Moved most modules into lib

1 files changed, 1859 insertions, 0 deletions

diff --git a/src/loop.cc b/src/loop.cc
new file mode 100644
index 0000000..f187a50
--- /dev/null
+++ b/src/loop.cc
@@ -0,0 +1,1859 @@
+/*****************************************************************************
+ Copyright (C) 2008 University of Southern California
+ Copyright (C) 2009-2010 University of Utah
+ All Rights Reserved.
+
+ Purpose:
+ Core loop transformation functionality.
+
+ Notes:
+ "level" (starting from 1) means loop level and it corresponds to "dim"
+ (starting from 0) in transformed iteration space [c_1,l_1,c_2,l_2,....,
+ c_n,l_n,c_(n+1)], e.g., l_2 is loop level 2 in generated code, dim 3
+ in transformed iteration space, and variable 4 in Omega relation.
+ All c's are constant numbers only and they will not show up as actual loops.
+ Formula:
+ dim = 2*level - 1
+ var = dim + 1
+
+ History:
+ 10/2005 Created by Chun Chen.
+ 09/2009 Expand tile functionality, -chun
+ 10/2009 Initialize unfusible loop nest without bailing out, -chun
+*****************************************************************************/
+
+#include <limits.h>
+#include <math.h>
+#include <code_gen/codegen.h>
+#include <code_gen/CG_utils.h>
+#include <iostream>
+#include <algorithm>
+#include <map>
+#include "loop.hh"
+#include "omegatools.hh"
+#include "irtools.hh"
+#include "chill_error.hh"
+#include <string.h>
+#include <list>
+using namespace omega;
+
+const std::string Loop::tmp_loop_var_name_prefix = std::string("chill_t"); // Manu:: In fortran, first character of a variable name must be a letter, so this change
+const std::string Loop::overflow_var_name_prefix = std::string("over");
+
+//-----------------------------------------------------------------------------
+// Class Loop
+//-----------------------------------------------------------------------------
+// --begin Anand: Added from CHiLL 0.2
+
+bool Loop::isInitialized() const {
+  return stmt.size() != 0 && !stmt[0].xform.is_null();
+}
+
+//--end Anand: added from CHiLL 0.2
+
+bool Loop::init_loop(std::vector<ir_tree_node *> &ir_tree,
+                     std::vector<ir_tree_node *> &ir_stmt) {
+
+  ir_stmt = extract_ir_stmts(ir_tree);
+  stmt_nesting_level_.resize(ir_stmt.size());
+  std::vector<int> stmt_nesting_level(ir_stmt.size());
+  for (int i = 0; i < ir_stmt.size(); i++) {
+    ir_stmt[i]->payload = i;
+    int t = 0;
+    ir_tree_node *itn = ir_stmt[i];
+    while (itn->parent != NULL) {
+      itn = itn->parent;
+      if (itn->content->type() == IR_CONTROL_LOOP)
+        t++;
+    }
+    stmt_nesting_level_[i] = t;
+    stmt_nesting_level[i] = t;
+  }
+  
+  stmt = std::vector<Statement>(ir_stmt.size());
+  int n_dim = -1;
+  int max_loc;
+  //std::vector<std::string> index;
+  for (int i = 0; i < ir_stmt.size(); i++) {
+    int max_nesting_level = -1;
+    int loc;
+    for (int j = 0; j < ir_stmt.size(); j++)
+      if (stmt_nesting_level[j] > max_nesting_level) {
+        max_nesting_level = stmt_nesting_level[j];
+        loc = j;
+      }
+    
+    // most deeply nested statement acting as a reference point
+    if (n_dim == -1) {
+      n_dim = max_nesting_level;
+      max_loc = loc;
+      
+      index = std::vector<std::string>(n_dim);
+      
+      ir_tree_node *itn = ir_stmt[loc];
+      int cur_dim = n_dim - 1;
+      while (itn->parent != NULL) {
+        itn = itn->parent;
+        if (itn->content->type() == IR_CONTROL_LOOP) {
+          index[cur_dim] =
+            static_cast<IR_Loop *>(itn->content)->index()->name();
+          itn->payload = cur_dim--;
+        }
+      }
+    }
+    
+    // align loops by names, temporary solution
+    ir_tree_node *itn = ir_stmt[loc];
+    int depth = stmt_nesting_level_[loc] - 1;
+    /*   while (itn->parent != NULL) {
+         itn = itn->parent;
+         if (itn->content->type() == IR_CONTROL_LOOP && itn->payload == -1) {
+         std::string name = static_cast<IR_Loop *>(itn->content)->index()->name();
+         for (int j = 0; j < n_dim; j++)
+         if (index[j] == name) {
+         itn->payload = j;
+         break;
+         }
+         if (itn->payload == -1)
+         throw loop_error("no complex alignment yet");
+         }
+         }
+    */
+    for (int t = depth; t >= 0; t--) {
+      int y = t;
+      ir_tree_node *itn = ir_stmt[loc];
+      
+      while ((itn->parent != NULL) && (y >= 0)) {
+        itn = itn->parent;
+        if (itn->content->type() == IR_CONTROL_LOOP)
+          y--;
+      }
+      
+      if (itn->content->type() == IR_CONTROL_LOOP && itn->payload == -1) {
+        CG_outputBuilder *ocg = ir->builder();
+        
+        itn->payload = depth - t;
+        
+        CG_outputRepr *code =
+          static_cast<IR_Block *>(ir_stmt[loc]->content)->extract();
+        
+        std::vector<CG_outputRepr *> index_expr;
+        std::vector<std::string> old_index;
+        CG_outputRepr *repl = ocg->CreateIdent(index[itn->payload]);
+        index_expr.push_back(repl);
+        old_index.push_back(
+          static_cast<IR_Loop *>(itn->content)->index()->name());
+        code = ocg->CreateSubstitutedStmt(0, code, old_index,
+                                          index_expr);
+        
+        replace.insert(std::pair<int, CG_outputRepr*>(loc, code));
+        //stmt[loc].code = code;
+        
+      }
+    }
+    
+    // set relation variable names
+    Relation r(n_dim);
+    F_And *f_root = r.add_and();
+    itn = ir_stmt[loc];
+    int temp_depth = depth;
+    while (itn->parent != NULL) {
+      
+      itn = itn->parent;
+      if (itn->content->type() == IR_CONTROL_LOOP) {
+        r.name_set_var(itn->payload + 1, index[temp_depth]);
+        
+        temp_depth--;
+      }
+      //static_cast<IR_Loop *>(itn->content)->index()->name());
+    }
+    
+    /*while (itn->parent != NULL) {
+      itn = itn->parent;
+      if (itn->content->type() == IR_CONTROL_LOOP)
+      r.name_set_var(itn->payload+1, static_cast<IR_Loop *>(itn->content)->index()->name());
+      }*/
+    
+    // extract information from loop/if structures
+    std::vector<bool> processed(n_dim, false);
+    std::vector<std::string> vars_to_be_reversed;
+    itn = ir_stmt[loc];
+    while (itn->parent != NULL) {
+      itn = itn->parent;
+      
+      switch (itn->content->type()) {
+      case IR_CONTROL_LOOP: {
+        IR_Loop *lp = static_cast<IR_Loop *>(itn->content);
+        Variable_ID v = r.set_var(itn->payload + 1);
+        int c;
+        
+        try {
+          c = lp->step_size();
+          if (c > 0) {
+            CG_outputRepr *lb = lp->lower_bound();
+            exp2formula(ir, r, f_root, freevar, lb, v, 's',
+                        IR_COND_GE, true);
+            CG_outputRepr *ub = lp->upper_bound();
+            IR_CONDITION_TYPE cond = lp->stop_cond();
+            if (cond == IR_COND_LT || cond == IR_COND_LE)
+              exp2formula(ir, r, f_root, freevar, ub, v, 's',
+                          cond, true);
+            else
+              throw ir_error("loop condition not supported");
+            
+          } else if (c < 0) {
+            CG_outputBuilder *ocg = ir->builder();
+            CG_outputRepr *lb = lp->lower_bound();
+            lb = ocg->CreateMinus(NULL, lb);
+            exp2formula(ir, r, f_root, freevar, lb, v, 's',
+                        IR_COND_GE, true);
+            CG_outputRepr *ub = lp->upper_bound();
+            ub = ocg->CreateMinus(NULL, ub);
+            IR_CONDITION_TYPE cond = lp->stop_cond();
+            if (cond == IR_COND_GE)
+              exp2formula(ir, r, f_root, freevar, ub, v, 's',
