//===- Reassociate.cpp - Reassociate binary expressions -------------------===// // // The LLVM Compiler Infrastructure // // This file was developed by the LLVM research group and 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... // // 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/Constants.h" #include "llvm/Function.h" #include "llvm/Instructions.h" #include "llvm/Pass.h" #include "llvm/Type.h" #include "llvm/Assembly/Writer.h" #include "llvm/Support/CFG.h" #include "llvm/Support/Debug.h" #include "llvm/ADT/PostOrderIterator.h" #include "llvm/ADT/Statistic.h" #include using namespace llvm; namespace { Statistic<> NumLinear ("reassociate","Number of insts linearized"); Statistic<> NumChanged("reassociate","Number of insts reassociated"); Statistic<> NumSwapped("reassociate","Number of insts with operands swapped"); Statistic<> NumAnnihil("reassociate","Number of expr tree annihilated"); 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. } class Reassociate : public FunctionPass { std::map RankMap; std::map ValueRankMap; bool MadeChange; public: bool runOnFunction(Function &F); virtual void getAnalysisUsage(AnalysisUsage &AU) const { AU.setPreservesCFG(); } private: void BuildRankMap(Function &F); unsigned getRank(Value *V); void RewriteExprTree(BinaryOperator *I, unsigned Idx, std::vector &Ops); void OptimizeExpression(unsigned Opcode, std::vector &Ops); void LinearizeExprTree(BinaryOperator *I, std::vector &Ops); void LinearizeExpr(BinaryOperator *I); void ReassociateBB(BasicBlock *BB); }; RegisterOpt X("reassociate", "Reassociate expressions"); } // Public interface to the Reassociate pass FunctionPass *llvm::createReassociatePass() { return new Reassociate(); } static bool isUnmovableInstruction(Instruction *I) { if (I->getOpcode() == Instruction::PHI || I->getOpcode() == Instruction::Alloca || I->getOpcode() == Instruction::Load || I->getOpcode() == Instruction::Malloc || I->getOpcode() == Instruction::Invoke || I->getOpcode() == Instruction::Call || I->getOpcode() == Instruction::Div || I->getOpcode() == Instruction::Rem) 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 RPOT(&F); for (ReversePostOrderTraversal::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) { if (isa(V)) return ValueRankMap[V]; // Function argument... Instruction *I = dyn_cast(V); if (I == 0) return 0; // Otherwise it's a global or constant, rank 0. unsigned &CachedRank = ValueRankMap[I]; if (CachedRank) return CachedRank; // 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()->isIntegral() || (!BinaryOperator::isNot(I) && !BinaryOperator::isNeg(I))) ++Rank; //DEBUG(std::cerr << "Calculated Rank[" << V->getName() << "] = " //<< Rank << "\n"); return CachedRank = Rank; } /// 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(V) && cast(V)->getOpcode() == Opcode) return cast(V); return 0; } /// LowerNegateToMultiply - Replace 0-X with X*-1. /// static Instruction *LowerNegateToMultiply(Instruction *Neg) { Constant *Cst; if (Neg->getType()->isFloatingPoint()) Cst = ConstantFP::get(Neg->getType(), -1); else Cst = ConstantInt::getAllOnesValue(Neg->getType()); std::string NegName = Neg->getName(); Neg->setName(""); Instruction *Res = BinaryOperator::createMul(Neg->getOperand(1), Cst, NegName, Neg); Neg->replaceAllUsesWith(Res); Neg->eraseFromParent(); return Res; } // Given an expression of the form '(A+B)+(D+C)', turn it into '(((A+B)+C)+D)'. // Note that if D is also part of the expression tree that we recurse to // linearize it as well. Besides that case, this does not recurse into A,B, or // C. void Reassociate::LinearizeExpr(BinaryOperator *I) { BinaryOperator *LHS = cast(I->getOperand(0)); BinaryOperator *RHS = cast(I->getOperand(1)); assert(isReassociableOp(LHS, I->getOpcode()) && isReassociableOp(RHS, I->getOpcode()) && "Not an expression that needs linearization?"); DEBUG(std::cerr << "Linear" << *LHS << *RHS << *I); // Move the RHS instruction to live immediately before I, avoiding breaking // dominator