Added support for KLEE index-based array optimization

5 files changed, 778 insertions, 0 deletions

diff --git a/lib/Expr/ArrayExprOptimizer.cpp b/lib/Expr/ArrayExprOptimizer.cpp
new file mode 100644
index 00000000..d3e8cbab
--- /dev/null
+++ b/lib/Expr/ArrayExprOptimizer.cpp
@@ -0,0 +1,135 @@
+#include "klee/ArrayExprOptimizer.h"
+
+#include "klee/ArrayExprRewriter.h"
+#include "klee/util/BitArray.h"
+
+#include <iostream>
+
+using namespace klee;
+
+namespace klee {
+llvm::cl::opt<ArrayOptimizationType> OptimizeArray(
+    "optimize-array",
+    llvm::cl::values(
+        clEnumValN(INDEX, "index", "Index-based transformation"),
+        clEnumValEnd),
+    llvm::cl::init(NONE),
+    llvm::cl::desc("Optimize accesses to either concrete or concrete/symbolic "
+                   "arrays. (default=off)"));
+};
+
+void ExprOptimizer::optimizeExpr(const ref<Expr> &e, ref<Expr> &result,
+                                 bool valueOnly) {
+  unsigned hash = e->hash();
+  if (cacheExprUnapplicable.find(hash) != cacheExprUnapplicable.end()) {
+    return;
+  }
+
+  // Find cached expressions
+  auto cached = cacheExprOptimized.find(hash);
+  if (cached != cacheExprOptimized.end()) {
+    result = cached->second;
+    return;
+  }
+
+  // ----------------------- INDEX-BASED OPTIMIZATION -------------------------
+  if (!valueOnly && OptimizeArray == INDEX) {
+    array2idx_ty arrays;
+    ConstantArrayExprVisitor aev(arrays);
+    aev.visit(e);
+
+    if (arrays.size() == 0 || aev.isIncompatible()) {
+      // We do not optimize expressions other than those with concrete
+      // arrays with a symbolic index
+      // If we cannot optimize the expression, we return a failure only
+      // when we are not combining the optimizations
+      if (OptimizeArray == INDEX) {
+        cacheExprUnapplicable.insert(hash);
+        return;
+      }
+    } else {
+      mapIndexOptimizedExpr_ty idx_valIdx;
+
+      // Compute those indexes s.t. orig_expr =equisat= (k==i|k==j|..)
+      if (computeIndexes(arrays, e, idx_valIdx)) {
+        if (idx_valIdx.size() > 0) {
+          // Create new expression on indexes
+          result = ExprRewriter::createOptExpr(e, arrays, idx_valIdx);
+        } else {
+          klee_warning("OPT_I: infeasible branch!");
+          result = ConstantExpr::create(0, Expr::Bool);
+        }
+        // Add new expression to cache
+        if (result.get()) {
+          klee_warning("OPT_I: successful");
+          cacheExprOptimized[hash] = result;
+        } else {
+          klee_warning("OPT_I: unsuccessful");
+        }
+      } else {
+        klee_warning("OPT_I: unsuccessful");
+        cacheExprUnapplicable.insert(hash);
+      }
+    }
+  }
+}
+
+bool ExprOptimizer::computeIndexes(array2idx_ty &arrays, const ref<Expr> &e,
+                                   mapIndexOptimizedExpr_ty &idx_valIdx) const {
+  bool success = false;
+  // For each constant array found
+  for (auto &element : arrays) {
+    const Array *arr = element.first;
+
+    assert(arr->isConstantArray() && "Array is not concrete");
+    assert(element.second.size() == 1 && "Multiple indexes on the same array");
+
+    IndexTransformationExprVisitor idxt_v(arr);
+    idxt_v.visit(e);
+    assert((idxt_v.getWidth() % arr->range == 0) && "Read is not aligned");
+    Expr::Width width = idxt_v.getWidth() / arr->range;
+
+    if (idxt_v.getMul().get()) {
+      // If we have a MulExpr in the index, we can optimize our search by
+      // skipping all those indexes that are not multiple of such value.
