view src/hotspot/share/opto/superword.hpp @ 52592:1ecc914fb707

8210829: Modularize allocations in C2 Reviewed-by: kvn, roland
author rkennke
date Wed, 19 Sep 2018 21:31:33 +0200
parents c035fbb1beb4
children 4bb6e0871bf7
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 * Copyright (c) 2007, 2018, Oracle and/or its affiliates. All rights reserved.
 * This code is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.
 * This code is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
 * version 2 for more details (a copy is included in the LICENSE file that
 * accompanied this code).
 * You should have received a copy of the GNU General Public License version
 * 2 along with this work; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
 * or visit if you need additional information or have any
 * questions.


#include "opto/loopnode.hpp"
#include "opto/node.hpp"
#include "opto/phaseX.hpp"
#include "opto/vectornode.hpp"
#include "utilities/growableArray.hpp"
#include "libadt/dict.hpp"

//                  S U P E R W O R D   T R A N S F O R M
// SuperWords are short, fixed length vectors.
// Algorithm from:
// Exploiting SuperWord Level Parallelism with
//   Multimedia Instruction Sets
// by
//   Samuel Larsen and Saman Amarasinghe
//   MIT Laboratory for Computer Science
// date
//   May 2000
// published in
//   ACM SIGPLAN Notices
//   Proceedings of ACM PLDI '00,  Volume 35 Issue 5
// Definition 3.1 A Pack is an n-tuple, <s1, ...,sn>, where
// s1,...,sn are independent isomorphic statements in a basic
// block.
// Definition 3.2 A PackSet is a set of Packs.
// Definition 3.3 A Pair is a Pack of size two, where the
// first statement is considered the left element, and the
// second statement is considered the right element.

class SWPointer;
class OrderedPair;

// ========================= Dependence Graph =====================

class DepMem;

// An edge in the dependence graph.  The edges incident to a dependence
// node are threaded through _next_in for incoming edges and _next_out
// for outgoing edges.
class DepEdge : public ResourceObj {
  DepMem* _pred;
  DepMem* _succ;
  DepEdge* _next_in;   // list of in edges, null terminated
  DepEdge* _next_out;  // list of out edges, null terminated

  DepEdge(DepMem* pred, DepMem* succ, DepEdge* next_in, DepEdge* next_out) :
    _pred(pred), _succ(succ), _next_in(next_in), _next_out(next_out) {}

  DepEdge* next_in()  { return _next_in; }
  DepEdge* next_out() { return _next_out; }
  DepMem*  pred()     { return _pred; }
  DepMem*  succ()     { return _succ; }

  void print();

// A node in the dependence graph.  _in_head starts the threaded list of
// incoming edges, and _out_head starts the list of outgoing edges.
class DepMem : public ResourceObj {
  Node*    _node;     // Corresponding ideal node
  DepEdge* _in_head;  // Head of list of in edges, null terminated
  DepEdge* _out_head; // Head of list of out edges, null terminated

  DepMem(Node* node) : _node(node), _in_head(NULL), _out_head(NULL) {}

  Node*    node()                { return _node;     }
  DepEdge* in_head()             { return _in_head;  }
  DepEdge* out_head()            { return _out_head; }
  void set_in_head(DepEdge* hd)  { _in_head = hd;    }
  void set_out_head(DepEdge* hd) { _out_head = hd;   }

  int in_cnt();  // Incoming edge count
  int out_cnt(); // Outgoing edge count

  void print();

class DepGraph {
  Arena* _arena;
  GrowableArray<DepMem*> _map;
  DepMem* _root;
  DepMem* _tail;

  DepGraph(Arena* a) : _arena(a), _map(a, 8,  0, NULL) {
    _root = new (_arena) DepMem(NULL);
    _tail = new (_arena) DepMem(NULL);

  DepMem* root() { return _root; }
  DepMem* tail() { return _tail; }

  // Return dependence node corresponding to an ideal node
  DepMem* dep(Node* node) { return>_idx); }

  // Make a new dependence graph node for an ideal node.
  DepMem* make_node(Node* node);

  // Make a new dependence graph edge dprec->dsucc
  DepEdge* make_edge(DepMem* dpred, DepMem* dsucc);

