ScalarEvolution.cpp revision b7ef72963b2215ca23c27fa8ea777bada06994d0
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 SCEVHandle 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/Analysis/ConstantFolding.h" 69#include "llvm/Analysis/Dominators.h" 70#include "llvm/Analysis/LoopInfo.h" 71#include "llvm/Assembly/Writer.h" 72#include "llvm/Target/TargetData.h" 73#include "llvm/Transforms/Scalar.h" 74#include "llvm/Support/CFG.h" 75#include "llvm/Support/CommandLine.h" 76#include "llvm/Support/Compiler.h" 77#include "llvm/Support/ConstantRange.h" 78#include "llvm/Support/GetElementPtrTypeIterator.h" 79#include "llvm/Support/InstIterator.h" 80#include "llvm/Support/ManagedStatic.h" 81#include "llvm/Support/MathExtras.h" 82#include "llvm/Support/raw_ostream.h" 83#include "llvm/ADT/Statistic.h" 84#include "llvm/ADT/STLExtras.h" 85#include <ostream> 86#include <algorithm> 87#include <cmath> 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 derived loop"), 103 cl::init(100)); 104 105static RegisterPass<ScalarEvolution> 106R("scalar-evolution", "Scalar Evolution Analysis", false, true); 107char ScalarEvolution::ID = 0; 108 109//===----------------------------------------------------------------------===// 110// SCEV class definitions 111//===----------------------------------------------------------------------===// 112 113//===----------------------------------------------------------------------===// 114// Implementation of the SCEV class. 115// 116SCEV::~SCEV() {} 117void SCEV::dump() const { 118 print(errs()); 119 errs() << '\n'; 120} 121 122void SCEV::print(std::ostream &o) const { 123 raw_os_ostream OS(o); 124 print(OS); 125} 126 127bool SCEV::isZero() const { 128 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 129 return SC->getValue()->isZero(); 130 return false; 131} 132 133 134SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {} 135 136bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 137 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 138 return false; 139} 140 141const Type *SCEVCouldNotCompute::getType() const { 142 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 143 return 0; 144} 145 146bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 147 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 148 return false; 149} 150 151SCEVHandle SCEVCouldNotCompute:: 152replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 153 const SCEVHandle &Conc, 154 ScalarEvolution &SE) const { 155 return this; 156} 157 158void SCEVCouldNotCompute::print(raw_ostream &OS) const { 159 OS << "***COULDNOTCOMPUTE***"; 160} 161 162bool SCEVCouldNotCompute::classof(const SCEV *S) { 163 return S->getSCEVType() == scCouldNotCompute; 164} 165 166 167// SCEVConstants - Only allow the creation of one SCEVConstant for any 168// particular value. Don't use a SCEVHandle here, or else the object will 169// never be deleted! 170static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants; 171 172 173SCEVConstant::~SCEVConstant() { 174 SCEVConstants->erase(V); 175} 176 177SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) { 178 SCEVConstant *&R = (*SCEVConstants)[V]; 179 if (R == 0) R = new SCEVConstant(V); 180 return R; 181} 182 183SCEVHandle ScalarEvolution::getConstant(const APInt& Val) { 184 return getConstant(ConstantInt::get(Val)); 185} 186 187const Type *SCEVConstant::getType() const { return V->getType(); } 188 189void SCEVConstant::print(raw_ostream &OS) const { 190 WriteAsOperand(OS, V, false); 191} 192 193// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any 194// particular input. Don't use a SCEVHandle here, or else the object will 195// never be deleted! 196static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 197 SCEVTruncateExpr*> > SCEVTruncates; 198 199SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty) 200 : SCEV(scTruncate), Op(op), Ty(ty) { 201 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 202 (Ty->isInteger() || isa<PointerType>(Ty)) && 203 "Cannot truncate non-integer value!"); 204 assert((!Op->getType()->isInteger() || !Ty->isInteger() || 205 Op->getType()->getPrimitiveSizeInBits() > 206 Ty->getPrimitiveSizeInBits()) && 207 "This is not a truncating conversion!"); 208} 209 210SCEVTruncateExpr::~SCEVTruncateExpr() { 211 SCEVTruncates->erase(std::make_pair(Op, Ty)); 212} 213 214bool SCEVTruncateExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 215 return Op->dominates(BB, DT); 216} 217 218void SCEVTruncateExpr::print(raw_ostream &OS) const { 219 OS << "(truncate " << *Op << " to " << *Ty << ")"; 220} 221 222// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any 223// particular input. Don't use a SCEVHandle here, or else the object will never 224// be deleted! 225static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 226 SCEVZeroExtendExpr*> > SCEVZeroExtends; 227 228SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty) 229 : SCEV(scZeroExtend), Op(op), Ty(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 235SCEVZeroExtendExpr::~SCEVZeroExtendExpr() { 236 SCEVZeroExtends->erase(std::make_pair(Op, Ty)); 237} 238 239bool SCEVZeroExtendExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 240 return Op->dominates(BB, DT); 241} 242 243void SCEVZeroExtendExpr::print(raw_ostream &OS) const { 244 OS << "(zeroextend " << *Op << " to " << *Ty << ")"; 245} 246 247// SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any 248// particular input. Don't use a SCEVHandle here, or else the object will never 249// be deleted! 250static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 251 SCEVSignExtendExpr*> > SCEVSignExtends; 252 253SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty) 254 : SCEV(scSignExtend), Op(op), Ty(ty) { 255 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 256 (Ty->isInteger() || isa<PointerType>(Ty)) && 257 "Cannot sign extend non-integer value!"); 258 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits() 259 && "This is not an extending conversion!"); 260} 261 262SCEVSignExtendExpr::~SCEVSignExtendExpr() { 263 SCEVSignExtends->erase(std::make_pair(Op, Ty)); 264} 265 266bool SCEVSignExtendExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 267 return Op->dominates(BB, DT); 268} 269 270void SCEVSignExtendExpr::print(raw_ostream &OS) const { 271 OS << "(signextend " << *Op << " to " << *Ty << ")"; 272} 273 274// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any 275// particular input. Don't use a SCEVHandle here, or else the object will never 276// be deleted! 277static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >, 278 SCEVCommutativeExpr*> > SCEVCommExprs; 279 280SCEVCommutativeExpr::~SCEVCommutativeExpr() { 281 SCEVCommExprs->erase(std::make_pair(getSCEVType(), 282 std::vector<SCEV*>(Operands.begin(), 283 Operands.end()))); 284} 285 286void SCEVCommutativeExpr::print(raw_ostream &OS) const { 287 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 288 const char *OpStr = getOperationStr(); 289 OS << "(" << *Operands[0]; 290 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 291 OS << OpStr << *Operands[i]; 292 OS << ")"; 293} 294 295SCEVHandle SCEVCommutativeExpr:: 296replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 297 const SCEVHandle &Conc, 298 ScalarEvolution &SE) const { 299 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 300 SCEVHandle H = 301 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 302 if (H != getOperand(i)) { 303 std::vector<SCEVHandle> NewOps; 304 NewOps.reserve(getNumOperands()); 305 for (unsigned j = 0; j != i; ++j) 306 NewOps.push_back(getOperand(j)); 307 NewOps.push_back(H); 308 for (++i; i != e; ++i) 309 NewOps.push_back(getOperand(i)-> 310 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 311 312 if (isa<SCEVAddExpr>(this)) 313 return SE.getAddExpr(NewOps); 314 else if (isa<SCEVMulExpr>(this)) 315 return SE.getMulExpr(NewOps); 316 else if (isa<SCEVSMaxExpr>(this)) 317 return SE.getSMaxExpr(NewOps); 318 else if (isa<SCEVUMaxExpr>(this)) 319 return SE.getUMaxExpr(NewOps); 320 else 321 assert(0 && "Unknown commutative expr!"); 322 } 323 } 324 return this; 325} 326 327bool SCEVCommutativeExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 328 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 329 if (!getOperand(i)->dominates(BB, DT)) 330 return false; 331 } 332 return true; 333} 334 335 336// SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular 337// input. Don't use a SCEVHandle here, or else the object will never be 338// deleted! 339static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>, 340 SCEVUDivExpr*> > SCEVUDivs; 341 342SCEVUDivExpr::~SCEVUDivExpr() { 343 SCEVUDivs->erase(std::make_pair(LHS, RHS)); 344} 345 346bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 347 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT); 348} 349 350void SCEVUDivExpr::print(raw_ostream &OS) const { 351 OS << "(" << *LHS << " /u " << *RHS << ")"; 352} 353 354const Type *SCEVUDivExpr::getType() const { 355 return LHS->getType(); 356} 357 358// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any 359// particular input. Don't use a SCEVHandle here, or else the object will never 360// be deleted! 361static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >, 362 SCEVAddRecExpr*> > SCEVAddRecExprs; 363 364SCEVAddRecExpr::~SCEVAddRecExpr() { 365 SCEVAddRecExprs->erase(std::make_pair(L, 366 std::vector<SCEV*>(Operands.begin(), 367 Operands.end()))); 368} 369 370bool SCEVAddRecExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 371 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 372 if (!getOperand(i)->dominates(BB, DT)) 373 return false; 374 } 375 return true; 376} 377 378 379SCEVHandle SCEVAddRecExpr:: 380replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 381 const SCEVHandle &Conc, 382 ScalarEvolution &SE) const { 383 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 384 SCEVHandle H = 385 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 386 if (H != getOperand(i)) { 387 std::vector<SCEVHandle> NewOps; 388 NewOps.reserve(getNumOperands()); 389 for (unsigned j = 0; j != i; ++j) 390 NewOps.push_back(getOperand(j)); 391 NewOps.push_back(H); 392 for (++i; i != e; ++i) 393 NewOps.push_back(getOperand(i)-> 394 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 395 396 return SE.getAddRecExpr(NewOps, L); 397 } 398 } 399 return this; 400} 401 402 403bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 404 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't 405 // contain L and if the start is invariant. 406 return !QueryLoop->contains(L->getHeader()) && 407 getOperand(0)->isLoopInvariant(QueryLoop); 408} 409 410 411void SCEVAddRecExpr::print(raw_ostream &OS) const { 412 OS << "{" << *Operands[0]; 413 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 414 OS << ",+," << *Operands[i]; 415 OS << "}<" << L->getHeader()->getName() + ">"; 416} 417 418// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular 419// value. Don't use a SCEVHandle here, or else the object will never be 420// deleted! 421static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns; 422 423SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); } 424 425bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 426 // All non-instruction values are loop invariant. All instructions are loop 427 // invariant if they are not contained in the specified loop. 428 if (Instruction *I = dyn_cast<Instruction>(V)) 429 return !L->contains(I->getParent()); 430 return true; 431} 432 433bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const { 434 if (Instruction *I = dyn_cast<Instruction>(getValue())) 435 return DT->dominates(I->getParent(), BB); 436 return true; 437} 438 439const Type *SCEVUnknown::getType() const { 440 return V->getType(); 441} 442 443void SCEVUnknown::print(raw_ostream &OS) const { 444 if (isa<PointerType>(V->getType())) 445 OS << "(ptrtoint " << *V->getType() << " "; 446 WriteAsOperand(OS, V, false); 447 if (isa<PointerType>(V->getType())) 448 OS << " to iPTR)"; 449} 450 451//===----------------------------------------------------------------------===// 452// SCEV Utilities 453//===----------------------------------------------------------------------===// 454 455namespace { 456 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 457 /// than the complexity of the RHS. This comparator is used to canonicalize 458 /// expressions. 459 struct VISIBILITY_HIDDEN SCEVComplexityCompare { 460 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 461 return LHS->getSCEVType() < RHS->getSCEVType(); 462 } 463 }; 464} 465 466/// GroupByComplexity - Given a list of SCEV objects, order them by their 467/// complexity, and group objects of the same complexity together by value. 468/// When this routine is finished, we know that any duplicates in the vector are 469/// consecutive and that complexity is monotonically increasing. 470/// 471/// Note that we go take special precautions to ensure that we get determinstic 472/// results from this routine. In other words, we don't want the results of 473/// this to depend on where the addresses of various SCEV objects happened to 474/// land in memory. 475/// 476static void GroupByComplexity(std::vector<SCEVHandle> &Ops) { 477 if (Ops.size() < 2) return; // Noop 478 if (Ops.size() == 2) { 479 // This is the common case, which also happens to be trivially simple. 480 // Special case it. 481 if (SCEVComplexityCompare()(Ops[1], Ops[0])) 482 std::swap(Ops[0], Ops[1]); 483 return; 484 } 485 486 // Do the rough sort by complexity. 487 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare()); 488 489 // Now that we are sorted by complexity, group elements of the same 490 // complexity. Note that this is, at worst, N^2, but the vector is likely to 491 // be extremely short in practice. Note that we take this approach because we 492 // do not want to depend on the addresses of the objects we are grouping. 493 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 494 SCEV *S = Ops[i]; 495 unsigned Complexity = S->getSCEVType(); 496 497 // If there are any objects of the same complexity and same value as this 498 // one, group them. 499 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 500 if (Ops[j] == S) { // Found a duplicate. 501 // Move it to immediately after i'th element. 502 std::swap(Ops[i+1], Ops[j]); 503 ++i; // no need to rescan it. 504 if (i == e-2) return; // Done! 505 } 506 } 507 } 508} 509 510 511 512//===----------------------------------------------------------------------===// 513// Simple SCEV method implementations 514//===----------------------------------------------------------------------===// 515 516/// BinomialCoefficient - Compute BC(It, K). The result has width W. 517// Assume, K > 0. 518static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K, 519 ScalarEvolution &SE, 520 const Type* ResultTy) { 521 // Handle the simplest case efficiently. 522 if (K == 1) 523 return SE.getTruncateOrZeroExtend(It, ResultTy); 524 525 // We are using the following formula for BC(It, K): 526 // 527 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 528 // 529 // Suppose, W is the bitwidth of the return value. We must be prepared for 530 // overflow. Hence, we must assure that the result of our computation is 531 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 532 // safe in modular arithmetic. 