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/ADT/DenseMap.h"
26 #include "llvm/ADT/PostOrderIterator.h"
27 #include "llvm/ADT/STLExtras.h"
28 #include "llvm/ADT/SetVector.h"
29 #include "llvm/ADT/Statistic.h"
30 #include "llvm/Assembly/Writer.h"
31 #include "llvm/IR/Constants.h"
32 #include "llvm/IR/DerivedTypes.h"
33 #include "llvm/IR/Function.h"
34 #include "llvm/IR/IRBuilder.h"
35 #include "llvm/IR/Instructions.h"
36 #include "llvm/IR/IntrinsicInst.h"
37 #include "llvm/Pass.h"
38 #include "llvm/Support/CFG.h"
39 #include "llvm/Support/Debug.h"
40 #include "llvm/Support/ValueHandle.h"
41 #include "llvm/Support/raw_ostream.h"
42 #include "llvm/Transforms/Utils/Local.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 typedef std::pair
<Value
*, APInt
> RepeatedValue
;
344 /// LinearizeExprTree - Given an associative binary expression, return the leaf
345 /// nodes in Ops along with their weights (how many times the leaf occurs). The
346 /// original expression is the same as
347 /// (Ops[0].first op Ops[0].first op ... Ops[0].first) <- Ops[0].second times
349 /// (Ops[1].first op Ops[1].first op ... Ops[1].first) <- Ops[1].second times
353 /// (Ops[N].first op Ops[N].first op ... Ops[N].first) <- Ops[N].second times
355 /// Note that the values Ops[0].first, ..., Ops[N].first are all distinct.
357 /// This routine may modify the function, in which case it returns 'true'. The
358 /// changes it makes may well be destructive, changing the value computed by 'I'
359 /// to something completely different. Thus if the routine returns 'true' then
360 /// you MUST either replace I with a new expression computed from the Ops array,
361 /// or use RewriteExprTree to put the values back in.
363 /// A leaf node is either not a binary operation of the same kind as the root
364 /// node 'I' (i.e. is not a binary operator at all, or is, but with a different
365 /// opcode), or is the same kind of binary operator but has a use which either
366 /// does not belong to the expression, or does belong to the expression but is
367 /// a leaf node. Every leaf node has at least one use that is a non-leaf node
368 /// of the expression, while for non-leaf nodes (except for the root 'I') every
369 /// use is a non-leaf node of the expression.
372 /// expression graph node names
382 /// The leaf nodes are C, E, F and G. The Ops array will contain (maybe not in
383 /// that order) (C, 1), (E, 1), (F, 2), (G, 2).
385 /// The expression is maximal: if some instruction is a binary operator of the
386 /// same kind as 'I', and all of its uses are non-leaf nodes of the expression,
387 /// then the instruction also belongs to the expression, is not a leaf node of
388 /// it, and its operands also belong to the expression (but may be leaf nodes).
390 /// NOTE: This routine will set operands of non-leaf non-root nodes to undef in
391 /// order to ensure that every non-root node in the expression has *exactly one*
392 /// use by a non-leaf node of the expression. This destruction means that the
393 /// caller MUST either replace 'I' with a new expression or use something like
394 /// RewriteExprTree to put the values back in if the routine indicates that it
395 /// made a change by returning 'true'.
397 /// In the above example either the right operand of A or the left operand of B
398 /// will be replaced by undef. If it is B's operand then this gives:
402 /// + + | A, B - operand of B replaced with undef
408 /// Note that such undef operands can only be reached by passing through 'I'.
409 /// For example, if you visit operands recursively starting from a leaf node
410 /// then you will never see such an undef operand unless you get back to 'I',
411 /// which requires passing through a phi node.
413 /// Note that this routine may also mutate binary operators of the wrong type
414 /// that have all uses inside the expression (i.e. only used by non-leaf nodes
415 /// of the expression) if it can turn them into binary operators of the right
416 /// type and thus make the expression bigger.
418 static bool LinearizeExprTree(BinaryOperator
*I
,
419 SmallVectorImpl
<RepeatedValue
> &Ops
) {
420 DEBUG(dbgs() << "LINEARIZE: " << *I
<< '\n');
421 unsigned Bitwidth
= I
->getType()->getScalarType()->getPrimitiveSizeInBits();
422 unsigned Opcode
= I
->getOpcode();
423 assert(Instruction::isAssociative(Opcode
) &&
424 Instruction::isCommutative(Opcode
) &&
425 "Expected an associative and commutative operation!");
427 // Visit all operands of the expression, keeping track of their weight (the
428 // number of paths from the expression root to the operand, or if you like
429 // the number of times that operand occurs in the linearized expression).
430 // For example, if I = X + A, where X = A + B, then I, X and B have weight 1
431 // while A has weight two.
433 // Worklist of non-leaf nodes (their operands are in the expression too) along
434 // with their weights, representing a certain number of paths to the operator.
435 // If an operator occurs in the worklist multiple times then we found multiple
436 // ways to get to it.
437 SmallVector
<std::pair
<BinaryOperator
*, APInt
>, 8> Worklist
; // (Op, Weight)
438 Worklist
.push_back(std::make_pair(I
, APInt(Bitwidth
, 1)));
439 bool MadeChange
= false;
441 // Leaves of the expression are values that either aren't the right kind of
442 // operation (eg: a constant, or a multiply in an add tree), or are, but have
443 // some uses that are not inside the expression. For example, in I = X + X,
444 // X = A + B, the value X has two uses (by I) that are in the expression. If
445 // X has any other uses, for example in a return instruction, then we consider
446 // X to be a leaf, and won't analyze it further. When we first visit a value,
447 // if it has more than one use then at first we conservatively consider it to
448 // be a leaf. Later, as the expression is explored, we may discover some more
449 // uses of the value from inside the expression. If all uses turn out to be
450 // from within the expression (and the value is a binary operator of the right
451 // kind) then the value is no longer considered to be a leaf, and its operands
454 // Leaves - Keeps track of the set of putative leaves as well as the number of
455 // paths to each leaf seen so far.
456 typedef DenseMap
<Value
*, APInt
> LeafMap
;
457 LeafMap Leaves
; // Leaf -> Total weight so far.
458 SmallVector
<Value
*, 8> LeafOrder
; // Ensure deterministic leaf output order.
461 SmallPtrSet
<Value
*, 8> Visited
; // For sanity checking the iteration scheme.
463 while (!Worklist
.empty()) {
464 std::pair
<BinaryOperator
*, APInt
> P
= Worklist
.pop_back_val();
465 I
= P
.first
; // We examine the operands of this binary operator.
467 for (unsigned OpIdx
= 0; OpIdx
< 2; ++OpIdx
) { // Visit operands.
468 Value
*Op
= I
->getOperand(OpIdx
);
469 APInt Weight
= P
.second
; // Number of paths to this operand.
470 DEBUG(dbgs() << "OPERAND: " << *Op
<< " (" << Weight
<< ")\n");
471 assert(!Op
->use_empty() && "No uses, so how did we get to it?!");
473 // If this is a binary operation of the right kind with only one use then
474 // add its operands to the expression.
