1 /*
   2  * Copyright (c) 1997, 2009, Oracle and/or its affiliates. All rights reserved.
   3  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
   4  *
   5  * This code is free software; you can redistribute it and/or modify it
   6  * under the terms of the GNU General Public License version 2 only, as
   7  * published by the Free Software Foundation.
   8  *
   9  * This code is distributed in the hope that it will be useful, but WITHOUT
  10  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
  11  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  12  * version 2 for more details (a copy is included in the LICENSE file that
  13  * accompanied this code).
  14  *
  15  * You should have received a copy of the GNU General Public License version
  16  * 2 along with this work; if not, write to the Free Software Foundation,
  17  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
  18  *
  19  * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
  20  * or visit www.oracle.com if you need additional information or have any
  21  * questions.
  22  *
  23  */
  24 
  25 class Compile;
  26 class ConINode;
  27 class ConLNode;
  28 class Node;
  29 class Type;
  30 class PhaseTransform;
  31 class   PhaseGVN;
  32 class     PhaseIterGVN;
  33 class       PhaseCCP;
  34 class   PhasePeephole;
  35 class   PhaseRegAlloc;
  36 
  37 
  38 //-----------------------------------------------------------------------------
  39 // Expandable closed hash-table of nodes, initialized to NULL.
  40 // Note that the constructor just zeros things
  41 // Storage is reclaimed when the Arena's lifetime is over.
  42 class NodeHash : public StackObj {
  43 protected:
  44   Arena *_a;                    // Arena to allocate in
  45   uint   _max;                  // Size of table (power of 2)
  46   uint   _inserts;              // For grow and debug, count of hash_inserts
  47   uint   _insert_limit;         // 'grow' when _inserts reaches _insert_limit
  48   Node **_table;                // Hash table of Node pointers
  49   Node  *_sentinel;             // Replaces deleted entries in hash table
  50 
  51 public:
  52   NodeHash(uint est_max_size);
  53   NodeHash(Arena *arena, uint est_max_size);
  54   NodeHash(NodeHash *use_this_state);
  55 #ifdef ASSERT
  56   ~NodeHash();                  // Unlock all nodes upon destruction of table.
  57   void operator=(const NodeHash&); // Unlock all nodes upon replacement of table.
  58 #endif
  59   Node  *hash_find(const Node*);// Find an equivalent version in hash table
  60   Node  *hash_find_insert(Node*);// If not in table insert else return found node
  61   void   hash_insert(Node*);    // Insert into hash table
  62   bool   hash_delete(const Node*);// Replace with _sentinel in hash table
  63   void   check_grow() {
  64     _inserts++;
  65     if( _inserts == _insert_limit ) { grow(); }
  66     assert( _inserts <= _insert_limit, "hash table overflow");
  67     assert( _inserts < _max, "hash table overflow" );
  68   }
  69   static uint round_up(uint);   // Round up to nearest power of 2
  70   void   grow();                // Grow _table to next power of 2 and rehash
  71   // Return 75% of _max, rounded up.
  72   uint   insert_limit() const { return _max - (_max>>2); }
  73 
  74   void   clear();               // Set all entries to NULL, keep storage.
  75   // Size of hash table
  76   uint   size()         const { return _max; }
  77   // Return Node* at index in table
  78   Node  *at(uint table_index) {
  79     assert(table_index < _max, "Must be within table");
  80     return _table[table_index];
  81   }
  82 
  83   void   remove_useless_nodes(VectorSet &useful); // replace with sentinel
  84 
  85   Node  *sentinel() { return _sentinel; }
  86 
  87 #ifndef PRODUCT
  88   Node  *find_index(uint idx);  // For debugging
  89   void   dump();                // For debugging, dump statistics
  90 #endif
  91   uint   _grows;                // For debugging, count of table grow()s
  92   uint   _look_probes;          // For debugging, count of hash probes
  93   uint   _lookup_hits;          // For debugging, count of hash_finds
  94   uint   _lookup_misses;        // For debugging, count of hash_finds
  95   uint   _insert_probes;        // For debugging, count of hash probes
  96   uint   _delete_probes;        // For debugging, count of hash probes for deletes
  97   uint   _delete_hits;          // For debugging, count of hash probes for deletes
  98   uint   _delete_misses;        // For debugging, count of hash probes for deletes
  99   uint   _total_inserts;        // For debugging, total inserts into hash table
 100   uint   _total_insert_probes;  // For debugging, total probes while inserting
 101 };
 102 
 103 
 104 //-----------------------------------------------------------------------------
 105 // Map dense integer indices to Types.  Uses classic doubling-array trick.
