ScalarEvolution.cpp revision eb490a7aa34c873b1bc401eb2c45a4d71a62be37
1//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===// 2// 3// The LLVM Compiler Infrastructure 4// 5// This file is distributed under the University of Illinois Open Source 6// License. See LICENSE.TXT for details. 7// 8//===----------------------------------------------------------------------===// 9// 10// This file contains the implementation of the scalar evolution analysis 11// engine, which is used primarily to analyze expressions involving induction 12// variables in loops. 13// 14// There are several aspects to this library. First is the representation of 15// scalar expressions, which are represented as subclasses of the SCEV class. 16// These classes are used to represent certain types of subexpressions that we 17// can handle. These classes are reference counted, managed by the const SCEV * 18// class. We only create one SCEV of a particular shape, so pointer-comparisons 19// for equality are legal. 20// 21// One important aspect of the SCEV objects is that they are never cyclic, even 22// if there is a cycle in the dataflow for an expression (ie, a PHI node). If 23// the PHI node is one of the idioms that we can represent (e.g., a polynomial 24// recurrence) then we represent it directly as a recurrence node, otherwise we 25// represent it as a SCEVUnknown node. 26// 27// In addition to being able to represent expressions of various types, we also 28// have folders that are used to build the *canonical* representation for a 29// particular expression. These folders are capable of using a variety of 30// rewrite rules to simplify the expressions. 31// 32// Once the folders are defined, we can implement the more interesting 33// higher-level code, such as the code that recognizes PHI nodes of various 34// types, computes the execution count of a loop, etc. 35// 36// TODO: We should use these routines and value representations to implement 37// dependence analysis! 38// 39//===----------------------------------------------------------------------===// 40// 41// There are several good references for the techniques used in this analysis. 42// 43// Chains of recurrences -- a method to expedite the evaluation 44// of closed-form functions 45// Olaf Bachmann, Paul S. Wang, Eugene V. Zima 46// 47// On computational properties of chains of recurrences 48// Eugene V. Zima 49// 50// Symbolic Evaluation of Chains of Recurrences for Loop Optimization 51// Robert A. van Engelen 52// 53// Efficient Symbolic Analysis for Optimizing Compilers 54// Robert A. van Engelen 55// 56// Using the chains of recurrences algebra for data dependence testing and 57// induction variable substitution 58// MS Thesis, Johnie Birch 59// 60//===----------------------------------------------------------------------===// 61 62#define DEBUG_TYPE "scalar-evolution" 63#include "llvm/Analysis/ScalarEvolutionExpressions.h" 64#include "llvm/Constants.h" 65#include "llvm/DerivedTypes.h" 66#include "llvm/GlobalVariable.h" 67#include "llvm/Instructions.h" 68#include "llvm/LLVMContext.h" 69#include "llvm/Operator.h" 70#include "llvm/Analysis/ConstantFolding.h" 71#include "llvm/Analysis/Dominators.h" 72#include "llvm/Analysis/LoopInfo.h" 73#include "llvm/Analysis/ValueTracking.h" 74#include "llvm/Assembly/Writer.h" 75#include "llvm/Target/TargetData.h" 76#include "llvm/Support/CommandLine.h" 77#include "llvm/Support/Compiler.h" 78#include "llvm/Support/ConstantRange.h" 79#include "llvm/Support/ErrorHandling.h" 80#include "llvm/Support/GetElementPtrTypeIterator.h" 81#include "llvm/Support/InstIterator.h" 82#include "llvm/Support/MathExtras.h" 83#include "llvm/Support/raw_ostream.h" 84#include "llvm/ADT/Statistic.h" 85#include "llvm/ADT/STLExtras.h" 86#include "llvm/ADT/SmallPtrSet.h" 87#include <algorithm> 88using namespace llvm; 89 90STATISTIC(NumArrayLenItCounts, 91 "Number of trip counts computed with array length"); 92STATISTIC(NumTripCountsComputed, 93 "Number of loops with predictable loop counts"); 94STATISTIC(NumTripCountsNotComputed, 95 "Number of loops without predictable loop counts"); 96STATISTIC(NumBruteForceTripCountsComputed, 97 "Number of loops with trip counts computed by force"); 98 99static cl::opt<unsigned> 100MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 101 cl::desc("Maximum number of iterations SCEV will " 102 "symbolically execute a constant " 103 "derived loop"), 104 cl::init(100)); 105 106static RegisterPass<ScalarEvolution> 107R("scalar-evolution", "Scalar Evolution Analysis", false, true); 108char ScalarEvolution::ID = 0; 109 110//===----------------------------------------------------------------------===// 111// SCEV class definitions 112//===----------------------------------------------------------------------===// 113 114//===----------------------------------------------------------------------===// 115// Implementation of the SCEV class. 116// 117 118SCEV::~SCEV() {} 119 120void SCEV::dump() const { 121 print(errs()); 122 errs() << '\n'; 123} 124 125void SCEV::print(std::ostream &o) const { 126 raw_os_ostream OS(o); 127 print(OS); 128} 129 130bool SCEV::isZero() const { 131 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 132 return SC->getValue()->isZero(); 133 return false; 134} 135 136bool SCEV::isOne() const { 137 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 138 return SC->getValue()->isOne(); 139 return false; 140} 141 142bool SCEV::isAllOnesValue() const { 143 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 144 return SC->getValue()->isAllOnesValue(); 145 return false; 146} 147 148SCEVCouldNotCompute::SCEVCouldNotCompute() : 149 SCEV(FoldingSetNodeID(), scCouldNotCompute) {} 150 151bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 152 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 153 return false; 154} 155 156const Type *SCEVCouldNotCompute::getType() const { 157 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 158 return 0; 159} 160 161bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 162 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 163 return false; 164} 165 166bool SCEVCouldNotCompute::hasOperand(const SCEV *) const { 167 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 168 return false; 169} 170 171void SCEVCouldNotCompute::print(raw_ostream &OS) const { 172 OS << "***COULDNOTCOMPUTE***"; 173} 174 175bool SCEVCouldNotCompute::classof(const SCEV *S) { 176 return S->getSCEVType() == scCouldNotCompute; 177} 178 179const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { 180 FoldingSetNodeID ID; 181 ID.AddInteger(scConstant); 182 ID.AddPointer(V); 183 void *IP = 0; 184 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 185 SCEV *S = SCEVAllocator.Allocate<SCEVConstant>(); 186 new (S) SCEVConstant(ID, V); 187 UniqueSCEVs.InsertNode(S, IP); 188 return S; 189} 190 191const SCEV *ScalarEvolution::getConstant(const APInt& Val) { 192 return getConstant(ConstantInt::get(getContext(), Val)); 193} 194 195const SCEV * 196ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) { 197 return getConstant( 198 ConstantInt::get(cast<IntegerType>(Ty), V, isSigned)); 199} 200 201const Type *SCEVConstant::getType() const { return V->getType(); } 202 203void SCEVConstant::print(raw_ostream &OS) const { 204 WriteAsOperand(OS, V, false); 205} 206 207SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeID &ID, 208 unsigned SCEVTy, const SCEV *op, const Type *ty) 209 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {} 210 211bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 212 return Op->dominates(BB, DT); 213} 214 215SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeID &ID, 216 const SCEV *op, const Type *ty) 217 : SCEVCastExpr(ID, scTruncate, op, ty) { 218 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 219 (Ty->isInteger() || isa<PointerType>(Ty)) && 220 "Cannot truncate non-integer value!"); 221} 222 223void SCEVTruncateExpr::print(raw_ostream &OS) const { 224 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 225} 226 227SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeID &ID, 228 const SCEV *op, const Type *ty) 229 : SCEVCastExpr(ID, scZeroExtend, op, ty) { 230 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 231 (Ty->isInteger() || isa<PointerType>(Ty)) && 232 "Cannot zero extend non-integer value!"); 233} 234 235void SCEVZeroExtendExpr::print(raw_ostream &OS) const { 236 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 237} 238 239SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeID &ID, 240 const SCEV *op, const Type *ty) 241 : SCEVCastExpr(ID, scSignExtend, op, ty) { 242 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 243 (Ty->isInteger() || isa<PointerType>(Ty)) && 244 "Cannot sign extend non-integer value!"); 245} 246 247void SCEVSignExtendExpr::print(raw_ostream &OS) const { 248 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 249} 250 251void SCEVCommutativeExpr::print(raw_ostream &OS) const { 252 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 253 const char *OpStr = getOperationStr(); 254 OS << "(" << *Operands[0]; 255 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 256 OS << OpStr << *Operands[i]; 257 OS << ")"; 258} 259 260bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 261 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 262 if (!getOperand(i)->dominates(BB, DT)) 263 return false; 264 } 265 return true; 266} 267 268bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 269 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT); 270} 271 272void SCEVUDivExpr::print(raw_ostream &OS) const { 273 OS << "(" << *LHS << " /u " << *RHS << ")"; 274} 275 276const Type *SCEVUDivExpr::getType() const { 277 // In most cases the types of LHS and RHS will be the same, but in some 278 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't 279 // depend on the type for correctness, but handling types carefully can 280 // avoid extra casts in the SCEVExpander. The LHS is more likely to be 281 // a pointer type than the RHS, so use the RHS' type here. 282 return RHS->getType(); 283} 284 285bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 286 // Add recurrences are never invariant in the function-body (null loop). 287 if (!QueryLoop) 288 return false; 289 290 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L. 291 if (QueryLoop->contains(L->getHeader())) 292 return false; 293 294 // This recurrence is variant w.r.t. QueryLoop if any of its operands 295 // are variant. 296 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 297 if (!getOperand(i)->isLoopInvariant(QueryLoop)) 298 return false; 299 300 // Otherwise it's loop-invariant. 301 return true; 302} 303 304void SCEVAddRecExpr::print(raw_ostream &OS) const { 305 OS << "{" << *Operands[0]; 306 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 307 OS << ",+," << *Operands[i]; 308 OS << "}<" << L->getHeader()->getName() + ">"; 309} 310 311bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 312 // All non-instruction values are loop invariant. All instructions are loop 313 // invariant if they are not contained in the specified loop. 314 // Instructions are never considered invariant in the function body 315 // (null loop) because they are defined within the "loop". 316 if (Instruction *I = dyn_cast<Instruction>(V)) 317 return L && !L->contains(I->getParent()); 318 return true; 319} 320 321bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const { 322 if (Instruction *I = dyn_cast<Instruction>(getValue())) 323 return DT->dominates(I->getParent(), BB); 324 return true; 325} 326 327const Type *SCEVUnknown::getType() const { 328 return V->getType(); 329} 330 331void SCEVUnknown::print(raw_ostream &OS) const { 332 WriteAsOperand(OS, V, false); 333} 334 335//===----------------------------------------------------------------------===// 336// SCEV Utilities 337//===----------------------------------------------------------------------===// 338 339namespace { 340 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 341 /// than the complexity of the RHS. This comparator is used to canonicalize 342 /// expressions. 343 class VISIBILITY_HIDDEN SCEVComplexityCompare { 344 LoopInfo *LI; 345 public: 346 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {} 347 348 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 349 // Primarily, sort the SCEVs by their getSCEVType(). 350 if (LHS->getSCEVType() != RHS->getSCEVType()) 351 return LHS->getSCEVType() < RHS->getSCEVType(); 352 353 // Aside from the getSCEVType() ordering, the particular ordering 354 // isn't very important except that it's beneficial to be consistent, 355 // so that (a + b) and (b + a) don't end up as different expressions. 356 357 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 358 // not as complete as it could be. 359 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) { 360 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 361 362 // Order pointer values after integer values. This helps SCEVExpander 363 // form GEPs. 364 if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType())) 365 return false; 366 if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType())) 367 return true; 368 369 // Compare getValueID values. 370 if (LU->getValue()->getValueID() != RU->getValue()->getValueID()) 371 return LU->getValue()->getValueID() < RU->getValue()->getValueID(); 372 373 // Sort arguments by their position. 374 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) { 375 const Argument *RA = cast<Argument>(RU->getValue()); 376 return LA->getArgNo() < RA->getArgNo(); 377 } 378 379 // For instructions, compare their loop depth, and their opcode. 380 // This is pretty loose. 381 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) { 382 Instruction *RV = cast<Instruction>(RU->getValue()); 383 384 // Compare loop depths. 385 if (LI->getLoopDepth(LV->getParent()) != 386 LI->getLoopDepth(RV->getParent())) 387 return LI->getLoopDepth(LV->getParent()) < 388 LI->getLoopDepth(RV->getParent()); 389 390 // Compare opcodes. 391 if (LV->getOpcode() != RV->getOpcode()) 392 return LV->getOpcode() < RV->getOpcode(); 393 394 // Compare the number of operands. 395 if (LV->getNumOperands() != RV->getNumOperands()) 396 return LV->getNumOperands() < RV->getNumOperands(); 397 } 398 399 return false; 400 } 401 402 // Compare constant values. 403 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) { 404 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 405 if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth()) 406 return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth(); 407 return LC->getValue()->getValue().ult(RC->getValue()->getValue()); 408 } 409 410 // Compare addrec loop depths. 411 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) { 412 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 413 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth()) 414 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth(); 415 } 416 417 // Lexicographically compare n-ary expressions. 418 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) { 419 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 420 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) { 421 if (i >= RC->getNumOperands()) 422 return false; 423 if (operator()(LC->getOperand(i), RC->getOperand(i))) 424 return true; 425 if (operator()(RC->getOperand(i), LC->getOperand(i))) 426 return false; 427 } 428 return LC->getNumOperands() < RC->getNumOperands(); 429 } 430 431 // Lexicographically compare udiv expressions. 432 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) { 433 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 434 if (operator()(LC->getLHS(), RC->getLHS())) 435 return true; 436 if (operator()(RC->getLHS(), LC->getLHS())) 437 return false; 438 if (operator()(LC->getRHS(), RC->getRHS())) 439 return true; 440 if (operator()(RC->getRHS(), LC->getRHS())) 441 return false; 442 return false; 443 } 444 445 // Compare cast expressions by operand. 446 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) { 447 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 448 return operator()(LC->getOperand(), RC->getOperand()); 449 } 450 451 llvm_unreachable("Unknown SCEV kind!"); 452 return false; 453 } 454 }; 455} 456 457/// GroupByComplexity - Given a list of SCEV objects, order them by their 458/// complexity, and group objects of the same complexity together by value. 459/// When this routine is finished, we know that any duplicates in the vector are 460/// consecutive and that complexity is monotonically increasing. 461/// 462/// Note that we go take special precautions to ensure that we get determinstic 463/// results from this routine. In other words, we don't want the results of 464/// this to depend on where the addresses of various SCEV objects happened to 465/// land in memory. 466/// 467static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 468 LoopInfo *LI) { 469 if (Ops.size() < 2) return; // Noop 470 if (Ops.size() == 2) { 471 // This is the common case, which also happens to be trivially simple. 472 // Special case it. 473 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0])) 474 std::swap(Ops[0], Ops[1]); 475 return; 476 } 477 478 // Do the rough sort by complexity. 479 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 480 481 // Now that we are sorted by complexity, group elements of the same 482 // complexity. Note that this is, at worst, N^2, but the vector is likely to 483 // be extremely short in practice. Note that we take this approach because we 484 // do not want to depend on the addresses of the objects we are grouping. 485 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 486 const SCEV *S = Ops[i]; 487 unsigned Complexity = S->getSCEVType(); 488 489 // If there are any objects of the same complexity and same value as this 490 // one, group them. 491 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 492 if (Ops[j] == S) { // Found a duplicate. 493 // Move it to immediately after i'th element. 494 std::swap(Ops[i+1], Ops[j]); 495 ++i; // no need to rescan it. 496 if (i == e-2) return; // Done! 497 } 498 } 499 } 500} 501 502 503 504//===----------------------------------------------------------------------===// 505// Simple SCEV method implementations 506//===----------------------------------------------------------------------===// 507 508/// BinomialCoefficient - Compute BC(It, K). The result has width W. 509/// Assume, K > 0. 510static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 511 ScalarEvolution &SE, 512 const Type* ResultTy) { 513 // Handle the simplest case efficiently. 514 if (K == 1) 515 return SE.getTruncateOrZeroExtend(It, ResultTy); 516 517 // We are using the following formula for BC(It, K): 518 // 519 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 520 // 521 // Suppose, W is the bitwidth of the return value. We must be prepared for 522 // overflow. Hence, we must assure that the result of our computation is 523 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 524 // safe in modular arithmetic. 525 // 526 // However, this code doesn't use exactly that formula; the formula it uses 527 // is something like the following, where T is the number of factors of 2 in 528 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 529 // exponentiation: 530 // 531 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 532 // 533 // This formula is trivially equivalent to the previous formula. However, 534 // this formula can be implemented much more efficiently. The trick is that 535 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 536 // arithmetic. To do exact division in modular arithmetic, all we have 537 // to do is multiply by the inverse. Therefore, this step can be done at 538 // width W. 539 // 540 // The next issue is how to safely do the division by 2^T. The way this 541 // is done is by doing the multiplication step at a width of at least W + T 542 // bits. This way, the bottom W+T bits of the product are accurate. Then, 543 // when we perform the division by 2^T (which is equivalent to a right shift 544 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 545 // truncated out after the division by 2^T. 546 // 547 // In comparison to just directly using the first formula, this technique 548 // is much more efficient; using the first formula requires W * K bits, 549 // but this formula less than W + K bits. Also, the first formula requires 550 // a division step, whereas this formula only requires multiplies and shifts. 551 // 552 // It doesn't matter whether the subtraction step is done in the calculation 553 // width or the input iteration count's width; if the subtraction overflows, 554 // the result must be zero anyway. We prefer here to do it in the width of 555 // the induction variable because it helps a lot for certain cases; CodeGen 556 // isn't smart enough to ignore the overflow, which leads to much less 557 // efficient code if the width of the subtraction is wider than the native 558 // register width. 559 // 560 // (It's possible to not widen at all by pulling out factors of 2 before 561 // the multiplication; for example, K=2 can be calculated as 562 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 563 // extra arithmetic, so it's not an obvious win, and it gets 564 // much more complicated for K > 3.) 565 566 // Protection from insane SCEVs; this bound is conservative, 567 // but it probably doesn't matter. 568 if (K > 1000) 569 return SE.getCouldNotCompute(); 570 571 unsigned W = SE.getTypeSizeInBits(ResultTy); 572 573 // Calculate K! / 2^T and T; we divide out the factors of two before 574 // multiplying for calculating K! / 2^T to avoid overflow. 575 // Other overflow doesn't matter because we only care about the bottom 576 // W bits of the result. 577 APInt OddFactorial(W, 1); 578 unsigned T = 1; 579 for (unsigned i = 3; i <= K; ++i) { 580 APInt Mult(W, i); 581 unsigned TwoFactors = Mult.countTrailingZeros(); 582 T += TwoFactors; 583 Mult = Mult.lshr(TwoFactors); 584 OddFactorial *= Mult; 585 } 586 587 // We need at least W + T bits for the multiplication step 588 unsigned CalculationBits = W + T; 589 590 // Calcuate 2^T, at width T+W. 591 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 592 593 // Calculate the multiplicative inverse of K! / 2^T; 594 // this multiplication factor will perform the exact division by 595 // K! / 2^T. 596 APInt Mod = APInt::getSignedMinValue(W+1); 597 APInt MultiplyFactor = OddFactorial.zext(W+1); 598 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 599 MultiplyFactor = MultiplyFactor.trunc(W); 600 601 // Calculate the product, at width T+W 602 const IntegerType *CalculationTy = IntegerType::get(CalculationBits); 603 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 604 for (unsigned i = 1; i != K; ++i) { 605 const SCEV *S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType())); 606 Dividend = SE.getMulExpr(Dividend, 607 SE.getTruncateOrZeroExtend(S, CalculationTy)); 608 } 609 610 // Divide by 2^T 611 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 612 613 // Truncate the result, and divide by K! / 2^T. 614 615 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 616 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 617} 618 619/// evaluateAtIteration - Return the value of this chain of recurrences at 620/// the specified iteration number. We can evaluate this recurrence by 621/// multiplying each element in the chain by the binomial coefficient 622/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 623/// 624/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 625/// 626/// where BC(It, k) stands for binomial coefficient. 627/// 628const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 629 ScalarEvolution &SE) const { 630 const SCEV *Result = getStart(); 631 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 632 // The computation is correct in the face of overflow provided that the 633 // multiplication is performed _after_ the evaluation of the binomial 634 // coefficient. 