diff --git a/examples/matrix.cpp b/examples/matrix.cpp
index 89d4aa9ec..78c8d7194 100644
--- a/examples/matrix.cpp
+++ b/examples/matrix.cpp
@@ -35,7 +35,8 @@ int main() {
    program->codegen(&module);
    llvm::LLVMContext llvm_context;
    llvm::Module llvm_module("test", llvm_context);
-   tdl::codegen::lowering(module, llvm_module);
+   tdl::codegen::selection selection;
+   selection.run(module, llvm_module);
    llvm::PrintModulePass print(llvm::outs());
    llvm::AnalysisManager<llvm::Module> analysis;
    print.run(llvm_module, analysis);
diff --git a/include/codegen/allocation.h b/include/codegen/allocation.h
index b2112b20b..d23b98501 100644
--- a/include/codegen/allocation.h
+++ b/include/codegen/allocation.h
@@ -1,9 +1,45 @@
 #ifndef TDL_INCLUDE_IR_CODEGEN_STORAGE_ALLOC_H
 #define TDL_INCLUDE_IR_CODEGEN_STORAGE_ALLOC_H
 
+#include <map>
+#include <set>
+
 namespace tdl{
+
+namespace ir{
+  class value;
+  class function;
+}
+
 namespace codegen{
 
+class layout;
+class target_tuner;
+class liveness;
+class loop_info;
+
+class allocation {
+public:
+  // accessors
+  unsigned get_num_bytes(ir::value *x) const;
+  unsigned get_offset(ir::value *x)    const { return offsets_.at(x); }
+  unsigned get_allocated_size()        const { return allocated_size_; }
+  bool has_double_buffer(ir::value *x) const { return double_buffer_.find(x) != double_buffer_.end(); }
+
+  // run
+  void run(ir::function &fn);
+
+private:
+  std::map<ir::value*, unsigned> offsets_;
+  std::set<ir::value*> double_buffer_;
+  std::map<ir::value*, unsigned> num_bytes_;
+  size_t allocated_size_;
+  // dependences
+  liveness *liveness_;
+  layout *layout_;
+  loop_info *loop_info_;
+};
+
 }
 }
 
diff --git a/include/codegen/layout.h b/include/codegen/layout.h
index 40227001c..1fd6deeda 100644
--- a/include/codegen/layout.h
+++ b/include/codegen/layout.h
@@ -1,9 +1,44 @@
 #ifndef TDL_INCLUDE_IR_CODEGEN_LAYOUT_H
 #define TDL_INCLUDE_IR_CODEGEN_LAYOUT_H
 
-namespace tdl{
+#include <vector>
+#include <map>
+
+namespace tdl {
+
+namespace ir {
+  class function;
+  class instruction;
+  class value;
+}
+
 namespace codegen{
 
+struct shared_view_info{
+  ir::value *usr;
+  bool has_dedicated_storage;
+};
+
+class layout {
+private:
+  typedef std::vector<shared_view_info> shared_view_val_t;
+
+  void add_phi_nodes(ir::value *v);
+  void add_shared_views(ir::value *v);
+
+public:
+  // accessors
+  unsigned get_num_shared_views(ir::value *v);
+  shared_view_info get_shared_view(ir::value *v, unsigned idx);
+
+  // run
+  bool run(ir::function &fn);
+
+private:
+  std::map<ir::value*, shared_view_val_t> shared_views_;
+};
+
+
 }
 }
 
diff --git a/include/codegen/liveness.h b/include/codegen/liveness.h
index 9afbc4e46..8a6806c2e 100644
--- a/include/codegen/liveness.h
+++ b/include/codegen/liveness.h
@@ -1,9 +1,61 @@
 #ifndef TDL_INCLUDE_IR_CODEGEN_LIVENESS_H
 #define TDL_INCLUDE_IR_CODEGEN_LIVENESS_H
 
+#include <map>
+
 namespace tdl{
+
+namespace ir{
+  class value;
+  class function;
+}
+
 namespace codegen{
 