475 if (BinaryOperator
*BO
= isReassociableOp(Op
, Opcode
)) {
476 assert(Visited
.insert(Op
) && "Not first visit!");
477 DEBUG(dbgs() << "DIRECT ADD: " << *Op
<< " (" << Weight
<< ")\n");
478 Worklist
.push_back(std::make_pair(BO
, Weight
));
482 // Appears to be a leaf. Is the operand already in the set of leaves?
483 LeafMap::iterator It
= Leaves
.find(Op
);
484 if (It
== Leaves
.end()) {
485 // Not in the leaf map. Must be the first time we saw this operand.
486 assert(Visited
.insert(Op
) && "Not first visit!");
487 if (!Op
->hasOneUse()) {
488 // This value has uses not accounted for by the expression, so it is
489 // not safe to modify. Mark it as being a leaf.
490 DEBUG(dbgs() << "ADD USES LEAF: " << *Op
<< " (" << Weight
<< ")\n");
491 LeafOrder
.push_back(Op
);
495 // No uses outside the expression, try morphing it.
496 } else if (It
!= Leaves
.end()) {
497 // Already in the leaf map.
498 assert(Visited
.count(Op
) && "In leaf map but not visited!");
500 // Update the number of paths to the leaf.
501 IncorporateWeight(It
->second
, Weight
, Opcode
);
503 #if 0 // TODO: Re-enable once PR13021 is fixed.
504 // The leaf already has one use from inside the expression. As we want
505 // exactly one such use, drop this new use of the leaf.
506 assert(!Op
->hasOneUse() && "Only one use, but we got here twice!");
507 I
->setOperand(OpIdx
, UndefValue::get(I
->getType()));
510 // If the leaf is a binary operation of the right kind and we now see
511 // that its multiple original uses were in fact all by nodes belonging
512 // to the expression, then no longer consider it to be a leaf and add
513 // its operands to the expression.
514 if (BinaryOperator
*BO
= isReassociableOp(Op
, Opcode
)) {
515 DEBUG(dbgs() << "UNLEAF: " << *Op
<< " (" << It
->second
<< ")\n");
516 Worklist
.push_back(std::make_pair(BO
, It
->second
));
522 // If we still have uses that are not accounted for by the expression
523 // then it is not safe to modify the value.
524 if (!Op
->hasOneUse())
527 // No uses outside the expression, try morphing it.
529 Leaves
.erase(It
); // Since the value may be morphed below.
532 // At this point we have a value which, first of all, is not a binary
533 // expression of the right kind, and secondly, is only used inside the
534 // expression. This means that it can safely be modified. See if we
535 // can usefully morph it into an expression of the right kind.
536 assert((!isa
<Instruction
>(Op
) ||
537 cast
<Instruction
>(Op
)->getOpcode() != Opcode
) &&
538 "Should have been handled above!");
539 assert(Op
->hasOneUse() && "Has uses outside the expression tree!");
541 // If this is a multiply expression, turn any internal negations into
542 // multiplies by -1 so they can be reassociated.
543 BinaryOperator
*BO
= dyn_cast
<BinaryOperator
>(Op
);
544 if (Opcode
== Instruction::Mul
&& BO
&& BinaryOperator::isNeg(BO
)) {
545 DEBUG(dbgs() << "MORPH LEAF: " << *Op
<< " (" << Weight
<< ") TO ");
546 BO
= LowerNegateToMultiply(BO
);
547 DEBUG(dbgs() << *BO
<< 'n');
548 Worklist
.push_back(std::make_pair(BO
, Weight
));
553 // Failed to morph into an expression of the right type. This really is
555 DEBUG(dbgs() << "ADD LEAF: " << *Op
<< " (" << Weight
<< ")\n");
556 assert(!isReassociableOp(Op
, Opcode
) && "Value was morphed?");
557 LeafOrder
.push_back(Op
);
562 // The leaves, repeated according to their weights, represent the linearized
563 // form of the expression.
564 for (unsigned i
= 0, e
= LeafOrder
.size(); i
!= e
; ++i
) {
565 Value
*V
= LeafOrder
[i
];
566 LeafMap::iterator It
= Leaves
.find(V
);
567 if (It
== Leaves
.end())
568 // Node initially thought to be a leaf wasn't.
570 assert(!isReassociableOp(V
, Opcode
) && "Shouldn't be a leaf!");
571 APInt Weight
= It
->second
;
572 if (Weight
.isMinValue())
573 // Leaf already output or weight reduction eliminated it.
575 // Ensure the leaf is only output once.
577 Ops
.push_back(std::make_pair(V
, Weight
));
580 // For nilpotent operations or addition there may be no operands, for example
581 // because the expression was "X xor X" or consisted of 2^Bitwidth additions:
582 // in both cases the weight reduces to 0 causing the value to be skipped.
584 Constant
*Identity
= ConstantExpr::getBinOpIdentity(Opcode
, I
->getType());
585 assert(Identity
&& "Associative operation without identity!");
586 Ops
.push_back(std::make_pair(Identity
, APInt(Bitwidth
, 1)));
592 // RewriteExprTree - Now that the operands for this expression tree are
593 // linearized and optimized, emit them in-order.
594 void Reassociate::RewriteExprTree(BinaryOperator
*I
,
595 SmallVectorImpl
<ValueEntry
> &Ops
) {
596 assert(Ops
.size() > 1 && "Single values should be used directly!");
598 // Since our optimizations should never increase the number of operations, the
599 // new expression can usually be written reusing the existing binary operators
600 // from the original expression tree, without creating any new instructions,
601 // though the rewritten expression may have a completely different topology.
602 // We take care to not change anything if the new expression will be the same
603 // as the original. If more than trivial changes (like commuting operands)
604 // were made then we are obliged to clear out any optional subclass data like
607 /// NodesToRewrite - Nodes from the original expression available for writing
608 /// the new expression into.
609 SmallVector
<BinaryOperator
*, 8> NodesToRewrite
;
610 unsigned Opcode
= I
->getOpcode();
611 BinaryOperator
*Op
= I
;
613 /// NotRewritable - The operands being written will be the leaves of the new
614 /// expression and must not be used as inner nodes (via NodesToRewrite) by
615 /// mistake. Inner nodes are always reassociable, and usually leaves are not
616 /// (if they were they would have been incorporated into the expression and so
617 /// would not be leaves), so most of the time there is no danger of this. But
618 /// in rare cases a leaf may become reassociable if an optimization kills uses
619 /// of it, or it may momentarily become reassociable during rewriting (below)
620 /// due it being removed as an operand of one of its uses. Ensure that misuse
621 /// of leaf nodes as inner nodes cannot occur by remembering all of the future
622 /// leaves and refusing to reuse any of them as inner nodes.
623 SmallPtrSet
<Value
*, 8> NotRewritable
;
624 for (unsigned i
= 0, e
= Ops
.size(); i
!= e
; ++i
)
625 NotRewritable
.insert(Ops
[i
].Op
);
627 // ExpressionChanged - Non-null if the rewritten expression differs from the
628 // original in some non-trivial way, requiring the clearing of optional flags.
629 // Flags are cleared from the operator in ExpressionChanged up to I inclusive.
