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+# Lab4 实验文档
+- [Lab4 实验文档](#lab4-实验文档)
+  - [0. 前言](#0-前言)
+  - [1. GVN 基础知识](#1-gvn-基础知识)
+    - [1.1 GVN 简介](#11-gvn-简介)
+    - [1.2 GVN 相关概念](#12-gvn-相关概念)
+      - [1. IR 假设](#1-ir-假设)
+      - [2. Expression 概念](#2-expression-概念)
+      - [3. 等价概念](#3-等价概念)
+      - [4. Value Expression 概念](#4-value-expression-概念)
+      - [5. Value phi-function 概念](#5-value-phi-function-概念)
+      - [6. Partition](#6-partition)
+      - [7. Join 操作](#7-join-操作)
+      - [8. 变量等价与表达式等价](#8-变量等价与表达式等价)
+      - [9. Transfer Function](#9-transfer-function)
+  - [2. GVN 算法（论文中提供的伪代码）](#2-gvn-算法论文中提供的伪代码)
+  - [3. 实验内容](#3-实验内容)
+    - [3.1 GVN pass 实现内容要求](#31-gvn-pass-实现内容要求)
+    - [3.2 GVN 辅助类](#32-gvn-辅助类)
+    - [3.3 注册及运行 GVN Pass](#33-注册及运行-gvn-pass)
+      - [注册 Pass](#注册-pass)
+      - [运行 Pass](#运行-pass)
+    - [3.3 自动测试](#33-自动测试)
+    - [3.4 Tips](#34-tips)
+  - [4. 提交要求](#4-提交要求)
+    - [目录结构](#目录结构)
+    - [提交要求和评分标准](#提交要求和评分标准)
+## 0. 前言
+
+在 Lab4.1 中，我们介绍了 SSA IR，并阐明了其优势。本次实验中我们需要在 SSA IR 基础上，实现一个基于数据流分析的冗余消除的优化 Pass : Global Value Numbering（全局值编号）。
+## 1. GVN 基础知识
+
+### 1.1 GVN 简介
+
+GVN(Global Value Numbering) 全局值编号，是一个基于 SSA 格式的优化，通过建立变量，表达式到值编号的映射关系，从而检测到冗余计算代码并删除。本次实验采用的算法参考论文为：**[Detection of Redundant Expressions: A Complete and Polynomial-Time Algorithm in SSA](./gvn.pdf)** 在该论文中，提出了一种适合 SSA IR ，多项式算法复杂度的数据流分析方式的算法，能够实现对冗余代码完备的检测。本次实验中，我们将在`Light IR` 上实现该数据流分析算法，并根据数据流分析结果删掉冗余代码，达到优化目的。
+
+### 1.2 GVN 相关概念
+
+#### 1. IR 假设
+
+将IR抽象为具有空的`entry block`与`exit block`的控制流图（CFG）。块内包含形式为`x = e`的赋值语句，其中`e`为表达式，`x`为变量。每个bb块最多可以有两个前驱，有两个前驱的bb块被称为`join block`。
+
+#### 2. Expression 概念
+
+一个`Expression`（表达式）可以是一个常量，一个变量，或者是$`x⊕y`$的形式，其中 x 与 y 是常量或者变量， ⊕ 代表一个通用的二元运算符。一个`Expression`也可以是 $`\phi_k(x,y)`$ 的形式，其中 x, y 是变量，并且 k 表示 join block。这种形式的 `Expression`被称作 `phi` 函数。基于 Lab4.1 对`phi`指令概念的理解，我们知道 phi 函数是出现在 join block 的起始处，而在实际的数据流分析过程中，我们会将 `phi` 指令作为 join block 前驱的赋值指令进行处理。
+
+**注**：如下例子所示：形如$`x_3=\phi(x_{1},x_{2})`$的 phi 指令。
+
+```asm
+bb1:
+    x1 = 1 + 1
+    br bb3
+
+bb2:
+    x2 = 2 + 2
+    br bb3
+
+bb3:
+    x3=phi(x1,x2)
+    ...
+```
+
+为了实现 SSA 上 GVN 分析的完备性，我们在数据流分析中，将 phi 指令在对应前驱中转化为 $`x_3 = x_1`$, $`x_3 = x_2`$ 两条赋值语句处理。如下例子所示：
+
+```asm
+bb1:
+    x1 = 1 + 1
+    x3 = x1
+    br bb3
+
+bb2:
+    x2 = 2 + 2
+    x3 = x2
+    br bb3
+
+bb3:
+	...
+```
+
+#### 3. 等价概念
+
+两个表达式 `e1`,`e2` 如果被称作等价的，那么他们有着相同的运算符，并且操作数也是对应等价的。
+
+#### 4. Value Expression 概念
+
+一个 Value Expression（值表达式），$`vi⊕vj`$ 代表了值编号为vi，vj的两个等价类之间的运算。$`vi⊕vj=\{x⊕y;x\in C_i,C_i是一系列变量等价的等价类集合，值编号为v_i;y\in C_j,C_j是一系列变量等价的等价类的集合, 值编号是v_j\}`$
+
+#### 5. Value phi-function 概念
+
+与值表达式类似，value phi-function 视作为一系列等价的 phi-function 的抽象。在本次 GVN 实验中，需要扩展 phi-function 的理解，例如如下ir片段的例子：
+
+```asm
+bb1:
+    y=x1+1
+    br bb3
+
+bb2:
+    z=x2+1
+    br bb3
+
+bb3:
+    x3=phi(x1,x2)
+    w3=x3+1
+```
+
+对于 变量 w3 对应的 Expression x3+1，由于x3是phi function，因此可以通过[expression 概念](#2-expression-概念)中对phi function的处理探测出：w3，y在bb1中等价，w3，z在bb2中等价，因此可以将 w3 视作是变量 y 与变量 z 在 bb3 处的合并，可以用 $`\phi_{bb_3}(y,z)`$ 来表示w3对应的 value phi-function。
+
+#### 6. Partition
+
+一个 Partition （分区）由一系列等价类组成，一个等价类是由一个值编号，和一系列成员组成。每个成员可以是：变量，常量，值表达式。同时，一个等价类可能会关联一个 value-phi-function。
+
+#### 7. Join 操作
+Join 操作检测到达此处的所有路径共有的等价项。在 SSA 格式的 IR 中，变量只会被赋值一次，当程序点 p 支配 join block 时，在 p 点成立的等价关系，在 join block 处仍然成立。通过对 join block 的前驱 Partition 取交集，可以保留所有支配 join block 的程序点的等价关系。对于在每个路径的等价的探测，我们将在[2.GVN算法](#2-gvn-算法论文中提供的伪代码)中通过伪代码进行阐述。对于表达式的等价关系与变量等价关系的检测与判定，我们会分别阐述。
+
+#### 8. 变量等价与表达式等价
+
+例如如下代码段：
+
+```asm
+bb1:
+    x1=1+1
+    y1=2+2
+    z1=x1+y1
+    br bb3
+
+bb2:
+    x2=2+2
+    y2=3+3
+    z2=x2+y2
+    br bb3
+
+bb3:
+    x3=phi(x1,x2)
+    y3=phi(y1,y2)
+    z3=phi(z1,z2)
+    z4=x3+y3
+```
+
+在左分支bb1中，通过将 x3=phi(x1, x2)语句转换为前驱的复制语句 x3=x1 ，可以检测出，x3与x1在左分支路径上的等价性。同理也有x3与x2在右分支上的等价性。此为**变量等价**
+
+同时，通过对z4=x3+y3的分析，可以看出，x3+y3 这个表达式，在bb1中与x1+y1等价，在bb2中与x2+y2等价，此为**表达式等价**，通过这个表达式等价的关系，可以分析出，z4与z1在bb1中变量等价，z4与z2在bb2中变量等价，因此可以建立z4的phi函数为phi(z1,z2)，进而可以导出z3与z4的**变量等价**，从而消除z3与z4的冗余。
+
+#### 9. Transfer Function
+
+TransferFunction 作用于一条语句s：x=e 上，接受 partition 记为 $`PIN_s`$ 并探测 e 与到达此处程序点所有 path 上是否有等价的 expression。TransferFunction 通过更新原有的等价类，或者创建新的等价类来在 partition $`PIN_s`$ 基础上修改并输出 partition 记为 $`POUT_s`$。在后面给出的伪代码可以看出，TransferFunction先在$`PIN_s`$检测是否存在 expression e 的 value expression，然后会继续检查 e 是否可以表达为不同表达式的合并。考虑如下例子（沿用了在变量等价中的例子）：
+
+```asm
+bb1:
+    x1=1+1
+    y1=2+2
+    z1=x1+y1
+    br bb3
+
+bb2:
+    x2=2+2
+    y2=3+3
+    z2=x2+y2
+    br bb3
+
+bb3:
+    x3=phi(x1,x2)
+    y3=phi(y1,y2)
+    z3=phi(z1,z2)
+    z4=x3+y3
+```
+
+在对`z4=x3+y3`这个表达式执行$`\text{TransferFunction}(x=e, PIN_s)`$:
+
+其中，x 为 z4, e 为 `x3+y3`
+$`PIN_{bb3}=\{\{v_1,x_1,1+1:\text{non-phi}\},\{v_2,y_1,2+2:\text{non-phi}\},\{v_3,z_1,x_1+y_1:\text{non-phi}\},\{v_4,x_2,2+2:\text{non-phi}\},\{v_5,y_2,3+3:\text{non-phi}\},\{v_6,z_2,x_2+y_2:\text{non-phi}\},\{v_7,x_3:\phi(x_1,x_2)\},\{v_8,y_3:\phi(y_1,y_2)\},\{v_9,z_3:\phi(z_1,z_2)\}\}`$
+
+在 $`PIN_{bb3}`$ 中找不到 `x3+y3` 对应的 expression 表达式。
+
+但是，对 `x3+y3` 进一步分析可以得到：因为`x3`和`y3`都是`phi`，`x3+y3`可以表示为 `bb1` 中 `x1+y1` 与 `bb2` 中 `x2+y2` 的两个表达式的合并，因此可以记为 phi(`x1+y1`, `x2+y2`)
+
+接下来，可以检测到变量 z1 与 `x1+y1` expression 在`bb3`前驱`bb1`中的等价关系，变量 z2 与 `x2+y2` expression 在`bb3`前驱`bb2`中的等价关系。因此可以检测到 phi(`x1+y1`, `x2+y2`)与 phi（z1,z2）的等价关系。
+
+进而得到 变量 z3 与 z4 是等价的，`x3 + y3` expression 的计算是冗余的。
+
+注：这里的 $`PIN_{bb3}`$ 的例子仅仅是为了说明 TransferFunction 的职能和 partition 的结构式样，不代表最终迭代稳定后的结果。
+
+## 2. GVN 算法（论文中提供的伪代码）
+
+本小节附上了原论文中附的伪代码，伪代码中给出了五个主函数的逻辑，这里自顶向下梳理一下：
+
+`detectEquivalences(G)`  包含了最主要的数据流迭代过程，传入参数 G 为抽象的数据流分析的 CFG 图结构，实现中可以以函数为分析的基本单位来执行此函数，迭代初始时，将各个 Partition 初始化为顶元`Top`， 定义为`Join(P, Top) = P = Join(Top, P)`
+
+注：此函数中的 statement 的概念对应前述的一条语句
+
+```clike
+detectEquivalences(G)
+    PIN1 = {} // “1” is the first statement in the program
+    POUT1 = transferFunction(PIN1)
+    for each statement s other than the first statement in the program
+        POUTs = Top
+    while changes to any POUT occur // i.e. changes in equivalences
+        for each statement s other than the first statement in the program
+            if s appears in block b that has two predecessors
+            then
+                PINs = Join(POUTs1, POUTs2) // s1 and s2 are last statements in respective predecessors
+            else
+                PINs = POUTs3    // s3 the statement just before s
+            POUTs = transferFunction(PINs) // apply transferFunction on each statement in the block
+```
+
+`Join` 操作仅仅在某个语句有两个前驱时被触发，注意：在join操作执行之前，join block 中的 phi 语句会作为 copy statement 加入 join block 对应的两个前驱末尾处。细节处理方式见[expression 概念](#2-expression-概念)的注栏。
+
+```clike
+Join(P1, P2)
+    P = {}
+    for each pair of classes Ci ∈ P1 and Cj ∈ P2
+        Ck = Intersect(Ci, Cj)
+        P = P ∪ Ck // Ignore when Ck is empty
+    return P
+
+Intersect(Ci, Cj)
+    Ck = Ci ∩ Cj // set intersection
+    if Ck ！= {} and Ck does not have value number
+    then
+        Ck = Ck ∪ {vk} // vk is new value number
+        Ck = (Ck − {vpf}) ∪ {φb(vi, vj)}
+        // vpf is value φ-function in Ck, vi ∈ Ci, vj ∈ Cj, b is join block
+    return Ck
+```
+
+`TransferFunction` 接受一个赋值语句 x=e（x是变量，e为表达式），与一个 partition $`PIN_s`$ 。其中 getVN 从一个 partition 中根据 e 来找到对应的编号。
+
+注： 在 lightir 的设计中，普通语句的 x 与 e 存在同一个类中，而 phi 语句中需要经转换为 copy 语句，x 与 e 与普通语句会有一些不同，需要仔细思考区分一下。
+
+```clike
+TransferFunction(x = e, PINs)
+    POUTs = PINs
+    if x is in a class Ci in POUTs
+        then Ci = Ci − {x}
+    ve = valueExpr(e)
+    vpf = valuePhiFunc(ve,PINs) // can be NULL
+    if ve or vpf is in a class Ci in POUTs // ignore vpf when NULL
+    then
+        Ci = Ci ∪ {x, ve} // set union
+    else
+        POUTs = POUTs ∪ {vn, x, ve : vpf} // vn is new value number
+    return POUTs
+
+valuePhiFunc(ve,P)
+    if ve is of the form φk(vi1, vj1) ⊕ φk(vi2, vj2)
+    then
+        // process left edge
+        vi = getVN(POUTkl, vi1 ⊕ vi2)
+        if vi is NULL
+        then vi = valuePhiFunc(vi1 ⊕ vi2, POUTkl)
+        // process right edge
+        vj = getVN(POUTkr, vj1 ⊕ vj2)
+        if vj is NULL
+        then vj = valuePhiFunc(vj1 ⊕ vj2, POUTkr)
+
+    if vi is not NULL and vj is not NULL
+    then return φk(vi, vj)
+    else return NULL
+```
+
+## 3. 实验内容
+
+在本次实验中，请仔细阅读[3.2 GVN pass 实现内容要求](#32-gvn-pass-实现内容要求)，根据要求补全`src/optimization/GVN.cpp`，`include/optimization/GVN.cpp`中关于 GVN pass 数据流分析部分，同时需要在 `Reports/4-ir-opt/` 目录下撰写实验报告。**为了在评测中统一分析结果，请大家采用 lab3 的 TA-impl 分支提供的答案来继续后续实验。**
+### 3.1 GVN pass 实现内容要求
+
+GVN 通过数据流分析来检测冗余的变量和计算，通过替换和死代码删除结合，实现优化效果。前述的例子中主要以二元运算语句来解释原理，且助教为大家提供了代码替换和删除的逻辑，除此之外，需要完成的方向有：
+
+1. 对冗余指令的检测与消除包括（二元运算指令，cmp，gep，类型转换指令）
+
+2. 对纯函数的冗余调用消除（助教提供了纯函数分析，见[FuncInfo.h](../../include/optimization/FuncInfo.h)）
+
+    该 Pass 的接口`is_pure_function`接受一个lightIR Function，判断该函数是否为纯函数；对于纯函数，如果其参数等价，对这个纯函数的不同调用也等价。
+
+3. 常量传播
+
+   在数据流分析的过程中，可以使用常量折叠来实现常量传播，从而将可在编译时计算的结果计算好，减少运行时开销。（助教提供了常量折叠类，在辅助类的介绍中）
+
+我们会在测试样例中对这三点进行考察。
+
+**注**：我们为大家提供了冗余删除的函数 `GVN::replace_cc_members` ，只需要正确填充在 `GVN` 类中的 `pout` 变量，我们的替换逻辑将会根据每个 bb 的 pout 自行使用`CongruenceClass` 的 `leader_` 成员来替换在此 bb 内与其等价其他指令。
+
+### 3.2 GVN 辅助类
+
+在上述对 GVN 概念的介绍中，为了能让大家专注于核心数据流分析逻辑的实现，我们为大家提供了一些相应实现的辅助类，并在注释里解释了其相应用途，请注意与前述的 GVN 的抽象概念结合，理解其设计，并补充必要的类成员的实现。
+
+`GVN.h`:
+
+```c++
+class ConstFolder; // 常量折叠类，用于折叠操作数都是常量的指令
+
+// 该 namespace 下，包含了用于判断 expression 等价的结构，我们提供了 binary expression，phi expression，constant expression 的结构，请根据测试用例添加你需要的其他 expression 的结构，具体细节请据 GVN.h 结合代码与注释理解
+namespace GVNExpression {
+class Expression; // 所有 expression 类型的基类
+class ConstantExpression; // 常量 expression 类型
+class BinaryExpression; // 二元运算 expression 包括 + - * /
+class PhiExpression; // phi expression 类型，表示不同路径的 expression 在此的合并
+}
+
+struct CongruenceClass; // 对应伪代码中等价类的概念，分析结果会根据此类 dump 至 json 文件中，代码替换与消除逻辑也根据此结构实现
+
+class GVN; // GVN pass核心实现逻辑，除一些用的上的辅助函数外，重点补齐此处与伪代码对应的核心函数，其中run()函数是 pass 启动的入口，已经为大家补充好。
+```
+
+`GVN.cpp`:
+
+```c++
+namespace utils // 一些用于输出的函数，可方便调试，以及将结果 dump 到 json 文件中的方法
+```
+
+### 3.3 注册及运行 GVN Pass
+
+#### 注册 Pass
+
+本次实验使用了由 C++ 编写的 `LightIR` 来在 IR 层面完成优化化简，在`include/optimization/PassManager.hpp`中，定义了一个用于管理 Pass 的类`PassManager`。它的作用是注册与运行 Pass 。它提供了以下接口：
+
+```cpp
+PassManager pm(module.get())
+pm.add_Pass<GVN>(emit, dump_json)    // 注册Pass，emit为true时打印优化后的IR
+pm.run()    // 按照注册的顺序运行 Pass 的 run() 函数
+```
+
+#### 运行 Pass
+
+```sh
+mkdir build && cd build
+cmake ..
+make -j
+make install
+```
+
+为了便于大家进行实验，助教对之前的`cminusfc`增加了选项，用来选择是否开启某种优化，通过`-mem2reg`开关来控制优化 Pass 的使用，当需要对 `.cminus` 文件测试时，可以这样使用：
+
+```bash
+./cminusfc [ -mem2reg ] [ -gvn [ -dump-json ] ] <input-file>
+```
+
+其中，gvn pass 需要在 mem2reg pass 运行后运行。
+
+### 3.3 自动测试
+
+助教贴心地为大家准备了自动测试脚本，它在 `tests/4-ir-opt` 目录下，使用方法如下：
+
+```bash
+python3 lab4_evals.py [ -gvn-analysis ] [ -gvn ]
+```
+
+该脚本可以在任意目录下运行
+
+```bash
+python3 tests/4-ir-opt/lab4_evals.py [ -gvn-analysis ] [ -gvn ]
+```
+
+其中 `-gvn-analysis` 对 GVN 分析结果的正确性进行判断，执行结果如下所示：
+
+```bash
+========== GlobalValueNumberAnalysis ==========
+Compiling  -mem2reg -emit-llvm -gvn -dump-json
+  0%|                       | 0/4 [00:00<?, ?it/s]
+Compile bin.cminus  success
+generate json bin.cminus  success
+ 25%|███▊           | 1/4 [00:00<00:00,  8.38it/s]
+Compile loop3.cminus  success
+generate json loop3.cminus  success
+ 50%|███████▌       | 2/4 [00:00<00:00,  7.21it/s]
+Compile pure_func.cminus  success
+generate json pure_func.cminus  success
+ 75%|███████████▎   | 3/4 [00:00<00:00,  4.08it/s]
+Compile single_bb1.cminus  success
+generate json single_bb1.cminus  success
+100%|███████████████| 4/4 [00:00<00:00,  4.64it/s]
+bin.cminus: 1.0
+loop3.cminus: 1.0
+pure_func.cminus: 1.0
+single_bb1.cminus: 1.0
+```
+
+`-gvn` 会执行测试文件，比对你实现的 GVN 算法优化后的程序，与助教的基准程序的运行时间。
+
+```bash
+========== GlobalValueNumber ==========
+Compiling  -mem2reg
+100%|███████████████| 2/2 [00:00<00:00,  8.22it/s]
+Evalution
+100%|███████████████| 2/2 [00:17<00:00,  6.44s/it]
+Compiling  -mem2reg -gvn
+100%|███████████████| 2/2 [00:00<00:00,  5.67it/s]
+Evalution
+100%|███████████████| 2/2 [00:13<00:00,  4.36s/it]
+Compiling baseline files
+100%|███████████████| 2/2 [00:00<00:00, 13.70it/s]
+Evalution
+100%|███████████████| 2/2 [00:09<00:00,  3.24s/it]
+testcase         before optimization     after optimization      baseline
+constant.cminus                 0.70                    0.24              0.24
+transpose.cminus                3.72                    3.04              3.03
+root@3fd22a9ed627:/labs/2022fall-compiler_cminus-taversion/tests/4-ir-opt#
+```
+
+如果要增加样例，直接在样例目录中添加文件即可，命名参考目录下的其他文件。
+
+### 3.4 Tips
+
+1. 为了大家能够循序渐进地实现 GVN pass，助教给出一个实现上的规划：
+
+   1. 使用 GVN pass 分析单一基本块的程序 case
+      
+        补充 `detectEquivalences` 函数（无需处理 Join ），在转移方程`transferFunction`中，为每个变量创建等价类。
+
+   2. 使用 GVN pass 分析带有冗余计算的单一基本块的程序 case，并在分析过程中进行常量传播
+
+        依照伪代码补全转移方程`transferFunction`，得到正确的等价类，将输出结构 dump 至 json 文件，与手动推算结果进行比对。
+
+   3. 使用 GVN pass 分析带有选择语句的程序 case，处理phi语句之间的冗余
+
+        完善 `detectEquivalences` ，实现合并两个前驱分区的合并算法 `Join`，和 `valuePhiFunc`，注意本次实验只考察`phi(a+b, c+d)`与`phi(a,c)+phi(b,d)`之间的冗余。
+
+   4. 正确分析带有循环的程序
+
+        完成了前三点后，你的 GVN 应该比较完整了，可以根据带循环的简单程序来调试。 
+
+2. **Lab3** 的测试样例仍然可以用来测试优化正确性
+
+3. 使用 logging 工具来打印调试信息，以及 GDB 等软件进行单步调试来检查错误的原因
+
+    [logging](../common/logging.md) 是帮助大家打印调试信息的工具，如有需求可以阅读文档后进行使用
+
+4. 你有可能会遇到智能指针相关的问题，详见[C++文档](https://zh.cppreference.com/w/cpp/memory/shared_ptr)，以及[段错误调试指北](../common/simple_cpp.md#debugging-seg-fault)
+
+## 4. 提交要求
+
+### 目录结构
+
+```
+.
+├── CMakeLists.txt
+├── Documentations
+│   ├── ...
+│   ├── common
+│   |   ├── LightIR.md                  LightIR 相关文档
+│   |   ├── logging.md                  logging 工具相关文档
+│   |   └── cminusf.md                  cminus-f 的语法和语义文档
+│   └── 4.2-gvn
+│       ├── gvn.pdf                     本实验参考文献原文
+│       └── README.md                   Lab4 实验文档说明（你在这里）
+├── include                             实验所需的头文件
+│   ├── ...
+│   ├── optimization
+│   │   ├── Mem2Reg.hpp                 Mem2Reg
+│   │   ├── Dominators.hpp              支配树
+│   │   └── GVN.h                       GVN								 	 <--- 修改并提交
+│   ├── cminusf_builder.hpp
+|   └── ast.hpp
+├── Reports
+│   ├── ...
+│   └── 4.2-gvn
+│       └── report.md            		lab4 本次实验报告模板					<--- 修改并提交
+│  
+├── src
+│   ├── ...
+│   └── optimization
+│       ├── Mem2Reg.cpp                  Mem2Reg
+│       ├── Dominators.cpp               支配树
+│       └── GVN.cpp                      GVN								 <--- 修改并提交
+│
+└── tests
+    ├── ...
+    └── 4-ir-opt
+        ├── testcases                    助教提供的测试样例
+        └── lab4_test.py                 助教提供的测试脚本
+
+```
+### 提交要求和评分标准
+
+* 提交要求
+  本实验是个人实验，需要将代码上传至gitlab实验仓库，并在希冀评测平台上提交仓库链接。
+
+  * 需要填补
+
+    `include/optimization/GVN.h`, `src/optimization/GVN.cpp`，在 `Reports/4.2-gvn/report.md` 中撰写实验报告。
+
+    - 实验报告内容包括
+        实验要求、实验难点、实验设计、实验结果验证、思考题、实验反馈等，具体见 `Reports/4.2-gvn/report.md`
+
+  * 本次实验不提供希冀平台在线测试通道，将在 soft ddl 时收取同学仓库 `master` 分支下`include/optimization/GVN.h`，`src/optimization/GVN.cpp` 文件，请同学们在ddl前将自己的最新分支push到 git 仓库上
+
+  * 本次实验报告以 pdf 格式提交到希冀平台对应提交通道
+
+* 评分标准: 实验完成分（总分 60 分）组成如下：
+  * 实验报告 (5 分) 
+
+    需要回答 Reports 目录下实验报告模板的思考题。
+
+  * easy case（40分）
+
+    助教提供了 4 个公开测试用例，并保留 4 个隐藏用例，根据每个用例 dump 出来的分析结果正误给分。json 文件判断的逻辑如下，仅对每个bb的 pout 进行判断。
+
+    例如：
+  
+    ```json
+    "pout": {
+        "label_entry": [["%op0", ], ["%op1", ], ["%op2", ], ],
+        "label3": [["%op0", ], ["%op1", ], ["%op2", ], ["%op4", "%op10", ], ["%op5", "%op9", ], ["%op6", "%op8", ], ],
+        "label7": [["%op0", ], ["%op1", ], ["%op2", ], ["%op10", ], ["%op9", ], ["%op11", "%op8", ], ],
+        "label12": [["%op0", ], ["%op1", ], ["%op2", ], ["%op13", "%op10", ], ["%op14", "%op9", ], ["%op15", "%op8", ], ],}
+    ```
+    对于分值为 x，n 个基本块的程序，每个 bb 分析结果为$`x/n`$分，某个bb的分析结果多或者少一个等价类，或有分析错误的等价类，该 bb 分析结果没有分值。
+
+
+  * performance case（15分）
+
+    助教提供了 2 个公开case，并保留 2 个隐藏用例。以及助教实现优化后的 baseline.ll ，优化效果按照如下方式给分（执行结果不正确则此项分数为0）
+
+    ```
+    对于每一个testcase:
+    (before_optimization-after_optimization)/(before_optimization-baseline) > 0.8 得满分
+    (before_optimization-after_optimization)/(before_optimization-baseline) > 0.5 得85%分数
+    (before_optimization-after_optimization)/(before_optimization-baseline) > 0.2 得60%分数
+    ```
+
+  * 禁止执行恶意代码，违者本次实验0分处理
+
+* 迟交规定
+
+  * `Soft Deadline`: 2022/12/12 23:59:59 (北京标准时间，UTC+8)
+
+  * `Hard Deadline`: 2022/12/19 23:59:59 (北京标准时间，UTC+8)
+
+  * 迟交需要邮件通知 TA :
+    * 邮箱:
+    chen16614@mail.ustc.edu.cn 抄送 farmerzhang1@mail.ustc.edu.cn
+    * 邮件主题: lab4.2迟交-学号
+    * 内容: 包括迟交原因、最后版本commitID、迟交时间等
+
+  * 迟交分数
+    * x为迟交天数(对于`Soft Deadline`而言)，grade为满分
+      ``` bash
+      final_grade = grade, x = 0
+      final_grade = grade * (0.9)^x, 0 < x <= 7
+      final_grade = 0, x > 7 # 这一条严格执行,请对自己负责
+      ```
+
+* 关于抄袭和雷同
+  经过助教和老师判定属于实验抄袭或雷同情况，所有参与方一律零分，不接受任何解释和反驳（严禁对开源代码或者其他同学代码的直接搬运）。
+  如有任何问题，欢迎提issue进行批判指正。
diff --git a/Documentations/4.2-gvn/gvn.pdf b/Documentations/4.2-gvn/gvn.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..87b2c577f0674df1b6ebbcaf9669b949ddea7030
Binary files /dev/null and b/Documentations/4.2-gvn/gvn.pdf differ
diff --git a/Documentations/common/simple_cpp.md b/Documentations/common/simple_cpp.md
index 60a07e2dccfeead09e7e8aa2b522d6b78bd3caad..42c88f897d98af3a58d9a39b434cd631a3c60597 100644
--- a/Documentations/common/simple_cpp.md
+++ b/Documentations/common/simple_cpp.md
@@ -106,3 +106,13 @@ C中，只能使用标准库中的`malloc`与`free`来进行内存分配，并
 1. `std::shared_ptr`: 引用计数智能指针，使用一个共享变量来记录指针管理的对象被引用了几次。当对象引用计数为0时，说明当前该对象不再有引用，并且进程也无法再通过其它方式来引用它，也就意味着可以回收内存，这相当于低级的垃圾回收策略。
 2. `std::unique_ptr`: 表示所有权的智能指针，该指针要求它所管理的对象智能有一次引用，主要用于语义上不允许共享的对象（比如`llvm::Module`）。当引用计数为0时，它也会回收内存。
 