+class layout;
+
+typedef unsigned slot_index;
+
+struct segment {
+  slot_index start;
+  slot_index end;
+
+  bool contains(slot_index idx) const {
+    return start <= idx && idx < end;
+  }
+
+  bool intersect(const segment &Other){
+    return contains(Other.start) || Other.contains(start);
+  }
+};
+
+class liveness {
+private:
+  typedef std::map<ir::value*, slot_index> indices_map_t;
+  typedef std::map<ir::value*, segment>    intervals_map_t;
+  typedef std::map<ir::value*, bool>       has_storage_map_t;
+
+public:
+  /// Intervals iterators...
+  using iterator = intervals_map_t::iterator;
+  using const_iterator = intervals_map_t::const_iterator;
+
+public:
+
+  // accessors
+  const intervals_map_t& intervals() const { return intervals_; }
+  segment get_interval(ir::value* v) const { return intervals_.at(v); }
+
+  // run
+  void run(ir::function *fn);
+
+private:
+  has_storage_map_t has_dedicated_storage_;
+  indices_map_t indices_;
+  intervals_map_t intervals_;
+  layout* layouts_;
+};
+
 }
 }
 
diff --git a/include/codegen/selection.h b/include/codegen/selection.h
index 5c2bff41e..b55725c05 100644
--- a/include/codegen/selection.h
+++ b/include/codegen/selection.h
@@ -9,191 +9,35 @@
 #include "ir/type.h"
 
 
+namespace llvm{
+  class Type;
+  class Value;
+  class Instruction;
+  class Constant;
+  class LLVMContext;
+}
+
 namespace tdl{
 namespace codegen{
 
-using namespace llvm;
+class selection{
+  typedef std::map<ir::value *, llvm::Value *> vmap_t;
+  typedef std::map<ir::basic_block *, llvm::BasicBlock *> bmap_t;
 
-/* convert ir::type to Type */
-Type *llvm_type(ir::type *ty, LLVMContext &ctx) {
-  // function
-  if(auto* tt = dynamic_cast<ir::function_type*>(ty)){
-    Type *return_ty = llvm_type(tt->get_return_ty(), ctx);
-    std::vector<Type*> param_tys;
-    std::transform(tt->params_begin(), tt->params_end(), std::back_inserter(param_tys),
-                   [&ctx](ir::type* t){ return llvm_type(t, ctx);});
-    return FunctionType::get(return_ty, param_tys, false);
-  }
-  // pointer
-  if(ty->is_pointer_ty()){
-    Type *elt_ty = llvm_type(ty->get_pointer_element_ty(), ctx);
-    unsigned addr_space = ty->get_pointer_address_space();
-    return PointerType::get(elt_ty, addr_space);
-  }
-  // integer
-  if(ty->is_integer_ty()){
-    unsigned bitwidth = ty->get_integer_bitwidth();
-    return IntegerType::get(ctx, bitwidth);
-  }
-  // primitive types
-  switch(ty->get_type_id()){
-    case ir::type::VoidTyID:      return Type::getVoidTy(ctx);
-    case ir::type::HalfTyID:      return Type::getHalfTy(ctx);
-    case ir::type::FloatTyID:     return Type::getFloatTy(ctx);
-    case ir::type::DoubleTyID:    return Type::getDoubleTy(ctx);
-    case ir::type::X86_FP80TyID:  return Type::getX86_FP80Ty(ctx);
-    case ir::type::PPC_FP128TyID: return Type::getPPC_FP128Ty(ctx);
-    case ir::type::LabelTyID:     return Type::getLabelTy(ctx);
-    case ir::type::MetadataTyID:  return Type::getMetadataTy(ctx);
-    case ir::type::TokenTyID:     return Type::getTokenTy(ctx);
-    default: break;
-  }
-  // unknown type
-  throw std::runtime_error("unknown conversion from ir::type to Type");
-}
+private:
+  llvm::Type*        llvm_type(ir::type *ty, llvm::LLVMContext &ctx);
+  llvm::Value*       llvm_value(ir::value *v,llvm:: LLVMContext &ctx);
+  llvm::Instruction* llvm_inst(ir::instruction *inst, llvm::LLVMContext &ctx);
+  llvm::Constant*    llvm_constant(ir::constant *cst, llvm::LLVMContext &ctx);
 
