Reassociate.cpp revision 256281
133965Sjdp//===- Reassociate.cpp - Reassociate binary expressions -------------------===// 289857Sobrien// 333965Sjdp// The LLVM Compiler Infrastructure 433965Sjdp// 533965Sjdp// This file is distributed under the University of Illinois Open Source 633965Sjdp// License. See LICENSE.TXT for details. 733965Sjdp// 833965Sjdp//===----------------------------------------------------------------------===// 933965Sjdp// 1033965Sjdp// This pass reassociates commutative expressions in an order that is designed 1133965Sjdp// to promote better constant propagation, GCSE, LICM, PRE, etc. 1233965Sjdp// 1333965Sjdp// For example: 4 + (x + 5) -> x + (4 + 5) 1433965Sjdp// 1533965Sjdp// In the implementation of this algorithm, constants are assigned rank = 0, 1633965Sjdp// function arguments are rank = 1, and other values are assigned ranks 17218822Sdim// corresponding to the reverse post order traversal of current function 18218822Sdim// (starting at 2), which effectively gives values in deep loops higher rank 1933965Sjdp// than values not in loops. 2089857Sobrien// 21218822Sdim//===----------------------------------------------------------------------===// 22218822Sdim 23218822Sdim#define DEBUG_TYPE "reassociate" 2433965Sjdp#include "llvm/Transforms/Scalar.h" 25130561Sobrien#include "llvm/ADT/DenseMap.h" 2633965Sjdp#include "llvm/ADT/PostOrderIterator.h" 27130561Sobrien#include "llvm/ADT/STLExtras.h" 28130561Sobrien#include "llvm/ADT/SetVector.h" 29130561Sobrien#include "llvm/ADT/Statistic.h" 30130561Sobrien#include "llvm/Assembly/Writer.h" 31104834Sobrien#include "llvm/IR/Constants.h" 3233965Sjdp#include "llvm/IR/DerivedTypes.h" 33104834Sobrien#include "llvm/IR/Function.h" 34104834Sobrien#include "llvm/IR/IRBuilder.h" 35104834Sobrien#include "llvm/IR/Instructions.h" 36104834Sobrien#include "llvm/IR/IntrinsicInst.h" 37104834Sobrien#include "llvm/Pass.h" 38104834Sobrien#include "llvm/Support/CFG.h" 39104834Sobrien#include "llvm/Support/Debug.h" 40104834Sobrien#include "llvm/Support/ValueHandle.h" 41104834Sobrien#include "llvm/Support/raw_ostream.h" 42104834Sobrien#include "llvm/Transforms/Utils/Local.h" 43104834Sobrien#include <algorithm> 44104834Sobrienusing namespace llvm; 45104834Sobrien 46104834SobrienSTATISTIC(NumChanged, "Number of insts reassociated"); 47104834SobrienSTATISTIC(NumAnnihil, "Number of expr tree annihilated"); 48104834SobrienSTATISTIC(NumFactor , "Number of multiplies factored"); 49104834Sobrien 50218822Sdimnamespace { 51104834Sobrien struct ValueEntry { 52104834Sobrien unsigned Rank; 53218822Sdim Value *Op; 54104834Sobrien ValueEntry(unsigned R, Value *O) : Rank(R), Op(O) {} 55104834Sobrien }; 56104834Sobrien inline bool operator<(const ValueEntry &LHS, const ValueEntry &RHS) { 57130561Sobrien return LHS.Rank > RHS.Rank; // Sort so that highest rank goes to start. 58130561Sobrien } 59130561Sobrien} 60130561Sobrien 61130561Sobrien#ifndef NDEBUG 62130561Sobrien/// PrintOps - Print out the expression identified in the Ops list. 63104834Sobrien/// 64104834Sobrienstatic void PrintOps(Instruction *I, const SmallVectorImpl<ValueEntry> &Ops) { 65104834Sobrien Module *M = I->getParent()->getParent()->getParent(); 66104834Sobrien dbgs() << Instruction::getOpcodeName(I->getOpcode()) << " " 67104834Sobrien << *Ops[0].Op->getType() << '\t'; 68104834Sobrien for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 69104834Sobrien dbgs() << "[ "; 70104834Sobrien WriteAsOperand(dbgs(), Ops[i].Op, false, M); 71104834Sobrien dbgs() << ", #" << Ops[i].Rank << "] "; 7289857Sobrien } 73130561Sobrien} 7489857Sobrien#endif 75130561Sobrien 7633965Sjdpnamespace { 7789857Sobrien /// \brief Utility class representing a base and exponent pair which form one 7889857Sobrien /// factor of some product. 7989857Sobrien struct Factor { 8089857Sobrien Value *Base; 8189857Sobrien unsigned Power; 8289857Sobrien 8389857Sobrien Factor(Value *Base, unsigned Power) : Base(Base), Power(Power) {} 8489857Sobrien 8589857Sobrien /// \brief Sort factors by their Base. 8689857Sobrien struct BaseSorter { 8789857Sobrien bool operator()(const Factor &LHS, const Factor &RHS) { 8889857Sobrien return LHS.Base < RHS.Base; 8989857Sobrien } 9089857Sobrien }; 9189857Sobrien 9289857Sobrien /// \brief Compare factors for equal bases. 9389857Sobrien struct BaseEqual { 9489857Sobrien bool operator()(const Factor &LHS, const Factor &RHS) { 9589857Sobrien return LHS.Base == RHS.Base; 9689857Sobrien } 9789857Sobrien }; 9889857Sobrien 9989857Sobrien /// \brief Sort factors in descending order by their power. 10089857Sobrien struct PowerDescendingSorter { 10189857Sobrien bool operator()(const Factor &LHS, const Factor &RHS) { 10289857Sobrien return LHS.Power > RHS.Power; 10389857Sobrien } 10489857Sobrien }; 10589857Sobrien 10689857Sobrien /// \brief Compare factors for equal powers. 10789857Sobrien struct PowerEqual { 10889857Sobrien bool operator()(const Factor &LHS, const Factor &RHS) { 10989857Sobrien return LHS.Power == RHS.Power; 11089857Sobrien } 11189857Sobrien }; 11289857Sobrien }; 11389857Sobrien 11489857Sobrien /// Utility class representing a non-constant Xor-operand. We classify 11589857Sobrien /// non-constant Xor-Operands into two categories: 11689857Sobrien /// C1) The operand is in the form "X & C", where C is a constant and C != ~0 11789857Sobrien /// C2) 11889857Sobrien /// C2.1) The operand is in the form of "X | C", where C is a non-zero 11989857Sobrien /// constant. 12089857Sobrien /// C2.2) Any operand E which doesn't fall into C1 and C2.1, we view this 12189857Sobrien /// operand as "E | 0" 12289857Sobrien class XorOpnd { 12389857Sobrien public: 12489857Sobrien XorOpnd(Value *V); 12589857Sobrien const XorOpnd &operator=(const XorOpnd &That); 12689857Sobrien 12789857Sobrien bool isInvalid() const { return SymbolicPart == 0; } 12889857Sobrien bool isOrExpr() const { return isOr; } 12989857Sobrien Value *getValue() const { return OrigVal; } 13089857Sobrien Value *getSymbolicPart() const { return SymbolicPart; } 13189857Sobrien unsigned getSymbolicRank() const { return SymbolicRank; } 13289857Sobrien const APInt &getConstPart() const { return ConstPart; } 13389857Sobrien 13489857Sobrien void Invalidate() { SymbolicPart = OrigVal = 0; } 13589857Sobrien void setSymbolicRank(unsigned R) { SymbolicRank = R; } 13689857Sobrien 13789857Sobrien // Sort the XorOpnd-Pointer in ascending order of symbolic-value-rank. 13889857Sobrien // The purpose is twofold: 13989857Sobrien // 1) Cluster together the operands sharing the same symbolic-value. 14089857Sobrien // 2) Operand having smaller symbolic-value-rank is permuted earlier, which 14189857Sobrien // could potentially shorten crital path, and expose more loop-invariants. 14289857Sobrien // Note that values' rank are basically defined in RPO order (FIXME). 14389857Sobrien // So, if Rank(X) < Rank(Y) < Rank(Z), it means X is defined earlier 14489857Sobrien // than Y which is defined earlier than Z. Permute "x | 1", "Y & 2", 14589857Sobrien // "z" in the order of X-Y-Z is better than any other orders. 14689857Sobrien struct PtrSortFunctor { 14789857Sobrien bool operator()(XorOpnd * const &LHS, XorOpnd * const &RHS) { 14889857Sobrien return LHS->getSymbolicRank() < RHS->getSymbolicRank(); 14989857Sobrien } 150104834Sobrien }; 151104834Sobrien private: 15289857Sobrien Value *OrigVal; 153104834Sobrien Value *SymbolicPart; 154130561Sobrien APInt ConstPart; 155104834Sobrien unsigned SymbolicRank; 15689857Sobrien bool isOr; 157104834Sobrien }; 158104834Sobrien} 159218822Sdim 160104834Sobriennamespace { 161104834Sobrien class Reassociate : public FunctionPass { 162104834Sobrien DenseMap<BasicBlock*, unsigned> RankMap; 163104834Sobrien DenseMap<AssertingVH<Value>, unsigned> ValueRankMap; 164104834Sobrien SetVector<AssertingVH<Instruction> > RedoInsts; 165104834Sobrien bool MadeChange; 166104834Sobrien public: 167104834Sobrien static char ID; // Pass identification, replacement for typeid 168104834Sobrien Reassociate() : FunctionPass(ID) { 169104834Sobrien initializeReassociatePass(*PassRegistry::getPassRegistry()); 170104834Sobrien } 171104834Sobrien 172104834Sobrien bool runOnFunction(Function &F); 173104834Sobrien 174104834Sobrien virtual void getAnalysisUsage(AnalysisUsage &AU) const { 175104834Sobrien AU.setPreservesCFG(); 176104834Sobrien } 177104834Sobrien private: 178104834Sobrien void BuildRankMap(Function &F); 179104834Sobrien unsigned getRank(Value *V); 180104834Sobrien void ReassociateExpression(BinaryOperator *I); 181104834Sobrien void RewriteExprTree(BinaryOperator *I, SmallVectorImpl<ValueEntry> &Ops); 182104834Sobrien Value *OptimizeExpression(BinaryOperator *I, 183104834Sobrien SmallVectorImpl<ValueEntry> &Ops); 184104834Sobrien Value *OptimizeAdd(Instruction *I, SmallVectorImpl<ValueEntry> &Ops); 185104834Sobrien Value *OptimizeXor(Instruction *I, SmallVectorImpl<ValueEntry> &Ops); 186104834Sobrien bool CombineXorOpnd(Instruction *I, XorOpnd *Opnd1, APInt &ConstOpnd, 187104834Sobrien Value *&Res); 188104834Sobrien bool CombineXorOpnd(Instruction *I, XorOpnd *Opnd1, XorOpnd *Opnd2, 189104834Sobrien APInt &ConstOpnd, Value *&Res); 190104834Sobrien bool collectMultiplyFactors(SmallVectorImpl<ValueEntry> &Ops, 191104834Sobrien SmallVectorImpl<Factor> &Factors); 192104834Sobrien Value *buildMinimalMultiplyDAG(IRBuilder<> &Builder, 193 SmallVectorImpl<Factor> &Factors); 194 Value *OptimizeMul(BinaryOperator *I, SmallVectorImpl<ValueEntry> &Ops); 195 Value *RemoveFactorFromExpression(Value *V, Value *Factor); 196 void EraseInst(Instruction *I); 197 void OptimizeInst(Instruction *I); 198 }; 199} 200 201XorOpnd::XorOpnd(Value *V) { 202 assert(!isa<ConstantInt>(V) && "No ConstantInt"); 203 OrigVal = V; 204 Instruction *I = dyn_cast<Instruction>(V); 205 SymbolicRank = 0; 206 207 if (I && (I->getOpcode() == Instruction::Or || 208 I->getOpcode() == Instruction::And)) { 209 Value *V0 = I->getOperand(0); 210 Value *V1 = I->getOperand(1); 211 if (isa<ConstantInt>(V0)) 212 std::swap(V0, V1); 213 214 if (ConstantInt *C = dyn_cast<ConstantInt>(V1)) { 215 ConstPart = C->getValue(); 216 SymbolicPart = V0; 217 isOr = (I->getOpcode() == Instruction::Or); 218 return; 219 } 220 } 221 222 // view the operand as "V | 0" 223 SymbolicPart = V; 224 ConstPart = APInt::getNullValue(V->getType()->getIntegerBitWidth()); 225 isOr = true; 226} 227 228const XorOpnd &XorOpnd::operator=(const XorOpnd &That) { 229 OrigVal = That.OrigVal; 230 SymbolicPart = That.SymbolicPart; 231 ConstPart = That.ConstPart; 232 SymbolicRank = That.SymbolicRank; 233 isOr = That.isOr; 234 return *this; 235} 236 237char Reassociate::ID = 0; 238INITIALIZE_PASS(Reassociate, "reassociate", 239 "Reassociate expressions", false, false) 240 241// Public interface to the Reassociate pass 242FunctionPass *llvm::createReassociatePass() { return new Reassociate(); } 243 244/// isReassociableOp - Return true if V is an instruction of the specified 245/// opcode and if it only has one use. 246static BinaryOperator *isReassociableOp(Value *V, unsigned Opcode) { 247 if (V->hasOneUse() && isa<Instruction>(V) && 248 cast<Instruction>(V)->getOpcode() == Opcode) 249 return cast<BinaryOperator>(V); 250 return 0; 251} 252 253static bool isUnmovableInstruction(Instruction *I) { 254 if (I->getOpcode() == Instruction::PHI || 255 I->getOpcode() == Instruction::LandingPad || 256 I->getOpcode() == Instruction::Alloca || 257 I->getOpcode() == Instruction::Load || 258 I->getOpcode() == Instruction::Invoke || 259 (I->getOpcode() == Instruction::Call && 260 !isa<DbgInfoIntrinsic>(I)) || 261 I->getOpcode() == Instruction::UDiv || 262 I->getOpcode() == Instruction::SDiv || 263 I->getOpcode() == Instruction::FDiv || 264 I->getOpcode() == Instruction::URem || 265 I->getOpcode() == Instruction::SRem || 266 I->getOpcode() == Instruction::FRem) 267 return true; 268 return false; 269} 270 271void Reassociate::BuildRankMap(Function &F) { 272 unsigned i = 2; 273 274 // Assign distinct ranks to function arguments 275 for (Function::arg_iterator I = F.arg_begin(), E = F.arg_end(); I != E; ++I) 276 ValueRankMap[&*I] = ++i; 277 278 ReversePostOrderTraversal<Function*> RPOT(&F); 279 for (ReversePostOrderTraversal<Function*>::rpo_iterator I = RPOT.begin(), 280 E = RPOT.end(); I != E; ++I) { 281 BasicBlock *BB = *I; 282 unsigned BBRank = RankMap[BB] = ++i << 16; 283 284 // Walk the basic block, adding precomputed ranks for any instructions that 285 // we cannot move. This ensures that the ranks for these instructions are 286 // all different in the block. 287 for (BasicBlock::iterator I = BB->begin(), E = BB->end(); I != E; ++I) 288 if (isUnmovableInstruction(I)) 289 ValueRankMap[&*I] = ++BBRank; 290 } 291} 292 293unsigned Reassociate::getRank(Value *V) { 294 Instruction *I = dyn_cast<Instruction>(V); 295 if (I == 0) { 296 if (isa<Argument>(V)) return ValueRankMap[V]; // Function argument. 297 return 0; // Otherwise it's a global or constant, rank 0. 298 } 299 300 if (unsigned Rank = ValueRankMap[I]) 301 return Rank; // Rank already known? 302 303 // If this is an expression, return the 1+MAX(rank(LHS), rank(RHS)) so that 304 // we can reassociate expressions for code motion! Since we do not recurse 305 // for PHI nodes, we cannot have infinite recursion here, because there 306 // cannot be loops in the value graph that do not go through PHI nodes. 307 unsigned Rank = 0, MaxRank = RankMap[I->getParent()]; 308 for (unsigned i = 0, e = I->getNumOperands(); 309 i != e && Rank != MaxRank; ++i) 310 Rank = std::max(Rank, getRank(I->getOperand(i))); 311 312 // If this is a not or neg instruction, do not count it for rank. This 313 // assures us that X and ~X will have the same rank. 314 if (!I->getType()->isIntegerTy() || 315 (!BinaryOperator::isNot(I) && !BinaryOperator::isNeg(I))) 316 ++Rank; 317 318 //DEBUG(dbgs() << "Calculated Rank[" << V->getName() << "] = " 319 // << Rank << "\n"); 320 321 return ValueRankMap[I] = Rank; 322} 323 324/// LowerNegateToMultiply - Replace 0-X with X*-1. 325/// 326static BinaryOperator *LowerNegateToMultiply(Instruction *Neg) { 327 Constant *Cst = Constant::getAllOnesValue(Neg->getType()); 328 329 BinaryOperator *Res = 330 BinaryOperator::CreateMul(Neg->getOperand(1), Cst, "",Neg); 331 Neg->setOperand(1, Constant::getNullValue(Neg->getType())); // Drop use of op. 332 Res->takeName(Neg); 333 Neg->replaceAllUsesWith(Res); 334 Res->setDebugLoc(Neg->getDebugLoc()); 335 return Res; 336} 337 338/// CarmichaelShift - Returns k such that lambda(2^Bitwidth) = 2^k, where lambda 339/// is the Carmichael function. This means that x^(2^k) === 1 mod 2^Bitwidth for 340/// every odd x, i.e. x^(2^k) = 1 for every odd x in Bitwidth-bit arithmetic. 341/// Note that 0 <= k < Bitwidth, and if Bitwidth > 3 then x^(2^k) = 0 for every 342/// even x in Bitwidth-bit arithmetic. 343static unsigned CarmichaelShift(unsigned Bitwidth) { 344 if (Bitwidth < 3) 345 return Bitwidth - 1; 346 return Bitwidth - 2; 347} 348 349/// IncorporateWeight - Add the extra weight 'RHS' to the existing weight 'LHS', 350/// reducing the combined weight using any special properties of the operation. 351/// The existing weight LHS represents the computation X op X op ... op X where 352/// X occurs LHS times. The combined weight represents X op X op ... op X with 353/// X occurring LHS + RHS times. If op is "Xor" for example then the combined 354/// operation is equivalent to X if LHS + RHS is odd, or 0 if LHS + RHS is even; 355/// the routine returns 1 in LHS in the first case, and 0 in LHS in the second. 356static void IncorporateWeight(APInt &LHS, const APInt &RHS, unsigned Opcode) { 357 // If we were working with infinite precision arithmetic then the combined 358 // weight would be LHS + RHS. But we are using finite precision arithmetic, 359 // and the APInt sum LHS + RHS may not be correct if it wraps (it is correct 360 // for nilpotent operations and addition, but not for idempotent operations 361 // and multiplication), so it is important to correctly reduce the combined 362 // weight back into range if wrapping would be wrong. 363 364 // If RHS is zero then the weight didn't change. 365 if (RHS.isMinValue()) 366 return; 367 // If LHS is zero then the combined weight is RHS. 368 if (LHS.isMinValue()) { 369 LHS = RHS; 370 return; 371 } 372 // From this point on we know that neither LHS nor RHS is zero. 373 374 if (Instruction::isIdempotent(Opcode)) { 375 // Idempotent means X op X === X, so any non-zero weight is equivalent to a 376 // weight of 1. Keeping weights at zero or one also means that wrapping is 377 // not a problem. 378 assert(LHS == 1 && RHS == 1 && "Weights not reduced!"); 379 return; // Return a weight of 1. 380 } 381 if (Instruction::isNilpotent(Opcode)) { 382 // Nilpotent means X op X === 0, so reduce weights modulo 2. 383 assert(LHS == 1 && RHS == 1 && "Weights not reduced!"); 384 LHS = 0; // 1 + 1 === 0 modulo 2. 385 return; 386 } 387 if (Opcode == Instruction::Add) { 388 // TODO: Reduce the weight by exploiting nsw/nuw? 389 LHS += RHS; 390 return; 391 } 392 393 assert(Opcode == Instruction::Mul && "Unknown associative operation!"); 394 unsigned Bitwidth = LHS.getBitWidth(); 395 // If CM is the Carmichael number then a weight W satisfying W >= CM+Bitwidth 396 // can be replaced with W-CM. That's because x^W=x^(W-CM) for every Bitwidth 397 // bit number x, since either x is odd in which case x^CM = 1, or x is even in 398 // which case both x^W and x^(W - CM) are zero. By subtracting off multiples 399 // of CM like this weights can always be reduced to the range [0, CM+Bitwidth) 400 // which by a happy accident means that they can always be represented using 401 // Bitwidth bits. 402 // TODO: Reduce the weight by exploiting nsw/nuw? (Could do much better than 403 // the Carmichael number). 404 if (Bitwidth > 3) { 405 /// CM - The value of Carmichael's lambda function. 406 APInt CM = APInt::getOneBitSet(Bitwidth, CarmichaelShift(Bitwidth)); 407 // Any weight W >= Threshold can be replaced with W - CM. 408 APInt Threshold = CM + Bitwidth; 409 assert(LHS.ult(Threshold) && RHS.ult(Threshold) && "Weights not reduced!"); 410 // For Bitwidth 4 or more the following sum does not overflow. 411 LHS += RHS; 412 while (LHS.uge(Threshold)) 413 LHS -= CM; 414 } else { 415 // To avoid problems with overflow do everything the same as above but using 416 // a larger type. 417 unsigned CM = 1U << CarmichaelShift(Bitwidth); 418 unsigned Threshold = CM + Bitwidth; 419 assert(LHS.getZExtValue() < Threshold && RHS.getZExtValue() < Threshold && 420 "Weights not reduced!"); 421 unsigned Total = LHS.getZExtValue() + RHS.getZExtValue(); 422 while (Total >= Threshold) 423 Total -= CM; 424 LHS = Total; 425 } 426} 427 428typedef std::pair<Value*, APInt> RepeatedValue; 429 430/// LinearizeExprTree - Given an associative binary expression, return the leaf 431/// nodes in Ops along with their weights (how many times the leaf occurs). The 432/// original expression is the same as 433/// (Ops[0].first op Ops[0].first op ... Ops[0].first) <- Ops[0].second times 434/// op 435/// (Ops[1].first op Ops[1].first op ... Ops[1].first) <- Ops[1].second times 436/// op 437/// ... 438/// op 439/// (Ops[N].first op Ops[N].first op ... Ops[N].first) <- Ops[N].second times 440/// 441/// Note that the values Ops[0].first, ..., Ops[N].first are all distinct. 442/// 443/// This routine may modify the function, in which case it returns 'true'. The 444/// changes it makes may well be destructive, changing the value computed by 'I' 445/// to something completely different. Thus if the routine returns 'true' then 446/// you MUST either replace I with a new expression computed from the Ops array, 447/// or use RewriteExprTree to put the values back in. 448/// 449/// A leaf node is either not a binary operation of the same kind as the root 450/// node 'I' (i.e. is not a binary operator at all, or is, but with a different 451/// opcode), or is the same kind of binary operator but has a use which either 452/// does not belong to the expression, or does belong to the expression but is 453/// a leaf node. Every leaf node has at least one use that is a non-leaf node 454/// of the expression, while for non-leaf nodes (except for the root 'I') every 455/// use is a non-leaf node of the expression. 