1 //===- SyncDependenceAnalysis.cpp - Divergent Branch Dependence Calculation
4 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
5 // See https://llvm.org/LICENSE.txt for license information.
6 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
8 //===----------------------------------------------------------------------===//
10 // This file implements an algorithm that returns for a divergent branch
11 // the set of basic blocks whose phi nodes become divergent due to divergent
12 // control. These are the blocks that are reachable by two disjoint paths from
13 // the branch or loop exits that have a reaching path that is disjoint from a
14 // path to the loop latch.
16 // The SyncDependenceAnalysis is used in the DivergenceAnalysis to model
17 // control-induced divergence in phi nodes.
20 // The SyncDependenceAnalysis lazily computes sync dependences [3].
21 // The analysis evaluates the disjoint path criterion [2] by a reduction
22 // to SSA construction. The SSA construction algorithm is implemented as
23 // a simple data-flow analysis [1].
25 // [1] "A Simple, Fast Dominance Algorithm", SPI '01, Cooper, Harvey and Kennedy
26 // [2] "Efficiently Computing Static Single Assignment Form
27 // and the Control Dependence Graph", TOPLAS '91,
28 // Cytron, Ferrante, Rosen, Wegman and Zadeck
29 // [3] "Improving Performance of OpenCL on CPUs", CC '12, Karrenberg and Hack
30 // [4] "Divergence Analysis", TOPLAS '13, Sampaio, Souza, Collange and Pereira
32 // -- Sync dependence --
33 // Sync dependence [4] characterizes the control flow aspect of the
34 // propagation of branch divergence. For example,
36 // %cond = icmp slt i32 %tid, 10
37 // br i1 %cond, label %then, label %else
43 // %a = phi i32 [ 0, %then ], [ 1, %else ]
45 // Suppose %tid holds the thread ID. Although %a is not data dependent on %tid
46 // because %tid is not on its use-def chains, %a is sync dependent on %tid
47 // because the branch "br i1 %cond" depends on %tid and affects which value %a
50 // -- Reduction to SSA construction --
51 // There are two disjoint paths from A to X, if a certain variant of SSA
52 // construction places a phi node in X under the following set-up scheme [2].
54 // This variant of SSA construction ignores incoming undef values.
55 // That is paths from the entry without a definition do not result in
67 // Assume that A contains a divergent branch. We are interested
68 // in the set of all blocks where each block is reachable from A
69 // via two disjoint paths. This would be the set {D, F} in this
71 // To generally reduce this query to SSA construction we introduce
72 // a virtual variable x and assign to x different values in each
73 // successor block of A.
83 // Our flavor of SSA construction for x will construct the following
93 // The blocks D and F contain phi nodes and are thus each reachable
94 // by two disjoins paths from A.
97 // In case of loop exits we need to check the disjoint path criterion for loops
98 // [2]. To this end, we check whether the definition of x differs between the
99 // loop exit and the loop header (_after_ SSA construction).
101 //===----------------------------------------------------------------------===//
102 #include "llvm/ADT/PostOrderIterator.h"
103 #include "llvm/ADT/SmallPtrSet.h"
104 #include "llvm/Analysis/PostDominators.h"
105 #include "llvm/Analysis/SyncDependenceAnalysis.h"
106 #include "llvm/IR/BasicBlock.h"
107 #include "llvm/IR/CFG.h"
108 #include "llvm/IR/Dominators.h"
109 #include "llvm/IR/Function.h"
112 #include <unordered_set>
114 #define DEBUG_TYPE "sync-dependence"
118 ConstBlockSet
SyncDependenceAnalysis::EmptyBlockSet
;
120 SyncDependenceAnalysis::SyncDependenceAnalysis(const DominatorTree
&DT
,
121 const PostDominatorTree
&PDT
,
123 : FuncRPOT(DT
.getRoot()->getParent()), DT(DT
), PDT(PDT
), LI(LI
) {}
125 SyncDependenceAnalysis::~SyncDependenceAnalysis() {}
127 using FunctionRPOT
= ReversePostOrderTraversal
<const Function
*>;
129 // divergence propagator for reducible CFGs
130 struct DivergencePropagator
{
131 const FunctionRPOT
&FuncRPOT
;
132 const DominatorTree
&DT
;
133 const PostDominatorTree
&PDT
;
136 // identified join points
137 std::unique_ptr
<ConstBlockSet
> JoinBlocks
;
139 // reached loop exits (by a path disjoint to a path to the loop header)
140 SmallPtrSet
<const BasicBlock
*, 4> ReachedLoopExits
;
142 // if DefMap[B] == C then C is the dominating definition at block B
143 // if DefMap[B] ~ undef then we haven't seen B yet
144 // if DefMap[B] == B then B is a join point of disjoint paths from X or B is
145 // an immediate successor of X (initial value).