630 BinaryOperator
*ExpressionChanged
= 0;
631 for (unsigned i
= 0; ; ++i
) {
632 // The last operation (which comes earliest in the IR) is special as both
633 // operands will come from Ops, rather than just one with the other being
635 if (i
+2 == Ops
.size()) {
636 Value
*NewLHS
= Ops
[i
].Op
;
637 Value
*NewRHS
= Ops
[i
+1].Op
;
638 Value
*OldLHS
= Op
->getOperand(0);
639 Value
*OldRHS
= Op
->getOperand(1);
641 if (NewLHS
== OldLHS
&& NewRHS
== OldRHS
)
642 // Nothing changed, leave it alone.
645 if (NewLHS
== OldRHS
&& NewRHS
== OldLHS
) {
646 // The order of the operands was reversed. Swap them.
647 DEBUG(dbgs() << "RA: " << *Op
<< '\n');
649 DEBUG(dbgs() << "TO: " << *Op
<< '\n');
655 // The new operation differs non-trivially from the original. Overwrite
656 // the old operands with the new ones.
657 DEBUG(dbgs() << "RA: " << *Op
<< '\n');
658 if (NewLHS
!= OldLHS
) {
659 BinaryOperator
*BO
= isReassociableOp(OldLHS
, Opcode
);
660 if (BO
&& !NotRewritable
.count(BO
))
661 NodesToRewrite
.push_back(BO
);
662 Op
->setOperand(0, NewLHS
);
664 if (NewRHS
!= OldRHS
) {
665 BinaryOperator
*BO
= isReassociableOp(OldRHS
, Opcode
);
666 if (BO
&& !NotRewritable
.count(BO
))
667 NodesToRewrite
.push_back(BO
);
668 Op
->setOperand(1, NewRHS
);
670 DEBUG(dbgs() << "TO: " << *Op
<< '\n');
672 ExpressionChanged
= Op
;
679 // Not the last operation. The left-hand side will be a sub-expression
680 // while the right-hand side will be the current element of Ops.
681 Value
*NewRHS
= Ops
[i
].Op
;
682 if (NewRHS
!= Op
->getOperand(1)) {
683 DEBUG(dbgs() << "RA: " << *Op
<< '\n');
684 if (NewRHS
== Op
->getOperand(0)) {
685 // The new right-hand side was already present as the left operand. If
686 // we are lucky then swapping the operands will sort out both of them.
689 // Overwrite with the new right-hand side.
690 BinaryOperator
*BO
= isReassociableOp(Op
->getOperand(1), Opcode
);
691 if (BO
&& !NotRewritable
.count(BO
))
692 NodesToRewrite
.push_back(BO
);
693 Op
->setOperand(1, NewRHS
);
694 ExpressionChanged
= Op
;
696 DEBUG(dbgs() << "TO: " << *Op
<< '\n');
701 // Now deal with the left-hand side. If this is already an operation node
702 // from the original expression then just rewrite the rest of the expression
704 BinaryOperator
*BO
= isReassociableOp(Op
->getOperand(0), Opcode
);
705 if (BO
&& !NotRewritable
.count(BO
)) {
710 // Otherwise, grab a spare node from the original expression and use that as
711 // the left-hand side. If there are no nodes left then the optimizers made
712 // an expression with more nodes than the original! This usually means that
713 // they did something stupid but it might mean that the problem was just too
714 // hard (finding the mimimal number of multiplications needed to realize a
715 // multiplication expression is NP-complete). Whatever the reason, smart or
716 // stupid, create a new node if there are none left.
717 BinaryOperator
*NewOp
;
718 if (NodesToRewrite
.empty()) {
719 Constant
*Undef
= UndefValue::get(I
->getType());
720 NewOp
= BinaryOperator::Create(Instruction::BinaryOps(Opcode
),
721 Undef
, Undef
, "", I
);
723 NewOp
= NodesToRewrite
.pop_back_val();
726 DEBUG(dbgs() << "RA: " << *Op
<< '\n');
727 Op
->setOperand(0, NewOp
);
728 DEBUG(dbgs() << "TO: " << *Op
<< '\n');
729 ExpressionChanged
= Op
;
735 // If the expression changed non-trivially then clear out all subclass data
736 // starting from the operator specified in ExpressionChanged, and compactify
737 // the operators to just before the expression root to guarantee that the
738 // expression tree is dominated by all of Ops.
739 if (ExpressionChanged
)
741 ExpressionChanged
->clearSubclassOptionalData();
742 if (ExpressionChanged
== I
)
744 ExpressionChanged
->moveBefore(I
);
745 ExpressionChanged
= cast
<BinaryOperator
>(*ExpressionChanged
->use_begin());
748 // Throw away any left over nodes from the original expression.
749 for (unsigned i
= 0, e
= NodesToRewrite
.size(); i
!= e
; ++i
)
750 RedoInsts
.insert(NodesToRewrite
[i
]);
753 /// NegateValue - Insert instructions before the instruction pointed to by BI,
754 /// that computes the negative version of the value specified. The negative
755 /// version of the value is returned, and BI is left pointing at the instruction
756 /// that should be processed next by the reassociation pass.
757 static Value
*NegateValue(Value
*V
, Instruction
*BI
) {
758 if (Constant
*C
= dyn_cast
<Constant
>(V
))
759 return ConstantExpr::getNeg(C
);
761 // We are trying to expose opportunity for reassociation. One of the things
762 // that we want to do to achieve this is to push a negation as deep into an
763 // expression chain as possible, to expose the add instructions. In practice,
764 // this means that we turn this:
765 // X = -(A+12+C+D) into X = -A + -12 + -C + -D = -12 + -A + -C + -D
766 // so that later, a: Y = 12+X could get reassociated with the -12 to eliminate
767 // the constants. We assume that instcombine will clean up the mess later if
768 // we introduce tons of unnecessary negation instructions.
770 if (BinaryOperator
*I
= isReassociableOp(V
, Instruction::Add
)) {
771 // Push the negates through the add.
772 I
->setOperand(0, NegateValue(I
->getOperand(0), BI
));
773 I
->setOperand(1, NegateValue(I
->getOperand(1), BI
));
775 // We must move the add instruction here, because the neg instructions do
776 // not dominate the old add instruction in general. By moving it, we are
777 // assured that the neg instructions we just inserted dominate the
778 // instruction we are about to insert after them.
781 I
->setName(I
->getName()+".neg");
785 // Okay, we need to materialize a negated version of V with an instruction.
786 // Scan the use lists of V to see if we have one already.
787 for (Value::use_iterator UI
= V
->use_begin(), E
= V
->use_end(); UI
!= E
;++UI
){
789 if (!BinaryOperator::isNeg(U
)) continue;
791 // We found one! Now we have to make sure that the definition dominates
792 // this use. We do this by moving it to the entry block (if it is a
793 // non-instruction value) or right after the definition. These negates will
794 // be zapped by reassociate later, so we don't need much finesse here.
795 BinaryOperator
*TheNeg
= cast
<BinaryOperator
>(U
);
797 // Verify that the negate is in this function, V might be a constant expr.
