1 //===- Reassociate.cpp - Reassociate binary expressions -------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This pass reassociates commutative expressions in an order that is designed
11 // to promote better constant propagation, GCSE, LICM, PRE, etc.
13 // For example: 4 + (x + 5) -> x + (4 + 5)
15 // In the implementation of this algorithm, constants are assigned rank = 0,
16 // function arguments are rank = 1, and other values are assigned ranks
17 // corresponding to the reverse post order traversal of current function
18 // (starting at 2), which effectively gives values in deep loops higher rank
19 // than values not in loops.
21 //===----------------------------------------------------------------------===//
23 #include "llvm/Transforms/Scalar/Reassociate.h"
24 #include "llvm/ADT/APFloat.h"
25 #include "llvm/ADT/APInt.h"
26 #include "llvm/ADT/DenseMap.h"
27 #include "llvm/ADT/PostOrderIterator.h"
28 #include "llvm/ADT/SetVector.h"
29 #include "llvm/ADT/SmallPtrSet.h"
30 #include "llvm/ADT/SmallSet.h"
31 #include "llvm/ADT/SmallVector.h"
32 #include "llvm/ADT/Statistic.h"
33 #include "llvm/Analysis/GlobalsModRef.h"
34 #include "llvm/Transforms/Utils/Local.h"
35 #include "llvm/Analysis/ValueTracking.h"
36 #include "llvm/IR/Argument.h"
37 #include "llvm/IR/BasicBlock.h"
38 #include "llvm/IR/CFG.h"
39 #include "llvm/IR/Constant.h"
40 #include "llvm/IR/Constants.h"
41 #include "llvm/IR/Function.h"
42 #include "llvm/IR/IRBuilder.h"
43 #include "llvm/IR/InstrTypes.h"
44 #include "llvm/IR/Instruction.h"
45 #include "llvm/IR/Instructions.h"
46 #include "llvm/IR/IntrinsicInst.h"
47 #include "llvm/IR/Operator.h"
48 #include "llvm/IR/PassManager.h"
49 #include "llvm/IR/PatternMatch.h"
50 #include "llvm/IR/Type.h"
51 #include "llvm/IR/User.h"
52 #include "llvm/IR/Value.h"
53 #include "llvm/IR/ValueHandle.h"
54 #include "llvm/Pass.h"
55 #include "llvm/Support/Casting.h"
56 #include "llvm/Support/Debug.h"
57 #include "llvm/Support/ErrorHandling.h"
58 #include "llvm/Support/raw_ostream.h"
59 #include "llvm/Transforms/Scalar.h"
65 using namespace reassociate;
67 #define DEBUG_TYPE "reassociate"
69 STATISTIC(NumChanged, "Number of insts reassociated");
70 STATISTIC(NumAnnihil, "Number of expr tree annihilated");
71 STATISTIC(NumFactor , "Number of multiplies factored");
74 /// Print out the expression identified in the Ops list.
75 static void PrintOps(Instruction *I, const SmallVectorImpl<ValueEntry> &Ops) {
76 Module *M = I->getModule();
77 dbgs() << Instruction::getOpcodeName(I->getOpcode()) << " "
78 << *Ops[0].Op->getType() << '\t';
79 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
81 Ops[i].Op->printAsOperand(dbgs(), false, M);
82 dbgs() << ", #" << Ops[i].Rank << "] ";
87 /// Utility class representing a non-constant Xor-operand. We classify
88 /// non-constant Xor-Operands into two categories:
89 /// C1) The operand is in the form "X & C", where C is a constant and C != ~0
91 /// C2.1) The operand is in the form of "X | C", where C is a non-zero
93 /// C2.2) Any operand E which doesn't fall into C1 and C2.1, we view this
94 /// operand as "E | 0"
95 class llvm::reassociate::XorOpnd {
99 bool isInvalid() const { return SymbolicPart == nullptr; }
100 bool isOrExpr() const { return isOr; }
101 Value *getValue() const { return OrigVal; }
102 Value *getSymbolicPart() const { return SymbolicPart; }
103 unsigned getSymbolicRank() const { return SymbolicRank; }
104 const APInt &getConstPart() const { return ConstPart; }
106 void Invalidate() { SymbolicPart = OrigVal = nullptr; }
107 void setSymbolicRank(unsigned R) { SymbolicRank = R; }
113 unsigned SymbolicRank;
117 XorOpnd::XorOpnd(Value *V) {
118 assert(!isa<ConstantInt>(V) && "No ConstantInt");
120 Instruction *I = dyn_cast<Instruction>(V);
123 if (I && (I->getOpcode() == Instruction::Or ||
124 I->getOpcode() == Instruction::And)) {
125 Value *V0 = I->getOperand(0);
126 Value *V1 = I->getOperand(1);
128 if (match(V0, PatternMatch::m_APInt(C)))
131 if (match(V1, PatternMatch::m_APInt(C))) {
134 isOr = (I->getOpcode() == Instruction::Or);
139 // view the operand as "V | 0"
141 ConstPart = APInt::getNullValue(V->getType()->getScalarSizeInBits());
145 /// Return true if V is an instruction of the specified opcode and if it
146 /// only has one use.
147 static BinaryOperator *isReassociableOp(Value *V, unsigned Opcode) {
148 auto *I = dyn_cast<Instruction>(V);
149 if (I && I->hasOneUse() && I->getOpcode() == Opcode)
150 if (!isa<FPMathOperator>(I) || I->isFast())
151 return cast<BinaryOperator>(I);
155 static BinaryOperator *isReassociableOp(Value *V, unsigned Opcode1,
157 auto *I = dyn_cast<Instruction>(V);
158 if (I && I->hasOneUse() &&
159 (I->getOpcode() == Opcode1 || I->getOpcode() == Opcode2))
160 if (!isa<FPMathOperator>(I) || I->isFast())
161 return cast<BinaryOperator>(I);
165 void ReassociatePass::BuildRankMap(Function &F,
166 ReversePostOrderTraversal<Function*> &RPOT) {
169 // Assign distinct ranks to function arguments.
170 for (auto &Arg : F.args()) {
171 ValueRankMap[&Arg] = ++Rank;
172 LLVM_DEBUG(dbgs() << "Calculated Rank[" << Arg.getName() << "] = " << Rank
176 // Traverse basic blocks in ReversePostOrder
177 for (BasicBlock *BB : RPOT) {
178 unsigned BBRank = RankMap[BB] = ++Rank << 16;
180 // Walk the basic block, adding precomputed ranks for any instructions that
181 // we cannot move. This ensures that the ranks for these instructions are
182 // all different in the block.
183 for (Instruction &I : *BB)
184 if (mayBeMemoryDependent(I))
185 ValueRankMap[&I] = ++BBRank;
189 unsigned ReassociatePass::getRank(Value *V) {
190 Instruction *I = dyn_cast<Instruction>(V);
192 if (isa<Argument>(V)) return ValueRankMap[V]; // Function argument.
193 return 0; // Otherwise it's a global or constant, rank 0.
196 if (unsigned Rank = ValueRankMap[I])
197 return Rank; // Rank already known?
199 // If this is an expression, return the 1+MAX(rank(LHS), rank(RHS)) so that
200 // we can reassociate expressions for code motion! Since we do not recurse
201 // for PHI nodes, we cannot have infinite recursion here, because there
202 // cannot be loops in the value graph that do not go through PHI nodes.
203 unsigned Rank = 0, MaxRank = RankMap[I->getParent()];
204 for (unsigned i = 0, e = I->getNumOperands(); i != e && Rank != MaxRank; ++i)
205 Rank = std::max(Rank, getRank(I->getOperand(i)));
207 // If this is a not or neg instruction, do not count it for rank. This
208 // assures us that X and ~X will have the same rank.
209 if (!BinaryOperator::isNot(I) && !BinaryOperator::isNeg(I) &&
210 !BinaryOperator::isFNeg(I))
213 LLVM_DEBUG(dbgs() << "Calculated Rank[" << V->getName() << "] = " << Rank
216 return ValueRankMap[I] = Rank;
219 // Canonicalize constants to RHS. Otherwise, sort the operands by rank.
220 void ReassociatePass::canonicalizeOperands(Instruction *I) {
221 assert(isa<BinaryOperator>(I) && "Expected binary operator.");
222 assert(I->isCommutative() && "Expected commutative operator.");
224 Value *LHS = I->getOperand(0);
225 Value *RHS = I->getOperand(1);
226 if (LHS == RHS || isa<Constant>(RHS))
228 if (isa<Constant>(LHS) || getRank(RHS) < getRank(LHS))
229 cast<BinaryOperator>(I)->swapOperands();
232 static BinaryOperator *CreateAdd(Value *S1, Value *S2, const Twine &Name,
233 Instruction *InsertBefore, Value *FlagsOp) {
234 if (S1->getType()->isIntOrIntVectorTy())
235 return BinaryOperator::CreateAdd(S1, S2, Name, InsertBefore);
237 BinaryOperator *Res =
238 BinaryOperator::CreateFAdd(S1, S2, Name, InsertBefore);
239 Res->setFastMathFlags(cast<FPMathOperator>(FlagsOp)->getFastMathFlags());
244 static BinaryOperator *CreateMul(Value *S1, Value *S2, const Twine &Name,
245 Instruction *InsertBefore, Value *FlagsOp) {
246 if (S1->getType()->isIntOrIntVectorTy())
247 return BinaryOperator::CreateMul(S1, S2, Name, InsertBefore);
249 BinaryOperator *Res =
250 BinaryOperator::CreateFMul(S1, S2, Name, InsertBefore);
251 Res->setFastMathFlags(cast<FPMathOperator>(FlagsOp)->getFastMathFlags());
256 static BinaryOperator *CreateNeg(Value *S1, const Twine &Name,
257 Instruction *InsertBefore, Value *FlagsOp) {
258 if (S1->getType()->isIntOrIntVectorTy())
259 return BinaryOperator::CreateNeg(S1, Name, InsertBefore);
261 BinaryOperator *Res = BinaryOperator::CreateFNeg(S1, Name, InsertBefore);
262 Res->setFastMathFlags(cast<FPMathOperator>(FlagsOp)->getFastMathFlags());
267 /// Replace 0-X with X*-1.
268 static BinaryOperator *LowerNegateToMultiply(Instruction *Neg) {
269 Type *Ty = Neg->getType();
270 Constant *NegOne = Ty->isIntOrIntVectorTy() ?
271 ConstantInt::getAllOnesValue(Ty) : ConstantFP::get(Ty, -1.0);
273 BinaryOperator *Res = CreateMul(Neg->getOperand(1), NegOne, "", Neg, Neg);
274 Neg->setOperand(1, Constant::getNullValue(Ty)); // Drop use of op.
276 Neg->replaceAllUsesWith(Res);
277 Res->setDebugLoc(Neg->getDebugLoc());
281 /// Returns k such that lambda(2^Bitwidth) = 2^k, where lambda is the Carmichael
282 /// function. This means that x^(2^k) === 1 mod 2^Bitwidth for
283 /// every odd x, i.e. x^(2^k) = 1 for every odd x in Bitwidth-bit arithmetic.
284 /// Note that 0 <= k < Bitwidth, and if Bitwidth > 3 then x^(2^k) = 0 for every
285 /// even x in Bitwidth-bit arithmetic.
286 static unsigned CarmichaelShift(unsigned Bitwidth) {
292 /// Add the extra weight 'RHS' to the existing weight 'LHS',
293 /// reducing the combined weight using any special properties of the operation.
294 /// The existing weight LHS represents the computation X op X op ... op X where
295 /// X occurs LHS times. The combined weight represents X op X op ... op X with
296 /// X occurring LHS + RHS times. If op is "Xor" for example then the combined
297 /// operation is equivalent to X if LHS + RHS is odd, or 0 if LHS + RHS is even;
298 /// the routine returns 1 in LHS in the first case, and 0 in LHS in the second.
