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 #define DEBUG_TYPE "reassociate"
24 #include "llvm/Transforms/Scalar.h"
25 #include "llvm/Transforms/Utils/Local.h"
26 #include "llvm/Constants.h"
27 #include "llvm/DerivedTypes.h"
28 #include "llvm/Function.h"
29 #include "llvm/IRBuilder.h"
30 #include "llvm/Instructions.h"
31 #include "llvm/IntrinsicInst.h"
32 #include "llvm/Pass.h"
33 #include "llvm/ADT/DenseMap.h"
34 #include "llvm/ADT/PostOrderIterator.h"
35 #include "llvm/ADT/STLExtras.h"
36 #include "llvm/ADT/SetVector.h"
37 #include "llvm/ADT/Statistic.h"
38 #include "llvm/Assembly/Writer.h"
39 #include "llvm/Support/CFG.h"
40 #include "llvm/Support/Debug.h"
41 #include "llvm/Support/ValueHandle.h"
42 #include "llvm/Support/raw_ostream.h"
46 STATISTIC(NumChanged, "Number of insts reassociated");
47 STATISTIC(NumAnnihil, "Number of expr tree annihilated");
48 STATISTIC(NumFactor , "Number of multiplies factored");
54 ValueEntry(unsigned R, Value *O) : Rank(R), Op(O) {}
56 inline bool operator<(const ValueEntry &LHS, const ValueEntry &RHS) {
57 return LHS.Rank > RHS.Rank; // Sort so that highest rank goes to start.
62 /// PrintOps - Print out the expression identified in the Ops list.
64 static void PrintOps(Instruction *I, const SmallVectorImpl<ValueEntry> &Ops) {
65 Module *M = I->getParent()->getParent()->getParent();
66 dbgs() << Instruction::getOpcodeName(I->getOpcode()) << " "
67 << *Ops[0].Op->getType() << '\t';
68 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
70 WriteAsOperand(dbgs(), Ops[i].Op, false, M);
71 dbgs() << ", #" << Ops[i].Rank << "] ";
77 /// \brief Utility class representing a base and exponent pair which form one
78 /// factor of some product.
83 Factor(Value *Base, unsigned Power) : Base(Base), Power(Power) {}
85 /// \brief Sort factors by their Base.
87 bool operator()(const Factor &LHS, const Factor &RHS) {
88 return LHS.Base < RHS.Base;
92 /// \brief Compare factors for equal bases.
94 bool operator()(const Factor &LHS, const Factor &RHS) {
95 return LHS.Base == RHS.Base;
99 /// \brief Sort factors in descending order by their power.
100 struct PowerDescendingSorter {
101 bool operator()(const Factor &LHS, const Factor &RHS) {
102 return LHS.Power > RHS.Power;
106 /// \brief Compare factors for equal powers.
108 bool operator()(const Factor &LHS, const Factor &RHS) {
109 return LHS.Power == RHS.Power;
116 class Reassociate : public FunctionPass {
117 DenseMap<BasicBlock*, unsigned> RankMap;
118 DenseMap<AssertingVH<Value>, unsigned> ValueRankMap;
119 SetVector<AssertingVH<Instruction> > RedoInsts;
122 static char ID; // Pass identification, replacement for typeid
123 Reassociate() : FunctionPass(ID) {
124 initializeReassociatePass(*PassRegistry::getPassRegistry());
127 bool runOnFunction(Function &F);
129 virtual void getAnalysisUsage(AnalysisUsage &AU) const {
130 AU.setPreservesCFG();
133 void BuildRankMap(Function &F);
134 unsigned getRank(Value *V);
135 void ReassociateExpression(BinaryOperator *I);
136 void RewriteExprTree(BinaryOperator *I, SmallVectorImpl<ValueEntry> &Ops);
137 Value *OptimizeExpression(BinaryOperator *I,
138 SmallVectorImpl<ValueEntry> &Ops);
139 Value *OptimizeAdd(Instruction *I, SmallVectorImpl<ValueEntry> &Ops);
140 bool collectMultiplyFactors(SmallVectorImpl<ValueEntry> &Ops,
141 SmallVectorImpl<Factor> &Factors);
142 Value *buildMinimalMultiplyDAG(IRBuilder<> &Builder,
143 SmallVectorImpl<Factor> &Factors);
144 Value *OptimizeMul(BinaryOperator *I, SmallVectorImpl<ValueEntry> &Ops);
145 Value *RemoveFactorFromExpression(Value *V, Value *Factor);
146 void EraseInst(Instruction *I);
147 void OptimizeInst(Instruction *I);
151 char Reassociate::ID = 0;
152 INITIALIZE_PASS(Reassociate, "reassociate",
153 "Reassociate expressions", false, false)
155 // Public interface to the Reassociate pass
156 FunctionPass *llvm::createReassociatePass() { return new Reassociate(); }
158 /// isReassociableOp - Return true if V is an instruction of the specified
159 /// opcode and if it only has one use.
160 static BinaryOperator *isReassociableOp(Value *V, unsigned Opcode) {
161 if (V->hasOneUse() && isa<Instruction>(V) &&
162 cast<Instruction>(V)->getOpcode() == Opcode)
163 return cast<BinaryOperator>(V);
167 static bool isUnmovableInstruction(Instruction *I) {
168 if (I->getOpcode() == Instruction::PHI ||
169 I->getOpcode() == Instruction::LandingPad ||
170 I->getOpcode() == Instruction::Alloca ||
171 I->getOpcode() == Instruction::Load ||
172 I->getOpcode() == Instruction::Invoke ||
173 (I->getOpcode() == Instruction::Call &&
174 !isa<DbgInfoIntrinsic>(I)) ||
175 I->getOpcode() == Instruction::UDiv ||
176 I->getOpcode() == Instruction::SDiv ||
177 I->getOpcode() == Instruction::FDiv ||
178 I->getOpcode() == Instruction::URem ||
179 I->getOpcode() == Instruction::SRem ||
180 I->getOpcode() == Instruction::FRem)
185 void Reassociate::BuildRankMap(Function &F) {
188 // Assign distinct ranks to function arguments
189 for (Function::arg_iterator I = F.arg_begin(), E = F.arg_end(); I != E; ++I)
190 ValueRankMap[&*I] = ++i;
192 ReversePostOrderTraversal<Function*> RPOT(&F);
193 for (ReversePostOrderTraversal<Function*>::rpo_iterator I = RPOT.begin(),
194 E = RPOT.end(); I != E; ++I) {
196 unsigned BBRank = RankMap[BB] = ++i << 16;
198 // Walk the basic block, adding precomputed ranks for any instructions that
199 // we cannot move. This ensures that the ranks for these instructions are
200 // all different in the block.
201 for (BasicBlock::iterator I = BB->begin(), E = BB->end(); I != E; ++I)
202 if (isUnmovableInstruction(I))
203 ValueRankMap[&*I] = ++BBRank;
207 unsigned Reassociate::getRank(Value *V) {
208 Instruction *I = dyn_cast<Instruction>(V);
210 if (isa<Argument>(V)) return ValueRankMap[V]; // Function argument.
211 return 0; // Otherwise it's a global or constant, rank 0.
214 if (unsigned Rank = ValueRankMap[I])
215 return Rank; // Rank already known?
217 // If this is an expression, return the 1+MAX(rank(LHS), rank(RHS)) so that
218 // we can reassociate expressions for code motion! Since we do not recurse
219 // for PHI nodes, we cannot have infinite recursion here, because there
220 // cannot be loops in the value graph that do not go through PHI nodes.
221 unsigned Rank = 0, MaxRank = RankMap[I->getParent()];
222 for (unsigned i = 0, e = I->getNumOperands();
223 i != e && Rank != MaxRank; ++i)
224 Rank = std::max(Rank, getRank(I->getOperand(i)));
226 // If this is a not or neg instruction, do not count it for rank. This
227 // assures us that X and ~X will have the same rank.
228 if (!I->getType()->isIntegerTy() ||
229 (!BinaryOperator::isNot(I) && !BinaryOperator::isNeg(I)))
232 //DEBUG(dbgs() << "Calculated Rank[" << V->getName() << "] = "
235 return ValueRankMap[I] = Rank;
238 /// LowerNegateToMultiply - Replace 0-X with X*-1.