533 // 534 // However, this code doesn't use exactly that formula; the formula it uses 535 // is something like the following, where T is the number of factors of 2 in 536 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 537 // exponentiation: 538 // 539 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 540 // 541 // This formula is trivially equivalent to the previous formula. However, 542 // this formula can be implemented much more efficiently. The trick is that 543 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 544 // arithmetic. To do exact division in modular arithmetic, all we have 545 // to do is multiply by the inverse. Therefore, this step can be done at 546 // width W. 547 // 548 // The next issue is how to safely do the division by 2^T. The way this 549 // is done is by doing the multiplication step at a width of at least W + T 550 // bits. This way, the bottom W+T bits of the product are accurate. Then, 551 // when we perform the division by 2^T (which is equivalent to a right shift 552 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 553 // truncated out after the division by 2^T. 554 // 555 // In comparison to just directly using the first formula, this technique 556 // is much more efficient; using the first formula requires W * K bits, 557 // but this formula less than W + K bits. Also, the first formula requires 558 // a division step, whereas this formula only requires multiplies and shifts. 559 // 560 // It doesn't matter whether the subtraction step is done in the calculation 561 // width or the input iteration count's width; if the subtraction overflows, 562 // the result must be zero anyway. We prefer here to do it in the width of 563 // the induction variable because it helps a lot for certain cases; CodeGen 564 // isn't smart enough to ignore the overflow, which leads to much less 565 // efficient code if the width of the subtraction is wider than the native 566 // register width. 567 // 568 // (It's possible to not widen at all by pulling out factors of 2 before 569 // the multiplication; for example, K=2 can be calculated as 570 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 571 // extra arithmetic, so it's not an obvious win, and it gets 572 // much more complicated for K > 3.) 573 574 // Protection from insane SCEVs; this bound is conservative, 575 // but it probably doesn't matter. 576 if (K > 1000) 577 return SE.getCouldNotCompute(); 578 579 unsigned W = SE.getTargetData().getTypeSizeInBits(ResultTy); 580 581 // Calculate K! / 2^T and T; we divide out the factors of two before 582 // multiplying for calculating K! / 2^T to avoid overflow. 583 // Other overflow doesn't matter because we only care about the bottom 584 // W bits of the result. 585 APInt OddFactorial(W, 1); 586 unsigned T = 1; 587 for (unsigned i = 3; i <= K; ++i) { 588 APInt Mult(W, i); 589 unsigned TwoFactors = Mult.countTrailingZeros(); 590 T += TwoFactors; 591 Mult = Mult.lshr(TwoFactors); 592 OddFactorial *= Mult; 593 } 594 595 // We need at least W + T bits for the multiplication step 596 unsigned CalculationBits = W + T; 597 598 // Calcuate 2^T, at width T+W. 599 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 600 601 // Calculate the multiplicative inverse of K! / 2^T; 602 // this multiplication factor will perform the exact division by 603 // K! / 2^T. 604 APInt Mod = APInt::getSignedMinValue(W+1); 605 APInt MultiplyFactor = OddFactorial.zext(W+1); 606 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 607 MultiplyFactor = MultiplyFactor.trunc(W); 608 609 // Calculate the product, at width T+W 610 const IntegerType *CalculationTy = IntegerType::get(CalculationBits); 611 SCEVHandle Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 612 for (unsigned i = 1; i != K; ++i) { 613 SCEVHandle S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType())); 614 Dividend = SE.getMulExpr(Dividend, 615 SE.getTruncateOrZeroExtend(S, CalculationTy)); 616 } 617 618 // Divide by 2^T 619 SCEVHandle DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 620 621 // Truncate the result, and divide by K! / 2^T. 622 623 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 624 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 625} 626 627/// evaluateAtIteration - Return the value of this chain of recurrences at 628/// the specified iteration number. We can evaluate this recurrence by 629/// multiplying each element in the chain by the binomial coefficient 630/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 631/// 632/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 633/// 634/// where BC(It, k) stands for binomial coefficient. 635/// 636SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It, 637 ScalarEvolution &SE) const { 638 SCEVHandle Result = getStart(); 639 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 640 // The computation is correct in the face of overflow provided that the 641 // multiplication is performed _after_ the evaluation of the binomial 642 // coefficient. 643 SCEVHandle Coeff = BinomialCoefficient(It, i, SE, getType()); 644 if (isa<SCEVCouldNotCompute>(Coeff)) 645 return Coeff; 646 647 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 648 } 649 return Result; 650} 651 652//===----------------------------------------------------------------------===// 653// SCEV Expression folder implementations 654//===----------------------------------------------------------------------===// 655 656SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op, const Type *Ty) { 657 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 658 return getUnknown( 659 ConstantExpr::getTrunc(SC->getValue(), Ty)); 660 661 // If the input value is a chrec scev made out of constants, truncate 662 // all of the constants. 663 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 664 std::vector<SCEVHandle> Operands; 665 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 666 // FIXME: This should allow truncation of other expression types! 667 if (isa<SCEVConstant>(AddRec->getOperand(i))) 668 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 669 else 670 break; 671 if (Operands.size() == AddRec->getNumOperands()) 672 return getAddRecExpr(Operands, AddRec->getLoop()); 673 } 674 675 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)]; 676 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty); 677 return Result; 678} 679 680SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op, 681 const Type *Ty) { 682 assert(getTargetData().getTypeSizeInBits(Op->getType()) < 683 getTargetData().getTypeSizeInBits(Ty) && 684 "This is not an extending conversion!"); 685 686 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 687 const Type *IntTy = Ty; 688 if (isa<PointerType>(IntTy)) IntTy = getTargetData().getIntPtrType(); 689 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy); 690 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 691 return getUnknown(C); 692 } 693 694 // FIXME: If the input value is a chrec scev, and we can prove that the value 695 // did not overflow the old, smaller, value, we can zero extend all of the 696 // operands (often constants). This would allow analysis of something like 697 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 698 699 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)]; 700 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty); 701 return Result; 702} 703 704SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op, const Type *Ty) { 705 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 706 const Type *IntTy = Ty; 707 if (isa<PointerType>(IntTy)) IntTy = getTargetData().getIntPtrType(); 708 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy); 709 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 710 return getUnknown(C); 711 } 712 713 // FIXME: If the input value is a chrec scev, and we can prove that the value 714 // did not overflow the old, smaller, value, we can sign extend all of the 715 // operands (often constants). This would allow analysis of something like 716 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 717 718 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)]; 719 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty); 720 return Result; 721} 722 723// get - Get a canonical add expression, or something simpler if possible. 724SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) { 725 assert(!Ops.empty() && "Cannot get empty add!"); 726 if (Ops.size() == 1) return Ops[0]; 727 728 // Sort by complexity, this groups all similar expression types together. 729 GroupByComplexity(Ops); 730 731 // If there are any constants, fold them together. 732 unsigned Idx = 0; 733 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 734 ++Idx; 735 assert(Idx < Ops.size()); 736 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 737 // We found two constants, fold them together! 738 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() + 739 RHSC->getValue()->getValue()); 740 Ops[0] = getConstant(Fold); 741 Ops.erase(Ops.begin()+1); // Erase the folded element 742 if (Ops.size() == 1) return Ops[0]; 743 LHSC = cast<SCEVConstant>(Ops[0]); 744 } 745 746 // If we are left with a constant zero being added, strip it off. 747 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 748 Ops.erase(Ops.begin()); 749 --Idx; 750 } 751 } 752 753 if (Ops.size() == 1) return Ops[0]; 754 755 // Okay, check to see if the same value occurs in the operand list twice. If 756 // so, merge them together into an multiply expression. Since we sorted the 757 // list, these values are required to be adjacent. 758 const Type *Ty = Ops[0]->getType(); 759 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 760 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 761 // Found a match, merge the two values into a multiply, and add any 762 // remaining values to the result. 763 SCEVHandle Two = getIntegerSCEV(2, Ty); 764 SCEVHandle Mul = getMulExpr(Ops[i], Two); 765 if (Ops.size() == 2) 766 return Mul; 767 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 768 Ops.push_back(Mul); 769 return getAddExpr(Ops); 770 } 771 772 // Now we know the first non-constant operand. Skip past any cast SCEVs. 773 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 774 ++Idx; 775 776 // If there are add operands they would be next. 777 if (Idx < Ops.size()) { 778 bool DeletedAdd = false; 779 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 780 // If we have an add, expand the add operands onto the end of the operands 781 // list. 782 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 783 Ops.erase(Ops.begin()+Idx); 784 DeletedAdd = true; 785 } 786 787 // If we deleted at least one add, we added operands to the end of the list, 788 // and they are not necessarily sorted. Recurse to resort and resimplify 789 // any operands we just aquired. 790 if (DeletedAdd) 791 return getAddExpr(Ops); 792 } 793 794 // Skip over the add expression until we get to a multiply. 795 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 796 ++Idx; 797 798 // If we are adding something to a multiply expression, make sure the 799 // something is not already an operand of the multiply. If so, merge it into 800 // the multiply. 801 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 802 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 803 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 804 SCEV *MulOpSCEV = Mul->getOperand(MulOp); 805 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 806 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) { 807 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 808 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 809 if (Mul->getNumOperands() != 2) { 810 // If the multiply has more than two operands, we must get the 811 // Y*Z term. 812 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 813 MulOps.erase(MulOps.begin()+MulOp); 814 InnerMul = getMulExpr(MulOps); 815 } 816 SCEVHandle One = getIntegerSCEV(1, Ty); 817 SCEVHandle AddOne = getAddExpr(InnerMul, One); 818 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]); 819 if (Ops.size() == 2) return OuterMul; 820 if (AddOp < Idx) { 821 Ops.erase(Ops.begin()+AddOp); 822 Ops.erase(Ops.begin()+Idx-1); 823 } else { 824 Ops.erase(Ops.begin()+Idx); 825 Ops.erase(Ops.begin()+AddOp-1); 826 } 827 Ops.push_back(OuterMul); 828 return getAddExpr(Ops); 829 } 830 831 // Check this multiply against other multiplies being added together. 832 for (unsigned OtherMulIdx = Idx+1; 833 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 834 ++OtherMulIdx) { 835 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 836 // If MulOp occurs in OtherMul, we can fold the two multiplies 837 // together. 838 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 839 OMulOp != e; ++OMulOp) 840 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 841 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 842 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 843 if (Mul->getNumOperands() != 2) { 844 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 845 MulOps.erase(MulOps.begin()+MulOp); 846 InnerMul1 = getMulExpr(MulOps); 847 } 848 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 849 if (OtherMul->getNumOperands() != 2) { 850 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 851 OtherMul->op_end()); 852 MulOps.erase(MulOps.begin()+OMulOp); 853 InnerMul2 = getMulExpr(MulOps); 854 } 855 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 856 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 857 if (Ops.size() == 2) return OuterMul; 858 Ops.erase(Ops.begin()+Idx); 859 Ops.erase(Ops.begin()+OtherMulIdx-1); 860 Ops.push_back(OuterMul); 861 return getAddExpr(Ops); 862 } 863 } 864 } 865 } 866 867 // If there are any add recurrences in the operands list, see if any other 868 // added values are loop invariant. If so, we can fold them into the 869 // recurrence. 870 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 871 ++Idx; 872 873 // Scan over all recurrences, trying to fold loop invariants into them. 874 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 875 // Scan all of the other operands to this add and add them to the vector if 876 // they are loop invariant w.r.t. the recurrence. 877 std::vector<SCEVHandle> LIOps; 878 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 879 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 880 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 881 LIOps.push_back(Ops[i]); 882 Ops.erase(Ops.begin()+i); 883 --i; --e; 884 } 885 886 // If we found some loop invariants, fold them into the recurrence. 887 if (!LIOps.empty()) { 888 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 889 LIOps.push_back(AddRec->getStart()); 890 891 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 892 AddRecOps[0] = getAddExpr(LIOps); 893 894 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 895 // If all of the other operands were loop invariant, we are done. 896 if (Ops.size() == 1) return NewRec; 897 898 // Otherwise, add the folded AddRec by the non-liv parts. 