146 using DefiningBlockMap
= std::map
<const BasicBlock
*, const BasicBlock
*>;
147 DefiningBlockMap DefMap
;
149 // all blocks with pending visits
150 std::unordered_set
<const BasicBlock
*> PendingUpdates
;
152 DivergencePropagator(const FunctionRPOT
&FuncRPOT
, const DominatorTree
&DT
,
153 const PostDominatorTree
&PDT
, const LoopInfo
&LI
)
154 : FuncRPOT(FuncRPOT
), DT(DT
), PDT(PDT
), LI(LI
),
155 JoinBlocks(new ConstBlockSet
) {}
157 // set the definition at @block and mark @block as pending for a visit
158 void addPending(const BasicBlock
&Block
, const BasicBlock
&DefBlock
) {
159 bool WasAdded
= DefMap
.emplace(&Block
, &DefBlock
).second
;
161 PendingUpdates
.insert(&Block
);
164 void printDefs(raw_ostream
&Out
) {
165 Out
<< "Propagator::DefMap {\n";
166 for (const auto *Block
: FuncRPOT
) {
167 auto It
= DefMap
.find(Block
);
168 Out
<< Block
->getName() << " : ";
169 if (It
== DefMap
.end()) {
172 const auto *DefBlock
= It
->second
;
173 Out
<< (DefBlock
? DefBlock
->getName() : "<null>") << "\n";
179 // process @succBlock with reaching definition @defBlock
180 // the original divergent branch was in @parentLoop (if any)
181 void visitSuccessor(const BasicBlock
&SuccBlock
, const Loop
*ParentLoop
,
182 const BasicBlock
&DefBlock
) {
184 // @succBlock is a loop exit
185 if (ParentLoop
&& !ParentLoop
->contains(&SuccBlock
)) {
186 DefMap
.emplace(&SuccBlock
, &DefBlock
);
187 ReachedLoopExits
.insert(&SuccBlock
);
191 // first reaching def?
192 auto ItLastDef
= DefMap
.find(&SuccBlock
);
193 if (ItLastDef
== DefMap
.end()) {
194 addPending(SuccBlock
, DefBlock
);
198 // a join of at least two definitions
199 if (ItLastDef
->second
!= &DefBlock
) {
200 // do we know this join already?
201 if (!JoinBlocks
->insert(&SuccBlock
).second
)
204 // update the definition
205 addPending(SuccBlock
, SuccBlock
);
209 // find all blocks reachable by two disjoint paths from @rootTerm.
210 // This method works for both divergent terminators and loops with
212 // @rootBlock is either the block containing the branch or the header of the
214 // @nodeSuccessors is the set of successors of the node (Loop or Terminator)
215 // headed by @rootBlock.
216 // @parentLoop is the parent loop of the Loop or the loop that contains the
218 template <typename SuccessorIterable
>
219 std::unique_ptr
<ConstBlockSet
>
220 computeJoinPoints(const BasicBlock
&RootBlock
,
221 SuccessorIterable NodeSuccessors
, const Loop
*ParentLoop
) {
224 // immediate post dominator (no join block beyond that block)
225 const auto *PdNode
= PDT
.getNode(const_cast<BasicBlock
*>(&RootBlock
));
226 const auto *IpdNode
= PdNode
->getIDom();
227 const auto *PdBoundBlock
= IpdNode
? IpdNode
->getBlock() : nullptr;
229 // bootstrap with branch targets
230 for (const auto *SuccBlock
: NodeSuccessors
) {
231 DefMap
.emplace(SuccBlock
, SuccBlock
);
233 if (ParentLoop
&& !ParentLoop
->contains(SuccBlock
)) {
234 // immediate loop exit from node.
