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authorAlex Auvolat <alex@adnab.me>2018-07-20 15:15:05 +0200
committerAlex Auvolat <alex@adnab.me>2018-07-20 15:15:05 +0200
commita624a8504c722a2c561ce147f64c2a1a0bb6f4b0 (patch)
treeec179769d2cbc3a299ad064c3d46d7e5d17004b8
parent8e77ababa95035e65fddbc8e331d62ceb7ab4507 (diff)
downloadshard-a624a8504c722a2c561ce147f64c2a1a0bb6f4b0.tar.gz
shard-a624a8504c722a2c561ce147f64c2a1a0bb6f4b0.zip
Merkle search tree
-rw-r--r--lib/data/merklesearchtree.ex181
-rw-r--r--test/mst_test.exs35
2 files changed, 216 insertions, 0 deletions
diff --git a/lib/data/merklesearchtree.ex b/lib/data/merklesearchtree.ex
new file mode 100644
index 0000000..d23e8a7
--- /dev/null
+++ b/lib/data/merklesearchtree.ex
@@ -0,0 +1,181 @@
+defmodule SData.MerkleSearchTree do
+ @moduledoc"""
+ A Merkle search tree.
+
+ A node of the tree is
+ {
+ level,
+ hash_of_node | nil,
+ [
+ { k_low_bound, v, hash_of_node | nil },
+ { k_low_bound, v, hash_of_node | nil },
+ ...
+ }
+ }
+ """
+
+ defstruct [:root, :store]
+
+ def new() do
+ %SData.MerkleSearchTree{
+ root: nil,
+ store: %{}
+ }
+ end
+
+ def insert(state, key, value) do
+ level = calc_level(key)
+ {hash, store} = insert_at(state.store, state.root, key, level, value)
+ %{ state | root: hash, store: store }
+ end
+
+ def remove(_state, _key) do
+ # TODO
+ end
+
+ defp insert_at(store, root, key, level, value) do
+ {new_page, store} = if root == nil do
+ { { level, nil, [ { key, value, nil } ] }, store }
+ else
+ { plevel, low, lst } = store[root]
+ [ { k0, _, _} | _ ] = lst
+ cond do
+ plevel < level ->
+ {low, high, store} = split(store, root, key)
+ { { level, low, [ { key, value, high } ] }, store }
+ plevel == level ->
+ store = Map.delete(store, root)
+ if key < k0 do
+ {low2a, low2b, store} = split(store, low, key)
+ { { level, low2a, [ { key, value, low2b } | lst] }, store }
+ else
+ {new_lst, store} = aux_insert_after_first(store, lst, key, value)
+ { { plevel, low, new_lst }, store }
+ end
+ plevel > level ->
+ store = Map.delete(store, root)
+ if key < k0 do
+ {new_low, store} = insert_at(store, low, key, level, value)
+ { { plevel, new_low, lst }, store }
+ else
+ {new_lst, store} = aux_insert_sub_after_first(store, lst, key, level, value)
+ { { plevel, low, new_lst }, store }
+ end
+ end
+ end
+ hash = SData.term_hash new_page
+ store = Map.put(store, hash, new_page)
+ { hash, store }
+ end
+
+ defp split(store, hash, key) do
+ if hash == nil do
+ {nil, nil, store}
+ else
+ { level, low, lst } = store[hash]
+ store = Map.delete(store, hash)
+ [ { k0, _, _} | _ ] = lst
+ cond do
+ key < k0 ->
+ {lowlow, lowhi, store} = split(store, low, key)
+ newp2 = { level, lowhi, lst }
+ newp2h = SData.term_hash newp2
+ store = Map.put(store, newp2h, newp2)
+ {lowlow, newp2h, store}
+ key > k0 ->
+ {lst1, p2, store} = split_aux(store, lst, key, level)
+ newp1 = {level, low, lst1}
+ newp1h = SData.term_hash newp1
+ store = Map.put(store, newp1h, newp1)
+ {newp1h, p2, store}
+ end
+ end
+ end
+
+ defp split_aux(store, lst, key, level) do
+ case lst do
+ [ {k1, _, _} | _ ] when k1 == key ->
+ raise "Bad logic"
+ [ {k1, v1, r1} ] ->
+ {r1l, r1h, store} = split(store, r1, key)
+ { [{k1, v1, r1l}], r1h, store }