240 static BinaryOperator *LowerNegateToMultiply(Instruction *Neg) {
241 Constant *Cst = Constant::getAllOnesValue(Neg->getType());
243 BinaryOperator *Res =
244 BinaryOperator::CreateMul(Neg->getOperand(1), Cst, "",Neg);
245 Neg->setOperand(1, Constant::getNullValue(Neg->getType())); // Drop use of op.
247 Neg->replaceAllUsesWith(Res);
248 Res->setDebugLoc(Neg->getDebugLoc());
252 /// CarmichaelShift - Returns k such that lambda(2^Bitwidth) = 2^k, where lambda
253 /// is the Carmichael function. This means that x^(2^k) === 1 mod 2^Bitwidth for
254 /// every odd x, i.e. x^(2^k) = 1 for every odd x in Bitwidth-bit arithmetic.
255 /// Note that 0 <= k < Bitwidth, and if Bitwidth > 3 then x^(2^k) = 0 for every
256 /// even x in Bitwidth-bit arithmetic.
257 static unsigned CarmichaelShift(unsigned Bitwidth) {
263 /// IncorporateWeight - Add the extra weight 'RHS' to the existing weight 'LHS',
264 /// reducing the combined weight using any special properties of the operation.
265 /// The existing weight LHS represents the computation X op X op ... op X where
266 /// X occurs LHS times. The combined weight represents X op X op ... op X with
267 /// X occurring LHS + RHS times. If op is "Xor" for example then the combined
268 /// operation is equivalent to X if LHS + RHS is odd, or 0 if LHS + RHS is even;
269 /// the routine returns 1 in LHS in the first case, and 0 in LHS in the second.
270 static void IncorporateWeight(APInt &LHS, const APInt &RHS, unsigned Opcode) {
271 // If we were working with infinite precision arithmetic then the combined
272 // weight would be LHS + RHS. But we are using finite precision arithmetic,
273 // and the APInt sum LHS + RHS may not be correct if it wraps (it is correct
274 // for nilpotent operations and addition, but not for idempotent operations
275 // and multiplication), so it is important to correctly reduce the combined
276 // weight back into range if wrapping would be wrong.
278 // If RHS is zero then the weight didn't change.
279 if (RHS.isMinValue())
281 // If LHS is zero then the combined weight is RHS.
282 if (LHS.isMinValue()) {
286 // From this point on we know that neither LHS nor RHS is zero.
288 if (Instruction::isIdempotent(Opcode)) {
289 // Idempotent means X op X === X, so any non-zero weight is equivalent to a
290 // weight of 1. Keeping weights at zero or one also means that wrapping is
292 assert(LHS == 1 && RHS == 1 && "Weights not reduced!");
293 return; // Return a weight of 1.
295 if (Instruction::isNilpotent(Opcode)) {
296 // Nilpotent means X op X === 0, so reduce weights modulo 2.
297 assert(LHS == 1 && RHS == 1 && "Weights not reduced!");
298 LHS = 0; // 1 + 1 === 0 modulo 2.
301 if (Opcode == Instruction::Add) {
302 // TODO: Reduce the weight by exploiting nsw/nuw?
307 assert(Opcode == Instruction::Mul && "Unknown associative operation!");
308 unsigned Bitwidth = LHS.getBitWidth();
309 // If CM is the Carmichael number then a weight W satisfying W >= CM+Bitwidth
310 // can be replaced with W-CM. That's because x^W=x^(W-CM) for every Bitwidth
311 // bit number x, since either x is odd in which case x^CM = 1, or x is even in
312 // which case both x^W and x^(W - CM) are zero. By subtracting off multiples
313 // of CM like this weights can always be reduced to the range [0, CM+Bitwidth)
314 // which by a happy accident means that they can always be represented using
316 // TODO: Reduce the weight by exploiting nsw/nuw? (Could do much better than
317 // the Carmichael number).
319 /// CM - The value of Carmichael's lambda function.
320 APInt CM = APInt::getOneBitSet(Bitwidth, CarmichaelShift(Bitwidth));
321 // Any weight W >= Threshold can be replaced with W - CM.
322 APInt Threshold = CM + Bitwidth;
323 assert(LHS.ult(Threshold) && RHS.ult(Threshold) && "Weights not reduced!");
324 // For Bitwidth 4 or more the following sum does not overflow.
326 while (LHS.uge(Threshold))
329 // To avoid problems with overflow do everything the same as above but using
331 unsigned CM = 1U << CarmichaelShift(Bitwidth);
332 unsigned Threshold = CM + Bitwidth;
333 assert(LHS.getZExtValue() < Threshold && RHS.getZExtValue() < Threshold &&
334 "Weights not reduced!");
335 unsigned Total = LHS.getZExtValue() + RHS.getZExtValue();
336 while (Total >= Threshold)
342 /// EvaluateRepeatedConstant - Compute C op C op ... op C where the constant C
343 /// is repeated Weight times.
344 static Constant *EvaluateRepeatedConstant(unsigned Opcode, Constant *C,
346 // For addition the result can be efficiently computed as the product of the
347 // constant and the weight.
348 if (Opcode == Instruction::Add)
349 return ConstantExpr::getMul(C, ConstantInt::get(C->getContext(), Weight));
351 // The weight might be huge, so compute by repeated squaring to ensure that
352 // compile time is proportional to the logarithm of the weight.
353 Constant *Result = 0;
354 Constant *Power = C; // Successively C, C op C, (C op C) op (C op C) etc.
355 // Visit the bits in Weight.
356 while (Weight != 0) {
357 // If the current bit in Weight is non-zero do Result = Result op Power.
359 Result = Result ? ConstantExpr::get(Opcode, Result, Power) : Power;
360 // Move on to the next bit if any more are non-zero.
361 Weight = Weight.lshr(1);
362 if (Weight.isMinValue())
365 Power = ConstantExpr::get(Opcode, Power, Power);
368 assert(Result && "Only positive weights supported!");
372 typedef std::pair<Value*, APInt> RepeatedValue;
374 /// LinearizeExprTree - 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, and
386 /// they are all non-constant except possibly for the last one, which if it is
387 /// constant will have weight one (Ops[N].second === 1).
389 /// This routine may modify the function, in which case it returns 'true'. The
390 /// changes it makes may well be destructive, changing the value computed by 'I'
391 /// to something completely different. Thus if the routine returns 'true' then
392 /// you MUST either replace I with a new expression computed from the Ops array,
393 /// or use RewriteExprTree to put the values back in.
395 /// A leaf node is either not a binary operation of the same kind as the root
396 /// node 'I' (i.e. is not a binary operator at all, or is, but with a different
397 /// opcode), or is the same kind of binary operator but has a use which either
398 /// does not belong to the expression, or does belong to the expression but is
399 /// a leaf node. Every leaf node has at least one use that is a non-leaf node
400 /// of the expression, while for non-leaf nodes (except for the root 'I') every
401 /// use is a non-leaf node of the expression.
404 /// expression graph node names
414 /// The leaf nodes are C, E, F and G. The Ops array will contain (maybe not in
415 /// that order) (C, 1), (E, 1), (F, 2), (G, 2).
417 /// The expression is maximal: if some instruction is a binary operator of the
418 /// same kind as 'I', and all of its uses are non-leaf nodes of the expression,
419 /// then the instruction also belongs to the expression, is not a leaf node of
420 /// it, and its operands also belong to the expression (but may be leaf nodes).
422 /// NOTE: This routine will set operands of non-leaf non-root nodes to undef in
423 /// order to ensure that every non-root node in the expression has *exactly one*
424 /// use by a non-leaf node of the expression. This destruction means that the
425 /// caller MUST either replace 'I' with a new expression or use something like
426 /// RewriteExprTree to put the values back in if the routine indicates that it
427 /// made a change by returning 'true'.
429 /// In the above example either the right operand of A or the left operand of B
430 /// will be replaced by undef. If it is B's operand then this gives:
434 /// + + | A, B - operand of B replaced with undef
440 /// Note that such undef operands can only be reached by passing through 'I'.
441 /// For example, if you visit operands recursively starting from a leaf node
442 /// then you will never see such an undef operand unless you get back to 'I',
443 /// which requires passing through a phi node.
