New memory-tag commands

Add new commands under the "memory-tag" prefix to allow users to inspect,
modify and check memory tags in different ways.

The available subcommands are the following:

- memory-tag print-logical-tag <expression>: Prints the logical tag for a
  particular address.

- memory-tag withltag <expression> <tag>: Prints the address tagged with the
  logical tag <tag>.

- memory-tag print-allocation-tag <expression>: Prints the allocation tag for
  a particular address.

- memory-tag setatag <expression> <length> <tags>: Sets one or more allocation
  tags to the specified tags.

- memory-tag check <expression>: Checks if the logical tag in <address>
  matches its allocation tag.

These commands make use of the memory tagging gdbarch methods, and are still
available, but disabled, when memory tagging is not supported by the
architecture.

I've pondered about a way to make these commands invisible when memory tagging
is not available, but given the check is at runtime (and support may come and go
based on a process' configuration), that is a bit too late in the process to
either not include the commands or get rid of them.

Ideas are welcome.

gdb/ChangeLog:

2021-03-24  Luis Machado  <luis.machado@linaro.org>

	* printcmd.c: Include gdbsupport/rsp-low.h.
	(memory_tag_list): New static global.
	(process_print_command_args): Factored out of
	print_command_1.
	(print_command_1): Use process_print_command_args.
	(show_addr_not_tagged, show_memory_tagging_unsupported)
	(memory_tag_command, memory_tag_print_tag_command)
	(memory_tag_print_logical_tag_command)
	(memory_tag_print_allocation_tag_command, parse_with_logical_tag_input)
	(memory_tag_with_logical_tag_command, parse_set_allocation_tag_input)
	(memory_tag_set_allocation_tag_command, memory_tag_check_command): New
	functions.
	(_initialize_printcmd): Add "memory-tag" prefix and subcommands.

gdbsupport/ChangeLog:

2021-03-24  Luis Machado  <luis.machado@linaro.org>

	* rsp-low.cc (fromhex, hex2bin): Move to ...
	* common-utils.cc: ... here.
	(fromhex) Change error message text to not be RSP-specific.
	* rsp-low.h (fromhex, hex2bin): Move to ...
	* common-utils.h: ... here.

gdb/ChangeLog

@@ -1,3 +1,19 @@
+2021-03-24  Luis Machado  <luis.machado@linaro.org>
+
+	* printcmd.c: Include gdbsupport/rsp-low.h.
+	(memory_tag_list): New static global.
+	(process_print_command_args): Factored out of
+	print_command_1.
+	(print_command_1): Use process_print_command_args.
+	(show_addr_not_tagged, show_memory_tagging_unsupported)
+	(memory_tag_command, memory_tag_print_tag_command)
+	(memory_tag_print_logical_tag_command)
+	(memory_tag_print_allocation_tag_command, parse_with_logical_tag_input)
+	(memory_tag_with_logical_tag_command, parse_set_allocation_tag_input)
+	(memory_tag_set_allocation_tag_command, memory_tag_check_command): New
+	functions.
+	(_initialize_printcmd): Add "memory-tag" prefix and subcommands.
+
 2021-03-24  Luis Machado  <luis.machado@linaro.org>
 
 	* aarch64-linux-tdep.c

gdb/printcmd.c

@@ -54,6 +54,11 @@
 #include "gdbsupport/byte-vector.h"
 #include "gdbsupport/gdb_optional.h"
 #include "safe-ctype.h"
+#include "gdbsupport/rsp-low.h"
+
+/* Chain containing all defined memory-tag subcommands.  */
+
+static struct cmd_list_element *memory_tag_list;
 
 /* Last specified output format.  */
 
@@ -1203,21 +1208,19 @@ print_value (value *val, const value_print_options &opts)
   annotate_value_history_end ();
 }
 
-/* Implementation of the "print" and "call" commands.  */
+/* Helper for parsing arguments for print_command_1.  */
 
-static void
+static struct value *
-print_command_1 (const char *args, bool voidprint)
+process_print_command_args (const char *args, value_print_options *print_opts,
+			    bool voidprint)
 {
-  struct value *val;
+  get_user_print_options (print_opts);
-  value_print_options print_opts;
-
-  get_user_print_options (&print_opts);
   /* Override global settings with explicit options, if any.  */
-  auto group = make_value_print_options_def_group (&print_opts);
+  auto group = make_value_print_options_def_group (print_opts);
   gdb::option::process_options
     (&args, gdb::option::PROCESS_OPTIONS_REQUIRE_DELIMITER, group);
 
