Reassociate.cpp revision 249423
158551Skris//===- Reassociate.cpp - Reassociate binary expressions -------------------===// 258551Skris// 3228060Sbapt// The LLVM Compiler Infrastructure 4228060Sbapt// 5228060Sbapt// This file is distributed under the University of Illinois Open Source 658551Skris// License. See LICENSE.TXT for details. 7228060Sbapt// 858551Skris//===----------------------------------------------------------------------===// 9228060Sbapt// 10228060Sbapt// This pass reassociates commutative expressions in an order that is designed 11228060Sbapt// to promote better constant propagation, GCSE, LICM, PRE, etc. 12228060Sbapt// 1358551Skris// For example: 4 + (x + 5) -> x + (4 + 5) 14228060Sbapt// 15228060Sbapt// In the implementation of this algorithm, constants are assigned rank = 0, 16228060Sbapt// function arguments are rank = 1, and other values are assigned ranks 17228060Sbapt// corresponding to the reverse post order traversal of current function 1858551Skris// (starting at 2), which effectively gives values in deep loops higher rank 19228060Sbapt// than values not in loops. 20228060Sbapt// 21228060Sbapt//===----------------------------------------------------------------------===// 22228060Sbapt 2358551Skris#define DEBUG_TYPE "reassociate" 24228060Sbapt#include "llvm/Transforms/Scalar.h" 25228060Sbapt#include "llvm/ADT/DenseMap.h" 26228060Sbapt#include "llvm/ADT/PostOrderIterator.h" 27228060Sbapt#include "llvm/ADT/STLExtras.h" 28228060Sbapt#include "llvm/ADT/SetVector.h" 29#include "llvm/ADT/Statistic.h" 30#include "llvm/Assembly/Writer.h" 31#include "llvm/IR/Constants.h" 32#include "llvm/IR/DerivedTypes.h" 33#include "llvm/IR/Function.h" 34#include "llvm/IR/IRBuilder.h" 35#include "llvm/IR/Instructions.h" 36#include "llvm/IR/IntrinsicInst.h" 37#include "llvm/Pass.h" 38#include "llvm/Support/CFG.h" 39#include "llvm/Support/Debug.h" 40#include "llvm/Support/ValueHandle.h" 41#include "llvm/Support/raw_ostream.h" 42#include "llvm/Transforms/Utils/Local.h" 43#include <algorithm> 44using namespace llvm; 45 46STATISTIC(NumChanged, "Number of insts reassociated"); 47STATISTIC(NumAnnihil, "Number of expr tree annihilated"); 48STATISTIC(NumFactor , "Number of multiplies factored"); 49 50namespace { 51 struct ValueEntry { 52 unsigned Rank; 53 Value *Op; 54 ValueEntry(unsigned R, Value *O) : Rank(R), Op(O) {} 55 }; 56 inline bool operator<(const ValueEntry &LHS, const ValueEntry &RHS) { 57 return LHS.Rank > RHS.Rank; // Sort so that highest rank goes to start. 58 } 59} 60 61#ifndef NDEBUG 62/// PrintOps - Print out the expression identified in the Ops list. 63/// 64static void PrintOps(Instruction *I, const SmallVectorImpl<ValueEntry> &Ops) { 65 Module *M = I->getParent()->getParent()->getParent(); 66 dbgs() << Instruction::getOpcodeName(I->getOpcode()) << " " 67 << *Ops[0].Op->getType() << '\t'; 68 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 69 dbgs() << "[ "; 70 WriteAsOperand(dbgs(), Ops[i].Op, false, M); 71 dbgs() << ", #" << Ops[i].Rank << "] "; 72 } 73} 74#endif 75 76namespace { 77 /// \brief Utility class representing a base and exponent pair which form one 78 /// factor of some product. 79 struct Factor { 80 Value *Base; 81 unsigned Power; 82 83 Factor(Value *Base, unsigned Power) : Base(Base), Power(Power) {} 84 85 /// \brief Sort factors by their Base. 86 struct BaseSorter { 87 bool operator()(const Factor &LHS, const Factor &RHS) { 88 return LHS.Base < RHS.Base; 89 } 90 }; 91 92 /// \brief Compare factors for equal bases. 93 struct BaseEqual { 94 bool operator()(const Factor &LHS, const Factor &RHS) { 95 return LHS.Base == RHS.Base; 96 } 97 }; 98 99 /// \brief Sort factors in descending order by their power. 100 struct PowerDescendingSorter { 101 bool operator()(const Factor &LHS, const Factor &RHS) { 102 return LHS.Power > RHS.Power; 103 } 104 }; 105 106 /// \brief Compare factors for equal powers. 107 struct PowerEqual { 108 bool operator()(const Factor &LHS, const Factor &RHS) { 109 return LHS.Power == RHS.Power; 110 } 111 }; 112 }; 113 114 /// Utility class representing a non-constant Xor-operand. We classify 115 /// non-constant Xor-Operands into two categories: 116 /// C1) The operand is in the form "X & C", where C is a constant and C != ~0 117 /// C2) 118 /// C2.1) The operand is in the form of "X | C", where C is a non-zero 119 /// constant. 120 /// C2.2) Any operand E which doesn't fall into C1 and C2.1, we view this 121 /// operand as "E | 0" 122 class XorOpnd { 123 public: 124 XorOpnd(Value *V); 125 const XorOpnd &operator=(const XorOpnd &That); 126 127 bool isInvalid() const { return SymbolicPart == 0; } 128 bool isOrExpr() const { return isOr; } 129 Value *getValue() const { return OrigVal; } 130 Value *getSymbolicPart() const { return SymbolicPart; } 131 unsigned getSymbolicRank() const { return SymbolicRank; } 132 const APInt &getConstPart() const { return ConstPart; } 133 134 void Invalidate() { SymbolicPart = OrigVal = 0; } 135 void setSymbolicRank(unsigned R) { SymbolicRank = R; } 136 137 // Sort the XorOpnd-Pointer in ascending order of symbolic-value-rank. 138 // The purpose is twofold: 139 // 1) Cluster together the operands sharing the same symbolic-value. 140 // 2) Operand having smaller symbolic-value-rank is permuted earlier, which 141 // could potentially shorten crital path, and expose more loop-invariants. 142 // Note that values' rank are basically defined in RPO order (FIXME). 143 // So, if Rank(X) < Rank(Y) < Rank(Z), it means X is defined earlier 144 // than Y which is defined earlier than Z. Permute "x | 1", "Y & 2", 145 // "z" in the order of X-Y-Z is better than any other orders. 146 class PtrSortFunctor { 147 ArrayRef<XorOpnd> A; 148 149 public: 150 PtrSortFunctor(ArrayRef<XorOpnd> Array) : A(Array) {} 151 bool operator()(unsigned LHSIndex, unsigned RHSIndex) { 152 return A[LHSIndex].getSymbolicRank() < A[RHSIndex].getSymbolicRank(); 153 } 154 }; 155 private: 156 Value *OrigVal; 157 Value *SymbolicPart; 158 APInt ConstPart; 159 unsigned SymbolicRank; 160 bool isOr; 161 }; 162} 163 164namespace { 165 class Reassociate : public FunctionPass { 166 DenseMap<BasicBlock*, unsigned> RankMap; 167 DenseMap<AssertingVH<Value>, unsigned> ValueRankMap; 168 SetVector<AssertingVH<Instruction> > RedoInsts; 169 bool MadeChange; 170 public: 171 static char ID; // Pass identification, replacement for typeid 172 Reassociate() : FunctionPass(ID) { 173 initializeReassociatePass(*PassRegistry::getPassRegistry()); 174 } 175 176 bool runOnFunction(Function &F); 177 178 virtual void getAnalysisUsage(AnalysisUsage &AU) const { 179 AU.setPreservesCFG(); 180 } 181 private: 182 void BuildRankMap(Function &F); 183 unsigned getRank(Value *V); 184 void ReassociateExpression(BinaryOperator *I); 185 void RewriteExprTree(BinaryOperator *I, SmallVectorImpl<ValueEntry> &Ops); 186 Value *OptimizeExpression(BinaryOperator *I, 187 SmallVectorImpl<ValueEntry> &Ops); 188 Value *OptimizeAdd(Instruction *I, SmallVectorImpl<ValueEntry> &Ops); 189 Value *OptimizeXor(Instruction *I, SmallVectorImpl<ValueEntry> &Ops); 190 bool CombineXorOpnd(Instruction *I, XorOpnd *Opnd1, APInt &ConstOpnd, 191 Value *&Res); 192 bool CombineXorOpnd(Instruction *I, XorOpnd *Opnd1, XorOpnd *Opnd2, 193 APInt &ConstOpnd, Value *&Res); 194 bool collectMultiplyFactors(SmallVectorImpl<ValueEntry> &Ops, 195 SmallVectorImpl<Factor> &Factors); 196 Value *buildMinimalMultiplyDAG(IRBuilder<> &Builder, 197 SmallVectorImpl<Factor> &Factors); 198 Value *OptimizeMul(BinaryOperator *I, SmallVectorImpl<ValueEntry> &Ops); 199 Value *RemoveFactorFromExpression(Value *V, Value *Factor); 200 void EraseInst(Instruction *I); 201 void OptimizeInst(Instruction *I); 202 }; 203} 204 205XorOpnd::XorOpnd(Value *V) { 206 assert(!isa<ConstantInt>(V) && "No ConstantInt"); 207 OrigVal = V; 208 Instruction *I = dyn_cast<Instruction>(V); 209 SymbolicRank = 0; 210 211 if (I && (I->getOpcode() == Instruction::Or || 212 I->getOpcode() == Instruction::And)) { 213 Value *V0 = I->getOperand(0); 214 Value *V1 = I->getOperand(1); 215 if (isa<ConstantInt>(V0)) 216 std::swap(V0, V1); 217 218 if (ConstantInt *C = dyn_cast<ConstantInt>(V1)) { 219 ConstPart = C->getValue(); 220 SymbolicPart = V0; 221 isOr = (I->getOpcode() == Instruction::Or); 222 return; 223 } 224 } 225 226 // view the operand as "V | 0" 227 SymbolicPart = V; 228 ConstPart = APInt::getNullValue(V->getType()->getIntegerBitWidth()); 229 isOr = true; 230} 231 232const XorOpnd &XorOpnd::operator=(const XorOpnd &That) { 233 OrigVal = That.OrigVal; 234 SymbolicPart = That.SymbolicPart; 235 ConstPart = That.ConstPart; 236 SymbolicRank = That.SymbolicRank; 237 isOr = That.isOr; 238 return *this; 239} 240 241char Reassociate::ID = 0; 242INITIALIZE_PASS(Reassociate, "reassociate", 243 "Reassociate expressions", false, false) 244 245// Public interface to the Reassociate pass 246FunctionPass *llvm::createReassociatePass() { return new Reassociate(); } 247 248/// isReassociableOp - Return true if V is an instruction of the specified 249/// opcode and if it only has one use. 250static BinaryOperator *isReassociableOp(Value *V, unsigned Opcode) { 251 if (V->hasOneUse() && isa<Instruction>(V) && 252 cast<Instruction>(V)->getOpcode() == Opcode) 253 return cast<BinaryOperator>(V); 254 return 0; 255} 256 257static bool isUnmovableInstruction(Instruction *I) { 258 if (I->getOpcode() == Instruction::PHI || 259 I->getOpcode() == Instruction::LandingPad || 260 I->getOpcode() == Instruction::Alloca || 261 I->getOpcode() == Instruction::Load || 262 I->getOpcode() == Instruction::Invoke || 263 (I->getOpcode() == Instruction::Call && 264 !isa<DbgInfoIntrinsic>(I)) || 265 I->getOpcode() == Instruction::UDiv || 266 I->getOpcode() == Instruction::SDiv || 267 I->getOpcode() == Instruction::FDiv || 268 I->getOpcode() == Instruction::URem || 269 I->getOpcode() == Instruction::SRem || 270 I->getOpcode() == Instruction::FRem) 271 return true; 272 return false; 273} 274 275void Reassociate::BuildRankMap(Function &F) { 276 unsigned i = 2; 277 278 // Assign distinct ranks to function arguments 279 for (Function::arg_iterator I = F.arg_begin(), E = F.arg_end(); I != E; ++I) 280 ValueRankMap[&*I] = ++i; 281 282 ReversePostOrderTraversal<Function*> RPOT(&F); 283 for (ReversePostOrderTraversal<Function*>::rpo_iterator I = RPOT.begin(), 284 E = RPOT.end(); I != E; ++I) { 285 BasicBlock *BB = *I; 286 unsigned BBRank = RankMap[BB] = ++i << 16; 287 288 // Walk the basic block, adding precomputed ranks for any instructions that 289 // we cannot move. This ensures that the ranks for these instructions are 290 // all different in the block. 