798 if (TheNeg
->getParent()->getParent() != BI
->getParent()->getParent())
801 BasicBlock::iterator InsertPt
;
802 if (Instruction
*InstInput
= dyn_cast
<Instruction
>(V
)) {
803 if (InvokeInst
*II
= dyn_cast
<InvokeInst
>(InstInput
)) {
804 InsertPt
= II
->getNormalDest()->begin();
806 InsertPt
= InstInput
;
809 while (isa
<PHINode
>(InsertPt
)) ++InsertPt
;
811 InsertPt
= TheNeg
->getParent()->getParent()->getEntryBlock().begin();
813 TheNeg
->moveBefore(InsertPt
);
817 // Insert a 'neg' instruction that subtracts the value from zero to get the
819 return BinaryOperator::CreateNeg(V
, V
->getName() + ".neg", BI
);
822 /// ShouldBreakUpSubtract - Return true if we should break up this subtract of
823 /// X-Y into (X + -Y).
824 static bool ShouldBreakUpSubtract(Instruction
*Sub
) {
825 // If this is a negation, we can't split it up!
826 if (BinaryOperator::isNeg(Sub
))
829 // Don't bother to break this up unless either the LHS is an associable add or
830 // subtract or if this is only used by one.
831 if (isReassociableOp(Sub
->getOperand(0), Instruction::Add
) ||
832 isReassociableOp(Sub
->getOperand(0), Instruction::Sub
))
834 if (isReassociableOp(Sub
->getOperand(1), Instruction::Add
) ||
835 isReassociableOp(Sub
->getOperand(1), Instruction::Sub
))
837 if (Sub
->hasOneUse() &&
838 (isReassociableOp(Sub
->use_back(), Instruction::Add
) ||
839 isReassociableOp(Sub
->use_back(), Instruction::Sub
)))
845 /// BreakUpSubtract - If we have (X-Y), and if either X is an add, or if this is
846 /// only used by an add, transform this into (X+(0-Y)) to promote better
848 static BinaryOperator
*BreakUpSubtract(Instruction
*Sub
) {
849 // Convert a subtract into an add and a neg instruction. This allows sub
850 // instructions to be commuted with other add instructions.
852 // Calculate the negative value of Operand 1 of the sub instruction,
853 // and set it as the RHS of the add instruction we just made.
855 Value
*NegVal
= NegateValue(Sub
->getOperand(1), Sub
);
856 BinaryOperator
*New
=
857 BinaryOperator::CreateAdd(Sub
->getOperand(0), NegVal
, "", Sub
);
858 Sub
->setOperand(0, Constant::getNullValue(Sub
->getType())); // Drop use of op.
859 Sub
->setOperand(1, Constant::getNullValue(Sub
->getType())); // Drop use of op.
862 // Everyone now refers to the add instruction.
863 Sub
->replaceAllUsesWith(New
);
864 New
->setDebugLoc(Sub
->getDebugLoc());
866 DEBUG(dbgs() << "Negated: " << *New
<< '\n');
870 /// ConvertShiftToMul - If this is a shift of a reassociable multiply or is used
871 /// by one, change this into a multiply by a constant to assist with further
873 static BinaryOperator
*ConvertShiftToMul(Instruction
*Shl
) {
874 Constant
*MulCst
= ConstantInt::get(Shl
->getType(), 1);
875 MulCst
= ConstantExpr::getShl(MulCst
, cast
<Constant
>(Shl
->getOperand(1)));
877 BinaryOperator
*Mul
=
878 BinaryOperator::CreateMul(Shl
->getOperand(0), MulCst
, "", Shl
);
879 Shl
->setOperand(0, UndefValue::get(Shl
->getType())); // Drop use of op.
881 Shl
->replaceAllUsesWith(Mul
);
882 Mul
->setDebugLoc(Shl
->getDebugLoc());
886 /// FindInOperandList - Scan backwards and forwards among values with the same
887 /// rank as element i to see if X exists. If X does not exist, return i. This
888 /// is useful when scanning for 'x' when we see '-x' because they both get the
890 static unsigned FindInOperandList(SmallVectorImpl
<ValueEntry
> &Ops
, unsigned i
,
892 unsigned XRank
= Ops
[i
].Rank
;
893 unsigned e
= Ops
.size();
894 for (unsigned j
= i
+1; j
!= e
&& Ops
[j
].Rank
== XRank
; ++j
)
898 for (unsigned j
= i
-1; j
!= ~0U && Ops
[j
].Rank
== XRank
; --j
)
904 /// EmitAddTreeOfValues - Emit a tree of add instructions, summing Ops together
905 /// and returning the result. Insert the tree before I.
906 static Value
*EmitAddTreeOfValues(Instruction
*I
,
907 SmallVectorImpl
<WeakVH
> &Ops
){
908 if (Ops
.size() == 1) return Ops
.back();
910 Value
*V1
= Ops
.back();
912 Value
*V2
= EmitAddTreeOfValues(I
, Ops
);
913 return BinaryOperator::CreateAdd(V2
, V1
, "tmp", I
);
916 /// RemoveFactorFromExpression - If V is an expression tree that is a
917 /// multiplication sequence, and if this sequence contains a multiply by Factor,
918 /// remove Factor from the tree and return the new tree.
919 Value
*Reassociate::RemoveFactorFromExpression(Value
*V
, Value
*Factor
) {
920 BinaryOperator
*BO
= isReassociableOp(V
, Instruction::Mul
);
923 SmallVector
<RepeatedValue
, 8> Tree
;
924 MadeChange
|= LinearizeExprTree(BO
, Tree
);
925 SmallVector
<ValueEntry
, 8> Factors
;
926 Factors
.reserve(Tree
.size());
927 for (unsigned i
= 0, e
= Tree
.size(); i
!= e
; ++i
) {
928 RepeatedValue E
= Tree
[i
];
929 Factors
.append(E
.second
.getZExtValue(),
930 ValueEntry(getRank(E
.first
), E
.first
));
933 bool FoundFactor
= false;
934 bool NeedsNegate
= false;
935 for (unsigned i
= 0, e
= Factors
.size(); i
!= e
; ++i
) {
936 if (Factors
[i
].Op
== Factor
) {
938 Factors
.erase(Factors
.begin()+i
);
942 // If this is a negative version of this factor, remove it.
943 if (ConstantInt
*FC1
= dyn_cast
<ConstantInt
>(Factor
))
944 if (ConstantInt
*FC2
= dyn_cast
<ConstantInt
>(Factors
[i
].Op
))
945 if (FC1
->getValue() == -FC2
->getValue()) {
946 FoundFactor
= NeedsNegate
= true;
947 Factors
.erase(Factors
.begin()+i
);
953 // Make sure to restore the operands to the expression tree.
954 RewriteExprTree(BO
, Factors
);
958 BasicBlock::iterator InsertPt
= BO
; ++InsertPt
;
960 // If this was just a single multiply, remove the multiply and return the only
961 // remaining operand.
962 if (Factors
.size() == 1) {
963 RedoInsts
.insert(BO
);
966 RewriteExprTree(BO
, Factors
);
971 V
= BinaryOperator::CreateNeg(V
, "neg", InsertPt
);
976 /// FindSingleUseMultiplyFactors - If V is a single-use multiply, recursively
977 /// add its operands as factors, otherwise add V to the list of factors.
979 /// Ops is the top-level list of add operands we're trying to factor.
980 static void FindSingleUseMultiplyFactors(Value
*V
,
981 SmallVectorImpl
<Value
*> &Factors
,
982 const SmallVectorImpl
<ValueEntry
> &Ops
) {
983 BinaryOperator
*BO
= isReassociableOp(V
, Instruction::Mul
);
985 Factors
.push_back(V
);
989 // Otherwise, add the LHS and RHS to the list of factors.