-  print_command_parse_format (&args, "print", &print_opts);
+  print_command_parse_format (&args, "print", print_opts);
 
   const char *exp = args;
 
@@ -1226,10 +1229,20 @@ print_command_1 (const char *args, bool voidprint)
       /* VOIDPRINT is true to indicate that we do want to print a void
 	 value, so invert it for parse_expression.  */
       expression_up expr = parse_expression (exp, nullptr, !voidprint);
-      val = evaluate_expression (expr.get ());
+      return evaluate_expression (expr.get ());
     }
-  else
+
-    val = access_value_history (0);
+  return access_value_history (0);
+}
+
+/* Implementation of the "print" and "call" commands.  */
+
+static void
+print_command_1 (const char *args, int voidprint)
+{
+  value_print_options print_opts;
+
+  struct value *val = process_print_command_args (args, &print_opts, voidprint);
 
   if (voidprint || (val && value_type (val) &&
 		    value_type (val)->code () != TYPE_CODE_VOID))
@@ -2778,6 +2791,293 @@ eval_command (const char *arg, int from_tty)
   execute_command (expanded.c_str (), from_tty);
 }
 
+/* Convenience function for error checking in memory-tag commands.  */
+
+static void
+show_addr_not_tagged (CORE_ADDR address)
+{
+  error (_("Address %s not in a region mapped with a memory tagging flag."),
+	 paddress (target_gdbarch (), address));
+}
+
+/* Convenience function for error checking in memory-tag commands.  */
+
+static void
+show_memory_tagging_unsupported (void)
+{
+  error (_("Memory tagging not supported or disabled by the current"
+	   " architecture."));
+}
+
+/* Implement the "memory-tag" prefix command.  */
+
+static void
+memory_tag_command (const char *arg, int from_tty)
+{
+  help_list (memory_tag_list, "memory-tag ", all_commands, gdb_stdout);
+}
+
+/* Helper for print-logical-tag and print-allocation-tag.  */
+
+static void
+memory_tag_print_tag_command (const char *args, enum memtag_type tag_type)
+{
+  if (args == nullptr)
+    error_no_arg (_("address or pointer"));
+
+  /* Parse args into a value.  If the value is a pointer or an address,
+     then fetch the logical or allocation tag.  */
+  value_print_options print_opts;
+
+  struct value *val = process_print_command_args (args, &print_opts, true);
+
+  /* If the address is not in a region memory mapped with a memory tagging
+     flag, it is no use trying to access/manipulate its allocation tag.
+
+     It is OK to manipulate the logical tag though.  */
+  if (tag_type == memtag_type::allocation
+      && !gdbarch_tagged_address_p (target_gdbarch (), val))
+    show_addr_not_tagged (value_as_address (val));
+
+  struct value *tag_value
+    = gdbarch_get_memtag (target_gdbarch (), val, tag_type);
+  std::string tag = gdbarch_memtag_to_string (target_gdbarch (), tag_value);
+
+  if (tag.empty ())
+    printf_filtered (_("%s tag unavailable.\n"),
+		     tag_type
+		       == memtag_type::logical? "Logical" : "Allocation");
+
+  struct value *v_tag = process_print_command_args (tag.c_str (),
+						    &print_opts,
+						    true);
+  print_opts.output_format = 'x';
+  print_value (v_tag, print_opts);
+}
+
+/* Implement the "memory-tag print-logical-tag" command.  */
+
+static void
+memory_tag_print_logical_tag_command (const char *args, int from_tty)
+{
+  if (!target_supports_memory_tagging ())
+    show_memory_tagging_unsupported ();
+
+  memory_tag_print_tag_command (args, memtag_type::logical);
+}
+
+/* Implement the "memory-tag print-allocation-tag" command.  */
+
+static void
+memory_tag_print_allocation_tag_command (const char *args, int from_tty)
+{
+  if (!target_supports_memory_tagging ())
+    show_memory_tagging_unsupported ();
+
+  memory_tag_print_tag_command (args, memtag_type::allocation);
+}
+
+/* Parse ARGS and extract ADDR and TAG.
+   ARGS should have format <expression> <tag bytes>.  */
+
+static void
+parse_with_logical_tag_input (const char *args, struct value **val,
+			      gdb::byte_vector &tags,
+			      value_print_options *print_opts)
+{
+  /* Fetch the address.  */
+  std::string address_string = extract_string_maybe_quoted (&args);
+
+  /* Parse the address into a value.  */
+  *val = process_print_command_args (address_string.c_str (), print_opts,
+				     true);
+
+  /* Fetch the tag bytes.  */
+  std::string tag_string = extract_string_maybe_quoted (&args);
+
+  /* Validate the input.  */
+  if (address_string.empty () || tag_string.empty ())
+    error (_("Missing arguments."));
+
+  if (tag_string.length () != 2)
+    error (_("Error parsing tags argument. The tag should be 2 digits."));
