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/Instructions.h"
30 #include "llvm/IntrinsicInst.h"
31 #include "llvm/Pass.h"
32 #include "llvm/Assembly/Writer.h"
33 #include "llvm/Support/CFG.h"
34 #include "llvm/Support/IRBuilder.h"
35 #include "llvm/Support/Debug.h"
36 #include "llvm/Support/ValueHandle.h"
37 #include "llvm/Support/raw_ostream.h"
38 #include "llvm/ADT/DenseMap.h"
39 #include "llvm/ADT/PostOrderIterator.h"
40 #include "llvm/ADT/SetVector.h"
41 #include "llvm/ADT/SmallMap.h"
42 #include "llvm/ADT/STLExtras.h"
43 #include "llvm/ADT/Statistic.h"
47 STATISTIC(NumChanged, "Number of insts reassociated");
48 STATISTIC(NumAnnihil, "Number of expr tree annihilated");
49 STATISTIC(NumFactor , "Number of multiplies factored");
55 ValueEntry(unsigned R, Value *O) : Rank(R), Op(O) {}
57 inline bool operator<(const ValueEntry &LHS, const ValueEntry &RHS) {
58 return LHS.Rank > RHS.Rank; // Sort so that highest rank goes to start.
63 /// PrintOps - Print out the expression identified in the Ops list.
65 static void PrintOps(Instruction *I, const SmallVectorImpl<ValueEntry> &Ops) {
66 Module *M = I->getParent()->getParent()->getParent();
67 dbgs() << Instruction::getOpcodeName(I->getOpcode()) << " "
68 << *Ops[0].Op->getType() << '\t';
69 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
71 WriteAsOperand(dbgs(), Ops[i].Op, false, M);
72 dbgs() << ", #" << Ops[i].Rank << "] ";
78 /// \brief Utility class representing a base and exponent pair which form one
79 /// factor of some product.
84 Factor(Value *Base, unsigned Power) : Base(Base), Power(Power) {}
86 /// \brief Sort factors by their Base.
88 bool operator()(const Factor &LHS, const Factor &RHS) {
89 return LHS.Base < RHS.Base;
93 /// \brief Compare factors for equal bases.
95 bool operator()(const Factor &LHS, const Factor &RHS) {
96 return LHS.Base == RHS.Base;
100 /// \brief Sort factors in descending order by their power.
101 struct PowerDescendingSorter {
102 bool operator()(const Factor &LHS, const Factor &RHS) {
103 return LHS.Power > RHS.Power;
107 /// \brief Compare factors for equal powers.
109 bool operator()(const Factor &LHS, const Factor &RHS) {
110 return LHS.Power == RHS.Power;
117 class Reassociate : public FunctionPass {
118 DenseMap<BasicBlock*, unsigned> RankMap;
119 DenseMap<AssertingVH<Value>, unsigned> ValueRankMap;
120 SetVector<AssertingVH<Instruction> > RedoInsts;
123 static char ID; // Pass identification, replacement for typeid
124 Reassociate() : FunctionPass(ID) {
125 initializeReassociatePass(*PassRegistry::getPassRegistry());
128 bool runOnFunction(Function &F);
130 virtual void getAnalysisUsage(AnalysisUsage &AU) const {
131 AU.setPreservesCFG();
134 void BuildRankMap(Function &F);
135 unsigned getRank(Value *V);
136 Value *ReassociateExpression(BinaryOperator *I);
137 void RewriteExprTree(BinaryOperator *I, SmallVectorImpl<ValueEntry> &Ops);
138 Value *OptimizeExpression(BinaryOperator *I,
139 SmallVectorImpl<ValueEntry> &Ops);
140 Value *OptimizeAdd(Instruction *I, SmallVectorImpl<ValueEntry> &Ops);
141 bool collectMultiplyFactors(SmallVectorImpl<ValueEntry> &Ops,
142 SmallVectorImpl<Factor> &Factors);
143 Value *buildMinimalMultiplyDAG(IRBuilder<> &Builder,
144 SmallVectorImpl<Factor> &Factors);
145 Value *OptimizeMul(BinaryOperator *I, SmallVectorImpl<ValueEntry> &Ops);
146 Value *RemoveFactorFromExpression(Value *V, Value *Factor);
147 void EraseInst(Instruction *I);
148 void OptimizeInst(Instruction *I);
152 char Reassociate::ID = 0;
153 INITIALIZE_PASS(Reassociate, "reassociate",
154 "Reassociate expressions", false, false)
156 // Public interface to the Reassociate pass
157 FunctionPass *llvm::createReassociatePass() { return new Reassociate(); }
159 /// isReassociableOp - Return true if V is an instruction of the specified
160 /// opcode and if it only has one use.
161 static BinaryOperator *isReassociableOp(Value *V, unsigned Opcode) {
162 if (V->hasOneUse() && isa<Instruction>(V) &&
163 cast<Instruction>(V)->getOpcode() == Opcode)
164 return cast<BinaryOperator>(V);
168 static bool isUnmovableInstruction(Instruction *I) {
169 if (I->getOpcode() == Instruction::PHI ||
170 I->getOpcode() == Instruction::LandingPad ||
171 I->getOpcode() == Instruction::Alloca ||
172 I->getOpcode() == Instruction::Load ||
173 I->getOpcode() == Instruction::Invoke ||
174 (I->getOpcode() == Instruction::Call &&
175 !isa<DbgInfoIntrinsic>(I)) ||
176 I->getOpcode() == Instruction::UDiv ||
177 I->getOpcode() == Instruction::SDiv ||
178 I->getOpcode() == Instruction::FDiv ||
179 I->getOpcode() == Instruction::URem ||
180 I->getOpcode() == Instruction::SRem ||
181 I->getOpcode() == Instruction::FRem)
186 void Reassociate::BuildRankMap(Function &F) {
189 // Assign distinct ranks to function arguments
190 for (Function::arg_iterator I = F.arg_begin(), E = F.arg_end(); I != E; ++I)
191 ValueRankMap[&*I] = ++i;
193 ReversePostOrderTraversal<Function*> RPOT(&F);
194 for (ReversePostOrderTraversal<Function*>::rpo_iterator I = RPOT.begin(),
195 E = RPOT.end(); I != E; ++I) {
197 unsigned BBRank = RankMap[BB] = ++i << 16;
199 // Walk the basic block, adding precomputed ranks for any instructions that
200 // we cannot move. This ensures that the ranks for these instructions are
201 // all different in the block.
202 for (BasicBlock::iterator I = BB->begin(), E = BB->end(); I != E; ++I)
203 if (isUnmovableInstruction(I))
204 ValueRankMap[&*I] = ++BBRank;
208 unsigned Reassociate::getRank(Value *V) {
209 Instruction *I = dyn_cast<Instruction>(V);
211 if (isa<Argument>(V)) return ValueRankMap[V]; // Function argument.
212 return 0; // Otherwise it's a global or constant, rank 0.
215 if (unsigned Rank = ValueRankMap[I])
216 return Rank; // Rank already known?
218 // If this is an expression, return the 1+MAX(rank(LHS), rank(RHS)) so that
219 // we can reassociate expressions for code motion! Since we do not recurse
220 // for PHI nodes, we cannot have infinite recursion here, because there
221 // cannot be loops in the value graph that do not go through PHI nodes.
222 unsigned Rank = 0, MaxRank = RankMap[I->getParent()];
223 for (unsigned i = 0, e = I->getNumOperands();
224 i != e && Rank != MaxRank; ++i)
225 Rank = std::max(Rank, getRank(I->getOperand(i)));
227 // If this is a not or neg instruction, do not count it for rank. This
228 // assures us that X and ~X will have the same rank.
229 if (!I->getType()->isIntegerTy() ||
230 (!BinaryOperator::isNot(I) && !BinaryOperator::isNeg(I)))
233 //DEBUG(dbgs() << "Calculated Rank[" << V->getName() << "] = "
236 return ValueRankMap[I] = Rank;
239 /// LowerNegateToMultiply - Replace 0-X with X*-1.