635 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 636 if (isa<SCEVCouldNotCompute>(Coeff)) 637 return Coeff; 638 639 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 640 } 641 return Result; 642} 643 644//===----------------------------------------------------------------------===// 645// SCEV Expression folder implementations 646//===----------------------------------------------------------------------===// 647 648const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 649 const Type *Ty) { 650 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 651 "This is not a truncating conversion!"); 652 assert(isSCEVable(Ty) && 653 "This is not a conversion to a SCEVable type!"); 654 Ty = getEffectiveSCEVType(Ty); 655 656 FoldingSetNodeID ID; 657 ID.AddInteger(scTruncate); 658 ID.AddPointer(Op); 659 ID.AddPointer(Ty); 660 void *IP = 0; 661 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 662 663 // Fold if the operand is constant. 664 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 665 return getConstant( 666 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty))); 667 668 // trunc(trunc(x)) --> trunc(x) 669 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 670 return getTruncateExpr(ST->getOperand(), Ty); 671 672 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 673 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 674 return getTruncateOrSignExtend(SS->getOperand(), Ty); 675 676 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 677 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 678 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 679 680 // If the input value is a chrec scev, truncate the chrec's operands. 681 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 682 SmallVector<const SCEV *, 4> Operands; 683 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 684 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 685 return getAddRecExpr(Operands, AddRec->getLoop()); 686 } 687 688 // The cast wasn't folded; create an explicit cast node. 689 // Recompute the insert position, as it may have been invalidated. 690 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 691 SCEV *S = SCEVAllocator.Allocate<SCEVTruncateExpr>(); 692 new (S) SCEVTruncateExpr(ID, Op, Ty); 693 UniqueSCEVs.InsertNode(S, IP); 694 return S; 695} 696 697const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 698 const Type *Ty) { 699 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 700 "This is not an extending conversion!"); 701 assert(isSCEVable(Ty) && 702 "This is not a conversion to a SCEVable type!"); 703 Ty = getEffectiveSCEVType(Ty); 704 705 // Fold if the operand is constant. 706 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 707 const Type *IntTy = getEffectiveSCEVType(Ty); 708 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy); 709 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 710 return getConstant(cast<ConstantInt>(C)); 711 } 712 713 // zext(zext(x)) --> zext(x) 714 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 715 return getZeroExtendExpr(SZ->getOperand(), Ty); 716 717 // Before doing any expensive analysis, check to see if we've already 718 // computed a SCEV for this Op and Ty. 719 FoldingSetNodeID ID; 720 ID.AddInteger(scZeroExtend); 721 ID.AddPointer(Op); 722 ID.AddPointer(Ty); 723 void *IP = 0; 724 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 725 726 // If the input value is a chrec scev, and we can prove that the value 727 // did not overflow the old, smaller, value, we can zero extend all of the 728 // operands (often constants). This allows analysis of something like 729 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 730 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 731 if (AR->isAffine()) { 732 const SCEV *Start = AR->getStart(); 733 const SCEV *Step = AR->getStepRecurrence(*this); 734 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 735 const Loop *L = AR->getLoop(); 736 737 // If we have special knowledge that this addrec won't overflow, 738 // we don't need to do any further analysis. 739 if (AR->hasNoUnsignedOverflow()) 740 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 741 getZeroExtendExpr(Step, Ty), 742 L); 743 744 // Check whether the backedge-taken count is SCEVCouldNotCompute. 745 // Note that this serves two purposes: It filters out loops that are 746 // simply not analyzable, and it covers the case where this code is 747 // being called from within backedge-taken count analysis, such that 748 // attempting to ask for the backedge-taken count would likely result 749 // in infinite recursion. In the later case, the analysis code will 750 // cope with a conservative value, and it will take care to purge 751 // that value once it has finished. 752 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 753 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 754 // Manually compute the final value for AR, checking for 755 // overflow. 756 757 // Check whether the backedge-taken count can be losslessly casted to 758 // the addrec's type. The count is always unsigned. 759 const SCEV *CastedMaxBECount = 760 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 761 const SCEV *RecastedMaxBECount = 762 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 763 if (MaxBECount == RecastedMaxBECount) { 764 const Type *WideTy = IntegerType::get(BitWidth * 2); 765 // Check whether Start+Step*MaxBECount has no unsigned overflow. 766 const SCEV *ZMul = 767 getMulExpr(CastedMaxBECount, 768 getTruncateOrZeroExtend(Step, Start->getType())); 769 const SCEV *Add = getAddExpr(Start, ZMul); 770 const SCEV *OperandExtendedAdd = 771 getAddExpr(getZeroExtendExpr(Start, WideTy), 772 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 773 getZeroExtendExpr(Step, WideTy))); 774 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 775 // Return the expression with the addrec on the outside. 776 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 777 getZeroExtendExpr(Step, Ty), 778 L); 779 780 // Similar to above, only this time treat the step value as signed. 781 // This covers loops that count down. 782 const SCEV *SMul = 783 getMulExpr(CastedMaxBECount, 784 getTruncateOrSignExtend(Step, Start->getType())); 785 Add = getAddExpr(Start, SMul); 786 OperandExtendedAdd = 787 getAddExpr(getZeroExtendExpr(Start, WideTy), 788 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 789 getSignExtendExpr(Step, WideTy))); 790 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 791 // Return the expression with the addrec on the outside. 792 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 793 getSignExtendExpr(Step, Ty), 794 L); 795 } 796 797 // If the backedge is guarded by a comparison with the pre-inc value 798 // the addrec is safe. Also, if the entry is guarded by a comparison 799 // with the start value and the backedge is guarded by a comparison 800 // with the post-inc value, the addrec is safe. 801 if (isKnownPositive(Step)) { 802 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 803 getUnsignedRange(Step).getUnsignedMax()); 804 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 805 (isLoopGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 806 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 807 AR->getPostIncExpr(*this), N))) 808 // Return the expression with the addrec on the outside. 809 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 810 getZeroExtendExpr(Step, Ty), 811 L); 812 } else if (isKnownNegative(Step)) { 813 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 814 getSignedRange(Step).getSignedMin()); 815 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) && 816 (isLoopGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) || 817 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 818 AR->getPostIncExpr(*this), N))) 819 // Return the expression with the addrec on the outside. 820 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 821 getSignExtendExpr(Step, Ty), 822 L); 823 } 824 } 825 } 826 827 // The cast wasn't folded; create an explicit cast node. 828 // Recompute the insert position, as it may have been invalidated. 829 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 830 SCEV *S = SCEVAllocator.Allocate<SCEVZeroExtendExpr>(); 831 new (S) SCEVZeroExtendExpr(ID, Op, Ty); 832 UniqueSCEVs.InsertNode(S, IP); 833 return S; 834} 835 836const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 837 const Type *Ty) { 838 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 839 "This is not an extending conversion!"); 840 assert(isSCEVable(Ty) && 841 "This is not a conversion to a SCEVable type!"); 842 Ty = getEffectiveSCEVType(Ty); 843 844 // Fold if the operand is constant. 845 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 846 const Type *IntTy = getEffectiveSCEVType(Ty); 847 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy); 848 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 849 return getConstant(cast<ConstantInt>(C)); 850 } 851 852 // sext(sext(x)) --> sext(x) 853 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 854 return getSignExtendExpr(SS->getOperand(), Ty); 855 856 // Before doing any expensive analysis, check to see if we've already 857 // computed a SCEV for this Op and Ty. 858 FoldingSetNodeID ID; 859 ID.AddInteger(scSignExtend); 860 ID.AddPointer(Op); 861 ID.AddPointer(Ty); 862 void *IP = 0; 863 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 864 865 // If the input value is a chrec scev, and we can prove that the value 866 // did not overflow the old, smaller, value, we can sign extend all of the 867 // operands (often constants). This allows analysis of something like 868 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 869 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 870 if (AR->isAffine()) { 871 const SCEV *Start = AR->getStart(); 872 const SCEV *Step = AR->getStepRecurrence(*this); 873 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 874 const Loop *L = AR->getLoop(); 875 876 // If we have special knowledge that this addrec won't overflow, 877 // we don't need to do any further analysis. 878 if (AR->hasNoSignedOverflow()) 879 return getAddRecExpr(getSignExtendExpr(Start, Ty), 880 getSignExtendExpr(Step, Ty), 881 L); 882 883 // Check whether the backedge-taken count is SCEVCouldNotCompute. 884 // Note that this serves two purposes: It filters out loops that are 885 // simply not analyzable, and it covers the case where this code is 886 // being called from within backedge-taken count analysis, such that 887 // attempting to ask for the backedge-taken count would likely result 888 // in infinite recursion. In the later case, the analysis code will 889 // cope with a conservative value, and it will take care to purge 890 // that value once it has finished. 891 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 892 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 893 // Manually compute the final value for AR, checking for 894 // overflow. 895 896 // Check whether the backedge-taken count can be losslessly casted to 897 // the addrec's type. The count is always unsigned. 898 const SCEV *CastedMaxBECount = 899 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 900 const SCEV *RecastedMaxBECount = 901 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 902 if (MaxBECount == RecastedMaxBECount) { 903 const Type *WideTy = IntegerType::get(BitWidth * 2); 904 // Check whether Start+Step*MaxBECount has no signed overflow. 905 const SCEV *SMul = 906 getMulExpr(CastedMaxBECount, 907 getTruncateOrSignExtend(Step, Start->getType())); 908 const SCEV *Add = getAddExpr(Start, SMul); 909 const SCEV *OperandExtendedAdd = 910 getAddExpr(getSignExtendExpr(Start, WideTy), 911 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 912 getSignExtendExpr(Step, WideTy))); 913 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 914 // Return the expression with the addrec on the outside. 915 return getAddRecExpr(getSignExtendExpr(Start, Ty), 916 getSignExtendExpr(Step, Ty), 917 L); 918 919 // Similar to above, only this time treat the step value as unsigned. 920 // This covers loops that count up with an unsigned step. 921 const SCEV *UMul = 922 getMulExpr(CastedMaxBECount, 923 getTruncateOrZeroExtend(Step, Start->getType())); 924 Add = getAddExpr(Start, UMul); 925 OperandExtendedAdd = 926 getAddExpr(getZeroExtendExpr(Start, WideTy), 927 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 928 getZeroExtendExpr(Step, WideTy))); 929 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 930 // Return the expression with the addrec on the outside. 931 return getAddRecExpr(getSignExtendExpr(Start, Ty), 932 getZeroExtendExpr(Step, Ty), 933 L); 934 } 935 936 // If the backedge is guarded by a comparison with the pre-inc value 937 // the addrec is safe. Also, if the entry is guarded by a comparison 938 // with the start value and the backedge is guarded by a comparison 939 // with the post-inc value, the addrec is safe. 940 if (isKnownPositive(Step)) { 941 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) - 942 getSignedRange(Step).getSignedMax()); 943 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) || 944 (isLoopGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) && 945 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, 946 AR->getPostIncExpr(*this), N))) 947 // Return the expression with the addrec on the outside. 948 return getAddRecExpr(getSignExtendExpr(Start, Ty), 949 getSignExtendExpr(Step, Ty), 950 L); 951 } else if (isKnownNegative(Step)) { 952 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) - 953 getSignedRange(Step).getSignedMin()); 954 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) || 955 (isLoopGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) && 956 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, 957 AR->getPostIncExpr(*this), N))) 958 // Return the expression with the addrec on the outside. 959 return getAddRecExpr(getSignExtendExpr(Start, Ty), 960 getSignExtendExpr(Step, Ty), 961 L); 962 } 963 } 964 } 965 966 // The cast wasn't folded; create an explicit cast node. 967 // Recompute the insert position, as it may have been invalidated. 968 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 969 SCEV *S = SCEVAllocator.Allocate<SCEVSignExtendExpr>(); 970 new (S) SCEVSignExtendExpr(ID, Op, Ty); 971 UniqueSCEVs.InsertNode(S, IP); 972 return S; 973} 974 975/// getAnyExtendExpr - Return a SCEV for the given operand extended with 976/// unspecified bits out to the given type. 977/// 978const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 979 const Type *Ty) { 980 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 981 "This is not an extending conversion!"); 982 assert(isSCEVable(Ty) && 983 "This is not a conversion to a SCEVable type!"); 984 Ty = getEffectiveSCEVType(Ty); 985 986 // Sign-extend negative constants. 987 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 988 if (SC->getValue()->getValue().isNegative()) 989 return getSignExtendExpr(Op, Ty); 990 991 // Peel off a truncate cast. 992 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 993 const SCEV *NewOp = T->getOperand(); 994 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 995 return getAnyExtendExpr(NewOp, Ty); 996 return getTruncateOrNoop(NewOp, Ty); 997 } 998 999 // Next try a zext cast. If the cast is folded, use it. 1000 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1001 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1002 return ZExt; 1003 1004 // Next try a sext cast. If the cast is folded, use it. 1005 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1006 if (!isa<SCEVSignExtendExpr>(SExt)) 1007 return SExt; 1008 1009 // If the expression is obviously signed, use the sext cast value. 1010 if (isa<SCEVSMaxExpr>(Op)) 1011 return SExt; 1012 1013 // Absent any other information, use the zext cast value. 1014 return ZExt; 1015} 1016 1017/// CollectAddOperandsWithScales - Process the given Ops list, which is 1018/// a list of operands to be added under the given scale, update the given 1019/// map. This is a helper function for getAddRecExpr. As an example of 1020/// what it does, given a sequence of operands that would form an add 1021/// expression like this: 1022/// 1023/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1024/// 1025/// where A and B are constants, update the map with these values: 1026/// 1027/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1028/// 1029/// and add 13 + A*B*29 to AccumulatedConstant. 1030/// This will allow getAddRecExpr to produce this: 1031/// 1032/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1033/// 1034/// This form often exposes folding opportunities that are hidden in 1035/// the original operand list. 1036/// 1037/// Return true iff it appears that any interesting folding opportunities 1038/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1039/// the common case where no interesting opportunities are present, and 1040/// is also used as a check to avoid infinite recursion. 1041/// 1042static bool 1043CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1044 SmallVector<const SCEV *, 8> &NewOps, 1045 APInt &AccumulatedConstant, 1046 const SmallVectorImpl<const SCEV *> &Ops, 1047 const APInt &Scale, 1048 ScalarEvolution &SE) { 1049 bool Interesting = false; 1050 1051 // Iterate over the add operands. 1052 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1053 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1054 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1055 APInt NewScale = 1056 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1057 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1058 // A multiplication of a constant with another add; recurse. 1059 Interesting |= 1060 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1061 cast<SCEVAddExpr>(Mul->getOperand(1)) 1062 ->getOperands(), 1063 NewScale, SE); 1064 } else { 1065 // A multiplication of a constant with some other value. Update 1066 // the map. 1067 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1068 const SCEV *Key = SE.getMulExpr(MulOps); 1069 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1070 M.insert(std::make_pair(Key, NewScale)); 1071 if (Pair.second) { 1072 NewOps.push_back(Pair.first->first); 1073 } else { 1074 Pair.first->second += NewScale; 1075 // The map already had an entry for this value, which may indicate 1076 // a folding opportunity. 1077 Interesting = true; 1078 } 1079 } 1080 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1081 // Pull a buried constant out to the outside. 1082 if (Scale != 1 || AccumulatedConstant != 0 || C->isZero()) 1083 Interesting = true; 1084 AccumulatedConstant += Scale * C->getValue()->getValue(); 1085 } else { 1086 // An ordinary operand. Update the map. 1087 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1088 M.insert(std::make_pair(Ops[i], Scale)); 1089 if (Pair.second) { 1090 NewOps.push_back(Pair.first->first); 1091 } else { 1092 Pair.first->second += Scale; 1093 // The map already had an entry for this value, which may indicate 1094 // a folding opportunity. 1095 Interesting = true; 1096 } 1097 } 1098 } 1099 1100 return Interesting; 1101} 1102 1103namespace { 1104 struct APIntCompare { 1105 bool operator()(const APInt &LHS, const APInt &RHS) const { 1106 return LHS.ult(RHS); 1107 } 1108 }; 1109} 1110 1111/// getAddExpr - Get a canonical add expression, or something simpler if 1112/// possible. 1113const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops) { 1114 assert(!Ops.empty() && "Cannot get empty add!"); 1115 if (Ops.size() == 1) return Ops[0]; 1116#ifndef NDEBUG 1117 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1118 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1119 getEffectiveSCEVType(Ops[0]->getType()) && 1120 "SCEVAddExpr operand types don't match!"); 1121#endif 1122 1123 // Sort by complexity, this groups all similar expression types together. 1124 GroupByComplexity(Ops, LI); 1125 1126 // If there are any constants, fold them together. 1127 unsigned Idx = 0; 1128 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1129 ++Idx; 1130 assert(Idx < Ops.size()); 1131 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1132 // We found two constants, fold them together! 1133 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1134 RHSC->getValue()->getValue()); 1135 if (Ops.size() == 2) return Ops[0]; 1136 Ops.erase(Ops.begin()+1); // Erase the folded element 1137 LHSC = cast<SCEVConstant>(Ops[0]); 1138 } 1139 1140 // If we are left with a constant zero being added, strip it off. 1141 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1142 Ops.erase(Ops.begin()); 1143 --Idx; 1144 } 1145 } 1146 1147 if (Ops.size() == 1) return Ops[0]; 1148 1149 // Okay, check to see if the same value occurs in the operand list twice. If 1150 // so, merge them together into an multiply expression. Since we sorted the 1151 // list, these values are required to be adjacent. 1152 const Type *Ty = Ops[0]->getType(); 1153 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1154 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1155 // Found a match, merge the two values into a multiply, and add any 1156 // remaining values to the result. 1157 const SCEV *Two = getIntegerSCEV(2, Ty); 1158 const SCEV *Mul = getMulExpr(Ops[i], Two); 1159 if (Ops.size() == 2) 1160 return Mul; 1161 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 1162 Ops.push_back(Mul); 1163 return getAddExpr(Ops); 1164 } 1165 1166 // Check for truncates. If all the operands are truncated from the same 1167 // type, see if factoring out the truncate would permit the result to be 1168 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1169 // if the contents of the resulting outer trunc fold to something simple. 1170 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1171 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1172 const Type *DstType = Trunc->getType(); 1173 const Type *SrcType = Trunc->getOperand()->getType(); 1174 SmallVector<const SCEV *, 8> LargeOps; 1175 bool Ok = true; 1176 // Check all the operands to see if they can be represented in the 1177 // source type of the truncate. 1178 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1179 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1180 if (T->getOperand()->getType() != SrcType) { 1181 Ok = false; 1182 break; 1183 } 1184 LargeOps.push_back(T->getOperand()); 1185 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1186 // This could be either sign or zero extension, but sign extension 1187 // is much more likely to be foldable here. 1188 LargeOps.push_back(getSignExtendExpr(C, SrcType)); 1189 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1190 SmallVector<const SCEV *, 8> LargeMulOps; 1191 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1192 if (const SCEVTruncateExpr *T = 1193 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1194 if (T->getOperand()->getType() != SrcType) { 1195 Ok = false; 1196 break; 1197 } 1198 LargeMulOps.push_back(T->getOperand()); 1199 } else if (const SCEVConstant *C = 1200 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1201 // This could be either sign or zero extension, but sign extension 1202 // is much more likely to be foldable here. 1203 LargeMulOps.push_back(getSignExtendExpr(C, SrcType)); 1204 } else { 1205 Ok = false; 1206 break; 1207 } 1208 } 1209 if (Ok) 1210 LargeOps.push_back(getMulExpr(LargeMulOps)); 1211 } else { 1212 Ok = false; 1213 break; 1214 } 1215 } 1216 if (Ok) { 1217 // Evaluate the expression in the larger type. 1218 const SCEV *Fold = getAddExpr(LargeOps); 1219 // If it folds to something simple, use it. Otherwise, don't. 1220 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1221 return getTruncateExpr(Fold, DstType); 1222 } 1223 } 1224 1225 // Skip past any other cast SCEVs. 1226 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1227 ++Idx; 1228 1229 // If there are add operands they would be next. 1230 if (Idx < Ops.size()) { 1231 bool DeletedAdd = false; 1232 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1233 // If we have an add, expand the add operands onto the end of the operands 1234 // list. 1235 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 1236 Ops.erase(Ops.begin()+Idx); 1237 DeletedAdd = true; 1238 } 1239 1240 // If we deleted at least one add, we added operands to the end of the list, 1241 // and they are not necessarily sorted. Recurse to resort and resimplify 1242 // any operands we just aquired. 