 106 // Abstractly provides an infinite array of Type*'s, initialized to NULL.
 107 // Note that the constructor just zeros things, and since I use Arena
 108 // allocation I do not need a destructor to reclaim storage.
 109 // Despite the general name, this class is customized for use by PhaseTransform.
 110 class Type_Array : public StackObj {
 111   Arena *_a;                    // Arena to allocate in
 112   uint   _max;
 113   const Type **_types;
 114   void grow( uint i );          // Grow array node to fit
 115   const Type *operator[] ( uint i ) const // Lookup, or NULL for not mapped
 116   { return (i<_max) ? _types[i] : (Type*)NULL; }
 117   friend class PhaseTransform;
 118 public:
 119   Type_Array(Arena *a) : _a(a), _max(0), _types(0) {}
 120   Type_Array(Type_Array *ta) : _a(ta->_a), _max(ta->_max), _types(ta->_types) { }
 121   const Type *fast_lookup(uint i) const{assert(i<_max,"oob");return _types[i];}
 122   // Extend the mapping: index i maps to Type *n.
 123   void map( uint i, const Type *n ) { if( i>=_max ) grow(i); _types[i] = n; }
 124   uint Size() const { return _max; }
 125 #ifndef PRODUCT
 126   void dump() const;
 127 #endif
 128 };
 129 
 130 
 131 //------------------------------PhaseRemoveUseless-----------------------------
 132 // Remove useless nodes from GVN hash-table, worklist, and graph
 133 class PhaseRemoveUseless : public Phase {
 134 protected:
 135   Unique_Node_List _useful;   // Nodes reachable from root
 136                               // list is allocated from current resource area
 137 public:
 138   PhaseRemoveUseless( PhaseGVN *gvn, Unique_Node_List *worklist );
 139 
 140   Unique_Node_List *get_useful() { return &_useful; }
 141 };
 142 
 143 
 144 //------------------------------PhaseTransform---------------------------------
 145 // Phases that analyze, then transform.  Constructing the Phase object does any
 146 // global or slow analysis.  The results are cached later for a fast
 147 // transformation pass.  When the Phase object is deleted the cached analysis
 148 // results are deleted.
 149 class PhaseTransform : public Phase {
 150 protected:
 151   Arena*     _arena;
 152   Node_Array _nodes;           // Map old node indices to new nodes.
 153   Type_Array _types;           // Map old node indices to Types.
 154 
 155   // ConNode caches:
 156   enum { _icon_min = -1 * HeapWordSize,
 157          _icon_max = 16 * HeapWordSize,
 158          _lcon_min = _icon_min,
 159          _lcon_max = _icon_max,
 160          _zcon_max = (uint)T_CONFLICT
 161   };
 162   ConINode* _icons[_icon_max - _icon_min + 1];   // cached jint constant nodes
 163   ConLNode* _lcons[_lcon_max - _lcon_min + 1];   // cached jlong constant nodes
 164   ConNode*  _zcons[_zcon_max + 1];               // cached is_zero_type nodes
 165   void init_con_caches();
 166 
 167   // Support both int and long caches because either might be an intptr_t,
 168   // so they show up frequently in address computations.
 169 
 170 public:
 171   PhaseTransform( PhaseNumber pnum );
 172   PhaseTransform( Arena *arena, PhaseNumber pnum );
 173   PhaseTransform( PhaseTransform *phase, PhaseNumber pnum );
 174 
 175   Arena*      arena()   { return _arena; }
 176   Type_Array& types()   { return _types; }
 177   // _nodes is used in varying ways by subclasses, which define local accessors
 178 
 179 public:
 180   // Get a previously recorded type for the node n.
 181   // This type must already have been recorded.
 182   // If you want the type of a very new (untransformed) node,
 183   // you must use type_or_null, and test the result for NULL.