properties. I->getParent()->getInstList().splice(I, RHS->getParent()->getInstList(), RHS); // Move operands around to do the linearization. I->setOperand(1, RHS->getOperand(0)); RHS->setOperand(0, LHS); I->setOperand(0, RHS); ++NumLinear; MadeChange = true; DEBUG(std::cerr << "Linearized: " << *I); // If D is part of this expression tree, tail recurse. if (isReassociableOp(I->getOperand(1), I->getOpcode())) LinearizeExpr(I); } /// LinearizeExprTree - Given an associative binary expression tree, traverse /// all of the uses putting it into canonical form. This forces a left-linear /// form of the the expression (((a+b)+c)+d), and collects information about the /// rank of the non-tree operands. /// /// This returns the rank of the RHS operand, which is known to be the highest /// rank value in the expression tree. /// void Reassociate::LinearizeExprTree(BinaryOperator *I, std::vector &Ops) { Value *LHS = I->getOperand(0), *RHS = I->getOperand(1); unsigned Opcode = I->getOpcode(); // First step, linearize the expression if it is in ((A+B)+(C+D)) form. BinaryOperator *LHSBO = isReassociableOp(LHS, Opcode); BinaryOperator *RHSBO = isReassociableOp(RHS, Opcode); // If this is a multiply expression tree and it contains internal negations, // transform them into multiplies by -1 so they can be reassociated. if (I->getOpcode() == Instruction::Mul) { if (!LHSBO && LHS->hasOneUse() && BinaryOperator::isNeg(LHS)) { LHS = LowerNegateToMultiply(cast(LHS)); LHSBO = isReassociableOp(LHS, Opcode); } if (!RHSBO && RHS->hasOneUse() && BinaryOperator::isNeg(RHS)) { RHS = LowerNegateToMultiply(cast(RHS)); RHSBO = isReassociableOp(RHS, Opcode); } } if (!LHSBO) { if (!RHSBO) { // Neither the LHS or RHS as part of the tree, thus this is a leaf. As // such, just remember these operands and their rank. Ops.push_back(ValueEntry(getRank(LHS), LHS)); Ops.push_back(ValueEntry(getRank(RHS), RHS)); return; } else { // Turn X+(Y+Z) -> (Y+Z)+X std::swap(LHSBO, RHSBO); std::swap(LHS, RHS); bool Success = !I->swapOperands(); assert(Success && "swapOperands failed"); MadeChange = true; } } else if (RHSBO) { // Turn (A+B)+(C+D) -> (((A+B)+C)+D). This guarantees the the RHS is not // part of the expression tree. LinearizeExpr(I); LHS = LHSBO = cast(I->getOperand(0)); RHS = I->getOperand(1); RHSBO = 0; } // Okay, now we know that the LHS is a nested expression and that the RHS is // not. Perform reassociation. assert(!isReassociableOp(RHS, Opcode) && "LinearizeExpr failed!"); // Move LHS right before I to make sure that the tree expression dominates all // values. I->getParent()->getInstList().splice(I, LHSBO->getParent()->getInstList(), LHSBO); // Linearize the expression tree on the LHS. LinearizeExprTree(LHSBO, Ops); // Remember the RHS operand and its rank. Ops.push_back(ValueEntry(getRank(RHS), RHS)); } // RewriteExprTree - Now that the operands for this expression tree are // linearized and optimized, emit them in-order. This function is written to be // tail recursive. void Reassociate::RewriteExprTree(BinaryOperator *I, unsigned i, std::vector &Ops) { if (i+2 == Ops.size()) { if (I->getOperand(0) != Ops[i].Op || I->getOperand(1) != Ops[i+1].Op) { DEBUG(std::cerr << "RA: " << *I); I->setOperand(0, Ops[i].Op); I->setOperand(1, Ops[i+1].Op); DEBUG(std::cerr << "TO: " << *I); MadeChange = true; ++NumChanged; } return; } assert(i+2 < Ops.size() && "Ops index out of range!"); if (I->getOperand(1) != Ops[i].Op) { DEBUG(std::cerr << "RA: " << *I); I->setOperand(1, Ops[i].Op); DEBUG(std::cerr << "TO: " << *I); MadeChange = true; ++NumChanged; } RewriteExprTree(cast(I->getOperand(0)), i+1, Ops); } // 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) { // 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 (Instruction *I = dyn_cast(V)) if (I->getOpcode() == Instruction::Add && I->hasOneUse()) { Value *RHS = NegateValue(I->getOperand(1), BI); Value *LHS = NegateValue(I->getOperand(0), BI); // We must actually insert a new add instruction here, because the neg // instructions do not dominate the old add instruction