1 // Copyright (c) 2015-2016 The Khronos Group Inc.
2 //
3 // Licensed under the Apache License, Version 2.0 (the "License");
4 // you may not use this file except in compliance with the License.
5 // You may obtain a copy of the License at
6 //
7 // http://www.apache.org/licenses/LICENSE-2.0
8 //
9 // Unless required by applicable law or agreed to in writing, software
10 // distributed under the License is distributed on an "AS IS" BASIS,
11 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12 // See the License for the specific language governing permissions and
13 // limitations under the License.
14
15 #ifndef SPVTOOLS_CFA_H_
16 #define SPVTOOLS_CFA_H_
17
18 #include <algorithm>
19 #include <cassert>
20 #include <functional>
21 #include <map>
22 #include <unordered_map>
23 #include <unordered_set>
24 #include <utility>
25 #include <vector>
26
27 using std::find;
28 using std::function;
29 using std::get;
30 using std::pair;
31 using std::unordered_map;
32 using std::unordered_set;
33 using std::vector;
34
35 namespace spvtools {
36
37 // Control Flow Analysis of control flow graphs of basic block nodes |BB|.
38 template<class BB> class CFA {
39 using bb_ptr = BB*;
40 using cbb_ptr = const BB*;
41 using bb_iter = typename std::vector<BB*>::const_iterator;
42 using get_blocks_func =
43 std::function<const std::vector<BB*>*(const BB*)>;
44
45 struct block_info {
46 cbb_ptr block; ///< pointer to the block
47 bb_iter iter; ///< Iterator to the current child node being processed
48 };
49
50 /// Returns true if a block with @p id is found in the @p work_list vector
51 ///
52 /// @param[in] work_list Set of blocks visited in the the depth first traversal
53 /// of the CFG
54 /// @param[in] id The ID of the block being checked
55 ///
56 /// @return true if the edge work_list.back().block->id() => id is a back-edge
57 static bool FindInWorkList(
58 const std::vector<block_info>& work_list, uint32_t id);
59
60 public:
61 /// @brief Depth first traversal starting from the \p entry BasicBlock
62 ///
63 /// This function performs a depth first traversal from the \p entry
64 /// BasicBlock and calls the pre/postorder functions when it needs to process
65 /// the node in pre order, post order. It also calls the backedge function
66 /// when a back edge is encountered.
67 ///
68 /// @param[in] entry The root BasicBlock of a CFG
69 /// @param[in] successor_func A function which will return a pointer to the
70 /// successor nodes
71 /// @param[in] preorder A function that will be called for every block in a
72 /// CFG following preorder traversal semantics
73 /// @param[in] postorder A function that will be called for every block in a
74 /// CFG following postorder traversal semantics
75 /// @param[in] backedge A function that will be called when a backedge is
76 /// encountered during a traversal
77 /// NOTE: The @p successor_func and predecessor_func each return a pointer to a
78 /// collection such that iterators to that collection remain valid for the
79 /// lifetime of the algorithm.
80 static void DepthFirstTraversal(const BB* entry,
81 get_blocks_func successor_func,
82 std::function<void(cbb_ptr)> preorder,
83 std::function<void(cbb_ptr)> postorder,
84 std::function<void(cbb_ptr, cbb_ptr)> backedge);
85
86 /// @brief Calculates dominator edges for a set of blocks
87 ///
88 /// Computes dominators using the algorithm of Cooper, Harvey, and Kennedy
89 /// "A Simple, Fast Dominance Algorithm", 2001.
90 ///
91 /// The algorithm assumes there is a unique root node (a node without
92 /// predecessors), and it is therefore at the end of the postorder vector.
93 ///
94 /// This function calculates the dominator edges for a set of blocks in the CFG.
95 /// Uses the dominator algorithm by Cooper et al.
96 ///
97 /// @param[in] postorder A vector of blocks in post order traversal order
98 /// in a CFG
99 /// @param[in] predecessor_func Function used to get the predecessor nodes of a
100 /// block
101 ///
102 /// @return the dominator tree of the graph, as a vector of pairs of nodes.
103 /// The first node in the pair is a node in the graph. The second node in the
104 /// pair is its immediate dominator in the sense of Cooper et.al., where a block
105 /// without predecessors (such as the root node) is its own immediate dominator.
106 static vector<pair<BB*, BB*>> CalculateDominators(
107 const vector<cbb_ptr>& postorder, get_blocks_func predecessor_func);
108
109 // Computes a minimal set of root nodes required to traverse, in the forward
110 // direction, the CFG represented by the given vector of blocks, and successor
111 // and predecessor functions. When considering adding two nodes, each having
112 // predecessors, favour using the one that appears earlier on the input blocks
113 // list.