291 for (BasicBlock::iterator I = BB->begin(), E = BB->end(); I != E; ++I) 292 if (isUnmovableInstruction(I)) 293 ValueRankMap[&*I] = ++BBRank; 294 } 295} 296 297unsigned Reassociate::getRank(Value *V) { 298 Instruction *I = dyn_cast<Instruction>(V); 299 if (I == 0) { 300 if (isa<Argument>(V)) return ValueRankMap[V]; // Function argument. 301 return 0; // Otherwise it's a global or constant, rank 0. 302 } 303 304 if (unsigned Rank = ValueRankMap[I]) 305 return Rank; // Rank already known? 306 307 // If this is an expression, return the 1+MAX(rank(LHS), rank(RHS)) so that 308 // we can reassociate expressions for code motion! Since we do not recurse 309 // for PHI nodes, we cannot have infinite recursion here, because there 310 // cannot be loops in the value graph that do not go through PHI nodes. 311 unsigned Rank = 0, MaxRank = RankMap[I->getParent()]; 312 for (unsigned i = 0, e = I->getNumOperands(); 313 i != e && Rank != MaxRank; ++i) 314 Rank = std::max(Rank, getRank(I->getOperand(i))); 315 316 // If this is a not or neg instruction, do not count it for rank. This 317 // assures us that X and ~X will have the same rank. 318 if (!I->getType()->isIntegerTy() || 319 (!BinaryOperator::isNot(I) && !BinaryOperator::isNeg(I))) 320 ++Rank; 321 322 //DEBUG(dbgs() << "Calculated Rank[" << V->getName() << "] = " 323 // << Rank << "\n"); 324 325 return ValueRankMap[I] = Rank; 326} 327 328/// LowerNegateToMultiply - Replace 0-X with X*-1. 329/// 330static BinaryOperator *LowerNegateToMultiply(Instruction *Neg) { 331 Constant *Cst = Constant::getAllOnesValue(Neg->getType()); 332 333 BinaryOperator *Res = 334 BinaryOperator::CreateMul(Neg->getOperand(1), Cst, "",Neg); 335 Neg->setOperand(1, Constant::getNullValue(Neg->getType())); // Drop use of op. 336 Res->takeName(Neg); 337 Neg->replaceAllUsesWith(Res); 338 Res->setDebugLoc(Neg->getDebugLoc()); 339 return Res; 340} 341 342/// CarmichaelShift - Returns k such that lambda(2^Bitwidth) = 2^k, where lambda 343/// is the Carmichael function. This means that x^(2^k) === 1 mod 2^Bitwidth for 344/// every odd x, i.e. x^(2^k) = 1 for every odd x in Bitwidth-bit arithmetic. 345/// Note that 0 <= k < Bitwidth, and if Bitwidth > 3 then x^(2^k) = 0 for every 346/// even x in Bitwidth-bit arithmetic. 347static unsigned CarmichaelShift(unsigned Bitwidth) { 348 if (Bitwidth < 3) 349 return Bitwidth - 1; 350 return Bitwidth - 2; 351} 352 353/// IncorporateWeight - Add the extra weight 'RHS' to the existing weight 'LHS', 354/// reducing the combined weight using any special properties of the operation. 355/// The existing weight LHS represents the computation X op X op ... op X where 356/// X occurs LHS times. The combined weight represents X op X op ... op X with 357/// X occurring LHS + RHS times. If op is "Xor" for example then the combined 358/// operation is equivalent to X if LHS + RHS is odd, or 0 if LHS + RHS is even; 359/// the routine returns 1 in LHS in the first case, and 0 in LHS in the second. 360static void IncorporateWeight(APInt &LHS, const APInt &RHS, unsigned Opcode) { 361 // If we were working with infinite precision arithmetic then the combined 362 // weight would be LHS + RHS. But we are using finite precision arithmetic, 363 // and the APInt sum LHS + RHS may not be correct if it wraps (it is correct 364 // for nilpotent operations and addition, but not for idempotent operations 365 // and multiplication), so it is important to correctly reduce the combined 366 // weight back into range if wrapping would be wrong. 367 368 // If RHS is zero then the weight didn't change. 369 if (RHS.isMinValue()) 370 return; 371 // If LHS is zero then the combined weight is RHS. 372 if (LHS.isMinValue()) { 373 LHS = RHS; 374 return; 375 } 376 // From this point on we know that neither LHS nor RHS is zero. 377 378 if (Instruction::isIdempotent(Opcode)) { 379 // Idempotent means X op X === X, so any non-zero weight is equivalent to a 380 // weight of 1. Keeping weights at zero or one also means that wrapping is 381 // not a problem. 382 assert(LHS == 1 && RHS == 1 && "Weights not reduced!"); 383 return; // Return a weight of 1. 384 } 385 if (Instruction::isNilpotent(Opcode)) { 386 // Nilpotent means X op X === 0, so reduce weights modulo 2. 387 assert(LHS == 1 && RHS == 1 && "Weights not reduced!"); 388 LHS = 0; // 1 + 1 === 0 modulo 2. 389 return; 390 } 391 if (Opcode == Instruction::Add) { 392 // TODO: Reduce the weight by exploiting nsw/nuw? 393 LHS += RHS; 394 return; 395 } 396 397 assert(Opcode == Instruction::Mul && "Unknown associative operation!"); 398 unsigned Bitwidth = LHS.getBitWidth(); 399 // If CM is the Carmichael number then a weight W satisfying W >= CM+Bitwidth 400 // can be replaced with W-CM. That's because x^W=x^(W-CM) for every Bitwidth 401 // bit number x, since either x is odd in which case x^CM = 1, or x is even in 402 // which case both x^W and x^(W - CM) are zero. By subtracting off multiples 403 // of CM like this weights can always be reduced to the range [0, CM+Bitwidth) 404 // which by a happy accident means that they can always be represented using 405 // Bitwidth bits. 406 // TODO: Reduce the weight by exploiting nsw/nuw? (Could do much better than 407 // the Carmichael number). 408 if (Bitwidth > 3) { 409 /// CM - The value of Carmichael's lambda function. 410 APInt CM = APInt::getOneBitSet(Bitwidth, CarmichaelShift(Bitwidth)); 411 // Any weight W >= Threshold can be replaced with W - CM. 412 APInt Threshold = CM + Bitwidth; 413 assert(LHS.ult(Threshold) && RHS.ult(Threshold) && "Weights not reduced!"); 414 // For Bitwidth 4 or more the following sum does not overflow. 415 LHS += RHS; 416 while (LHS.uge(Threshold)) 417 LHS -= CM; 418 } else { 419 // To avoid problems with overflow do everything the same as above but using 420 // a larger type. 421 unsigned CM = 1U << CarmichaelShift(Bitwidth); 422 unsigned Threshold = CM + Bitwidth; 423 assert(LHS.getZExtValue() < Threshold && RHS.getZExtValue() < Threshold && 424 "Weights not reduced!"); 425 unsigned Total = LHS.getZExtValue() + RHS.getZExtValue(); 426 while (Total >= Threshold) 427 Total -= CM; 428 LHS = Total; 429 } 430} 431 432typedef std::pair<Value*, APInt> RepeatedValue; 433 434/// LinearizeExprTree - Given an associative binary expression, return the leaf 435/// nodes in Ops along with their weights (how many times the leaf occurs). The 436/// original expression is the same as 437/// (Ops[0].first op Ops[0].first op ... Ops[0].first) <- Ops[0].second times 438/// op 439/// (Ops[1].first op Ops[1].first op ... Ops[1].first) <- Ops[1].second times 440/// op 441/// ... 442/// op 443/// (Ops[N].first op Ops[N].first op ... Ops[N].first) <- Ops[N].second times 444/// 445/// Note that the values Ops[0].first, ..., Ops[N].first are all distinct. 446/// 447/// This routine may modify the function, in which case it returns 'true'. The 448/// changes it makes may well be destructive, changing the value computed by 'I' 449/// to something completely different. Thus if the routine returns 'true' then 450/// you MUST either replace I with a new expression computed from the Ops array, 451/// or use RewriteExprTree to put the values back in. 452/// 453/// A leaf node is either not a binary operation of the same kind as the root 454/// node 'I' (i.e. is not a binary operator at all, or is, but with a different 455/// opcode), or is the same kind of binary operator but has a use which either 456/// does not belong to the expression, or does belong to the expression but is 457/// a leaf node. Every leaf node has at least one use that is a non-leaf node 458/// of the expression, while for non-leaf nodes (except for the root 'I') every 459/// use is a non-leaf node of the expression. 460/// 461/// For example: 462/// expression graph node names 463/// 464/// + | I 465/// / \ | 466/// + + | A, B 467/// / \ / \ | 468/// * + * | C, D, E 469/// / \ / \ / \ | 470/// + * | F, G 471/// 472/// The leaf nodes are C, E, F and G. The Ops array will contain (maybe not in 473/// that order) (C, 1), (E, 1), (F, 2), (G, 2). 474/// 475/// The expression is maximal: if some instruction is a binary operator of the 476/// same kind as 'I', and all of its uses are non-leaf nodes of the expression, 477/// then the instruction also belongs to the expression, is not a leaf node of 478/// it, and its operands also belong to the expression (but may be leaf nodes). 479/// 480/// NOTE: This routine will set operands of non-leaf non-root nodes to undef in 481/// order to ensure that every non-root node in the expression has *exactly one* 482/// use by a non-leaf node of the expression. This destruction means that the 483/// caller MUST either replace 'I' with a new expression or use something like 484/// RewriteExprTree to put the values back in if the routine indicates that it 485/// made a change by returning 'true'. 