1243 if (DeletedAdd) 1244 return getAddExpr(Ops); 1245 } 1246 1247 // Skip over the add expression until we get to a multiply. 1248 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1249 ++Idx; 1250 1251 // Check to see if there are any folding opportunities present with 1252 // operands multiplied by constant values. 1253 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1254 uint64_t BitWidth = getTypeSizeInBits(Ty); 1255 DenseMap<const SCEV *, APInt> M; 1256 SmallVector<const SCEV *, 8> NewOps; 1257 APInt AccumulatedConstant(BitWidth, 0); 1258 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1259 Ops, APInt(BitWidth, 1), *this)) { 1260 // Some interesting folding opportunity is present, so its worthwhile to 1261 // re-generate the operands list. Group the operands by constant scale, 1262 // to avoid multiplying by the same constant scale multiple times. 1263 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1264 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(), 1265 E = NewOps.end(); I != E; ++I) 1266 MulOpLists[M.find(*I)->second].push_back(*I); 1267 // Re-generate the operands list. 1268 Ops.clear(); 1269 if (AccumulatedConstant != 0) 1270 Ops.push_back(getConstant(AccumulatedConstant)); 1271 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1272 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1273 if (I->first != 0) 1274 Ops.push_back(getMulExpr(getConstant(I->first), 1275 getAddExpr(I->second))); 1276 if (Ops.empty()) 1277 return getIntegerSCEV(0, Ty); 1278 if (Ops.size() == 1) 1279 return Ops[0]; 1280 return getAddExpr(Ops); 1281 } 1282 } 1283 1284 // If we are adding something to a multiply expression, make sure the 1285 // something is not already an operand of the multiply. If so, merge it into 1286 // the multiply. 1287 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1288 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1289 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1290 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1291 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1292 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) { 1293 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1294 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1295 if (Mul->getNumOperands() != 2) { 1296 // If the multiply has more than two operands, we must get the 1297 // Y*Z term. 1298 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end()); 1299 MulOps.erase(MulOps.begin()+MulOp); 1300 InnerMul = getMulExpr(MulOps); 1301 } 1302 const SCEV *One = getIntegerSCEV(1, Ty); 1303 const SCEV *AddOne = getAddExpr(InnerMul, One); 1304 const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]); 1305 if (Ops.size() == 2) return OuterMul; 1306 if (AddOp < Idx) { 1307 Ops.erase(Ops.begin()+AddOp); 1308 Ops.erase(Ops.begin()+Idx-1); 1309 } else { 1310 Ops.erase(Ops.begin()+Idx); 1311 Ops.erase(Ops.begin()+AddOp-1); 1312 } 1313 Ops.push_back(OuterMul); 1314 return getAddExpr(Ops); 1315 } 1316 1317 // Check this multiply against other multiplies being added together. 1318 for (unsigned OtherMulIdx = Idx+1; 1319 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1320 ++OtherMulIdx) { 1321 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1322 // If MulOp occurs in OtherMul, we can fold the two multiplies 1323 // together. 1324 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1325 OMulOp != e; ++OMulOp) 1326 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1327 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1328 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1329 if (Mul->getNumOperands() != 2) { 1330 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1331 Mul->op_end()); 1332 MulOps.erase(MulOps.begin()+MulOp); 1333 InnerMul1 = getMulExpr(MulOps); 1334 } 1335 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1336 if (OtherMul->getNumOperands() != 2) { 1337 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1338 OtherMul->op_end()); 1339 MulOps.erase(MulOps.begin()+OMulOp); 1340 InnerMul2 = getMulExpr(MulOps); 1341 } 1342 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1343 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1344 if (Ops.size() == 2) return OuterMul; 1345 Ops.erase(Ops.begin()+Idx); 1346 Ops.erase(Ops.begin()+OtherMulIdx-1); 1347 Ops.push_back(OuterMul); 1348 return getAddExpr(Ops); 1349 } 1350 } 1351 } 1352 } 1353 1354 // If there are any add recurrences in the operands list, see if any other 1355 // added values are loop invariant. If so, we can fold them into the 1356 // recurrence. 1357 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1358 ++Idx; 1359 1360 // Scan over all recurrences, trying to fold loop invariants into them. 1361 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1362 // Scan all of the other operands to this add and add them to the vector if 1363 // they are loop invariant w.r.t. the recurrence. 1364 SmallVector<const SCEV *, 8> LIOps; 1365 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1366 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1367 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1368 LIOps.push_back(Ops[i]); 1369 Ops.erase(Ops.begin()+i); 1370 --i; --e; 1371 } 1372 1373 // If we found some loop invariants, fold them into the recurrence. 1374 if (!LIOps.empty()) { 1375 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1376 LIOps.push_back(AddRec->getStart()); 1377 1378 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1379 AddRec->op_end()); 1380 AddRecOps[0] = getAddExpr(LIOps); 1381 1382 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 1383 // If all of the other operands were loop invariant, we are done. 1384 if (Ops.size() == 1) return NewRec; 1385 1386 // Otherwise, add the folded AddRec by the non-liv parts. 1387 for (unsigned i = 0;; ++i) 1388 if (Ops[i] == AddRec) { 1389 Ops[i] = NewRec; 1390 break; 1391 } 1392 return getAddExpr(Ops); 1393 } 1394 1395 // Okay, if there weren't any loop invariants to be folded, check to see if 1396 // there are multiple AddRec's with the same loop induction variable being 1397 // added together. If so, we can fold them. 1398 for (unsigned OtherIdx = Idx+1; 1399 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1400 if (OtherIdx != Idx) { 1401 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1402 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1403 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 1404 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(), 1405 AddRec->op_end()); 1406 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 1407 if (i >= NewOps.size()) { 1408 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 1409 OtherAddRec->op_end()); 1410 break; 1411 } 1412 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 1413 } 1414 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1415 1416 if (Ops.size() == 2) return NewAddRec; 1417 1418 Ops.erase(Ops.begin()+Idx); 1419 Ops.erase(Ops.begin()+OtherIdx-1); 1420 Ops.push_back(NewAddRec); 1421 return getAddExpr(Ops); 1422 } 1423 } 1424 1425 // Otherwise couldn't fold anything into this recurrence. Move onto the 1426 // next one. 1427 } 1428 1429 // Okay, it looks like we really DO need an add expr. Check to see if we 1430 // already have one, otherwise create a new one. 1431 FoldingSetNodeID ID; 1432 ID.AddInteger(scAddExpr); 1433 ID.AddInteger(Ops.size()); 1434 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1435 ID.AddPointer(Ops[i]); 1436 void *IP = 0; 1437 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1438 SCEV *S = SCEVAllocator.Allocate<SCEVAddExpr>(); 1439 new (S) SCEVAddExpr(ID, Ops); 1440 UniqueSCEVs.InsertNode(S, IP); 1441 return S; 1442} 1443 1444 1445/// getMulExpr - Get a canonical multiply expression, or something simpler if 1446/// possible. 1447const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops) { 1448 assert(!Ops.empty() && "Cannot get empty mul!"); 1449#ifndef NDEBUG 1450 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1451 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1452 getEffectiveSCEVType(Ops[0]->getType()) && 1453 "SCEVMulExpr operand types don't match!"); 1454#endif 1455 1456 // Sort by complexity, this groups all similar expression types together. 1457 GroupByComplexity(Ops, LI); 1458 1459 // If there are any constants, fold them together. 1460 unsigned Idx = 0; 1461 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1462 1463 // C1*(C2+V) -> C1*C2 + C1*V 1464 if (Ops.size() == 2) 1465 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1466 if (Add->getNumOperands() == 2 && 1467 isa<SCEVConstant>(Add->getOperand(0))) 1468 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1469 getMulExpr(LHSC, Add->getOperand(1))); 1470 1471 1472 ++Idx; 1473 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1474 // We found two constants, fold them together! 1475 ConstantInt *Fold = ConstantInt::get(getContext(), 1476 LHSC->getValue()->getValue() * 1477 RHSC->getValue()->getValue()); 1478 Ops[0] = getConstant(Fold); 1479 Ops.erase(Ops.begin()+1); // Erase the folded element 1480 if (Ops.size() == 1) return Ops[0]; 1481 LHSC = cast<SCEVConstant>(Ops[0]); 1482 } 1483 1484 // If we are left with a constant one being multiplied, strip it off. 1485 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1486 Ops.erase(Ops.begin()); 1487 --Idx; 1488 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1489 // If we have a multiply of zero, it will always be zero. 1490 return Ops[0]; 1491 } 1492 } 1493 1494 // Skip over the add expression until we get to a multiply. 1495 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1496 ++Idx; 1497 1498 if (Ops.size() == 1) 1499 return Ops[0]; 1500 1501 // If there are mul operands inline them all into this expression. 1502 if (Idx < Ops.size()) { 1503 bool DeletedMul = false; 1504 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1505 // If we have an mul, expand the mul operands onto the end of the operands 1506 // list. 1507 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 1508 Ops.erase(Ops.begin()+Idx); 1509 DeletedMul = true; 1510 } 1511 1512 // If we deleted at least one mul, we added operands to the end of the list, 1513 // and they are not necessarily sorted. Recurse to resort and resimplify 1514 // any operands we just aquired. 1515 if (DeletedMul) 1516 return getMulExpr(Ops); 1517 } 1518 1519 // If there are any add recurrences in the operands list, see if any other 1520 // added values are loop invariant. If so, we can fold them into the 1521 // recurrence. 1522 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1523 ++Idx; 1524 1525 // Scan over all recurrences, trying to fold loop invariants into them. 1526 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1527 // Scan all of the other operands to this mul and add them to the vector if 1528 // they are loop invariant w.r.t. the recurrence. 1529 SmallVector<const SCEV *, 8> LIOps; 1530 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1531 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1532 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1533 LIOps.push_back(Ops[i]); 1534 Ops.erase(Ops.begin()+i); 1535 --i; --e; 1536 } 1537 1538 // If we found some loop invariants, fold them into the recurrence. 1539 if (!LIOps.empty()) { 1540 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1541 SmallVector<const SCEV *, 4> NewOps; 1542 NewOps.reserve(AddRec->getNumOperands()); 1543 if (LIOps.size() == 1) { 1544 const SCEV *Scale = LIOps[0]; 1545 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1546 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1547 } else { 1548 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1549 SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end()); 1550 MulOps.push_back(AddRec->getOperand(i)); 1551 NewOps.push_back(getMulExpr(MulOps)); 1552 } 1553 } 1554 1555 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1556 1557 // If all of the other operands were loop invariant, we are done. 1558 if (Ops.size() == 1) return NewRec; 1559 1560 // Otherwise, multiply the folded AddRec by the non-liv parts. 1561 for (unsigned i = 0;; ++i) 1562 if (Ops[i] == AddRec) { 1563 Ops[i] = NewRec; 1564 break; 1565 } 1566 return getMulExpr(Ops); 1567 } 1568 1569 // Okay, if there weren't any loop invariants to be folded, check to see if 1570 // there are multiple AddRec's with the same loop induction variable being 1571 // multiplied together. If so, we can fold them. 1572 for (unsigned OtherIdx = Idx+1; 1573 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1574 if (OtherIdx != Idx) { 1575 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1576 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1577 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1578 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1579 const SCEV *NewStart = getMulExpr(F->getStart(), 1580 G->getStart()); 1581 const SCEV *B = F->getStepRecurrence(*this); 1582 const SCEV *D = G->getStepRecurrence(*this); 1583 const SCEV *NewStep = getAddExpr(getMulExpr(F, D), 1584 getMulExpr(G, B), 1585 getMulExpr(B, D)); 1586 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, 1587 F->getLoop()); 1588 if (Ops.size() == 2) return NewAddRec; 1589 1590 Ops.erase(Ops.begin()+Idx); 1591 Ops.erase(Ops.begin()+OtherIdx-1); 1592 Ops.push_back(NewAddRec); 1593 return getMulExpr(Ops); 1594 } 1595 } 1596 1597 // Otherwise couldn't fold anything into this recurrence. Move onto the 1598 // next one. 1599 } 1600 1601 // Okay, it looks like we really DO need an mul expr. Check to see if we 1602 // already have one, otherwise create a new one. 1603 FoldingSetNodeID ID; 1604 ID.AddInteger(scMulExpr); 1605 ID.AddInteger(Ops.size()); 1606 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1607 ID.AddPointer(Ops[i]); 1608 void *IP = 0; 1609 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1610 SCEV *S = SCEVAllocator.Allocate<SCEVMulExpr>(); 1611 new (S) SCEVMulExpr(ID, Ops); 1612 UniqueSCEVs.InsertNode(S, IP); 1613 return S; 1614} 1615 1616/// getUDivExpr - Get a canonical multiply expression, or something simpler if 1617/// possible. 1618const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 1619 const SCEV *RHS) { 1620 assert(getEffectiveSCEVType(LHS->getType()) == 1621 getEffectiveSCEVType(RHS->getType()) && 1622 "SCEVUDivExpr operand types don't match!"); 1623 1624 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1625 if (RHSC->getValue()->equalsInt(1)) 1626 return LHS; // X udiv 1 --> x 1627 if (RHSC->isZero()) 1628 return getIntegerSCEV(0, LHS->getType()); // value is undefined 1629 1630 // Determine if the division can be folded into the operands of 1631 // its operands. 1632 // TODO: Generalize this to non-constants by using known-bits information. 1633 const Type *Ty = LHS->getType(); 1634 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1635 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ; 1636 // For non-power-of-two values, effectively round the value up to the 1637 // nearest power of two. 1638 if (!RHSC->getValue()->getValue().isPowerOf2()) 1639 ++MaxShiftAmt; 1640 const IntegerType *ExtTy = 1641 IntegerType::get(getTypeSizeInBits(Ty) + MaxShiftAmt); 1642 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1643 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1644 if (const SCEVConstant *Step = 1645 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1646 if (!Step->getValue()->getValue() 1647 .urem(RHSC->getValue()->getValue()) && 1648 getZeroExtendExpr(AR, ExtTy) == 1649 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1650 getZeroExtendExpr(Step, ExtTy), 1651 AR->getLoop())) { 1652 SmallVector<const SCEV *, 4> Operands; 1653 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1654 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1655 return getAddRecExpr(Operands, AR->getLoop()); 1656 } 1657 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1658 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1659 SmallVector<const SCEV *, 4> Operands; 1660 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1661 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1662 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1663 // Find an operand that's safely divisible. 1664 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1665 const SCEV *Op = M->getOperand(i); 1666 const SCEV *Div = getUDivExpr(Op, RHSC); 1667 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1668 const SmallVectorImpl<const SCEV *> &MOperands = M->getOperands(); 1669 Operands = SmallVector<const SCEV *, 4>(MOperands.begin(), 1670 MOperands.end()); 1671 Operands[i] = Div; 1672 return getMulExpr(Operands); 1673 } 1674 } 1675 } 1676 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 1677 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 1678 SmallVector<const SCEV *, 4> Operands; 1679 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 1680 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 1681 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 1682 Operands.clear(); 1683 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 1684 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 1685 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i)) 1686 break; 1687 Operands.push_back(Op); 1688 } 1689 if (Operands.size() == A->getNumOperands()) 1690 return getAddExpr(Operands); 1691 } 1692 } 1693 1694 // Fold if both operands are constant. 1695 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1696 Constant *LHSCV = LHSC->getValue(); 1697 Constant *RHSCV = RHSC->getValue(); 1698 return getConstant(cast<ConstantInt>(getContext().getConstantExprUDiv(LHSCV, 1699 RHSCV))); 1700 } 1701 } 1702 1703 FoldingSetNodeID ID; 1704 ID.AddInteger(scUDivExpr); 1705 ID.AddPointer(LHS); 1706 ID.AddPointer(RHS); 1707 void *IP = 0; 1708 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1709 SCEV *S = SCEVAllocator.Allocate<SCEVUDivExpr>(); 1710 new (S) SCEVUDivExpr(ID, LHS, RHS); 1711 UniqueSCEVs.InsertNode(S, IP); 1712 return S; 1713} 1714 1715 1716/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1717/// Simplify the expression as much as possible. 1718const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, 1719 const SCEV *Step, const Loop *L) { 1720 SmallVector<const SCEV *, 4> Operands; 1721 Operands.push_back(Start); 1722 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1723 if (StepChrec->getLoop() == L) { 1724 Operands.insert(Operands.end(), StepChrec->op_begin(), 1725 StepChrec->op_end()); 1726 return getAddRecExpr(Operands, L); 1727 } 1728 1729 Operands.push_back(Step); 1730 return getAddRecExpr(Operands, L); 1731} 1732 1733/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1734/// Simplify the expression as much as possible. 1735const SCEV * 1736ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 1737 const Loop *L) { 1738 if (Operands.size() == 1) return Operands[0]; 1739#ifndef NDEBUG 1740 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 1741 assert(getEffectiveSCEVType(Operands[i]->getType()) == 1742 getEffectiveSCEVType(Operands[0]->getType()) && 1743 "SCEVAddRecExpr operand types don't match!"); 1744#endif 1745 1746 if (Operands.back()->isZero()) { 1747 Operands.pop_back(); 1748 return getAddRecExpr(Operands, L); // {X,+,0} --> X 1749 } 1750 1751 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 1752 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 1753 const Loop* NestedLoop = NestedAR->getLoop(); 1754 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) { 1755 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 1756 NestedAR->op_end()); 1757 Operands[0] = NestedAR->getStart(); 1758 // AddRecs require their operands be loop-invariant with respect to their 1759 // loops. Don't perform this transformation if it would break this 1760 // requirement. 1761 bool AllInvariant = true; 1762 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1763 if (!Operands[i]->isLoopInvariant(L)) { 1764 AllInvariant = false; 1765 break; 1766 } 1767 if (AllInvariant) { 1768 NestedOperands[0] = getAddRecExpr(Operands, L); 1769 AllInvariant = true; 1770 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 1771 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) { 1772 AllInvariant = false; 1773 break; 1774 } 1775 if (AllInvariant) 1776 // Ok, both add recurrences are valid after the transformation. 1777 return getAddRecExpr(NestedOperands, NestedLoop); 1778 } 1779 // Reset Operands to its original state. 1780 Operands[0] = NestedAR; 1781 } 1782 } 1783 1784 FoldingSetNodeID ID; 1785 ID.AddInteger(scAddRecExpr); 1786 ID.AddInteger(Operands.size()); 1787 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1788 ID.AddPointer(Operands[i]); 1789 ID.AddPointer(L); 1790 void *IP = 0; 1791 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1792 SCEV *S = SCEVAllocator.Allocate<SCEVAddRecExpr>(); 1793 new (S) SCEVAddRecExpr(ID, Operands, L); 1794 UniqueSCEVs.InsertNode(S, IP); 1795 return S; 1796} 1797 1798const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 1799 const SCEV *RHS) { 1800 SmallVector<const SCEV *, 2> Ops; 1801 Ops.push_back(LHS); 1802 Ops.push_back(RHS); 1803 return getSMaxExpr(Ops); 1804} 1805 1806const SCEV * 1807ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 1808 assert(!Ops.empty() && "Cannot get empty smax!"); 1809 if (Ops.size() == 1) return Ops[0]; 1810#ifndef NDEBUG 1811 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1812 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1813 getEffectiveSCEVType(Ops[0]->getType()) && 1814 "SCEVSMaxExpr operand types don't match!"); 1815#endif 1816 1817 // Sort by complexity, this groups all similar expression types together. 1818 GroupByComplexity(Ops, LI); 1819 1820 // If there are any constants, fold them together. 1821 unsigned Idx = 0; 1822 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1823 ++Idx; 1824 assert(Idx < Ops.size()); 1825 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1826 // We found two constants, fold them together! 1827 ConstantInt *Fold = ConstantInt::get(getContext(), 1828 APIntOps::smax(LHSC->getValue()->getValue(), 1829 RHSC->getValue()->getValue())); 1830 Ops[0] = getConstant(Fold); 1831 Ops.erase(Ops.begin()+1); // Erase the folded element 1832 if (Ops.size() == 1) return Ops[0]; 1833 LHSC = cast<SCEVConstant>(Ops[0]); 1834 } 1835 1836 // If we are left with a constant minimum-int, strip it off. 1837 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 1838 Ops.erase(Ops.begin()); 1839 --Idx; 1840 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 1841 // If we have an smax with a constant maximum-int, it will always be 1842 // maximum-int. 1843 return Ops[0]; 1844 } 1845 } 1846 1847 if (Ops.size() == 1) return Ops[0]; 1848 1849 // Find the first SMax 1850 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 1851 ++Idx; 1852 1853 // Check to see if one of the operands is an SMax. If so, expand its operands 1854 // onto our operand list, and recurse to simplify. 1855 if (Idx < Ops.size()) { 1856 bool DeletedSMax = false; 1857 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 1858 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 1859 Ops.erase(Ops.begin()+Idx); 1860 DeletedSMax = true; 1861 } 1862 1863 if (DeletedSMax) 1864 return getSMaxExpr(Ops); 1865 } 1866 1867 // Okay, check to see if the same value occurs in the operand list twice. If 1868 // so, delete one. Since we sorted the list, these values are required to 1869 // be adjacent. 