990 FindSingleUseMultiplyFactors(BO
->getOperand(1), Factors
, Ops
);
991 FindSingleUseMultiplyFactors(BO
->getOperand(0), Factors
, Ops
);
994 /// OptimizeAndOrXor - Optimize a series of operands to an 'and', 'or', or 'xor'
995 /// instruction. This optimizes based on identities. If it can be reduced to
996 /// a single Value, it is returned, otherwise the Ops list is mutated as
998 static Value
*OptimizeAndOrXor(unsigned Opcode
,
999 SmallVectorImpl
<ValueEntry
> &Ops
) {
1000 // Scan the operand lists looking for X and ~X pairs, along with X,X pairs.
1001 // If we find any, we can simplify the expression. X&~X == 0, X|~X == -1.
1002 for (unsigned i
= 0, e
= Ops
.size(); i
!= e
; ++i
) {
1003 // First, check for X and ~X in the operand list.
1004 assert(i
< Ops
.size());
1005 if (BinaryOperator::isNot(Ops
[i
].Op
)) { // Cannot occur for ^.
1006 Value
*X
= BinaryOperator::getNotArgument(Ops
[i
].Op
);
1007 unsigned FoundX
= FindInOperandList(Ops
, i
, X
);
1009 if (Opcode
== Instruction::And
) // ...&X&~X = 0
1010 return Constant::getNullValue(X
->getType());
1012 if (Opcode
== Instruction::Or
) // ...|X|~X = -1
1013 return Constant::getAllOnesValue(X
->getType());
1017 // Next, check for duplicate pairs of values, which we assume are next to
1018 // each other, due to our sorting criteria.
1019 assert(i
< Ops
.size());
1020 if (i
+1 != Ops
.size() && Ops
[i
+1].Op
== Ops
[i
].Op
) {
1021 if (Opcode
== Instruction::And
|| Opcode
== Instruction::Or
) {
1022 // Drop duplicate values for And and Or.
1023 Ops
.erase(Ops
.begin()+i
);
1029 // Drop pairs of values for Xor.
1030 assert(Opcode
== Instruction::Xor
);
1032 return Constant::getNullValue(Ops
[0].Op
->getType());
1035 Ops
.erase(Ops
.begin()+i
, Ops
.begin()+i
+2);
1043 /// OptimizeAdd - Optimize a series of operands to an 'add' instruction. This
1044 /// optimizes based on identities. If it can be reduced to a single Value, it
1045 /// is returned, otherwise the Ops list is mutated as necessary.
1046 Value
*Reassociate::OptimizeAdd(Instruction
*I
,
1047 SmallVectorImpl
<ValueEntry
> &Ops
) {
1048 // Scan the operand lists looking for X and -X pairs. If we find any, we
1049 // can simplify the expression. X+-X == 0. While we're at it, scan for any
1050 // duplicates. We want to canonicalize Y+Y+Y+Z -> 3*Y+Z.
1052 // TODO: We could handle "X + ~X" -> "-1" if we wanted, since "-X = ~X+1".
1054 for (unsigned i
= 0, e
= Ops
.size(); i
!= e
; ++i
) {
1055 Value
*TheOp
= Ops
[i
].Op
;
1056 // Check to see if we've seen this operand before. If so, we factor all
1057 // instances of the operand together. Due to our sorting criteria, we know
1058 // that these need to be next to each other in the vector.
1059 if (i
+1 != Ops
.size() && Ops
[i
+1].Op
== TheOp
) {
1060 // Rescan the list, remove all instances of this operand from the expr.
1061 unsigned NumFound
= 0;
1063 Ops
.erase(Ops
.begin()+i
);
1065 } while (i
!= Ops
.size() && Ops
[i
].Op
== TheOp
);
1067 DEBUG(errs() << "\nFACTORING [" << NumFound
<< "]: " << *TheOp
<< '\n');
1070 // Insert a new multiply.
1071 Value
*Mul
= ConstantInt::get(cast
<IntegerType
>(I
->getType()), NumFound
);
1072 Mul
= BinaryOperator::CreateMul(TheOp
, Mul
, "factor", I
);
1074 // Now that we have inserted a multiply, optimize it. This allows us to
1075 // handle cases that require multiple factoring steps, such as this:
1076 // (X*2) + (X*2) + (X*2) -> (X*2)*3 -> X*6
1077 RedoInsts
.insert(cast
<Instruction
>(Mul
));
1079 // If every add operand was a duplicate, return the multiply.
1083 // Otherwise, we had some input that didn't have the dupe, such as
1084 // "A + A + B" -> "A*2 + B". Add the new multiply to the list of
1085 // things being added by this operation.
1086 Ops
.insert(Ops
.begin(), ValueEntry(getRank(Mul
), Mul
));
1093 // Check for X and -X in the operand list.
1094 if (!BinaryOperator::isNeg(TheOp
))
1097 Value
*X
= BinaryOperator::getNegArgument(TheOp
);
1098 unsigned FoundX
= FindInOperandList(Ops
, i
, X
);
1102 // Remove X and -X from the operand list.
1103 if (Ops
.size() == 2)
1104 return Constant::getNullValue(X
->getType());
1106 Ops
.erase(Ops
.begin()+i
);
1110 --i
; // Need to back up an extra one.
1111 Ops
.erase(Ops
.begin()+FoundX
);
1113 --i
; // Revisit element.
1114 e
-= 2; // Removed two elements.
1117 // Scan the operand list, checking to see if there are any common factors
1118 // between operands. Consider something like A*A+A*B*C+D. We would like to
1119 // reassociate this to A*(A+B*C)+D, which reduces the number of multiplies.
1120 // To efficiently find this, we count the number of times a factor occurs
1121 // for any ADD operands that are MULs.
1122 DenseMap
<Value
*, unsigned> FactorOccurrences
;
1124 // Keep track of each multiply we see, to avoid triggering on (X*4)+(X*4)
1125 // where they are actually the same multiply.
1126 unsigned MaxOcc
= 0;
1127 Value
*MaxOccVal
= 0;
1128 for (unsigned i
= 0, e
= Ops
.size(); i
!= e
; ++i
) {
1129 BinaryOperator
*BOp
= isReassociableOp(Ops
[i
].Op
, Instruction::Mul
);
1133 // Compute all of the factors of this added value.
1134 SmallVector
<Value
*, 8> Factors
;
1135 FindSingleUseMultiplyFactors(BOp
, Factors
, Ops
);
1136 assert(Factors
.size() > 1 && "Bad linearize!");
1138 // Add one to FactorOccurrences for each unique factor in this op.
1139 SmallPtrSet
<Value
*, 8> Duplicates
;
1140 for (unsigned i
= 0, e
= Factors
.size(); i
!= e
; ++i
) {
1141 Value
*Factor
= Factors
[i
];
1142 if (!Duplicates
.insert(Factor
)) continue;
1144 unsigned Occ
= ++FactorOccurrences
[Factor
];
1145 if (Occ
> MaxOcc
) { MaxOcc
= Occ
; MaxOccVal
= Factor
; }
1147 // If Factor is a negative constant, add the negated value as a factor
1148 // because we can percolate the negate out. Watch for minint, which
1149 // cannot be positivified.