486/// 487/// In the above example either the right operand of A or the left operand of B 488/// will be replaced by undef. If it is B's operand then this gives: 489/// 490/// + | I 491/// / \ | 492/// + + | A, B - operand of B replaced with undef 493/// / \ \ | 494/// * + * | C, D, E 495/// / \ / \ / \ | 496/// + * | F, G 497/// 498/// Note that such undef operands can only be reached by passing through 'I'. 499/// For example, if you visit operands recursively starting from a leaf node 500/// then you will never see such an undef operand unless you get back to 'I', 501/// which requires passing through a phi node. 502/// 503/// Note that this routine may also mutate binary operators of the wrong type 504/// that have all uses inside the expression (i.e. only used by non-leaf nodes 505/// of the expression) if it can turn them into binary operators of the right 506/// type and thus make the expression bigger. 507 508static bool LinearizeExprTree(BinaryOperator *I, 509 SmallVectorImpl<RepeatedValue> &Ops) { 510 DEBUG(dbgs() << "LINEARIZE: " << *I << '\n'); 511 unsigned Bitwidth = I->getType()->getScalarType()->getPrimitiveSizeInBits(); 512 unsigned Opcode = I->getOpcode(); 513 assert(Instruction::isAssociative(Opcode) && 514 Instruction::isCommutative(Opcode) && 515 "Expected an associative and commutative operation!"); 516 517 // Visit all operands of the expression, keeping track of their weight (the 518 // number of paths from the expression root to the operand, or if you like 519 // the number of times that operand occurs in the linearized expression). 520 // For example, if I = X + A, where X = A + B, then I, X and B have weight 1 521 // while A has weight two. 522 523 // Worklist of non-leaf nodes (their operands are in the expression too) along 524 // with their weights, representing a certain number of paths to the operator. 525 // If an operator occurs in the worklist multiple times then we found multiple 526 // ways to get to it. 527 SmallVector<std::pair<BinaryOperator*, APInt>, 8> Worklist; // (Op, Weight) 528 Worklist.push_back(std::make_pair(I, APInt(Bitwidth, 1))); 529 bool MadeChange = false; 530 531 // Leaves of the expression are values that either aren't the right kind of 532 // operation (eg: a constant, or a multiply in an add tree), or are, but have 533 // some uses that are not inside the expression. For example, in I = X + X, 534 // X = A + B, the value X has two uses (by I) that are in the expression. If 535 // X has any other uses, for example in a return instruction, then we consider 536 // X to be a leaf, and won't analyze it further. When we first visit a value, 537 // if it has more than one use then at first we conservatively consider it to 538 // be a leaf. Later, as the expression is explored, we may discover some more 539 // uses of the value from inside the expression. If all uses turn out to be 540 // from within the expression (and the value is a binary operator of the right 541 // kind) then the value is no longer considered to be a leaf, and its operands 542 // are explored. 543 544 // Leaves - Keeps track of the set of putative leaves as well as the number of 545 // paths to each leaf seen so far. 546 typedef DenseMap<Value*, APInt> LeafMap; 547 LeafMap Leaves; // Leaf -> Total weight so far. 548 SmallVector<Value*, 8> LeafOrder; // Ensure deterministic leaf output order. 549 550#ifndef NDEBUG 551 SmallPtrSet<Value*, 8> Visited; // For sanity checking the iteration scheme. 552#endif 553 while (!Worklist.empty()) { 554 std::pair<BinaryOperator*, APInt> P = Worklist.pop_back_val(); 555 I = P.first; // We examine the operands of this binary operator. 556 557 for (unsigned OpIdx = 0; OpIdx < 2; ++OpIdx) { // Visit operands. 558 Value *Op = I->getOperand(OpIdx); 559 APInt Weight = P.second; // Number of paths to this operand. 560 DEBUG(dbgs() << "OPERAND: " << *Op << " (" << Weight << ")\n"); 561 assert(!Op->use_empty() && "No uses, so how did we get to it?!"); 562 563 // If this is a binary operation of the right kind with only one use then 564 // add its operands to the expression. 565 if (BinaryOperator *BO = isReassociableOp(Op, Opcode)) { 566 assert(Visited.insert(Op) && "Not first visit!"); 567 DEBUG(dbgs() << "DIRECT ADD: " << *Op << " (" << Weight << ")\n"); 568 Worklist.push_back(std::make_pair(BO, Weight)); 569 continue; 570 } 571 572 // Appears to be a leaf. Is the operand already in the set of leaves? 573 LeafMap::iterator It = Leaves.find(Op); 574 if (It == Leaves.end()) { 575 // Not in the leaf map. Must be the first time we saw this operand. 576 assert(Visited.insert(Op) && "Not first visit!"); 577 if (!Op->hasOneUse()) { 578 // This value has uses not accounted for by the expression, so it is 579 // not safe to modify. Mark it as being a leaf. 580 DEBUG(dbgs() << "ADD USES LEAF: " << *Op << " (" << Weight << ")\n"); 581 LeafOrder.push_back(Op); 582 Leaves[Op] = Weight; 583 continue; 584 } 585 // No uses outside the expression, try morphing it. 586 } else if (It != Leaves.end()) { 587 // Already in the leaf map. 588 assert(Visited.count(Op) && "In leaf map but not visited!"); 589 590 // Update the number of paths to the leaf. 591 IncorporateWeight(It->second, Weight, Opcode); 592 593#if 0 // TODO: Re-enable once PR13021 is fixed. 594 // The leaf already has one use from inside the expression. As we want 595 // exactly one such use, drop this new use of the leaf. 596 assert(!Op->hasOneUse() && "Only one use, but we got here twice!"); 597 I->setOperand(OpIdx, UndefValue::get(I->getType())); 598 MadeChange = true; 599 600 // If the leaf is a binary operation of the right kind and we now see 601 // that its multiple original uses were in fact all by nodes belonging 602 // to the expression, then no longer consider it to be a leaf and add 603 // its operands to the expression. 604 if (BinaryOperator *BO = isReassociableOp(Op, Opcode)) { 605 DEBUG(dbgs() << "UNLEAF: " << *Op << " (" << It->second << ")\n"); 606 Worklist.push_back(std::make_pair(BO, It->second)); 607 Leaves.erase(It); 608 continue; 609 } 610#endif 611 612 // If we still have uses that are not accounted for by the expression 613 // then it is not safe to modify the value. 614 if (!Op->hasOneUse()) 615 continue; 616 617 // No uses outside the expression, try morphing it. 618 Weight = It->second; 619 Leaves.erase(It); // Since the value may be morphed below. 620 } 621 622 // At this point we have a value which, first of all, is not a binary 623 // expression of the right kind, and secondly, is only used inside the 624 // expression. This means that it can safely be modified. See if we 625 // can usefully morph it into an expression of the right kind. 626 assert((!isa<Instruction>(Op) || 627 cast<Instruction>(Op)->getOpcode() != Opcode) && 628 "Should have been handled above!"); 629 assert(Op->hasOneUse() && "Has uses outside the expression tree!"); 630 631 // If this is a multiply expression, turn any internal negations into 632 // multiplies by -1 so they can be reassociated. 633 BinaryOperator *BO = dyn_cast<BinaryOperator>(Op); 634 if (Opcode == Instruction::Mul && BO && BinaryOperator::isNeg(BO)) { 635 DEBUG(dbgs() << "MORPH LEAF: " << *Op << " (" << Weight << ") TO "); 636 BO = LowerNegateToMultiply(BO); 637 DEBUG(dbgs() << *BO << 'n'); 638 Worklist.push_back(std::make_pair(BO, Weight)); 639 MadeChange = true; 640 continue; 641 } 642 643 // Failed to morph into an expression of the right type. This really is 644 // a leaf. 645 DEBUG(dbgs() << "ADD LEAF: " << *Op << " (" << Weight << ")\n"); 646 assert(!isReassociableOp(Op, Opcode) && "Value was morphed?"); 647 LeafOrder.push_back(Op); 648 Leaves[Op] = Weight; 649 } 650 } 651 652 // The leaves, repeated according to their weights, represent the linearized 653 // form of the expression. 654 for (unsigned i = 0, e = LeafOrder.size(); i != e; ++i) { 655 Value *V = LeafOrder[i]; 656 LeafMap::iterator It = Leaves.find(V); 657 if (It == Leaves.end()) 658 // Node initially thought to be a leaf wasn't. 659 continue; 660 assert(!isReassociableOp(V, Opcode) && "Shouldn't be a leaf!"); 661 APInt Weight = It->second; 662 if (Weight.isMinValue()) 663 // Leaf already output or weight reduction eliminated it. 664 continue; 665 // Ensure the leaf is only output once. 666 It->second = 0; 667 Ops.push_back(std::make_pair(V, Weight)); 668 } 669 670 // For nilpotent operations or addition there may be no operands, for example 671 // because the expression was "X xor X" or consisted of 2^Bitwidth additions: 672 // in both cases the weight reduces to 0 causing the value to be skipped. 673 if (Ops.empty()) { 674 Constant *Identity = ConstantExpr::getBinOpIdentity(Opcode, I->getType()); 675 assert(Identity && "Associative operation without identity!"); 676 Ops.push_back(std::make_pair(Identity, APInt(Bitwidth, 1))); 677 } 678 679 return MadeChange; 680} 681 682// RewriteExprTree - Now that the operands for this expression tree are 683// linearized and optimized, emit them in-order. 684void Reassociate::RewriteExprTree(BinaryOperator *I, 685 SmallVectorImpl<ValueEntry> &Ops) { 686 assert(Ops.size() > 1 && "Single values should be used directly!"); 687 688 // Since our optimizations should never increase the number of operations, the 689 // new expression can usually be written reusing the existing binary operators 690 // from the original expression tree, without creating any new instructions, 691 // though the rewritten expression may have a completely different topology. 692 // We take care to not change anything if the new expression will be the same 693 // as the original. If more than trivial changes (like commuting operands) 694 // were made then we are obliged to clear out any optional subclass data like 695 // nsw flags. 