241 static BinaryOperator *LowerNegateToMultiply(Instruction *Neg) {
242 Constant *Cst = Constant::getAllOnesValue(Neg->getType());
244 BinaryOperator *Res =
245 BinaryOperator::CreateMul(Neg->getOperand(1), Cst, "",Neg);
246 Neg->setOperand(1, Constant::getNullValue(Neg->getType())); // Drop use of op.
248 Neg->replaceAllUsesWith(Res);
249 Res->setDebugLoc(Neg->getDebugLoc());
253 /// CarmichaelShift - Returns k such that lambda(2^Bitwidth) = 2^k, where lambda
254 /// is the Carmichael function. This means that x^(2^k) === 1 mod 2^Bitwidth for
255 /// every odd x, i.e. x^(2^k) = 1 for every odd x in Bitwidth-bit arithmetic.
256 /// Note that 0 <= k < Bitwidth, and if Bitwidth > 3 then x^(2^k) = 0 for every
257 /// even x in Bitwidth-bit arithmetic.
258 static unsigned CarmichaelShift(unsigned Bitwidth) {
264 /// IncorporateWeight - Add the extra weight 'RHS' to the existing weight 'LHS',
265 /// reducing the combined weight using any special properties of the operation.
266 /// The existing weight LHS represents the computation X op X op ... op X where
267 /// X occurs LHS times. The combined weight represents X op X op ... op X with
268 /// X occurring LHS + RHS times. If op is "Xor" for example then the combined
269 /// operation is equivalent to X if LHS + RHS is odd, or 0 if LHS + RHS is even;
270 /// the routine returns 1 in LHS in the first case, and 0 in LHS in the second.
271 static void IncorporateWeight(APInt &LHS, const APInt &RHS, unsigned Opcode) {
272 // If we were working with infinite precision arithmetic then the combined
273 // weight would be LHS + RHS. But we are using finite precision arithmetic,
274 // and the APInt sum LHS + RHS may not be correct if it wraps (it is correct
275 // for nilpotent operations and addition, but not for idempotent operations
276 // and multiplication), so it is important to correctly reduce the combined
277 // weight back into range if wrapping would be wrong.
279 // If RHS is zero then the weight didn't change.
280 if (RHS.isMinValue())
282 // If LHS is zero then the combined weight is RHS.
283 if (LHS.isMinValue()) {
287 // From this point on we know that neither LHS nor RHS is zero.
289 if (Instruction::isIdempotent(Opcode)) {
290 // Idempotent means X op X === X, so any non-zero weight is equivalent to a
291 // weight of 1. Keeping weights at zero or one also means that wrapping is
293 assert(LHS == 1 && RHS == 1 && "Weights not reduced!");
294 return; // Return a weight of 1.
296 if (Instruction::isNilpotent(Opcode)) {
297 // Nilpotent means X op X === 0, so reduce weights modulo 2.
298 assert(LHS == 1 && RHS == 1 && "Weights not reduced!");
299 LHS = 0; // 1 + 1 === 0 modulo 2.
302 if (Opcode == Instruction::Add) {
303 // TODO: Reduce the weight by exploiting nsw/nuw?
308 assert(Opcode == Instruction::Mul && "Unknown associative operation!");
309 unsigned Bitwidth = LHS.getBitWidth();
310 // If CM is the Carmichael number then a weight W satisfying W >= CM+Bitwidth
311 // can be replaced with W-CM. That's because x^W=x^(W-CM) for every Bitwidth
312 // bit number x, since either x is odd in which case x^CM = 1, or x is even in
313 // which case both x^W and x^(W - CM) are zero. By subtracting off multiples
314 // of CM like this weights can always be reduced to the range [0, CM+Bitwidth)
315 // which by a happy accident means that they can always be represented using
317 // TODO: Reduce the weight by exploiting nsw/nuw? (Could do much better than
318 // the Carmichael number).
320 /// CM - The value of Carmichael's lambda function.
321 APInt CM = APInt::getOneBitSet(Bitwidth, CarmichaelShift(Bitwidth));
322 // Any weight W >= Threshold can be replaced with W - CM.
323 APInt Threshold = CM + Bitwidth;
324 assert(LHS.ult(Threshold) && RHS.ult(Threshold) && "Weights not reduced!");
325 // For Bitwidth 4 or more the following sum does not overflow.
327 while (LHS.uge(Threshold))
330 // To avoid problems with overflow do everything the same as above but using
332 unsigned CM = 1U << CarmichaelShift(Bitwidth);
333 unsigned Threshold = CM + Bitwidth;
334 assert(LHS.getZExtValue() < Threshold && RHS.getZExtValue() < Threshold &&
335 "Weights not reduced!");
336 unsigned Total = LHS.getZExtValue() + RHS.getZExtValue();
337 while (Total >= Threshold)
343 /// EvaluateRepeatedConstant - Compute C op C op ... op C where the constant C
344 /// is repeated Weight times.
345 static Constant *EvaluateRepeatedConstant(unsigned Opcode, Constant *C,
347 // For addition the result can be efficiently computed as the product of the
348 // constant and the weight.
349 if (Opcode == Instruction::Add)
350 return ConstantExpr::getMul(C, ConstantInt::get(C->getContext(), Weight));
352 // The weight might be huge, so compute by repeated squaring to ensure that
353 // compile time is proportional to the logarithm of the weight.
354 Constant *Result = 0;
355 Constant *Power = C; // Successively C, C op C, (C op C) op (C op C) etc.
356 // Visit the bits in Weight.
357 while (Weight != 0) {
358 // If the current bit in Weight is non-zero do Result = Result op Power.
360 Result = Result ? ConstantExpr::get(Opcode, Result, Power) : Power;
361 // Move on to the next bit if any more are non-zero.
362 Weight = Weight.lshr(1);
363 if (Weight.isMinValue())
366 Power = ConstantExpr::get(Opcode, Power, Power);
369 assert(Result && "Only positive weights supported!");
373 typedef std::pair<Value*, APInt> RepeatedValue;
375 /// LinearizeExprTree - Given an associative binary expression, return the leaf
376 /// nodes in Ops along with their weights (how many times the leaf occurs). The
377 /// original expression is the same as
378 /// (Ops[0].first op Ops[0].first op ... Ops[0].first) <- Ops[0].second times
380 /// (Ops[1].first op Ops[1].first op ... Ops[1].first) <- Ops[1].second times
384 /// (Ops[N].first op Ops[N].first op ... Ops[N].first) <- Ops[N].second times
386 /// Note that the values Ops[0].first, ..., Ops[N].first are all distinct, and
387 /// they are all non-constant except possibly for the last one, which if it is
388 /// constant will have weight one (Ops[N].second === 1).
390 /// This routine may modify the function, in which case it returns 'true'. The
391 /// changes it makes may well be destructive, changing the value computed by 'I'
392 /// to something completely different. Thus if the routine returns 'true' then
393 /// you MUST either replace I with a new expression computed from the Ops array,
394 /// or use RewriteExprTree to put the values back in.
396 /// A leaf node is either not a binary operation of the same kind as the root
397 /// node 'I' (i.e. is not a binary operator at all, or is, but with a different
398 /// opcode), or is the same kind of binary operator but has a use which either
399 /// does not belong to the expression, or does belong to the expression but is
400 /// a leaf node. Every leaf node has at least one use that is a non-leaf node
401 /// of the expression, while for non-leaf nodes (except for the root 'I') every
402 /// use is a non-leaf node of the expression.
405 /// expression graph node names
415 /// The leaf nodes are C, E, F and G. The Ops array will contain (maybe not in
416 /// that order) (C, 1), (E, 1), (F, 2), (G, 2).
418 /// The expression is maximal: if some instruction is a binary operator of the
419 /// same kind as 'I', and all of its uses are non-leaf nodes of the expression,
420 /// then the instruction also belongs to the expression, is not a leaf node of
421 /// it, and its operands also belong to the expression (but may be leaf nodes).
423 /// NOTE: This routine will set operands of non-leaf non-root nodes to undef in
424 /// order to ensure that every non-root node in the expression has *exactly one*
425 /// use by a non-leaf node of the expression. This destruction means that the
426 /// caller MUST either replace 'I' with a new expression or use something like
427 /// RewriteExprTree to put the values back in if the routine indicates that it
428 /// made a change by returning 'true'.
430 /// In the above example either the right operand of A or the left operand of B
431 /// will be replaced by undef. If it is B's operand then this gives:
435 /// + + | A, B - operand of B replaced with undef
441 /// Note that such undef operands can only be reached by passing through 'I'.
