nitg-s: removed useless LiveEntryColoring since there is no more generic tree option
[nit.git] / src / coloring.nit
index 08c63a1..877c993 100644 (file)
 # Graph coloring tools
 module coloring
 
-import rapid_type_analysis # for type coloration
+import typing
 
-abstract class AbstractColoring[E: Object]
+# Layouts
 
-       private var sorter: AbstractSorter[E]
-       private var reverse_sorter: AbstractSorter[E]
+class TypingLayout[E]
+       # Unic ids or each element
+       var ids: Map[E, Int] = new HashMap[E, Int]
+       # Fixed positions of each element in all tables
+       var pos: Map[E, Int] = new HashMap[E, Int]
+end
+
+class PHTypingLayout[E]
+       super TypingLayout[E]
+       # Masks used by hash function
+       var masks: Map[E, Int] = new HashMap[E, Int]
+       # Positions of each element for each tables
+       var hashes: Map[E, Map[E, Int]] = new HashMap[E, Map[E, Int]]
+end
 
-       private var core: OrderedSet[E] = new OrderedSet[E]
-       private var crown: OrderedSet[E] = new OrderedSet[E]
-       private var border: OrderedSet[E] = new OrderedSet[E]
+# Builders
 
-       private var coloration_result: Map[E, Int] = new HashMap[E, Int]
-       private var conflicts_graph_cache: nullable HashMap[E, Set[E]]
+abstract class TypingLayoutBuilder[E]
+
+       type LAYOUT: TypingLayout[E]
+
+       private var mmodule: MModule
+       init(mmodule: MModule) do self.mmodule = mmodule
+
+       # Compute elements ids and position
+       fun build_layout(elements: Set[E]): LAYOUT is abstract
+
+       # Give each MType a unic id using a descending linearization of the `mtypes` set
+       private fun compute_ids(elements: Set[E]): Map[E, Int] do
+               var ids = new HashMap[E, Int]
+               var lin = self.reverse_linearize(elements)
+               for element in lin do
+                       ids[element] = ids.length
+               end
+               return ids
+       end
+
+       private fun reverse_linearize(elements: Set[E]): Array[E] is abstract
+end
+
+# Layout builder for MType using Binary Matrix (BM)
+class BMTypeLayoutBuilder
+       super TypingLayoutBuilder[MType]
+
+       init(mmodule: MModule) do super
+
+       # Compute mtypes ids and position using BM
+       redef fun build_layout(mtypes) do
+               var result = new TypingLayout[MType]
+               result.ids = self.compute_ids(mtypes)
+               result.pos = result.ids
+               return result
+       end
+
+       redef fun reverse_linearize(elements) do return self.mmodule.reverse_linearize_mtypes(elements)
+end
+
+# Layout builder for MType using Coloring (CL)
+class CLTypeLayoutBuilder
+       super TypingLayoutBuilder[MType]
+
+       private var colorer: MTypeColorer
+
+       init(mmodule: MModule) do
+               super
+               self.colorer = new MTypeColorer(mmodule)
+       end
+
+       # Compute mtypes ids and position using BM
+       redef fun build_layout(mtypes) do
+               var result = new TypingLayout[MType]
+               result.ids = self.compute_ids(mtypes)
+               result.pos = self.colorer.colorize(mtypes)
+               return result
+       end
+
+       redef fun reverse_linearize(elements) do return self.mmodule.reverse_linearize_mtypes(elements)
+end
+
+# Layout builder for MType using Perfect Hashing (PH)
+class PHTypeLayoutBuilder
+       super TypingLayoutBuilder[MType]
+
+       redef type LAYOUT: PHTypingLayout[MType]
+
+       private var hasher: MTypeHasher
+
+       init(mmodule: MModule, operator: PHOperator) do
+               super
+               self.hasher = new MTypeHasher(mmodule, operator)
+       end
+
+       # Compute mtypes ids and position using BM
+       redef fun build_layout(mtypes) do
+               var result = new PHTypingLayout[MType]
+               result.ids = self.compute_ids(mtypes)
+               result.masks = self.hasher.compute_masks(mtypes, result.ids)
+               result.hashes = self.hasher.compute_hashes(mtypes, result.ids, result.masks)
+               return result
+       end
+
+       # Ids start from 1 instead of 0
+       redef fun compute_ids(mtypes) do
+               var ids = new HashMap[MType, Int]
+               var lin = self.mmodule.reverse_linearize_mtypes(mtypes)
+               for mtype in lin do
+                       ids[mtype] = ids.length + 1
+               end
+               return ids
+       end
+
+       redef fun reverse_linearize(elements) do return self.mmodule.reverse_linearize_mtypes(elements)
+end
+
+# Layout builder for MClass using Binary Matrix (BM)
+class BMClassLayoutBuilder
+       super TypingLayoutBuilder[MClass]
+
+       init(mmodule: MModule) do super
+
+       # Compute mclasses ids and position using BM
+       redef fun build_layout(mclasses) do
+               var result = new TypingLayout[MClass]
+               result.ids = self.compute_ids(mclasses)
+               result.pos = result.ids
+               return result
+       end
+
+       redef fun reverse_linearize(elements) do return self.mmodule.reverse_linearize_mclasses(elements)
+end
+
+# Layout builder for MClass using Coloring (CL)
+class CLClassLayoutBuilder
+       super TypingLayoutBuilder[MClass]
+
+       private var colorer: MClassColorer
 
-       init(sorter: AbstractSorter[E], reverse_sorter: AbstractSorter[E]) do
-               self.sorter = sorter
-               self.reverse_sorter = reverse_sorter
+       init(mmodule: MModule) do
+               super
+               self.colorer = new MClassColorer(mmodule)
        end
 
-       fun colorize(elements: Collection[E]): Map[E, Int] do
-               # tag each element as part of group core, crown or border
-               for e in elements do
-                       tag_element(e)
+       # Compute mclasses ids and position using BM
+       redef fun build_layout(mclasses) do
+               var result = new TypingLayout[MClass]
+               result.ids = self.compute_ids(mclasses)
+               result.pos = self.colorer.colorize(mclasses)
+               return result
+       end
+
+       redef fun reverse_linearize(elements) do return self.mmodule.reverse_linearize_mclasses(elements)
+end
+
+# Layout builder for MClass using Perfect Hashing (PH)
+class PHClassLayoutBuilder
+       super TypingLayoutBuilder[MClass]
+
+       redef type LAYOUT: PHTypingLayout[MClass]
+
+       private var hasher: MClassHasher
+
+       init(mmodule: MModule, operator: PHOperator) do
+               super
+               self.hasher = new MClassHasher(mmodule, operator)
+       end
+
+       # Compute mclasses ids and position using BM
+       redef fun build_layout(mclasses) do
+               var result = new PHTypingLayout[MClass]
+               result.ids = self.compute_ids(mclasses)
+               result.masks = self.hasher.compute_masks(mclasses, result.ids)
+               result.hashes = self.hasher.compute_hashes(mclasses, result.ids, result.masks)
+               return result
+       end
+
+       # Ids start from 1 instead of 0
+       redef fun compute_ids(mclasses) do
+               var ids = new HashMap[MClass, Int]
+               var lin = self.mmodule.reverse_linearize_mclasses(mclasses)
+               for mclass in lin do
+                       ids[mclass] = ids.length + 1
                end
+               return ids
+       end
+
+       redef fun reverse_linearize(elements) do return self.mmodule.reverse_linearize_mclasses(elements)
+end
+
+# Colorers
+
+abstract class AbstractColorer[E: Object]
 