899 for (unsigned i = 0;; ++i) 900 if (Ops[i] == AddRec) { 901 Ops[i] = NewRec; 902 break; 903 } 904 return getAddExpr(Ops); 905 } 906 907 // Okay, if there weren't any loop invariants to be folded, check to see if 908 // there are multiple AddRec's with the same loop induction variable being 909 // added together. If so, we can fold them. 910 for (unsigned OtherIdx = Idx+1; 911 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 912 if (OtherIdx != Idx) { 913 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 914 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 915 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 916 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 917 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 918 if (i >= NewOps.size()) { 919 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 920 OtherAddRec->op_end()); 921 break; 922 } 923 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 924 } 925 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 926 927 if (Ops.size() == 2) return NewAddRec; 928 929 Ops.erase(Ops.begin()+Idx); 930 Ops.erase(Ops.begin()+OtherIdx-1); 931 Ops.push_back(NewAddRec); 932 return getAddExpr(Ops); 933 } 934 } 935 936 // Otherwise couldn't fold anything into this recurrence. Move onto the 937 // next one. 938 } 939 940 // Okay, it looks like we really DO need an add expr. Check to see if we 941 // already have one, otherwise create a new one. 942 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 943 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr, 944 SCEVOps)]; 945 if (Result == 0) Result = new SCEVAddExpr(Ops); 946 return Result; 947} 948 949 950SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) { 951 assert(!Ops.empty() && "Cannot get empty mul!"); 952 953 // Sort by complexity, this groups all similar expression types together. 954 GroupByComplexity(Ops); 955 956 // If there are any constants, fold them together. 957 unsigned Idx = 0; 958 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 959 960 // C1*(C2+V) -> C1*C2 + C1*V 961 if (Ops.size() == 2) 962 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 963 if (Add->getNumOperands() == 2 && 964 isa<SCEVConstant>(Add->getOperand(0))) 965 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 966 getMulExpr(LHSC, Add->getOperand(1))); 967 968 969 ++Idx; 970 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 971 // We found two constants, fold them together! 972 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() * 973 RHSC->getValue()->getValue()); 974 Ops[0] = getConstant(Fold); 975 Ops.erase(Ops.begin()+1); // Erase the folded element 976 if (Ops.size() == 1) return Ops[0]; 977 LHSC = cast<SCEVConstant>(Ops[0]); 978 } 979 980 // If we are left with a constant one being multiplied, strip it off. 981 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 982 Ops.erase(Ops.begin()); 983 --Idx; 984 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 985 // If we have a multiply of zero, it will always be zero. 986 return Ops[0]; 987 } 988 } 989 990 // Skip over the add expression until we get to a multiply. 991 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 992 ++Idx; 993 994 if (Ops.size() == 1) 995 return Ops[0]; 996 997 // If there are mul operands inline them all into this expression. 998 if (Idx < Ops.size()) { 999 bool DeletedMul = false; 1000 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1001 // If we have an mul, expand the mul operands onto the end of the operands 1002 // list. 1003 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 1004 Ops.erase(Ops.begin()+Idx); 1005 DeletedMul = true; 1006 } 1007 1008 // If we deleted at least one mul, we added operands to the end of the list, 1009 // and they are not necessarily sorted. Recurse to resort and resimplify 1010 // any operands we just aquired. 1011 if (DeletedMul) 1012 return getMulExpr(Ops); 1013 } 1014 1015 // If there are any add recurrences in the operands list, see if any other 1016 // added values are loop invariant. If so, we can fold them into the 1017 // recurrence. 1018 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1019 ++Idx; 1020 1021 // Scan over all recurrences, trying to fold loop invariants into them. 1022 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1023 // Scan all of the other operands to this mul and add them to the vector if 1024 // they are loop invariant w.r.t. the recurrence. 1025 std::vector<SCEVHandle> LIOps; 1026 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1027 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1028 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1029 LIOps.push_back(Ops[i]); 1030 Ops.erase(Ops.begin()+i); 1031 --i; --e; 1032 } 1033 1034 // If we found some loop invariants, fold them into the recurrence. 1035 if (!LIOps.empty()) { 1036 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1037 std::vector<SCEVHandle> NewOps; 1038 NewOps.reserve(AddRec->getNumOperands()); 1039 if (LIOps.size() == 1) { 1040 SCEV *Scale = LIOps[0]; 1041 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1042 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1043 } else { 1044 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1045 std::vector<SCEVHandle> MulOps(LIOps); 1046 MulOps.push_back(AddRec->getOperand(i)); 1047 NewOps.push_back(getMulExpr(MulOps)); 1048 } 1049 } 1050 1051 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1052 1053 // If all of the other operands were loop invariant, we are done. 1054 if (Ops.size() == 1) return NewRec; 1055 1056 // Otherwise, multiply the folded AddRec by the non-liv parts. 1057 for (unsigned i = 0;; ++i) 1058 if (Ops[i] == AddRec) { 1059 Ops[i] = NewRec; 1060 break; 1061 } 1062 return getMulExpr(Ops); 1063 } 1064 1065 // Okay, if there weren't any loop invariants to be folded, check to see if 1066 // there are multiple AddRec's with the same loop induction variable being 1067 // multiplied together. If so, we can fold them. 1068 for (unsigned OtherIdx = Idx+1; 1069 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1070 if (OtherIdx != Idx) { 1071 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1072 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1073 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1074 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1075 SCEVHandle NewStart = getMulExpr(F->getStart(), 1076 G->getStart()); 1077 SCEVHandle B = F->getStepRecurrence(*this); 1078 SCEVHandle D = G->getStepRecurrence(*this); 1079 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D), 1080 getMulExpr(G, B), 1081 getMulExpr(B, D)); 1082 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep, 1083 F->getLoop()); 1084 if (Ops.size() == 2) return NewAddRec; 1085 1086 Ops.erase(Ops.begin()+Idx); 1087 Ops.erase(Ops.begin()+OtherIdx-1); 1088 Ops.push_back(NewAddRec); 1089 return getMulExpr(Ops); 1090 } 1091 } 1092 1093 // Otherwise couldn't fold anything into this recurrence. Move onto the 1094 // next one. 1095 } 1096 1097 // Okay, it looks like we really DO need an mul expr. Check to see if we 1098 // already have one, otherwise create a new one. 1099 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1100 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr, 1101 SCEVOps)]; 1102 if (Result == 0) 1103 Result = new SCEVMulExpr(Ops); 1104 return Result; 1105} 1106 1107SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS, const SCEVHandle &RHS) { 1108 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1109 if (RHSC->getValue()->equalsInt(1)) 1110 return LHS; // X udiv 1 --> x 1111 1112 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1113 Constant *LHSCV = LHSC->getValue(); 1114 Constant *RHSCV = RHSC->getValue(); 1115 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV)); 1116 } 1117 } 1118 1119 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow. 1120 1121 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)]; 1122 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS); 1123 return Result; 1124} 1125 1126 1127/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1128/// specified loop. Simplify the expression as much as possible. 1129SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start, 1130 const SCEVHandle &Step, const Loop *L) { 1131 std::vector<SCEVHandle> Operands; 1132 Operands.push_back(Start); 1133 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1134 if (StepChrec->getLoop() == L) { 1135 Operands.insert(Operands.end(), StepChrec->op_begin(), 1136 StepChrec->op_end()); 1137 return getAddRecExpr(Operands, L); 1138 } 1139 1140 Operands.push_back(Step); 1141 return getAddRecExpr(Operands, L); 1142} 1143 1144/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1145/// specified loop. Simplify the expression as much as possible. 1146SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands, 1147 const Loop *L) { 1148 if (Operands.size() == 1) return Operands[0]; 1149 1150 if (Operands.back()->isZero()) { 1151 Operands.pop_back(); 1152 return getAddRecExpr(Operands, L); // {X,+,0} --> X 1153 } 1154 1155 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 1156 if (SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 1157 const Loop* NestedLoop = NestedAR->getLoop(); 1158 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) { 1159 std::vector<SCEVHandle> NestedOperands(NestedAR->op_begin(), 1160 NestedAR->op_end()); 1161 SCEVHandle NestedARHandle(NestedAR); 1162 Operands[0] = NestedAR->getStart(); 1163 NestedOperands[0] = getAddRecExpr(Operands, L); 1164 return getAddRecExpr(NestedOperands, NestedLoop); 1165 } 1166 } 1167 1168 SCEVAddRecExpr *&Result = 1169 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(), 1170 Operands.end()))]; 1171 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 1172 return Result; 1173} 1174 1175SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS, 1176 const SCEVHandle &RHS) { 1177 std::vector<SCEVHandle> Ops; 1178 Ops.push_back(LHS); 1179 Ops.push_back(RHS); 1180 return getSMaxExpr(Ops); 1181} 1182 1183SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) { 1184 assert(!Ops.empty() && "Cannot get empty smax!"); 1185 if (Ops.size() == 1) return Ops[0]; 1186 1187 // Sort by complexity, this groups all similar expression types together. 1188 GroupByComplexity(Ops); 1189 1190 // If there are any constants, fold them together. 1191 unsigned Idx = 0; 1192 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1193 ++Idx; 1194 assert(Idx < Ops.size()); 1195 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1196 // We found two constants, fold them together! 1197 ConstantInt *Fold = ConstantInt::get( 1198 APIntOps::smax(LHSC->getValue()->getValue(), 1199 RHSC->getValue()->getValue())); 1200 Ops[0] = getConstant(Fold); 1201 Ops.erase(Ops.begin()+1); // Erase the folded element 1202 if (Ops.size() == 1) return Ops[0]; 1203 LHSC = cast<SCEVConstant>(Ops[0]); 1204 } 1205 1206 // If we are left with a constant -inf, strip it off. 1207 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 1208 Ops.erase(Ops.begin()); 1209 --Idx; 1210 } 1211 } 1212 1213 if (Ops.size() == 1) return Ops[0]; 1214 1215 // Find the first SMax 1216 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 1217 ++Idx; 1218 1219 // Check to see if one of the operands is an SMax. If so, expand its operands 1220 // onto our operand list, and recurse to simplify. 1221 if (Idx < Ops.size()) { 1222 bool DeletedSMax = false; 1223 while (SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 1224 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 1225 Ops.erase(Ops.begin()+Idx); 1226 DeletedSMax = true; 1227 } 1228 1229 if (DeletedSMax) 1230 return getSMaxExpr(Ops); 1231 } 1232 1233 // Okay, check to see if the same value occurs in the operand list twice. If 1234 // so, delete one. Since we sorted the list, these values are required to 1235 // be adjacent. 1236 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1237 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 1238 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1239 --i; --e; 1240 } 1241 1242 if (Ops.size() == 1) return Ops[0]; 1243 1244 assert(!Ops.empty() && "Reduced smax down to nothing!"); 1245 1246 // Okay, it looks like we really DO need an smax expr. Check to see if we 1247 // already have one, otherwise create a new one. 1248 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1249 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr, 1250 SCEVOps)]; 1251 if (Result == 0) Result = new SCEVSMaxExpr(Ops); 1252 return Result; 1253} 1254 1255SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS, 1256 const SCEVHandle &RHS) { 1257 std::vector<SCEVHandle> Ops; 1258 Ops.push_back(LHS); 1259 Ops.push_back(RHS); 1260 return getUMaxExpr(Ops); 1261} 1262 1263SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) { 1264 assert(!Ops.empty() && "Cannot get empty umax!"); 1265 if (Ops.size() == 1) return Ops[0]; 1266 1267 // Sort by complexity, this groups all similar expression types together. 1268 GroupByComplexity(Ops); 1269 1270 // If there are any constants, fold them together. 1271 unsigned Idx = 0; 1272 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1273 ++Idx; 1274 assert(Idx < Ops.size()); 1275 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1276 // We found two constants, fold them together! 1277 ConstantInt *Fold = ConstantInt::get( 1278 APIntOps::umax(LHSC->getValue()->getValue(), 1279 RHSC->getValue()->getValue())); 1280 Ops[0] = getConstant(Fold); 1281 Ops.erase(Ops.begin()+1); // Erase the folded element 1282 if (Ops.size() == 1) return Ops[0]; 1283 LHSC = cast<SCEVConstant>(Ops[0]); 1284 } 1285 1286 // If we are left with a constant zero, strip it off. 1287 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 1288 Ops.erase(Ops.begin()); 1289 --Idx; 1290 } 1291 } 1292 1293 if (Ops.size() == 1) return Ops[0]; 1294 1295 // Find the first UMax 1296 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 1297 ++Idx; 1298 1299 // Check to see if one of the operands is a UMax. If so, expand its operands 1300 // onto our operand list, and recurse to simplify. 1301 if (Idx < Ops.size()) { 1302 bool DeletedUMax = false; 1303 while (SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 1304 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 1305 Ops.erase(Ops.begin()+Idx); 1306 DeletedUMax = true; 1307 } 1308 1309 if (DeletedUMax) 1310 return getUMaxExpr(Ops); 1311 } 1312 1313 // Okay, check to see if the same value occurs in the operand list twice. If 1314 // so, delete one. Since we sorted the list, these values are required to 1315 // be adjacent. 1316 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1317 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y 1318 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1319 --i; --e; 1320 } 1321 1322 if (Ops.size() == 1) return Ops[0]; 1323 1324 assert(!Ops.empty() && "Reduced umax down to nothing!"); 1325 1326 // Okay, it looks like we really DO need a umax expr. Check to see if we 1327 // already have one, otherwise create a new one. 1328 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1329 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr, 1330 SCEVOps)]; 1331 if (Result == 0) Result = new SCEVUMaxExpr(Ops); 1332 return Result; 1333} 1334 1335SCEVHandle ScalarEvolution::getUnknown(Value *V) { 1336 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 1337 return getConstant(CI); 1338 if (isa<ConstantPointerNull>(V)) 1339 return getIntegerSCEV(0, V->getType()); 1340 SCEVUnknown *&Result = (*SCEVUnknowns)[V]; 1341 if (Result == 0) Result = new SCEVUnknown(V); 1342 return Result; 1343} 1344 1345//===----------------------------------------------------------------------===// 1346// ScalarEvolutionsImpl Definition and Implementation 1347//===----------------------------------------------------------------------===// 1348// 1349/// ScalarEvolutionsImpl - This class implements the main driver for the scalar 1350/// evolution code. 1351/// 1352namespace { 1353 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl { 1354 /// SE - A reference to the public ScalarEvolution object. 1355 ScalarEvolution &SE; 1356 1357 /// F - The function we are analyzing. 