442 /// For example, if you visit operands recursively starting from a leaf node
443 /// then you will never see such an undef operand unless you get back to 'I',
444 /// which requires passing through a phi node.
446 /// Note that this routine may also mutate binary operators of the wrong type
447 /// that have all uses inside the expression (i.e. only used by non-leaf nodes
448 /// of the expression) if it can turn them into binary operators of the right
449 /// type and thus make the expression bigger.
451 static bool LinearizeExprTree(BinaryOperator *I,
452 SmallVectorImpl<RepeatedValue> &Ops) {
453 DEBUG(dbgs() << "LINEARIZE: " << *I << '\n');
454 unsigned Bitwidth = I->getType()->getScalarType()->getPrimitiveSizeInBits();
455 unsigned Opcode = I->getOpcode();
456 assert(Instruction::isAssociative(Opcode) &&
457 Instruction::isCommutative(Opcode) &&
458 "Expected an associative and commutative operation!");
460 // Visit all operands of the expression, keeping track of their weight (the
461 // number of paths from the expression root to the operand, or if you like
462 // the number of times that operand occurs in the linearized expression).
463 // For example, if I = X + A, where X = A + B, then I, X and B have weight 1
464 // while A has weight two.
466 // Worklist of non-leaf nodes (their operands are in the expression too) along
467 // with their weights, representing a certain number of paths to the operator.
468 // If an operator occurs in the worklist multiple times then we found multiple
469 // ways to get to it.
470 SmallVector<std::pair<BinaryOperator*, APInt>, 8> Worklist; // (Op, Weight)
471 Worklist.push_back(std::make_pair(I, APInt(Bitwidth, 1)));
472 bool MadeChange = false;
474 // Leaves of the expression are values that either aren't the right kind of
475 // operation (eg: a constant, or a multiply in an add tree), or are, but have
476 // some uses that are not inside the expression. For example, in I = X + X,
477 // X = A + B, the value X has two uses (by I) that are in the expression. If
478 // X has any other uses, for example in a return instruction, then we consider
479 // X to be a leaf, and won't analyze it further. When we first visit a value,
480 // if it has more than one use then at first we conservatively consider it to
481 // be a leaf. Later, as the expression is explored, we may discover some more
482 // uses of the value from inside the expression. If all uses turn out to be
483 // from within the expression (and the value is a binary operator of the right
484 // kind) then the value is no longer considered to be a leaf, and its operands
487 // Leaves - Keeps track of the set of putative leaves as well as the number of
488 // paths to each leaf seen so far.
489 typedef SmallMap<Value*, APInt, 8> LeafMap;
490 LeafMap Leaves; // Leaf -> Total weight so far.
491 SmallVector<Value*, 8> LeafOrder; // Ensure deterministic leaf output order.
494 SmallPtrSet<Value*, 8> Visited; // For sanity checking the iteration scheme.
496 while (!Worklist.empty()) {
497 std::pair<BinaryOperator*, APInt> P = Worklist.pop_back_val();
498 I = P.first; // We examine the operands of this binary operator.
500 for (unsigned OpIdx = 0; OpIdx < 2; ++OpIdx) { // Visit operands.
501 Value *Op = I->getOperand(OpIdx);
502 APInt Weight = P.second; // Number of paths to this operand.
503 DEBUG(dbgs() << "OPERAND: " << *Op << " (" << Weight << ")\n");
504 assert(!Op->use_empty() && "No uses, so how did we get to it?!");
506 // If this is a binary operation of the right kind with only one use then
507 // add its operands to the expression.
508 if (BinaryOperator *BO = isReassociableOp(Op, Opcode)) {
509 assert(Visited.insert(Op) && "Not first visit!");
510 DEBUG(dbgs() << "DIRECT ADD: " << *Op << " (" << Weight << ")\n");
511 Worklist.push_back(std::make_pair(BO, Weight));
515 // Appears to be a leaf. Is the operand already in the set of leaves?
516 LeafMap::iterator It = Leaves.find(Op);
517 if (It == Leaves.end()) {
518 // Not in the leaf map. Must be the first time we saw this operand.
519 assert(Visited.insert(Op) && "Not first visit!");
520 if (!Op->hasOneUse()) {
521 // This value has uses not accounted for by the expression, so it is
522 // not safe to modify. Mark it as being a leaf.
523 DEBUG(dbgs() << "ADD USES LEAF: " << *Op << " (" << Weight << ")\n");
524 LeafOrder.push_back(Op);
528 // No uses outside the expression, try morphing it.
529 } else if (It != Leaves.end()) {
530 // Already in the leaf map.
531 assert(Visited.count(Op) && "In leaf map but not visited!");
533 // Update the number of paths to the leaf.
534 IncorporateWeight(It->second, Weight, Opcode);
536 // The leaf already has one use from inside the expression. As we want
537 // exactly one such use, drop this new use of the leaf.
538 assert(!Op->hasOneUse() && "Only one use, but we got here twice!");
539 I->setOperand(OpIdx, UndefValue::get(I->getType()));
542 // If the leaf is a binary operation of the right kind and we now see
543 // that its multiple original uses were in fact all by nodes belonging
544 // to the expression, then no longer consider it to be a leaf and add
545 // its operands to the expression.
546 if (BinaryOperator *BO = isReassociableOp(Op, Opcode)) {
547 DEBUG(dbgs() << "UNLEAF: " << *Op << " (" << It->second << ")\n");
548 Worklist.push_back(std::make_pair(BO, It->second));
553 // If we still have uses that are not accounted for by the expression
554 // then it is not safe to modify the value.
555 if (!Op->hasOneUse())
558 // No uses outside the expression, try morphing it.
560 Leaves.erase(It); // Since the value may be morphed below.
563 // At this point we have a value which, first of all, is not a binary
564 // expression of the right kind, and secondly, is only used inside the
565 // expression. This means that it can safely be modified. See if we
566 // can usefully morph it into an expression of the right kind.
567 assert((!isa<Instruction>(Op) ||
568 cast<Instruction>(Op)->getOpcode() != Opcode) &&
569 "Should have been handled above!");
570 assert(Op->hasOneUse() && "Has uses outside the expression tree!");
572 // If this is a multiply expression, turn any internal negations into
573 // multiplies by -1 so they can be reassociated.
574 BinaryOperator *BO = dyn_cast<BinaryOperator>(Op);
575 if (Opcode == Instruction::Mul && BO && BinaryOperator::isNeg(BO)) {
576 DEBUG(dbgs() << "MORPH LEAF: " << *Op << " (" << Weight << ") TO ");
577 BO = LowerNegateToMultiply(BO);
578 DEBUG(dbgs() << *BO << 'n');
579 Worklist.push_back(std::make_pair(BO, Weight));
584 // Failed to morph into an expression of the right type. This really is
586 DEBUG(dbgs() << "ADD LEAF: " << *Op << " (" << Weight << ")\n");
587 assert(!isReassociableOp(Op, Opcode) && "Value was morphed?");
588 LeafOrder.push_back(Op);
593 // The leaves, repeated according to their weights, represent the linearized
594 // form of the expression.
595 Constant *Cst = 0; // Accumulate constants here.
596 for (unsigned i = 0, e = LeafOrder.size(); i != e; ++i) {
597 Value *V = LeafOrder[i];
598 LeafMap::iterator It = Leaves.find(V);
599 if (It == Leaves.end())
600 // Node initially thought to be a leaf wasn't.
602 assert(!isReassociableOp(V, Opcode) && "Shouldn't be a leaf!");
603 APInt Weight = It->second;
604 if (Weight.isMinValue())
605 // Leaf already output or weight reduction eliminated it.
607 // Ensure the leaf is only output once.
609 // Glob all constants together into Cst.
610 if (Constant *C = dyn_cast<Constant>(V)) {
611 C = EvaluateRepeatedConstant(Opcode, C, Weight);
612 Cst = Cst ? ConstantExpr::get(Opcode, Cst, C) : C;
616 Ops.push_back(std::make_pair(V, Weight));
619 // Add any constants back into Ops, all globbed together and reduced to having
620 // weight 1 for the convenience of users.
621 if (Cst && Cst != ConstantExpr::getBinOpIdentity(Opcode, I->getType()))
622 Ops.push_back(std::make_pair(Cst, APInt(Bitwidth, 1)));
624 // For nilpotent operations or addition there may be no operands, for example
625 // because the expression was "X xor X" or consisted of 2^Bitwidth additions:
626 // in both cases the weight reduces to 0 causing the value to be skipped.
