1 //===- Reassociate.cpp - Reassociate binary expressions -------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This pass reassociates commutative expressions in an order that is designed
11 // to promote better constant propagation, GCSE, LICM, PRE, etc.
13 // For example: 4 + (x + 5) -> x + (4 + 5)
15 // In the implementation of this algorithm, constants are assigned rank = 0,
16 // function arguments are rank = 1, and other values are assigned ranks
17 // corresponding to the reverse post order traversal of current function
18 // (starting at 2), which effectively gives values in deep loops higher rank
19 // than values not in loops.
21 //===----------------------------------------------------------------------===//
23 #define DEBUG_TYPE "reassociate"
24 #include "llvm/Transforms/Scalar.h"
25 #include "llvm/Transforms/Utils/Local.h"
26 #include "llvm/Constants.h"
27 #include "llvm/DerivedTypes.h"
28 #include "llvm/Function.h"
29 #include "llvm/IRBuilder.h"
30 #include "llvm/Instructions.h"
31 #include "llvm/IntrinsicInst.h"
32 #include "llvm/Pass.h"
33 #include "llvm/ADT/DenseMap.h"
34 #include "llvm/ADT/PostOrderIterator.h"
35 #include "llvm/ADT/STLExtras.h"
36 #include "llvm/ADT/SetVector.h"
37 #include "llvm/ADT/Statistic.h"
38 #include "llvm/Assembly/Writer.h"
39 #include "llvm/Support/CFG.h"
40 #include "llvm/Support/Debug.h"
41 #include "llvm/Support/ValueHandle.h"
42 #include "llvm/Support/raw_ostream.h"
46 STATISTIC(NumChanged
, "Number of insts reassociated");
47 STATISTIC(NumAnnihil
, "Number of expr tree annihilated");
48 STATISTIC(NumFactor
, "Number of multiplies factored");
54 ValueEntry(unsigned R
, Value
*O
) : Rank(R
), Op(O
) {}
56 inline bool operator<(const ValueEntry
&LHS
, const ValueEntry
&RHS
) {
57 return LHS
.Rank
> RHS
.Rank
; // Sort so that highest rank goes to start.
62 /// PrintOps - Print out the expression identified in the Ops list.
64 static void PrintOps(Instruction
*I
, const SmallVectorImpl
<ValueEntry
> &Ops
) {
65 Module
*M
= I
->getParent()->getParent()->getParent();
66 dbgs() << Instruction::getOpcodeName(I
->getOpcode()) << " "
67 << *Ops
[0].Op
->getType() << '\t';
68 for (unsigned i
= 0, e
= Ops
.size(); i
!= e
; ++i
) {
70 WriteAsOperand(dbgs(), Ops
[i
].Op
, false, M
);
71 dbgs() << ", #" << Ops
[i
].Rank
<< "] ";
77 /// \brief Utility class representing a base and exponent pair which form one
78 /// factor of some product.
83 Factor(Value
*Base
, unsigned Power
) : Base(Base
), Power(Power
) {}
85 /// \brief Sort factors by their Base.
87 bool operator()(const Factor
&LHS
, const Factor
&RHS
) {
88 return LHS
.Base
< RHS
.Base
;
92 /// \brief Compare factors for equal bases.
94 bool operator()(const Factor
&LHS
, const Factor
&RHS
) {
95 return LHS
.Base
== RHS
.Base
;
99 /// \brief Sort factors in descending order by their power.
100 struct PowerDescendingSorter
{
101 bool operator()(const Factor
&LHS
, const Factor
&RHS
) {
102 return LHS
.Power
> RHS
.Power
;
106 /// \brief Compare factors for equal powers.
108 bool operator()(const Factor
&LHS
, const Factor
&RHS
) {
109 return LHS
.Power
== RHS
.Power
;
116 class Reassociate
: public FunctionPass
{
117 DenseMap
<BasicBlock
*, unsigned> RankMap
;
118 DenseMap
<AssertingVH
<Value
>, unsigned> ValueRankMap
;
119 SetVector
<AssertingVH
<Instruction
> > RedoInsts
;
122 static char ID
; // Pass identification, replacement for typeid
123 Reassociate() : FunctionPass(ID
) {
124 initializeReassociatePass(*PassRegistry::getPassRegistry());
127 bool runOnFunction(Function
&F
);
129 virtual void getAnalysisUsage(AnalysisUsage
&AU
) const {
130 AU
.setPreservesCFG();
133 void BuildRankMap(Function
&F
);
134 unsigned getRank(Value
*V
);
135 void ReassociateExpression(BinaryOperator
*I
);
136 void RewriteExprTree(BinaryOperator
*I
, SmallVectorImpl
<ValueEntry
> &Ops
);
137 Value
*OptimizeExpression(BinaryOperator
*I
,
138 SmallVectorImpl
<ValueEntry
> &Ops
);
139 Value
*OptimizeAdd(Instruction
*I
, SmallVectorImpl
<ValueEntry
> &Ops
);
140 bool collectMultiplyFactors(SmallVectorImpl
<ValueEntry
> &Ops
,
141 SmallVectorImpl
<Factor
> &Factors
);
142 Value
*buildMinimalMultiplyDAG(IRBuilder
<> &Builder
,
143 SmallVectorImpl
<Factor
> &Factors
);
144 Value
*OptimizeMul(BinaryOperator
*I
, SmallVectorImpl
<ValueEntry
> &Ops
);
145 Value
*RemoveFactorFromExpression(Value
*V
, Value
*Factor
);
146 void EraseInst(Instruction
*I
);
147 void OptimizeInst(Instruction
*I
);
151 char Reassociate::ID
= 0;
152 INITIALIZE_PASS(Reassociate
, "reassociate",
153 "Reassociate expressions", false, false)
155 // Public interface to the Reassociate pass
156 FunctionPass
*llvm::createReassociatePass() { return new Reassociate(); }
158 /// isReassociableOp - Return true if V is an instruction of the specified
159 /// opcode and if it only has one use.
160 static BinaryOperator
*isReassociableOp(Value
*V
, unsigned Opcode
) {
161 if (V
->hasOneUse() && isa
<Instruction
>(V
) &&
162 cast
<Instruction
>(V
)->getOpcode() == Opcode
)
163 return cast
<BinaryOperator
>(V
);
167 static bool isUnmovableInstruction(Instruction
*I
) {
168 if (I
->getOpcode() == Instruction::PHI
||
169 I
->getOpcode() == Instruction::LandingPad
||
170 I
->getOpcode() == Instruction::Alloca
||
171 I
->getOpcode() == Instruction::Load
||
172 I
->getOpcode() == Instruction::Invoke
||
173 (I
->getOpcode() == Instruction::Call
&&
174 !isa
<DbgInfoIntrinsic
>(I
)) ||
175 I
->getOpcode() == Instruction::UDiv
||
176 I
->getOpcode() == Instruction::SDiv
||
177 I
->getOpcode() == Instruction::FDiv
||
178 I
->getOpcode() == Instruction::URem
||
179 I
->getOpcode() == Instruction::SRem
||
180 I
->getOpcode() == Instruction::FRem
)
185 void Reassociate::BuildRankMap(Function
&F
) {
188 // Assign distinct ranks to function arguments
189 for (Function::arg_iterator I
= F
.arg_begin(), E
= F
.arg_end(); I
!= E
; ++I
)
190 ValueRankMap
[&*I
] = ++i
;
192 ReversePostOrderTraversal
<Function
*> RPOT(&F
);
193 for (ReversePostOrderTraversal
<Function
*>::rpo_iterator I
= RPOT
.begin(),
194 E
= RPOT
.end(); I
!= E
; ++I
) {
196 unsigned BBRank
= RankMap
[BB
] = ++i
<< 16;
198 // Walk the basic block, adding precomputed ranks for any instructions that
199 // we cannot move. This ensures that the ranks for these instructions are
200 // all different in the block.
201 for (BasicBlock::iterator I
= BB
->begin(), E
= BB
->end(); I
!= E
; ++I
)
202 if (isUnmovableInstruction(I
))
203 ValueRankMap
[&*I
] = ++BBRank
;
207 unsigned Reassociate::getRank(Value
*V
) {
208 Instruction
*I
= dyn_cast
<Instruction
>(V
);
210 if (isa
<Argument
>(V
)) return ValueRankMap
[V
]; // Function argument.
211 return 0; // Otherwise it's a global or constant, rank 0.
214 if (unsigned Rank
= ValueRankMap
[I
])
215 return Rank
; // Rank already known?
217 // If this is an expression, return the 1+MAX(rank(LHS), rank(RHS)) so that
218 // we can reassociate expressions for code motion! Since we do not recurse
219 // for PHI nodes, we cannot have infinite recursion here, because there
220 // cannot be loops in the value graph that do not go through PHI nodes.
221 unsigned Rank
= 0, MaxRank
= RankMap
[I
->getParent()];
222 for (unsigned i
= 0, e
= I
->getNumOperands();
223 i
!= e
&& Rank
!= MaxRank
; ++i
)
224 Rank
= std::max(Rank
, getRank(I
->getOperand(i
)));
226 // If this is a not or neg instruction, do not count it for rank. This
227 // assures us that X and ~X will have the same rank.