-               #print "core: {core.join(", ")}"
-               #print "border: {border.join(", ")}"
-               #print "crown: {crown.join(", ")}"
+       private var core: Set[E] = new HashSet[E]
+       private var crown: Set[E] = new HashSet[E]
+       private var border: Set[E] = new HashSet[E]
 
-               # sort by reverse linearization order
-               reverse_sorter.sort(core)
-               reverse_sorter.sort(border)
-               reverse_sorter.sort(crown)
+       private var coloration_result: Map[E, Int] = new HashMap[E, Int]
 
-               #print "conflicts"
-               #for k, v in conflicts_graph do
-               #       if k isa MType then
-               #               print "{k}: {v.join(", ")}"
-               #       end
-               #end
+       init do end
 
-               # colorize graph
+       fun colorize(elements: Set[E]): Map[E, Int] do
+               tag_elements(elements)
+               build_conflicts_graph(elements)
                colorize_elements(core)
                colorize_elements(border)
                colorize_elements(crown)
-
                return coloration_result
        end
 
        # Colorize a collection of elements
-       private fun colorize_elements(elements: Collection[E]) do
+       private fun colorize_elements(elements: Set[E]) do
                var min_color = 0
 
-               for element in elements do
+               var lin = reverse_linearize(elements)
+               for element in lin do
                        var color = min_color
-                       while not self.is_color_free(element, color) do
+                       while not self.is_color_free(element, elements, color) do
                                color += 1
                        end
                        coloration_result[element] = color
@@ -79,215 +244,241 @@ abstract class AbstractColoring[E: Object]
        end
 
        # Check if a related element to the element already use the color
-       private fun is_color_free(element: E, color: Int): Bool do
+       private fun is_color_free(element: E, elements: Set[E], color: Int): Bool do
                if conflicts_graph.has_key(element) then
                        for st in conflicts_graph[element] do
                                if coloration_result.has_key(st) and coloration_result[st] == color then return false
                        end
                end
-               for st in self.super_elements(element) do
+               for st in self.super_elements(element, elements) do
                        if coloration_result.has_key(st) and coloration_result[st] == color then return false
                end
                return true
        end
 
-       # Tag element as core, crown or border
-       private fun tag_element(element: E) do
-               # Check if sub elements are all in single inheritance
-               var all_subelements_si = true
-               for subelem in self.sub_elements(element) do
-                       if self.is_element_mi(subelem) then
-                               all_subelements_si = false
-                               break
+       # Tag elements as core, crown or border
+       private fun tag_elements(elements: Set[E]) do
+               for element in elements do
+                       # Check if sub elements are all in single inheritance
+                       var all_subelements_si = true
+                       for subelem in self.sub_elements(element, elements) do
+                               if self.is_element_mi(subelem, elements) then
+                                       all_subelements_si = false
+                                       break
+                               end
                        end
-               end
 
-               # Tag as core, crown or border
-               if self.is_element_mi(element) then
-                       core.add_all(self.super_elements(element))
-                       core.add(element)
-                       if all_subelements_si then
-                               border.add(element)
+                       # Tag as core, crown or border
+                       if self.is_element_mi(element, elements) then
+                               core.add_all(self.super_elements(element, elements))
+                               core.add(element)
+                               if all_subelements_si then
+                                       border.add(element)
+                               end
+                       else if not all_subelements_si then
+                               core.add_all(self.super_elements(element, elements))
+                               core.add(element)
+                       else
+                               crown.add(element)
                        end
-               else if not all_subelements_si then
-                       core.add_all(self.super_elements(element))
-                       core.add(element)
-               else
-                       crown.add(element)
                end
        end
 
        # Conflicts graph of elements hierarchy (two types are in conflict if they have common subelements)
-       private fun conflicts_graph: Map[E, Set[E]] do
-               if self.conflicts_graph_cache == null then
-                       self.conflicts_graph_cache = new HashMap[E, HashSet[E]]
-                       for t in self.core do
-                               for i in self.linear_extension(t) do
-                                       if t == i then continue
-
-                                       var lin_i = self.linear_extension(i)
-
-                                       for j in self.linear_extension(t) do
-                                               if i == j or j == t then continue
-                                               var lin_j = self.linear_extension(j)
-
-                                               var d_ij = lin_i - lin_j
-                                               var d_ji = lin_j - lin_i
-
-                                               for ed1 in d_ij do
-                                                       if not conflicts_graph_cache.has_key(ed1) then conflicts_graph_cache[ed1] = new HashSet[E]
-                                                       # add ed1 x ed2 to conflicts graph
-                                                       for ed2 in d_ji do conflicts_graph_cache[ed1].add(ed2)
-                                               end
-                                               for ed1 in d_ij do
-                                                       if not conflicts_graph_cache.has_key(ed1) then conflicts_graph_cache[ed1] = new HashSet[E]
-                                                       # add ed1 x ed2 to conflicts graph
-                                                       for ed2 in d_ji do conflicts_graph_cache[ed1].add(ed2)
-                                               end
+       private fun build_conflicts_graph(elements: Set[E]) do
+               self.conflicts_graph = new HashMap[E, HashSet[E]]
+               var core = reverse_linearize(self.core)
+               for t in core do
+                       for i in self.linear_extension(t, elements) do
+                               if t == i then continue
+
+                               var lin_i = self.linear_extension(i, elements)
+
+                               for j in self.linear_extension(t, elements) do
+                                       if i == j or j == t then continue
+                                       var lin_j = self.linear_extension(j, elements)
+
+                                       var d_ij = lin_i - lin_j
+                                       var d_ji = lin_j - lin_i
+
+                                       for ed1 in d_ij do
+                                               if not conflicts_graph.has_key(ed1) then conflicts_graph[ed1] = new HashSet[E]
+                                               # add ed1 x ed2 to conflicts graph
+                                               for ed2 in d_ji do conflicts_graph[ed1].add(ed2)
+                                       end
+                                       for ed1 in d_ij do
+                                               if not conflicts_graph.has_key(ed1) then conflicts_graph[ed1] = new HashSet[E]
+                                               # add ed1 x ed2 to conflicts graph
+                                               for ed2 in d_ji do conflicts_graph[ed1].add(ed2)
                                        end
                                end
                        end
                end
-               return conflicts_graph_cache.as(not null)
        end
 
+       private var conflicts_graph: nullable HashMap[E, Set[E]]
+
        # cache for linear_extensions
-       private var linear_extensions_cache: Map[E, OrderedSet[E]] = new HashMap[E, OrderedSet[E]]
+       private var linear_extensions_cache: Map[E, Array[E]] = new HashMap[E, Array[E]]
 
        # Return a linear_extension of super_elements of the element
-       private fun linear_extension(element: E): OrderedSet[E] do
+       private fun linear_extension(element: E, elements: Set[E]): Array[E] do
                if not self.linear_extensions_cache.has_key(element) then
-                       var lin = new OrderedSet[E]
-                       lin.add(element)
-                       lin.add_all(self.super_elements(element))
-                       self.sorter.sort(lin)
-                       self.linear_extensions_cache[element] = lin
+                       var supers = new HashSet[E]
+                       supers.add(element)
+                       supers.add_all(self.super_elements(element, elements))
+                       self.linear_extensions_cache[element] = self.linearize(supers)
                end
                return self.linear_extensions_cache[element]
        end
 