628 Constant *Identity = ConstantExpr::getBinOpIdentity(Opcode, I->getType());
629 Ops.push_back(std::make_pair(Identity, APInt(Bitwidth, 1)));
635 // RewriteExprTree - Now that the operands for this expression tree are
636 // linearized and optimized, emit them in-order.
637 void Reassociate::RewriteExprTree(BinaryOperator *I,
638 SmallVectorImpl<ValueEntry> &Ops) {
639 assert(Ops.size() > 1 && "Single values should be used directly!");
641 // Since our optimizations never increase the number of operations, the new
642 // expression can always be written by reusing the existing binary operators
643 // from the original expression tree, without creating any new instructions,
644 // though the rewritten expression may have a completely different topology.
645 // We take care to not change anything if the new expression will be the same
646 // as the original. If more than trivial changes (like commuting operands)
647 // were made then we are obliged to clear out any optional subclass data like
650 /// NodesToRewrite - Nodes from the original expression available for writing
651 /// the new expression into.
652 SmallVector<BinaryOperator*, 8> NodesToRewrite;
653 unsigned Opcode = I->getOpcode();
654 NodesToRewrite.push_back(I);
656 // ExpressionChanged - Non-null if the rewritten expression differs from the
657 // original in some non-trivial way, requiring the clearing of optional flags.
658 // Flags are cleared from the operator in ExpressionChanged up to I inclusive.
659 BinaryOperator *ExpressionChanged = 0;
660 BinaryOperator *Previous;
661 BinaryOperator *Op = 0;
662 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
663 assert(!NodesToRewrite.empty() &&
664 "Optimized expressions has more nodes than original!");
665 Previous = Op; Op = NodesToRewrite.pop_back_val();
666 if (ExpressionChanged)
667 // Compactify the tree instructions together with each other to guarantee
668 // that the expression tree is dominated by all of Ops.
669 Op->moveBefore(Previous);
671 // The last operation (which comes earliest in the IR) is special as both
672 // operands will come from Ops, rather than just one with the other being
674 if (i+2 == Ops.size()) {
675 Value *NewLHS = Ops[i].Op;
676 Value *NewRHS = Ops[i+1].Op;
677 Value *OldLHS = Op->getOperand(0);
678 Value *OldRHS = Op->getOperand(1);
680 if (NewLHS == OldLHS && NewRHS == OldRHS)
681 // Nothing changed, leave it alone.
684 if (NewLHS == OldRHS && NewRHS == OldLHS) {
685 // The order of the operands was reversed. Swap them.
686 DEBUG(dbgs() << "RA: " << *Op << '\n');
688 DEBUG(dbgs() << "TO: " << *Op << '\n');
694 // The new operation differs non-trivially from the original. Overwrite
695 // the old operands with the new ones.
696 DEBUG(dbgs() << "RA: " << *Op << '\n');
697 if (NewLHS != OldLHS) {
698 if (BinaryOperator *BO = isReassociableOp(OldLHS, Opcode))
699 NodesToRewrite.push_back(BO);
700 Op->setOperand(0, NewLHS);
702 if (NewRHS != OldRHS) {
703 if (BinaryOperator *BO = isReassociableOp(OldRHS, Opcode))
704 NodesToRewrite.push_back(BO);
705 Op->setOperand(1, NewRHS);
707 DEBUG(dbgs() << "TO: " << *Op << '\n');
709 ExpressionChanged = Op;
716 // Not the last operation. The left-hand side will be a sub-expression
717 // while the right-hand side will be the current element of Ops.
718 Value *NewRHS = Ops[i].Op;
719 if (NewRHS != Op->getOperand(1)) {
720 DEBUG(dbgs() << "RA: " << *Op << '\n');
721 if (NewRHS == Op->getOperand(0)) {
722 // The new right-hand side was already present as the left operand. If
723 // we are lucky then swapping the operands will sort out both of them.
726 // Overwrite with the new right-hand side.
727 if (BinaryOperator *BO = isReassociableOp(Op->getOperand(1), Opcode))
728 NodesToRewrite.push_back(BO);
729 Op->setOperand(1, NewRHS);
730 ExpressionChanged = Op;
732 DEBUG(dbgs() << "TO: " << *Op << '\n');
737 // Now deal with the left-hand side. If this is already an operation node
738 // from the original expression then just rewrite the rest of the expression
740 if (BinaryOperator *BO = isReassociableOp(Op->getOperand(0), Opcode)) {
741 NodesToRewrite.push_back(BO);
745 // Otherwise, grab a spare node from the original expression and use that as
746 // the left-hand side.
747 assert(!NodesToRewrite.empty() &&
748 "Optimized expressions has more nodes than original!");
749 DEBUG(dbgs() << "RA: " << *Op << '\n');
750 Op->setOperand(0, NodesToRewrite.back());
751 DEBUG(dbgs() << "TO: " << *Op << '\n');
752 ExpressionChanged = Op;
757 // If the expression changed non-trivially then clear out all subclass data
758 // starting from the operator specified in ExpressionChanged.
759 if (ExpressionChanged) {
761 ExpressionChanged->clearSubclassOptionalData();
762 if (ExpressionChanged == I)
764 ExpressionChanged = cast<BinaryOperator>(*ExpressionChanged->use_begin());
768 // Throw away any left over nodes from the original expression.
769 for (unsigned i = 0, e = NodesToRewrite.size(); i != e; ++i)
770 RedoInsts.insert(NodesToRewrite[i]);
773 /// NegateValue - Insert instructions before the instruction pointed to by BI,
774 /// that computes the negative version of the value specified. The negative
775 /// version of the value is returned, and BI is left pointing at the instruction
776 /// that should be processed next by the reassociation pass.
777 static Value *NegateValue(Value *V, Instruction *BI) {
778 if (Constant *C = dyn_cast<Constant>(V))
779 return ConstantExpr::getNeg(C);
781 // We are trying to expose opportunity for reassociation. One of the things
782 // that we want to do to achieve this is to push a negation as deep into an
783 // expression chain as possible, to expose the add instructions. In practice,
784 // this means that we turn this:
785 // X = -(A+12+C+D) into X = -A + -12 + -C + -D = -12 + -A + -C + -D
786 // so that later, a: Y = 12+X could get reassociated with the -12 to eliminate
787 // the constants. We assume that instcombine will clean up the mess later if
788 // we introduce tons of unnecessary negation instructions.
790 if (BinaryOperator *I = isReassociableOp(V, Instruction::Add)) {
791 // Push the negates through the add.
792 I->setOperand(0, NegateValue(I->getOperand(0), BI));
793 I->setOperand(1, NegateValue(I->getOperand(1), BI));
795 // We must move the add instruction here, because the neg instructions do
796 // not dominate the old add instruction in general. By moving it, we are
797 // assured that the neg instructions we just inserted dominate the
798 // instruction we are about to insert after them.
801 I->setName(I->getName()+".neg");
805 // Okay, we need to materialize a negated version of V with an instruction.
806 // Scan the use lists of V to see if we have one already.
807 for (Value::use_iterator UI = V->use_begin(), E = V->use_end(); UI != E;++UI){
809 if (!BinaryOperator::isNeg(U)) continue;
811 // We found one! Now we have to make sure that the definition dominates
812 // this use. We do this by moving it to the entry block (if it is a
813 // non-instruction value) or right after the definition. These negates will
814 // be zapped by reassociate later, so we don't need much finesse here.
815 BinaryOperator *TheNeg = cast<BinaryOperator>(U);
817 // Verify that the negate is in this function, V might be a constant expr.
818 if (TheNeg->getParent()->getParent() != BI->getParent()->getParent())
821 BasicBlock::iterator InsertPt;
822 if (Instruction *InstInput = dyn_cast<Instruction>(V)) {
823 if (InvokeInst *II = dyn_cast<InvokeInst>(InstInput)) {
824 InsertPt = II->getNormalDest()->begin();
826 InsertPt = InstInput;
829 while (isa<PHINode>(InsertPt)) ++InsertPt;
831 InsertPt = TheNeg->getParent()->getParent()->getEntryBlock().begin();
833 TheNeg->moveBefore(InsertPt);
837 // Insert a 'neg' instruction that subtracts the value from zero to get the
839 return BinaryOperator::CreateNeg(V, V->getName() + ".neg", BI);
842 /// ShouldBreakUpSubtract - Return true if we should break up this subtract of
843 /// X-Y into (X + -Y).