228 if (!I
->getType()->isIntegerTy() ||
229 (!BinaryOperator::isNot(I
) && !BinaryOperator::isNeg(I
)))
232 //DEBUG(dbgs() << "Calculated Rank[" << V->getName() << "] = "
235 return ValueRankMap
[I
] = Rank
;
238 /// LowerNegateToMultiply - Replace 0-X with X*-1.
240 static BinaryOperator
*LowerNegateToMultiply(Instruction
*Neg
) {
241 Constant
*Cst
= Constant::getAllOnesValue(Neg
->getType());
243 BinaryOperator
*Res
=
244 BinaryOperator::CreateMul(Neg
->getOperand(1), Cst
, "",Neg
);
245 Neg
->setOperand(1, Constant::getNullValue(Neg
->getType())); // Drop use of op.
247 Neg
->replaceAllUsesWith(Res
);
248 Res
->setDebugLoc(Neg
->getDebugLoc());
252 /// CarmichaelShift - Returns k such that lambda(2^Bitwidth) = 2^k, where lambda
253 /// is the Carmichael function. This means that x^(2^k) === 1 mod 2^Bitwidth for
254 /// every odd x, i.e. x^(2^k) = 1 for every odd x in Bitwidth-bit arithmetic.
255 /// Note that 0 <= k < Bitwidth, and if Bitwidth > 3 then x^(2^k) = 0 for every
256 /// even x in Bitwidth-bit arithmetic.
257 static unsigned CarmichaelShift(unsigned Bitwidth
) {
263 /// IncorporateWeight - Add the extra weight 'RHS' to the existing weight 'LHS',
264 /// reducing the combined weight using any special properties of the operation.
265 /// The existing weight LHS represents the computation X op X op ... op X where
266 /// X occurs LHS times. The combined weight represents X op X op ... op X with
267 /// X occurring LHS + RHS times. If op is "Xor" for example then the combined
268 /// operation is equivalent to X if LHS + RHS is odd, or 0 if LHS + RHS is even;
269 /// the routine returns 1 in LHS in the first case, and 0 in LHS in the second.
270 static void IncorporateWeight(APInt
&LHS
, const APInt
&RHS
, unsigned Opcode
) {
271 // If we were working with infinite precision arithmetic then the combined
272 // weight would be LHS + RHS. But we are using finite precision arithmetic,
273 // and the APInt sum LHS + RHS may not be correct if it wraps (it is correct
274 // for nilpotent operations and addition, but not for idempotent operations
275 // and multiplication), so it is important to correctly reduce the combined
276 // weight back into range if wrapping would be wrong.
278 // If RHS is zero then the weight didn't change.
279 if (RHS
.isMinValue())
281 // If LHS is zero then the combined weight is RHS.
282 if (LHS
.isMinValue()) {
286 // From this point on we know that neither LHS nor RHS is zero.
288 if (Instruction::isIdempotent(Opcode
)) {
289 // Idempotent means X op X === X, so any non-zero weight is equivalent to a
290 // weight of 1. Keeping weights at zero or one also means that wrapping is
292 assert(LHS
== 1 && RHS
== 1 && "Weights not reduced!");
293 return; // Return a weight of 1.
295 if (Instruction::isNilpotent(Opcode
)) {
296 // Nilpotent means X op X === 0, so reduce weights modulo 2.
297 assert(LHS
== 1 && RHS
== 1 && "Weights not reduced!");
298 LHS
= 0; // 1 + 1 === 0 modulo 2.
301 if (Opcode
== Instruction::Add
) {
302 // TODO: Reduce the weight by exploiting nsw/nuw?
307 assert(Opcode
== Instruction::Mul
&& "Unknown associative operation!");
308 unsigned Bitwidth
= LHS
.getBitWidth();
309 // If CM is the Carmichael number then a weight W satisfying W >= CM+Bitwidth
310 // can be replaced with W-CM. That's because x^W=x^(W-CM) for every Bitwidth
311 // bit number x, since either x is odd in which case x^CM = 1, or x is even in
312 // which case both x^W and x^(W - CM) are zero. By subtracting off multiples
313 // of CM like this weights can always be reduced to the range [0, CM+Bitwidth)
314 // which by a happy accident means that they can always be represented using
316 // TODO: Reduce the weight by exploiting nsw/nuw? (Could do much better than
317 // the Carmichael number).
319 /// CM - The value of Carmichael's lambda function.
320 APInt CM
= APInt::getOneBitSet(Bitwidth
, CarmichaelShift(Bitwidth
));
321 // Any weight W >= Threshold can be replaced with W - CM.
322 APInt Threshold
= CM
+ Bitwidth
;
323 assert(LHS
.ult(Threshold
) && RHS
.ult(Threshold
) && "Weights not reduced!");
324 // For Bitwidth 4 or more the following sum does not overflow.
326 while (LHS
.uge(Threshold
))
329 // To avoid problems with overflow do everything the same as above but using
331 unsigned CM
= 1U << CarmichaelShift(Bitwidth
);
332 unsigned Threshold
= CM
+ Bitwidth
;
333 assert(LHS
.getZExtValue() < Threshold
&& RHS
.getZExtValue() < Threshold
&&
334 "Weights not reduced!");
335 unsigned Total
= LHS
.getZExtValue() + RHS
.getZExtValue();
336 while (Total
>= Threshold
)
342 /// EvaluateRepeatedConstant - Compute C op C op ... op C where the constant C
343 /// is repeated Weight times.
344 static Constant
*EvaluateRepeatedConstant(unsigned Opcode
, Constant
*C
,
346 // For addition the result can be efficiently computed as the product of the
347 // constant and the weight.
348 if (Opcode
== Instruction::Add
)
349 return ConstantExpr::getMul(C
, ConstantInt::get(C
->getContext(), Weight
));
351 // The weight might be huge, so compute by repeated squaring to ensure that
352 // compile time is proportional to the logarithm of the weight.
353 Constant
*Result
= 0;
354 Constant
*Power
= C
; // Successively C, C op C, (C op C) op (C op C) etc.
355 // Visit the bits in Weight.
356 while (Weight
!= 0) {
357 // If the current bit in Weight is non-zero do Result = Result op Power.
359 Result
= Result
? ConstantExpr::get(Opcode
, Result
, Power
) : Power
;
360 // Move on to the next bit if any more are non-zero.
361 Weight
= Weight
.lshr(1);
362 if (Weight
.isMinValue())
365 Power
= ConstantExpr::get(Opcode
, Power
, Power
);
368 assert(Result
&& "Only positive weights supported!");
372 typedef std::pair
<Value
*, APInt
> RepeatedValue
;
374 /// LinearizeExprTree - Given an associative binary expression, return the leaf
375 /// nodes in Ops along with their weights (how many times the leaf occurs). The
376 /// original expression is the same as
377 /// (Ops[0].first op Ops[0].first op ... Ops[0].first) <- Ops[0].second times
379 /// (Ops[1].first op Ops[1].first op ... Ops[1].first) <- Ops[1].second times
383 /// (Ops[N].first op Ops[N].first op ... Ops[N].first) <- Ops[N].second times
385 /// Note that the values Ops[0].first, ..., Ops[N].first are all distinct, and
386 /// they are all non-constant except possibly for the last one, which if it is
387 /// constant will have weight one (Ops[N].second === 1).
389 /// This routine may modify the function, in which case it returns 'true'. The
390 /// changes it makes may well be destructive, changing the value computed by 'I'
391 /// to something completely different. Thus if the routine returns 'true' then
392 /// you MUST either replace I with a new expression computed from the Ops array,
393 /// or use RewriteExprTree to put the values back in.
395 /// A leaf node is either not a binary operation of the same kind as the root
396 /// node 'I' (i.e. is not a binary operator at all, or is, but with a different
397 /// opcode), or is the same kind of binary operator but has a use which either
398 /// does not belong to the expression, or does belong to the expression but is
399 /// a leaf node. Every leaf node has at least one use that is a non-leaf node
400 /// of the expression, while for non-leaf nodes (except for the root 'I') every
401 /// use is a non-leaf node of the expression.
404 /// expression graph node names
414 /// The leaf nodes are C, E, F and G. The Ops array will contain (maybe not in
415 /// that order) (C, 1), (E, 1), (F, 2), (G, 2).
417 /// The expression is maximal: if some instruction is a binary operator of the
418 /// same kind as 'I', and all of its uses are non-leaf nodes of the expression,
419 /// then the instruction also belongs to the expression, is not a leaf node of
420 /// it, and its operands also belong to the expression (but may be leaf nodes).
422 /// NOTE: This routine will set operands of non-leaf non-root nodes to undef in
423 /// order to ensure that every non-root node in the expression has *exactly one*
424 /// use by a non-leaf node of the expression. This destruction means that the
425 /// caller MUST either replace 'I' with a new expression or use something like
426 /// RewriteExprTree to put the values back in if the routine indicates that it
427 /// made a change by returning 'true'.