-       # Return all super elements (directs and indirects) of an element
-       private fun super_elements(element: E): Collection[E] is abstract
+       private fun super_elements(element: E, elements: Set[E]): Set[E] is abstract
+       private fun sub_elements(element: E, elements: Set[E]): Set[E] is abstract
+       private fun is_element_mi(element: E, elements: Set[E]): Bool is abstract
+       private fun linearize(elements: Set[E]): Array[E] is abstract
+       private fun reverse_linearize(elements: Set[E]): Array[E] is abstract
+end
 
-       # Return all sub elements (directs and indirects) of an element
-       private fun sub_elements(element: E): Collection[E] is abstract
+# MType coloring
+private class MTypeColorer
+       super AbstractColorer[MType]
 
-       # Is the element in multiple inheritance ?
-       private fun is_element_mi(element: E): Bool is abstract
-end
+       var mmodule: MModule
+
+       init(mmodule: MModule) do self.mmodule = mmodule
 
-# MClassType coloring
-class TypeColoring
-       super AbstractColoring[MType]
+       redef fun super_elements(element, elements) do return self.mmodule.super_mtypes(element, elements)
+       redef fun is_element_mi(element, elements) do return self.super_elements(element, elements).length > 1
+       redef fun sub_elements(element, elements) do do return self.mmodule.sub_mtypes(element, elements)
+       redef fun linearize(elements) do return self.mmodule.linearize_mtypes(elements)
+       redef fun reverse_linearize(elements) do return self.mmodule.reverse_linearize_mtypes(elements)
+end
 
-       type T: MType
+# MClass coloring
+private class MClassColorer
+       super AbstractColorer[MClass]
 
        private var mmodule: MModule
-       private var mtypes: Set[T]
 
-       # caches
-       private var super_elements_cache: Map[T, Set[T]] = new HashMap[T, Set[T]]
-       private var sub_elements_cache: Map[T, Set[T]] = new HashMap[T, Set[T]]
+       init(mmodule: MModule) do self.mmodule = mmodule
 
-       init(mainmodule: MModule, mtypes: Set[T]) do
-               super(new TypeSorter(mainmodule), new ReverseTypeSorter(mainmodule))
-               self.mmodule = mainmodule
-               self.mtypes = mtypes
-       end
+       redef fun super_elements(element, elements) do return self.mmodule.super_mclasses(element)
+       fun parent_elements(element: MClass): Set[MClass] do return self.mmodule.parent_mclasses(element)
+       redef fun is_element_mi(element, elements) do return self.parent_elements(element).length > 1
+       redef fun sub_elements(element, elements) do do return self.mmodule.sub_mclasses(element)
+       redef fun linearize(elements) do return self.mmodule.linearize_mclasses(elements)
+       redef fun reverse_linearize(elements) do return self.mmodule.reverse_linearize_mclasses(elements)
+end
 
-       # Build type tables
-       private fun build_type_tables(mtypes: Set[T], colors: Map[T, Int]): Map[T, Array[nullable T]] do
-               var tables = new HashMap[T, Array[nullable T]]
+# Perfect hashers
 
-               for mtype in mtypes do
-                       var table = new Array[nullable T]
-                       var supers = new HashSet[T]
-                       supers.add_all(self.super_elements(mtype))
-                       supers.add(mtype)
-                       for sup in supers do
-                               var color = colors[sup]
-                               if table.length <= color then
-                                       for i in [table.length .. color[ do
-                                               table[i] = null
-                                       end
-                               end
-                               table[color] = sup
-                       end
-                       tables[mtype] = table
+# Abstract Perfect Hashing
+private abstract class AbstractHasher[E: Object]
+
+       var operator: PHOperator
+
+       init(operator: PHOperator) do self.operator = operator
+
+       fun compute_masks(elements: Set[E], ids: Map[E, Int]): Map[E, Int] do
+               var masks = new HashMap[E, Int]
+               for element in elements do
+                       var supers = new HashSet[E]
+                       supers.add_all(self.super_elements(element, elements))
+                       supers.add(element)
+                       masks[element] = compute_mask(supers, ids)
                end
-               return tables
+               return masks
        end
 
-       redef fun super_elements(element) do
-               if not self.super_elements_cache.has_key(element) then
-                       var supers = new HashSet[T]
-                       for mtype in self.mtypes do
-                               if element == mtype then continue
-                               if element.is_subtype(self.mmodule, null, mtype) then
-                                       supers.add(mtype)
+       fun compute_mask(supers: Set[E], ids: Map[E, Int]): Int do
+               var mask = 0
+               loop
+                       var used = new List[Int]
+                       for sup in supers do
+                               var res = operator.op(mask, ids[sup])
+                               if used.has(res) then
+                                       break
+                               else
+                                       used.add(res)
                                end
                        end
-                       self.super_elements_cache[element] = supers
+                       if used.length == supers.length then break
+                       mask += 1
                end
-               return self.super_elements_cache[element]
-       end
-
-       # Return all direct super elements of an element
-       redef fun is_element_mi(element) do
-               return self.super_elements(element).length > 1
+               return mask
        end
 
-       # Return all sub elements (directs and indirects) of an element
-       redef fun sub_elements(element) do
-               if not self.sub_elements_cache.has_key(element) then
-                       var subs = new HashSet[T]
-                       for mtype in self.mtypes do
-                               if element == mtype then continue
-                               if mtype.is_subtype(self.mmodule, null, element) then
-                                       subs.add(mtype)
-                               end
+       fun compute_hashes(elements: Set[E], ids: Map[E, Int], masks: Map[E, Int]): Map[E, Map[E, Int]] do
+               var hashes = new HashMap[E, Map[E, Int]]
+               for element in elements do
+                       var supers = new HashSet[E]
+                       supers.add_all(self.super_elements(element, elements))
+                       supers.add(element)
+                       var inhashes = new HashMap[E, Int]
+                       var mask = masks[element]
+                       for sup in supers do
+                               inhashes[sup] = operator.op(mask, ids[sup])
                        end
-                       self.sub_elements_cache[element] = subs
+                       hashes[element] = inhashes
                end
-               return self.sub_elements_cache[element]
+               return hashes
        end
+
+       fun super_elements(element: E, elements: Set[E]): Set[E] is abstract
 end
 
-# A sorter for linearize list of types
-private class TypeSorter
-       super AbstractSorter[MType]
+# Abstract operator used for perfect hashing
+abstract class PHOperator
+       fun op(mask: Int, id:Int): Int is abstract
+end
 
-       private var mmodule: MModule
+# Hashing using modulo (MOD) operator
+# slower but compact
+class PHModOperator
+       super PHOperator
+       init do end
+       redef fun op(mask, id) do return mask % id
+end
 
-       init(mmodule: MModule) do self.mmodule = mmodule
+# Hashing using binary and (AND) operator
+# faster but sparse
+class PHAndOperator
+       super PHOperator
+       init do end
+       redef fun op(mask, id) do return mask.bin_and(id)
+end
 
-       redef fun compare(a, b) do
-               if a == b then
-                       return 0
-               else if a.is_subtype(self.mmodule, null, b) then
-                       return -1
-               end
-               return 1
+# MType Perfect Hashing
+private class MTypeHasher
+       super AbstractHasher[MType]
+
+       var mmodule: MModule
+
+       init(mmodule: MModule, operator: PHOperator) do
+               super(operator)
+               self.mmodule = mmodule
        end
+
+       redef fun super_elements(element, elements) do return self.mmodule.super_mtypes(element, elements)
 end
 