1870 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1871 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 1872 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1873 --i; --e; 1874 } 1875 1876 if (Ops.size() == 1) return Ops[0]; 1877 1878 assert(!Ops.empty() && "Reduced smax down to nothing!"); 1879 1880 // Okay, it looks like we really DO need an smax expr. Check to see if we 1881 // already have one, otherwise create a new one. 1882 FoldingSetNodeID ID; 1883 ID.AddInteger(scSMaxExpr); 1884 ID.AddInteger(Ops.size()); 1885 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1886 ID.AddPointer(Ops[i]); 1887 void *IP = 0; 1888 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1889 SCEV *S = SCEVAllocator.Allocate<SCEVSMaxExpr>(); 1890 new (S) SCEVSMaxExpr(ID, Ops); 1891 UniqueSCEVs.InsertNode(S, IP); 1892 return S; 1893} 1894 1895const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 1896 const SCEV *RHS) { 1897 SmallVector<const SCEV *, 2> Ops; 1898 Ops.push_back(LHS); 1899 Ops.push_back(RHS); 1900 return getUMaxExpr(Ops); 1901} 1902 1903const SCEV * 1904ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 1905 assert(!Ops.empty() && "Cannot get empty umax!"); 1906 if (Ops.size() == 1) return Ops[0]; 1907#ifndef NDEBUG 1908 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1909 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1910 getEffectiveSCEVType(Ops[0]->getType()) && 1911 "SCEVUMaxExpr operand types don't match!"); 1912#endif 1913 1914 // Sort by complexity, this groups all similar expression types together. 1915 GroupByComplexity(Ops, LI); 1916 1917 // If there are any constants, fold them together. 1918 unsigned Idx = 0; 1919 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1920 ++Idx; 1921 assert(Idx < Ops.size()); 1922 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1923 // We found two constants, fold them together! 1924 ConstantInt *Fold = ConstantInt::get(getContext(), 1925 APIntOps::umax(LHSC->getValue()->getValue(), 1926 RHSC->getValue()->getValue())); 1927 Ops[0] = getConstant(Fold); 1928 Ops.erase(Ops.begin()+1); // Erase the folded element 1929 if (Ops.size() == 1) return Ops[0]; 1930 LHSC = cast<SCEVConstant>(Ops[0]); 1931 } 1932 1933 // If we are left with a constant minimum-int, strip it off. 1934 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 1935 Ops.erase(Ops.begin()); 1936 --Idx; 1937 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 1938 // If we have an umax with a constant maximum-int, it will always be 1939 // maximum-int. 1940 return Ops[0]; 1941 } 1942 } 1943 1944 if (Ops.size() == 1) return Ops[0]; 1945 1946 // Find the first UMax 1947 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 1948 ++Idx; 1949 1950 // Check to see if one of the operands is a UMax. If so, expand its operands 1951 // onto our operand list, and recurse to simplify. 1952 if (Idx < Ops.size()) { 1953 bool DeletedUMax = false; 1954 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 1955 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 1956 Ops.erase(Ops.begin()+Idx); 1957 DeletedUMax = true; 1958 } 1959 1960 if (DeletedUMax) 1961 return getUMaxExpr(Ops); 1962 } 1963 1964 // Okay, check to see if the same value occurs in the operand list twice. If 1965 // so, delete one. Since we sorted the list, these values are required to 1966 // be adjacent. 1967 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1968 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y 1969 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1970 --i; --e; 1971 } 1972 1973 if (Ops.size() == 1) return Ops[0]; 1974 1975 assert(!Ops.empty() && "Reduced umax down to nothing!"); 1976 1977 // Okay, it looks like we really DO need a umax expr. Check to see if we 1978 // already have one, otherwise create a new one. 1979 FoldingSetNodeID ID; 1980 ID.AddInteger(scUMaxExpr); 1981 ID.AddInteger(Ops.size()); 1982 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1983 ID.AddPointer(Ops[i]); 1984 void *IP = 0; 1985 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1986 SCEV *S = SCEVAllocator.Allocate<SCEVUMaxExpr>(); 1987 new (S) SCEVUMaxExpr(ID, Ops); 1988 UniqueSCEVs.InsertNode(S, IP); 1989 return S; 1990} 1991 1992const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 1993 const SCEV *RHS) { 1994 // ~smax(~x, ~y) == smin(x, y). 1995 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 1996} 1997 1998const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 1999 const SCEV *RHS) { 2000 // ~umax(~x, ~y) == umin(x, y) 2001 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2002} 2003 2004const SCEV *ScalarEvolution::getUnknown(Value *V) { 2005 // Don't attempt to do anything other than create a SCEVUnknown object 2006 // here. createSCEV only calls getUnknown after checking for all other 2007 // interesting possibilities, and any other code that calls getUnknown 2008 // is doing so in order to hide a value from SCEV canonicalization. 2009 2010 FoldingSetNodeID ID; 2011 ID.AddInteger(scUnknown); 2012 ID.AddPointer(V); 2013 void *IP = 0; 2014 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2015 SCEV *S = SCEVAllocator.Allocate<SCEVUnknown>(); 2016 new (S) SCEVUnknown(ID, V); 2017 UniqueSCEVs.InsertNode(S, IP); 2018 return S; 2019} 2020 2021//===----------------------------------------------------------------------===// 2022// Basic SCEV Analysis and PHI Idiom Recognition Code 2023// 2024 2025/// isSCEVable - Test if values of the given type are analyzable within 2026/// the SCEV framework. This primarily includes integer types, and it 2027/// can optionally include pointer types if the ScalarEvolution class 2028/// has access to target-specific information. 2029bool ScalarEvolution::isSCEVable(const Type *Ty) const { 2030 // Integers are always SCEVable. 2031 if (Ty->isInteger()) 2032 return true; 2033 2034 // Pointers are SCEVable if TargetData information is available 2035 // to provide pointer size information. 2036 if (isa<PointerType>(Ty)) 2037 return TD != NULL; 2038 2039 // Otherwise it's not SCEVable. 2040 return false; 2041} 2042 2043/// getTypeSizeInBits - Return the size in bits of the specified type, 2044/// for which isSCEVable must return true. 2045uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 2046 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2047 2048 // If we have a TargetData, use it! 2049 if (TD) 2050 return TD->getTypeSizeInBits(Ty); 2051 2052 // Otherwise, we support only integer types. 2053 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!"); 2054 return Ty->getPrimitiveSizeInBits(); 2055} 2056 2057/// getEffectiveSCEVType - Return a type with the same bitwidth as 2058/// the given type and which represents how SCEV will treat the given 2059/// type, for which isSCEVable must return true. For pointer types, 2060/// this is the pointer-sized integer type. 2061const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 2062 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2063 2064 if (Ty->isInteger()) 2065 return Ty; 2066 2067 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!"); 2068 return TD->getIntPtrType(); 2069} 2070 2071const SCEV *ScalarEvolution::getCouldNotCompute() { 2072 return &CouldNotCompute; 2073} 2074 2075/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2076/// expression and create a new one. 2077const SCEV *ScalarEvolution::getSCEV(Value *V) { 2078 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2079 2080 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V); 2081 if (I != Scalars.end()) return I->second; 2082 const SCEV *S = createSCEV(V); 2083 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2084 return S; 2085} 2086 2087/// getIntegerSCEV - Given a SCEVable type, create a constant for the 2088/// specified signed integer value and return a SCEV for the constant. 2089const SCEV *ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) { 2090 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 2091 return getConstant(ConstantInt::get(ITy, Val)); 2092} 2093 2094/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2095/// 2096const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2097 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2098 return getConstant( 2099 cast<ConstantInt>(getContext().getConstantExprNeg(VC->getValue()))); 2100 2101 const Type *Ty = V->getType(); 2102 Ty = getEffectiveSCEVType(Ty); 2103 return getMulExpr(V, 2104 getConstant(cast<ConstantInt>(getContext().getAllOnesValue(Ty)))); 2105} 2106 2107/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2108const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2109 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2110 return getConstant( 2111 cast<ConstantInt>(getContext().getConstantExprNot(VC->getValue()))); 2112 2113 const Type *Ty = V->getType(); 2114 Ty = getEffectiveSCEVType(Ty); 2115 const SCEV *AllOnes = 2116 getConstant(cast<ConstantInt>(getContext().getAllOnesValue(Ty))); 2117 return getMinusSCEV(AllOnes, V); 2118} 2119 2120/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 2121/// 2122const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, 2123 const SCEV *RHS) { 2124 // X - Y --> X + -Y 2125 return getAddExpr(LHS, getNegativeSCEV(RHS)); 2126} 2127 2128/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2129/// input value to the specified type. If the type must be extended, it is zero 2130/// extended. 2131const SCEV * 2132ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, 2133 const Type *Ty) { 2134 const Type *SrcTy = V->getType(); 2135 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2136 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2137 "Cannot truncate or zero extend with non-integer arguments!"); 2138 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2139 return V; // No conversion 2140 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2141 return getTruncateExpr(V, Ty); 2142 return getZeroExtendExpr(V, Ty); 2143} 2144 2145/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2146/// input value to the specified type. If the type must be extended, it is sign 2147/// extended. 2148const SCEV * 2149ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2150 const Type *Ty) { 2151 const Type *SrcTy = V->getType(); 2152 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2153 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2154 "Cannot truncate or zero extend with non-integer arguments!"); 2155 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2156 return V; // No conversion 2157 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2158 return getTruncateExpr(V, Ty); 2159 return getSignExtendExpr(V, Ty); 2160} 2161 2162/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2163/// input value to the specified type. If the type must be extended, it is zero 2164/// extended. The conversion must not be narrowing. 2165const SCEV * 2166ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { 2167 const Type *SrcTy = V->getType(); 2168 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2169 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2170 "Cannot noop or zero extend with non-integer arguments!"); 2171 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2172 "getNoopOrZeroExtend cannot truncate!"); 2173 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2174 return V; // No conversion 2175 return getZeroExtendExpr(V, Ty); 2176} 2177 2178/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2179/// input value to the specified type. If the type must be extended, it is sign 2180/// extended. The conversion must not be narrowing. 2181const SCEV * 2182ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { 2183 const Type *SrcTy = V->getType(); 2184 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2185 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2186 "Cannot noop or sign extend with non-integer arguments!"); 2187 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2188 "getNoopOrSignExtend cannot truncate!"); 2189 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2190 return V; // No conversion 2191 return getSignExtendExpr(V, Ty); 2192} 2193 2194/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2195/// the input value to the specified type. If the type must be extended, 2196/// it is extended with unspecified bits. The conversion must not be 2197/// narrowing. 2198const SCEV * 2199ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { 2200 const Type *SrcTy = V->getType(); 2201 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2202 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2203 "Cannot noop or any extend with non-integer arguments!"); 2204 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2205 "getNoopOrAnyExtend cannot truncate!"); 2206 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2207 return V; // No conversion 2208 return getAnyExtendExpr(V, Ty); 2209} 2210 2211/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2212/// input value to the specified type. The conversion must not be widening. 2213const SCEV * 2214ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { 2215 const Type *SrcTy = V->getType(); 2216 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2217 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2218 "Cannot truncate or noop with non-integer arguments!"); 2219 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2220 "getTruncateOrNoop cannot extend!"); 2221 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2222 return V; // No conversion 2223 return getTruncateExpr(V, Ty); 2224} 2225 2226/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2227/// the types using zero-extension, and then perform a umax operation 2228/// with them. 2229const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2230 const SCEV *RHS) { 2231 const SCEV *PromotedLHS = LHS; 2232 const SCEV *PromotedRHS = RHS; 2233 2234 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2235 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2236 else 2237 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2238 2239 return getUMaxExpr(PromotedLHS, PromotedRHS); 2240} 2241 2242/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2243/// the types using zero-extension, and then perform a umin operation 2244/// with them. 2245const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2246 const SCEV *RHS) { 2247 const SCEV *PromotedLHS = LHS; 2248 const SCEV *PromotedRHS = RHS; 2249 2250 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2251 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2252 else 2253 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2254 2255 return getUMinExpr(PromotedLHS, PromotedRHS); 2256} 2257 2258/// PushDefUseChildren - Push users of the given Instruction 2259/// onto the given Worklist. 2260static void 2261PushDefUseChildren(Instruction *I, 2262 SmallVectorImpl<Instruction *> &Worklist) { 2263 // Push the def-use children onto the Worklist stack. 2264 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2265 UI != UE; ++UI) 2266 Worklist.push_back(cast<Instruction>(UI)); 2267} 2268 2269/// ForgetSymbolicValue - This looks up computed SCEV values for all 2270/// instructions that depend on the given instruction and removes them from 2271/// the Scalars map if they reference SymName. This is used during PHI 2272/// resolution. 2273void 2274ScalarEvolution::ForgetSymbolicName(Instruction *I, const SCEV *SymName) { 2275 SmallVector<Instruction *, 16> Worklist; 2276 PushDefUseChildren(I, Worklist); 2277 2278 SmallPtrSet<Instruction *, 8> Visited; 2279 Visited.insert(I); 2280 while (!Worklist.empty()) { 2281 Instruction *I = Worklist.pop_back_val(); 2282 if (!Visited.insert(I)) continue; 2283 2284 std::map<SCEVCallbackVH, const SCEV*>::iterator It = 2285 Scalars.find(static_cast<Value *>(I)); 2286 if (It != Scalars.end()) { 2287 // Short-circuit the def-use traversal if the symbolic name 2288 // ceases to appear in expressions. 2289 if (!It->second->hasOperand(SymName)) 2290 continue; 2291 2292 // SCEVUnknown for a PHI either means that it has an unrecognized 2293 // structure, or it's a PHI that's in the progress of being computed 2294 // by createNodeForPHI. In the former case, additional loop trip 2295 // count information isn't going to change anything. In the later 2296 // case, createNodeForPHI will perform the necessary updates on its 2297 // own when it gets to that point. 2298 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) 2299 Scalars.erase(It); 2300 ValuesAtScopes.erase(I); 2301 } 2302 2303 PushDefUseChildren(I, Worklist); 2304 } 2305} 2306 2307/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2308/// a loop header, making it a potential recurrence, or it doesn't. 2309/// 2310const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2311 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 2312 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2313 if (L->getHeader() == PN->getParent()) { 2314 // If it lives in the loop header, it has two incoming values, one 2315 // from outside the loop, and one from inside. 2316 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 2317 unsigned BackEdge = IncomingEdge^1; 2318 2319 // While we are analyzing this PHI node, handle its value symbolically. 2320 const SCEV *SymbolicName = getUnknown(PN); 2321 assert(Scalars.find(PN) == Scalars.end() && 2322 "PHI node already processed?"); 2323 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2324 2325 // Using this symbolic name for the PHI, analyze the value coming around 2326 // the back-edge. 2327 Value *BEValueV = PN->getIncomingValue(BackEdge); 2328 const SCEV *BEValue = getSCEV(BEValueV); 2329 2330 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2331 // has a special value for the first iteration of the loop. 2332 2333 // If the value coming around the backedge is an add with the symbolic 2334 // value we just inserted, then we found a simple induction variable! 2335 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2336 // If there is a single occurrence of the symbolic value, replace it 2337 // with a recurrence. 2338 unsigned FoundIndex = Add->getNumOperands(); 2339 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2340 if (Add->getOperand(i) == SymbolicName) 2341 if (FoundIndex == e) { 2342 FoundIndex = i; 2343 break; 2344 } 2345 2346 if (FoundIndex != Add->getNumOperands()) { 2347 // Create an add with everything but the specified operand. 2348 SmallVector<const SCEV *, 8> Ops; 2349 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2350 if (i != FoundIndex) 2351 Ops.push_back(Add->getOperand(i)); 2352 const SCEV *Accum = getAddExpr(Ops); 2353 2354 // This is not a valid addrec if the step amount is varying each 2355 // loop iteration, but is not itself an addrec in this loop. 2356 if (Accum->isLoopInvariant(L) || 2357 (isa<SCEVAddRecExpr>(Accum) && 2358 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2359 const SCEV *StartVal = 2360 getSCEV(PN->getIncomingValue(IncomingEdge)); 2361 const SCEVAddRecExpr *PHISCEV = 2362 cast<SCEVAddRecExpr>(getAddRecExpr(StartVal, Accum, L)); 2363 2364 // If the increment doesn't overflow, then neither the addrec nor the 2365 // post-increment will overflow. 2366 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) 2367 if (OBO->getOperand(0) == PN && 2368 getSCEV(OBO->getOperand(1)) == 2369 PHISCEV->getStepRecurrence(*this)) { 2370 const SCEVAddRecExpr *PostInc = PHISCEV->getPostIncExpr(*this); 2371 if (OBO->hasNoUnsignedOverflow()) { 2372 const_cast<SCEVAddRecExpr *>(PHISCEV) 2373 ->setHasNoUnsignedOverflow(true); 2374 const_cast<SCEVAddRecExpr *>(PostInc) 2375 ->setHasNoUnsignedOverflow(true); 2376 } 2377 if (OBO->hasNoSignedOverflow()) { 2378 const_cast<SCEVAddRecExpr *>(PHISCEV) 2379 ->setHasNoSignedOverflow(true); 2380 const_cast<SCEVAddRecExpr *>(PostInc) 2381 ->setHasNoSignedOverflow(true); 2382 } 2383 } 2384 2385 // Okay, for the entire analysis of this edge we assumed the PHI 2386 // to be symbolic. We now need to go back and purge all of the 2387 // entries for the scalars that use the symbolic expression. 2388 ForgetSymbolicName(PN, SymbolicName); 2389 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; 2390 return PHISCEV; 2391 } 2392 } 2393 } else if (const SCEVAddRecExpr *AddRec = 2394 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2395 // Otherwise, this could be a loop like this: 2396 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2397 // In this case, j = {1,+,1} and BEValue is j. 2398 // Because the other in-value of i (0) fits the evolution of BEValue 2399 // i really is an addrec evolution. 2400 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2401 const SCEV *StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 2402 2403 // If StartVal = j.start - j.stride, we can use StartVal as the 2404 // initial step of the addrec evolution. 2405 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2406 AddRec->getOperand(1))) { 2407 const SCEV *PHISCEV = 2408 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2409 2410 // Okay, for the entire analysis of this edge we assumed the PHI 2411 // to be symbolic. We now need to go back and purge all of the 2412 // entries for the scalars that use the symbolic expression. 2413 ForgetSymbolicName(PN, SymbolicName); 2414 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; 2415 return PHISCEV; 2416 } 2417 } 2418 } 2419 2420 return SymbolicName; 2421 } 2422 2423 // It's tempting to recognize PHIs with a unique incoming value, however 2424 // this leads passes like indvars to break LCSSA form. Fortunately, such 2425 // PHIs are rare, as instcombine zaps them. 2426 2427 // If it's not a loop phi, we can't handle it yet. 2428 return getUnknown(PN); 2429} 2430 2431/// createNodeForGEP - Expand GEP instructions into add and multiply 2432/// operations. This allows them to be analyzed by regular SCEV code. 2433/// 2434const SCEV *ScalarEvolution::createNodeForGEP(Operator *GEP) { 2435 2436 const Type *IntPtrTy = TD->getIntPtrType(); 2437 Value *Base = GEP->getOperand(0); 2438 // Don't attempt to analyze GEPs over unsized objects. 2439 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2440 return getUnknown(GEP); 2441 const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy); 2442 gep_type_iterator GTI = gep_type_begin(GEP); 2443 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()), 2444 E = GEP->op_end(); 2445 I != E; ++I) { 2446 Value *Index = *I; 2447 // Compute the (potentially symbolic) offset in bytes for this index. 2448 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2449 // For a struct, add the member offset. 2450 const StructLayout &SL = *TD->getStructLayout(STy); 2451 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2452 uint64_t Offset = SL.getElementOffset(FieldNo); 2453 TotalOffset = getAddExpr(TotalOffset, getIntegerSCEV(Offset, IntPtrTy)); 2454 } else { 2455 // For an array, add the element offset, explicitly scaled. 2456 const SCEV *LocalOffset = getSCEV(Index); 2457 if (!isa<PointerType>(LocalOffset->getType())) 2458 // Getelementptr indicies are signed. 2459 LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy); 2460 LocalOffset = 2461 getMulExpr(LocalOffset, 2462 getIntegerSCEV(TD->getTypeAllocSize(*GTI), IntPtrTy)); 2463 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 2464 } 2465 } 2466 return getAddExpr(getSCEV(Base), TotalOffset); 2467} 2468 2469/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2470/// guaranteed to end in (at every loop iteration). It is, at the same time, 2471/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2472/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2473uint32_t 2474ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 2475 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2476 return C->getValue()->getValue().countTrailingZeros(); 2477 2478 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2479 return std::min(GetMinTrailingZeros(T->getOperand()), 2480 (uint32_t)getTypeSizeInBits(T->getType())); 2481 2482 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 2483 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2484 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2485 getTypeSizeInBits(E->getType()) : OpRes; 2486 } 2487 2488 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 2489 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2490 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2491 getTypeSizeInBits(E->getType()) : OpRes; 2492 } 2493 2494 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2495 // The result is the min of all operands results. 2496 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2497 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2498 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2499 return MinOpRes; 2500 } 2501 2502 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2503 // The result is the sum of all operands results. 