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ara-mdk / platform / external / llvm / 7abc88bc83d2b1a0e576fa5cf92de5017d90a792 / . / lib / Transforms / Scalar / Reassociate.cpp
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//===- Reassociate.cpp - Reassociate binary expressions -------------------===//
//
// The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This pass reassociates commutative expressions in an order that is designed
// to promote better constant propagation, GCSE, LICM, PRE, etc.
//
// For example: 4 + (x + 5) -> x + (4 + 5)
//
// In the implementation of this algorithm, constants are assigned rank = 0,
// function arguments are rank = 1, and other values are assigned ranks
// corresponding to the reverse post order traversal of current function
// (starting at 2), which effectively gives values in deep loops higher rank
// than values not in loops.
//
//===----------------------------------------------------------------------===//
#define DEBUG_TYPE "reassociate"
#include "llvm/Transforms/Scalar.h"
#include "llvm/ADT/DenseMap.h"
#include "llvm/ADT/PostOrderIterator.h"
#include "llvm/ADT/STLExtras.h"
#include "llvm/ADT/SetVector.h"
#include "llvm/ADT/Statistic.h"
#include "llvm/Assembly/Writer.h"
#include "llvm/IR/Constants.h"
#include "llvm/IR/DerivedTypes.h"
#include "llvm/IR/Function.h"
#include "llvm/IR/IRBuilder.h"
#include "llvm/IR/Instructions.h"
#include "llvm/IR/IntrinsicInst.h"
#include "llvm/Pass.h"
#include "llvm/Support/CFG.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/ValueHandle.h"
#include "llvm/Support/raw_ostream.h"
#include "llvm/Transforms/Utils/Local.h"
#include <algorithm>
using namespace llvm;
STATISTIC(NumChanged, "Number of insts reassociated");
STATISTIC(NumAnnihil, "Number of expr tree annihilated");
STATISTIC(NumFactor , "Number of multiplies factored");
namespace {
struct ValueEntry {
unsigned Rank;
Value *Op;
ValueEntry(unsigned R, Value *O) : Rank(R), Op(O) {}
};
inline bool operator<(const ValueEntry &LHS, const ValueEntry &RHS) {
return LHS.Rank > RHS.Rank; // Sort so that highest rank goes to start.
}
}
#ifndef NDEBUG
/// PrintOps - Print out the expression identified in the Ops list.
///
static void PrintOps(Instruction *I, const SmallVectorImpl<ValueEntry> &Ops) {
Module *M = I->getParent()->getParent()->getParent();
dbgs() << Instruction::getOpcodeName(I->getOpcode()) << " "
<< *Ops[0].Op->getType() << '\t';
for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
dbgs() << "[ ";
WriteAsOperand(dbgs(), Ops[i].Op, false, M);
dbgs() << ", #" << Ops[i].Rank << "] ";
}
}
#endif
namespace {
/// \brief Utility class representing a base and exponent pair which form one
/// factor of some product.
struct Factor {
Value *Base;
unsigned Power;
Factor(Value *Base, unsigned Power) : Base(Base), Power(Power) {}
/// \brief Sort factors by their Base.
struct BaseSorter {
bool operator()(const Factor &LHS, const Factor &RHS) {
return LHS.Base < RHS.Base;
}
};
/// \brief Compare factors for equal bases.
struct BaseEqual {
bool operator()(const Factor &LHS, const Factor &RHS) {
return LHS.Base == RHS.Base;
}
};
/// \brief Sort factors in descending order by their power.
struct PowerDescendingSorter {
bool operator()(const Factor &LHS, const Factor &RHS) {
return LHS.Power > RHS.Power;
}
};
/// \brief Compare factors for equal powers.
struct PowerEqual {
bool operator()(const Factor &LHS, const Factor &RHS) {
return LHS.Power == RHS.Power;
}
};
};
}
namespace {
class Reassociate : public FunctionPass {
DenseMap<BasicBlock*, unsigned> RankMap;
DenseMap<AssertingVH<Value>, unsigned> ValueRankMap;
SetVector<AssertingVH<Instruction> > RedoInsts;
bool MadeChange;
public:
static char ID; // Pass identification, replacement for typeid
Reassociate() : FunctionPass(ID) {
initializeReassociatePass(*PassRegistry::getPassRegistry());
}
bool runOnFunction(Function &F);
virtual void getAnalysisUsage(AnalysisUsage &AU) const {
AU.setPreservesCFG();
}
private:
void BuildRankMap(Function &F);
unsigned getRank(Value *V);
void ReassociateExpression(BinaryOperator *I);
void RewriteExprTree(BinaryOperator *I, SmallVectorImpl<ValueEntry> &Ops);
Value *OptimizeExpression(BinaryOperator *I,
SmallVectorImpl<ValueEntry> &Ops);
Value *OptimizeAdd(Instruction *I, SmallVectorImpl<ValueEntry> &Ops);
bool collectMultiplyFactors(SmallVectorImpl<ValueEntry> &Ops,
SmallVectorImpl<Factor> &Factors);
Value *buildMinimalMultiplyDAG(IRBuilder<> &Builder,
SmallVectorImpl<Factor> &Factors);
Value *OptimizeMul(BinaryOperator *I, SmallVectorImpl<ValueEntry> &Ops);
Value *RemoveFactorFromExpression(Value *V, Value *Factor);
void EraseInst(Instruction *I);
void OptimizeInst(Instruction *I);
};
}
char Reassociate::ID = 0;
INITIALIZE_PASS(Reassociate, "reassociate",
"Reassociate expressions", false, false)
// Public interface to the Reassociate pass
FunctionPass *llvm::createReassociatePass() { return new Reassociate(); }
/// isReassociableOp - Return true if V is an instruction of the specified
/// opcode and if it only has one use.
static BinaryOperator *isReassociableOp(Value *V, unsigned Opcode) {
if (V->hasOneUse() && isa<Instruction>(V) &&
cast<Instruction>(V)->getOpcode() == Opcode)
return cast<BinaryOperator>(V);
return 0;
}
static bool isUnmovableInstruction(Instruction *I) {
if (I->getOpcode() == Instruction::PHI ||
I->getOpcode() == Instruction::LandingPad ||
I->getOpcode() == Instruction::Alloca ||
I->getOpcode() == Instruction::Load ||
I->getOpcode() == Instruction::Invoke ||
(I->getOpcode() == Instruction::Call &&
!isa<DbgInfoIntrinsic>(I)) ||
I->getOpcode() == Instruction::UDiv ||
I->getOpcode() == Instruction::SDiv ||
I->getOpcode() == Instruction::FDiv ||
I->getOpcode() == Instruction::URem ||
I->getOpcode() == Instruction::SRem ||
I->getOpcode() == Instruction::FRem)
return true;
return false;
}
void Reassociate::BuildRankMap(Function &F) {
unsigned i = 2;
// Assign distinct ranks to function arguments
for (Function::arg_iterator I = F.arg_begin(), E = F.arg_end(); I != E; ++I)
ValueRankMap[&*I] = ++i;
ReversePostOrderTraversal<Function*> RPOT(&F);
for (ReversePostOrderTraversal<Function*>::rpo_iterator I = RPOT.begin(),
E = RPOT.end(); I != E; ++I) {
BasicBlock *BB = *I;
unsigned BBRank = RankMap[BB] = ++i << 16;
// Walk the basic block, adding precomputed ranks for any instructions that
// we cannot move. This ensures that the ranks for these instructions are
// all different in the block.
for (BasicBlock::iterator I = BB->begin(), E = BB->end(); I != E; ++I)
if (isUnmovableInstruction(I))
ValueRankMap[&*I] = ++BBRank;
}
}
unsigned Reassociate::getRank(Value *V) {
Instruction *I = dyn_cast<Instruction>(V);
if (I == 0) {
if (isa<Argument>(V)) return ValueRankMap[V]; // Function argument.
return 0; // Otherwise it's a global or constant, rank 0.
}
if (unsigned Rank = ValueRankMap[I])
return Rank; // Rank already known?