456/// 457/// For example: 458/// expression graph node names 459/// 460/// + | I 461/// / \ | 462/// + + | A, B 463/// / \ / \ | 464/// * + * | C, D, E 465/// / \ / \ / \ | 466/// + * | F, G 467/// 468/// The leaf nodes are C, E, F and G. The Ops array will contain (maybe not in 469/// that order) (C, 1), (E, 1), (F, 2), (G, 2). 470/// 471/// The expression is maximal: if some instruction is a binary operator of the 472/// same kind as 'I', and all of its uses are non-leaf nodes of the expression, 473/// then the instruction also belongs to the expression, is not a leaf node of 474/// it, and its operands also belong to the expression (but may be leaf nodes). 475/// 476/// NOTE: This routine will set operands of non-leaf non-root nodes to undef in 477/// order to ensure that every non-root node in the expression has *exactly one* 478/// use by a non-leaf node of the expression. This destruction means that the 479/// caller MUST either replace 'I' with a new expression or use something like 480/// RewriteExprTree to put the values back in if the routine indicates that it 481/// made a change by returning 'true'. 482/// 483/// In the above example either the right operand of A or the left operand of B 484/// will be replaced by undef. If it is B's operand then this gives: 485/// 486/// + | I 487/// / \ | 488/// + + | A, B - operand of B replaced with undef 489/// / \ \ | 490/// * + * | C, D, E 491/// / \ / \ / \ | 492/// + * | F, G 493/// 494/// Note that such undef operands can only be reached by passing through 'I'. 495/// For example, if you visit operands recursively starting from a leaf node 496/// then you will never see such an undef operand unless you get back to 'I', 497/// which requires passing through a phi node. 498/// 499/// Note that this routine may also mutate binary operators of the wrong type 500/// that have all uses inside the expression (i.e. only used by non-leaf nodes 501/// of the expression) if it can turn them into binary operators of the right 502/// type and thus make the expression bigger. 503 504static bool LinearizeExprTree(BinaryOperator *I, 505 SmallVectorImpl<RepeatedValue> &Ops) { 506 DEBUG(dbgs() << "LINEARIZE: " << *I << '\n'); 507 unsigned Bitwidth = I->getType()->getScalarType()->getPrimitiveSizeInBits(); 508 unsigned Opcode = I->getOpcode(); 509 assert(Instruction::isAssociative(Opcode) && 510 Instruction::isCommutative(Opcode) && 511 "Expected an associative and commutative operation!"); 512 513 // Visit all operands of the expression, keeping track of their weight (the 514 // number of paths from the expression root to the operand, or if you like 515 // the number of times that operand occurs in the linearized expression). 516 // For example, if I = X + A, where X = A + B, then I, X and B have weight 1 517 // while A has weight two. 518 519 // Worklist of non-leaf nodes (their operands are in the expression too) along 520 // with their weights, representing a certain number of paths to the operator. 521 // If an operator occurs in the worklist multiple times then we found multiple 522 // ways to get to it. 523 SmallVector<std::pair<BinaryOperator*, APInt>, 8> Worklist; // (Op, Weight) 524 Worklist.push_back(std::make_pair(I, APInt(Bitwidth, 1))); 525 bool MadeChange = false; 526 527 // Leaves of the expression are values that either aren't the right kind of 528 // operation (eg: a constant, or a multiply in an add tree), or are, but have 529 // some uses that are not inside the expression. For example, in I = X + X, 530 // X = A + B, the value X has two uses (by I) that are in the expression. If 531 // X has any other uses, for example in a return instruction, then we consider 532 // X to be a leaf, and won't analyze it further. When we first visit a value, 533 // if it has more than one use then at first we conservatively consider it to 534 // be a leaf. Later, as the expression is explored, we may discover some more 535 // uses of the value from inside the expression. If all uses turn out to be 536 // from within the expression (and the value is a binary operator of the right 537 // kind) then the value is no longer considered to be a leaf, and its operands 538 // are explored. 539 540 // Leaves - Keeps track of the set of putative leaves as well as the number of 541 // paths to each leaf seen so far. 542 typedef DenseMap<Value*, APInt> LeafMap; 543 LeafMap Leaves; // Leaf -> Total weight so far. 544 SmallVector<Value*, 8> LeafOrder; // Ensure deterministic leaf output order. 545 546#ifndef NDEBUG 547 SmallPtrSet<Value*, 8> Visited; // For sanity checking the iteration scheme. 548#endif 549 while (!Worklist.empty()) { 550 std::pair<BinaryOperator*, APInt> P = Worklist.pop_back_val(); 551 I = P.first; // We examine the operands of this binary operator. 552 553 for (unsigned OpIdx = 0; OpIdx < 2; ++OpIdx) { // Visit operands. 554 Value *Op = I->getOperand(OpIdx); 555 APInt Weight = P.second; // Number of paths to this operand. 556 DEBUG(dbgs() << "OPERAND: " << *Op << " (" << Weight << ")\n"); 557 assert(!Op->use_empty() && "No uses, so how did we get to it?!"); 558 559 // If this is a binary operation of the right kind with only one use then 560 // add its operands to the expression. 561 if (BinaryOperator *BO = isReassociableOp(Op, Opcode)) { 562 assert(Visited.insert(Op) && "Not first visit!"); 563 DEBUG(dbgs() << "DIRECT ADD: " << *Op << " (" << Weight << ")\n"); 564 Worklist.push_back(std::make_pair(BO, Weight)); 565 continue; 566 } 567 568 // Appears to be a leaf. Is the operand already in the set of leaves? 569 LeafMap::iterator It = Leaves.find(Op); 570 if (It == Leaves.end()) { 571 // Not in the leaf map. Must be the first time we saw this operand. 572 assert(Visited.insert(Op) && "Not first visit!"); 573 if (!Op->hasOneUse()) { 574 // This value has uses not accounted for by the expression, so it is 575 // not safe to modify. Mark it as being a leaf. 576 DEBUG(dbgs() << "ADD USES LEAF: " << *Op << " (" << Weight << ")\n"); 577 LeafOrder.push_back(Op); 578 Leaves[Op] = Weight; 579 continue; 580 } 581 // No uses outside the expression, try morphing it. 582 } else if (It != Leaves.end()) { 583 // Already in the leaf map. 584 assert(Visited.count(Op) && "In leaf map but not visited!"); 585 586 // Update the number of paths to the leaf. 587 IncorporateWeight(It->second, Weight, Opcode); 588 589#if 0 // TODO: Re-enable once PR13021 is fixed. 590 // The leaf already has one use from inside the expression. As we want 591 // exactly one such use, drop this new use of the leaf. 592 assert(!Op->hasOneUse() && "Only one use, but we got here twice!"); 593 I->setOperand(OpIdx, UndefValue::get(I->getType())); 594 MadeChange = true; 595 596 // If the leaf is a binary operation of the right kind and we now see 597 // that its multiple original uses were in fact all by nodes belonging 598 // to the expression, then no longer consider it to be a leaf and add 599 // its operands to the expression. 600 if (BinaryOperator *BO = isReassociableOp(Op, Opcode)) { 601 DEBUG(dbgs() << "UNLEAF: " << *Op << " (" << It->second << ")\n"); 602 Worklist.push_back(std::make_pair(BO, It->second)); 603 Leaves.erase(It); 604 continue; 605 } 606#endif 607 608 // If we still have uses that are not accounted for by the expression 609 // then it is not safe to modify the value. 610 if (!Op->hasOneUse()) 611 continue; 612 613 // No uses outside the expression, try morphing it. 614 Weight = It->second; 615 Leaves.erase(It); // Since the value may be morphed below. 616 } 617 618 // At this point we have a value which, first of all, is not a binary 619 // expression of the right kind, and secondly, is only used inside the 620 // expression. This means that it can safely be modified. See if we 621 // can usefully morph it into an expression of the right kind. 622 assert((!isa<Instruction>(Op) || 623 cast<Instruction>(Op)->getOpcode() != Opcode) && 624 "Should have been handled above!"); 625 assert(Op->hasOneUse() && "Has uses outside the expression tree!"); 626 627 // If this is a multiply expression, turn any internal negations into 628 // multiplies by -1 so they can be reassociated. 629 BinaryOperator *BO = dyn_cast<BinaryOperator>(Op); 630 if (Opcode == Instruction::Mul && BO && BinaryOperator::isNeg(BO)) { 631 DEBUG(dbgs() << "MORPH LEAF: " << *Op << " (" << Weight << ") TO "); 632 BO = LowerNegateToMultiply(BO); 633 DEBUG(dbgs() << *BO << 'n'); 634 Worklist.push_back(std::make_pair(BO, Weight)); 635 MadeChange = true; 636 continue; 637 } 638 639 // Failed to morph into an expression of the right type. This really is 640 // a leaf. 641 DEBUG(dbgs() << "ADD LEAF: " << *Op << " (" << Weight << ")\n"); 642 assert(!isReassociableOp(Op, Opcode) && "Value was morphed?"); 643 LeafOrder.push_back(Op); 644 Leaves[Op] = Weight; 645 } 646 } 647 648 // The leaves, repeated according to their weights, represent the linearized 649 // form of the expression. 650 for (unsigned i = 0, e = LeafOrder.size(); i != e; ++i) { 651 Value *V = LeafOrder[i]; 652 LeafMap::iterator It = Leaves.find(V); 653 if (It == Leaves.end()) 654 // Node initially thought to be a leaf wasn't. 655 continue; 656 assert(!isReassociableOp(V, Opcode) && "Shouldn't be a leaf!"); 657 APInt Weight = It->second; 658 if (Weight.isMinValue()) 659 // Leaf already output or weight reduction eliminated it. 660 continue; 661 // Ensure the leaf is only output once. 662 It->second = 0; 663 Ops.push_back(std::make_pair(V, Weight)); 664 } 665 666 // For nilpotent operations or addition there may be no operands, for example 667 // because the expression was "X xor X" or consisted of 2^Bitwidth additions: 668 // in both cases the weight reduces to 0 causing the value to be skipped. 669 if (Ops.empty()) { 670 Constant *Identity = ConstantExpr::getBinOpIdentity(Opcode, I->getType()); 671 assert(Identity && "Associative operation without identity!"); 672 Ops.push_back(std::make_pair(Identity, APInt(Bitwidth, 1))); 673 } 674 675 return MadeChange; 676} 677 678// RewriteExprTree - Now that the operands for this expression tree are 679// linearized and optimized, emit them in-order. 