429 /// In the above example either the right operand of A or the left operand of B
430 /// will be replaced by undef. If it is B's operand then this gives:
434 /// + + | A, B - operand of B replaced with undef
440 /// Note that such undef operands can only be reached by passing through 'I'.
441 /// For example, if you visit operands recursively starting from a leaf node
442 /// then you will never see such an undef operand unless you get back to 'I',
443 /// which requires passing through a phi node.
445 /// Note that this routine may also mutate binary operators of the wrong type
446 /// that have all uses inside the expression (i.e. only used by non-leaf nodes
447 /// of the expression) if it can turn them into binary operators of the right
448 /// type and thus make the expression bigger.
450 static bool LinearizeExprTree(BinaryOperator
*I
,
451 SmallVectorImpl
<RepeatedValue
> &Ops
) {
452 DEBUG(dbgs() << "LINEARIZE: " << *I
<< '\n');
453 unsigned Bitwidth
= I
->getType()->getScalarType()->getPrimitiveSizeInBits();
454 unsigned Opcode
= I
->getOpcode();
455 assert(Instruction::isAssociative(Opcode
) &&
456 Instruction::isCommutative(Opcode
) &&
457 "Expected an associative and commutative operation!");
458 // If we see an absorbing element then the entire expression must be equal to
459 // it. For example, if this is a multiplication expression and zero occurs as
460 // an operand somewhere in it then the result of the expression must be zero.
461 Constant
*Absorber
= ConstantExpr::getBinOpAbsorber(Opcode
, I
->getType());
463 // Visit all operands of the expression, keeping track of their weight (the
464 // number of paths from the expression root to the operand, or if you like
465 // the number of times that operand occurs in the linearized expression).
466 // For example, if I = X + A, where X = A + B, then I, X and B have weight 1
467 // while A has weight two.
469 // Worklist of non-leaf nodes (their operands are in the expression too) along
470 // with their weights, representing a certain number of paths to the operator.
471 // If an operator occurs in the worklist multiple times then we found multiple
472 // ways to get to it.
473 SmallVector
<std::pair
<BinaryOperator
*, APInt
>, 8> Worklist
; // (Op, Weight)
474 Worklist
.push_back(std::make_pair(I
, APInt(Bitwidth
, 1)));
475 bool MadeChange
= false;
477 // Leaves of the expression are values that either aren't the right kind of
478 // operation (eg: a constant, or a multiply in an add tree), or are, but have
479 // some uses that are not inside the expression. For example, in I = X + X,
480 // X = A + B, the value X has two uses (by I) that are in the expression. If
481 // X has any other uses, for example in a return instruction, then we consider
482 // X to be a leaf, and won't analyze it further. When we first visit a value,
483 // if it has more than one use then at first we conservatively consider it to
484 // be a leaf. Later, as the expression is explored, we may discover some more
485 // uses of the value from inside the expression. If all uses turn out to be
486 // from within the expression (and the value is a binary operator of the right
487 // kind) then the value is no longer considered to be a leaf, and its operands
490 // Leaves - Keeps track of the set of putative leaves as well as the number of
491 // paths to each leaf seen so far.
492 typedef DenseMap
<Value
*, APInt
> LeafMap
;
493 LeafMap Leaves
; // Leaf -> Total weight so far.
494 SmallVector
<Value
*, 8> LeafOrder
; // Ensure deterministic leaf output order.
497 SmallPtrSet
<Value
*, 8> Visited
; // For sanity checking the iteration scheme.
499 while (!Worklist
.empty()) {
500 std::pair
<BinaryOperator
*, APInt
> P
= Worklist
.pop_back_val();
501 I
= P
.first
; // We examine the operands of this binary operator.
503 for (unsigned OpIdx
= 0; OpIdx
< 2; ++OpIdx
) { // Visit operands.
504 Value
*Op
= I
->getOperand(OpIdx
);
505 APInt Weight
= P
.second
; // Number of paths to this operand.
506 DEBUG(dbgs() << "OPERAND: " << *Op
<< " (" << Weight
<< ")\n");
507 assert(!Op
->use_empty() && "No uses, so how did we get to it?!");
509 // If the expression contains an absorbing element then there is no need
510 // to analyze it further: it must evaluate to the absorbing element.
511 if (Op
== Absorber
&& !Weight
.isMinValue()) {
512 Ops
.push_back(std::make_pair(Absorber
, APInt(Bitwidth
, 1)));
516 // If this is a binary operation of the right kind with only one use then
517 // add its operands to the expression.
518 if (BinaryOperator
*BO
= isReassociableOp(Op
, Opcode
)) {
519 assert(Visited
.insert(Op
) && "Not first visit!");
520 DEBUG(dbgs() << "DIRECT ADD: " << *Op
<< " (" << Weight
<< ")\n");
521 Worklist
.push_back(std::make_pair(BO
, Weight
));
525 // Appears to be a leaf. Is the operand already in the set of leaves?
526 LeafMap::iterator It
= Leaves
.find(Op
);
527 if (It
== Leaves
.end()) {
528 // Not in the leaf map. Must be the first time we saw this operand.
529 assert(Visited
.insert(Op
) && "Not first visit!");
530 if (!Op
->hasOneUse()) {
531 // This value has uses not accounted for by the expression, so it is
532 // not safe to modify. Mark it as being a leaf.
533 DEBUG(dbgs() << "ADD USES LEAF: " << *Op
<< " (" << Weight
<< ")\n");
534 LeafOrder
.push_back(Op
);
538 // No uses outside the expression, try morphing it.
539 } else if (It
!= Leaves
.end()) {
540 // Already in the leaf map.
541 assert(Visited
.count(Op
) && "In leaf map but not visited!");
543 // Update the number of paths to the leaf.
544 IncorporateWeight(It
->second
, Weight
, Opcode
);
546 #if 0 // TODO: Re-enable once PR13021 is fixed.
547 // The leaf already has one use from inside the expression. As we want
548 // exactly one such use, drop this new use of the leaf.
549 assert(!Op
->hasOneUse() && "Only one use, but we got here twice!");
550 I
->setOperand(OpIdx
, UndefValue::get(I
->getType()));
553 // If the leaf is a binary operation of the right kind and we now see
554 // that its multiple original uses were in fact all by nodes belonging
555 // to the expression, then no longer consider it to be a leaf and add
556 // its operands to the expression.
557 if (BinaryOperator
*BO
= isReassociableOp(Op
, Opcode
)) {
558 DEBUG(dbgs() << "UNLEAF: " << *Op
<< " (" << It
->second
<< ")\n");
559 Worklist
.push_back(std::make_pair(BO
, It
->second
));
565 // If we still have uses that are not accounted for by the expression
566 // then it is not safe to modify the value.
567 if (!Op
->hasOneUse())
570 // No uses outside the expression, try morphing it.
572 Leaves
.erase(It
); // Since the value may be morphed below.
575 // At this point we have a value which, first of all, is not a binary
576 // expression of the right kind, and secondly, is only used inside the
577 // expression. This means that it can safely be modified. See if we
578 // can usefully morph it into an expression of the right kind.
579 assert((!isa
<Instruction
>(Op
) ||
580 cast
<Instruction
>(Op
)->getOpcode() != Opcode
) &&
581 "Should have been handled above!");
582 assert(Op
->hasOneUse() && "Has uses outside the expression tree!");
584 // If this is a multiply expression, turn any internal negations into
585 // multiplies by -1 so they can be reassociated.
586 BinaryOperator
*BO
= dyn_cast
<BinaryOperator
>(Op
);
587 if (Opcode
== Instruction::Mul
&& BO
&& BinaryOperator::isNeg(BO
)) {
588 DEBUG(dbgs() << "MORPH LEAF: " << *Op
<< " (" << Weight
<< ") TO ");
589 BO
= LowerNegateToMultiply(BO
);
590 DEBUG(dbgs() << *BO
<< 'n');
591 Worklist
.push_back(std::make_pair(BO
, Weight
));
596 // Failed to morph into an expression of the right type. This really is
598 DEBUG(dbgs() << "ADD LEAF: " << *Op
<< " (" << Weight
<< ")\n");
599 assert(!isReassociableOp(Op
, Opcode
) && "Value was morphed?");
600 LeafOrder
.push_back(Op
);
605 // The leaves, repeated according to their weights, represent the linearized
606 // form of the expression.
607 Constant
*Cst
= 0; // Accumulate constants here.
608 for (unsigned i
= 0, e
= LeafOrder
.size(); i
!= e
; ++i
) {
609 Value
*V
= LeafOrder
[i
];
610 LeafMap::iterator It
= Leaves
.find(V
);
611 if (It
== Leaves
.end())
612 // Node initially thought to be a leaf wasn't.
614 assert(!isReassociableOp(V
, Opcode
) && "Shouldn't be a leaf!");
615 APInt Weight
= It
->second
;
616 if (Weight
.isMinValue())
617 // Leaf already output or weight reduction eliminated it.