299 static void IncorporateWeight(APInt &LHS, const APInt &RHS, unsigned Opcode) {
300 // If we were working with infinite precision arithmetic then the combined
301 // weight would be LHS + RHS. But we are using finite precision arithmetic,
302 // and the APInt sum LHS + RHS may not be correct if it wraps (it is correct
303 // for nilpotent operations and addition, but not for idempotent operations
304 // and multiplication), so it is important to correctly reduce the combined
305 // weight back into range if wrapping would be wrong.
307 // If RHS is zero then the weight didn't change.
308 if (RHS.isMinValue())
310 // If LHS is zero then the combined weight is RHS.
311 if (LHS.isMinValue()) {
315 // From this point on we know that neither LHS nor RHS is zero.
317 if (Instruction::isIdempotent(Opcode)) {
318 // Idempotent means X op X === X, so any non-zero weight is equivalent to a
319 // weight of 1. Keeping weights at zero or one also means that wrapping is
321 assert(LHS == 1 && RHS == 1 && "Weights not reduced!");
322 return; // Return a weight of 1.
324 if (Instruction::isNilpotent(Opcode)) {
325 // Nilpotent means X op X === 0, so reduce weights modulo 2.
326 assert(LHS == 1 && RHS == 1 && "Weights not reduced!");
327 LHS = 0; // 1 + 1 === 0 modulo 2.
330 if (Opcode == Instruction::Add || Opcode == Instruction::FAdd) {
331 // TODO: Reduce the weight by exploiting nsw/nuw?
336 assert((Opcode == Instruction::Mul || Opcode == Instruction::FMul) &&
337 "Unknown associative operation!");
338 unsigned Bitwidth = LHS.getBitWidth();
339 // If CM is the Carmichael number then a weight W satisfying W >= CM+Bitwidth
340 // can be replaced with W-CM. That's because x^W=x^(W-CM) for every Bitwidth
341 // bit number x, since either x is odd in which case x^CM = 1, or x is even in
342 // which case both x^W and x^(W - CM) are zero. By subtracting off multiples
343 // of CM like this weights can always be reduced to the range [0, CM+Bitwidth)
344 // which by a happy accident means that they can always be represented using
346 // TODO: Reduce the weight by exploiting nsw/nuw? (Could do much better than
347 // the Carmichael number).
349 /// CM - The value of Carmichael's lambda function.
350 APInt CM = APInt::getOneBitSet(Bitwidth, CarmichaelShift(Bitwidth));
351 // Any weight W >= Threshold can be replaced with W - CM.
352 APInt Threshold = CM + Bitwidth;
353 assert(LHS.ult(Threshold) && RHS.ult(Threshold) && "Weights not reduced!");
354 // For Bitwidth 4 or more the following sum does not overflow.
356 while (LHS.uge(Threshold))
359 // To avoid problems with overflow do everything the same as above but using
361 unsigned CM = 1U << CarmichaelShift(Bitwidth);
362 unsigned Threshold = CM + Bitwidth;
363 assert(LHS.getZExtValue() < Threshold && RHS.getZExtValue() < Threshold &&
364 "Weights not reduced!");
365 unsigned Total = LHS.getZExtValue() + RHS.getZExtValue();
366 while (Total >= Threshold)
372 using RepeatedValue = std::pair<Value*, APInt>;
374 /// Given an associative binary expression, return the leaf
375 /// nodes in Ops along with their weights (how many times the leaf occurs). The
376 /// original expression is the same as
377 /// (Ops[0].first op Ops[0].first op ... Ops[0].first) <- Ops[0].second times
379 /// (Ops[1].first op Ops[1].first op ... Ops[1].first) <- Ops[1].second times
383 /// (Ops[N].first op Ops[N].first op ... Ops[N].first) <- Ops[N].second times
385 /// Note that the values Ops[0].first, ..., Ops[N].first are all distinct.
387 /// This routine may modify the function, in which case it returns 'true'. The
388 /// changes it makes may well be destructive, changing the value computed by 'I'
389 /// to something completely different. Thus if the routine returns 'true' then
390 /// you MUST either replace I with a new expression computed from the Ops array,
391 /// or use RewriteExprTree to put the values back in.
393 /// A leaf node is either not a binary operation of the same kind as the root
394 /// node 'I' (i.e. is not a binary operator at all, or is, but with a different
395 /// opcode), or is the same kind of binary operator but has a use which either
396 /// does not belong to the expression, or does belong to the expression but is
397 /// a leaf node. Every leaf node has at least one use that is a non-leaf node
398 /// of the expression, while for non-leaf nodes (except for the root 'I') every
399 /// use is a non-leaf node of the expression.
402 /// expression graph node names
412 /// The leaf nodes are C, E, F and G. The Ops array will contain (maybe not in
413 /// that order) (C, 1), (E, 1), (F, 2), (G, 2).
415 /// The expression is maximal: if some instruction is a binary operator of the
416 /// same kind as 'I', and all of its uses are non-leaf nodes of the expression,
417 /// then the instruction also belongs to the expression, is not a leaf node of
418 /// it, and its operands also belong to the expression (but may be leaf nodes).
420 /// NOTE: This routine will set operands of non-leaf non-root nodes to undef in
421 /// order to ensure that every non-root node in the expression has *exactly one*
422 /// use by a non-leaf node of the expression. This destruction means that the
423 /// caller MUST either replace 'I' with a new expression or use something like
424 /// RewriteExprTree to put the values back in if the routine indicates that it
425 /// made a change by returning 'true'.
427 /// In the above example either the right operand of A or the left operand of B
428 /// will be replaced by undef. If it is B's operand then this gives:
432 /// + + | A, B - operand of B replaced with undef
438 /// Note that such undef operands can only be reached by passing through 'I'.
439 /// For example, if you visit operands recursively starting from a leaf node
440 /// then you will never see such an undef operand unless you get back to 'I',
441 /// which requires passing through a phi node.
443 /// Note that this routine may also mutate binary operators of the wrong type
444 /// that have all uses inside the expression (i.e. only used by non-leaf nodes
445 /// of the expression) if it can turn them into binary operators of the right
446 /// type and thus make the expression bigger.
447 static bool LinearizeExprTree(BinaryOperator *I,
448 SmallVectorImpl<RepeatedValue> &Ops) {
449 LLVM_DEBUG(dbgs() << "LINEARIZE: " << *I << '\n');
450 unsigned Bitwidth = I->getType()->getScalarType()->getPrimitiveSizeInBits();
451 unsigned Opcode = I->getOpcode();
452 assert(I->isAssociative() && I->isCommutative() &&
453 "Expected an associative and commutative operation!");
455 // Visit all operands of the expression, keeping track of their weight (the
456 // number of paths from the expression root to the operand, or if you like
457 // the number of times that operand occurs in the linearized expression).
458 // For example, if I = X + A, where X = A + B, then I, X and B have weight 1
459 // while A has weight two.
461 // Worklist of non-leaf nodes (their operands are in the expression too) along
462 // with their weights, representing a certain number of paths to the operator.
463 // If an operator occurs in the worklist multiple times then we found multiple
464 // ways to get to it.
465 SmallVector<std::pair<BinaryOperator*, APInt>, 8> Worklist; // (Op, Weight)
466 Worklist.push_back(std::make_pair(I, APInt(Bitwidth, 1)));
467 bool Changed = false;
469 // Leaves of the expression are values that either aren't the right kind of
470 // operation (eg: a constant, or a multiply in an add tree), or are, but have
471 // some uses that are not inside the expression. For example, in I = X + X,
472 // X = A + B, the value X has two uses (by I) that are in the expression. If
473 // X has any other uses, for example in a return instruction, then we consider
474 // X to be a leaf, and won't analyze it further. When we first visit a value,
475 // if it has more than one use then at first we conservatively consider it to
476 // be a leaf. Later, as the expression is explored, we may discover some more
477 // uses of the value from inside the expression. If all uses turn out to be
478 // from within the expression (and the value is a binary operator of the right
479 // kind) then the value is no longer considered to be a leaf, and its operands
482 // Leaves - Keeps track of the set of putative leaves as well as the number of
483 // paths to each leaf seen so far.
484 using LeafMap = DenseMap<Value *, APInt>;
485 LeafMap Leaves; // Leaf -> Total weight so far.
486 SmallVector<Value *, 8> LeafOrder; // Ensure deterministic leaf output order.
489 SmallPtrSet<Value *, 8> Visited; // For sanity checking the iteration scheme.
491 while (!Worklist.empty()) {
492 std::pair<BinaryOperator*, APInt> P = Worklist.pop_back_val();
493 I = P.first; // We examine the operands of this binary operator.
495 for (unsigned OpIdx = 0; OpIdx < 2; ++OpIdx) { // Visit operands.
496 Value *Op = I->getOperand(OpIdx);
497 APInt Weight = P.second; // Number of paths to this operand.
498 LLVM_DEBUG(dbgs() << "OPERAND: " << *Op << " (" << Weight << ")\n");
499 assert(!Op->use_empty() && "No uses, so how did we get to it?!");
501 // If this is a binary operation of the right kind with only one use then
502 // add its operands to the expression.
503 if (BinaryOperator *BO = isReassociableOp(Op, Opcode)) {
504 assert(Visited.insert(Op).second && "Not first visit!");
505 LLVM_DEBUG(dbgs() << "DIRECT ADD: " << *Op << " (" << Weight << ")\n");
506 Worklist.push_back(std::make_pair(BO, Weight));
510 // Appears to be a leaf. Is the operand already in the set of leaves?
511 LeafMap::iterator It = Leaves.find(Op);
512 if (It == Leaves.end()) {
513 // Not in the leaf map. Must be the first time we saw this operand.
514 assert(Visited.insert(Op).second && "Not first visit!");
515 if (!Op->hasOneUse()) {
516 // This value has uses not accounted for by the expression, so it is
517 // not safe to modify. Mark it as being a leaf.
519 << "ADD USES LEAF: " << *Op << " (" << Weight << ")\n");
520 LeafOrder.push_back(Op);
524 // No uses outside the expression, try morphing it.
526 // Already in the leaf map.
527 assert(It != Leaves.end() && Visited.count(Op) &&
528 "In leaf map but not visited!");
530 // Update the number of paths to the leaf.
531 IncorporateWeight(It->second, Weight, Opcode);
533 #if 0 // TODO: Re-enable once PR13021 is fixed.
534 // The leaf already has one use from inside the expression. As we want
535 // exactly one such use, drop this new use of the leaf.
536 assert(!Op->hasOneUse() && "Only one use, but we got here twice!");
537 I->setOperand(OpIdx, UndefValue::get(I->getType()));
540 // If the leaf is a binary operation of the right kind and we now see
541 // that its multiple original uses were in fact all by nodes belonging
542 // to the expression, then no longer consider it to be a leaf and add
543 // its operands to the expression.
544 if (BinaryOperator *BO = isReassociableOp(Op, Opcode)) {
545 LLVM_DEBUG(dbgs() << "UNLEAF: " << *Op << " (" << It->second << ")\n");
546 Worklist.push_back(std::make_pair(BO, It->second));
552 // If we still have uses that are not accounted for by the expression
553 // then it is not safe to modify the value.
554 if (!Op->hasOneUse())
557 // No uses outside the expression, try morphing it.
559 Leaves.erase(It); // Since the value may be morphed below.
562 // At this point we have a value which, first of all, is not a binary
563 // expression of the right kind, and secondly, is only used inside the
564 // expression. This means that it can safely be modified. See if we
565 // can usefully morph it into an expression of the right kind.
566 assert((!isa<Instruction>(Op) ||
567 cast<Instruction>(Op)->getOpcode() != Opcode
568 || (isa<FPMathOperator>(Op) &&
569 !cast<Instruction>(Op)->isFast())) &&
570 "Should have been handled above!");
571 assert(Op->hasOneUse() && "Has uses outside the expression tree!");
573 // If this is a multiply expression, turn any internal negations into
574 // multiplies by -1 so they can be reassociated.