680void Reassociate::RewriteExprTree(BinaryOperator *I, 681 SmallVectorImpl<ValueEntry> &Ops) { 682 assert(Ops.size() > 1 && "Single values should be used directly!"); 683 684 // Since our optimizations should never increase the number of operations, the 685 // new expression can usually be written reusing the existing binary operators 686 // from the original expression tree, without creating any new instructions, 687 // though the rewritten expression may have a completely different topology. 688 // We take care to not change anything if the new expression will be the same 689 // as the original. If more than trivial changes (like commuting operands) 690 // were made then we are obliged to clear out any optional subclass data like 691 // nsw flags. 692 693 /// NodesToRewrite - Nodes from the original expression available for writing 694 /// the new expression into. 695 SmallVector<BinaryOperator*, 8> NodesToRewrite; 696 unsigned Opcode = I->getOpcode(); 697 BinaryOperator *Op = I; 698 699 /// NotRewritable - The operands being written will be the leaves of the new 700 /// expression and must not be used as inner nodes (via NodesToRewrite) by 701 /// mistake. Inner nodes are always reassociable, and usually leaves are not 702 /// (if they were they would have been incorporated into the expression and so 703 /// would not be leaves), so most of the time there is no danger of this. But 704 /// in rare cases a leaf may become reassociable if an optimization kills uses 705 /// of it, or it may momentarily become reassociable during rewriting (below) 706 /// due it being removed as an operand of one of its uses. Ensure that misuse 707 /// of leaf nodes as inner nodes cannot occur by remembering all of the future 708 /// leaves and refusing to reuse any of them as inner nodes. 709 SmallPtrSet<Value*, 8> NotRewritable; 710 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 711 NotRewritable.insert(Ops[i].Op); 712 713 // ExpressionChanged - Non-null if the rewritten expression differs from the 714 // original in some non-trivial way, requiring the clearing of optional flags. 715 // Flags are cleared from the operator in ExpressionChanged up to I inclusive. 716 BinaryOperator *ExpressionChanged = 0; 717 for (unsigned i = 0; ; ++i) { 718 // The last operation (which comes earliest in the IR) is special as both 719 // operands will come from Ops, rather than just one with the other being 720 // a subexpression. 721 if (i+2 == Ops.size()) { 722 Value *NewLHS = Ops[i].Op; 723 Value *NewRHS = Ops[i+1].Op; 724 Value *OldLHS = Op->getOperand(0); 725 Value *OldRHS = Op->getOperand(1); 726 727 if (NewLHS == OldLHS && NewRHS == OldRHS) 728 // Nothing changed, leave it alone. 729 break; 730 731 if (NewLHS == OldRHS && NewRHS == OldLHS) { 732 // The order of the operands was reversed. Swap them. 733 DEBUG(dbgs() << "RA: " << *Op << '\n'); 734 Op->swapOperands(); 735 DEBUG(dbgs() << "TO: " << *Op << '\n'); 736 MadeChange = true; 737 ++NumChanged; 738 break; 739 } 740 741 // The new operation differs non-trivially from the original. Overwrite 742 // the old operands with the new ones. 743 DEBUG(dbgs() << "RA: " << *Op << '\n'); 744 if (NewLHS != OldLHS) { 745 BinaryOperator *BO = isReassociableOp(OldLHS, Opcode); 746 if (BO && !NotRewritable.count(BO)) 747 NodesToRewrite.push_back(BO); 748 Op->setOperand(0, NewLHS); 749 } 750 if (NewRHS != OldRHS) { 751 BinaryOperator *BO = isReassociableOp(OldRHS, Opcode); 752 if (BO && !NotRewritable.count(BO)) 753 NodesToRewrite.push_back(BO); 754 Op->setOperand(1, NewRHS); 755 } 756 DEBUG(dbgs() << "TO: " << *Op << '\n'); 757 758 ExpressionChanged = Op; 759 MadeChange = true; 760 ++NumChanged; 761 762 break; 763 } 764 765 // Not the last operation. The left-hand side will be a sub-expression 766 // while the right-hand side will be the current element of Ops. 767 Value *NewRHS = Ops[i].Op; 768 if (NewRHS != Op->getOperand(1)) { 769 DEBUG(dbgs() << "RA: " << *Op << '\n'); 770 if (NewRHS == Op->getOperand(0)) { 771 // The new right-hand side was already present as the left operand. If 772 // we are lucky then swapping the operands will sort out both of them. 773 Op->swapOperands(); 774 } else { 775 // Overwrite with the new right-hand side. 776 BinaryOperator *BO = isReassociableOp(Op->getOperand(1), Opcode); 777 if (BO && !NotRewritable.count(BO)) 778 NodesToRewrite.push_back(BO); 779 Op->setOperand(1, NewRHS); 780 ExpressionChanged = Op; 781 } 782 DEBUG(dbgs() << "TO: " << *Op << '\n'); 783 MadeChange = true; 784 ++NumChanged; 785 } 786 787 // Now deal with the left-hand side. If this is already an operation node 788 // from the original expression then just rewrite the rest of the expression 789 // into it. 790 BinaryOperator *BO = isReassociableOp(Op->getOperand(0), Opcode); 791 if (BO && !NotRewritable.count(BO)) { 792 Op = BO; 793 continue; 794 } 795 796 // Otherwise, grab a spare node from the original expression and use that as 797 // the left-hand side. If there are no nodes left then the optimizers made 798 // an expression with more nodes than the original! This usually means that 799 // they did something stupid but it might mean that the problem was just too 800 // hard (finding the mimimal number of multiplications needed to realize a 801 // multiplication expression is NP-complete). Whatever the reason, smart or 802 // stupid, create a new node if there are none left. 803 BinaryOperator *NewOp; 804 if (NodesToRewrite.empty()) { 805 Constant *Undef = UndefValue::get(I->getType()); 806 NewOp = BinaryOperator::Create(Instruction::BinaryOps(Opcode), 807 Undef, Undef, "", I); 808 } else { 809 NewOp = NodesToRewrite.pop_back_val(); 810 } 811 812 DEBUG(dbgs() << "RA: " << *Op << '\n'); 813 Op->setOperand(0, NewOp); 814 DEBUG(dbgs() << "TO: " << *Op << '\n'); 815 ExpressionChanged = Op; 816 MadeChange = true; 817 ++NumChanged; 818 Op = NewOp; 819 } 820 821 // If the expression changed non-trivially then clear out all subclass data 822 // starting from the operator specified in ExpressionChanged, and compactify 823 // the operators to just before the expression root to guarantee that the 824 // expression tree is dominated by all of Ops. 825 if (ExpressionChanged) 826 do { 827 ExpressionChanged->clearSubclassOptionalData(); 828 if (ExpressionChanged == I) 829 break; 830 ExpressionChanged->moveBefore(I); 831 ExpressionChanged = cast<BinaryOperator>(*ExpressionChanged->use_begin()); 832 } while (1); 833 834 // Throw away any left over nodes from the original expression. 835 for (unsigned i = 0, e = NodesToRewrite.size(); i != e; ++i) 836 RedoInsts.insert(NodesToRewrite[i]); 837} 838 839/// NegateValue - Insert instructions before the instruction pointed to by BI, 840/// that computes the negative version of the value specified. The negative 841/// version of the value is returned, and BI is left pointing at the instruction 842/// that should be processed next by the reassociation pass. 843static Value *NegateValue(Value *V, Instruction *BI) { 844 if (Constant *C = dyn_cast<Constant>(V)) 845 return ConstantExpr::getNeg(C); 846 847 // We are trying to expose opportunity for reassociation. One of the things 848 // that we want to do to achieve this is to push a negation as deep into an 849 // expression chain as possible, to expose the add instructions. In practice, 850 // this means that we turn this: 851 // X = -(A+12+C+D) into X = -A + -12 + -C + -D = -12 + -A + -C + -D 852 // so that later, a: Y = 12+X could get reassociated with the -12 to eliminate 853 // the constants. We assume that instcombine will clean up the mess later if 854 // we introduce tons of unnecessary negation instructions. 855 // 856 if (BinaryOperator *I = isReassociableOp(V, Instruction::Add)) { 857 // Push the negates through the add. 858 I->setOperand(0, NegateValue(I->getOperand(0), BI)); 859 I->setOperand(1, NegateValue(I->getOperand(1), BI)); 860 861 // We must move the add instruction here, because the neg instructions do 862 // not dominate the old add instruction in general. By moving it, we are 863 // assured that the neg instructions we just inserted dominate the 864 // instruction we are about to insert after them. 865 // 866 I->moveBefore(BI); 867 I->setName(I->getName()+".neg"); 868 return I; 869 } 870 871 // Okay, we need to materialize a negated version of V with an instruction. 872 // Scan the use lists of V to see if we have one already. 873 for (Value::use_iterator UI = V->use_begin(), E = V->use_end(); UI != E;++UI){ 874 User *U = *UI; 875 if (!BinaryOperator::isNeg(U)) continue; 876 877 // We found one! Now we have to make sure that the definition dominates 878 // this use. We do this by moving it to the entry block (if it is a 879 // non-instruction value) or right after the definition. These negates will 880 // be zapped by reassociate later, so we don't need much finesse here. 881 BinaryOperator *TheNeg = cast<BinaryOperator>(U); 882 883 // Verify that the negate is in this function, V might be a constant expr. 884 if (TheNeg->getParent()->getParent() != BI->getParent()->getParent()) 885 continue; 886 887 BasicBlock::iterator InsertPt; 888 if (Instruction *InstInput = dyn_cast<Instruction>(V)) { 889 if (InvokeInst *II = dyn_cast<InvokeInst>(InstInput)) { 890 InsertPt = II->getNormalDest()->begin(); 891 } else { 892 InsertPt = InstInput; 893 ++InsertPt; 894 } 895 while (isa<PHINode>(InsertPt)) ++InsertPt; 896 } else { 897 InsertPt = TheNeg->getParent()->getParent()->getEntryBlock().begin(); 898 } 899 TheNeg->moveBefore(InsertPt); 900 return TheNeg; 901 } 902 903 // Insert a 'neg' instruction that subtracts the value from zero to get the 904 // negation. 905 return BinaryOperator::CreateNeg(V, V->getName() + ".neg", BI); 906} 907 908/// ShouldBreakUpSubtract - Return true if we should break up this subtract of 909/// X-Y into (X + -Y). 