2504 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2505 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2506 for (unsigned i = 1, e = M->getNumOperands(); 2507 SumOpRes != BitWidth && i != e; ++i) 2508 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2509 BitWidth); 2510 return SumOpRes; 2511 } 2512 2513 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2514 // The result is the min of all operands results. 2515 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2516 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2517 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2518 return MinOpRes; 2519 } 2520 2521 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2522 // The result is the min of all operands results. 2523 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2524 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2525 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2526 return MinOpRes; 2527 } 2528 2529 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2530 // The result is the min of all operands results. 2531 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2532 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2533 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2534 return MinOpRes; 2535 } 2536 2537 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2538 // For a SCEVUnknown, ask ValueTracking. 2539 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2540 APInt Mask = APInt::getAllOnesValue(BitWidth); 2541 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2542 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 2543 return Zeros.countTrailingOnes(); 2544 } 2545 2546 // SCEVUDivExpr 2547 return 0; 2548} 2549 2550/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 2551/// 2552ConstantRange 2553ScalarEvolution::getUnsignedRange(const SCEV *S) { 2554 2555 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2556 return ConstantRange(C->getValue()->getValue()); 2557 2558 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2559 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 2560 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2561 X = X.add(getUnsignedRange(Add->getOperand(i))); 2562 return X; 2563 } 2564 2565 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2566 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 2567 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2568 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 2569 return X; 2570 } 2571 2572 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2573 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 2574 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2575 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 2576 return X; 2577 } 2578 2579 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 2580 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 2581 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 2582 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 2583 return X; 2584 } 2585 2586 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 2587 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 2588 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 2589 return X.udiv(Y); 2590 } 2591 2592 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 2593 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 2594 return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth()); 2595 } 2596 2597 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 2598 ConstantRange X = getUnsignedRange(SExt->getOperand()); 2599 return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth()); 2600 } 2601 2602 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 2603 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 2604 return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth()); 2605 } 2606 2607 ConstantRange FullSet(getTypeSizeInBits(S->getType()), true); 2608 2609 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 2610 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop()); 2611 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T); 2612 if (!Trip) return FullSet; 2613 2614 // TODO: non-affine addrec 2615 if (AddRec->isAffine()) { 2616 const Type *Ty = AddRec->getType(); 2617 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 2618 if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) { 2619 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 2620 2621 const SCEV *Start = AddRec->getStart(); 2622 const SCEV *Step = AddRec->getStepRecurrence(*this); 2623 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this); 2624 2625 // Check for overflow. 2626 // TODO: This is very conservative. 2627 if (!(Step->isOne() && 2628 isKnownPredicate(ICmpInst::ICMP_ULT, Start, End)) && 2629 !(Step->isAllOnesValue() && 2630 isKnownPredicate(ICmpInst::ICMP_UGT, Start, End))) 2631 return FullSet; 2632 2633 ConstantRange StartRange = getUnsignedRange(Start); 2634 ConstantRange EndRange = getUnsignedRange(End); 2635 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 2636 EndRange.getUnsignedMin()); 2637 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 2638 EndRange.getUnsignedMax()); 2639 if (Min.isMinValue() && Max.isMaxValue()) 2640 return FullSet; 2641 return ConstantRange(Min, Max+1); 2642 } 2643 } 2644 } 2645 2646 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2647 // For a SCEVUnknown, ask ValueTracking. 2648 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2649 APInt Mask = APInt::getAllOnesValue(BitWidth); 2650 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2651 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 2652 if (Ones == ~Zeros + 1) 2653 return FullSet; 2654 return ConstantRange(Ones, ~Zeros + 1); 2655 } 2656 2657 return FullSet; 2658} 2659 2660/// getSignedRange - Determine the signed range for a particular SCEV. 2661/// 2662ConstantRange 2663ScalarEvolution::getSignedRange(const SCEV *S) { 2664 2665 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2666 return ConstantRange(C->getValue()->getValue()); 2667 2668 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2669 ConstantRange X = getSignedRange(Add->getOperand(0)); 2670 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2671 X = X.add(getSignedRange(Add->getOperand(i))); 2672 return X; 2673 } 2674 2675 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2676 ConstantRange X = getSignedRange(Mul->getOperand(0)); 2677 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2678 X = X.multiply(getSignedRange(Mul->getOperand(i))); 2679 return X; 2680 } 2681 2682 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2683 ConstantRange X = getSignedRange(SMax->getOperand(0)); 2684 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2685 X = X.smax(getSignedRange(SMax->getOperand(i))); 2686 return X; 2687 } 2688 2689 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 2690 ConstantRange X = getSignedRange(UMax->getOperand(0)); 2691 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 2692 X = X.umax(getSignedRange(UMax->getOperand(i))); 2693 return X; 2694 } 2695 2696 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 2697 ConstantRange X = getSignedRange(UDiv->getLHS()); 2698 ConstantRange Y = getSignedRange(UDiv->getRHS()); 2699 return X.udiv(Y); 2700 } 2701 2702 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 2703 ConstantRange X = getSignedRange(ZExt->getOperand()); 2704 return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth()); 2705 } 2706 2707 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 2708 ConstantRange X = getSignedRange(SExt->getOperand()); 2709 return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth()); 2710 } 2711 2712 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 2713 ConstantRange X = getSignedRange(Trunc->getOperand()); 2714 return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth()); 2715 } 2716 2717 ConstantRange FullSet(getTypeSizeInBits(S->getType()), true); 2718 2719 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 2720 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop()); 2721 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T); 2722 if (!Trip) return FullSet; 2723 2724 // TODO: non-affine addrec 2725 if (AddRec->isAffine()) { 2726 const Type *Ty = AddRec->getType(); 2727 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 2728 if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) { 2729 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 2730 2731 const SCEV *Start = AddRec->getStart(); 2732 const SCEV *Step = AddRec->getStepRecurrence(*this); 2733 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this); 2734 2735 // Check for overflow. 2736 // TODO: This is very conservative. 2737 if (!(Step->isOne() && 2738 isKnownPredicate(ICmpInst::ICMP_SLT, Start, End)) && 2739 !(Step->isAllOnesValue() && 2740 isKnownPredicate(ICmpInst::ICMP_SGT, Start, End))) 2741 return FullSet; 2742 2743 ConstantRange StartRange = getSignedRange(Start); 2744 ConstantRange EndRange = getSignedRange(End); 2745 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 2746 EndRange.getSignedMin()); 2747 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 2748 EndRange.getSignedMax()); 2749 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 2750 return FullSet; 2751 return ConstantRange(Min, Max+1); 2752 } 2753 } 2754 } 2755 2756 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2757 // For a SCEVUnknown, ask ValueTracking. 2758 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2759 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 2760 if (NS == 1) 2761 return FullSet; 2762 return 2763 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 2764 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1); 2765 } 2766 2767 return FullSet; 2768} 2769 2770/// createSCEV - We know that there is no SCEV for the specified value. 2771/// Analyze the expression. 2772/// 2773const SCEV *ScalarEvolution::createSCEV(Value *V) { 2774 if (!isSCEVable(V->getType())) 2775 return getUnknown(V); 2776 2777 unsigned Opcode = Instruction::UserOp1; 2778 if (Instruction *I = dyn_cast<Instruction>(V)) 2779 Opcode = I->getOpcode(); 2780 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 2781 Opcode = CE->getOpcode(); 2782 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 2783 return getConstant(CI); 2784 else if (isa<ConstantPointerNull>(V)) 2785 return getIntegerSCEV(0, V->getType()); 2786 else if (isa<UndefValue>(V)) 2787 return getIntegerSCEV(0, V->getType()); 2788 else 2789 return getUnknown(V); 2790 2791 Operator *U = cast<Operator>(V); 2792 switch (Opcode) { 2793 case Instruction::Add: 2794 return getAddExpr(getSCEV(U->getOperand(0)), 2795 getSCEV(U->getOperand(1))); 2796 case Instruction::Mul: 2797 return getMulExpr(getSCEV(U->getOperand(0)), 2798 getSCEV(U->getOperand(1))); 2799 case Instruction::UDiv: 2800 return getUDivExpr(getSCEV(U->getOperand(0)), 2801 getSCEV(U->getOperand(1))); 2802 case Instruction::Sub: 2803 return getMinusSCEV(getSCEV(U->getOperand(0)), 2804 getSCEV(U->getOperand(1))); 2805 case Instruction::And: 2806 // For an expression like x&255 that merely masks off the high bits, 2807 // use zext(trunc(x)) as the SCEV expression. 2808 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2809 if (CI->isNullValue()) 2810 return getSCEV(U->getOperand(1)); 2811 if (CI->isAllOnesValue()) 2812 return getSCEV(U->getOperand(0)); 2813 const APInt &A = CI->getValue(); 2814 2815 // Instcombine's ShrinkDemandedConstant may strip bits out of 2816 // constants, obscuring what would otherwise be a low-bits mask. 2817 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 2818 // knew about to reconstruct a low-bits mask value. 2819 unsigned LZ = A.countLeadingZeros(); 2820 unsigned BitWidth = A.getBitWidth(); 2821 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 2822 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 2823 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 2824 2825 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 2826 2827 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 2828 return 2829 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 2830 IntegerType::get(BitWidth - LZ)), 2831 U->getType()); 2832 } 2833 break; 2834 2835 case Instruction::Or: 2836 // If the RHS of the Or is a constant, we may have something like: 2837 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 2838 // optimizations will transparently handle this case. 2839 // 2840 // In order for this transformation to be safe, the LHS must be of the 2841 // form X*(2^n) and the Or constant must be less than 2^n. 2842 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2843 const SCEV *LHS = getSCEV(U->getOperand(0)); 2844 const APInt &CIVal = CI->getValue(); 2845 if (GetMinTrailingZeros(LHS) >= 2846 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) 2847 return getAddExpr(LHS, getSCEV(U->getOperand(1))); 2848 } 2849 break; 2850 case Instruction::Xor: 2851 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2852 // If the RHS of the xor is a signbit, then this is just an add. 2853 // Instcombine turns add of signbit into xor as a strength reduction step. 2854 if (CI->getValue().isSignBit()) 2855 return getAddExpr(getSCEV(U->getOperand(0)), 2856 getSCEV(U->getOperand(1))); 2857 2858 // If the RHS of xor is -1, then this is a not operation. 2859 if (CI->isAllOnesValue()) 2860 return getNotSCEV(getSCEV(U->getOperand(0))); 2861 2862 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 2863 // This is a variant of the check for xor with -1, and it handles 2864 // the case where instcombine has trimmed non-demanded bits out 2865 // of an xor with -1. 2866 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 2867 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 2868 if (BO->getOpcode() == Instruction::And && 2869 LCI->getValue() == CI->getValue()) 2870 if (const SCEVZeroExtendExpr *Z = 2871 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 2872 const Type *UTy = U->getType(); 2873 const SCEV *Z0 = Z->getOperand(); 2874 const Type *Z0Ty = Z0->getType(); 2875 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 2876 2877 // If C is a low-bits mask, the zero extend is zerving to 2878 // mask off the high bits. Complement the operand and 2879 // re-apply the zext. 2880 if (APIntOps::isMask(Z0TySize, CI->getValue())) 2881 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 2882 2883 // If C is a single bit, it may be in the sign-bit position 2884 // before the zero-extend. In this case, represent the xor 2885 // using an add, which is equivalent, and re-apply the zext. 2886 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize); 2887 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() && 2888 Trunc.isSignBit()) 2889 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 2890 UTy); 2891 } 2892 } 2893 break; 2894 2895 case Instruction::Shl: 2896 // Turn shift left of a constant amount into a multiply. 2897 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 2898 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 2899 Constant *X = ConstantInt::get(getContext(), 2900 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 2901 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 2902 } 2903 break; 2904 2905 case Instruction::LShr: 2906 // Turn logical shift right of a constant into a unsigned divide. 2907 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 2908 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 2909 Constant *X = ConstantInt::get(getContext(), 2910 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 2911 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 2912 } 2913 break; 2914 2915 case Instruction::AShr: 2916 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 2917 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 2918 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0))) 2919 if (L->getOpcode() == Instruction::Shl && 2920 L->getOperand(1) == U->getOperand(1)) { 2921 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2922 uint64_t Amt = BitWidth - CI->getZExtValue(); 2923 if (Amt == BitWidth) 2924 return getSCEV(L->getOperand(0)); // shift by zero --> noop 2925 if (Amt > BitWidth) 2926 return getIntegerSCEV(0, U->getType()); // value is undefined 2927 return 2928 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 2929 IntegerType::get(Amt)), 2930 U->getType()); 2931 } 2932 break; 2933 2934 case Instruction::Trunc: 2935 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 2936 2937 case Instruction::ZExt: 2938 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 2939 2940 case Instruction::SExt: 2941 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 2942 2943 case Instruction::BitCast: 2944 // BitCasts are no-op casts so we just eliminate the cast. 2945 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 2946 return getSCEV(U->getOperand(0)); 2947 break; 2948 2949 // It's tempting to handle inttoptr and ptrtoint, however this can 2950 // lead to pointer expressions which cannot be expanded to GEPs 2951 // (because they may overflow). For now, the only pointer-typed 2952 // expressions we handle are GEPs and address literals. 2953 2954 case Instruction::GetElementPtr: 2955 if (!TD) break; // Without TD we can't analyze pointers. 2956 return createNodeForGEP(U); 2957 2958 case Instruction::PHI: 2959 return createNodeForPHI(cast<PHINode>(U)); 2960 2961 case Instruction::Select: 2962 // This could be a smax or umax that was lowered earlier. 2963 // Try to recover it. 2964 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 2965 Value *LHS = ICI->getOperand(0); 2966 Value *RHS = ICI->getOperand(1); 2967 switch (ICI->getPredicate()) { 2968 case ICmpInst::ICMP_SLT: 2969 case ICmpInst::ICMP_SLE: 2970 std::swap(LHS, RHS); 2971 // fall through 2972 case ICmpInst::ICMP_SGT: 2973 case ICmpInst::ICMP_SGE: 2974 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 2975 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 2976 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 2977 return getSMinExpr(getSCEV(LHS), getSCEV(RHS)); 2978 break; 2979 case ICmpInst::ICMP_ULT: 2980 case ICmpInst::ICMP_ULE: 2981 std::swap(LHS, RHS); 2982 // fall through 2983 case ICmpInst::ICMP_UGT: 2984 case ICmpInst::ICMP_UGE: 2985 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 2986 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 2987 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 2988 return getUMinExpr(getSCEV(LHS), getSCEV(RHS)); 2989 break; 2990 case ICmpInst::ICMP_NE: 2991 // n != 0 ? n : 1 -> umax(n, 1) 2992 if (LHS == U->getOperand(1) && 2993 isa<ConstantInt>(U->getOperand(2)) && 2994 cast<ConstantInt>(U->getOperand(2))->isOne() && 2995 isa<ConstantInt>(RHS) && 2996 cast<ConstantInt>(RHS)->isZero()) 2997 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2))); 2998 break; 2999 case ICmpInst::ICMP_EQ: 3000 // n == 0 ? 1 : n -> umax(n, 1) 3001 if (LHS == U->getOperand(2) && 3002 isa<ConstantInt>(U->getOperand(1)) && 3003 cast<ConstantInt>(U->getOperand(1))->isOne() && 3004 isa<ConstantInt>(RHS) && 3005 cast<ConstantInt>(RHS)->isZero()) 3006 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1))); 3007 break; 3008 default: 3009 break; 3010 } 3011 } 3012 3013 default: // We cannot analyze this expression. 3014 break; 3015 } 3016 3017 return getUnknown(V); 3018} 3019 3020 3021 3022//===----------------------------------------------------------------------===// 3023// Iteration Count Computation Code 3024// 3025 3026/// getBackedgeTakenCount - If the specified loop has a predictable 3027/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3028/// object. The backedge-taken count is the number of times the loop header 3029/// will be branched to from within the loop. This is one less than the 3030/// trip count of the loop, since it doesn't count the first iteration, 3031/// when the header is branched to from outside the loop. 3032/// 3033/// Note that it is not valid to call this method on a loop without a 3034/// loop-invariant backedge-taken count (see 3035/// hasLoopInvariantBackedgeTakenCount). 3036/// 3037const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3038 return getBackedgeTakenInfo(L).Exact; 3039} 3040 3041/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3042/// return the least SCEV value that is known never to be less than the 3043/// actual backedge taken count. 3044const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3045 return getBackedgeTakenInfo(L).Max; 3046} 3047 3048/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3049/// onto the given Worklist. 3050static void 3051PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3052 BasicBlock *Header = L->getHeader(); 3053 3054 // Push all Loop-header PHIs onto the Worklist stack. 3055 for (BasicBlock::iterator I = Header->begin(); 3056 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3057 Worklist.push_back(PN); 3058} 3059 3060const ScalarEvolution::BackedgeTakenInfo & 3061ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3062 // Initially insert a CouldNotCompute for this loop. If the insertion 3063 // succeeds, procede to actually compute a backedge-taken count and 3064 // update the value. The temporary CouldNotCompute value tells SCEV 3065 // code elsewhere that it shouldn't attempt to request a new 3066 // backedge-taken count, which could result in infinite recursion. 3067 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair = 3068 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 3069 if (Pair.second) { 3070 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L); 3071 if (ItCount.Exact != getCouldNotCompute()) { 3072 assert(ItCount.Exact->isLoopInvariant(L) && 3073 ItCount.Max->isLoopInvariant(L) && 3074 "Computed trip count isn't loop invariant for loop!"); 3075 ++NumTripCountsComputed; 3076 3077 // Update the value in the map. 3078 Pair.first->second = ItCount; 3079 } else { 3080 if (ItCount.Max != getCouldNotCompute()) 3081 // Update the value in the map. 3082 Pair.first->second = ItCount; 3083 if (isa<PHINode>(L->getHeader()->begin())) 3084 // Only count loops that have phi nodes as not being computable. 3085 ++NumTripCountsNotComputed; 3086 } 3087 3088 // Now that we know more about the trip count for this loop, forget any 3089 // existing SCEV values for PHI nodes in this loop since they are only 3090 // conservative estimates made without the benefit of trip count 3091 // information. This is similar to the code in 3092 // forgetLoopBackedgeTakenCount, except that it handles SCEVUnknown PHI 3093 // nodes specially. 3094 if (ItCount.hasAnyInfo()) { 3095 SmallVector<Instruction *, 16> Worklist; 3096 PushLoopPHIs(L, Worklist); 3097 3098 SmallPtrSet<Instruction *, 8> Visited; 3099 while (!Worklist.empty()) { 3100 Instruction *I = Worklist.pop_back_val(); 3101 if (!Visited.insert(I)) continue; 3102 3103 std::map<SCEVCallbackVH, const SCEV*>::iterator It = 3104 Scalars.find(static_cast<Value *>(I)); 3105 if (It != Scalars.end()) { 3106 // SCEVUnknown for a PHI either means that it has an unrecognized 3107 // structure, or it's a PHI that's in the progress of being computed 3108 // by createNodeForPHI. In the former case, additional loop trip 3109 // count information isn't going to change anything. In the later 3110 // case, createNodeForPHI will perform the necessary updates on its 3111 // own when it gets to that point. 3112 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) 3113 Scalars.erase(It); 3114 ValuesAtScopes.erase(I); 3115 if (PHINode *PN = dyn_cast<PHINode>(I)) 3116 ConstantEvolutionLoopExitValue.erase(PN); 3117 } 3118 3119 PushDefUseChildren(I, Worklist); 3120 } 3121 } 3122 } 3123 return Pair.first->second; 3124} 3125 3126/// forgetLoopBackedgeTakenCount - This method should be called by the 3127/// client when it has changed a loop in a way that may effect 3128/// ScalarEvolution's ability to compute a trip count, or if the loop 3129/// is deleted. 3130void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) { 3131 BackedgeTakenCounts.erase(L); 3132 3133 SmallVector<Instruction *, 16> Worklist; 3134 PushLoopPHIs(L, Worklist); 3135 3136 SmallPtrSet<Instruction *, 8> Visited; 3137 while (!Worklist.empty()) { 3138 Instruction *I = Worklist.pop_back_val(); 3139 if (!Visited.insert(I)) continue; 3140 3141 std::map<SCEVCallbackVH, const SCEV*>::iterator It = 3142 Scalars.find(static_cast<Value *>(I)); 3143 if (It != Scalars.end()) { 3144 Scalars.erase(It); 3145 ValuesAtScopes.erase(I); 3146 if (PHINode *PN = dyn_cast<PHINode>(I)) 3147 ConstantEvolutionLoopExitValue.erase(PN); 3148 } 3149 3150 PushDefUseChildren(I, Worklist); 3151 } 3152} 3153 3154/// ComputeBackedgeTakenCount - Compute the number of times the backedge 3155/// of the specified loop will execute. 