  DepEdge* make_edge(Node* pred,   Node* succ)   { return make_edge(dep(pred), dep(succ)); }
  DepEdge* make_edge(DepMem* pred, Node* succ)   { return make_edge(pred,      dep(succ)); }
  DepEdge* make_edge(Node* pred,   DepMem* succ) { return make_edge(dep(pred), succ);      }

  void init() { _map.clear(); } // initialize

  void print(Node* n)   { dep(n)->print(); }
  void print(DepMem* d) { d->print(); }

// Iterator over predecessors in the dependence graph and
// non-memory-graph inputs of ideal nodes.
class DepPreds : public StackObj {
  Node*    _n;
  int      _next_idx, _end_idx;
  DepEdge* _dep_next;
  Node*    _current;
  bool     _done;

  DepPreds(Node* n, DepGraph& dg);
  Node* current() { return _current; }
  bool  done()    { return _done; }
  void  next();

// Iterator over successors in the dependence graph and
// non-memory-graph outputs of ideal nodes.
class DepSuccs : public StackObj {
  Node*    _n;
  int      _next_idx, _end_idx;
  DepEdge* _dep_next;
  Node*    _current;
  bool     _done;

  DepSuccs(Node* n, DepGraph& dg);
  Node* current() { return _current; }
  bool  done()    { return _done; }
  void  next();

// ========================= SuperWord =====================

// -----------------------------SWNodeInfo---------------------------------
// Per node info needed by SuperWord
class SWNodeInfo {
  int         _alignment; // memory alignment for a node
  int         _depth;     // Max expression (DAG) depth from block start
  const Type* _velt_type; // vector element type
  Node_List*  _my_pack;   // pack containing this node

  SWNodeInfo() : _alignment(-1), _depth(0), _velt_type(NULL), _my_pack(NULL) {}
  static const SWNodeInfo initial;

class SuperWord;
class CMoveKit {
 friend class SuperWord;
  SuperWord* _sw;
  Dict* _dict;
  CMoveKit(Arena* a, SuperWord* sw) : _sw(sw)  {_dict = new Dict(cmpkey, hashkey, a);}
  void*     _2p(Node* key)        const  { return (void*)(intptr_t)key; } // 2 conversion functions to make gcc happy
  Dict*     dict()                const  { return _dict; }
  void map(Node* key, Node_List* val)    { assert(_dict->operator[](_2p(key)) == NULL, "key existed"); _dict->Insert(_2p(key), (void*)val); }
  void unmap(Node* key)                  { _dict->Delete(_2p(key)); }
  Node_List* pack(Node* key)      const  { return (Node_List*)_dict->operator[](_2p(key)); }
  Node* is_Bool_candidate(Node* nd) const; // if it is the right candidate return corresponding CMove* ,
  Node* is_CmpD_candidate(Node* nd) const; // otherwise return NULL
  Node_List* make_cmovevd_pack(Node_List* cmovd_pk);
  bool test_cmpd_pack(Node_List* cmpd_pk, Node_List* cmovd_pk);
};//class CMoveKit

// JVMCI: OrderedPair is moved up to deal with compilation issues on Windows
// Ordered pair of Node*.
class OrderedPair {
  Node* _p1;
  Node* _p2;
  OrderedPair() : _p1(NULL), _p2(NULL) {}
  OrderedPair(Node* p1, Node* p2) {
    if (p1->_idx < p2->_idx) {
      _p1 = p1; _p2 = p2;
    } else {
      _p1 = p2; _p2 = p1;

  bool operator==(const OrderedPair &rhs) {
    return _p1 == rhs._p1 && _p2 == rhs._p2;
  void print() { tty->print("  (%d, %d)", _p1->_idx, _p2->_idx); }

  static const OrderedPair initial;

// -----------------------------SuperWord---------------------------------
// Transforms scalar operations into packed (superword) operations.
class SuperWord : public ResourceObj {
 friend class SWPointer;
 friend class CMoveKit;
  PhaseIdealLoop* _phase;
  Arena*          _arena;
  PhaseIterGVN   &_igvn;

  enum consts { top_align = -1, bottom_align = -666 };