+
+  tags = hex2bin (tag_string.c_str ());
+}
+
+/* Implement the "memory-tag with-logical-tag" command.  */
+
+static void
+memory_tag_with_logical_tag_command (const char *args, int from_tty)
+{
+  if (!target_supports_memory_tagging ())
+    show_memory_tagging_unsupported ();
+
+  if (args == nullptr)
+    error_no_arg (_("<address> <tag>"));
+
+  gdb::byte_vector tags;
+  struct value *val;
+  value_print_options print_opts;
+
+  /* Parse the input.  */
+  parse_with_logical_tag_input (args, &val, tags, &print_opts);
+
+  /* Setting the logical tag is just a local operation that does not touch
+     any memory from the target.  Given an input value, we modify the value
+     to include the appropriate tag.
+
+     For this reason we need to cast the argument value to a
+     (void *) pointer.  This is so we have the right type for the gdbarch
+     hook to manipulate the value and insert the tag.
+
+     Otherwise, this would fail if, for example, GDB parsed the argument value
+     into an int-sized value and the pointer value has a type of greater
+     length.  */
+
+  /* Cast to (void *).  */
+  val = value_cast (builtin_type (target_gdbarch ())->builtin_data_ptr,
+		    val);
+
+  /* Length doesn't matter for a logical tag.  Pass 0.  */
+  if (!gdbarch_set_memtags (target_gdbarch (), val, 0, tags,
+			    memtag_type::logical))
+    printf_filtered (_("Could not update the logical tag data.\n"));
+  else
+    {
+      /* Always print it in hex format.  */
+      print_opts.output_format = 'x';
+      print_value (val, print_opts);
+    }
+}
+
+/* Parse ARGS and extract ADDR, LENGTH and TAGS.  */
+
+static void
+parse_set_allocation_tag_input (const char *args, struct value **val,
+				size_t *length, gdb::byte_vector &tags)
+{
+  /* Fetch the address.  */
+  std::string address_string = extract_string_maybe_quoted (&args);
+
+  /* Parse the address into a value.  */
+  value_print_options print_opts;
+  *val = process_print_command_args (address_string.c_str (), &print_opts,
+				     true);
+
+  /* Fetch the length.  */
+  std::string length_string = extract_string_maybe_quoted (&args);
+
+  /* Fetch the tag bytes.  */
+  std::string tags_string = extract_string_maybe_quoted (&args);
+
+  /* Validate the input.  */
+  if (address_string.empty () || length_string.empty () || tags_string.empty ())
+    error (_("Missing arguments."));
+
+  errno = 0;
+  const char *trailer = nullptr;
+  LONGEST parsed_length = strtoulst (length_string.c_str (), &trailer, 10);
+
+  if (errno != 0 || (trailer != nullptr && trailer[0] != '\0'))
+    error (_("Error parsing length argument."));
+
+  if (parsed_length <= 0)
+    error (_("Invalid zero or negative length."));
+
+  *length = parsed_length;
+
+  if (tags_string.length () % 2)
+    error (_("Error parsing tags argument. Tags should be 2 digits per byte."));
+
+  tags = hex2bin (tags_string.c_str ());
+
+  /* If the address is not in a region memory mapped with a memory tagging
+     flag, it is no use trying to access/manipulate its allocation tag.  */
+  if (!gdbarch_tagged_address_p (target_gdbarch (), *val))
+    show_addr_not_tagged (value_as_address (*val));
+}
+
+/* Implement the "memory-tag set-allocation-tag" command.
+   ARGS should be in the format <address> <length> <tags>.  */
+
+static void
+memory_tag_set_allocation_tag_command (const char *args, int from_tty)
+{
+  if (!target_supports_memory_tagging ())
+    show_memory_tagging_unsupported ();
+
+  if (args == nullptr)
+    error_no_arg (_("<starting address> <length> <tag bytes>"));
+
+  gdb::byte_vector tags;
+  size_t length = 0;
+  struct value *val;
+
+  /* Parse the input.  */
+  parse_set_allocation_tag_input (args, &val, &length, tags);
+
+  if (!gdbarch_set_memtags (target_gdbarch (), val, length, tags,
+			    memtag_type::allocation))
+    printf_filtered (_("Could not update the allocation tag(s).\n"));
+  else
+    printf_filtered (_("Allocation tag(s) updated successfully.\n"));
+}
+
+/* Implement the "memory-tag check" command.  */
+
+static void
+memory_tag_check_command (const char *args, int from_tty)
+{
+  if (!target_supports_memory_tagging ())
+    show_memory_tagging_unsupported ();
+
+  if (args == nullptr)
+    error (_("Argument required (address or pointer)"));
+
+  /* Parse the expression into a value.  If the value is an address or
+     pointer, then check its logical tag against the allocation tag.  */
+  value_print_options print_opts;
+
+  struct value *val = process_print_command_args (args, &print_opts, true);