1150 if (ConstantInt
*CI
= dyn_cast
<ConstantInt
>(Factor
))
1151 if (CI
->isNegative() && !CI
->isMinValue(true)) {
1152 Factor
= ConstantInt::get(CI
->getContext(), -CI
->getValue());
1153 assert(!Duplicates
.count(Factor
) &&
1154 "Shouldn't have two constant factors, missed a canonicalize");
1156 unsigned Occ
= ++FactorOccurrences
[Factor
];
1157 if (Occ
> MaxOcc
) { MaxOcc
= Occ
; MaxOccVal
= Factor
; }
1162 // If any factor occurred more than one time, we can pull it out.
1164 DEBUG(errs() << "\nFACTORING [" << MaxOcc
<< "]: " << *MaxOccVal
<< '\n');
1167 // Create a new instruction that uses the MaxOccVal twice. If we don't do
1168 // this, we could otherwise run into situations where removing a factor
1169 // from an expression will drop a use of maxocc, and this can cause
1170 // RemoveFactorFromExpression on successive values to behave differently.
1171 Instruction
*DummyInst
= BinaryOperator::CreateAdd(MaxOccVal
, MaxOccVal
);
1172 SmallVector
<WeakVH
, 4> NewMulOps
;
1173 for (unsigned i
= 0; i
!= Ops
.size(); ++i
) {
1174 // Only try to remove factors from expressions we're allowed to.
1175 BinaryOperator
*BOp
= isReassociableOp(Ops
[i
].Op
, Instruction::Mul
);
1179 if (Value
*V
= RemoveFactorFromExpression(Ops
[i
].Op
, MaxOccVal
)) {
1180 // The factorized operand may occur several times. Convert them all in
1182 for (unsigned j
= Ops
.size(); j
!= i
;) {
1184 if (Ops
[j
].Op
== Ops
[i
].Op
) {
1185 NewMulOps
.push_back(V
);
1186 Ops
.erase(Ops
.begin()+j
);
1193 // No need for extra uses anymore.
1196 unsigned NumAddedValues
= NewMulOps
.size();
1197 Value
*V
= EmitAddTreeOfValues(I
, NewMulOps
);
1199 // Now that we have inserted the add tree, optimize it. This allows us to
1200 // handle cases that require multiple factoring steps, such as this:
1201 // A*A*B + A*A*C --> A*(A*B+A*C) --> A*(A*(B+C))
1202 assert(NumAddedValues
> 1 && "Each occurrence should contribute a value");
1203 (void)NumAddedValues
;
1204 if (Instruction
*VI
= dyn_cast
<Instruction
>(V
))
1205 RedoInsts
.insert(VI
);
1207 // Create the multiply.
1208 Instruction
*V2
= BinaryOperator::CreateMul(V
, MaxOccVal
, "tmp", I
);
1210 // Rerun associate on the multiply in case the inner expression turned into
1211 // a multiply. We want to make sure that we keep things in canonical form.
1212 RedoInsts
.insert(V2
);
1214 // If every add operand included the factor (e.g. "A*B + A*C"), then the
1215 // entire result expression is just the multiply "A*(B+C)".
1219 // Otherwise, we had some input that didn't have the factor, such as
1220 // "A*B + A*C + D" -> "A*(B+C) + D". Add the new multiply to the list of
1221 // things being added by this operation.
1222 Ops
.insert(Ops
.begin(), ValueEntry(getRank(V2
), V2
));
1229 /// \brief Predicate tests whether a ValueEntry's op is in a map.
1230 struct IsValueInMap
{
1231 const DenseMap
<Value
*, unsigned> &Map
;
1233 IsValueInMap(const DenseMap
<Value
*, unsigned> &Map
) : Map(Map
) {}
1235 bool operator()(const ValueEntry
&Entry
) {
1236 return Map
.find(Entry
.Op
) != Map
.end();
1241 /// \brief Build up a vector of value/power pairs factoring a product.
1243 /// Given a series of multiplication operands, build a vector of factors and
1244 /// the powers each is raised to when forming the final product. Sort them in
1245 /// the order of descending power.
1247 /// (x*x) -> [(x, 2)]
1248 /// ((x*x)*x) -> [(x, 3)]
1249 /// ((((x*y)*x)*y)*x) -> [(x, 3), (y, 2)]
1251 /// \returns Whether any factors have a power greater than one.
1252 bool Reassociate::collectMultiplyFactors(SmallVectorImpl
<ValueEntry
> &Ops
,
1253 SmallVectorImpl
<Factor
> &Factors
) {
1254 // FIXME: Have Ops be (ValueEntry, Multiplicity) pairs, simplifying this.
1255 // Compute the sum of powers of simplifiable factors.
1256 unsigned FactorPowerSum
= 0;
1257 for (unsigned Idx
= 1, Size
= Ops
.size(); Idx
< Size
; ++Idx
) {
1258 Value
*Op
= Ops
[Idx
-1].Op
;
1260 // Count the number of occurrences of this value.
1262 for (; Idx
< Size
&& Ops
[Idx
].Op
== Op
; ++Idx
)
1264 // Track for simplification all factors which occur 2 or more times.
1266 FactorPowerSum
+= Count
;
1269 // We can only simplify factors if the sum of the powers of our simplifiable
1270 // factors is 4 or higher. When that is the case, we will *always* have
1271 // a simplification. This is an important invariant to prevent cyclicly
1272 // trying to simplify already minimal formations.
1273 if (FactorPowerSum
< 4)
1276 // Now gather the simplifiable factors, removing them from Ops.
1278 for (unsigned Idx
= 1; Idx
< Ops
.size(); ++Idx
) {
1279 Value
*Op
= Ops
[Idx
-1].Op
;
1281 // Count the number of occurrences of this value.
1283 for (; Idx
< Ops
.size() && Ops
[Idx
].Op
== Op
; ++Idx
)
1287 // Move an even number of occurrences to Factors.
1290 FactorPowerSum
+= Count
;
1291 Factors
.push_back(Factor(Op
, Count
));
1292 Ops
.erase(Ops
.begin()+Idx
, Ops
.begin()+Idx
+Count
);
1295 // None of the adjustments above should have reduced the sum of factor powers
1296 // below our mininum of '4'.
1297 assert(FactorPowerSum
>= 4);
1299 std::sort(Factors
.begin(), Factors
.end(), Factor::PowerDescendingSorter());
1303 /// \brief Build a tree of multiplies, computing the product of Ops.
1304 static Value
*buildMultiplyTree(IRBuilder
<> &Builder
,
1305 SmallVectorImpl
<Value
*> &Ops
) {
1306 if (Ops
.size() == 1)
1309 Value
*LHS
= Ops
.pop_back_val();
1311 LHS
= Builder
.CreateMul(LHS
, Ops
.pop_back_val());
1312 } while (!Ops
.empty());
1317 /// \brief Build a minimal multiplication DAG for (a^x)*(b^y)*(c^z)*...
