diff --git a/lib/lua/vm/executor.ex b/lib/lua/vm/executor.ex
index d0c1227..79d102e 100644
--- a/lib/lua/vm/executor.ex
+++ b/lib/lua/vm/executor.ex
@@ -735,39 +735,80 @@ defmodule Lua.VM.Executor do
 
   # Bitwise operations
   defp do_execute([{:bitwise_and, dest, a, b} | rest], regs, upvalues, proto, state) do
-    result = Bitwise.band(trunc(elem(regs, a)), trunc(elem(regs, b)))
+    val_a = elem(regs, a)
+    val_b = elem(regs, b)
+
+    {result, new_state} =
+      try_binary_metamethod("__band", val_a, val_b, state, fn ->
+        Bitwise.band(to_integer!(val_a), to_integer!(val_b))
+      end)
+
     regs = put_elem(regs, dest, result)
-    do_execute(rest, regs, upvalues, proto, state)
+    do_execute(rest, regs, upvalues, proto, new_state)
   end
 
   defp do_execute([{:bitwise_or, dest, a, b} | rest], regs, upvalues, proto, state) do
-    result = Bitwise.bor(trunc(elem(regs, a)), trunc(elem(regs, b)))
+    val_a = elem(regs, a)
+    val_b = elem(regs, b)
+
+    {result, new_state} =
+      try_binary_metamethod("__bor", val_a, val_b, state, fn ->
+        Bitwise.bor(to_integer!(val_a), to_integer!(val_b))
+      end)
+
     regs = put_elem(regs, dest, result)
-    do_execute(rest, regs, upvalues, proto, state)
+    do_execute(rest, regs, upvalues, proto, new_state)
   end
 
   defp do_execute([{:bitwise_xor, dest, a, b} | rest], regs, upvalues, proto, state) do
-    result = Bitwise.bxor(trunc(elem(regs, a)), trunc(elem(regs, b)))
+    val_a = elem(regs, a)
+    val_b = elem(regs, b)
+
+    {result, new_state} =
+      try_binary_metamethod("__bxor", val_a, val_b, state, fn ->
+        Bitwise.bxor(to_integer!(val_a), to_integer!(val_b))
+      end)
+
     regs = put_elem(regs, dest, result)
-    do_execute(rest, regs, upvalues, proto, state)
+    do_execute(rest, regs, upvalues, proto, new_state)
   end
 
   defp do_execute([{:shift_left, dest, a, b} | rest], regs, upvalues, proto, state) do
-    result = Bitwise.bsl(trunc(elem(regs, a)), trunc(elem(regs, b)))
+    val_a = elem(regs, a)
+    val_b = elem(regs, b)
+
+    {result, new_state} =
+      try_binary_metamethod("__shl", val_a, val_b, state, fn ->
+        lua_shift_left(to_integer!(val_a), to_integer!(val_b))
+      end)
+
     regs = put_elem(regs, dest, result)
-    do_execute(rest, regs, upvalues, proto, state)
+    do_execute(rest, regs, upvalues, proto, new_state)
   end
 
   defp do_execute([{:shift_right, dest, a, b} | rest], regs, upvalues, proto, state) do
-    result = Bitwise.bsr(trunc(elem(regs, a)), trunc(elem(regs, b)))
+    val_a = elem(regs, a)
+    val_b = elem(regs, b)
+
+    {result, new_state} =
+      try_binary_metamethod("__shr", val_a, val_b, state, fn ->
+        lua_shift_right(to_integer!(val_a), to_integer!(val_b))
+      end)
+
     regs = put_elem(regs, dest, result)
-    do_execute(rest, regs, upvalues, proto, state)
+    do_execute(rest, regs, upvalues, proto, new_state)
   end
 
   defp do_execute([{:bitwise_not, dest, source} | rest], regs, upvalues, proto, state) do
-    result = Bitwise.bnot(trunc(elem(regs, source)))
+    val = elem(regs, source)
+
+    {result, new_state} =
+      try_unary_metamethod("__bnot", val, state, fn ->
+        Bitwise.bnot(to_integer!(val))
+      end)
+
     regs = put_elem(regs, dest, result)
-    do_execute(rest, regs, upvalues, proto, state)
+    do_execute(rest, regs, upvalues, proto, new_state)
   end
 