+## Debugging Seg Fault
+Lab3/4 中，你可能会各种各样的段错误，不要害怕！clang 提供了一个工具来帮助我们解决内存泄漏。
+```bash
+cd build
+cmake .. -DCMAKE_BUILD_TYPE=Asan
+make
+```
+然后再次运行你的错误代码， Asan 会提供更详细的报错信息。
+
+注：要更换到别的 build type （如Debug或Release）时需要显式指定，否则 cmake 会使用 cached 的版本。
diff --git a/Reports/4.2-gvn/report.md b/Reports/4.2-gvn/report.md
new file mode 100644
index 0000000000000000000000000000000000000000..d290e359f9533ec66fe37e41d1cefaed08ed8b1a
--- /dev/null
+++ b/Reports/4.2-gvn/report.md
@@ -0,0 +1,28 @@
+# Lab4.2 实验报告
+
+姓名 学号
+
+## 实验要求
+
+请按照自己的理解，写明本次实验需要做什么
+
+## 实验难点
+
+实验中遇到哪些挑战
+
+## 实验设计
+实现思路，相应代码，优化前后的IR对比（举一个例子）并辅以简单说明
+
+### 思考题
+1. 请简要分析你的算法复杂度
+2. `std::shared_ptr`如果存在环形引用，则无法正确释放内存，你的 Expression 类是否存在 circular reference?
+3. 尽管本次实验已经写了很多代码，但是在算法上和工程上仍然可以对 GVN 进行改进，请简述你的 GVN 实现可以改进的地方
+
+## 实验总结
+
+此次实验有什么收获
+
+## 实验反馈（可选 不会评分）
+
+对本次实验的建议
+
diff --git a/include/lightir/Instruction.h b/include/lightir/Instruction.h
index ccf46c50efe5b9444f9f8bbd50cdc184805cf715..738aad63f12fc33f8aff7539c2f43249e6365233 100644
--- a/include/lightir/Instruction.h
+++ b/include/lightir/Instruction.h
@@ -55,8 +55,8 @@ class Instruction : public User, public llvm::ilist_node<Instruction> {
     Module *get_module();
 