+      // In fact, they will be rejected by the MulExpr interpreter since it
+      // will not find any integer solution
+      Expr &e = *idxt_v.getMul();
+      ConstantExpr &ce = static_cast<ConstantExpr &>(e);
+      uint64_t mulVal = (*ce.getAPValue().getRawData());
+      // So far we try to limit this optimization, but we may try some more
+      // aggressive conditions (i.e. mulVal > width)
+      if (width == 1 && mulVal > 1)
+        width = mulVal;
+    }
+
+    // For each concrete value 'i' stored in the array
+    for (size_t aIdx = 0; aIdx < arr->constantValues.size(); aIdx += width) {
+      Assignment *a = new Assignment();
+      v_arr_ty objects;
+      std::vector<std::vector<unsigned char> > values;
+
+      // For each symbolic index Expr(k) found
+      for (auto &index_it : element.second) {
+        ref<Expr> idx = index_it;
+        ref<Expr> val = ConstantExpr::alloc(aIdx, arr->getDomain());
+        // We create a partial assignment on 'k' s.t. Expr(k)==i
+        bool assignmentSuccess =
+            AssignmentGenerator::generatePartialAssignment(idx, val, a);
+        success |= assignmentSuccess;
+
+        // If the assignment satisfies both the expression 'e' and the PC
+        ref<Expr> evaluation = a->evaluate(e);
+        if (assignmentSuccess && evaluation->isTrue()) {
+          if (idx_valIdx.find(idx) == idx_valIdx.end()) {
+            idx_valIdx.insert(std::make_pair(idx, std::vector<ref<Expr> >()));
+          }
+          idx_valIdx[idx]
+              .push_back(ConstantExpr::alloc(aIdx, arr->getDomain()));
+        }
+      }
+      delete a;
+    }
+  }
+  return success;
+}
diff --git a/lib/Expr/ArrayExprRewriter.cpp b/lib/Expr/ArrayExprRewriter.cpp
new file mode 100644
index 00000000..d4dc9a21
--- /dev/null
+++ b/lib/Expr/ArrayExprRewriter.cpp
@@ -0,0 +1,141 @@
+#include "klee/ArrayExprRewriter.h"
+
+#include "klee/util/BitArray.h"
+
+#include "llvm/Support/CommandLine.h"
+
+using namespace klee;
+
+ref<Expr> ExprRewriter::createOptExpr(const ref<Expr> &e,
+		const array2idx_ty &arrays,
+		const mapIndexOptimizedExpr_ty &idx_valIdx) {
+    return rewrite(e, arrays, idx_valIdx);
+}
+
+ref<Expr>
+ExprRewriter::rewrite(const ref<Expr> &e,
+                                   const array2idx_ty &arrays,
+                                   const mapIndexOptimizedExpr_ty &idx_valIdx) {
+  ref<Expr> notFound;
+  std::vector<ref<Expr> > eqExprs;
+  bool invert = false;
+  for (auto &element : arrays) {
+	const Array* arr = element.first;
+	std::vector<ref<Expr> > indexes = element.second;
+
+	IndexTransformationExprVisitor idxt_v(arr);
+	idxt_v.visit(e);
+
+	assert((idxt_v.getWidth() % element.first->range == 0) && "Read is not aligned");
+
+	Expr::Width width = idxt_v.getWidth() / element.first->range;
+	if (idxt_v.getMul().get()) {
+	  // If we have a MulExpr in the index, we can optimize our search by
+	  // skipping all those indexes that are not multiple of such value.