619 // Ensure the leaf is only output once.
621 // Glob all constants together into Cst.
622 if (Constant
*C
= dyn_cast
<Constant
>(V
)) {
623 C
= EvaluateRepeatedConstant(Opcode
, C
, Weight
);
624 Cst
= Cst
? ConstantExpr::get(Opcode
, Cst
, C
) : C
;
628 Ops
.push_back(std::make_pair(V
, Weight
));
631 // Add any constants back into Ops, all globbed together and reduced to having
632 // weight 1 for the convenience of users.
633 Constant
*Identity
= ConstantExpr::getBinOpIdentity(Opcode
, I
->getType());
634 if (Cst
&& Cst
!= Identity
) {
635 // If combining multiple constants resulted in the absorber then the entire
636 // expression must evaluate to the absorber.
639 Ops
.push_back(std::make_pair(Cst
, APInt(Bitwidth
, 1)));
642 // For nilpotent operations or addition there may be no operands, for example
643 // because the expression was "X xor X" or consisted of 2^Bitwidth additions:
644 // in both cases the weight reduces to 0 causing the value to be skipped.
646 assert(Identity
&& "Associative operation without identity!");
647 Ops
.push_back(std::make_pair(Identity
, APInt(Bitwidth
, 1)));
653 // RewriteExprTree - Now that the operands for this expression tree are
654 // linearized and optimized, emit them in-order.
655 void Reassociate::RewriteExprTree(BinaryOperator
*I
,
656 SmallVectorImpl
<ValueEntry
> &Ops
) {
657 assert(Ops
.size() > 1 && "Single values should be used directly!");
659 // Since our optimizations never increase the number of operations, the new
660 // expression can always be written by reusing the existing binary operators
661 // from the original expression tree, without creating any new instructions,
662 // though the rewritten expression may have a completely different topology.
663 // We take care to not change anything if the new expression will be the same
664 // as the original. If more than trivial changes (like commuting operands)
665 // were made then we are obliged to clear out any optional subclass data like
668 /// NodesToRewrite - Nodes from the original expression available for writing
669 /// the new expression into.
670 SmallVector
<BinaryOperator
*, 8> NodesToRewrite
;
671 unsigned Opcode
= I
->getOpcode();
672 BinaryOperator
*Op
= I
;
674 // ExpressionChanged - Non-null if the rewritten expression differs from the
675 // original in some non-trivial way, requiring the clearing of optional flags.
676 // Flags are cleared from the operator in ExpressionChanged up to I inclusive.
677 BinaryOperator
*ExpressionChanged
= 0;
678 for (unsigned i
= 0; ; ++i
) {
679 // The last operation (which comes earliest in the IR) is special as both
680 // operands will come from Ops, rather than just one with the other being
682 if (i
+2 == Ops
.size()) {
683 Value
*NewLHS
= Ops
[i
].Op
;
684 Value
*NewRHS
= Ops
[i
+1].Op
;
685 Value
*OldLHS
= Op
->getOperand(0);
686 Value
*OldRHS
= Op
->getOperand(1);
688 if (NewLHS
== OldLHS
&& NewRHS
== OldRHS
)
689 // Nothing changed, leave it alone.
692 if (NewLHS
== OldRHS
&& NewRHS
== OldLHS
) {
693 // The order of the operands was reversed. Swap them.
694 DEBUG(dbgs() << "RA: " << *Op
<< '\n');
696 DEBUG(dbgs() << "TO: " << *Op
<< '\n');
702 // The new operation differs non-trivially from the original. Overwrite
703 // the old operands with the new ones.
704 DEBUG(dbgs() << "RA: " << *Op
<< '\n');
705 if (NewLHS
!= OldLHS
) {
706 if (BinaryOperator
*BO
= isReassociableOp(OldLHS
, Opcode
))
707 NodesToRewrite
.push_back(BO
);
708 Op
->setOperand(0, NewLHS
);
710 if (NewRHS
!= OldRHS
) {
711 if (BinaryOperator
*BO
= isReassociableOp(OldRHS
, Opcode
))
712 NodesToRewrite
.push_back(BO
);
713 Op
->setOperand(1, NewRHS
);
715 DEBUG(dbgs() << "TO: " << *Op
<< '\n');
717 ExpressionChanged
= Op
;
724 // Not the last operation. The left-hand side will be a sub-expression
725 // while the right-hand side will be the current element of Ops.
726 Value
*NewRHS
= Ops
[i
].Op
;
727 if (NewRHS
!= Op
->getOperand(1)) {
728 DEBUG(dbgs() << "RA: " << *Op
<< '\n');
729 if (NewRHS
== Op
->getOperand(0)) {
730 // The new right-hand side was already present as the left operand. If
731 // we are lucky then swapping the operands will sort out both of them.
734 // Overwrite with the new right-hand side.
735 if (BinaryOperator
*BO
= isReassociableOp(Op
->getOperand(1), Opcode
))
736 NodesToRewrite
.push_back(BO
);
737 Op
->setOperand(1, NewRHS
);
738 ExpressionChanged
= Op
;
740 DEBUG(dbgs() << "TO: " << *Op
<< '\n');
745 // Now deal with the left-hand side. If this is already an operation node
746 // from the original expression then just rewrite the rest of the expression
748 if (BinaryOperator
*BO
= isReassociableOp(Op
->getOperand(0), Opcode
)) {
753 // Otherwise, grab a spare node from the original expression and use that as
754 // the left-hand side. If there are no nodes left then the optimizers made
755 // an expression with more nodes than the original! This usually means that
756 // they did something stupid but it might mean that the problem was just too
757 // hard (finding the mimimal number of multiplications needed to realize a
758 // multiplication expression is NP-complete). Whatever the reason, smart or
759 // stupid, create a new node if there are none left.
760 BinaryOperator
*NewOp
;
761 if (NodesToRewrite
.empty()) {
762 Constant
*Undef
= UndefValue::get(I
->getType());
763 NewOp
= BinaryOperator::Create(Instruction::BinaryOps(Opcode
),
764 Undef
, Undef
, "", I
);
766 NewOp
= NodesToRewrite
.pop_back_val();
769 DEBUG(dbgs() << "RA: " << *Op
<< '\n');
770 Op
->setOperand(0, NewOp
);
771 DEBUG(dbgs() << "TO: " << *Op
<< '\n');
772 ExpressionChanged
= Op
;
778 // If the expression changed non-trivially then clear out all subclass data
779 // starting from the operator specified in ExpressionChanged, and compactify
780 // the operators to just before the expression root to guarantee that the
781 // expression tree is dominated by all of Ops.
782 if (ExpressionChanged
)
784 ExpressionChanged
->clearSubclassOptionalData();
785 if (ExpressionChanged
== I
)
787 ExpressionChanged
->moveBefore(I
);
788 ExpressionChanged
= cast
<BinaryOperator
>(*ExpressionChanged
->use_begin());
791 // Throw away any left over nodes from the original expression.
792 for (unsigned i
= 0, e
= NodesToRewrite
.size(); i
!= e
; ++i
)
793 RedoInsts
.insert(NodesToRewrite
[i
]);
796 /// NegateValue - Insert instructions before the instruction pointed to by BI,
797 /// that computes the negative version of the value specified. The negative
798 /// version of the value is returned, and BI is left pointing at the instruction
799 /// that should be processed next by the reassociation pass.
800 static Value
*NegateValue(Value
*V
, Instruction
*BI
) {
801 if (Constant
*C
= dyn_cast
<Constant
>(V
))
802 return ConstantExpr::getNeg(C
);
804 // We are trying to expose opportunity for reassociation. One of the things
805 // that we want to do to achieve this is to push a negation as deep into an
806 // expression chain as possible, to expose the add instructions. In practice,
807 // this means that we turn this:
808 // X = -(A+12+C+D) into X = -A + -12 + -C + -D = -12 + -A + -C + -D
809 // so that later, a: Y = 12+X could get reassociated with the -12 to eliminate
810 // the constants. We assume that instcombine will clean up the mess later if
811 // we introduce tons of unnecessary negation instructions.
813 if (BinaryOperator
*I
= isReassociableOp(V
, Instruction::Add
)) {
814 // Push the negates through the add.
815 I
->setOperand(0, NegateValue(I
->getOperand(0), BI
));
816 I
->setOperand(1, NegateValue(I
->getOperand(1), BI
));
818 // We must move the add instruction here, because the neg instructions do
819 // not dominate the old add instruction in general. By moving it, we are
820 // assured that the neg instructions we just inserted dominate the
821 // instruction we are about to insert after them.
824 I
->setName(I
->getName()+".neg");
828 // Okay, we need to materialize a negated version of V with an instruction.
829 // Scan the use lists of V to see if we have one already.
830 for (Value::use_iterator UI
= V
->use_begin(), E
= V
->use_end(); UI
!= E
;++UI
){
832 if (!BinaryOperator::isNeg(U
)) continue;
834 // We found one! Now we have to make sure that the definition dominates
835 // this use. We do this by moving it to the entry block (if it is a
836 // non-instruction value) or right after the definition. These negates will
837 // be zapped by reassociate later, so we don't need much finesse here.