     OpID get_instr_type() const { return op_id_; }
-    std::string get_instr_op_name() {
-        switch (op_id_) {
+    static std::string get_instr_op_name(OpID id) {
+        switch (id) {
         case ret: return "ret"; break;
         case br: return "br"; break;
         case add: return "add"; break;
@@ -82,6 +82,7 @@ class Instruction : public User, public llvm::ilist_node<Instruction> {
         default: return ""; break;
         }
     }
+    std::string get_instr_op_name() { return get_instr_op_name(op_id_); }
 
     bool is_void() {
         return ((op_id_ == ret) || (op_id_ == br) || (op_id_ == store) ||
diff --git a/include/lightir/Value.h b/include/lightir/Value.h
index 4eeb018231e7c79cfdb36535dba5982b9aef6ef9..5fb6a8850bcef3d782d176c045aa5a916e2cf7d8 100644
--- a/include/lightir/Value.h
+++ b/include/lightir/Value.h
@@ -1,12 +1,14 @@
 #ifndef SYSYC_VALUE_H
 #define SYSYC_VALUE_H
 
+#include <functional>
 #include <iostream>
 #include <list>
 #include <string>
 
 class Type;
 class Value;
+class User;
 
 struct Use {
     Value *val_;
@@ -35,6 +37,8 @@ class Value {
     std::string get_name() const;
 
     void replace_all_use_with(Value *new_val);
+    /// replace `value` with `new_val` when the user of value satisfies predicate `pred`
+    void replace_use_with_when(Value *new_val, std::function<bool(User *)> pred);
     void remove_use(Value *val);
 
     virtual std::string print() = 0;
diff --git a/include/optimization/DeadCode.h b/include/optimization/DeadCode.h
new file mode 100644
index 0000000000000000000000000000000000000000..ef5a80380c6b9640d2a9b08d40872a7882be347d
--- /dev/null
+++ b/include/optimization/DeadCode.h
@@ -0,0 +1,106 @@
+#pragma once
+#include "FuncInfo.h"
+#include "Function.h"
+#include "Instruction.h"
+#include "PassManager.hpp"
+#include "logging.hpp"
+
+/**
+ * 死代码消除：参见 https://www.clear.rice.edu/comp512/Lectures/10Dead-Clean-SCCP.pdf
+ **/
+class DeadCode : public Pass {
+  public:
+    DeadCode(Module *m) : Pass(m), func_info(std::make_shared<FuncInfo>(m)) {}
+
+    // 处理流程：两趟处理，mark 标记有用变量，sweep 删除无用指令
+    void run() {
+        bool changed{};
+        func_info->run();
+        do {
+            changed = false;
+            for (auto &F : m_->get_functions()) {
+                auto func = &F;
+                mark(func);
+                changed |= sweep(func);
+            }
+        } while (changed);
+        LOG_INFO << "dead code pass erased " << ins_count << " instructions";
+    }
+
+  private:
+    std::shared_ptr<FuncInfo> func_info;
+    void mark(Function *func) {
+        work_list.clear();
+        marked.clear();
+
+        for (auto &bb : func->get_basic_blocks()) {
+            for (auto &ins : bb.get_instructions()) {
+                if (is_critical(&ins)) {
+                    marked[&ins] = true;
+                    work_list.push_back(&ins);
+                }
+            }
+        }
+
+        while (work_list.empty() == false) {
+            auto now = work_list.front();
+            work_list.pop_front();
+
+            mark(now);
+        }
+    }
+    void mark(Instruction *ins) {
+        for (auto op : ins->get_operands()) {
+            auto def = dynamic_cast<Instruction *>(op);
+            if (def == nullptr)
+                continue;
+            if (marked[def])
+                continue;
+            if (def->get_function() != ins->get_function())
+                continue;
+            marked[def] = true;
+            work_list.push_back(def);
+        }
+    }
+    bool sweep(Function *func) {
+        std::unordered_set<Instruction *> wait_del{};
+        for (auto &bb : func->get_basic_blocks()) {
+            for (auto it = bb.get_instructions().begin(); it != bb.get_instructions().end();) {
+                if (marked[&*it]) {
+                    ++it;
+                    continue;
+                } else {
+                    auto tmp = &*it;
+                    wait_del.insert(tmp);
+                    it++;
+                }
+            }
+        }
+        for (auto inst : wait_del)
+            inst->remove_use_of_ops();
+        for (auto inst : wait_del)
+            inst->get_parent()->get_instructions().erase(inst);
+        ins_count += wait_del.size();
+        return not wait_del.empty(); // changed
+    }
+    bool is_critical(Instruction *ins) {
+        // 对纯函数的无用调用也可以在删除之列
+        if (ins->is_call()) {
+            auto call_inst = dynamic_cast<CallInst *>(ins);
+            auto callee = dynamic_cast<Function *>(call_inst->get_operand(0));
+            if (func_info->is_pure_function(callee))
+                return false;
+            return true;
+        }
+        if (ins->is_br() || ins->is_ret())
+            return true;
+        if (ins->is_store())
+            return true;
+        return false;
+    }
+
+    // 用以衡量死代码消除的性能
+    int ins_count{0};
+    std::deque<Instruction *> work_list{};
+    std::unordered_map<Instruction *, bool> marked{};
+};
diff --git a/include/optimization/FuncInfo.h b/include/optimization/FuncInfo.h
new file mode 100644
index 0000000000000000000000000000000000000000..1ffe1289da0b7d39a47e4db1397a4eab2d1ccdb6
--- /dev/null
+++ b/include/optimization/FuncInfo.h
@@ -0,0 +1,131 @@
+#pragma once
+#include "Function.h"
+#include "PassManager.hpp"
+#include "logging.hpp"
+
+#include <deque>
+#include <unordered_map>
+#include <unordered_set>
+
+/**
+ * 计算哪些函数是纯函数
+ * WARN: 假定所有函数都是纯函数，除非他写入了全局变量、修改了传入的数组、或者直接间接调用了非纯函数
+ */
+class FuncInfo : public Pass {
+  public:
+    FuncInfo(Module *m) : Pass(m) {}
+
+    void run() {
+        for (auto &f : m_->get_functions()) {
+            auto func = &f;
+            trivial_mark(func);
+            if (not is_pure[func])
+                worklist.push_back(func);
+        }
+        while (worklist.empty() == false) {
+            auto now = worklist.front();
+            worklist.pop_front();
+            process(now);
+        }
+        log();
+    }
+
+    bool is_pure_function(Function *func) const {
+        // exit_if(is_pure.find(func) == is_pure.end(), ERROR_IN_PURE_FUNCTION_ANALYSIS);
+        return is_pure.at(func);
+    }
+
+    void log() {
+        for (auto it : is_pure) {
+            LOG_INFO << it.first->get_name() << " is pure? " << it.second;
+        }
+    }
+
+  private:
+    // 有 store 操作的函数非纯函数来处理
+    void trivial_mark(Function *func) {
+        if (func->is_declaration() or func->get_name() == "main") {
+            is_pure[func] = false;
+            return;
+        }
+        // 只要传入数组，都作为非纯函数处理
+        for (auto it = func->get_function_type()->param_begin(); it != func->get_function_type()->param_end(); ++it) {
+            auto arg_type = *it;
+            if (arg_type->is_integer_type() == false and arg_type->is_float_type() == false) {
+                is_pure[func] = false;
+                return;
+            }
+        }
+        for (auto &bb : func->get_basic_blocks())
+            for (auto &inst : bb.get_instructions()) {
+                if (is_side_effect_inst(&inst)) {
+                    is_pure[func] = false;
+                    return;
+                }
+            }
+        is_pure[func] = true;
+    }
+
+    void process(Function *func) {
+        for (auto &use : func->get_use_list()) {
+            LOG_INFO << use.val_->print() << " uses func: " << func->get_name();
+            if (auto inst = dynamic_cast<Instruction *>(use.val_)) {
+                auto func = (inst->get_parent()->get_parent());
+                if (is_pure[func]) {
+                    is_pure[func] = false;
+                    worklist.push_back(func);
+                }
+            } else
+                LOG_WARNING << "Value besides instruction uses a function";
+        }
+    }
+
+    // 对局部变量进行 store 没有副作用
+    bool is_side_effect_inst(Instruction *inst) {
+        if (inst->is_store()) {
+            if (is_local_store(dynamic_cast<StoreInst *>(inst)))
+                return false;
+            return true;
+        }
+        if (inst->is_load()) {
+            if (is_local_load(dynamic_cast<LoadInst *>(inst)))
+                return false;
+            return true;
+        }
+        // call 指令的副作用会在后续 bfs 中计算
+        return false;
+    }
+
+    bool is_local_load(LoadInst *inst) {
+        auto addr = dynamic_cast<Instruction *>(get_first_addr(inst->get_operand(0)));
+        if (addr and addr->is_alloca())
+            return true;
+        return false;
+    }
+
+    bool is_local_store(StoreInst *inst) {
+        auto addr = dynamic_cast<Instruction *>(get_first_addr(inst->get_lval()));
+        if (addr and addr->is_alloca())
+            return true;
+        return false;
+    }
+    Value *get_first_addr(Value *val) {
+        if (auto inst = dynamic_cast<Instruction *>(val)) {
+            if (inst->is_alloca())
+                return inst;
+            if (inst->is_gep())
+                return get_first_addr(inst->get_operand(0));
+            if (inst->is_load())
+                return val;
+            LOG_WARNING << "FuncInfo: try to determine addr in operands";
+            for (auto op : inst->get_operands()) {
+                if (op->get_type()->is_pointer_type())
+                    return get_first_addr(op);
+            }
+        }
+        return val;
+    }
+
+    std::deque<Function *> worklist;
+    std::unordered_map<Function *, bool> is_pure;
+};
diff --git a/include/optimization/GVN.h b/include/optimization/GVN.h
new file mode 100644
index 0000000000000000000000000000000000000000..6b794acc8ddb7991b1fd42f0f9d1c1c0d6902f85
--- /dev/null
+++ b/include/optimization/GVN.h
@@ -0,0 +1,189 @@
+#pragma once
+#include "BasicBlock.h"
+#include "Constant.h"
+#include "DeadCode.h"
+#include "FuncInfo.h"
+#include "Function.h"
+#include "Instruction.h"
+#include "Module.h"
+#include "PassManager.hpp"
+#include "Value.h"
+
+#include <cstddef>
+#include <cstdint>
+#include <memory>
+#include <optional>
+#include <string>
+#include <tuple>
+#include <unordered_map>
+#include <utility>
+#include <vector>
+
+namespace GVNExpression {
+
+// fold the constant value
+class ConstFolder {
+  public:
+    ConstFolder(Module *m) : module_(m) {}
+    Constant *compute(Instruction *instr, Constant *value1, Constant *value2);
+    Constant *compute(Instruction *instr, Constant *value1);
+
+  private:
+    Module *module_;
+};
+
+/**
+ * for constructor of class derived from `Expression`, we make it public
+ * because `std::make_shared` needs the constructor to be publicly available,
+ * but you should call the static factory method `create` instead the constructor itself to get the desired data
+ */
+class Expression {
+  public:
+    // TODO: you need to extend expression types according to testcases
+    enum gvn_expr_t { e_constant, e_bin, e_phi };
+    Expression(gvn_expr_t t) : expr_type(t) {}
+    virtual ~Expression() = default;
+    virtual std::string print() = 0;
+    gvn_expr_t get_expr_type() const { return expr_type; }
+
+  private:
+    gvn_expr_t expr_type;
+};
+
+bool operator==(const std::shared_ptr<Expression> &lhs, const std::shared_ptr<Expression> &rhs);
+bool operator==(const GVNExpression::Expression &lhs, const GVNExpression::Expression &rhs);
+
+class ConstantExpression : public Expression {
+  public:
+    static std::shared_ptr<ConstantExpression> create(Constant *c) { return std::make_shared<ConstantExpression>(c); }
+    virtual std::string print() { return c_->print(); }
+    // we leverage the fact that constants in lightIR have unique addresses
+    bool equiv(const ConstantExpression *other) const { return c_ == other->c_; }
+    ConstantExpression(Constant *c) : Expression(e_constant), c_(c) {}
+
+  private:
+    Constant *c_;
+};
+
+// arithmetic expression
+class BinaryExpression : public Expression {
+  public:
+    static std::shared_ptr<BinaryExpression> create(Instruction::OpID op,
+                                                    std::shared_ptr<Expression> lhs,
+                                                    std::shared_ptr<Expression> rhs) {
+        return std::make_shared<BinaryExpression>(op, lhs, rhs);
+    }
+    virtual std::string print() {
+        return "(" + Instruction::get_instr_op_name(op_) + " " + lhs_->print() + " " + rhs_->print() + ")";
+    }
+
+    bool equiv(const BinaryExpression *other) const {
+        if (op_ == other->op_ and *lhs_ == *other->lhs_ and *rhs_ == *other->rhs_)
+            return true;
+        else
+            return false;
+    }
+
+    BinaryExpression(Instruction::OpID op, std::shared_ptr<Expression> lhs, std::shared_ptr<Expression> rhs)
+        : Expression(e_bin), op_(op), lhs_(lhs), rhs_(rhs) {}
+
+  private:
+    Instruction::OpID op_;
+    std::shared_ptr<Expression> lhs_, rhs_;
+};
+
+class PhiExpression : public Expression {
+  public:
+    static std::shared_ptr<PhiExpression> create(std::shared_ptr<Expression> lhs, std::shared_ptr<Expression> rhs) {
+        return std::make_shared<PhiExpression>(lhs, rhs);
+    }
+    virtual std::string print() { return "(phi " + lhs_->print() + " " + rhs_->print() + ")"; }
+    bool equiv(const PhiExpression *other) const {
+        if (*lhs_ == *other->lhs_ and *rhs_ == *other->rhs_)
+            return true;
+        else
+            return false;
+    }
+    PhiExpression(std::shared_ptr<Expression> lhs, std::shared_ptr<Expression> rhs)
+        : Expression(e_phi), lhs_(lhs), rhs_(rhs) {}
+
+  private:
+    std::shared_ptr<Expression> lhs_, rhs_;
+};
+} // namespace GVNExpression
+
+/**
+ * Congruence class in each partitions
+ * note: for constant propagation, you might need to add other fields
+ * and for load/store redundancy detection, you most certainly need to modify the class
+ */
+struct CongruenceClass {
+    size_t index_;
+    // representative of the congruence class, used to replace all the members (except itself) when analysis is done
+    Value *leader_;
+    // value expression in congruence class
+    std::shared_ptr<GVNExpression::Expression> value_expr_;
+    // value φ-function is an annotation of the congruence class
+    std::shared_ptr<GVNExpression::PhiExpression> value_phi_;
+    // equivalent variables in one congruence class
+    std::set<Value *> members_;
+
+    CongruenceClass(size_t index) : index_(index), leader_{}, value_expr_{}, value_phi_{}, members_{} {}
+
+    bool operator<(const CongruenceClass &other) const { return this->index_ < other.index_; }
+    bool operator==(const CongruenceClass &other) const;
+};
+
+namespace std {
+template <>
+// overload std::less for std::shared_ptr<CongruenceClass>, i.e. how to sort the congruence classes
+struct less<std::shared_ptr<CongruenceClass>> {
+    bool operator()(const std::shared_ptr<CongruenceClass> &a, const std::shared_ptr<CongruenceClass> &b) const {
+        // nullptrs should never appear in partitions, so we just dereference it
+        return *a < *b;
+    }
+};
+} // namespace std
+
+class GVN : public Pass {
+  public:
+    using partitions = std::set<std::shared_ptr<CongruenceClass>>;
+    GVN(Module *m, bool dump_json) : Pass(m), dump_json_(dump_json) {}
+    // pass start
+    void run() override;
+    // init for pass metadata;
+    void initPerFunction();
+
+    // fill the following functions according to Pseudocode, **you might need to add more arguments**
+    void detectEquivalences();
+    partitions join(const partitions &P1, const partitions &P2);
+    std::shared_ptr<CongruenceClass> intersect(std::shared_ptr<CongruenceClass>, std::shared_ptr<CongruenceClass>);
+    partitions transferFunction(Instruction *x, Value *e, partitions pin);
+    std::shared_ptr<GVNExpression::PhiExpression> valuePhiFunc(std::shared_ptr<GVNExpression::Expression>,
+                                                               const partitions &);
+    std::shared_ptr<GVNExpression::Expression> valueExpr(Instruction *instr);
+    std::shared_ptr<GVNExpression::Expression> getVN(const partitions &pout,
+                                                     std::shared_ptr<GVNExpression::Expression> ve);
+
+    // replace cc members with leader
+    void replace_cc_members();
+
+    // note: be careful when to use copy constructor or clone
+    partitions clone(const partitions &p);
+
+    // create congruence class helper
+    std::shared_ptr<CongruenceClass> createCongruenceClass(size_t index = 0) {
+        return std::make_shared<CongruenceClass>(index);
+    }
+
+  private:
+    bool dump_json_;
+    std::uint64_t next_value_number_ = 1;
+    Function *func_;
+    std::map<BasicBlock *, partitions> pin_, pout_;
+    std::unique_ptr<FuncInfo> func_info_;
+    std::unique_ptr<GVNExpression::ConstFolder> folder_;
+    std::unique_ptr<DeadCode> dce_;
+};
+
+bool operator==(const GVN::partitions &p1, const GVN::partitions &p2);
diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index 8875e3d24b68de59843a57bb0fbf38170d0e5d61..bae084948786aa6d4062be6371567dd7f4b0f4b7 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -3,4 +3,4 @@ add_subdirectory(common)
 add_subdirectory(io)
 add_subdirectory(lightir)
 add_subdirectory(cminusfc)
-add_subdirectory(optimization)
\ No newline at end of file
+add_subdirectory(optimization)
diff --git a/src/cminusfc/cminusfc.cpp b/src/cminusfc/cminusfc.cpp
index 880d879cc62469172dafe668b7f43ca161358528..7c705a2583635c0d33e114c55c51ed5994bf99e1 100644
--- a/src/cminusfc/cminusfc.cpp
+++ b/src/cminusfc/cminusfc.cpp
@@ -1,4 +1,5 @@
 #include "Dominators.h"
+#include "GVN.h"
 #include "Mem2Reg.hpp"
 #include "PassManager.hpp"
 #include "cminusf_builder.hpp"
@@ -11,7 +12,8 @@
 using namespace std::literals::string_literals;
 
