diff --git a/include/optimization/GVN.h b/include/optimization/GVN.h
index 9e0a82caf4ed5090557914e790a7165df3c46fc1..f4872d33136a450725eb8a3cb9e2d02630336826 100644
--- a/include/optimization/GVN.h
+++ b/include/optimization/GVN.h
@@ -69,6 +69,8 @@ class ConstantExpression : public Expression {
     }
     ConstantExpression(Constant *c) : Expression(e_constant), c_(c) {}
 
+    Constant *get_val() { return c_; }
+
   private:
     Constant *c_;
 };
@@ -199,20 +201,24 @@ class GEPExpression : public Expression {
 // unique expression: not equal to any one else
 class UniqueExpression : public Expression {
   public:
-    static std::shared_ptr<UniqueExpression> create(Instruction *instr) {
-        return std::make_shared<UniqueExpression>(instr);
+    static std::shared_ptr<UniqueExpression> create(Instruction *instr,
+                                                    size_t index) {
+        return std::make_shared<UniqueExpression>(instr, index);
     }
-    virtual std::string print() { return "(UNIQUE " + instr_->print() + ")"; }
+    // virtual std::string print() { return "(UNIQUE " + instr_->print() + ")";
+    // }
+    virtual std::string print() { return "v" + std::to_string(index_); }
 
     bool equiv(const UniqueExpression *other) const {
         return instr_ == other->instr_;
     }
 
-    UniqueExpression(Instruction *instr)
-        : Expression(e_unique), instr_(instr) {}
+    UniqueExpression(Instruction *instr, size_t index)
+        : Expression(e_unique), instr_(instr), index_(index) {}
 
   private:
     Instruction *instr_;
+    size_t index_;
 };
 } // namespace GVNExpression
 
@@ -276,7 +282,8 @@ class GVN : public Pass {
     partitions transferFunction(BasicBlock *bb);
     std::shared_ptr<GVNExpression::PhiExpression> valuePhiFunc(
         std::shared_ptr<GVNExpression::Expression>,
-        BasicBlock *bb);
+        BasicBlock *bb,
+        Instruction *instr);
     std::shared_ptr<GVNExpression::Expression> valueExpr(
         Instruction *instr,
         const partitions &part);
@@ -308,6 +315,7 @@ class GVN : public Pass {
     std::map<BasicBlock *, bool> _TOP;
     partitions join_helper(BasicBlock *pre1, BasicBlock *pre2);
     BasicBlock *curr_bb;
+    std::map<std::pair<Instruction *, Value *>, size_t> start_idx_;
     //
     // self add function
     //
@@ -317,11 +325,17 @@ class GVN : public Pass {
         Value *v,
         const partitions &part);
 
-    std::vector<std::shared_ptr<GVNExpression::Expression>> core_(
+    std::vector<std::shared_ptr<GVNExpression::Expression>> valueExpr_core_(
         Instruction *instr,
         const partitions &part,
-        size_t count,
+        const size_t count,
         bool fold_ = true);
+    Constant *constFold_core(const size_t count,
+                             const partitions &part,
+                             Instruction *instr,
+                             const std::vector<Value *> &operands);
+    void assign_start_idx_();
+    void dump_tmp(Function &);
 };
 
 bool operator==(const GVN::partitions &p1, const GVN::partitions &p2);
diff --git a/src/optimization/GVN.cpp b/src/optimization/GVN.cpp
index aee69a63ca5cbdc5e1521cfc1dd7734ecc010cc1..d53b95ff05d93f19c452524641138ff7de8d1ff0 100644
--- a/src/optimization/GVN.cpp
+++ b/src/optimization/GVN.cpp
@@ -199,6 +199,8 @@ dump_bb2partition(const std::map<BasicBlock *, GVN::partitions> &map) {
 static void
 print_partitions(const GVN::partitions &p) {
     if (p.empty()) {
+        // to del
+        // std::cout << "empty partitions\n";
         LOG_DEBUG << "empty partitions\n";
         return;
     }
@@ -206,13 +208,14 @@ print_partitions(const GVN::partitions &p) {
     for (auto &cc : p)
         log += print_congruence_class(*cc);
     LOG_DEBUG << log; // please don't use std::cout
+    // to del
+    // std::cout << log;
 }
 } // namespace utils
 