3156ScalarEvolution::BackedgeTakenInfo 3157ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 3158 SmallVector<BasicBlock*, 8> ExitingBlocks; 3159 L->getExitingBlocks(ExitingBlocks); 3160 3161 // Examine all exits and pick the most conservative values. 3162 const SCEV *BECount = getCouldNotCompute(); 3163 const SCEV *MaxBECount = getCouldNotCompute(); 3164 bool CouldNotComputeBECount = false; 3165 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 3166 BackedgeTakenInfo NewBTI = 3167 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 3168 3169 if (NewBTI.Exact == getCouldNotCompute()) { 3170 // We couldn't compute an exact value for this exit, so 3171 // we won't be able to compute an exact value for the loop. 3172 CouldNotComputeBECount = true; 3173 BECount = getCouldNotCompute(); 3174 } else if (!CouldNotComputeBECount) { 3175 if (BECount == getCouldNotCompute()) 3176 BECount = NewBTI.Exact; 3177 else 3178 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 3179 } 3180 if (MaxBECount == getCouldNotCompute()) 3181 MaxBECount = NewBTI.Max; 3182 else if (NewBTI.Max != getCouldNotCompute()) 3183 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 3184 } 3185 3186 return BackedgeTakenInfo(BECount, MaxBECount); 3187} 3188 3189/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 3190/// of the specified loop will execute if it exits via the specified block. 3191ScalarEvolution::BackedgeTakenInfo 3192ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 3193 BasicBlock *ExitingBlock) { 3194 3195 // Okay, we've chosen an exiting block. See what condition causes us to 3196 // exit at this block. 3197 // 3198 // FIXME: we should be able to handle switch instructions (with a single exit) 3199 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 3200 if (ExitBr == 0) return getCouldNotCompute(); 3201 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 3202 3203 // At this point, we know we have a conditional branch that determines whether 3204 // the loop is exited. However, we don't know if the branch is executed each 3205 // time through the loop. If not, then the execution count of the branch will 3206 // not be equal to the trip count of the loop. 3207 // 3208 // Currently we check for this by checking to see if the Exit branch goes to 3209 // the loop header. If so, we know it will always execute the same number of 3210 // times as the loop. We also handle the case where the exit block *is* the 3211 // loop header. This is common for un-rotated loops. 3212 // 3213 // If both of those tests fail, walk up the unique predecessor chain to the 3214 // header, stopping if there is an edge that doesn't exit the loop. If the 3215 // header is reached, the execution count of the branch will be equal to the 3216 // trip count of the loop. 3217 // 3218 // More extensive analysis could be done to handle more cases here. 3219 // 3220 if (ExitBr->getSuccessor(0) != L->getHeader() && 3221 ExitBr->getSuccessor(1) != L->getHeader() && 3222 ExitBr->getParent() != L->getHeader()) { 3223 // The simple checks failed, try climbing the unique predecessor chain 3224 // up to the header. 3225 bool Ok = false; 3226 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3227 BasicBlock *Pred = BB->getUniquePredecessor(); 3228 if (!Pred) 3229 return getCouldNotCompute(); 3230 TerminatorInst *PredTerm = Pred->getTerminator(); 3231 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3232 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3233 if (PredSucc == BB) 3234 continue; 3235 // If the predecessor has a successor that isn't BB and isn't 3236 // outside the loop, assume the worst. 3237 if (L->contains(PredSucc)) 3238 return getCouldNotCompute(); 3239 } 3240 if (Pred == L->getHeader()) { 3241 Ok = true; 3242 break; 3243 } 3244 BB = Pred; 3245 } 3246 if (!Ok) 3247 return getCouldNotCompute(); 3248 } 3249 3250 // Procede to the next level to examine the exit condition expression. 3251 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 3252 ExitBr->getSuccessor(0), 3253 ExitBr->getSuccessor(1)); 3254} 3255 3256/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 3257/// backedge of the specified loop will execute if its exit condition 3258/// were a conditional branch of ExitCond, TBB, and FBB. 3259ScalarEvolution::BackedgeTakenInfo 3260ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 3261 Value *ExitCond, 3262 BasicBlock *TBB, 3263 BasicBlock *FBB) { 3264 // Check if the controlling expression for this loop is an And or Or. 3265 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 3266 if (BO->getOpcode() == Instruction::And) { 3267 // Recurse on the operands of the and. 3268 BackedgeTakenInfo BTI0 = 3269 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3270 BackedgeTakenInfo BTI1 = 3271 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3272 const SCEV *BECount = getCouldNotCompute(); 3273 const SCEV *MaxBECount = getCouldNotCompute(); 3274 if (L->contains(TBB)) { 3275 // Both conditions must be true for the loop to continue executing. 3276 // Choose the less conservative count. 3277 if (BTI0.Exact == getCouldNotCompute() || 3278 BTI1.Exact == getCouldNotCompute()) 3279 BECount = getCouldNotCompute(); 3280 else 3281 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3282 if (BTI0.Max == getCouldNotCompute()) 3283 MaxBECount = BTI1.Max; 3284 else if (BTI1.Max == getCouldNotCompute()) 3285 MaxBECount = BTI0.Max; 3286 else 3287 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3288 } else { 3289 // Both conditions must be true for the loop to exit. 3290 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 3291 if (BTI0.Exact != getCouldNotCompute() && 3292 BTI1.Exact != getCouldNotCompute()) 3293 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3294 if (BTI0.Max != getCouldNotCompute() && 3295 BTI1.Max != getCouldNotCompute()) 3296 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3297 } 3298 3299 return BackedgeTakenInfo(BECount, MaxBECount); 3300 } 3301 if (BO->getOpcode() == Instruction::Or) { 3302 // Recurse on the operands of the or. 3303 BackedgeTakenInfo BTI0 = 3304 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3305 BackedgeTakenInfo BTI1 = 3306 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3307 const SCEV *BECount = getCouldNotCompute(); 3308 const SCEV *MaxBECount = getCouldNotCompute(); 3309 if (L->contains(FBB)) { 3310 // Both conditions must be false for the loop to continue executing. 3311 // Choose the less conservative count. 3312 if (BTI0.Exact == getCouldNotCompute() || 3313 BTI1.Exact == getCouldNotCompute()) 3314 BECount = getCouldNotCompute(); 3315 else 3316 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3317 if (BTI0.Max == getCouldNotCompute()) 3318 MaxBECount = BTI1.Max; 3319 else if (BTI1.Max == getCouldNotCompute()) 3320 MaxBECount = BTI0.Max; 3321 else 3322 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3323 } else { 3324 // Both conditions must be false for the loop to exit. 3325 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 3326 if (BTI0.Exact != getCouldNotCompute() && 3327 BTI1.Exact != getCouldNotCompute()) 3328 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3329 if (BTI0.Max != getCouldNotCompute() && 3330 BTI1.Max != getCouldNotCompute()) 3331 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3332 } 3333 3334 return BackedgeTakenInfo(BECount, MaxBECount); 3335 } 3336 } 3337 3338 // With an icmp, it may be feasible to compute an exact backedge-taken count. 3339 // Procede to the next level to examine the icmp. 3340 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 3341 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 3342 3343 // If it's not an integer or pointer comparison then compute it the hard way. 3344 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3345} 3346 3347/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 3348/// backedge of the specified loop will execute if its exit condition 3349/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 3350ScalarEvolution::BackedgeTakenInfo 3351ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 3352 ICmpInst *ExitCond, 3353 BasicBlock *TBB, 3354 BasicBlock *FBB) { 3355 3356 // If the condition was exit on true, convert the condition to exit on false 3357 ICmpInst::Predicate Cond; 3358 if (!L->contains(FBB)) 3359 Cond = ExitCond->getPredicate(); 3360 else 3361 Cond = ExitCond->getInversePredicate(); 3362 3363 // Handle common loops like: for (X = "string"; *X; ++X) 3364 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 3365 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 3366 const SCEV *ItCnt = 3367 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 3368 if (!isa<SCEVCouldNotCompute>(ItCnt)) { 3369 unsigned BitWidth = getTypeSizeInBits(ItCnt->getType()); 3370 return BackedgeTakenInfo(ItCnt, 3371 isa<SCEVConstant>(ItCnt) ? ItCnt : 3372 getConstant(APInt::getMaxValue(BitWidth)-1)); 3373 } 3374 } 3375 3376 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 3377 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 3378 3379 // Try to evaluate any dependencies out of the loop. 3380 LHS = getSCEVAtScope(LHS, L); 3381 RHS = getSCEVAtScope(RHS, L); 3382 3383 // At this point, we would like to compute how many iterations of the 3384 // loop the predicate will return true for these inputs. 3385 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 3386 // If there is a loop-invariant, force it into the RHS. 3387 std::swap(LHS, RHS); 3388 Cond = ICmpInst::getSwappedPredicate(Cond); 3389 } 3390 3391 // If we have a comparison of a chrec against a constant, try to use value 3392 // ranges to answer this query. 3393 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 3394 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 3395 if (AddRec->getLoop() == L) { 3396 // Form the constant range. 3397 ConstantRange CompRange( 3398 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 3399 3400 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 3401 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 3402 } 3403 3404 switch (Cond) { 3405 case ICmpInst::ICMP_NE: { // while (X != Y) 3406 // Convert to: while (X-Y != 0) 3407 const SCEV *TC = HowFarToZero(getMinusSCEV(LHS, RHS), L); 3408 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 3409 break; 3410 } 3411 case ICmpInst::ICMP_EQ: { 3412 // Convert to: while (X-Y == 0) // while (X == Y) 3413 const SCEV *TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 3414 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 3415 break; 3416 } 3417 case ICmpInst::ICMP_SLT: { 3418 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 3419 if (BTI.hasAnyInfo()) return BTI; 3420 break; 3421 } 3422 case ICmpInst::ICMP_SGT: { 3423 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3424 getNotSCEV(RHS), L, true); 3425 if (BTI.hasAnyInfo()) return BTI; 3426 break; 3427 } 3428 case ICmpInst::ICMP_ULT: { 3429 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 3430 if (BTI.hasAnyInfo()) return BTI; 3431 break; 3432 } 3433 case ICmpInst::ICMP_UGT: { 3434 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3435 getNotSCEV(RHS), L, false); 3436 if (BTI.hasAnyInfo()) return BTI; 3437 break; 3438 } 3439 default: 3440#if 0 3441 errs() << "ComputeBackedgeTakenCount "; 3442 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 3443 errs() << "[unsigned] "; 3444 errs() << *LHS << " " 3445 << Instruction::getOpcodeName(Instruction::ICmp) 3446 << " " << *RHS << "\n"; 3447#endif 3448 break; 3449 } 3450 return 3451 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3452} 3453 3454static ConstantInt * 3455EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 3456 ScalarEvolution &SE) { 3457 const SCEV *InVal = SE.getConstant(C); 3458 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 3459 assert(isa<SCEVConstant>(Val) && 3460 "Evaluation of SCEV at constant didn't fold correctly?"); 3461 return cast<SCEVConstant>(Val)->getValue(); 3462} 3463 3464/// GetAddressedElementFromGlobal - Given a global variable with an initializer 3465/// and a GEP expression (missing the pointer index) indexing into it, return 3466/// the addressed element of the initializer or null if the index expression is 3467/// invalid. 3468static Constant * 3469GetAddressedElementFromGlobal(LLVMContext &Context, GlobalVariable *GV, 3470 const std::vector<ConstantInt*> &Indices) { 3471 Constant *Init = GV->getInitializer(); 3472 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 3473 uint64_t Idx = Indices[i]->getZExtValue(); 3474 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 3475 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 3476 Init = cast<Constant>(CS->getOperand(Idx)); 3477 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 3478 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 3479 Init = cast<Constant>(CA->getOperand(Idx)); 3480 } else if (isa<ConstantAggregateZero>(Init)) { 3481 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 3482 assert(Idx < STy->getNumElements() && "Bad struct index!"); 3483 Init = Context.getNullValue(STy->getElementType(Idx)); 3484 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 3485 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 3486 Init = Context.getNullValue(ATy->getElementType()); 3487 } else { 3488 llvm_unreachable("Unknown constant aggregate type!"); 3489 } 3490 return 0; 3491 } else { 3492 return 0; // Unknown initializer type 3493 } 3494 } 3495 return Init; 3496} 3497 3498/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 3499/// 'icmp op load X, cst', try to see if we can compute the backedge 3500/// execution count. 3501const SCEV * 3502ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 3503 LoadInst *LI, 3504 Constant *RHS, 3505 const Loop *L, 3506 ICmpInst::Predicate predicate) { 3507 if (LI->isVolatile()) return getCouldNotCompute(); 3508 3509 // Check to see if the loaded pointer is a getelementptr of a global. 3510 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 3511 if (!GEP) return getCouldNotCompute(); 3512 3513 // Make sure that it is really a constant global we are gepping, with an 3514 // initializer, and make sure the first IDX is really 0. 3515 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 3516 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 3517 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 3518 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 3519 return getCouldNotCompute(); 3520 3521 // Okay, we allow one non-constant index into the GEP instruction. 3522 Value *VarIdx = 0; 3523 std::vector<ConstantInt*> Indexes; 3524 unsigned VarIdxNum = 0; 3525 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 3526 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 3527 Indexes.push_back(CI); 3528 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 3529 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 3530 VarIdx = GEP->getOperand(i); 3531 VarIdxNum = i-2; 3532 Indexes.push_back(0); 3533 } 3534 3535 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 3536 // Check to see if X is a loop variant variable value now. 3537 const SCEV *Idx = getSCEV(VarIdx); 3538 Idx = getSCEVAtScope(Idx, L); 3539 3540 // We can only recognize very limited forms of loop index expressions, in 3541 // particular, only affine AddRec's like {C1,+,C2}. 3542 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 3543 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 3544 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 3545 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 3546 return getCouldNotCompute(); 3547 3548 unsigned MaxSteps = MaxBruteForceIterations; 3549 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 3550 ConstantInt *ItCst = ConstantInt::get( 3551 cast<IntegerType>(IdxExpr->getType()), IterationNum); 3552 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 3553 3554 // Form the GEP offset. 3555 Indexes[VarIdxNum] = Val; 3556 3557 Constant *Result = GetAddressedElementFromGlobal(getContext(), GV, Indexes); 3558 if (Result == 0) break; // Cannot compute! 3559 3560 // Evaluate the condition for this iteration. 3561 Result = ConstantExpr::getICmp(predicate, Result, RHS); 3562 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 3563 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 3564#if 0 3565 errs() << "\n***\n*** Computed loop count " << *ItCst 3566 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 3567 << "***\n"; 3568#endif 3569 ++NumArrayLenItCounts; 3570 return getConstant(ItCst); // Found terminating iteration! 3571 } 3572 } 3573 return getCouldNotCompute(); 3574} 3575 3576 3577/// CanConstantFold - Return true if we can constant fold an instruction of the 3578/// specified type, assuming that all operands were constants. 3579static bool CanConstantFold(const Instruction *I) { 3580 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 3581 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 3582 return true; 3583 3584 if (const CallInst *CI = dyn_cast<CallInst>(I)) 3585 if (const Function *F = CI->getCalledFunction()) 3586 return canConstantFoldCallTo(F); 3587 return false; 3588} 3589 3590/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 3591/// in the loop that V is derived from. We allow arbitrary operations along the 3592/// way, but the operands of an operation must either be constants or a value 3593/// derived from a constant PHI. If this expression does not fit with these 3594/// constraints, return null. 3595static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 3596 // If this is not an instruction, or if this is an instruction outside of the 3597 // loop, it can't be derived from a loop PHI. 3598 Instruction *I = dyn_cast<Instruction>(V); 3599 if (I == 0 || !L->contains(I->getParent())) return 0; 3600 3601 if (PHINode *PN = dyn_cast<PHINode>(I)) { 3602 if (L->getHeader() == I->getParent()) 3603 return PN; 3604 else 3605 // We don't currently keep track of the control flow needed to evaluate 3606 // PHIs, so we cannot handle PHIs inside of loops. 3607 return 0; 3608 } 3609 3610 // If we won't be able to constant fold this expression even if the operands 3611 // are constants, return early. 3612 if (!CanConstantFold(I)) return 0; 3613 3614 // Otherwise, we can evaluate this instruction if all of its operands are 3615 // constant or derived from a PHI node themselves. 3616 PHINode *PHI = 0; 3617 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 3618 if (!(isa<Constant>(I->getOperand(Op)) || 3619 isa<GlobalValue>(I->getOperand(Op)))) { 3620 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 3621 if (P == 0) return 0; // Not evolving from PHI 3622 if (PHI == 0) 3623 PHI = P; 3624 else if (PHI != P) 3625 return 0; // Evolving from multiple different PHIs. 3626 } 3627 3628 // This is a expression evolving from a constant PHI! 3629 return PHI; 3630} 3631 3632/// EvaluateExpression - Given an expression that passes the 3633/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 3634/// in the loop has the value PHIVal. If we can't fold this expression for some 3635/// reason, return null. 3636static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 3637 if (isa<PHINode>(V)) return PHIVal; 3638 if (Constant *C = dyn_cast<Constant>(V)) return C; 3639 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV; 3640 Instruction *I = cast<Instruction>(V); 3641 LLVMContext &Context = I->getParent()->getContext(); 3642 3643 std::vector<Constant*> Operands; 3644 Operands.resize(I->getNumOperands()); 3645 3646 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 3647 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 3648 if (Operands[i] == 0) return 0; 3649 } 3650 3651 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 3652 return ConstantFoldCompareInstOperands(CI->getPredicate(), 3653 &Operands[0], Operands.size(), 3654 Context); 3655 else 3656 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 3657 &Operands[0], Operands.size(), 3658 Context); 3659} 3660 3661/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 3662/// in the header of its containing loop, we know the loop executes a 3663/// constant number of times, and the PHI node is just a recurrence 3664/// involving constants, fold it. 3665Constant * 3666ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 3667 const APInt& BEs, 3668 const Loop *L) { 3669 std::map<PHINode*, Constant*>::iterator I = 3670 ConstantEvolutionLoopExitValue.find(PN); 3671 if (I != ConstantEvolutionLoopExitValue.end()) 3672 return I->second; 3673 3674 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations))) 3675 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 3676 3677 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 3678 3679 // Since the loop is canonicalized, the PHI node must have two entries. One 3680 // entry must be a constant (coming in from outside of the loop), and the 3681 // second must be derived from the same PHI. 3682 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 3683 Constant *StartCST = 3684 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 3685 if (StartCST == 0) 3686 return RetVal = 0; // Must be a constant. 3687 3688 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 3689 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 3690 if (PN2 != PN) 3691 return RetVal = 0; // Not derived from same PHI. 3692 3693 // Execute the loop symbolically to determine the exit value. 3694 if (BEs.getActiveBits() >= 32) 3695 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 3696 3697 unsigned NumIterations = BEs.getZExtValue(); // must be in range 3698 unsigned IterationNum = 0; 3699 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 3700 if (IterationNum == NumIterations) 3701 return RetVal = PHIVal; // Got exit value! 3702 3703 // Compute the value of the PHI node for the next iteration. 3704 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 3705 if (NextPHI == PHIVal) 3706 return RetVal = NextPHI; // Stopped evolving! 3707 if (NextPHI == 0) 3708 return 0; // Couldn't evaluate! 3709 PHIVal = NextPHI; 3710 } 3711} 3712 3713/// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a 3714/// constant number of times (the condition evolves only from constants), 3715/// try to evaluate a few iterations of the loop until we get the exit 3716/// condition gets a value of ExitWhen (true or false). If we cannot 3717/// evaluate the trip count of the loop, return getCouldNotCompute(). 3718const SCEV * 3719ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 3720 Value *Cond, 3721 bool ExitWhen) { 3722 PHINode *PN = getConstantEvolvingPHI(Cond, L); 3723 if (PN == 0) return getCouldNotCompute(); 3724 3725 // Since the loop is canonicalized, the PHI node must have two entries. One 3726 // entry must be a constant (coming in from outside of the loop), and the 3727 // second must be derived from the same PHI. 3728 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 3729 Constant *StartCST = 3730 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 3731 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 3732 3733 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 3734 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 3735 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI. 3736 3737 // Okay, we find a PHI node that defines the trip count of this loop. Execute 3738 // the loop symbolically to determine when the condition gets a value of 3739 // "ExitWhen". 3740 unsigned IterationNum = 0; 3741 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 3742 for (Constant *PHIVal = StartCST; 3743 IterationNum != MaxIterations; ++IterationNum) { 3744 ConstantInt *CondVal = 3745 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 3746 3747 // Couldn't symbolically evaluate. 