844 static bool ShouldBreakUpSubtract(Instruction *Sub) {
845 // If this is a negation, we can't split it up!
846 if (BinaryOperator::isNeg(Sub))
849 // Don't bother to break this up unless either the LHS is an associable add or
850 // subtract or if this is only used by one.
851 if (isReassociableOp(Sub->getOperand(0), Instruction::Add) ||
852 isReassociableOp(Sub->getOperand(0), Instruction::Sub))
854 if (isReassociableOp(Sub->getOperand(1), Instruction::Add) ||
855 isReassociableOp(Sub->getOperand(1), Instruction::Sub))
857 if (Sub->hasOneUse() &&
858 (isReassociableOp(Sub->use_back(), Instruction::Add) ||
859 isReassociableOp(Sub->use_back(), Instruction::Sub)))
865 /// BreakUpSubtract - If we have (X-Y), and if either X is an add, or if this is
866 /// only used by an add, transform this into (X+(0-Y)) to promote better
868 static BinaryOperator *BreakUpSubtract(Instruction *Sub) {
869 // Convert a subtract into an add and a neg instruction. This allows sub
870 // instructions to be commuted with other add instructions.
872 // Calculate the negative value of Operand 1 of the sub instruction,
873 // and set it as the RHS of the add instruction we just made.
875 Value *NegVal = NegateValue(Sub->getOperand(1), Sub);
876 BinaryOperator *New =
877 BinaryOperator::CreateAdd(Sub->getOperand(0), NegVal, "", Sub);
878 Sub->setOperand(0, Constant::getNullValue(Sub->getType())); // Drop use of op.
879 Sub->setOperand(1, Constant::getNullValue(Sub->getType())); // Drop use of op.
882 // Everyone now refers to the add instruction.
883 Sub->replaceAllUsesWith(New);
884 New->setDebugLoc(Sub->getDebugLoc());
886 DEBUG(dbgs() << "Negated: " << *New << '\n');
890 /// ConvertShiftToMul - If this is a shift of a reassociable multiply or is used
891 /// by one, change this into a multiply by a constant to assist with further
893 static BinaryOperator *ConvertShiftToMul(Instruction *Shl) {
894 Constant *MulCst = ConstantInt::get(Shl->getType(), 1);
895 MulCst = ConstantExpr::getShl(MulCst, cast<Constant>(Shl->getOperand(1)));
897 BinaryOperator *Mul =
898 BinaryOperator::CreateMul(Shl->getOperand(0), MulCst, "", Shl);
899 Shl->setOperand(0, UndefValue::get(Shl->getType())); // Drop use of op.
901 Shl->replaceAllUsesWith(Mul);
902 Mul->setDebugLoc(Shl->getDebugLoc());
906 /// FindInOperandList - Scan backwards and forwards among values with the same
907 /// rank as element i to see if X exists. If X does not exist, return i. This
908 /// is useful when scanning for 'x' when we see '-x' because they both get the
910 static unsigned FindInOperandList(SmallVectorImpl<ValueEntry> &Ops, unsigned i,
912 unsigned XRank = Ops[i].Rank;
913 unsigned e = Ops.size();
914 for (unsigned j = i+1; j != e && Ops[j].Rank == XRank; ++j)
918 for (unsigned j = i-1; j != ~0U && Ops[j].Rank == XRank; --j)
924 /// EmitAddTreeOfValues - Emit a tree of add instructions, summing Ops together
925 /// and returning the result. Insert the tree before I.
926 static Value *EmitAddTreeOfValues(Instruction *I,
927 SmallVectorImpl<WeakVH> &Ops){
928 if (Ops.size() == 1) return Ops.back();
930 Value *V1 = Ops.back();
932 Value *V2 = EmitAddTreeOfValues(I, Ops);
933 return BinaryOperator::CreateAdd(V2, V1, "tmp", I);
936 /// RemoveFactorFromExpression - If V is an expression tree that is a
937 /// multiplication sequence, and if this sequence contains a multiply by Factor,
938 /// remove Factor from the tree and return the new tree.
939 Value *Reassociate::RemoveFactorFromExpression(Value *V, Value *Factor) {
940 BinaryOperator *BO = isReassociableOp(V, Instruction::Mul);
943 SmallVector<RepeatedValue, 8> Tree;
944 MadeChange |= LinearizeExprTree(BO, Tree);
945 SmallVector<ValueEntry, 8> Factors;
946 Factors.reserve(Tree.size());
947 for (unsigned i = 0, e = Tree.size(); i != e; ++i) {
948 RepeatedValue E = Tree[i];
949 Factors.append(E.second.getZExtValue(),
950 ValueEntry(getRank(E.first), E.first));
953 bool FoundFactor = false;
954 bool NeedsNegate = false;
955 for (unsigned i = 0, e = Factors.size(); i != e; ++i) {
956 if (Factors[i].Op == Factor) {
958 Factors.erase(Factors.begin()+i);
962 // If this is a negative version of this factor, remove it.
963 if (ConstantInt *FC1 = dyn_cast<ConstantInt>(Factor))
964 if (ConstantInt *FC2 = dyn_cast<ConstantInt>(Factors[i].Op))
965 if (FC1->getValue() == -FC2->getValue()) {
966 FoundFactor = NeedsNegate = true;
967 Factors.erase(Factors.begin()+i);
973 // Make sure to restore the operands to the expression tree.
974 RewriteExprTree(BO, Factors);
978 BasicBlock::iterator InsertPt = BO; ++InsertPt;
980 // If this was just a single multiply, remove the multiply and return the only
981 // remaining operand.
982 if (Factors.size() == 1) {
983 RedoInsts.insert(BO);
986 RewriteExprTree(BO, Factors);
991 V = BinaryOperator::CreateNeg(V, "neg", InsertPt);
996 /// FindSingleUseMultiplyFactors - If V is a single-use multiply, recursively
997 /// add its operands as factors, otherwise add V to the list of factors.
999 /// Ops is the top-level list of add operands we're trying to factor.
1000 static void FindSingleUseMultiplyFactors(Value *V,
1001 SmallVectorImpl<Value*> &Factors,
1002 const SmallVectorImpl<ValueEntry> &Ops) {
1003 BinaryOperator *BO = isReassociableOp(V, Instruction::Mul);
1005 Factors.push_back(V);
1009 // Otherwise, add the LHS and RHS to the list of factors.
1010 FindSingleUseMultiplyFactors(BO->getOperand(1), Factors, Ops);
1011 FindSingleUseMultiplyFactors(BO->getOperand(0), Factors, Ops);
1014 /// OptimizeAndOrXor - Optimize a series of operands to an 'and', 'or', or 'xor'
1015 /// instruction. This optimizes based on identities. If it can be reduced to
1016 /// a single Value, it is returned, otherwise the Ops list is mutated as
1018 static Value *OptimizeAndOrXor(unsigned Opcode,
1019 SmallVectorImpl<ValueEntry> &Ops) {
1020 // Scan the operand lists looking for X and ~X pairs, along with X,X pairs.
1021 // If we find any, we can simplify the expression. X&~X == 0, X|~X == -1.
1022 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1023 // First, check for X and ~X in the operand list.
1024 assert(i < Ops.size());
1025 if (BinaryOperator::isNot(Ops[i].Op)) { // Cannot occur for ^.
1026 Value *X = BinaryOperator::getNotArgument(Ops[i].Op);
1027 unsigned FoundX = FindInOperandList(Ops, i, X);
1029 if (Opcode == Instruction::And) // ...&X&~X = 0
1030 return Constant::getNullValue(X->getType());
1032 if (Opcode == Instruction::Or) // ...|X|~X = -1
1033 return Constant::getAllOnesValue(X->getType());
1037 // Next, check for duplicate pairs of values, which we assume are next to
1038 // each other, due to our sorting criteria.
1039 assert(i < Ops.size());
1040 if (i+1 != Ops.size() && Ops[i+1].Op == Ops[i].Op) {
1041 if (Opcode == Instruction::And || Opcode == Instruction::Or) {
1042 // Drop duplicate values for And and Or.
1043 Ops.erase(Ops.begin()+i);
1049 // Drop pairs of values for Xor.