575 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(Op))
576 if ((Opcode == Instruction::Mul && BinaryOperator::isNeg(BO)) ||
577 (Opcode == Instruction::FMul && BinaryOperator::isFNeg(BO))) {
579 << "MORPH LEAF: " << *Op << " (" << Weight << ") TO ");
580 BO = LowerNegateToMultiply(BO);
581 LLVM_DEBUG(dbgs() << *BO << '\n');
582 Worklist.push_back(std::make_pair(BO, Weight));
587 // Failed to morph into an expression of the right type. This really is
589 LLVM_DEBUG(dbgs() << "ADD LEAF: " << *Op << " (" << Weight << ")\n");
590 assert(!isReassociableOp(Op, Opcode) && "Value was morphed?");
591 LeafOrder.push_back(Op);
596 // The leaves, repeated according to their weights, represent the linearized
597 // form of the expression.
598 for (unsigned i = 0, e = LeafOrder.size(); i != e; ++i) {
599 Value *V = LeafOrder[i];
600 LeafMap::iterator It = Leaves.find(V);
601 if (It == Leaves.end())
602 // Node initially thought to be a leaf wasn't.
604 assert(!isReassociableOp(V, Opcode) && "Shouldn't be a leaf!");
605 APInt Weight = It->second;
606 if (Weight.isMinValue())
607 // Leaf already output or weight reduction eliminated it.
609 // Ensure the leaf is only output once.
611 Ops.push_back(std::make_pair(V, Weight));
614 // For nilpotent operations or addition there may be no operands, for example
615 // because the expression was "X xor X" or consisted of 2^Bitwidth additions:
616 // in both cases the weight reduces to 0 causing the value to be skipped.
618 Constant *Identity = ConstantExpr::getBinOpIdentity(Opcode, I->getType());
619 assert(Identity && "Associative operation without identity!");
620 Ops.emplace_back(Identity, APInt(Bitwidth, 1));
626 /// Now that the operands for this expression tree are
627 /// linearized and optimized, emit them in-order.
628 void ReassociatePass::RewriteExprTree(BinaryOperator *I,
629 SmallVectorImpl<ValueEntry> &Ops) {
630 assert(Ops.size() > 1 && "Single values should be used directly!");
632 // Since our optimizations should never increase the number of operations, the
633 // new expression can usually be written reusing the existing binary operators
634 // from the original expression tree, without creating any new instructions,
635 // though the rewritten expression may have a completely different topology.
636 // We take care to not change anything if the new expression will be the same
637 // as the original. If more than trivial changes (like commuting operands)
638 // were made then we are obliged to clear out any optional subclass data like
641 /// NodesToRewrite - Nodes from the original expression available for writing
642 /// the new expression into.
643 SmallVector<BinaryOperator*, 8> NodesToRewrite;
644 unsigned Opcode = I->getOpcode();
645 BinaryOperator *Op = I;
647 /// NotRewritable - The operands being written will be the leaves of the new
648 /// expression and must not be used as inner nodes (via NodesToRewrite) by
649 /// mistake. Inner nodes are always reassociable, and usually leaves are not
650 /// (if they were they would have been incorporated into the expression and so
651 /// would not be leaves), so most of the time there is no danger of this. But
652 /// in rare cases a leaf may become reassociable if an optimization kills uses
653 /// of it, or it may momentarily become reassociable during rewriting (below)
654 /// due it being removed as an operand of one of its uses. Ensure that misuse
655 /// of leaf nodes as inner nodes cannot occur by remembering all of the future
656 /// leaves and refusing to reuse any of them as inner nodes.
657 SmallPtrSet<Value*, 8> NotRewritable;
658 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
659 NotRewritable.insert(Ops[i].Op);
661 // ExpressionChanged - Non-null if the rewritten expression differs from the
662 // original in some non-trivial way, requiring the clearing of optional flags.
663 // Flags are cleared from the operator in ExpressionChanged up to I inclusive.
664 BinaryOperator *ExpressionChanged = nullptr;
665 for (unsigned i = 0; ; ++i) {
666 // The last operation (which comes earliest in the IR) is special as both
667 // operands will come from Ops, rather than just one with the other being
669 if (i+2 == Ops.size()) {
670 Value *NewLHS = Ops[i].Op;
671 Value *NewRHS = Ops[i+1].Op;
672 Value *OldLHS = Op->getOperand(0);
673 Value *OldRHS = Op->getOperand(1);
675 if (NewLHS == OldLHS && NewRHS == OldRHS)
676 // Nothing changed, leave it alone.
679 if (NewLHS == OldRHS && NewRHS == OldLHS) {
680 // The order of the operands was reversed. Swap them.
681 LLVM_DEBUG(dbgs() << "RA: " << *Op << '\n');
683 LLVM_DEBUG(dbgs() << "TO: " << *Op << '\n');
689 // The new operation differs non-trivially from the original. Overwrite
690 // the old operands with the new ones.
691 LLVM_DEBUG(dbgs() << "RA: " << *Op << '\n');
692 if (NewLHS != OldLHS) {
693 BinaryOperator *BO = isReassociableOp(OldLHS, Opcode);
694 if (BO && !NotRewritable.count(BO))
695 NodesToRewrite.push_back(BO);
696 Op->setOperand(0, NewLHS);
698 if (NewRHS != OldRHS) {
699 BinaryOperator *BO = isReassociableOp(OldRHS, Opcode);
700 if (BO && !NotRewritable.count(BO))
701 NodesToRewrite.push_back(BO);
702 Op->setOperand(1, NewRHS);
704 LLVM_DEBUG(dbgs() << "TO: " << *Op << '\n');
706 ExpressionChanged = Op;
713 // Not the last operation. The left-hand side will be a sub-expression
714 // while the right-hand side will be the current element of Ops.
715 Value *NewRHS = Ops[i].Op;
716 if (NewRHS != Op->getOperand(1)) {
717 LLVM_DEBUG(dbgs() << "RA: " << *Op << '\n');
718 if (NewRHS == Op->getOperand(0)) {
719 // The new right-hand side was already present as the left operand. If
720 // we are lucky then swapping the operands will sort out both of them.
723 // Overwrite with the new right-hand side.
724 BinaryOperator *BO = isReassociableOp(Op->getOperand(1), Opcode);
725 if (BO && !NotRewritable.count(BO))
726 NodesToRewrite.push_back(BO);
727 Op->setOperand(1, NewRHS);
728 ExpressionChanged = Op;
730 LLVM_DEBUG(dbgs() << "TO: " << *Op << '\n');
735 // Now deal with the left-hand side. If this is already an operation node
736 // from the original expression then just rewrite the rest of the expression
738 BinaryOperator *BO = isReassociableOp(Op->getOperand(0), Opcode);
739 if (BO && !NotRewritable.count(BO)) {
744 // Otherwise, grab a spare node from the original expression and use that as
745 // the left-hand side. If there are no nodes left then the optimizers made
746 // an expression with more nodes than the original! This usually means that
747 // they did something stupid but it might mean that the problem was just too
748 // hard (finding the mimimal number of multiplications needed to realize a
749 // multiplication expression is NP-complete). Whatever the reason, smart or
750 // stupid, create a new node if there are none left.
751 BinaryOperator *NewOp;
752 if (NodesToRewrite.empty()) {
753 Constant *Undef = UndefValue::get(I->getType());
754 NewOp = BinaryOperator::Create(Instruction::BinaryOps(Opcode),
755 Undef, Undef, "", I);
756 if (NewOp->getType()->isFPOrFPVectorTy())
757 NewOp->setFastMathFlags(I->getFastMathFlags());
759 NewOp = NodesToRewrite.pop_back_val();
762 LLVM_DEBUG(dbgs() << "RA: " << *Op << '\n');
763 Op->setOperand(0, NewOp);
764 LLVM_DEBUG(dbgs() << "TO: " << *Op << '\n');
765 ExpressionChanged = Op;
771 // If the expression changed non-trivially then clear out all subclass data
772 // starting from the operator specified in ExpressionChanged, and compactify
773 // the operators to just before the expression root to guarantee that the
774 // expression tree is dominated by all of Ops.
775 if (ExpressionChanged)
777 // Preserve FastMathFlags.
778 if (isa<FPMathOperator>(I)) {
779 FastMathFlags Flags = I->getFastMathFlags();
780 ExpressionChanged->clearSubclassOptionalData();
781 ExpressionChanged->setFastMathFlags(Flags);
783 ExpressionChanged->clearSubclassOptionalData();
785 if (ExpressionChanged == I)
788 // Discard any debug info related to the expressions that has changed (we
789 // can leave debug infor related to the root, since the result of the
790 // expression tree should be the same even after reassociation).
791 SmallVector<DbgInfoIntrinsic *, 1> DbgUsers;
792 findDbgUsers(DbgUsers, ExpressionChanged);
793 for (auto *DII : DbgUsers) {
794 Value *Undef = UndefValue::get(ExpressionChanged->getType());
795 DII->setOperand(0, MetadataAsValue::get(DII->getContext(),
796 ValueAsMetadata::get(Undef)));
799 ExpressionChanged->moveBefore(I);
800 ExpressionChanged = cast<BinaryOperator>(*ExpressionChanged->user_begin());
803 // Throw away any left over nodes from the original expression.
804 for (unsigned i = 0, e = NodesToRewrite.size(); i != e; ++i)
805 RedoInsts.insert(NodesToRewrite[i]);
808 /// Insert instructions before the instruction pointed to by BI,
809 /// that computes the negative version of the value specified. The negative
810 /// version of the value is returned, and BI is left pointing at the instruction
811 /// that should be processed next by the reassociation pass.
812 /// Also add intermediate instructions to the redo list that are modified while
813 /// pushing the negates through adds. These will be revisited to see if
814 /// additional opportunities have been exposed.
815 static Value *NegateValue(Value *V, Instruction *BI,
816 ReassociatePass::OrderedSet &ToRedo) {
817 if (auto *C = dyn_cast<Constant>(V))
818 return C->getType()->isFPOrFPVectorTy() ? ConstantExpr::getFNeg(C) :
819 ConstantExpr::getNeg(C);
821 // We are trying to expose opportunity for reassociation. One of the things
822 // that we want to do to achieve this is to push a negation as deep into an
823 // expression chain as possible, to expose the add instructions. In practice,
824 // this means that we turn this:
825 // X = -(A+12+C+D) into X = -A + -12 + -C + -D = -12 + -A + -C + -D
826 // so that later, a: Y = 12+X could get reassociated with the -12 to eliminate
827 // the constants. We assume that instcombine will clean up the mess later if
828 // we introduce tons of unnecessary negation instructions.
830 if (BinaryOperator *I =
831 isReassociableOp(V, Instruction::Add, Instruction::FAdd)) {
832 // Push the negates through the add.
833 I->setOperand(0, NegateValue(I->getOperand(0), BI, ToRedo));
834 I->setOperand(1, NegateValue(I->getOperand(1), BI, ToRedo));
835 if (I->getOpcode() == Instruction::Add) {
836 I->setHasNoUnsignedWrap(false);
837 I->setHasNoSignedWrap(false);
840 // We must move the add instruction here, because the neg instructions do
841 // not dominate the old add instruction in general. By moving it, we are
842 // assured that the neg instructions we just inserted dominate the
843 // instruction we are about to insert after them.
846 I->setName(I->getName()+".neg");
848 // Add the intermediate negates to the redo list as processing them later
849 // could expose more reassociating opportunities.
854 // Okay, we need to materialize a negated version of V with an instruction.
855 // Scan the use lists of V to see if we have one already.
856 for (User *U : V->users()) {
857 if (!BinaryOperator::isNeg(U) && !BinaryOperator::isFNeg(U))
860 // We found one! Now we have to make sure that the definition dominates
861 // this use. We do this by moving it to the entry block (if it is a
862 // non-instruction value) or right after the definition. These negates will
863 // be zapped by reassociate later, so we don't need much finesse here.
864 BinaryOperator *TheNeg = cast<BinaryOperator>(U);
866 // Verify that the negate is in this function, V might be a constant expr.