// If this is an expression, return the 1+MAX(rank(LHS), rank(RHS)) so that
// we can reassociate expressions for code motion! Since we do not recurse
// for PHI nodes, we cannot have infinite recursion here, because there
// cannot be loops in the value graph that do not go through PHI nodes.
unsigned Rank = 0, MaxRank = RankMap[I->getParent()];
for (unsigned i = 0, e = I->getNumOperands();
i != e && Rank != MaxRank; ++i)
Rank = std::max(Rank, getRank(I->getOperand(i)));
// If this is a not or neg instruction, do not count it for rank. This
// assures us that X and ~X will have the same rank.
if (!I->getType()->isIntegerTy() ||
(!BinaryOperator::isNot(I) && !BinaryOperator::isNeg(I)))
++Rank;
//DEBUG(dbgs() << "Calculated Rank[" << V->getName() << "] = "
// << Rank << "\n");
return ValueRankMap[I] = Rank;
}
/// LowerNegateToMultiply - Replace 0-X with X*-1.
///
static BinaryOperator *LowerNegateToMultiply(Instruction *Neg) {
Constant *Cst = Constant::getAllOnesValue(Neg->getType());
BinaryOperator *Res =
BinaryOperator::CreateMul(Neg->getOperand(1), Cst, "",Neg);
Neg->setOperand(1, Constant::getNullValue(Neg->getType())); // Drop use of op.
Res->takeName(Neg);
Neg->replaceAllUsesWith(Res);
Res->setDebugLoc(Neg->getDebugLoc());
return Res;
}
/// CarmichaelShift - Returns k such that lambda(2^Bitwidth) = 2^k, where lambda
/// is the Carmichael function. This means that x^(2^k) === 1 mod 2^Bitwidth for
/// every odd x, i.e. x^(2^k) = 1 for every odd x in Bitwidth-bit arithmetic.
/// Note that 0 <= k < Bitwidth, and if Bitwidth > 3 then x^(2^k) = 0 for every
/// even x in Bitwidth-bit arithmetic.
static unsigned CarmichaelShift(unsigned Bitwidth) {
if (Bitwidth < 3)
return Bitwidth - 1;
return Bitwidth - 2;
}
/// IncorporateWeight - Add the extra weight 'RHS' to the existing weight 'LHS',
/// reducing the combined weight using any special properties of the operation.
/// The existing weight LHS represents the computation X op X op ... op X where
/// X occurs LHS times. The combined weight represents X op X op ... op X with
/// X occurring LHS + RHS times. If op is "Xor" for example then the combined
/// operation is equivalent to X if LHS + RHS is odd, or 0 if LHS + RHS is even;
/// the routine returns 1 in LHS in the first case, and 0 in LHS in the second.
static void IncorporateWeight(APInt &LHS, const APInt &RHS, unsigned Opcode) {
// If we were working with infinite precision arithmetic then the combined
// weight would be LHS + RHS. But we are using finite precision arithmetic,
// and the APInt sum LHS + RHS may not be correct if it wraps (it is correct
// for nilpotent operations and addition, but not for idempotent operations
// and multiplication), so it is important to correctly reduce the combined
// weight back into range if wrapping would be wrong.
// If RHS is zero then the weight didn't change.
if (RHS.isMinValue())
return;
// If LHS is zero then the combined weight is RHS.
if (LHS.isMinValue()) {
LHS = RHS;
return;
}
// From this point on we know that neither LHS nor RHS is zero.
if (Instruction::isIdempotent(Opcode)) {
// Idempotent means X op X === X, so any non-zero weight is equivalent to a
// weight of 1. Keeping weights at zero or one also means that wrapping is
// not a problem.
assert(LHS == 1 && RHS == 1 && "Weights not reduced!");
return; // Return a weight of 1.
}
if (Instruction::isNilpotent(Opcode)) {
// Nilpotent means X op X === 0, so reduce weights modulo 2.
assert(LHS == 1 && RHS == 1 && "Weights not reduced!");
LHS = 0; // 1 + 1 === 0 modulo 2.
return;
}
if (Opcode == Instruction::Add) {
// TODO: Reduce the weight by exploiting nsw/nuw?
LHS += RHS;
return;
}
assert(Opcode == Instruction::Mul && "Unknown associative operation!");
unsigned Bitwidth = LHS.getBitWidth();
// If CM is the Carmichael number then a weight W satisfying W >= CM+Bitwidth
// can be replaced with W-CM. That's because x^W=x^(W-CM) for every Bitwidth
// bit number x, since either x is odd in which case x^CM = 1, or x is even in
// which case both x^W and x^(W - CM) are zero. By subtracting off multiples
// of CM like this weights can always be reduced to the range [0, CM+Bitwidth)
// which by a happy accident means that they can always be represented using
// Bitwidth bits.
// TODO: Reduce the weight by exploiting nsw/nuw? (Could do much better than
// the Carmichael number).
if (Bitwidth > 3) {
/// CM - The value of Carmichael's lambda function.
APInt CM = APInt::getOneBitSet(Bitwidth, CarmichaelShift(Bitwidth));
// Any weight W >= Threshold can be replaced with W - CM.
APInt Threshold = CM + Bitwidth;
assert(LHS.ult(Threshold) && RHS.ult(Threshold) && "Weights not reduced!");
// For Bitwidth 4 or more the following sum does not overflow.
LHS += RHS;
while (LHS.uge(Threshold))
LHS -= CM;
} else {
// To avoid problems with overflow do everything the same as above but using
// a larger type.
unsigned CM = 1U << CarmichaelShift(Bitwidth);
unsigned Threshold = CM + Bitwidth;
assert(LHS.getZExtValue() < Threshold && RHS.getZExtValue() < Threshold &&
"Weights not reduced!");
unsigned Total = LHS.getZExtValue() + RHS.getZExtValue();
while (Total >= Threshold)
Total -= CM;
LHS = Total;
}
}
typedef std::pair<Value*, APInt> RepeatedValue;
/// LinearizeExprTree - Given an associative binary expression, return the leaf
/// nodes in Ops along with their weights (how many times the leaf occurs). The
/// original expression is the same as
/// (Ops[0].first op Ops[0].first op ... Ops[0].first) <- Ops[0].second times
/// op
/// (Ops[1].first op Ops[1].first op ... Ops[1].first) <- Ops[1].second times
/// op
/// ...
/// op
/// (Ops[N].first op Ops[N].first op ... Ops[N].first) <- Ops[N].second times
///
/// Note that the values Ops[0].first, ..., Ops[N].first are all distinct.
///
/// This routine may modify the function, in which case it returns 'true'. The
/// changes it makes may well be destructive, changing the value computed by 'I'
/// to something completely different. Thus if the routine returns 'true' then
/// you MUST either replace I with a new expression computed from the Ops array,
/// or use RewriteExprTree to put the values back in.
///
/// A leaf node is either not a binary operation of the same kind as the root
/// node 'I' (i.e. is not a binary operator at all, or is, but with a different
/// opcode), or is the same kind of binary operator but has a use which either
/// does not belong to the expression, or does belong to the expression but is
/// a leaf node. Every leaf node has at least one use that is a non-leaf node
/// of the expression, while for non-leaf nodes (except for the root 'I') every
/// use is a non-leaf node of the expression.
///
/// For example:
/// expression graph node names
///
/// + | I
/// / \ |
/// + + | A, B
/// / \ / \ |
/// * + * | C, D, E
/// / \ / \ / \ |
/// + * | F, G
///
/// The leaf nodes are C, E, F and G. The Ops array will contain (maybe not in
/// that order) (C, 1), (E, 1), (F, 2), (G, 2).
///
/// The expression is maximal: if some instruction is a binary operator of the
/// same kind as 'I', and all of its uses are non-leaf nodes of the expression,
/// then the instruction also belongs to the expression, is not a leaf node of
/// it, and its operands also belong to the expression (but may be leaf nodes).
///
/// NOTE: This routine will set operands of non-leaf non-root nodes to undef in
/// order to ensure that every non-root node in the expression has *exactly one*
/// use by a non-leaf node of the expression. This destruction means that the
/// caller MUST either replace 'I' with a new expression or use something like
/// RewriteExprTree to put the values back in if the routine indicates that it
/// made a change by returning 'true'.
///
/// In the above example either the right operand of A or the left operand of B
/// will be replaced by undef. If it is B's operand then this gives:
///
/// + | I
/// / \ |
/// + + | A, B - operand of B replaced with undef
/// / \ \ |
/// * + * | C, D, E
/// / \ / \ / \ |
/// + * | F, G
///
/// Note that such undef operands can only be reached by passing through 'I'.