838 BinaryOperator
*TheNeg
= cast
<BinaryOperator
>(U
);
840 // Verify that the negate is in this function, V might be a constant expr.
841 if (TheNeg
->getParent()->getParent() != BI
->getParent()->getParent())
844 BasicBlock::iterator InsertPt
;
845 if (Instruction
*InstInput
= dyn_cast
<Instruction
>(V
)) {
846 if (InvokeInst
*II
= dyn_cast
<InvokeInst
>(InstInput
)) {
847 InsertPt
= II
->getNormalDest()->begin();
849 InsertPt
= InstInput
;
852 while (isa
<PHINode
>(InsertPt
)) ++InsertPt
;
854 InsertPt
= TheNeg
->getParent()->getParent()->getEntryBlock().begin();
856 TheNeg
->moveBefore(InsertPt
);
860 // Insert a 'neg' instruction that subtracts the value from zero to get the
862 return BinaryOperator::CreateNeg(V
, V
->getName() + ".neg", BI
);
865 /// ShouldBreakUpSubtract - Return true if we should break up this subtract of
866 /// X-Y into (X + -Y).
867 static bool ShouldBreakUpSubtract(Instruction
*Sub
) {
868 // If this is a negation, we can't split it up!
869 if (BinaryOperator::isNeg(Sub
))
872 // Don't bother to break this up unless either the LHS is an associable add or
873 // subtract or if this is only used by one.
874 if (isReassociableOp(Sub
->getOperand(0), Instruction::Add
) ||
875 isReassociableOp(Sub
->getOperand(0), Instruction::Sub
))
877 if (isReassociableOp(Sub
->getOperand(1), Instruction::Add
) ||
878 isReassociableOp(Sub
->getOperand(1), Instruction::Sub
))
880 if (Sub
->hasOneUse() &&
881 (isReassociableOp(Sub
->use_back(), Instruction::Add
) ||
882 isReassociableOp(Sub
->use_back(), Instruction::Sub
)))
888 /// BreakUpSubtract - If we have (X-Y), and if either X is an add, or if this is
889 /// only used by an add, transform this into (X+(0-Y)) to promote better
891 static BinaryOperator
*BreakUpSubtract(Instruction
*Sub
) {
892 // Convert a subtract into an add and a neg instruction. This allows sub
893 // instructions to be commuted with other add instructions.
895 // Calculate the negative value of Operand 1 of the sub instruction,
896 // and set it as the RHS of the add instruction we just made.
898 Value
*NegVal
= NegateValue(Sub
->getOperand(1), Sub
);
899 BinaryOperator
*New
=
900 BinaryOperator::CreateAdd(Sub
->getOperand(0), NegVal
, "", Sub
);
901 Sub
->setOperand(0, Constant::getNullValue(Sub
->getType())); // Drop use of op.
902 Sub
->setOperand(1, Constant::getNullValue(Sub
->getType())); // Drop use of op.
905 // Everyone now refers to the add instruction.
906 Sub
->replaceAllUsesWith(New
);
907 New
->setDebugLoc(Sub
->getDebugLoc());
909 DEBUG(dbgs() << "Negated: " << *New
<< '\n');
913 /// ConvertShiftToMul - If this is a shift of a reassociable multiply or is used
914 /// by one, change this into a multiply by a constant to assist with further
916 static BinaryOperator
*ConvertShiftToMul(Instruction
*Shl
) {
917 Constant
*MulCst
= ConstantInt::get(Shl
->getType(), 1);
918 MulCst
= ConstantExpr::getShl(MulCst
, cast
<Constant
>(Shl
->getOperand(1)));
920 BinaryOperator
*Mul
=
921 BinaryOperator::CreateMul(Shl
->getOperand(0), MulCst
, "", Shl
);
922 Shl
->setOperand(0, UndefValue::get(Shl
->getType())); // Drop use of op.
924 Shl
->replaceAllUsesWith(Mul
);
925 Mul
->setDebugLoc(Shl
->getDebugLoc());
929 /// FindInOperandList - Scan backwards and forwards among values with the same
930 /// rank as element i to see if X exists. If X does not exist, return i. This
931 /// is useful when scanning for 'x' when we see '-x' because they both get the
933 static unsigned FindInOperandList(SmallVectorImpl
<ValueEntry
> &Ops
, unsigned i
,
935 unsigned XRank
= Ops
[i
].Rank
;
936 unsigned e
= Ops
.size();
937 for (unsigned j
= i
+1; j
!= e
&& Ops
[j
].Rank
== XRank
; ++j
)
941 for (unsigned j
= i
-1; j
!= ~0U && Ops
[j
].Rank
== XRank
; --j
)
947 /// EmitAddTreeOfValues - Emit a tree of add instructions, summing Ops together
948 /// and returning the result. Insert the tree before I.
949 static Value
*EmitAddTreeOfValues(Instruction
*I
,
950 SmallVectorImpl
<WeakVH
> &Ops
){
951 if (Ops
.size() == 1) return Ops
.back();
953 Value
*V1
= Ops
.back();
955 Value
*V2
= EmitAddTreeOfValues(I
, Ops
);
956 return BinaryOperator::CreateAdd(V2
, V1
, "tmp", I
);
959 /// RemoveFactorFromExpression - If V is an expression tree that is a
960 /// multiplication sequence, and if this sequence contains a multiply by Factor,
961 /// remove Factor from the tree and return the new tree.
962 Value
*Reassociate::RemoveFactorFromExpression(Value
*V
, Value
*Factor
) {
963 BinaryOperator
*BO
= isReassociableOp(V
, Instruction::Mul
);
966 SmallVector
<RepeatedValue
, 8> Tree
;
967 MadeChange
|= LinearizeExprTree(BO
, Tree
);
968 SmallVector
<ValueEntry
, 8> Factors
;
969 Factors
.reserve(Tree
.size());
970 for (unsigned i
= 0, e
= Tree
.size(); i
!= e
; ++i
) {
971 RepeatedValue E
= Tree
[i
];
972 Factors
.append(E
.second
.getZExtValue(),
973 ValueEntry(getRank(E
.first
), E
.first
));
976 bool FoundFactor
= false;
977 bool NeedsNegate
= false;
978 for (unsigned i
= 0, e
= Factors
.size(); i
!= e
; ++i
) {
979 if (Factors
[i
].Op
== Factor
) {
981 Factors
.erase(Factors
.begin()+i
);
985 // If this is a negative version of this factor, remove it.
986 if (ConstantInt
*FC1
= dyn_cast
<ConstantInt
>(Factor
))
987 if (ConstantInt
*FC2
= dyn_cast
<ConstantInt
>(Factors
[i
].Op
))
988 if (FC1
->getValue() == -FC2
->getValue()) {
989 FoundFactor
= NeedsNegate
= true;
990 Factors
.erase(Factors
.begin()+i
);
996 // Make sure to restore the operands to the expression tree.
997 RewriteExprTree(BO
, Factors
);
1001 BasicBlock::iterator InsertPt
= BO
; ++InsertPt
;
1003 // If this was just a single multiply, remove the multiply and return the only
1004 // remaining operand.
1005 if (Factors
.size() == 1) {
1006 RedoInsts
.insert(BO
);
1009 RewriteExprTree(BO
, Factors
);
1014 V
= BinaryOperator::CreateNeg(V
, "neg", InsertPt
);
1019 /// FindSingleUseMultiplyFactors - If V is a single-use multiply, recursively
1020 /// add its operands as factors, otherwise add V to the list of factors.
1022 /// Ops is the top-level list of add operands we're trying to factor.
1023 static void FindSingleUseMultiplyFactors(Value
*V
,
1024 SmallVectorImpl
<Value
*> &Factors
,
1025 const SmallVectorImpl
<ValueEntry
> &Ops
) {
1026 BinaryOperator
*BO
= isReassociableOp(V
, Instruction::Mul
);
1028 Factors
.push_back(V
);
1032 // Otherwise, add the LHS and RHS to the list of factors.
1033 FindSingleUseMultiplyFactors(BO
->getOperand(1), Factors
, Ops
);
1034 FindSingleUseMultiplyFactors(BO
->getOperand(0), Factors
, Ops
);
1037 /// OptimizeAndOrXor - Optimize a series of operands to an 'and', 'or', or 'xor'
1038 /// instruction. This optimizes based on identities. If it can be reduced to
1039 /// a single Value, it is returned, otherwise the Ops list is mutated as
1041 static Value
*OptimizeAndOrXor(unsigned Opcode
,
1042 SmallVectorImpl
<ValueEntry
> &Ops
) {
1043 // Scan the operand lists looking for X and ~X pairs, along with X,X pairs.
1044 // If we find any, we can simplify the expression. X&~X == 0, X|~X == -1.
1045 for (unsigned i
= 0, e
= Ops
.size(); i
!= e
; ++i
) {
1046 // First, check for X and ~X in the operand list.