445 /// Note that this routine may also mutate binary operators of the wrong type
446 /// that have all uses inside the expression (i.e. only used by non-leaf nodes
447 /// of the expression) if it can turn them into binary operators of the right
448 /// type and thus make the expression bigger.
450 static bool LinearizeExprTree(BinaryOperator *I,
451 SmallVectorImpl<RepeatedValue> &Ops) {
452 DEBUG(dbgs() << "LINEARIZE: " << *I << '\n');
453 unsigned Bitwidth = I->getType()->getScalarType()->getPrimitiveSizeInBits();
454 unsigned Opcode = I->getOpcode();
455 assert(Instruction::isAssociative(Opcode) &&
456 Instruction::isCommutative(Opcode) &&
457 "Expected an associative and commutative operation!");
458 // If we see an absorbing element then the entire expression must be equal to
459 // it. For example, if this is a multiplication expression and zero occurs as
460 // an operand somewhere in it then the result of the expression must be zero.
461 Constant *Absorber = ConstantExpr::getBinOpAbsorber(Opcode, I->getType());
463 // Visit all operands of the expression, keeping track of their weight (the
464 // number of paths from the expression root to the operand, or if you like
465 // the number of times that operand occurs in the linearized expression).
466 // For example, if I = X + A, where X = A + B, then I, X and B have weight 1
467 // while A has weight two.
469 // Worklist of non-leaf nodes (their operands are in the expression too) along
470 // with their weights, representing a certain number of paths to the operator.
471 // If an operator occurs in the worklist multiple times then we found multiple
472 // ways to get to it.
473 SmallVector<std::pair<BinaryOperator*, APInt>, 8> Worklist; // (Op, Weight)
474 Worklist.push_back(std::make_pair(I, APInt(Bitwidth, 1)));
475 bool MadeChange = false;
477 // Leaves of the expression are values that either aren't the right kind of
478 // operation (eg: a constant, or a multiply in an add tree), or are, but have
479 // some uses that are not inside the expression. For example, in I = X + X,
480 // X = A + B, the value X has two uses (by I) that are in the expression. If
481 // X has any other uses, for example in a return instruction, then we consider
482 // X to be a leaf, and won't analyze it further. When we first visit a value,
483 // if it has more than one use then at first we conservatively consider it to
484 // be a leaf. Later, as the expression is explored, we may discover some more
485 // uses of the value from inside the expression. If all uses turn out to be
486 // from within the expression (and the value is a binary operator of the right
487 // kind) then the value is no longer considered to be a leaf, and its operands
490 // Leaves - Keeps track of the set of putative leaves as well as the number of
491 // paths to each leaf seen so far.
492 typedef DenseMap<Value*, APInt> LeafMap;
493 LeafMap Leaves; // Leaf -> Total weight so far.
494 SmallVector<Value*, 8> LeafOrder; // Ensure deterministic leaf output order.
497 SmallPtrSet<Value*, 8> Visited; // For sanity checking the iteration scheme.
499 while (!Worklist.empty()) {
500 std::pair<BinaryOperator*, APInt> P = Worklist.pop_back_val();
501 I = P.first; // We examine the operands of this binary operator.
503 for (unsigned OpIdx = 0; OpIdx < 2; ++OpIdx) { // Visit operands.
504 Value *Op = I->getOperand(OpIdx);
505 APInt Weight = P.second; // Number of paths to this operand.
506 DEBUG(dbgs() << "OPERAND: " << *Op << " (" << Weight << ")\n");
507 assert(!Op->use_empty() && "No uses, so how did we get to it?!");
509 // If the expression contains an absorbing element then there is no need
510 // to analyze it further: it must evaluate to the absorbing element.
511 if (Op == Absorber && !Weight.isMinValue()) {
512 Ops.push_back(std::make_pair(Absorber, APInt(Bitwidth, 1)));
516 // If this is a binary operation of the right kind with only one use then
517 // add its operands to the expression.
518 if (BinaryOperator *BO = isReassociableOp(Op, Opcode)) {
519 assert(Visited.insert(Op) && "Not first visit!");
520 DEBUG(dbgs() << "DIRECT ADD: " << *Op << " (" << Weight << ")\n");
521 Worklist.push_back(std::make_pair(BO, Weight));
525 // Appears to be a leaf. Is the operand already in the set of leaves?
526 LeafMap::iterator It = Leaves.find(Op);
527 if (It == Leaves.end()) {
528 // Not in the leaf map. Must be the first time we saw this operand.
529 assert(Visited.insert(Op) && "Not first visit!");
530 if (!Op->hasOneUse()) {
531 // This value has uses not accounted for by the expression, so it is
532 // not safe to modify. Mark it as being a leaf.
533 DEBUG(dbgs() << "ADD USES LEAF: " << *Op << " (" << Weight << ")\n");
534 LeafOrder.push_back(Op);
538 // No uses outside the expression, try morphing it.
539 } else if (It != Leaves.end()) {
540 // Already in the leaf map.
541 assert(Visited.count(Op) && "In leaf map but not visited!");
543 // Update the number of paths to the leaf.
544 IncorporateWeight(It->second, Weight, Opcode);
546 // The leaf already has one use from inside the expression. As we want
547 // exactly one such use, drop this new use of the leaf.
548 assert(!Op->hasOneUse() && "Only one use, but we got here twice!");
549 I->setOperand(OpIdx, UndefValue::get(I->getType()));
552 // If the leaf is a binary operation of the right kind and we now see
553 // that its multiple original uses were in fact all by nodes belonging
554 // to the expression, then no longer consider it to be a leaf and add
555 // its operands to the expression.
556 if (BinaryOperator *BO = isReassociableOp(Op, Opcode)) {
557 DEBUG(dbgs() << "UNLEAF: " << *Op << " (" << It->second << ")\n");
558 Worklist.push_back(std::make_pair(BO, It->second));
563 // If we still have uses that are not accounted for by the expression
564 // then it is not safe to modify the value.
565 if (!Op->hasOneUse())
568 // No uses outside the expression, try morphing it.
570 Leaves.erase(It); // Since the value may be morphed below.
573 // At this point we have a value which, first of all, is not a binary
574 // expression of the right kind, and secondly, is only used inside the
575 // expression. This means that it can safely be modified. See if we
576 // can usefully morph it into an expression of the right kind.
577 assert((!isa<Instruction>(Op) ||
578 cast<Instruction>(Op)->getOpcode() != Opcode) &&
579 "Should have been handled above!");
580 assert(Op->hasOneUse() && "Has uses outside the expression tree!");
582 // If this is a multiply expression, turn any internal negations into
583 // multiplies by -1 so they can be reassociated.
584 BinaryOperator *BO = dyn_cast<BinaryOperator>(Op);
585 if (Opcode == Instruction::Mul && BO && BinaryOperator::isNeg(BO)) {
586 DEBUG(dbgs() << "MORPH LEAF: " << *Op << " (" << Weight << ") TO ");
587 BO = LowerNegateToMultiply(BO);
588 DEBUG(dbgs() << *BO << 'n');
589 Worklist.push_back(std::make_pair(BO, Weight));
594 // Failed to morph into an expression of the right type. This really is
596 DEBUG(dbgs() << "ADD LEAF: " << *Op << " (" << Weight << ")\n");
597 assert(!isReassociableOp(Op, Opcode) && "Value was morphed?");
598 LeafOrder.push_back(Op);
603 // The leaves, repeated according to their weights, represent the linearized
604 // form of the expression.
605 Constant *Cst = 0; // Accumulate constants here.
606 for (unsigned i = 0, e = LeafOrder.size(); i != e; ++i) {
607 Value *V = LeafOrder[i];
608 LeafMap::iterator It = Leaves.find(V);
609 if (It == Leaves.end())
610 // Node initially thought to be a leaf wasn't.
612 assert(!isReassociableOp(V, Opcode) && "Shouldn't be a leaf!");
613 APInt Weight = It->second;
614 if (Weight.isMinValue())
615 // Leaf already output or weight reduction eliminated it.
617 // Ensure the leaf is only output once.
619 // Glob all constants together into Cst.
620 if (Constant *C = dyn_cast<Constant>(V)) {
621 C = EvaluateRepeatedConstant(Opcode, C, Weight);
622 Cst = Cst ? ConstantExpr::get(Opcode, Cst, C) : C;
626 Ops.push_back(std::make_pair(V, Weight));
629 // Add any constants back into Ops, all globbed together and reduced to having
630 // weight 1 for the convenience of users.