696 697 /// NodesToRewrite - Nodes from the original expression available for writing 698 /// the new expression into. 699 SmallVector<BinaryOperator*, 8> NodesToRewrite; 700 unsigned Opcode = I->getOpcode(); 701 BinaryOperator *Op = I; 702 703 /// NotRewritable - The operands being written will be the leaves of the new 704 /// expression and must not be used as inner nodes (via NodesToRewrite) by 705 /// mistake. Inner nodes are always reassociable, and usually leaves are not 706 /// (if they were they would have been incorporated into the expression and so 707 /// would not be leaves), so most of the time there is no danger of this. But 708 /// in rare cases a leaf may become reassociable if an optimization kills uses 709 /// of it, or it may momentarily become reassociable during rewriting (below) 710 /// due it being removed as an operand of one of its uses. Ensure that misuse 711 /// of leaf nodes as inner nodes cannot occur by remembering all of the future 712 /// leaves and refusing to reuse any of them as inner nodes. 713 SmallPtrSet<Value*, 8> NotRewritable; 714 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 715 NotRewritable.insert(Ops[i].Op); 716 717 // ExpressionChanged - Non-null if the rewritten expression differs from the 718 // original in some non-trivial way, requiring the clearing of optional flags. 719 // Flags are cleared from the operator in ExpressionChanged up to I inclusive. 720 BinaryOperator *ExpressionChanged = 0; 721 for (unsigned i = 0; ; ++i) { 722 // The last operation (which comes earliest in the IR) is special as both 723 // operands will come from Ops, rather than just one with the other being 724 // a subexpression. 725 if (i+2 == Ops.size()) { 726 Value *NewLHS = Ops[i].Op; 727 Value *NewRHS = Ops[i+1].Op; 728 Value *OldLHS = Op->getOperand(0); 729 Value *OldRHS = Op->getOperand(1); 730 731 if (NewLHS == OldLHS && NewRHS == OldRHS) 732 // Nothing changed, leave it alone. 733 break; 734 735 if (NewLHS == OldRHS && NewRHS == OldLHS) { 736 // The order of the operands was reversed. Swap them. 737 DEBUG(dbgs() << "RA: " << *Op << '\n'); 738 Op->swapOperands(); 739 DEBUG(dbgs() << "TO: " << *Op << '\n'); 740 MadeChange = true; 741 ++NumChanged; 742 break; 743 } 744 745 // The new operation differs non-trivially from the original. Overwrite 746 // the old operands with the new ones. 747 DEBUG(dbgs() << "RA: " << *Op << '\n'); 748 if (NewLHS != OldLHS) { 749 BinaryOperator *BO = isReassociableOp(OldLHS, Opcode); 750 if (BO && !NotRewritable.count(BO)) 751 NodesToRewrite.push_back(BO); 752 Op->setOperand(0, NewLHS); 753 } 754 if (NewRHS != OldRHS) { 755 BinaryOperator *BO = isReassociableOp(OldRHS, Opcode); 756 if (BO && !NotRewritable.count(BO)) 757 NodesToRewrite.push_back(BO); 758 Op->setOperand(1, NewRHS); 759 } 760 DEBUG(dbgs() << "TO: " << *Op << '\n'); 761 762 ExpressionChanged = Op; 763 MadeChange = true; 764 ++NumChanged; 765 766 break; 767 } 768 769 // Not the last operation. The left-hand side will be a sub-expression 770 // while the right-hand side will be the current element of Ops. 771 Value *NewRHS = Ops[i].Op; 772 if (NewRHS != Op->getOperand(1)) { 773 DEBUG(dbgs() << "RA: " << *Op << '\n'); 774 if (NewRHS == Op->getOperand(0)) { 775 // The new right-hand side was already present as the left operand. If 776 // we are lucky then swapping the operands will sort out both of them. 777 Op->swapOperands(); 778 } else { 779 // Overwrite with the new right-hand side. 780 BinaryOperator *BO = isReassociableOp(Op->getOperand(1), Opcode); 781 if (BO && !NotRewritable.count(BO)) 782 NodesToRewrite.push_back(BO); 783 Op->setOperand(1, NewRHS); 784 ExpressionChanged = Op; 785 } 786 DEBUG(dbgs() << "TO: " << *Op << '\n'); 787 MadeChange = true; 788 ++NumChanged; 789 } 790 791 // Now deal with the left-hand side. If this is already an operation node 792 // from the original expression then just rewrite the rest of the expression 793 // into it. 794 BinaryOperator *BO = isReassociableOp(Op->getOperand(0), Opcode); 795 if (BO && !NotRewritable.count(BO)) { 796 Op = BO; 797 continue; 798 } 799 800 // Otherwise, grab a spare node from the original expression and use that as 801 // the left-hand side. If there are no nodes left then the optimizers made 802 // an expression with more nodes than the original! This usually means that 803 // they did something stupid but it might mean that the problem was just too 804 // hard (finding the mimimal number of multiplications needed to realize a 805 // multiplication expression is NP-complete). Whatever the reason, smart or 806 // stupid, create a new node if there are none left. 807 BinaryOperator *NewOp; 808 if (NodesToRewrite.empty()) { 809 Constant *Undef = UndefValue::get(I->getType()); 810 NewOp = BinaryOperator::Create(Instruction::BinaryOps(Opcode), 811 Undef, Undef, "", I); 812 } else { 813 NewOp = NodesToRewrite.pop_back_val(); 814 } 815 816 DEBUG(dbgs() << "RA: " << *Op << '\n'); 817 Op->setOperand(0, NewOp); 818 DEBUG(dbgs() << "TO: " << *Op << '\n'); 819 ExpressionChanged = Op; 820 MadeChange = true; 821 ++NumChanged; 822 Op = NewOp; 823 } 824 825 // If the expression changed non-trivially then clear out all subclass data 826 // starting from the operator specified in ExpressionChanged, and compactify 827 // the operators to just before the expression root to guarantee that the 828 // expression tree is dominated by all of Ops. 829 if (ExpressionChanged) 830 do { 831 ExpressionChanged->clearSubclassOptionalData(); 832 if (ExpressionChanged == I) 833 break; 834 ExpressionChanged->moveBefore(I); 835 ExpressionChanged = cast<BinaryOperator>(*ExpressionChanged->use_begin()); 836 } while (1); 837 838 // Throw away any left over nodes from the original expression. 839 for (unsigned i = 0, e = NodesToRewrite.size(); i != e; ++i) 840 RedoInsts.insert(NodesToRewrite[i]); 841} 842 843/// NegateValue - Insert instructions before the instruction pointed to by BI, 844/// that computes the negative version of the value specified. The negative 845/// version of the value is returned, and BI is left pointing at the instruction 846/// that should be processed next by the reassociation pass. 847static Value *NegateValue(Value *V, Instruction *BI) { 848 if (Constant *C = dyn_cast<Constant>(V)) 849 return ConstantExpr::getNeg(C); 850 851 // We are trying to expose opportunity for reassociation. One of the things 852 // that we want to do to achieve this is to push a negation as deep into an 853 // expression chain as possible, to expose the add instructions. In practice, 854 // this means that we turn this: 855 // X = -(A+12+C+D) into X = -A + -12 + -C + -D = -12 + -A + -C + -D 856 // so that later, a: Y = 12+X could get reassociated with the -12 to eliminate 857 // the constants. We assume that instcombine will clean up the mess later if 858 // we introduce tons of unnecessary negation instructions. 859 // 860 if (BinaryOperator *I = isReassociableOp(V, Instruction::Add)) { 861 // Push the negates through the add. 862 I->setOperand(0, NegateValue(I->getOperand(0), BI)); 863 I->setOperand(1, NegateValue(I->getOperand(1), BI)); 864 865 // We must move the add instruction here, because the neg instructions do 866 // not dominate the old add instruction in general. By moving it, we are 867 // assured that the neg instructions we just inserted dominate the 868 // instruction we are about to insert after them. 869 // 870 I->moveBefore(BI); 871 I->setName(I->getName()+".neg"); 872 return I; 873 } 874 875 // Okay, we need to materialize a negated version of V with an instruction. 876 // Scan the use lists of V to see if we have one already. 877 for (Value::use_iterator UI = V->use_begin(), E = V->use_end(); UI != E;++UI){ 878 User *U = *UI; 879 if (!BinaryOperator::isNeg(U)) continue; 880 881 // We found one! Now we have to make sure that the definition dominates 882 // this use. We do this by moving it to the entry block (if it is a 883 // non-instruction value) or right after the definition. These negates will 884 // be zapped by reassociate later, so we don't need much finesse here. 885 BinaryOperator *TheNeg = cast<BinaryOperator>(U); 886 887 // Verify that the negate is in this function, V might be a constant expr. 888 if (TheNeg->getParent()->getParent() != BI->getParent()->getParent()) 889 continue; 890 891 BasicBlock::iterator InsertPt; 892 if (Instruction *InstInput = dyn_cast<Instruction>(V)) { 893 if (InvokeInst *II = dyn_cast<InvokeInst>(InstInput)) { 894 InsertPt = II->getNormalDest()->begin(); 895 } else { 896 InsertPt = InstInput; 897 ++InsertPt; 898 } 899 while (isa<PHINode>(InsertPt)) ++InsertPt; 900 } else { 901 InsertPt = TheNeg->getParent()->getParent()->getEntryBlock().begin(); 902 } 903 TheNeg->moveBefore(InsertPt); 904 return TheNeg; 905 } 906 907 // Insert a 'neg' instruction that subtracts the value from zero to get the 908 // negation. 909 return BinaryOperator::CreateNeg(V, V->getName() + ".neg", BI); 910} 911 912/// ShouldBreakUpSubtract - Return true if we should break up this subtract of 913/// X-Y into (X + -Y). 914static bool ShouldBreakUpSubtract(Instruction *Sub) { 915 // If this is a negation, we can't split it up! 916 if (BinaryOperator::isNeg(Sub)) 917 return false; 918 919 // Don't bother to break this up unless either the LHS is an associable add or 920 // subtract or if this is only used by one. 921 if (isReassociableOp(Sub->getOperand(0), Instruction::Add) || 922 isReassociableOp(Sub->getOperand(0), Instruction::Sub)) 923 return true; 924 if (isReassociableOp(Sub->getOperand(1), Instruction::Add) || 925 isReassociableOp(Sub->getOperand(1), Instruction::Sub)) 926 return true; 927 if (Sub->hasOneUse() && 928 (isReassociableOp(Sub->use_back(), Instruction::Add) || 929 isReassociableOp(Sub->use_back(), Instruction::Sub))) 930 return true; 931 932 return false; 933} 934 935/// BreakUpSubtract - If we have (X-Y), and if either X is an add, or if this is 936/// only used by an add, transform this into (X+(0-Y)) to promote better 937/// reassociation. 