-Value* llvm_value(ir::value *v, LLVMContext &ctx,
-                        std::map<ir::value*, Value*> &vmap,
-                        std::map<ir::basic_block*, BasicBlock*> &bmap);
+public:
+  void run(ir::module &src, llvm::Module &dst);
 
-/* convert ir::constant to Constant */
-Constant *llvm_constant(ir::constant *cst, LLVMContext &ctx) {
-  Type *dst_ty = llvm_type(cst->get_type(), ctx);
-  if(auto* cc = dynamic_cast<ir::constant_int*>(cst))
-    return ConstantInt::get(dst_ty, cc->get_value());
-  if(auto* cc = dynamic_cast<ir::constant_fp*>(cst))
-    return ConstantFP::get(dst_ty, cc->get_value());
-  // unknown constant
-  throw std::runtime_error("unknown conversion from ir::constant to Constant");
-}
-
-
-/* convert ir::instruction to Instruction */
-Instruction *llvm_inst(ir::instruction *inst, LLVMContext & ctx,
-                             std::map<ir::value*, Value*> &vmap,
-                             std::map<ir::basic_block*, BasicBlock*> &bmap) {
-  auto value = [&](ir::value *x) { return llvm_value(x, ctx, vmap, bmap); };
-  auto block = [&](ir::basic_block *x) { return bmap.at(x); };
-  auto type = [&](ir::type *x) { return llvm_type(x, ctx); };
-  if(auto* ii = dynamic_cast<ir::cond_branch_inst*>(inst)){
-    BasicBlock *true_dest  = block(ii->get_true_dest());
-    BasicBlock *false_dest = block(ii->get_false_dest());
-    Value *cond = value(ii->get_cond());
-    return BranchInst::Create(true_dest, false_dest, cond);
-  }
-  if(auto* ii = dynamic_cast<ir::uncond_branch_inst*>(inst)){
-    BasicBlock *dest = block(ii->get_dest());
-    return BranchInst::Create(dest);
-  }
-  if(auto* ii = dynamic_cast<ir::phi_node*>(inst)){
-    Type *ty = type(ii->get_type());
-    unsigned num_ops = ii->get_num_operands();
-    return PHINode::Create(ty, num_ops, ii->get_name());
-  }
-  if(auto* ii = dynamic_cast<ir::return_inst*>(inst)){
-    ir::value *ret_val = ii->get_return_value();
-    return ReturnInst::Create(ctx, ret_val?value(ret_val):nullptr);
-  }
-  if(auto* ii = dynamic_cast<ir::binary_operator*>(inst)){
-    Value *lhs = value(ii->get_operand(0));
-    Value *rhs = value(ii->get_operand(1));
-    return BinaryOperator::Create(ii->get_op(), lhs, rhs, ii->get_name());
-  }
-  if(auto* ii = dynamic_cast<ir::icmp_inst*>(inst)){
-    CmpInst::Predicate pred = ii->get_pred();
-    Value *lhs = value(ii->get_operand(0));
-    Value *rhs = value(ii->get_operand(1));
-    return CmpInst::Create(Instruction::ICmp, pred, lhs, rhs, ii->get_name());
-  }
-  if(auto* ii = dynamic_cast<ir::fcmp_inst*>(inst)){
-    CmpInst::Predicate pred = ii->get_pred();
-    Value *lhs = value(ii->get_operand(0));
-    Value *rhs = value(ii->get_operand(1));
-    return FCmpInst::Create(Instruction::FCmp, pred, lhs, rhs, ii->get_name());
-  }
-  if(auto* ii = dynamic_cast<ir::cast_inst*>(inst)){
-    Value *arg = value(ii->get_operand(0));
-    Type *dst_ty = type(ii->get_type());
-    return CastInst::Create(ii->get_op(), arg, dst_ty, ii->get_name());
-  }
-  if(auto* ii = dynamic_cast<ir::getelementptr_inst*>(inst)){
-    std::vector<Value*> idx_vals;
-    std::transform(ii->idx_begin(), ii->idx_end(), std::back_inserter(idx_vals),