631 Constant *Identity = ConstantExpr::getBinOpIdentity(Opcode, I->getType());
632 if (Cst && Cst != Identity) {
633 // If combining multiple constants resulted in the absorber then the entire
634 // expression must evaluate to the absorber.
637 Ops.push_back(std::make_pair(Cst, APInt(Bitwidth, 1)));
640 // For nilpotent operations or addition there may be no operands, for example
641 // because the expression was "X xor X" or consisted of 2^Bitwidth additions:
642 // in both cases the weight reduces to 0 causing the value to be skipped.
644 assert(Identity && "Associative operation without identity!");
645 Ops.push_back(std::make_pair(Identity, APInt(Bitwidth, 1)));
651 // RewriteExprTree - Now that the operands for this expression tree are
652 // linearized and optimized, emit them in-order.
653 void Reassociate::RewriteExprTree(BinaryOperator *I,
654 SmallVectorImpl<ValueEntry> &Ops) {
655 assert(Ops.size() > 1 && "Single values should be used directly!");
657 // Since our optimizations never increase the number of operations, the new
658 // expression can always be written by reusing the existing binary operators
659 // from the original expression tree, without creating any new instructions,
660 // though the rewritten expression may have a completely different topology.
661 // We take care to not change anything if the new expression will be the same
662 // as the original. If more than trivial changes (like commuting operands)
663 // were made then we are obliged to clear out any optional subclass data like
666 /// NodesToRewrite - Nodes from the original expression available for writing
667 /// the new expression into.
668 SmallVector<BinaryOperator*, 8> NodesToRewrite;
669 unsigned Opcode = I->getOpcode();
670 BinaryOperator *Op = I;
672 // ExpressionChanged - Non-null if the rewritten expression differs from the
673 // original in some non-trivial way, requiring the clearing of optional flags.
674 // Flags are cleared from the operator in ExpressionChanged up to I inclusive.
675 BinaryOperator *ExpressionChanged = 0;
676 for (unsigned i = 0; ; ++i) {
677 // The last operation (which comes earliest in the IR) is special as both
678 // operands will come from Ops, rather than just one with the other being
680 if (i+2 == Ops.size()) {
681 Value *NewLHS = Ops[i].Op;
682 Value *NewRHS = Ops[i+1].Op;
683 Value *OldLHS = Op->getOperand(0);
684 Value *OldRHS = Op->getOperand(1);
686 if (NewLHS == OldLHS && NewRHS == OldRHS)
687 // Nothing changed, leave it alone.
690 if (NewLHS == OldRHS && NewRHS == OldLHS) {
691 // The order of the operands was reversed. Swap them.
692 DEBUG(dbgs() << "RA: " << *Op << '\n');
694 DEBUG(dbgs() << "TO: " << *Op << '\n');
700 // The new operation differs non-trivially from the original. Overwrite
701 // the old operands with the new ones.
702 DEBUG(dbgs() << "RA: " << *Op << '\n');
703 if (NewLHS != OldLHS) {
704 if (BinaryOperator *BO = isReassociableOp(OldLHS, Opcode))
705 NodesToRewrite.push_back(BO);
706 Op->setOperand(0, NewLHS);
708 if (NewRHS != OldRHS) {
709 if (BinaryOperator *BO = isReassociableOp(OldRHS, Opcode))
710 NodesToRewrite.push_back(BO);
711 Op->setOperand(1, NewRHS);
713 DEBUG(dbgs() << "TO: " << *Op << '\n');
715 ExpressionChanged = Op;
722 // Not the last operation. The left-hand side will be a sub-expression
723 // while the right-hand side will be the current element of Ops.
724 Value *NewRHS = Ops[i].Op;
725 if (NewRHS != Op->getOperand(1)) {
726 DEBUG(dbgs() << "RA: " << *Op << '\n');
727 if (NewRHS == Op->getOperand(0)) {
728 // The new right-hand side was already present as the left operand. If
729 // we are lucky then swapping the operands will sort out both of them.
732 // Overwrite with the new right-hand side.
733 if (BinaryOperator *BO = isReassociableOp(Op->getOperand(1), Opcode))
734 NodesToRewrite.push_back(BO);
735 Op->setOperand(1, NewRHS);
736 ExpressionChanged = Op;
738 DEBUG(dbgs() << "TO: " << *Op << '\n');
743 // Now deal with the left-hand side. If this is already an operation node
744 // from the original expression then just rewrite the rest of the expression
746 if (BinaryOperator *BO = isReassociableOp(Op->getOperand(0), Opcode)) {
751 // Otherwise, grab a spare node from the original expression and use that as
752 // the left-hand side. If there are no nodes left then the optimizers made
753 // an expression with more nodes than the original! This usually means that
754 // they did something stupid but it might mean that the problem was just too
755 // hard (finding the mimimal number of multiplications needed to realize a
756 // multiplication expression is NP-complete). Whatever the reason, smart or
757 // stupid, create a new node if there are none left.
758 BinaryOperator *NewOp;
759 if (NodesToRewrite.empty()) {
760 Constant *Undef = UndefValue::get(I->getType());
761 NewOp = BinaryOperator::Create(Instruction::BinaryOps(Opcode),
762 Undef, Undef, "", I);
764 NewOp = NodesToRewrite.pop_back_val();
767 DEBUG(dbgs() << "RA: " << *Op << '\n');
768 Op->setOperand(0, NewOp);
769 DEBUG(dbgs() << "TO: " << *Op << '\n');
770 ExpressionChanged = Op;
776 // If the expression changed non-trivially then clear out all subclass data
777 // starting from the operator specified in ExpressionChanged, and compactify
778 // the operators to just before the expression root to guarantee that the
779 // expression tree is dominated by all of Ops.
780 if (ExpressionChanged)
782 ExpressionChanged->clearSubclassOptionalData();
783 if (ExpressionChanged == I)
785 ExpressionChanged->moveBefore(I);
786 ExpressionChanged = cast<BinaryOperator>(*ExpressionChanged->use_begin());
789 // Throw away any left over nodes from the original expression.
790 for (unsigned i = 0, e = NodesToRewrite.size(); i != e; ++i)
791 RedoInsts.insert(NodesToRewrite[i]);
794 /// NegateValue - Insert instructions before the instruction pointed to by BI,
795 /// that computes the negative version of the value specified. The negative
796 /// version of the value is returned, and BI is left pointing at the instruction
797 /// that should be processed next by the reassociation pass.
798 static Value *NegateValue(Value *V, Instruction *BI) {
799 if (Constant *C = dyn_cast<Constant>(V))
800 return ConstantExpr::getNeg(C);
802 // We are trying to expose opportunity for reassociation. One of the things
803 // that we want to do to achieve this is to push a negation as deep into an
804 // expression chain as possible, to expose the add instructions. In practice,
805 // this means that we turn this:
806 // X = -(A+12+C+D) into X = -A + -12 + -C + -D = -12 + -A + -C + -D
807 // so that later, a: Y = 12+X could get reassociated with the -12 to eliminate
808 // the constants. We assume that instcombine will clean up the mess later if
809 // we introduce tons of unnecessary negation instructions.
811 if (BinaryOperator *I = isReassociableOp(V, Instruction::Add)) {
812 // Push the negates through the add.
813 I->setOperand(0, NegateValue(I->getOperand(0), BI));
814 I->setOperand(1, NegateValue(I->getOperand(1), BI));
816 // We must move the add instruction here, because the neg instructions do
817 // not dominate the old add instruction in general. By moving it, we are
818 // assured that the neg instructions we just inserted dominate the
819 // instruction we are about to insert after them.
822 I->setName(I->getName()+".neg");
826 // Okay, we need to materialize a negated version of V with an instruction.
827 // Scan the use lists of V to see if we have one already.
828 for (Value::use_iterator UI = V->use_begin(), E = V->use_end(); UI != E;++UI){
830 if (!BinaryOperator::isNeg(U)) continue;
832 // We found one! Now we have to make sure that the definition dominates
833 // this use. We do this by moving it to the entry block (if it is a
834 // non-instruction value) or right after the definition. These negates will
835 // be zapped by reassociate later, so we don't need much finesse here.