/// For example, if you visit operands recursively starting from a leaf node
/// then you will never see such an undef operand unless you get back to 'I',
/// which requires passing through a phi node.
///
/// Note that this routine may also mutate binary operators of the wrong type
/// that have all uses inside the expression (i.e. only used by non-leaf nodes
/// of the expression) if it can turn them into binary operators of the right
/// type and thus make the expression bigger.
static bool LinearizeExprTree(BinaryOperator *I,
SmallVectorImpl<RepeatedValue> &Ops) {
DEBUG(dbgs() << "LINEARIZE: " << *I << '\n');
unsigned Bitwidth = I->getType()->getScalarType()->getPrimitiveSizeInBits();
unsigned Opcode = I->getOpcode();
assert(Instruction::isAssociative(Opcode) &&
Instruction::isCommutative(Opcode) &&
"Expected an associative and commutative operation!");
// Visit all operands of the expression, keeping track of their weight (the
// number of paths from the expression root to the operand, or if you like
// the number of times that operand occurs in the linearized expression).
// For example, if I = X + A, where X = A + B, then I, X and B have weight 1
// while A has weight two.
// Worklist of non-leaf nodes (their operands are in the expression too) along
// with their weights, representing a certain number of paths to the operator.
// If an operator occurs in the worklist multiple times then we found multiple
// ways to get to it.
SmallVector<std::pair<BinaryOperator*, APInt>, 8> Worklist; // (Op, Weight)
Worklist.push_back(std::make_pair(I, APInt(Bitwidth, 1)));
bool MadeChange = false;
// Leaves of the expression are values that either aren't the right kind of
// operation (eg: a constant, or a multiply in an add tree), or are, but have
// some uses that are not inside the expression. For example, in I = X + X,
// X = A + B, the value X has two uses (by I) that are in the expression. If
// X has any other uses, for example in a return instruction, then we consider
// X to be a leaf, and won't analyze it further. When we first visit a value,
// if it has more than one use then at first we conservatively consider it to
// be a leaf. Later, as the expression is explored, we may discover some more
// uses of the value from inside the expression. If all uses turn out to be
// from within the expression (and the value is a binary operator of the right
// kind) then the value is no longer considered to be a leaf, and its operands
// are explored.
// Leaves - Keeps track of the set of putative leaves as well as the number of
// paths to each leaf seen so far.
typedef DenseMap<Value*, APInt> LeafMap;
LeafMap Leaves; // Leaf -> Total weight so far.
SmallVector<Value*, 8> LeafOrder; // Ensure deterministic leaf output order.
#ifndef NDEBUG
SmallPtrSet<Value*, 8> Visited; // For sanity checking the iteration scheme.
#endif
while (!Worklist.empty()) {
std::pair<BinaryOperator*, APInt> P = Worklist.pop_back_val();
I = P.first; // We examine the operands of this binary operator.
for (unsigned OpIdx = 0; OpIdx < 2; ++OpIdx) { // Visit operands.
Value *Op = I->getOperand(OpIdx);
APInt Weight = P.second; // Number of paths to this operand.
DEBUG(dbgs() << "OPERAND: " << *Op << " (" << Weight << ")\n");
assert(!Op->use_empty() && "No uses, so how did we get to it?!");
// If this is a binary operation of the right kind with only one use then
// add its operands to the expression.
if (BinaryOperator *BO = isReassociableOp(Op, Opcode)) {
assert(Visited.insert(Op) && "Not first visit!");
DEBUG(dbgs() << "DIRECT ADD: " << *Op << " (" << Weight << ")\n");
Worklist.push_back(std::make_pair(BO, Weight));
continue;
}
// Appears to be a leaf. Is the operand already in the set of leaves?
LeafMap::iterator It = Leaves.find(Op);
if (It == Leaves.end()) {
// Not in the leaf map. Must be the first time we saw this operand.
assert(Visited.insert(Op) && "Not first visit!");
if (!Op->hasOneUse()) {
// This value has uses not accounted for by the expression, so it is
// not safe to modify. Mark it as being a leaf.
DEBUG(dbgs() << "ADD USES LEAF: " << *Op << " (" << Weight << ")\n");
LeafOrder.push_back(Op);
Leaves[Op] = Weight;
continue;
}
// No uses outside the expression, try morphing it.
} else if (It != Leaves.end()) {
// Already in the leaf map.
assert(Visited.count(Op) && "In leaf map but not visited!");
// Update the number of paths to the leaf.
IncorporateWeight(It->second, Weight, Opcode);
#if 0 // TODO: Re-enable once PR13021 is fixed.
// The leaf already has one use from inside the expression. As we want
// exactly one such use, drop this new use of the leaf.
assert(!Op->hasOneUse() && "Only one use, but we got here twice!");
I->setOperand(OpIdx, UndefValue::get(I->getType()));
MadeChange = true;
// If the leaf is a binary operation of the right kind and we now see
// that its multiple original uses were in fact all by nodes belonging
// to the expression, then no longer consider it to be a leaf and add
// its operands to the expression.
if (BinaryOperator *BO = isReassociableOp(Op, Opcode)) {
DEBUG(dbgs() << "UNLEAF: " << *Op << " (" << It->second << ")\n");
Worklist.push_back(std::make_pair(BO, It->second));
Leaves.erase(It);
continue;
}
#endif
// If we still have uses that are not accounted for by the expression
// then it is not safe to modify the value.
if (!Op->hasOneUse())
continue;
// No uses outside the expression, try morphing it.
Weight = It->second;
Leaves.erase(It); // Since the value may be morphed below.
}
// At this point we have a value which, first of all, is not a binary
// expression of the right kind, and secondly, is only used inside the
// expression. This means that it can safely be modified. See if we
// can usefully morph it into an expression of the right kind.
assert((!isa<Instruction>(Op) ||
cast<Instruction>(Op)->getOpcode() != Opcode) &&
"Should have been handled above!");
assert(Op->hasOneUse() && "Has uses outside the expression tree!");
// If this is a multiply expression, turn any internal negations into
// multiplies by -1 so they can be reassociated.
BinaryOperator *BO = dyn_cast<BinaryOperator>(Op);
if (Opcode == Instruction::Mul && BO && BinaryOperator::isNeg(BO)) {
DEBUG(dbgs() << "MORPH LEAF: " << *Op << " (" << Weight << ") TO ");
BO = LowerNegateToMultiply(BO);
DEBUG(dbgs() << *BO << 'n');
Worklist.push_back(std::make_pair(BO, Weight));
MadeChange = true;
continue;
}
// Failed to morph into an expression of the right type. This really is
// a leaf.
DEBUG(dbgs() << "ADD LEAF: " << *Op << " (" << Weight << ")\n");
assert(!isReassociableOp(Op, Opcode) && "Value was morphed?");
LeafOrder.push_back(Op);
Leaves[Op] = Weight;
}
}
// The leaves, repeated according to their weights, represent the linearized
// form of the expression.
for (unsigned i = 0, e = LeafOrder.size(); i != e; ++i) {
Value *V = LeafOrder[i];
LeafMap::iterator It = Leaves.find(V);
if (It == Leaves.end())
// Node initially thought to be a leaf wasn't.
continue;
assert(!isReassociableOp(V, Opcode) && "Shouldn't be a leaf!");
APInt Weight = It->second;
if (Weight.isMinValue())
// Leaf already output or weight reduction eliminated it.
continue;
// Ensure the leaf is only output once.
It->second = 0;
Ops.push_back(std::make_pair(V, Weight));
}
// For nilpotent operations or addition there may be no operands, for example
// because the expression was "X xor X" or consisted of 2^Bitwidth additions:
// in both cases the weight reduces to 0 causing the value to be skipped.
if (Ops.empty()) {
Constant *Identity = ConstantExpr::getBinOpIdentity(Opcode, I->getType());
assert(Identity && "Associative operation without identity!");
Ops.push_back(std::make_pair(Identity, APInt(Bitwidth, 1)));
}
return MadeChange;
}
// RewriteExprTree - Now that the operands for this expression tree are
// linearized and optimized, emit them in-order.
void Reassociate::RewriteExprTree(BinaryOperator *I,
SmallVectorImpl<ValueEntry> &Ops) {
assert(Ops.size() > 1 && "Single values should be used directly!");
// Since our optimizations should never increase the number of operations, the
// new expression can usually be written reusing the existing binary operators
// from the original expression tree, without creating any new instructions,
// though the rewritten expression may have a completely different topology.