-# A sorter for reverse linearization
-private class ReverseTypeSorter
-       super TypeSorter
+# MClass Perfect Hashing
+private class MClassHasher
+       super AbstractHasher[MClass]
 
-       redef fun compare(a, b) do
-               if a == b then
-                       return 0
-               else if a.is_subtype(self.mmodule, null, b) then
-                       return 1
-               end
-               return -1
+       private var mmodule: MModule
+
+       init(mmodule: MModule, operator: PHOperator) do
+               super(operator)
+               self.mmodule = mmodule
        end
+
+       redef fun super_elements(element, elements) do return self.mmodule.super_mclasses(element)
 end
 
 # MClass coloring
 class ClassColoring
-       super AbstractColoring[MClass]
+       super AbstractColorer[MClass]
 
        type T: MClass
 
@@ -298,113 +489,14 @@ class ClassColoring
        private var parent_elements_cache: Map[T, Set[T]] = new HashMap[T, Set[T]]
        private var sub_elements_cache: Map[T, Set[T]] = new HashMap[T, Set[T]]
 
-       init(mainmodule: MModule) do
-               super(new ClassSorter(mainmodule), new ReverseClassSorter(mainmodule))
-               self.mmodule = mainmodule
-       end
-
-       # Build type tables
-       private fun build_type_tables(mclasses: Array[T], colors: Map[T, Int]): Map[T, Array[nullable T]] do
-               var tables = new HashMap[T, Array[nullable T]]
-
-               for mclasse in mclasses do
-                       var table = new Array[nullable T]
-                       var supers = new HashSet[T]
-                       supers.add_all(self.super_elements(mclasse))
-                       supers.add(mclasse)
-                       for sup in supers do
-                               var color = colors[sup]
-                               if table.length <= color then
-                                       for i in [table.length .. color[ do
-                                               table[i] = null
-                                       end
-                               end
-                               table[color] = sup
-                       end
-                       tables[mclasse] = table
-               end
-               return tables
-       end
-
-       redef fun super_elements(element) do
-               if not self.super_elements_cache.has_key(element) then
-                       var supers = new HashSet[T]
-                       if self.mmodule.flatten_mclass_hierarchy.has(element) then
-                               for sup in self.mmodule.flatten_mclass_hierarchy[element].greaters do
-                                       if element == sup then continue
-                                       supers.add(sup)
-                               end
-                       end
-                       self.super_elements_cache[element] = supers
-               end
-               return self.super_elements_cache[element]
-       end
-
-       private fun parent_elements(element: T): Set[T] do
-               if not self.parent_elements_cache.has_key(element) then
-                       var parents = new HashSet[T]
-                       if self.mmodule.flatten_mclass_hierarchy.has(element) then
-                               for parent in self.mmodule.flatten_mclass_hierarchy[element].direct_greaters do
-                                       if element == parent then continue
-                                       parents.add(parent)
-                               end
-                       end
-                       self.parent_elements_cache[element] = parents
-               end
-               return self.parent_elements_cache[element]
-       end
-
-       # Return all sub elements (directs and indirects) of an element
-       redef fun sub_elements(element) do
-               if not self.sub_elements_cache.has_key(element) then
-                       var subs = new HashSet[T]
-                       if self.mmodule.flatten_mclass_hierarchy.has(element) then
-                               for sub in self.mmodule.flatten_mclass_hierarchy[element].smallers do
-                                       subs.add(sub)
-                               end
-                       end
-                       self.sub_elements_cache[element] = subs
-               end
-               return self.sub_elements_cache[element]
-       end
-
-       # Return all direct super elements of an element
-       redef fun is_element_mi(element) do
-               if not self.mmodule.flatten_mclass_hierarchy.has(element) then return false
-               return self.mmodule.flatten_mclass_hierarchy[element].direct_greaters.length > 1
-       end
-end
-
-# A sorter for linearize list of classes
-private class ClassSorter
-       super AbstractSorter[MClass]
-
-       var mmodule: MModule
-
-       redef fun compare(a, b) do
-               if a == b then
-                       return 0
-               else if self.mmodule.flatten_mclass_hierarchy.has(a) and self.mmodule.flatten_mclass_hierarchy[a].greaters.has(b) then
-                       return -1
-               end
-               return 1
-       end
-end
-
-# A sorter for reverse linearization
-private class ReverseClassSorter
-       super AbstractSorter[MClass]
-
-       var mmodule: MModule
+       init(mainmodule: MModule) do self.mmodule = mainmodule
 
-       redef fun compare(a, b) do
-               if a == b then
-                       return 0
-               else if self.mmodule.flatten_mclass_hierarchy.has(a) and self.mmodule.flatten_mclass_hierarchy[a].greaters.has(b) then
-                       return 1
-               end
-               return -1
-       end
+       redef fun super_elements(element, elements) do return self.mmodule.super_mclasses(element)
+       fun parent_elements(element: MClass): Set[MClass] do return self.mmodule.parent_mclasses(element)
+       redef fun is_element_mi(element, elements) do return self.parent_elements(element).length > 1
+       redef fun sub_elements(element, elements) do do return self.mmodule.sub_mclasses(element)
+       redef fun linearize(elements) do return self.mmodule.linearize_mclasses(elements)
+       redef fun reverse_linearize(elements) do return self.mmodule.reverse_linearize_mclasses(elements)
 end
 
 # MProperty coloring
@@ -413,63 +505,21 @@ class PropertyColoring
        type MPROP: MProperty
        type MPROPDEF: MPropDef
 
+       private var mmodule: MModule
        private var class_coloring: ClassColoring
        private var coloration_result: Map[MPROP, Int] = new HashMap[MPROP, Int]
 
-       init(class_coloring: ClassColoring) do
+       init(mmodule: MModule, class_coloring: ClassColoring) do
+               self.mmodule = mmodule
                self.class_coloring = class_coloring
        end
 
-       private fun colorize: Map[MPROP, Int] do
+       fun colorize: Map[MPROP, Int] do
                colorize_core_properties
                colorize_crown_properties
                return self.coloration_result
        end
 
-       private fun build_property_tables: Map[MClass, Array[nullable MPROPDEF]] do
-               var tables = new HashMap[MClass, Array[nullable MPROPDEF]]
-
-               for mclass in self.class_coloring.coloration_result.keys do
-                       var table = new Array[nullable MPROPDEF]
-                       # first, fill table from parents by reverse linearization order
-                       var parents = new OrderedSet[MClass]
-                       parents.add_all(self.class_coloring.super_elements(mclass))
-                       self.class_coloring.reverse_sorter.sort(parents)
-                       for parent in parents do
-                               for mproperty in self.properties(parent) do
-                                       var color = self.coloration_result[mproperty]
-                                       if table.length <= color then
-                                               for i in [table.length .. color[ do
-                                                       table[i] = null
-                                               end
-                                       end
-                                       for mpropdef in mproperty.mpropdefs do
-                                               if mpropdef.mclassdef.mclass == parent then
-                                                       table[color] = mpropdef
-                                               end
-                                       end
-                               end
-                       end
-
-                       # then override with local properties
-                       for mproperty in self.properties(mclass) do
-                               var color = self.coloration_result[mproperty]
-                               if table.length <= color then
-                                       for i in [table.length .. color[ do
-                                               table[i] = null
-                                       end
-                               end
-                               for mpropdef in mproperty.mpropdefs do
-                                       if mpropdef.mclassdef.mclass == mclass then
-                                               table[color] = mpropdef
-                                       end
-                               end
-                       end
-                       tables[mclass] = table
-               end
-               return tables
-       end
-
        # Colorize properties of the core hierarchy
        private fun colorize_core_properties do
                var mclasses = self.class_coloring.core
@@ -526,31 +576,15 @@ class PropertyColoring
                return max_color
        end
 