836 BinaryOperator *TheNeg = cast<BinaryOperator>(U);
838 // Verify that the negate is in this function, V might be a constant expr.
839 if (TheNeg->getParent()->getParent() != BI->getParent()->getParent())
842 BasicBlock::iterator InsertPt;
843 if (Instruction *InstInput = dyn_cast<Instruction>(V)) {
844 if (InvokeInst *II = dyn_cast<InvokeInst>(InstInput)) {
845 InsertPt = II->getNormalDest()->begin();
847 InsertPt = InstInput;
850 while (isa<PHINode>(InsertPt)) ++InsertPt;
852 InsertPt = TheNeg->getParent()->getParent()->getEntryBlock().begin();
854 TheNeg->moveBefore(InsertPt);
858 // Insert a 'neg' instruction that subtracts the value from zero to get the
860 return BinaryOperator::CreateNeg(V, V->getName() + ".neg", BI);
863 /// ShouldBreakUpSubtract - Return true if we should break up this subtract of
864 /// X-Y into (X + -Y).
865 static bool ShouldBreakUpSubtract(Instruction *Sub) {
866 // If this is a negation, we can't split it up!
867 if (BinaryOperator::isNeg(Sub))
870 // Don't bother to break this up unless either the LHS is an associable add or
871 // subtract or if this is only used by one.
872 if (isReassociableOp(Sub->getOperand(0), Instruction::Add) ||
873 isReassociableOp(Sub->getOperand(0), Instruction::Sub))
875 if (isReassociableOp(Sub->getOperand(1), Instruction::Add) ||
876 isReassociableOp(Sub->getOperand(1), Instruction::Sub))
878 if (Sub->hasOneUse() &&
879 (isReassociableOp(Sub->use_back(), Instruction::Add) ||
880 isReassociableOp(Sub->use_back(), Instruction::Sub)))
886 /// BreakUpSubtract - If we have (X-Y), and if either X is an add, or if this is
887 /// only used by an add, transform this into (X+(0-Y)) to promote better
889 static BinaryOperator *BreakUpSubtract(Instruction *Sub) {
890 // Convert a subtract into an add and a neg instruction. This allows sub
891 // instructions to be commuted with other add instructions.
893 // Calculate the negative value of Operand 1 of the sub instruction,
894 // and set it as the RHS of the add instruction we just made.
896 Value *NegVal = NegateValue(Sub->getOperand(1), Sub);
897 BinaryOperator *New =
898 BinaryOperator::CreateAdd(Sub->getOperand(0), NegVal, "", Sub);
899 Sub->setOperand(0, Constant::getNullValue(Sub->getType())); // Drop use of op.
900 Sub->setOperand(1, Constant::getNullValue(Sub->getType())); // Drop use of op.
903 // Everyone now refers to the add instruction.
904 Sub->replaceAllUsesWith(New);
905 New->setDebugLoc(Sub->getDebugLoc());
907 DEBUG(dbgs() << "Negated: " << *New << '\n');
911 /// ConvertShiftToMul - If this is a shift of a reassociable multiply or is used
912 /// by one, change this into a multiply by a constant to assist with further
914 static BinaryOperator *ConvertShiftToMul(Instruction *Shl) {
915 Constant *MulCst = ConstantInt::get(Shl->getType(), 1);
916 MulCst = ConstantExpr::getShl(MulCst, cast<Constant>(Shl->getOperand(1)));
918 BinaryOperator *Mul =
919 BinaryOperator::CreateMul(Shl->getOperand(0), MulCst, "", Shl);
920 Shl->setOperand(0, UndefValue::get(Shl->getType())); // Drop use of op.
922 Shl->replaceAllUsesWith(Mul);
923 Mul->setDebugLoc(Shl->getDebugLoc());
927 /// FindInOperandList - Scan backwards and forwards among values with the same
928 /// rank as element i to see if X exists. If X does not exist, return i. This
929 /// is useful when scanning for 'x' when we see '-x' because they both get the
931 static unsigned FindInOperandList(SmallVectorImpl<ValueEntry> &Ops, unsigned i,
933 unsigned XRank = Ops[i].Rank;
934 unsigned e = Ops.size();
935 for (unsigned j = i+1; j != e && Ops[j].Rank == XRank; ++j)
939 for (unsigned j = i-1; j != ~0U && Ops[j].Rank == XRank; --j)
945 /// EmitAddTreeOfValues - Emit a tree of add instructions, summing Ops together
946 /// and returning the result. Insert the tree before I.
947 static Value *EmitAddTreeOfValues(Instruction *I,
948 SmallVectorImpl<WeakVH> &Ops){
949 if (Ops.size() == 1) return Ops.back();
951 Value *V1 = Ops.back();
953 Value *V2 = EmitAddTreeOfValues(I, Ops);
954 return BinaryOperator::CreateAdd(V2, V1, "tmp", I);
957 /// RemoveFactorFromExpression - If V is an expression tree that is a
958 /// multiplication sequence, and if this sequence contains a multiply by Factor,
959 /// remove Factor from the tree and return the new tree.
960 Value *Reassociate::RemoveFactorFromExpression(Value *V, Value *Factor) {
961 BinaryOperator *BO = isReassociableOp(V, Instruction::Mul);
964 SmallVector<RepeatedValue, 8> Tree;
965 MadeChange |= LinearizeExprTree(BO, Tree);
966 SmallVector<ValueEntry, 8> Factors;
967 Factors.reserve(Tree.size());
968 for (unsigned i = 0, e = Tree.size(); i != e; ++i) {
969 RepeatedValue E = Tree[i];
970 Factors.append(E.second.getZExtValue(),
971 ValueEntry(getRank(E.first), E.first));
974 bool FoundFactor = false;
975 bool NeedsNegate = false;
976 for (unsigned i = 0, e = Factors.size(); i != e; ++i) {
977 if (Factors[i].Op == Factor) {
979 Factors.erase(Factors.begin()+i);
983 // If this is a negative version of this factor, remove it.
984 if (ConstantInt *FC1 = dyn_cast<ConstantInt>(Factor))
985 if (ConstantInt *FC2 = dyn_cast<ConstantInt>(Factors[i].Op))
986 if (FC1->getValue() == -FC2->getValue()) {
987 FoundFactor = NeedsNegate = true;
988 Factors.erase(Factors.begin()+i);
994 // Make sure to restore the operands to the expression tree.
995 RewriteExprTree(BO, Factors);
999 BasicBlock::iterator InsertPt = BO; ++InsertPt;
1001 // If this was just a single multiply, remove the multiply and return the only
1002 // remaining operand.
1003 if (Factors.size() == 1) {
1004 RedoInsts.insert(BO);
1007 RewriteExprTree(BO, Factors);
1012 V = BinaryOperator::CreateNeg(V, "neg", InsertPt);
1017 /// FindSingleUseMultiplyFactors - If V is a single-use multiply, recursively
1018 /// add its operands as factors, otherwise add V to the list of factors.
1020 /// Ops is the top-level list of add operands we're trying to factor.
1021 static void FindSingleUseMultiplyFactors(Value *V,
1022 SmallVectorImpl<Value*> &Factors,
1023 const SmallVectorImpl<ValueEntry> &Ops) {
1024 BinaryOperator *BO = isReassociableOp(V, Instruction::Mul);
1026 Factors.push_back(V);
1030 // Otherwise, add the LHS and RHS to the list of factors.
1031 FindSingleUseMultiplyFactors(BO->getOperand(1), Factors, Ops);
1032 FindSingleUseMultiplyFactors(BO->getOperand(0), Factors, Ops);
1035 /// OptimizeAndOrXor - Optimize a series of operands to an 'and', 'or', or 'xor'
1036 /// instruction. This optimizes based on identities. If it can be reduced to
1037 /// a single Value, it is returned, otherwise the Ops list is mutated as
1039 static Value *OptimizeAndOrXor(unsigned Opcode,
1040 SmallVectorImpl<ValueEntry> &Ops) {
1041 // Scan the operand lists looking for X and ~X pairs, along with X,X pairs.
1042 // If we find any, we can simplify the expression. X&~X == 0, X|~X == -1.
1043 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1044 // First, check for X and ~X in the operand list.
1045 assert(i < Ops.size());
1046 if (BinaryOperator::isNot(Ops[i].Op)) { // Cannot occur for ^.