1358 /// 1359 Function &F; 1360 1361 /// LI - The loop information for the function we are currently analyzing. 1362 /// 1363 LoopInfo &LI; 1364 1365 /// TD - The target data information for the target we are targetting. 1366 /// 1367 TargetData &TD; 1368 1369 /// UnknownValue - This SCEV is used to represent unknown trip counts and 1370 /// things. 1371 SCEVHandle UnknownValue; 1372 1373 /// Scalars - This is a cache of the scalars we have analyzed so far. 1374 /// 1375 std::map<Value*, SCEVHandle> Scalars; 1376 1377 /// BackedgeTakenCounts - Cache the backedge-taken count of the loops for 1378 /// this function as they are computed. 1379 std::map<const Loop*, SCEVHandle> BackedgeTakenCounts; 1380 1381 /// ConstantEvolutionLoopExitValue - This map contains entries for all of 1382 /// the PHI instructions that we attempt to compute constant evolutions for. 1383 /// This allows us to avoid potentially expensive recomputation of these 1384 /// properties. An instruction maps to null if we are unable to compute its 1385 /// exit value. 1386 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue; 1387 1388 public: 1389 ScalarEvolutionsImpl(ScalarEvolution &se, Function &f, LoopInfo &li, 1390 TargetData &td) 1391 : SE(se), F(f), LI(li), TD(td), UnknownValue(new SCEVCouldNotCompute()) {} 1392 1393 SCEVHandle getCouldNotCompute(); 1394 1395 /// getIntegerSCEV - Given an integer or FP type, create a constant for the 1396 /// specified signed integer value and return a SCEV for the constant. 1397 SCEVHandle getIntegerSCEV(int Val, const Type *Ty); 1398 1399 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 1400 /// 1401 SCEVHandle getNegativeSCEV(const SCEVHandle &V); 1402 1403 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 1404 /// 1405 SCEVHandle getNotSCEV(const SCEVHandle &V); 1406 1407 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 1408 /// 1409 SCEVHandle getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS); 1410 1411 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion 1412 /// of the input value to the specified type. If the type must be extended, 1413 /// it is zero extended. 1414 SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty); 1415 1416 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion 1417 /// of the input value to the specified type. If the type must be extended, 1418 /// it is sign extended. 1419 SCEVHandle getTruncateOrSignExtend(const SCEVHandle &V, const Type *Ty); 1420 1421 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1422 /// expression and create a new one. 1423 SCEVHandle getSCEV(Value *V); 1424 1425 /// hasSCEV - Return true if the SCEV for this value has already been 1426 /// computed. 1427 bool hasSCEV(Value *V) const { 1428 return Scalars.count(V); 1429 } 1430 1431 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for 1432 /// the specified value. 1433 void setSCEV(Value *V, const SCEVHandle &H) { 1434 bool isNew = Scalars.insert(std::make_pair(V, H)).second; 1435 assert(isNew && "This entry already existed!"); 1436 isNew = false; 1437 } 1438 1439 1440 /// getSCEVAtScope - Compute the value of the specified expression within 1441 /// the indicated loop (which may be null to indicate in no loop). If the 1442 /// expression cannot be evaluated, return UnknownValue itself. 1443 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L); 1444 1445 1446 /// isLoopGuardedByCond - Test whether entry to the loop is protected by 1447 /// a conditional between LHS and RHS. 1448 bool isLoopGuardedByCond(const Loop *L, ICmpInst::Predicate Pred, 1449 SCEV *LHS, SCEV *RHS); 1450 1451 /// hasLoopInvariantBackedgeTakenCount - Return true if the specified loop 1452 /// has an analyzable loop-invariant backedge-taken count. 1453 bool hasLoopInvariantBackedgeTakenCount(const Loop *L); 1454 1455 /// forgetLoopBackedgeTakenCount - This method should be called by the 1456 /// client when it has changed a loop in a way that may effect 1457 /// ScalarEvolution's ability to compute a trip count, or if the loop 1458 /// is deleted. 1459 void forgetLoopBackedgeTakenCount(const Loop *L); 1460 1461 /// getBackedgeTakenCount - If the specified loop has a predictable 1462 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 1463 /// object. The backedge-taken count is the number of times the loop header 1464 /// will be branched to from within the loop. This is one less than the 1465 /// trip count of the loop, since it doesn't count the first iteration, 1466 /// when the header is branched to from outside the loop. 1467 /// 1468 /// Note that it is not valid to call this method on a loop without a 1469 /// loop-invariant backedge-taken count (see 1470 /// hasLoopInvariantBackedgeTakenCount). 1471 /// 1472 SCEVHandle getBackedgeTakenCount(const Loop *L); 1473 1474 /// deleteValueFromRecords - This method should be called by the 1475 /// client before it removes a value from the program, to make sure 1476 /// that no dangling references are left around. 1477 void deleteValueFromRecords(Value *V); 1478 1479 /// getTargetData - Return the TargetData. 1480 const TargetData &getTargetData() const; 1481 1482 private: 1483 /// createSCEV - We know that there is no SCEV for the specified value. 1484 /// Analyze the expression. 1485 SCEVHandle createSCEV(Value *V); 1486 1487 /// createNodeForPHI - Provide the special handling we need to analyze PHI 1488 /// SCEVs. 1489 SCEVHandle createNodeForPHI(PHINode *PN); 1490 1491 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value 1492 /// for the specified instruction and replaces any references to the 1493 /// symbolic value SymName with the specified value. This is used during 1494 /// PHI resolution. 1495 void ReplaceSymbolicValueWithConcrete(Instruction *I, 1496 const SCEVHandle &SymName, 1497 const SCEVHandle &NewVal); 1498 1499 /// ComputeBackedgeTakenCount - Compute the number of times the specified 1500 /// loop will iterate. 1501 SCEVHandle ComputeBackedgeTakenCount(const Loop *L); 1502 1503 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition 1504 /// of 'icmp op load X, cst', try to see if we can compute the trip count. 1505 SCEVHandle 1506 ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, 1507 Constant *RHS, 1508 const Loop *L, 1509 ICmpInst::Predicate p); 1510 1511 /// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute 1512 /// a constant number of times (the condition evolves only from constants), 1513 /// try to evaluate a few iterations of the loop until we get the exit 1514 /// condition gets a value of ExitWhen (true or false). If we cannot 1515 /// evaluate the trip count of the loop, return UnknownValue. 1516 SCEVHandle ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, 1517 bool ExitWhen); 1518 1519 /// HowFarToZero - Return the number of times a backedge comparing the 1520 /// specified value to zero will execute. If not computable, return 1521 /// UnknownValue. 1522 SCEVHandle HowFarToZero(SCEV *V, const Loop *L); 1523 1524 /// HowFarToNonZero - Return the number of times a backedge checking the 1525 /// specified value for nonzero will execute. If not computable, return 1526 /// UnknownValue. 1527 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L); 1528 1529 /// HowManyLessThans - Return the number of times a backedge containing the 1530 /// specified less-than comparison will execute. If not computable, return 1531 /// UnknownValue. isSigned specifies whether the less-than is signed. 1532 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, 1533 bool isSigned); 1534 1535 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 1536 /// (which may not be an immediate predecessor) which has exactly one 1537 /// successor from which BB is reachable, or null if no such block is 1538 /// found. 1539 BasicBlock* getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB); 1540 1541 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1542 /// in the header of its containing loop, we know the loop executes a 1543 /// constant number of times, and the PHI node is just a recurrence 1544 /// involving constants, fold it. 1545 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, 1546 const Loop *L); 1547 }; 1548} 1549 1550//===----------------------------------------------------------------------===// 1551// Basic SCEV Analysis and PHI Idiom Recognition Code 1552// 1553 1554/// deleteValueFromRecords - This method should be called by the 1555/// client before it removes an instruction from the program, to make sure 1556/// that no dangling references are left around. 1557void ScalarEvolutionsImpl::deleteValueFromRecords(Value *V) { 1558 SmallVector<Value *, 16> Worklist; 1559 1560 if (Scalars.erase(V)) { 1561 if (PHINode *PN = dyn_cast<PHINode>(V)) 1562 ConstantEvolutionLoopExitValue.erase(PN); 1563 Worklist.push_back(V); 1564 } 1565 1566 while (!Worklist.empty()) { 1567 Value *VV = Worklist.back(); 1568 Worklist.pop_back(); 1569 1570 for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end(); 1571 UI != UE; ++UI) { 1572 Instruction *Inst = cast<Instruction>(*UI); 1573 if (Scalars.erase(Inst)) { 1574 if (PHINode *PN = dyn_cast<PHINode>(VV)) 1575 ConstantEvolutionLoopExitValue.erase(PN); 1576 Worklist.push_back(Inst); 1577 } 1578 } 1579 } 1580} 1581 1582const TargetData &ScalarEvolutionsImpl::getTargetData() const { 1583 return TD; 1584} 1585 1586SCEVHandle ScalarEvolutionsImpl::getCouldNotCompute() { 1587 return UnknownValue; 1588} 1589 1590/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1591/// expression and create a new one. 1592SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) { 1593 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!"); 1594 1595 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V); 1596 if (I != Scalars.end()) return I->second; 1597 SCEVHandle S = createSCEV(V); 1598 Scalars.insert(std::make_pair(V, S)); 1599 return S; 1600} 1601 1602/// getIntegerSCEV - Given an integer or FP type, create a constant for the 1603/// specified signed integer value and return a SCEV for the constant. 1604SCEVHandle ScalarEvolutionsImpl::getIntegerSCEV(int Val, const Type *Ty) { 1605 if (isa<PointerType>(Ty)) 1606 Ty = TD.getIntPtrType(); 1607 Constant *C; 1608 if (Val == 0) 1609 C = Constant::getNullValue(Ty); 1610 else if (Ty->isFloatingPoint()) 1611 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle : 1612 APFloat::IEEEdouble, Val)); 1613 else 1614 C = ConstantInt::get(Ty, Val); 1615 return SE.getUnknown(C); 1616} 1617 1618/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 1619/// 1620SCEVHandle ScalarEvolutionsImpl::getNegativeSCEV(const SCEVHandle &V) { 1621 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 1622 return SE.getUnknown(ConstantExpr::getNeg(VC->getValue())); 1623 1624 const Type *Ty = V->getType(); 1625 if (isa<PointerType>(Ty)) 1626 Ty = TD.getIntPtrType(); 1627 return SE.getMulExpr(V, SE.getConstant(ConstantInt::getAllOnesValue(Ty))); 1628} 1629 1630/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 1631SCEVHandle ScalarEvolutionsImpl::getNotSCEV(const SCEVHandle &V) { 1632 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 1633 return SE.getUnknown(ConstantExpr::getNot(VC->getValue())); 1634 1635 const Type *Ty = V->getType(); 1636 if (isa<PointerType>(Ty)) 1637 Ty = TD.getIntPtrType(); 1638 SCEVHandle AllOnes = SE.getConstant(ConstantInt::getAllOnesValue(Ty)); 1639 return getMinusSCEV(AllOnes, V); 1640} 1641 1642/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 1643/// 1644SCEVHandle ScalarEvolutionsImpl::getMinusSCEV(const SCEVHandle &LHS, 1645 const SCEVHandle &RHS) { 1646 // X - Y --> X + -Y 1647 return SE.getAddExpr(LHS, SE.getNegativeSCEV(RHS)); 1648} 1649 1650/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 1651/// input value to the specified type. If the type must be extended, it is zero 1652/// extended. 1653SCEVHandle 1654ScalarEvolutionsImpl::getTruncateOrZeroExtend(const SCEVHandle &V, 1655 const Type *Ty) { 1656 const Type *SrcTy = V->getType(); 1657 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 1658 (Ty->isInteger() || isa<PointerType>(Ty)) && 1659 "Cannot truncate or zero extend with non-integer arguments!"); 1660 if (TD.getTypeSizeInBits(SrcTy) == TD.getTypeSizeInBits(Ty)) 1661 return V; // No conversion 1662 if (TD.getTypeSizeInBits(SrcTy) > TD.getTypeSizeInBits(Ty)) 1663 return SE.getTruncateExpr(V, Ty); 1664 return SE.getZeroExtendExpr(V, Ty); 1665} 1666 1667/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 1668/// input value to the specified type. If the type must be extended, it is sign 1669/// extended. 1670SCEVHandle 1671ScalarEvolutionsImpl::getTruncateOrSignExtend(const SCEVHandle &V, 1672 const Type *Ty) { 1673 const Type *SrcTy = V->getType(); 1674 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 1675 (Ty->isInteger() || isa<PointerType>(Ty)) && 1676 "Cannot truncate or zero extend with non-integer arguments!"); 1677 if (TD.getTypeSizeInBits(SrcTy) == TD.getTypeSizeInBits(Ty)) 1678 return V; // No conversion 1679 if (TD.getTypeSizeInBits(SrcTy) > TD.getTypeSizeInBits(Ty)) 1680 return SE.getTruncateExpr(V, Ty); 1681 return SE.getSignExtendExpr(V, Ty); 1682} 1683 1684/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 1685/// the specified instruction and replaces any references to the symbolic value 1686/// SymName with the specified value. This is used during PHI resolution. 1687void ScalarEvolutionsImpl:: 1688ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName, 1689 const SCEVHandle &NewVal) { 1690 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I); 1691 if (SI == Scalars.end()) return; 1692 1693 SCEVHandle NV = 1694 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, SE); 1695 if (NV == SI->second) return; // No change. 1696 1697 SI->second = NV; // Update the scalars map! 1698 1699 // Any instruction values that use this instruction might also need to be 1700 // updated! 1701 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1702 UI != E; ++UI) 1703 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 1704} 1705 1706/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1707/// a loop header, making it a potential recurrence, or it doesn't. 1708/// 1709SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) { 1710 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1711 if (const Loop *L = LI.getLoopFor(PN->getParent())) 1712 if (L->getHeader() == PN->getParent()) { 1713 // If it lives in the loop header, it has two incoming values, one 1714 // from outside the loop, and one from inside. 1715 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1716 unsigned BackEdge = IncomingEdge^1; 1717 1718 // While we are analyzing this PHI node, handle its value symbolically. 1719 SCEVHandle SymbolicName = SE.getUnknown(PN); 1720 assert(Scalars.find(PN) == Scalars.end() && 1721 "PHI node already processed?"); 1722 Scalars.insert(std::make_pair(PN, SymbolicName)); 1723 1724 // Using this symbolic name for the PHI, analyze the value coming around 1725 // the back-edge. 1726 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1727 1728 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1729 // has a special value for the first iteration of the loop. 1730 1731 // If the value coming around the backedge is an add with the symbolic 1732 // value we just inserted, then we found a simple induction variable! 1733 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1734 // If there is a single occurrence of the symbolic value, replace it 1735 // with a recurrence. 