-       # properties cache
-       private var properties_cache: Map[MClass, Set[MPROP]] = new HashMap[MClass, Set[MPROP]]
-
        # All 'mproperties' associated to all 'mclassdefs' of the class
        private fun properties(mclass: MClass): Set[MPROP] do
-               if not self.properties_cache.has_key(mclass) then
-                       var properties = new HashSet[MPROP]
-                       var parents = self.class_coloring.super_elements(mclass)
-                       for parent in parents do
-                               properties.add_all(self.properties(parent))
-                       end
-
-                       for mclassdef in mclass.mclassdefs do
-                               for mpropdef in mclassdef.mpropdefs do
-                                       var mproperty = mpropdef.mproperty
-                                       if mproperty isa MPROP then
-                                               properties.add(mproperty)
-                                       end
-                               end
-                       end
-                       self.properties_cache[mclass] = properties
-               end
-               return properties_cache[mclass]
-       end
-end
+               var properties = new HashSet[MPROP]
+               for mprop in self.mmodule.properties(mclass) do
+                       if mprop isa MPROP then properties.add(mprop)
+               end
+               return properties
+       end
+end
 
 # MMethod coloring
 class MethodColoring
@@ -558,7 +592,7 @@ class MethodColoring
 
        redef type MPROP: MMethod
        redef type MPROPDEF: MMethodDef
-       init(class_coloring: ClassColoring) do end
+       init(mmodule: MModule, class_coloring: ClassColoring) do super
 end
 
 # MAttribute coloring
@@ -567,7 +601,7 @@ class AttributeColoring
 
        redef type MPROP: MAttribute
        redef type MPROPDEF: MAttributeDef
-       init(class_coloring: ClassColoring) do end
+       init(mmodule: MModule, class_coloring: ClassColoring) do super
 end
 
 # MVirtualTypeProp coloring
@@ -576,7 +610,135 @@ class VTColoring
 
        redef type MPROP: MVirtualTypeProp
        redef type MPROPDEF: MVirtualTypeDef
-       init(class_coloring: ClassColoring) do end
+       init(mmodule: MModule, class_coloring: ClassColoring) do super
+end
+
+class NaiveVTColoring
+       super VTColoring
+
+       init(mmodule: MModule, class_coloring: ClassColoring) do super
+
+       redef fun colorize: Map[MPROP, Int] do
+               var mclasses = new HashSet[MClass]
+               mclasses.add_all(self.class_coloring.core)
+               mclasses.add_all(self.class_coloring.crown)
+               var min_color = 0
+
+               for mclass in mclasses do
+                       min_color = max_color(min_color, mclasses)
+                       colorize_elements(self.properties(mclass), min_color)
+               end
+               return self.coloration_result
+       end
+end
+
+abstract class VTPerfectHashing
+       super VTColoring
+
+       private var masks: Map[MClass, Int] = new HashMap[MClass, Int]
+
+       init(mmodule: MModule, class_coloring: ClassColoring) do super
+
+       redef fun colorize: Map[MPROP, Int] do
+               var mclasses = new HashSet[MClass]
+               mclasses.add_all(self.class_coloring.core)
+               mclasses.add_all(self.class_coloring.crown)
+               for mclass in mclasses do
+                       var vts = self.properties(mclass)
+                       for vt in vts do
+                               if coloration_result.has_key(vt) then continue
+                               coloration_result[vt] = coloration_result.length + 1
+                       end
+               end
+               return self.coloration_result
+       end
+
+       fun compute_masks: Map[MClass, Int] do
+               var mclasses = new HashSet[MClass]
+               mclasses.add_all(self.class_coloring.core)
+               mclasses.add_all(self.class_coloring.crown)
+               for mclass in mclasses do
+                       self.masks[mclass] = compute_mask(self.properties(mclass))
+               end
+               return self.masks
+       end
+
+       private fun compute_mask(vts: Set[MPROP]): Int do
+               var mask = 0
+               loop
+                       var used = new List[Int]
+                       for vt in vts do
+                               var res = op(mask, self.coloration_result[vt])
+                               if used.has(res) then
+                                       break
+                               else
+                                       used.add(res)
+                               end
+                       end
+                       if used.length == vts.length then break
+                       mask += 1
+               end
+               return mask
+       end
+
+       fun build_property_tables: Map[MClass, Array[nullable MPROPDEF]] do
+               var tables = new HashMap[MClass, Array[nullable MPROPDEF]]
+
+               for mclass in self.class_coloring.coloration_result.keys do
+                       var table = new Array[nullable MPROPDEF]
+                       # first, fill table from parents by reverse linearization order
+                       var parents = self.class_coloring.mmodule.super_mclasses(mclass)
+                       var lin = self.class_coloring.reverse_linearize(parents)
+                       for parent in lin do
+                               for mproperty in self.properties(parent) do
+                                       var color = phash(self.coloration_result[mproperty], masks[mclass])
+                                       if table.length <= color then
+                                               for i in [table.length .. color[ do
+                                                       table[i] = null
+                                               end
+                                       end
+                                       for mpropdef in mproperty.mpropdefs do
+                                               if mpropdef.mclassdef.mclass == parent then
+                                                       table[color] = mpropdef
+                                               end
+                                       end
+                               end
+                       end
+
+                       # then override with local properties
+                       for mproperty in self.properties(mclass) do
+                               var color = phash(self.coloration_result[mproperty], masks[mclass])
+                               if table.length <= color then
+                                       for i in [table.length .. color[ do
+                                               table[i] = null
+                                       end
+                               end
+                               for mpropdef in mproperty.mpropdefs do
+                                       if mpropdef.mclassdef.mclass == mclass then
+                                               table[color] = mpropdef
+                                       end
+                               end
+                       end
+                       tables[mclass] = table
+               end
+               return tables
+       end
+
+       private fun op(mask: Int, id:Int): Int is abstract
+       private fun phash(id: Int, mask: Int): Int do return op(mask, id)
+
+end
+
+class VTModPerfectHashing
+       super VTPerfectHashing
+       init(mmodule: MModule, class_coloring: ClassColoring) do super
+       redef fun op(mask, id) do return mask % id
+end
+
+class VTAndPerfectHashing
+       super VTPerfectHashing
+       init(mmodule: MModule, class_coloring: ClassColoring) do super
+       redef fun op(mask, id) do return mask.bin_and(id)
 end
 
 # MParameterType coloring
@@ -588,7 +750,7 @@ class FTColoring
                self.class_coloring = class_coloring
        end
 
-       private fun colorize: Map[MParameterType, Int] do
+       fun colorize: Map[MParameterType, Int] do
                colorize_core_properties
                colorize_crown_properties
                return self.coloration_result
@@ -666,14 +828,15 @@ class FTColoring
                return fts_cache[mclass]
        end
 
-       private fun build_ft_tables: Map[MClass, Array[nullable MParameterType]] do
+       fun build_ft_tables: Map[MClass, Array[nullable MParameterType]] do
                var tables = new HashMap[MClass, Array[nullable MParameterType]]
 
                for mclass in self.class_coloring.coloration_result.keys do
                        var table = new Array[nullable MParameterType]
 