938static BinaryOperator *BreakUpSubtract(Instruction *Sub) { 939 // Convert a subtract into an add and a neg instruction. This allows sub 940 // instructions to be commuted with other add instructions. 941 // 942 // Calculate the negative value of Operand 1 of the sub instruction, 943 // and set it as the RHS of the add instruction we just made. 944 // 945 Value *NegVal = NegateValue(Sub->getOperand(1), Sub); 946 BinaryOperator *New = 947 BinaryOperator::CreateAdd(Sub->getOperand(0), NegVal, "", Sub); 948 Sub->setOperand(0, Constant::getNullValue(Sub->getType())); // Drop use of op. 949 Sub->setOperand(1, Constant::getNullValue(Sub->getType())); // Drop use of op. 950 New->takeName(Sub); 951 952 // Everyone now refers to the add instruction. 953 Sub->replaceAllUsesWith(New); 954 New->setDebugLoc(Sub->getDebugLoc()); 955 956 DEBUG(dbgs() << "Negated: " << *New << '\n'); 957 return New; 958} 959 960/// ConvertShiftToMul - If this is a shift of a reassociable multiply or is used 961/// by one, change this into a multiply by a constant to assist with further 962/// reassociation. 963static BinaryOperator *ConvertShiftToMul(Instruction *Shl) { 964 Constant *MulCst = ConstantInt::get(Shl->getType(), 1); 965 MulCst = ConstantExpr::getShl(MulCst, cast<Constant>(Shl->getOperand(1))); 966 967 BinaryOperator *Mul = 968 BinaryOperator::CreateMul(Shl->getOperand(0), MulCst, "", Shl); 969 Shl->setOperand(0, UndefValue::get(Shl->getType())); // Drop use of op. 970 Mul->takeName(Shl); 971 Shl->replaceAllUsesWith(Mul); 972 Mul->setDebugLoc(Shl->getDebugLoc()); 973 return Mul; 974} 975 976/// FindInOperandList - Scan backwards and forwards among values with the same 977/// rank as element i to see if X exists. If X does not exist, return i. This 978/// is useful when scanning for 'x' when we see '-x' because they both get the 979/// same rank. 980static unsigned FindInOperandList(SmallVectorImpl<ValueEntry> &Ops, unsigned i, 981 Value *X) { 982 unsigned XRank = Ops[i].Rank; 983 unsigned e = Ops.size(); 984 for (unsigned j = i+1; j != e && Ops[j].Rank == XRank; ++j) 985 if (Ops[j].Op == X) 986 return j; 987 // Scan backwards. 988 for (unsigned j = i-1; j != ~0U && Ops[j].Rank == XRank; --j) 989 if (Ops[j].Op == X) 990 return j; 991 return i; 992} 993 994/// EmitAddTreeOfValues - Emit a tree of add instructions, summing Ops together 995/// and returning the result. Insert the tree before I. 996static Value *EmitAddTreeOfValues(Instruction *I, 997 SmallVectorImpl<WeakVH> &Ops){ 998 if (Ops.size() == 1) return Ops.back(); 999 1000 Value *V1 = Ops.back(); 1001 Ops.pop_back(); 1002 Value *V2 = EmitAddTreeOfValues(I, Ops); 1003 return BinaryOperator::CreateAdd(V2, V1, "tmp", I); 1004} 1005 1006/// RemoveFactorFromExpression - If V is an expression tree that is a 1007/// multiplication sequence, and if this sequence contains a multiply by Factor, 1008/// remove Factor from the tree and return the new tree. 1009Value *Reassociate::RemoveFactorFromExpression(Value *V, Value *Factor) { 1010 BinaryOperator *BO = isReassociableOp(V, Instruction::Mul); 1011 if (!BO) return 0; 1012 1013 SmallVector<RepeatedValue, 8> Tree; 1014 MadeChange |= LinearizeExprTree(BO, Tree); 1015 SmallVector<ValueEntry, 8> Factors; 1016 Factors.reserve(Tree.size()); 1017 for (unsigned i = 0, e = Tree.size(); i != e; ++i) { 1018 RepeatedValue E = Tree[i]; 1019 Factors.append(E.second.getZExtValue(), 1020 ValueEntry(getRank(E.first), E.first)); 1021 } 1022 1023 bool FoundFactor = false; 1024 bool NeedsNegate = false; 1025 for (unsigned i = 0, e = Factors.size(); i != e; ++i) { 1026 if (Factors[i].Op == Factor) { 1027 FoundFactor = true; 1028 Factors.erase(Factors.begin()+i); 1029 break; 1030 } 1031 1032 // If this is a negative version of this factor, remove it. 1033 if (ConstantInt *FC1 = dyn_cast<ConstantInt>(Factor)) 1034 if (ConstantInt *FC2 = dyn_cast<ConstantInt>(Factors[i].Op)) 1035 if (FC1->getValue() == -FC2->getValue()) { 1036 FoundFactor = NeedsNegate = true; 1037 Factors.erase(Factors.begin()+i); 1038 break; 1039 } 1040 } 1041 1042 if (!FoundFactor) { 1043 // Make sure to restore the operands to the expression tree. 1044 RewriteExprTree(BO, Factors); 1045 return 0; 1046 } 1047 1048 BasicBlock::iterator InsertPt = BO; ++InsertPt; 1049 1050 // If this was just a single multiply, remove the multiply and return the only 1051 // remaining operand. 1052 if (Factors.size() == 1) { 1053 RedoInsts.insert(BO); 1054 V = Factors[0].Op; 1055 } else { 1056 RewriteExprTree(BO, Factors); 1057 V = BO; 1058 } 1059 1060 if (NeedsNegate) 1061 V = BinaryOperator::CreateNeg(V, "neg", InsertPt); 1062 1063 return V; 1064} 1065 1066/// FindSingleUseMultiplyFactors - If V is a single-use multiply, recursively 1067/// add its operands as factors, otherwise add V to the list of factors. 1068/// 1069/// Ops is the top-level list of add operands we're trying to factor. 1070static void FindSingleUseMultiplyFactors(Value *V, 1071 SmallVectorImpl<Value*> &Factors, 1072 const SmallVectorImpl<ValueEntry> &Ops) { 1073 BinaryOperator *BO = isReassociableOp(V, Instruction::Mul); 1074 if (!BO) { 1075 Factors.push_back(V); 1076 return; 1077 } 1078 1079 // Otherwise, add the LHS and RHS to the list of factors. 1080 FindSingleUseMultiplyFactors(BO->getOperand(1), Factors, Ops); 1081 FindSingleUseMultiplyFactors(BO->getOperand(0), Factors, Ops); 1082} 1083 1084/// OptimizeAndOrXor - Optimize a series of operands to an 'and', 'or', or 'xor' 1085/// instruction. This optimizes based on identities. If it can be reduced to 1086/// a single Value, it is returned, otherwise the Ops list is mutated as 1087/// necessary. 1088static Value *OptimizeAndOrXor(unsigned Opcode, 1089 SmallVectorImpl<ValueEntry> &Ops) { 1090 // Scan the operand lists looking for X and ~X pairs, along with X,X pairs. 1091 // If we find any, we can simplify the expression. X&~X == 0, X|~X == -1. 1092 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1093 // First, check for X and ~X in the operand list. 1094 assert(i < Ops.size()); 1095 if (BinaryOperator::isNot(Ops[i].Op)) { // Cannot occur for ^. 1096 Value *X = BinaryOperator::getNotArgument(Ops[i].Op); 1097 unsigned FoundX = FindInOperandList(Ops, i, X); 1098 if (FoundX != i) { 1099 if (Opcode == Instruction::And) // ...&X&~X = 0 1100 return Constant::getNullValue(X->getType()); 1101 1102 if (Opcode == Instruction::Or) // ...|X|~X = -1 1103 return Constant::getAllOnesValue(X->getType()); 1104 } 1105 } 1106 1107 // Next, check for duplicate pairs of values, which we assume are next to 1108 // each other, due to our sorting criteria. 1109 assert(i < Ops.size()); 1110 if (i+1 != Ops.size() && Ops[i+1].Op == Ops[i].Op) { 1111 if (Opcode == Instruction::And || Opcode == Instruction::Or) { 1112 // Drop duplicate values for And and Or. 1113 Ops.erase(Ops.begin()+i); 1114 --i; --e; 1115 ++NumAnnihil; 1116 continue; 1117 } 1118 1119 // Drop pairs of values for Xor. 1120 assert(Opcode == Instruction::Xor); 1121 if (e == 2) 1122 return Constant::getNullValue(Ops[0].Op->getType()); 1123 1124 // Y ^ X^X -> Y 1125 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 1126 i -= 1; e -= 2; 1127 ++NumAnnihil; 1128 } 1129 } 1130 return 0; 1131} 1132 1133/// Helper funciton of CombineXorOpnd(). It creates a bitwise-and 1134/// instruction with the given two operands, and return the resulting 1135/// instruction. There are two special cases: 1) if the constant operand is 0, 1136/// it will return NULL. 2) if the constant is ~0, the symbolic operand will 1137/// be returned. 1138static Value *createAndInstr(Instruction *InsertBefore, Value *Opnd, 1139 const APInt &ConstOpnd) { 1140 if (ConstOpnd != 0) { 1141 if (!ConstOpnd.isAllOnesValue()) { 1142 LLVMContext &Ctx = Opnd->getType()->getContext(); 1143 Instruction *I; 1144 I = BinaryOperator::CreateAnd(Opnd, ConstantInt::get(Ctx, ConstOpnd), 1145 "and.ra", InsertBefore); 1146 I->setDebugLoc(InsertBefore->getDebugLoc()); 1147 return I; 1148 } 1149 return Opnd; 1150 } 1151 return 0; 1152} 1153 1154// Helper function of OptimizeXor(). It tries to simplify "Opnd1 ^ ConstOpnd" 1155// into "R ^ C", where C would be 0, and R is a symbolic value. 1156// 1157// If it was successful, true is returned, and the "R" and "C" is returned 1158// via "Res" and "ConstOpnd", respectively; otherwise, false is returned, 1159// and both "Res" and "ConstOpnd" remain unchanged. 1160// 1161bool Reassociate::CombineXorOpnd(Instruction *I, XorOpnd *Opnd1, 1162 APInt &ConstOpnd, Value *&Res) { 1163 // Xor-Rule 1: (x | c1) ^ c2 = (x | c1) ^ (c1 ^ c1) ^ c2 1164 // = ((x | c1) ^ c1) ^ (c1 ^ c2) 1165 // = (x & ~c1) ^ (c1 ^ c2) 1166 // It is useful only when c1 == c2. 1167 if (Opnd1->isOrExpr() && Opnd1->getConstPart() != 0) { 1168 if (!Opnd1->getValue()->hasOneUse()) 1169 return false; 1170 1171 const APInt &C1 = Opnd1->getConstPart(); 1172 if (C1 != ConstOpnd) 1173 return false; 1174 1175 Value *X = Opnd1->getSymbolicPart(); 1176 Res = createAndInstr(I, X, ~C1); 1177 // ConstOpnd was C2, now C1 ^ C2. 1178 ConstOpnd ^= C1; 1179 1180 if (Instruction *T = dyn_cast<Instruction>(Opnd1->getValue())) 1181 RedoInsts.insert(T); 1182 return true; 1183 } 1184 return false; 1185} 1186 1187 1188// Helper function of OptimizeXor(). It tries to simplify 1189// "Opnd1 ^ Opnd2 ^ ConstOpnd" into "R ^ C", where C would be 0, and R is a 1190// symbolic value. 1191// 1192// If it was successful, true is returned, and the "R" and "C" is returned 1193// via "Res" and "ConstOpnd", respectively (If the entire expression is 1194// evaluated to a constant, the Res is set to NULL); otherwise, false is 1195// returned, and both "Res" and "ConstOpnd" remain unchanged. 