 184   const Type* type(const Node* n) const {
 185     const Type* t = _types.fast_lookup(n->_idx);
 186     assert(t != NULL, "must set before get");
 187     return t;
 188   }
 189   // Get a previously recorded type for the node n,
 190   // or else return NULL if there is none.
 191   const Type* type_or_null(const Node* n) const {
 192     return _types.fast_lookup(n->_idx);
 193   }
 194   // Record a type for a node.
 195   void    set_type(const Node* n, const Type *t) {
 196     assert(t != NULL, "type must not be null");
 197     _types.map(n->_idx, t);
 198   }
 199   // Record an initial type for a node, the node's bottom type.
 200   void    set_type_bottom(const Node* n) {
 201     // Use this for initialization when bottom_type() (or better) is not handy.
 202     // Usually the initialization shoudl be to n->Value(this) instead,
 203     // or a hand-optimized value like Type::MEMORY or Type::CONTROL.
 204     assert(_types[n->_idx] == NULL, "must set the initial type just once");
 205     _types.map(n->_idx, n->bottom_type());
 206   }
 207   // Make sure the types array is big enough to record a size for the node n.
 208   // (In product builds, we never want to do range checks on the types array!)
 209   void ensure_type_or_null(const Node* n) {
 210     if (n->_idx >= _types.Size())
 211       _types.map(n->_idx, NULL);   // Grow the types array as needed.
 212   }
 213 
 214   // Utility functions:
 215   const TypeInt*  find_int_type( Node* n);
 216   const TypeLong* find_long_type(Node* n);
 217   jint  find_int_con( Node* n, jint  value_if_unknown) {
 218     const TypeInt* t = find_int_type(n);
 219     return (t != NULL && t->is_con()) ? t->get_con() : value_if_unknown;
 220   }
 221   jlong find_long_con(Node* n, jlong value_if_unknown) {
 222     const TypeLong* t = find_long_type(n);
 223     return (t != NULL && t->is_con()) ? t->get_con() : value_if_unknown;
 224   }
 225 
 226   // Make an idealized constant, i.e., one of ConINode, ConPNode, ConFNode, etc.
 227   // Same as transform(ConNode::make(t)).
 228   ConNode* makecon(const Type* t);
 229   virtual ConNode* uncached_makecon(const Type* t)  // override in PhaseValues
 230   { ShouldNotCallThis(); return NULL; }
 231 
 232   // Fast int or long constant.  Same as TypeInt::make(i) or TypeLong::make(l).
 233   ConINode* intcon(jint i);
 234   ConLNode* longcon(jlong l);
 235 
 236   // Fast zero or null constant.  Same as makecon(Type::get_zero_type(bt)).
 237   ConNode* zerocon(BasicType bt);
 238 
 239   // Return a node which computes the same function as this node, but
 240   // in a faster or cheaper fashion.
 241   virtual Node *transform( Node *n ) = 0;
 242 
 243   // Return whether two Nodes are equivalent.
 244   // Must not be recursive, since the recursive version is built from this.
 245   // For pessimistic optimizations this is simply pointer equivalence.
 246   bool eqv(const Node* n1, const Node* n2) const { return n1 == n2; }
 247 
 248   // Return whether two Nodes are equivalent, after stripping casting.
 249   bool eqv_uncast(const Node* n1, const Node* n2) const {
 250     return eqv(n1->uncast(), n2->uncast());
 251   }
 252 
 253   // For pessimistic passes, the return type must monotonically narrow.
 254   // For optimistic  passes, the return type must monotonically widen.
 255   // It is possible to get into a "death march" in either type of pass,
 256   // where the types are continually moving but it will take 2**31 or
 257   // more steps to converge.  This doesn't happen on most normal loops.
 258   //
 259   // Here is an example of a deadly loop for an optimistic pass, along
 260   // with a partial trace of inferred types:
 261   //    x = phi(0,x'); L: x' = x+1; if (x' >= 0) goto L;
 262   //    0                 1                join([0..max], 1)
 263   //    [0..1]            [1..2]           join([0..max], [1..2])
 264   //    [0..2]            [1..3]           join([0..max], [1..3])
 265   //      ... ... ...
