hipe_sdi: Use segment trees to represent PARENTS

This speeds up parentsOfChild/2 from O(n) to O(lg n + k).

A new module misc/hipe_segment_trees.erl is introduced.

1 files changed, 150 insertions, 0 deletions

diff --git a/lib/hipe/misc/hipe_segment_trees.erl b/lib/hipe/misc/hipe_segment_trees.erl
new file mode 100644
index 0000000000..cbee328125
--- /dev/null
+++ b/lib/hipe/misc/hipe_segment_trees.erl
@@ -0,0 +1,150 @@
+%%%
+%%% %CopyrightBegin%
+%%%
+%%% Copyright Ericsson AB 2016. All Rights Reserved.
+%%%
+%%% 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.
+%%%
+%%% %CopyrightEnd%
+%%%
+%%% Segment trees.
+%%%
+%%% Keys are the (0-based) indices into the list passed to build/1.
+%%%
+%%% Range bounds are inclusive.
+%%%
+%%% TODO: Change the shape of the tree to a perfect binary tree, and pack it as
+%%% an implicit data structure into tuples (like a binary heap would be) for
+%%% improved efficiency.
+
+-module(hipe_segment_trees).
+
+-export([build/1, intersect/2]).
+
+-record(segment_tree, {
+	  lo            :: integer(),
+	  hi            :: integer(),
+	  root          :: tnode()
+	 }).
+
+%% X =< Mid belongs in Left
+-define(NODE(Left, Right, Mid, Segments), {Left, Right, Mid, Segments}).
+
+-define(POINT_LEAF(Val), Val).
+-define(RANGE_LEAF(Lo, Hi), {Lo, Hi}).
+
+-type segments() :: [non_neg_integer()].
+-type leaf()     :: segments().
+-type tnode()    :: ?NODE(tnode(), tnode(), integer(), segments()) | leaf().
+
+-opaque tree() :: #segment_tree{} | nil.
+-export_type([tree/0]).
+
+%% @doc Builds a segment tree of the given intervals.
+-spec build([{integer(), integer()}]) -> tree().
+build(ListOfIntervals) ->
+    case
+	lists:usort(
+	  lists:append(
+	    [[Lo, Hi] || {Lo, Hi} <- ListOfIntervals, Lo =< Hi]))
+    of
+	[] -> nil;
+	Endpoints ->
+	    Tree0 = empty_tree_from_endpoints(Endpoints),
+	    [Lo|_] = Endpoints,
+	    Hi = lists:last(Endpoints),
+	    Tree1 = insert_intervals(0, ListOfIntervals, Lo, Hi, Tree0),
+	    Tree = squash_empty_subtrees(Tree1),
+	    #segment_tree{lo=Lo, hi=Hi, root=Tree}
+    end.
+
+empty_tree_from_endpoints(Endpoints) ->
+    Leaves = leaves(Endpoints),
+    {T, [], _, _} = balanced_bst(Leaves, length(Leaves)),
+    T.
+
+leaves([Endpoint]) -> [?POINT_LEAF(Endpoint)];
+leaves([A | [B|_] = Tail]) ->
+    %% We could omit the range leaf if it's empty, but we want to pack this data
+    %% structure into an array (tuple) eventually, and then we *really* want
+    %% every other leaf to be a range
+    case A<B-1 of
+	true  -> [?POINT_LEAF(A),?RANGE_LEAF(A+1,B-1) | leaves(Tail)];
+	false -> [?POINT_LEAF(A) | leaves(Tail)]
+    end.
+
+balanced_bst(L, S) when S > 1 ->
+    Sm = S, %% - 1
+    S2 = Sm div 2,
+    S1 = Sm - S2,
+    {Left, L1, LeftLo, LeftHi} = balanced_bst(L, S1),
+    {Right, L2, _, RightHi} = balanced_bst(L1, S2),
+    T = ?NODE(Left, Right, LeftHi, []),
+    {T, L2, LeftLo, RightHi};
+balanced_bst([?RANGE_LEAF(Lo, Hi) | L], 1) ->
+    {[], L, Lo, Hi};
+balanced_bst([?POINT_LEAF(Val) | L], 1) ->
+    {[], L, Val, Val}.
+
+insert_intervals(_Ix, [], _Lo, _Hi, Tree) -> Tree;
+insert_intervals(Ix, [Int|Ints], Lo, Hi, Tree) ->
+    insert_intervals(Ix + 1, Ints, Lo, Hi,
+		     insert_interval(Ix, Int, Lo, Hi, Tree)).
+
+insert_interval(_, {Lo, Hi}, _, _, Node) when Lo > Hi -> Node;
+insert_interval(I, Int={Lo,Hi}, NLo, NHi,
+		?NODE(Left0, Right0, Mid, Segments)) ->
+    if Lo =< NLo, NHi =< Hi ->
+	    ?NODE(Left0, Right0, Mid, [I|Segments]);
+       true ->
+	    Left = case intervals_intersect(Lo, Hi,    NLo, Mid) of
+		       true -> insert_interval(I, Int, NLo, Mid, Left0);
+		       false -> Left0
+		   end,
+	    Right = case intervals_intersect(Lo, Hi,    Mid+1, NHi) of
+			true -> insert_interval(I, Int, Mid+1, NHi, Right0);
+			false -> Right0
+		   end,
+	    ?NODE(Left, Right, Mid, Segments)
+    end;
+insert_interval(I, {_Lo,_Hi}, _NLo, _NHi, Leaf) -> [I|Leaf].
+
+intervals_intersect(ALo, AHi, BLo, BHi) ->
+    (ALo =< AHi) andalso (BLo =< BHi) %% both nonempty
+	andalso (BLo =< AHi) andalso (ALo =< BHi).
+
+%% Purely optional optimisation
+squash_empty_subtrees(?NODE(Left0, Right0, Mid, Segs)) ->
+    build_squash_node(squash_empty_subtrees(Left0),
+		      squash_empty_subtrees(Right0),
+		      Mid, Segs);
+squash_empty_subtrees(Leaf) -> Leaf.
+
+build_squash_node([], [], _, Segs) -> Segs;
+build_squash_node(Left, Right, Mid, Segs) ->
+    ?NODE(Left, Right, Mid, Segs).
+
+%% @doc Returns the indices of the intervals in the tree that contains Point.
+-spec intersect(integer(), tree()) -> [non_neg_integer()].
+intersect(Point, nil) when is_integer(Point) -> [];
+intersect(Point, #segment_tree{lo=Lo, hi=Hi, root=Root})
+  when is_integer(Point) ->
+    case Lo =< Point andalso Point =< Hi of
+	false -> [];
+	true -> intersect_1(Point, Root, [])
+    end.
+
+intersect_1(Point, ?NODE(Left, Right, Mid, Segs), Acc0) ->
+    Child = if Point =< Mid -> Left; true -> Right end,
+    intersect_1(Point, Child, Segs ++ Acc0);
+intersect_1(_, LeafSegs, Acc) -> LeafSegs ++ Acc.