1196bool Reassociate::CombineXorOpnd(Instruction *I, XorOpnd *Opnd1, XorOpnd *Opnd2, 1197 APInt &ConstOpnd, Value *&Res) { 1198 Value *X = Opnd1->getSymbolicPart(); 1199 if (X != Opnd2->getSymbolicPart()) 1200 return false; 1201 1202 const APInt &C1 = Opnd1->getConstPart(); 1203 const APInt &C2 = Opnd2->getConstPart(); 1204 1205 // This many instruction become dead.(At least "Opnd1 ^ Opnd2" will die.) 1206 int DeadInstNum = 1; 1207 if (Opnd1->getValue()->hasOneUse()) 1208 DeadInstNum++; 1209 if (Opnd2->getValue()->hasOneUse()) 1210 DeadInstNum++; 1211 1212 // Xor-Rule 2: 1213 // (x | c1) ^ (x & c2) 1214 // = (x|c1) ^ (x&c2) ^ (c1 ^ c1) = ((x|c1) ^ c1) ^ (x & c2) ^ c1 1215 // = (x & ~c1) ^ (x & c2) ^ c1 // Xor-Rule 1 1216 // = (x & c3) ^ c1, where c3 = ~c1 ^ c2 // Xor-rule 3 1217 // 1218 if (Opnd1->isOrExpr() != Opnd2->isOrExpr()) { 1219 if (Opnd2->isOrExpr()) 1220 std::swap(Opnd1, Opnd2); 1221 1222 APInt C3((~C1) ^ C2); 1223 1224 // Do not increase code size! 1225 if (C3 != 0 && !C3.isAllOnesValue()) { 1226 int NewInstNum = ConstOpnd != 0 ? 1 : 2; 1227 if (NewInstNum > DeadInstNum) 1228 return false; 1229 } 1230 1231 Res = createAndInstr(I, X, C3); 1232 ConstOpnd ^= C1; 1233 1234 } else if (Opnd1->isOrExpr()) { 1235 // Xor-Rule 3: (x | c1) ^ (x | c2) = (x & c3) ^ c3 where c3 = c1 ^ c2 1236 // 1237 APInt C3 = C1 ^ C2; 1238 1239 // Do not increase code size 1240 if (C3 != 0 && !C3.isAllOnesValue()) { 1241 int NewInstNum = ConstOpnd != 0 ? 1 : 2; 1242 if (NewInstNum > DeadInstNum) 1243 return false; 1244 } 1245 1246 Res = createAndInstr(I, X, C3); 1247 ConstOpnd ^= C3; 1248 } else { 1249 // Xor-Rule 4: (x & c1) ^ (x & c2) = (x & (c1^c2)) 1250 // 1251 APInt C3 = C1 ^ C2; 1252 Res = createAndInstr(I, X, C3); 1253 } 1254 1255 // Put the original operands in the Redo list; hope they will be deleted 1256 // as dead code. 1257 if (Instruction *T = dyn_cast<Instruction>(Opnd1->getValue())) 1258 RedoInsts.insert(T); 1259 if (Instruction *T = dyn_cast<Instruction>(Opnd2->getValue())) 1260 RedoInsts.insert(T); 1261 1262 return true; 1263} 1264 1265/// Optimize a series of operands to an 'xor' instruction. If it can be reduced 1266/// to a single Value, it is returned, otherwise the Ops list is mutated as 1267/// necessary. 1268Value *Reassociate::OptimizeXor(Instruction *I, 1269 SmallVectorImpl<ValueEntry> &Ops) { 1270 if (Value *V = OptimizeAndOrXor(Instruction::Xor, Ops)) 1271 return V; 1272 1273 if (Ops.size() == 1) 1274 return 0; 1275 1276 SmallVector<XorOpnd, 8> Opnds; 1277 SmallVector<unsigned, 8> OpndIndices; 1278 Type *Ty = Ops[0].Op->getType(); 1279 APInt ConstOpnd(Ty->getIntegerBitWidth(), 0); 1280 1281 // Step 1: Convert ValueEntry to XorOpnd 1282 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1283 Value *V = Ops[i].Op; 1284 if (!isa<ConstantInt>(V)) { 1285 XorOpnd O(V); 1286 O.setSymbolicRank(getRank(O.getSymbolicPart())); 1287 Opnds.push_back(O); 1288 OpndIndices.push_back(Opnds.size() - 1); 1289 } else 1290 ConstOpnd ^= cast<ConstantInt>(V)->getValue(); 1291 } 1292 1293 // Step 2: Sort the Xor-Operands in a way such that the operands containing 1294 // the same symbolic value cluster together. For instance, the input operand 1295 // sequence ("x | 123", "y & 456", "x & 789") will be sorted into: 1296 // ("x | 123", "x & 789", "y & 456"). 1297 std::sort(OpndIndices.begin(), OpndIndices.end(), 1298 XorOpnd::PtrSortFunctor(Opnds)); 1299 1300 // Step 3: Combine adjacent operands 1301 XorOpnd *PrevOpnd = 0; 1302 bool Changed = false; 1303 for (unsigned i = 0, e = Opnds.size(); i < e; i++) { 1304 XorOpnd *CurrOpnd = &Opnds[OpndIndices[i]]; 1305 // The combined value 1306 Value *CV; 1307 1308 // Step 3.1: Try simplifying "CurrOpnd ^ ConstOpnd" 1309 if (ConstOpnd != 0 && CombineXorOpnd(I, CurrOpnd, ConstOpnd, CV)) { 1310 Changed = true; 1311 if (CV) 1312 *CurrOpnd = XorOpnd(CV); 1313 else { 1314 CurrOpnd->Invalidate(); 1315 continue; 1316 } 1317 } 1318 1319 if (!PrevOpnd || CurrOpnd->getSymbolicPart() != PrevOpnd->getSymbolicPart()) { 1320 PrevOpnd = CurrOpnd; 1321 continue; 1322 } 1323 1324 // step 3.2: When previous and current operands share the same symbolic 1325 // value, try to simplify "PrevOpnd ^ CurrOpnd ^ ConstOpnd" 1326 // 1327 if (CombineXorOpnd(I, CurrOpnd, PrevOpnd, ConstOpnd, CV)) { 1328 // Remove previous operand 1329 PrevOpnd->Invalidate(); 1330 if (CV) { 1331 *CurrOpnd = XorOpnd(CV); 1332 PrevOpnd = CurrOpnd; 1333 } else { 1334 CurrOpnd->Invalidate(); 1335 PrevOpnd = 0; 1336 } 1337 Changed = true; 1338 } 1339 } 1340 1341 // Step 4: Reassemble the Ops 1342 if (Changed) { 1343 Ops.clear(); 1344 for (unsigned int i = 0, e = Opnds.size(); i < e; i++) { 1345 XorOpnd &O = Opnds[i]; 1346 if (O.isInvalid()) 1347 continue; 1348 ValueEntry VE(getRank(O.getValue()), O.getValue()); 1349 Ops.push_back(VE); 1350 } 1351 if (ConstOpnd != 0) { 1352 Value *C = ConstantInt::get(Ty->getContext(), ConstOpnd); 1353 ValueEntry VE(getRank(C), C); 1354 Ops.push_back(VE); 1355 } 1356 int Sz = Ops.size(); 1357 if (Sz == 1) 1358 return Ops.back().Op; 1359 else if (Sz == 0) { 1360 assert(ConstOpnd == 0); 1361 return ConstantInt::get(Ty->getContext(), ConstOpnd); 1362 } 1363 } 1364 1365 return 0; 1366} 1367 1368/// OptimizeAdd - Optimize a series of operands to an 'add' instruction. This 1369/// optimizes based on identities. If it can be reduced to a single Value, it 1370/// is returned, otherwise the Ops list is mutated as necessary. 1371Value *Reassociate::OptimizeAdd(Instruction *I, 1372 SmallVectorImpl<ValueEntry> &Ops) { 1373 // Scan the operand lists looking for X and -X pairs. If we find any, we 1374 // can simplify the expression. X+-X == 0. While we're at it, scan for any 1375 // duplicates. We want to canonicalize Y+Y+Y+Z -> 3*Y+Z. 1376 // 1377 // TODO: We could handle "X + ~X" -> "-1" if we wanted, since "-X = ~X+1". 1378 // 1379 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1380 Value *TheOp = Ops[i].Op; 1381 // Check to see if we've seen this operand before. If so, we factor all 1382 // instances of the operand together. Due to our sorting criteria, we know 1383 // that these need to be next to each other in the vector. 1384 if (i+1 != Ops.size() && Ops[i+1].Op == TheOp) { 1385 // Rescan the list, remove all instances of this operand from the expr. 1386 unsigned NumFound = 0; 1387 do { 1388 Ops.erase(Ops.begin()+i); 1389 ++NumFound; 1390 } while (i != Ops.size() && Ops[i].Op == TheOp); 1391 1392 DEBUG(errs() << "\nFACTORING [" << NumFound << "]: " << *TheOp << '\n'); 1393 ++NumFactor; 1394 1395 // Insert a new multiply. 1396 Value *Mul = ConstantInt::get(cast<IntegerType>(I->getType()), NumFound); 1397 Mul = BinaryOperator::CreateMul(TheOp, Mul, "factor", I); 1398 1399 // Now that we have inserted a multiply, optimize it. This allows us to 1400 // handle cases that require multiple factoring steps, such as this: 1401 // (X*2) + (X*2) + (X*2) -> (X*2)*3 -> X*6 1402 RedoInsts.insert(cast<Instruction>(Mul)); 1403 1404 // If every add operand was a duplicate, return the multiply. 1405 if (Ops.empty()) 1406 return Mul; 1407 1408 // Otherwise, we had some input that didn't have the dupe, such as 1409 // "A + A + B" -> "A*2 + B". Add the new multiply to the list of 1410 // things being added by this operation. 1411 Ops.insert(Ops.begin(), ValueEntry(getRank(Mul), Mul)); 1412 1413 --i; 1414 e = Ops.size(); 1415 continue; 1416 } 1417 1418 // Check for X and -X in the operand list. 1419 if (!BinaryOperator::isNeg(TheOp)) 1420 continue; 1421 1422 Value *X = BinaryOperator::getNegArgument(TheOp); 1423 unsigned FoundX = FindInOperandList(Ops, i, X); 1424 if (FoundX == i) 1425 continue; 1426 1427 // Remove X and -X from the operand list. 1428 if (Ops.size() == 2) 1429 return Constant::getNullValue(X->getType()); 1430 1431 Ops.erase(Ops.begin()+i); 1432 if (i < FoundX) 1433 --FoundX; 1434 else 1435 --i; // Need to back up an extra one. 1436 Ops.erase(Ops.begin()+FoundX); 1437 ++NumAnnihil; 1438 --i; // Revisit element. 1439 e -= 2; // Removed two elements. 1440 } 1441 1442 // Scan the operand list, checking to see if there are any common factors 1443 // between operands. Consider something like A*A+A*B*C+D. We would like to 1444 // reassociate this to A*(A+B*C)+D, which reduces the number of multiplies. 1445 // To efficiently find this, we count the number of times a factor occurs 1446 // for any ADD operands that are MULs. 1447 DenseMap<Value*, unsigned> FactorOccurrences; 1448 1449 // Keep track of each multiply we see, to avoid triggering on (X*4)+(X*4) 1450 // where they are actually the same multiply. 1451 unsigned MaxOcc = 0; 1452 Value *MaxOccVal = 0; 1453 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1454 BinaryOperator *BOp = isReassociableOp(Ops[i].Op, Instruction::Mul); 1455 if (!BOp) 1456 continue; 1457 1458 // Compute all of the factors of this added value. 1459 SmallVector<Value*, 8> Factors; 1460 FindSingleUseMultiplyFactors(BOp, Factors, Ops); 1461 assert(Factors.size() > 1 && "Bad linearize!"); 1462 1463 // Add one to FactorOccurrences for each unique factor in this op. 1464 SmallPtrSet<Value*, 8> Duplicates; 1465 for (unsigned i = 0, e = Factors.size(); i != e; ++i) { 1466 Value *Factor = Factors[i]; 1467 if (!Duplicates.insert(Factor)) continue; 1468 1469 unsigned Occ = ++FactorOccurrences[Factor]; 1470 if (Occ > MaxOcc) { MaxOcc = Occ; MaxOccVal = Factor; } 1471 1472 // If Factor is a negative constant, add the negated value as a factor 1473 // because we can percolate the negate out. Watch for minint, which 1474 // cannot be positivified. 