// We take care to not change anything if the new expression will be the same
// as the original. If more than trivial changes (like commuting operands)
// were made then we are obliged to clear out any optional subclass data like
// nsw flags.
/// NodesToRewrite - Nodes from the original expression available for writing
/// the new expression into.
SmallVector<BinaryOperator*, 8> NodesToRewrite;
unsigned Opcode = I->getOpcode();
BinaryOperator *Op = I;
/// NotRewritable - The operands being written will be the leaves of the new
/// expression and must not be used as inner nodes (via NodesToRewrite) by
/// mistake. Inner nodes are always reassociable, and usually leaves are not
/// (if they were they would have been incorporated into the expression and so
/// would not be leaves), so most of the time there is no danger of this. But
/// in rare cases a leaf may become reassociable if an optimization kills uses
/// of it, or it may momentarily become reassociable during rewriting (below)
/// due it being removed as an operand of one of its uses. Ensure that misuse
/// of leaf nodes as inner nodes cannot occur by remembering all of the future
/// leaves and refusing to reuse any of them as inner nodes.
SmallPtrSet<Value*, 8> NotRewritable;
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
NotRewritable.insert(Ops[i].Op);
// ExpressionChanged - Non-null if the rewritten expression differs from the
// original in some non-trivial way, requiring the clearing of optional flags.
// Flags are cleared from the operator in ExpressionChanged up to I inclusive.
BinaryOperator *ExpressionChanged = 0;
for (unsigned i = 0; ; ++i) {
// The last operation (which comes earliest in the IR) is special as both
// operands will come from Ops, rather than just one with the other being
// a subexpression.
if (i+2 == Ops.size()) {
Value *NewLHS = Ops[i].Op;
Value *NewRHS = Ops[i+1].Op;
Value *OldLHS = Op->getOperand(0);
Value *OldRHS = Op->getOperand(1);
if (NewLHS == OldLHS && NewRHS == OldRHS)
// Nothing changed, leave it alone.
break;
if (NewLHS == OldRHS && NewRHS == OldLHS) {
// The order of the operands was reversed. Swap them.
DEBUG(dbgs() << "RA: " << *Op << '\n');
Op->swapOperands();
DEBUG(dbgs() << "TO: " << *Op << '\n');
MadeChange = true;
++NumChanged;
break;
}
// The new operation differs non-trivially from the original. Overwrite
// the old operands with the new ones.
DEBUG(dbgs() << "RA: " << *Op << '\n');
if (NewLHS != OldLHS) {
BinaryOperator *BO = isReassociableOp(OldLHS, Opcode);
if (BO && !NotRewritable.count(BO))
NodesToRewrite.push_back(BO);
Op->setOperand(0, NewLHS);
}
if (NewRHS != OldRHS) {
BinaryOperator *BO = isReassociableOp(OldRHS, Opcode);
if (BO && !NotRewritable.count(BO))
NodesToRewrite.push_back(BO);
Op->setOperand(1, NewRHS);
}
DEBUG(dbgs() << "TO: " << *Op << '\n');
ExpressionChanged = Op;
MadeChange = true;
++NumChanged;
break;
}
// Not the last operation. The left-hand side will be a sub-expression
// while the right-hand side will be the current element of Ops.
Value *NewRHS = Ops[i].Op;
if (NewRHS != Op->getOperand(1)) {
DEBUG(dbgs() << "RA: " << *Op << '\n');
if (NewRHS == Op->getOperand(0)) {
// The new right-hand side was already present as the left operand. If
// we are lucky then swapping the operands will sort out both of them.
Op->swapOperands();
} else {
// Overwrite with the new right-hand side.
BinaryOperator *BO = isReassociableOp(Op->getOperand(1), Opcode);
if (BO && !NotRewritable.count(BO))
NodesToRewrite.push_back(BO);
Op->setOperand(1, NewRHS);
ExpressionChanged = Op;
}
DEBUG(dbgs() << "TO: " << *Op << '\n');
MadeChange = true;
++NumChanged;
}
// Now deal with the left-hand side. If this is already an operation node
// from the original expression then just rewrite the rest of the expression
// into it.
BinaryOperator *BO = isReassociableOp(Op->getOperand(0), Opcode);
if (BO && !NotRewritable.count(BO)) {
Op = BO;
continue;
}
// Otherwise, grab a spare node from the original expression and use that as
// the left-hand side. If there are no nodes left then the optimizers made
// an expression with more nodes than the original! This usually means that
// they did something stupid but it might mean that the problem was just too
// hard (finding the mimimal number of multiplications needed to realize a
// multiplication expression is NP-complete). Whatever the reason, smart or
// stupid, create a new node if there are none left.
BinaryOperator *NewOp;
if (NodesToRewrite.empty()) {
Constant *Undef = UndefValue::get(I->getType());
NewOp = BinaryOperator::Create(Instruction::BinaryOps(Opcode),
Undef, Undef, "", I);
} else {
NewOp = NodesToRewrite.pop_back_val();
}
DEBUG(dbgs() << "RA: " << *Op << '\n');
Op->setOperand(0, NewOp);
DEBUG(dbgs() << "TO: " << *Op << '\n');
ExpressionChanged = Op;
MadeChange = true;
++NumChanged;
Op = NewOp;
}
// If the expression changed non-trivially then clear out all subclass data
// starting from the operator specified in ExpressionChanged, and compactify
// the operators to just before the expression root to guarantee that the
// expression tree is dominated by all of Ops.
if (ExpressionChanged)
do {
ExpressionChanged->clearSubclassOptionalData();
if (ExpressionChanged == I)
break;
ExpressionChanged->moveBefore(I);
ExpressionChanged = cast<BinaryOperator>(*ExpressionChanged->use_begin());
} while (1);
// Throw away any left over nodes from the original expression.
for (unsigned i = 0, e = NodesToRewrite.size(); i != e; ++i)
RedoInsts.insert(NodesToRewrite[i]);
}
/// NegateValue - Insert instructions before the instruction pointed to by BI,
/// that computes the negative version of the value specified. The negative
/// version of the value is returned, and BI is left pointing at the instruction
/// that should be processed next by the reassociation pass.
static Value *NegateValue(Value *V, Instruction *BI) {
if (Constant *C = dyn_cast<Constant>(V))
return ConstantExpr::getNeg(C);
// We are trying to expose opportunity for reassociation. One of the things
// that we want to do to achieve this is to push a negation as deep into an
// expression chain as possible, to expose the add instructions. In practice,
// this means that we turn this:
// X = -(A+12+C+D) into X = -A + -12 + -C + -D = -12 + -A + -C + -D
// so that later, a: Y = 12+X could get reassociated with the -12 to eliminate
// the constants. We assume that instcombine will clean up the mess later if
// we introduce tons of unnecessary negation instructions.
//
if (BinaryOperator *I = isReassociableOp(V, Instruction::Add)) {
// Push the negates through the add.
I->setOperand(0, NegateValue(I->getOperand(0), BI));
I->setOperand(1, NegateValue(I->getOperand(1), BI));
// We must move the add instruction here, because the neg instructions do
// not dominate the old add instruction in general. By moving it, we are
// assured that the neg instructions we just inserted dominate the
// instruction we are about to insert after them.
//
I->moveBefore(BI);
I->setName(I->getName()+".neg");
return I;
}
// Okay, we need to materialize a negated version of V with an instruction.
// Scan the use lists of V to see if we have one already.
for (Value::use_iterator UI = V->use_begin(), E = V->use_end(); UI != E;++UI){
User *U = *UI;
if (!BinaryOperator::isNeg(U)) continue;
// We found one! Now we have to make sure that the definition dominates
// this use. We do this by moving it to the entry block (if it is a
// non-instruction value) or right after the definition. These negates will
// be zapped by reassociate later, so we don't need much finesse here.