1050 assert(Opcode == Instruction::Xor);
1052 return Constant::getNullValue(Ops[0].Op->getType());
1055 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
1063 /// OptimizeAdd - Optimize a series of operands to an 'add' instruction. This
1064 /// optimizes based on identities. If it can be reduced to a single Value, it
1065 /// is returned, otherwise the Ops list is mutated as necessary.
1066 Value *Reassociate::OptimizeAdd(Instruction *I,
1067 SmallVectorImpl<ValueEntry> &Ops) {
1068 // Scan the operand lists looking for X and -X pairs. If we find any, we
1069 // can simplify the expression. X+-X == 0. While we're at it, scan for any
1070 // duplicates. We want to canonicalize Y+Y+Y+Z -> 3*Y+Z.
1072 // TODO: We could handle "X + ~X" -> "-1" if we wanted, since "-X = ~X+1".
1074 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1075 Value *TheOp = Ops[i].Op;
1076 // Check to see if we've seen this operand before. If so, we factor all
1077 // instances of the operand together. Due to our sorting criteria, we know
1078 // that these need to be next to each other in the vector.
1079 if (i+1 != Ops.size() && Ops[i+1].Op == TheOp) {
1080 // Rescan the list, remove all instances of this operand from the expr.
1081 unsigned NumFound = 0;
1083 Ops.erase(Ops.begin()+i);
1085 } while (i != Ops.size() && Ops[i].Op == TheOp);
1087 DEBUG(errs() << "\nFACTORING [" << NumFound << "]: " << *TheOp << '\n');
1090 // Insert a new multiply.
1091 Value *Mul = ConstantInt::get(cast<IntegerType>(I->getType()), NumFound);
1092 Mul = BinaryOperator::CreateMul(TheOp, Mul, "factor", I);
1094 // Now that we have inserted a multiply, optimize it. This allows us to
1095 // handle cases that require multiple factoring steps, such as this:
1096 // (X*2) + (X*2) + (X*2) -> (X*2)*3 -> X*6
1097 RedoInsts.insert(cast<Instruction>(Mul));
1099 // If every add operand was a duplicate, return the multiply.
1103 // Otherwise, we had some input that didn't have the dupe, such as
1104 // "A + A + B" -> "A*2 + B". Add the new multiply to the list of
1105 // things being added by this operation.
1106 Ops.insert(Ops.begin(), ValueEntry(getRank(Mul), Mul));
1113 // Check for X and -X in the operand list.
1114 if (!BinaryOperator::isNeg(TheOp))
1117 Value *X = BinaryOperator::getNegArgument(TheOp);
1118 unsigned FoundX = FindInOperandList(Ops, i, X);
1122 // Remove X and -X from the operand list.
1123 if (Ops.size() == 2)
1124 return Constant::getNullValue(X->getType());
1126 Ops.erase(Ops.begin()+i);
1130 --i; // Need to back up an extra one.
1131 Ops.erase(Ops.begin()+FoundX);
1133 --i; // Revisit element.
1134 e -= 2; // Removed two elements.
1137 // Scan the operand list, checking to see if there are any common factors
1138 // between operands. Consider something like A*A+A*B*C+D. We would like to
1139 // reassociate this to A*(A+B*C)+D, which reduces the number of multiplies.
1140 // To efficiently find this, we count the number of times a factor occurs
1141 // for any ADD operands that are MULs.
1142 DenseMap<Value*, unsigned> FactorOccurrences;
1144 // Keep track of each multiply we see, to avoid triggering on (X*4)+(X*4)
1145 // where they are actually the same multiply.
1146 unsigned MaxOcc = 0;
1147 Value *MaxOccVal = 0;
1148 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1149 BinaryOperator *BOp = isReassociableOp(Ops[i].Op, Instruction::Mul);
1153 // Compute all of the factors of this added value.
1154 SmallVector<Value*, 8> Factors;
1155 FindSingleUseMultiplyFactors(BOp, Factors, Ops);
1156 assert(Factors.size() > 1 && "Bad linearize!");
1158 // Add one to FactorOccurrences for each unique factor in this op.
1159 SmallPtrSet<Value*, 8> Duplicates;
1160 for (unsigned i = 0, e = Factors.size(); i != e; ++i) {
1161 Value *Factor = Factors[i];
1162 if (!Duplicates.insert(Factor)) continue;
1164 unsigned Occ = ++FactorOccurrences[Factor];
1165 if (Occ > MaxOcc) { MaxOcc = Occ; MaxOccVal = Factor; }
1167 // If Factor is a negative constant, add the negated value as a factor
1168 // because we can percolate the negate out. Watch for minint, which
1169 // cannot be positivified.
1170 if (ConstantInt *CI = dyn_cast<ConstantInt>(Factor))
1171 if (CI->isNegative() && !CI->isMinValue(true)) {
1172 Factor = ConstantInt::get(CI->getContext(), -CI->getValue());
1173 assert(!Duplicates.count(Factor) &&
1174 "Shouldn't have two constant factors, missed a canonicalize");
1176 unsigned Occ = ++FactorOccurrences[Factor];
1177 if (Occ > MaxOcc) { MaxOcc = Occ; MaxOccVal = Factor; }
1182 // If any factor occurred more than one time, we can pull it out.
1184 DEBUG(errs() << "\nFACTORING [" << MaxOcc << "]: " << *MaxOccVal << '\n');
1187 // Create a new instruction that uses the MaxOccVal twice. If we don't do
1188 // this, we could otherwise run into situations where removing a factor
1189 // from an expression will drop a use of maxocc, and this can cause
1190 // RemoveFactorFromExpression on successive values to behave differently.
1191 Instruction *DummyInst = BinaryOperator::CreateAdd(MaxOccVal, MaxOccVal);
1192 SmallVector<WeakVH, 4> NewMulOps;
1193 for (unsigned i = 0; i != Ops.size(); ++i) {
1194 // Only try to remove factors from expressions we're allowed to.
1195 BinaryOperator *BOp = isReassociableOp(Ops[i].Op, Instruction::Mul);
1199 if (Value *V = RemoveFactorFromExpression(Ops[i].Op, MaxOccVal)) {
1200 // The factorized operand may occur several times. Convert them all in
1202 for (unsigned j = Ops.size(); j != i;) {
1204 if (Ops[j].Op == Ops[i].Op) {
1205 NewMulOps.push_back(V);
1206 Ops.erase(Ops.begin()+j);
1213 // No need for extra uses anymore.
1216 unsigned NumAddedValues = NewMulOps.size();
1217 Value *V = EmitAddTreeOfValues(I, NewMulOps);
1219 // Now that we have inserted the add tree, optimize it. This allows us to
1220 // handle cases that require multiple factoring steps, such as this:
1221 // A*A*B + A*A*C --> A*(A*B+A*C) --> A*(A*(B+C))
1222 assert(NumAddedValues > 1 && "Each occurrence should contribute a value");
1223 (void)NumAddedValues;
1224 if (Instruction *VI = dyn_cast<Instruction>(V))
1225 RedoInsts.insert(VI);
1227 // Create the multiply.
1228 Instruction *V2 = BinaryOperator::CreateMul(V, MaxOccVal, "tmp", I);
1230 // Rerun associate on the multiply in case the inner expression turned into
1231 // a multiply. We want to make sure that we keep things in canonical form.
1232 RedoInsts.insert(V2);
1234 // If every add operand included the factor (e.g. "A*B + A*C"), then the
1235 // entire result expression is just the multiply "A*(B+C)".
1239 // Otherwise, we had some input that didn't have the factor, such as
1240 // "A*B + A*C + D" -> "A*(B+C) + D". Add the new multiply to the list of
1241 // things being added by this operation.
1242 Ops.insert(Ops.begin(), ValueEntry(getRank(V2), V2));
1249 /// \brief Predicate tests whether a ValueEntry's op is in a map.
1250 struct IsValueInMap {
1251 const DenseMap<Value *, unsigned> ⤅
1253 IsValueInMap(const DenseMap<Value *, unsigned> &Map) : Map(Map) {}
1255 bool operator()(const ValueEntry &Entry) {
1256 return Map.find(Entry.Op) != Map.end();
1261 /// \brief Build up a vector of value/power pairs factoring a product.