1736 unsigned FoundIndex = Add->getNumOperands(); 1737 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1738 if (Add->getOperand(i) == SymbolicName) 1739 if (FoundIndex == e) { 1740 FoundIndex = i; 1741 break; 1742 } 1743 1744 if (FoundIndex != Add->getNumOperands()) { 1745 // Create an add with everything but the specified operand. 1746 std::vector<SCEVHandle> Ops; 1747 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1748 if (i != FoundIndex) 1749 Ops.push_back(Add->getOperand(i)); 1750 SCEVHandle Accum = SE.getAddExpr(Ops); 1751 1752 // This is not a valid addrec if the step amount is varying each 1753 // loop iteration, but is not itself an addrec in this loop. 1754 if (Accum->isLoopInvariant(L) || 1755 (isa<SCEVAddRecExpr>(Accum) && 1756 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1757 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1758 SCEVHandle PHISCEV = SE.getAddRecExpr(StartVal, Accum, L); 1759 1760 // Okay, for the entire analysis of this edge we assumed the PHI 1761 // to be symbolic. We now need to go back and update all of the 1762 // entries for the scalars that use the PHI (except for the PHI 1763 // itself) to use the new analyzed value instead of the "symbolic" 1764 // value. 1765 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1766 return PHISCEV; 1767 } 1768 } 1769 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) { 1770 // Otherwise, this could be a loop like this: 1771 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 1772 // In this case, j = {1,+,1} and BEValue is j. 1773 // Because the other in-value of i (0) fits the evolution of BEValue 1774 // i really is an addrec evolution. 1775 if (AddRec->getLoop() == L && AddRec->isAffine()) { 1776 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1777 1778 // If StartVal = j.start - j.stride, we can use StartVal as the 1779 // initial step of the addrec evolution. 1780 if (StartVal == SE.getMinusSCEV(AddRec->getOperand(0), 1781 AddRec->getOperand(1))) { 1782 SCEVHandle PHISCEV = 1783 SE.getAddRecExpr(StartVal, AddRec->getOperand(1), L); 1784 1785 // Okay, for the entire analysis of this edge we assumed the PHI 1786 // to be symbolic. We now need to go back and update all of the 1787 // entries for the scalars that use the PHI (except for the PHI 1788 // itself) to use the new analyzed value instead of the "symbolic" 1789 // value. 1790 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1791 return PHISCEV; 1792 } 1793 } 1794 } 1795 1796 return SymbolicName; 1797 } 1798 1799 // If it's not a loop phi, we can't handle it yet. 1800 return SE.getUnknown(PN); 1801} 1802 1803/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 1804/// guaranteed to end in (at every loop iteration). It is, at the same time, 1805/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 1806/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 1807static uint32_t GetMinTrailingZeros(SCEVHandle S, const TargetData &TD) { 1808 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 1809 return C->getValue()->getValue().countTrailingZeros(); 1810 1811 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 1812 return std::min(GetMinTrailingZeros(T->getOperand(), TD), 1813 (uint32_t)TD.getTypeSizeInBits(T->getType())); 1814 1815 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 1816 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), TD); 1817 return OpRes == TD.getTypeSizeInBits(E->getOperand()->getType()) ? 1818 TD.getTypeSizeInBits(E->getOperand()->getType()) : OpRes; 1819 } 1820 1821 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 1822 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), TD); 1823 return OpRes == TD.getTypeSizeInBits(E->getOperand()->getType()) ? 1824 TD.getTypeSizeInBits(E->getOperand()->getType()) : OpRes; 1825 } 1826 1827 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 1828 // The result is the min of all operands results. 1829 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), TD); 1830 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1831 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), TD)); 1832 return MinOpRes; 1833 } 1834 1835 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 1836 // The result is the sum of all operands results. 1837 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0), TD); 1838 uint32_t BitWidth = TD.getTypeSizeInBits(M->getType()); 1839 for (unsigned i = 1, e = M->getNumOperands(); 1840 SumOpRes != BitWidth && i != e; ++i) 1841 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i), TD), 1842 BitWidth); 1843 return SumOpRes; 1844 } 1845 1846 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 1847 // The result is the min of all operands results. 1848 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), TD); 1849 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1850 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), TD)); 1851 return MinOpRes; 1852 } 1853 1854 if (SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 1855 // The result is the min of all operands results. 1856 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), TD); 1857 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 1858 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), TD)); 1859 return MinOpRes; 1860 } 1861 1862 if (SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 1863 // The result is the min of all operands results. 1864 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), TD); 1865 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 1866 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), TD)); 1867 return MinOpRes; 1868 } 1869 1870 // SCEVUDivExpr, SCEVUnknown 1871 return 0; 1872} 1873 1874/// createSCEV - We know that there is no SCEV for the specified value. 1875/// Analyze the expression. 1876/// 1877SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) { 1878 if (!isa<IntegerType>(V->getType()) && 1879 !isa<PointerType>(V->getType())) 1880 return SE.getUnknown(V); 1881 1882 unsigned Opcode = Instruction::UserOp1; 1883 if (Instruction *I = dyn_cast<Instruction>(V)) 1884 Opcode = I->getOpcode(); 1885 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 1886 Opcode = CE->getOpcode(); 1887 else 1888 return SE.getUnknown(V); 1889 1890 User *U = cast<User>(V); 1891 switch (Opcode) { 1892 case Instruction::Add: 1893 return SE.getAddExpr(getSCEV(U->getOperand(0)), 1894 getSCEV(U->getOperand(1))); 1895 case Instruction::Mul: 1896 return SE.getMulExpr(getSCEV(U->getOperand(0)), 1897 getSCEV(U->getOperand(1))); 1898 case Instruction::UDiv: 1899 return SE.getUDivExpr(getSCEV(U->getOperand(0)), 1900 getSCEV(U->getOperand(1))); 1901 case Instruction::Sub: 1902 return SE.getMinusSCEV(getSCEV(U->getOperand(0)), 1903 getSCEV(U->getOperand(1))); 1904 case Instruction::Or: 1905 // If the RHS of the Or is a constant, we may have something like: 1906 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 1907 // optimizations will transparently handle this case. 1908 // 1909 // In order for this transformation to be safe, the LHS must be of the 1910 // form X*(2^n) and the Or constant must be less than 2^n. 1911 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 1912 SCEVHandle LHS = getSCEV(U->getOperand(0)); 1913 const APInt &CIVal = CI->getValue(); 1914 if (GetMinTrailingZeros(LHS, TD) >= 1915 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) 1916 return SE.getAddExpr(LHS, getSCEV(U->getOperand(1))); 1917 } 1918 break; 1919 case Instruction::Xor: 1920 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 1921 // If the RHS of the xor is a signbit, then this is just an add. 1922 // Instcombine turns add of signbit into xor as a strength reduction step. 1923 if (CI->getValue().isSignBit()) 1924 return SE.getAddExpr(getSCEV(U->getOperand(0)), 1925 getSCEV(U->getOperand(1))); 1926 1927 // If the RHS of xor is -1, then this is a not operation. 1928 else if (CI->isAllOnesValue()) 1929 return SE.getNotSCEV(getSCEV(U->getOperand(0))); 1930 } 1931 break; 1932 1933 case Instruction::Shl: 1934 // Turn shift left of a constant amount into a multiply. 1935 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 1936 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 1937 Constant *X = ConstantInt::get( 1938 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 1939 return SE.getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 1940 } 1941 break; 1942 1943 case Instruction::LShr: 1944 // Turn logical shift right of a constant into a unsigned divide. 1945 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 1946 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 1947 Constant *X = ConstantInt::get( 1948 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 1949 return SE.getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 1950 } 1951 break; 1952 1953 case Instruction::Trunc: 1954 return SE.getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 1955 1956 case Instruction::ZExt: 1957 return SE.getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 1958 1959 case Instruction::SExt: 1960 return SE.getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 1961 1962 case Instruction::BitCast: 1963 // BitCasts are no-op casts so we just eliminate the cast. 1964 if ((U->getType()->isInteger() || 1965 isa<PointerType>(U->getType())) && 1966 (U->getOperand(0)->getType()->isInteger() || 1967 isa<PointerType>(U->getOperand(0)->getType()))) 1968 return getSCEV(U->getOperand(0)); 1969 break; 1970 1971 case Instruction::IntToPtr: 1972 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 1973 TD.getIntPtrType()); 1974 1975 case Instruction::PtrToInt: 1976 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 1977 U->getType()); 1978 1979 case Instruction::GetElementPtr: { 1980 const Type *IntPtrTy = TD.getIntPtrType(); 1981 Value *Base = U->getOperand(0); 1982 SCEVHandle TotalOffset = SE.getIntegerSCEV(0, IntPtrTy); 1983 gep_type_iterator GTI = gep_type_begin(U); 1984 for (GetElementPtrInst::op_iterator I = next(U->op_begin()), 1985 E = U->op_end(); 1986 I != E; ++I) { 1987 Value *Index = *I; 1988 // Compute the (potentially symbolic) offset in bytes for this index. 1989 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 1990 // For a struct, add the member offset. 1991 const StructLayout &SL = *TD.getStructLayout(STy); 1992 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 1993 uint64_t Offset = SL.getElementOffset(FieldNo); 1994 TotalOffset = SE.getAddExpr(TotalOffset, 1995 SE.getIntegerSCEV(Offset, IntPtrTy)); 1996 } else { 1997 // For an array, add the element offset, explicitly scaled. 1998 SCEVHandle LocalOffset = getSCEV(Index); 1999 if (!isa<PointerType>(LocalOffset->getType())) 2000 // Getelementptr indicies are signed. 2001 LocalOffset = getTruncateOrSignExtend(LocalOffset, 2002 IntPtrTy); 2003 LocalOffset = 2004 SE.getMulExpr(LocalOffset, 2005 SE.getIntegerSCEV(TD.getTypePaddedSize(*GTI), 2006 IntPtrTy)); 2007 TotalOffset = SE.getAddExpr(TotalOffset, LocalOffset); 2008 } 2009 } 2010 return SE.getAddExpr(getSCEV(Base), TotalOffset); 2011 } 2012 2013 case Instruction::PHI: 2014 return createNodeForPHI(cast<PHINode>(U)); 2015 2016 case Instruction::Select: 2017 // This could be a smax or umax that was lowered earlier. 2018 // Try to recover it. 2019 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 2020 Value *LHS = ICI->getOperand(0); 2021 Value *RHS = ICI->getOperand(1); 2022 switch (ICI->getPredicate()) { 2023 case ICmpInst::ICMP_SLT: 2024 case ICmpInst::ICMP_SLE: 2025 std::swap(LHS, RHS); 2026 // fall through 2027 case ICmpInst::ICMP_SGT: 2028 case ICmpInst::ICMP_SGE: 2029 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 2030 return SE.getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 2031 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 2032 // ~smax(~x, ~y) == smin(x, y). 2033 return SE.getNotSCEV(SE.getSMaxExpr( 2034 SE.getNotSCEV(getSCEV(LHS)), 2035 SE.getNotSCEV(getSCEV(RHS)))); 2036 break; 2037 case ICmpInst::ICMP_ULT: 2038 case ICmpInst::ICMP_ULE: 2039 std::swap(LHS, RHS); 2040 // fall through 2041 case ICmpInst::ICMP_UGT: 2042 case ICmpInst::ICMP_UGE: 2043 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 2044 return SE.getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 2045 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 2046 // ~umax(~x, ~y) == umin(x, y) 2047 return SE.getNotSCEV(SE.getUMaxExpr(SE.getNotSCEV(getSCEV(LHS)), 2048 SE.getNotSCEV(getSCEV(RHS)))); 2049 break; 2050 default: 2051 break; 2052 } 2053 } 2054 2055 default: // We cannot analyze this expression. 2056 break; 2057 } 2058 2059 return SE.getUnknown(V); 2060} 2061 2062 2063 2064//===----------------------------------------------------------------------===// 2065// Iteration Count Computation Code 2066// 2067 2068/// getBackedgeTakenCount - If the specified loop has a predictable 2069/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 2070/// object. The backedge-taken count is the number of times the loop header 2071/// will be branched to from within the loop. This is one less than the 2072/// trip count of the loop, since it doesn't count the first iteration, 2073/// when the header is branched to from outside the loop. 2074/// 2075/// Note that it is not valid to call this method on a loop without a 2076/// loop-invariant backedge-taken count (see 2077/// hasLoopInvariantBackedgeTakenCount). 2078/// 2079SCEVHandle ScalarEvolutionsImpl::getBackedgeTakenCount(const Loop *L) { 2080 std::map<const Loop*, SCEVHandle>::iterator I = BackedgeTakenCounts.find(L); 2081 if (I == BackedgeTakenCounts.end()) { 2082 SCEVHandle ItCount = ComputeBackedgeTakenCount(L); 2083 I = BackedgeTakenCounts.insert(std::make_pair(L, ItCount)).first; 2084 if (ItCount != UnknownValue) { 2085 assert(ItCount->isLoopInvariant(L) && 2086 "Computed trip count isn't loop invariant for loop!"); 2087 ++NumTripCountsComputed; 2088 } else if (isa<PHINode>(L->getHeader()->begin())) { 2089 // Only count loops that have phi nodes as not being computable. 2090 ++NumTripCountsNotComputed; 2091 } 2092 } 2093 return I->second; 2094} 2095 2096/// forgetLoopBackedgeTakenCount - This method should be called by the 2097/// client when it has changed a loop in a way that may effect 2098/// ScalarEvolution's ability to compute a trip count, or if the loop 2099/// is deleted. 2100void ScalarEvolutionsImpl::forgetLoopBackedgeTakenCount(const Loop *L) { 2101 BackedgeTakenCounts.erase(L); 2102} 2103 2104/// ComputeBackedgeTakenCount - Compute the number of times the backedge 2105/// of the specified loop will execute. 2106SCEVHandle ScalarEvolutionsImpl::ComputeBackedgeTakenCount(const Loop *L) { 2107 // If the loop has a non-one exit block count, we can't analyze it. 2108 SmallVector<BasicBlock*, 8> ExitBlocks; 2109 L->getExitBlocks(ExitBlocks); 2110 if (ExitBlocks.size() != 1) return UnknownValue; 2111 2112 // Okay, there is one exit block. Try to find the condition that causes the 2113 // loop to be exited. 2114 BasicBlock *ExitBlock = ExitBlocks[0]; 2115 2116 BasicBlock *ExitingBlock = 0; 2117 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 2118 PI != E; ++PI) 2119 if (L->contains(*PI)) { 2120 if (ExitingBlock == 0) 2121 ExitingBlock = *PI; 2122 else 2123 return UnknownValue; // More than one block exiting! 