 GVN::partitions
 GVN::join_helper(BasicBlock *pre1, BasicBlock *pre2) {
     assert(not _TOP[pre1] or not _TOP[pre2] && "should flow here, not jump");
-
     if (_TOP[pre1])
         return pout_[pre2];
     else if (_TOP[pre2])
@@ -260,25 +263,70 @@ GVN::intersect(shared_ptr<CongruenceClass> ci, shared_ptr<CongruenceClass> cj) {
     if (c->members_.size()) // not empty
     {
         if (c->index_ == 0) {
-            c->index_ = new_number();
+            // it must be a phi instruction
+            // and be separated to 2 copy statement
+            // we should use the copy-stmt int the previous block
+            auto instr = static_cast<Instruction *>(*c->members_.begin());
+            auto instr_phi = dynamic_cast<PhiInst *>(instr);
+            int exact_idx;
+            // trick here: use the exact value number
+            if (instr_phi) {
+                auto exact_pre_bb =
+                    *(instr_phi->get_parent()->get_pre_basic_blocks().begin());
+                auto e = instr_phi->get_operand(
+                    pretend_copy_stmt(instr_phi, exact_pre_bb));
+                exact_idx = start_idx_.at(std::make_pair(instr_phi, e));
+            } else {
+                exact_idx = start_idx_.at(std::make_pair(instr, nullptr));
+            }
+            c->index_ = exact_idx;
             c->value_expr_ = c->value_phi_ =
                 PhiExpression::create(ci->value_expr_, cj->value_expr_);
         }
+        // ??
         c->leader_ = *c->members_.begin();
     }
 
     return c;
 }
 
+// assign start index for each instruction, including copy statement
+// ther logic here:
+// - use the same traver order as main run
+// - assign an incremental number for each instruction
+void
+GVN::assign_start_idx_() {
+    int res;
+    for (auto &bb : func_->get_basic_blocks()) {
+        for (auto &instr : bb.get_instructions()) {
+            if (not instr.is_phi() and not instr.is_void())
+                start_idx_[std::make_pair(&instr, nullptr)] = new_number();
+        }
+        // and the phi instruction in all the successors
+        for (auto succ : bb.get_succ_basic_blocks()) {
+            for (auto &instr : succ->get_instructions()) {
+                if (instr.is_phi()) {
+                    if ((res = pretend_copy_stmt(&instr, &bb)) == -1)
+                        continue;
+                    start_idx_[std::make_pair(&instr, instr.get_operand(res))] =
+                        new_number();
+                }
+            }
+        }
+    }
+    next_value_number_ = 1;
+}
+
 void
 GVN::detectEquivalences() {
+    int times = 0;
     bool changed;
     std::cout << "all the instruction address:" << std::endl;
     for (auto &bb : func_->get_basic_blocks()) {
         for (auto &instr : bb.get_instructions())
             std::cout << &instr << "\t" << instr.print() << std::endl;
     }
-
+    assign_start_idx_();
     // initialize pout with top
     for (auto &bb : func_->get_basic_blocks()) {
         _TOP[&bb] = true;
@@ -293,6 +341,7 @@ GVN::detectEquivalences() {
     // iterate until converge
     do {
         changed = false;
+        std::cout << ++times << "th iteration" << std::endl;
         for (auto &_bb : func_->get_basic_blocks()) {
             auto bb = &_bb;
             if (bb == Entry)
@@ -306,12 +355,12 @@ GVN::detectEquivalences() {
                     case 2: {
                         auto pre_1 = *pre_bbs_.begin();
                         auto pre_2 = *(++pre_bbs_.begin());
-                        pin_[bb] = join_helper(pre_1, pre_2);
+                        pin_[bb] = clone(join_helper(pre_1, pre_2));
                         break;
                     }
                     case 1: {
                         auto pre = *(pre_bbs_.begin());
-                        pin_[bb] = pout_[pre];
+                        pin_[bb] = clone(pout_[pre]);
                         break;
                     }
                     default:
@@ -324,9 +373,15 @@ GVN::detectEquivalences() {
 