+                          IR_COND_LE, true);
+            else if (cond == IR_COND_GT)
+              exp2formula(ir, r, f_root, freevar, ub, v, 's',
+                          IR_COND_LT, true);
+            else
+              throw ir_error("loop condition not supported");
+            
+            vars_to_be_reversed.push_back(lp->index()->name());
+          } else
+            throw ir_error("loop step size zero");
+        } catch (const ir_error &e) {
+          for (int i = 0; i < itn->children.size(); i++)
+            delete itn->children[i];
+          itn->children = std::vector<ir_tree_node *>();
+          itn->content = itn->content->convert();
+          return false;
+        }
+        
+        if (abs(c) != 1) {
+          F_Exists *f_exists = f_root->add_exists();
+          Variable_ID e = f_exists->declare();
+          F_And *f_and = f_exists->add_and();
+          Stride_Handle h = f_and->add_stride(abs(c));
+          if (c > 0)
+            h.update_coef(e, 1);
+          else
+            h.update_coef(e, -1);
+          h.update_coef(v, -1);
+          CG_outputRepr *lb = lp->lower_bound();
+          exp2formula(ir, r, f_and, freevar, lb, e, 's', IR_COND_EQ,
+                      true);
+        }
+        
+        processed[itn->payload] = true;
+        break;
+      }
+      case IR_CONTROL_IF: {
+        CG_outputRepr *cond =
+          static_cast<IR_If *>(itn->content)->condition();
+        try {
+          if (itn->payload % 2 == 1)
+            exp2constraint(ir, r, f_root, freevar, cond, true);
+          else {
+            F_Not *f_not = f_root->add_not();
+            F_And *f_and = f_not->add_and();
+            exp2constraint(ir, r, f_and, freevar, cond, true);
+          }
+        } catch (const ir_error &e) {
+          std::vector<ir_tree_node *> *t;
+          if (itn->parent == NULL)
+            t = &ir_tree;
+          else
+            t = &(itn->parent->children);
+          int id = itn->payload;
+          int i = t->size() - 1;
+          while (i >= 0) {
+            if ((*t)[i] == itn) {
+              for (int j = 0; j < itn->children.size(); j++)
+                delete itn->children[j];
+              itn->children = std::vector<ir_tree_node *>();
+              itn->content = itn->content->convert();
+            } else if ((*t)[i]->payload >> 1 == id >> 1) {
+              delete (*t)[i];
+              t->erase(t->begin() + i);
+            }
+            i--;
+          }
+          return false;
+        }
+        
+        break;
+      }
+      default:
+        for (int i = 0; i < itn->children.size(); i++)
+          delete itn->children[i];
+        itn->children = std::vector<ir_tree_node *>();
+        itn->content = itn->content->convert();
+        return false;
+      }
+    }
+    
+    // add information for missing loops
+    for (int j = 0; j < n_dim; j++)
+      if (!processed[j]) {
+        ir_tree_node *itn = ir_stmt[max_loc];
+        while (itn->parent != NULL) {
+          itn = itn->parent;
+          if (itn->content->type() == IR_CONTROL_LOOP
+              && itn->payload == j)
+            break;
+        }
+        
+        Variable_ID v = r.set_var(j + 1);
+        if (loc < max_loc) {
+          
+          CG_outputBuilder *ocg = ir->builder();
+          
+          CG_outputRepr *lb =
+            static_cast<IR_Loop *>(itn->content)->lower_bound();
+          
+          exp2formula(ir, r, f_root, freevar, lb, v, 's', IR_COND_EQ,
+                      false);
+          
+          /*    if (ir->QueryExpOperation(
+                static_cast<IR_Loop *>(itn->content)->lower_bound())
+                == IR_OP_VARIABLE) {
+                IR_ScalarRef *ref =
+                static_cast<IR_ScalarRef *>(ir->Repr2Ref(
+                static_cast<IR_Loop *>(itn->content)->lower_bound()));
+                std::string name_ = ref->name();
+                
+                for (int i = 0; i < index.size(); i++)
+                if (index[i] == name_) {
+                exp2formula(ir, r, f_root, freevar, lb, v, 's',
+                IR_COND_GE, false);
+                
+                CG_outputRepr *ub =
+                static_cast<IR_Loop *>(itn->content)->upper_bound();
+                IR_CONDITION_TYPE cond =
+                static_cast<IR_Loop *>(itn->content)->stop_cond();
+                if (cond == IR_COND_LT || cond == IR_COND_LE)
+                exp2formula(ir, r, f_root, freevar, ub, v,
+                's', cond, false);
+                
+                
+                
+                }
+                
+                }
+          */
+          
+        } else { // loc > max_loc
+          
+          CG_outputBuilder *ocg = ir->builder();
+          CG_outputRepr *ub =
+            static_cast<IR_Loop *>(itn->content)->upper_bound();
+          
+          exp2formula(ir, r, f_root, freevar, ub, v, 's', IR_COND_EQ,
+                      false);
+          /*if (ir->QueryExpOperation(
+            static_cast<IR_Loop *>(itn->content)->upper_bound())
+            == IR_OP_VARIABLE) {
+            IR_ScalarRef *ref =
+            static_cast<IR_ScalarRef *>(ir->Repr2Ref(
+            static_cast<IR_Loop *>(itn->content)->upper_bound()));
+            std::string name_ = ref->name();
+            
+            for (int i = 0; i < index.size(); i++)
+            if (index[i] == name_) {
+            
+            CG_outputRepr *lb =
+            static_cast<IR_Loop *>(itn->content)->lower_bound();
+            
+            exp2formula(ir, r, f_root, freevar, lb, v, 's',
+            IR_COND_GE, false);
+            
+            CG_outputRepr *ub =
+            static_cast<IR_Loop *>(itn->content)->upper_bound();
+            IR_CONDITION_TYPE cond =
+            static_cast<IR_Loop *>(itn->content)->stop_cond();
+            if (cond == IR_COND_LT || cond == IR_COND_LE)
+            exp2formula(ir, r, f_root, freevar, ub, v,
+            's', cond, false);
+            
+            
+            }
+            }
+          */
+        }
+      }
+    
+    r.setup_names();
+    r.simplify();
+    
+    // insert the statement
+    CG_outputBuilder *ocg = ir->builder();
+    std::vector<CG_outputRepr *> reverse_expr;
+    for (int j = 1; j <= vars_to_be_reversed.size(); j++) {
+      CG_outputRepr *repl = ocg->CreateIdent(vars_to_be_reversed[j]);
+      repl = ocg->CreateMinus(NULL, repl);
+      reverse_expr.push_back(repl);
+    }
+    CG_outputRepr *code =
+      static_cast<IR_Block *>(ir_stmt[loc]->content)->extract();
+    code = ocg->CreateSubstitutedStmt(0, code, vars_to_be_reversed,
+                                      reverse_expr);
+    stmt[loc].code = code;
+    stmt[loc].IS = r;
+    stmt[loc].loop_level = std::vector<LoopLevel>(n_dim);
+    stmt[loc].ir_stmt_node = ir_stmt[loc];
+    for (int i = 0; i < n_dim; i++) {
+      stmt[loc].loop_level[i].type = LoopLevelOriginal;
+      stmt[loc].loop_level[i].payload = i;
+      stmt[loc].loop_level[i].parallel_level = 0;
+    }
+    
+    stmt_nesting_level[loc] = -1;
+  }
+  
+  return true;
+}
+
+Loop::Loop(const IR_Control *control) {
+
+  last_compute_cgr_ = NULL;
+  last_compute_cg_ = NULL;
+  
+  ir = const_cast<IR_Code *>(control->ir_);
+  init_code = NULL;
+  cleanup_code = NULL;
+  tmp_loop_var_name_counter = 1;
+  overflow_var_name_counter = 1;
+  known = Relation::True(0);
+  
+  ir_tree = build_ir_tree(control->clone(), NULL);
+  //    std::vector<ir_tree_node *> ir_stmt;
+  
+  while (!init_loop(ir_tree, ir_stmt)) {
+  }
+
+  
+  
+  for (int i = 0; i < stmt.size(); i++) {