867 if (TheNeg->getParent()->getParent() != BI->getParent()->getParent())
870 BasicBlock::iterator InsertPt;
871 if (Instruction *InstInput = dyn_cast<Instruction>(V)) {
872 if (InvokeInst *II = dyn_cast<InvokeInst>(InstInput)) {
873 InsertPt = II->getNormalDest()->begin();
875 InsertPt = ++InstInput->getIterator();
877 while (isa<PHINode>(InsertPt)) ++InsertPt;
879 InsertPt = TheNeg->getParent()->getParent()->getEntryBlock().begin();
881 TheNeg->moveBefore(&*InsertPt);
882 if (TheNeg->getOpcode() == Instruction::Sub) {
883 TheNeg->setHasNoUnsignedWrap(false);
884 TheNeg->setHasNoSignedWrap(false);
886 TheNeg->andIRFlags(BI);
888 ToRedo.insert(TheNeg);
892 // Insert a 'neg' instruction that subtracts the value from zero to get the
894 BinaryOperator *NewNeg = CreateNeg(V, V->getName() + ".neg", BI, BI);
895 ToRedo.insert(NewNeg);
899 /// Return true if we should break up this subtract of X-Y into (X + -Y).
900 static bool ShouldBreakUpSubtract(Instruction *Sub) {
901 // If this is a negation, we can't split it up!
902 if (BinaryOperator::isNeg(Sub) || BinaryOperator::isFNeg(Sub))
905 // Don't breakup X - undef.
906 if (isa<UndefValue>(Sub->getOperand(1)))
909 // Don't bother to break this up unless either the LHS is an associable add or
910 // subtract or if this is only used by one.
911 Value *V0 = Sub->getOperand(0);
912 if (isReassociableOp(V0, Instruction::Add, Instruction::FAdd) ||
913 isReassociableOp(V0, Instruction::Sub, Instruction::FSub))
915 Value *V1 = Sub->getOperand(1);
916 if (isReassociableOp(V1, Instruction::Add, Instruction::FAdd) ||
917 isReassociableOp(V1, Instruction::Sub, Instruction::FSub))
919 Value *VB = Sub->user_back();
920 if (Sub->hasOneUse() &&
921 (isReassociableOp(VB, Instruction::Add, Instruction::FAdd) ||
922 isReassociableOp(VB, Instruction::Sub, Instruction::FSub)))
928 /// If we have (X-Y), and if either X is an add, or if this is only used by an
929 /// add, transform this into (X+(0-Y)) to promote better reassociation.
930 static BinaryOperator *BreakUpSubtract(Instruction *Sub,
931 ReassociatePass::OrderedSet &ToRedo) {
932 // Convert a subtract into an add and a neg instruction. This allows sub
933 // instructions to be commuted with other add instructions.
935 // Calculate the negative value of Operand 1 of the sub instruction,
936 // and set it as the RHS of the add instruction we just made.
937 Value *NegVal = NegateValue(Sub->getOperand(1), Sub, ToRedo);
938 BinaryOperator *New = CreateAdd(Sub->getOperand(0), NegVal, "", Sub, Sub);
939 Sub->setOperand(0, Constant::getNullValue(Sub->getType())); // Drop use of op.
940 Sub->setOperand(1, Constant::getNullValue(Sub->getType())); // Drop use of op.
943 // Everyone now refers to the add instruction.
944 Sub->replaceAllUsesWith(New);
945 New->setDebugLoc(Sub->getDebugLoc());
947 LLVM_DEBUG(dbgs() << "Negated: " << *New << '\n');
951 /// If this is a shift of a reassociable multiply or is used by one, change
952 /// this into a multiply by a constant to assist with further reassociation.
953 static BinaryOperator *ConvertShiftToMul(Instruction *Shl) {
954 Constant *MulCst = ConstantInt::get(Shl->getType(), 1);
955 MulCst = ConstantExpr::getShl(MulCst, cast<Constant>(Shl->getOperand(1)));
957 BinaryOperator *Mul =
958 BinaryOperator::CreateMul(Shl->getOperand(0), MulCst, "", Shl);
959 Shl->setOperand(0, UndefValue::get(Shl->getType())); // Drop use of op.
962 // Everyone now refers to the mul instruction.
963 Shl->replaceAllUsesWith(Mul);
964 Mul->setDebugLoc(Shl->getDebugLoc());
966 // We can safely preserve the nuw flag in all cases. It's also safe to turn a
967 // nuw nsw shl into a nuw nsw mul. However, nsw in isolation requires special
969 bool NSW = cast<BinaryOperator>(Shl)->hasNoSignedWrap();
970 bool NUW = cast<BinaryOperator>(Shl)->hasNoUnsignedWrap();
972 Mul->setHasNoSignedWrap(true);
973 Mul->setHasNoUnsignedWrap(NUW);
977 /// Scan backwards and forwards among values with the same rank as element i
978 /// to see if X exists. If X does not exist, return i. This is useful when
979 /// scanning for 'x' when we see '-x' because they both get the same rank.
980 static unsigned FindInOperandList(const SmallVectorImpl<ValueEntry> &Ops,
981 unsigned i, Value *X) {
982 unsigned XRank = Ops[i].Rank;
983 unsigned e = Ops.size();
984 for (unsigned j = i+1; j != e && Ops[j].Rank == XRank; ++j) {
987 if (Instruction *I1 = dyn_cast<Instruction>(Ops[j].Op))
988 if (Instruction *I2 = dyn_cast<Instruction>(X))
989 if (I1->isIdenticalTo(I2))
993 for (unsigned j = i-1; j != ~0U && Ops[j].Rank == XRank; --j) {
996 if (Instruction *I1 = dyn_cast<Instruction>(Ops[j].Op))
997 if (Instruction *I2 = dyn_cast<Instruction>(X))
998 if (I1->isIdenticalTo(I2))
1004 /// Emit a tree of add instructions, summing Ops together
1005 /// and returning the result. Insert the tree before I.
1006 static Value *EmitAddTreeOfValues(Instruction *I,
1007 SmallVectorImpl<WeakTrackingVH> &Ops) {
1008 if (Ops.size() == 1) return Ops.back();
1010 Value *V1 = Ops.back();
1012 Value *V2 = EmitAddTreeOfValues(I, Ops);
1013 return CreateAdd(V2, V1, "reass.add", I, I);
1016 /// If V is an expression tree that is a multiplication sequence,
1017 /// and if this sequence contains a multiply by Factor,
1018 /// remove Factor from the tree and return the new tree.
1019 Value *ReassociatePass::RemoveFactorFromExpression(Value *V, Value *Factor) {
1020 BinaryOperator *BO = isReassociableOp(V, Instruction::Mul, Instruction::FMul);
1024 SmallVector<RepeatedValue, 8> Tree;
1025 MadeChange |= LinearizeExprTree(BO, Tree);
1026 SmallVector<ValueEntry, 8> Factors;
1027 Factors.reserve(Tree.size());
1028 for (unsigned i = 0, e = Tree.size(); i != e; ++i) {
1029 RepeatedValue E = Tree[i];
1030 Factors.append(E.second.getZExtValue(),
1031 ValueEntry(getRank(E.first), E.first));
1034 bool FoundFactor = false;
1035 bool NeedsNegate = false;
1036 for (unsigned i = 0, e = Factors.size(); i != e; ++i) {
1037 if (Factors[i].Op == Factor) {
1039 Factors.erase(Factors.begin()+i);
1043 // If this is a negative version of this factor, remove it.
1044 if (ConstantInt *FC1 = dyn_cast<ConstantInt>(Factor)) {
1045 if (ConstantInt *FC2 = dyn_cast<ConstantInt>(Factors[i].Op))
1046 if (FC1->getValue() == -FC2->getValue()) {
1047 FoundFactor = NeedsNegate = true;
1048 Factors.erase(Factors.begin()+i);
1051 } else if (ConstantFP *FC1 = dyn_cast<ConstantFP>(Factor)) {
1052 if (ConstantFP *FC2 = dyn_cast<ConstantFP>(Factors[i].Op)) {
1053 const APFloat &F1 = FC1->getValueAPF();
1054 APFloat F2(FC2->getValueAPF());
1056 if (F1.compare(F2) == APFloat::cmpEqual) {
1057 FoundFactor = NeedsNegate = true;
1058 Factors.erase(Factors.begin() + i);
1066 // Make sure to restore the operands to the expression tree.
1067 RewriteExprTree(BO, Factors);
1071 BasicBlock::iterator InsertPt = ++BO->getIterator();
1073 // If this was just a single multiply, remove the multiply and return the only
1074 // remaining operand.
1075 if (Factors.size() == 1) {
1076 RedoInsts.insert(BO);
1079 RewriteExprTree(BO, Factors);
1084 V = CreateNeg(V, "neg", &*InsertPt, BO);
1089 /// If V is a single-use multiply, recursively add its operands as factors,
1090 /// otherwise add V to the list of factors.
1092 /// Ops is the top-level list of add operands we're trying to factor.
1093 static void FindSingleUseMultiplyFactors(Value *V,
1094 SmallVectorImpl<Value*> &Factors) {
1095 BinaryOperator *BO = isReassociableOp(V, Instruction::Mul, Instruction::FMul);
1097 Factors.push_back(V);
1101 // Otherwise, add the LHS and RHS to the list of factors.
1102 FindSingleUseMultiplyFactors(BO->getOperand(1), Factors);
1103 FindSingleUseMultiplyFactors(BO->getOperand(0), Factors);
1106 /// Optimize a series of operands to an 'and', 'or', or 'xor' instruction.
1107 /// This optimizes based on identities. If it can be reduced to a single Value,
1108 /// it is returned, otherwise the Ops list is mutated as necessary.
1109 static Value *OptimizeAndOrXor(unsigned Opcode,
1110 SmallVectorImpl<ValueEntry> &Ops) {
1111 // Scan the operand lists looking for X and ~X pairs, along with X,X pairs.
1112 // If we find any, we can simplify the expression. X&~X == 0, X|~X == -1.
1113 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1114 // First, check for X and ~X in the operand list.
1115 assert(i < Ops.size());
1116 if (BinaryOperator::isNot(Ops[i].Op)) { // Cannot occur for ^.
1117 Value *X = BinaryOperator::getNotArgument(Ops[i].Op);
1118 unsigned FoundX = FindInOperandList(Ops, i, X);
1120 if (Opcode == Instruction::And) // ...&X&~X = 0
1121 return Constant::getNullValue(X->getType());
1123 if (Opcode == Instruction::Or) // ...|X|~X = -1
1124 return Constant::getAllOnesValue(X->getType());
1128 // Next, check for duplicate pairs of values, which we assume are next to
1129 // each other, due to our sorting criteria.
1130 assert(i < Ops.size());
1131 if (i+1 != Ops.size() && Ops[i+1].Op == Ops[i].Op) {
1132 if (Opcode == Instruction::And || Opcode == Instruction::Or) {
1133 // Drop duplicate values for And and Or.
1134 Ops.erase(Ops.begin()+i);
1140 // Drop pairs of values for Xor.
1141 assert(Opcode == Instruction::Xor);
1143 return Constant::getNullValue(Ops[0].Op->getType());
1146 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
1154 /// Helper function of CombineXorOpnd(). It creates a bitwise-and
1155 /// instruction with the given two operands, and return the resulting
1156 /// instruction. There are two special cases: 1) if the constant operand is 0,
1157 /// it will return NULL. 2) if the constant is ~0, the symbolic operand will
1159 static Value *createAndInstr(Instruction *InsertBefore, Value *Opnd,
1160 const APInt &ConstOpnd) {
1161 if (ConstOpnd.isNullValue())
1164 if (ConstOpnd.isAllOnesValue())
1167 Instruction *I = BinaryOperator::CreateAnd(
1168 Opnd, ConstantInt::get(Opnd->getType(), ConstOpnd), "and.ra",
1170 I->setDebugLoc(InsertBefore->getDebugLoc());
1174 // Helper function of OptimizeXor(). It tries to simplify "Opnd1 ^ ConstOpnd"
1175 // into "R ^ C", where C would be 0, and R is a symbolic value.