 266   //    [0..max]          [min]u[1..max]   join([0..max], [min..max])
 267   //    [0..max] ==> fixpoint
 268   // We would have proven, the hard way, that the iteration space is all
 269   // non-negative ints, with the loop terminating due to 32-bit overflow.
 270   //
 271   // Here is the corresponding example for a pessimistic pass:
 272   //    x = phi(0,x'); L: x' = x-1; if (x' >= 0) goto L;
 273   //    int               int              join([0..max], int)
 274   //    [0..max]          [-1..max-1]      join([0..max], [-1..max-1])
 275   //    [0..max-1]        [-1..max-2]      join([0..max], [-1..max-2])
 276   //      ... ... ...
 277   //    [0..1]            [-1..0]          join([0..max], [-1..0])
 278   //    0                 -1               join([0..max], -1)
 279   //    0 == fixpoint
 280   // We would have proven, the hard way, that the iteration space is {0}.
 281   // (Usually, other optimizations will make the "if (x >= 0)" fold up
 282   // before we get into trouble.  But not always.)
 283   //
 284   // It's a pleasant thing to observe that the pessimistic pass
 285   // will make short work of the optimistic pass's deadly loop,
 286   // and vice versa.  That is a good example of the complementary
 287   // purposes of the CCP (optimistic) vs. GVN (pessimistic) phases.
 288   //
 289   // In any case, only widen or narrow a few times before going to the
 290   // correct flavor of top or bottom.
 291   //
 292   // This call only needs to be made once as the data flows around any
 293   // given cycle.  We do it at Phis, and nowhere else.
 294   // The types presented are the new type of a phi (computed by PhiNode::Value)
 295   // and the previously computed type, last time the phi was visited.
 296   //
 297   // The third argument is upper limit for the saturated value,
 298   // if the phase wishes to widen the new_type.
 299   // If the phase is narrowing, the old type provides a lower limit.
 300   // Caller guarantees that old_type and new_type are no higher than limit_type.
 301   virtual const Type* saturate(const Type* new_type, const Type* old_type,
 302                                const Type* limit_type) const
 303   { ShouldNotCallThis(); return NULL; }
 304 
 305 #ifndef PRODUCT
 306   void dump_old2new_map() const;
 307   void dump_new( uint new_lidx ) const;
 308   void dump_types() const;
 309   void dump_nodes_and_types(const Node *root, uint depth, bool only_ctrl = true);
 310   void dump_nodes_and_types_recur( const Node *n, uint depth, bool only_ctrl, VectorSet &visited);
 311 
 312   uint   _count_progress;       // For profiling, count transforms that make progress
 313   void   set_progress()        { ++_count_progress; assert( allow_progress(),"No progress allowed during verification"); }
 314   void   clear_progress()      { _count_progress = 0; }
 315   uint   made_progress() const { return _count_progress; }
 316 
 317   uint   _count_transforms;     // For profiling, count transforms performed
 318   void   set_transforms()      { ++_count_transforms; }
 319   void   clear_transforms()    { _count_transforms = 0; }
 320   uint   made_transforms() const{ return _count_transforms; }
 321 
 322   bool   _allow_progress;      // progress not allowed during verification pass
 323   void   set_allow_progress(bool allow) { _allow_progress = allow; }
 324   bool   allow_progress()               { return _allow_progress; }
 325 #endif
 326 };
 327 
 328 //------------------------------PhaseValues------------------------------------
 329 // Phase infrastructure to support values
 330 class PhaseValues : public PhaseTransform {
 331 protected:
 332   NodeHash  _table;             // Hash table for value-numbering
 333 
 334 public:
 335   PhaseValues( Arena *arena, uint est_max_size );
 336   PhaseValues( PhaseValues *pt );
 337   PhaseValues( PhaseValues *ptv, const char *dummy );
 338   NOT_PRODUCT( ~PhaseValues(); )
 339   virtual PhaseIterGVN *is_IterGVN() { return 0; }
 340 
 341   // Some Ideal and other transforms delete --> modify --> insert values
 342   bool   hash_delete(Node *n)     { return _table.hash_delete(n); }
 343   void   hash_insert(Node *n)     { _table.hash_insert(n); }
 344   Node  *hash_find_insert(Node *n){ return _table.hash_find_insert(n); }
 345   Node  *hash_find(const Node *n) { return _table.hash_find(n); }
 346 
 347   // Used after parsing to eliminate values that are no longer in program
 348   void   remove_useless_nodes(VectorSet &useful) {
 349     _table.remove_useless_nodes(useful);
 350     // this may invalidate cached cons so reset the cache
 351     init_con_caches();
 352   }
 353 
 354   virtual ConNode* uncached_makecon(const Type* t);  // override from PhaseTransform
 355 
 356   virtual const Type* saturate(const Type* new_type, const Type* old_type,
 357                                const Type* limit_type) const
 358   { return new_type; }
 359 
 360 #ifndef PRODUCT
 361   uint   _count_new_values;     // For profiling, count new values produced
 362   void    inc_new_values()        { ++_count_new_values; }
 363   void    clear_new_values()      { _count_new_values = 0; }
 364   uint    made_new_values() const { return _count_new_values; }
 365 #endif
 366 };
 367 
 368 
 369 //------------------------------PhaseGVN---------------------------------------
 370 // Phase for performing local, pessimistic GVN-style optimizations.