2124 } 2125 assert(ExitingBlock && "No exits from loop, something is broken!"); 2126 2127 // Okay, we've computed the exiting block. See what condition causes us to 2128 // exit. 2129 // 2130 // FIXME: we should be able to handle switch instructions (with a single exit) 2131 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 2132 if (ExitBr == 0) return UnknownValue; 2133 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 2134 2135 // At this point, we know we have a conditional branch that determines whether 2136 // the loop is exited. However, we don't know if the branch is executed each 2137 // time through the loop. If not, then the execution count of the branch will 2138 // not be equal to the trip count of the loop. 2139 // 2140 // Currently we check for this by checking to see if the Exit branch goes to 2141 // the loop header. If so, we know it will always execute the same number of 2142 // times as the loop. We also handle the case where the exit block *is* the 2143 // loop header. This is common for un-rotated loops. More extensive analysis 2144 // could be done to handle more cases here. 2145 if (ExitBr->getSuccessor(0) != L->getHeader() && 2146 ExitBr->getSuccessor(1) != L->getHeader() && 2147 ExitBr->getParent() != L->getHeader()) 2148 return UnknownValue; 2149 2150 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition()); 2151 2152 // If it's not an integer comparison then compute it the hard way. 2153 // Note that ICmpInst deals with pointer comparisons too so we must check 2154 // the type of the operand. 2155 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType())) 2156 return ComputeBackedgeTakenCountExhaustively(L, ExitBr->getCondition(), 2157 ExitBr->getSuccessor(0) == ExitBlock); 2158 2159 // If the condition was exit on true, convert the condition to exit on false 2160 ICmpInst::Predicate Cond; 2161 if (ExitBr->getSuccessor(1) == ExitBlock) 2162 Cond = ExitCond->getPredicate(); 2163 else 2164 Cond = ExitCond->getInversePredicate(); 2165 2166 // Handle common loops like: for (X = "string"; *X; ++X) 2167 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 2168 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 2169 SCEVHandle ItCnt = 2170 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 2171 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 2172 } 2173 2174 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 2175 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 2176 2177 // Try to evaluate any dependencies out of the loop. 2178 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 2179 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 2180 Tmp = getSCEVAtScope(RHS, L); 2181 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 2182 2183 // At this point, we would like to compute how many iterations of the 2184 // loop the predicate will return true for these inputs. 2185 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 2186 // If there is a loop-invariant, force it into the RHS. 2187 std::swap(LHS, RHS); 2188 Cond = ICmpInst::getSwappedPredicate(Cond); 2189 } 2190 2191 // FIXME: think about handling pointer comparisons! i.e.: 2192 // while (P != P+100) ++P; 2193 2194 // If we have a comparison of a chrec against a constant, try to use value 2195 // ranges to answer this query. 2196 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 2197 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 2198 if (AddRec->getLoop() == L) { 2199 // Form the comparison range using the constant of the correct type so 2200 // that the ConstantRange class knows to do a signed or unsigned 2201 // comparison. 2202 ConstantInt *CompVal = RHSC->getValue(); 2203 const Type *RealTy = ExitCond->getOperand(0)->getType(); 2204 CompVal = dyn_cast<ConstantInt>( 2205 ConstantExpr::getBitCast(CompVal, RealTy)); 2206 if (CompVal) { 2207 // Form the constant range. 2208 ConstantRange CompRange( 2209 ICmpInst::makeConstantRange(Cond, CompVal->getValue())); 2210 2211 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, SE); 2212 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 2213 } 2214 } 2215 2216 switch (Cond) { 2217 case ICmpInst::ICMP_NE: { // while (X != Y) 2218 // Convert to: while (X-Y != 0) 2219 SCEVHandle TC = HowFarToZero(SE.getMinusSCEV(LHS, RHS), L); 2220 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2221 break; 2222 } 2223 case ICmpInst::ICMP_EQ: { 2224 // Convert to: while (X-Y == 0) // while (X == Y) 2225 SCEVHandle TC = HowFarToNonZero(SE.getMinusSCEV(LHS, RHS), L); 2226 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2227 break; 2228 } 2229 case ICmpInst::ICMP_SLT: { 2230 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true); 2231 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2232 break; 2233 } 2234 case ICmpInst::ICMP_SGT: { 2235 SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS), 2236 SE.getNotSCEV(RHS), L, true); 2237 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2238 break; 2239 } 2240 case ICmpInst::ICMP_ULT: { 2241 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false); 2242 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2243 break; 2244 } 2245 case ICmpInst::ICMP_UGT: { 2246 SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS), 2247 SE.getNotSCEV(RHS), L, false); 2248 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2249 break; 2250 } 2251 default: 2252#if 0 2253 errs() << "ComputeBackedgeTakenCount "; 2254 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 2255 errs() << "[unsigned] "; 2256 errs() << *LHS << " " 2257 << Instruction::getOpcodeName(Instruction::ICmp) 2258 << " " << *RHS << "\n"; 2259#endif 2260 break; 2261 } 2262 return 2263 ComputeBackedgeTakenCountExhaustively(L, ExitCond, 2264 ExitBr->getSuccessor(0) == ExitBlock); 2265} 2266 2267static ConstantInt * 2268EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 2269 ScalarEvolution &SE) { 2270 SCEVHandle InVal = SE.getConstant(C); 2271 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE); 2272 assert(isa<SCEVConstant>(Val) && 2273 "Evaluation of SCEV at constant didn't fold correctly?"); 2274 return cast<SCEVConstant>(Val)->getValue(); 2275} 2276 2277/// GetAddressedElementFromGlobal - Given a global variable with an initializer 2278/// and a GEP expression (missing the pointer index) indexing into it, return 2279/// the addressed element of the initializer or null if the index expression is 2280/// invalid. 2281static Constant * 2282GetAddressedElementFromGlobal(GlobalVariable *GV, 2283 const std::vector<ConstantInt*> &Indices) { 2284 Constant *Init = GV->getInitializer(); 2285 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 2286 uint64_t Idx = Indices[i]->getZExtValue(); 2287 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 2288 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 2289 Init = cast<Constant>(CS->getOperand(Idx)); 2290 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 2291 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 2292 Init = cast<Constant>(CA->getOperand(Idx)); 2293 } else if (isa<ConstantAggregateZero>(Init)) { 2294 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 2295 assert(Idx < STy->getNumElements() && "Bad struct index!"); 2296 Init = Constant::getNullValue(STy->getElementType(Idx)); 2297 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 2298 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 2299 Init = Constant::getNullValue(ATy->getElementType()); 2300 } else { 2301 assert(0 && "Unknown constant aggregate type!"); 2302 } 2303 return 0; 2304 } else { 2305 return 0; // Unknown initializer type 2306 } 2307 } 2308 return Init; 2309} 2310 2311/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 2312/// 'icmp op load X, cst', try to see if we can compute the backedge 2313/// execution count. 2314SCEVHandle ScalarEvolutionsImpl:: 2315ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS, 2316 const Loop *L, 2317 ICmpInst::Predicate predicate) { 2318 if (LI->isVolatile()) return UnknownValue; 2319 2320 // Check to see if the loaded pointer is a getelementptr of a global. 2321 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 2322 if (!GEP) return UnknownValue; 2323 2324 // Make sure that it is really a constant global we are gepping, with an 2325 // initializer, and make sure the first IDX is really 0. 2326 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 2327 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 2328 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 2329 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 2330 return UnknownValue; 2331 2332 // Okay, we allow one non-constant index into the GEP instruction. 2333 Value *VarIdx = 0; 2334 std::vector<ConstantInt*> Indexes; 2335 unsigned VarIdxNum = 0; 2336 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 2337 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 2338 Indexes.push_back(CI); 2339 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 2340 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 2341 VarIdx = GEP->getOperand(i); 2342 VarIdxNum = i-2; 2343 Indexes.push_back(0); 2344 } 2345 2346 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 2347 // Check to see if X is a loop variant variable value now. 2348 SCEVHandle Idx = getSCEV(VarIdx); 2349 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 2350 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 2351 2352 // We can only recognize very limited forms of loop index expressions, in 2353 // particular, only affine AddRec's like {C1,+,C2}. 2354 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 2355 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 2356 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 2357 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 2358 return UnknownValue; 2359 2360 unsigned MaxSteps = MaxBruteForceIterations; 2361 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 2362 ConstantInt *ItCst = 2363 ConstantInt::get(IdxExpr->getType(), IterationNum); 2364 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, SE); 2365 2366 // Form the GEP offset. 2367 Indexes[VarIdxNum] = Val; 2368 2369 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 2370 if (Result == 0) break; // Cannot compute! 2371 2372 // Evaluate the condition for this iteration. 2373 Result = ConstantExpr::getICmp(predicate, Result, RHS); 2374 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 2375 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 2376#if 0 2377 errs() << "\n***\n*** Computed loop count " << *ItCst 2378 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 2379 << "***\n"; 2380#endif 2381 ++NumArrayLenItCounts; 2382 return SE.getConstant(ItCst); // Found terminating iteration! 2383 } 2384 } 2385 return UnknownValue; 2386} 2387 2388 2389/// CanConstantFold - Return true if we can constant fold an instruction of the 2390/// specified type, assuming that all operands were constants. 2391static bool CanConstantFold(const Instruction *I) { 2392 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 2393 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 2394 return true; 2395 2396 if (const CallInst *CI = dyn_cast<CallInst>(I)) 2397 if (const Function *F = CI->getCalledFunction()) 2398 return canConstantFoldCallTo(F); 2399 return false; 2400} 2401 2402/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 2403/// in the loop that V is derived from. We allow arbitrary operations along the 2404/// way, but the operands of an operation must either be constants or a value 2405/// derived from a constant PHI. If this expression does not fit with these 2406/// constraints, return null. 2407static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 2408 // If this is not an instruction, or if this is an instruction outside of the 2409 // loop, it can't be derived from a loop PHI. 2410 Instruction *I = dyn_cast<Instruction>(V); 2411 if (I == 0 || !L->contains(I->getParent())) return 0; 2412 2413 if (PHINode *PN = dyn_cast<PHINode>(I)) { 2414 if (L->getHeader() == I->getParent()) 2415 return PN; 2416 else 2417 // We don't currently keep track of the control flow needed to evaluate 2418 // PHIs, so we cannot handle PHIs inside of loops. 2419 return 0; 2420 } 2421 2422 // If we won't be able to constant fold this expression even if the operands 2423 // are constants, return early. 2424 if (!CanConstantFold(I)) return 0; 2425 2426 // Otherwise, we can evaluate this instruction if all of its operands are 2427 // constant or derived from a PHI node themselves. 2428 PHINode *PHI = 0; 2429 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 2430 if (!(isa<Constant>(I->getOperand(Op)) || 2431 isa<GlobalValue>(I->getOperand(Op)))) { 2432 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 2433 if (P == 0) return 0; // Not evolving from PHI 2434 if (PHI == 0) 2435 PHI = P; 2436 else if (PHI != P) 2437 return 0; // Evolving from multiple different PHIs. 2438 } 2439 2440 // This is a expression evolving from a constant PHI! 2441 return PHI; 2442} 2443 2444/// EvaluateExpression - Given an expression that passes the 2445/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 2446/// in the loop has the value PHIVal. If we can't fold this expression for some 2447/// reason, return null. 2448static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 2449 if (isa<PHINode>(V)) return PHIVal; 2450 if (Constant *C = dyn_cast<Constant>(V)) return C; 2451 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV; 2452 Instruction *I = cast<Instruction>(V); 2453 2454 std::vector<Constant*> Operands; 2455 Operands.resize(I->getNumOperands()); 2456 2457 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2458 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 2459 if (Operands[i] == 0) return 0; 2460 } 2461 2462 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2463 return ConstantFoldCompareInstOperands(CI->getPredicate(), 2464 &Operands[0], Operands.size()); 2465 else 2466 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2467 &Operands[0], Operands.size()); 2468} 2469 2470/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 2471/// in the header of its containing loop, we know the loop executes a 2472/// constant number of times, and the PHI node is just a recurrence 2473/// involving constants, fold it. 2474Constant *ScalarEvolutionsImpl:: 2475getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, const Loop *L){ 2476 std::map<PHINode*, Constant*>::iterator I = 2477 ConstantEvolutionLoopExitValue.find(PN); 2478 if (I != ConstantEvolutionLoopExitValue.end()) 2479 return I->second; 2480 2481 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations))) 2482 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 2483 2484 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 2485 2486 // Since the loop is canonicalized, the PHI node must have two entries. One 2487 // entry must be a constant (coming in from outside of the loop), and the 2488 // second must be derived from the same PHI. 2489 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2490 Constant *StartCST = 2491 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2492 if (StartCST == 0) 2493 return RetVal = 0; // Must be a constant. 2494 2495 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2496 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2497 if (PN2 != PN) 2498 return RetVal = 0; // Not derived from same PHI. 2499 2500 // Execute the loop symbolically to determine the exit value. 2501 if (BEs.getActiveBits() >= 32) 2502 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 2503 2504 unsigned NumIterations = BEs.getZExtValue(); // must be in range 2505 unsigned IterationNum = 0; 2506 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 2507 if (IterationNum == NumIterations) 2508 return RetVal = PHIVal; // Got exit value! 