 void print_help(std::string exe_name) {
-    std::cout << "Usage: " << exe_name << " [ -h | --help ] [ -o <target-file> ] [ -emit-llvm ] [-mem2reg] <input-file>"
+    std::cout << "Usage: " << exe_name
+              << " [ -h | --help ] [ -o <target-file> ] [ -emit-llvm ] [-mem2reg] [-gvn] [-dump-json] <input-file>"
               << std::endl;
 }
 
@@ -20,6 +22,8 @@ int main(int argc, char **argv) {
     std::string input_path;
 
     bool mem2reg = false;
+    bool gvn = false;
+    bool dump_json = false;
     bool emit = false;
 
     for (int i = 1; i < argc; ++i) {
@@ -38,6 +42,10 @@ int main(int argc, char **argv) {
             emit = true;
         } else if (argv[i] == "-mem2reg"s) {
             mem2reg = true;
+        } else if (argv[i] == "-gvn"s) {
+            gvn = true;
+        } else if (argv[i] == "-dump-json"s) {
+            dump_json = true;
         } else {
             if (input_path.empty()) {
                 input_path = argv[i];
@@ -47,6 +55,8 @@ int main(int argc, char **argv) {
             }
         }
     }
+    if (gvn and not mem2reg)
+        LOG_WARNING << "Enabling GVN without mem2reg";
     if (input_path.empty()) {
         print_help(argv[0]);
         return 0;
@@ -77,12 +87,15 @@ int main(int argc, char **argv) {
 
     auto m = builder.getModule();
 
-    m->set_print_name();
+    // m->set_print_name();
     PassManager PM(m.get());
 
     if (mem2reg) {
         PM.add_pass<Mem2Reg>(emit);
     }
+    if (gvn)
+        PM.add_pass<GVN>(emit, dump_json);
+
     PM.run();
 