BinaryOperator *TheNeg = cast<BinaryOperator>(U);
// Verify that the negate is in this function, V might be a constant expr.
if (TheNeg->getParent()->getParent() != BI->getParent()->getParent())
continue;
BasicBlock::iterator InsertPt;
if (Instruction *InstInput = dyn_cast<Instruction>(V)) {
if (InvokeInst *II = dyn_cast<InvokeInst>(InstInput)) {
InsertPt = II->getNormalDest()->begin();
} else {
InsertPt = InstInput;
++InsertPt;
}
while (isa<PHINode>(InsertPt)) ++InsertPt;
} else {
InsertPt = TheNeg->getParent()->getParent()->getEntryBlock().begin();
}
TheNeg->moveBefore(InsertPt);
return TheNeg;
}
// Insert a 'neg' instruction that subtracts the value from zero to get the
// negation.
return BinaryOperator::CreateNeg(V, V->getName() + ".neg", BI);
}
/// ShouldBreakUpSubtract - Return true if we should break up this subtract of
/// X-Y into (X + -Y).
static bool ShouldBreakUpSubtract(Instruction *Sub) {
// If this is a negation, we can't split it up!
if (BinaryOperator::isNeg(Sub))
return false;
// Don't bother to break this up unless either the LHS is an associable add or
// subtract or if this is only used by one.
if (isReassociableOp(Sub->getOperand(0), Instruction::Add) ||
isReassociableOp(Sub->getOperand(0), Instruction::Sub))
return true;
if (isReassociableOp(Sub->getOperand(1), Instruction::Add) ||
isReassociableOp(Sub->getOperand(1), Instruction::Sub))
return true;
if (Sub->hasOneUse() &&
(isReassociableOp(Sub->use_back(), Instruction::Add) ||
isReassociableOp(Sub->use_back(), Instruction::Sub)))
return true;
return false;
}
/// BreakUpSubtract - If we have (X-Y), and if either X is an add, or if this is
/// only used by an add, transform this into (X+(0-Y)) to promote better
/// reassociation.
static BinaryOperator *BreakUpSubtract(Instruction *Sub) {
// Convert a subtract into an add and a neg instruction. This allows sub
// instructions to be commuted with other add instructions.
//
// Calculate the negative value of Operand 1 of the sub instruction,
// and set it as the RHS of the add instruction we just made.
//
Value *NegVal = NegateValue(Sub->getOperand(1), Sub);
BinaryOperator *New =
BinaryOperator::CreateAdd(Sub->getOperand(0), NegVal, "", Sub);
Sub->setOperand(0, Constant::getNullValue(Sub->getType())); // Drop use of op.
Sub->setOperand(1, Constant::getNullValue(Sub->getType())); // Drop use of op.
New->takeName(Sub);
// Everyone now refers to the add instruction.
Sub->replaceAllUsesWith(New);
New->setDebugLoc(Sub->getDebugLoc());
DEBUG(dbgs() << "Negated: " << *New << '\n');
return New;
}
/// ConvertShiftToMul - If this is a shift of a reassociable multiply or is used
/// by one, change this into a multiply by a constant to assist with further
/// reassociation.
static BinaryOperator *ConvertShiftToMul(Instruction *Shl) {
Constant *MulCst = ConstantInt::get(Shl->getType(), 1);
MulCst = ConstantExpr::getShl(MulCst, cast<Constant>(Shl->getOperand(1)));
BinaryOperator *Mul =
BinaryOperator::CreateMul(Shl->getOperand(0), MulCst, "", Shl);
Shl->setOperand(0, UndefValue::get(Shl->getType())); // Drop use of op.
Mul->takeName(Shl);
Shl->replaceAllUsesWith(Mul);
Mul->setDebugLoc(Shl->getDebugLoc());
return Mul;
}
/// FindInOperandList - Scan backwards and forwards among values with the same
/// rank as element i to see if X exists. If X does not exist, return i. This
/// is useful when scanning for 'x' when we see '-x' because they both get the
/// same rank.
static unsigned FindInOperandList(SmallVectorImpl<ValueEntry> &Ops, unsigned i,
Value *X) {
unsigned XRank = Ops[i].Rank;
unsigned e = Ops.size();
for (unsigned j = i+1; j != e && Ops[j].Rank == XRank; ++j)
if (Ops[j].Op == X)
return j;
// Scan backwards.
for (unsigned j = i-1; j != ~0U && Ops[j].Rank == XRank; --j)
if (Ops[j].Op == X)
return j;
return i;
}
/// EmitAddTreeOfValues - Emit a tree of add instructions, summing Ops together
/// and returning the result. Insert the tree before I.
static Value *EmitAddTreeOfValues(Instruction *I,
SmallVectorImpl<WeakVH> &Ops){
if (Ops.size() == 1) return Ops.back();
Value *V1 = Ops.back();
Ops.pop_back();
Value *V2 = EmitAddTreeOfValues(I, Ops);
return BinaryOperator::CreateAdd(V2, V1, "tmp", I);
}
/// RemoveFactorFromExpression - If V is an expression tree that is a
/// multiplication sequence, and if this sequence contains a multiply by Factor,
/// remove Factor from the tree and return the new tree.
Value *Reassociate::RemoveFactorFromExpression(Value *V, Value *Factor) {
BinaryOperator *BO = isReassociableOp(V, Instruction::Mul);
if (!BO) return 0;
SmallVector<RepeatedValue, 8> Tree;
MadeChange |= LinearizeExprTree(BO, Tree);
SmallVector<ValueEntry, 8> Factors;
Factors.reserve(Tree.size());
for (unsigned i = 0, e = Tree.size(); i != e; ++i) {
RepeatedValue E = Tree[i];
Factors.append(E.second.getZExtValue(),
ValueEntry(getRank(E.first), E.first));
}
bool FoundFactor = false;
bool NeedsNegate = false;
for (unsigned i = 0, e = Factors.size(); i != e; ++i) {
if (Factors[i].Op == Factor) {
FoundFactor = true;
Factors.erase(Factors.begin()+i);
break;
}
// If this is a negative version of this factor, remove it.
if (ConstantInt *FC1 = dyn_cast<ConstantInt>(Factor))
if (ConstantInt *FC2 = dyn_cast<ConstantInt>(Factors[i].Op))
if (FC1->getValue() == -FC2->getValue()) {
FoundFactor = NeedsNegate = true;
Factors.erase(Factors.begin()+i);
break;
}
}
if (!FoundFactor) {
// Make sure to restore the operands to the expression tree.
RewriteExprTree(BO, Factors);
return 0;
}
BasicBlock::iterator InsertPt = BO; ++InsertPt;
// If this was just a single multiply, remove the multiply and return the only
// remaining operand.
if (Factors.size() == 1) {
RedoInsts.insert(BO);
V = Factors[0].Op;
} else {
RewriteExprTree(BO, Factors);
V = BO;
}
if (NeedsNegate)
V = BinaryOperator::CreateNeg(V, "neg", InsertPt);
return V;
}
/// FindSingleUseMultiplyFactors - If V is a single-use multiply, recursively
/// add its operands as factors, otherwise add V to the list of factors.
///
/// Ops is the top-level list of add operands we're trying to factor.
static void FindSingleUseMultiplyFactors(Value *V,
SmallVectorImpl<Value*> &Factors,
const SmallVectorImpl<ValueEntry> &Ops) {
BinaryOperator *BO = isReassociableOp(V, Instruction::Mul);
if (!BO) {
Factors.push_back(V);
return;
}
// Otherwise, add the LHS and RHS to the list of factors.
FindSingleUseMultiplyFactors(BO->getOperand(1), Factors, Ops);
FindSingleUseMultiplyFactors(BO->getOperand(0), Factors, Ops);
}
/// OptimizeAndOrXor - Optimize a series of operands to an 'and', 'or', or 'xor'
/// instruction. This optimizes based on identities. If it can be reduced to
/// a single Value, it is returned, otherwise the Ops list is mutated as
/// necessary.
static Value *OptimizeAndOrXor(unsigned Opcode,
SmallVectorImpl<ValueEntry> &Ops) {
// Scan the operand lists looking for X and ~X pairs, along with X,X pairs.
// If we find any, we can simplify the expression. X&~X == 0, X|~X == -1.
for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
// First, check for X and ~X in the operand list.
assert(i < Ops.size());
if (BinaryOperator::isNot(Ops[i].Op)) { // Cannot occur for ^.