3748 if (!CondVal) return getCouldNotCompute(); 3749 3750 if (CondVal->getValue() == uint64_t(ExitWhen)) { 3751 ++NumBruteForceTripCountsComputed; 3752 return getConstant(Type::Int32Ty, IterationNum); 3753 } 3754 3755 // Compute the value of the PHI node for the next iteration. 3756 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 3757 if (NextPHI == 0 || NextPHI == PHIVal) 3758 return getCouldNotCompute();// Couldn't evaluate or not making progress... 3759 PHIVal = NextPHI; 3760 } 3761 3762 // Too many iterations were needed to evaluate. 3763 return getCouldNotCompute(); 3764} 3765 3766/// getSCEVAtScope - Return a SCEV expression handle for the specified value 3767/// at the specified scope in the program. The L value specifies a loop 3768/// nest to evaluate the expression at, where null is the top-level or a 3769/// specified loop is immediately inside of the loop. 3770/// 3771/// This method can be used to compute the exit value for a variable defined 3772/// in a loop by querying what the value will hold in the parent loop. 3773/// 3774/// In the case that a relevant loop exit value cannot be computed, the 3775/// original value V is returned. 3776const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 3777 // FIXME: this should be turned into a virtual method on SCEV! 3778 3779 if (isa<SCEVConstant>(V)) return V; 3780 3781 // If this instruction is evolved from a constant-evolving PHI, compute the 3782 // exit value from the loop without using SCEVs. 3783 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 3784 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 3785 const Loop *LI = (*this->LI)[I->getParent()]; 3786 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 3787 if (PHINode *PN = dyn_cast<PHINode>(I)) 3788 if (PN->getParent() == LI->getHeader()) { 3789 // Okay, there is no closed form solution for the PHI node. Check 3790 // to see if the loop that contains it has a known backedge-taken 3791 // count. If so, we may be able to force computation of the exit 3792 // value. 3793 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 3794 if (const SCEVConstant *BTCC = 3795 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 3796 // Okay, we know how many times the containing loop executes. If 3797 // this is a constant evolving PHI node, get the final value at 3798 // the specified iteration number. 3799 Constant *RV = getConstantEvolutionLoopExitValue(PN, 3800 BTCC->getValue()->getValue(), 3801 LI); 3802 if (RV) return getSCEV(RV); 3803 } 3804 } 3805 3806 // Okay, this is an expression that we cannot symbolically evaluate 3807 // into a SCEV. Check to see if it's possible to symbolically evaluate 3808 // the arguments into constants, and if so, try to constant propagate the 3809 // result. This is particularly useful for computing loop exit values. 3810 if (CanConstantFold(I)) { 3811 // Check to see if we've folded this instruction at this loop before. 3812 std::map<const Loop *, Constant *> &Values = ValuesAtScopes[I]; 3813 std::pair<std::map<const Loop *, Constant *>::iterator, bool> Pair = 3814 Values.insert(std::make_pair(L, static_cast<Constant *>(0))); 3815 if (!Pair.second) 3816 return Pair.first->second ? &*getSCEV(Pair.first->second) : V; 3817 3818 std::vector<Constant*> Operands; 3819 Operands.reserve(I->getNumOperands()); 3820 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 3821 Value *Op = I->getOperand(i); 3822 if (Constant *C = dyn_cast<Constant>(Op)) { 3823 Operands.push_back(C); 3824 } else { 3825 // If any of the operands is non-constant and if they are 3826 // non-integer and non-pointer, don't even try to analyze them 3827 // with scev techniques. 3828 if (!isSCEVable(Op->getType())) 3829 return V; 3830 3831 const SCEV* OpV = getSCEVAtScope(Op, L); 3832 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) { 3833 Constant *C = SC->getValue(); 3834 if (C->getType() != Op->getType()) 3835 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 3836 Op->getType(), 3837 false), 3838 C, Op->getType()); 3839 Operands.push_back(C); 3840 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 3841 if (Constant *C = dyn_cast<Constant>(SU->getValue())) { 3842 if (C->getType() != Op->getType()) 3843 C = 3844 ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 3845 Op->getType(), 3846 false), 3847 C, Op->getType()); 3848 Operands.push_back(C); 3849 } else 3850 return V; 3851 } else { 3852 return V; 3853 } 3854 } 3855 } 3856 3857 Constant *C; 3858 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 3859 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 3860 &Operands[0], Operands.size(), 3861 getContext()); 3862 else 3863 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 3864 &Operands[0], Operands.size(), 3865 getContext()); 3866 Pair.first->second = C; 3867 return getSCEV(C); 3868 } 3869 } 3870 3871 // This is some other type of SCEVUnknown, just return it. 3872 return V; 3873 } 3874 3875 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 3876 // Avoid performing the look-up in the common case where the specified 3877 // expression has no loop-variant portions. 3878 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 3879 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 3880 if (OpAtScope != Comm->getOperand(i)) { 3881 // Okay, at least one of these operands is loop variant but might be 3882 // foldable. Build a new instance of the folded commutative expression. 3883 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 3884 Comm->op_begin()+i); 3885 NewOps.push_back(OpAtScope); 3886 3887 for (++i; i != e; ++i) { 3888 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 3889 NewOps.push_back(OpAtScope); 3890 } 3891 if (isa<SCEVAddExpr>(Comm)) 3892 return getAddExpr(NewOps); 3893 if (isa<SCEVMulExpr>(Comm)) 3894 return getMulExpr(NewOps); 3895 if (isa<SCEVSMaxExpr>(Comm)) 3896 return getSMaxExpr(NewOps); 3897 if (isa<SCEVUMaxExpr>(Comm)) 3898 return getUMaxExpr(NewOps); 3899 llvm_unreachable("Unknown commutative SCEV type!"); 3900 } 3901 } 3902 // If we got here, all operands are loop invariant. 3903 return Comm; 3904 } 3905 3906 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 3907 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 3908 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 3909 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 3910 return Div; // must be loop invariant 3911 return getUDivExpr(LHS, RHS); 3912 } 3913 3914 // If this is a loop recurrence for a loop that does not contain L, then we 3915 // are dealing with the final value computed by the loop. 3916 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 3917 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 3918 // To evaluate this recurrence, we need to know how many times the AddRec 3919 // loop iterates. Compute this now. 3920 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 3921 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 3922 3923 // Then, evaluate the AddRec. 3924 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 3925 } 3926 return AddRec; 3927 } 3928 3929 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 3930 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 3931 if (Op == Cast->getOperand()) 3932 return Cast; // must be loop invariant 3933 return getZeroExtendExpr(Op, Cast->getType()); 3934 } 3935 3936 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 3937 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 3938 if (Op == Cast->getOperand()) 3939 return Cast; // must be loop invariant 3940 return getSignExtendExpr(Op, Cast->getType()); 3941 } 3942 3943 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 3944 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 3945 if (Op == Cast->getOperand()) 3946 return Cast; // must be loop invariant 3947 return getTruncateExpr(Op, Cast->getType()); 3948 } 3949 3950 llvm_unreachable("Unknown SCEV type!"); 3951 return 0; 3952} 3953 3954/// getSCEVAtScope - This is a convenience function which does 3955/// getSCEVAtScope(getSCEV(V), L). 3956const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 3957 return getSCEVAtScope(getSCEV(V), L); 3958} 3959 3960/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 3961/// following equation: 3962/// 3963/// A * X = B (mod N) 3964/// 3965/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 3966/// A and B isn't important. 3967/// 3968/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 3969static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 3970 ScalarEvolution &SE) { 3971 uint32_t BW = A.getBitWidth(); 3972 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 3973 assert(A != 0 && "A must be non-zero."); 3974 3975 // 1. D = gcd(A, N) 3976 // 3977 // The gcd of A and N may have only one prime factor: 2. The number of 3978 // trailing zeros in A is its multiplicity 3979 uint32_t Mult2 = A.countTrailingZeros(); 3980 // D = 2^Mult2 3981 3982 // 2. Check if B is divisible by D. 3983 // 3984 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 3985 // is not less than multiplicity of this prime factor for D. 3986 if (B.countTrailingZeros() < Mult2) 3987 return SE.getCouldNotCompute(); 3988 3989 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 3990 // modulo (N / D). 3991 // 3992 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 3993 // bit width during computations. 3994 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 3995 APInt Mod(BW + 1, 0); 3996 Mod.set(BW - Mult2); // Mod = N / D 3997 APInt I = AD.multiplicativeInverse(Mod); 3998 3999 // 4. Compute the minimum unsigned root of the equation: 4000 // I * (B / D) mod (N / D) 4001 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 4002 4003 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 4004 // bits. 4005 return SE.getConstant(Result.trunc(BW)); 4006} 4007 4008/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 4009/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 4010/// might be the same) or two SCEVCouldNotCompute objects. 4011/// 4012static std::pair<const SCEV *,const SCEV *> 4013SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 4014 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 4015 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 4016 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 4017 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 4018 4019 // We currently can only solve this if the coefficients are constants. 4020 if (!LC || !MC || !NC) { 4021 const SCEV *CNC = SE.getCouldNotCompute(); 4022 return std::make_pair(CNC, CNC); 4023 } 4024 4025 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 4026 const APInt &L = LC->getValue()->getValue(); 4027 const APInt &M = MC->getValue()->getValue(); 4028 const APInt &N = NC->getValue()->getValue(); 4029 APInt Two(BitWidth, 2); 4030 APInt Four(BitWidth, 4); 4031 4032 { 4033 using namespace APIntOps; 4034 const APInt& C = L; 4035 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 4036 // The B coefficient is M-N/2 4037 APInt B(M); 4038 B -= sdiv(N,Two); 4039 4040 // The A coefficient is N/2 4041 APInt A(N.sdiv(Two)); 4042 4043 // Compute the B^2-4ac term. 4044 APInt SqrtTerm(B); 4045 SqrtTerm *= B; 4046 SqrtTerm -= Four * (A * C); 4047 4048 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 4049 // integer value or else APInt::sqrt() will assert. 4050 APInt SqrtVal(SqrtTerm.sqrt()); 4051 4052 // Compute the two solutions for the quadratic formula. 4053 // The divisions must be performed as signed divisions. 4054 APInt NegB(-B); 4055 APInt TwoA( A << 1 ); 4056 if (TwoA.isMinValue()) { 4057 const SCEV *CNC = SE.getCouldNotCompute(); 4058 return std::make_pair(CNC, CNC); 4059 } 4060 4061 LLVMContext &Context = SE.getContext(); 4062 4063 ConstantInt *Solution1 = 4064 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 4065 ConstantInt *Solution2 = 4066 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 4067 4068 return std::make_pair(SE.getConstant(Solution1), 4069 SE.getConstant(Solution2)); 4070 } // end APIntOps namespace 4071} 4072 4073/// HowFarToZero - Return the number of times a backedge comparing the specified 4074/// value to zero will execute. If not computable, return CouldNotCompute. 4075const SCEV *ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 4076 // If the value is a constant 4077 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4078 // If the value is already zero, the branch will execute zero times. 4079 if (C->getValue()->isZero()) return C; 4080 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4081 } 4082 4083 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 4084 if (!AddRec || AddRec->getLoop() != L) 4085 return getCouldNotCompute(); 4086 4087 if (AddRec->isAffine()) { 4088 // If this is an affine expression, the execution count of this branch is 4089 // the minimum unsigned root of the following equation: 4090 // 4091 // Start + Step*N = 0 (mod 2^BW) 4092 // 4093 // equivalent to: 4094 // 4095 // Step*N = -Start (mod 2^BW) 4096 // 4097 // where BW is the common bit width of Start and Step. 4098 4099 // Get the initial value for the loop. 4100 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), 4101 L->getParentLoop()); 4102 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), 4103 L->getParentLoop()); 4104 4105 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 4106 // For now we handle only constant steps. 4107 4108 // First, handle unitary steps. 4109 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 4110 return getNegativeSCEV(Start); // N = -Start (as unsigned) 4111 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 4112 return Start; // N = Start (as unsigned) 4113 4114 // Then, try to solve the above equation provided that Start is constant. 4115 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 4116 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 4117 -StartC->getValue()->getValue(), 4118 *this); 4119 } 4120 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 4121 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 4122 // the quadratic equation to solve it. 4123 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec, 4124 *this); 4125 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4126 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4127 if (R1) { 4128#if 0 4129 errs() << "HFTZ: " << *V << " - sol#1: " << *R1 4130 << " sol#2: " << *R2 << "\n"; 4131#endif 4132 // Pick the smallest positive root value. 4133 if (ConstantInt *CB = 4134 dyn_cast<ConstantInt>(getContext().getConstantExprICmp(ICmpInst::ICMP_ULT, 4135 R1->getValue(), R2->getValue()))) { 4136 if (CB->getZExtValue() == false) 4137 std::swap(R1, R2); // R1 is the minimum root now. 4138 4139 // We can only use this value if the chrec ends up with an exact zero 4140 // value at this index. When solving for "X*X != 5", for example, we 4141 // should not accept a root of 2. 4142 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 4143 if (Val->isZero()) 4144 return R1; // We found a quadratic root! 4145 } 4146 } 4147 } 4148 4149 return getCouldNotCompute(); 4150} 4151 4152/// HowFarToNonZero - Return the number of times a backedge checking the 4153/// specified value for nonzero will execute. If not computable, return 4154/// CouldNotCompute 4155const SCEV *ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 4156 // Loops that look like: while (X == 0) are very strange indeed. We don't 4157 // handle them yet except for the trivial case. This could be expanded in the 4158 // future as needed. 4159 4160 // If the value is a constant, check to see if it is known to be non-zero 4161 // already. If so, the backedge will execute zero times. 4162 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4163 if (!C->getValue()->isNullValue()) 4164 return getIntegerSCEV(0, C->getType()); 4165 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4166 } 4167 4168 // We could implement others, but I really doubt anyone writes loops like 4169 // this, and if they did, they would already be constant folded. 4170 return getCouldNotCompute(); 4171} 4172 4173/// getLoopPredecessor - If the given loop's header has exactly one unique 4174/// predecessor outside the loop, return it. Otherwise return null. 4175/// 4176BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) { 4177 BasicBlock *Header = L->getHeader(); 4178 BasicBlock *Pred = 0; 4179 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header); 4180 PI != E; ++PI) 4181 if (!L->contains(*PI)) { 4182 if (Pred && Pred != *PI) return 0; // Multiple predecessors. 4183 Pred = *PI; 4184 } 4185 return Pred; 4186} 4187 4188/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 4189/// (which may not be an immediate predecessor) which has exactly one 4190/// successor from which BB is reachable, or null if no such block is 4191/// found. 4192/// 4193BasicBlock * 4194ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 4195 // If the block has a unique predecessor, then there is no path from the 4196 // predecessor to the block that does not go through the direct edge 4197 // from the predecessor to the block. 4198 if (BasicBlock *Pred = BB->getSinglePredecessor()) 4199 return Pred; 4200 4201 // A loop's header is defined to be a block that dominates the loop. 4202 // If the header has a unique predecessor outside the loop, it must be 4203 // a block that has exactly one successor that can reach the loop. 4204 if (Loop *L = LI->getLoopFor(BB)) 4205 return getLoopPredecessor(L); 4206 4207 return 0; 4208} 4209 4210/// HasSameValue - SCEV structural equivalence is usually sufficient for 4211/// testing whether two expressions are equal, however for the purposes of 4212/// looking for a condition guarding a loop, it can be useful to be a little 4213/// more general, since a front-end may have replicated the controlling 4214/// expression. 4215/// 4216static bool HasSameValue(const SCEV *A, const SCEV *B) { 4217 // Quick check to see if they are the same SCEV. 4218 if (A == B) return true; 4219 4220 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 4221 // two different instructions with the same value. Check for this case. 4222 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 4223 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 4224 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 4225 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 4226 if (AI->isIdenticalTo(BI)) 4227 return true; 4228 4229 // Otherwise assume they may have a different value. 4230 return false; 4231} 4232 4233bool ScalarEvolution::isKnownNegative(const SCEV *S) { 4234 return getSignedRange(S).getSignedMax().isNegative(); 4235} 4236 4237bool ScalarEvolution::isKnownPositive(const SCEV *S) { 4238 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 4239} 4240 4241bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 4242 return !getSignedRange(S).getSignedMin().isNegative(); 4243} 4244 4245bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 4246 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 4247} 4248 4249bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 4250 return isKnownNegative(S) || isKnownPositive(S); 4251} 4252 4253bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 4254 const SCEV *LHS, const SCEV *RHS) { 4255 4256 if (HasSameValue(LHS, RHS)) 4257 return ICmpInst::isTrueWhenEqual(Pred); 4258 4259 switch (Pred) { 4260 default: 4261 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4262 break; 4263 case ICmpInst::ICMP_SGT: 4264 Pred = ICmpInst::ICMP_SLT; 4265 std::swap(LHS, RHS); 4266 case ICmpInst::ICMP_SLT: { 4267 ConstantRange LHSRange = getSignedRange(LHS); 4268 ConstantRange RHSRange = getSignedRange(RHS); 4269 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 4270 return true; 4271 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 4272 return false; 4273 break; 4274 } 4275 case ICmpInst::ICMP_SGE: 4276 Pred = ICmpInst::ICMP_SLE; 4277 std::swap(LHS, RHS); 4278 case ICmpInst::ICMP_SLE: { 4279 ConstantRange LHSRange = getSignedRange(LHS); 4280 ConstantRange RHSRange = getSignedRange(RHS); 4281 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 4282 return true; 4283 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 4284 return false; 4285 break; 4286 } 4287 case ICmpInst::ICMP_UGT: 4288 Pred = ICmpInst::ICMP_ULT; 4289 std::swap(LHS, RHS); 4290 case ICmpInst::ICMP_ULT: { 4291 ConstantRange LHSRange = getUnsignedRange(LHS); 4292 ConstantRange RHSRange = getUnsignedRange(RHS); 4293 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 4294 return true; 4295 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 4296 return false; 4297 break; 4298 } 4299 case ICmpInst::ICMP_UGE: 4300 Pred = ICmpInst::ICMP_ULE; 4301 std::swap(LHS, RHS); 4302 case ICmpInst::ICMP_ULE: { 4303 ConstantRange LHSRange = getUnsignedRange(LHS); 4304 ConstantRange RHSRange = getUnsignedRange(RHS); 4305 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 4306 return true; 4307 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 4308 return false; 4309 break; 4310 } 4311 case ICmpInst::ICMP_NE: { 4312 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 4313 return true; 4314 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 4315 return true; 4316 4317 const SCEV *Diff = getMinusSCEV(LHS, RHS); 4318 if (isKnownNonZero(Diff)) 4319 return true; 4320 break; 4321 } 4322 case ICmpInst::ICMP_EQ: 4323 // The check at the top of the function catches the case where 4324 // the values are known to be equal. 4325 break; 4326 } 4327 return false; 4328} 4329 4330/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 4331/// protected by a conditional between LHS and RHS. This is used to 4332/// to eliminate casts. 4333bool 4334ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 4335 ICmpInst::Predicate Pred, 4336 const SCEV *LHS, const SCEV *RHS) { 4337 // Interpret a null as meaning no loop, where there is obviously no guard 4338 // (interprocedural conditions notwithstanding). 4339 if (!L) return true; 4340 4341 BasicBlock *Latch = L->getLoopLatch(); 4342 if (!Latch) 4343 return false; 4344 4345 BranchInst *LoopContinuePredicate = 4346 dyn_cast<BranchInst>(Latch->getTerminator()); 4347 if (!LoopContinuePredicate || 4348 LoopContinuePredicate->isUnconditional()) 4349 return false; 4350 4351 return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS, 4352 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 4353} 4354 4355/// isLoopGuardedByCond - Test whether entry to the loop is protected 4356/// by a conditional between LHS and RHS. This is used to help avoid max 4357/// expressions in loop trip counts, and to eliminate casts. 4358bool 4359ScalarEvolution::isLoopGuardedByCond(const Loop *L, 4360 ICmpInst::Predicate Pred, 4361 const SCEV *LHS, const SCEV *RHS) { 4362 // Interpret a null as meaning no loop, where there is obviously no guard 4363 // (interprocedural conditions notwithstanding). 4364 if (!L) return false; 4365 4366 BasicBlock *Predecessor = getLoopPredecessor(L); 4367 BasicBlock *PredecessorDest = L->getHeader(); 4368 4369 // Starting at the loop predecessor, climb up the predecessor chain, as long 4370 // as there are predecessors that can be found that have unique successors 4371 // leading to the original header. 4372 for (; Predecessor; 4373 PredecessorDest = Predecessor, 4374 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) { 4375 4376 BranchInst *LoopEntryPredicate = 4377 dyn_cast<BranchInst>(Predecessor->getTerminator()); 4378 if (!LoopEntryPredicate || 4379 LoopEntryPredicate->isUnconditional()) 4380 continue; 4381 4382 if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS, 4383 LoopEntryPredicate->getSuccessor(0) != PredecessorDest)) 4384 return true; 4385 } 4386 4387 return false; 4388} 4389 4390/// isImpliedCond - Test whether the condition described by Pred, LHS, 4391/// and RHS is true whenever the given Cond value evaluates to true. 4392bool ScalarEvolution::isImpliedCond(Value *CondValue, 4393 ICmpInst::Predicate Pred, 4394 const SCEV *LHS, const SCEV *RHS, 4395 bool Inverse) { 4396 // Recursivly handle And and Or conditions. 