Merge monty@192.168.0.9:/my/mysql-5.0

into  mysql.com:/home/my/mysql-5.0

configure.in

@@ -356,6 +356,9 @@ then
   # mysqld requires -fno-implicit-templates.
   # Disable exceptions as they seams to create problems with gcc and threads.
   # mysqld doesn't use run-time-type-checking, so we disable it.
+  # We should use -Wno-invalid-offsetof flag to disable some warnings from gcc
+  # regarding offset() usage in C++ which are done in a safe manner in the
+  # server
   CXXFLAGS="$CXXFLAGS -fno-implicit-templates -fno-exceptions -fno-rtti"
   AC_DEFINE([HAVE_EXPLICIT_TEMPLATE_INSTANTIATION],
     [1], [Defined by configure. Use explicit template instantiation.])

ndb/include/ndbapi/NdbDictionary.hpp

@@ -61,12 +61,15 @@ typedef struct charset_info_st CHARSET_INFO;
  */
 class NdbDictionary {
 public:
+  NdbDictionary() {}                          /* Remove gcc warning */
   /**
    * @class Object
    * @brief Meta information about a database object (a table, index, etc)
    */
   class Object {
   public:
+    Object() {}                               /* Remove gcc warning */
+    virtual ~Object() {}                      /* Remove gcc warning */
     /**
      * Status of object
      */

sql/field.cc

@@ -5262,7 +5262,7 @@ int Field_date::store(longlong nr, bool unsigned_val)
   }
 
   if (nr >= 19000000000000.0 && nr <= 99991231235959.0)
-    nr=floor(nr/1000000.0);			// Timestamp to date
+    nr= (longlong) floor(nr/1000000.0);         // Timestamp to date
 
   if (error)
     set_datetime_warning(MYSQL_ERROR::WARN_LEVEL_WARN,

sql/handler.h

@@ -231,6 +231,7 @@ struct xid_t {
   long bqual_length;
   char data[XIDDATASIZE];  // not \0-terminated !
 
+  xid_t() {}                                /* Remove gcc warning */  
   bool eq(struct xid_t *xid)
   { return eq(xid->gtrid_length, xid->bqual_length, xid->data); }
   bool eq(long g, long b, const char *d)
@@ -463,6 +464,7 @@ typedef class Item COND;
 
 typedef struct st_ha_check_opt
 {
+  st_ha_check_opt() {}                        /* Remove gcc warning */
   ulong sort_buffer_size;
   uint flags;       /* isam layer flags (e.g. for myisamchk) */
   uint sql_flags;   /* sql layer flags - for something myisamchk cannot do */

sql/item.h

@@ -164,7 +164,8 @@ struct Hybrid_type_traits
   virtual my_decimal *val_decimal(Hybrid_type *val, my_decimal *buf) const;
   virtual String *val_str(Hybrid_type *val, String *buf, uint8 decimals) const;
   static const Hybrid_type_traits *instance();
-  Hybrid_type_traits() {};
+  Hybrid_type_traits() {}
+  virtual ~Hybrid_type_traits() {}
 };
 
 
@@ -339,6 +340,7 @@ private:
   bool        save_resolve_in_select_list;
 
 public:
+  Name_resolution_context_state() {}          /* Remove gcc warning */
   TABLE_LIST *save_next_local;
 
 public:
@@ -1015,6 +1017,7 @@ bool agg_item_charsets(DTCollation &c, const char *name,
 class Item_num: public Item
 {
 public:
+  Item_num() {}                               /* Remove gcc warning */
   virtual Item_num *neg()= 0;
   Item *safe_charset_converter(CHARSET_INFO *tocs);
 };