             // check changes in pout
             changed |= not(part == pout_[bb]);
-            pout_[bb] = part;
+            pout_[bb] = clone(part);
             _TOP[bb] = false;
+
+            /* std::cout << "//-------\n"
+             *           << "//after transferFunction(basic-block="
+             *           << bb->get_name() << "), all pout:" << std::endl; */
+            // dump_tmp(*func_);
         }
+        // reset value number
     } while (changed);
 }
 
@@ -343,12 +398,52 @@ GVN::search_ve(Value *v, const GVN::partitions &part) {
     return nullptr;
 }
 
+// try constant fold for `count` operands
+// the related instr is `instr`
+Constant *
+GVN::constFold_core(const size_t count,
+                    const partitions &part,
+                    Instruction *instr,
+                    const std::vector<Value *> &operands) {
+    assert(count == 1 or count == 2);
+    Constant *res = nullptr;
+
+    // the first operand
+    auto op0_const_value = dynamic_cast<Constant *>(operands[0]);
+    auto op0_search_ = search_ve(operands[0], part);
+    auto op0_const_expr =
+        op0_search_ ? dynamic_cast<ConstantExpression *>(op0_search_.get())
+                    : nullptr;
+    if ((op0_const_value or op0_const_expr)) {
+        auto op0_const =
+            op0_const_value ? op0_const_value : op0_const_expr->get_val();
+        // by now: the type cast instruction can do constant fold
+        if (count == 1)
+            res = folder_->compute(instr, op0_const);
+        if (count == 2) {
+            // the second operand
+            auto op1_const_value = dynamic_cast<Constant *>(operands[1]);
+            auto op1_search_ = search_ve(operands[1], part);
+            auto op1_const_expr =
+                op1_search_
+                    ? dynamic_cast<ConstantExpression *>(op1_search_.get())
+                    : nullptr;
+            if (op1_const_value or op1_const_expr) {
+                auto op1_const = op1_const_value ? op1_const_value
+                                                 : op1_const_expr->get_val();
+                res = folder_->compute(instr, op0_const, op1_const);
+            }
+        }
+    }
+    return res;
+}
+
 // for each op, try to find the
 std::vector<shared_ptr<Expression>>
-GVN::core_(Instruction *instr,
-           const partitions &part,
-           size_t count,
-           bool fold_) {
+GVN::valueExpr_core_(Instruction *instr,
+                     const partitions &part,
+                     const size_t count,
+                     bool fold_) {
     assert(not(fold_ and count > 2));
 
     Value *v;
@@ -357,22 +452,12 @@ GVN::core_(Instruction *instr,
     std::vector<shared_ptr<Expression>> ret;
 
     // if able to fold, then fold
-    fold_ &= bool(dynamic_cast<Constant *>(operands[0]));
-    if (count == 2)
-        fold_ &= bool(dynamic_cast<Constant *>(operands[1]));
     if (fold_) {
-        Constant *res;
-        if (count == 1) {
-            res =
-                folder_->compute(instr, dynamic_cast<Constant *>(operands[0]));
-        } else {
-            // count == 2
-            res = folder_->compute(instr,
-                                   dynamic_cast<Constant *>(operands[0]),
-                                   dynamic_cast<Constant *>(operands[1]));
+        Constant *res = nullptr;
+        if ((res = constFold_core(count, part, instr, operands))) {
+            ret.push_back(ConstantExpression::create(res));
+            return ret;
         }
-        ret.push_back(ConstantExpression::create(res));
-        return ret;
     }
 