in general. By // adding it now, we are assured that the neg instructions we just // inserted dominate the instruction we are about to insert after them. // return BinaryOperator::create(Instruction::Add, LHS, RHS, I->getName()+".neg", BI); } // Insert a 'neg' instruction that subtracts the value from zero to get the // negation. // return BinaryOperator::createNeg(V, V->getName() + ".neg", BI); } /// 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 Instruction *BreakUpSubtract(Instruction *Sub) { // Reject cases where it is pointless to do this. if (Sub->getType()->isFloatingPoint()) return 0; // Floating point adds are not associative. // Don't bother to break this up unless either the LHS is an associable add or // if this is only used by one. if (!isReassociableOp(Sub->getOperand(0), Instruction::Add) && !isReassociableOp(Sub->getOperand(1), Instruction::Add) && !(Sub->hasOneUse() &&isReassociableOp(Sub->use_back(), Instruction::Add))) return 0; // Convert a subtract into an add and a neg instruction... so that sub // instructions can 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... // std::string Name = Sub->getName(); Sub->setName(""); Value *NegVal = NegateValue(Sub->getOperand(1), Sub); Instruction *New = BinaryOperator::createAdd(Sub->getOperand(0), NegVal, Name, Sub); // Everyone now refers to the add instruction. Sub->replaceAllUsesWith(New); Sub->eraseFromParent(); DEBUG(std::cerr << "Negated: " << *New); 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 Instruction *ConvertShiftToMul(Instruction *Shl) { if (!isReassociableOp(Shl->getOperand(0), Instruction::Mul) && !(Shl->hasOneUse() && isReassociableOp(Shl->use_back(),Instruction::Mul))) return 0; Constant *MulCst = ConstantInt::get(Shl->getType(), 1); MulCst = ConstantExpr::getShl(MulCst, cast(Shl->getOperand(1))); std::string Name = Shl->getName(); Shl->setName(""); Instruction *Mul = BinaryOperator::createMul(Shl->getOperand(0), MulCst, Name, Shl); Shl->replaceAllUsesWith(Mul); Shl->eraseFromParent(); return Mul; } // 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. static unsigned FindInOperandList(std::vector &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; } void Reassociate::OptimizeExpression(unsigned Opcode, std::vector &Ops) { // Now that we have the linearized expression tree, try to optimize it. // Start by folding any constants that we found. bool IterateOptimization = false; if (Ops.size() == 1) return; if (Constant *V1 = dyn_cast(Ops[Ops.size()-2].Op)) if (Constant *V2 = dyn_cast(Ops.back().Op)) { Ops.pop_back(); Ops.back().Op = ConstantExpr::get(Opcode, V1, V2); OptimizeExpression(Opcode, Ops); return; } // Check for destructive annihilation due to a constant being used. if (ConstantIntegral *CstVal = dyn_cast(Ops.back().Op)) switch (Opcode) { default: break; case Instruction::And: if (CstVal->isNullValue()) { // ... & 0 -> 0 Ops[0].Op = CstVal; Ops.erase(Ops.begin()+1, Ops.end()); ++NumAnnihil; return; } else if (CstVal->isAllOnesValue()) { // ... & -1 -> ... Ops.pop_back(); } break; case Instruction::Mul: if (CstVal->isNullValue()) { // ... * 0 -> 0 Ops[0].Op = CstVal; Ops.erase(Ops.begin()+1, Ops.end()); ++NumAnnihil; return; } else if (cast(CstVal)->getRawValue() == 1) { Ops.pop_back(); // ... * 1 -> ... } break; case Instruction::Or: if (CstVal->isAllOnesValue()) { // ... | -1 -> -1 Ops[0].Op = CstVal; Ops.erase(Ops.begin()+1, Ops.end()); ++NumAnnihil; return; } // FALLTHROUGH! case Instruction::Add: case Instruction::Xor: if (CstVal->isNullValue()) // ... [|^+] 0 -> ... Ops.pop_back(); break; } // Handle destructive annihilation do to identities between elements in the // argument list here. switch (Opcode) { default: break; case Instruction::And: case Instruction::Or: case Instruction::Xor: // 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. 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 Ops[0].Op = Constant::getNullValue(X->getType()); Ops.erase(Ops.begin()+1, Ops.end()); ++NumAnnihil; return; } else if (Opcode == Instruction::Or) { // ...