  GrowableArray<Node_List*> _packset;    // Packs for the current block

  GrowableArray<int> _bb_idx;            // Map from Node _idx to index within block

  GrowableArray<Node*> _block;           // Nodes in current block
  GrowableArray<Node*> _post_block;      // Nodes in post loop block
  GrowableArray<Node*> _data_entry;      // Nodes with all inputs from outside
  GrowableArray<Node*> _mem_slice_head;  // Memory slice head nodes
  GrowableArray<Node*> _mem_slice_tail;  // Memory slice tail nodes
  GrowableArray<Node*> _iteration_first; // nodes in the generation that has deps from phi
  GrowableArray<Node*> _iteration_last;  // nodes in the generation that has deps to   phi
  GrowableArray<SWNodeInfo> _node_info;  // Info needed per node
  CloneMap&            _clone_map;       // map of nodes created in cloning
  CMoveKit             _cmovev_kit;      // support for vectorization of CMov
  MemNode* _align_to_ref;                // Memory reference that pre-loop will align to

  GrowableArray<OrderedPair> _disjoint_ptrs; // runtime disambiguated pointer pairs

  DepGraph _dg; // Dependence graph

  // Scratch pads
  VectorSet    _visited;       // Visited set
  VectorSet    _post_visited;  // Post-visited set
  Node_Stack   _n_idx_list;    // List of (node,index) pairs
  GrowableArray<Node*> _nlist; // List of nodes
  GrowableArray<Node*> _stk;   // Stack of nodes

  SuperWord(PhaseIdealLoop* phase);

  void transform_loop(IdealLoopTree* lpt, bool do_optimization);

  void unrolling_analysis(int &local_loop_unroll_factor);

  // Accessors for SWPointer
  PhaseIdealLoop* phase()          { return _phase; }
  IdealLoopTree* lpt()             { return _lpt; }
  PhiNode* iv()                    { return _iv; }

  bool early_return()              { return _early_return; }

#ifndef PRODUCT
  bool     is_debug()              { return _vector_loop_debug > 0; }
  bool     is_trace_alignment()    { return (_vector_loop_debug & 2) > 0; }
  bool     is_trace_mem_slice()    { return (_vector_loop_debug & 4) > 0; }
  bool     is_trace_loop()         { return (_vector_loop_debug & 8) > 0; }
  bool     is_trace_adjacent()     { return (_vector_loop_debug & 16) > 0; }
  bool     is_trace_cmov()         { return (_vector_loop_debug & 32) > 0; }
  bool     is_trace_loop_reverse() { return (_vector_loop_debug & 64) > 0; }
  bool     do_vector_loop()        { return _do_vector_loop; }
  bool     do_reserve_copy()       { return _do_reserve_copy; }
  IdealLoopTree* _lpt;             // Current loop tree node
  LoopNode*      _lp;              // Current LoopNode
  Node*          _bb;              // Current basic block
  PhiNode*       _iv;              // Induction var
  bool           _race_possible;   // In cases where SDMU is true
  bool           _early_return;    // True if we do not initialize
  bool           _do_vector_loop;  // whether to do vectorization/simd style
  bool           _do_reserve_copy; // do reserve copy of the graph(loop) before final modification in output
  int            _num_work_vecs;   // Number of non memory vector operations
  int            _num_reductions;  // Number of reduction expressions applied
  int            _ii_first;        // generation with direct deps from mem phi
  int            _ii_last;         // generation with direct deps to   mem phi
  GrowableArray<int> _ii_order;
#ifndef PRODUCT
  uintx          _vector_loop_debug; // provide more printing in debug mode

  // Accessors
  Arena* arena()                   { return _arena; }

  Node* bb()                       { return _bb; }
  void  set_bb(Node* bb)           { _bb = bb; }

  void set_lpt(IdealLoopTree* lpt) { _lpt = lpt; }

  LoopNode* lp()                   { return _lp; }
  void      set_lp(LoopNode* lp)   { _lp = lp;
                                     _iv = lp->as_CountedLoop()->phi()->as_Phi(); }
  int      iv_stride()             { return lp()->as_CountedLoop()->stride_con(); }

  int vector_width(Node* n) {
    BasicType bt = velt_basic_type(n);
    return MIN2(ABS(iv_stride()), Matcher::max_vector_size(bt));
  int vector_width_in_bytes(Node* n) {
    BasicType bt = velt_basic_type(n);
    return vector_width(n)*type2aelembytes(bt);
  MemNode* align_to_ref()            { return _align_to_ref; }
  void  set_align_to_ref(MemNode* m) { _align_to_ref = m; }