     // normal case:
@@ -405,7 +490,7 @@ GVN::valueExpr(Instruction *instr, const partitions &part) {
         return tmp;
 
     if (instr->isBinary() or instr->is_cmp() or instr->is_fcmp()) {
-        res = core_(instr, part, 2);
+        res = valueExpr_core_(instr, part, 2);
         if (res.size() == 1) // constant fold
             return res[0];
         else
@@ -414,7 +499,7 @@ GVN::valueExpr(Instruction *instr, const partitions &part) {
     } else if (instr->is_phi()) {
         err = "phi";
     } else if (instr->is_fp2si() or instr->is_si2fp() or instr->is_zext()) {
-        res = core_(instr, part, 1);
+        res = valueExpr_core_(instr, part, 1);
         if (res[0]->get_expr_type() == Expression::e_constant)
             return res[0];
         Type *dest_type;
@@ -439,12 +524,16 @@ GVN::valueExpr(Instruction *instr, const partitions &part) {
                 instr->get_instr_type(), res[0], dest_type);
         }
     } else if (instr->is_gep()) {
-        res = core_(instr, part, instr->get_operands().size(), false);
+        res = valueExpr_core_(instr, part, instr->get_operands().size(), false);
         auto ptr = res[0];
         res.erase(res.begin());
         return GEPExpression::create(ptr, res);
     } else if (instr->is_load() or instr->is_alloca() or instr->is_call()) {
-        return UniqueExpression::create(instr);
+        auto ret = search_ve(instr, part);
+        if (ret)
+            return ret;
+        else
+            return UniqueExpression::create(instr, next_value_number_);
     }
 
     std::cerr << "Undefined case: " << err << std::endl;
@@ -459,8 +548,10 @@ GVN::valueExpr(Instruction *instr, const partitions &part) {
 //
 /// \param bb basic block in which the transfer function is called
 GVN::partitions
-GVN::transferFunction(Instruction *x, Value *e, partitions pin) {
-    partitions pout = pin;
+GVN::transferFunction(Instruction *instr, Value *e, partitions pin) {
+    next_value_number_ = start_idx_[std::make_pair(instr, e)];
+
+    partitions pout = clone(pin);
     // TODO: deal with copy-stmt case
     // ?? deal with copy statement
     auto e_instr = dynamic_cast<Instruction *>(e);
@@ -469,10 +560,13 @@ GVN::transferFunction(Instruction *x, Value *e, partitions pin) {
            "A value must be from an instruction or constant");
     // erase the old record for x
     std::set<Value *>::iterator it;
-    for (auto c : pin)
-        if ((it = std::find(c->members_.begin(), c->members_.end(), x)) !=
+    for (auto c : pout)
+        if ((it = std::find(c->members_.begin(), c->members_.end(), instr)) !=
             c->members_.end()) {
             c->members_.erase(it);
+            if (c->members_.empty())
+                pout.erase(c);
+            break;
         }
 
     // TODO: get different ValueExpr by Instruction::OpID, modify pout
@@ -483,25 +577,29 @@ GVN::transferFunction(Instruction *x, Value *e, partitions pin) {
         if (e_const)
             ve = ConstantExpression::create(e_const);
         else
-            ve = valueExpr(e_instr, pin);
+            ve = valueExpr(e_instr, pout);
     } else
-        ve = valueExpr(x, pin);
-    auto vpf = valuePhiFunc(ve, curr_bb);
+        ve = valueExpr(instr, pout);
+    auto vpf = valuePhiFunc(ve, curr_bb, instr);
 
     // TODO: set leader
     for (auto c : pout) {
         if (ve == c->value_expr_ or
             (vpf and c->value_phi_ and *vpf == *c->value_phi_)) {
-            c->value_expr_ = ve;
-            c->members_.insert(x);
+            // c->value_expr_ = ve;
+            c->members_.insert(instr);
             return pout;
         }
     }
     auto c = createCongruenceClass(new_number());
-    c->members_.insert(x);
-    c->leader_ = x;
+    c->members_.insert(instr);
     c->value_expr_ = ve;
     c->value_phi_ = vpf;
+    if (c->value_expr_->get_expr_type() == Expression::e_constant)
+        c->leader_ =
+            static_cast<ConstantExpression *>(c->value_expr_.get())->get_val();
+    else
+        c->leader_ = instr;
     pout.insert(c);
     return pout;
 }
@@ -520,8 +618,6 @@ GVN::transferFunction(BasicBlock *bb) {
      * utils::print_partitions(pin_[bb]);
      * LOG_INFO << "pout before:\n";
      * utils::print_partitions(pout_[bb]);  */
-    std::cout << "for basic block " << bb->get_name() << ", pin:" << std::endl;
-    utils::print_partitions(pin_[bb]);
 