1263 /// Given a series of multiplication operands, build a vector of factors and
1264 /// the powers each is raised to when forming the final product. Sort them in
1265 /// the order of descending power.
1267 /// (x*x) -> [(x, 2)]
1268 /// ((x*x)*x) -> [(x, 3)]
1269 /// ((((x*y)*x)*y)*x) -> [(x, 3), (y, 2)]
1271 /// \returns Whether any factors have a power greater than one.
1272 bool Reassociate::collectMultiplyFactors(SmallVectorImpl<ValueEntry> &Ops,
1273 SmallVectorImpl<Factor> &Factors) {
1274 // FIXME: Have Ops be (ValueEntry, Multiplicity) pairs, simplifying this.
1275 // Compute the sum of powers of simplifiable factors.
1276 unsigned FactorPowerSum = 0;
1277 for (unsigned Idx = 1, Size = Ops.size(); Idx < Size; ++Idx) {
1278 Value *Op = Ops[Idx-1].Op;
1280 // Count the number of occurrences of this value.
1282 for (; Idx < Size && Ops[Idx].Op == Op; ++Idx)
1284 // Track for simplification all factors which occur 2 or more times.
1286 FactorPowerSum += Count;
1289 // We can only simplify factors if the sum of the powers of our simplifiable
1290 // factors is 4 or higher. When that is the case, we will *always* have
1291 // a simplification. This is an important invariant to prevent cyclicly
1292 // trying to simplify already minimal formations.
1293 if (FactorPowerSum < 4)
1296 // Now gather the simplifiable factors, removing them from Ops.
1298 for (unsigned Idx = 1; Idx < Ops.size(); ++Idx) {
1299 Value *Op = Ops[Idx-1].Op;
1301 // Count the number of occurrences of this value.
1303 for (; Idx < Ops.size() && Ops[Idx].Op == Op; ++Idx)
1307 // Move an even number of occurrences to Factors.
1310 FactorPowerSum += Count;
1311 Factors.push_back(Factor(Op, Count));
1312 Ops.erase(Ops.begin()+Idx, Ops.begin()+Idx+Count);
1315 // None of the adjustments above should have reduced the sum of factor powers
1316 // below our mininum of '4'.
1317 assert(FactorPowerSum >= 4);
1319 std::sort(Factors.begin(), Factors.end(), Factor::PowerDescendingSorter());
1323 /// \brief Build a tree of multiplies, computing the product of Ops.
1324 static Value *buildMultiplyTree(IRBuilder<> &Builder,
1325 SmallVectorImpl<Value*> &Ops) {
1326 if (Ops.size() == 1)
1329 Value *LHS = Ops.pop_back_val();
1331 LHS = Builder.CreateMul(LHS, Ops.pop_back_val());
1332 } while (!Ops.empty());
1337 /// \brief Build a minimal multiplication DAG for (a^x)*(b^y)*(c^z)*...
1339 /// Given a vector of values raised to various powers, where no two values are
1340 /// equal and the powers are sorted in decreasing order, compute the minimal
1341 /// DAG of multiplies to compute the final product, and return that product
1343 Value *Reassociate::buildMinimalMultiplyDAG(IRBuilder<> &Builder,
1344 SmallVectorImpl<Factor> &Factors) {
1345 assert(Factors[0].Power);
1346 SmallVector<Value *, 4> OuterProduct;
1347 for (unsigned LastIdx = 0, Idx = 1, Size = Factors.size();
1348 Idx < Size && Factors[Idx].Power > 0; ++Idx) {
1349 if (Factors[Idx].Power != Factors[LastIdx].Power) {
1354 // We want to multiply across all the factors with the same power so that
1355 // we can raise them to that power as a single entity. Build a mini tree
1357 SmallVector<Value *, 4> InnerProduct;
1358 InnerProduct.push_back(Factors[LastIdx].Base);
1360 InnerProduct.push_back(Factors[Idx].Base);
1362 } while (Idx < Size && Factors[Idx].Power == Factors[LastIdx].Power);
1364 // Reset the base value of the first factor to the new expression tree.
1365 // We'll remove all the factors with the same power in a second pass.
1366 Value *M = Factors[LastIdx].Base = buildMultiplyTree(Builder, InnerProduct);
1367 if (Instruction *MI = dyn_cast<Instruction>(M))
1368 RedoInsts.insert(MI);
1372 // Unique factors with equal powers -- we've folded them into the first one's
1374 Factors.erase(std::unique(Factors.begin(), Factors.end(),
1375 Factor::PowerEqual()),
1378 // Iteratively collect the base of each factor with an add power into the
1379 // outer product, and halve each power in preparation for squaring the
1381 for (unsigned Idx = 0, Size = Factors.size(); Idx != Size; ++Idx) {
1382 if (Factors[Idx].Power & 1)
1383 OuterProduct.push_back(Factors[Idx].Base);
1384 Factors[Idx].Power >>= 1;
1386 if (Factors[0].Power) {
1387 Value *SquareRoot = buildMinimalMultiplyDAG(Builder, Factors);
1388 OuterProduct.push_back(SquareRoot);
1389 OuterProduct.push_back(SquareRoot);
1391 if (OuterProduct.size() == 1)
1392 return OuterProduct.front();
1394 Value *V = buildMultiplyTree(Builder, OuterProduct);
1398 Value *Reassociate::OptimizeMul(BinaryOperator *I,
1399 SmallVectorImpl<ValueEntry> &Ops) {
1400 // We can only optimize the multiplies when there is a chain of more than
1401 // three, such that a balanced tree might require fewer total multiplies.
1405 // Try to turn linear trees of multiplies without other uses of the
1406 // intermediate stages into minimal multiply DAGs with perfect sub-expression
1408 SmallVector<Factor, 4> Factors;
1409 if (!collectMultiplyFactors(Ops, Factors))
1410 return 0; // All distinct factors, so nothing left for us to do.
1412 IRBuilder<> Builder(I);
1413 Value *V = buildMinimalMultiplyDAG(Builder, Factors);
1417 ValueEntry NewEntry = ValueEntry(getRank(V), V);
1418 Ops.insert(std::lower_bound(Ops.begin(), Ops.end(), NewEntry), NewEntry);
1422 Value *Reassociate::OptimizeExpression(BinaryOperator *I,
1423 SmallVectorImpl<ValueEntry> &Ops) {
1424 // Now that we have the linearized expression tree, try to optimize it.
1425 // Start by folding any constants that we found.
1426 if (Ops.size() == 1) return Ops[0].Op;
1428 unsigned Opcode = I->getOpcode();
1430 if (Constant *V1 = dyn_cast<Constant>(Ops[Ops.size()-2].Op))
1431 if (Constant *V2 = dyn_cast<Constant>(Ops.back().Op)) {
1433 Ops.back().Op = ConstantExpr::get(Opcode, V1, V2);
1434 return OptimizeExpression(I, Ops);
1437 // Check for destructive annihilation due to a constant being used.
1438 if (ConstantInt *CstVal = dyn_cast<ConstantInt>(Ops.back().Op))
1441 case Instruction::And:
1442 if (CstVal->isZero()) // X & 0 -> 0
1444 if (CstVal->isAllOnesValue()) // X & -1 -> X
1447 case Instruction::Mul:
1448 if (CstVal->isZero()) { // X * 0 -> 0
1453 if (cast<ConstantInt>(CstVal)->isOne())
1454 Ops.pop_back(); // X * 1 -> X
1456 case Instruction::Or:
1457 if (CstVal->isAllOnesValue()) // X | -1 -> -1
1460 case Instruction::Add:
1461 case Instruction::Xor:
1462 if (CstVal->isZero()) // X [|^+] 0 -> X
1466 if (Ops.size() == 1) return Ops[0].Op;
1468 // Handle destructive annihilation due to identities between elements in the
1469 // argument list here.
1470 unsigned NumOps = Ops.size();
1473 case Instruction::And:
1474 case Instruction::Or:
1475 case Instruction::Xor:
1476 if (Value *Result = OptimizeAndOrXor(Opcode, Ops))
1480 case Instruction::Add:
1481 if (Value *Result = OptimizeAdd(I, Ops))
1485 case Instruction::Mul:
1486 if (Value *Result = OptimizeMul(I, Ops))
1491 if (Ops.size() != NumOps)
1492 return OptimizeExpression(I, Ops);
1496 /// EraseInst - Zap the given instruction, adding interesting operands to the
1498 void Reassociate::EraseInst(Instruction *I) {
1499 assert(isInstructionTriviallyDead(I) && "Trivially dead instructions only!");
1500 SmallVector<Value*, 8> Ops(I->op_begin(), I->op_end());
1501 // Erase the dead instruction.