1047 Value *X = BinaryOperator::getNotArgument(Ops[i].Op);
1048 unsigned FoundX = FindInOperandList(Ops, i, X);
1050 if (Opcode == Instruction::And) // ...&X&~X = 0
1051 return Constant::getNullValue(X->getType());
1053 if (Opcode == Instruction::Or) // ...|X|~X = -1
1054 return Constant::getAllOnesValue(X->getType());
1058 // Next, check for duplicate pairs of values, which we assume are next to
1059 // each other, due to our sorting criteria.
1060 assert(i < Ops.size());
1061 if (i+1 != Ops.size() && Ops[i+1].Op == Ops[i].Op) {
1062 if (Opcode == Instruction::And || Opcode == Instruction::Or) {
1063 // Drop duplicate values for And and Or.
1064 Ops.erase(Ops.begin()+i);
1070 // Drop pairs of values for Xor.
1071 assert(Opcode == Instruction::Xor);
1073 return Constant::getNullValue(Ops[0].Op->getType());
1076 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
1084 /// OptimizeAdd - Optimize a series of operands to an 'add' instruction. This
1085 /// optimizes based on identities. If it can be reduced to a single Value, it
1086 /// is returned, otherwise the Ops list is mutated as necessary.
1087 Value *Reassociate::OptimizeAdd(Instruction *I,
1088 SmallVectorImpl<ValueEntry> &Ops) {
1089 // Scan the operand lists looking for X and -X pairs. If we find any, we
1090 // can simplify the expression. X+-X == 0. While we're at it, scan for any
1091 // duplicates. We want to canonicalize Y+Y+Y+Z -> 3*Y+Z.
1093 // TODO: We could handle "X + ~X" -> "-1" if we wanted, since "-X = ~X+1".
1095 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1096 Value *TheOp = Ops[i].Op;
1097 // Check to see if we've seen this operand before. If so, we factor all
1098 // instances of the operand together. Due to our sorting criteria, we know
1099 // that these need to be next to each other in the vector.
1100 if (i+1 != Ops.size() && Ops[i+1].Op == TheOp) {
1101 // Rescan the list, remove all instances of this operand from the expr.
1102 unsigned NumFound = 0;
1104 Ops.erase(Ops.begin()+i);
1106 } while (i != Ops.size() && Ops[i].Op == TheOp);
1108 DEBUG(errs() << "\nFACTORING [" << NumFound << "]: " << *TheOp << '\n');
1111 // Insert a new multiply.
1112 Value *Mul = ConstantInt::get(cast<IntegerType>(I->getType()), NumFound);
1113 Mul = BinaryOperator::CreateMul(TheOp, Mul, "factor", I);
1115 // Now that we have inserted a multiply, optimize it. This allows us to
1116 // handle cases that require multiple factoring steps, such as this:
1117 // (X*2) + (X*2) + (X*2) -> (X*2)*3 -> X*6
1118 RedoInsts.insert(cast<Instruction>(Mul));
1120 // If every add operand was a duplicate, return the multiply.
1124 // Otherwise, we had some input that didn't have the dupe, such as
1125 // "A + A + B" -> "A*2 + B". Add the new multiply to the list of
1126 // things being added by this operation.
1127 Ops.insert(Ops.begin(), ValueEntry(getRank(Mul), Mul));
1134 // Check for X and -X in the operand list.
1135 if (!BinaryOperator::isNeg(TheOp))
1138 Value *X = BinaryOperator::getNegArgument(TheOp);
1139 unsigned FoundX = FindInOperandList(Ops, i, X);
1143 // Remove X and -X from the operand list.
1144 if (Ops.size() == 2)
1145 return Constant::getNullValue(X->getType());
1147 Ops.erase(Ops.begin()+i);
1151 --i; // Need to back up an extra one.
1152 Ops.erase(Ops.begin()+FoundX);
1154 --i; // Revisit element.
1155 e -= 2; // Removed two elements.
1158 // Scan the operand list, checking to see if there are any common factors
1159 // between operands. Consider something like A*A+A*B*C+D. We would like to
1160 // reassociate this to A*(A+B*C)+D, which reduces the number of multiplies.
1161 // To efficiently find this, we count the number of times a factor occurs
1162 // for any ADD operands that are MULs.
1163 DenseMap<Value*, unsigned> FactorOccurrences;
1165 // Keep track of each multiply we see, to avoid triggering on (X*4)+(X*4)
1166 // where they are actually the same multiply.
1167 unsigned MaxOcc = 0;
1168 Value *MaxOccVal = 0;
1169 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1170 BinaryOperator *BOp = isReassociableOp(Ops[i].Op, Instruction::Mul);
1174 // Compute all of the factors of this added value.
1175 SmallVector<Value*, 8> Factors;
1176 FindSingleUseMultiplyFactors(BOp, Factors, Ops);
1177 assert(Factors.size() > 1 && "Bad linearize!");
1179 // Add one to FactorOccurrences for each unique factor in this op.
1180 SmallPtrSet<Value*, 8> Duplicates;
1181 for (unsigned i = 0, e = Factors.size(); i != e; ++i) {
1182 Value *Factor = Factors[i];
1183 if (!Duplicates.insert(Factor)) continue;
1185 unsigned Occ = ++FactorOccurrences[Factor];
1186 if (Occ > MaxOcc) { MaxOcc = Occ; MaxOccVal = Factor; }
1188 // If Factor is a negative constant, add the negated value as a factor
1189 // because we can percolate the negate out. Watch for minint, which
1190 // cannot be positivified.
1191 if (ConstantInt *CI = dyn_cast<ConstantInt>(Factor))
1192 if (CI->isNegative() && !CI->isMinValue(true)) {
1193 Factor = ConstantInt::get(CI->getContext(), -CI->getValue());
1194 assert(!Duplicates.count(Factor) &&
1195 "Shouldn't have two constant factors, missed a canonicalize");
1197 unsigned Occ = ++FactorOccurrences[Factor];
1198 if (Occ > MaxOcc) { MaxOcc = Occ; MaxOccVal = Factor; }
1203 // If any factor occurred more than one time, we can pull it out.
1205 DEBUG(errs() << "\nFACTORING [" << MaxOcc << "]: " << *MaxOccVal << '\n');
1208 // Create a new instruction that uses the MaxOccVal twice. If we don't do
1209 // this, we could otherwise run into situations where removing a factor
1210 // from an expression will drop a use of maxocc, and this can cause
1211 // RemoveFactorFromExpression on successive values to behave differently.
1212 Instruction *DummyInst = BinaryOperator::CreateAdd(MaxOccVal, MaxOccVal);
1213 SmallVector<WeakVH, 4> NewMulOps;
1214 for (unsigned i = 0; i != Ops.size(); ++i) {
1215 // Only try to remove factors from expressions we're allowed to.
1216 BinaryOperator *BOp = isReassociableOp(Ops[i].Op, Instruction::Mul);
1220 if (Value *V = RemoveFactorFromExpression(Ops[i].Op, MaxOccVal)) {
1221 // The factorized operand may occur several times. Convert them all in
1223 for (unsigned j = Ops.size(); j != i;) {
1225 if (Ops[j].Op == Ops[i].Op) {
1226 NewMulOps.push_back(V);
1227 Ops.erase(Ops.begin()+j);
1234 // No need for extra uses anymore.
1237 unsigned NumAddedValues = NewMulOps.size();
1238 Value *V = EmitAddTreeOfValues(I, NewMulOps);
1240 // Now that we have inserted the add tree, optimize it. This allows us to
1241 // handle cases that require multiple factoring steps, such as this:
1242 // A*A*B + A*A*C --> A*(A*B+A*C) --> A*(A*(B+C))
1243 assert(NumAddedValues > 1 && "Each occurrence should contribute a value");
1244 (void)NumAddedValues;
1245 if (Instruction *VI = dyn_cast<Instruction>(V))
1246 RedoInsts.insert(VI);
1248 // Create the multiply.
1249 Instruction *V2 = BinaryOperator::CreateMul(V, MaxOccVal, "tmp", I);
1251 // Rerun associate on the multiply in case the inner expression turned into
1252 // a multiply. We want to make sure that we keep things in canonical form.
1253 RedoInsts.insert(V2);
1255 // If every add operand included the factor (e.g. "A*B + A*C"), then the
1256 // entire result expression is just the multiply "A*(B+C)".