+	  // In fact, they will be rejected by the MulExpr interpreter since it
+	  // will not find any integer solution
+	  Expr &e = *idxt_v.getMul();
+	  ConstantExpr &ce = static_cast<ConstantExpr &>(e);
+	  llvm::APInt val = ce.getAPValue();
+	  uint64_t mulVal = val.getZExtValue();
+	  // So far we try to limit this optimization, but we may try some more
+	  // aggressive conditions (i.e. mulVal > width)
+	  if (width == 1 && mulVal > 1)
+		width = mulVal;
+	}
+
+	for (std::vector<ref<Expr> >::const_iterator index_it = indexes.begin();
+		 index_it != indexes.end(); ++index_it) {
+	  if (idx_valIdx.find((*index_it)) == idx_valIdx.end()) {
+		continue;
+	  }
+	  auto opt_indexes = idx_valIdx.at((*index_it));
+	  if (opt_indexes.size() == 0) {
+		// We continue with other solutions
+		continue;
+	  } else if (opt_indexes.size() == 1) {
+		// We treat this case as a special one, and we create an EqExpr (e.g. k==i)
+		eqExprs.push_back(createEqExpr((*index_it), opt_indexes[0]));
+	  } else {
+		Expr::Width idxWidth = (*index_it).get()->getWidth();
+		unsigned set = 0;
+		BitArray ba(arr->size/width);
+		for (auto &vals : opt_indexes) {
+		  ConstantExpr &ce = static_cast<ConstantExpr &>(*vals);
+		  llvm::APInt v = ce.getAPValue();
+		  ba.set(v.getZExtValue() / width);
+		  set++;
+		}
+		if (set > 0 && set < arr->size/width)
+		  invert = ((float)set / (float)(arr->size/width)) > 0.5 ? true : false;
+		int start = -1;
+		for (unsigned i = 0; i < arr->size/width; ++i) {
+		  if ((!invert && ba.get(i)) || (invert && !ba.get(i))) {
+			if (start < 0)
+			  start = i;
+		  } else {
+			if (start >= 0) {
+			  if (i - start == 1) {
+				eqExprs.push_back(createEqExpr((*index_it), ConstantExpr::create(start*width, idxWidth)));
+			  } else {
+				// create range expr
+				ref<Expr> s = ConstantExpr::create(start*width, idxWidth);
+				ref<Expr> e = ConstantExpr::create((i-1)*width, idxWidth);
+				eqExprs.push_back(createRangeExpr((*index_it), s, e));
+			  }
+			  start = -1;
+			}
+		  }
+		}
+		if (start >= 0) {
+		  if ((arr->size/width) - start == 1) {
+			eqExprs.push_back(createEqExpr((*index_it), ConstantExpr::create(start*width, idxWidth)));
+		  } else {
+			// create range expr
+			ref<Expr> s = ConstantExpr::create(start*width, idxWidth);
+			ref<Expr> e = ConstantExpr::create(((arr->size/width) - 1)*width, idxWidth);
+			eqExprs.push_back(createRangeExpr((*index_it), s, e));
+		  }
+		}
+	  }
+	}
+  }
+  if (eqExprs.size() == 0) {
+	return notFound;
+  } else if (eqExprs.size() == 1) {
+	if (isa<AndExpr>(eqExprs[0])) {
+	  return EqExpr::alloc(ConstantExpr::alloc(invert ? 0 : 1, (eqExprs[0])->getWidth()),
+						   eqExprs[0]);
+	}
+	return invert ? NotExpr::alloc(eqExprs[0]) : eqExprs[0];
+  } else {
+	// We have found at least 2 indexes, we combine them using an OrExpr (e.g. k==i|k==j)
+	ref<Expr> orExpr = concatenateOrExpr(eqExprs.begin(), eqExprs.end());
+	// Create Eq expression for true branch
+	return EqExpr::alloc(ConstantExpr::alloc(invert ? 0 : 1, (orExpr)->getWidth()), orExpr);
+  }
+}
+
+ref<Expr> ExprRewriter::concatenateOrExpr(
+    const std::vector<ref<Expr> >::const_iterator begin,
+    const std::vector<ref<Expr> >::const_iterator end) {
+  if (begin + 2 == end) {
+    return OrExpr::alloc(ZExtExpr::alloc((*begin), Expr::Int32),
+                         ZExtExpr::alloc((*(begin + 1)), Expr::Int32));
+  } else {
+    return OrExpr::alloc(ZExtExpr::alloc((*begin), Expr::Int32),
+                         concatenateOrExpr(begin + 1, end));