2509 2510 // Compute the value of the PHI node for the next iteration. 2511 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2512 if (NextPHI == PHIVal) 2513 return RetVal = NextPHI; // Stopped evolving! 2514 if (NextPHI == 0) 2515 return 0; // Couldn't evaluate! 2516 PHIVal = NextPHI; 2517 } 2518} 2519 2520/// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a 2521/// constant number of times (the condition evolves only from constants), 2522/// try to evaluate a few iterations of the loop until we get the exit 2523/// condition gets a value of ExitWhen (true or false). If we cannot 2524/// evaluate the trip count of the loop, return UnknownValue. 2525SCEVHandle ScalarEvolutionsImpl:: 2526ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 2527 PHINode *PN = getConstantEvolvingPHI(Cond, L); 2528 if (PN == 0) return UnknownValue; 2529 2530 // Since the loop is canonicalized, the PHI node must have two entries. One 2531 // entry must be a constant (coming in from outside of the loop), and the 2532 // second must be derived from the same PHI. 2533 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2534 Constant *StartCST = 2535 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2536 if (StartCST == 0) return UnknownValue; // Must be a constant. 2537 2538 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2539 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2540 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 2541 2542 // Okay, we find a PHI node that defines the trip count of this loop. Execute 2543 // the loop symbolically to determine when the condition gets a value of 2544 // "ExitWhen". 2545 unsigned IterationNum = 0; 2546 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 2547 for (Constant *PHIVal = StartCST; 2548 IterationNum != MaxIterations; ++IterationNum) { 2549 ConstantInt *CondVal = 2550 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 2551 2552 // Couldn't symbolically evaluate. 2553 if (!CondVal) return UnknownValue; 2554 2555 if (CondVal->getValue() == uint64_t(ExitWhen)) { 2556 ConstantEvolutionLoopExitValue[PN] = PHIVal; 2557 ++NumBruteForceTripCountsComputed; 2558 return SE.getConstant(ConstantInt::get(Type::Int32Ty, IterationNum)); 2559 } 2560 2561 // Compute the value of the PHI node for the next iteration. 2562 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2563 if (NextPHI == 0 || NextPHI == PHIVal) 2564 return UnknownValue; // Couldn't evaluate or not making progress... 2565 PHIVal = NextPHI; 2566 } 2567 2568 // Too many iterations were needed to evaluate. 2569 return UnknownValue; 2570} 2571 2572/// getSCEVAtScope - Compute the value of the specified expression within the 2573/// indicated loop (which may be null to indicate in no loop). If the 2574/// expression cannot be evaluated, return UnknownValue. 2575SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) { 2576 // FIXME: this should be turned into a virtual method on SCEV! 2577 2578 if (isa<SCEVConstant>(V)) return V; 2579 2580 // If this instruction is evolved from a constant-evolving PHI, compute the 2581 // exit value from the loop without using SCEVs. 2582 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 2583 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 2584 const Loop *LI = this->LI[I->getParent()]; 2585 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 2586 if (PHINode *PN = dyn_cast<PHINode>(I)) 2587 if (PN->getParent() == LI->getHeader()) { 2588 // Okay, there is no closed form solution for the PHI node. Check 2589 // to see if the loop that contains it has a known backedge-taken 2590 // count. If so, we may be able to force computation of the exit 2591 // value. 2592 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(LI); 2593 if (SCEVConstant *BTCC = 2594 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 2595 // Okay, we know how many times the containing loop executes. If 2596 // this is a constant evolving PHI node, get the final value at 2597 // the specified iteration number. 2598 Constant *RV = getConstantEvolutionLoopExitValue(PN, 2599 BTCC->getValue()->getValue(), 2600 LI); 2601 if (RV) return SE.getUnknown(RV); 2602 } 2603 } 2604 2605 // Okay, this is an expression that we cannot symbolically evaluate 2606 // into a SCEV. Check to see if it's possible to symbolically evaluate 2607 // the arguments into constants, and if so, try to constant propagate the 2608 // result. This is particularly useful for computing loop exit values. 2609 if (CanConstantFold(I)) { 2610 std::vector<Constant*> Operands; 2611 Operands.reserve(I->getNumOperands()); 2612 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2613 Value *Op = I->getOperand(i); 2614 if (Constant *C = dyn_cast<Constant>(Op)) { 2615 Operands.push_back(C); 2616 } else { 2617 // If any of the operands is non-constant and if they are 2618 // non-integer and non-pointer, don't even try to analyze them 2619 // with scev techniques. 2620 if (!isa<IntegerType>(Op->getType()) && 2621 !isa<PointerType>(Op->getType())) 2622 return V; 2623 2624 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 2625 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 2626 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(), 2627 Op->getType(), 2628 false)); 2629 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 2630 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 2631 Operands.push_back(ConstantExpr::getIntegerCast(C, 2632 Op->getType(), 2633 false)); 2634 else 2635 return V; 2636 } else { 2637 return V; 2638 } 2639 } 2640 } 2641 2642 Constant *C; 2643 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2644 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 2645 &Operands[0], Operands.size()); 2646 else 2647 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2648 &Operands[0], Operands.size()); 2649 return SE.getUnknown(C); 2650 } 2651 } 2652 2653 // This is some other type of SCEVUnknown, just return it. 2654 return V; 2655 } 2656 2657 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 2658 // Avoid performing the look-up in the common case where the specified 2659 // expression has no loop-variant portions. 2660 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 2661 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2662 if (OpAtScope != Comm->getOperand(i)) { 2663 if (OpAtScope == UnknownValue) return UnknownValue; 2664 // Okay, at least one of these operands is loop variant but might be 2665 // foldable. Build a new instance of the folded commutative expression. 2666 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 2667 NewOps.push_back(OpAtScope); 2668 2669 for (++i; i != e; ++i) { 2670 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2671 if (OpAtScope == UnknownValue) return UnknownValue; 2672 NewOps.push_back(OpAtScope); 2673 } 2674 if (isa<SCEVAddExpr>(Comm)) 2675 return SE.getAddExpr(NewOps); 2676 if (isa<SCEVMulExpr>(Comm)) 2677 return SE.getMulExpr(NewOps); 2678 if (isa<SCEVSMaxExpr>(Comm)) 2679 return SE.getSMaxExpr(NewOps); 2680 if (isa<SCEVUMaxExpr>(Comm)) 2681 return SE.getUMaxExpr(NewOps); 2682 assert(0 && "Unknown commutative SCEV type!"); 2683 } 2684 } 2685 // If we got here, all operands are loop invariant. 2686 return Comm; 2687 } 2688 2689 if (SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 2690 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L); 2691 if (LHS == UnknownValue) return LHS; 2692 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L); 2693 if (RHS == UnknownValue) return RHS; 2694 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 2695 return Div; // must be loop invariant 2696 return SE.getUDivExpr(LHS, RHS); 2697 } 2698 2699 // If this is a loop recurrence for a loop that does not contain L, then we 2700 // are dealing with the final value computed by the loop. 2701 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 2702 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 2703 // To evaluate this recurrence, we need to know how many times the AddRec 2704 // loop iterates. Compute this now. 2705 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 2706 if (BackedgeTakenCount == UnknownValue) return UnknownValue; 2707 2708 // Then, evaluate the AddRec. 2709 return AddRec->evaluateAtIteration(BackedgeTakenCount, SE); 2710 } 2711 return UnknownValue; 2712 } 2713 2714 //assert(0 && "Unknown SCEV type!"); 2715 return UnknownValue; 2716} 2717 2718/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 2719/// following equation: 2720/// 2721/// A * X = B (mod N) 2722/// 2723/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 2724/// A and B isn't important. 2725/// 2726/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 2727static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 2728 ScalarEvolution &SE) { 2729 uint32_t BW = A.getBitWidth(); 2730 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 2731 assert(A != 0 && "A must be non-zero."); 2732 2733 // 1. D = gcd(A, N) 2734 // 2735 // The gcd of A and N may have only one prime factor: 2. The number of 2736 // trailing zeros in A is its multiplicity 2737 uint32_t Mult2 = A.countTrailingZeros(); 2738 // D = 2^Mult2 2739 2740 // 2. Check if B is divisible by D. 2741 // 2742 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 2743 // is not less than multiplicity of this prime factor for D. 2744 if (B.countTrailingZeros() < Mult2) 2745 return SE.getCouldNotCompute(); 2746 2747 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 2748 // modulo (N / D). 2749 // 2750 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 2751 // bit width during computations. 2752 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 2753 APInt Mod(BW + 1, 0); 2754 Mod.set(BW - Mult2); // Mod = N / D 2755 APInt I = AD.multiplicativeInverse(Mod); 2756 2757 // 4. Compute the minimum unsigned root of the equation: 2758 // I * (B / D) mod (N / D) 2759 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 2760 2761 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 2762 // bits. 2763 return SE.getConstant(Result.trunc(BW)); 2764} 2765 2766/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 2767/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 2768/// might be the same) or two SCEVCouldNotCompute objects. 2769/// 2770static std::pair<SCEVHandle,SCEVHandle> 2771SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 2772 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 2773 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 2774 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 2775 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 2776 2777 // We currently can only solve this if the coefficients are constants. 2778 if (!LC || !MC || !NC) { 2779 SCEV *CNC = SE.getCouldNotCompute(); 2780 return std::make_pair(CNC, CNC); 2781 } 2782 2783 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 2784 const APInt &L = LC->getValue()->getValue(); 2785 const APInt &M = MC->getValue()->getValue(); 2786 const APInt &N = NC->getValue()->getValue(); 2787 APInt Two(BitWidth, 2); 2788 APInt Four(BitWidth, 4); 2789 2790 { 2791 using namespace APIntOps; 2792 const APInt& C = L; 2793 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 2794 // The B coefficient is M-N/2 2795 APInt B(M); 2796 B -= sdiv(N,Two); 2797 2798 // The A coefficient is N/2 2799 APInt A(N.sdiv(Two)); 2800 2801 // Compute the B^2-4ac term. 2802 APInt SqrtTerm(B); 2803 SqrtTerm *= B; 2804 SqrtTerm -= Four * (A * C); 2805 2806 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 2807 // integer value or else APInt::sqrt() will assert. 2808 APInt SqrtVal(SqrtTerm.sqrt()); 2809 2810 // Compute the two solutions for the quadratic formula. 2811 // The divisions must be performed as signed divisions. 2812 APInt NegB(-B); 2813 APInt TwoA( A << 1 ); 2814 if (TwoA.isMinValue()) { 2815 SCEV *CNC = SE.getCouldNotCompute(); 2816 return std::make_pair(CNC, CNC); 2817 } 2818 2819 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA)); 2820 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA)); 2821 2822 return std::make_pair(SE.getConstant(Solution1), 2823 SE.getConstant(Solution2)); 2824 } // end APIntOps namespace 2825} 2826 2827/// HowFarToZero - Return the number of times a backedge comparing the specified 2828/// value to zero will execute. If not computable, return UnknownValue 2829SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) { 2830 // If the value is a constant 2831 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2832 // If the value is already zero, the branch will execute zero times. 2833 if (C->getValue()->isZero()) return C; 2834 return UnknownValue; // Otherwise it will loop infinitely. 2835 } 2836 2837 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 2838 if (!AddRec || AddRec->getLoop() != L) 2839 return UnknownValue; 2840 2841 if (AddRec->isAffine()) { 2842 // If this is an affine expression, the execution count of this branch is 2843 // the minimum unsigned root of the following equation: 2844 // 2845 // Start + Step*N = 0 (mod 2^BW) 2846 // 2847 // equivalent to: 2848 // 2849 // Step*N = -Start (mod 2^BW) 2850 // 2851 // where BW is the common bit width of Start and Step. 2852 2853 // Get the initial value for the loop. 2854 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 2855 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 2856 2857 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop()); 2858 2859 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 2860 // For now we handle only constant steps. 2861 2862 // First, handle unitary steps. 2863 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 2864 return SE.getNegativeSCEV(Start); // N = -Start (as unsigned) 2865 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 2866 return Start; // N = Start (as unsigned) 2867 2868 // Then, try to solve the above equation provided that Start is constant. 2869 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 2870 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 2871 -StartC->getValue()->getValue(),SE); 2872 } 2873 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 2874 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 2875 // the quadratic equation to solve it. 2876 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec, SE); 2877 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2878 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2879 if (R1) { 2880#if 0 2881 errs() << "HFTZ: " << *V << " - sol#1: " << *R1 2882 << " sol#2: " << *R2 << "\n"; 2883#endif 2884 // Pick the smallest positive root value. 2885 if (ConstantInt *CB = 2886 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2887 R1->getValue(), R2->getValue()))) { 2888 if (CB->getZExtValue() == false) 2889 std::swap(R1, R2); // R1 is the minimum root now. 2890 2891 // We can only use this value if the chrec ends up with an exact zero 2892 // value at this index. When solving for "X*X != 5", for example, we 2893 // should not accept a root of 2. 2894 SCEVHandle Val = AddRec->evaluateAtIteration(R1, SE); 2895 if (Val->isZero()) 2896 return R1; // We found a quadratic root! 2897 } 2898 } 2899 } 2900 2901 return UnknownValue; 2902} 2903 2904/// HowFarToNonZero - Return the number of times a backedge checking the 2905/// specified value for nonzero will execute. If not computable, return 2906/// UnknownValue 2907SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) { 2908 // Loops that look like: while (X == 0) are very strange indeed. We don't 2909 // handle them yet except for the trivial case. This could be expanded in the 2910 // future as needed. 