 371 class PhaseGVN : public PhaseValues {
 372 public:
 373   PhaseGVN( Arena *arena, uint est_max_size ) : PhaseValues( arena, est_max_size ) {}
 374   PhaseGVN( PhaseGVN *gvn ) : PhaseValues( gvn ) {}
 375   PhaseGVN( PhaseGVN *gvn, const char *dummy ) : PhaseValues( gvn, dummy ) {}
 376 
 377   // Return a node which computes the same function as this node, but
 378   // in a faster or cheaper fashion.
 379   Node  *transform( Node *n );
 380   Node  *transform_no_reclaim( Node *n );
 381 
 382   // Check for a simple dead loop when a data node references itself.
 383   DEBUG_ONLY(void dead_loop_check(Node *n);)
 384 };
 385 
 386 //------------------------------PhaseIterGVN-----------------------------------
 387 // Phase for iteratively performing local, pessimistic GVN-style optimizations.
 388 // and ideal transformations on the graph.
 389 class PhaseIterGVN : public PhaseGVN {
 390  private:
 391   bool _delay_transform;  // When true simply register the node when calling transform
 392                           // instead of actually optimizing it
 393 
 394   // Idealize old Node 'n' with respect to its inputs and its value
 395   virtual Node *transform_old( Node *a_node );
 396 
 397   // Subsume users of node 'old' into node 'nn'
 398   void subsume_node( Node *old, Node *nn );
 399 
 400 protected:
 401 
 402   // Idealize new Node 'n' with respect to its inputs and its value
 403   virtual Node *transform( Node *a_node );
 404 
 405   // Warm up hash table, type table and initial worklist
 406   void init_worklist( Node *a_root );
 407 
 408   virtual const Type* saturate(const Type* new_type, const Type* old_type,
 409                                const Type* limit_type) const;
 410   // Usually returns new_type.  Returns old_type if new_type is only a slight
 411   // improvement, such that it would take many (>>10) steps to reach 2**32.
 412 
 413 public:
 414   PhaseIterGVN( PhaseIterGVN *igvn ); // Used by CCP constructor
 415   PhaseIterGVN( PhaseGVN *gvn ); // Used after Parser
 416   PhaseIterGVN( PhaseIterGVN *igvn, const char *dummy ); // Used after +VerifyOpto
 417 
 418   virtual PhaseIterGVN *is_IterGVN() { return this; }
 419 
 420   Unique_Node_List _worklist;       // Iterative worklist
 421 
 422   // Given def-use info and an initial worklist, apply Node::Ideal,
 423   // Node::Value, Node::Identity, hash-based value numbering, Node::Ideal_DU
 424   // and dominator info to a fixed point.
 425   void optimize();
 426 
 427   // Register a new node with the iter GVN pass without transforming it.
 428   // Used when we need to restructure a Region/Phi area and all the Regions
 429   // and Phis need to complete this one big transform before any other
 430   // transforms can be triggered on the region.
 431   // Optional 'orig' is an earlier version of this node.
 432   // It is significant only for debugging and profiling.
 433   Node* register_new_node_with_optimizer(Node* n, Node* orig = NULL);
 434 
 435   // Kill a globally dead Node.   It is allowed to have uses which are
 436   // assumed dead and left 'in limbo'.