+    std::map<int, CG_outputRepr*>::iterator it = replace.find(i);
+    
+    if (it != replace.end())
+      stmt[i].code = it->second;
+    else
+      stmt[i].code = stmt[i].code;
+  }
+  
+  if (stmt.size() != 0)
+    dep = DependenceGraph(stmt[0].IS.n_set());
+  else
+    dep = DependenceGraph(0);
+  // init the dependence graph
+  for (int i = 0; i < stmt.size(); i++)
+    dep.insert();
+  
+  for (int i = 0; i < stmt.size(); i++)
+    for (int j = i; j < stmt.size(); j++) {
+      std::pair<std::vector<DependenceVector>,
+        std::vector<DependenceVector> > dv = test_data_dependences(
+          ir, stmt[i].code, stmt[i].IS, stmt[j].code, stmt[j].IS,
+          freevar, index, stmt_nesting_level_[i],
+          stmt_nesting_level_[j]);
+      
+      for (int k = 0; k < dv.first.size(); k++) {
+        if (is_dependence_valid(ir_stmt[i], ir_stmt[j], dv.first[k],
+                                true))
+          dep.connect(i, j, dv.first[k]);
+        else {
+          dep.connect(j, i, dv.first[k].reverse());
+        }
+        
+      }
+      for (int k = 0; k < dv.second.size(); k++)
+        if (is_dependence_valid(ir_stmt[j], ir_stmt[i], dv.second[k],
+                                false))
+          dep.connect(j, i, dv.second[k]);
+        else {
+          dep.connect(i, j, dv.second[k].reverse());
+        }
+      // std::pair<std::vector<DependenceVector>,
+      //                std::vector<DependenceVector> > dv_ = test_data_dependences(
+      
+    }
+  
+
+
+  // init dumb transformation relations e.g. [i, j] -> [ 0, i, 0, j, 0]
+  for (int i = 0; i < stmt.size(); i++) {
+    int n = stmt[i].IS.n_set();
+    stmt[i].xform = Relation(n, 2 * n + 1);
+    F_And *f_root = stmt[i].xform.add_and();
+    
+    for (int j = 1; j <= n; j++) {
+      EQ_Handle h = f_root->add_EQ();
+      h.update_coef(stmt[i].xform.output_var(2 * j), 1);
+      h.update_coef(stmt[i].xform.input_var(j), -1);
+    }
+    
+    for (int j = 1; j <= 2 * n + 1; j += 2) {
+      EQ_Handle h = f_root->add_EQ();
+      h.update_coef(stmt[i].xform.output_var(j), 1);
+    }
+    stmt[i].xform.simplify();
+  }
+  
+  if (stmt.size() != 0)
+    num_dep_dim = stmt[0].IS.n_set();
+  else
+    num_dep_dim = 0;
+  // debug
+  /*for (int i = 0; i < stmt.size(); i++) {
+    std::cout << i << ": ";
+    //stmt[i].xform.print();
+    stmt[i].IS.print();
+    std::cout << std::endl;
+    
+    }*/
+  //end debug
+}
+
+Loop::~Loop() {
+  
+  delete last_compute_cgr_;
+  delete last_compute_cg_;
+  
+  for (int i = 0; i < stmt.size(); i++)
+    if (stmt[i].code != NULL) {
+      stmt[i].code->clear();
+      delete stmt[i].code;
+    }
+  
+  for (int i = 0; i < ir_tree.size(); i++)
+    delete ir_tree[i];
+  
+  if (init_code != NULL) {
+    init_code->clear();
+    delete init_code;
+  }
+  if (cleanup_code != NULL) {
+    cleanup_code->clear();
+    delete cleanup_code;
+  }
+}
+
+int Loop::get_dep_dim_of(int stmt_num, int level) const {
+  if (stmt_num < 0 || stmt_num >= stmt.size())
+    throw std::invalid_argument("invaid statement " + to_string(stmt_num));
+  
+  if (level < 1 || level > stmt[stmt_num].loop_level.size())
+    return -1;
+  
+  int trip_count = 0;
+  while (true) {
+    switch (stmt[stmt_num].loop_level[level - 1].type) {
+    case LoopLevelOriginal:
+      return stmt[stmt_num].loop_level[level - 1].payload;
+    case LoopLevelTile:
+      level = stmt[stmt_num].loop_level[level - 1].payload;
+      if (level < 1)
+        return -1;
+      if (level > stmt[stmt_num].loop_level.size())
+        throw loop_error(
+          "incorrect loop level information for statement "
+          + to_string(stmt_num));
+      break;
+    default:
+      throw loop_error(
+        "unknown loop level information for statement "
+        + to_string(stmt_num));
+    }
+    trip_count++;
+    if (trip_count >= stmt[stmt_num].loop_level.size())
+      throw loop_error(
+        "incorrect loop level information for statement "
+        + to_string(stmt_num));
+  }
+}
+
+int Loop::get_last_dep_dim_before(int stmt_num, int level) const {
+  if (stmt_num < 0 || stmt_num >= stmt.size())
+    throw std::invalid_argument("invaid statement " + to_string(stmt_num));
+  
+  if (level < 1)
+    return -1;
+  if (level > stmt[stmt_num].loop_level.size())
+    level = stmt[stmt_num].loop_level.size() + 1;
+  
+  for (int i = level - 1; i >= 1; i--)
+    if (stmt[stmt_num].loop_level[i - 1].type == LoopLevelOriginal)
+      return stmt[stmt_num].loop_level[i - 1].payload;
+  
+  return -1;
+}
+
+void Loop::print_internal_loop_structure() const {
+  for (int i = 0; i < stmt.size(); i++) {
+    std::vector<int> lex = getLexicalOrder(i);
+    std::cout << "s" << i + 1 << ": ";
+    for (int j = 0; j < stmt[i].loop_level.size(); j++) {
+      if (2 * j < lex.size())
+        std::cout << lex[2 * j];
+      switch (stmt[i].loop_level[j].type) {
+      case LoopLevelOriginal:
+        std::cout << "(dim:" << stmt[i].loop_level[j].payload << ")";
+        break;
+      case LoopLevelTile:
+        std::cout << "(tile:" << stmt[i].loop_level[j].payload << ")";
+        break;
+      default:
+        std::cout << "(unknown)";
+      }
+      std::cout << ' ';
+    }
+    for (int j = 2 * stmt[i].loop_level.size(); j < lex.size(); j += 2) {
+      std::cout << lex[j];
+      if (j != lex.size() - 1)
+        std::cout << ' ';
+    }
+    std::cout << std::endl;
+  }
+}
+
+CG_outputRepr *Loop::getCode(int effort) const {
+  const int m = stmt.size();
+  if (m == 0)
+    return NULL;
+  const int n = stmt[0].xform.n_out();
+  
+  if (last_compute_cg_ == NULL) {
+    std::vector<Relation> IS(m);
+    std::vector<Relation> xforms(m);
+    for (int i = 0; i < m; i++) {
+      IS[i] = stmt[i].IS;
+      xforms[i] = stmt[i].xform;
+    }
+    Relation known = Extend_Set(copy(this->known), n - this->known.n_set());
+    
+    last_compute_cg_ = new CodeGen(xforms, IS, known);
+    delete last_compute_cgr_;
+    last_compute_cgr_ = NULL;
+  }
+  
+  if (last_compute_cgr_ == NULL || last_compute_effort_ != effort) {
+    delete last_compute_cgr_;
+    last_compute_cgr_ = last_compute_cg_->buildAST(effort);
+    last_compute_effort_ = effort;
+  }
+  
+  std::vector<CG_outputRepr *> stmts(m);
+  for (int i = 0; i < m; i++)
+    stmts[i] = stmt[i].code;
+  CG_outputBuilder *ocg = ir->builder();
+  CG_outputRepr *repr = last_compute_cgr_->printRepr(ocg, stmts);
+  
+  if (init_code != NULL)
+    repr = ocg->StmtListAppend(init_code->clone(), repr);
+  if (cleanup_code != NULL)
+    repr = ocg->StmtListAppend(repr, cleanup_code->clone());
+  
+  return repr;
+}
+
+void Loop::printCode(int effort) const {
+  const int m = stmt.size();
+  if (m == 0)
+    return;
+  const int n = stmt[0].xform.n_out();
+  
+  if (last_compute_cg_ == NULL) {
+    std::vector<Relation> IS(m);
+    std::vector<Relation> xforms(m);
+    for (int i = 0; i < m; i++) {
+      IS[i] = stmt[i].IS;
+      xforms[i] = stmt[i].xform;
+    }
+    Relation known = Extend_Set(copy(this->known), n - this->known.n_set());
+    
+    last_compute_cg_ = new CodeGen(xforms, IS, known);
+    delete last_compute_cgr_;
+    last_compute_cgr_ = NULL;
+  }
+  
+  if (last_compute_cgr_ == NULL || last_compute_effort_ != effort) {
+    delete last_compute_cgr_;
+    last_compute_cgr_ = last_compute_cg_->buildAST(effort);
+    last_compute_effort_ = effort;
+  }
+  
+  std::string repr = last_compute_cgr_->printString();
+  std::cout << repr << std::endl;
+}
+
+void Loop::printIterationSpace() const {
+  for (int i = 0; i < stmt.size(); i++) {
+    std::cout << "s" << i << ": ";