  Node* ctrl(Node* n) const { return _phase->has_ctrl(n) ? _phase->get_ctrl(n) : n; }

  // block accessors
  bool in_bb(Node* n)      { return n != NULL && n->outcnt() > 0 && ctrl(n) == _bb; }
  int  bb_idx(Node* n)     { assert(in_bb(n), "must be"); return>_idx); }
  void set_bb_idx(Node* n, int i) { _bb_idx.at_put_grow(n->_idx, i); }

  // visited set accessors
  void visited_clear()           { _visited.Clear(); }
  void visited_set(Node* n)      { return _visited.set(bb_idx(n)); }
  int visited_test(Node* n)      { return _visited.test(bb_idx(n)); }
  int visited_test_set(Node* n)  { return _visited.test_set(bb_idx(n)); }
  void post_visited_clear()      { _post_visited.Clear(); }
  void post_visited_set(Node* n) { return _post_visited.set(bb_idx(n)); }
  int post_visited_test(Node* n) { return _post_visited.test(bb_idx(n)); }

  // Ensure node_info contains element "i"
  void grow_node_info(int i) { if (i >= _node_info.length()) _node_info.at_put_grow(i, SWNodeInfo::initial); }

  // memory alignment for a node
  int alignment(Node* n)                     { return _node_info.adr_at(bb_idx(n))->_alignment; }
  void set_alignment(Node* n, int a)         { int i = bb_idx(n); grow_node_info(i); _node_info.adr_at(i)->_alignment = a; }

  // Max expression (DAG) depth from beginning of the block for each node
  int depth(Node* n)                         { return _node_info.adr_at(bb_idx(n))->_depth; }
  void set_depth(Node* n, int d)             { int i = bb_idx(n); grow_node_info(i); _node_info.adr_at(i)->_depth = d; }

  // vector element type
  const Type* velt_type(Node* n)             { return _node_info.adr_at(bb_idx(n))->_velt_type; }
  BasicType velt_basic_type(Node* n)         { return velt_type(n)->array_element_basic_type(); }
  void set_velt_type(Node* n, const Type* t) { int i = bb_idx(n); grow_node_info(i); _node_info.adr_at(i)->_velt_type = t; }
  bool same_velt_type(Node* n1, Node* n2);

  // my_pack
  Node_List* my_pack(Node* n)                 { return !in_bb(n) ? NULL : _node_info.adr_at(bb_idx(n))->_my_pack; }
  void set_my_pack(Node* n, Node_List* p)     { int i = bb_idx(n); grow_node_info(i); _node_info.adr_at(i)->_my_pack = p; }
  // is pack good for converting into one vector node replacing 12 nodes of Cmp, Bool, CMov
  bool is_cmov_pack(Node_List* p);
  bool is_cmov_pack_internal_node(Node_List* p, Node* nd) { return is_cmov_pack(p) && !nd->is_CMove(); }
  // For pack p, are all idx operands the same?
  bool same_inputs(Node_List* p, int idx);
  // CloneMap utilities
  bool same_origin_idx(Node* a, Node* b) const;
  bool same_generation(Node* a, Node* b) const;