                        # first, fill table from parents
-                       for parent in self.class_coloring.super_elements(mclass) do
+                       var parents = self.class_coloring.mmodule.super_mclasses(mclass)
+                       for parent in parents do
                                for ft in self.fts(parent) do
                                        var color = self.coloration_result[ft]
                                        if table.length <= color then
@@ -701,94 +864,176 @@ class FTColoring
        end
 end
 
-# Live Entries coloring
-class LiveEntryColoring
+class NaiveFTColoring
+       super FTColoring
 
-       private var coloration_result: Map[MType, Int] = new HashMap[MType, Int]
-       private var conflicts_graph_cache: nullable HashMap[MType, Set[MType]]
-       var livetypes_tables_sizes: nullable Map[MClass, Array[Int]]
+       init(class_coloring: ClassColoring) do end
 
-       init do end
+       redef fun colorize: Map[MParameterType, Int] do
+               var mclasses = new HashSet[MClass]
+               mclasses.add_all(self.class_coloring.core)
+               mclasses.add_all(self.class_coloring.crown)
+               var min_color = 0
 
-       fun colorize(elements: Collection[MType]): Map[MType, Int] do
-               # compute conflicts
-               build_conflicts_graph(elements)
+               for mclass in mclasses do
+                       min_color = max_color(min_color, mclasses)
+                       colorize_elements(self.fts(mclass), min_color)
+               end
+               return self.coloration_result
+       end
+end
 
-               # colorize graph
-               colorize_elements(elements)
+abstract class FTPerfectHashing
+       super FTColoring
 
-               return coloration_result
+       private var masks: Map[MClass, Int] = new HashMap[MClass, Int]
+
+       init(class_coloring: ClassColoring) do end
+
+       redef fun colorize: Map[MParameterType, Int] do
+               var mclasses = new HashSet[MClass]
+               mclasses.add_all(self.class_coloring.core)
+               mclasses.add_all(self.class_coloring.crown)
+               for mclass in mclasses do
+                       for ft in self.fts(mclass) do
+                               if coloration_result.has_key(ft) then continue
+                               coloration_result[ft] = coloration_result.length + 1
+                       end
+               end
+               return self.coloration_result
        end
 
-       # Build type tables
-       private fun build_livetype_tables(mtypes: Set[MType]): Map[MClass, Array[nullable Object]] do
-               var livetypes_tables = new HashMap[MClass, Array[nullable Object]]
-               self.livetypes_tables_sizes = new HashMap[MClass, Array[Int]]
+       fun compute_masks: Map[MClass, Int] do
+               var mclasses = new HashSet[MClass]
+               mclasses.add_all(self.class_coloring.core)
+               mclasses.add_all(self.class_coloring.crown)
+               for mclass in mclasses do
+                       var fts = new HashSet[MParameterType]
+                       var parents = self.class_coloring.mmodule.super_mclasses(mclass)
+                       for parent in parents do
+                               fts.add_all(self.fts(parent))
+                       end
+                       fts.add_all(self.fts(mclass))
+                       self.masks[mclass] = compute_mask(fts)
+               end
+               return self.masks
+       end
 
-               for mtype in mtypes do
-                       if mtype isa MGenericType then
-                               var table: Array[nullable Object]
-                               var sizes: Array[Int]
-                               if livetypes_tables.has_key(mtype.mclass) then
-                                       table = livetypes_tables[mtype.mclass]
-                               else
-                                       table = new Array[nullable Object]
-                                       livetypes_tables[mtype.mclass] = table
-                               end
-                               if livetypes_tables_sizes.has_key(mtype.mclass) then
-                                       sizes = livetypes_tables_sizes[mtype.mclass]
+       private fun compute_mask(fts: Set[MParameterType]): Int do
+               var mask = 0
+               loop
+                       var used = new List[Int]
+                       for ft in fts do
+                               var res = op(mask, self.coloration_result[ft])
+                               if used.has(res) then
+                                       break
                                else
-                                       sizes = new Array[Int]
-                                       livetypes_tables_sizes[mtype.mclass] = sizes
+                                       used.add(res)
                                end
-                               build_livetype_table(mtype, 0, table, sizes)
                        end
+                       if used.length == fts.length then break
+                       mask += 1
                end
-
-               return livetypes_tables
+               return mask
        end
 
-       # Build live gentype table recursively
-       private fun build_livetype_table(mtype: MGenericType, current_rank: Int, table: Array[nullable Object], sizes: Array[Int]) do
-               var ft = mtype.arguments[current_rank]
-               if not self.coloration_result.has_key(ft) then return
-               var color = self.coloration_result[ft]
+       redef fun build_ft_tables do
+               var tables = new HashMap[MClass, Array[nullable MParameterType]]
 
-               if current_rank >= sizes.length then
-                       sizes[current_rank] = color + 1
-               else if color >= sizes[current_rank] then
-                       sizes[current_rank] = color + 1
-               end
+               for mclass in self.class_coloring.coloration_result.keys do
+                       var table = new Array[nullable MParameterType]
+
+                       # first, fill table from parents
+                       var parents = self.class_coloring.mmodule.super_mclasses(mclass)
+                       for parent in parents do
+                               for ft in self.fts(parent) do
+                                       var color = phash(self.coloration_result[ft], masks[mclass])
+                                       if table.length <= color then
+                                               for i in [table.length .. color[ do
+                                                       table[i] = null
+                                               end
+                                       end
+                                       table[color] = ft
+                               end
+                       end
 
-               if color > table.length then
-                       for i in [table.length .. color[ do table[i] = null
+                       # then override with local properties
+                       for ft in self.fts(mclass) do
+                               var color = phash(self.coloration_result[ft], masks[mclass])
+                               if table.length <= color then
+                                       for i in [table.length .. color[ do
+                                               table[i] = null
+                                       end
+                               end
+                               table[color] = ft
+                       end
+                       tables[mclass] = table
                end
+               return tables
+       end
 
-               if current_rank == mtype.arguments.length - 1 then
-                       table[color] = mtype
-               else
-                       var ft_table: Array[nullable Object]
-                       if color < table.length and table[color] != null then
-                               ft_table = table[color].as(Array[nullable Object])
-                       else
-                               ft_table = new Array[nullable Object]
+       private fun op(mask: Int, id:Int): Int is abstract
+       private fun phash(id: Int, mask: Int): Int do return op(mask, id)
+end
+
+class FTModPerfectHashing
+       super FTPerfectHashing
+       init(class_coloring: ClassColoring) do end
+       redef fun op(mask, id) do return mask % id
+end
+
+class FTAndPerfectHashing
+       super FTPerfectHashing
+       init(class_coloring: ClassColoring) do end
+       redef fun op(mask, id) do return mask.bin_and(id)
+end
+
+# live unanchored coloring
+class UnanchoredTypeColoring
+
+       private var coloration_result: Map[MType, Int] = new HashMap[MType, Int]
+       private var conflicts_graph: Map[MType, Set[MType]] = new HashMap[MType, Set[MType]]
+
+       init do end
+
+       fun colorize(elements: Map[MClassType, Set[MType]]): Map[MType, Int] do
+               build_conflicts_graph(elements)
+               colorize_elements(elements)
+               return coloration_result
+       end
+
+       fun build_tables(elements: Map[MClassType, Set[MType]]): Map[MClassType, Array[nullable MType]] do
+               var tables = new HashMap[MClassType, Array[nullable MType]]
+
+               for mclasstype, mtypes in elements do
+                       var table = new Array[nullable MType]
+                       for mtype in mtypes do
+                               var color = self.coloration_result[mtype]
+                               if table.length <= color then
+                                       for i in [table.length .. color[ do
+                                               table[i] = null
+                                       end
+                               end
+                               table[color] = mtype
                        end
-                       table[color] = ft_table
-                       build_livetype_table(mtype, current_rank + 1, ft_table, sizes)
+                       tables[mclasstype] = table
                end
+               return tables
        end
 