1177 // If it was successful, true is returned, and the "R" and "C" is returned
1178 // via "Res" and "ConstOpnd", respectively; otherwise, false is returned,
1179 // and both "Res" and "ConstOpnd" remain unchanged.
1180 bool ReassociatePass::CombineXorOpnd(Instruction *I, XorOpnd *Opnd1,
1181 APInt &ConstOpnd, Value *&Res) {
1182 // Xor-Rule 1: (x | c1) ^ c2 = (x | c1) ^ (c1 ^ c1) ^ c2
1183 // = ((x | c1) ^ c1) ^ (c1 ^ c2)
1184 // = (x & ~c1) ^ (c1 ^ c2)
1185 // It is useful only when c1 == c2.
1186 if (!Opnd1->isOrExpr() || Opnd1->getConstPart().isNullValue())
1189 if (!Opnd1->getValue()->hasOneUse())
1192 const APInt &C1 = Opnd1->getConstPart();
1193 if (C1 != ConstOpnd)
1196 Value *X = Opnd1->getSymbolicPart();
1197 Res = createAndInstr(I, X, ~C1);
1198 // ConstOpnd was C2, now C1 ^ C2.
1201 if (Instruction *T = dyn_cast<Instruction>(Opnd1->getValue()))
1202 RedoInsts.insert(T);
1206 // Helper function of OptimizeXor(). It tries to simplify
1207 // "Opnd1 ^ Opnd2 ^ ConstOpnd" into "R ^ C", where C would be 0, and R is a
1210 // If it was successful, true is returned, and the "R" and "C" is returned
1211 // via "Res" and "ConstOpnd", respectively (If the entire expression is
1212 // evaluated to a constant, the Res is set to NULL); otherwise, false is
1213 // returned, and both "Res" and "ConstOpnd" remain unchanged.
1214 bool ReassociatePass::CombineXorOpnd(Instruction *I, XorOpnd *Opnd1,
1215 XorOpnd *Opnd2, APInt &ConstOpnd,
1217 Value *X = Opnd1->getSymbolicPart();
1218 if (X != Opnd2->getSymbolicPart())
1221 // This many instruction become dead.(At least "Opnd1 ^ Opnd2" will die.)
1222 int DeadInstNum = 1;
1223 if (Opnd1->getValue()->hasOneUse())
1225 if (Opnd2->getValue()->hasOneUse())
1229 // (x | c1) ^ (x & c2)
1230 // = (x|c1) ^ (x&c2) ^ (c1 ^ c1) = ((x|c1) ^ c1) ^ (x & c2) ^ c1
1231 // = (x & ~c1) ^ (x & c2) ^ c1 // Xor-Rule 1
1232 // = (x & c3) ^ c1, where c3 = ~c1 ^ c2 // Xor-rule 3
1234 if (Opnd1->isOrExpr() != Opnd2->isOrExpr()) {
1235 if (Opnd2->isOrExpr())
1236 std::swap(Opnd1, Opnd2);
1238 const APInt &C1 = Opnd1->getConstPart();
1239 const APInt &C2 = Opnd2->getConstPart();
1240 APInt C3((~C1) ^ C2);
1242 // Do not increase code size!
1243 if (!C3.isNullValue() && !C3.isAllOnesValue()) {
1244 int NewInstNum = ConstOpnd.getBoolValue() ? 1 : 2;
1245 if (NewInstNum > DeadInstNum)
1249 Res = createAndInstr(I, X, C3);
1251 } else if (Opnd1->isOrExpr()) {
1252 // Xor-Rule 3: (x | c1) ^ (x | c2) = (x & c3) ^ c3 where c3 = c1 ^ c2
1254 const APInt &C1 = Opnd1->getConstPart();
1255 const APInt &C2 = Opnd2->getConstPart();
1258 // Do not increase code size
1259 if (!C3.isNullValue() && !C3.isAllOnesValue()) {
1260 int NewInstNum = ConstOpnd.getBoolValue() ? 1 : 2;
1261 if (NewInstNum > DeadInstNum)
1265 Res = createAndInstr(I, X, C3);
1268 // Xor-Rule 4: (x & c1) ^ (x & c2) = (x & (c1^c2))
1270 const APInt &C1 = Opnd1->getConstPart();
1271 const APInt &C2 = Opnd2->getConstPart();
1273 Res = createAndInstr(I, X, C3);
1276 // Put the original operands in the Redo list; hope they will be deleted
1278 if (Instruction *T = dyn_cast<Instruction>(Opnd1->getValue()))
1279 RedoInsts.insert(T);
1280 if (Instruction *T = dyn_cast<Instruction>(Opnd2->getValue()))
1281 RedoInsts.insert(T);
1286 /// Optimize a series of operands to an 'xor' instruction. If it can be reduced
1287 /// to a single Value, it is returned, otherwise the Ops list is mutated as
1289 Value *ReassociatePass::OptimizeXor(Instruction *I,
1290 SmallVectorImpl<ValueEntry> &Ops) {
1291 if (Value *V = OptimizeAndOrXor(Instruction::Xor, Ops))
1294 if (Ops.size() == 1)
1297 SmallVector<XorOpnd, 8> Opnds;
1298 SmallVector<XorOpnd*, 8> OpndPtrs;
1299 Type *Ty = Ops[0].Op->getType();
1300 APInt ConstOpnd(Ty->getScalarSizeInBits(), 0);
1302 // Step 1: Convert ValueEntry to XorOpnd
1303 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1304 Value *V = Ops[i].Op;
1306 // TODO: Support non-splat vectors.
1307 if (match(V, PatternMatch::m_APInt(C))) {
1311 O.setSymbolicRank(getRank(O.getSymbolicPart()));
1316 // NOTE: From this point on, do *NOT* add/delete element to/from "Opnds".
1317 // It would otherwise invalidate the "Opnds"'s iterator, and hence invalidate
1318 // the "OpndPtrs" as well. For the similar reason, do not fuse this loop
1319 // with the previous loop --- the iterator of the "Opnds" may be invalidated
1320 // when new elements are added to the vector.
1321 for (unsigned i = 0, e = Opnds.size(); i != e; ++i)
1322 OpndPtrs.push_back(&Opnds[i]);
1324 // Step 2: Sort the Xor-Operands in a way such that the operands containing
1325 // the same symbolic value cluster together. For instance, the input operand
1326 // sequence ("x | 123", "y & 456", "x & 789") will be sorted into:
1327 // ("x | 123", "x & 789", "y & 456").
1329 // The purpose is twofold:
1330 // 1) Cluster together the operands sharing the same symbolic-value.
1331 // 2) Operand having smaller symbolic-value-rank is permuted earlier, which
1332 // could potentially shorten crital path, and expose more loop-invariants.
1333 // Note that values' rank are basically defined in RPO order (FIXME).
1334 // So, if Rank(X) < Rank(Y) < Rank(Z), it means X is defined earlier
1335 // than Y which is defined earlier than Z. Permute "x | 1", "Y & 2",
1336 // "z" in the order of X-Y-Z is better than any other orders.
1337 std::stable_sort(OpndPtrs.begin(), OpndPtrs.end(),
1338 [](XorOpnd *LHS, XorOpnd *RHS) {
1339 return LHS->getSymbolicRank() < RHS->getSymbolicRank();
1342 // Step 3: Combine adjacent operands
1343 XorOpnd *PrevOpnd = nullptr;
1344 bool Changed = false;
1345 for (unsigned i = 0, e = Opnds.size(); i < e; i++) {
1346 XorOpnd *CurrOpnd = OpndPtrs[i];
1347 // The combined value
1350 // Step 3.1: Try simplifying "CurrOpnd ^ ConstOpnd"
1351 if (!ConstOpnd.isNullValue() &&
1352 CombineXorOpnd(I, CurrOpnd, ConstOpnd, CV)) {
1355 *CurrOpnd = XorOpnd(CV);
1357 CurrOpnd->Invalidate();
1362 if (!PrevOpnd || CurrOpnd->getSymbolicPart() != PrevOpnd->getSymbolicPart()) {
1363 PrevOpnd = CurrOpnd;
1367 // step 3.2: When previous and current operands share the same symbolic
1368 // value, try to simplify "PrevOpnd ^ CurrOpnd ^ ConstOpnd"
1369 if (CombineXorOpnd(I, CurrOpnd, PrevOpnd, ConstOpnd, CV)) {
1370 // Remove previous operand
1371 PrevOpnd->Invalidate();
1373 *CurrOpnd = XorOpnd(CV);
1374 PrevOpnd = CurrOpnd;
1376 CurrOpnd->Invalidate();
1383 // Step 4: Reassemble the Ops
1386 for (unsigned int i = 0, e = Opnds.size(); i < e; i++) {
1387 XorOpnd &O = Opnds[i];
1390 ValueEntry VE(getRank(O.getValue()), O.getValue());
1393 if (!ConstOpnd.isNullValue()) {
1394 Value *C = ConstantInt::get(Ty, ConstOpnd);
1395 ValueEntry VE(getRank(C), C);
1398 unsigned Sz = Ops.size();
1400 return Ops.back().Op;
1402 assert(ConstOpnd.isNullValue());
1403 return ConstantInt::get(Ty, ConstOpnd);
1410 /// Optimize a series of operands to an 'add' instruction. This
1411 /// optimizes based on identities. If it can be reduced to a single Value, it
1412 /// is returned, otherwise the Ops list is mutated as necessary.
1413 Value *ReassociatePass::OptimizeAdd(Instruction *I,
1414 SmallVectorImpl<ValueEntry> &Ops) {
1415 // Scan the operand lists looking for X and -X pairs. If we find any, we
1416 // can simplify expressions like X+-X == 0 and X+~X ==-1. While we're at it,
1418 // duplicates. We want to canonicalize Y+Y+Y+Z -> 3*Y+Z.
1420 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1421 Value *TheOp = Ops[i].Op;
1422 // Check to see if we've seen this operand before. If so, we factor all
1423 // instances of the operand together. Due to our sorting criteria, we know
1424 // that these need to be next to each other in the vector.
1425 if (i+1 != Ops.size() && Ops[i+1].Op == TheOp) {
1426 // Rescan the list, remove all instances of this operand from the expr.
1427 unsigned NumFound = 0;
1429 Ops.erase(Ops.begin()+i);
1431 } while (i != Ops.size() && Ops[i].Op == TheOp);
1433 LLVM_DEBUG(dbgs() << "\nFACTORING [" << NumFound << "]: " << *TheOp
1437 // Insert a new multiply.
1438 Type *Ty = TheOp->getType();
1439 Constant *C = Ty->isIntOrIntVectorTy() ?
1440 ConstantInt::get(Ty, NumFound) : ConstantFP::get(Ty, NumFound);
1441 Instruction *Mul = CreateMul(TheOp, C, "factor", I, I);
1443 // Now that we have inserted a multiply, optimize it. This allows us to
1444 // handle cases that require multiple factoring steps, such as this:
1445 // (X*2) + (X*2) + (X*2) -> (X*2)*3 -> X*6
1446 RedoInsts.insert(Mul);
1448 // If every add operand was a duplicate, return the multiply.
1452 // Otherwise, we had some input that didn't have the dupe, such as
1453 // "A + A + B" -> "A*2 + B". Add the new multiply to the list of
1454 // things being added by this operation.
1455 Ops.insert(Ops.begin(), ValueEntry(getRank(Mul), Mul));
1462 // Check for X and -X or X and ~X in the operand list.
1463 if (!BinaryOperator::isNeg(TheOp) && !BinaryOperator::isFNeg(TheOp) &&
1464 !BinaryOperator::isNot(TheOp))
1468 if (BinaryOperator::isNeg(TheOp) || BinaryOperator::isFNeg(TheOp))
1469 X = BinaryOperator::getNegArgument(TheOp);
1470 else if (BinaryOperator::isNot(TheOp))
1471 X = BinaryOperator::getNotArgument(TheOp);
1473 unsigned FoundX = FindInOperandList(Ops, i, X);
1477 // Remove X and -X from the operand list.