  // methods

  // Extract the superword level parallelism
  void SLP_extract();
  // Find the adjacent memory references and create pack pairs for them.
  void find_adjacent_refs();
  // Tracing support
  #ifndef PRODUCT
  void find_adjacent_refs_trace_1(Node* best_align_to_mem_ref, int best_iv_adjustment);
  void print_loop(bool whole);
  // Find a memory reference to align the loop induction variable to.
  MemNode* find_align_to_ref(Node_List &memops);
  // Calculate loop's iv adjustment for this memory ops.
  int get_iv_adjustment(MemNode* mem);
  // Can the preloop align the reference to position zero in the vector?
  bool ref_is_alignable(SWPointer& p);
  // rebuild the graph so all loads in different iterations of cloned loop become dependant on phi node (in _do_vector_loop only)
  bool hoist_loads_in_graph();
  // Test whether MemNode::Memory dependency to the same load but in the first iteration of this loop is coming from memory phi
  // Return false if failed
  Node* find_phi_for_mem_dep(LoadNode* ld);
  // Return same node but from the first generation. Return 0, if not found
  Node* first_node(Node* nd);
  // Return same node as this but from the last generation. Return 0, if not found
  Node* last_node(Node* n);
  // Mark nodes belonging to first and last generation
  // returns first generation index or -1 if vectorization/simd is impossible
  int mark_generations();
  // swapping inputs of commutative instruction (Add or Mul)
  bool fix_commutative_inputs(Node* gold, Node* fix);
  // make packs forcefully (in _do_vector_loop only)
  bool pack_parallel();
  // Construct dependency graph.
  void dependence_graph();
  // Return a memory slice (node list) in predecessor order starting at "start"
  void mem_slice_preds(Node* start, Node* stop, GrowableArray<Node*> &preds);
  // Can s1 and s2 be in a pack with s1 immediately preceding s2 and  s1 aligned at "align"
  bool stmts_can_pack(Node* s1, Node* s2, int align);
  // Does s exist in a pack at position pos?
  bool exists_at(Node* s, uint pos);
  // Is s1 immediately before s2 in memory?
  bool are_adjacent_refs(Node* s1, Node* s2);
  // Are s1 and s2 similar?
  bool isomorphic(Node* s1, Node* s2);
  // Is there no data path from s1 to s2 or s2 to s1?
  bool independent(Node* s1, Node* s2);
  // For a node pair (s1, s2) which is isomorphic and independent,
  // do s1 and s2 have similar input edges?
  bool have_similar_inputs(Node* s1, Node* s2);
  // Is there a data path between s1 and s2 and both are reductions?
  bool reduction(Node* s1, Node* s2);
  // Helper for independent
  bool independent_path(Node* shallow, Node* deep, uint dp=0);
  void set_alignment(Node* s1, Node* s2, int align);
  int data_size(Node* s);
  // Extend packset by following use->def and def->use links from pack members.
  void extend_packlist();
  // Extend the packset by visiting operand definitions of nodes in pack p
  bool follow_use_defs(Node_List* p);
  // Extend the packset by visiting uses of nodes in pack p
  bool follow_def_uses(Node_List* p);
  // For extended packsets, ordinally arrange uses packset by major component
  void order_def_uses(Node_List* p);
  // Estimate the savings from executing s1 and s2 as a pack
  int est_savings(Node* s1, Node* s2);
  int adjacent_profit(Node* s1, Node* s2);
  int pack_cost(int ct);
  int unpack_cost(int ct);
  // Combine packs A and B with A.last == B.first into A.first..,A.last,B.second,..B.last
  void combine_packs();
  // Construct the map from nodes to packs.
  void construct_my_pack_map();
  // Remove packs that are not implemented or not profitable.
  void filter_packs();
  // Merge CMoveD into new vector-nodes
  void merge_packs_to_cmovd();
  // Adjust the memory graph for the packed operations
  void schedule();
  // Remove "current" from its current position in the memory graph and insert
  // it after the appropriate insert points (lip or uip);
  void remove_and_insert(MemNode *current, MemNode *prev, MemNode *lip, Node *uip, Unique_Node_List &schd_before);
  // Within a store pack, schedule stores together by moving out the sandwiched memory ops according
  // to dependence info; and within a load pack, move loads down to the last executed load.
  void co_locate_pack(Node_List* p);
  // Convert packs into vector node operations
  void output();
  // Create a vector operand for the nodes in pack p for operand: in(opd_idx)
  Node* vector_opd(Node_List* p, int opd_idx);
  // Can code be generated for pack p?
  bool implemented(Node_List* p);
  // For pack p, are all operands and all uses (with in the block) vector?
  bool profitable(Node_List* p);
  // If a use of pack p is not a vector use, then replace the use with an extract operation.
  void insert_extracts(Node_List* p);
  // Is use->in(u_idx) a vector use?
  bool is_vector_use(Node* use, int u_idx);
  // Construct reverse postorder list of block members
  bool construct_bb();
  // Initialize per node info
  void initialize_bb();
  // Insert n into block after pos
  void bb_insert_after(Node* n, int pos);
  // Compute max depth for expressions from beginning of block
  void compute_max_depth();
  // Compute necessary vector element type for expressions
  void compute_vector_element_type();
  // Are s1 and s2 in a pack pair and ordered as s1,s2?
  bool in_packset(Node* s1, Node* s2);
  // Is s in pack p?
  Node_List* in_pack(Node* s, Node_List* p);
  // Remove the pack at position pos in the packset
  void remove_pack_at(int pos);
  // Return the node executed first in pack p.
  Node* executed_first(Node_List* p);
  // Return the node executed last in pack p.
  Node* executed_last(Node_List* p);
  static LoadNode::ControlDependency control_dependency(Node_List* p);
  // Alignment within a vector memory reference
  int memory_alignment(MemNode* s, int iv_adjust);
  // (Start, end] half-open range defining which operands are vector
  void vector_opd_range(Node* n, uint* start, uint* end);
  // Smallest type containing range of values
  const Type* container_type(Node* n);
  // Adjust pre-loop limit so that in main loop, a load/store reference
  // to align_to_ref will be a position zero in the vector.
  void align_initial_loop_index(MemNode* align_to_ref);
  // Find pre loop end from main loop.  Returns null if none.
  CountedLoopEndNode* get_pre_loop_end(CountedLoopNode *cl);
  // Is the use of d1 in u1 at the same operand position as d2 in u2?
  bool opnd_positions_match(Node* d1, Node* u1, Node* d2, Node* u2);
  void init();
  // clean up some basic structures - used if the ideal graph was rebuilt
  void restart();

