coloring: add `POSetConflictGraph:order`

[nit.git] / src / compiler / coloring.nit

# This file is part of NIT ( http://www.nitlanguage.org ).
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

module coloring

import poset

# Build a conflict graph from a POSet
class POSetConflictGraph[E: Object]

        # Core is composed by:
        #  * elements that have mutiple direct parents
        #  * parents of elements that have multiple direct parents
        # REQUIRE: is_colored
        var core = new HashSet[E]

        # Border is composed by minimal elements of the core:
        #  * that have multiple direct parents
        #  * but whose subelements are all in single inheritance
        # REQUIRE: is_colored
        var border = new HashSet[E]

        # The crown is composed by the elements that are:
        #  * not part of the core nor the border
        #  * are in single inheritance
        # REQUIRE: is_colored
        var crown = new HashSet[E]

        # Conflict graph of the POSet
        # Elements X and Y are in conflict if either:
        #  * X and Y are the same element
        #  * Y is a subelement of X
        #  * X and Y have common sub elements
        # REQUIRE: is_colored
        var conflicts = new HashMap[E, Set[E]]

        var poset: POSet[E]

        # The linearisation order to visit elements in the poset
        var order: Array[E] is noinit

        init do
                extract_core
                extract_border
                extract_crown
                compute_conflicts
                order = poset.linearize(poset)
        end

        # Compute the set of elements forming the core of the poset hierarchy.
        private fun extract_core do
                core.clear
                for e in poset do
                        if poset[e].direct_greaters.length > 1 then
                                core.add_all(poset[e].greaters)
                        end
                end
        end

        # Compute the set of elements composing the border of the core
        # Elements belonging to the `border` are removed from the `core`
        private fun extract_border do
                border.clear
                for e in core do
                        if not is_border(e) then continue
                        border.add(e)
                end
                for e in border do core.remove(e)
        end

        private fun is_border(e: E): Bool do
                for child in poset[e].direct_smallers do
                        if core.has(child) then return false
                end
                return true
        end

        # Compute the set of elements belonging to the crown of the inheritance hierarchy.
        private fun extract_crown do
                crown.clear
                for e in poset do
                        if not core.has(e) and not border.has(e) then crown.add(e)
                end
        end

        # Check for conflict in the core.
        # Start from border and tag every ancestors
        private fun compute_conflicts do
                conflicts.clear
                for e in border do add_conflicts(poset[e].greaters)
        end

        private fun add_conflict(e, o: E) do
                if not conflicts.has_key(e) then conflicts[e] = new HashSet[E]
                if not conflicts.has_key(o) then conflicts[o] = new HashSet[E]
                conflicts[e].add(o)
                conflicts[o].add(e)
        end

        private fun add_conflicts(es: Collection[E]) do
                for e1 in es do
                        for e2 in es do add_conflict(e1, e2)
                end
        end

        # Used for debugging only
        fun pretty_print do
                #print "core: {core.join(" ")} ({core.length})"
                #print "border: {border.join(" ")} ({border.length})"
                #print "crown: {crown.join(" ")} ({crown.length})"
                print "conflicts:"
                for e, c in conflicts do print "  {e}: {c.join(" ")}"
        end
end

# Colorize elements from a POSet
# Two elements from a POSet cannot have the same color if they share common subelements
#
# Example:
#
# ~~~raw
#       A
#     / | \
#    /  |  \
#   B   C   D
#   |  /|   |
#   | / |   |
#   |/  |   |
#   E   F   G
#   |
#   H
# ~~~
#
# Conflicts:
#
# * A: {B, C, D, E, F, G, H}
# * B: {A, C, E, H}
# * C: {A, E, H, F}
# * D: {A, G}
# * E: {A, B, C, H}
# * F: {A, C}
# * G: {A, D}
# * H: {A, B, C, E}
#
# Possible colors:
#
# * A:0, B:1, C: 2, D: 1, E: 3, F:3, G:2, H:4
#
# see: Ducournau, R. (2011).
# Coloring, a versatile technique for implementing object-oriented languages.
# Software: Practice and Experience, 41(6), 627–659.
class POSetColorer[E: Object]

        # Is the poset already colored?
        var is_colored = false

        # Resulting ids
        # REQUIRE: is_colored
        fun ids: Map[E, Int] do
                assert is_colored
                return ids_cache
        end
        private var ids_cache = new HashMap[E, Int]

        # Resulting colors
        # REQUIRE: is_colored
        fun colors: Map[E, Int] do
                assert is_colored
                return colors_cache
        end
        private var colors_cache = new HashMap[E, Int]

        # REQUIRE: is_colored
        fun poset: POSet[E] do
                assert is_colored
                return poset_cache
        end
        private var poset_cache: POSet[E] is noinit

        # REQUIRE: is_colored
        fun conflicts: Map[E, Set[E]] do
                assert is_colored
                return conflicts_cache
        end
        private var conflicts_cache: Map[E, Set[E]] is noinit

        private var graph: POSetConflictGraph[E] is noinit

        # Start coloring on given POSet
        fun colorize(poset: POSet[E]) do
                poset_cache = poset
                graph = new POSetConflictGraph[E](poset)
                allocate_ids
                compute_colors
                conflicts_cache = graph.conflicts
                is_colored = true
        end

        private fun allocate_ids do
                ids_cache.clear
                var elements = new HashSet[E].from(poset_cache.to_a)
                for e in poset_cache.linearize(elements) do
                        ids_cache[e] = ids_cache.length
                end
        end