1478 if (Ops.size() == 2 &&
1479 (BinaryOperator::isNeg(TheOp) || BinaryOperator::isFNeg(TheOp)))
1480 return Constant::getNullValue(X->getType());
1482 // Remove X and ~X from the operand list.
1483 if (Ops.size() == 2 && BinaryOperator::isNot(TheOp))
1484 return Constant::getAllOnesValue(X->getType());
1486 Ops.erase(Ops.begin()+i);
1490 --i; // Need to back up an extra one.
1491 Ops.erase(Ops.begin()+FoundX);
1493 --i; // Revisit element.
1494 e -= 2; // Removed two elements.
1496 // if X and ~X we append -1 to the operand list.
1497 if (BinaryOperator::isNot(TheOp)) {
1498 Value *V = Constant::getAllOnesValue(X->getType());
1499 Ops.insert(Ops.end(), ValueEntry(getRank(V), V));
1504 // Scan the operand list, checking to see if there are any common factors
1505 // between operands. Consider something like A*A+A*B*C+D. We would like to
1506 // reassociate this to A*(A+B*C)+D, which reduces the number of multiplies.
1507 // To efficiently find this, we count the number of times a factor occurs
1508 // for any ADD operands that are MULs.
1509 DenseMap<Value*, unsigned> FactorOccurrences;
1511 // Keep track of each multiply we see, to avoid triggering on (X*4)+(X*4)
1512 // where they are actually the same multiply.
1513 unsigned MaxOcc = 0;
1514 Value *MaxOccVal = nullptr;
1515 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1516 BinaryOperator *BOp =
1517 isReassociableOp(Ops[i].Op, Instruction::Mul, Instruction::FMul);
1521 // Compute all of the factors of this added value.
1522 SmallVector<Value*, 8> Factors;
1523 FindSingleUseMultiplyFactors(BOp, Factors);
1524 assert(Factors.size() > 1 && "Bad linearize!");
1526 // Add one to FactorOccurrences for each unique factor in this op.
1527 SmallPtrSet<Value*, 8> Duplicates;
1528 for (unsigned i = 0, e = Factors.size(); i != e; ++i) {
1529 Value *Factor = Factors[i];
1530 if (!Duplicates.insert(Factor).second)
1533 unsigned Occ = ++FactorOccurrences[Factor];
1539 // If Factor is a negative constant, add the negated value as a factor
1540 // because we can percolate the negate out. Watch for minint, which
1541 // cannot be positivified.
1542 if (ConstantInt *CI = dyn_cast<ConstantInt>(Factor)) {
1543 if (CI->isNegative() && !CI->isMinValue(true)) {
1544 Factor = ConstantInt::get(CI->getContext(), -CI->getValue());
1545 if (!Duplicates.insert(Factor).second)
1547 unsigned Occ = ++FactorOccurrences[Factor];
1553 } else if (ConstantFP *CF = dyn_cast<ConstantFP>(Factor)) {
1554 if (CF->isNegative()) {
1555 APFloat F(CF->getValueAPF());
1557 Factor = ConstantFP::get(CF->getContext(), F);
1558 if (!Duplicates.insert(Factor).second)
1560 unsigned Occ = ++FactorOccurrences[Factor];
1570 // If any factor occurred more than one time, we can pull it out.
1572 LLVM_DEBUG(dbgs() << "\nFACTORING [" << MaxOcc << "]: " << *MaxOccVal
1576 // Create a new instruction that uses the MaxOccVal twice. If we don't do
1577 // this, we could otherwise run into situations where removing a factor
1578 // from an expression will drop a use of maxocc, and this can cause
1579 // RemoveFactorFromExpression on successive values to behave differently.
1580 Instruction *DummyInst =
1581 I->getType()->isIntOrIntVectorTy()
1582 ? BinaryOperator::CreateAdd(MaxOccVal, MaxOccVal)
1583 : BinaryOperator::CreateFAdd(MaxOccVal, MaxOccVal);
1585 SmallVector<WeakTrackingVH, 4> NewMulOps;
1586 for (unsigned i = 0; i != Ops.size(); ++i) {
1587 // Only try to remove factors from expressions we're allowed to.
1588 BinaryOperator *BOp =
1589 isReassociableOp(Ops[i].Op, Instruction::Mul, Instruction::FMul);
1593 if (Value *V = RemoveFactorFromExpression(Ops[i].Op, MaxOccVal)) {
1594 // The factorized operand may occur several times. Convert them all in
1596 for (unsigned j = Ops.size(); j != i;) {
1598 if (Ops[j].Op == Ops[i].Op) {
1599 NewMulOps.push_back(V);
1600 Ops.erase(Ops.begin()+j);
1607 // No need for extra uses anymore.
1608 DummyInst->deleteValue();
1610 unsigned NumAddedValues = NewMulOps.size();
1611 Value *V = EmitAddTreeOfValues(I, NewMulOps);
1613 // Now that we have inserted the add tree, optimize it. This allows us to
1614 // handle cases that require multiple factoring steps, such as this:
1615 // A*A*B + A*A*C --> A*(A*B+A*C) --> A*(A*(B+C))
1616 assert(NumAddedValues > 1 && "Each occurrence should contribute a value");
1617 (void)NumAddedValues;
1618 if (Instruction *VI = dyn_cast<Instruction>(V))
1619 RedoInsts.insert(VI);
1621 // Create the multiply.
1622 Instruction *V2 = CreateMul(V, MaxOccVal, "reass.mul", I, I);
1624 // Rerun associate on the multiply in case the inner expression turned into
1625 // a multiply. We want to make sure that we keep things in canonical form.
1626 RedoInsts.insert(V2);
1628 // If every add operand included the factor (e.g. "A*B + A*C"), then the
1629 // entire result expression is just the multiply "A*(B+C)".
1633 // Otherwise, we had some input that didn't have the factor, such as
1634 // "A*B + A*C + D" -> "A*(B+C) + D". Add the new multiply to the list of
1635 // things being added by this operation.
1636 Ops.insert(Ops.begin(), ValueEntry(getRank(V2), V2));
1642 /// Build up a vector of value/power pairs factoring a product.
1644 /// Given a series of multiplication operands, build a vector of factors and
1645 /// the powers each is raised to when forming the final product. Sort them in
1646 /// the order of descending power.
1648 /// (x*x) -> [(x, 2)]
1649 /// ((x*x)*x) -> [(x, 3)]
1650 /// ((((x*y)*x)*y)*x) -> [(x, 3), (y, 2)]
1652 /// \returns Whether any factors have a power greater than one.
1653 static bool collectMultiplyFactors(SmallVectorImpl<ValueEntry> &Ops,
1654 SmallVectorImpl<Factor> &Factors) {
1655 // FIXME: Have Ops be (ValueEntry, Multiplicity) pairs, simplifying this.
1656 // Compute the sum of powers of simplifiable factors.
1657 unsigned FactorPowerSum = 0;
1658 for (unsigned Idx = 1, Size = Ops.size(); Idx < Size; ++Idx) {
1659 Value *Op = Ops[Idx-1].Op;
1661 // Count the number of occurrences of this value.
1663 for (; Idx < Size && Ops[Idx].Op == Op; ++Idx)
1665 // Track for simplification all factors which occur 2 or more times.
1667 FactorPowerSum += Count;
1670 // We can only simplify factors if the sum of the powers of our simplifiable
1671 // factors is 4 or higher. When that is the case, we will *always* have
1672 // a simplification. This is an important invariant to prevent cyclicly
1673 // trying to simplify already minimal formations.
1674 if (FactorPowerSum < 4)
1677 // Now gather the simplifiable factors, removing them from Ops.
1679 for (unsigned Idx = 1; Idx < Ops.size(); ++Idx) {
1680 Value *Op = Ops[Idx-1].Op;
1682 // Count the number of occurrences of this value.
1684 for (; Idx < Ops.size() && Ops[Idx].Op == Op; ++Idx)
1688 // Move an even number of occurrences to Factors.
1691 FactorPowerSum += Count;
1692 Factors.push_back(Factor(Op, Count));
1693 Ops.erase(Ops.begin()+Idx, Ops.begin()+Idx+Count);
1696 // None of the adjustments above should have reduced the sum of factor powers
1697 // below our mininum of '4'.
1698 assert(FactorPowerSum >= 4);
1700 std::stable_sort(Factors.begin(), Factors.end(),
1701 [](const Factor &LHS, const Factor &RHS) {
1702 return LHS.Power > RHS.Power;
1707 /// Build a tree of multiplies, computing the product of Ops.
1708 static Value *buildMultiplyTree(IRBuilder<> &Builder,
1709 SmallVectorImpl<Value*> &Ops) {
1710 if (Ops.size() == 1)
1713 Value *LHS = Ops.pop_back_val();
1715 if (LHS->getType()->isIntOrIntVectorTy())
1716 LHS = Builder.CreateMul(LHS, Ops.pop_back_val());
1718 LHS = Builder.CreateFMul(LHS, Ops.pop_back_val());
1719 } while (!Ops.empty());
1724 /// Build a minimal multiplication DAG for (a^x)*(b^y)*(c^z)*...
1726 /// Given a vector of values raised to various powers, where no two values are
1727 /// equal and the powers are sorted in decreasing order, compute the minimal
1728 /// DAG of multiplies to compute the final product, and return that product
1731 ReassociatePass::buildMinimalMultiplyDAG(IRBuilder<> &Builder,
1732 SmallVectorImpl<Factor> &Factors) {
1733 assert(Factors[0].Power);
1734 SmallVector<Value *, 4> OuterProduct;
1735 for (unsigned LastIdx = 0, Idx = 1, Size = Factors.size();
1736 Idx < Size && Factors[Idx].Power > 0; ++Idx) {
1737 if (Factors[Idx].Power != Factors[LastIdx].Power) {
1742 // We want to multiply across all the factors with the same power so that
1743 // we can raise them to that power as a single entity. Build a mini tree
1745 SmallVector<Value *, 4> InnerProduct;
1746 InnerProduct.push_back(Factors[LastIdx].Base);
1748 InnerProduct.push_back(Factors[Idx].Base);
1750 } while (Idx < Size && Factors[Idx].Power == Factors[LastIdx].Power);
1752 // Reset the base value of the first factor to the new expression tree.
1753 // We'll remove all the factors with the same power in a second pass.
1754 Value *M = Factors[LastIdx].Base = buildMultiplyTree(Builder, InnerProduct);
1755 if (Instruction *MI = dyn_cast<Instruction>(M))
1756 RedoInsts.insert(MI);
1760 // Unique factors with equal powers -- we've folded them into the first one's
1762 Factors.erase(std::unique(Factors.begin(), Factors.end(),
1763 [](const Factor &LHS, const Factor &RHS) {
1764 return LHS.Power == RHS.Power;
1768 // Iteratively collect the base of each factor with an add power into the
1769 // outer product, and halve each power in preparation for squaring the
1771 for (unsigned Idx = 0, Size = Factors.size(); Idx != Size; ++Idx) {
1772 if (Factors[Idx].Power & 1)
1773 OuterProduct.push_back(Factors[Idx].Base);
1774 Factors[Idx].Power >>= 1;
1776 if (Factors[0].Power) {
1777 Value *SquareRoot = buildMinimalMultiplyDAG(Builder, Factors);
1778 OuterProduct.push_back(SquareRoot);
1779 OuterProduct.push_back(SquareRoot);
1781 if (OuterProduct.size() == 1)
1782 return OuterProduct.front();
1784 Value *V = buildMultiplyTree(Builder, OuterProduct);
1788 Value *ReassociatePass::OptimizeMul(BinaryOperator *I,
1789 SmallVectorImpl<ValueEntry> &Ops) {
1790 // We can only optimize the multiplies when there is a chain of more than
1791 // three, such that a balanced tree might require fewer total multiplies.
1795 // Try to turn linear trees of multiplies without other uses of the
1796 // intermediate stages into minimal multiply DAGs with perfect sub-expression
1798 SmallVector<Factor, 4> Factors;
1799 if (!collectMultiplyFactors(Ops, Factors))
1800 return nullptr; // All distinct factors, so nothing left for us to do.