   # Comparison operations
@@ -1585,6 +1626,49 @@ defmodule Lua.VM.Executor do
 
   defp to_number(v), do: {:error, v}
 
+  # Convert value to integer for bitwise operations (with string coercion)
+  defp to_integer!(v) when is_integer(v), do: v
+  defp to_integer!(v) when is_float(v), do: trunc(v)
+
+  defp to_integer!(v) when is_binary(v) do
+    case Value.parse_number(v) do
+      nil ->
+        raise TypeError,
+          value: "attempt to perform bitwise operation on a string value",
+          error_kind: :bitwise_on_non_integer,
+          value_type: :string
+
+      n ->
+        trunc(n)
+    end
+  end
+
+  defp to_integer!(v) do
+    raise TypeError,
+      value: "attempt to perform bitwise operation on a #{Value.type_name(v)} value",
+      error_kind: :bitwise_on_non_integer,
+      value_type: value_type(v)
+  end
+
+  # Lua 5.3 shift semantics: negative shift reverses direction, shift >= 64 yields 0
+  defp lua_shift_left(_val, shift) when shift >= 64, do: 0
+  defp lua_shift_left(_val, shift) when shift <= -64, do: 0
+  defp lua_shift_left(val, shift) when shift < 0, do: lua_shift_right(val, -shift)
+
+  defp lua_shift_left(val, shift) do
+    Bitwise.band(Bitwise.bsl(val, shift), 0xFFFFFFFFFFFFFFFF)
+  end
+
+  defp lua_shift_right(_val, shift) when shift >= 64, do: 0
+  defp lua_shift_right(_val, shift) when shift <= -64, do: 0
+  defp lua_shift_right(val, shift) when shift < 0, do: lua_shift_left(val, -shift)
+
+  defp lua_shift_right(val, shift) do
+    # Unsigned right shift - mask to 64-bit first
+    unsigned_val = Bitwise.band(val, 0xFFFFFFFFFFFFFFFF)
+    Bitwise.bsr(unsigned_val, shift)
+  end
+
   # Helper to determine Lua type from Elixir value
   defp value_type(nil), do: nil
   defp value_type(v) when is_boolean(v), do: :boolean
diff --git a/lib/lua/vm/stdlib.ex b/lib/lua/vm/stdlib.ex
index 2aaae74..1597383 100644
--- a/lib/lua/vm/stdlib.ex
+++ b/lib/lua/vm/stdlib.ex
@@ -40,10 +40,14 @@ defmodule Lua.VM.Stdlib do
     |> State.register_function("select", &lua_select/2)
     |> State.register_function("load", &lua_load/2)
     |> State.register_function("require", &lua_require/2)
+    |> State.register_function("collectgarbage", &lua_collectgarbage/2)
+    |> State.register_function("dofile", &lua_dofile/2)
+    |> State.set_global("_VERSION", "Lua 5.3")
     |> install_package_table()
     |> Lua.VM.Stdlib.String.install()
     |> Lua.VM.Stdlib.Math.install()
     |> Lua.VM.Stdlib.Table.install()
+    |> install_unpack_alias()
     |> install_global_g()
   end
 
@@ -626,4 +630,43 @@ defmodule Lua.VM.Stdlib do
         {Value.to_string(value), state}
     end
   end
+
+  # collectgarbage stub — no-op accepting all standard modes
+  defp lua_collectgarbage(args, state) do
+    mode = List.first(args) || "collect"
+
+    case mode do
+      "count" ->
+        # Return plausible memory usage in KB and remainder bytes
+        {[0.0, 0], state}
+
+      "isrunning" ->
+        {[true], state}
+
+      _ ->
+        # "collect", "stop", "restart", "step", "setpause", "setstepmul", "generational", "incremental"
+        {[0], state}
+    end
+  end
+
+  # dofile stub — not supported in embedded mode
+  defp lua_dofile(_args, _state) do
+    raise RuntimeError, value: "dofile not supported in embedded mode"
+  end
+
+  # Install global 'unpack' as alias for table.unpack
+  defp install_unpack_alias(state) do
+    case Map.get(state.globals, "table") do
+      {:tref, id} ->
+        table = Map.fetch!(state.tables, id)
+
+        case Map.get(table.data, "unpack") do
+          nil -> state
+          unpack_fn -> State.set_global(state, "unpack", unpack_fn)
+        end
+
+      _ ->
+        state
+    end
+  end
 end
diff --git a/lib/lua/vm/stdlib/math.ex b/lib/lua/vm/stdlib/math.ex
index 856c4fc..91a962a 100644
--- a/lib/lua/vm/stdlib/math.ex
+++ b/lib/lua/vm/stdlib/math.ex
@@ -150,7 +150,7 @@ defmodule Lua.VM.Stdlib.Math do
 
