* identified by the algorithm in 'iter_over_machine'.
*)
-type ownership = unit
+(* General binary tree type. Data 'a is stored in the leaves and 'b
+ * is stored in the nodes.
+ *)
+type ('a,'b) binary_tree =
+ | Leaf of 'a
+ | Node of ('a,'b) binary_tree * 'b * ('a,'b) binary_tree
+
+(* This prints out the binary tree in graphviz dot format. *)
+let print_binary_tree leaf_printer node_printer tree =
+ (* Assign a unique, fixed label to each node. *)
+ let label =
+ let i = ref 0 in
+ let hash = Hashtbl.create 13 in
+ fun node ->
+ try Hashtbl.find hash node
+ with Not_found ->
+ let i = incr i; !i in
+ let label = "n" ^ string_of_int i in
+ Hashtbl.add hash node label;
+ label
+ in
+ (* Recursively generate the graphviz file. *)
+ let rec print = function
+ | (Leaf a as leaf) ->
+ eprintf " %s [shape=box, label=\"%s\"];\n"
+ (label leaf) (leaf_printer a)
+ | (Node (left,b,right) as node) ->
+ eprintf " %s [label=\"%s\"];\n"
+ (label node) (node_printer b);
+ eprintf " %s -> %s [tailport=sw];\n" (label node) (label left);
+ eprintf " %s -> %s [tailport=se];\n" (label node) (label right);
+ print left;
+ print right;
+ in
+ eprintf "/* Use 'dot -Tpng foo.dot > foo.png' to convert to a png file. */\n";
+ eprintf "digraph G {\n";
+ print tree;
+ eprintf "}\n";
+
+(* A segment describes the owner of a range of disk addresses. *)
+type segment =
+ int63 * int63 * (* disk offset, size of segment *)
+ [ `Filesystem of filesystem
+ | `Partitions of partitions
+ | `PhysicalVolume of pv ] * (* owner *)
+ int63 (* owner offset *)
+
+type interval = int63 * int63 (* start point, end point (bytes) *)
+
+(* The special segment tree structure that we construct in create_ownership. *)
+type segment_tree =
+ (interval * segment list, interval * segment list) binary_tree
+
+type ownership =
+ (device * (* block_device (disk) *)
+ segment_tree) list (* segment tree for this disk *)
(* List of owned segments before we build the segment tree. *)
type ownership_list =
(device * (* block_device (disk) *)
- int63 * int63 * (* disk offset, size of segment *)
- [ `Filesystem of filesystem
- | `Partitions of partitions
- | `PhysicalVolume of pv ] * (* owner *)
- int63 (* owner offset *)
- ) list
+ segment) list
(* Ownership tables. *)
let create_ownership machine =
let ownership =
List.fold_left (
fun ownership (disk, disk_offset) ->
- let elem = disk, disk_offset, extent, owner, offset in
+ let elem = disk, (disk_offset, extent, owner, offset) in
elem :: ownership
) ownership devs in
loop ownership (offset +^ extent)
| `Partitions { parts_plugin_id = parts_plugin_id } ->
parts_plugin_id
in
- let ownership = iter_over_machine machine in
+
+ (* Build the list of segments. *)
+ let ownership : ownership_list = iter_over_machine machine in
+
+ (* Group the segments together by disk. *)
+ let ownership =
+ let ownership = List.sort ownership in
+ group_by ownership in
(* If debugging, print the segments that we found. *)
if !debug then (
- let ownership = List.rev ownership in
- eprintf "ownership segment list of %s:\n" machine.m_name;
List.iter (
- fun (disk, disk_offset, size, owner, owner_offset) ->
- let blocksize = disk#blocksize in
- let disk_offset_in_blocks, disk_offset_in_block =
- disk_offset /^ blocksize, disk_offset %^ blocksize in
- let size_in_blocks, size_in_block =
- size /^ blocksize, size %^ blocksize in
-
- eprintf "%s %s[%s:%s] %s[%s:%s] %s@%s\n"
- disk#name
- (Int63.to_string disk_offset)
- (Int63.to_string disk_offset_in_blocks)
- (Int63.to_string disk_offset_in_block)
- (Int63.to_string size)
- (Int63.to_string size_in_blocks)
- (Int63.to_string size_in_block)
- (string_of_owner owner)
- (Int63.to_string owner_offset)
+ fun (disk, segments) ->
+ eprintf "ownership segment list of %s %s:\n" machine.m_name disk#name;
+ List.iter (
+ fun (disk_offset, size, owner, owner_offset) ->
+ let blocksize = disk#blocksize in
+ let disk_offset_in_blocks, disk_offset_in_block =
+ disk_offset /^ blocksize, disk_offset %^ blocksize in
+ let size_in_blocks, size_in_block =
+ size /^ blocksize, size %^ blocksize in
+
+ eprintf " %s[%s:%s] %s[%s:%s] %s@%s\n"
+ (Int63.to_string disk_offset)
+ (Int63.to_string disk_offset_in_blocks)
+ (Int63.to_string disk_offset_in_block)
+ (Int63.to_string size)
+ (Int63.to_string size_in_blocks)
+ (Int63.to_string size_in_block)
+ (string_of_owner owner)
+ (Int63.to_string owner_offset)
+ ) segments
) ownership
- )
+ );
+
+ (* Build the segment tree from the ownership list (of segments).