+  }
+}
+
+ref<Expr> ExprRewriter::createEqExpr(const ref<Expr> &index,
+                                     const ref<Expr> &valIndex) {
+  return EqExpr::alloc(valIndex, index);
+}
+
+ref<Expr> ExprRewriter::createRangeExpr(const ref<Expr> &index,
+                                        const ref<Expr> &valStart,
+                                        const ref<Expr> &valEnd) {
+  return AndExpr::alloc(UleExpr::alloc(valStart, index),
+                        UleExpr::alloc(index, valEnd));
+}
diff --git a/lib/Expr/ArrayExprVisitor.cpp b/lib/Expr/ArrayExprVisitor.cpp
new file mode 100644
index 00000000..26ddbb95
--- /dev/null
+++ b/lib/Expr/ArrayExprVisitor.cpp
@@ -0,0 +1,171 @@
+#include "klee/util/ArrayExprVisitor.h"
+
+#include "klee/Internal/Support/ErrorHandling.h"
+
+#include <algorithm>
+
+using namespace klee;
+
+//------------------------------ HELPER FUNCTIONS ---------------------------//
+bool ArrayExprHelper::isReadExprAtOffset(ref<Expr> e, const ReadExpr *base,
+                                         ref<Expr> offset) {
+  const ReadExpr *re = dyn_cast<ReadExpr>(e.get());
+  if (!re || (re->getWidth() != Expr::Int8))
+    return false;
+  return SubExpr::create(re->index, base->index) == offset;
+}
+
+ReadExpr *ArrayExprHelper::hasOrderedReads(const ConcatExpr &ce) {
+  const ReadExpr *base = dyn_cast<ReadExpr>(ce.getKid(0));
+
+  // right now, all Reads are byte reads but some
+  // transformations might change this
+  if (!base || base->getWidth() != Expr::Int8)
+    return NULL;
+
+  // Get stride expr in proper index width.
+  Expr::Width idxWidth = base->index->getWidth();
+  ref<Expr> strideExpr = ConstantExpr::alloc(-1, idxWidth);
+  ref<Expr> offset = ConstantExpr::create(0, idxWidth);
+
+  ref<Expr> e = ce.getKid(1);
+
+  // concat chains are unbalanced to the right
+  while (e->getKind() == Expr::Concat) {
+    offset = AddExpr::create(offset, strideExpr);
+    if (!isReadExprAtOffset(e->getKid(0), base, offset))
+      return NULL;
+    e = e->getKid(1);
+  }
+
+  offset = AddExpr::create(offset, strideExpr);
+  if (!isReadExprAtOffset(e, base, offset))
+    return NULL;
+
+  return cast<ReadExpr>(e.get());
+}
+
+//--------------------------- INDEX-BASED OPTIMIZATION-----------------------//
+ExprVisitor::Action
+ConstantArrayExprVisitor::visitConcat(const ConcatExpr &ce) {
+  ReadExpr *base = ArrayExprHelper::hasOrderedReads(ce);
+  if (base) {
+    // It is an interesting ReadExpr if it contains a concrete array
+    // that is read at a symbolic index
+    if (base->updates.root->isConstantArray() &&
+        !isa<ConstantExpr>(base->index)) {
+      for (const UpdateNode *un = base->updates.head; un; un = un->next) {
+        if (!isa<ConstantExpr>(un->index) || !isa<ConstantExpr>(un->value)) {
+          incompatible = true;
+          return Action::skipChildren();
+        }
+      }
+      IndexCompatibilityExprVisitor compatible;
+      compatible.visit(base->index);
+      if (compatible.isCompatible() &&
+          addedIndexes.find(base->index.get()->hash()) == addedIndexes.end()) {
+        if (arrays.find(base->updates.root) == arrays.end()) {
+          arrays.insert(
+              std::make_pair(base->updates.root, std::vector<ref<Expr> >()));
+        } else {
+          // Another possible index to resolve, currently unsupported
+          incompatible = true;
+          return Action::skipChildren();
+        }
+        arrays.find(base->updates.root)->second.push_back(base->index);