+    Relation r = getNewIS(i);
+    for (int j = 1; j <= r.n_inp(); j++)
+      r.name_input_var(j, CodeGen::loop_var_name_prefix + to_string(j));
+    r.setup_names();
+    r.print();
+  }
+}
+
+void Loop::printDependenceGraph() const {
+  if (dep.edgeCount() == 0)
+    std::cout << "no dependence exists" << std::endl;
+  else {
+    std::cout << "dependence graph:" << std::endl;
+    std::cout << dep;
+  }
+}
+
+Relation Loop::getNewIS(int stmt_num) const {
+  Relation result;
+  
+  if (stmt[stmt_num].xform.is_null()) {
+    Relation known = Extend_Set(copy(this->known),
+                                stmt[stmt_num].IS.n_set() - this->known.n_set());
+    result = Intersection(copy(stmt[stmt_num].IS), known);
+  } else {
+    Relation known = Extend_Set(copy(this->known),
+                                stmt[stmt_num].xform.n_out() - this->known.n_set());
+    result = Intersection(
+      Range(
+        Restrict_Domain(copy(stmt[stmt_num].xform),
+                        copy(stmt[stmt_num].IS))), known);
+  }
+  
+  result.simplify(2, 4);
+  
+  return result;
+}
+
+std::vector<Relation> Loop::getNewIS() const {
+  const int m = stmt.size();
+  
+  std::vector<Relation> new_IS(m);
+  for (int i = 0; i < m; i++)
+    new_IS[i] = getNewIS(i);
+  
+  return new_IS;
+}
+
+void Loop::pragma(int stmt_num, int level, const std::string &pragmaText) {
+	// check sanity of parameters
+	if(stmt_num < 0)
+		throw std::invalid_argument("invalid statement " + to_string(stmt_num));
+	
+	CG_outputBuilder *ocg = ir->builder();
+	CG_outputRepr *code = stmt[stmt_num].code;
+	ocg->CreatePragmaAttribute(code, level, pragmaText);
+}
+
+void Loop::prefetch(int stmt_num, int level, const std::string &arrName, int hint) {
+	// check sanity of parameters
+	if(stmt_num < 0)
+		throw std::invalid_argument("invalid statement " + to_string(stmt_num));
+
+	CG_outputBuilder *ocg = ir->builder();
+	CG_outputRepr *code = stmt[stmt_num].code;
+	ocg->CreatePrefetchAttribute(code, level, arrName, hint);
+}
+
+std::vector<int> Loop::getLexicalOrder(int stmt_num) const {
+  assert(stmt_num < stmt.size());
+  
+  const int n = stmt[stmt_num].xform.n_out();
+  std::vector<int> lex(n, 0);
+  
+  for (int i = 0; i < n; i += 2)
+    lex[i] = get_const(stmt[stmt_num].xform, i, Output_Var);
+  
+  return lex;
+}
+
+// find the sub loop nest specified by stmt_num and level,
+// only iteration space satisfiable statements returned.
+std::set<int> Loop::getSubLoopNest(int stmt_num, int level) const {
+  assert(stmt_num >= 0 && stmt_num < stmt.size());
+  assert(level > 0 && level <= stmt[stmt_num].loop_level.size());
+  
+  std::set<int> working;
+  for (int i = 0; i < stmt.size(); i++)
+    if (const_cast<Loop *>(this)->stmt[i].IS.is_upper_bound_satisfiable()
+        && stmt[i].loop_level.size() >= level)
+      working.insert(i);
+  
+  for (int i = 1; i <= level; i++) {
+    int a = getLexicalOrder(stmt_num, i);
+    for (std::set<int>::iterator j = working.begin(); j != working.end();) {
+      int b = getLexicalOrder(*j, i);
+      if (b != a)
+        working.erase(j++);
+      else
+        ++j;
+    }
+  }
+  
+  return working;
+}
+
+int Loop::getLexicalOrder(int stmt_num, int level) const {
+  assert(stmt_num >= 0 && stmt_num < stmt.size());
+  assert(level > 0 && level <= stmt[stmt_num].loop_level.size()+1);
+  
+  Relation &r = const_cast<Loop *>(this)->stmt[stmt_num].xform;
+  for (EQ_Iterator e(r.single_conjunct()->EQs()); e; e++)
+    if (abs((*e).get_coef(r.output_var(2 * level - 1))) == 1) {
+      bool is_const = true;
+      for (Constr_Vars_Iter cvi(*e); cvi; cvi++)
+        if (cvi.curr_var() != r.output_var(2 * level - 1)) {
+          is_const = false;
+          break;
+        }
+      if (is_const) {
+        int t = static_cast<int>((*e).get_const());
+        return (*e).get_coef(r.output_var(2 * level - 1)) > 0 ? -t : t;
+      }
+    }
+  
+  throw loop_error(
+    "can't find lexical order for statement " + to_string(stmt_num)
+    + "'s loop level " + to_string(level));
+}
+
+std::set<int> Loop::getStatements(const std::vector<int> &lex, int dim) const {
+  const int m = stmt.size();
+  
+  std::set<int> same_loops;
+  for (int i = 0; i < m; i++) {
+    if (dim < 0)
+      same_loops.insert(i);
+    else {
+      std::vector<int> a_lex = getLexicalOrder(i);
+      int j;
+      for (j = 0; j <= dim; j += 2)
+        if (lex[j] != a_lex[j])
+          break;
+      if (j > dim)
+        same_loops.insert(i);
+    }
+    
+  }
+  
+  return same_loops;
+}
+
+void Loop::shiftLexicalOrder(const std::vector<int> &lex, int dim, int amount) {
+  const int m = stmt.size();
+  
+  if (amount == 0)
+    return;
+  
+  for (int i = 0; i < m; i++) {
+    std::vector<int> lex2 = getLexicalOrder(i);
+    
+    bool need_shift = true;
+    
+    for (int j = 0; j < dim; j++)
+      if (lex2[j] != lex[j]) {
+        need_shift = false;
+        break;
+      }
+    
+    if (!need_shift)
+      continue;
+    
+    if (amount > 0) {
+      if (lex2[dim] < lex[dim])
+        continue;
+    } else if (amount < 0) {
+      if (lex2[dim] > lex[dim])
+        continue;
+    }
+    
+    assign_const(stmt[i].xform, dim, lex2[dim] + amount);
+  }
+}
+
+std::vector<std::set<int> > Loop::sort_by_same_loops(std::set<int> active,
+                                                     int level) {
+  
+  std::set<int> not_nested_at_this_level;
+  std::map<ir_tree_node*, std::set<int> > sorted_by_loop;
+  std::map<int, std::set<int> > sorted_by_lex_order;
+  std::vector<std::set<int> > to_return;
+  bool lex_order_already_set = false;
+  for (std::set<int>::iterator it = active.begin(); it != active.end();
+       it++) {
+    
+    if (stmt[*it].ir_stmt_node == NULL)
+      lex_order_already_set = true;
+  }
+  
+  if (lex_order_already_set) {
+    
+    for (std::set<int>::iterator it = active.begin(); it != active.end();
+         it++) {
+      std::map<int, std::set<int> >::iterator it2 =
+        sorted_by_lex_order.find(
+          get_const(stmt[*it].xform, 2 * (level - 1),
+                    Output_Var));
+      
+      if (it2 != sorted_by_lex_order.end())
+        it2->second.insert(*it);
+      else {
+        
+        std::set<int> to_insert;
+        
+        to_insert.insert(*it);
+        
+        sorted_by_lex_order.insert(
+          std::pair<int, std::set<int> >(
+            get_const(stmt[*it].xform, 2 * (level - 1),
+                      Output_Var), to_insert));
+        
+      }
+      
+    }
+    
+    for (std::map<int, std::set<int> >::iterator it2 =
+           sorted_by_lex_order.begin(); it2 != sorted_by_lex_order.end();
+         it2++)
+      to_return.push_back(it2->second);
+    
+  } else {
+    
+    for (std::set<int>::iterator it = active.begin(); it != active.end();
+         it++) {
+      
+      ir_tree_node* itn = stmt[*it].ir_stmt_node;
+      itn = itn->parent;
+      while ((itn != NULL) && (itn->payload != level - 1))
+        itn = itn->parent;
+      
+      if (itn == NULL)
+        not_nested_at_this_level.insert(*it);
+      else {
+        std::map<ir_tree_node*, std::set<int> >::iterator it2 =
+          sorted_by_loop.find(itn);
+        
+        if (it2 != sorted_by_loop.end())
+          it2->second.insert(*it);
+        else {
+          std::set<int> to_insert;
+          
+          to_insert.insert(*it);
+          
+          sorted_by_loop.insert(
+            std::pair<ir_tree_node*, std::set<int> >(itn,
+                                                     to_insert));
+          
+        }
+        
+      }
+      
+    }
+    if (not_nested_at_this_level.size() > 0) {