1802 IRBuilder<> Builder(I);
1803 // The reassociate transformation for FP operations is performed only
1804 // if unsafe algebra is permitted by FastMathFlags. Propagate those flags
1805 // to the newly generated operations.
1806 if (auto FPI = dyn_cast<FPMathOperator>(I))
1807 Builder.setFastMathFlags(FPI->getFastMathFlags());
1809 Value *V = buildMinimalMultiplyDAG(Builder, Factors);
1813 ValueEntry NewEntry = ValueEntry(getRank(V), V);
1814 Ops.insert(std::lower_bound(Ops.begin(), Ops.end(), NewEntry), NewEntry);
1818 Value *ReassociatePass::OptimizeExpression(BinaryOperator *I,
1819 SmallVectorImpl<ValueEntry> &Ops) {
1820 // Now that we have the linearized expression tree, try to optimize it.
1821 // Start by folding any constants that we found.
1822 Constant *Cst = nullptr;
1823 unsigned Opcode = I->getOpcode();
1824 while (!Ops.empty() && isa<Constant>(Ops.back().Op)) {
1825 Constant *C = cast<Constant>(Ops.pop_back_val().Op);
1826 Cst = Cst ? ConstantExpr::get(Opcode, C, Cst) : C;
1828 // If there was nothing but constants then we are done.
1832 // Put the combined constant back at the end of the operand list, except if
1833 // there is no point. For example, an add of 0 gets dropped here, while a
1834 // multiplication by zero turns the whole expression into zero.
1835 if (Cst && Cst != ConstantExpr::getBinOpIdentity(Opcode, I->getType())) {
1836 if (Cst == ConstantExpr::getBinOpAbsorber(Opcode, I->getType()))
1838 Ops.push_back(ValueEntry(0, Cst));
1841 if (Ops.size() == 1) return Ops[0].Op;
1843 // Handle destructive annihilation due to identities between elements in the
1844 // argument list here.
1845 unsigned NumOps = Ops.size();
1848 case Instruction::And:
1849 case Instruction::Or:
1850 if (Value *Result = OptimizeAndOrXor(Opcode, Ops))
1854 case Instruction::Xor:
1855 if (Value *Result = OptimizeXor(I, Ops))
1859 case Instruction::Add:
1860 case Instruction::FAdd:
1861 if (Value *Result = OptimizeAdd(I, Ops))
1865 case Instruction::Mul:
1866 case Instruction::FMul:
1867 if (Value *Result = OptimizeMul(I, Ops))
1872 if (Ops.size() != NumOps)
1873 return OptimizeExpression(I, Ops);
1877 // Remove dead instructions and if any operands are trivially dead add them to
1878 // Insts so they will be removed as well.
1879 void ReassociatePass::RecursivelyEraseDeadInsts(Instruction *I,
1880 OrderedSet &Insts) {
1881 assert(isInstructionTriviallyDead(I) && "Trivially dead instructions only!");
1882 SmallVector<Value *, 4> Ops(I->op_begin(), I->op_end());
1883 ValueRankMap.erase(I);
1885 RedoInsts.remove(I);
1886 I->eraseFromParent();
1888 if (Instruction *OpInst = dyn_cast<Instruction>(Op))
1889 if (OpInst->use_empty())
1890 Insts.insert(OpInst);
1893 /// Zap the given instruction, adding interesting operands to the work list.
1894 void ReassociatePass::EraseInst(Instruction *I) {
1895 assert(isInstructionTriviallyDead(I) && "Trivially dead instructions only!");
1896 LLVM_DEBUG(dbgs() << "Erasing dead inst: "; I->dump());
1898 SmallVector<Value*, 8> Ops(I->op_begin(), I->op_end());
1899 // Erase the dead instruction.
1900 ValueRankMap.erase(I);
1901 RedoInsts.remove(I);
1902 I->eraseFromParent();
1903 // Optimize its operands.
1904 SmallPtrSet<Instruction *, 8> Visited; // Detect self-referential nodes.
1905 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1906 if (Instruction *Op = dyn_cast<Instruction>(Ops[i])) {
1907 // If this is a node in an expression tree, climb to the expression root
1908 // and add that since that's where optimization actually happens.
1909 unsigned Opcode = Op->getOpcode();
1910 while (Op->hasOneUse() && Op->user_back()->getOpcode() == Opcode &&
1911 Visited.insert(Op).second)
1912 Op = Op->user_back();
1914 // The instruction we're going to push may be coming from a
1915 // dead block, and Reassociate skips the processing of unreachable
1916 // blocks because it's a waste of time and also because it can
1917 // lead to infinite loop due to LLVM's non-standard definition
1919 if (ValueRankMap.find(Op) != ValueRankMap.end())
1920 RedoInsts.insert(Op);
1926 // Canonicalize expressions of the following form:
1927 // x + (-Constant * y) -> x - (Constant * y)
1928 // x - (-Constant * y) -> x + (Constant * y)
1929 Instruction *ReassociatePass::canonicalizeNegConstExpr(Instruction *I) {
1930 if (!I->hasOneUse() || I->getType()->isVectorTy())
1933 // Must be a fmul or fdiv instruction.
1934 unsigned Opcode = I->getOpcode();
1935 if (Opcode != Instruction::FMul && Opcode != Instruction::FDiv)
1938 auto *C0 = dyn_cast<ConstantFP>(I->getOperand(0));
1939 auto *C1 = dyn_cast<ConstantFP>(I->getOperand(1));
1941 // Both operands are constant, let it get constant folded away.
1945 ConstantFP *CF = C0 ? C0 : C1;
1947 // Must have one constant operand.
1951 // Must be a negative ConstantFP.
1952 if (!CF->isNegative())
1955 // User must be a binary operator with one or more uses.
1956 Instruction *User = I->user_back();
1957 if (!isa<BinaryOperator>(User) || User->use_empty())
1960 unsigned UserOpcode = User->getOpcode();
1961 if (UserOpcode != Instruction::FAdd && UserOpcode != Instruction::FSub)
1964 // Subtraction is not commutative. Explicitly, the following transform is
1965 // not valid: (-Constant * y) - x -> x + (Constant * y)
1966 if (!User->isCommutative() && User->getOperand(1) != I)
1969 // Don't canonicalize x + (-Constant * y) -> x - (Constant * y), if the
1970 // resulting subtract will be broken up later. This can get us into an
1971 // infinite loop during reassociation.
1972 if (UserOpcode == Instruction::FAdd && ShouldBreakUpSubtract(User))
1975 // Change the sign of the constant.
1976 APFloat Val = CF->getValueAPF();
1978 I->setOperand(C0 ? 0 : 1, ConstantFP::get(CF->getContext(), Val));
1980 // Canonicalize I to RHS to simplify the next bit of logic. E.g.,
1981 // ((-Const*y) + x) -> (x + (-Const*y)).
1982 if (User->getOperand(0) == I && User->isCommutative())
1983 cast<BinaryOperator>(User)->swapOperands();
1985 Value *Op0 = User->getOperand(0);
1986 Value *Op1 = User->getOperand(1);
1988 switch (UserOpcode) {
1990 llvm_unreachable("Unexpected Opcode!");
1991 case Instruction::FAdd:
1992 NI = BinaryOperator::CreateFSub(Op0, Op1);
1993 NI->setFastMathFlags(cast<FPMathOperator>(User)->getFastMathFlags());
1995 case Instruction::FSub:
1996 NI = BinaryOperator::CreateFAdd(Op0, Op1);
1997 NI->setFastMathFlags(cast<FPMathOperator>(User)->getFastMathFlags());
2001 NI->insertBefore(User);
2002 NI->setName(User->getName());
2003 User->replaceAllUsesWith(NI);
2004 NI->setDebugLoc(I->getDebugLoc());
2005 RedoInsts.insert(I);
2010 /// Inspect and optimize the given instruction. Note that erasing
2011 /// instructions is not allowed.
2012 void ReassociatePass::OptimizeInst(Instruction *I) {
2013 // Only consider operations that we understand.
2014 if (!isa<BinaryOperator>(I))
2017 if (I->getOpcode() == Instruction::Shl && isa<ConstantInt>(I->getOperand(1)))
2018 // If an operand of this shift is a reassociable multiply, or if the shift
2019 // is used by a reassociable multiply or add, turn into a multiply.
2020 if (isReassociableOp(I->getOperand(0), Instruction::Mul) ||
2022 (isReassociableOp(I->user_back(), Instruction::Mul) ||
2023 isReassociableOp(I->user_back(), Instruction::Add)))) {
2024 Instruction *NI = ConvertShiftToMul(I);
2025 RedoInsts.insert(I);
2030 // Canonicalize negative constants out of expressions.
2031 if (Instruction *Res = canonicalizeNegConstExpr(I))
2034 // Commute binary operators, to canonicalize the order of their operands.
2035 // This can potentially expose more CSE opportunities, and makes writing other
2036 // transformations simpler.
2037 if (I->isCommutative())
2038 canonicalizeOperands(I);
2040 // Don't optimize floating-point instructions unless they are 'fast'.
2041 if (I->getType()->isFPOrFPVectorTy() && !I->isFast())
2044 // Do not reassociate boolean (i1) expressions. We want to preserve the
2045 // original order of evaluation for short-circuited comparisons that
2046 // SimplifyCFG has folded to AND/OR expressions. If the expression
2047 // is not further optimized, it is likely to be transformed back to a
2048 // short-circuited form for code gen, and the source order may have been
2049 // optimized for the most likely conditions.
2050 if (I->getType()->isIntegerTy(1))
2053 // If this is a subtract instruction which is not already in negate form,
2054 // see if we can convert it to X+-Y.
2055 if (I->getOpcode() == Instruction::Sub) {
2056 if (ShouldBreakUpSubtract(I)) {
2057 Instruction *NI = BreakUpSubtract(I, RedoInsts);
2058 RedoInsts.insert(I);
2061 } else if (BinaryOperator::isNeg(I)) {
2062 // Otherwise, this is a negation. See if the operand is a multiply tree
2063 // and if this is not an inner node of a multiply tree.
2064 if (isReassociableOp(I->getOperand(1), Instruction::Mul) &&
2066 !isReassociableOp(I->user_back(), Instruction::Mul))) {
2067 Instruction *NI = LowerNegateToMultiply(I);
2068 // If the negate was simplified, revisit the users to see if we can
2069 // reassociate further.
2070 for (User *U : NI->users()) {
2071 if (BinaryOperator *Tmp = dyn_cast<BinaryOperator>(U))
2072 RedoInsts.insert(Tmp);
2074 RedoInsts.insert(I);
2079 } else if (I->getOpcode() == Instruction::FSub) {
2080 if (ShouldBreakUpSubtract(I)) {
2081 Instruction *NI = BreakUpSubtract(I, RedoInsts);
2082 RedoInsts.insert(I);
2085 } else if (BinaryOperator::isFNeg(I)) {
2086 // Otherwise, this is a negation. See if the operand is a multiply tree
2087 // and if this is not an inner node of a multiply tree.
2088 if (isReassociableOp(I->getOperand(1), Instruction::FMul) &&
2090 !isReassociableOp(I->user_back(), Instruction::FMul))) {
2091 // If the negate was simplified, revisit the users to see if we can
2092 // reassociate further.
2093 Instruction *NI = LowerNegateToMultiply(I);
2094 for (User *U : NI->users()) {
2095 if (BinaryOperator *Tmp = dyn_cast<BinaryOperator>(U))
2096 RedoInsts.insert(Tmp);
2098 RedoInsts.insert(I);
2105 // If this instruction is an associative binary operator, process it.
2106 if (!I->isAssociative()) return;
2107 BinaryOperator *BO = cast<BinaryOperator>(I);
2109 // If this is an interior node of a reassociable tree, ignore it until we
2110 // get to the root of the tree, to avoid N^2 analysis.
