]}; // single-point interval
     }
     else
     {
-        interval.low = interval_split[0];
         if (interval_split[1] == "*")
-            interval.high = "";
+            interval = Interval{interval_split[0]};
         else
-            interval.high = interval_split[1];
+            interval = Interval{interval_split[0], interval_split[1]};
     }
 
     return interval;
@@ -72,6 +71,9 @@ static Interval read_interval( std::string str)
 
 TotalisticRuleEntry::TotalisticRuleEntry(std::string rule_string)
 {
+    std::fill(result_cache_bitmap.begin(), result_cache_bitmap.end(), false);
+    m_initial_variable = '\0';
+
     rule_string.erase(std::remove_if(rule_string.begin(), rule_string.end(), ::isspace), rule_string.end());
 
     auto arrow_tokens = split(rule_string, "->");
@@ -92,7 +94,7 @@ TotalisticRuleEntry::TotalisticRuleEntry(std::string rule_string)
     else
     {
         m_initial_state_is_variable = true;
-        m_initial_variable = comma_tokens[0];
+        m_initial_variable = comma_tokens[0][0];
     }
 
     for (size_t i = 1; i < comma_tokens.size(); ++i)
@@ -100,7 +102,7 @@ TotalisticRuleEntry::TotalisticRuleEntry(std::string rule_string)
         auto colon_tokens = split(comma_tokens[i], ":");
         if (colon_tokens.size() != 2)
             throw TotalisticRuleException("Invalid rule entry format");
-        m_constraints[colon_tokens[0]] = read_interval(colon_tokens[1]);
+        m_constraints.push_back({MathExpr(colon_tokens[0]), read_interval(colon_tokens[1])});
     }
 
     m_result_state = arrow_tokens[1];
@@ -114,8 +116,7 @@ bool TotalisticRuleEntry::accept(unsigned initial_state, const Neighborhood &nei
     bool entry_accepted = true;
     for (const auto& constraint : m_constraints)
     {
-        unsigned state_to_test = eval_math(constraint.first, {{m_initial_variable, initial_state}});
-        if (!constraint.second.contains(neighborhood.getNb(state_to_test)))
+        if (!constraint.valid(m_initial_variable, initial_state, neighborhood))
         {
             entry_accepted = false;
             break;
@@ -124,7 +125,18 @@ bool TotalisticRuleEntry::accept(unsigned initial_state, const Neighborhood &nei
 
     if (entry_accepted)
     {
-        next = eval_math(m_result_state, {{m_initial_variable, initial_state}});
+        if (result_cache_bitmap[initial_state])
+        {
+            next = result_cache[initial_state];
+        }
+        else
+        {
+            if (m_initial_state_is_variable)
+                m_result_state.set_var(m_initial_variable, initial_state);
+
+            result_cache_bitmap[initial_state] = true;
+            next = result_cache[initial_state] = m_result_state.eval();
+        }
         return true;
     }
     else
diff --git a/tests/totalistictransition_test.cpp b/tests/totalistictransition_test.cpp
index e55abcf..a0540f3 100644
--- a/tests/totalistictransition_test.cpp
+++ b/tests/totalistictransition_test.cpp
@@ -13,8 +13,8 @@ void CellulutTests::test_totalistictransition()
     QCOMPARE(eval_math("5 * 6+3"), 33);
     QCOMPARE(eval_math("(5+6) * 3"), 33);
 
-    QCOMPARE(eval_math("(i+1)%4", {{"i", 2}}), 3);
-    QCOMPARE(eval_math("(i+1)%4", {{"i", 3}}), 0);
+    QCOMPARE(eval_math("(i+1)%4", {{'i', 2}}), 3);
+    QCOMPARE(eval_math("(i+1)%4", {{'i', 3}}), 0);
 
 
     {
-- 
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