+        addedIndexes.insert(base->index.get()->hash());
+      } else if (compatible.hasInnerReads()) {
+        // This Read has an inner Read, we want to optimize the inner one
+        // to create a cascading effect during assignment evaluation
+        return Action::doChildren();
+      }
+      return Action::skipChildren();
+    }
+  }
+  return Action::doChildren();
+}
+ExprVisitor::Action ConstantArrayExprVisitor::visitRead(const ReadExpr &re) {
+  // It is an interesting ReadExpr if it contains a concrete array
+  // that is read at a symbolic index
+  if (re.updates.root->isConstantArray() && !isa<ConstantExpr>(re.index)) {
+    for (const UpdateNode *un = re.updates.head; un; un = un->next) {
+      if (!isa<ConstantExpr>(un->index) || !isa<ConstantExpr>(un->value)) {
+        incompatible = true;
+        return Action::skipChildren();
+      }
+    }
+    IndexCompatibilityExprVisitor compatible;
+    compatible.visit(re.index);
+    if (compatible.isCompatible() &&
+        addedIndexes.find(re.index.get()->hash()) == addedIndexes.end()) {
+      if (arrays.find(re.updates.root) == arrays.end()) {
+        arrays.insert(
+            std::make_pair(re.updates.root, std::vector<ref<Expr> >()));
+      } else {
+        // Another possible index to resolve, currently unsupported
+        incompatible = true;
+        return Action::skipChildren();
+      }
+      arrays.find(re.updates.root)->second.push_back(re.index);
+      addedIndexes.insert(re.index.get()->hash());
+    } else if (compatible.hasInnerReads()) {
+      // This Read has an inner Read, we want to optimize the inner one
+      // to create a cascading effect during assignment evaluation
+      return Action::doChildren();
+    }
+    return Action::skipChildren();
+  } else if (re.updates.root->isSymbolicArray()) {
+    incompatible = true;
+  }
+
+  return Action::doChildren();
+}
+
+ExprVisitor::Action
+IndexCompatibilityExprVisitor::visitRead(const ReadExpr &re) {
+  if (re.updates.head) {
+    compatible = false;
+    return Action::skipChildren();
+  } else if (re.updates.root->isConstantArray() &&
+             !isa<ConstantExpr>(re.index)) {
+    compatible = false;
+    inner = true;
+    return Action::skipChildren();
+  }
+  return Action::doChildren();
+}
+ExprVisitor::Action IndexCompatibilityExprVisitor::visitURem(const URemExpr &) {
+  compatible = false;
+  return Action::skipChildren();
+}
+ExprVisitor::Action IndexCompatibilityExprVisitor::visitSRem(const SRemExpr &) {
+  compatible = false;
+  return Action::skipChildren();
+}
+ExprVisitor::Action IndexCompatibilityExprVisitor::visitOr(const OrExpr &) {
+  compatible = false;
+  return Action::skipChildren();
+}
+
+ExprVisitor::Action
+IndexTransformationExprVisitor::visitConcat(const ConcatExpr &ce) {
+  if (ReadExpr *re = dyn_cast<ReadExpr>(ce.getKid(0))) {
+    if (re->updates.root->hash() == array->hash() && width < ce.getWidth()) {
+      if (width == Expr::InvalidWidth)
+        width = ce.getWidth();
+    }
+  } else if (ReadExpr *re = dyn_cast<ReadExpr>(ce.getKid(1))) {
+    if (re->updates.root->hash() == array->hash() && width < ce.getWidth()) {
+      if (width == Expr::InvalidWidth)
+        width = ce.getWidth();
+    }
+  }
+  return Action::doChildren();
+}
+ExprVisitor::Action IndexTransformationExprVisitor::visitMul(const MulExpr &e) {
+  if (isa<ConstantExpr>(e.getKid(0)))
+    mul = e.getKid(0);
+  else if (isa<ConstantExpr>(e.getKid(0)))
+    mul = e.getKid(1);
+  return Action::doChildren();