     // iterate through all instructions in the block
     for (auto &instr : bb->get_instructions()) {
@@ -539,39 +635,88 @@ GVN::transferFunction(BasicBlock *bb) {
             }
         }
     }
-    /* LOG_INFO << "pout after:\n";
-     * utils::print_partitions(part);
-     * std::cout << std::endl; */
+    std::cout << "-------\n"
+              << "for basic block " << bb->get_name() << ", pout:" << std::endl;
+    utils::print_partitions(part);
     return part;
 }
 
+// NOTE: only instruction op matter
 shared_ptr<PhiExpression>
-GVN::valuePhiFunc(shared_ptr<Expression> ve, BasicBlock *bb) {
+GVN::valuePhiFunc(shared_ptr<Expression> ve,
+                  BasicBlock *bb,
+                  Instruction *instr) {
     // TODO
+    // get 2 predecessors
+    auto pre_bbs_ = bb->get_pre_basic_blocks();
+    if (pre_bbs_.size() == 1)
+        return nullptr;
+    auto pre_1 = *pre_bbs_.begin();
+    auto pre_2 = *(++pre_bbs_.begin());
+
+    // check expression form
     if (ve->get_expr_type() != Expression::e_bin)
         return nullptr;
     auto ve_bin = static_cast<BinaryExpression *>(ve.get());
-    if (ve_bin->lhs_->get_expr_type() != Expression::e_phi or
+    if (ve_bin->lhs_->get_expr_type() != Expression::e_phi and
         ve_bin->rhs_->get_expr_type() != Expression::e_phi)
         return nullptr;
 
+    shared_ptr<Expression> vi{}, vj{};
+    shared_ptr<BinaryExpression> vl_merge{}, vr_merge{};
+    shared_ptr<Expression> vl_merge_E{}, vr_merge_E{};
     // get 2 phi expressions
-    auto lhs = static_cast<PhiExpression *>(ve_bin->lhs_.get());
-    auto rhs = static_cast<PhiExpression *>(ve_bin->rhs_.get());
-    // get 2 predecessors
-    auto pre_bbs_ = bb->get_pre_basic_blocks();
-    auto pre_1 = *pre_bbs_.begin();
-    auto pre_2 = *(++pre_bbs_.begin());
+    auto lhs_phi = dynamic_cast<PhiExpression *>(ve_bin->lhs_.get());
+    auto rhs_phi = dynamic_cast<PhiExpression *>(ve_bin->rhs_.get());
+
+    // set vl_merge and vr_merge
+    if (ve_bin->lhs_->get_expr_type() == Expression::e_phi and
+        ve_bin->rhs_->get_expr_type() == Expression::e_phi) {
+        // try to get the merged value expression
+        vl_merge =
+            BinaryExpression::create(ve_bin->op_, lhs_phi->lhs_, rhs_phi->lhs_);
+        vr_merge =
+            BinaryExpression::create(ve_bin->op_, lhs_phi->rhs_, rhs_phi->rhs_);
+    } else if (ve_bin->lhs_->get_expr_type() == Expression::e_phi) {
+        vl_merge =
+            BinaryExpression::create(ve_bin->op_, lhs_phi->lhs_, ve_bin->rhs_);
+        vr_merge =
+            BinaryExpression::create(ve_bin->op_, lhs_phi->rhs_, ve_bin->rhs_);
+    } else {
+        vl_merge =
+            BinaryExpression::create(ve_bin->op_, ve_bin->lhs_, rhs_phi->lhs_);
+        vr_merge =
+            BinaryExpression::create(ve_bin->op_, ve_bin->lhs_, rhs_phi->rhs_);
+    }
+
+    // constant fold
+    if (vl_merge->lhs_->get_expr_type() == Expression::e_constant and
+        vl_merge->rhs_->get_expr_type() == Expression::e_constant) {
+        auto vl_merge_l =
+            dynamic_cast<ConstantExpression *>(vl_merge->lhs_.get());
+        auto vl_merge_r =
+            dynamic_cast<ConstantExpression *>(vl_merge->rhs_.get());
+        vl_merge_E = ConstantExpression::create(folder_->compute(
+            instr, vl_merge_l->get_val(), vl_merge_r->get_val()));
+    } else
+        vl_merge_E = vl_merge;
+    if (vr_merge->lhs_->get_expr_type() == Expression::e_constant and
+        vr_merge->rhs_->get_expr_type() == Expression::e_constant) {
+        auto vr_merge_l =
+            dynamic_cast<ConstantExpression *>(vr_merge->lhs_.get());
+        auto vr_merge_r =
+            dynamic_cast<ConstantExpression *>(vr_merge->rhs_.get());
+        vr_merge_E = ConstantExpression::create(folder_->compute(
+            instr, vr_merge_l->get_val(), vr_merge_r->get_val()));
+    } else
+        vr_merge_E = vr_merge;
 