+      for (std::set<int>::iterator it = not_nested_at_this_level.begin();
+           it != not_nested_at_this_level.end(); it++) {
+        std::set<int> temp;
+        temp.insert(*it);
+        to_return.push_back(temp);
+        
+      }
+    }
+    for (std::map<ir_tree_node*, std::set<int> >::iterator it2 =
+           sorted_by_loop.begin(); it2 != sorted_by_loop.end(); it2++)
+      to_return.push_back(it2->second);
+  }
+  return to_return;
+}
+
+void update_successors(int n, int node_num[], int cant_fuse_with[],
+                       Graph<std::set<int>, bool> &g, std::list<int> &work_list) {
+  
+  std::set<int> disconnect;
+  for (Graph<std::set<int>, bool>::EdgeList::iterator i =
+         g.vertex[n].second.begin(); i != g.vertex[n].second.end(); i++) {
+    int m = i->first;
+    
+    if (node_num[m] != -1)
+      throw loop_error("Graph input for fusion has cycles not a DAG!!");
+    
+    std::vector<bool> check_ = g.getEdge(n, m);
+    
+    bool has_bad_edge_path = false;
+    for (int i = 0; i < check_.size(); i++)
+      if (!check_[i]) {
+        has_bad_edge_path = true;
+        break;
+      }
+    if (has_bad_edge_path)
+      cant_fuse_with[m] = std::max(cant_fuse_with[m], node_num[n]);
+    else
+      cant_fuse_with[m] = std::max(cant_fuse_with[m], cant_fuse_with[n]);
+    disconnect.insert(m);
+  }
+  
+  
+  for (std::set<int>::iterator i = disconnect.begin(); i != disconnect.end();
+       i++) {
+    g.disconnect(n, *i);
+    
+    bool no_incoming_edges = true;
+    for (int j = 0; j < g.vertex.size(); j++)
+      if (j != *i)
+        if (g.hasEdge(j, *i)) {
+          no_incoming_edges = false;
+          break;
+        }
+    
+    
+    if (no_incoming_edges)
+      work_list.push_back(*i);
+  }
+  
+}
+
+Graph<std::set<int>, bool> Loop::construct_induced_graph_at_level(
+  std::vector<std::set<int> > s, DependenceGraph dep, int dep_dim) {
+  Graph<std::set<int>, bool> g;
+  
+  for (int i = 0; i < s.size(); i++)
+    g.insert(s[i]);
+  
+  for (int i = 0; i < s.size(); i++) {
+    
+    for (int j = i + 1; j < s.size(); j++) {
+      bool has_true_edge_i_to_j = false;
+      bool has_true_edge_j_to_i = false;
+      bool is_connected_i_to_j = false;
+      bool is_connected_j_to_i = false;
+      for (std::set<int>::iterator ii = s[i].begin(); ii != s[i].end();
+           ii++) {
+        
+        for (std::set<int>::iterator jj = s[j].begin();
+             jj != s[j].end(); jj++) {
+          
+          std::vector<DependenceVector> dvs = dep.getEdge(*ii, *jj);
+          for (int k = 0; k < dvs.size(); k++)
+            if (dvs[k].is_control_dependence()
+                || (dvs[k].is_data_dependence()
+                    && dvs[k].has_been_carried_at(dep_dim))) {
+              
+              if (dvs[k].is_data_dependence()
+                  && dvs[k].has_negative_been_carried_at(
+                    dep_dim)) {
+                //g.connect(i, j, false);
+                is_connected_i_to_j = true;
+                break;
+              } else {
+                //g.connect(i, j, true);
+                
+                has_true_edge_i_to_j = true;
+                //break
+              }
+            }
+          
+          //if (is_connected)
+          
+          //    break;
+          //        if (has_true_edge_i_to_j && !is_connected_i_to_j)
+          //                g.connect(i, j, true);
+          dvs = dep.getEdge(*jj, *ii);
+          for (int k = 0; k < dvs.size(); k++)
+            if (dvs[k].is_control_dependence()
+                || (dvs[k].is_data_dependence()
+                    && dvs[k].has_been_carried_at(dep_dim))) {
+              
+              if (is_connected_i_to_j || has_true_edge_i_to_j)
+                throw loop_error(
+                  "Graph input for fusion has cycles not a DAG!!");
+              
+              if (dvs[k].is_data_dependence()
+                  && dvs[k].has_negative_been_carried_at(
+                    dep_dim)) {
+                //g.connect(i, j, false);
+                is_connected_j_to_i = true;
+                break;
+              } else {
+                //g.connect(i, j, true);
+                
+                has_true_edge_j_to_i = true;
+                //break;
+              }
+            }
+          
+          //    if (is_connected)
+          //break;
+          //    if (is_connected)
+          //break;
+        }
+        
+        
+        //if (is_connected)
+        //  break;
+      }
+      
+      
+      if (is_connected_i_to_j)
+        g.connect(i, j, false);
+      else if (has_true_edge_i_to_j)
+        g.connect(i, j, true);
+      
+      if (is_connected_j_to_i)
+        g.connect(j, i, false);
+      else if (has_true_edge_j_to_i)
+        g.connect(j, i, true);
+      
+      
+    }
+  }
+  return g;
+}
+
+std::vector<std::set<int> > Loop::typed_fusion(Graph<std::set<int>, bool> g) {
+  
+  bool roots[g.vertex.size()];
+  
+  for (int i = 0; i < g.vertex.size(); i++)
+    roots[i] = true;
+  
+  for (int i = 0; i < g.vertex.size(); i++)
+    for (int j = i + 1; j < g.vertex.size(); j++) {
+      
+      if (g.hasEdge(i, j))
+        roots[j] = false;
+      
+      if (g.hasEdge(j, i))
+        roots[i] = false;
+      
+    }
+  
+  std::list<int> work_list;
+  int cant_fuse_with[g.vertex.size()];
+  std::vector<std::set<int> > s;
+  //Each Fused set's representative node
+  
+  int node_to_fused_nodes[g.vertex.size()];
+  int node_num[g.vertex.size()];
+  for (int i = 0; i < g.vertex.size(); i++) {
+    if (roots[i] == true)
+      work_list.push_back(i);
+    cant_fuse_with[i] = 0;
+    node_to_fused_nodes[i] = 0;
+    node_num[i] = -1;
+  }
+  // topological sort according to chun's permute algorithm
+  //   std::vector<std::set<int> > s = g.topoSort();
+  std::vector<std::set<int> > s2 = g.topoSort();
+  if (work_list.empty() || (s2.size() != g.vertex.size())) {
+    
+    std::cout << s2.size() << "\t" << g.vertex.size() << std::endl;
+    throw loop_error("Input for fusion not a DAG!!");
+    
+    
+  }
+  int fused_nodes_counter = 0;
+  while (!work_list.empty()) {
+    int n = work_list.front();
+    //int n_ = g.vertex[n].first;
+    work_list.pop_front();
+    int node;
+    if (cant_fuse_with[n] == 0)
+      node = 0;
+    else
+      node = cant_fuse_with[n];
+    
+    if ((fused_nodes_counter != 0) && (node != fused_nodes_counter)) {
+      int rep_node = node_to_fused_nodes[node];
+      node_num[n] = node_num[rep_node];
+      
+      try {
+        update_successors(n, node_num, cant_fuse_with, g, work_list);
+      } catch (const loop_error &e) {
+        
+        throw loop_error(
+          "statements cannot be fused together due to negative dependence");
+        
+        
+      }
+      for (std::set<int>::iterator it = g.vertex[n].first.begin();
+           it != g.vertex[n].first.end(); it++)
+        s[node].insert(*it);
+    } else {
+      //std::set<int> new_node;
+      //new_node.insert(n_);
+      s.push_back(g.vertex[n].first);
+      node_to_fused_nodes[node] = n;
+      node_num[n] = ++node;
+      try {
+        update_successors(n, node_num, cant_fuse_with, g, work_list);
+      } catch (const loop_error &e) {
+        
+        throw loop_error(
+          "statements cannot be fused together due to negative dependence");
+        
+        
+      }
+      fused_nodes_counter++;
+    }
+  }
+  
+  return s;
+}
+
+void Loop::setLexicalOrder(int dim, const std::set<int> &active,
+                           int starting_order, std::vector<std::vector<std::string> > idxNames) {