2111 unsigned Opcode = BO->getOpcode();
2112 if (BO->hasOneUse() && BO->user_back()->getOpcode() == Opcode) {
2113 // During the initial run we will get to the root of the tree.
2114 // But if we get here while we are redoing instructions, there is no
2115 // guarantee that the root will be visited. So Redo later
2116 if (BO->user_back() != BO &&
2117 BO->getParent() == BO->user_back()->getParent())
2118 RedoInsts.insert(BO->user_back());
2122 // If this is an add tree that is used by a sub instruction, ignore it
2123 // until we process the subtract.
2124 if (BO->hasOneUse() && BO->getOpcode() == Instruction::Add &&
2125 cast<Instruction>(BO->user_back())->getOpcode() == Instruction::Sub)
2127 if (BO->hasOneUse() && BO->getOpcode() == Instruction::FAdd &&
2128 cast<Instruction>(BO->user_back())->getOpcode() == Instruction::FSub)
2131 ReassociateExpression(BO);
2134 void ReassociatePass::ReassociateExpression(BinaryOperator *I) {
2135 // First, walk the expression tree, linearizing the tree, collecting the
2136 // operand information.
2137 SmallVector<RepeatedValue, 8> Tree;
2138 MadeChange |= LinearizeExprTree(I, Tree);
2139 SmallVector<ValueEntry, 8> Ops;
2140 Ops.reserve(Tree.size());
2141 for (unsigned i = 0, e = Tree.size(); i != e; ++i) {
2142 RepeatedValue E = Tree[i];
2143 Ops.append(E.second.getZExtValue(),
2144 ValueEntry(getRank(E.first), E.first));
2147 LLVM_DEBUG(dbgs() << "RAIn:\t"; PrintOps(I, Ops); dbgs() << '\n');
2149 // Now that we have linearized the tree to a list and have gathered all of
2150 // the operands and their ranks, sort the operands by their rank. Use a
2151 // stable_sort so that values with equal ranks will have their relative
2152 // positions maintained (and so the compiler is deterministic). Note that
2153 // this sorts so that the highest ranking values end up at the beginning of
2155 std::stable_sort(Ops.begin(), Ops.end());
2157 // Now that we have the expression tree in a convenient
2158 // sorted form, optimize it globally if possible.
2159 if (Value *V = OptimizeExpression(I, Ops)) {
2161 // Self-referential expression in unreachable code.
2163 // This expression tree simplified to something that isn't a tree,
2165 LLVM_DEBUG(dbgs() << "Reassoc to scalar: " << *V << '\n');
2166 I->replaceAllUsesWith(V);
2167 if (Instruction *VI = dyn_cast<Instruction>(V))
2168 if (I->getDebugLoc())
2169 VI->setDebugLoc(I->getDebugLoc());
2170 RedoInsts.insert(I);
2175 // We want to sink immediates as deeply as possible except in the case where
2176 // this is a multiply tree used only by an add, and the immediate is a -1.
2177 // In this case we reassociate to put the negation on the outside so that we
2178 // can fold the negation into the add: (-X)*Y + Z -> Z-X*Y
2179 if (I->hasOneUse()) {
2180 if (I->getOpcode() == Instruction::Mul &&
2181 cast<Instruction>(I->user_back())->getOpcode() == Instruction::Add &&
2182 isa<ConstantInt>(Ops.back().Op) &&
2183 cast<ConstantInt>(Ops.back().Op)->isMinusOne()) {
2184 ValueEntry Tmp = Ops.pop_back_val();
2185 Ops.insert(Ops.begin(), Tmp);
2186 } else if (I->getOpcode() == Instruction::FMul &&
2187 cast<Instruction>(I->user_back())->getOpcode() ==
2188 Instruction::FAdd &&
2189 isa<ConstantFP>(Ops.back().Op) &&
2190 cast<ConstantFP>(Ops.back().Op)->isExactlyValue(-1.0)) {
2191 ValueEntry Tmp = Ops.pop_back_val();
2192 Ops.insert(Ops.begin(), Tmp);
2196 LLVM_DEBUG(dbgs() << "RAOut:\t"; PrintOps(I, Ops); dbgs() << '\n');
2198 if (Ops.size() == 1) {
2200 // Self-referential expression in unreachable code.
2203 // This expression tree simplified to something that isn't a tree,
2205 I->replaceAllUsesWith(Ops[0].Op);
2206 if (Instruction *OI = dyn_cast<Instruction>(Ops[0].Op))
2207 OI->setDebugLoc(I->getDebugLoc());
2208 RedoInsts.insert(I);
2212 if (Ops.size() > 2 && Ops.size() <= GlobalReassociateLimit) {
2213 // Find the pair with the highest count in the pairmap and move it to the
2214 // back of the list so that it can later be CSE'd.
2217 // if c*e is the most "popular" pair, we can express this as
2220 unsigned BestRank = 0;
2221 std::pair<unsigned, unsigned> BestPair;
2222 unsigned Idx = I->getOpcode() - Instruction::BinaryOpsBegin;
2223 for (unsigned i = 0; i < Ops.size() - 1; ++i)
2224 for (unsigned j = i + 1; j < Ops.size(); ++j) {
2226 Value *Op0 = Ops[i].Op;
2227 Value *Op1 = Ops[j].Op;
2228 if (std::less<Value *>()(Op1, Op0))
2229 std::swap(Op0, Op1);
2230 auto it = PairMap[Idx].find({Op0, Op1});
2231 if (it != PairMap[Idx].end())
2232 Score += it->second;
2234 unsigned MaxRank = std::max(Ops[i].Rank, Ops[j].Rank);
2235 if (Score > Max || (Score == Max && MaxRank < BestRank)) {
2242 auto Op0 = Ops[BestPair.first];
2243 auto Op1 = Ops[BestPair.second];
2244 Ops.erase(&Ops[BestPair.second]);
2245 Ops.erase(&Ops[BestPair.first]);
2250 // Now that we ordered and optimized the expressions, splat them back into
2251 // the expression tree, removing any unneeded nodes.
2252 RewriteExprTree(I, Ops);
2256 ReassociatePass::BuildPairMap(ReversePostOrderTraversal<Function *> &RPOT) {
2257 // Make a "pairmap" of how often each operand pair occurs.
2258 for (BasicBlock *BI : RPOT) {
2259 for (Instruction &I : *BI) {
2260 if (!I.isAssociative())
2263 // Ignore nodes that aren't at the root of trees.
2264 if (I.hasOneUse() && I.user_back()->getOpcode() == I.getOpcode())
2267 // Collect all operands in a single reassociable expression.
2268 // Since Reassociate has already been run once, we can assume things
2269 // are already canonical according to Reassociation's regime.
2270 SmallVector<Value *, 8> Worklist = { I.getOperand(0), I.getOperand(1) };
2271 SmallVector<Value *, 8> Ops;
2272 while (!Worklist.empty() && Ops.size() <= GlobalReassociateLimit) {
2273 Value *Op = Worklist.pop_back_val();
2274 Instruction *OpI = dyn_cast<Instruction>(Op);
2275 if (!OpI || OpI->getOpcode() != I.getOpcode() || !OpI->hasOneUse()) {
2279 // Be paranoid about self-referencing expressions in unreachable code.
2280 if (OpI->getOperand(0) != OpI)
2281 Worklist.push_back(OpI->getOperand(0));
2282 if (OpI->getOperand(1) != OpI)
2283 Worklist.push_back(OpI->getOperand(1));
2285 // Skip extremely long expressions.
2286 if (Ops.size() > GlobalReassociateLimit)
2289 // Add all pairwise combinations of operands to the pair map.
2290 unsigned BinaryIdx = I.getOpcode() - Instruction::BinaryOpsBegin;
2291 SmallSet<std::pair<Value *, Value*>, 32> Visited;
2292 for (unsigned i = 0; i < Ops.size() - 1; ++i) {
2293 for (unsigned j = i + 1; j < Ops.size(); ++j) {
2294 // Canonicalize operand orderings.
2295 Value *Op0 = Ops[i];
2296 Value *Op1 = Ops[j];
2297 if (std::less<Value *>()(Op1, Op0))
2298 std::swap(Op0, Op1);
2299 if (!Visited.insert({Op0, Op1}).second)
2301 auto res = PairMap[BinaryIdx].insert({{Op0, Op1}, 1});
2303 ++res.first->second;
2310 PreservedAnalyses ReassociatePass::run(Function &F, FunctionAnalysisManager &) {
2311 // Get the functions basic blocks in Reverse Post Order. This order is used by
2312 // BuildRankMap to pre calculate ranks correctly. It also excludes dead basic
2313 // blocks (it has been seen that the analysis in this pass could hang when
2314 // analysing dead basic blocks).
2315 ReversePostOrderTraversal<Function *> RPOT(&F);
2317 // Calculate the rank map for F.
2318 BuildRankMap(F, RPOT);
2320 // Build the pair map before running reassociate.
2321 // Technically this would be more accurate if we did it after one round
2322 // of reassociation, but in practice it doesn't seem to help much on
2323 // real-world code, so don't waste the compile time running reassociate
2325 // If a user wants, they could expicitly run reassociate twice in their
2326 // pass pipeline for further potential gains.
2327 // It might also be possible to update the pair map during runtime, but the
2328 // overhead of that may be large if there's many reassociable chains.
2333 // Traverse the same blocks that were analysed by BuildRankMap.
2334 for (BasicBlock *BI : RPOT) {
2335 assert(RankMap.count(&*BI) && "BB should be ranked.");
2336 // Optimize every instruction in the basic block.
2337 for (BasicBlock::iterator II = BI->begin(), IE = BI->end(); II != IE;)
2338 if (isInstructionTriviallyDead(&*II)) {
2342 assert(II->getParent() == &*BI && "Moved to a different block!");
2346 // Make a copy of all the instructions to be redone so we can remove dead
2348 OrderedSet ToRedo(RedoInsts);
2349 // Iterate over all instructions to be reevaluated and remove trivially dead
2350 // instructions. If any operand of the trivially dead instruction becomes
2351 // dead mark it for deletion as well. Continue this process until all
2352 // trivially dead instructions have been removed.
2353 while (!ToRedo.empty()) {
2354 Instruction *I = ToRedo.pop_back_val();
2355 if (isInstructionTriviallyDead(I)) {
2356 RecursivelyEraseDeadInsts(I, ToRedo);
2361 // Now that we have removed dead instructions, we can reoptimize the
2362 // remaining instructions.
2363 while (!RedoInsts.empty()) {
2364 Instruction *I = RedoInsts.front();
2365 RedoInsts.erase(RedoInsts.begin());
2366 if (isInstructionTriviallyDead(I))
2373 // We are done with the rank map and pair map.
2375 ValueRankMap.clear();
2376 for (auto &Entry : PairMap)
2380 PreservedAnalyses PA;
2381 PA.preserveSet<CFGAnalyses>();
2382 PA.preserve<GlobalsAA>();
2386 return PreservedAnalyses::all();
2391 class ReassociateLegacyPass : public FunctionPass {
2392 ReassociatePass Impl;
2395 static char ID; // Pass identification, replacement for typeid
2397 ReassociateLegacyPass() : FunctionPass(ID) {
2398 initializeReassociateLegacyPassPass(*PassRegistry::getPassRegistry());
2401 bool runOnFunction(Function &F) override {
2402 if (skipFunction(F))
2405 FunctionAnalysisManager DummyFAM;
2406 auto PA = Impl.run(F, DummyFAM);
2407 return !PA.areAllPreserved();
2410 void getAnalysisUsage(AnalysisUsage &AU) const override {
2411 AU.setPreservesCFG();
2412 AU.addPreserved<GlobalsAAWrapperPass>();
2416 } // end anonymous namespace
2418 char ReassociateLegacyPass::ID = 0;
2420 INITIALIZE_PASS(ReassociateLegacyPass, "reassociate",
2421 "Reassociate expressions", false, false)
2423 // Public interface to the Reassociate pass
2424 FunctionPass *llvm::createReassociatePass() {
2425 return new ReassociateLegacyPass();