     auto IR = m->print();
@@ -95,11 +108,13 @@ int main(int argc, char **argv) {
     output_stream << IR;
     output_stream.close();
     if (!emit) {
-        std::string lib_path = argv[0];
+        std::string lib_path = " -L"s + argv[0];
         auto idx = lib_path.rfind('/');
         if (idx != std::string::npos)
-            lib_path.erase(lib_path.rfind('/'));
-        auto cmd_str = "clang -O0 -w "s + target_path + ".ll -o " + target_path + " -L" + lib_path + " -lcminus_io";
+            lib_path.erase(idx);
+        else
+            lib_path.clear();
+        auto cmd_str = "clang -O0 -w -no-pie "s + target_path + ".ll -o " + target_path + lib_path + " -lcminus_io";
         int re_code0 = std::system(cmd_str.c_str());
         cmd_str = "rm "s + target_path + ".ll";
         int re_code1 = std::system(cmd_str.c_str());
@@ -108,5 +123,6 @@ int main(int argc, char **argv) {
         else
             return 1;
     }
+
     return 0;
 }
diff --git a/src/lightir/Value.cpp b/src/lightir/Value.cpp
index 06297e142da28779ac2701c4cb762d959adb7929..0ccc6bde0f5487c57f3ed30b3b9f51bf58e9baf8 100644
--- a/src/lightir/Value.cpp
+++ b/src/lightir/Value.cpp
@@ -24,3 +24,17 @@ void Value::remove_use(Value *val) {
     auto is_val = [val](const Use &use) { return use.val_ == val; };
     use_list_.remove_if(is_val);
 }
+
+void Value::replace_use_with_when(Value *new_val, std::function<bool(User *)> pred) {
+    for (auto it = use_list_.begin(); it != use_list_.end();) {
+        auto use = *it;
+        auto val = dynamic_cast<User *>(use.val_);
+        assert(val && "new_val is not a user");
+        if (not pred(val)) {
+            ++it;
+            continue;
+        }
+        val->set_operand(use.arg_no_, new_val);
+        it = use_list_.erase(it);
+    }
+}
diff --git a/src/optimization/CMakeLists.txt b/src/optimization/CMakeLists.txt
index 102c5e8a2afcdef2030817c359734b2fcd8c8090..8e969b3c6f1f340b763191a70970003afa904b9c 100644
--- a/src/optimization/CMakeLists.txt
+++ b/src/optimization/CMakeLists.txt
@@ -2,4 +2,5 @@ add_library(
         OP_lib STATIC
         Dominators.cpp
         Mem2Reg.cpp
+        GVN.cpp
 )
diff --git a/src/optimization/GVN.cpp b/src/optimization/GVN.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..e10dda3b9c2c6801b99695fc72818080caf9bd7b
--- /dev/null
+++ b/src/optimization/GVN.cpp
@@ -0,0 +1,306 @@
+#include "GVN.h"
+
+#include "BasicBlock.h"
+#include "Constant.h"
+#include "DeadCode.h"
+#include "FuncInfo.h"
+#include "Function.h"
+#include "Instruction.h"
+#include "logging.hpp"
+
+#include <algorithm>
+#include <cstddef>
+#include <cstdint>
+#include <fstream>
+#include <memory>
+#include <sstream>
+#include <tuple>
+#include <utility>
+#include <vector>
+
+using namespace GVNExpression;
+using std::string_literals::operator""s;
+using std::shared_ptr;
+
+static auto get_const_int_value = [](Value *v) { return dynamic_cast<ConstantInt *>(v)->get_value(); };
+static auto get_const_fp_value = [](Value *v) { return dynamic_cast<ConstantFP *>(v)->get_value(); };
+// Constant Propagation helper, folders are done for you
+Constant *ConstFolder::compute(Instruction *instr, Constant *value1, Constant *value2) {
+    auto op = instr->get_instr_type();
+    switch (op) {
+    case Instruction::add: return ConstantInt::get(get_const_int_value(value1) + get_const_int_value(value2), module_);
+    case Instruction::sub: return ConstantInt::get(get_const_int_value(value1) - get_const_int_value(value2), module_);
+    case Instruction::mul: return ConstantInt::get(get_const_int_value(value1) * get_const_int_value(value2), module_);
+    case Instruction::sdiv: return ConstantInt::get(get_const_int_value(value1) / get_const_int_value(value2), module_);
+    case Instruction::fadd: return ConstantFP::get(get_const_fp_value(value1) + get_const_fp_value(value2), module_);
+    case Instruction::fsub: return ConstantFP::get(get_const_fp_value(value1) - get_const_fp_value(value2), module_);
+    case Instruction::fmul: return ConstantFP::get(get_const_fp_value(value1) * get_const_fp_value(value2), module_);
+    case Instruction::fdiv: return ConstantFP::get(get_const_fp_value(value1) / get_const_fp_value(value2), module_);
+
+    case Instruction::cmp:
+        switch (dynamic_cast<CmpInst *>(instr)->get_cmp_op()) {
+        case CmpInst::EQ: return ConstantInt::get(get_const_int_value(value1) == get_const_int_value(value2), module_);
+        case CmpInst::NE: return ConstantInt::get(get_const_int_value(value1) != get_const_int_value(value2), module_);
+        case CmpInst::GT: return ConstantInt::get(get_const_int_value(value1) > get_const_int_value(value2), module_);
+        case CmpInst::GE: return ConstantInt::get(get_const_int_value(value1) >= get_const_int_value(value2), module_);
+        case CmpInst::LT: return ConstantInt::get(get_const_int_value(value1) < get_const_int_value(value2), module_);
+        case CmpInst::LE: return ConstantInt::get(get_const_int_value(value1) <= get_const_int_value(value2), module_);
+        }
+    case Instruction::fcmp:
+        switch (dynamic_cast<FCmpInst *>(instr)->get_cmp_op()) {
+        case FCmpInst::EQ: return ConstantInt::get(get_const_fp_value(value1) == get_const_fp_value(value2), module_);
+        case FCmpInst::NE: return ConstantInt::get(get_const_fp_value(value1) != get_const_fp_value(value2), module_);
+        case FCmpInst::GT: return ConstantInt::get(get_const_fp_value(value1) > get_const_fp_value(value2), module_);
+        case FCmpInst::GE: return ConstantInt::get(get_const_fp_value(value1) >= get_const_fp_value(value2), module_);
+        case FCmpInst::LT: return ConstantInt::get(get_const_fp_value(value1) < get_const_fp_value(value2), module_);
+        case FCmpInst::LE: return ConstantInt::get(get_const_fp_value(value1) <= get_const_fp_value(value2), module_);
+        }
+    default: return nullptr;
+    }
+}
+
+Constant *ConstFolder::compute(Instruction *instr, Constant *value1) {
+    auto op = instr->get_instr_type();
+    switch (op) {
+    case Instruction::sitofp: return ConstantFP::get((float)get_const_int_value(value1), module_);
+    case Instruction::fptosi: return ConstantInt::get((int)get_const_fp_value(value1), module_);
+    case Instruction::zext: return ConstantInt::get((int)get_const_int_value(value1), module_);
+    default: return nullptr;
+    }
+}
+
+namespace utils {
+static std::string print_congruence_class(const CongruenceClass &cc) {
+    std::stringstream ss;
+    if (cc.index_ == 0) {
+        ss << "top class\n";
+        return ss.str();
+    }
+    ss << "\nindex: " << cc.index_ << "\nleader: " << cc.leader_->print()
+       << "\nvalue phi: " << (cc.value_phi_ ? cc.value_phi_->print() : "nullptr"s)
+       << "\nvalue expr: " << (cc.value_expr_ ? cc.value_expr_->print() : "nullptr"s) << "\nmembers: {";
+    for (auto &member : cc.members_)
+        ss << member->print() << "; ";
+    ss << "}\n";
+    return ss.str();
+}
+
+static std::string dump_cc_json(const CongruenceClass &cc) {
+    std::string json;
+    json += "[";
+    for (auto member : cc.members_) {
+        if (auto c = dynamic_cast<Constant *>(member))
+            json += member->print() + ", ";
+        else
+            json += "\"%" + member->get_name() + "\", ";
+    }
+    json += "]";
+    return json;
+}
+
+static std::string dump_partition_json(const GVN::partitions &p) {
+    std::string json;
+    json += "[";
+    for (auto cc : p)
+        json += dump_cc_json(*cc) + ", ";
+    json += "]";
+    return json;
+}
+
+static std::string dump_bb2partition(const std::map<BasicBlock *, GVN::partitions> &map) {
+    std::string json;
+    json += "{";
+    for (auto [bb, p] : map)
+        json += "\"" + bb->get_name() + "\": " + dump_partition_json(p) + ",";
+    json += "}";
+    return json;
+}
+
+// logging utility for you
+static void print_partitions(const GVN::partitions &p) {
+    if (p.empty()) {
+        LOG_DEBUG << "empty partitions\n";
+        return;
+    }
+    std::string log;
+    for (auto &cc : p)
+        log += print_congruence_class(*cc);
+    LOG_DEBUG << log; // please don't use std::cout
+}
+} // namespace utils
+
+GVN::partitions GVN::join(const partitions &P1, const partitions &P2) {
+    // TODO: do intersection pair-wise
+    return {};
+}
+
+std::shared_ptr<CongruenceClass> GVN::intersect(std::shared_ptr<CongruenceClass> Ci,
+                                                std::shared_ptr<CongruenceClass> Cj) {
+    // TODO
+    return {};
+}
+
+void GVN::detectEquivalences() {
+    bool changed = false;
+    // initialize pout with top
+    // iterate until converge
+    do {
+        // see the pseudo code in documentation
+        for (auto &bb : func_->get_basic_blocks()) { // you might need to visit the blocks in depth-first order
+            // get PIN of bb by predecessor(s)
+            // iterate through all instructions in the block
+            // and the phi instruction in all the successors
+
+            // check changes in pout
+        }
+    } while (changed);
+}
+
+shared_ptr<Expression> GVN::valueExpr(Instruction *instr) {
+    // TODO
+    return {};
+}
+
+// instruction of the form `x = e`, mostly x is just e (SSA), but for copy stmt x is a phi instruction in the
+// successor. Phi values (not copy stmt) should be handled in detectEquiv
+/// \param bb basic block in which the transfer function is called
+GVN::partitions GVN::transferFunction(Instruction *x, Value *e, partitions pin) {
+    partitions pout = clone(pin);
+    // TODO: get different ValueExpr by Instruction::OpID, modify pout
+    return pout;
+}
+
+shared_ptr<PhiExpression> GVN::valuePhiFunc(shared_ptr<Expression> ve, const partitions &P) {
+    // TODO
+    return {};
+}
+
+shared_ptr<Expression> GVN::getVN(const partitions &pout, shared_ptr<Expression> ve) {
+    // TODO: return what?
+    for (auto it = pout.begin(); it != pout.end(); it++)
+        if ((*it)->value_expr_ and *(*it)->value_expr_ == *ve)
+            return {};
+    return nullptr;
+}
+
+void GVN::initPerFunction() {
+    next_value_number_ = 1;
+    pin_.clear();
+    pout_.clear();
+}
+
+void GVN::replace_cc_members() {
+    for (auto &[_bb, part] : pout_) {
+        auto bb = _bb; // workaround: structured bindings can't be captured in C++17
+        for (auto &cc : part) {
+            if (cc->index_ == 0)
+                continue;
+            // if you are planning to do constant propagation, leaders should be set to constant at some point
+            for (auto &member : cc->members_) {
+                bool member_is_phi = dynamic_cast<PhiInst *>(member);
+                bool value_phi = cc->value_phi_ != nullptr;
+                if (member != cc->leader_ and (value_phi or !member_is_phi)) {
+                    // only replace the members if users are in the same block as bb
+                    member->replace_use_with_when(cc->leader_, [bb](User *user) {
+                        if (auto instr = dynamic_cast<Instruction *>(user)) {
+                            auto parent = instr->get_parent();
+                            auto &bb_pre = parent->get_pre_basic_blocks();
+                            if (instr->is_phi()) // as copy stmt, the phi belongs to this block
+                                return std::find(bb_pre.begin(), bb_pre.end(), bb) != bb_pre.end();
+                            else
+                                return parent == bb;
+                        }
+                        return false;
+                    });
+                }
+            }
+        }
+    }
+    return;
+}
+
+// top-level function, done for you
+void GVN::run() {
+    std::ofstream gvn_json;
+    if (dump_json_) {
+        gvn_json.open("gvn.json", std::ios::out);
+        gvn_json << "[";
+    }
+
+    folder_ = std::make_unique<ConstFolder>(m_);
+    func_info_ = std::make_unique<FuncInfo>(m_);
+    func_info_->run();
+    dce_ = std::make_unique<DeadCode>(m_);
+    dce_->run(); // let dce take care of some dead phis with undef
+
+    for (auto &f : m_->get_functions()) {
+        if (f.get_basic_blocks().empty())
+            continue;
+        func_ = &f;
+        initPerFunction();
+        LOG_INFO << "Processing " << f.get_name();
+        detectEquivalences();
+        LOG_INFO << "===============pin=========================\n";
+        for (auto &[bb, part] : pin_) {
+            LOG_INFO << "\n===============bb: " << bb->get_name() << "=========================\npartitionIn: ";
+            for (auto &cc : part)
+                LOG_INFO << utils::print_congruence_class(*cc);
+        }
+        LOG_INFO << "\n===============pout=========================\n";
+        for (auto &[bb, part] : pout_) {
+            LOG_INFO << "\n=====bb: " << bb->get_name() << "=====\npartitionOut: ";
+            for (auto &cc : part)
+                LOG_INFO << utils::print_congruence_class(*cc);
+        }
+        if (dump_json_) {
+            gvn_json << "{\n\"function\": ";
+            gvn_json << "\"" << f.get_name() << "\", ";
+            gvn_json << "\n\"pout\": " << utils::dump_bb2partition(pout_);
+            gvn_json << "},";
+        }
+        replace_cc_members(); // don't delete instructions, just replace them
+    }
+    dce_->run(); // let dce do that for us
+    if (dump_json_)
+        gvn_json << "]";
+}
+
+template <typename T>
+static bool equiv_as(const Expression &lhs, const Expression &rhs) {
+    // we use static_cast because we are very sure that both operands are actually T, not other types.
+    return static_cast<const T *>(&lhs)->equiv(static_cast<const T *>(&rhs));
+}
+
+bool GVNExpression::operator==(const Expression &lhs, const Expression &rhs) {
+    if (lhs.get_expr_type() != rhs.get_expr_type())
+        return false;
+    switch (lhs.get_expr_type()) {
+    case Expression::e_constant: return equiv_as<ConstantExpression>(lhs, rhs);
+    case Expression::e_bin: return equiv_as<BinaryExpression>(lhs, rhs);
+    case Expression::e_phi: return equiv_as<PhiExpression>(lhs, rhs);
+    }
+}
+
+bool GVNExpression::operator==(const shared_ptr<Expression> &lhs, const shared_ptr<Expression> &rhs) {
+    if (lhs == nullptr and rhs == nullptr) // is the nullptr check necessary here?
+        return true;
+    return lhs and rhs and *lhs == *rhs;
+}
+
+GVN::partitions GVN::clone(const partitions &p) {
+    partitions data;
+    for (auto &cc : p) {
+        data.insert(std::make_shared<CongruenceClass>(*cc));
+    }
+    return data;
+}
+
+bool operator==(const GVN::partitions &p1, const GVN::partitions &p2) {
+    // TODO: how to compare partitions?
+    return false;
+}
+
+bool CongruenceClass::operator==(const CongruenceClass &other) const {
+    // TODO: which fields need to be compared?
+    return false;
+}
diff --git a/tests/4-ir-opt/lab4_evals.py b/tests/4-ir-opt/lab4_evals.py
new file mode 100755
index 0000000000000000000000000000000000000000..013ff9080cfc923544bb50118318c51d8426cbdb
--- /dev/null
+++ b/tests/4-ir-opt/lab4_evals.py
@@ -0,0 +1,349 @@
+#!/usr/bin/env python3
+import subprocess
+import os
+import argparse
+import re
+import time
+import glob
+import json5
+from pathlib import Path
+
+# you can run the script from anywhere!
+cminusfc_path = Path(__file__).absolute().parents[2] / "build/cminusfc"
+cminusfc = str(cminusfc_path)
+
+try:
+    from tqdm import tqdm
+except Exception as _:
+    os.system("apt install -y python3-tqdm || python3 -m pip install tqdm")
+    from tqdm import tqdm
+repeated_time = 3
+
+
+def init_args():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--GlobalValueNumber", "-gvn", action="store_true")
+    parser.add_argument(
+        "--GlobalValueNumberAnalysis", "-gvn-analysis", action="store_true"
+    )
+    args = parser.parse_args()
+    return args
+
+
+def get_raw_testcases(root_path):
+    file_names = glob.glob(root_path + "/*.cminus")
+    # pattern=r'[0-9]+'
+    # file_names.sort(key= lambda item:int(re.findall(pattern, os.path.basename(item))[0]))
+    return file_names
+
+
+def get_baseline_files(root_path):
+    file_names = glob.glob(root_path + "/*.ll")
+    # pattern=r'[0-9]+'
+    # file_names.sort(key= lambda item:int(re.findall(pattern, os.path.basename(item))[0]))
+    return file_names
+
+
+def compile_baseline_files(file_lists):
+    print("Compiling baseline files")
+    progess_bar = tqdm(total=len(file_lists), ncols=50)
+    exec_files = list()
+    for each in file_lists:
+        exec_file, _ = os.path.splitext(each)
+        COMMAND = "clang -O0 -w " + each + " -o " + exec_file + " -L. -lcminus_io"
+        try:
+            result = subprocess.run(
+                COMMAND,
+                stdout=subprocess.PIPE,
+                stderr=subprocess.PIPE,
+                shell=True,
+                timeout=1,
+            )
+            if result.returncode == 0:
+                exec_files.append(exec_file)
+            else:
+                exec_files.append(None)
+                print(
+                    f"\nCompile {each.split('/')[-1]} \033[31;1m failed\033[0m")
+        except Exception as _:
+            exec_files.append(None)
+            print(f"Compile {each.split('/')[-1]} \033[31;1m failed\033[0m")
+        progess_bar.update(1)
+    progess_bar.close()
+    return exec_files
+
+
+def compile_testcases(file_lists, option):
+    COMMAND = cminusfc + " " + option + " "
+    exec_files = list()
+    print("Compiling ", option)
+    progess_bar = tqdm(total=len(file_lists), ncols=50)
+
+    for each in file_lists:
+
+        try:
+            result = subprocess.run(
+                COMMAND + each,
+                stdout=subprocess.PIPE,
+                stderr=subprocess.PIPE,
+                shell=True,
+                timeout=1,
+            )
+            if result.returncode == 0:
+                exec_file, _ = os.path.splitext(each)
+                exec_files.append(exec_file)
+            else:
+                exec_files.append(None)
+                print(
+                    f"\nCompile {each.split('/')[-1]} \033[31;1m failed\033[0m")
+        except Exception as _:
+            exec_files.append(None)
+            print(f"Compile {each.split('/')[-1]} \033[31;1m failed\033[0m")
+
+        progess_bar.update(1)
+    progess_bar.close()
+    return exec_files
+
+
+def gvn_evaluate(file_lists, metric_func, check_mode=True):
+    result = list()
+    print("Evalution ")
+    progess_bar = tqdm(total=len(file_lists), ncols=50)