910static bool ShouldBreakUpSubtract(Instruction *Sub) { 911 // If this is a negation, we can't split it up! 912 if (BinaryOperator::isNeg(Sub)) 913 return false; 914 915 // Don't bother to break this up unless either the LHS is an associable add or 916 // subtract or if this is only used by one. 917 if (isReassociableOp(Sub->getOperand(0), Instruction::Add) || 918 isReassociableOp(Sub->getOperand(0), Instruction::Sub)) 919 return true; 920 if (isReassociableOp(Sub->getOperand(1), Instruction::Add) || 921 isReassociableOp(Sub->getOperand(1), Instruction::Sub)) 922 return true; 923 if (Sub->hasOneUse() && 924 (isReassociableOp(Sub->use_back(), Instruction::Add) || 925 isReassociableOp(Sub->use_back(), Instruction::Sub))) 926 return true; 927 928 return false; 929} 930 931/// BreakUpSubtract - If we have (X-Y), and if either X is an add, or if this is 932/// only used by an add, transform this into (X+(0-Y)) to promote better 933/// reassociation. 934static BinaryOperator *BreakUpSubtract(Instruction *Sub) { 935 // Convert a subtract into an add and a neg instruction. This allows sub 936 // instructions to be commuted with other add instructions. 937 // 938 // Calculate the negative value of Operand 1 of the sub instruction, 939 // and set it as the RHS of the add instruction we just made. 940 // 941 Value *NegVal = NegateValue(Sub->getOperand(1), Sub); 942 BinaryOperator *New = 943 BinaryOperator::CreateAdd(Sub->getOperand(0), NegVal, "", Sub); 944 Sub->setOperand(0, Constant::getNullValue(Sub->getType())); // Drop use of op. 945 Sub->setOperand(1, Constant::getNullValue(Sub->getType())); // Drop use of op. 946 New->takeName(Sub); 947 948 // Everyone now refers to the add instruction. 949 Sub->replaceAllUsesWith(New); 950 New->setDebugLoc(Sub->getDebugLoc()); 951 952 DEBUG(dbgs() << "Negated: " << *New << '\n'); 953 return New; 954} 955 956/// ConvertShiftToMul - If this is a shift of a reassociable multiply or is used 957/// by one, change this into a multiply by a constant to assist with further 958/// reassociation. 959static BinaryOperator *ConvertShiftToMul(Instruction *Shl) { 960 Constant *MulCst = ConstantInt::get(Shl->getType(), 1); 961 MulCst = ConstantExpr::getShl(MulCst, cast<Constant>(Shl->getOperand(1))); 962 963 BinaryOperator *Mul = 964 BinaryOperator::CreateMul(Shl->getOperand(0), MulCst, "", Shl); 965 Shl->setOperand(0, UndefValue::get(Shl->getType())); // Drop use of op. 966 Mul->takeName(Shl); 967 Shl->replaceAllUsesWith(Mul); 968 Mul->setDebugLoc(Shl->getDebugLoc()); 969 return Mul; 970} 971 972/// FindInOperandList - Scan backwards and forwards among values with the same 973/// rank as element i to see if X exists. If X does not exist, return i. This 974/// is useful when scanning for 'x' when we see '-x' because they both get the 975/// same rank. 976static unsigned FindInOperandList(SmallVectorImpl<ValueEntry> &Ops, unsigned i, 977 Value *X) { 978 unsigned XRank = Ops[i].Rank; 979 unsigned e = Ops.size(); 980 for (unsigned j = i+1; j != e && Ops[j].Rank == XRank; ++j) 981 if (Ops[j].Op == X) 982 return j; 983 // Scan backwards. 984 for (unsigned j = i-1; j != ~0U && Ops[j].Rank == XRank; --j) 985 if (Ops[j].Op == X) 986 return j; 987 return i; 988} 989 990/// EmitAddTreeOfValues - Emit a tree of add instructions, summing Ops together 991/// and returning the result. Insert the tree before I. 992static Value *EmitAddTreeOfValues(Instruction *I, 993 SmallVectorImpl<WeakVH> &Ops){ 994 if (Ops.size() == 1) return Ops.back(); 995 996 Value *V1 = Ops.back(); 997 Ops.pop_back(); 998 Value *V2 = EmitAddTreeOfValues(I, Ops); 999 return BinaryOperator::CreateAdd(V2, V1, "tmp", I); 1000} 1001 1002/// RemoveFactorFromExpression - If V is an expression tree that is a 1003/// multiplication sequence, and if this sequence contains a multiply by Factor, 1004/// remove Factor from the tree and return the new tree. 1005Value *Reassociate::RemoveFactorFromExpression(Value *V, Value *Factor) { 1006 BinaryOperator *BO = isReassociableOp(V, Instruction::Mul); 1007 if (!BO) return 0; 1008 1009 SmallVector<RepeatedValue, 8> Tree; 1010 MadeChange |= LinearizeExprTree(BO, Tree); 1011 SmallVector<ValueEntry, 8> Factors; 1012 Factors.reserve(Tree.size()); 1013 for (unsigned i = 0, e = Tree.size(); i != e; ++i) { 1014 RepeatedValue E = Tree[i]; 1015 Factors.append(E.second.getZExtValue(), 1016 ValueEntry(getRank(E.first), E.first)); 1017 } 1018 1019 bool FoundFactor = false; 1020 bool NeedsNegate = false; 1021 for (unsigned i = 0, e = Factors.size(); i != e; ++i) { 1022 if (Factors[i].Op == Factor) { 1023 FoundFactor = true; 1024 Factors.erase(Factors.begin()+i); 1025 break; 1026 } 1027 1028 // If this is a negative version of this factor, remove it. 1029 if (ConstantInt *FC1 = dyn_cast<ConstantInt>(Factor)) 1030 if (ConstantInt *FC2 = dyn_cast<ConstantInt>(Factors[i].Op)) 1031 if (FC1->getValue() == -FC2->getValue()) { 1032 FoundFactor = NeedsNegate = true; 1033 Factors.erase(Factors.begin()+i); 1034 break; 1035 } 1036 } 1037 1038 if (!FoundFactor) { 1039 // Make sure to restore the operands to the expression tree. 1040 RewriteExprTree(BO, Factors); 1041 return 0; 1042 } 1043 1044 BasicBlock::iterator InsertPt = BO; ++InsertPt; 1045 1046 // If this was just a single multiply, remove the multiply and return the only 1047 // remaining operand. 1048 if (Factors.size() == 1) { 1049 RedoInsts.insert(BO); 1050 V = Factors[0].Op; 1051 } else { 1052 RewriteExprTree(BO, Factors); 1053 V = BO; 1054 } 1055 1056 if (NeedsNegate) 1057 V = BinaryOperator::CreateNeg(V, "neg", InsertPt); 1058 1059 return V; 1060} 1061 1062/// FindSingleUseMultiplyFactors - If V is a single-use multiply, recursively 1063/// add its operands as factors, otherwise add V to the list of factors. 1064/// 1065/// Ops is the top-level list of add operands we're trying to factor. 1066static void FindSingleUseMultiplyFactors(Value *V, 1067 SmallVectorImpl<Value*> &Factors, 1068 const SmallVectorImpl<ValueEntry> &Ops) { 1069 BinaryOperator *BO = isReassociableOp(V, Instruction::Mul); 1070 if (!BO) { 1071 Factors.push_back(V); 1072 return; 1073 } 1074 1075 // Otherwise, add the LHS and RHS to the list of factors. 1076 FindSingleUseMultiplyFactors(BO->getOperand(1), Factors, Ops); 1077 FindSingleUseMultiplyFactors(BO->getOperand(0), Factors, Ops); 1078} 1079 1080/// OptimizeAndOrXor - Optimize a series of operands to an 'and', 'or', or 'xor' 1081/// instruction. This optimizes based on identities. If it can be reduced to 1082/// a single Value, it is returned, otherwise the Ops list is mutated as 1083/// necessary. 1084static Value *OptimizeAndOrXor(unsigned Opcode, 1085 SmallVectorImpl<ValueEntry> &Ops) { 1086 // Scan the operand lists looking for X and ~X pairs, along with X,X pairs. 1087 // If we find any, we can simplify the expression. X&~X == 0, X|~X == -1. 1088 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1089 // First, check for X and ~X in the operand list. 1090 assert(i < Ops.size()); 1091 if (BinaryOperator::isNot(Ops[i].Op)) { // Cannot occur for ^. 1092 Value *X = BinaryOperator::getNotArgument(Ops[i].Op); 1093 unsigned FoundX = FindInOperandList(Ops, i, X); 1094 if (FoundX != i) { 1095 if (Opcode == Instruction::And) // ...&X&~X = 0 1096 return Constant::getNullValue(X->getType()); 1097 1098 if (Opcode == Instruction::Or) // ...|X|~X = -1 1099 return Constant::getAllOnesValue(X->getType()); 1100 } 1101 } 1102 1103 // Next, check for duplicate pairs of values, which we assume are next to 1104 // each other, due to our sorting criteria. 1105 assert(i < Ops.size()); 1106 if (i+1 != Ops.size() && Ops[i+1].Op == Ops[i].Op) { 1107 if (Opcode == Instruction::And || Opcode == Instruction::Or) { 1108 // Drop duplicate values for And and Or. 1109 Ops.erase(Ops.begin()+i); 1110 --i; --e; 1111 ++NumAnnihil; 1112 continue; 1113 } 1114 1115 // Drop pairs of values for Xor. 1116 assert(Opcode == Instruction::Xor); 1117 if (e == 2) 1118 return Constant::getNullValue(Ops[0].Op->getType()); 1119 1120 // Y ^ X^X -> Y 1121 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 1122 i -= 1; e -= 2; 1123 ++NumAnnihil; 1124 } 1125 } 1126 return 0; 1127} 1128 1129/// Helper funciton of CombineXorOpnd(). It creates a bitwise-and 1130/// instruction with the given two operands, and return the resulting 1131/// instruction. There are two special cases: 1) if the constant operand is 0, 1132/// it will return NULL. 2) if the constant is ~0, the symbolic operand will 1133/// be returned. 1134static Value *createAndInstr(Instruction *InsertBefore, Value *Opnd, 1135 const APInt &ConstOpnd) { 1136 if (ConstOpnd != 0) { 1137 if (!ConstOpnd.isAllOnesValue()) { 1138 LLVMContext &Ctx = Opnd->getType()->getContext(); 1139 Instruction *I; 1140 I = BinaryOperator::CreateAnd(Opnd, ConstantInt::get(Ctx, ConstOpnd), 1141 "and.ra", InsertBefore); 1142 I->setDebugLoc(InsertBefore->getDebugLoc()); 1143 return I; 1144 } 1145 return Opnd; 1146 } 1147 return 0; 1148} 1149 1150// Helper function of OptimizeXor(). It tries to simplify "Opnd1 ^ ConstOpnd" 1151// into "R ^ C", where C would be 0, and R is a symbolic value. 1152// 1153// If it was successful, true is returned, and the "R" and "C" is returned 1154// via "Res" and "ConstOpnd", respectively; otherwise, false is returned, 1155// and both "Res" and "ConstOpnd" remain unchanged. 1156// 1157bool Reassociate::CombineXorOpnd(Instruction *I, XorOpnd *Opnd1, 1158 APInt &ConstOpnd, Value *&Res) { 1159 // Xor-Rule 1: (x | c1) ^ c2 = (x | c1) ^ (c1 ^ c1) ^ c2 1160 // = ((x | c1) ^ c1) ^ (c1 ^ c2) 1161 // = (x & ~c1) ^ (c1 ^ c2) 1162 // It is useful only when c1 == c2. 1163 if (Opnd1->isOrExpr() && Opnd1->getConstPart() != 0) { 1164 if (!Opnd1->getValue()->hasOneUse()) 1165 return false; 1166 1167 const APInt &C1 = Opnd1->getConstPart(); 1168 if (C1 != ConstOpnd) 1169 return false; 1170 1171 Value *X = Opnd1->getSymbolicPart(); 1172 Res = createAndInstr(I, X, ~C1); 1173 // ConstOpnd was C2, now C1 ^ C2. 1174 ConstOpnd ^= C1; 1175 1176 if (Instruction *T = dyn_cast<Instruction>(Opnd1->getValue())) 1177 RedoInsts.insert(T); 1178 return true; 1179 } 1180 return false; 1181} 1182 1183 1184// Helper function of OptimizeXor(). It tries to simplify 1185// "Opnd1 ^ Opnd2 ^ ConstOpnd" into "R ^ C", where C would be 0, and R is a 1186// symbolic value. 