        # Colorize core, border and crown in that order
        private fun compute_colors do
                colors_cache.clear
                colorize_core
                colorize_set(graph.border)
                colorize_set(graph.crown)
        end

        # Core elements cannot have the same color than:
        #  * one of their parents
        #  * one of their conflicting elements
        private fun colorize_core do
                for e in poset_cache.linearize(graph.core) do
                        var color = min_color(e)
                        var conflicts = graph.conflicts[e]
                        while not is_color_free(color, conflicts) do
                                color += 1
                        end
                        colors_cache[e] = color
                end
        end

        # Other elements inherit color fron their direct parents
        private fun colorize_set(set: Set[E]) do
                for e in poset_cache.linearize(set) do colors_cache[e] = min_color(e)
        end

        # Get the next minimal color from direct parents
        private fun min_color(e: E): Int do
                var max_color = -1
                for p in poset_cache[e].direct_greaters do
                        if not colors_cache.has_key(p) then continue
                        var color = colors_cache[p]
                        if color > max_color then max_color = color
                end
                return max_color + 1
        end

        private fun is_color_free(color: Int, set: Collection[E]): Bool do
                for e in set do
                        if colors_cache.has_key(e) and colors_cache[e] == color then return false
                end
                return true
        end

        # Used for debugging only
        fun pretty_print do
                print "ids:"
                for e, id in ids do print "  {e}: {id}"
                print "colors:"
                for e, c in colors do print "  {e}: {c}"
        end
end

# Colorize a collection of buckets
# Two elements cannot have the same color if they both appear in the same bucket
# No coloring order is garantied
#
# Example:
#       buckets[A] = {x1, x2}
#   buckets[B] = {x1, x3, x4}
#       buckets[C] = {x2, x3}
# Conflicts:
#       x1: {x2, x3, x4}
#   x2: {x1, x3}
#   x3: {x1, x2, x4}
#   x4: {x1, x3}
# Possible colors:
#       x1: 0, x2: 1, x3: 2, x4: 1
class BucketsColorer[H: Object, E: Object]
        private var colors = new HashMap[E, Int]
        private var conflicts = new HashMap[E, Set[E]]

        # Start bucket coloring
        fun colorize(buckets: Map[H, Set[E]]): Map[E, Int] do
                compute_conflicts(buckets)
                var min_color = 0
                for holder, hbuckets in buckets do
                        for bucket in hbuckets do
                                if colors.has_key(bucket) then continue
                                var color = min_color
                                while not is_color_free(bucket, color) do
                                        color += 1
                                end
                                colors[bucket] = color
                                color = min_color
                        end
                end
                return colors
        end

        private fun is_color_free(bucket: E, color: Int): Bool do
                if conflicts.has_key(bucket) then
                        for other in conflicts[bucket] do
                                if colors.has_key(other) and colors[other] == color then return false
                        end
                end
                return true
        end

        private fun compute_conflicts(buckets: Map[H, Set[E]]) do
                conflicts.clear
                for holder, hbuckets in buckets do
                        for bucket in hbuckets do
                                if not conflicts.has_key(bucket) then conflicts[bucket] = new HashSet[E]
                                for obucket in hbuckets do
                                        if obucket == bucket then continue
                                        if not conflicts.has_key(obucket) then conflicts[obucket] = new HashSet[E]
                                        conflicts[bucket].add(obucket)
                                        conflicts[obucket].add(bucket)
                                end
                        end
                end
        end
end

# Colorize a collection of buckets using a poset and a conflict graph
# Two elements cannot have the same color if they both appear in the same bucket
# The use of a POSet hierarchy optimize the coloring
# Buckets elements are colored using linearization order starting
class POSetBucketsColorer[H: Object, E: Object]
        private var colors = new HashMap[E, Int]
        private var poset: POSet[H]
        private var conflicts: Map[H, Set[H]]

        # Colorize buckets using the POSet and conflict graph
        fun colorize(buckets: Map[H, Set[E]]): Map[E, Int] do
                colors.clear
                for h in poset.linearize(buckets.keys) do
                        var color = min_color(poset[h].direct_greaters, buckets)
                        for bucket in buckets[h] do
                                if colors.has_key(bucket) then continue
                                while not is_color_free(color, h, buckets) do color += 1
                                colors[bucket] = color
                                color += 1
                        end
                end
                return colors
        end

        # Get the next available color considering used colors by other buckets
        private fun min_color(others: Collection[H], buckets: Map[H, Set[E]]): Int do
                var min = -1
                for holder in others do
                        var color = max_color(holder, buckets)
                        if color > min then min = color
                end
                return min + 1
        end

        # Return the max color used by a class
        private fun max_color(holder: H, buckets: Map[H, Set[E]]): Int do
                var max = -1
                for bucket in buckets[holder] do
                        if not colors.has_key(bucket) then continue
                        var color = colors[bucket]
                        if color > max then max = color
                end
                return max
        end

        # Check if the color is free for this holder
        private fun is_color_free(color: Int, holder: H, buckets: Map[H, Set[E]]): Bool do
                if not conflicts.has_key(holder) then return true
                for conflict in conflicts[holder] do
                        for bucket in buckets[conflict] do
                                if not colors.has_key(bucket) then continue
                                if colors[bucket] == color then return false
                        end
                end
                return true
        end
end