114 static std::vector<BB*> TraversalRoots(
115 const std::vector<BB*>& blocks,
116 get_blocks_func succ_func,
117 get_blocks_func pred_func);
118
119 static void ComputeAugmentedCFG(
120 std::vector<BB*>& ordered_blocks,
121 BB* pseudo_entry_block,
122 BB* pseudo_exit_block,
123 std::unordered_map<const BB*, std::vector<BB*>>* augmented_successors_map,
124 std::unordered_map<const BB*, std::vector<BB*>>* augmented_predecessors_map,
125 get_blocks_func succ_func,
126 get_blocks_func pred_func);
127 };
128
FindInWorkList(const vector<block_info> & work_list,uint32_t id)129 template<class BB> bool CFA<BB>::FindInWorkList(const vector<block_info>& work_list,
130 uint32_t id) {
131 for (const auto b : work_list) {
132 if (b.block->id() == id) return true;
133 }
134 return false;
135 }
136
DepthFirstTraversal(const BB * entry,get_blocks_func successor_func,function<void (cbb_ptr)> preorder,function<void (cbb_ptr)> postorder,function<void (cbb_ptr,cbb_ptr)> backedge)137 template<class BB> void CFA<BB>::DepthFirstTraversal(const BB* entry,
138 get_blocks_func successor_func,
139 function<void(cbb_ptr)> preorder,
140 function<void(cbb_ptr)> postorder,
141 function<void(cbb_ptr, cbb_ptr)> backedge) {
142 unordered_set<uint32_t> processed;
143
144 /// NOTE: work_list is the sequence of nodes from the root node to the node
145 /// being processed in the traversal
146 vector<block_info> work_list;
147 work_list.reserve(10);
148
149 work_list.push_back({ entry, begin(*successor_func(entry)) });
150 preorder(entry);
151 processed.insert(entry->id());
152
153 while (!work_list.empty()) {
154 block_info& top = work_list.back();
155 if (top.iter == end(*successor_func(top.block))) {
156 postorder(top.block);
157 work_list.pop_back();
158 }
159 else {
160 BB* child = *top.iter;
161 top.iter++;
162 if (FindInWorkList(work_list, child->id())) {
163 backedge(top.block, child);
164 }
165 if (processed.count(child->id()) == 0) {
166 preorder(child);
167 work_list.emplace_back(
168 block_info{ child, begin(*successor_func(child)) });
169 processed.insert(child->id());
170 }
171 }
172 }
173 }
174
175 template<class BB>
CalculateDominators(const vector<cbb_ptr> & postorder,get_blocks_func predecessor_func)176 vector<pair<BB*, BB*>> CFA<BB>::CalculateDominators(
177 const vector<cbb_ptr>& postorder, get_blocks_func predecessor_func) {
178 struct block_detail {
179 size_t dominator; ///< The index of blocks's dominator in post order array
180 size_t postorder_index; ///< The index of the block in the post order array
181 };
182 const size_t undefined_dom = postorder.size();
183
184 unordered_map<cbb_ptr, block_detail> idoms;
185 for (size_t i = 0; i < postorder.size(); i++) {
186 idoms[postorder[i]] = { undefined_dom, i };
187 }
188 idoms[postorder.back()].dominator = idoms[postorder.back()].postorder_index;
189
190 bool changed = true;
191 while (changed) {
192 changed = false;
193 for (auto b = postorder.rbegin() + 1; b != postorder.rend(); ++b) {
194 const vector<BB*>& predecessors = *predecessor_func(*b);
195 // Find the first processed/reachable predecessor that is reachable
196 // in the forward traversal.
197 auto res = find_if(begin(predecessors), end(predecessors),
198 [&idoms, undefined_dom](BB* pred) {
199 return idoms.count(pred) &&
200 idoms[pred].dominator != undefined_dom;
201 });
202 if (res == end(predecessors)) continue;
203 const BB* idom = *res;
204 size_t idom_idx = idoms[idom].postorder_index;
205
206 // all other predecessors
207 for (const auto* p : predecessors) {
208 if (idom == p) continue;
209 // Only consider nodes reachable in the forward traversal.
210 // Otherwise the intersection doesn't make sense and will never
211 // terminate.