+
+  /* If the address is not in a region memory mapped with a memory tagging
+     flag, it is no use trying to access/manipulate its allocation tag.  */
+  if (!gdbarch_tagged_address_p (target_gdbarch (), val))
+    show_addr_not_tagged (value_as_address (val));
+
+  CORE_ADDR addr = value_as_address (val);
+
+  /* Check if the tag is valid.  */
+  if (!gdbarch_memtag_matches_p (target_gdbarch (), val))
+    {
+      struct value *tag
+	= gdbarch_get_memtag (target_gdbarch (), val, memtag_type::logical);
+      std::string ltag
+	= gdbarch_memtag_to_string (target_gdbarch (), tag);
+
+      tag = gdbarch_get_memtag (target_gdbarch (), val,
+				memtag_type::allocation);
+      std::string atag
+	= gdbarch_memtag_to_string (target_gdbarch (), tag);
+
+      printf_filtered (_("Logical tag (%s) does not match"
+			 " the allocation tag (%s) for address %s.\n"),
+		       ltag.c_str (), atag.c_str (),
+		       paddress (target_gdbarch (), addr));
+    }
+  else
+    {
+      struct value *tag
+	= gdbarch_get_memtag (target_gdbarch (), val, memtag_type::logical);
+      std::string ltag
+	= gdbarch_memtag_to_string (target_gdbarch (), tag);
+
+      printf_filtered (_("Memory tags for address %s match (%s).\n"),
+		       paddress (target_gdbarch (), addr), ltag.c_str ());
+    }
+}
+
 void _initialize_printcmd ();
 void
 _initialize_printcmd ()
@@ -2980,4 +3280,61 @@ Construct a GDB command and then evaluate it.\n\
 Usage: eval \"format string\", ARG1, ARG2, ARG3, ..., ARGN\n\
 Convert the arguments to a string as \"printf\" would, but then\n\
 treat this string as a command line, and evaluate it."));
+
+  /* Memory tagging commands.  */
+  add_prefix_cmd ("memory-tag", class_vars, memory_tag_command, _("\
+Generic command for printing and manipulating memory tag properties."),
+		  &memory_tag_list, "memory-tag ", 0, &cmdlist);
+  add_cmd ("print-logical-tag", class_vars,
+	   memory_tag_print_logical_tag_command,
+	   ("Print the logical tag from POINTER.\n\
+Usage: memory-tag print-logical-tag <POINTER>.\n\
+<POINTER> is an expression that evaluates to a pointer.\n\
+Print the logical tag contained in POINTER.  The tag interpretation is\n\
+architecture-specific."),
+	   &memory_tag_list);
+  add_cmd ("print-allocation-tag", class_vars,
+	   memory_tag_print_allocation_tag_command,
+	   _("Print the allocation tag for ADDRESS.\n\
+Usage: memory-tag print-allocation-tag <ADDRESS>.\n\
+<ADDRESS> is an expression that evaluates to a memory address.\n\
+Print the allocation tag associated with the memory address ADDRESS.\n\
+The tag interpretation is architecture-specific."),
+	   &memory_tag_list);
+  add_cmd ("with-logical-tag", class_vars, memory_tag_with_logical_tag_command,
+	   _("Print a POINTER with a specific logical TAG.\n\
+Usage: memory-tag with-logical-tag <POINTER> <TAG>\n\
+<POINTER> is an expression that evaluates to a pointer.\n\
+<TAG> is a sequence of hex bytes that is interpreted by the architecture\n\
+as a single memory tag."),
+	   &memory_tag_list);
+  add_cmd ("set-allocation-tag", class_vars,
+	   memory_tag_set_allocation_tag_command,
+	   _("Set the allocation tag(s) for a memory range.\n\
+Usage: memory-tag set-allocation-tag <ADDRESS> <LENGTH> <TAG_BYTES>\n\
+<ADDRESS> is an expression that evaluates to a memory address\n\
+<LENGTH> is the number of bytes that is added to <ADDRESS> to calculate\n\
+the memory range.\n\
+<TAG_BYTES> is a sequence of hex bytes that is interpreted by the\n\
+architecture as one or more memory tags.\n\
+Sets the tags of the memory range [ADDRESS, ADDRESS + LENGTH)\n\
+to TAG_BYTES.\n\
+\n\
+If the number of tags is greater than or equal to the number of tag granules\n\
+in the [ADDRESS, ADDRESS + LENGTH) range, only the tags up to the\n\
+number of tag granules are updated.\n\
+\n\
+If the number of tags is less than the number of tag granules, then the\n\
+command is a fill operation.  The TAG_BYTES are interpreted as a pattern\n\
+that gets repeated until the number of tag granules in the memory range\n\
+[ADDRESS, ADDRESS + LENGTH) is updated."),
+	   &memory_tag_list);
+  add_cmd ("check", class_vars, memory_tag_check_command,
+	   _("Validate a pointer's logical tag against the allocation tag.\n\
+Usage: memory-tag check <POINTER>\n\
+<POINTER> is an expression that evaluates to a pointer\n\
+Fetch the logical and allocation tags for POINTER and compare them\n\
+for equality.  If the tags do not match, print additional information about\n\
+the tag mismatch."),
+	   &memory_tag_list);
 }