1319 /// Given a vector of values raised to various powers, where no two values are
1320 /// equal and the powers are sorted in decreasing order, compute the minimal
1321 /// DAG of multiplies to compute the final product, and return that product
1323 Value
*Reassociate::buildMinimalMultiplyDAG(IRBuilder
<> &Builder
,
1324 SmallVectorImpl
<Factor
> &Factors
) {
1325 assert(Factors
[0].Power
);
1326 SmallVector
<Value
*, 4> OuterProduct
;
1327 for (unsigned LastIdx
= 0, Idx
= 1, Size
= Factors
.size();
1328 Idx
< Size
&& Factors
[Idx
].Power
> 0; ++Idx
) {
1329 if (Factors
[Idx
].Power
!= Factors
[LastIdx
].Power
) {
1334 // We want to multiply across all the factors with the same power so that
1335 // we can raise them to that power as a single entity. Build a mini tree
1337 SmallVector
<Value
*, 4> InnerProduct
;
1338 InnerProduct
.push_back(Factors
[LastIdx
].Base
);
1340 InnerProduct
.push_back(Factors
[Idx
].Base
);
1342 } while (Idx
< Size
&& Factors
[Idx
].Power
== Factors
[LastIdx
].Power
);
1344 // Reset the base value of the first factor to the new expression tree.
1345 // We'll remove all the factors with the same power in a second pass.
1346 Value
*M
= Factors
[LastIdx
].Base
= buildMultiplyTree(Builder
, InnerProduct
);
1347 if (Instruction
*MI
= dyn_cast
<Instruction
>(M
))
1348 RedoInsts
.insert(MI
);
1352 // Unique factors with equal powers -- we've folded them into the first one's
1354 Factors
.erase(std::unique(Factors
.begin(), Factors
.end(),
1355 Factor::PowerEqual()),
1358 // Iteratively collect the base of each factor with an add power into the
1359 // outer product, and halve each power in preparation for squaring the
1361 for (unsigned Idx
= 0, Size
= Factors
.size(); Idx
!= Size
; ++Idx
) {
1362 if (Factors
[Idx
].Power
& 1)
1363 OuterProduct
.push_back(Factors
[Idx
].Base
);
1364 Factors
[Idx
].Power
>>= 1;
1366 if (Factors
[0].Power
) {
1367 Value
*SquareRoot
= buildMinimalMultiplyDAG(Builder
, Factors
);
1368 OuterProduct
.push_back(SquareRoot
);
1369 OuterProduct
.push_back(SquareRoot
);
1371 if (OuterProduct
.size() == 1)
1372 return OuterProduct
.front();
1374 Value
*V
= buildMultiplyTree(Builder
, OuterProduct
);
1378 Value
*Reassociate::OptimizeMul(BinaryOperator
*I
,
1379 SmallVectorImpl
<ValueEntry
> &Ops
) {
1380 // We can only optimize the multiplies when there is a chain of more than
1381 // three, such that a balanced tree might require fewer total multiplies.
1385 // Try to turn linear trees of multiplies without other uses of the
1386 // intermediate stages into minimal multiply DAGs with perfect sub-expression
1388 SmallVector
<Factor
, 4> Factors
;
1389 if (!collectMultiplyFactors(Ops
, Factors
))
1390 return 0; // All distinct factors, so nothing left for us to do.
1392 IRBuilder
<> Builder(I
);
1393 Value
*V
= buildMinimalMultiplyDAG(Builder
, Factors
);
1397 ValueEntry NewEntry
= ValueEntry(getRank(V
), V
);
1398 Ops
.insert(std::lower_bound(Ops
.begin(), Ops
.end(), NewEntry
), NewEntry
);
1402 Value
*Reassociate::OptimizeExpression(BinaryOperator
*I
,
1403 SmallVectorImpl
<ValueEntry
> &Ops
) {
1404 // Now that we have the linearized expression tree, try to optimize it.
1405 // Start by folding any constants that we found.
1407 unsigned Opcode
= I
->getOpcode();
1408 while (!Ops
.empty() && isa
<Constant
>(Ops
.back().Op
)) {
1409 Constant
*C
= cast
<Constant
>(Ops
.pop_back_val().Op
);
1410 Cst
= Cst
? ConstantExpr::get(Opcode
, C
, Cst
) : C
;
1412 // If there was nothing but constants then we are done.
1416 // Put the combined constant back at the end of the operand list, except if
1417 // there is no point. For example, an add of 0 gets dropped here, while a
1418 // multiplication by zero turns the whole expression into zero.
1419 if (Cst
&& Cst
!= ConstantExpr::getBinOpIdentity(Opcode
, I
->getType())) {
1420 if (Cst
== ConstantExpr::getBinOpAbsorber(Opcode
, I
->getType()))
1422 Ops
.push_back(ValueEntry(0, Cst
));
1425 if (Ops
.size() == 1) return Ops
[0].Op
;
1427 // Handle destructive annihilation due to identities between elements in the
1428 // argument list here.
1429 unsigned NumOps
= Ops
.size();
1432 case Instruction::And
:
1433 case Instruction::Or
:
1434 case Instruction::Xor
:
1435 if (Value
*Result
= OptimizeAndOrXor(Opcode
, Ops
))
1439 case Instruction::Add
:
1440 if (Value
*Result
= OptimizeAdd(I
, Ops
))
1444 case Instruction::Mul
:
1445 if (Value
*Result
= OptimizeMul(I
, Ops
))
1450 if (Ops
.size() != NumOps
)
1451 return OptimizeExpression(I
, Ops
);
1455 /// EraseInst - Zap the given instruction, adding interesting operands to the
1457 void Reassociate::EraseInst(Instruction
*I
) {
1458 assert(isInstructionTriviallyDead(I
) && "Trivially dead instructions only!");
1459 SmallVector
<Value
*, 8> Ops(I
->op_begin(), I
->op_end());
1460 // Erase the dead instruction.
1461 ValueRankMap
.erase(I
);
1462 RedoInsts
.remove(I
);
1463 I
->eraseFromParent();
1464 // Optimize its operands.
1465 SmallPtrSet
<Instruction
*, 8> Visited
; // Detect self-referential nodes.
1466 for (unsigned i
= 0, e
= Ops
.size(); i
!= e
; ++i
)
1467 if (Instruction
*Op
= dyn_cast
<Instruction
>(Ops
[i
])) {
1468 // If this is a node in an expression tree, climb to the expression root
1469 // and add that since that's where optimization actually happens.
1470 unsigned Opcode
= Op
->getOpcode();
1471 while (Op
->hasOneUse() && Op
->use_back()->getOpcode() == Opcode
&&
1473 Op
= Op
->use_back();
1474 RedoInsts
.insert(Op
);
1478 /// OptimizeInst - Inspect and optimize the given instruction. Note that erasing
1479 /// instructions is not allowed.
1480 void Reassociate::OptimizeInst(Instruction
*I
) {
1481 // Only consider operations that we understand.
1482 if (!isa
<BinaryOperator
>(I
))
1485 if (I
->getOpcode() == Instruction::Shl
&&
1486 isa
<ConstantInt
>(I
->getOperand(1)))
1487 // If an operand of this shift is a reassociable multiply, or if the shift
1488 // is used by a reassociable multiply or add, turn into a multiply.
1489 if (isReassociableOp(I
->getOperand(0), Instruction::Mul
) ||
1491 (isReassociableOp(I
->use_back(), Instruction::Mul
) ||
1492 isReassociableOp(I
->use_back(), Instruction::Add
)))) {
1493 Instruction
*NI
= ConvertShiftToMul(I
);
1494 RedoInsts
.insert(I
);
1499 // Floating point binary operators are not associative, but we can still
1500 // commute (some) of them, to canonicalize the order of their operands.