1502 ValueRankMap.erase(I);
1503 I->eraseFromParent();
1504 // Optimize its operands.
1505 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1506 if (Instruction *Op = dyn_cast<Instruction>(Ops[i])) {
1507 // If this is a node in an expression tree, climb to the expression root
1508 // and add that since that's where optimization actually happens.
1509 unsigned Opcode = Op->getOpcode();
1510 while (Op->hasOneUse() && Op->use_back()->getOpcode() == Opcode)
1511 Op = Op->use_back();
1512 RedoInsts.insert(Op);
1516 /// OptimizeInst - Inspect and optimize the given instruction. Note that erasing
1517 /// instructions is not allowed.
1518 void Reassociate::OptimizeInst(Instruction *I) {
1519 // Only consider operations that we understand.
1520 if (!isa<BinaryOperator>(I))
1523 if (I->getOpcode() == Instruction::Shl &&
1524 isa<ConstantInt>(I->getOperand(1)))
1525 // If an operand of this shift is a reassociable multiply, or if the shift
1526 // is used by a reassociable multiply or add, turn into a multiply.
1527 if (isReassociableOp(I->getOperand(0), Instruction::Mul) ||
1529 (isReassociableOp(I->use_back(), Instruction::Mul) ||
1530 isReassociableOp(I->use_back(), Instruction::Add)))) {
1531 Instruction *NI = ConvertShiftToMul(I);
1532 RedoInsts.insert(I);
1537 // Floating point binary operators are not associative, but we can still
1538 // commute (some) of them, to canonicalize the order of their operands.
1539 // This can potentially expose more CSE opportunities, and makes writing
1540 // other transformations simpler.
1541 if ((I->getType()->isFloatingPointTy() || I->getType()->isVectorTy())) {
1542 // FAdd and FMul can be commuted.
1543 if (I->getOpcode() != Instruction::FMul &&
1544 I->getOpcode() != Instruction::FAdd)
1547 Value *LHS = I->getOperand(0);
1548 Value *RHS = I->getOperand(1);
1549 unsigned LHSRank = getRank(LHS);
1550 unsigned RHSRank = getRank(RHS);
1552 // Sort the operands by rank.
1553 if (RHSRank < LHSRank) {
1554 I->setOperand(0, RHS);
1555 I->setOperand(1, LHS);
1561 // Do not reassociate boolean (i1) expressions. We want to preserve the
1562 // original order of evaluation for short-circuited comparisons that
1563 // SimplifyCFG has folded to AND/OR expressions. If the expression
1564 // is not further optimized, it is likely to be transformed back to a
1565 // short-circuited form for code gen, and the source order may have been
1566 // optimized for the most likely conditions.
1567 if (I->getType()->isIntegerTy(1))
1570 // If this is a subtract instruction which is not already in negate form,
1571 // see if we can convert it to X+-Y.
1572 if (I->getOpcode() == Instruction::Sub) {
1573 if (ShouldBreakUpSubtract(I)) {
1574 Instruction *NI = BreakUpSubtract(I);
1575 RedoInsts.insert(I);
1578 } else if (BinaryOperator::isNeg(I)) {
1579 // Otherwise, this is a negation. See if the operand is a multiply tree
1580 // and if this is not an inner node of a multiply tree.
1581 if (isReassociableOp(I->getOperand(1), Instruction::Mul) &&
1583 !isReassociableOp(I->use_back(), Instruction::Mul))) {
1584 Instruction *NI = LowerNegateToMultiply(I);
1585 RedoInsts.insert(I);
1592 // If this instruction is an associative binary operator, process it.
1593 if (!I->isAssociative()) return;
1594 BinaryOperator *BO = cast<BinaryOperator>(I);
1596 // If this is an interior node of a reassociable tree, ignore it until we
1597 // get to the root of the tree, to avoid N^2 analysis.
1598 if (BO->hasOneUse() && BO->use_back()->getOpcode() == BO->getOpcode())
1601 // If this is an add tree that is used by a sub instruction, ignore it
1602 // until we process the subtract.
1603 if (BO->hasOneUse() && BO->getOpcode() == Instruction::Add &&
1604 cast<Instruction>(BO->use_back())->getOpcode() == Instruction::Sub)
1607 ReassociateExpression(BO);
1610 Value *Reassociate::ReassociateExpression(BinaryOperator *I) {
1612 // First, walk the expression tree, linearizing the tree, collecting the
1613 // operand information.
1614 SmallVector<RepeatedValue, 8> Tree;
1615 MadeChange |= LinearizeExprTree(I, Tree);
1616 SmallVector<ValueEntry, 8> Ops;
1617 Ops.reserve(Tree.size());
1618 for (unsigned i = 0, e = Tree.size(); i != e; ++i) {
1619 RepeatedValue E = Tree[i];
1620 Ops.append(E.second.getZExtValue(),
1621 ValueEntry(getRank(E.first), E.first));
1624 DEBUG(dbgs() << "RAIn:\t"; PrintOps(I, Ops); dbgs() << '\n');
1626 // Now that we have linearized the tree to a list and have gathered all of
1627 // the operands and their ranks, sort the operands by their rank. Use a
1628 // stable_sort so that values with equal ranks will have their relative
1629 // positions maintained (and so the compiler is deterministic). Note that
1630 // this sorts so that the highest ranking values end up at the beginning of
1632 std::stable_sort(Ops.begin(), Ops.end());
1634 // OptimizeExpression - Now that we have the expression tree in a convenient
1635 // sorted form, optimize it globally if possible.
1636 if (Value *V = OptimizeExpression(I, Ops)) {
1637 // This expression tree simplified to something that isn't a tree,
1639 DEBUG(dbgs() << "Reassoc to scalar: " << *V << '\n');
1640 I->replaceAllUsesWith(V);
1641 if (Instruction *VI = dyn_cast<Instruction>(V))
1642 VI->setDebugLoc(I->getDebugLoc());
1643 RedoInsts.insert(I);
1648 // We want to sink immediates as deeply as possible except in the case where
1649 // this is a multiply tree used only by an add, and the immediate is a -1.
1650 // In this case we reassociate to put the negation on the outside so that we
1651 // can fold the negation into the add: (-X)*Y + Z -> Z-X*Y
1652 if (I->getOpcode() == Instruction::Mul && I->hasOneUse() &&
1653 cast<Instruction>(I->use_back())->getOpcode() == Instruction::Add &&
1654 isa<ConstantInt>(Ops.back().Op) &&
1655 cast<ConstantInt>(Ops.back().Op)->isAllOnesValue()) {
1656 ValueEntry Tmp = Ops.pop_back_val();
1657 Ops.insert(Ops.begin(), Tmp);
1660 DEBUG(dbgs() << "RAOut:\t"; PrintOps(I, Ops); dbgs() << '\n');
1662 if (Ops.size() == 1) {
1663 // This expression tree simplified to something that isn't a tree,
1665 I->replaceAllUsesWith(Ops[0].Op);
1666 if (Instruction *OI = dyn_cast<Instruction>(Ops[0].Op))
1667 OI->setDebugLoc(I->getDebugLoc());
1668 RedoInsts.insert(I);
1672 // Now that we ordered and optimized the expressions, splat them back into
1673 // the expression tree, removing any unneeded nodes.
1674 RewriteExprTree(I, Ops);
1678 bool Reassociate::runOnFunction(Function &F) {
1679 // Calculate the rank map for F
1683 for (Function::iterator BI = F.begin(), BE = F.end(); BI != BE; ++BI) {
1684 // Optimize every instruction in the basic block.
1685 for (BasicBlock::iterator II = BI->begin(), IE = BI->end(); II != IE; )
1686 if (isInstructionTriviallyDead(II)) {
1690 assert(II->getParent() == BI && "Moved to a different block!");
1694 // If this produced extra instructions to optimize, handle them now.
1695 while (!RedoInsts.empty()) {
1696 Instruction *I = RedoInsts.pop_back_val();
1697 if (isInstructionTriviallyDead(I))
1704 // We are done with the rank map.
1706 ValueRankMap.clear();