        # Colorize a collection of elements
-       fun colorize_elements(elements: Collection[MType]) do
+       fun colorize_elements(elements: Map[MClassType, Set[MType]]) do
                var min_color = 0
-
-               for element in elements do
-                       var color = min_color
-                       while not self.is_color_free(element, color) do
-                               color += 1
+               for mclasstype, mclasstypes in elements do
+                       for element in mclasstypes do
+                               if self.coloration_result.has_key(element) then continue
+                               var color = min_color
+                               while not self.is_color_free(element, color) do
+                                       color += 1
+                               end
+                               coloration_result[element] = color
+                               color = min_color
                        end
-                       coloration_result[element] = color
-                       color = min_color
                end
        end
 
@@ -802,44 +1047,13 @@ class LiveEntryColoring
                return true
        end
 
-       # look for types in the same generic signatures
-       private fun build_conflicts_graph(elements: Collection[MType]) do
-               # regroup types by classes
-               var genclasses = new HashMap[MClass, Set[MType]]
-               for e in elements do
-                       if e isa MGenericType then
-                               if not genclasses.has_key(e.mclass) then
-                                       genclasses[e.mclass] = new HashSet[MType]
-                               end
-                               genclasses[e.mclass].add(e)
-                       end
-               end
-
-               # for each class
-               self.conflicts_graph_cache = new HashMap[MType, Set[MType]]
-               for mclass, mtypes in genclasses do
-                       # for each rank
-                       for rank in [0..mclass.arity[ do
-                               # for each live type
-                               for mtype in mtypes do
-                                       var mclasstype: MClassType
-                                       if mtype isa MNullableType then
-                                               mclasstype = mtype.mtype.as(MClassType)
-                                       else
-                                               mclasstype = mtype.as(MClassType)
-                                       end
-                                       var ft = mclasstype.arguments[rank]
-                                       for otype in mtypes do
-                                               if mtype == otype then continue
-                                               var oclasstype: MClassType
-                                               if otype isa MNullableType then
-                                                       oclasstype = otype.mtype.as(MClassType)
-                                               else
-                                                       oclasstype = otype.as(MClassType)
-                                               end
-                                               var oft = oclasstype.arguments[rank]
-                                               self.add_conflict(ft, oft)
-                                       end
+       # look for unanchored types generated by the same type
+       private fun build_conflicts_graph(elements: Map[MClassType, Set[MType]]) do
+               for mclasstype, mtypes in elements do
+                       for mtype in mtypes do
+                               for otype in mtypes do
+                                       if otype == mtype then continue
+                                       self.add_conflict(mtype, otype)
                                end
                        end
                end
@@ -847,30 +1061,333 @@ class LiveEntryColoring
 
        private fun add_conflict(mtype: MType, otype: MType) do
                if mtype == otype then return
-               if not self.conflicts_graph_cache.has_key(mtype) then  self.conflicts_graph_cache[mtype] = new HashSet[MClassType]
-               self.conflicts_graph_cache[mtype].add(otype)
-               if not self.conflicts_graph_cache.has_key(otype) then  self.conflicts_graph_cache[otype] = new HashSet[MClassType]
-               self.conflicts_graph_cache[otype].add(mtype)
+               if not self.conflicts_graph.has_key(mtype) then  self.conflicts_graph[mtype] = new HashSet[MType]
+               self.conflicts_graph[mtype].add(otype)
+               if not self.conflicts_graph.has_key(otype) then  self.conflicts_graph[otype] = new HashSet[MType]
+               self.conflicts_graph[otype].add(mtype)
        end
-       private fun conflicts_graph: Map[MType, Set[MType]] do return conflicts_graph_cache.as(not null)
 end
 
-# Utils
+class NaiveUnanchoredTypeColoring
+       super UnanchoredTypeColoring
+
+       init do end
+
+       redef fun colorize_elements(elements: Map[MClassType, Set[MType]]) do
+               var color = 0
+               for mclasstype, mclasstypes in elements do
+                       for element in mclasstypes do
+                               coloration_result[element] = color
+                               color += 1
+                       end
+               end
+       end
+end
+
+abstract class UnanchoredTypePerfectHashing
+       super NaiveUnanchoredTypeColoring
+
+       private var masks: Map[MClassType, Int] = new HashMap[MClassType, Int]
+
+       init do end
+
+       redef fun colorize_elements(elements: Map[MClassType, Set[MType]]) do
+               var color = 1
+               for mclasstype, mclasstypes in elements do
+                       for element in mclasstypes do
+                               coloration_result[element] = color
+                               color += 1
+                       end
+               end
+       end
 
-# An ordered set
-private class OrderedSet[E]
-       super Array[E]
+       fun compute_masks(elements: Map[MClassType, Set[MType]]): Map[MClassType, Int] do
+               for mclasstype, mtypes in elements do
+                       self.masks[mclasstype] = compute_mask(mtypes)
+               end
+               return self.masks
+       end
 
-       redef fun add(e) do
-               if not self.has(e) then
-                       super(e)
+       private fun compute_mask(mtypes: Set[MType]): Int do
+               var mask = 0
+               loop
+                       var used = new List[Int]
+                       for mtype in mtypes do
+                               var res = op(mask, self.coloration_result[mtype])
+                               if used.has(res) then
+                                       break
+                               else
+                                       used.add(res)
+                               end
+                       end
+                       if used.length == mtypes.length then break
+                       mask += 1
+               end
+               return mask
+       end
+
+       redef fun build_tables(elements: Map[MClassType, Set[MType]]): Map[MClassType, Array[nullable MType]] do
+               var tables = new HashMap[MClassType, Array[nullable MType]]
+
+               for mclasstype, mtypes in elements do
+                       var table = new Array[nullable MType]
+                       for mtype in mtypes do
+                               var color = phash(self.coloration_result[mtype], masks[mclasstype])
+                               if table.length <= color then
+                                       for i in [table.length .. color[ do
+                                               table[i] = null
+                                       end
+                               end
+                               table[color] = mtype
+                       end
+                       tables[mclasstype] = table
                end
+               return tables
+       end
+
+       private fun op(mask: Int, id:Int): Int is abstract
+       private fun phash(id: Int, mask: Int): Int do return op(mask, id)
+end
+
+class UnanchoredTypeModPerfectHashing
+       super UnanchoredTypePerfectHashing
+       init do end
+       redef fun op(mask, id) do return mask % id
+end
+
+class UnanchoredTypeAndPerfectHashing
+       super UnanchoredTypePerfectHashing
+       init do end
+       redef fun op(mask, id) do return mask.bin_and(id)
+end
+
+
+# Utils
+
+redef class HashSet[E]
+       init from(elements: Collection[E]) do
+               init
+               self.add_all(elements)
+       end
+end
+
+redef class Array[E]
+       init from(elements: Collection[E]) do
+               init
+               self.add_all(elements)
        end
 