 437   void remove_globally_dead_node( Node *dead );
 438 
 439   // Kill all inputs to a dead node, recursively making more dead nodes.
 440   // The Node must be dead locally, i.e., have no uses.
 441   void remove_dead_node( Node *dead ) {
 442     assert(dead->outcnt() == 0 && !dead->is_top(), "node must be dead");
 443     remove_globally_dead_node(dead);
 444   }
 445 
 446   // Add users of 'n' to worklist
 447   void add_users_to_worklist0( Node *n );
 448   void add_users_to_worklist ( Node *n );
 449 
 450   // Replace old node with new one.
 451   void replace_node( Node *old, Node *nn ) {
 452     add_users_to_worklist(old);
 453     hash_delete(old); // Yank from hash before hacking edges
 454     subsume_node(old, nn);
 455   }
 456 
 457   bool delay_transform() const { return _delay_transform; }
 458 
 459   void set_delay_transform(bool delay) {
 460     _delay_transform = delay;
 461   }
 462 
 463 #ifndef PRODUCT
 464 protected:
 465   // Sub-quadratic implementation of VerifyIterativeGVN.
 466   unsigned long _verify_counter;
 467   unsigned long _verify_full_passes;
 468   enum { _verify_window_size = 30 };
 469   Node* _verify_window[_verify_window_size];
 470   void verify_step(Node* n);
 471 #endif
 472 };
 473 
 474 //------------------------------PhaseCCP---------------------------------------
 475 // Phase for performing global Conditional Constant Propagation.
 476 // Should be replaced with combined CCP & GVN someday.
 477 class PhaseCCP : public PhaseIterGVN {
 478   // Non-recursive.  Use analysis to transform single Node.
 479   virtual Node *transform_once( Node *n );
 480 
 481 public:
 482   PhaseCCP( PhaseIterGVN *igvn ); // Compute conditional constants
 483   NOT_PRODUCT( ~PhaseCCP(); )
 484 
 485   // Worklist algorithm identifies constants
 486   void analyze();
 487   // Recursive traversal of program.  Used analysis to modify program.
 488   virtual Node *transform( Node *n );
 489   // Do any transformation after analysis
 490   void          do_transform();
 491 
 492   virtual const Type* saturate(const Type* new_type, const Type* old_type,
 493                                const Type* limit_type) const;
 494   // Returns new_type->widen(old_type), which increments the widen bits until
 495   // giving up with TypeInt::INT or TypeLong::LONG.
 496   // Result is clipped to limit_type if necessary.
 497 
 498 #ifndef PRODUCT
 499   static uint _total_invokes;    // For profiling, count invocations
 500   void    inc_invokes()          { ++PhaseCCP::_total_invokes; }
 501 
 502   static uint _total_constants;  // For profiling, count constants found
 503   uint   _count_constants;
 504   void    clear_constants()      { _count_constants = 0; }
 505   void    inc_constants()        { ++_count_constants; }
 506   uint    count_constants() const { return _count_constants; }
 507 
 508   static void print_statistics();
 509 #endif
 510 };
 511 
 512 
 513 //------------------------------PhasePeephole----------------------------------
 514 // Phase for performing peephole optimizations on register allocated basic blocks.
 515 class PhasePeephole : public PhaseTransform {
 516   PhaseRegAlloc *_regalloc;
 517   PhaseCFG     &_cfg;
 518   // Recursive traversal of program.  Pure function is unused in this phase
 519   virtual Node *transform( Node *n );
 520 
 521 public:
 522   PhasePeephole( PhaseRegAlloc *regalloc, PhaseCFG &cfg );
 523   NOT_PRODUCT( ~PhasePeephole(); )
 524 
 525   // Do any transformation after analysis
 526   void          do_transform();
 527 
 528 #ifndef PRODUCT
 529   static uint _total_peepholes;  // For profiling, count peephole rules applied
 530   uint   _count_peepholes;
 531   void    clear_peepholes()      { _count_peepholes = 0; }
 532   void    inc_peepholes()        { ++_count_peepholes; }
 533   uint    count_peepholes() const { return _count_peepholes; }
 534 
 535   static void print_statistics();
 536 #endif
 537 };