+ [ {k1, v1, r1}, {k2, v2, r2} | rst ] when key < k2->
+ {r1l, r1h, store} = split(store, r1, key)
+ p2 = { level, r1h, [ {k2, v2, r2} | rst ] }
+ p2h = SData.term_hash p2
+ store = store
+ |> Map.put(p2h, p2)
+ { [{k1, v1, r1l}], p2h, store }
+ [ fst | rst ] ->
+ {rst2, hi, store} = split_aux(store, rst, key, level)
+ { [ fst | rst2 ], hi, store }
+ end
+ end
+
+ defp aux_insert_after_first(store, lst, key, value) do
+ case lst do
+ [ {k1, _, r1} | rst ] when k1 == key ->
+ { [ {k1, value, r1} | rst ], store }
+ [ {k1, v1, r1} ] ->
+ {r1a, r1b, new_store} = split(store, r1, key)
+ { [ {k1, v1, r1a}, {key, value, r1b} ], new_store }
+ [ {k1, v1, r1}, {k2, v2, r2} | rst ] when key < k2->
+ {r1a, r1b, new_store} = split(store, r1, key)
+ { [ {k1, v1, r1a}, {key, value, r1b}, {k2, v2, r2} | rst ], new_store }
+ [ fst | rst ] ->
+ {rst2, new_store} = aux_insert_after_first(store, rst, key, value)
+ { [ fst | rst2 ], new_store }
+ end
+ end
+
+ defp aux_insert_sub_after_first(store, lst, key, level, value) do
+ case lst do
+ [ {k1, _, _} | _ ] when k1 == key ->
+ raise "Bad logic"
+ [ {k1, v1, r1} ] ->
+ {r1new, store_new} = insert_at(store, r1, key, level, value)
+ { [{k1, v1, r1new}], store_new }
+ [ {k1, v1, r1}, {k2, v2, r2} | rst ] when key < k2->
+ {r1new, store_new} = insert_at(store, r1, key, level, value)
+ { [{k1, v1, r1new}, {k2, v2, r2} | rst], store_new }
+ [ fst | rst ] ->
+ {rst2, new_store} = aux_insert_sub_after_first(store, rst, key, level, value)
+ { [ fst | rst2 ], new_store }
+ end
+ end
+
+ def dump(state) do
+ dump(state.store, state.root, "")
+ end
+
+ defp dump(store, root, lvl) do
+ case root do
+ nil ->
+ IO.puts(lvl <> "nil")
+ _ ->
+ { level, low, lst} = store[root]
+ IO.puts(lvl <> "#{root|>Base.encode16} (#{level})")
+ dump(store, low, lvl <> " ")
+ for {k, v, r} <- lst do
+ IO.puts(lvl<>"- #{inspect k} => #{inspect v}")
+ dump(store, r, lvl <> " ")
+ end
+ end
+ end
+
+ defp calc_level(key) do
+ key
+ |> SData.term_hash
+ |> Base.encode16
+ |> String.to_charlist
+ |> count_leading_zeroes
+ end
+
+ defp count_leading_zeroes('0' ++ rest) do
+ 1 + count_leading_zeroes(rest)
+ end
+ defp count_leading_zeroes(_) do
+ 0
+ end
+
+end
diff --git a/test/mst_test.exs b/test/mst_test.exs
new file mode 100644
index 0000000..68886c7
--- /dev/null
+++ b/test/mst_test.exs
@@ -0,0 +1,35 @@
+defmodule ShardTest.MST do
+ use ExUnit.Case
+ alias SData.MerkleSearchTree, as: MST
+ doctest Shard.Application
+
+ test "merkle search tree 1" do
+ y = Enum.reduce(0..1000, MST.new(),
+ fn i, acc -> MST.insert(acc, i, i) end)
+
+
+ z = Enum.reduce(Enum.shuffle(0..1000), MST.new(),
+ fn i, acc -> MST.insert(acc, i, i) end)
+
+ IO.puts "y.root: #{y.root|>Base.encode16}"
+ IO.puts "z.root: #{z.root|>Base.encode16}"
+ assert y.root == z.root
+ end
+
+ test "merkle search tree 2" do
+ items = for i <- 0..1000 do
+ h = SData.term_hash i
+ {h, SData.term_hash h}
+ end
+
+ y = Enum.reduce(items, MST.new(),
+ fn {k, v}, acc -> MST.insert(acc, k, v) end)
+
+ z = Enum.reduce(Enum.shuffle(items), MST.new(),
+ fn {k, v}, acc -> MST.insert(acc, k, v) end)
+
+ IO.puts "y.root: #{y.root|>Base.encode16}"
+ IO.puts "z.root: #{z.root|>Base.encode16}"
+ assert y.root == z.root
+ end
+end