4397 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) { 4398 if (BO->getOpcode() == Instruction::And) { 4399 if (!Inverse) 4400 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4401 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4402 } else if (BO->getOpcode() == Instruction::Or) { 4403 if (Inverse) 4404 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4405 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4406 } 4407 } 4408 4409 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue); 4410 if (!ICI) return false; 4411 4412 // Bail if the ICmp's operands' types are wider than the needed type 4413 // before attempting to call getSCEV on them. This avoids infinite 4414 // recursion, since the analysis of widening casts can require loop 4415 // exit condition information for overflow checking, which would 4416 // lead back here. 4417 if (getTypeSizeInBits(LHS->getType()) < 4418 getTypeSizeInBits(ICI->getOperand(0)->getType())) 4419 return false; 4420 4421 // Now that we found a conditional branch that dominates the loop, check to 4422 // see if it is the comparison we are looking for. 4423 ICmpInst::Predicate FoundPred; 4424 if (Inverse) 4425 FoundPred = ICI->getInversePredicate(); 4426 else 4427 FoundPred = ICI->getPredicate(); 4428 4429 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 4430 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 4431 4432 // Balance the types. The case where FoundLHS' type is wider than 4433 // LHS' type is checked for above. 4434 if (getTypeSizeInBits(LHS->getType()) > 4435 getTypeSizeInBits(FoundLHS->getType())) { 4436 if (CmpInst::isSigned(Pred)) { 4437 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 4438 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 4439 } else { 4440 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 4441 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 4442 } 4443 } 4444 4445 // Canonicalize the query to match the way instcombine will have 4446 // canonicalized the comparison. 4447 // First, put a constant operand on the right. 4448 if (isa<SCEVConstant>(LHS)) { 4449 std::swap(LHS, RHS); 4450 Pred = ICmpInst::getSwappedPredicate(Pred); 4451 } 4452 // Then, canonicalize comparisons with boundary cases. 4453 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 4454 const APInt &RA = RC->getValue()->getValue(); 4455 switch (Pred) { 4456 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4457 case ICmpInst::ICMP_EQ: 4458 case ICmpInst::ICMP_NE: 4459 break; 4460 case ICmpInst::ICMP_UGE: 4461 if ((RA - 1).isMinValue()) { 4462 Pred = ICmpInst::ICMP_NE; 4463 RHS = getConstant(RA - 1); 4464 break; 4465 } 4466 if (RA.isMaxValue()) { 4467 Pred = ICmpInst::ICMP_EQ; 4468 break; 4469 } 4470 if (RA.isMinValue()) return true; 4471 break; 4472 case ICmpInst::ICMP_ULE: 4473 if ((RA + 1).isMaxValue()) { 4474 Pred = ICmpInst::ICMP_NE; 4475 RHS = getConstant(RA + 1); 4476 break; 4477 } 4478 if (RA.isMinValue()) { 4479 Pred = ICmpInst::ICMP_EQ; 4480 break; 4481 } 4482 if (RA.isMaxValue()) return true; 4483 break; 4484 case ICmpInst::ICMP_SGE: 4485 if ((RA - 1).isMinSignedValue()) { 4486 Pred = ICmpInst::ICMP_NE; 4487 RHS = getConstant(RA - 1); 4488 break; 4489 } 4490 if (RA.isMaxSignedValue()) { 4491 Pred = ICmpInst::ICMP_EQ; 4492 break; 4493 } 4494 if (RA.isMinSignedValue()) return true; 4495 break; 4496 case ICmpInst::ICMP_SLE: 4497 if ((RA + 1).isMaxSignedValue()) { 4498 Pred = ICmpInst::ICMP_NE; 4499 RHS = getConstant(RA + 1); 4500 break; 4501 } 4502 if (RA.isMinSignedValue()) { 4503 Pred = ICmpInst::ICMP_EQ; 4504 break; 4505 } 4506 if (RA.isMaxSignedValue()) return true; 4507 break; 4508 case ICmpInst::ICMP_UGT: 4509 if (RA.isMinValue()) { 4510 Pred = ICmpInst::ICMP_NE; 4511 break; 4512 } 4513 if ((RA + 1).isMaxValue()) { 4514 Pred = ICmpInst::ICMP_EQ; 4515 RHS = getConstant(RA + 1); 4516 break; 4517 } 4518 if (RA.isMaxValue()) return false; 4519 break; 4520 case ICmpInst::ICMP_ULT: 4521 if (RA.isMaxValue()) { 4522 Pred = ICmpInst::ICMP_NE; 4523 break; 4524 } 4525 if ((RA - 1).isMinValue()) { 4526 Pred = ICmpInst::ICMP_EQ; 4527 RHS = getConstant(RA - 1); 4528 break; 4529 } 4530 if (RA.isMinValue()) return false; 4531 break; 4532 case ICmpInst::ICMP_SGT: 4533 if (RA.isMinSignedValue()) { 4534 Pred = ICmpInst::ICMP_NE; 4535 break; 4536 } 4537 if ((RA + 1).isMaxSignedValue()) { 4538 Pred = ICmpInst::ICMP_EQ; 4539 RHS = getConstant(RA + 1); 4540 break; 4541 } 4542 if (RA.isMaxSignedValue()) return false; 4543 break; 4544 case ICmpInst::ICMP_SLT: 4545 if (RA.isMaxSignedValue()) { 4546 Pred = ICmpInst::ICMP_NE; 4547 break; 4548 } 4549 if ((RA - 1).isMinSignedValue()) { 4550 Pred = ICmpInst::ICMP_EQ; 4551 RHS = getConstant(RA - 1); 4552 break; 4553 } 4554 if (RA.isMinSignedValue()) return false; 4555 break; 4556 } 4557 } 4558 4559 // Check to see if we can make the LHS or RHS match. 4560 if (LHS == FoundRHS || RHS == FoundLHS) { 4561 if (isa<SCEVConstant>(RHS)) { 4562 std::swap(FoundLHS, FoundRHS); 4563 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 4564 } else { 4565 std::swap(LHS, RHS); 4566 Pred = ICmpInst::getSwappedPredicate(Pred); 4567 } 4568 } 4569 4570 // Check whether the found predicate is the same as the desired predicate. 4571 if (FoundPred == Pred) 4572 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 4573 4574 // Check whether swapping the found predicate makes it the same as the 4575 // desired predicate. 4576 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 4577 if (isa<SCEVConstant>(RHS)) 4578 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 4579 else 4580 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 4581 RHS, LHS, FoundLHS, FoundRHS); 4582 } 4583 4584 // Check whether the actual condition is beyond sufficient. 4585 if (FoundPred == ICmpInst::ICMP_EQ) 4586 if (ICmpInst::isTrueWhenEqual(Pred)) 4587 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 4588 return true; 4589 if (Pred == ICmpInst::ICMP_NE) 4590 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 4591 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 4592 return true; 4593 4594 // Otherwise assume the worst. 4595 return false; 4596} 4597 4598/// isImpliedCondOperands - Test whether the condition described by Pred, 4599/// LHS, and RHS is true whenever the condition desribed by Pred, FoundLHS, 4600/// and FoundRHS is true. 4601bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 4602 const SCEV *LHS, const SCEV *RHS, 4603 const SCEV *FoundLHS, 4604 const SCEV *FoundRHS) { 4605 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 4606 FoundLHS, FoundRHS) || 4607 // ~x < ~y --> x > y 4608 isImpliedCondOperandsHelper(Pred, LHS, RHS, 4609 getNotSCEV(FoundRHS), 4610 getNotSCEV(FoundLHS)); 4611} 4612 4613/// isImpliedCondOperandsHelper - Test whether the condition described by 4614/// Pred, LHS, and RHS is true whenever the condition desribed by Pred, 4615/// FoundLHS, and FoundRHS is true. 4616bool 4617ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 4618 const SCEV *LHS, const SCEV *RHS, 4619 const SCEV *FoundLHS, 4620 const SCEV *FoundRHS) { 4621 switch (Pred) { 4622 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4623 case ICmpInst::ICMP_EQ: 4624 case ICmpInst::ICMP_NE: 4625 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 4626 return true; 4627 break; 4628 case ICmpInst::ICMP_SLT: 4629 case ICmpInst::ICMP_SLE: 4630 if (isKnownPredicate(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 4631 isKnownPredicate(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 4632 return true; 4633 break; 4634 case ICmpInst::ICMP_SGT: 4635 case ICmpInst::ICMP_SGE: 4636 if (isKnownPredicate(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 4637 isKnownPredicate(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 4638 return true; 4639 break; 4640 case ICmpInst::ICMP_ULT: 4641 case ICmpInst::ICMP_ULE: 4642 if (isKnownPredicate(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 4643 isKnownPredicate(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 4644 return true; 4645 break; 4646 case ICmpInst::ICMP_UGT: 4647 case ICmpInst::ICMP_UGE: 4648 if (isKnownPredicate(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 4649 isKnownPredicate(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 4650 return true; 4651 break; 4652 } 4653 4654 return false; 4655} 4656 4657/// getBECount - Subtract the end and start values and divide by the step, 4658/// rounding up, to get the number of times the backedge is executed. Return 4659/// CouldNotCompute if an intermediate computation overflows. 4660const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 4661 const SCEV *End, 4662 const SCEV *Step) { 4663 const Type *Ty = Start->getType(); 4664 const SCEV *NegOne = getIntegerSCEV(-1, Ty); 4665 const SCEV *Diff = getMinusSCEV(End, Start); 4666 const SCEV *RoundUp = getAddExpr(Step, NegOne); 4667 4668 // Add an adjustment to the difference between End and Start so that 4669 // the division will effectively round up. 4670 const SCEV *Add = getAddExpr(Diff, RoundUp); 4671 4672 // Check Add for unsigned overflow. 4673 // TODO: More sophisticated things could be done here. 4674 const Type *WideTy = getContext().getIntegerType(getTypeSizeInBits(Ty) + 1); 4675 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 4676 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 4677 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 4678 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 4679 return getCouldNotCompute(); 4680 4681 return getUDivExpr(Add, Step); 4682} 4683 4684/// HowManyLessThans - Return the number of times a backedge containing the 4685/// specified less-than comparison will execute. If not computable, return 4686/// CouldNotCompute. 4687ScalarEvolution::BackedgeTakenInfo 4688ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 4689 const Loop *L, bool isSigned) { 4690 // Only handle: "ADDREC < LoopInvariant". 4691 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute(); 4692 4693 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 4694 if (!AddRec || AddRec->getLoop() != L) 4695 return getCouldNotCompute(); 4696 4697 if (AddRec->isAffine()) { 4698 // FORNOW: We only support unit strides. 4699 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 4700 const SCEV *Step = AddRec->getStepRecurrence(*this); 4701 4702 // TODO: handle non-constant strides. 4703 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step); 4704 if (!CStep || CStep->isZero()) 4705 return getCouldNotCompute(); 4706 if (CStep->isOne()) { 4707 // With unit stride, the iteration never steps past the limit value. 4708 } else if (CStep->getValue()->getValue().isStrictlyPositive()) { 4709 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) { 4710 // Test whether a positive iteration iteration can step past the limit 4711 // value and past the maximum value for its type in a single step. 4712 if (isSigned) { 4713 APInt Max = APInt::getSignedMaxValue(BitWidth); 4714 if ((Max - CStep->getValue()->getValue()) 4715 .slt(CLimit->getValue()->getValue())) 4716 return getCouldNotCompute(); 4717 } else { 4718 APInt Max = APInt::getMaxValue(BitWidth); 4719 if ((Max - CStep->getValue()->getValue()) 4720 .ult(CLimit->getValue()->getValue())) 4721 return getCouldNotCompute(); 4722 } 4723 } else 4724 // TODO: handle non-constant limit values below. 4725 return getCouldNotCompute(); 4726 } else 4727 // TODO: handle negative strides below. 4728 return getCouldNotCompute(); 4729 4730 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 4731 // m. So, we count the number of iterations in which {n,+,s} < m is true. 4732 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 4733 // treat m-n as signed nor unsigned due to overflow possibility. 4734 4735 // First, we get the value of the LHS in the first iteration: n 4736 const SCEV *Start = AddRec->getOperand(0); 4737 4738 // Determine the minimum constant start value. 4739 const SCEV *MinStart = getConstant(isSigned ? 4740 getSignedRange(Start).getSignedMin() : 4741 getUnsignedRange(Start).getUnsignedMin()); 4742 4743 // If we know that the condition is true in order to enter the loop, 4744 // then we know that it will run exactly (m-n)/s times. Otherwise, we 4745 // only know that it will execute (max(m,n)-n)/s times. In both cases, 4746 // the division must round up. 4747 const SCEV *End = RHS; 4748 if (!isLoopGuardedByCond(L, 4749 isSigned ? ICmpInst::ICMP_SLT : 4750 ICmpInst::ICMP_ULT, 4751 getMinusSCEV(Start, Step), RHS)) 4752 End = isSigned ? getSMaxExpr(RHS, Start) 4753 : getUMaxExpr(RHS, Start); 4754 4755 // Determine the maximum constant end value. 4756 const SCEV *MaxEnd = getConstant(isSigned ? 4757 getSignedRange(End).getSignedMax() : 4758 getUnsignedRange(End).getUnsignedMax()); 4759 4760 // Finally, we subtract these two values and divide, rounding up, to get 4761 // the number of times the backedge is executed. 4762 const SCEV *BECount = getBECount(Start, End, Step); 4763 4764 // The maximum backedge count is similar, except using the minimum start 4765 // value and the maximum end value. 4766 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step); 4767 4768 return BackedgeTakenInfo(BECount, MaxBECount); 4769 } 4770 4771 return getCouldNotCompute(); 4772} 4773 4774/// getNumIterationsInRange - Return the number of iterations of this loop that 4775/// produce values in the specified constant range. Another way of looking at 4776/// this is that it returns the first iteration number where the value is not in 4777/// the condition, thus computing the exit count. If the iteration count can't 4778/// be computed, an instance of SCEVCouldNotCompute is returned. 4779const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 4780 ScalarEvolution &SE) const { 4781 if (Range.isFullSet()) // Infinite loop. 4782 return SE.getCouldNotCompute(); 4783 4784 // If the start is a non-zero constant, shift the range to simplify things. 4785 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 4786 if (!SC->getValue()->isZero()) { 4787 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 4788 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 4789 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop()); 4790 if (const SCEVAddRecExpr *ShiftedAddRec = 4791 dyn_cast<SCEVAddRecExpr>(Shifted)) 4792 return ShiftedAddRec->getNumIterationsInRange( 4793 Range.subtract(SC->getValue()->getValue()), SE); 4794 // This is strange and shouldn't happen. 4795 return SE.getCouldNotCompute(); 4796 } 4797 4798 // The only time we can solve this is when we have all constant indices. 4799 // Otherwise, we cannot determine the overflow conditions. 4800 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 4801 if (!isa<SCEVConstant>(getOperand(i))) 4802 return SE.getCouldNotCompute(); 4803 4804 4805 // Okay at this point we know that all elements of the chrec are constants and 4806 // that the start element is zero. 4807 4808 // First check to see if the range contains zero. If not, the first 4809 // iteration exits. 4810 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 4811 if (!Range.contains(APInt(BitWidth, 0))) 4812 return SE.getIntegerSCEV(0, getType()); 4813 4814 if (isAffine()) { 4815 // If this is an affine expression then we have this situation: 4816 // Solve {0,+,A} in Range === Ax in Range 4817 4818 // We know that zero is in the range. If A is positive then we know that 4819 // the upper value of the range must be the first possible exit value. 4820 // If A is negative then the lower of the range is the last possible loop 4821 // value. Also note that we already checked for a full range. 4822 APInt One(BitWidth,1); 4823 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 4824 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 4825 4826 // The exit value should be (End+A)/A. 4827 APInt ExitVal = (End + A).udiv(A); 4828 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 4829 4830 // Evaluate at the exit value. If we really did fall out of the valid 4831 // range, then we computed our trip count, otherwise wrap around or other 4832 // things must have happened. 4833 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 4834 if (Range.contains(Val->getValue())) 4835 return SE.getCouldNotCompute(); // Something strange happened 4836 4837 // Ensure that the previous value is in the range. This is a sanity check. 4838 assert(Range.contains( 4839 EvaluateConstantChrecAtConstant(this, 4840 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 4841 "Linear scev computation is off in a bad way!"); 4842 return SE.getConstant(ExitValue); 4843 } else if (isQuadratic()) { 4844 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 4845 // quadratic equation to solve it. To do this, we must frame our problem in 4846 // terms of figuring out when zero is crossed, instead of when 4847 // Range.getUpper() is crossed. 4848 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 4849 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 4850 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 4851 4852 // Next, solve the constructed addrec 4853 std::pair<const SCEV *,const SCEV *> Roots = 4854 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 4855 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4856 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4857 if (R1) { 4858 // Pick the smallest positive root value. 4859 if (ConstantInt *CB = 4860 dyn_cast<ConstantInt>( 4861 SE.getContext().getConstantExprICmp(ICmpInst::ICMP_ULT, 4862 R1->getValue(), R2->getValue()))) { 4863 if (CB->getZExtValue() == false) 4864 std::swap(R1, R2); // R1 is the minimum root now. 4865 4866 // Make sure the root is not off by one. The returned iteration should 4867 // not be in the range, but the previous one should be. When solving 4868 // for "X*X < 5", for example, we should not return a root of 2. 4869 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 4870 R1->getValue(), 4871 SE); 4872 if (Range.contains(R1Val->getValue())) { 4873 // The next iteration must be out of the range... 4874 ConstantInt *NextVal = 4875 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 4876 4877 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 4878 if (!Range.contains(R1Val->getValue())) 4879 return SE.getConstant(NextVal); 4880 return SE.getCouldNotCompute(); // Something strange happened 4881 } 4882 4883 // If R1 was not in the range, then it is a good return value. Make 4884 // sure that R1-1 WAS in the range though, just in case. 4885 ConstantInt *NextVal = 4886 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 4887 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 4888 if (Range.contains(R1Val->getValue())) 4889 return R1; 4890 return SE.getCouldNotCompute(); // Something strange happened 4891 } 4892 } 4893 } 4894 4895 return SE.getCouldNotCompute(); 4896} 4897 4898 4899 4900//===----------------------------------------------------------------------===// 4901// SCEVCallbackVH Class Implementation 4902//===----------------------------------------------------------------------===// 4903 4904void ScalarEvolution::SCEVCallbackVH::deleted() { 4905 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 4906 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 4907 SE->ConstantEvolutionLoopExitValue.erase(PN); 4908 if (Instruction *I = dyn_cast<Instruction>(getValPtr())) 4909 SE->ValuesAtScopes.erase(I); 4910 SE->Scalars.erase(getValPtr()); 4911 // this now dangles! 4912} 4913 4914void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) { 4915 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 4916 4917 // Forget all the expressions associated with users of the old value, 4918 // so that future queries will recompute the expressions using the new 4919 // value. 4920 SmallVector<User *, 16> Worklist; 4921 SmallPtrSet<User *, 8> Visited; 4922 Value *Old = getValPtr(); 4923 bool DeleteOld = false; 4924 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 4925 UI != UE; ++UI) 4926 Worklist.push_back(*UI); 4927 while (!Worklist.empty()) { 4928 User *U = Worklist.pop_back_val(); 4929 // Deleting the Old value will cause this to dangle. Postpone 4930 // that until everything else is done. 4931 if (U == Old) { 4932 DeleteOld = true; 4933 continue; 4934 } 4935 if (!Visited.insert(U)) 4936 continue; 4937 if (PHINode *PN = dyn_cast<PHINode>(U)) 4938 SE->ConstantEvolutionLoopExitValue.erase(PN); 4939 if (Instruction *I = dyn_cast<Instruction>(U)) 4940 SE->ValuesAtScopes.erase(I); 4941 SE->Scalars.erase(U); 4942 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 4943 UI != UE; ++UI) 4944 Worklist.push_back(*UI); 4945 } 4946 // Delete the Old value if it (indirectly) references itself. 4947 if (DeleteOld) { 4948 if (PHINode *PN = dyn_cast<PHINode>(Old)) 4949 SE->ConstantEvolutionLoopExitValue.erase(PN); 4950 if (Instruction *I = dyn_cast<Instruction>(Old)) 4951 SE->ValuesAtScopes.erase(I); 4952 SE->Scalars.erase(Old); 4953 // this now dangles! 4954 } 4955 // this may dangle! 4956} 4957 4958ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 4959 : CallbackVH(V), SE(se) {} 4960 4961//===----------------------------------------------------------------------===// 4962// ScalarEvolution Class Implementation 4963//===----------------------------------------------------------------------===// 4964 4965ScalarEvolution::ScalarEvolution() 4966 : FunctionPass(&ID) { 4967} 4968 4969bool ScalarEvolution::runOnFunction(Function &F) { 4970 this->F = &F; 4971 LI = &getAnalysis<LoopInfo>(); 4972 TD = getAnalysisIfAvailable<TargetData>(); 4973 return false; 4974} 4975 4976void ScalarEvolution::releaseMemory() { 4977 Scalars.clear(); 4978 BackedgeTakenCounts.clear(); 4979 ConstantEvolutionLoopExitValue.clear(); 4980 ValuesAtScopes.clear(); 4981 UniqueSCEVs.clear(); 4982 SCEVAllocator.Reset(); 4983} 4984 4985void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 4986 AU.setPreservesAll(); 4987 AU.addRequiredTransitive<LoopInfo>(); 4988} 4989 4990bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 4991 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 4992} 4993 4994static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 4995 const Loop *L) { 4996 // Print all inner loops first 4997 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 4998 PrintLoopInfo(OS, SE, *I); 4999 5000 OS << "Loop " << L->getHeader()->getName() << ": "; 5001 5002 SmallVector<BasicBlock*, 8> ExitBlocks; 5003 L->getExitBlocks(ExitBlocks); 5004 if (ExitBlocks.size() != 1) 5005 OS << "<multiple exits> "; 5006 5007 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 5008 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 5009 } else { 5010 OS << "Unpredictable backedge-taken count. "; 5011 } 5012 5013 OS << "\n"; 5014 OS << "Loop " << L->getHeader()->getName() << ": "; 5015 5016 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 5017 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 5018 } else { 5019 OS << "Unpredictable max backedge-taken count. "; 5020 } 5021 5022 OS << "\n"; 5023} 5024 5025void ScalarEvolution::print(raw_ostream &OS, const Module* ) const { 5026 // ScalarEvolution's implementaiton of the print method is to print 5027 // out SCEV values of all instructions that are interesting. Doing 5028 // this potentially causes it to create new SCEV objects though, 5029 // which technically conflicts with the const qualifier. This isn't 5030 // observable from outside the class though, so casting away the 5031 // const isn't dangerous. 5032 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this); 5033 5034 OS << "Classifying expressions for: " << F->getName() << "\n"; 5035 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 5036 if (isSCEVable(I->getType())) { 5037 OS << *I << '\n'; 5038 OS << " --> "; 5039 const SCEV *SV = SE.getSCEV(&*I); 5040 SV->print(OS); 5041 5042 const Loop *L = LI->getLoopFor((*I).getParent()); 5043 5044 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 5045 if (AtUse != SV) { 5046 OS << " --> "; 5047 AtUse->print(OS); 5048 } 5049 5050 if (L) { 5051 OS << "\t\t" "Exits: "; 5052 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 5053 if (!ExitValue->isLoopInvariant(L)) { 5054 OS << "<<Unknown>>"; 5055 } else { 5056 OS << *ExitValue; 5057 } 5058 } 5059 5060 OS << "\n"; 5061 } 5062 5063 OS << "Determining loop execution counts for: " << F->getName() << "\n"; 5064 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 5065 PrintLoopInfo(OS, &SE, *I); 5066} 5067 5068void ScalarEvolution::print(std::ostream &o, const Module *M) const { 5069 raw_os_ostream OS(o); 5070 print(OS, M); 5071} 5072