1187// 1188// If it was successful, true is returned, and the "R" and "C" is returned 1189// via "Res" and "ConstOpnd", respectively (If the entire expression is 1190// evaluated to a constant, the Res is set to NULL); otherwise, false is 1191// returned, and both "Res" and "ConstOpnd" remain unchanged. 1192bool Reassociate::CombineXorOpnd(Instruction *I, XorOpnd *Opnd1, XorOpnd *Opnd2, 1193 APInt &ConstOpnd, Value *&Res) { 1194 Value *X = Opnd1->getSymbolicPart(); 1195 if (X != Opnd2->getSymbolicPart()) 1196 return false; 1197 1198 // This many instruction become dead.(At least "Opnd1 ^ Opnd2" will die.) 1199 int DeadInstNum = 1; 1200 if (Opnd1->getValue()->hasOneUse()) 1201 DeadInstNum++; 1202 if (Opnd2->getValue()->hasOneUse()) 1203 DeadInstNum++; 1204 1205 // Xor-Rule 2: 1206 // (x | c1) ^ (x & c2) 1207 // = (x|c1) ^ (x&c2) ^ (c1 ^ c1) = ((x|c1) ^ c1) ^ (x & c2) ^ c1 1208 // = (x & ~c1) ^ (x & c2) ^ c1 // Xor-Rule 1 1209 // = (x & c3) ^ c1, where c3 = ~c1 ^ c2 // Xor-rule 3 1210 // 1211 if (Opnd1->isOrExpr() != Opnd2->isOrExpr()) { 1212 if (Opnd2->isOrExpr()) 1213 std::swap(Opnd1, Opnd2); 1214 1215 const APInt &C1 = Opnd1->getConstPart(); 1216 const APInt &C2 = Opnd2->getConstPart(); 1217 APInt C3((~C1) ^ C2); 1218 1219 // Do not increase code size! 1220 if (C3 != 0 && !C3.isAllOnesValue()) { 1221 int NewInstNum = ConstOpnd != 0 ? 1 : 2; 1222 if (NewInstNum > DeadInstNum) 1223 return false; 1224 } 1225 1226 Res = createAndInstr(I, X, C3); 1227 ConstOpnd ^= C1; 1228 1229 } else if (Opnd1->isOrExpr()) { 1230 // Xor-Rule 3: (x | c1) ^ (x | c2) = (x & c3) ^ c3 where c3 = c1 ^ c2 1231 // 1232 const APInt &C1 = Opnd1->getConstPart(); 1233 const APInt &C2 = Opnd2->getConstPart(); 1234 APInt C3 = C1 ^ C2; 1235 1236 // Do not increase code size 1237 if (C3 != 0 && !C3.isAllOnesValue()) { 1238 int NewInstNum = ConstOpnd != 0 ? 1 : 2; 1239 if (NewInstNum > DeadInstNum) 1240 return false; 1241 } 1242 1243 Res = createAndInstr(I, X, C3); 1244 ConstOpnd ^= C3; 1245 } else { 1246 // Xor-Rule 4: (x & c1) ^ (x & c2) = (x & (c1^c2)) 1247 // 1248 const APInt &C1 = Opnd1->getConstPart(); 1249 const APInt &C2 = Opnd2->getConstPart(); 1250 APInt C3 = C1 ^ C2; 1251 Res = createAndInstr(I, X, C3); 1252 } 1253 1254 // Put the original operands in the Redo list; hope they will be deleted 1255 // as dead code. 1256 if (Instruction *T = dyn_cast<Instruction>(Opnd1->getValue())) 1257 RedoInsts.insert(T); 1258 if (Instruction *T = dyn_cast<Instruction>(Opnd2->getValue())) 1259 RedoInsts.insert(T); 1260 1261 return true; 1262} 1263 1264/// Optimize a series of operands to an 'xor' instruction. If it can be reduced 1265/// to a single Value, it is returned, otherwise the Ops list is mutated as 1266/// necessary. 1267Value *Reassociate::OptimizeXor(Instruction *I, 1268 SmallVectorImpl<ValueEntry> &Ops) { 1269 if (Value *V = OptimizeAndOrXor(Instruction::Xor, Ops)) 1270 return V; 1271 1272 if (Ops.size() == 1) 1273 return 0; 1274 1275 SmallVector<XorOpnd, 8> Opnds; 1276 SmallVector<XorOpnd*, 8> OpndPtrs; 1277 Type *Ty = Ops[0].Op->getType(); 1278 APInt ConstOpnd(Ty->getIntegerBitWidth(), 0); 1279 1280 // Step 1: Convert ValueEntry to XorOpnd 1281 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1282 Value *V = Ops[i].Op; 1283 if (!isa<ConstantInt>(V)) { 1284 XorOpnd O(V); 1285 O.setSymbolicRank(getRank(O.getSymbolicPart())); 1286 Opnds.push_back(O); 1287 } else 1288 ConstOpnd ^= cast<ConstantInt>(V)->getValue(); 1289 } 1290 1291 // NOTE: From this point on, do *NOT* add/delete element to/from "Opnds". 1292 // It would otherwise invalidate the "Opnds"'s iterator, and hence invalidate 1293 // the "OpndPtrs" as well. For the similar reason, do not fuse this loop 1294 // with the previous loop --- the iterator of the "Opnds" may be invalidated 1295 // when new elements are added to the vector. 1296 for (unsigned i = 0, e = Opnds.size(); i != e; ++i) 1297 OpndPtrs.push_back(&Opnds[i]); 1298 1299 // Step 2: Sort the Xor-Operands in a way such that the operands containing 1300 // the same symbolic value cluster together. For instance, the input operand 1301 // sequence ("x | 123", "y & 456", "x & 789") will be sorted into: 1302 // ("x | 123", "x & 789", "y & 456"). 1303 std::sort(OpndPtrs.begin(), OpndPtrs.end(), XorOpnd::PtrSortFunctor()); 1304 1305 // Step 3: Combine adjacent operands 1306 XorOpnd *PrevOpnd = 0; 1307 bool Changed = false; 1308 for (unsigned i = 0, e = Opnds.size(); i < e; i++) { 1309 XorOpnd *CurrOpnd = OpndPtrs[i]; 1310 // The combined value 1311 Value *CV; 1312 1313 // Step 3.1: Try simplifying "CurrOpnd ^ ConstOpnd" 1314 if (ConstOpnd != 0 && CombineXorOpnd(I, CurrOpnd, ConstOpnd, CV)) { 1315 Changed = true; 1316 if (CV) 1317 *CurrOpnd = XorOpnd(CV); 1318 else { 1319 CurrOpnd->Invalidate(); 1320 continue; 1321 } 1322 } 1323 1324 if (!PrevOpnd || CurrOpnd->getSymbolicPart() != PrevOpnd->getSymbolicPart()) { 1325 PrevOpnd = CurrOpnd; 1326 continue; 1327 } 1328 1329 // step 3.2: When previous and current operands share the same symbolic 1330 // value, try to simplify "PrevOpnd ^ CurrOpnd ^ ConstOpnd" 1331 // 1332 if (CombineXorOpnd(I, CurrOpnd, PrevOpnd, ConstOpnd, CV)) { 1333 // Remove previous operand 1334 PrevOpnd->Invalidate(); 1335 if (CV) { 1336 *CurrOpnd = XorOpnd(CV); 1337 PrevOpnd = CurrOpnd; 1338 } else { 1339 CurrOpnd->Invalidate(); 1340 PrevOpnd = 0; 1341 } 1342 Changed = true; 1343 } 1344 } 1345 1346 // Step 4: Reassemble the Ops 1347 if (Changed) { 1348 Ops.clear(); 1349 for (unsigned int i = 0, e = Opnds.size(); i < e; i++) { 1350 XorOpnd &O = Opnds[i]; 1351 if (O.isInvalid()) 1352 continue; 1353 ValueEntry VE(getRank(O.getValue()), O.getValue()); 1354 Ops.push_back(VE); 1355 } 1356 if (ConstOpnd != 0) { 1357 Value *C = ConstantInt::get(Ty->getContext(), ConstOpnd); 1358 ValueEntry VE(getRank(C), C); 1359 Ops.push_back(VE); 1360 } 1361 int Sz = Ops.size(); 1362 if (Sz == 1) 1363 return Ops.back().Op; 1364 else if (Sz == 0) { 1365 assert(ConstOpnd == 0); 1366 return ConstantInt::get(Ty->getContext(), ConstOpnd); 1367 } 1368 } 1369 1370 return 0; 1371} 1372 1373/// OptimizeAdd - Optimize a series of operands to an 'add' instruction. This 1374/// optimizes based on identities. If it can be reduced to a single Value, it 1375/// is returned, otherwise the Ops list is mutated as necessary. 1376Value *Reassociate::OptimizeAdd(Instruction *I, 1377 SmallVectorImpl<ValueEntry> &Ops) { 1378 // Scan the operand lists looking for X and -X pairs. If we find any, we 1379 // can simplify the expression. X+-X == 0. While we're at it, scan for any 1380 // duplicates. We want to canonicalize Y+Y+Y+Z -> 3*Y+Z. 1381 // 1382 // TODO: We could handle "X + ~X" -> "-1" if we wanted, since "-X = ~X+1". 1383 // 1384 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1385 Value *TheOp = Ops[i].Op; 1386 // Check to see if we've seen this operand before. If so, we factor all 1387 // instances of the operand together. Due to our sorting criteria, we know 1388 // that these need to be next to each other in the vector. 1389 if (i+1 != Ops.size() && Ops[i+1].Op == TheOp) { 1390 // Rescan the list, remove all instances of this operand from the expr. 1391 unsigned NumFound = 0; 1392 do { 1393 Ops.erase(Ops.begin()+i); 1394 ++NumFound; 1395 } while (i != Ops.size() && Ops[i].Op == TheOp); 1396 1397 DEBUG(errs() << "\nFACTORING [" << NumFound << "]: " << *TheOp << '\n'); 1398 ++NumFactor; 1399 1400 // Insert a new multiply. 1401 Value *Mul = ConstantInt::get(cast<IntegerType>(I->getType()), NumFound); 1402 Mul = BinaryOperator::CreateMul(TheOp, Mul, "factor", I); 1403 1404 // Now that we have inserted a multiply, optimize it. This allows us to 1405 // handle cases that require multiple factoring steps, such as this: 1406 // (X*2) + (X*2) + (X*2) -> (X*2)*3 -> X*6 1407 RedoInsts.insert(cast<Instruction>(Mul)); 1408 1409 // If every add operand was a duplicate, return the multiply. 1410 if (Ops.empty()) 1411 return Mul; 1412 1413 // Otherwise, we had some input that didn't have the dupe, such as 1414 // "A + A + B" -> "A*2 + B". Add the new multiply to the list of 1415 // things being added by this operation. 1416 Ops.insert(Ops.begin(), ValueEntry(getRank(Mul), Mul)); 1417 1418 --i; 1419 e = Ops.size(); 1420 continue; 1421 } 1422 1423 // Check for X and -X in the operand list. 1424 if (!BinaryOperator::isNeg(TheOp)) 1425 continue; 1426 1427 Value *X = BinaryOperator::getNegArgument(TheOp); 1428 unsigned FoundX = FindInOperandList(Ops, i, X); 1429 if (FoundX == i) 1430 continue; 1431 1432 // Remove X and -X from the operand list. 1433 if (Ops.size() == 2) 1434 return Constant::getNullValue(X->getType()); 1435 1436 Ops.erase(Ops.begin()+i); 1437 if (i < FoundX) 1438 --FoundX; 1439 else 1440 --i; // Need to back up an extra one. 1441 Ops.erase(Ops.begin()+FoundX); 1442 ++NumAnnihil; 1443 --i; // Revisit element. 1444 e -= 2; // Removed two elements. 1445 } 1446 1447 // Scan the operand list, checking to see if there are any common factors 1448 // between operands. Consider something like A*A+A*B*C+D. We would like to 1449 // reassociate this to A*(A+B*C)+D, which reduces the number of multiplies. 1450 // To efficiently find this, we count the number of times a factor occurs 1451 // for any ADD operands that are MULs. 1452 DenseMap<Value*, unsigned> FactorOccurrences; 1453 1454 // Keep track of each multiply we see, to avoid triggering on (X*4)+(X*4) 1455 // where they are actually the same multiply. 1456 unsigned MaxOcc = 0; 1457 Value *MaxOccVal = 0; 1458 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1459 BinaryOperator *BOp = isReassociableOp(Ops[i].Op, Instruction::Mul); 1460 if (!BOp) 1461 continue; 1462 1463 // Compute all of the factors of this added value. 1464 SmallVector<Value*, 8> Factors; 1465 FindSingleUseMultiplyFactors(BOp, Factors, Ops); 1466 assert(Factors.size() > 1 && "Bad linearize!"); 1467 1468 // Add one to FactorOccurrences for each unique factor in this op. 1469 SmallPtrSet<Value*, 8> Duplicates; 1470 for (unsigned i = 0, e = Factors.size(); i != e; ++i) { 1471 Value *Factor = Factors[i]; 1472 if (!Duplicates.insert(Factor)) continue; 1473 1474 unsigned Occ = ++FactorOccurrences[Factor]; 1475 if (Occ > MaxOcc) { MaxOcc = Occ; MaxOccVal = Factor; } 1476 1477 // If Factor is a negative constant, add the negated value as a factor 1478 // because we can percolate the negate out. Watch for minint, which 1479 // cannot be positivified. 