+}
diff --git a/lib/Expr/AssignmentGenerator.cpp b/lib/Expr/AssignmentGenerator.cpp
new file mode 100644
index 00000000..755263f0
--- /dev/null
+++ b/lib/Expr/AssignmentGenerator.cpp
@@ -0,0 +1,327 @@
+#include "klee/AssignmentGenerator.h"
+
+#include "llvm/Support/raw_ostream.h"
+
+using namespace klee;
+
+bool AssignmentGenerator::generatePartialAssignment(const ref<Expr> &e,
+                                                    ref<Expr> &val,
+                                                    Assignment *&a) {
+  return helperGenerateAssignment(e, val, a, e->getWidth(), false);
+}
+
+bool AssignmentGenerator::helperGenerateAssignment(const ref<Expr> &e,
+                                                   ref<Expr> &val,
+                                                   Assignment *&a,
+                                                   Expr::Width width,
+                                                   bool sign) {
+  Expr &ep = *e.get();
+  switch (ep.getKind()) {
+
+  // ARITHMETIC
+  case Expr::Add: {
+    // val = val - kid
+    ref<Expr> kid_val;
+    ref<Expr> kid_expr;
+    if (isa<ConstantExpr>(ep.getKid(0))) {
+      kid_val = ep.getKid(0);
+      kid_expr = ep.getKid(1);
+    } else if (isa<ConstantExpr>(ep.getKid(1))) {
+      kid_val = ep.getKid(1);
+      kid_expr = ep.getKid(0);
+    } else {
+      return false;
+    }
+    if (!ExtractExpr::create(kid_val, kid_val.get()->getWidth() - 1, 1).get()->isZero()) {
+      // FIXME: really bad hack to support those cases in which KLEE creates
+      // Add expressions with negative values
+      val = createAddExpr(kid_val, val);
+    } else {
+      val = createSubExpr(kid_val, val);
+    }
+    return helperGenerateAssignment(kid_expr, val, a, width, sign);
+  }
+  case Expr::Sub: {
+    // val = val + kid
+    ref<Expr> kid_val;
+    ref<Expr> kid_expr;
+    if (isa<ConstantExpr>(ep.getKid(0))) {
+      kid_val = ep.getKid(0);
+      kid_expr = ep.getKid(1);
+    } else if (isa<ConstantExpr>(ep.getKid(1))) {
+      kid_val = ep.getKid(1);
+      kid_expr = ep.getKid(0);
+    } else {
+      return false;
+    }
+    val = createAddExpr(kid_val, val);
+    return helperGenerateAssignment(kid_expr, val, a, width, sign);
+  }
+  case Expr::Mul: {
+    // val = val / kid (check for sign)
+    ref<Expr> kid_val;
+    ref<Expr> kid_expr;
+    if (isa<ConstantExpr>(ep.getKid(0))) {
+      kid_val = ep.getKid(0);
+      kid_expr = ep.getKid(1);
+    } else if (isa<ConstantExpr>(ep.getKid(1))) {
+      kid_val = ep.getKid(1);
+      kid_expr = ep.getKid(0);
+    } else {
+      return false;
+    }
+
+    if (kid_val.get()->isZero()) {
+      return false;
+    } else if (!createDivRem(kid_val, val, sign)->isZero()) {
+      return false;
+    }
+    val = createDivExpr(kid_val, val, sign);
+    return helperGenerateAssignment(kid_expr, val, a, width, sign);
+  }
+  case Expr::UDiv:
+  // val = val * kid
+  // no break, falling down to case SDiv
+  case Expr::SDiv: {
+    // val = val * kid
+    ref<Expr> kid_val;
+    ref<Expr> kid_expr;
+    if (isa<ConstantExpr>(ep.getKid(0))) {
+      kid_val = ep.getKid(0);
+      kid_expr = ep.getKid(1);
+    } else if (isa<ConstantExpr>(ep.getKid(1))) {
+      kid_val = ep.getKid(1);
+      kid_expr = ep.getKid(0);
+    } else {
+      return false;
+    }
+    val = createMulExpr(kid_val, val);
+    return helperGenerateAssignment(kid_expr, val, a, width, sign);
+  }
+
+  // LOGICAL
+  case Expr::LShr: {
+    if (!isa<ConstantExpr>(ep.getKid(1))) {