-    // try to get the merged value expression
-    auto vl_merge = BinaryExpression::create(ve_bin->op_, lhs->lhs_, rhs->lhs_);
-    auto vr_merge = BinaryExpression::create(ve_bin->op_, lhs->rhs_, rhs->rhs_);
-    auto vi = getVN(pout_[pre_1], vl_merge);
-    auto vj = getVN(pout_[pre_2], vr_merge);
+    vi = getVN(pout_[pre_1], vl_merge_E);
+    vj = getVN(pout_[pre_2], vr_merge_E);
     if (vi == nullptr)
-        vi = valuePhiFunc(vl_merge, pre_1);
+        vi = valuePhiFunc(vl_merge_E, pre_1, instr);
     if (vj == nullptr)
-        vj = valuePhiFunc(vr_merge, pre_2);
+        vj = valuePhiFunc(vr_merge_E, pre_2, instr);
 
     if (vi and vj)
         return PhiExpression::create(vi, vj);
@@ -688,6 +833,19 @@ GVN::run() {
         gvn_json << "]";
 }
 
+void
+GVN::dump_tmp(Function &f) {
+    std::string gvn_json;
+    if (dump_json_) {
+        gvn_json += "{\n\"function\": ";
+        gvn_json += "\"" + f.get_name() + "\", ";
+        gvn_json += "\n\"pout\": " + utils::dump_bb2partition(pout_);
+        gvn_json += "},";
+    }
+    gvn_json += "]";
+    std::cout << gvn_json << std::endl;
+}
+
 template <typename T>
 static bool
 equiv_as(const Expression &lhs, const Expression &rhs) {
@@ -729,6 +887,7 @@ GVN::partitions
 GVN::clone(const partitions &p) {
     partitions data;
     for (auto &cc : p) {
+        assert(not cc->members_.empty());
         data.insert(std::make_shared<CongruenceClass>(*cc));
     }
     return data;
diff --git a/tests/4-ir-opt/testcases/GVN/functional/.gitignore b/tests/4-ir-opt/testcases/GVN/functional/.gitignore
index fd645655007deecf92e33c8371dd762c0251d69a..f6bb428e4bd7d8c3b7cfa32afd694d7f2754c818 100644
--- a/tests/4-ir-opt/testcases/GVN/functional/.gitignore
+++ b/tests/4-ir-opt/testcases/GVN/functional/.gitignore
@@ -1 +1,4 @@
 *.ll
+*th
+tmp*
+gvn.json
diff --git a/tests/4-ir-opt/testcases/GVN/functional/clear.sh b/tests/4-ir-opt/testcases/GVN/functional/clear.sh
index ddad120f63075b1c150ebe7fbe5425d96a901420..b3835ba9ab44c6b4611c5b3376767fe09c377ee8 100755
--- a/tests/4-ir-opt/testcases/GVN/functional/clear.sh
+++ b/tests/4-ir-opt/testcases/GVN/functional/clear.sh
@@ -1,4 +1,5 @@
 rm -rf *.ll
 rm -rf gvn.json
 rm -rf `ls | grep -v "\."`
+rm -rf tmp*