   # math.ceil(x)
   defp math_ceil([x], state) when is_number(x) do
-    {[Float.ceil(x / 1)], state}
+    {[trunc(Float.ceil(x / 1))], state}
   end
 
   defp math_ceil([x | _], _state) do
@@ -201,7 +201,7 @@ defmodule Lua.VM.Stdlib.Math do
 
   # math.floor(x)
   defp math_floor([x], state) when is_number(x) do
-    {[Float.floor(x / 1)], state}
+    {[trunc(Float.floor(x / 1))], state}
   end
 
   defp math_floor([x | _], _state) do
diff --git a/test/lua/vm/stdlib/math_test.exs b/test/lua/vm/stdlib/math_test.exs
index 935ce71..2be82bf 100644
--- a/test/lua/vm/stdlib/math_test.exs
+++ b/test/lua/vm/stdlib/math_test.exs
@@ -23,7 +23,7 @@ defmodule Lua.VM.Stdlib.MathTest do
       assert {:ok, proto} = Compiler.compile(ast, source: "test.lua")
       state = Stdlib.install(State.new())
 
-      assert {:ok, [4.0, -3.0, 5.0], _state} = VM.execute(proto, state)
+      assert {:ok, [4, -3, 5], _state} = VM.execute(proto, state)
     end
 
     test "math.floor rounds down" do
@@ -32,7 +32,7 @@ defmodule Lua.VM.Stdlib.MathTest do
       assert {:ok, proto} = Compiler.compile(ast, source: "test.lua")
       state = Stdlib.install(State.new())
 
-      assert {:ok, [3.0, -4.0, 5.0], _state} = VM.execute(proto, state)
+      assert {:ok, [3, -4, 5], _state} = VM.execute(proto, state)
     end
 
     test "math.max returns maximum" do
diff --git a/test/lua_test.exs b/test/lua_test.exs
index 8c22ef8..d120fcb 100644
--- a/test/lua_test.exs
+++ b/test/lua_test.exs
@@ -1766,6 +1766,84 @@ defmodule LuaTest do
     end
   end
 
+  describe "collectgarbage stub" do
+    setup do
+      %{lua: Lua.new(sandboxed: [])}
+    end
+
+    test "collectgarbage returns without error", %{lua: lua} do
+      code = """
+      collectgarbage()
+      collectgarbage("collect")
+      collectgarbage("stop")
+      return true
+      """
+
+      assert {[true], _} = Lua.eval!(lua, code)
+    end
+
+    test "collectgarbage 'count' returns a number", %{lua: lua} do
+      code = """
+      local k = collectgarbage("count")
+      return type(k)
+      """
+
+      assert {["number"], _} = Lua.eval!(lua, code)
+    end
+  end
+
+  describe "global stubs and constants" do
+    setup do
+      %{lua: Lua.new(sandboxed: [])}
+    end
+
+    test "_VERSION is Lua 5.3", %{lua: lua} do
+      assert {["Lua 5.3"], _} = Lua.eval!(lua, "return _VERSION")
+    end
+
+    test "unpack works as global alias", %{lua: lua} do
+      code = "return unpack({10, 20, 30})"
+      assert {[10, 20, 30], _} = Lua.eval!(lua, code)
+    end
+  end
+
+  describe "bitwise operation fixes" do
+    setup do
+      %{lua: Lua.new(sandboxed: [])}
+    end
+
+    test "string coercion for bitwise ops", %{lua: lua} do
+      code = ~S[return "0xff" | 0]
+      assert {[255], _} = Lua.eval!(lua, code)
+    end
+
+    test "shift edge cases", %{lua: lua} do
+      code = "return 1 << 64, 1 >> 64, 1 << -1"
+      assert {[0, 0, 0], _} = Lua.eval!(lua, code)
+    end
+
+    test "negative shift reverses direction", %{lua: lua} do
+      code = "return 8 >> -2"
+      assert {[32], _} = Lua.eval!(lua, code)
+    end
+  end
+
+  describe "math.floor and math.ceil return integers" do
+    setup do
+      %{lua: Lua.new(sandboxed: [])}
+    end
+
+    test "math.floor returns integer", %{lua: lua} do
+      code = "return math.type(math.floor(3.5))"
+      assert {["integer"], _} = Lua.eval!(lua, code)
+    end
+
+    test "math.ceil returns integer", %{lua: lua} do
+      code = "return math.type(math.ceil(3.5))"
+      assert {["integer"], _} = Lua.eval!(lua, code)
+    end
+  end
+
   defp test_file(name) do
     Path.join(["test", "fixtures", name])
   end