1480 if (ConstantInt *CI = dyn_cast<ConstantInt>(Factor)) 1481 if (CI->isNegative() && !CI->isMinValue(true)) { 1482 Factor = ConstantInt::get(CI->getContext(), -CI->getValue()); 1483 assert(!Duplicates.count(Factor) && 1484 "Shouldn't have two constant factors, missed a canonicalize"); 1485 1486 unsigned Occ = ++FactorOccurrences[Factor]; 1487 if (Occ > MaxOcc) { MaxOcc = Occ; MaxOccVal = Factor; } 1488 } 1489 } 1490 } 1491 1492 // If any factor occurred more than one time, we can pull it out. 1493 if (MaxOcc > 1) { 1494 DEBUG(errs() << "\nFACTORING [" << MaxOcc << "]: " << *MaxOccVal << '\n'); 1495 ++NumFactor; 1496 1497 // Create a new instruction that uses the MaxOccVal twice. If we don't do 1498 // this, we could otherwise run into situations where removing a factor 1499 // from an expression will drop a use of maxocc, and this can cause 1500 // RemoveFactorFromExpression on successive values to behave differently. 1501 Instruction *DummyInst = BinaryOperator::CreateAdd(MaxOccVal, MaxOccVal); 1502 SmallVector<WeakVH, 4> NewMulOps; 1503 for (unsigned i = 0; i != Ops.size(); ++i) { 1504 // Only try to remove factors from expressions we're allowed to. 1505 BinaryOperator *BOp = isReassociableOp(Ops[i].Op, Instruction::Mul); 1506 if (!BOp) 1507 continue; 1508 1509 if (Value *V = RemoveFactorFromExpression(Ops[i].Op, MaxOccVal)) { 1510 // The factorized operand may occur several times. Convert them all in 1511 // one fell swoop. 1512 for (unsigned j = Ops.size(); j != i;) { 1513 --j; 1514 if (Ops[j].Op == Ops[i].Op) { 1515 NewMulOps.push_back(V); 1516 Ops.erase(Ops.begin()+j); 1517 } 1518 } 1519 --i; 1520 } 1521 } 1522 1523 // No need for extra uses anymore. 1524 delete DummyInst; 1525 1526 unsigned NumAddedValues = NewMulOps.size(); 1527 Value *V = EmitAddTreeOfValues(I, NewMulOps); 1528 1529 // Now that we have inserted the add tree, optimize it. This allows us to 1530 // handle cases that require multiple factoring steps, such as this: 1531 // A*A*B + A*A*C --> A*(A*B+A*C) --> A*(A*(B+C)) 1532 assert(NumAddedValues > 1 && "Each occurrence should contribute a value"); 1533 (void)NumAddedValues; 1534 if (Instruction *VI = dyn_cast<Instruction>(V)) 1535 RedoInsts.insert(VI); 1536 1537 // Create the multiply. 1538 Instruction *V2 = BinaryOperator::CreateMul(V, MaxOccVal, "tmp", I); 1539 1540 // Rerun associate on the multiply in case the inner expression turned into 1541 // a multiply. We want to make sure that we keep things in canonical form. 1542 RedoInsts.insert(V2); 1543 1544 // If every add operand included the factor (e.g. "A*B + A*C"), then the 1545 // entire result expression is just the multiply "A*(B+C)". 1546 if (Ops.empty()) 1547 return V2; 1548 1549 // Otherwise, we had some input that didn't have the factor, such as 1550 // "A*B + A*C + D" -> "A*(B+C) + D". Add the new multiply to the list of 1551 // things being added by this operation. 1552 Ops.insert(Ops.begin(), ValueEntry(getRank(V2), V2)); 1553 } 1554 1555 return 0; 1556} 1557 1558namespace { 1559 /// \brief Predicate tests whether a ValueEntry's op is in a map. 1560 struct IsValueInMap { 1561 const DenseMap<Value *, unsigned> ⤅ 1562 1563 IsValueInMap(const DenseMap<Value *, unsigned> &Map) : Map(Map) {} 1564 1565 bool operator()(const ValueEntry &Entry) { 1566 return Map.find(Entry.Op) != Map.end(); 1567 } 1568 }; 1569} 1570 1571/// \brief Build up a vector of value/power pairs factoring a product. 1572/// 1573/// Given a series of multiplication operands, build a vector of factors and 1574/// the powers each is raised to when forming the final product. Sort them in 1575/// the order of descending power. 1576/// 1577/// (x*x) -> [(x, 2)] 1578/// ((x*x)*x) -> [(x, 3)] 1579/// ((((x*y)*x)*y)*x) -> [(x, 3), (y, 2)] 1580/// 1581/// \returns Whether any factors have a power greater than one. 1582bool Reassociate::collectMultiplyFactors(SmallVectorImpl<ValueEntry> &Ops, 1583 SmallVectorImpl<Factor> &Factors) { 1584 // FIXME: Have Ops be (ValueEntry, Multiplicity) pairs, simplifying this. 1585 // Compute the sum of powers of simplifiable factors. 1586 unsigned FactorPowerSum = 0; 1587 for (unsigned Idx = 1, Size = Ops.size(); Idx < Size; ++Idx) { 1588 Value *Op = Ops[Idx-1].Op; 1589 1590 // Count the number of occurrences of this value. 1591 unsigned Count = 1; 1592 for (; Idx < Size && Ops[Idx].Op == Op; ++Idx) 1593 ++Count; 1594 // Track for simplification all factors which occur 2 or more times. 1595 if (Count > 1) 1596 FactorPowerSum += Count; 1597 } 1598 1599 // We can only simplify factors if the sum of the powers of our simplifiable 1600 // factors is 4 or higher. When that is the case, we will *always* have 1601 // a simplification. This is an important invariant to prevent cyclicly 1602 // trying to simplify already minimal formations. 1603 if (FactorPowerSum < 4) 1604 return false; 1605 1606 // Now gather the simplifiable factors, removing them from Ops. 1607 FactorPowerSum = 0; 1608 for (unsigned Idx = 1; Idx < Ops.size(); ++Idx) { 1609 Value *Op = Ops[Idx-1].Op; 1610 1611 // Count the number of occurrences of this value. 1612 unsigned Count = 1; 1613 for (; Idx < Ops.size() && Ops[Idx].Op == Op; ++Idx) 1614 ++Count; 1615 if (Count == 1) 1616 continue; 1617 // Move an even number of occurrences to Factors. 1618 Count &= ~1U; 1619 Idx -= Count; 1620 FactorPowerSum += Count; 1621 Factors.push_back(Factor(Op, Count)); 1622 Ops.erase(Ops.begin()+Idx, Ops.begin()+Idx+Count); 1623 } 1624 1625 // None of the adjustments above should have reduced the sum of factor powers 1626 // below our mininum of '4'. 1627 assert(FactorPowerSum >= 4); 1628 1629 std::sort(Factors.begin(), Factors.end(), Factor::PowerDescendingSorter()); 1630 return true; 1631} 1632 1633/// \brief Build a tree of multiplies, computing the product of Ops. 1634static Value *buildMultiplyTree(IRBuilder<> &Builder, 1635 SmallVectorImpl<Value*> &Ops) { 1636 if (Ops.size() == 1) 1637 return Ops.back(); 1638 1639 Value *LHS = Ops.pop_back_val(); 1640 do { 1641 LHS = Builder.CreateMul(LHS, Ops.pop_back_val()); 1642 } while (!Ops.empty()); 1643 1644 return LHS; 1645} 1646 1647/// \brief Build a minimal multiplication DAG for (a^x)*(b^y)*(c^z)*... 1648/// 1649/// Given a vector of values raised to various powers, where no two values are 1650/// equal and the powers are sorted in decreasing order, compute the minimal 1651/// DAG of multiplies to compute the final product, and return that product 1652/// value. 1653Value *Reassociate::buildMinimalMultiplyDAG(IRBuilder<> &Builder, 1654 SmallVectorImpl<Factor> &Factors) { 1655 assert(Factors[0].Power); 1656 SmallVector<Value *, 4> OuterProduct; 1657 for (unsigned LastIdx = 0, Idx = 1, Size = Factors.size(); 1658 Idx < Size && Factors[Idx].Power > 0; ++Idx) { 1659 if (Factors[Idx].Power != Factors[LastIdx].Power) { 1660 LastIdx = Idx; 1661 continue; 1662 } 1663 1664 // We want to multiply across all the factors with the same power so that 1665 // we can raise them to that power as a single entity. Build a mini tree 1666 // for that. 1667 SmallVector<Value *, 4> InnerProduct; 1668 InnerProduct.push_back(Factors[LastIdx].Base); 1669 do { 1670 InnerProduct.push_back(Factors[Idx].Base); 1671 ++Idx; 1672 } while (Idx < Size && Factors[Idx].Power == Factors[LastIdx].Power); 1673 1674 // Reset the base value of the first factor to the new expression tree. 1675 // We'll remove all the factors with the same power in a second pass. 1676 Value *M = Factors[LastIdx].Base = buildMultiplyTree(Builder, InnerProduct); 1677 if (Instruction *MI = dyn_cast<Instruction>(M)) 1678 RedoInsts.insert(MI); 1679 1680 LastIdx = Idx; 1681 } 1682 // Unique factors with equal powers -- we've folded them into the first one's 1683 // base. 1684 Factors.erase(std::unique(Factors.begin(), Factors.end(), 1685 Factor::PowerEqual()), 1686 Factors.end()); 1687 1688 // Iteratively collect the base of each factor with an add power into the 1689 // outer product, and halve each power in preparation for squaring the 1690 // expression. 1691 for (unsigned Idx = 0, Size = Factors.size(); Idx != Size; ++Idx) { 1692 if (Factors[Idx].Power & 1) 1693 OuterProduct.push_back(Factors[Idx].Base); 1694 Factors[Idx].Power >>= 1; 1695 } 1696 if (Factors[0].Power) { 1697 Value *SquareRoot = buildMinimalMultiplyDAG(Builder, Factors); 1698 OuterProduct.push_back(SquareRoot); 1699 OuterProduct.push_back(SquareRoot); 1700 } 1701 if (OuterProduct.size() == 1) 1702 return OuterProduct.front(); 1703 1704 Value *V = buildMultiplyTree(Builder, OuterProduct); 1705 return V; 1706} 1707 1708Value *Reassociate::OptimizeMul(BinaryOperator *I, 1709 SmallVectorImpl<ValueEntry> &Ops) { 1710 // We can only optimize the multiplies when there is a chain of more than 1711 // three, such that a balanced tree might require fewer total multiplies. 1712 if (Ops.size() < 4) 1713 return 0; 1714 1715 // Try to turn linear trees of multiplies without other uses of the 1716 // intermediate stages into minimal multiply DAGs with perfect sub-expression 1717 // re-use. 1718 SmallVector<Factor, 4> Factors; 1719 if (!collectMultiplyFactors(Ops, Factors)) 1720 return 0; // All distinct factors, so nothing left for us to do. 1721 1722 IRBuilder<> Builder(I); 1723 Value *V = buildMinimalMultiplyDAG(Builder, Factors); 1724 if (Ops.empty()) 1725 return V; 1726 1727 ValueEntry NewEntry = ValueEntry(getRank(V), V); 1728 Ops.insert(std::lower_bound(Ops.begin(), Ops.end(), NewEntry), NewEntry); 1729 return 0; 1730} 1731 1732Value *Reassociate::OptimizeExpression(BinaryOperator *I, 1733 SmallVectorImpl<ValueEntry> &Ops) { 1734 // Now that we have the linearized expression tree, try to optimize it. 1735 // Start by folding any constants that we found. 