+    for each in file_lists:
+        if each == None:
+            result.append(None)
+            continue
+        if check_if_correct(each, check_mode):
+            base = 0
+            for _ in range(repeated_time):
+                re_value = metric_func(each)
+                if re_value != None:
+                    base += re_value / repeated_time
+                else:
+                    base = None
+                    break
+            result.append(base)
+        else:
+            result.append(None)
+
+        subprocess.call(["rm", "-rf", each])
+        progess_bar.update(1)
+    progess_bar.close()
+    return result
+
+
+def check_if_correct(exec_file, check_mode=True):
+    if check_mode:
+        input_option = None
+        if os.path.exists(exec_file + ".in"):
+            with open(exec_file + ".in", "rb") as fin:
+                input_option = fin.read()
+        try:
+            result = subprocess.run(
+                [exec_file],
+                input=input_option,
+                stdout=subprocess.PIPE,
+                stderr=subprocess.PIPE,
+                timeout=10,
+            )
+            with open(exec_file + ".out", "rb") as fout:
+                answer = fout.read()
+                if result.stdout == answer:
+                    return True
+                else:
+                    print(
+                        f"Execute {exec_file.split('/')[-1]} result is not correct! your output:{result.stdout}, but the answer is:{answer}"
+                    )
+                    return False
+
+        except Exception as e:
+            print(
+                f"Execute {exec_file.split('/')[-1]} \033[31;1m failed\033[0m")
+            return False
+    else:
+        return True
+
+
+def get_execute_time(exec_file):
+    try:
+        cmdline = "taskset -c 0 " + exec_file + " < " + exec_file + ".in" + " 2>&1"
+        input_option = None
+        start = time.time()
+        result = subprocess.run(
+            [cmdline],
+            shell=True,
+            stdout=subprocess.PIPE,
+            stderr=subprocess.PIPE,
+            universal_newlines=True,
+            timeout=10,
+        )
+        elapsed = time.time() - start
+        return elapsed
+    except Exception as e:
+        print(f"Execute {exec_file.split('/')[-1]} \033[31;1m failed\033[0m")
+        return None
+
+
+def table_print(testcase, before_optimization, after_optimization, baseline):
+    if len(before_optimization) == len(baseline) and len(before_optimization) == len(
+        after_optimization
+    ):
+        pass
+    else:
+        max_len = max(
+            [len(before_optimization), len(after_optimization), len(baseline)]
+        )
+        if len(before_optimization) < max_len:
+            before_optimization += [None] * \
+                (max_len - len(before_optimization))
+        if len(after_optimization) < max_len:
+            after_optimization += [None] * (max_len - len(after_optimization))
+        if len(baseline) < max_len:
+            baseline += [None] * (max_len - len(baseline))
+    print(
+        "\033[33;1mtestcase",
+        "\t",
+        "\033[31;1mbefore optimization\033[0m",
+        "\t",
+        "\033[32;1mafter optimization\033[0m",
+        "\t",
+        "\033[35;1mbaseline\033[0m",
+    )
+    for index, (result1, result2, result3) in enumerate(
+        zip(before_optimization, after_optimization, baseline)
+    ):
+        print(
+            testcase[index].split("/")[-1],
+            "\t\t%.2f" % result1 if result1 != None else "\t\tNone",
+            "\t\t\t%.2f" % result2 if result2 != None else "\t\t\tNone",
+            "\t\t  %.2f" % result3 if result3 != None else "\t\t  None",
+        )
+
+
+def calculate_gvn_bb_score(input_partition, answer_partition):
+    # score of every bb is either 0 or 1
+    if len(input_partition) != len(answer_partition):
+        return 0
+    score_cnt = 0
+    for in_cc in input_partition:
+        for ans_cc in answer_partition:
+            if set(in_cc) == set(ans_cc):
+                score_cnt += 1
+                break
+    if score_cnt == len(answer_partition):
+        return 1
+    return 0
+
+
+def calculate_gvn_score(input_functions, answer_functions):
+    # input & answer is dict from json
+    # calculate score use sum(score of every bb)/total_bb
+    # score of every bb is either 1 or 0
+    # total_bb is count of pout
+
+    total_bb = 0
+    for ans_func in answer_functions:
+        total_bb += len(ans_func["pout"])
+    cal_score = 0
+    for ans_func in answer_functions:
+        for in_func in input_functions:
+            if ans_func["function"] == in_func["function"]:
+                for ans_bb, ans_partition in ans_func["pout"].items():
+                    for in_bb, in_partition in in_func["pout"].items():
+                        if ans_bb == in_bb:
+                            cal_score += calculate_gvn_bb_score(
+                                in_partition, ans_partition
+                            )
+                        else:
+                            continue
+            else:
+                continue
+    return cal_score / total_bb
+
+
+if __name__ == "__main__":
+    script_path = os.path.join(os.getcwd(), __file__)
+    usr_args = init_args()
+
+    if usr_args.GlobalValueNumber:
+        print("=" * 10, "GlobalValueNumber", "=" * 10)
+        root_path = os.path.join(
+            os.path.dirname(script_path), "testcases/GVN/performance"
+        )
+        testcases = get_raw_testcases(root_path=root_path)
+        exec_files1 = compile_testcases(
+            file_lists=testcases, option="-mem2reg")
+        results1 = gvn_evaluate(file_lists=exec_files1,
+                                metric_func=get_execute_time)
+
+        exec_files2 = compile_testcases(
+            file_lists=testcases, option="-mem2reg -gvn")
+        results2 = gvn_evaluate(file_lists=exec_files2,
+                                metric_func=get_execute_time)
+
+        baseline_files = get_baseline_files(
+            os.path.join(root_path, "baseline"))
+        exec_files3 = compile_baseline_files(baseline_files)
+        results3 = gvn_evaluate(
+            file_lists=exec_files3, metric_func=get_execute_time, check_mode=False
+        )
+        table_print(
+            testcase=testcases,
+            before_optimization=results1,
+            after_optimization=results2,
+            baseline=results3,
+        )
+
+    if usr_args.GlobalValueNumberAnalysis:
+        print("=" * 10, "GlobalValueNumberAnalysis", "=" * 10)
+        root_path = os.path.join(
+            os.path.dirname(script_path), "testcases/GVN/functional"
+        )
+        testcases = get_raw_testcases(root_path=root_path)
+        option = "-mem2reg -emit-llvm -gvn -dump-json"
+        COMMAND = cminusfc + " " + option + " "
+        print("Compiling ", option)
+        progess_bar = tqdm(total=len(testcases), ncols=50)
+
+        score_list = []
+        i = 0
+        for each in testcases:
+            i += 1
+            try:
+                result = subprocess.run(
+                    COMMAND + each,
+                    stdout=subprocess.PIPE,
+                    stderr=subprocess.PIPE,
+                    shell=True,
+                    timeout=1,
+                )
+                if result.returncode == 0:
+                    exec_file, _ = os.path.splitext(each)
+                    each_base = each.split("/")[-1]
+                    print(f"\nCompile {each_base} \033[32;1m success\033[0m")
+                    with open("gvn.json", "r") as load_input:
+                        with open(exec_file + ".json", "r") as load_answer:
+                            print(
+                                f"generate json {each_base} \033[32;1m success\033[0m"
+                            )
+                            # here, input is a list of dict
+                            input_functions = json5.load(load_input)
+                            answer_functions = json5.load(load_answer)
+                            score = calculate_gvn_score(
+                                input_functions, answer_functions
+                            )
+                            score_list.append((each_base, score))
+                    subprocess.call(["rm", "-rf", exec_file + ".ll"])
+                else:
+                    print(
+                        f"\nnCompile {each.split('/')[-1]} \033[31;1m failed\033[0m")
+            except Exception as _:
+                print(
+                    f"Analyze {each.split('/')[-1]} \033[31;1m failed\033[0m")
+            progess_bar.update(1)
+        progess_bar.close()
+
+        i = 0
+        for file, score in score_list:
+            i += 1
+            print(file + ":", score)
diff --git a/tests/4-ir-opt/testcases/GVN/functional/bin.cminus b/tests/4-ir-opt/testcases/GVN/functional/bin.cminus
new file mode 100644
index 0000000000000000000000000000000000000000..e63686b7153405a4eba44d1ea1a80d203d5405e8
--- /dev/null
+++ b/tests/4-ir-opt/testcases/GVN/functional/bin.cminus
@@ -0,0 +1,19 @@
+/* c and d are redundant, and also check for constant propagation */
+int main(void) {
+    int a;
+    int b;
+    int c;
+    int d;
+    if (input() > input()) {
+        a = 33 + 33;
+        b = 44 + 44;
+        c = a + b;
+    } else {
+        a = 55 + 55;
+        b = 66 + 66;
+        c = a + b;
+    }
+    output(c);
+    d = a + b;
+    output(d);
+}
diff --git a/tests/4-ir-opt/testcases/GVN/functional/bin.json b/tests/4-ir-opt/testcases/GVN/functional/bin.json
new file mode 100644
index 0000000000000000000000000000000000000000..40c9cc3e9db0e590465c5fa452937c430be170ad
--- /dev/null
+++ b/tests/4-ir-opt/testcases/GVN/functional/bin.json
@@ -0,0 +1,109 @@
+[
+    {
+        "function": "main",
+        "pout": {
+            "label_entry": [
+                [
+                    "%op0",
+                ],
+                [
+                    "%op1",
+                ],
+                [
+                    "%op2",
+                ],
+                [
+                    "%op3",
+                ],
+                [
+                    "%op4",
+                ],
+            ],
+            "label5": [
+                [
+                    "%op0",
+                ],
+                [
+                    "%op1",
+                ],
+                [
+                    "%op2",
+                ],
+                [
+                    "%op3",
+                ],
+                [
+                    "%op4",
+                ],
+                [
+                    "%op6",
+                    "%op12",
+                ],
+                [
+                    "%op7",
+                    "%op11",
+                ],
+                [
+                    "%op8",
+                    "%op10",
+                ],
+            ],
+            "label9": [
+                [
+                    "%op0",
+                ],
+                [
+                    "%op1",
+                ],
+                [
+                    "%op2",
+                ],
+                [
+                    "%op3",
+                ],
+                [
+                    "%op4",
+                ],
+                [
+                    "%op12",
+                ],
+                [
+                    "%op11",
+                ],
+                [
+                    "%op13",
+                    "%op10",
+                ],
+            ],
+            "label14": [
+                [
+                    "%op0",
+                ],
+                [
+                    "%op1",
+                ],
+                [
+                    "%op2",
+                ],
+                [
+                    "%op3",
+                ],
+                [
+                    "%op4",
+                ],
+                [
+                    "%op15",
+                    "%op12",
+                ],
+                [
+                    "%op16",
+                    "%op11",
+                ],
+                [
+                    "%op17",
+                    "%op10",
+                ],
+            ],
+        }
+    },
+]
\ No newline at end of file
diff --git a/tests/4-ir-opt/testcases/GVN/functional/loop3.cminus b/tests/4-ir-opt/testcases/GVN/functional/loop3.cminus
new file mode 100644
index 0000000000000000000000000000000000000000..2567a98116a43bc8c5905dd8bbe7e59a4fb1a0fb
--- /dev/null
+++ b/tests/4-ir-opt/testcases/GVN/functional/loop3.cminus
@@ -0,0 +1,41 @@
+/* c and d are redundant, e and f are not redundant  */
+int main(void) {
+    int i;
+    int j;
+    int a;
+    int b;
+    int c;
+    int d;
+    int e;
+    int f;
+
+    a = 0;
+    b = 0;
+    c = 0;
+    d = 0;
+    e = 0;
+    f = 0;
+
+    i = 1;
+    while (i < 10) {
+        j = 1;
+        a = input();
+        b = input();
+        c = a + b;
+        while (j < 10) {
+            i = i + j;
+            j = i + j;
+            c = a + b;
+        }
+        d = a + b;
+        i = i + 1;
+
+        e = c + d;
+        output(c);
+        output(d);
+    }
+    f = c + d;
+    output(e);
+    output(f);
+    return 0;
+}
diff --git a/tests/4-ir-opt/testcases/GVN/functional/loop3.json b/tests/4-ir-opt/testcases/GVN/functional/loop3.json
new file mode 100644
index 0000000000000000000000000000000000000000..a80a9bdb344c85bd063e4c2ee3a2fa3549ecb6b6
--- /dev/null
+++ b/tests/4-ir-opt/testcases/GVN/functional/loop3.json
@@ -0,0 +1,244 @@
+[
+    {
+        "function": "main",
+        "pout": {
+            "label_entry": [
+                [
+                    0,
+                    "%op3",
+                    "%op2",
+                    "%op1",
+                ],
+                [
+                    1,
+                    "%op7",
+                ],
+            ],
+            "label0": [
+                [
+                    "%op3",
+                    "%op2",
+                ],
+                [
+                    "%op1",
+                ],
+                [
+                    "%op7",
+                ],
+                [
+                    "%op8",
+                ],
+                [
+                    "%op9",
+                ],
+                [
+                    "%op10",
+                ],
+            ],
+            "label11": [
+                [
+                    "%op3",
+                    "%op2",
+                ],
+                [
+                    "%op1",
+                ],
+                [
+                    "%op20",
+                    "%op7",
+                ],
+                [
+                    "%op8",
+                ],
+                [
+                    "%op9",
+                ],
+                [
+                    "%op10",
+                ],
+                [
+                    "%op12",
+                ],
+                [
+                    "%op13",
+                ],
+                [
+                    "%op14",
+                    "%op18",
+                ],
+                [
+                    1,
+                    "%op19",
+                ],
+            ],
+            "label15": [
+                [
+                    "%op3",
+                    "%op2",
+                ],
+                [
+                    "%op1",
+                ],
+                [
+                    "%op7",
+                ],
+                [
+                    "%op8",
+                ],
+                [
+                    "%op9",
+                ],
+                [
+                    "%op10",
+                ],
+                [
+                    "%op16",
+                ],
+            ],
+            "label17": [
+                [
+                    "%op12",
+                ],
+                [
+                    "%op13",
+                ],
+                [
+                    "%op3",
+                    "%op2",
+                ],
+                [
+                    "%op1",
+                ],
+                [
+                    "%op8",
+                ],
+                [
+                    "%op9",
+                ],
+                [
+                    "%op10",
+                ],
+                [
+                    "%op7",
+                ],
+                [
+                    "%op20",
+                ],
+                [
+                    "%op14",
+                    "%op18",
+                ],
+                [
+                    "%op19",
+                ],
+                [
+                    "%op21",
+                ],
+                [
+                    "%op22",
+                ],
+                [
+                    "%op23",
+                ],
+            ],
+            "label24": [
+                [
+                    "%op12",
+                ],
+                [
+                    "%op13",
+                ],
+                [
+                    "%op3",
+                    "%op2",
+                ],
+                [
+                    "%op1",
+                ],
+                [
+                    "%op8",
+                ],
+                [
+                    "%op9",
+                ],
+                [
+                    "%op10",
+                ],
+                [
+                    "%op7",
+                ],
+                [
+                    "%op14",
+                    "%op27",
+                    "%op18",
+                ],
+                [
+                    "%op21",
+                ],
+                [
+                    "%op22",
+                ],
+                [
+                    "%op23",
+                ],
+                [
+                    "%op25",
+                ],
+                [
+                    "%op26",
+                    "%op19",
+                ],
+                [
+                    "%op20",
+                ],
+            ],
+            "label28": [
+                [
+                    "%op12",
+                ],
+                [
+                    "%op13",
+                ],
+                [
+                    "%op8",
+                ],
+                [
+                    "%op9",
+                ],
+                [
+                    "%op10",
+                ],
+                [
+                    "%op20",
+                ],