sql/item_cmpfunc.h

@@ -128,6 +128,8 @@ public:
 class Comp_creator
 {
 public:
+  Comp_creator() {}                           /* Remove gcc warning */
+  virtual ~Comp_creator() {}                  /* Remove gcc warning */
   virtual Item_bool_func2* create(Item *a, Item *b) const = 0;
   virtual const char* symbol(bool invert) const = 0;
   virtual bool eqne_op() const = 0;
@@ -137,6 +139,8 @@ public:
 class Eq_creator :public Comp_creator
 {
 public:
+  Eq_creator() {}                             /* Remove gcc warning */
+  virtual ~Eq_creator() {}                    /* Remove gcc warning */
   virtual Item_bool_func2* create(Item *a, Item *b) const;
   virtual const char* symbol(bool invert) const { return invert? "<>" : "="; }
   virtual bool eqne_op() const { return 1; }
@@ -146,6 +150,8 @@ public:
 class Ne_creator :public Comp_creator
 {
 public:
+  Ne_creator() {}                             /* Remove gcc warning */
+  virtual ~Ne_creator() {}                    /* Remove gcc warning */
   virtual Item_bool_func2* create(Item *a, Item *b) const;
   virtual const char* symbol(bool invert) const { return invert? "=" : "<>"; }
   virtual bool eqne_op() const { return 1; }
@@ -155,6 +161,8 @@ public:
 class Gt_creator :public Comp_creator
 {
 public:
+  Gt_creator() {}                             /* Remove gcc warning */
+  virtual ~Gt_creator() {}                    /* Remove gcc warning */
   virtual Item_bool_func2* create(Item *a, Item *b) const;
   virtual const char* symbol(bool invert) const { return invert? "<=" : ">"; }
   virtual bool eqne_op() const { return 0; }
@@ -164,6 +172,8 @@ public:
 class Lt_creator :public Comp_creator
 {
 public:
+  Lt_creator() {}                             /* Remove gcc warning */
+  virtual ~Lt_creator() {}                    /* Remove gcc warning */
   virtual Item_bool_func2* create(Item *a, Item *b) const;
   virtual const char* symbol(bool invert) const { return invert? ">=" : "<"; }
   virtual bool eqne_op() const { return 0; }
@@ -173,6 +183,8 @@ public:
 class Ge_creator :public Comp_creator
 {
 public:
+  Ge_creator() {}                             /* Remove gcc warning */
+  virtual ~Ge_creator() {}                    /* Remove gcc warning */
   virtual Item_bool_func2* create(Item *a, Item *b) const;
   virtual const char* symbol(bool invert) const { return invert? "<" : ">="; }
   virtual bool eqne_op() const { return 0; }
@@ -182,6 +194,8 @@ public:
 class Le_creator :public Comp_creator
 {
 public:
+  Le_creator() {}                             /* Remove gcc warning */
+  virtual ~Le_creator() {}                    /* Remove gcc warning */
   virtual Item_bool_func2* create(Item *a, Item *b) const;
   virtual const char* symbol(bool invert) const { return invert? ">" : "<="; }
   virtual bool eqne_op() const { return 0; }
@@ -739,6 +753,7 @@ class cmp_item_int :public cmp_item
 {
   longlong value;
 public:
+  cmp_item_int() {}                           /* Remove gcc warning */
   void store_value(Item *item)
   {
     value= item->val_int();
@@ -759,6 +774,7 @@ class cmp_item_real :public cmp_item
 {
   double value;
 public:
+  cmp_item_real() {}                          /* Remove gcc warning */
   void store_value(Item *item)
   {
     value= item->val_real();
@@ -780,6 +796,7 @@ class cmp_item_decimal :public cmp_item
 {
   my_decimal value;
 public:
+  cmp_item_decimal() {}                       /* Remove gcc warning */
   void store_value(Item *item);
   int cmp(Item *arg);
   int compare(cmp_item *c);

sql/log_event.h

@@ -121,6 +121,7 @@ struct old_sql_ex
  ****************************************************************************/
 struct sql_ex_info
 {
+  sql_ex_info() {}                            /* Remove gcc warning */
   char* field_term;
   char* enclosed;
   char* line_term;

sql/mysql_priv.h

@@ -432,6 +432,7 @@ typedef struct st_sql_list {
   byte *first;
   byte **next;
 
+  st_sql_list() {}                              /* Remove gcc warning */
   inline void empty()
   {
     elements=0;
@@ -983,7 +984,7 @@ bool close_thread_table(THD *thd, TABLE **table_ptr);
 void close_temporary_tables(THD *thd);
 void close_tables_for_reopen(THD *thd, TABLE_LIST **tables);
 TABLE_LIST *find_table_in_list(TABLE_LIST *table,
-                               uint offset_to_list,
+                               st_table_list *TABLE_LIST::*link,
                                const char *db_name,
                                const char *table_name);
 TABLE_LIST *unique_table(THD *thd, TABLE_LIST *table, TABLE_LIST *table_list);
@@ -1024,7 +1025,7 @@ inline TABLE_LIST *find_table_in_global_list(TABLE_LIST *table,
                                              const char *db_name,
                                              const char *table_name)
 {
-  return find_table_in_list(table, offsetof(TABLE_LIST, next_global),
+  return find_table_in_list(table, &TABLE_LIST::next_global,
                             db_name, table_name);
 }
 