-                   [&value](ir::value* x){ return value(x);});
-    Type *source_ty = type(ii->get_source_elt_ty());
-    Value *arg = value(ii->get_operand(0));
-    return GetElementPtrInst::Create(source_ty, arg, idx_vals, ii->get_name());
-  }
-  if(ir::load_inst* ii = dynamic_cast<ir::load_inst*>(inst)){
-    Value *ptr = value(ii->get_pointer_operand());
-    return new LoadInst(ptr, ii->get_name());
-  }
-  // unknown instruction
-  throw std::runtime_error("unknown conversion from ir::type to Type");
-}
-
-Value* llvm_value(ir::value *v, LLVMContext &ctx,
-                        std::map<ir::value*, Value*> &vmap,
-                        std::map<ir::basic_block*, BasicBlock*> &bmap) {
-  if(vmap.find(v) != vmap.end())
-    return vmap.at(v);
-  // create operands
-  if(auto *uu = dynamic_cast<ir::user*>(v))
-    for(ir::value* u: uu->ops())
-      vmap[u] = llvm_value(u, ctx, vmap, bmap);
-  if(auto *cc = dynamic_cast<ir::constant*>(v))
-    return llvm_constant(cc, ctx);
-  // instruction
-  if(auto *ii = dynamic_cast<ir::instruction*>(v))
-    return llvm_inst(ii, ctx, vmap, bmap);
-  // unknown value
-  throw std::runtime_error("unknown conversion from ir::value to Value");
-}
-
-void lowering(ir::module &src, Module &dst){
-  std::map<ir::value*, Value*> vmap;
-  std::map<ir::basic_block*, BasicBlock*> bmap;
-  LLVMContext &dst_ctx = dst.getContext();
-  IRBuilder<> dst_builder(dst_ctx);
-  // iterate over functions
-  for(ir::function *fn: src.get_function_list()) {
-    // create LLVM function
-    FunctionType *fn_ty = (FunctionType*)llvm_type(fn->get_fn_type(), dst_ctx);
-    Function *dst_fn = Function::Create(fn_ty, Function::ExternalLinkage, "kernel", &dst);
-//    std::cout << ((FunctionType*)fn_ty)->getNumParams() << std::endl;
-    // map parameters
-    for(unsigned i = 0; i < fn->args().size(); i++)
-      vmap[fn->args()[i]] = &*(dst_fn->arg_begin() + i);
-    // create blocks
-    for(ir::basic_block *block: fn->blocks()) {
-      BasicBlock *dst_block = BasicBlock::Create(dst_ctx, block->get_name(), dst_fn);
-      bmap[block] = dst_block;
-    }
-    // iterate through block
-    for(ir::basic_block *block: fn->blocks()) {
-      dst_builder.SetInsertPoint(bmap[block]);
-      for(ir::instruction *inst: block->get_inst_list()) {
-        Instruction *dst_inst = llvm_inst(inst, dst_ctx, vmap, bmap);
-        vmap[inst] = dst_inst;
-        dst_builder.Insert(dst_inst);
-      }
-    }
-    // add phi operands
-    for(ir::basic_block *block: fn->blocks())
-    for(ir::instruction *inst: block->get_inst_list())
-    if(auto *phi = dynamic_cast<ir::phi_node*>(inst)){
-      PHINode *dst_phi = (PHINode*)vmap.at(phi);
-      for(unsigned i = 0; i < phi->get_num_incoming(); i++){
-        ir::value *inc_val = phi->get_incoming_value(i);
-        ir::basic_block *inc_block = phi->get_incoming_block(i);
-        Value *llvm_inc_val = llvm_value(inc_val, dst_ctx, vmap, bmap);
-        BasicBlock *llvm_block = bmap[inc_block];
-        dst_phi->addIncoming(llvm_inc_val, llvm_block);
-      }
-    }
-  }
-}
+private:
+  vmap_t vmap_;
+  bmap_t bmap_;
 