1047 assert(i
< Ops
.size());
1048 if (BinaryOperator::isNot(Ops
[i
].Op
)) { // Cannot occur for ^.
1049 Value
*X
= BinaryOperator::getNotArgument(Ops
[i
].Op
);
1050 unsigned FoundX
= FindInOperandList(Ops
, i
, X
);
1052 if (Opcode
== Instruction::And
) // ...&X&~X = 0
1053 return Constant::getNullValue(X
->getType());
1055 if (Opcode
== Instruction::Or
) // ...|X|~X = -1
1056 return Constant::getAllOnesValue(X
->getType());
1060 // Next, check for duplicate pairs of values, which we assume are next to
1061 // each other, due to our sorting criteria.
1062 assert(i
< Ops
.size());
1063 if (i
+1 != Ops
.size() && Ops
[i
+1].Op
== Ops
[i
].Op
) {
1064 if (Opcode
== Instruction::And
|| Opcode
== Instruction::Or
) {
1065 // Drop duplicate values for And and Or.
1066 Ops
.erase(Ops
.begin()+i
);
1072 // Drop pairs of values for Xor.
1073 assert(Opcode
== Instruction::Xor
);
1075 return Constant::getNullValue(Ops
[0].Op
->getType());
1078 Ops
.erase(Ops
.begin()+i
, Ops
.begin()+i
+2);
1086 /// OptimizeAdd - Optimize a series of operands to an 'add' instruction. This
1087 /// optimizes based on identities. If it can be reduced to a single Value, it
1088 /// is returned, otherwise the Ops list is mutated as necessary.
1089 Value
*Reassociate::OptimizeAdd(Instruction
*I
,
1090 SmallVectorImpl
<ValueEntry
> &Ops
) {
1091 // Scan the operand lists looking for X and -X pairs. If we find any, we
1092 // can simplify the expression. X+-X == 0. While we're at it, scan for any
1093 // duplicates. We want to canonicalize Y+Y+Y+Z -> 3*Y+Z.
1095 // TODO: We could handle "X + ~X" -> "-1" if we wanted, since "-X = ~X+1".
1097 for (unsigned i
= 0, e
= Ops
.size(); i
!= e
; ++i
) {
1098 Value
*TheOp
= Ops
[i
].Op
;
1099 // Check to see if we've seen this operand before. If so, we factor all
1100 // instances of the operand together. Due to our sorting criteria, we know
1101 // that these need to be next to each other in the vector.
1102 if (i
+1 != Ops
.size() && Ops
[i
+1].Op
== TheOp
) {
1103 // Rescan the list, remove all instances of this operand from the expr.
1104 unsigned NumFound
= 0;
1106 Ops
.erase(Ops
.begin()+i
);
1108 } while (i
!= Ops
.size() && Ops
[i
].Op
== TheOp
);
1110 DEBUG(errs() << "\nFACTORING [" << NumFound
<< "]: " << *TheOp
<< '\n');
1113 // Insert a new multiply.
1114 Value
*Mul
= ConstantInt::get(cast
<IntegerType
>(I
->getType()), NumFound
);
1115 Mul
= BinaryOperator::CreateMul(TheOp
, Mul
, "factor", I
);
1117 // Now that we have inserted a multiply, optimize it. This allows us to
1118 // handle cases that require multiple factoring steps, such as this:
1119 // (X*2) + (X*2) + (X*2) -> (X*2)*3 -> X*6
1120 RedoInsts
.insert(cast
<Instruction
>(Mul
));
1122 // If every add operand was a duplicate, return the multiply.
1126 // Otherwise, we had some input that didn't have the dupe, such as
1127 // "A + A + B" -> "A*2 + B". Add the new multiply to the list of
1128 // things being added by this operation.
1129 Ops
.insert(Ops
.begin(), ValueEntry(getRank(Mul
), Mul
));
1136 // Check for X and -X in the operand list.
1137 if (!BinaryOperator::isNeg(TheOp
))
1140 Value
*X
= BinaryOperator::getNegArgument(TheOp
);
1141 unsigned FoundX
= FindInOperandList(Ops
, i
, X
);
1145 // Remove X and -X from the operand list.
1146 if (Ops
.size() == 2)
1147 return Constant::getNullValue(X
->getType());
1149 Ops
.erase(Ops
.begin()+i
);
1153 --i
; // Need to back up an extra one.
1154 Ops
.erase(Ops
.begin()+FoundX
);
1156 --i
; // Revisit element.
1157 e
-= 2; // Removed two elements.
1160 // Scan the operand list, checking to see if there are any common factors
1161 // between operands. Consider something like A*A+A*B*C+D. We would like to
1162 // reassociate this to A*(A+B*C)+D, which reduces the number of multiplies.
1163 // To efficiently find this, we count the number of times a factor occurs
1164 // for any ADD operands that are MULs.
1165 DenseMap
<Value
*, unsigned> FactorOccurrences
;
1167 // Keep track of each multiply we see, to avoid triggering on (X*4)+(X*4)
1168 // where they are actually the same multiply.
1169 unsigned MaxOcc
= 0;
1170 Value
*MaxOccVal
= 0;
1171 for (unsigned i
= 0, e
= Ops
.size(); i
!= e
; ++i
) {
1172 BinaryOperator
*BOp
= isReassociableOp(Ops
[i
].Op
, Instruction::Mul
);
1176 // Compute all of the factors of this added value.
1177 SmallVector
<Value
*, 8> Factors
;
1178 FindSingleUseMultiplyFactors(BOp
, Factors
, Ops
);
1179 assert(Factors
.size() > 1 && "Bad linearize!");
1181 // Add one to FactorOccurrences for each unique factor in this op.
1182 SmallPtrSet
<Value
*, 8> Duplicates
;
1183 for (unsigned i
= 0, e
= Factors
.size(); i
!= e
; ++i
) {
1184 Value
*Factor
= Factors
[i
];
1185 if (!Duplicates
.insert(Factor
)) continue;
1187 unsigned Occ
= ++FactorOccurrences
[Factor
];
1188 if (Occ
> MaxOcc
) { MaxOcc
= Occ
; MaxOccVal
= Factor
; }
1190 // If Factor is a negative constant, add the negated value as a factor
1191 // because we can percolate the negate out. Watch for minint, which
1192 // cannot be positivified.
1193 if (ConstantInt
*CI
= dyn_cast
<ConstantInt
>(Factor
))
1194 if (CI
->isNegative() && !CI
->isMinValue(true)) {
1195 Factor
= ConstantInt::get(CI
->getContext(), -CI
->getValue());
1196 assert(!Duplicates
.count(Factor
) &&
1197 "Shouldn't have two constant factors, missed a canonicalize");
1199 unsigned Occ
= ++FactorOccurrences
[Factor
];
1200 if (Occ
> MaxOcc
) { MaxOcc
= Occ
; MaxOccVal
= Factor
; }
1205 // If any factor occurred more than one time, we can pull it out.
1207 DEBUG(errs() << "\nFACTORING [" << MaxOcc
<< "]: " << *MaxOccVal
<< '\n');
1210 // Create a new instruction that uses the MaxOccVal twice. If we don't do
1211 // this, we could otherwise run into situations where removing a factor
1212 // from an expression will drop a use of maxocc, and this can cause
1213 // RemoveFactorFromExpression on successive values to behave differently.
1214 Instruction
*DummyInst
= BinaryOperator::CreateAdd(MaxOccVal
, MaxOccVal
);
1215 SmallVector
<WeakVH
, 4> NewMulOps
;
1216 for (unsigned i
= 0; i
!= Ops
.size(); ++i
) {
1217 // Only try to remove factors from expressions we're allowed to.
1218 BinaryOperator
*BOp
= isReassociableOp(Ops
[i
].Op
, Instruction::Mul
);
1222 if (Value
*V
= RemoveFactorFromExpression(Ops
[i
].Op
, MaxOccVal
)) {
1223 // The factorized operand may occur several times. Convert them all in
1225 for (unsigned j
= Ops
.size(); j
!= i
;) {
1227 if (Ops
[j
].Op
== Ops
[i
].Op
) {
1228 NewMulOps
.push_back(V
);
1229 Ops
.erase(Ops
.begin()+j
);
1236 // No need for extra uses anymore.
1239 unsigned NumAddedValues
= NewMulOps
.size();
1240 Value
*V
= EmitAddTreeOfValues(I
, NewMulOps
);
1242 // Now that we have inserted the add tree, optimize it. This allows us to
1243 // handle cases that require multiple factoring steps, such as this:
1244 // A*A*B + A*A*C --> A*(A*B+A*C) --> A*(A*(B+C))
1245 assert(NumAddedValues
> 1 && "Each occurrence should contribute a value");
1246 (void)NumAddedValues
;
1247 if (Instruction
*VI
= dyn_cast
<Instruction
>(V
))
1248 RedoInsts
.insert(VI
);
1250 // Create the multiply.
1251 Instruction
*V2
= BinaryOperator::CreateMul(V
, MaxOccVal
, "tmp", I
);
1253 // Rerun associate on the multiply in case the inner expression turned into
1254 // a multiply. We want to make sure that we keep things in canonical form.