@@ -1032,7 +1033,7 @@ inline TABLE_LIST *find_table_in_local_list(TABLE_LIST *table,
                                             const char *db_name,
                                             const char *table_name)
 {
-  return find_table_in_list(table, offsetof(TABLE_LIST, next_local),
+  return find_table_in_list(table, &TABLE_LIST::next_local,
                             db_name, table_name);
 }
 

sql/opt_range.cc

@@ -1495,6 +1495,8 @@ public:
   { return (void*) alloc_root(mem_root, (uint) size); }
   static void operator delete(void *ptr,size_t size) { TRASH(ptr, size); }
   static void operator delete(void *ptr, MEM_ROOT *mem_root) { /* Never called */ }
+  virtual ~TABLE_READ_PLAN() {}               /* Remove gcc warning */
+
 };
 
 class TRP_ROR_INTERSECT;
@@ -1518,6 +1520,7 @@ public:
   TRP_RANGE(SEL_ARG *key_arg, uint idx_arg)
    : key(key_arg), key_idx(idx_arg)
   {}
+  virtual ~TRP_RANGE() {}                     /* Remove gcc warning */
 
   QUICK_SELECT_I *make_quick(PARAM *param, bool retrieve_full_rows,
                              MEM_ROOT *parent_alloc)
@@ -1539,6 +1542,8 @@ public:
 class TRP_ROR_INTERSECT : public TABLE_READ_PLAN
 {
 public:
+  TRP_ROR_INTERSECT() {}                      /* Remove gcc warning */
+  virtual ~TRP_ROR_INTERSECT() {}             /* Remove gcc warning */
   QUICK_SELECT_I *make_quick(PARAM *param, bool retrieve_full_rows,
                              MEM_ROOT *parent_alloc);
 
@@ -1560,6 +1565,8 @@ public:
 class TRP_ROR_UNION : public TABLE_READ_PLAN
 {
 public:
+  TRP_ROR_UNION() {}                          /* Remove gcc warning */
+  virtual ~TRP_ROR_UNION() {}                 /* Remove gcc warning */
   QUICK_SELECT_I *make_quick(PARAM *param, bool retrieve_full_rows,
                              MEM_ROOT *parent_alloc);
   TABLE_READ_PLAN **first_ror; /* array of ptrs to plans for merged scans */
@@ -1576,6 +1583,8 @@ public:
 class TRP_INDEX_MERGE : public TABLE_READ_PLAN
 {
 public:
+  TRP_INDEX_MERGE() {}                        /* Remove gcc warning */
+  virtual ~TRP_INDEX_MERGE() {}               /* Remove gcc warning */
   QUICK_SELECT_I *make_quick(PARAM *param, bool retrieve_full_rows,
                              MEM_ROOT *parent_alloc);
   TRP_RANGE **range_scans; /* array of ptrs to plans of merged scans */
@@ -1625,6 +1634,7 @@ public:
       if (key_infix_len)
         memcpy(this->key_infix, key_infix_arg, key_infix_len);
     }
+  virtual ~TRP_GROUP_MIN_MAX() {}             /* Remove gcc warning */
 
   QUICK_SELECT_I *make_quick(PARAM *param, bool retrieve_full_rows,
                              MEM_ROOT *parent_alloc);

sql/parse_file.h

@@ -49,6 +49,8 @@ struct File_option
 class Unknown_key_hook
 {
 public:
+  Unknown_key_hook() {}                       /* Remove gcc warning */
+  virtual ~Unknown_key_hook() {}              /* Remove gcc warning */
   virtual bool process_unknown_string(char *&unknown_key, gptr base,
                                       MEM_ROOT *mem_root, char *end)= 0;
 };
@@ -59,6 +61,7 @@ public:
 class File_parser_dummy_hook: public Unknown_key_hook
 {
 public:
+  File_parser_dummy_hook() {}                 /* Remove gcc warning */
   virtual bool process_unknown_string(char *&unknown_key, gptr base,
                                       MEM_ROOT *mem_root, char *end);
 };