1736 Constant *Cst = 0; 1737 unsigned Opcode = I->getOpcode(); 1738 while (!Ops.empty() && isa<Constant>(Ops.back().Op)) { 1739 Constant *C = cast<Constant>(Ops.pop_back_val().Op); 1740 Cst = Cst ? ConstantExpr::get(Opcode, C, Cst) : C; 1741 } 1742 // If there was nothing but constants then we are done. 1743 if (Ops.empty()) 1744 return Cst; 1745 1746 // Put the combined constant back at the end of the operand list, except if 1747 // there is no point. For example, an add of 0 gets dropped here, while a 1748 // multiplication by zero turns the whole expression into zero. 1749 if (Cst && Cst != ConstantExpr::getBinOpIdentity(Opcode, I->getType())) { 1750 if (Cst == ConstantExpr::getBinOpAbsorber(Opcode, I->getType())) 1751 return Cst; 1752 Ops.push_back(ValueEntry(0, Cst)); 1753 } 1754 1755 if (Ops.size() == 1) return Ops[0].Op; 1756 1757 // Handle destructive annihilation due to identities between elements in the 1758 // argument list here. 1759 unsigned NumOps = Ops.size(); 1760 switch (Opcode) { 1761 default: break; 1762 case Instruction::And: 1763 case Instruction::Or: 1764 if (Value *Result = OptimizeAndOrXor(Opcode, Ops)) 1765 return Result; 1766 break; 1767 1768 case Instruction::Xor: 1769 if (Value *Result = OptimizeXor(I, Ops)) 1770 return Result; 1771 break; 1772 1773 case Instruction::Add: 1774 if (Value *Result = OptimizeAdd(I, Ops)) 1775 return Result; 1776 break; 1777 1778 case Instruction::Mul: 1779 if (Value *Result = OptimizeMul(I, Ops)) 1780 return Result; 1781 break; 1782 } 1783 1784 if (Ops.size() != NumOps) 1785 return OptimizeExpression(I, Ops); 1786 return 0; 1787} 1788 1789/// EraseInst - Zap the given instruction, adding interesting operands to the 1790/// work list. 1791void Reassociate::EraseInst(Instruction *I) { 1792 assert(isInstructionTriviallyDead(I) && "Trivially dead instructions only!"); 1793 SmallVector<Value*, 8> Ops(I->op_begin(), I->op_end()); 1794 // Erase the dead instruction. 1795 ValueRankMap.erase(I); 1796 RedoInsts.remove(I); 1797 I->eraseFromParent(); 1798 // Optimize its operands. 1799 SmallPtrSet<Instruction *, 8> Visited; // Detect self-referential nodes. 1800 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1801 if (Instruction *Op = dyn_cast<Instruction>(Ops[i])) { 1802 // If this is a node in an expression tree, climb to the expression root 1803 // and add that since that's where optimization actually happens. 1804 unsigned Opcode = Op->getOpcode(); 1805 while (Op->hasOneUse() && Op->use_back()->getOpcode() == Opcode && 1806 Visited.insert(Op)) 1807 Op = Op->use_back(); 1808 RedoInsts.insert(Op); 1809 } 1810} 1811 1812/// OptimizeInst - Inspect and optimize the given instruction. Note that erasing 1813/// instructions is not allowed. 1814void Reassociate::OptimizeInst(Instruction *I) { 1815 // Only consider operations that we understand. 1816 if (!isa<BinaryOperator>(I)) 1817 return; 1818 1819 if (I->getOpcode() == Instruction::Shl && 1820 isa<ConstantInt>(I->getOperand(1))) 1821 // If an operand of this shift is a reassociable multiply, or if the shift 1822 // is used by a reassociable multiply or add, turn into a multiply. 1823 if (isReassociableOp(I->getOperand(0), Instruction::Mul) || 1824 (I->hasOneUse() && 1825 (isReassociableOp(I->use_back(), Instruction::Mul) || 1826 isReassociableOp(I->use_back(), Instruction::Add)))) { 1827 Instruction *NI = ConvertShiftToMul(I); 1828 RedoInsts.insert(I); 1829 MadeChange = true; 1830 I = NI; 1831 } 1832 1833 // Floating point binary operators are not associative, but we can still 1834 // commute (some) of them, to canonicalize the order of their operands. 1835 // This can potentially expose more CSE opportunities, and makes writing 1836 // other transformations simpler. 1837 if ((I->getType()->isFloatingPointTy() || I->getType()->isVectorTy())) { 1838 // FAdd and FMul can be commuted. 1839 if (I->getOpcode() != Instruction::FMul && 1840 I->getOpcode() != Instruction::FAdd) 1841 return; 1842 1843 Value *LHS = I->getOperand(0); 1844 Value *RHS = I->getOperand(1); 1845 unsigned LHSRank = getRank(LHS); 1846 unsigned RHSRank = getRank(RHS); 1847 1848 // Sort the operands by rank. 1849 if (RHSRank < LHSRank) { 1850 I->setOperand(0, RHS); 1851 I->setOperand(1, LHS); 1852 } 1853 1854 return; 1855 } 1856 1857 // Do not reassociate boolean (i1) expressions. We want to preserve the 1858 // original order of evaluation for short-circuited comparisons that 1859 // SimplifyCFG has folded to AND/OR expressions. If the expression 1860 // is not further optimized, it is likely to be transformed back to a 1861 // short-circuited form for code gen, and the source order may have been 1862 // optimized for the most likely conditions. 1863 if (I->getType()->isIntegerTy(1)) 1864 return; 1865 1866 // If this is a subtract instruction which is not already in negate form, 1867 // see if we can convert it to X+-Y. 1868 if (I->getOpcode() == Instruction::Sub) { 1869 if (ShouldBreakUpSubtract(I)) { 1870 Instruction *NI = BreakUpSubtract(I); 1871 RedoInsts.insert(I); 1872 MadeChange = true; 1873 I = NI; 1874 } else if (BinaryOperator::isNeg(I)) { 1875 // Otherwise, this is a negation. See if the operand is a multiply tree 1876 // and if this is not an inner node of a multiply tree. 1877 if (isReassociableOp(I->getOperand(1), Instruction::Mul) && 1878 (!I->hasOneUse() || 1879 !isReassociableOp(I->use_back(), Instruction::Mul))) { 1880 Instruction *NI = LowerNegateToMultiply(I); 1881 RedoInsts.insert(I); 1882 MadeChange = true; 1883 I = NI; 1884 } 1885 } 1886 } 1887 1888 // If this instruction is an associative binary operator, process it. 1889 if (!I->isAssociative()) return; 1890 BinaryOperator *BO = cast<BinaryOperator>(I); 1891 1892 // If this is an interior node of a reassociable tree, ignore it until we 1893 // get to the root of the tree, to avoid N^2 analysis. 1894 unsigned Opcode = BO->getOpcode(); 1895 if (BO->hasOneUse() && BO->use_back()->getOpcode() == Opcode) 1896 return; 1897 1898 // If this is an add tree that is used by a sub instruction, ignore it 1899 // until we process the subtract. 1900 if (BO->hasOneUse() && BO->getOpcode() == Instruction::Add && 1901 cast<Instruction>(BO->use_back())->getOpcode() == Instruction::Sub) 1902 return; 1903 1904 ReassociateExpression(BO); 1905} 1906 1907void Reassociate::ReassociateExpression(BinaryOperator *I) { 1908 1909 // First, walk the expression tree, linearizing the tree, collecting the 1910 // operand information. 1911 SmallVector<RepeatedValue, 8> Tree; 1912 MadeChange |= LinearizeExprTree(I, Tree); 1913 SmallVector<ValueEntry, 8> Ops; 1914 Ops.reserve(Tree.size()); 1915 for (unsigned i = 0, e = Tree.size(); i != e; ++i) { 1916 RepeatedValue E = Tree[i]; 1917 Ops.append(E.second.getZExtValue(), 1918 ValueEntry(getRank(E.first), E.first)); 1919 } 1920 1921 DEBUG(dbgs() << "RAIn:\t"; PrintOps(I, Ops); dbgs() << '\n'); 1922 1923 // Now that we have linearized the tree to a list and have gathered all of 1924 // the operands and their ranks, sort the operands by their rank. Use a 1925 // stable_sort so that values with equal ranks will have their relative 1926 // positions maintained (and so the compiler is deterministic). Note that 1927 // this sorts so that the highest ranking values end up at the beginning of 1928 // the vector. 1929 std::stable_sort(Ops.begin(), Ops.end()); 1930 1931 // OptimizeExpression - Now that we have the expression tree in a convenient 1932 // sorted form, optimize it globally if possible. 1933 if (Value *V = OptimizeExpression(I, Ops)) { 1934 if (V == I) 1935 // Self-referential expression in unreachable code. 1936 return; 1937 // This expression tree simplified to something that isn't a tree, 1938 // eliminate it. 1939 DEBUG(dbgs() << "Reassoc to scalar: " << *V << '\n'); 1940 I->replaceAllUsesWith(V); 1941 if (Instruction *VI = dyn_cast<Instruction>(V)) 1942 VI->setDebugLoc(I->getDebugLoc()); 1943 RedoInsts.insert(I); 1944 ++NumAnnihil; 1945 return; 1946 } 1947 1948 // We want to sink immediates as deeply as possible except in the case where 1949 // this is a multiply tree used only by an add, and the immediate is a -1. 1950 // In this case we reassociate to put the negation on the outside so that we 1951 // can fold the negation into the add: (-X)*Y + Z -> Z-X*Y 1952 if (I->getOpcode() == Instruction::Mul && I->hasOneUse() && 1953 cast<Instruction>(I->use_back())->getOpcode() == Instruction::Add && 1954 isa<ConstantInt>(Ops.back().Op) && 1955 cast<ConstantInt>(Ops.back().Op)->isAllOnesValue()) { 1956 ValueEntry Tmp = Ops.pop_back_val(); 1957 Ops.insert(Ops.begin(), Tmp); 1958 } 1959 1960 DEBUG(dbgs() << "RAOut:\t"; PrintOps(I, Ops); dbgs() << '\n'); 1961 1962 if (Ops.size() == 1) { 1963 if (Ops[0].Op == I) 1964 // Self-referential expression in unreachable code. 1965 return; 1966 1967 // This expression tree simplified to something that isn't a tree, 1968 // eliminate it. 1969 I->replaceAllUsesWith(Ops[0].Op); 1970 if (Instruction *OI = dyn_cast<Instruction>(Ops[0].Op)) 1971 OI->setDebugLoc(I->getDebugLoc()); 1972 RedoInsts.insert(I); 1973 return; 1974 } 1975 1976 // Now that we ordered and optimized the expressions, splat them back into 1977 // the expression tree, removing any unneeded nodes. 1978 RewriteExprTree(I, Ops); 1979} 1980 1981bool Reassociate::runOnFunction(Function &F) { 1982 // Calculate the rank map for F 1983 BuildRankMap(F); 1984 1985 MadeChange = false; 1986 for (Function::iterator BI = F.begin(), BE = F.end(); BI != BE; ++BI) { 1987 // Optimize every instruction in the basic block. 1988 for (BasicBlock::iterator II = BI->begin(), IE = BI->end(); II != IE; ) 1989 if (isInstructionTriviallyDead(II)) { 1990 EraseInst(II++); 1991 } else { 1992 OptimizeInst(II); 1993 assert(II->getParent() == BI && "Moved to a different block!"); 1994 ++II; 1995 } 1996 1997 // If this produced extra instructions to optimize, handle them now. 1998 while (!RedoInsts.empty()) { 1999 Instruction *I = RedoInsts.pop_back_val(); 2000 if (isInstructionTriviallyDead(I)) 2001 EraseInst(I); 2002 else 2003 OptimizeInst(I); 2004 } 2005 } 2006 2007 // We are done with the rank map. 2008 RankMap.clear(); 2009 ValueRankMap.clear(); 2010 2011 return MadeChange; 2012} 2013