  // print methods
  void print_packset();
  void print_pack(Node_List* p);
  void print_bb();
  void print_stmt(Node* s);
  char* blank(uint depth);

  void packset_sort(int n);

// Information about an address for dependence checking and vector alignment
class SWPointer {
  MemNode*   _mem;           // My memory reference node
  SuperWord* _slp;           // SuperWord class

  Node* _base;               // NULL if unsafe nonheap reference
  Node* _adr;                // address pointer
  jint  _scale;              // multiplier for iv (in bytes), 0 if no loop iv
  jint  _offset;             // constant offset (in bytes)
  Node* _invar;              // invariant offset (in bytes), NULL if none
  bool  _negate_invar;       // if true then use: (0 - _invar)
  Node_Stack* _nstack;       // stack used to record a swpointer trace of variants
  bool        _analyze_only; // Used in loop unrolling only for swpointer trace
  uint        _stack_idx;    // Used in loop unrolling only for swpointer trace

  PhaseIdealLoop* phase() { return _slp->phase(); }
  IdealLoopTree*  lpt()   { return _slp->lpt(); }
  PhiNode*        iv()    { return _slp->iv();  } // Induction var

  bool invariant(Node* n);

  // Match: k*iv + offset
  bool scaled_iv_plus_offset(Node* n);
  // Match: k*iv where k is a constant that's not zero
  bool scaled_iv(Node* n);
  // Match: offset is (k [+/- invariant])
  bool offset_plus_k(Node* n, bool negate = false);

  enum CMP {
    Less          = 1,
    Greater       = 2,
    Equal         = 4,
    NotEqual      = (Less | Greater),
    NotComparable = (Less | Greater | Equal)

  SWPointer(MemNode* mem, SuperWord* slp, Node_Stack *nstack, bool analyze_only);
  // Following is used to create a temporary object during
  // the pattern match of an address expression.
  SWPointer(SWPointer* p);

  bool valid()  { return _adr != NULL; }
  bool has_iv() { return _scale != 0; }

  Node* base()             { return _base; }
  Node* adr()              { return _adr; }
  MemNode* mem()           { return _mem; }
  int   scale_in_bytes()   { return _scale; }
  Node* invar()            { return _invar; }
  bool  negate_invar()     { return _negate_invar; }
  int   offset_in_bytes()  { return _offset; }
  int   memory_size()      { return _mem->memory_size(); }
  Node_Stack* node_stack() { return _nstack; }