1501 // This can potentially expose more CSE opportunities, and makes writing
1502 // other transformations simpler.
1503 if ((I
->getType()->isFloatingPointTy() || I
->getType()->isVectorTy())) {
1504 // FAdd and FMul can be commuted.
1505 if (I
->getOpcode() != Instruction::FMul
&&
1506 I
->getOpcode() != Instruction::FAdd
)
1509 Value
*LHS
= I
->getOperand(0);
1510 Value
*RHS
= I
->getOperand(1);
1511 unsigned LHSRank
= getRank(LHS
);
1512 unsigned RHSRank
= getRank(RHS
);
1514 // Sort the operands by rank.
1515 if (RHSRank
< LHSRank
) {
1516 I
->setOperand(0, RHS
);
1517 I
->setOperand(1, LHS
);
1523 // Do not reassociate boolean (i1) expressions. We want to preserve the
1524 // original order of evaluation for short-circuited comparisons that
1525 // SimplifyCFG has folded to AND/OR expressions. If the expression
1526 // is not further optimized, it is likely to be transformed back to a
1527 // short-circuited form for code gen, and the source order may have been
1528 // optimized for the most likely conditions.
1529 if (I
->getType()->isIntegerTy(1))
1532 // If this is a subtract instruction which is not already in negate form,
1533 // see if we can convert it to X+-Y.
1534 if (I
->getOpcode() == Instruction::Sub
) {
1535 if (ShouldBreakUpSubtract(I
)) {
1536 Instruction
*NI
= BreakUpSubtract(I
);
1537 RedoInsts
.insert(I
);
1540 } else if (BinaryOperator::isNeg(I
)) {
1541 // Otherwise, this is a negation. See if the operand is a multiply tree
1542 // and if this is not an inner node of a multiply tree.
1543 if (isReassociableOp(I
->getOperand(1), Instruction::Mul
) &&
1545 !isReassociableOp(I
->use_back(), Instruction::Mul
))) {
1546 Instruction
*NI
= LowerNegateToMultiply(I
);
1547 RedoInsts
.insert(I
);
1554 // If this instruction is an associative binary operator, process it.
1555 if (!I
->isAssociative()) return;
1556 BinaryOperator
*BO
= cast
<BinaryOperator
>(I
);
1558 // If this is an interior node of a reassociable tree, ignore it until we
1559 // get to the root of the tree, to avoid N^2 analysis.
1560 unsigned Opcode
= BO
->getOpcode();
1561 if (BO
->hasOneUse() && BO
->use_back()->getOpcode() == Opcode
)
1564 // If this is an add tree that is used by a sub instruction, ignore it
1565 // until we process the subtract.
1566 if (BO
->hasOneUse() && BO
->getOpcode() == Instruction::Add
&&
1567 cast
<Instruction
>(BO
->use_back())->getOpcode() == Instruction::Sub
)
1570 ReassociateExpression(BO
);
1573 void Reassociate::ReassociateExpression(BinaryOperator
*I
) {
1575 // First, walk the expression tree, linearizing the tree, collecting the
1576 // operand information.
1577 SmallVector
<RepeatedValue
, 8> Tree
;
1578 MadeChange
|= LinearizeExprTree(I
, Tree
);
1579 SmallVector
<ValueEntry
, 8> Ops
;
1580 Ops
.reserve(Tree
.size());
1581 for (unsigned i
= 0, e
= Tree
.size(); i
!= e
; ++i
) {
1582 RepeatedValue E
= Tree
[i
];
1583 Ops
.append(E
.second
.getZExtValue(),
1584 ValueEntry(getRank(E
.first
), E
.first
));
1587 DEBUG(dbgs() << "RAIn:\t"; PrintOps(I
, Ops
); dbgs() << '\n');
1589 // Now that we have linearized the tree to a list and have gathered all of
1590 // the operands and their ranks, sort the operands by their rank. Use a
1591 // stable_sort so that values with equal ranks will have their relative
1592 // positions maintained (and so the compiler is deterministic). Note that
1593 // this sorts so that the highest ranking values end up at the beginning of
1595 std::stable_sort(Ops
.begin(), Ops
.end());
1597 // OptimizeExpression - Now that we have the expression tree in a convenient
1598 // sorted form, optimize it globally if possible.
1599 if (Value
*V
= OptimizeExpression(I
, Ops
)) {
1601 // Self-referential expression in unreachable code.
1603 // This expression tree simplified to something that isn't a tree,
1605 DEBUG(dbgs() << "Reassoc to scalar: " << *V
<< '\n');
1606 I
->replaceAllUsesWith(V
);
1607 if (Instruction
*VI
= dyn_cast
<Instruction
>(V
))
1608 VI
->setDebugLoc(I
->getDebugLoc());
1609 RedoInsts
.insert(I
);
1614 // We want to sink immediates as deeply as possible except in the case where
1615 // this is a multiply tree used only by an add, and the immediate is a -1.
1616 // In this case we reassociate to put the negation on the outside so that we
1617 // can fold the negation into the add: (-X)*Y + Z -> Z-X*Y
1618 if (I
->getOpcode() == Instruction::Mul
&& I
->hasOneUse() &&
1619 cast
<Instruction
>(I
->use_back())->getOpcode() == Instruction::Add
&&
1620 isa
<ConstantInt
>(Ops
.back().Op
) &&
1621 cast
<ConstantInt
>(Ops
.back().Op
)->isAllOnesValue()) {
1622 ValueEntry Tmp
= Ops
.pop_back_val();
1623 Ops
.insert(Ops
.begin(), Tmp
);
1626 DEBUG(dbgs() << "RAOut:\t"; PrintOps(I
, Ops
); dbgs() << '\n');
1628 if (Ops
.size() == 1) {
1630 // Self-referential expression in unreachable code.
1633 // This expression tree simplified to something that isn't a tree,
1635 I
->replaceAllUsesWith(Ops
[0].Op
);
1636 if (Instruction
*OI
= dyn_cast
<Instruction
>(Ops
[0].Op
))
1637 OI
->setDebugLoc(I
->getDebugLoc());
1638 RedoInsts
.insert(I
);
1642 // Now that we ordered and optimized the expressions, splat them back into
1643 // the expression tree, removing any unneeded nodes.
1644 RewriteExprTree(I
, Ops
);
1647 bool Reassociate::runOnFunction(Function
&F
) {
1648 // Calculate the rank map for F
1652 for (Function::iterator BI
= F
.begin(), BE
= F
.end(); BI
!= BE
; ++BI
) {
1653 // Optimize every instruction in the basic block.
1654 for (BasicBlock::iterator II
= BI
->begin(), IE
= BI
->end(); II
!= IE
; )
1655 if (isInstructionTriviallyDead(II
)) {
1659 assert(II
->getParent() == BI
&& "Moved to a different block!");
1663 // If this produced extra instructions to optimize, handle them now.
1664 while (!RedoInsts
.empty()) {
1665 Instruction
*I
= RedoInsts
.pop_back_val();
1666 if (isInstructionTriviallyDead(I
))
1673 // We are done with the rank map.
1675 ValueRankMap
.clear();