1260 // Otherwise, we had some input that didn't have the factor, such as
1261 // "A*B + A*C + D" -> "A*(B+C) + D". Add the new multiply to the list of
1262 // things being added by this operation.
1263 Ops.insert(Ops.begin(), ValueEntry(getRank(V2), V2));
1270 /// \brief Predicate tests whether a ValueEntry's op is in a map.
1271 struct IsValueInMap {
1272 const DenseMap<Value *, unsigned> ⤅
1274 IsValueInMap(const DenseMap<Value *, unsigned> &Map) : Map(Map) {}
1276 bool operator()(const ValueEntry &Entry) {
1277 return Map.find(Entry.Op) != Map.end();
1282 /// \brief Build up a vector of value/power pairs factoring a product.
1284 /// Given a series of multiplication operands, build a vector of factors and
1285 /// the powers each is raised to when forming the final product. Sort them in
1286 /// the order of descending power.
1288 /// (x*x) -> [(x, 2)]
1289 /// ((x*x)*x) -> [(x, 3)]
1290 /// ((((x*y)*x)*y)*x) -> [(x, 3), (y, 2)]
1292 /// \returns Whether any factors have a power greater than one.
1293 bool Reassociate::collectMultiplyFactors(SmallVectorImpl<ValueEntry> &Ops,
1294 SmallVectorImpl<Factor> &Factors) {
1295 // FIXME: Have Ops be (ValueEntry, Multiplicity) pairs, simplifying this.
1296 // Compute the sum of powers of simplifiable factors.
1297 unsigned FactorPowerSum = 0;
1298 for (unsigned Idx = 1, Size = Ops.size(); Idx < Size; ++Idx) {
1299 Value *Op = Ops[Idx-1].Op;
1301 // Count the number of occurrences of this value.
1303 for (; Idx < Size && Ops[Idx].Op == Op; ++Idx)
1305 // Track for simplification all factors which occur 2 or more times.
1307 FactorPowerSum += Count;
1310 // We can only simplify factors if the sum of the powers of our simplifiable
1311 // factors is 4 or higher. When that is the case, we will *always* have
1312 // a simplification. This is an important invariant to prevent cyclicly
1313 // trying to simplify already minimal formations.
1314 if (FactorPowerSum < 4)
1317 // Now gather the simplifiable factors, removing them from Ops.
1319 for (unsigned Idx = 1; Idx < Ops.size(); ++Idx) {
1320 Value *Op = Ops[Idx-1].Op;
1322 // Count the number of occurrences of this value.
1324 for (; Idx < Ops.size() && Ops[Idx].Op == Op; ++Idx)
1328 // Move an even number of occurrences to Factors.
1331 FactorPowerSum += Count;
1332 Factors.push_back(Factor(Op, Count));
1333 Ops.erase(Ops.begin()+Idx, Ops.begin()+Idx+Count);
1336 // None of the adjustments above should have reduced the sum of factor powers
1337 // below our mininum of '4'.
1338 assert(FactorPowerSum >= 4);
1340 std::sort(Factors.begin(), Factors.end(), Factor::PowerDescendingSorter());
1344 /// \brief Build a tree of multiplies, computing the product of Ops.
1345 static Value *buildMultiplyTree(IRBuilder<> &Builder,
1346 SmallVectorImpl<Value*> &Ops) {
1347 if (Ops.size() == 1)
1350 Value *LHS = Ops.pop_back_val();
1352 LHS = Builder.CreateMul(LHS, Ops.pop_back_val());
1353 } while (!Ops.empty());
1358 /// \brief Build a minimal multiplication DAG for (a^x)*(b^y)*(c^z)*...
1360 /// Given a vector of values raised to various powers, where no two values are
1361 /// equal and the powers are sorted in decreasing order, compute the minimal
1362 /// DAG of multiplies to compute the final product, and return that product
1364 Value *Reassociate::buildMinimalMultiplyDAG(IRBuilder<> &Builder,
1365 SmallVectorImpl<Factor> &Factors) {
1366 assert(Factors[0].Power);
1367 SmallVector<Value *, 4> OuterProduct;
1368 for (unsigned LastIdx = 0, Idx = 1, Size = Factors.size();
1369 Idx < Size && Factors[Idx].Power > 0; ++Idx) {
1370 if (Factors[Idx].Power != Factors[LastIdx].Power) {
1375 // We want to multiply across all the factors with the same power so that
1376 // we can raise them to that power as a single entity. Build a mini tree
1378 SmallVector<Value *, 4> InnerProduct;
1379 InnerProduct.push_back(Factors[LastIdx].Base);
1381 InnerProduct.push_back(Factors[Idx].Base);
1383 } while (Idx < Size && Factors[Idx].Power == Factors[LastIdx].Power);
1385 // Reset the base value of the first factor to the new expression tree.
1386 // We'll remove all the factors with the same power in a second pass.
1387 Value *M = Factors[LastIdx].Base = buildMultiplyTree(Builder, InnerProduct);
1388 if (Instruction *MI = dyn_cast<Instruction>(M))
1389 RedoInsts.insert(MI);
1393 // Unique factors with equal powers -- we've folded them into the first one's
1395 Factors.erase(std::unique(Factors.begin(), Factors.end(),
1396 Factor::PowerEqual()),
1399 // Iteratively collect the base of each factor with an add power into the
1400 // outer product, and halve each power in preparation for squaring the
1402 for (unsigned Idx = 0, Size = Factors.size(); Idx != Size; ++Idx) {
1403 if (Factors[Idx].Power & 1)
1404 OuterProduct.push_back(Factors[Idx].Base);
1405 Factors[Idx].Power >>= 1;
1407 if (Factors[0].Power) {
1408 Value *SquareRoot = buildMinimalMultiplyDAG(Builder, Factors);
1409 OuterProduct.push_back(SquareRoot);
1410 OuterProduct.push_back(SquareRoot);
1412 if (OuterProduct.size() == 1)
1413 return OuterProduct.front();
1415 Value *V = buildMultiplyTree(Builder, OuterProduct);
1419 Value *Reassociate::OptimizeMul(BinaryOperator *I,
1420 SmallVectorImpl<ValueEntry> &Ops) {
1421 // We can only optimize the multiplies when there is a chain of more than
1422 // three, such that a balanced tree might require fewer total multiplies.
1426 // Try to turn linear trees of multiplies without other uses of the
1427 // intermediate stages into minimal multiply DAGs with perfect sub-expression
1429 SmallVector<Factor, 4> Factors;
1430 if (!collectMultiplyFactors(Ops, Factors))
1431 return 0; // All distinct factors, so nothing left for us to do.
1433 IRBuilder<> Builder(I);
1434 Value *V = buildMinimalMultiplyDAG(Builder, Factors);
1438 ValueEntry NewEntry = ValueEntry(getRank(V), V);
1439 Ops.insert(std::lower_bound(Ops.begin(), Ops.end(), NewEntry), NewEntry);
1443 Value *Reassociate::OptimizeExpression(BinaryOperator *I,
1444 SmallVectorImpl<ValueEntry> &Ops) {
1445 // Now that we have the linearized expression tree, try to optimize it.
1446 // Start by folding any constants that we found.
1447 if (Ops.size() == 1) return Ops[0].Op;
1449 unsigned Opcode = I->getOpcode();
1451 // Handle destructive annihilation due to identities between elements in the
1452 // argument list here.
1453 unsigned NumOps = Ops.size();
1456 case Instruction::And:
1457 case Instruction::Or:
1458 case Instruction::Xor:
1459 if (Value *Result = OptimizeAndOrXor(Opcode, Ops))
1463 case Instruction::Add:
1464 if (Value *Result = OptimizeAdd(I, Ops))
1468 case Instruction::Mul:
1469 if (Value *Result = OptimizeMul(I, Ops))
1474 if (Ops.size() != NumOps)
1475 return OptimizeExpression(I, Ops);
1479 /// EraseInst - Zap the given instruction, adding interesting operands to the
1481 void Reassociate::EraseInst(Instruction *I) {
1482 assert(isInstructionTriviallyDead(I) && "Trivially dead instructions only!");
1483 SmallVector<Value*, 8> Ops(I->op_begin(), I->op_end());
1484 // Erase the dead instruction.