  // Comparable?
  int cmp(SWPointer& q) {
    if (valid() && q.valid() &&
        (_adr == q._adr || (_base == _adr && q._base == q._adr)) &&
        _scale == q._scale   &&
        _invar == q._invar   &&
        _negate_invar == q._negate_invar) {
      bool overlap = q._offset <   _offset +   memory_size() &&
                       _offset < q._offset + q.memory_size();
      return overlap ? Equal : (_offset < q._offset ? Less : Greater);
    } else {
      return NotComparable;

  bool not_equal(SWPointer& q)    { return not_equal(cmp(q)); }
  bool equal(SWPointer& q)        { return equal(cmp(q)); }
  bool comparable(SWPointer& q)   { return comparable(cmp(q)); }
  static bool not_equal(int cmp)  { return cmp <= NotEqual; }
  static bool equal(int cmp)      { return cmp == Equal; }
  static bool comparable(int cmp) { return cmp < NotComparable; }

  void print();

#ifndef PRODUCT
  class Tracer {
    friend class SuperWord;
    friend class SWPointer;
    SuperWord*   _slp;
    static int   _depth;
    int _depth_save;
    void print_depth();
    int  depth() const    { return _depth; }
    void set_depth(int d) { _depth = d; }
    void inc_depth()      { _depth++;}
    void dec_depth()      { if (_depth > 0) _depth--;}
    void store_depth()    {_depth_save = _depth;}
    void restore_depth()  {_depth = _depth_save;}

    class Depth {
      friend class Tracer;
      friend class SWPointer;
      friend class SuperWord;
      Depth()  { ++_depth; }
      Depth(int x)  { _depth = 0; }
      ~Depth() { if (_depth > 0) --_depth;}
    Tracer (SuperWord* slp) : _slp(slp) {}

    // tracing functions
    void ctor_1(Node* mem);
    void ctor_2(Node* adr);
    void ctor_3(Node* adr, int i);
    void ctor_4(Node* adr, int i);
    void ctor_5(Node* adr, Node* base,  int i);
    void ctor_6(Node* mem);

    void invariant_1(Node *n, Node *n_c);

    void scaled_iv_plus_offset_1(Node* n);
    void scaled_iv_plus_offset_2(Node* n);
    void scaled_iv_plus_offset_3(Node* n);
    void scaled_iv_plus_offset_4(Node* n);
    void scaled_iv_plus_offset_5(Node* n);
    void scaled_iv_plus_offset_6(Node* n);
    void scaled_iv_plus_offset_7(Node* n);
    void scaled_iv_plus_offset_8(Node* n);

    void scaled_iv_1(Node* n);
    void scaled_iv_2(Node* n, int scale);
    void scaled_iv_3(Node* n, int scale);
    void scaled_iv_4(Node* n, int scale);
    void scaled_iv_5(Node* n, int scale);
    void scaled_iv_6(Node* n, int scale);
    void scaled_iv_7(Node* n);
    void scaled_iv_8(Node* n, SWPointer* tmp);
    void scaled_iv_9(Node* n, int _scale, int _offset, int mult);
    void scaled_iv_10(Node* n);

    void offset_plus_k_1(Node* n);
    void offset_plus_k_2(Node* n, int _offset);
    void offset_plus_k_3(Node* n, int _offset);
    void offset_plus_k_4(Node* n);
    void offset_plus_k_5(Node* n, Node* _invar);
    void offset_plus_k_6(Node* n, Node* _invar, bool _negate_invar, int _offset);
    void offset_plus_k_7(Node* n, Node* _invar, bool _negate_invar, int _offset);
    void offset_plus_k_8(Node* n, Node* _invar, bool _negate_invar, int _offset);
    void offset_plus_k_9(Node* n, Node* _invar, bool _negate_invar, int _offset);
    void offset_plus_k_10(Node* n, Node* _invar, bool _negate_invar, int _offset);
    void offset_plus_k_11(Node* n);

  } _tracer;//TRacer;