-       # Return a new OrderedSet with the elements only contened in 'self' and not in 'o'
-       fun -(o: OrderedSet[E]): OrderedSet[E] do
-               var res = new OrderedSet[E]
+       # Return a new Array with the elements only contened in 'self' and not in 'o'
+       fun -(o: Array[E]): Array[E] do
+               var res = new Array[E]
                for e in self do if not o.has(e) then res.add(e)
                return res
        end
-end
\ No newline at end of file
+end
+
+redef class MModule
+
+       # Return a linearization of a set of mtypes
+       private fun linearize_mtypes(mtypes: Set[MType]): Array[MType] do
+               var lin = new Array[MType].from(mtypes)
+               var sorter = new TypeSorter(self)
+               sorter.sort(lin)
+               return lin
+       end
+
+       # Return a reverse linearization of a set of mtypes
+       private fun reverse_linearize_mtypes(mtypes: Set[MType]): Array[MType] do
+               var lin = new Array[MType].from(mtypes)
+               var sorter = new ReverseTypeSorter(self)
+               sorter.sort(lin)
+               return lin
+       end
+
+       # Return super types of a `mtype` in `self`
+       private fun super_mtypes(mtype: MType, mtypes: Set[MType]): Set[MType] do
+               if not self.super_mtypes_cache.has_key(mtype) then
+                       var supers = new HashSet[MType]
+                       for otype in mtypes do
+                               if otype == mtype then continue
+                               if mtype.is_subtype(self, null, otype) then
+                                       supers.add(otype)
+                               end
+                       end
+                       self.super_mtypes_cache[mtype] = supers
+               end
+               return self.super_mtypes_cache[mtype]
+       end
+
+       private var super_mtypes_cache: Map[MType, Set[MType]] = new HashMap[MType, Set[MType]]
+
+       # Return all sub mtypes (directs and indirects) of a `mtype` in `self`
+       private fun sub_mtypes(mtype: MType, mtypes: Set[MType]): Set[MType] do
+               if not self.sub_mtypes_cache.has_key(mtype) then
+                       var subs = new HashSet[MType]
+                       for otype in mtypes do
+                               if otype == mtype then continue
+                               if otype.is_subtype(self, null, mtype) then
+                                       subs.add(otype)
+                               end
+                       end
+                       self.sub_mtypes_cache[mtype] = subs
+               end
+               return self.sub_mtypes_cache[mtype]
+       end
+
+       private var sub_mtypes_cache: Map[MType, Set[MType]] = new HashMap[MType, Set[MType]]
+
+       # Return a linearization of a set of mclasses
+       private fun linearize_mclasses(mclasses: Set[MClass]): Array[MClass] do
+               var lin = new Array[MClass].from(mclasses)
+               var sorter = new ClassSorter(self)
+               sorter.sort(lin)
+               return lin
+       end
+
+       # Return a reverse linearization of a set of mtypes
+       private fun reverse_linearize_mclasses(mclasses: Set[MClass]): Array[MClass] do
+               var lin = new Array[MClass].from(mclasses)
+               var sorter = new ReverseClassSorter(self)
+               sorter.sort(lin)
+               return lin
+       end
+
+       # Return all super mclasses (directs and indirects) of a `mclass` in `self`
+       private fun super_mclasses(mclass: MClass): Set[MClass] do
+               if not self.super_mclasses_cache.has_key(mclass) then
+                       var supers = new HashSet[MClass]
+                       if self.flatten_mclass_hierarchy.has(mclass) then
+                               for sup in self.flatten_mclass_hierarchy[mclass].greaters do
+                                       if sup == mclass then continue
+                                       supers.add(sup)
+                               end
+                       end
+                       self.super_mclasses_cache[mclass] = supers
+               end
+               return self.super_mclasses_cache[mclass]
+       end
+
+       private var super_mclasses_cache: Map[MClass, Set[MClass]] = new HashMap[MClass, Set[MClass]]
+
+       # Return all parents of a `mclass` in `self`
+       private fun parent_mclasses(mclass: MClass): Set[MClass] do
+               if not self.parent_mclasses_cache.has_key(mclass) then
+                       var parents = new HashSet[MClass]
+                       if self.flatten_mclass_hierarchy.has(mclass) then
+                               for sup in self.flatten_mclass_hierarchy[mclass].direct_greaters do
+                                       if sup == mclass then continue
+                                       parents.add(sup)
+                               end
+                       end
+                       self.parent_mclasses_cache[mclass] = parents
+               end
+               return self.parent_mclasses_cache[mclass]
+       end
+
+       private var parent_mclasses_cache: Map[MClass, Set[MClass]] = new HashMap[MClass, Set[MClass]]
+
+       # Return all sub mclasses (directs and indirects) of a `mclass` in `self`
+       private fun sub_mclasses(mclass: MClass): Set[MClass] do
+               if not self.sub_mclasses_cache.has_key(mclass) then
+                       var subs = new HashSet[MClass]
+                       if self.flatten_mclass_hierarchy.has(mclass) then
+                               for sub in self.flatten_mclass_hierarchy[mclass].smallers do
+                                       if sub == mclass then continue
+                                       subs.add(sub)
+                               end
+                       end
+                       self.sub_mclasses_cache[mclass] = subs
+               end
+               return self.sub_mclasses_cache[mclass]
+       end
+
+       private var sub_mclasses_cache: Map[MClass, Set[MClass]] = new HashMap[MClass, Set[MClass]]
+
+       # All 'mproperties' associated to all 'mclassdefs' of `mclass`
+       private fun properties(mclass: MClass): Set[MProperty] do
+               if not self.properties_cache.has_key(mclass) then
+                       var properties = new HashSet[MProperty]
+                       var parents = self.super_mclasses(mclass)
+                       for parent in parents do
+                               properties.add_all(self.properties(parent))
+                       end
+
+                       for mclassdef in mclass.mclassdefs do
+                               for mpropdef in mclassdef.mpropdefs do
+                                       properties.add(mpropdef.mproperty)
+                               end
+                       end
+                       self.properties_cache[mclass] = properties
+               end
+               return properties_cache[mclass]
+       end
+
+       private var properties_cache: Map[MClass, Set[MProperty]] = new HashMap[MClass, Set[MProperty]]
+end
+
+# A sorter for linearize list of types
+class TypeSorter
+       super AbstractSorter[MType]
+
+       private var mmodule: MModule
+
+       init(mmodule: MModule) do self.mmodule = mmodule
+
+       redef fun compare(a, b) do
+               if a == b then
+                       return 0
+               else if a.is_subtype(self.mmodule, null, b) then
+                       return -1
+               end
+               return 1
+       end
+end
+
+# A sorter for reverse linearization
+class ReverseTypeSorter
+       super TypeSorter
+
+       init(mmodule: MModule) do end
+
+       redef fun compare(a, b) do
+               if a == b then
+                       return 0
+               else if a.is_subtype(self.mmodule, null, b) then
+                       return 1
+               end
+               return -1
+       end
+end
+
+# A sorter for linearize list of classes
+private class ClassSorter
+       super AbstractSorter[MClass]
+
+       var mmodule: MModule
+
+       redef fun compare(a, b) do
+               if a == b then
+                       return 0
+               else if self.mmodule.flatten_mclass_hierarchy.has(a) and self.mmodule.flatten_mclass_hierarchy[a].greaters.has(b) then
+                       return -1
+               end
+               return 1
+       end
+end
+
+# A sorter for reverse linearization
+private class ReverseClassSorter
+       super AbstractSorter[MClass]
+
+       var mmodule: MModule
+
+       redef fun compare(a, b) do
+               if a == b then
+                       return 0
+               else if self.mmodule.flatten_mclass_hierarchy.has(a) and self.mmodule.flatten_mclass_hierarchy[a].greaters.has(b) then
+                       return 1
+               end
+               return -1
+       end
+end