gdbsupport/ChangeLog

@@ -1,3 +1,11 @@
+2021-03-24  Luis Machado  <luis.machado@linaro.org>
+
+	* rsp-low.cc (fromhex, hex2bin): Move to ...
+	* common-utils.cc: ... here.
+	(fromhex) Change error message text to not be RSP-specific.
+	* rsp-low.h (fromhex, hex2bin): Move to ...
+	* common-utils.h: ... here.
+
 2021-03-21  Alan Modra  <amodra@gmail.com>
 
 	* common-utils.h (startswith): Delete version now supplied by bfd.h.

gdbsupport/common-utils.cc

@@ -392,3 +392,52 @@ align_down (ULONGEST v, int n)
   gdb_assert (n && (n & (n-1)) == 0);
   return (v & -n);
 }
+
+/* See gdbsupport/common-utils.h.  */
+
+int
+fromhex (int a)
+{
+  if (a >= '0' && a <= '9')
+    return a - '0';
+  else if (a >= 'a' && a <= 'f')
+    return a - 'a' + 10;
+  else if (a >= 'A' && a <= 'F')
+    return a - 'A' + 10;
+  else
+    error (_("Invalid hex digit %d"), a);
+}
+
+/* See gdbsupport/common-utils.h.  */
+
+int
+hex2bin (const char *hex, gdb_byte *bin, int count)
+{
+  int i;
+
+  for (i = 0; i < count; i++)
+    {
+      if (hex[0] == 0 || hex[1] == 0)
+	{
+	  /* Hex string is short, or of uneven length.
+	     Return the count that has been converted so far.  */
+	  return i;
+	}
+      *bin++ = fromhex (hex[0]) * 16 + fromhex (hex[1]);
+      hex += 2;
+    }
+  return i;
+}
+
+/* See gdbsupport/common-utils.h.  */
+
+gdb::byte_vector
+hex2bin (const char *hex)
+{
+  size_t bin_len = strlen (hex) / 2;
+  gdb::byte_vector bin (bin_len);
+
+  hex2bin (hex, bin.data (), bin_len);
+
+  return bin;
+}

gdbsupport/common-utils.h

@@ -22,6 +22,7 @@
 
 #include <string>
 #include <vector>
+#include "gdbsupport/byte-vector.h"
 