sql/sp_rcontext.h

@@ -268,6 +268,7 @@ class Select_fetch_into_spvars: public select_result_interceptor
   List<struct sp_pvar> *spvar_list;
   uint field_count;
 public:
+  Select_fetch_into_spvars() {}               /* Remove gcc warning */
   uint get_field_count() { return field_count; }
   void set_spvar_list(List<struct sp_pvar> *vars) { spvar_list= vars; }
 

sql/spatial.h

@@ -165,6 +165,8 @@ struct Geometry_buffer;
 class Geometry
 {
 public:
+  Geometry() {}                               /* Remove gcc warning */
+  virtual ~Geometry() {}                        /* Remove gcc warning */
   static void *operator new(size_t size, void *buffer)
   {
     return buffer;
@@ -302,6 +304,8 @@ protected:
 class Gis_point: public Geometry
 {
 public:
+  Gis_point() {}                              /* Remove gcc warning */
+  virtual ~Gis_point() {}                     /* Remove gcc warning */
   uint32 get_data_size() const;
   bool init_from_wkt(Gis_read_stream *trs, String *wkb);
   uint init_from_wkb(const char *wkb, uint len, wkbByteOrder bo, String *res);
@@ -349,6 +353,8 @@ public:
 class Gis_line_string: public Geometry
 {
 public:
+  Gis_line_string() {}                        /* Remove gcc warning */
+  virtual ~Gis_line_string() {}               /* Remove gcc warning */
   uint32 get_data_size() const;
   bool init_from_wkt(Gis_read_stream *trs, String *wkb);
   uint init_from_wkb(const char *wkb, uint len, wkbByteOrder bo, String *res);
@@ -375,6 +381,8 @@ public:
 class Gis_polygon: public Geometry
 {
 public:
+  Gis_polygon() {}                            /* Remove gcc warning */
+  virtual ~Gis_polygon() {}                   /* Remove gcc warning */
   uint32 get_data_size() const;
   bool init_from_wkt(Gis_read_stream *trs, String *wkb);
   uint init_from_wkb(const char *wkb, uint len, wkbByteOrder bo, String *res);
@@ -401,6 +409,8 @@ public:
 class Gis_multi_point: public Geometry
 {
 public:
+  Gis_multi_point() {}                        /* Remove gcc warning */
+  virtual ~Gis_multi_point() {}               /* Remove gcc warning */
   uint32 get_data_size() const;
   bool init_from_wkt(Gis_read_stream *trs, String *wkb);
   uint init_from_wkb(const char *wkb, uint len, wkbByteOrder bo, String *res);
@@ -423,6 +433,8 @@ public:
 class Gis_multi_line_string: public Geometry
 {
 public:
+  Gis_multi_line_string() {}                  /* Remove gcc warning */
+  virtual ~Gis_multi_line_string() {}         /* Remove gcc warning */
   uint32 get_data_size() const;
   bool init_from_wkt(Gis_read_stream *trs, String *wkb);
   uint init_from_wkb(const char *wkb, uint len, wkbByteOrder bo, String *res);
@@ -447,6 +459,8 @@ public:
 class Gis_multi_polygon: public Geometry
 {
 public:
+  Gis_multi_polygon() {}                      /* Remove gcc warning */
+  virtual ~Gis_multi_polygon() {}             /* Remove gcc warning */
   uint32 get_data_size() const;
   bool init_from_wkt(Gis_read_stream *trs, String *wkb);
   uint init_from_wkb(const char *wkb, uint len, wkbByteOrder bo, String *res);
@@ -471,6 +485,8 @@ public:
 class Gis_geometry_collection: public Geometry
 {
 public:
+  Gis_geometry_collection() {}                /* Remove gcc warning */
+  virtual ~Gis_geometry_collection() {}       /* Remove gcc warning */
   uint32 get_data_size() const;
   bool init_from_wkt(Gis_read_stream *trs, String *wkb);
   uint init_from_wkb(const char *wkb, uint len, wkbByteOrder bo, String *res);