+  if (active.size() == 0)
+    return;
+  
+  // check for sanity of parameters
+  if (dim < 0 || dim % 2 != 0)
+    throw std::invalid_argument(
+      "invalid constant loop level to set lexicographical order");
+  std::vector<int> lex;
+  int ref_stmt_num;
+  for (std::set<int>::iterator i = active.begin(); i != active.end(); i++) {
+    if ((*i) < 0 || (*i) >= stmt.size())
+      throw std::invalid_argument(
+        "invalid statement number " + to_string(*i));
+    if (dim >= stmt[*i].xform.n_out())
+      throw std::invalid_argument(
+        "invalid constant loop level to set lexicographical order");
+    if (i == active.begin()) {
+      lex = getLexicalOrder(*i);
+      ref_stmt_num = *i;
+    } else {
+      std::vector<int> lex2 = getLexicalOrder(*i);
+      for (int j = 0; j < dim; j += 2)
+        if (lex[j] != lex2[j])
+          throw std::invalid_argument(
+            "statements are not in the same sub loop nest");
+    }
+  }
+  
+  // sepearate statements by current loop level types
+  int level = (dim + 2) / 2;
+  std::map<std::pair<LoopLevelType, int>, std::set<int> > active_by_level_type;
+  std::set<int> active_by_no_level;
+  for (std::set<int>::iterator i = active.begin(); i != active.end(); i++) {
+    if (level > stmt[*i].loop_level.size())
+      active_by_no_level.insert(*i);
+    else
+      active_by_level_type[std::make_pair(
+          stmt[*i].loop_level[level - 1].type,
+          stmt[*i].loop_level[level - 1].payload)].insert(*i);
+  }
+  
+  // further separate statements due to control dependences
+  std::vector<std::set<int> > active_by_level_type_splitted;
+  for (std::map<std::pair<LoopLevelType, int>, std::set<int> >::iterator i =
+         active_by_level_type.begin(); i != active_by_level_type.end(); i++)
+    active_by_level_type_splitted.push_back(i->second);
+  for (std::set<int>::iterator i = active_by_no_level.begin();
+       i != active_by_no_level.end(); i++)
+    for (int j = active_by_level_type_splitted.size() - 1; j >= 0; j--) {
+      std::set<int> controlled, not_controlled;
+      for (std::set<int>::iterator k =
+             active_by_level_type_splitted[j].begin();
+           k != active_by_level_type_splitted[j].end(); k++) {
+        std::vector<DependenceVector> dvs = dep.getEdge(*i, *k);
+        bool is_controlled = false;
+        for (int kk = 0; kk < dvs.size(); kk++)
+          if (dvs[kk].type = DEP_CONTROL) {
+            is_controlled = true;
+            break;
+          }
+        if (is_controlled)
+          controlled.insert(*k);
+        else
+          not_controlled.insert(*k);
+      }
+      if (controlled.size() != 0 && not_controlled.size() != 0) {
+        active_by_level_type_splitted.erase(
+          active_by_level_type_splitted.begin() + j);
+        active_by_level_type_splitted.push_back(controlled);
+        active_by_level_type_splitted.push_back(not_controlled);
+      }
+    }
+  
+  // set lexical order separating loops with different loop types first
+  if (active_by_level_type_splitted.size() + active_by_no_level.size() > 1) {
+    int dep_dim = get_last_dep_dim_before(ref_stmt_num, level) + 1;
+    
+    Graph<std::set<int>, Empty> g;
+    for (std::vector<std::set<int> >::iterator i =
+           active_by_level_type_splitted.begin();
+         i != active_by_level_type_splitted.end(); i++)
+      g.insert(*i);
+    for (std::set<int>::iterator i = active_by_no_level.begin();
+         i != active_by_no_level.end(); i++) {
+      std::set<int> t;
+      t.insert(*i);
+      g.insert(t);
+    }
+    for (int i = 0; i < g.vertex.size(); i++)
+      for (int j = i + 1; j < g.vertex.size(); j++) {
+        bool connected = false;
+        for (std::set<int>::iterator ii = g.vertex[i].first.begin();
+             ii != g.vertex[i].first.end(); ii++) {
+          for (std::set<int>::iterator jj = g.vertex[j].first.begin();
+               jj != g.vertex[j].first.end(); jj++) {
+            std::vector<DependenceVector> dvs = dep.getEdge(*ii,
+                                                            *jj);
+            for (int k = 0; k < dvs.size(); k++)
+              if (dvs[k].is_control_dependence()
+                  || (dvs[k].is_data_dependence()
+                      && !dvs[k].has_been_carried_before(
+                        dep_dim))) {
+                g.connect(i, j);
+                connected = true;
+                break;
+              }
+            if (connected)
+              break;
+          }
+          if (connected)
+            break;
+        }
+        connected = false;
+        for (std::set<int>::iterator ii = g.vertex[i].first.begin();
+             ii != g.vertex[i].first.end(); ii++) {
+          for (std::set<int>::iterator jj = g.vertex[j].first.begin();
+               jj != g.vertex[j].first.end(); jj++) {
+            std::vector<DependenceVector> dvs = dep.getEdge(*jj,
+                                                            *ii);
+            // find the sub loop nest specified by stmt_num and level,
+            // only iteration space satisfiable statements returned.
+            for (int k = 0; k < dvs.size(); k++)
+              if (dvs[k].is_control_dependence()
+                  || (dvs[k].is_data_dependence()
+                      && !dvs[k].has_been_carried_before(
+                        dep_dim))) {
+                g.connect(j, i);
+                connected = true;
+                break;
+              }
+            if (connected)
+              break;
+          }
+          if (connected)
+            break;
+        }
+      }
+    
+    std::vector<std::set<int> > s = g.topoSort();
+    if (s.size() != g.vertex.size())
+      throw loop_error(
+        "cannot separate statements with different loop types at loop level "
+        + to_string(level));
+    
+    // assign lexical order
+    int order = starting_order;
+    for (int i = 0; i < s.size(); i++) {
+      std::set<int> &cur_scc = g.vertex[*(s[i].begin())].first;
+      int sz = cur_scc.size();
+      if (sz == 1) {
+        int cur_stmt = *(cur_scc.begin());
+        assign_const(stmt[cur_stmt].xform, dim, order);
+        for (int j = dim + 2; j < stmt[cur_stmt].xform.n_out(); j += 2)
+          assign_const(stmt[cur_stmt].xform, j, 0);
+        order++;
+      } else {
+        setLexicalOrder(dim, cur_scc, order, idxNames);
+        order += sz;
+      }
+    }
+  }
+  // set lexical order seperating single iteration statements and loops
+  else {
+    std::set<int> true_singles;
+    std::set<int> nonsingles;
+    std::map<coef_t, std::set<int> > fake_singles;
+    std::set<int> fake_singles_;
+    
+    // sort out statements that do not require loops
+    for (std::set<int>::iterator i = active.begin(); i != active.end();
+         i++) {
+      Relation cur_IS = getNewIS(*i);
+      if (is_single_iteration(cur_IS, dim + 1)) {
+        bool is_all_single = true;
+        for (int j = dim + 3; j < stmt[*i].xform.n_out(); j += 2)
+          if (!is_single_iteration(cur_IS, j)) {
+            is_all_single = false;
+            break;
+          }
+        if (is_all_single)
+          true_singles.insert(*i);
+        else {
+          fake_singles_.insert(*i);
+          try {
+            fake_singles[get_const(cur_IS, dim + 1, Set_Var)].insert(
+              *i);
+          } catch (const std::exception &e) {
+            fake_singles[posInfinity].insert(*i);
+          }
+        }
+      } else
+        nonsingles.insert(*i);
+    }
+    
+    
+    // split nonsingles forcibly according to negative dependences present (loop unfusible)