Value *X = BinaryOperator::getNotArgument(Ops[i].Op);
unsigned FoundX = FindInOperandList(Ops, i, X);
if (FoundX != i) {
if (Opcode == Instruction::And) // ...&X&~X = 0
return Constant::getNullValue(X->getType());
if (Opcode == Instruction::Or) // ...|X|~X = -1
return Constant::getAllOnesValue(X->getType());
}
}
// Next, check for duplicate pairs of values, which we assume are next to
// each other, due to our sorting criteria.
assert(i < Ops.size());
if (i+1 != Ops.size() && Ops[i+1].Op == Ops[i].Op) {
if (Opcode == Instruction::And || Opcode == Instruction::Or) {
// Drop duplicate values for And and Or.
Ops.erase(Ops.begin()+i);
--i; --e;
++NumAnnihil;
continue;
}
// Drop pairs of values for Xor.
assert(Opcode == Instruction::Xor);
if (e == 2)
return Constant::getNullValue(Ops[0].Op->getType());
// Y ^ X^X -> Y
Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
i -= 1; e -= 2;
++NumAnnihil;
}
}
return 0;
}
/// OptimizeAdd - Optimize a series of operands to an 'add' instruction. This
/// optimizes based on identities. If it can be reduced to a single Value, it
/// is returned, otherwise the Ops list is mutated as necessary.
Value *Reassociate::OptimizeAdd(Instruction *I,
SmallVectorImpl<ValueEntry> &Ops) {
// Scan the operand lists looking for X and -X pairs. If we find any, we
// can simplify the expression. X+-X == 0. While we're at it, scan for any
// duplicates. We want to canonicalize Y+Y+Y+Z -> 3*Y+Z.
//
// TODO: We could handle "X + ~X" -> "-1" if we wanted, since "-X = ~X+1".
//
for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
Value *TheOp = Ops[i].Op;
// Check to see if we've seen this operand before. If so, we factor all
// instances of the operand together. Due to our sorting criteria, we know
// that these need to be next to each other in the vector.
if (i+1 != Ops.size() && Ops[i+1].Op == TheOp) {
// Rescan the list, remove all instances of this operand from the expr.
unsigned NumFound = 0;
do {
Ops.erase(Ops.begin()+i);
++NumFound;
} while (i != Ops.size() && Ops[i].Op == TheOp);
DEBUG(errs() << "\nFACTORING [" << NumFound << "]: " << *TheOp << '\n');
++NumFactor;
// Insert a new multiply.
Value *Mul = ConstantInt::get(cast<IntegerType>(I->getType()), NumFound);
Mul = BinaryOperator::CreateMul(TheOp, Mul, "factor", I);
// Now that we have inserted a multiply, optimize it. This allows us to
// handle cases that require multiple factoring steps, such as this:
// (X*2) + (X*2) + (X*2) -> (X*2)*3 -> X*6
RedoInsts.insert(cast<Instruction>(Mul));
// If every add operand was a duplicate, return the multiply.
if (Ops.empty())
return Mul;
// Otherwise, we had some input that didn't have the dupe, such as
// "A + A + B" -> "A*2 + B". Add the new multiply to the list of
// things being added by this operation.
Ops.insert(Ops.begin(), ValueEntry(getRank(Mul), Mul));
--i;
e = Ops.size();
continue;
}
// Check for X and -X in the operand list.
if (!BinaryOperator::isNeg(TheOp))
continue;
Value *X = BinaryOperator::getNegArgument(TheOp);
unsigned FoundX = FindInOperandList(Ops, i, X);
if (FoundX == i)
continue;
// Remove X and -X from the operand list.
if (Ops.size() == 2)
return Constant::getNullValue(X->getType());
Ops.erase(Ops.begin()+i);
if (i < FoundX)
--FoundX;
else
--i; // Need to back up an extra one.
Ops.erase(Ops.begin()+FoundX);
++NumAnnihil;
--i; // Revisit element.
e -= 2; // Removed two elements.
}
// Scan the operand list, checking to see if there are any common factors
// between operands. Consider something like A*A+A*B*C+D. We would like to
// reassociate this to A*(A+B*C)+D, which reduces the number of multiplies.
// To efficiently find this, we count the number of times a factor occurs
// for any ADD operands that are MULs.
DenseMap<Value*, unsigned> FactorOccurrences;
// Keep track of each multiply we see, to avoid triggering on (X*4)+(X*4)
// where they are actually the same multiply.
unsigned MaxOcc = 0;
Value *MaxOccVal = 0;
for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
BinaryOperator *BOp = isReassociableOp(Ops[i].Op, Instruction::Mul);
if (!BOp)
continue;
// Compute all of the factors of this added value.
SmallVector<Value*, 8> Factors;
FindSingleUseMultiplyFactors(BOp, Factors, Ops);
assert(Factors.size() > 1 && "Bad linearize!");
// Add one to FactorOccurrences for each unique factor in this op.
SmallPtrSet<Value*, 8> Duplicates;
for (unsigned i = 0, e = Factors.size(); i != e; ++i) {
Value *Factor = Factors[i];
if (!Duplicates.insert(Factor)) continue;
unsigned Occ = ++FactorOccurrences[Factor];
if (Occ > MaxOcc) { MaxOcc = Occ; MaxOccVal = Factor; }
// If Factor is a negative constant, add the negated value as a factor
// because we can percolate the negate out. Watch for minint, which
// cannot be positivified.
if (ConstantInt *CI = dyn_cast<ConstantInt>(Factor))
if (CI->isNegative() && !CI->isMinValue(true)) {
Factor = ConstantInt::get(CI->getContext(), -CI->getValue());
assert(!Duplicates.count(Factor) &&
"Shouldn't have two constant factors, missed a canonicalize");
unsigned Occ = ++FactorOccurrences[Factor];
if (Occ > MaxOcc) { MaxOcc = Occ; MaxOccVal = Factor; }
}
}
}
// If any factor occurred more than one time, we can pull it out.
if (MaxOcc > 1) {
DEBUG(errs() << "\nFACTORING [" << MaxOcc << "]: " << *MaxOccVal << '\n');
++NumFactor;
// Create a new instruction that uses the MaxOccVal twice. If we don't do
// this, we could otherwise run into situations where removing a factor
// from an expression will drop a use of maxocc, and this can cause
// RemoveFactorFromExpression on successive values to behave differently.
Instruction *DummyInst = BinaryOperator::CreateAdd(MaxOccVal, MaxOccVal);
SmallVector<WeakVH, 4> NewMulOps;
for (unsigned i = 0; i != Ops.size(); ++i) {
// Only try to remove factors from expressions we're allowed to.
BinaryOperator *BOp = isReassociableOp(Ops[i].Op, Instruction::Mul);
if (!BOp)
continue;
if (Value *V = RemoveFactorFromExpression(Ops[i].Op, MaxOccVal)) {
// The factorized operand may occur several times. Convert them all in
// one fell swoop.
for (unsigned j = Ops.size(); j != i;) {
--j;
if (Ops[j].Op == Ops[i].Op) {
NewMulOps.push_back(V);
Ops.erase(Ops.begin()+j);
}
}
--i;
}
}
// No need for extra uses anymore.
delete DummyInst;
unsigned NumAddedValues = NewMulOps.size();
Value *V = EmitAddTreeOfValues(I, NewMulOps);
// Now that we have inserted the add tree, optimize it. This allows us to
// handle cases that require multiple factoring steps, such as this:
// A*A*B + A*A*C --> A*(A*B+A*C) --> A*(A*(B+C))
assert(NumAddedValues > 1 && "Each occurrence should contribute a value");
(void)NumAddedValues;
if (Instruction *VI = dyn_cast<Instruction>(V))
RedoInsts.insert(VI);
// Create the multiply.
Instruction *V2 = BinaryOperator::CreateMul(V, MaxOccVal, "tmp", I);
// Rerun associate on the multiply in case the inner expression turned into
// a multiply. We want to make sure that we keep things in canonical form.
RedoInsts.insert(V2);
// If every add operand included the factor (e.g. "A*B + A*C"), then the
// entire result expression is just the multiply "A*(B+C)".
if (Ops.empty())
return V2;
// Otherwise, we had some input that didn't have the factor, such as
// "A*B + A*C + D" -> "A*(B+C) + D". Add the new multiply to the list of
// things being added by this operation.