sql/sql_base.cc

@@ -687,11 +687,11 @@ void close_temporary_tables(THD *thd)
 */
 
 TABLE_LIST *find_table_in_list(TABLE_LIST *table,
-                               uint offset,
+                               st_table_list *TABLE_LIST::*link,
                                const char *db_name,
                                const char *table_name)
 {
-  for (; table; table= *(TABLE_LIST **) ((char*) table + offset))
+  for (; table; table= table->*link )
   {
     if ((table->table == 0 || table->table->s->tmp_table == NO_TMP_TABLE) &&
         strcmp(table->db, db_name) == 0 &&

sql/sql_cache.h

@@ -69,6 +69,7 @@ class Query_cache;
 
 struct Query_cache_block_table
 {
+  Query_cache_block_table() {}                /* Remove gcc warning */
   TABLE_COUNTER_TYPE n;		// numbr in table (from 0)
   Query_cache_block_table *next, *prev;
   Query_cache_table *parent;
@@ -78,6 +79,7 @@ struct Query_cache_block_table
 
 struct Query_cache_block
 {
+  Query_cache_block() {}                      /* Remove gcc warning */
   enum block_type {FREE, QUERY, RESULT, RES_CONT, RES_BEG,
 		   RES_INCOMPLETE, TABLE, INCOMPLETE};
 
@@ -143,6 +145,7 @@ struct Query_cache_query
 
 struct Query_cache_table
 {
+  Query_cache_table() {}                      /* Remove gcc warning */
   char *tbl;
   uint32 key_len;
   uint8 table_type;
@@ -171,6 +174,7 @@ struct Query_cache_table
 
 struct Query_cache_result
 {
+  Query_cache_result() {}                     /* Remove gcc warning */
   Query_cache_block *query;
 
   inline gptr data()
@@ -197,6 +201,7 @@ extern "C" void query_cache_invalidate_by_MyISAM_filename(const char* filename);
 
 struct Query_cache_memory_bin
 {
+  Query_cache_memory_bin() {}                 /* Remove gcc warning */
 #ifndef DBUG_OFF
   ulong size;
 #endif
@@ -215,6 +220,7 @@ struct Query_cache_memory_bin
 
 struct Query_cache_memory_bin_step
 {
+  Query_cache_memory_bin_step() {}            /* Remove gcc warning */
   ulong size;
   ulong increment;
   uint idx;

sql/sql_class.h

@@ -69,7 +69,8 @@ class TC_LOG
 
 class TC_LOG_DUMMY: public TC_LOG // use it to disable the logging
 {
-  public:
+public:
+  TC_LOG_DUMMY() {}                           /* Remove gcc warning */
   int open(const char *opt_name)        { return 0; }
   void close()                          { }
   int log(THD *thd, my_xid xid)         { return 1; }
@@ -930,6 +931,7 @@ void xid_cache_delete(XID_STATE *xid_state);
 
 class Security_context {
 public:
+  Security_context() {}                       /* Remove gcc warning */
   /*
     host - host of the client
     user - user of the client, set to NULL until the user has been read from
@@ -1679,6 +1681,7 @@ public:
 class select_result_interceptor: public select_result
 {
 public:
+  select_result_interceptor() {}              /* Remove gcc warning */
   uint field_count(List<Item> &fields) const { return 0; }
   bool send_fields(List<Item> &fields, uint flag) { return FALSE; }
 };
@@ -1966,6 +1969,7 @@ class Table_ident :public Sql_alloc
 class user_var_entry
 {
  public:
+  user_var_entry() {}                         /* Remove gcc warning */
   LEX_STRING name;
   char *value;
   ulong length;

sql/sql_db.cc

@@ -1105,12 +1105,12 @@ bool mysql_change_db(THD *thd, const char *name, bool no_access_check)
 #ifndef NO_EMBEDDED_ACCESS_CHECKS
   ulong db_access;
   Security_context *sctx= thd->security_ctx;
+  LINT_INIT(db_access);
 #endif
   DBUG_ENTER("mysql_change_db");
   DBUG_PRINT("enter",("name: '%s'",name));
 
   LINT_INIT(db_length);
-  LINT_INIT(db_access);
 