212 if (!idoms.count(p)) continue;
213 if (idoms[p].dominator != undefined_dom) {
214 size_t finger1 = idoms[p].postorder_index;
215 size_t finger2 = idom_idx;
216 while (finger1 != finger2) {
217 while (finger1 < finger2) {
218 finger1 = idoms[postorder[finger1]].dominator;
219 }
220 while (finger2 < finger1) {
221 finger2 = idoms[postorder[finger2]].dominator;
222 }
223 }
224 idom_idx = finger1;
225 }
226 }
227 if (idoms[*b].dominator != idom_idx) {
228 idoms[*b].dominator = idom_idx;
229 changed = true;
230 }
231 }
232 }
233
234 vector<pair<bb_ptr, bb_ptr>> out;
235 for (auto idom : idoms) {
236 // NOTE: performing a const cast for convenient usage with
237 // UpdateImmediateDominators
238 out.push_back({ const_cast<BB*>(get<0>(idom)),
239 const_cast<BB*>(postorder[get<1>(idom).dominator]) });
240 }
241 return out;
242 }
243
244 template<class BB>
TraversalRoots(const std::vector<BB * > & blocks,get_blocks_func succ_func,get_blocks_func pred_func)245 std::vector<BB*> CFA<BB>::TraversalRoots(
246 const std::vector<BB*>& blocks,
247 get_blocks_func succ_func,
248 get_blocks_func pred_func) {
249 // The set of nodes which have been visited from any of the roots so far.
250 std::unordered_set<const BB*> visited;
251
252 auto mark_visited = [&visited](const BB* b) { visited.insert(b); };
253 auto ignore_block = [](const BB*) {};
254 auto ignore_blocks = [](const BB*, const BB*) {};
255
256
257 auto traverse_from_root = [&mark_visited, &succ_func, &ignore_block,
258 &ignore_blocks](const BB* entry) {
259 DepthFirstTraversal(
260 entry, succ_func, mark_visited, ignore_block, ignore_blocks);
261 };
262
263 std::vector<BB*> result;
264
265 // First collect nodes without predecessors.
266 for (auto block : blocks) {
267 if (pred_func(block)->empty()) {
268 assert(visited.count(block) == 0 && "Malformed graph!");
269 result.push_back(block);
270 traverse_from_root(block);
271 }
272 }
273
274 // Now collect other stranded nodes. These must be in unreachable cycles.
275 for (auto block : blocks) {
276 if (visited.count(block) == 0) {
277 result.push_back(block);
278 traverse_from_root(block);
279 }
280 }
281
282 return result;
283 }
284
285 template<class BB>
ComputeAugmentedCFG(std::vector<BB * > & ordered_blocks,BB * pseudo_entry_block,BB * pseudo_exit_block,std::unordered_map<const BB *,std::vector<BB * >> * augmented_successors_map,std::unordered_map<const BB *,std::vector<BB * >> * augmented_predecessors_map,get_blocks_func succ_func,get_blocks_func pred_func)286 void CFA<BB>::ComputeAugmentedCFG(
287 std::vector<BB*>& ordered_blocks,
288 BB* pseudo_entry_block, BB* pseudo_exit_block,
289 std::unordered_map<const BB*, std::vector<BB*>>* augmented_successors_map,
290 std::unordered_map<const BB*, std::vector<BB*>>* augmented_predecessors_map,
291 get_blocks_func succ_func,
292 get_blocks_func pred_func) {
293
294 // Compute the successors of the pseudo-entry block, and
295 // the predecessors of the pseudo exit block.
296 auto sources = TraversalRoots(ordered_blocks, succ_func, pred_func);
297
298 // For the predecessor traversals, reverse the order of blocks. This
299 // will affect the post-dominance calculation as follows:
300 // - Suppose you have blocks A and B, with A appearing before B in
301 // the list of blocks.
302 // - Also, A branches only to B, and B branches only to A.
303 // - We want to compute A as dominating B, and B as post-dominating B.
304 // By using reversed blocks for predecessor traversal roots discovery,
305 // we'll add an edge from B to the pseudo-exit node, rather than from A.
306 // All this is needed to correctly process the dominance/post-dominance
307 // constraint when A is a loop header that points to itself as its
308 // own continue target, and B is the latch block for the loop.
309 std::vector<BB*> reversed_blocks(ordered_blocks.rbegin(),
310 ordered_blocks.rend());
311 auto sinks = TraversalRoots(reversed_blocks, pred_func, succ_func);
312
313 // Wire up the pseudo entry block.
314 (*augmented_successors_map)[pseudo_entry_block] = sources;
315 for (auto block : sources) {
316 auto& augmented_preds = (*augmented_predecessors_map)[block];
317 const auto preds = pred_func(block);
318 augmented_preds.reserve(1 + preds->size());
319 augmented_preds.push_back(pseudo_entry_block);
320 augmented_preds.insert(augmented_preds.end(), preds->begin(), preds->end());
321 }
322
323 // Wire up the pseudo exit block.
324 (*augmented_predecessors_map)[pseudo_exit_block] = sinks;
325 for (auto block : sinks) {
326 auto& augmented_succ = (*augmented_successors_map)[block];
327 const auto succ = succ_func(block);
328 augmented_succ.reserve(1 + succ->size());
329 augmented_succ.push_back(pseudo_exit_block);
330 augmented_succ.insert(augmented_succ.end(), succ->begin(), succ->end());
331 }
332 };
333
334 } // namespace spvtools
335
336 #endif // SPVTOOLS_CFA_H_
337