+ * For an explanation of this process see:
+ * http://en.wikipedia.org/wiki/Segment_tree
+ *)
+ let ownership =
+ List.map (
+ fun (disk, segments) ->
+ (* Construct the list of distinct endpoints. *)
+ let eps =
+ List.map
+ (fun (start, size, _, _) -> [start; start +^ size])
+ segments in
+ let eps = sort_uniq (List.concat eps) in
+
+ (* Construct the elementary intervals. *)
+ let elints =
+ let elints, lastpoint =
+ List.fold_left (
+ fun (elints, prevpoint) point ->
+ ((point, point) :: (prevpoint, point) :: elints), point
+ ) ([], Int63.min_int) eps in
+ let elints = (lastpoint, Int63.max_int) :: elints in
+ List.rev elints in
+
+ if !debug then (
+ eprintf "elementary intervals for %s (%d in total):\n"
+ disk#name (List.length elints);
+ List.iter (
+ fun (startpoint, endpoint) ->
+ eprintf " %s %s\n"
+ (Int63.to_string startpoint) (Int63.to_string endpoint)
+ ) elints
+ );
+
+ (* Construct the binary tree of elementary intervals. *)
+ let tree =
+ (* Each elementary interval becomes a leaf. *)
+ let elints = List.map (fun elint -> Leaf elint) elints in
+ (* Recursively build this into a binary tree. *)
+ let rec make_layer = function
+ | [] -> []
+ | ([_] as x) -> x
+ (* Turn pairs of leaves at the bottom level into nodes. *)
+ | (Leaf _ as a) :: (Leaf _ as b) :: xs ->
+ let xs = make_layer xs in
+ Node (a, (), b) :: xs
+ (* Turn pairs of nodes at higher levels into nodes. *)
+ | (Node _ as left) :: ((Node _|Leaf _) as right) :: xs ->
+ let xs = make_layer xs in
+ Node (left, (), right) :: xs
+ | Leaf _ :: _ -> assert false (* never happens??? (I think) *)
+ in
+ let rec loop = function
+ | [] -> assert false
+ | [x] -> x
+ | xs -> loop (make_layer xs)
+ in
+ loop elints in
+
+ if !debug then (
+ let leaf_printer (startpoint, endpoint) =
+ sprintf "%s-%s"
+ (Int63.to_string startpoint) (Int63.to_string endpoint)
+ in
+ let node_printer () = "" in
+ print_binary_tree leaf_printer node_printer tree
+ );
+
+ (* Insert the segments into the tree one by one. *)
+ let tree =
+ (* For each node/leaf in the tree, add its interval and an
+ * empty list which will be used to store the segments.
+ *)
+ let rec interval_tree = function
+ | Leaf elint -> Leaf (elint, [])
+ | Node (left, (), right) ->
+ let left = interval_tree left in
+ let right = interval_tree right in
+ let (leftstart, _) = interval_of_node left in
+ let (_, rightend) = interval_of_node right in
+ let interval = leftstart, rightend in
+ Node (left, (interval, []), right)
+ and interval_of_node = function
+ | Leaf (elint, _) -> elint
+ | Node (_, (interval, _), _) -> interval
+ in
+
+ let tree = interval_tree tree in
+ (* This should always be true: *)
+ assert (interval_of_node tree = (Int63.min_int, Int63.max_int));
+
+ (* "Contained in" operator.
+ * 'a <-< b' iff 'a' is a subinterval of 'b'.
+ * |<---- a ---->|
+ * |<----------- b ----------->|
+ *)
+ let (<-<) (a1, a2) (b1, b2) = b1 <= a1 && a2 <= b2 in
+
+ (* "Intersects" operator.
+ * 'a /\ b' iff intervals 'a' and 'b' overlap, eg:
+ * |<---- a ---->|
+ * |<----------- b ----------->|
+ *)
+ let ( /\ ) (a1, a2) (b1, b2) = a2 > b1 || b2 > a1 in
+
+ let rec insert_segment tree segment =
+ let start, size, owner, owner_offset = segment in
+ let seginterval = start, start +^ size in
+ eprintf "inserting (%s,%s) ...\n"
+ (Int63.to_string (fst seginterval))
+ (Int63.to_string (snd seginterval));
+ match tree with
+ (* Test if we should insert into this leaf or node: *)
+ | Leaf (interval, segs) when interval <-< seginterval ->
+ Leaf (interval, segment :: segs)
+ | Node (left, (interval, segs), right)
+ when interval <-< seginterval ->
+ Node (left, (interval, segment :: segs), right)
+
+ | (Leaf _) as leaf -> leaf
+
+ (* Else, should we insert into left or right subtrees? *)
+ | Node (left, i, right) ->
+ let left =
+ if seginterval /\ interval_of_node left then
+ insert_segment left segment
+ else
+ left in
+ let right =
+ if seginterval /\ interval_of_node right then
+ insert_segment right segment
+ else
+ right in
+ Node (left, i, right)
+ in
+ let tree = List.fold_left insert_segment tree segments in
+ tree in
+
+ if !debug then (
+ let printer ((sp, ep), segments) =
+ sprintf "[%s-%s] " (Int63.to_string sp) (Int63.to_string ep) ^
+ String.concat ";"
+ (List.map (fun (_, _, owner,_) -> string_of_owner owner)
+ segments)
+ in
+ print_binary_tree printer printer tree
+ );
+ (disk, tree)
+ ) ownership in
+
+ (* Return the ownership structure. *)
+ ownership
git.annexia.org / virt-df.git / commitdiff