Ops.insert(Ops.begin(), ValueEntry(getRank(V2), V2));
}
return 0;
}
namespace {
/// \brief Predicate tests whether a ValueEntry's op is in a map.
struct IsValueInMap {
const DenseMap<Value *, unsigned> &Map;
IsValueInMap(const DenseMap<Value *, unsigned> &Map) : Map(Map) {}
bool operator()(const ValueEntry &Entry) {
return Map.find(Entry.Op) != Map.end();
}
};
}
/// \brief Build up a vector of value/power pairs factoring a product.
///
/// Given a series of multiplication operands, build a vector of factors and
/// the powers each is raised to when forming the final product. Sort them in
/// the order of descending power.
///
/// (x*x) -> [(x, 2)]
/// ((x*x)*x) -> [(x, 3)]
/// ((((x*y)*x)*y)*x) -> [(x, 3), (y, 2)]
///
/// \returns Whether any factors have a power greater than one.
bool Reassociate::collectMultiplyFactors(SmallVectorImpl<ValueEntry> &Ops,
SmallVectorImpl<Factor> &Factors) {
// FIXME: Have Ops be (ValueEntry, Multiplicity) pairs, simplifying this.
// Compute the sum of powers of simplifiable factors.
unsigned FactorPowerSum = 0;
for (unsigned Idx = 1, Size = Ops.size(); Idx < Size; ++Idx) {
Value *Op = Ops[Idx-1].Op;
// Count the number of occurrences of this value.
unsigned Count = 1;
for (; Idx < Size && Ops[Idx].Op == Op; ++Idx)
++Count;
// Track for simplification all factors which occur 2 or more times.
if (Count > 1)
FactorPowerSum += Count;
}
// We can only simplify factors if the sum of the powers of our simplifiable
// factors is 4 or higher. When that is the case, we will *always* have
// a simplification. This is an important invariant to prevent cyclicly
// trying to simplify already minimal formations.
if (FactorPowerSum < 4)
return false;
// Now gather the simplifiable factors, removing them from Ops.
FactorPowerSum = 0;
for (unsigned Idx = 1; Idx < Ops.size(); ++Idx) {
Value *Op = Ops[Idx-1].Op;
// Count the number of occurrences of this value.
unsigned Count = 1;
for (; Idx < Ops.size() && Ops[Idx].Op == Op; ++Idx)
++Count;
if (Count == 1)
continue;
// Move an even number of occurrences to Factors.
Count &= ~1U;
Idx -= Count;
FactorPowerSum += Count;
Factors.push_back(Factor(Op, Count));
Ops.erase(Ops.begin()+Idx, Ops.begin()+Idx+Count);
}
// None of the adjustments above should have reduced the sum of factor powers
// below our mininum of '4'.
assert(FactorPowerSum >= 4);
std::sort(Factors.begin(), Factors.end(), Factor::PowerDescendingSorter());
return true;
}
/// \brief Build a tree of multiplies, computing the product of Ops.
static Value *buildMultiplyTree(IRBuilder<> &Builder,
SmallVectorImpl<Value*> &Ops) {
if (Ops.size() == 1)
return Ops.back();
Value *LHS = Ops.pop_back_val();
do {
LHS = Builder.CreateMul(LHS, Ops.pop_back_val());
} while (!Ops.empty());
return LHS;
}
/// \brief Build a minimal multiplication DAG for (a^x)*(b^y)*(c^z)*...
///
/// Given a vector of values raised to various powers, where no two values are
/// equal and the powers are sorted in decreasing order, compute the minimal
/// DAG of multiplies to compute the final product, and return that product
/// value.
Value *Reassociate::buildMinimalMultiplyDAG(IRBuilder<> &Builder,
SmallVectorImpl<Factor> &Factors) {
assert(Factors[0].Power);
SmallVector<Value *, 4> OuterProduct;
for (unsigned LastIdx = 0, Idx = 1, Size = Factors.size();
Idx < Size && Factors[Idx].Power > 0; ++Idx) {
if (Factors[Idx].Power != Factors[LastIdx].Power) {
LastIdx = Idx;
continue;
}
// We want to multiply across all the factors with the same power so that
// we can raise them to that power as a single entity. Build a mini tree
// for that.
SmallVector<Value *, 4> InnerProduct;
InnerProduct.push_back(Factors[LastIdx].Base);
do {
InnerProduct.push_back(Factors[Idx].Base);
++Idx;
} while (Idx < Size && Factors[Idx].Power == Factors[LastIdx].Power);
// Reset the base value of the first factor to the new expression tree.
// We'll remove all the factors with the same power in a second pass.
Value *M = Factors[LastIdx].Base = buildMultiplyTree(Builder, InnerProduct);
if (Instruction *MI = dyn_cast<Instruction>(M))
RedoInsts.insert(MI);
LastIdx = Idx;
}
// Unique factors with equal powers -- we've folded them into the first one's
// base.
Factors.erase(std::unique(Factors.begin(), Factors.end(),
Factor::PowerEqual()),
Factors.end());
// Iteratively collect the base of each factor with an add power into the
// outer product, and halve each power in preparation for squaring the
// expression.
for (unsigned Idx = 0, Size = Factors.size(); Idx != Size; ++Idx) {
if (Factors[Idx].Power & 1)
OuterProduct.push_back(Factors[Idx].Base);
Factors[Idx].Power >>= 1;
}
if (Factors[0].Power) {
Value *SquareRoot = buildMinimalMultiplyDAG(Builder, Factors);
OuterProduct.push_back(SquareRoot);
OuterProduct.push_back(SquareRoot);
}
if (OuterProduct.size() == 1)
return OuterProduct.front();
Value *V = buildMultiplyTree(Builder, OuterProduct);
return V;
}
Value *Reassociate::OptimizeMul(BinaryOperator *I,
SmallVectorImpl<ValueEntry> &Ops) {
// We can only optimize the multiplies when there is a chain of more than
// three, such that a balanced tree might require fewer total multiplies.
if (Ops.size() < 4)
return 0;
// Try to turn linear trees of multiplies without other uses of the
// intermediate stages into minimal multiply DAGs with perfect sub-expression
// re-use.
SmallVector<Factor, 4> Factors;
if (!collectMultiplyFactors(Ops, Factors))
return 0; // All distinct factors, so nothing left for us to do.
IRBuilder<> Builder(I);
Value *V = buildMinimalMultiplyDAG(Builder, Factors);
if (Ops.empty())
return V;
ValueEntry NewEntry = ValueEntry(getRank(V), V);
Ops.insert(std::lower_bound(Ops.begin(), Ops.end(), NewEntry), NewEntry);
return 0;
}
Value *Reassociate::OptimizeExpression(BinaryOperator *I,
SmallVectorImpl<ValueEntry> &Ops) {
// Now that we have the linearized expression tree, try to optimize it.
// Start by folding any constants that we found.
Constant *Cst = 0;
unsigned Opcode = I->getOpcode();
while (!Ops.empty() && isa<Constant>(Ops.back().Op)) {
Constant *C = cast<Constant>(Ops.pop_back_val().Op);
Cst = Cst ? ConstantExpr::get(Opcode, C, Cst) : C;
}
// If there was nothing but constants then we are done.
if (Ops.empty())
return Cst;
// Put the combined constant back at the end of the operand list, except if
// there is no point. For example, an add of 0 gets dropped here, while a
// multiplication by zero turns the whole expression into zero.
if (Cst && Cst != ConstantExpr::getBinOpIdentity(Opcode, I->getType())) {
if (Cst == ConstantExpr::getBinOpAbsorber(Opcode, I->getType()))
return Cst;
Ops.push_back(ValueEntry(0, Cst));
}
if (Ops.size() == 1) return Ops[0].Op;
// Handle destructive annihilation due to identities between elements in the
// argument list here.
unsigned NumOps = Ops.size();
switch (Opcode) {
default: break;
case Instruction::And:
case Instruction::Or:
case Instruction::Xor:
if (Value *Result = OptimizeAndOrXor(Opcode, Ops))
return Result;
break;
case Instruction::Add:
if (Value *Result = OptimizeAdd(I, Ops))
return Result;
break;
case Instruction::Mul:
if (Value *Result = OptimizeMul(I, Ops))
return Result;
break;
}
if (Ops.size() != NumOps)
return OptimizeExpression(I, Ops);
return 0;
}
/// EraseInst - Zap the given instruction, adding interesting operands to the
/// work list.
void Reassociate::EraseInst(Instruction *I) {
assert(isInstructionTriviallyDead(I) && "Trivially dead instructions only!");
SmallVector<Value*, 8> Ops(I->op_begin(), I->op_end());
// Erase the dead instruction.