|X|~X = -1 Ops[0].Op = ConstantIntegral::getAllOnesValue(X->getType()); Ops.erase(Ops.begin()+1, Ops.end()); ++NumAnnihil; return; } } } // Next, check for duplicate pairs of values, which we assume are next to // each other, due to our sorting criteria. if (i+1 != Ops.size() && Ops[i+1].Op == Ops[i].Op) { if (Opcode == Instruction::And || Opcode == Instruction::Or) { // Drop duplicate values. Ops.erase(Ops.begin()+i); --i; --e; IterateOptimization = true; ++NumAnnihil; } else { assert(Opcode == Instruction::Xor); // ... X^X -> ... Ops.erase(Ops.begin()+i, Ops.begin()+i+2); i -= 2; e -= 2; IterateOptimization = true; ++NumAnnihil; } } } break; case Instruction::Add: // Scan the operand lists looking for X and -X pairs. If we find any, we // can simplify the expression. X+-X == 0 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { // Check for X and -X in the operand list. if (BinaryOperator::isNeg(Ops[i].Op)) { Value *X = BinaryOperator::getNegArgument(Ops[i].Op); unsigned FoundX = FindInOperandList(Ops, i, X); if (FoundX != i) { // Remove X and -X from the operand list. if (Ops.size() == 2) { Ops[0].Op = Constant::getNullValue(X->getType()); Ops.erase(Ops.begin()+1); ++NumAnnihil; return; } else { Ops.erase(Ops.begin()+i); if (i < FoundX) --FoundX; Ops.erase(Ops.begin()+FoundX); IterateOptimization = true; ++NumAnnihil; } } } } break; //case Instruction::Mul: } if (IterateOptimization) OptimizeExpression(Opcode, Ops); } /// PrintOps - Print out the expression identified in the Ops list. /// static void PrintOps(unsigned Opcode, const std::vector &Ops, BasicBlock *BB) { Module *M = BB->getParent()->getParent(); std::cerr << Instruction::getOpcodeName(Opcode) << " " << *Ops[0].Op->getType(); for (unsigned i = 0, e = Ops.size(); i != e; ++i) WriteAsOperand(std::cerr << " ", Ops[i].Op, false, true, M) << "," << Ops[i].Rank; } /// ReassociateBB - Inspect all of the instructions in this basic block, /// reassociating them as we go. void Reassociate::ReassociateBB(BasicBlock *BB) { for (BasicBlock::iterator BI = BB->begin(); BI != BB->end(); ++BI) { // If this is a subtract instruction which is not already in negate form, // see if we can convert it to X+-Y. if (BI->getOpcode() == Instruction::Sub) { if (!BinaryOperator::isNeg(BI)) { if (Instruction *NI = BreakUpSubtract(BI)) { MadeChange = true; BI = NI; } } else { // 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(BI->getOperand(1), Instruction::Mul) && (!BI->hasOneUse() || !isReassociableOp(BI->use_back(), Instruction::Mul))) { BI = LowerNegateToMultiply(BI); MadeChange = true; } } } if (BI->getOpcode() == Instruction::Shl && isa(BI->getOperand(1))) if (Instruction *NI = ConvertShiftToMul(BI)) { MadeChange = true; BI = NI; } // If this instruction is a commutative binary operator, process it. if (!BI->isAssociative()) continue; BinaryOperator *I = cast(BI); // 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. if (I->hasOneUse() && isReassociableOp(I->use_back(), I->getOpcode())) continue; // First, walk the expression tree, linearizing the tree, collecting std::vector Ops; LinearizeExprTree(I, Ops); DEBUG(std::cerr << "RAIn:\t"; PrintOps(I->getOpcode(), Ops, BB); std::cerr << "\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. OptimizeExpression(I->getOpcode(), Ops); DEBUG(std::cerr << "RAOut:\t"; PrintOps(I->getOpcode(), Ops, BB); std::cerr << "\n"); if (Ops.size() == 1) { // This expression tree simplified to something that isn't a tree, // eliminate it. I->replaceAllUsesWith(Ops[0].Op); } else { // Now that we ordered and optimized the expressions, splat them back into // the expression tree, removing any unneeded nodes. RewriteExprTree(I, 0, Ops); } } } bool Reassociate::runOnFunction(Function &F) { // Recalculate the rank map for F BuildRankMap(F); MadeChange = false; for (Function::iterator FI = F.begin(), FE = F.end(); FI != FE; ++FI) ReassociateBB(FI); // We are done with the rank map... RankMap.clear(); ValueRankMap.clear(); return MadeChange; }