   /* dbname can only be NULL if malloc failed */
   if (!dbname || !(db_length= strlen(dbname)))
@@ -1179,6 +1179,7 @@ end:
     x_free(thd->db);
   if (dbname && dbname[0] == 0)
   {
+    my_free(dbname, MYF(0));
     thd->db= NULL;
     thd->db_length= 0;
   }

sql/sql_parse.cc

@@ -5979,10 +5979,11 @@ TABLE_LIST *st_select_lex::add_table_to_list(THD *thd,
     /*
       table_list.next points to the last inserted TABLE_LIST->next_local'
       element
+      We don't use the offsetof() macro here to avoid warnings from gcc
     */
-    previous_table_ref= (TABLE_LIST*) (table_list.next -
-                                       offsetof(TABLE_LIST, next_local));
-    DBUG_ASSERT(previous_table_ref);
+    previous_table_ref= (TABLE_LIST*) ((char*) table_list.next -
+                                       ((char*) &(ptr->next_local) -
+                                        (char*) ptr));
     /*
       Set next_name_resolution_table of the previous table reference to point
       to the current table reference. In effect the list

sql/sql_select.h

@@ -104,6 +104,7 @@ typedef int (*Read_record_func)(struct st_join_table *tab);
 Next_select_func setup_end_select_func(JOIN *join);
 
 typedef struct st_join_table {
+  st_join_table() {}                          /* Remove gcc warning */
   TABLE		*table;
   KEYUSE	*keyuse;			/* pointer to first used key */
   SQL_SELECT	*select;
@@ -287,7 +288,7 @@ class JOIN :public Sql_alloc
   }
 
   JOIN(JOIN &join)
-    :fields_list(join.fields_list)
+    :Sql_alloc(), fields_list(join.fields_list)
   {
     init(join.thd, join.fields_list, join.select_options,
          join.result);

sql/sql_update.cc

@@ -1303,7 +1303,7 @@ bool multi_update::send_data(List<Item> &not_used_values)
       memcpy((char*) tmp_table->field[0]->ptr,
 	     (char*) table->file->ref, table->file->ref_length);
       /* Write row, ignoring duplicated updates to a row */
-      if (error= tmp_table->file->write_row(tmp_table->record[0]))
+      if ((error= tmp_table->file->write_row(tmp_table->record[0])))
       {
         if (error != HA_ERR_FOUND_DUPP_KEY &&
             error != HA_ERR_FOUND_DUPP_UNIQUE &&

sql/table.h

@@ -187,6 +187,8 @@ typedef struct st_table_share
 /* Information for one open table */
 
 struct st_table {
+  st_table() {}                               /* Remove gcc warning */
+
   TABLE_SHARE	*s;
   handler	*file;
 #ifdef NOT_YET
@@ -444,6 +446,7 @@ public:
 
 typedef struct st_table_list
 {
+  st_table_list() {}                          /* Remove gcc warning */
   /*
     List of tables local to a subquery (used by SQL_LIST). Considers
     views as leaves (unlike 'next_leaf' below). Created at parse time
@@ -675,6 +678,7 @@ class Item;
 class Field_iterator: public Sql_alloc
 {
 public:
+  Field_iterator() {}                         /* Remove gcc warning */
   virtual ~Field_iterator() {}
   virtual void set(TABLE_LIST *)= 0;
   virtual void next()= 0;

sql/tztime.cc

@@ -961,6 +961,7 @@ static const String tz_SYSTEM_name("SYSTEM", 6, &my_charset_latin1);
 class Time_zone_system : public Time_zone
 {
 public:
+  Time_zone_system() {}                       /* Remove gcc warning */
   virtual my_time_t TIME_to_gmt_sec(const TIME *t,
                                     my_bool *in_dst_time_gap) const;
   virtual void gmt_sec_to_TIME(TIME *tmp, my_time_t t) const;
@@ -1054,6 +1055,7 @@ Time_zone_system::get_name() const
 class Time_zone_utc : public Time_zone
 {
 public:
+  Time_zone_utc() {}                          /* Remove gcc warning */
   virtual my_time_t TIME_to_gmt_sec(const TIME *t,
                                     my_bool *in_dst_time_gap) const;
   virtual void gmt_sec_to_TIME(TIME *tmp, my_time_t t) const;

sql/tztime.h

@@ -30,6 +30,7 @@
 class Time_zone: public Sql_alloc 
 {
 public:
+  Time_zone() {}                              /* Remove gcc warning */
   /*
     Converts local time in broken down TIME representation to 
     my_time_t (UTC seconds since Epoch) represenation.