+                [
+                    "%op14",
+                    "%op29",
+                    "%op3",
+                    "%op18",
+                    "%op2",
+                ],
+                [
+                    "%op19",
+                ],
+                [
+                    "%op21",
+                ],
+                [
+                    "%op22",
+                ],
+                [
+                    "%op23",
+                ],
+                [
+                    "%op30",
+                    "%op7",
+                ],
+                [
+                    "%op31",
+                    "%op1",
+                ],
+            ],
+        }
+    },
+]
\ No newline at end of file
diff --git a/tests/4-ir-opt/testcases/GVN/functional/pure_func.cminus b/tests/4-ir-opt/testcases/GVN/functional/pure_func.cminus
new file mode 100644
index 0000000000000000000000000000000000000000..bd23964e0f3ea882b80197b6a5a747af85593038
--- /dev/null
+++ b/tests/4-ir-opt/testcases/GVN/functional/pure_func.cminus
@@ -0,0 +1,41 @@
+/* `max` is pure, can be detected using FuncInfo */
+int max(int a, int b) {
+    if (a > b)
+        return a;
+    return b;
+}
+
+int a[10000];
+int b[10000];
+
+void inputarray(int a[], int n) {
+    int i;
+    i = 0;
+    while (i < n) {
+        a[i] = input();
+        i = i + 1;
+    }
+}
+
+int main(void) {
+    int i;
+    int n;
+    n = input();
+    inputarray(a, n);
+    inputarray(b, n);
+    i = 0;
+    while (i < n) {
+        int ai;
+        int bi;
+        /* `gep a i` and `max(ai,bi)` are redundant */
+        ai = a[i];
+        bi = b[i];
+        a[i] = max(ai, bi) * max(ai, bi);
+        i = i + 1;
+    }
+    i = 0;
+    while (i < n) {
+        output(a[i]);
+        i = i + 1;
+    }
+}
\ No newline at end of file
diff --git a/tests/4-ir-opt/testcases/GVN/functional/pure_func.json b/tests/4-ir-opt/testcases/GVN/functional/pure_func.json
new file mode 100644
index 0000000000000000000000000000000000000000..6b1cf468c2f6dc091378531d5bff5934ac950de7
--- /dev/null
+++ b/tests/4-ir-opt/testcases/GVN/functional/pure_func.json
@@ -0,0 +1,863 @@
+[
+    {
+        "function": "max",
+        "pout": {
+            "label_entry": [
+                [
+                    "%arg0",
+                ],
+                [
+                    "%arg1",
+                ],
+                [
+                    "%a",
+                ],
+                [
+                    "%b",
+                ],
+                [
+                    "%op2",
+                ],
+                [
+                    "%op3",
+                ],
+                [
+                    "%op4",
+                ],
+            ],
+            "label5": [
+                [
+                    "%arg0",
+                ],
+                [
+                    "%arg1",
+                ],
+                [
+                    "%a",
+                ],
+                [
+                    "%b",
+                ],
+                [
+                    "%op2",
+                ],
+                [
+                    "%op3",
+                ],
+                [
+                    "%op4",
+                ],
+            ],
+            "label6": [
+                [
+                    "%arg0",
+                ],
+                [
+                    "%arg1",
+                ],
+                [
+                    "%a",
+                ],
+                [
+                    "%b",
+                ],
+                [
+                    "%op2",
+                ],
+                [
+                    "%op3",
+                ],
+                [
+                    "%op4",
+                ],
+            ],
+        }
+    },
+    {
+        "function": "inputarray",
+        "pout": {
+            "label_entry": [
+                [
+                    "%arg0",
+                ],
+                [
+                    "%arg1",
+                ],
+                [
+                    "%a",
+                ],
+                [
+                    "%b",
+                ],
+                [
+                    "%op4",
+                    0,
+                ],
+            ],
+            "label3": [
+                [
+                    "%arg0",
+                ],
+                [
+                    "%arg1",
+                ],
+                [
+                    "%a",
+                ],
+                [
+                    "%b",
+                ],
+                [
+                    "%op4",
+                ],
+                [
+                    "%op5",
+                ],
+                [
+                    "%op6",
+                ],
+                [
+                    "%op7",
+                ],
+            ],
+            "label8": [
+                [
+                    "%arg0",
+                ],
+                [
+                    "%arg1",
+                ],
+                [
+                    "%a",
+                ],
+                [
+                    "%b",
+                ],
+                [
+                    "%op4",
+                ],
+                [
+                    "%op5",
+                ],
+                [
+                    "%op6",
+                ],
+                [
+                    "%op7",
+                ],
+                [
+                    "%op9",
+                ],
+                [
+                    "%op10",
+                ],
+            ],
+            "label11": [
+                [
+                    "%arg0",
+                ],
+                [
+                    "%arg1",
+                ],
+                [
+                    "%a",
+                ],
+                [
+                    "%b",
+                ],
+                [
+                    "%op4",
+                ],
+                [
+                    "%op5",
+                ],
+                [
+                    "%op6",
+                ],
+                [
+                    "%op7",
+                ],
+            ],
+            "label12": [
+                [
+                    "%arg0",
+                ],
+                [
+                    "%arg1",
+                ],
+                [
+                    "%a",
+                ],
+                [
+                    "%b",
+                ],
+                [
+                    "%op4",
+                ],
+                [
+                    "%op5",
+                ],
+                [
+                    "%op6",
+                ],
+                [
+                    "%op7",
+                ],
+                [
+                    "%op9",
+                ],
+                [
+                    "%op10",
+                ],
+            ],
+            "label13": [
+                [
+                    "%arg0",
+                ],
+                [
+                    "%arg1",
+                ],
+                [
+                    "%a",
+                ],
+                [
+                    "%b",
+                ],
+                [
+                    "%op5",
+                ],
+                [
+                    "%op6",
+                ],
+                [
+                    "%op7",
+                ],
+                [
+                    "%op9",
+                ],
+                [
+                    "%op10",
+                ],
+                [
+                    "%op14",
+                ],
+                [
+                    "%op4",
+                    "%op15",
+                ],
+            ],
+        }
+    },
+    {
+        "function": "main",
+        "pout": {
+            "label_entry": [
+                [
+                    "%a",
+                ],
+                [
+                    "%b",
+                ],
+                [
+                    "%op0",
+                ],
+                [
+                    0,
+                    "%op6",
+                ],
+                [
+                    "%op1",
+                ],
+                [
+                    "%op2",
+                ],
+            ],
+            "label3": [
+                [
+                    "%a",
+                ],
+                [
+                    "%b",
+                ],
+                [
+                    "%op0",
+                ],
+                [
+                    "%op1",
+                ],
+                [
+                    "%op2",
+                ],
+                [
+                    "%op6",
+                ],
+                [
+                    "%op7",
+                ],
+                [
+                    "%op8",
+                ],
+                [
+                    "%op9",
+                ],
+            ],
+            "label10": [
+                [
+                    "%a",
+                ],
+                [
+                    "%b",
+                ],
+                [
+                    "%op0",
+                ],
+                [
+                    "%op1",
+                ],
+                [
+                    "%op2",
+                ],
+                [
+                    "%op6",
+                ],
+                [
+                    "%op7",
+                ],
+                [
+                    "%op8",
+                ],
+                [
+                    "%op9",
+                ],
+                [
+                    "%op11",
+                ],
+            ],
+            "label12": [
+                [
+                    "%a",
+                ],
+                [
+                    "%b",
+                ],
+                [
+                    "%op0",
+                ],
+                [
+                    "%op1",
+                ],
+                [
+                    "%op2",
+                ],
+                [
+                    "%op6",
+                ],
+                [
+                    "%op7",
+                ],
+                [
+                    "%op8",
+                ],
+                [
+                    "%op9",
+                ],
+                [
+                    0,
+                    "%op31",
+                ],
+            ],
+            "label13": [
+                [
+                    "%a",
+                ],
+                [
+                    "%b",
+                ],
+                [
+                    "%op0",
+                ],
+                [
+                    "%op1",
+                ],
+                [
+                    "%op2",
+                ],
+                [
+                    "%op6",
+                ],
+                [
+                    "%op7",
+                ],
+                [
+                    "%op8",
+                ],
+                [
+                    "%op9",
+                ],
+                [
+                    "%op11",
+                ],
+            ],
+            "label14": [
+                [
+                    "%a",
+                ],
+                [
+                    "%b",
+                ],
+                [
+                    "%op0",
+                ],
+                [
+                    "%op1",
+                ],
+                [
+                    "%op2",
+                ],
+                [
+                    "%op6",
+                ],
+                [
+                    "%op7",
+                ],
+                [
+                    "%op8",
+                ],
+                [
+                    "%op9",
+                ],
+                [
+                    "%op11",
+                    "%op17",
+                ],
+                [
+                    "%op15",
+                ],
+                [
+                    "%op16",
+                ],
+            ],
+            "label18": [
+                [
+                    "%a",
+                ],
+                [
+                    "%b",
+                ],
+                [
+                    "%op0",
+                ],
+                [
+                    "%op1",
+                ],
+                [
+                    "%op2",
+                ],
+                [
+                    "%op6",
+                ],
+                [
+                    "%op7",
+                ],
+                [
+                    "%op8",
+                ],
+                [
+                    "%op9",
+                ],
+                [
+                    "%op11",
+                    "%op17",
+                ],
+                [
+                    "%op15",
+                ],
+                [
+                    "%op16",
+                ],
+            ],
+            "label19": [
+                [
+                    "%a",
+                ],
+                [
+                    "%b",
+                ],
+                [
+                    "%op0",
+                ],
+                [
+                    "%op1",
+                ],
+                [
+                    "%op2",
+                ],
+                [
+                    "%op6",
+                ],
+                [
+                    "%op7",
+                ],
+                [
+                    "%op8",
+                ],
+                [
+                    "%op9",
+                ],
+                [
+                    "%op11",
+                    "%op17",
+                    "%op25",
+                ],
+                [
+                    "%op15",
+                ],
+                [
+                    "%op16",
+                ],
+                [
+                    "%op20",
+                ],
+                [
+                    "%op21",
+                ],
+                [
+                    "%op22",
+                    "%op23",
+                ],
+                [
+                    "%op24",
+                ],
+            ],
+            "label26": [
+                [
+                    "%a",
+                ],
+                [
+                    "%b",
+                ],
+                [
+                    "%op0",
+                ],
+                [
+                    "%op1",
+                ],
+                [
+                    "%op2",
+                ],
+                [
+                    "%op6",
+                ],
+                [
+                    "%op7",
+                ],
+                [
+                    "%op8",
+                ],
+                [
+                    "%op9",
+                ],
+                [
+                    "%op11",
+                    "%op17",
+                    "%op25",
+                ],
+                [
+                    "%op15",
+                ],
+                [
+                    "%op16",
+                ],
+                [
+                    "%op20",
+                ],
+                [
+                    "%op21",
+                ],
+                [
+                    "%op22",
+                    "%op23",
+                ],
+                [
+                    "%op24",
+                ],
+            ],
+            "label27": [
+                [
+                    "%a",
+                ],
+                [
+                    "%b",
+                ],
+                [
+                    "%op0",
+                ],
+                [
+                    "%op1",
+                ],
+                [
+                    "%op2",
+                ],
+                [
+                    "%op7",
+                ],
+                [
+                    "%op8",
+                ],
+                [
+                    "%op9",
+                ],
+                [
+                    "%op11",
+                    "%op17",
+                    "%op25",
+                ],
+                [
+                    "%op15",
+                    "%op28",
+                ],
+                [
+                    "%op16",
+                ],
+                [
+                    "%op20",
+                ],
+                [
+                    "%op21",
+                ],
+                [
+                    "%op22",
+                    "%op23",
+                ],
+                [
+                    "%op24",
+                ],
+                [
+                    "%op6",
+                    "%op29",
+                ],
+            ],
+            "label30": [
+                [
+                    "%a",
+                ],
+                [
+                    "%b",
+                ],
+                [
+                    "%op0",
+                ],
+                [
+                    "%op1",
+                ],
+                [
+                    "%op2",
+                ],
+                [
+                    "%op6",
+                ],
+                [
+                    "%op7",
+                ],
+                [
+                    "%op8",
+                ],
+                [
+                    "%op9",
+                ],
+                [
+                    "%op31",
+                ],
+                [
+                    "%op32",
+                ],
+                [
+                    "%op33",
+                ],
+                [
+                    "%op34",
+                ],
+            ],
+            "label35": [
+                [
+                    "%a",
+                ],
+                [
+                    "%b",
+                ],
+                [
+                    "%op0",
+                ],
+                [
+                    "%op1",
+                ],
+                [
+                    "%op2",
+                ],
+                [
+                    "%op6",
+                ],
+                [
+                    "%op7",
+                ],
+                [
+                    "%op8",
+                ],
+                [
+                    "%op9",
+                ],
+                [
+                    "%op31",
+                ],
+                [
+                    "%op32",
+                ],
+                [
+                    "%op33",
+                ],
+                [
+                    "%op34",
+                ],
+                [
+                    "%op36",
+                ],
+            ],
+            "label37": [