235 ReachedLoopExits
.insert(SuccBlock
);
239 PendingUpdates
.insert(SuccBlock
);
243 auto ItBeginRPO
= FuncRPOT
.begin();
245 // skip until term (TODO RPOT won't let us start at @term directly)
246 for (; *ItBeginRPO
!= &RootBlock
; ++ItBeginRPO
) {}
248 auto ItEndRPO
= FuncRPOT
.end();
249 assert(ItBeginRPO
!= ItEndRPO
);
251 // propagate definitions at the immediate successors of the node in RPO
252 auto ItBlockRPO
= ItBeginRPO
;
253 while (++ItBlockRPO
!= ItEndRPO
&& *ItBlockRPO
!= PdBoundBlock
) {
254 const auto *Block
= *ItBlockRPO
;
256 // skip @block if not pending update
257 auto ItPending
= PendingUpdates
.find(Block
);
258 if (ItPending
== PendingUpdates
.end())
260 PendingUpdates
.erase(ItPending
);
262 // propagate definition at @block to its successors
263 auto ItDef
= DefMap
.find(Block
);
264 const auto *DefBlock
= ItDef
->second
;
267 auto *BlockLoop
= LI
.getLoopFor(Block
);
269 (ParentLoop
!= BlockLoop
&& ParentLoop
->contains(BlockLoop
))) {
270 // if the successor is the header of a nested loop pretend its a
271 // single node with the loop's exits as successors
272 SmallVector
<BasicBlock
*, 4> BlockLoopExits
;
273 BlockLoop
->getExitBlocks(BlockLoopExits
);
274 for (const auto *BlockLoopExit
: BlockLoopExits
) {
275 visitSuccessor(*BlockLoopExit
, ParentLoop
, *DefBlock
);
279 // the successors are either on the same loop level or loop exits
280 for (const auto *SuccBlock
: successors(Block
)) {
281 visitSuccessor(*SuccBlock
, ParentLoop
, *DefBlock
);
286 // We need to know the definition at the parent loop header to decide
287 // whether the definition at the header is different from the definition at
288 // the loop exits, which would indicate a divergent loop exits.
292 // B // nested loop header
294 // C -> X (exit from B loop) -..-> (A latch)
296 // D -> back to B (B latch)
298 // proper exit from both loops
300 // D post-dominates B as it is the only proper exit from the "A loop".
301 // If C has a divergent branch, propagation will therefore stop at D.
302 // That implies that B will never receive a definition.
303 // But that definition can only be the same as at D (D itself in thise case)
304 // because all paths to anywhere have to pass through D.
306 const BasicBlock
*ParentLoopHeader
=
307 ParentLoop
? ParentLoop
->getHeader() : nullptr;
308 if (ParentLoop
&& ParentLoop
->contains(PdBoundBlock
)) {
309 DefMap
[ParentLoopHeader
] = DefMap
[PdBoundBlock
];
312 // analyze reached loop exits
313 if (!ReachedLoopExits
.empty()) {
315 const auto *HeaderDefBlock
= DefMap
[ParentLoopHeader
];
316 LLVM_DEBUG(printDefs(dbgs()));
317 assert(HeaderDefBlock
&& "no definition in header of carrying loop");
319 for (const auto *ExitBlock
: ReachedLoopExits
) {
320 auto ItExitDef
= DefMap
.find(ExitBlock
);
321 assert((ItExitDef
!= DefMap
.end()) &&
322 "no reaching def at reachable loop exit");
323 if (ItExitDef
->second
!= HeaderDefBlock
) {
324 JoinBlocks
->insert(ExitBlock
);
329 return std::move(JoinBlocks
);
333 const ConstBlockSet
&SyncDependenceAnalysis::join_blocks(const Loop
&Loop
) {
334 using LoopExitVec
= SmallVector
<BasicBlock
*, 4>;
335 LoopExitVec LoopExits
;
336 Loop
.getExitBlocks(LoopExits
);
337 if (LoopExits
.size() < 1) {
338 return EmptyBlockSet
;
341 // already available in cache?
342 auto ItCached
= CachedLoopExitJoins
.find(&Loop
);
343 if (ItCached
!= CachedLoopExitJoins
.end())
344 return *ItCached
->second
;
346 // compute all join points
347 DivergencePropagator Propagator
{FuncRPOT
, DT
, PDT
, LI
};
348 auto JoinBlocks
= Propagator
.computeJoinPoints
<const LoopExitVec
&>(
349 *Loop
.getHeader(), LoopExits
, Loop
.getParentLoop());
351 auto ItInserted
= CachedLoopExitJoins
.emplace(&Loop
, std::move(JoinBlocks
));
352 assert(ItInserted
.second
);
353 return *ItInserted
.first
->second
;
356 const ConstBlockSet
&
357 SyncDependenceAnalysis::join_blocks(const Instruction
&Term
) {
359 if (Term
.getNumSuccessors() < 1) {
360 return EmptyBlockSet
;
363 // already available in cache?
364 auto ItCached
= CachedBranchJoins
.find(&Term
);
365 if (ItCached
!= CachedBranchJoins
.end())
366 return *ItCached
->second
;
368 // compute all join points
369 DivergencePropagator Propagator
{FuncRPOT
, DT
, PDT
, LI
};
370 const auto &TermBlock
= *Term
.getParent();
371 auto JoinBlocks
= Propagator
.computeJoinPoints
<succ_const_range
>(
372 TermBlock
, successors(Term
.getParent()), LI
.getLoopFor(&TermBlock
));
374 auto ItInserted
= CachedBranchJoins
.emplace(&Term
, std::move(JoinBlocks
));
375 assert(ItInserted
.second
);
376 return *ItInserted
.first
->second
;