1475 if (ConstantInt *CI = dyn_cast<ConstantInt>(Factor)) 1476 if (CI->isNegative() && !CI->isMinValue(true)) { 1477 Factor = ConstantInt::get(CI->getContext(), -CI->getValue()); 1478 assert(!Duplicates.count(Factor) && 1479 "Shouldn't have two constant factors, missed a canonicalize"); 1480 1481 unsigned Occ = ++FactorOccurrences[Factor]; 1482 if (Occ > MaxOcc) { MaxOcc = Occ; MaxOccVal = Factor; } 1483 } 1484 } 1485 } 1486 1487 // If any factor occurred more than one time, we can pull it out. 1488 if (MaxOcc > 1) { 1489 DEBUG(errs() << "\nFACTORING [" << MaxOcc << "]: " << *MaxOccVal << '\n'); 1490 ++NumFactor; 1491 1492 // Create a new instruction that uses the MaxOccVal twice. If we don't do 1493 // this, we could otherwise run into situations where removing a factor 1494 // from an expression will drop a use of maxocc, and this can cause 1495 // RemoveFactorFromExpression on successive values to behave differently. 1496 Instruction *DummyInst = BinaryOperator::CreateAdd(MaxOccVal, MaxOccVal); 1497 SmallVector<WeakVH, 4> NewMulOps; 1498 for (unsigned i = 0; i != Ops.size(); ++i) { 1499 // Only try to remove factors from expressions we're allowed to. 1500 BinaryOperator *BOp = isReassociableOp(Ops[i].Op, Instruction::Mul); 1501 if (!BOp) 1502 continue; 1503 1504 if (Value *V = RemoveFactorFromExpression(Ops[i].Op, MaxOccVal)) { 1505 // The factorized operand may occur several times. Convert them all in 1506 // one fell swoop. 1507 for (unsigned j = Ops.size(); j != i;) { 1508 --j; 1509 if (Ops[j].Op == Ops[i].Op) { 1510 NewMulOps.push_back(V); 1511 Ops.erase(Ops.begin()+j); 1512 } 1513 } 1514 --i; 1515 } 1516 } 1517 1518 // No need for extra uses anymore. 1519 delete DummyInst; 1520 1521 unsigned NumAddedValues = NewMulOps.size(); 1522 Value *V = EmitAddTreeOfValues(I, NewMulOps); 1523 1524 // Now that we have inserted the add tree, optimize it. This allows us to 1525 // handle cases that require multiple factoring steps, such as this: 1526 // A*A*B + A*A*C --> A*(A*B+A*C) --> A*(A*(B+C)) 1527 assert(NumAddedValues > 1 && "Each occurrence should contribute a value"); 1528 (void)NumAddedValues; 1529 if (Instruction *VI = dyn_cast<Instruction>(V)) 1530 RedoInsts.insert(VI); 1531 1532 // Create the multiply. 1533 Instruction *V2 = BinaryOperator::CreateMul(V, MaxOccVal, "tmp", I); 1534 1535 // Rerun associate on the multiply in case the inner expression turned into 1536 // a multiply. We want to make sure that we keep things in canonical form. 1537 RedoInsts.insert(V2); 1538 1539 // If every add operand included the factor (e.g. "A*B + A*C"), then the 1540 // entire result expression is just the multiply "A*(B+C)". 1541 if (Ops.empty()) 1542 return V2; 1543 1544 // Otherwise, we had some input that didn't have the factor, such as 1545 // "A*B + A*C + D" -> "A*(B+C) + D". Add the new multiply to the list of 1546 // things being added by this operation. 1547 Ops.insert(Ops.begin(), ValueEntry(getRank(V2), V2)); 1548 } 1549 1550 return 0; 1551} 1552 1553namespace { 1554 /// \brief Predicate tests whether a ValueEntry's op is in a map. 1555 struct IsValueInMap { 1556 const DenseMap<Value *, unsigned> ⤅ 1557 1558 IsValueInMap(const DenseMap<Value *, unsigned> &Map) : Map(Map) {} 1559 1560 bool operator()(const ValueEntry &Entry) { 1561 return Map.find(Entry.Op) != Map.end(); 1562 } 1563 }; 1564} 1565 1566/// \brief Build up a vector of value/power pairs factoring a product. 1567/// 1568/// Given a series of multiplication operands, build a vector of factors and 1569/// the powers each is raised to when forming the final product. Sort them in 1570/// the order of descending power. 1571/// 1572/// (x*x) -> [(x, 2)] 1573/// ((x*x)*x) -> [(x, 3)] 1574/// ((((x*y)*x)*y)*x) -> [(x, 3), (y, 2)] 1575/// 1576/// \returns Whether any factors have a power greater than one. 1577bool Reassociate::collectMultiplyFactors(SmallVectorImpl<ValueEntry> &Ops, 1578 SmallVectorImpl<Factor> &Factors) { 1579 // FIXME: Have Ops be (ValueEntry, Multiplicity) pairs, simplifying this. 1580 // Compute the sum of powers of simplifiable factors. 1581 unsigned FactorPowerSum = 0; 1582 for (unsigned Idx = 1, Size = Ops.size(); Idx < Size; ++Idx) { 1583 Value *Op = Ops[Idx-1].Op; 1584 1585 // Count the number of occurrences of this value. 1586 unsigned Count = 1; 1587 for (; Idx < Size && Ops[Idx].Op == Op; ++Idx) 1588 ++Count; 1589 // Track for simplification all factors which occur 2 or more times. 1590 if (Count > 1) 1591 FactorPowerSum += Count; 1592 } 1593 1594 // We can only simplify factors if the sum of the powers of our simplifiable 1595 // factors is 4 or higher. When that is the case, we will *always* have 1596 // a simplification. This is an important invariant to prevent cyclicly 1597 // trying to simplify already minimal formations. 1598 if (FactorPowerSum < 4) 1599 return false; 1600 1601 // Now gather the simplifiable factors, removing them from Ops. 1602 FactorPowerSum = 0; 1603 for (unsigned Idx = 1; Idx < Ops.size(); ++Idx) { 1604 Value *Op = Ops[Idx-1].Op; 1605 1606 // Count the number of occurrences of this value. 1607 unsigned Count = 1; 1608 for (; Idx < Ops.size() && Ops[Idx].Op == Op; ++Idx) 1609 ++Count; 1610 if (Count == 1) 1611 continue; 1612 // Move an even number of occurrences to Factors. 1613 Count &= ~1U; 1614 Idx -= Count; 1615 FactorPowerSum += Count; 1616 Factors.push_back(Factor(Op, Count)); 1617 Ops.erase(Ops.begin()+Idx, Ops.begin()+Idx+Count); 1618 } 1619 1620 // None of the adjustments above should have reduced the sum of factor powers 1621 // below our mininum of '4'. 1622 assert(FactorPowerSum >= 4); 1623 1624 std::sort(Factors.begin(), Factors.end(), Factor::PowerDescendingSorter()); 1625 return true; 1626} 1627 1628/// \brief Build a tree of multiplies, computing the product of Ops. 1629static Value *buildMultiplyTree(IRBuilder<> &Builder, 1630 SmallVectorImpl<Value*> &Ops) { 1631 if (Ops.size() == 1) 1632 return Ops.back(); 1633 1634 Value *LHS = Ops.pop_back_val(); 1635 do { 1636 LHS = Builder.CreateMul(LHS, Ops.pop_back_val()); 1637 } while (!Ops.empty()); 1638 1639 return LHS; 1640} 1641 1642/// \brief Build a minimal multiplication DAG for (a^x)*(b^y)*(c^z)*... 1643/// 1644/// Given a vector of values raised to various powers, where no two values are 1645/// equal and the powers are sorted in decreasing order, compute the minimal 1646/// DAG of multiplies to compute the final product, and return that product 1647/// value. 1648Value *Reassociate::buildMinimalMultiplyDAG(IRBuilder<> &Builder, 1649 SmallVectorImpl<Factor> &Factors) { 1650 assert(Factors[0].Power); 1651 SmallVector<Value *, 4> OuterProduct; 1652 for (unsigned LastIdx = 0, Idx = 1, Size = Factors.size(); 1653 Idx < Size && Factors[Idx].Power > 0; ++Idx) { 1654 if (Factors[Idx].Power != Factors[LastIdx].Power) { 1655 LastIdx = Idx; 1656 continue; 1657 } 1658 1659 // We want to multiply across all the factors with the same power so that 1660 // we can raise them to that power as a single entity. Build a mini tree 1661 // for that. 1662 SmallVector<Value *, 4> InnerProduct; 1663 InnerProduct.push_back(Factors[LastIdx].Base); 1664 do { 1665 InnerProduct.push_back(Factors[Idx].Base); 1666 ++Idx; 1667 } while (Idx < Size && Factors[Idx].Power == Factors[LastIdx].Power); 1668 1669 // Reset the base value of the first factor to the new expression tree. 1670 // We'll remove all the factors with the same power in a second pass. 1671 Value *M = Factors[LastIdx].Base = buildMultiplyTree(Builder, InnerProduct); 1672 if (Instruction *MI = dyn_cast<Instruction>(M)) 1673 RedoInsts.insert(MI); 1674 1675 LastIdx = Idx; 1676 } 1677 // Unique factors with equal powers -- we've folded them into the first one's 1678 // base. 1679 Factors.erase(std::unique(Factors.begin(), Factors.end(), 1680 Factor::PowerEqual()), 1681 Factors.end()); 1682 1683 // Iteratively collect the base of each factor with an add power into the 1684 // outer product, and halve each power in preparation for squaring the 1685 // expression. 1686 for (unsigned Idx = 0, Size = Factors.size(); Idx != Size; ++Idx) { 1687 if (Factors[Idx].Power & 1) 1688 OuterProduct.push_back(Factors[Idx].Base); 1689 Factors[Idx].Power >>= 1; 1690 } 1691 if (Factors[0].Power) { 1692 Value *SquareRoot = buildMinimalMultiplyDAG(Builder, Factors); 1693 OuterProduct.push_back(SquareRoot); 1694 OuterProduct.push_back(SquareRoot); 1695 } 1696 if (OuterProduct.size() == 1) 1697 return OuterProduct.front(); 1698 1699 Value *V = buildMultiplyTree(Builder, OuterProduct); 1700 return V; 1701} 1702 1703Value *Reassociate::OptimizeMul(BinaryOperator *I, 1704 SmallVectorImpl<ValueEntry> &Ops) { 1705 // We can only optimize the multiplies when there is a chain of more than 1706 // three, such that a balanced tree might require fewer total multiplies. 1707 if (Ops.size() < 4) 1708 return 0; 1709 1710 // Try to turn linear trees of multiplies without other uses of the 1711 // intermediate stages into minimal multiply DAGs with perfect sub-expression 1712 // re-use. 1713 SmallVector<Factor, 4> Factors; 1714 if (!collectMultiplyFactors(Ops, Factors)) 1715 return 0; // All distinct factors, so nothing left for us to do. 1716 1717 IRBuilder<> Builder(I); 1718 Value *V = buildMinimalMultiplyDAG(Builder, Factors); 1719 if (Ops.empty()) 1720 return V; 1721 1722 ValueEntry NewEntry = ValueEntry(getRank(V), V); 1723 Ops.insert(std::lower_bound(Ops.begin(), Ops.end(), NewEntry), NewEntry); 1724 return 0; 1725} 1726 1727Value *Reassociate::OptimizeExpression(BinaryOperator *I, 1728 SmallVectorImpl<ValueEntry> &Ops) { 1729 // Now that we have the linearized expression tree, try to optimize it. 1730 // Start by folding any constants that we found. 