+                [
+                    "%a",
+                ],
+                [
+                    "%b",
+                ],
+                [
+                    "%op0",
+                ],
+                [
+                    "%op1",
+                ],
+                [
+                    "%op2",
+                ],
+                [
+                    "%op6",
+                ],
+                [
+                    "%op7",
+                ],
+                [
+                    "%op8",
+                ],
+                [
+                    "%op9",
+                ],
+                [
+                    "%op31",
+                ],
+                [
+                    "%op32",
+                ],
+                [
+                    "%op33",
+                ],
+                [
+                    "%op34",
+                ],
+            ],
+            "label38": [
+                [
+                    "%a",
+                ],
+                [
+                    "%b",
+                ],
+                [
+                    "%op0",
+                ],
+                [
+                    "%op1",
+                ],
+                [
+                    "%op2",
+                ],
+                [
+                    "%op6",
+                ],
+                [
+                    "%op7",
+                ],
+                [
+                    "%op8",
+                ],
+                [
+                    "%op9",
+                ],
+                [
+                    "%op31",
+                ],
+                [
+                    "%op32",
+                ],
+                [
+                    "%op33",
+                ],
+                [
+                    "%op34",
+                ],
+                [
+                    "%op36",
+                ],
+            ],
+            "label39": [
+                [
+                    "%a",
+                ],
+                [
+                    "%b",
+                ],
+                [
+                    "%op0",
+                ],
+                [
+                    "%op1",
+                ],
+                [
+                    "%op2",
+                ],
+                [
+                    "%op6",
+                ],
+                [
+                    "%op7",
+                ],
+                [
+                    "%op8",
+                ],
+                [
+                    "%op9",
+                ],
+                [
+                    "%op32",
+                ],
+                [
+                    "%op33",
+                ],
+                [
+                    "%op34",
+                ],
+                [
+                    "%op36",
+                ],
+                [
+                    "%op40",
+                ],
+                [
+                    "%op41",
+                ],
+                [
+                    "%op31",
+                    "%op42",
+                ],
+            ],
+        }
+    },
+]
\ No newline at end of file
diff --git a/tests/4-ir-opt/testcases/GVN/functional/single_bb1.cminus b/tests/4-ir-opt/testcases/GVN/functional/single_bb1.cminus
new file mode 100644
index 0000000000000000000000000000000000000000..fca23c17f4634e32bce4ae1e65ea0e9b4f7c28b8
--- /dev/null
+++ b/tests/4-ir-opt/testcases/GVN/functional/single_bb1.cminus
@@ -0,0 +1,12 @@
+/* check GVN on one-block input */
+int main(void) {
+    int a;
+    int b;
+    /* we provide a pure function analysis,
+       input is not side-effect free, so multiple calls to input are considered different */
+    a = input();
+    b = input();
+    output(a + b);
+    output(a + b);
+    return 0;
+}
diff --git a/tests/4-ir-opt/testcases/GVN/functional/single_bb1.json b/tests/4-ir-opt/testcases/GVN/functional/single_bb1.json
new file mode 100644
index 0000000000000000000000000000000000000000..5ea2140bbed93871dfbb1979e7498e42ccf71688
--- /dev/null
+++ b/tests/4-ir-opt/testcases/GVN/functional/single_bb1.json
@@ -0,0 +1,4 @@
+[{
+"function": "main", 
+"pout": {"label_entry": [["%op0", ], ["%op1", ], ["%op2", "%op3", ], ],
+}},]
\ No newline at end of file
diff --git a/tests/4-ir-opt/testcases/GVN/performance/baseline/const-prop.in b/tests/4-ir-opt/testcases/GVN/performance/baseline/const-prop.in
new file mode 100644
index 0000000000000000000000000000000000000000..ea600cb61b366b723c6e331e118865642391327f
--- /dev/null
+++ b/tests/4-ir-opt/testcases/GVN/performance/baseline/const-prop.in
@@ -0,0 +1 @@
+100000000
diff --git a/tests/4-ir-opt/testcases/GVN/performance/baseline/const-prop.ll b/tests/4-ir-opt/testcases/GVN/performance/baseline/const-prop.ll
new file mode 100644
index 0000000000000000000000000000000000000000..d8a1c73fd46a244f877ec88e25f43278a3b77236
--- /dev/null
+++ b/tests/4-ir-opt/testcases/GVN/performance/baseline/const-prop.ll
@@ -0,0 +1,26 @@
+declare i32 @input()
+
+declare void @output(i32)
+
+declare void @outputFloat(float)
+
+declare void @neg_idx_except()
+
+define void @main() {
+label_entry:
+  %op0 = call i32 @input()
+  br label %label1
+label1:                                                ; preds = %label_entry, %label11
+  %op2 = phi i32 [ 0, %label_entry ], [ 711082625, %label11 ]
+  %op7 = phi i32 [ 0, %label_entry ], [ %op37, %label11 ]
+  %op8 = icmp slt i32 %op7, %op0
+  %op9 = zext i1 %op8 to i32
+  %op10 = icmp ne i32 %op9, 0
+  br i1 %op10, label %label11, label %label38
+label11:                                                ; preds = %label1
+  %op37 = add i32 %op7, 1
+  br label %label1
+label38:                                                ; preds = %label1
+  call void @output(i32 %op2)
+  ret void
+}
diff --git a/tests/4-ir-opt/testcases/GVN/performance/baseline/transpose.in b/tests/4-ir-opt/testcases/GVN/performance/baseline/transpose.in
new file mode 100644
index 0000000000000000000000000000000000000000..f37548b30c57768e9549667d431165587c834a8e
--- /dev/null
+++ b/tests/4-ir-opt/testcases/GVN/performance/baseline/transpose.in
@@ -0,0 +1,32 @@
+10000000
+30
+2
+5
+4
+25
+8
+125
+16
+625
+32
+3125
+2
+5
+4
+25
+8
+125
+16
+625
+32
+3125
+2
+5
+4
+25
+8
+125
+16
+625
+32
+3125
diff --git a/tests/4-ir-opt/testcases/GVN/performance/baseline/transpose.ll b/tests/4-ir-opt/testcases/GVN/performance/baseline/transpose.ll
new file mode 100644
index 0000000000000000000000000000000000000000..154e7f3f82312e5f0d391112a362643d1a7d729f
--- /dev/null
+++ b/tests/4-ir-opt/testcases/GVN/performance/baseline/transpose.ll
@@ -0,0 +1,192 @@
+; ModuleID = 'cminus'
+source_filename = "./test.cminus"
+
+@matrix = global [20000000 x i32] zeroinitializer
+@ad = global [100000 x i32] zeroinitializer
+@len = global i32 zeroinitializer
+declare i32 @input()
+
+declare void @output(i32)
+
+declare void @outputFloat(float)
+
+declare void @neg_idx_except()
+
+define void @readarray() {
+label_entry:
+  br label %label0
+label0:                                                ; preds = %label_entry, %label11
+  %op1 = phi i32 [ 0, %label_entry ], [ %op13, %label11 ]
+  %op2 = load i32, i32* @len
+  %op3 = icmp slt i32 %op1, %op2
+  %op4 = zext i1 %op3 to i32
+  %op5 = icmp ne i32 %op4, 0
+  br i1 %op5, label %label6, label %label9
+label6:                                                ; preds = %label0
+  %op7 = call i32 @input()
+  %op8 = icmp slt i32 %op1, 0
+  br i1 %op8, label %label10, label %label11
+label9:                                                ; preds = %label0
+  ret void
+label10:                                                ; preds = %label6
+  call void @neg_idx_except()
+  ret void
+label11:                                                ; preds = %label6
+  %op12 = getelementptr [100000 x i32], [100000 x i32]* @ad, i32 0, i32 %op1
+  store i32 %op7, i32* %op12
+  %op13 = add i32 %op1, 1
+  br label %label0
+}
+define i32 @transpose(i32 %arg0, i32* %arg1, i32 %arg2) {
+label_entry:
+  %op4 = sdiv i32 %arg0, %arg2
+  br label %label5
+label5:                                                ; preds = %label_entry, %label25
+  %op8 = phi i32 [ 0, %label_entry ], [ %op26, %label25 ]
+  %op9 = icmp slt i32 %op8, %op4
+  %op10 = zext i1 %op9 to i32
+  %op11 = icmp ne i32 %op10, 0
+  br i1 %op11, label %label12, label %label13
+label12:                                                ; preds = %label5
+  br label %label15
+label13:                                                ; preds = %label5
+  ret i32 -1
+label15:                                                ; preds = %label12, %label29
+  %op17 = phi i32 [ 0, %label12 ], [ %op31, %label29 ]
+  %op18 = icmp slt i32 %op17, %arg2
+  %op19 = zext i1 %op18 to i32
+  %op20 = icmp ne i32 %op19, 0
+  br i1 %op20, label %label21, label %label25
+label21:                                                ; preds = %label15
+  %op22 = icmp slt i32 %op8, %op17
+  %op23 = zext i1 %op22 to i32
+  %op24 = icmp ne i32 %op23, 0
+  br i1 %op24, label %label27, label %label32
+label25:                                                ; preds = %label15
+  %op26 = add i32 %op8, 1
+  br label %label5
+label27:                                                ; preds = %label21
+  %op28 = add i32 %op17, 1
+  br label %label29
+label29:                                                ; preds = %label27, %label57
+  %op31 = phi i32 [ %op28, %label27 ], [ %op59, %label57 ]
+  br label %label15
+label32:                                                ; preds = %label21
+  %op33 = mul i32 %op8, %arg2
+  %op34 = add i32 %op33, %op17
+  %op35 = icmp slt i32 %op34, 0
+  br i1 %op35, label %label36, label %label37
+label36:                                                ; preds = %label32
+  call void @neg_idx_except()
+  ret i32 0
+label37:                                                ; preds = %label32
+  %op38 = getelementptr i32, i32* %arg1, i32 %op34
+  %op39 = load i32, i32* %op38
+  br i1 %op35, label %label43, label %label44
+label43:                                                ; preds = %label37
+  call void @neg_idx_except()
+  ret i32 0
+label44:                                                ; preds = %label37
+  %op46 = load i32, i32* %op38
+  %op47 = mul i32 %op17, %op4
+  %op48 = add i32 %op47, %op8
+  %op49 = icmp slt i32 %op48, 0
+  br i1 %op49, label %label50, label %label51
+label50:                                                ; preds = %label44
+  call void @neg_idx_except()
+  ret i32 0
+label51:                                                ; preds = %label44
+  %op52 = getelementptr i32, i32* %arg1, i32 %op48
+  store i32 %op46, i32* %op52
+  br i1 %op35, label %label56, label %label57
+label56:                                                ; preds = %label51
+  call void @neg_idx_except()
+  ret i32 0
+label57:                                                ; preds = %label51
+  store i32 %op39, i32* %op38
+  %op59 = add i32 %op17, 1
+  br label %label29
+}
+define i32 @main() {
+label_entry:
+  %op0 = call i32 @input()
+  %op1 = call i32 @input()
+  store i32 %op1, i32* @len
+  call void @readarray()
+  br label %label2
+label2:                                                ; preds = %label_entry, %label11
+  %op3 = phi i32 [ 0, %label_entry ], [ %op13, %label11 ]
+  %op4 = icmp slt i32 %op3, %op0
+  %op5 = zext i1 %op4 to i32
+  %op6 = icmp ne i32 %op5, 0
+  br i1 %op6, label %label7, label %label9
+label7:                                                ; preds = %label2
+  %op8 = icmp slt i32 %op3, 0
+  br i1 %op8, label %label10, label %label11
+label9:                                                ; preds = %label2
+  br label %label14
+label10:                                                ; preds = %label7
+  call void @neg_idx_except()
+  ret i32 0
+label11:                                                ; preds = %label7
+  %op12 = getelementptr [20000000 x i32], [20000000 x i32]* @matrix, i32 0, i32 %op3
+  store i32 %op3, i32* %op12
+  %op13 = add i32 %op3, 1
+  br label %label2
+label14:                                                ; preds = %label9, %label25
+  %op15 = phi i32 [ 0, %label9 ], [ %op29, %label25 ]
+  %op16 = load i32, i32* @len
+  %op17 = icmp slt i32 %op15, %op16
+  %op18 = zext i1 %op17 to i32
+  %op19 = icmp ne i32 %op18, 0
+  br i1 %op19, label %label20, label %label23
+label20:                                                ; preds = %label14
+  %op21 = getelementptr [20000000 x i32], [20000000 x i32]* @matrix, i32 0, i32 0
+  %op22 = icmp slt i32 %op15, 0
+  br i1 %op22, label %label24, label %label25
+label23:                                                ; preds = %label14
+  br label %label30
+label24:                                                ; preds = %label20
+  call void @neg_idx_except()
+  ret i32 0
+label25:                                                ; preds = %label20
+  %op26 = getelementptr [100000 x i32], [100000 x i32]* @ad, i32 0, i32 %op15
+  %op27 = load i32, i32* %op26
+  %op28 = call i32 @transpose(i32 %op0, i32* %op21, i32 %op27)
+  %op29 = add i32 %op15, 1
+  br label %label14
+label30:                                                ; preds = %label23, %label45
+  %op31 = phi i32 [ 0, %label23 ], [ %op49, %label45 ]
+  %op32 = phi i32 [ 0, %label23 ], [ %op50, %label45 ]
+  %op33 = load i32, i32* @len
+  %op34 = icmp slt i32 %op32, %op33
+  %op35 = zext i1 %op34 to i32
+  %op36 = icmp ne i32 %op35, 0
+  br i1 %op36, label %label37, label %label40
+label37:                                                ; preds = %label30
+  %op38 = mul i32 %op32, %op32
+  %op39 = icmp slt i32 %op32, 0
+  br i1 %op39, label %label44, label %label45
+label40:                                                ; preds = %label30
+  %op41 = icmp slt i32 %op31, 0
+  %op42 = zext i1 %op41 to i32
+  %op43 = icmp ne i32 %op42, 0
+  br i1 %op43, label %label51, label %label53
+label44:                                                ; preds = %label37
+  call void @neg_idx_except()
+  ret i32 0
+label45:                                                ; preds = %label37
+  %op46 = getelementptr [20000000 x i32], [20000000 x i32]* @matrix, i32 0, i32 %op32
+  %op47 = load i32, i32* %op46
+  %op48 = mul i32 %op38, %op47
+  %op49 = add i32 %op31, %op48
+  %op50 = add i32 %op32, 1
+  br label %label30
+label51:                                                ; preds = %label40
+  %op52 = sub i32 0, %op31
+  br label %label53
+label53:                                                ; preds = %label40, %label51
+  %op54 = phi i32 [ %op31, %label40 ], [ %op52, %label51 ]
+  call void @output(i32 %op54)
+  ret i32 0
+}
diff --git a/tests/4-ir-opt/testcases/GVN/performance/const-prop.cminus b/tests/4-ir-opt/testcases/GVN/performance/const-prop.cminus
new file mode 100644
index 0000000000000000000000000000000000000000..93d726f539fbb965d46b3c44f17ac8b1755740d7
--- /dev/null
+++ b/tests/4-ir-opt/testcases/GVN/performance/const-prop.cminus
@@ -0,0 +1,23 @@
+void main(void) {
+    int c;
+    int a;
+    int b;
+    int d;
+    int f;
+    int g;
+    int loopCnt;
+    loopCnt = input();
+    c = 0;
+    a = 0;
+    g = 0;
+    while (c < loopCnt) {
+        a = 1.23456 * 5.73478 * 2.3333 * 4.3673 * 6.34636;
+        b = a * a * a * a * a * a;
+        d = b * b * b * b * b * b;
+        f = d * d * d * d * d * d;
+        g = f * f * f * f * f * f;
+        c = c + 1;
+    }
+    output(g);
+    return;
+}
\ No newline at end of file
diff --git a/tests/4-ir-opt/testcases/GVN/performance/const-prop.in b/tests/4-ir-opt/testcases/GVN/performance/const-prop.in
new file mode 100644
index 0000000000000000000000000000000000000000..ea600cb61b366b723c6e331e118865642391327f
--- /dev/null
+++ b/tests/4-ir-opt/testcases/GVN/performance/const-prop.in
@@ -0,0 +1 @@
+100000000
diff --git a/tests/4-ir-opt/testcases/GVN/performance/const-prop.out b/tests/4-ir-opt/testcases/GVN/performance/const-prop.out
new file mode 100644
index 0000000000000000000000000000000000000000..79f74f4d2fc0b5c963f85bb11827c88073a3733b
--- /dev/null
+++ b/tests/4-ir-opt/testcases/GVN/performance/const-prop.out
@@ -0,0 +1 @@
+711082625
diff --git a/tests/4-ir-opt/testcases/GVN/performance/transpose.cminus b/tests/4-ir-opt/testcases/GVN/performance/transpose.cminus
new file mode 100644
index 0000000000000000000000000000000000000000..0aff64fd0996534f1612c3203c41dbf26b9a9812
--- /dev/null
+++ b/tests/4-ir-opt/testcases/GVN/performance/transpose.cminus
@@ -0,0 +1,70 @@
+int matrix[20000000];
+int ad[100000];
+
+int len;
+
+void readarray(void) {
+    int cnt;
+    cnt = 0;
+    while (cnt < len) {
+        ad[cnt] = input();
+        cnt = cnt + 1;
+    }
+}
+
+int transpose(int n, int matrix[], int rowsize) {
+    int colsize;
+    int i;
+    int j;
+    int curr;
+    colsize = n / rowsize;
+    i = 0;
+    j = 0;
+    while (i < colsize) {
+        j = 0;
+        while (j < rowsize) {
+            if (i < j) {
+                j = j + 1;
+            } else {
+                curr = matrix[i * rowsize + j];
+                matrix[j * colsize + i] = matrix[i * rowsize + j];
+                matrix[i * rowsize + j] = curr;
+                j = j + 1;
+            }
+        }
+        i = i + 1;
+    }
+    return 0 - 1;
+}
+
+int main(void) {
+    int n;
+    int i;
+    int ans;
+    n = input();
+    len = input();
+    readarray();
+    i = 0;
+
+    while (i < n) {
+        matrix[i] = i;
+        i = i + 1;
+    }
+    i = 0;
+    while (i < len) {
+        transpose(n, matrix, ad[i]);
+        i = i + 1;
+    }
+
+    ans = 0;
+    i = 0;
+    while (i < len) {
+        ans = ans + i * i * matrix[i];
+        i = i + 1;
+    }
+    if (ans < 0) {
+        ans = 0 - ans;
+    }
+    output(ans);
+    return 0;
+}
diff --git a/tests/4-ir-opt/testcases/GVN/performance/transpose.in b/tests/4-ir-opt/testcases/GVN/performance/transpose.in
new file mode 100644
index 0000000000000000000000000000000000000000..f37548b30c57768e9549667d431165587c834a8e
--- /dev/null
+++ b/tests/4-ir-opt/testcases/GVN/performance/transpose.in
@@ -0,0 +1,32 @@
+10000000
+30
+2
+5
+4
+25
+8
+125
+16
+625
+32
+3125
+2
+5
+4
+25
+8
+125
+16
+625
+32
+3125
+2
+5
+4
+25
+8
+125
+16
+625
+32
+3125
diff --git a/tests/4-ir-opt/testcases/GVN/performance/transpose.out b/tests/4-ir-opt/testcases/GVN/performance/transpose.out
new file mode 100644
index 0000000000000000000000000000000000000000..006d9b56fdab13cdcc3256d4da57476307ee6049
--- /dev/null
+++ b/tests/4-ir-opt/testcases/GVN/performance/transpose.out
@@ -0,0 +1 @@
+1042523985