+};
 
 }
 }
diff --git a/include/codegen/tune.h b/include/codegen/tune.h
index f1871167a..98ba7e327 100644
--- a/include/codegen/tune.h
+++ b/include/codegen/tune.h
@@ -1,10 +1,56 @@
-#ifndef TDL_INCLUDE_IR_CODEGEN_TUNE_H
-#define TDL_INCLUDE_IR_CODEGEN_TUNE_H
+//#ifndef TDL_INCLUDE_IR_CODEGEN_TUNE_H
+//#define TDL_INCLUDE_IR_CODEGEN_TUNE_H
 
-namespace tdl{
-namespace codegen{
+//namespace tdl{
+//namespace codegen{
 
-}
-}
+//// Layout binding pass
+//class TLVMAddTunerParams: public FunctionPass {
+//private:
+//  enum CType{
+//    Layout = 0, Shape = 1
+//  };
+//  // Params pool
+//  SmallVector<MDNode*, 8> LParamsPool;
+//  // Constraints
+//  typedef std::pair<Value*, unsigned> CNodeType;
+//  typedef DenseMap<CNodeType, DenseSet<CNodeType>> CGraphType;
+//  // Layout constraints
+//  CGraphType LCGraph;
+//  DenseSet<CNodeType> LCNodes;
+//  // Shape constraints
+//  CGraphType SCGraph;
+//  DenseSet<CNodeType> SCNodes;
+//  // Relational
+//  std::map<std::pair<Value*, std::string>, std::function<unsigned* ()>> ExtraParams;
+//  DenseSet<unsigned> Constants;
 
-#endif
+//  void addConstraint(CNodeType X, CNodeType Y, CType CT);
+//  void initCPhi(Instruction *I);
+//  void initCGraph(Instruction *V);
+//  void connectedComponents(CNodeType X, ArrayRef<MDNode *> Vals, CType CT, DenseSet<CNodeType> &Nodes, CGraphType &Graph);
+
+//public:
+//  static char ID;
+//  TLVMAddTunerParams(): FunctionPass(ID){ }
+
+//  void getAnalysisUsage(AnalysisUsage & AU) const override;
+//  bool runOnFunction(Function &F) override;
+
+//private:
+//  std::map<std::pair<Instruction*, std::string>, Constant*> KnownParams;
+//};
+
+//class TLVMAddTunerConstraints: public FunctionPass {
+//public:
+//  static char ID;
+//  TLVMAddTunerConstraints(): FunctionPass(ID){ }
+
+//  void getAnalysisUsage(AnalysisUsage & AU) const override;
+//  bool runOnFunction(Function &F) override;
+//};
+
+//}
+//}
+
+//#endif
diff --git a/include/ir/instructions.h b/include/ir/instructions.h
index 875b2b0a0..9d390b8cb 100644
--- a/include/ir/instructions.h
+++ b/include/ir/instructions.h
@@ -332,6 +332,11 @@ public:
 };
 
 
+// matmul
+
+class matmul_inst: public instruction {
+
+};
 
 }
 }
diff --git a/include/ir/type.h b/include/ir/type.h
index fb268326a..ab7b20ef1 100644
--- a/include/ir/type.h
+++ b/include/ir/type.h
@@ -51,8 +51,10 @@ public:
   // type attributes
   unsigned get_fp_mantissa_width() const;
   unsigned get_integer_bitwidth() const;
+  unsigned get_size_in_bits() const;
   type *get_scalar_ty() const;
   const std::vector<unsigned> &get_tile_shapes() const;
+  unsigned get_tile_num_elements() const;
   type *get_tile_element_ty() const;
   unsigned get_pointer_address_space() const;
   type *get_pointer_element_ty() const;
@@ -135,6 +137,7 @@ private:
 public:
   // accessors
   const std::vector<unsigned>& get_shapes() const { return shapes_; }
+  unsigned get_num_elements();
 
   // factory methods
   static tile_type* get(type *ty, const std::vector<unsigned> &shapes);