1731 Constant *Cst = 0; 1732 unsigned Opcode = I->getOpcode(); 1733 while (!Ops.empty() && isa<Constant>(Ops.back().Op)) { 1734 Constant *C = cast<Constant>(Ops.pop_back_val().Op); 1735 Cst = Cst ? ConstantExpr::get(Opcode, C, Cst) : C; 1736 } 1737 // If there was nothing but constants then we are done. 1738 if (Ops.empty()) 1739 return Cst; 1740 1741 // Put the combined constant back at the end of the operand list, except if 1742 // there is no point. For example, an add of 0 gets dropped here, while a 1743 // multiplication by zero turns the whole expression into zero. 1744 if (Cst && Cst != ConstantExpr::getBinOpIdentity(Opcode, I->getType())) { 1745 if (Cst == ConstantExpr::getBinOpAbsorber(Opcode, I->getType())) 1746 return Cst; 1747 Ops.push_back(ValueEntry(0, Cst)); 1748 } 1749 1750 if (Ops.size() == 1) return Ops[0].Op; 1751 1752 // Handle destructive annihilation due to identities between elements in the 1753 // argument list here. 1754 unsigned NumOps = Ops.size(); 1755 switch (Opcode) { 1756 default: break; 1757 case Instruction::And: 1758 case Instruction::Or: 1759 if (Value *Result = OptimizeAndOrXor(Opcode, Ops)) 1760 return Result; 1761 break; 1762 1763 case Instruction::Xor: 1764 if (Value *Result = OptimizeXor(I, Ops)) 1765 return Result; 1766 break; 1767 1768 case Instruction::Add: 1769 if (Value *Result = OptimizeAdd(I, Ops)) 1770 return Result; 1771 break; 1772 1773 case Instruction::Mul: 1774 if (Value *Result = OptimizeMul(I, Ops)) 1775 return Result; 1776 break; 1777 } 1778 1779 if (Ops.size() != NumOps) 1780 return OptimizeExpression(I, Ops); 1781 return 0; 1782} 1783 1784/// EraseInst - Zap the given instruction, adding interesting operands to the 1785/// work list. 1786void Reassociate::EraseInst(Instruction *I) { 1787 assert(isInstructionTriviallyDead(I) && "Trivially dead instructions only!"); 1788 SmallVector<Value*, 8> Ops(I->op_begin(), I->op_end()); 1789 // Erase the dead instruction. 1790 ValueRankMap.erase(I); 1791 RedoInsts.remove(I); 1792 I->eraseFromParent(); 1793 // Optimize its operands. 1794 SmallPtrSet<Instruction *, 8> Visited; // Detect self-referential nodes. 1795 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1796 if (Instruction *Op = dyn_cast<Instruction>(Ops[i])) { 1797 // If this is a node in an expression tree, climb to the expression root 1798 // and add that since that's where optimization actually happens. 1799 unsigned Opcode = Op->getOpcode(); 1800 while (Op->hasOneUse() && Op->use_back()->getOpcode() == Opcode && 1801 Visited.insert(Op)) 1802 Op = Op->use_back(); 1803 RedoInsts.insert(Op); 1804 } 1805} 1806 1807/// OptimizeInst - Inspect and optimize the given instruction. Note that erasing 1808/// instructions is not allowed. 1809void Reassociate::OptimizeInst(Instruction *I) { 1810 // Only consider operations that we understand. 1811 if (!isa<BinaryOperator>(I)) 1812 return; 1813 1814 if (I->getOpcode() == Instruction::Shl && 1815 isa<ConstantInt>(I->getOperand(1))) 1816 // If an operand of this shift is a reassociable multiply, or if the shift 1817 // is used by a reassociable multiply or add, turn into a multiply. 1818 if (isReassociableOp(I->getOperand(0), Instruction::Mul) || 1819 (I->hasOneUse() && 1820 (isReassociableOp(I->use_back(), Instruction::Mul) || 1821 isReassociableOp(I->use_back(), Instruction::Add)))) { 1822 Instruction *NI = ConvertShiftToMul(I); 1823 RedoInsts.insert(I); 1824 MadeChange = true; 1825 I = NI; 1826 } 1827 1828 // Floating point binary operators are not associative, but we can still 1829 // commute (some) of them, to canonicalize the order of their operands. 1830 // This can potentially expose more CSE opportunities, and makes writing 1831 // other transformations simpler. 1832 if ((I->getType()->isFloatingPointTy() || I->getType()->isVectorTy())) { 1833 // FAdd and FMul can be commuted. 1834 if (I->getOpcode() != Instruction::FMul && 1835 I->getOpcode() != Instruction::FAdd) 1836 return; 1837 1838 Value *LHS = I->getOperand(0); 1839 Value *RHS = I->getOperand(1); 1840 unsigned LHSRank = getRank(LHS); 1841 unsigned RHSRank = getRank(RHS); 1842 1843 // Sort the operands by rank. 1844 if (RHSRank < LHSRank) { 1845 I->setOperand(0, RHS); 1846 I->setOperand(1, LHS); 1847 } 1848 1849 return; 1850 } 1851 1852 // Do not reassociate boolean (i1) expressions. We want to preserve the 1853 // original order of evaluation for short-circuited comparisons that 1854 // SimplifyCFG has folded to AND/OR expressions. If the expression 1855 // is not further optimized, it is likely to be transformed back to a 1856 // short-circuited form for code gen, and the source order may have been 1857 // optimized for the most likely conditions. 1858 if (I->getType()->isIntegerTy(1)) 1859 return; 1860 1861 // If this is a subtract instruction which is not already in negate form, 1862 // see if we can convert it to X+-Y. 1863 if (I->getOpcode() == Instruction::Sub) { 1864 if (ShouldBreakUpSubtract(I)) { 1865 Instruction *NI = BreakUpSubtract(I); 1866 RedoInsts.insert(I); 1867 MadeChange = true; 1868 I = NI; 1869 } else if (BinaryOperator::isNeg(I)) { 1870 // Otherwise, this is a negation. See if the operand is a multiply tree 1871 // and if this is not an inner node of a multiply tree. 1872 if (isReassociableOp(I->getOperand(1), Instruction::Mul) && 1873 (!I->hasOneUse() || 1874 !isReassociableOp(I->use_back(), Instruction::Mul))) { 1875 Instruction *NI = LowerNegateToMultiply(I); 1876 RedoInsts.insert(I); 1877 MadeChange = true; 1878 I = NI; 1879 } 1880 } 1881 } 1882 1883 // If this instruction is an associative binary operator, process it. 1884 if (!I->isAssociative()) return; 1885 BinaryOperator *BO = cast<BinaryOperator>(I); 1886 1887 // If this is an interior node of a reassociable tree, ignore it until we 1888 // get to the root of the tree, to avoid N^2 analysis. 1889 unsigned Opcode = BO->getOpcode(); 1890 if (BO->hasOneUse() && BO->use_back()->getOpcode() == Opcode) 1891 return; 1892 1893 // If this is an add tree that is used by a sub instruction, ignore it 1894 // until we process the subtract. 1895 if (BO->hasOneUse() && BO->getOpcode() == Instruction::Add && 1896 cast<Instruction>(BO->use_back())->getOpcode() == Instruction::Sub) 1897 return; 1898 1899 ReassociateExpression(BO); 1900} 1901 1902void Reassociate::ReassociateExpression(BinaryOperator *I) { 1903 1904 // First, walk the expression tree, linearizing the tree, collecting the 1905 // operand information. 1906 SmallVector<RepeatedValue, 8> Tree; 1907 MadeChange |= LinearizeExprTree(I, Tree); 1908 SmallVector<ValueEntry, 8> Ops; 1909 Ops.reserve(Tree.size()); 1910 for (unsigned i = 0, e = Tree.size(); i != e; ++i) { 1911 RepeatedValue E = Tree[i]; 1912 Ops.append(E.second.getZExtValue(), 1913 ValueEntry(getRank(E.first), E.first)); 1914 } 1915 1916 DEBUG(dbgs() << "RAIn:\t"; PrintOps(I, Ops); dbgs() << '\n'); 1917 1918 // Now that we have linearized the tree to a list and have gathered all of 1919 // the operands and their ranks, sort the operands by their rank. Use a 1920 // stable_sort so that values with equal ranks will have their relative 1921 // positions maintained (and so the compiler is deterministic). Note that 1922 // this sorts so that the highest ranking values end up at the beginning of 1923 // the vector. 1924 std::stable_sort(Ops.begin(), Ops.end()); 1925 1926 // OptimizeExpression - Now that we have the expression tree in a convenient 1927 // sorted form, optimize it globally if possible. 1928 if (Value *V = OptimizeExpression(I, Ops)) { 1929 if (V == I) 1930 // Self-referential expression in unreachable code. 1931 return; 1932 // This expression tree simplified to something that isn't a tree, 1933 // eliminate it. 1934 DEBUG(dbgs() << "Reassoc to scalar: " << *V << '\n'); 1935 I->replaceAllUsesWith(V); 1936 if (Instruction *VI = dyn_cast<Instruction>(V)) 1937 VI->setDebugLoc(I->getDebugLoc()); 1938 RedoInsts.insert(I); 1939 ++NumAnnihil; 1940 return; 1941 } 1942 1943 // We want to sink immediates as deeply as possible except in the case where 1944 // this is a multiply tree used only by an add, and the immediate is a -1. 1945 // In this case we reassociate to put the negation on the outside so that we 1946 // can fold the negation into the add: (-X)*Y + Z -> Z-X*Y 1947 if (I->getOpcode() == Instruction::Mul && I->hasOneUse() && 1948 cast<Instruction>(I->use_back())->getOpcode() == Instruction::Add && 1949 isa<ConstantInt>(Ops.back().Op) && 1950 cast<ConstantInt>(Ops.back().Op)->isAllOnesValue()) { 1951 ValueEntry Tmp = Ops.pop_back_val(); 1952 Ops.insert(Ops.begin(), Tmp); 1953 } 1954 1955 DEBUG(dbgs() << "RAOut:\t"; PrintOps(I, Ops); dbgs() << '\n'); 1956 1957 if (Ops.size() == 1) { 1958 if (Ops[0].Op == I) 1959 // Self-referential expression in unreachable code. 1960 return; 1961 1962 // This expression tree simplified to something that isn't a tree, 1963 // eliminate it. 1964 I->replaceAllUsesWith(Ops[0].Op); 1965 if (Instruction *OI = dyn_cast<Instruction>(Ops[0].Op)) 1966 OI->setDebugLoc(I->getDebugLoc()); 1967 RedoInsts.insert(I); 1968 return; 1969 } 1970 1971 // Now that we ordered and optimized the expressions, splat them back into 1972 // the expression tree, removing any unneeded nodes. 1973 RewriteExprTree(I, Ops); 1974} 1975 1976bool Reassociate::runOnFunction(Function &F) { 1977 // Calculate the rank map for F 1978 BuildRankMap(F); 1979 1980 MadeChange = false; 1981 for (Function::iterator BI = F.begin(), BE = F.end(); BI != BE; ++BI) { 1982 // Optimize every instruction in the basic block. 1983 for (BasicBlock::iterator II = BI->begin(), IE = BI->end(); II != IE; ) 1984 if (isInstructionTriviallyDead(II)) { 1985 EraseInst(II++); 1986 } else { 1987 OptimizeInst(II); 1988 assert(II->getParent() == BI && "Moved to a different block!"); 1989 ++II; 1990 } 1991 1992 // If this produced extra instructions to optimize, handle them now. 1993 while (!RedoInsts.empty()) { 1994 Instruction *I = RedoInsts.pop_back_val(); 1995 if (isInstructionTriviallyDead(I)) 1996 EraseInst(I); 1997 else 1998 OptimizeInst(I); 1999 } 2000 } 2001 2002 // We are done with the rank map. 2003 RankMap.clear(); 2004 ValueRankMap.clear(); 2005 2006 return MadeChange; 2007} 2008