1255 RedoInsts
.insert(V2
);
1257 // If every add operand included the factor (e.g. "A*B + A*C"), then the
1258 // entire result expression is just the multiply "A*(B+C)".
1262 // Otherwise, we had some input that didn't have the factor, such as
1263 // "A*B + A*C + D" -> "A*(B+C) + D". Add the new multiply to the list of
1264 // things being added by this operation.
1265 Ops
.insert(Ops
.begin(), ValueEntry(getRank(V2
), V2
));
1272 /// \brief Predicate tests whether a ValueEntry's op is in a map.
1273 struct IsValueInMap
{
1274 const DenseMap
<Value
*, unsigned> &Map
;
1276 IsValueInMap(const DenseMap
<Value
*, unsigned> &Map
) : Map(Map
) {}
1278 bool operator()(const ValueEntry
&Entry
) {
1279 return Map
.find(Entry
.Op
) != Map
.end();
1284 /// \brief Build up a vector of value/power pairs factoring a product.
1286 /// Given a series of multiplication operands, build a vector of factors and
1287 /// the powers each is raised to when forming the final product. Sort them in
1288 /// the order of descending power.
1290 /// (x*x) -> [(x, 2)]
1291 /// ((x*x)*x) -> [(x, 3)]
1292 /// ((((x*y)*x)*y)*x) -> [(x, 3), (y, 2)]
1294 /// \returns Whether any factors have a power greater than one.
1295 bool Reassociate::collectMultiplyFactors(SmallVectorImpl
<ValueEntry
> &Ops
,
1296 SmallVectorImpl
<Factor
> &Factors
) {
1297 // FIXME: Have Ops be (ValueEntry, Multiplicity) pairs, simplifying this.
1298 // Compute the sum of powers of simplifiable factors.
1299 unsigned FactorPowerSum
= 0;
1300 for (unsigned Idx
= 1, Size
= Ops
.size(); Idx
< Size
; ++Idx
) {
1301 Value
*Op
= Ops
[Idx
-1].Op
;
1303 // Count the number of occurrences of this value.
1305 for (; Idx
< Size
&& Ops
[Idx
].Op
== Op
; ++Idx
)
1307 // Track for simplification all factors which occur 2 or more times.
1309 FactorPowerSum
+= Count
;
1312 // We can only simplify factors if the sum of the powers of our simplifiable
1313 // factors is 4 or higher. When that is the case, we will *always* have
1314 // a simplification. This is an important invariant to prevent cyclicly
1315 // trying to simplify already minimal formations.
1316 if (FactorPowerSum
< 4)
1319 // Now gather the simplifiable factors, removing them from Ops.
1321 for (unsigned Idx
= 1; Idx
< Ops
.size(); ++Idx
) {
1322 Value
*Op
= Ops
[Idx
-1].Op
;
1324 // Count the number of occurrences of this value.
1326 for (; Idx
< Ops
.size() && Ops
[Idx
].Op
== Op
; ++Idx
)
1330 // Move an even number of occurrences to Factors.
1333 FactorPowerSum
+= Count
;
1334 Factors
.push_back(Factor(Op
, Count
));
1335 Ops
.erase(Ops
.begin()+Idx
, Ops
.begin()+Idx
+Count
);
1338 // None of the adjustments above should have reduced the sum of factor powers
1339 // below our mininum of '4'.
1340 assert(FactorPowerSum
>= 4);
1342 std::sort(Factors
.begin(), Factors
.end(), Factor::PowerDescendingSorter());
1346 /// \brief Build a tree of multiplies, computing the product of Ops.
1347 static Value
*buildMultiplyTree(IRBuilder
<> &Builder
,
1348 SmallVectorImpl
<Value
*> &Ops
) {
1349 if (Ops
.size() == 1)
1352 Value
*LHS
= Ops
.pop_back_val();
1354 LHS
= Builder
.CreateMul(LHS
, Ops
.pop_back_val());
1355 } while (!Ops
.empty());
1360 /// \brief Build a minimal multiplication DAG for (a^x)*(b^y)*(c^z)*...
1362 /// Given a vector of values raised to various powers, where no two values are
1363 /// equal and the powers are sorted in decreasing order, compute the minimal
1364 /// DAG of multiplies to compute the final product, and return that product
1366 Value
*Reassociate::buildMinimalMultiplyDAG(IRBuilder
<> &Builder
,
1367 SmallVectorImpl
<Factor
> &Factors
) {
1368 assert(Factors
[0].Power
);
1369 SmallVector
<Value
*, 4> OuterProduct
;
1370 for (unsigned LastIdx
= 0, Idx
= 1, Size
= Factors
.size();
1371 Idx
< Size
&& Factors
[Idx
].Power
> 0; ++Idx
) {
1372 if (Factors
[Idx
].Power
!= Factors
[LastIdx
].Power
) {
1377 // We want to multiply across all the factors with the same power so that
1378 // we can raise them to that power as a single entity. Build a mini tree
1380 SmallVector
<Value
*, 4> InnerProduct
;
1381 InnerProduct
.push_back(Factors
[LastIdx
].Base
);
1383 InnerProduct
.push_back(Factors
[Idx
].Base
);
1385 } while (Idx
< Size
&& Factors
[Idx
].Power
== Factors
[LastIdx
].Power
);
1387 // Reset the base value of the first factor to the new expression tree.
1388 // We'll remove all the factors with the same power in a second pass.
1389 Value
*M
= Factors
[LastIdx
].Base
= buildMultiplyTree(Builder
, InnerProduct
);
1390 if (Instruction
*MI
= dyn_cast
<Instruction
>(M
))
1391 RedoInsts
.insert(MI
);
1395 // Unique factors with equal powers -- we've folded them into the first one's
1397 Factors
.erase(std::unique(Factors
.begin(), Factors
.end(),
1398 Factor::PowerEqual()),
1401 // Iteratively collect the base of each factor with an add power into the
1402 // outer product, and halve each power in preparation for squaring the
1404 for (unsigned Idx
= 0, Size
= Factors
.size(); Idx
!= Size
; ++Idx
) {
1405 if (Factors
[Idx
].Power
& 1)
1406 OuterProduct
.push_back(Factors
[Idx
].Base
);
1407 Factors
[Idx
].Power
>>= 1;
1409 if (Factors
[0].Power
) {
1410 Value
*SquareRoot
= buildMinimalMultiplyDAG(Builder
, Factors
);
1411 OuterProduct
.push_back(SquareRoot
);
1412 OuterProduct
.push_back(SquareRoot
);
1414 if (OuterProduct
.size() == 1)
1415 return OuterProduct
.front();
1417 Value
*V
= buildMultiplyTree(Builder
, OuterProduct
);
1421 Value
*Reassociate::OptimizeMul(BinaryOperator
*I
,
1422 SmallVectorImpl
<ValueEntry
> &Ops
) {
1423 // We can only optimize the multiplies when there is a chain of more than
1424 // three, such that a balanced tree might require fewer total multiplies.
1428 // Try to turn linear trees of multiplies without other uses of the
1429 // intermediate stages into minimal multiply DAGs with perfect sub-expression
1431 SmallVector
<Factor
, 4> Factors
;
1432 if (!collectMultiplyFactors(Ops
, Factors
))
1433 return 0; // All distinct factors, so nothing left for us to do.
1435 IRBuilder
<> Builder(I
);
1436 Value
*V
= buildMinimalMultiplyDAG(Builder
, Factors
);
1440 ValueEntry NewEntry
= ValueEntry(getRank(V
), V
);
1441 Ops
.insert(std::lower_bound(Ops
.begin(), Ops
.end(), NewEntry
), NewEntry
);
1445 Value
*Reassociate::OptimizeExpression(BinaryOperator
*I
,
1446 SmallVectorImpl
<ValueEntry
> &Ops
) {
1447 // Now that we have the linearized expression tree, try to optimize it.
1448 // Start by folding any constants that we found.
1449 if (Ops
.size() == 1) return Ops
[0].Op
;
1451 unsigned Opcode
= I
->getOpcode();
1453 // Handle destructive annihilation due to identities between elements in the
1454 // argument list here.
1455 unsigned NumOps
= Ops
.size();
1458 case Instruction::And
:
1459 case Instruction::Or
:
1460 case Instruction::Xor
:
1461 if (Value
*Result
= OptimizeAndOrXor(Opcode
, Ops
))
1465 case Instruction::Add
:
1466 if (Value
*Result
= OptimizeAdd(I
, Ops
))
1470 case Instruction::Mul
:
1471 if (Value
*Result
= OptimizeMul(I
, Ops
))
1476 if (Ops
.size() != NumOps
)
1477 return OptimizeExpression(I
, Ops
);
1481 /// EraseInst - Zap the given instruction, adding interesting operands to the
1483 void Reassociate::EraseInst(Instruction
*I
) {
1484 assert(isInstructionTriviallyDead(I
) && "Trivially dead instructions only!");
1485 SmallVector
<Value
*, 8> Ops(I
->op_begin(), I
->op_end());
1486 // Erase the dead instruction.