+    int dep_dim = get_dep_dim_of(ref_stmt_num, level);
+    
+    if (dim < stmt[ref_stmt_num].xform.n_out() - 1) {
+      
+      bool dummy_level_found = false;
+      
+      std::vector<std::set<int> > s;
+      
+      s = sort_by_same_loops(active, level);
+      bool further_levels_exist = false;
+      
+      if (!idxNames.empty())
+        if (level <= idxNames[ref_stmt_num].size())
+          if (idxNames[ref_stmt_num][level - 1].length() == 0) {
+            //  && s.size() == 1) {
+            int order1 = 0;
+            dummy_level_found = true;
+            
+            for (int i = level; i < idxNames[ref_stmt_num].size();
+                 i++)
+              if (idxNames[ref_stmt_num][i].length() > 0)
+                further_levels_exist = true;
+            
+          }
+      
+      //if (!dummy_level_found) {
+      
+      if (s.size() > 1) {
+        
+        Graph<std::set<int>, bool> g = construct_induced_graph_at_level(
+          s, dep, dep_dim);
+        s = typed_fusion(g);
+      }
+      int order = 0;
+      for (int i = 0; i < s.size(); i++) {
+        
+        for (std::set<int>::iterator it = s[i].begin();
+             it != s[i].end(); it++)
+          assign_const(stmt[*it].xform, dim, order);
+        
+        if ((dim + 2) <= (stmt[ref_stmt_num].xform.n_out() - 1))
+          setLexicalOrder(dim + 2, s[i], order, idxNames);
+        
+        order++;
+      }
+      //}
+      /*    else {
+            
+            int order1 = 0;
+            int order = 0;
+            for (std::set<int>::iterator i = active.begin();
+            i != active.end(); i++) {
+            if (!further_levels_exist)
+            assign_const(stmt[*i].xform, dim, order1++);
+            else
+            assign_const(stmt[*i].xform, dim, order1);
+            
+            }
+            
+            if ((dim + 2) <= (stmt[ref_stmt_num].xform.n_out() - 1) && further_levels_exist)
+            setLexicalOrder(dim + 2, active, order, idxNames);
+            }
+      */
+    } else {
+      int dummy_order = 0;
+      for (std::set<int>::iterator i = active.begin(); i != active.end();
+           i++)
+        assign_const(stmt[*i].xform, dim, dummy_order++);
+    }
+    /*for (int i = 0; i < g2.vertex.size(); i++)
+      for (int j = i+1; j < g2.vertex.size(); j++) {
+      std::vector<DependenceVector> dvs = dep.getEdge(g2.vertex[i].first, g2.vertex[j].first);
+      for (int k = 0; k < dvs.size(); k++)
+      if (dvs[k].is_control_dependence() ||
+      (dvs[k].is_data_dependence() && dvs[k].has_negative_been_carried_at(dep_dim))) {
+      g2.connect(i, j);
+      break;
+      }
+      dvs = dep.getEdge(g2.vertex[j].first, g2.vertex[i].first);
+      for (int k = 0; k < dvs.size(); k++)
+      if (dvs[k].is_control_dependence() ||
+      (dvs[k].is_data_dependence() && dvs[k].has_negative_been_carried_at(dep_dim))) {
+      g2.connect(j, i);
+      break;
+      }
+      }
+      
+      std::vector<std::set<int> > s2 = g2.packed_topoSort();
+      
+      std::vector<std::set<int> > splitted_nonsingles;
+      for (int i = 0; i < s2.size(); i++) {
+      std::set<int> cur_scc;
+      for (std::set<int>::iterator j = s2[i].begin(); j != s2[i].end(); j++)
+      cur_scc.insert(g2.vertex[*j].first);
+      splitted_nonsingles.push_back(cur_scc);
+      }
+    */
+    //convert to dependence graph for grouped statements
+    //dep_dim = get_last_dep_dim_before(ref_stmt_num, level) + 1;
+    /*int order = 0;
+      for (std::set<int>::iterator j = active.begin(); j != active.end();
+      j++) {
+      std::set<int> continuous;
+      std::cout<< active.size()<<std::endl;
+      while (nonsingles.find(*j) != nonsingles.end() && j != active.end()) {
+      continuous.insert(*j);
+      j++;
+      }
+      
+      printf("continuous size is %d\n", continuous.size());
+      
+      
+      
+      if (continuous.size() > 0) {
+      std::vector<std::set<int> > s = typed_fusion(continuous, dep,
+      dep_dim);
+      
+      for (int i = 0; i < s.size(); i++) {
+      for (std::set<int>::iterator l = s[i].begin();
+      l != s[i].end(); l++) {
+      assign_const(stmt[*l].xform, dim + 2, order);
+      setLexicalOrder(dim + 2, s[i]);
+      }
+      order++;
+      }
+      }
+      
+      if (j != active.end()) {
+      assign_const(stmt[*j].xform, dim + 2, order);
+      
+      for (int k = dim + 4; k < stmt[*j].xform.n_out(); k += 2)
+      assign_const(stmt[*j].xform, k, 0);
+      order++;
+      }
+      
+      if( j == active.end())
+      break;
+      }
+    */
+    
+    
+    // assign lexical order
+    /*int order = starting_order;
+      for (int i = 0; i < s.size(); i++) {
+      // translate each SCC into original statements
+      std::set<int> cur_scc;
+      for (std::set<int>::iterator j = s[i].begin(); j != s[i].end(); j++)
+      copy(s[i].begin(), s[i].end(),
+      inserter(cur_scc, cur_scc.begin()));
+      
+      // now assign the constant
+      for (std::set<int>::iterator j = cur_scc.begin();
+      j != cur_scc.end(); j++)
+      assign_const(stmt[*j].xform, dim, order);
+      
+      if (cur_scc.size() > 1)
+      setLexicalOrder(dim + 2, cur_scc);
+      else if (cur_scc.size() == 1) {
+      int cur_stmt = *(cur_scc.begin());
+      for (int j = dim + 2; j < stmt[cur_stmt].xform.n_out(); j += 2)
+      assign_const(stmt[cur_stmt].xform, j, 0);
+      }
+      
+      if (cur_scc.size() > 0)
+      order++;
+      }
+    */
+  }
+}
+
+void Loop::apply_xform() {
+  std::set<int> active;
+  for (int i = 0; i < stmt.size(); i++)
+    active.insert(i);
+  apply_xform(active);
+}
+
+void Loop::apply_xform(int stmt_num) {
+  std::set<int> active;
+  active.insert(stmt_num);
+  apply_xform(active);
+}
+
+void Loop::apply_xform(std::set<int> &active) {
+  int max_n = 0;
+  
+  CG_outputBuilder *ocg = ir->builder();
+  for (std::set<int>::iterator i = active.begin(); i != active.end(); i++) {
+    int n = stmt[*i].loop_level.size();
+    if (n > max_n)
+      max_n = n;
+    
+    std::vector<int> lex = getLexicalOrder(*i);
+    
+    Relation mapping(2 * n + 1, n);
+    F_And *f_root = mapping.add_and();
+    for (int j = 1; j <= n; j++) {
+      EQ_Handle h = f_root->add_EQ();
+      h.update_coef(mapping.output_var(j), 1);
+      h.update_coef(mapping.input_var(2 * j), -1);
+    }
+    mapping = Composition(mapping, stmt[*i].xform);
+    mapping.simplify();
+    
+    // match omega input/output variables to variable names in the code
+    for (int j = 1; j <= stmt[*i].IS.n_set(); j++)
+      mapping.name_input_var(j, stmt[*i].IS.set_var(j)->name());
+    for (int j = 1; j <= n; j++)
+      mapping.name_output_var(j,
+                              tmp_loop_var_name_prefix
+                              + to_string(tmp_loop_var_name_counter + j - 1));
+    mapping.setup_names();
+    
+    Relation known = Extend_Set(copy(this->known),
+                                mapping.n_out() - this->known.n_set());
+    //stmt[*i].code = outputStatement(ocg, stmt[*i].code, 0, mapping, known, std::vector<CG_outputRepr *>(mapping.n_out(), NULL));
+    std::vector<std::string> loop_vars;
+    for (int j = 1; j <= stmt[*i].IS.n_set(); j++)
+      loop_vars.push_back(stmt[*i].IS.set_var(j)->name());
+    std::vector<CG_outputRepr *> subs = output_substitutions(ocg,
+                                                             Inverse(copy(mapping)),
+                                                             std::vector<std::pair<CG_outputRepr *, int> >(mapping.n_out(),