+      return false;
+    }
+    ref<Expr> kid_val = ep.getKid(1);
+    val = createShlExpr(val, kid_val);
+    return helperGenerateAssignment(ep.getKid(0), val, a, width, sign);
+  }
+  case Expr::Shl: {
+    if (!isa<ConstantExpr>(ep.getKid(1))) {
+      return false;
+    }
+    ref<Expr> kid_val = ep.getKid(1);
+    val = createLShrExpr(val, kid_val);
+    return helperGenerateAssignment(ep.getKid(0), val, a, width, sign);
+  }
+  case Expr::Not: {
+    return helperGenerateAssignment(ep.getKid(0), val, a, width, sign);
+  }
+  case Expr::And: {
+    // val = val & kid
+    ref<Expr> kid_val;
+    ref<Expr> kid_expr;
+    if (isa<ConstantExpr>(ep.getKid(0))) {
+      kid_val = ep.getKid(0);
+      kid_expr = ep.getKid(1);
+    } else if (isa<ConstantExpr>(ep.getKid(1))) {
+      kid_val = ep.getKid(1);
+      kid_expr = ep.getKid(0);
+    } else {
+      return false;
+    }
+    val = createAndExpr(kid_val, val);
+    return helperGenerateAssignment(kid_expr, val, a, width, sign);
+  }
+
+  // CASTING
+  case Expr::ZExt: {
+    val = createExtractExpr(ep.getKid(0), val);
+    return helperGenerateAssignment(ep.getKid(0), val, a, width, false);
+  }
+  case Expr::SExt: {
+    val = createExtractExpr(ep.getKid(0), val);
+    return helperGenerateAssignment(ep.getKid(0), val, a, width, true);
+  }
+
+  // SPECIAL
+  case Expr::Concat: {
+    ReadExpr *base = hasOrderedReads(&ep);
+    if (base) {
+      return helperGenerateAssignment(ref<Expr>(base), val, a, ep.getWidth(),
+                                      sign);
+    } else {
+      klee_warning("Not supported");
+      ep.printKind(llvm::errs(), ep.getKind());
+      return false;
+    }
+  }
+  case Expr::Extract: {
+    val = createExtendExpr(ep.getKid(0), val);
+    return helperGenerateAssignment(ep.getKid(0), val, a, width, sign);
+  }
+
+  // READ
+  case Expr::Read: {
+    ReadExpr &re = static_cast<ReadExpr &>(ep);
+    if (isa<ConstantExpr>(re.index)) {
+      if (re.updates.root->isSymbolicArray()) {
+        ConstantExpr &index = static_cast<ConstantExpr &>(*re.index.get());
+        std::vector<unsigned char> c_value =
+            getIndexedValue(getByteValue(val), index, re.updates.root->size);
+        if (c_value.size() == 0) {
+          return false;
+        }
+        if (a->bindings.find(re.updates.root) == a->bindings.end()) {
+          a->bindings.insert(std::make_pair(re.updates.root, c_value));
+        } else {
+          return false;
+        }
+      }
+    } else {
+      return helperGenerateAssignment(re.index, val, a, width, sign);
+    }
+    return true;
+  }
+  default:
+    std::string type_str;
+    llvm::raw_string_ostream rso(type_str);
+    ep.printKind(rso, ep.getKind());
+    klee_warning("%s is not supported", rso.str().c_str());
+    return false;
+  }
+}
+
+bool AssignmentGenerator::isReadExprAtOffset(ref<Expr> e, const ReadExpr *base,
+                                             ref<Expr> offset) {
+  const ReadExpr *re = dyn_cast<ReadExpr>(e.get());
+  if (!re || (re->getWidth() != Expr::Int8))
+    return false;
+  return SubExpr::create(re->index, base->index) == offset;
+}
+
+ReadExpr *AssignmentGenerator::hasOrderedReads(ref<Expr> e) {
+  assert(e->getKind() == Expr::Concat);
+
+  const ReadExpr *base = dyn_cast<ReadExpr>(e->getKid(0));
+
+  // right now, all Reads are byte reads but some
+  // transformations might change this
+  if (!base || base->getWidth() != Expr::Int8)
+    return NULL;
+
+  // Get stride expr in proper index width.