 #include "poison.h"
 
@@ -191,4 +192,18 @@ in_inclusive_range (T value, T low, T high)
 extern ULONGEST align_up (ULONGEST v, int n);
 extern ULONGEST align_down (ULONGEST v, int n);
 
+/* Convert hex digit A to a number, or throw an exception.  */
+extern int fromhex (int a);
+
+/* HEX is a string of characters representing hexadecimal digits.
+   Convert pairs of hex digits to bytes and store sequentially into
+   BIN.  COUNT is the maximum number of characters to convert.  This
+   will convert fewer characters if the number of hex characters
+   actually seen is odd, or if HEX terminates before COUNT characters.
+   Returns the number of characters actually converted.  */
+extern int hex2bin (const char *hex, gdb_byte *bin, int count);
+
+/* Like the above, but return a gdb::byte_vector.  */
+gdb::byte_vector hex2bin (const char *hex);
+
 #endif /* COMMON_COMMON_UTILS_H */

gdbsupport/rsp-low.cc

@@ -22,21 +22,6 @@
 
 /* See rsp-low.h.  */
 
-int
-fromhex (int a)
-{
-  if (a >= '0' && a <= '9')
-    return a - '0';
-  else if (a >= 'a' && a <= 'f')
-    return a - 'a' + 10;
-  else if (a >= 'A' && a <= 'F')
-    return a - 'A' + 10;
-  else
-    error (_("Reply contains invalid hex digit %d"), a);
-}
-
-/* See rsp-low.h.  */
-
 int
 tohex (int nib)
 {
@@ -111,40 +96,6 @@ unpack_varlen_hex (const char *buff,	/* packet to parse */
 
 /* See rsp-low.h.  */
 
-int
-hex2bin (const char *hex, gdb_byte *bin, int count)
-{
-  int i;
-
-  for (i = 0; i < count; i++)
-    {
-      if (hex[0] == 0 || hex[1] == 0)
-	{
-	  /* Hex string is short, or of uneven length.
-	     Return the count that has been converted so far.  */
-	  return i;
-	}
-      *bin++ = fromhex (hex[0]) * 16 + fromhex (hex[1]);
-      hex += 2;
-    }
-  return i;
-}
-
-/* See rsp-low.h.  */
-
-gdb::byte_vector
-hex2bin (const char *hex)
-{
-  size_t bin_len = strlen (hex) / 2;
-  gdb::byte_vector bin (bin_len);
-
-  hex2bin (hex, bin.data (), bin_len);
-
-  return bin;
-}
-
-/* See rsp-low.h.  */
-
 std::string
 hex2str (const char *hex)
 {

gdbsupport/rsp-low.h

@@ -20,12 +20,6 @@
 #ifndef COMMON_RSP_LOW_H
 #define COMMON_RSP_LOW_H
 
-#include "gdbsupport/byte-vector.h"
-
-/* Convert hex digit A to a number, or throw an exception.  */
-
-extern int fromhex (int a);
-
 /* Convert number NIB to a hex digit.  */
 
 extern int tohex (int nib);
@@ -45,19 +39,6 @@ extern char *pack_hex_byte (char *pkt, int byte);
 
 extern const char *unpack_varlen_hex (const char *buff, ULONGEST *result);
 
-/* HEX is a string of characters representing hexadecimal digits.
-   Convert pairs of hex digits to bytes and store sequentially into
-   BIN.  COUNT is the maximum number of characters to convert.  This
-   will convert fewer characters if the number of hex characters
-   actually seen is odd, or if HEX terminates before COUNT characters.
-   Returns the number of characters actually converted.  */
-
-extern int hex2bin (const char *hex, gdb_byte *bin, int count);
-
-/* Like the above, but return a gdb::byte_vector.  */
-
-gdb::byte_vector hex2bin (const char *hex);
-
 /* Like hex2bin, but return a std::string.  */
 
 extern std::string hex2str (const char *hex);