+                                                                                                           std::make_pair(static_cast<CG_outputRepr *>(NULL), 0)));
+    stmt[*i].code = ocg->CreateSubstitutedStmt(0, stmt[*i].code, loop_vars,
+                                               subs);
+    stmt[*i].IS = Range(Restrict_Domain(mapping, stmt[*i].IS));
+    stmt[*i].IS.simplify();
+    
+    // replace original transformation relation with straight 1-1 mapping
+    mapping = Relation(n, 2 * n + 1);
+    f_root = mapping.add_and();
+    for (int j = 1; j <= n; j++) {
+      EQ_Handle h = f_root->add_EQ();
+      h.update_coef(mapping.output_var(2 * j), 1);
+      h.update_coef(mapping.input_var(j), -1);
+    }
+    for (int j = 1; j <= 2 * n + 1; j += 2) {
+      EQ_Handle h = f_root->add_EQ();
+      h.update_coef(mapping.output_var(j), 1);
+      h.update_const(-lex[j - 1]);
+    }
+    stmt[*i].xform = mapping;
+  }
+  
+  tmp_loop_var_name_counter += max_n;
+}
+
+void Loop::addKnown(const Relation &cond) {
+  
+  // invalidate saved codegen computation
+  delete last_compute_cgr_;
+  last_compute_cgr_ = NULL;
+  delete last_compute_cg_;
+  last_compute_cg_ = NULL;
+  
+  int n1 = this->known.n_set();
+  
+  Relation r = copy(cond);
+  int n2 = r.n_set();
+  
+  if (n1 < n2)
+    this->known = Extend_Set(this->known, n2 - n1);
+  else if (n1 > n2)
+    r = Extend_Set(r, n1 - n2);
+  
+  this->known = Intersection(this->known, r);
+}
+
+void Loop::removeDependence(int stmt_num_from, int stmt_num_to) {
+  // check for sanity of parameters
+  if (stmt_num_from >= stmt.size())
+    throw std::invalid_argument(
+      "invalid statement number " + to_string(stmt_num_from));
+  if (stmt_num_to >= stmt.size())
+    throw std::invalid_argument(
+      "invalid statement number " + to_string(stmt_num_to));
+  
+  dep.disconnect(stmt_num_from, stmt_num_to);
+}
+
+void Loop::dump() const {
+  for (int i = 0; i < stmt.size(); i++) {
+    std::vector<int> lex = getLexicalOrder(i);
+    std::cout << "s" << i + 1 << ": ";
+    for (int j = 0; j < stmt[i].loop_level.size(); j++) {
+      if (2 * j < lex.size())
+        std::cout << lex[2 * j];
+      switch (stmt[i].loop_level[j].type) {
+      case LoopLevelOriginal:
+        std::cout << "(dim:" << stmt[i].loop_level[j].payload << ")";
+        break;
+      case LoopLevelTile:
+        std::cout << "(tile:" << stmt[i].loop_level[j].payload << ")";
+        break;
+      default:
+        std::cout << "(unknown)";
+      }
+      std::cout << ' ';
+    }
+    for (int j = 2 * stmt[i].loop_level.size(); j < lex.size(); j += 2) {
+      std::cout << lex[j];
+      if (j != lex.size() - 1)
+        std::cout << ' ';
+    }
+    std::cout << std::endl;
+  }
+}
+
+bool Loop::nonsingular(const std::vector<std::vector<int> > &T) {
+  if (stmt.size() == 0)
+    return true;
+  
+  // check for sanity of parameters
+  for (int i = 0; i < stmt.size(); i++) {
+    if (stmt[i].loop_level.size() != num_dep_dim)
+      throw std::invalid_argument(
+        "nonsingular loop transformations must be applied to original perfect loop nest");
+    for (int j = 0; j < stmt[i].loop_level.size(); j++)
+      if (stmt[i].loop_level[j].type != LoopLevelOriginal)
+        throw std::invalid_argument(
+          "nonsingular loop transformations must be applied to original perfect loop nest");
+  }
+  if (T.size() != num_dep_dim)
+    throw std::invalid_argument("invalid transformation matrix");
+  for (int i = 0; i < stmt.size(); i++)
+    if (T[i].size() != num_dep_dim + 1 && T[i].size() != num_dep_dim)
+      throw std::invalid_argument("invalid transformation matrix");
+  // invalidate saved codegen computation
+  delete last_compute_cgr_;
+  last_compute_cgr_ = NULL;
+  delete last_compute_cg_;
+  last_compute_cg_ = NULL;
+  // build relation from matrix
+  Relation mapping(2 * num_dep_dim + 1, 2 * num_dep_dim + 1);
+  F_And *f_root = mapping.add_and();
+  for (int i = 0; i < num_dep_dim; i++) {
+    EQ_Handle h = f_root->add_EQ();
+    h.update_coef(mapping.output_var(2 * (i + 1)), -1);
+    for (int j = 0; j < num_dep_dim; j++)
+      if (T[i][j] != 0)
+        h.update_coef(mapping.input_var(2 * (j + 1)), T[i][j]);
+    if (T[i].size() == num_dep_dim + 1)
+      h.update_const(T[i][num_dep_dim]);
+  }
+  for (int i = 1; i <= 2 * num_dep_dim + 1; i += 2) {
+    EQ_Handle h = f_root->add_EQ();
+    h.update_coef(mapping.output_var(i), -1);
+    h.update_coef(mapping.input_var(i), 1);
+  }
+  
+  // update transformation relations
+  for (int i = 0; i < stmt.size(); i++)
+    stmt[i].xform = Composition(copy(mapping), stmt[i].xform);
+  
+  // update dependence graph
+  for (int i = 0; i < dep.vertex.size(); i++)
+    for (DependenceGraph::EdgeList::iterator j =
+           dep.vertex[i].second.begin(); j != dep.vertex[i].second.end();
+         j++) {
+      std::vector<DependenceVector> dvs = j->second;
+      for (int k = 0; k < dvs.size(); k++) {
+        DependenceVector &dv = dvs[k];
+        switch (dv.type) {
+        case DEP_W2R:
+        case DEP_R2W:
+        case DEP_W2W:
+        case DEP_R2R: {
+          std::vector<coef_t> lbounds(num_dep_dim), ubounds(
+            num_dep_dim);
+          for (int p = 0; p < num_dep_dim; p++) {
+            coef_t lb = 0;
+            coef_t ub = 0;
+            for (int q = 0; q < num_dep_dim; q++) {
+              if (T[p][q] > 0) {
+                if (lb == -posInfinity
+                    || dv.lbounds[q] == -posInfinity)
+                  lb = -posInfinity;
+                else
+                  lb += T[p][q] * dv.lbounds[q];
+                if (ub == posInfinity
+                    || dv.ubounds[q] == posInfinity)
+                  ub = posInfinity;
+                else
+                  ub += T[p][q] * dv.ubounds[q];
+              } else if (T[p][q] < 0) {
+                if (lb == -posInfinity
+                    || dv.ubounds[q] == posInfinity)
+                  lb = -posInfinity;
+                else
+                  lb += T[p][q] * dv.ubounds[q];
+                if (ub == posInfinity
+                    || dv.lbounds[q] == -posInfinity)
+                  ub = posInfinity;
+                else
+                  ub += T[p][q] * dv.lbounds[q];
+              }
+            }
+            if (T[p].size() == num_dep_dim + 1) {
+              if (lb != -posInfinity)
+                lb += T[p][num_dep_dim];
+              if (ub != posInfinity)
+                ub += T[p][num_dep_dim];
+            }
+            lbounds[p] = lb;
+            ubounds[p] = ub;
+          }
+          dv.lbounds = lbounds;
+          dv.ubounds = ubounds;
+          
+          break;
+        }
+        default:
+          ;
+        }
+      }
+      j->second = dvs;
+    }
+  
+  // set constant loop values
+  std::set<int> active;
+  for (int i = 0; i < stmt.size(); i++)
+    active.insert(i);
+  setLexicalOrder(0, active);
+  
+  return true;
+}
+
+
+bool Loop::is_dependence_valid_based_on_lex_order(int i, int j,
+                                                  const DependenceVector &dv, bool before) {
+  std::vector<int> lex_i = getLexicalOrder(i);
+  std::vector<int> lex_j = getLexicalOrder(j);
+  int last_dim;
+  if (!dv.is_scalar_dependence) {
+    for (last_dim = 0;
+         last_dim < lex_i.size() && (lex_i[last_dim] == lex_j[last_dim]);
+         last_dim++)
+      ;
+    last_dim = last_dim / 2;
+    if (last_dim == 0)
+      return true;
+    
+    for (int i = 0; i < last_dim; i++) {
+      if (dv.lbounds[i] > 0)
+        return true;
+      else if (dv.lbounds[i] < 0)
+        return false;
+    }
+  }
+  if (before)
+    return true;
+  
+  return false;
+  
+}
+