+  Expr::Width idxWidth = base->index->getWidth();
+  ref<Expr> strideExpr = ConstantExpr::alloc(-1, idxWidth);
+  ref<Expr> offset = ConstantExpr::create(0, idxWidth);
+
+  e = e->getKid(1);
+
+  // concat chains are unbalanced to the right
+  while (e->getKind() == Expr::Concat) {
+    offset = AddExpr::create(offset, strideExpr);
+    if (!isReadExprAtOffset(e->getKid(0), base, offset))
+      return NULL;
+    e = e->getKid(1);
+  }
+
+  offset = AddExpr::create(offset, strideExpr);
+  if (!isReadExprAtOffset(e, base, offset))
+    return NULL;
+
+  return cast<ReadExpr>(e.get());
+}
+
+ref<Expr> AssignmentGenerator::createSubExpr(const ref<Expr> &l, ref<Expr> &r) {
+  return SubExpr::create(r, l);
+}
+
+ref<Expr> AssignmentGenerator::createAddExpr(const ref<Expr> &l, ref<Expr> &r) {
+  return AddExpr::create(r, l);
+}
+
+ref<Expr> AssignmentGenerator::createMulExpr(const ref<Expr> &l, ref<Expr> &r) {
+  return MulExpr::create(r, l);
+}
+
+ref<Expr> AssignmentGenerator::createDivRem(const ref<Expr> &l, ref<Expr> &r,
+                                            bool sign) {
+  if (sign)
+    return SRemExpr::create(r, l);
+  else
+    return URemExpr::create(r, l);
+}
+
+ref<Expr> AssignmentGenerator::createDivExpr(const ref<Expr> &l, ref<Expr> &r,
+                                             bool sign) {
+  if (sign)
+    return SDivExpr::create(r, l);
+  else
+    return UDivExpr::create(r, l);
+}
+
+ref<Expr> AssignmentGenerator::createShlExpr(const ref<Expr> &l, ref<Expr> &r) {
+  return ShlExpr::create(r, l);
+}
+
+ref<Expr> AssignmentGenerator::createLShrExpr(const ref<Expr> &l,
+                                              ref<Expr> &r) {
+  return LShrExpr::create(r, l);
+}
+
+ref<Expr> AssignmentGenerator::createAndExpr(const ref<Expr> &l, ref<Expr> &r) {
+  return AndExpr::create(r, l);
+}
+
+ref<Expr> AssignmentGenerator::createExtractExpr(const ref<Expr> &l,
+                                                 ref<Expr> &r) {
+  return ExtractExpr::create(r, 0, l.get()->getWidth());
+}
+
+ref<Expr> AssignmentGenerator::createExtendExpr(const ref<Expr> &l,
+                                                ref<Expr> &r) {
+  if (l.get()->getKind() == Expr::ZExt) {
+    return ZExtExpr::create(r, l.get()->getWidth());
+  } else {
+    return SExtExpr::create(r, l.get()->getWidth());
+  }
+}
+
+std::vector<unsigned char> AssignmentGenerator::getByteValue(ref<Expr> &val) {
+  std::vector<unsigned char> toReturn;
+  if (ConstantExpr *value = dyn_cast<ConstantExpr>(val)) {
+    for (unsigned w = 0; w < val.get()->getWidth() / 8; ++w) {
+      ref<ConstantExpr> byte = value->Extract(w * 8, Expr::Int8);
+      unsigned char mem_val;
+      byte->toMemory(&mem_val);
+      toReturn.push_back(mem_val);
+    }
+  }
+  return toReturn;
+}
+
+std::vector<unsigned char>
+AssignmentGenerator::getIndexedValue(const std::vector<unsigned char> &c_val,
+                                     ConstantExpr &index,
+                                     const unsigned int size) {
+  std::vector<unsigned char> toReturn;
+  const llvm::APInt index_val = index.getAPValue();
+  assert(!index_val.isSignBit() && "Negative index");
+  const uint64_t id = index_val.getZExtValue() / c_val.size();
+  uint64_t arraySize = size / c_val.size();
+  for (uint64_t i = 0; i < arraySize; ++i) {
+    if (i == id) {
+      for (unsigned arr_i = 0; arr_i < c_val.size(); ++arr_i) {
+        toReturn.push_back(c_val[arr_i]);
+      }
+    } else {
+      for (unsigned arr_i = 0; arr_i < c_val.size(); ++arr_i) {
+        toReturn.push_back(0);
+      }
+    }
+  }
+
+  return toReturn;
+}
diff --git a/lib/Expr/CMakeLists.txt b/lib/Expr/CMakeLists.txt
index 4c63fe5b..74407295 100644
--- a/lib/Expr/CMakeLists.txt
+++ b/lib/Expr/CMakeLists.txt
@@ -8,7 +8,11 @@
 #===------------------------------------------------------------------------===#
 klee_add_component(kleaverExpr
   ArrayCache.cpp
+  ArrayExprOptimizer.cpp
+  ArrayExprRewriter.cpp
+  ArrayExprVisitor.cpp
   Assigment.cpp
+  AssignmentGenerator.cpp
   Constraints.cpp
   ExprBuilder.cpp
   Expr.cpp