1487 ValueRankMap
.erase(I
);
1488 RedoInsts
.remove(I
);
1489 I
->eraseFromParent();
1490 // Optimize its operands.
1491 SmallPtrSet
<Instruction
*, 8> Visited
; // Detect self-referential nodes.
1492 for (unsigned i
= 0, e
= Ops
.size(); i
!= e
; ++i
)
1493 if (Instruction
*Op
= dyn_cast
<Instruction
>(Ops
[i
])) {
1494 // If this is a node in an expression tree, climb to the expression root
1495 // and add that since that's where optimization actually happens.
1496 unsigned Opcode
= Op
->getOpcode();
1497 while (Op
->hasOneUse() && Op
->use_back()->getOpcode() == Opcode
&&
1499 Op
= Op
->use_back();
1500 RedoInsts
.insert(Op
);
1504 /// OptimizeInst - Inspect and optimize the given instruction. Note that erasing
1505 /// instructions is not allowed.
1506 void Reassociate::OptimizeInst(Instruction
*I
) {
1507 // Only consider operations that we understand.
1508 if (!isa
<BinaryOperator
>(I
))
1511 if (I
->getOpcode() == Instruction::Shl
&&
1512 isa
<ConstantInt
>(I
->getOperand(1)))
1513 // If an operand of this shift is a reassociable multiply, or if the shift
1514 // is used by a reassociable multiply or add, turn into a multiply.
1515 if (isReassociableOp(I
->getOperand(0), Instruction::Mul
) ||
1517 (isReassociableOp(I
->use_back(), Instruction::Mul
) ||
1518 isReassociableOp(I
->use_back(), Instruction::Add
)))) {
1519 Instruction
*NI
= ConvertShiftToMul(I
);
1520 RedoInsts
.insert(I
);
1525 // Floating point binary operators are not associative, but we can still
1526 // commute (some) of them, to canonicalize the order of their operands.
1527 // This can potentially expose more CSE opportunities, and makes writing
1528 // other transformations simpler.
1529 if ((I
->getType()->isFloatingPointTy() || I
->getType()->isVectorTy())) {
1530 // FAdd and FMul can be commuted.
1531 if (I
->getOpcode() != Instruction::FMul
&&
1532 I
->getOpcode() != Instruction::FAdd
)
1535 Value
*LHS
= I
->getOperand(0);
1536 Value
*RHS
= I
->getOperand(1);
1537 unsigned LHSRank
= getRank(LHS
);
1538 unsigned RHSRank
= getRank(RHS
);
1540 // Sort the operands by rank.
1541 if (RHSRank
< LHSRank
) {
1542 I
->setOperand(0, RHS
);
1543 I
->setOperand(1, LHS
);
1549 // Do not reassociate boolean (i1) expressions. We want to preserve the
1550 // original order of evaluation for short-circuited comparisons that
1551 // SimplifyCFG has folded to AND/OR expressions. If the expression
1552 // is not further optimized, it is likely to be transformed back to a
1553 // short-circuited form for code gen, and the source order may have been
1554 // optimized for the most likely conditions.
1555 if (I
->getType()->isIntegerTy(1))
1558 // If this is a subtract instruction which is not already in negate form,
1559 // see if we can convert it to X+-Y.
1560 if (I
->getOpcode() == Instruction::Sub
) {
1561 if (ShouldBreakUpSubtract(I
)) {
1562 Instruction
*NI
= BreakUpSubtract(I
);
1563 RedoInsts
.insert(I
);
1566 } else if (BinaryOperator::isNeg(I
)) {
1567 // Otherwise, this is a negation. See if the operand is a multiply tree
1568 // and if this is not an inner node of a multiply tree.
1569 if (isReassociableOp(I
->getOperand(1), Instruction::Mul
) &&
1571 !isReassociableOp(I
->use_back(), Instruction::Mul
))) {
1572 Instruction
*NI
= LowerNegateToMultiply(I
);
1573 RedoInsts
.insert(I
);
1580 // If this instruction is an associative binary operator, process it.
1581 if (!I
->isAssociative()) return;
1582 BinaryOperator
*BO
= cast
<BinaryOperator
>(I
);
1584 // If this is an interior node of a reassociable tree, ignore it until we
1585 // get to the root of the tree, to avoid N^2 analysis.
1586 unsigned Opcode
= BO
->getOpcode();
1587 if (BO
->hasOneUse() && BO
->use_back()->getOpcode() == Opcode
)
1590 // If this is an add tree that is used by a sub instruction, ignore it
1591 // until we process the subtract.
1592 if (BO
->hasOneUse() && BO
->getOpcode() == Instruction::Add
&&
1593 cast
<Instruction
>(BO
->use_back())->getOpcode() == Instruction::Sub
)
1596 ReassociateExpression(BO
);
1599 void Reassociate::ReassociateExpression(BinaryOperator
*I
) {
1601 // First, walk the expression tree, linearizing the tree, collecting the
1602 // operand information.
1603 SmallVector
<RepeatedValue
, 8> Tree
;
1604 MadeChange
|= LinearizeExprTree(I
, Tree
);
1605 SmallVector
<ValueEntry
, 8> Ops
;
1606 Ops
.reserve(Tree
.size());
1607 for (unsigned i
= 0, e
= Tree
.size(); i
!= e
; ++i
) {
1608 RepeatedValue E
= Tree
[i
];
1609 Ops
.append(E
.second
.getZExtValue(),
1610 ValueEntry(getRank(E
.first
), E
.first
));
1613 DEBUG(dbgs() << "RAIn:\t"; PrintOps(I
, Ops
); dbgs() << '\n');
1615 // Now that we have linearized the tree to a list and have gathered all of
1616 // the operands and their ranks, sort the operands by their rank. Use a
1617 // stable_sort so that values with equal ranks will have their relative
1618 // positions maintained (and so the compiler is deterministic). Note that
1619 // this sorts so that the highest ranking values end up at the beginning of
1621 std::stable_sort(Ops
.begin(), Ops
.end());
1623 // OptimizeExpression - Now that we have the expression tree in a convenient
1624 // sorted form, optimize it globally if possible.
1625 if (Value
*V
= OptimizeExpression(I
, Ops
)) {
1627 // Self-referential expression in unreachable code.
1629 // This expression tree simplified to something that isn't a tree,
1631 DEBUG(dbgs() << "Reassoc to scalar: " << *V
<< '\n');
1632 I
->replaceAllUsesWith(V
);
1633 if (Instruction
*VI
= dyn_cast
<Instruction
>(V
))
1634 VI
->setDebugLoc(I
->getDebugLoc());
1635 RedoInsts
.insert(I
);
1640 // We want to sink immediates as deeply as possible except in the case where
1641 // this is a multiply tree used only by an add, and the immediate is a -1.
1642 // In this case we reassociate to put the negation on the outside so that we
1643 // can fold the negation into the add: (-X)*Y + Z -> Z-X*Y
1644 if (I
->getOpcode() == Instruction::Mul
&& I
->hasOneUse() &&
1645 cast
<Instruction
>(I
->use_back())->getOpcode() == Instruction::Add
&&
1646 isa
<ConstantInt
>(Ops
.back().Op
) &&
1647 cast
<ConstantInt
>(Ops
.back().Op
)->isAllOnesValue()) {
1648 ValueEntry Tmp
= Ops
.pop_back_val();
1649 Ops
.insert(Ops
.begin(), Tmp
);
1652 DEBUG(dbgs() << "RAOut:\t"; PrintOps(I
, Ops
); dbgs() << '\n');
1654 if (Ops
.size() == 1) {
1656 // Self-referential expression in unreachable code.
1659 // This expression tree simplified to something that isn't a tree,
1661 I
->replaceAllUsesWith(Ops
[0].Op
);
1662 if (Instruction
*OI
= dyn_cast
<Instruction
>(Ops
[0].Op
))
1663 OI
->setDebugLoc(I
->getDebugLoc());
1664 RedoInsts
.insert(I
);
1668 // Now that we ordered and optimized the expressions, splat them back into
1669 // the expression tree, removing any unneeded nodes.
1670 RewriteExprTree(I
, Ops
);
1673 bool Reassociate::runOnFunction(Function
&F
) {
1674 // Calculate the rank map for F
1678 for (Function::iterator BI
= F
.begin(), BE
= F
.end(); BI
!= BE
; ++BI
) {
1679 // Optimize every instruction in the basic block.
1680 for (BasicBlock::iterator II
= BI
->begin(), IE
= BI
->end(); II
!= IE
; )
1681 if (isInstructionTriviallyDead(II
)) {
1685 assert(II
->getParent() == BI
&& "Moved to a different block!");
1689 // If this produced extra instructions to optimize, handle them now.
1690 while (!RedoInsts
.empty()) {
1691 Instruction
*I
= RedoInsts
.pop_back_val();
1692 if (isInstructionTriviallyDead(I
))
1699 // We are done with the rank map.
1701 ValueRankMap
.clear();