1485 ValueRankMap.erase(I);
1486 RedoInsts.remove(I);
1487 I->eraseFromParent();
1488 // Optimize its operands.
1489 SmallPtrSet<Instruction *, 8> Visited; // Detect self-referential nodes.
1490 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1491 if (Instruction *Op = dyn_cast<Instruction>(Ops[i])) {
1492 // If this is a node in an expression tree, climb to the expression root
1493 // and add that since that's where optimization actually happens.
1494 unsigned Opcode = Op->getOpcode();
1495 while (Op->hasOneUse() && Op->use_back()->getOpcode() == Opcode &&
1497 Op = Op->use_back();
1498 RedoInsts.insert(Op);
1502 /// OptimizeInst - Inspect and optimize the given instruction. Note that erasing
1503 /// instructions is not allowed.
1504 void Reassociate::OptimizeInst(Instruction *I) {
1505 // Only consider operations that we understand.
1506 if (!isa<BinaryOperator>(I))
1509 if (I->getOpcode() == Instruction::Shl &&
1510 isa<ConstantInt>(I->getOperand(1)))
1511 // If an operand of this shift is a reassociable multiply, or if the shift
1512 // is used by a reassociable multiply or add, turn into a multiply.
1513 if (isReassociableOp(I->getOperand(0), Instruction::Mul) ||
1515 (isReassociableOp(I->use_back(), Instruction::Mul) ||
1516 isReassociableOp(I->use_back(), Instruction::Add)))) {
1517 Instruction *NI = ConvertShiftToMul(I);
1518 RedoInsts.insert(I);
1523 // Floating point binary operators are not associative, but we can still
1524 // commute (some) of them, to canonicalize the order of their operands.
1525 // This can potentially expose more CSE opportunities, and makes writing
1526 // other transformations simpler.
1527 if ((I->getType()->isFloatingPointTy() || I->getType()->isVectorTy())) {
1528 // FAdd and FMul can be commuted.
1529 if (I->getOpcode() != Instruction::FMul &&
1530 I->getOpcode() != Instruction::FAdd)
1533 Value *LHS = I->getOperand(0);
1534 Value *RHS = I->getOperand(1);
1535 unsigned LHSRank = getRank(LHS);
1536 unsigned RHSRank = getRank(RHS);
1538 // Sort the operands by rank.
1539 if (RHSRank < LHSRank) {
1540 I->setOperand(0, RHS);
1541 I->setOperand(1, LHS);
1547 // Do not reassociate boolean (i1) expressions. We want to preserve the
1548 // original order of evaluation for short-circuited comparisons that
1549 // SimplifyCFG has folded to AND/OR expressions. If the expression
1550 // is not further optimized, it is likely to be transformed back to a
1551 // short-circuited form for code gen, and the source order may have been
1552 // optimized for the most likely conditions.
1553 if (I->getType()->isIntegerTy(1))
1556 // If this is a subtract instruction which is not already in negate form,
1557 // see if we can convert it to X+-Y.
1558 if (I->getOpcode() == Instruction::Sub) {
1559 if (ShouldBreakUpSubtract(I)) {
1560 Instruction *NI = BreakUpSubtract(I);
1561 RedoInsts.insert(I);
1564 } else if (BinaryOperator::isNeg(I)) {
1565 // Otherwise, this is a negation. See if the operand is a multiply tree
1566 // and if this is not an inner node of a multiply tree.
1567 if (isReassociableOp(I->getOperand(1), Instruction::Mul) &&
1569 !isReassociableOp(I->use_back(), Instruction::Mul))) {
1570 Instruction *NI = LowerNegateToMultiply(I);
1571 RedoInsts.insert(I);
1578 // If this instruction is an associative binary operator, process it.
1579 if (!I->isAssociative()) return;
1580 BinaryOperator *BO = cast<BinaryOperator>(I);
1582 // If this is an interior node of a reassociable tree, ignore it until we
1583 // get to the root of the tree, to avoid N^2 analysis.
1584 if (BO->hasOneUse() && BO->use_back()->getOpcode() == BO->getOpcode())
1587 // If this is an add tree that is used by a sub instruction, ignore it
1588 // until we process the subtract.
1589 if (BO->hasOneUse() && BO->getOpcode() == Instruction::Add &&
1590 cast<Instruction>(BO->use_back())->getOpcode() == Instruction::Sub)
1593 ReassociateExpression(BO);
1596 void Reassociate::ReassociateExpression(BinaryOperator *I) {
1598 // First, walk the expression tree, linearizing the tree, collecting the
1599 // operand information.
1600 SmallVector<RepeatedValue, 8> Tree;
1601 MadeChange |= LinearizeExprTree(I, Tree);
1602 SmallVector<ValueEntry, 8> Ops;
1603 Ops.reserve(Tree.size());
1604 for (unsigned i = 0, e = Tree.size(); i != e; ++i) {
1605 RepeatedValue E = Tree[i];
1606 Ops.append(E.second.getZExtValue(),
1607 ValueEntry(getRank(E.first), E.first));
1610 DEBUG(dbgs() << "RAIn:\t"; PrintOps(I, Ops); dbgs() << '\n');
1612 // Now that we have linearized the tree to a list and have gathered all of
1613 // the operands and their ranks, sort the operands by their rank. Use a
1614 // stable_sort so that values with equal ranks will have their relative
1615 // positions maintained (and so the compiler is deterministic). Note that
1616 // this sorts so that the highest ranking values end up at the beginning of
1618 std::stable_sort(Ops.begin(), Ops.end());
1620 // OptimizeExpression - Now that we have the expression tree in a convenient
1621 // sorted form, optimize it globally if possible.
1622 if (Value *V = OptimizeExpression(I, Ops)) {
1624 // Self-referential expression in unreachable code.
1626 // This expression tree simplified to something that isn't a tree,
1628 DEBUG(dbgs() << "Reassoc to scalar: " << *V << '\n');
1629 I->replaceAllUsesWith(V);
1630 if (Instruction *VI = dyn_cast<Instruction>(V))
1631 VI->setDebugLoc(I->getDebugLoc());
1632 RedoInsts.insert(I);
1637 // We want to sink immediates as deeply as possible except in the case where
1638 // this is a multiply tree used only by an add, and the immediate is a -1.
1639 // In this case we reassociate to put the negation on the outside so that we
1640 // can fold the negation into the add: (-X)*Y + Z -> Z-X*Y
1641 if (I->getOpcode() == Instruction::Mul && I->hasOneUse() &&
1642 cast<Instruction>(I->use_back())->getOpcode() == Instruction::Add &&
1643 isa<ConstantInt>(Ops.back().Op) &&
1644 cast<ConstantInt>(Ops.back().Op)->isAllOnesValue()) {
1645 ValueEntry Tmp = Ops.pop_back_val();
1646 Ops.insert(Ops.begin(), Tmp);
1649 DEBUG(dbgs() << "RAOut:\t"; PrintOps(I, Ops); dbgs() << '\n');
1651 if (Ops.size() == 1) {
1653 // Self-referential expression in unreachable code.
1656 // This expression tree simplified to something that isn't a tree,
1658 I->replaceAllUsesWith(Ops[0].Op);
1659 if (Instruction *OI = dyn_cast<Instruction>(Ops[0].Op))
1660 OI->setDebugLoc(I->getDebugLoc());
1661 RedoInsts.insert(I);
1665 // Now that we ordered and optimized the expressions, splat them back into
1666 // the expression tree, removing any unneeded nodes.
1667 RewriteExprTree(I, Ops);
1670 bool Reassociate::runOnFunction(Function &F) {
1671 // Calculate the rank map for F
1675 for (Function::iterator BI = F.begin(), BE = F.end(); BI != BE; ++BI) {
1676 // Optimize every instruction in the basic block.
1677 for (BasicBlock::iterator II = BI->begin(), IE = BI->end(); II != IE; )
1678 if (isInstructionTriviallyDead(II)) {
1682 assert(II->getParent() == BI && "Moved to a different block!");
1686 // If this produced extra instructions to optimize, handle them now.
1687 while (!RedoInsts.empty()) {
1688 Instruction *I = RedoInsts.pop_back_val();
1689 if (isInstructionTriviallyDead(I))
1696 // We are done with the rank map.
1698 ValueRankMap.clear();