ValueRankMap.erase(I);
RedoInsts.remove(I);
I->eraseFromParent();
// Optimize its operands.
SmallPtrSet<Instruction *, 8> Visited; // Detect self-referential nodes.
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
if (Instruction *Op = dyn_cast<Instruction>(Ops[i])) {
// If this is a node in an expression tree, climb to the expression root
// and add that since that's where optimization actually happens.
unsigned Opcode = Op->getOpcode();
while (Op->hasOneUse() && Op->use_back()->getOpcode() == Opcode &&
Visited.insert(Op))
Op = Op->use_back();
RedoInsts.insert(Op);
}
}
/// OptimizeInst - Inspect and optimize the given instruction. Note that erasing
/// instructions is not allowed.
void Reassociate::OptimizeInst(Instruction *I) {
// Only consider operations that we understand.
if (!isa<BinaryOperator>(I))
return;
if (I->getOpcode() == Instruction::Shl &&
isa<ConstantInt>(I->getOperand(1)))
// If an operand of this shift is a reassociable multiply, or if the shift
// is used by a reassociable multiply or add, turn into a multiply.
if (isReassociableOp(I->getOperand(0), Instruction::Mul) ||
(I->hasOneUse() &&
(isReassociableOp(I->use_back(), Instruction::Mul) ||
isReassociableOp(I->use_back(), Instruction::Add)))) {
Instruction *NI = ConvertShiftToMul(I);
RedoInsts.insert(I);
MadeChange = true;
I = NI;
}
// Floating point binary operators are not associative, but we can still
// commute (some) of them, to canonicalize the order of their operands.
// This can potentially expose more CSE opportunities, and makes writing
// other transformations simpler.
if ((I->getType()->isFloatingPointTy() || I->getType()->isVectorTy())) {
// FAdd and FMul can be commuted.
if (I->getOpcode() != Instruction::FMul &&
I->getOpcode() != Instruction::FAdd)
return;
Value *LHS = I->getOperand(0);
Value *RHS = I->getOperand(1);
unsigned LHSRank = getRank(LHS);
unsigned RHSRank = getRank(RHS);
// Sort the operands by rank.
if (RHSRank < LHSRank) {
I->setOperand(0, RHS);
I->setOperand(1, LHS);
}
return;
}
// Do not reassociate boolean (i1) expressions. We want to preserve the
// original order of evaluation for short-circuited comparisons that
// SimplifyCFG has folded to AND/OR expressions. If the expression
// is not further optimized, it is likely to be transformed back to a
// short-circuited form for code gen, and the source order may have been
// optimized for the most likely conditions.
if (I->getType()->isIntegerTy(1))
return;
// If this is a subtract instruction which is not already in negate form,
// see if we can convert it to X+-Y.
if (I->getOpcode() == Instruction::Sub) {
if (ShouldBreakUpSubtract(I)) {
Instruction *NI = BreakUpSubtract(I);
RedoInsts.insert(I);
MadeChange = true;
I = NI;
} else if (BinaryOperator::isNeg(I)) {
// Otherwise, this is a negation. See if the operand is a multiply tree
// and if this is not an inner node of a multiply tree.
if (isReassociableOp(I->getOperand(1), Instruction::Mul) &&
(!I->hasOneUse() ||
!isReassociableOp(I->use_back(), Instruction::Mul))) {
Instruction *NI = LowerNegateToMultiply(I);
RedoInsts.insert(I);
MadeChange = true;
I = NI;
}
}
}
// If this instruction is an associative binary operator, process it.
if (!I->isAssociative()) return;
BinaryOperator *BO = cast<BinaryOperator>(I);
// If this is an interior node of a reassociable tree, ignore it until we
// get to the root of the tree, to avoid N^2 analysis.
unsigned Opcode = BO->getOpcode();
if (BO->hasOneUse() && BO->use_back()->getOpcode() == Opcode)
return;
// If this is an add tree that is used by a sub instruction, ignore it
// until we process the subtract.
if (BO->hasOneUse() && BO->getOpcode() == Instruction::Add &&
cast<Instruction>(BO->use_back())->getOpcode() == Instruction::Sub)
return;
ReassociateExpression(BO);
}
void Reassociate::ReassociateExpression(BinaryOperator *I) {
// First, walk the expression tree, linearizing the tree, collecting the
// operand information.
SmallVector<RepeatedValue, 8> Tree;
MadeChange |= LinearizeExprTree(I, Tree);
SmallVector<ValueEntry, 8> Ops;
Ops.reserve(Tree.size());
for (unsigned i = 0, e = Tree.size(); i != e; ++i) {
RepeatedValue E = Tree[i];
Ops.append(E.second.getZExtValue(),
ValueEntry(getRank(E.first), E.first));
}
DEBUG(dbgs() << "RAIn:\t"; PrintOps(I, Ops); dbgs() << '\n');
// Now that we have linearized the tree to a list and have gathered all of
// the operands and their ranks, sort the operands by their rank. Use a
// stable_sort so that values with equal ranks will have their relative
// positions maintained (and so the compiler is deterministic). Note that
// this sorts so that the highest ranking values end up at the beginning of
// the vector.
std::stable_sort(Ops.begin(), Ops.end());
// OptimizeExpression - Now that we have the expression tree in a convenient
// sorted form, optimize it globally if possible.
if (Value *V = OptimizeExpression(I, Ops)) {
if (V == I)
// Self-referential expression in unreachable code.
return;
// This expression tree simplified to something that isn't a tree,
// eliminate it.
DEBUG(dbgs() << "Reassoc to scalar: " << *V << '\n');
I->replaceAllUsesWith(V);
if (Instruction *VI = dyn_cast<Instruction>(V))
VI->setDebugLoc(I->getDebugLoc());
RedoInsts.insert(I);
++NumAnnihil;
return;
}
// We want to sink immediates as deeply as possible except in the case where
// this is a multiply tree used only by an add, and the immediate is a -1.
// In this case we reassociate to put the negation on the outside so that we
// can fold the negation into the add: (-X)*Y + Z -> Z-X*Y
if (I->getOpcode() == Instruction::Mul && I->hasOneUse() &&
cast<Instruction>(I->use_back())->getOpcode() == Instruction::Add &&
isa<ConstantInt>(Ops.back().Op) &&
cast<ConstantInt>(Ops.back().Op)->isAllOnesValue()) {
ValueEntry Tmp = Ops.pop_back_val();
Ops.insert(Ops.begin(), Tmp);
}
DEBUG(dbgs() << "RAOut:\t"; PrintOps(I, Ops); dbgs() << '\n');
if (Ops.size() == 1) {
if (Ops[0].Op == I)
// Self-referential expression in unreachable code.
return;
// This expression tree simplified to something that isn't a tree,
// eliminate it.
I->replaceAllUsesWith(Ops[0].Op);
if (Instruction *OI = dyn_cast<Instruction>(Ops[0].Op))
OI->setDebugLoc(I->getDebugLoc());
RedoInsts.insert(I);
return;
}
// Now that we ordered and optimized the expressions, splat them back into
// the expression tree, removing any unneeded nodes.
RewriteExprTree(I, Ops);
}
bool Reassociate::runOnFunction(Function &F) {
// Calculate the rank map for F
BuildRankMap(F);
MadeChange = false;
for (Function::iterator BI = F.begin(), BE = F.end(); BI != BE; ++BI) {
// Optimize every instruction in the basic block.
for (BasicBlock::iterator II = BI->begin(), IE = BI->end(); II != IE; )
if (isInstructionTriviallyDead(II)) {
EraseInst(II++);
} else {
OptimizeInst(II);
assert(II->getParent() == BI && "Moved to a different block!");
++II;
}
// If this produced extra instructions to optimize, handle them now.
while (!RedoInsts.empty()) {
Instruction *I = RedoInsts.pop_back_val();
if (isInstructionTriviallyDead(I))
EraseInst(I);
else
OptimizeInst(I);
}
}
// We are done with the rank map.
RankMap.clear();
ValueRankMap.clear();
return MadeChange;
}