Implement dominator_tree analysis pass

Add support to build a dominator tree for a given CFG, and add APIs to
use the dominator tree to find idoms and dominance information.

include/blocks/basic_blocks.h

@@ -15,6 +15,7 @@ class basic_block {
         block::expr::Ptr branch_expr;
         block::stmt::Ptr parent;
         unsigned int index;
+        unsigned int id;
         std::string name;
 };
 

include/blocks/dominance.h

@@ -0,0 +1,34 @@
+#ifndef DOMINANCE_H
+#define DOMINANCE_H
+#include "blocks/block_visitor.h"
+#include "blocks/basic_blocks.h"
+#include "blocks/stmt.h"
+#include <vector>
+#include <stack>
+#include <string>
+#include <bitset>
+#include <algorithm>
+
+class dominator_tree {
+    public:
+        dominator_tree(std::vector<std::shared_ptr<basic_block>> &cfg);
+        std::vector<int> &get_postorder_bb_map();
+        std::vector<int> &get_postorder();
+        std::vector<int> &get_idom();
+        int get_idom(int bb_id);
+        bool dominates(int bb1_id, int bb2_id);
+        bool is_reachable_from_entry(int bb_id);
+        void analyze();
+
+    private:
+        std::vector<int> idom;
+        std::vector<int> postorder;
+        std::vector<int> postorder_bb_map;
+        std::vector<std::shared_ptr<basic_block>> &cfg_;
+        void postorder_dfs_helper(std::vector<bool> &visited_bbs, int id);
+        void postorder_dfs();
+        int intersect(int bb1_id, int bb2_id);
+};
+
+
+#endif

include/builder/builder_context.h

@@ -1,6 +1,7 @@
 #ifndef BUILDER_CONTEXT
 #define BUILDER_CONTEXT
 #include "blocks/basic_blocks.h"
+#include "blocks/dominance.h"
 #include "blocks/expr.h"
 #include "blocks/stmt.h"
 #include "builder/forward_declarations.h"

src/blocks/basic_blocks.cpp

@@ -169,5 +169,10 @@ std::vector<std::shared_ptr<basic_block>> generate_basic_blocks(block::stmt_bloc
         }
     }
 
+    // step 6: assign each basic_block an id
+    for (unsigned int i = 0; i < return_list.size(); i++) {
+        return_list[i]->id = i;
+    }
+
     return return_list;
 }

src/blocks/dominance.cpp

@@ -0,0 +1,116 @@
+#include "blocks/dominance.h"
+
+using namespace block;
+
+dominator_tree::dominator_tree(std::vector<std::shared_ptr<basic_block>> &cfg) : cfg_(cfg) {
+    // TODO: Add a check for size, it should be greater than 2.
+    idom.reserve(cfg_.size());
+    idom.assign(cfg_.size(), -1);
+    postorder.reserve(cfg_.size());
+    postorder_bb_map.reserve(cfg_.size());
+    postorder_bb_map.assign(cfg_.size(), -1);
+
+    // and call the anaylse function
+    analyze();
+}
+
+void dominator_tree::postorder_dfs_helper(std::vector<bool> &visited_bbs, int id) {
+    for (auto child: cfg_[id]->successor) {
+        if (!visited_bbs[child->id]) {
+            visited_bbs[child->id] = true;
+            postorder_dfs_helper(visited_bbs, child->id);
+            postorder.push_back(child->id);
+        }
+    }    
+}
+void dominator_tree::postorder_dfs() {
+    std::vector<bool> visited_bbs(cfg_.size());
+    visited_bbs.assign(visited_bbs.size(), false);
+    visited_bbs[0] = true;
+
+    postorder_dfs_helper(visited_bbs, 0);
+    postorder.push_back(0);
+}
+
+std::vector<int> &dominator_tree::get_postorder_bb_map() {
+    return postorder_bb_map;
+}
+
+std::vector<int> &dominator_tree::get_postorder() {
+    return postorder;
+}
+
+std::vector<int> &dominator_tree::get_idom() {
+    return idom;
+}
+
+int dominator_tree::get_idom(int bb_id) {
+    if (bb_id >= 0 && bb_id < idom.size()) {
+        return -1;
+    }
+
+    return idom[bb_id];
+}
+bool dominator_tree::dominates(int bb1_id, int bb2_id) {
+    if (bb1_id == 0) {
+        return true;
+    }
+
+    int pointer = idom[bb2_id];
+    while (pointer != 0) {
+        if (pointer == bb1_id) {
+            return true;
+        }
+        pointer = idom[pointer];
+    }
+
+    return false;
+}
+
+bool dominator_tree::is_reachable_from_entry(int bb_id) {
+    return dominates(0, bb_id);
+}
+
+int dominator_tree::intersect(int bb1_id, int bb2_id) {
+    while (bb1_id != bb2_id) {
+        if (postorder_bb_map[bb1_id] < postorder_bb_map[bb2_id]) {
+            bb1_id = idom[bb1_id];
+        }
+        else {
+            bb2_id = idom[bb2_id];
+        }
+    }
+
+    return bb1_id;
+}
+
+void dominator_tree::analyze() {
+    postorder_dfs();
+    for (unsigned int i = 0; i < postorder.size(); i++) {
+        postorder_bb_map[postorder[i]] = i;
+    }
+
+    idom[0] = 0;
+    bool change = false;
+
+    do {
+        change = 0;
+        for (int i = postorder.size() - 2; i >= 0; i--) {
+            int postorder_bb_num = postorder[i];
+            std::shared_ptr<basic_block> bb = cfg_[postorder_bb_num];
+            int bb_id_idom = bb->predecessor[0]->id;
+
+            for (unsigned int j = 1; j < bb->predecessor.size(); j++) {
+                int bb_id_idom_next = bb->predecessor[j]->id;
+                if (idom[bb_id_idom_next] != -1) {
+                    bb_id_idom = intersect(bb_id_idom, bb_id_idom_next);
+                }
+            }
+
+            if (idom[postorder_bb_num] != bb_id_idom) {
+                idom[postorder_bb_num] = bb_id_idom;
+                change = 1;
+            }
+        }
+    } while(change);
+}

src/builder/builder_context.cpp

@@ -296,7 +296,7 @@ block::stmt::Ptr builder_context::extract_ast_from_function_impl(void) {
 
 	std::cerr << "++++++ basic blocks ++++++ \n";
 	for (auto bb: BBs) {
-		std::cerr << bb->name << ":" << "  ; ";
+		std::cerr << bb->id << ":" << bb->name << ":" << "  ; ";
 		for (auto pred: bb->predecessor) {
 			std::cerr << pred->name << ", ";
 		}
@@ -314,6 +314,28 @@ block::stmt::Ptr builder_context::extract_ast_from_function_impl(void) {
 	}
 	std::cerr << "++++++ basic blocks ++++++ \n";
 
+	std::cerr << "++++++ dominance ++++++ \n";
+	dominator_tree dom(BBs);
+
+	std::cerr << "== postorder map ==\n";
+	for (int i: dom.get_postorder_bb_map()) {
+		std::cerr << i << "\n";
+	}
+	std::cerr << "== postorder map ==\n";
+
+	std::cerr << "== postorder ==\n";
+	for (int i: dom.get_postorder()) {
+		std::cerr << i << "\n";
+	}
+	std::cerr << "== postorder ==\n";
+
+	std::cerr << "== idom ==\n";
+	for (int i: dom.get_idom()) {
+		std::cerr << i << "\n";
+	}
+	std::cerr << "== idom ==\n";
+	std::cerr << "++++++ dominance ++++++ \n";
+
 	if (feature_unstructured)
 		return ast;