2911 2912 // If the value is a constant, check to see if it is known to be non-zero 2913 // already. If so, the backedge will execute zero times. 2914 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2915 if (!C->getValue()->isNullValue()) 2916 return SE.getIntegerSCEV(0, C->getType()); 2917 return UnknownValue; // Otherwise it will loop infinitely. 2918 } 2919 2920 // We could implement others, but I really doubt anyone writes loops like 2921 // this, and if they did, they would already be constant folded. 2922 return UnknownValue; 2923} 2924 2925/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 2926/// (which may not be an immediate predecessor) which has exactly one 2927/// successor from which BB is reachable, or null if no such block is 2928/// found. 2929/// 2930BasicBlock * 2931ScalarEvolutionsImpl::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 2932 // If the block has a unique predecessor, the predecessor must have 2933 // no other successors from which BB is reachable. 2934 if (BasicBlock *Pred = BB->getSinglePredecessor()) 2935 return Pred; 2936 2937 // A loop's header is defined to be a block that dominates the loop. 2938 // If the loop has a preheader, it must be a block that has exactly 2939 // one successor that can reach BB. This is slightly more strict 2940 // than necessary, but works if critical edges are split. 2941 if (Loop *L = LI.getLoopFor(BB)) 2942 return L->getLoopPreheader(); 2943 2944 return 0; 2945} 2946 2947/// isLoopGuardedByCond - Test whether entry to the loop is protected by 2948/// a conditional between LHS and RHS. 2949bool ScalarEvolutionsImpl::isLoopGuardedByCond(const Loop *L, 2950 ICmpInst::Predicate Pred, 2951 SCEV *LHS, SCEV *RHS) { 2952 BasicBlock *Preheader = L->getLoopPreheader(); 2953 BasicBlock *PreheaderDest = L->getHeader(); 2954 2955 // Starting at the preheader, climb up the predecessor chain, as long as 2956 // there are predecessors that can be found that have unique successors 2957 // leading to the original header. 2958 for (; Preheader; 2959 PreheaderDest = Preheader, 2960 Preheader = getPredecessorWithUniqueSuccessorForBB(Preheader)) { 2961 2962 BranchInst *LoopEntryPredicate = 2963 dyn_cast<BranchInst>(Preheader->getTerminator()); 2964 if (!LoopEntryPredicate || 2965 LoopEntryPredicate->isUnconditional()) 2966 continue; 2967 2968 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition()); 2969 if (!ICI) continue; 2970 2971 // Now that we found a conditional branch that dominates the loop, check to 2972 // see if it is the comparison we are looking for. 2973 Value *PreCondLHS = ICI->getOperand(0); 2974 Value *PreCondRHS = ICI->getOperand(1); 2975 ICmpInst::Predicate Cond; 2976 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest) 2977 Cond = ICI->getPredicate(); 2978 else 2979 Cond = ICI->getInversePredicate(); 2980 2981 if (Cond == Pred) 2982 ; // An exact match. 2983 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE) 2984 ; // The actual condition is beyond sufficient. 2985 else 2986 // Check a few special cases. 2987 switch (Cond) { 2988 case ICmpInst::ICMP_UGT: 2989 if (Pred == ICmpInst::ICMP_ULT) { 2990 std::swap(PreCondLHS, PreCondRHS); 2991 Cond = ICmpInst::ICMP_ULT; 2992 break; 2993 } 2994 continue; 2995 case ICmpInst::ICMP_SGT: 2996 if (Pred == ICmpInst::ICMP_SLT) { 2997 std::swap(PreCondLHS, PreCondRHS); 2998 Cond = ICmpInst::ICMP_SLT; 2999 break; 3000 } 3001 continue; 3002 case ICmpInst::ICMP_NE: 3003 // Expressions like (x >u 0) are often canonicalized to (x != 0), 3004 // so check for this case by checking if the NE is comparing against 3005 // a minimum or maximum constant. 3006 if (!ICmpInst::isTrueWhenEqual(Pred)) 3007 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) { 3008 const APInt &A = CI->getValue(); 3009 switch (Pred) { 3010 case ICmpInst::ICMP_SLT: 3011 if (A.isMaxSignedValue()) break; 3012 continue; 3013 case ICmpInst::ICMP_SGT: 3014 if (A.isMinSignedValue()) break; 3015 continue; 3016 case ICmpInst::ICMP_ULT: 3017 if (A.isMaxValue()) break; 3018 continue; 3019 case ICmpInst::ICMP_UGT: 3020 if (A.isMinValue()) break; 3021 continue; 3022 default: 3023 continue; 3024 } 3025 Cond = ICmpInst::ICMP_NE; 3026 // NE is symmetric but the original comparison may not be. Swap 3027 // the operands if necessary so that they match below. 3028 if (isa<SCEVConstant>(LHS)) 3029 std::swap(PreCondLHS, PreCondRHS); 3030 break; 3031 } 3032 continue; 3033 default: 3034 // We weren't able to reconcile the condition. 3035 continue; 3036 } 3037 3038 if (!PreCondLHS->getType()->isInteger()) continue; 3039 3040 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS); 3041 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS); 3042 if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) || 3043 (LHS == SE.getNotSCEV(PreCondRHSSCEV) && 3044 RHS == SE.getNotSCEV(PreCondLHSSCEV))) 3045 return true; 3046 } 3047 3048 return false; 3049} 3050 3051/// HowManyLessThans - Return the number of times a backedge containing the 3052/// specified less-than comparison will execute. If not computable, return 3053/// UnknownValue. 3054SCEVHandle ScalarEvolutionsImpl:: 3055HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) { 3056 // Only handle: "ADDREC < LoopInvariant". 3057 if (!RHS->isLoopInvariant(L)) return UnknownValue; 3058 3059 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 3060 if (!AddRec || AddRec->getLoop() != L) 3061 return UnknownValue; 3062 3063 if (AddRec->isAffine()) { 3064 // FORNOW: We only support unit strides. 3065 SCEVHandle One = SE.getIntegerSCEV(1, RHS->getType()); 3066 if (AddRec->getOperand(1) != One) 3067 return UnknownValue; 3068 3069 // We know the LHS is of the form {n,+,1} and the RHS is some loop-invariant 3070 // m. So, we count the number of iterations in which {n,+,1} < m is true. 3071 // Note that we cannot simply return max(m-n,0) because it's not safe to 3072 // treat m-n as signed nor unsigned due to overflow possibility. 3073 3074 // First, we get the value of the LHS in the first iteration: n 3075 SCEVHandle Start = AddRec->getOperand(0); 3076 3077 if (isLoopGuardedByCond(L, 3078 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT, 3079 SE.getMinusSCEV(AddRec->getOperand(0), One), RHS)) { 3080 // Since we know that the condition is true in order to enter the loop, 3081 // we know that it will run exactly m-n times. 3082 return SE.getMinusSCEV(RHS, Start); 3083 } else { 3084 // Then, we get the value of the LHS in the first iteration in which the 3085 // above condition doesn't hold. This equals to max(m,n). 3086 SCEVHandle End = isSigned ? SE.getSMaxExpr(RHS, Start) 3087 : SE.getUMaxExpr(RHS, Start); 3088 3089 // Finally, we subtract these two values to get the number of times the 3090 // backedge is executed: max(m,n)-n. 3091 return SE.getMinusSCEV(End, Start); 3092 } 3093 } 3094 3095 return UnknownValue; 3096} 3097 3098/// getNumIterationsInRange - Return the number of iterations of this loop that 3099/// produce values in the specified constant range. Another way of looking at 3100/// this is that it returns the first iteration number where the value is not in 3101/// the condition, thus computing the exit count. If the iteration count can't 3102/// be computed, an instance of SCEVCouldNotCompute is returned. 3103SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 3104 ScalarEvolution &SE) const { 3105 if (Range.isFullSet()) // Infinite loop. 3106 return SE.getCouldNotCompute(); 3107 3108 // If the start is a non-zero constant, shift the range to simplify things. 3109 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 3110 if (!SC->getValue()->isZero()) { 3111 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 3112 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 3113 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop()); 3114 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 3115 return ShiftedAddRec->getNumIterationsInRange( 3116 Range.subtract(SC->getValue()->getValue()), SE); 3117 // This is strange and shouldn't happen. 3118 return SE.getCouldNotCompute(); 3119 } 3120 3121 // The only time we can solve this is when we have all constant indices. 3122 // Otherwise, we cannot determine the overflow conditions. 3123 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 3124 if (!isa<SCEVConstant>(getOperand(i))) 3125 return SE.getCouldNotCompute(); 3126 3127 3128 // Okay at this point we know that all elements of the chrec are constants and 3129 // that the start element is zero. 3130 3131 // First check to see if the range contains zero. If not, the first 3132 // iteration exits. 3133 unsigned BitWidth = SE.getTargetData().getTypeSizeInBits(getType()); 3134 if (!Range.contains(APInt(BitWidth, 0))) 3135 return SE.getConstant(ConstantInt::get(getType(),0)); 3136 3137 if (isAffine()) { 3138 // If this is an affine expression then we have this situation: 3139 // Solve {0,+,A} in Range === Ax in Range 3140 3141 // We know that zero is in the range. If A is positive then we know that 3142 // the upper value of the range must be the first possible exit value. 3143 // If A is negative then the lower of the range is the last possible loop 3144 // value. Also note that we already checked for a full range. 3145 APInt One(BitWidth,1); 3146 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 3147 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 3148 3149 // The exit value should be (End+A)/A. 3150 APInt ExitVal = (End + A).udiv(A); 3151 ConstantInt *ExitValue = ConstantInt::get(ExitVal); 3152 3153 // Evaluate at the exit value. If we really did fall out of the valid 3154 // range, then we computed our trip count, otherwise wrap around or other 3155 // things must have happened. 3156 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 3157 if (Range.contains(Val->getValue())) 3158 return SE.getCouldNotCompute(); // Something strange happened 3159 3160 // Ensure that the previous value is in the range. This is a sanity check. 3161 assert(Range.contains( 3162 EvaluateConstantChrecAtConstant(this, 3163 ConstantInt::get(ExitVal - One), SE)->getValue()) && 3164 "Linear scev computation is off in a bad way!"); 3165 return SE.getConstant(ExitValue); 3166 } else if (isQuadratic()) { 3167 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 3168 // quadratic equation to solve it. To do this, we must frame our problem in 3169 // terms of figuring out when zero is crossed, instead of when 3170 // Range.getUpper() is crossed. 3171 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 3172 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 3173 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 3174 3175 // Next, solve the constructed addrec 3176 std::pair<SCEVHandle,SCEVHandle> Roots = 3177 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 3178 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 3179 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 3180 if (R1) { 3181 // Pick the smallest positive root value. 3182 if (ConstantInt *CB = 3183 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 3184 R1->getValue(), R2->getValue()))) { 3185 if (CB->getZExtValue() == false) 3186 std::swap(R1, R2); // R1 is the minimum root now. 3187 3188 // Make sure the root is not off by one. The returned iteration should 3189 // not be in the range, but the previous one should be. When solving 3190 // for "X*X < 5", for example, we should not return a root of 2. 3191 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 3192 R1->getValue(), 3193 SE); 3194 if (Range.contains(R1Val->getValue())) { 3195 // The next iteration must be out of the range... 3196 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1); 3197 3198 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 3199 if (!Range.contains(R1Val->getValue())) 3200 return SE.getConstant(NextVal); 3201 return SE.getCouldNotCompute(); // Something strange happened 3202 } 3203 3204 // If R1 was not in the range, then it is a good return value. Make 3205 // sure that R1-1 WAS in the range though, just in case. 3206 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1); 3207 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 3208 if (Range.contains(R1Val->getValue())) 3209 return R1; 3210 return SE.getCouldNotCompute(); // Something strange happened 3211 } 3212 } 3213 } 3214 3215 return SE.getCouldNotCompute(); 3216} 3217 3218 3219 3220//===----------------------------------------------------------------------===// 3221// ScalarEvolution Class Implementation 3222//===----------------------------------------------------------------------===// 3223 3224bool ScalarEvolution::runOnFunction(Function &F) { 3225 Impl = new ScalarEvolutionsImpl(*this, F, 3226 getAnalysis<LoopInfo>(), 3227 getAnalysis<TargetData>()); 3228 return false; 3229} 3230 3231void ScalarEvolution::releaseMemory() { 3232 delete (ScalarEvolutionsImpl*)Impl; 3233 Impl = 0; 3234} 3235 3236void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 3237 AU.setPreservesAll(); 3238 AU.addRequiredTransitive<LoopInfo>(); 3239 AU.addRequiredTransitive<TargetData>(); 3240} 3241 3242const TargetData &ScalarEvolution::getTargetData() const { 3243 return ((ScalarEvolutionsImpl*)Impl)->getTargetData(); 3244} 3245 3246SCEVHandle ScalarEvolution::getCouldNotCompute() { 3247 return ((ScalarEvolutionsImpl*)Impl)->getCouldNotCompute(); 3248} 3249 3250SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) { 3251 return ((ScalarEvolutionsImpl*)Impl)->getIntegerSCEV(Val, Ty); 3252} 3253 3254SCEVHandle ScalarEvolution::getSCEV(Value *V) const { 3255 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V); 3256} 3257 3258/// hasSCEV - Return true if the SCEV for this value has already been 3259/// computed. 3260bool ScalarEvolution::hasSCEV(Value *V) const { 3261 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V); 3262} 3263 3264 3265/// setSCEV - Insert the specified SCEV into the map of current SCEVs for 3266/// the specified value. 3267void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) { 3268 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H); 3269} 3270 3271/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 3272/// 3273SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) { 3274 return ((ScalarEvolutionsImpl*)Impl)->getNegativeSCEV(V); 3275} 3276 3277/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 3278/// 3279SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) { 3280 return ((ScalarEvolutionsImpl*)Impl)->getNotSCEV(V); 3281} 3282 3283/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 3284/// 3285SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS, 3286 const SCEVHandle &RHS) { 3287 return ((ScalarEvolutionsImpl*)Impl)->getMinusSCEV(LHS, RHS); 3288} 3289 3290/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion 3291/// of the input value to the specified type. If the type must be 3292/// extended, it is zero extended. 3293SCEVHandle ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V, 3294 const Type *Ty) { 3295 return ((ScalarEvolutionsImpl*)Impl)->getTruncateOrZeroExtend(V, Ty); 3296} 3297 3298/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion 3299/// of the input value to the specified type. If the type must be 3300/// extended, it is sign extended. 3301SCEVHandle ScalarEvolution::getTruncateOrSignExtend(const SCEVHandle &V, 3302 const Type *Ty) { 3303 return ((ScalarEvolutionsImpl*)Impl)->getTruncateOrSignExtend(V, Ty); 3304} 3305 3306 3307bool ScalarEvolution::isLoopGuardedByCond(const Loop *L, 3308 ICmpInst::Predicate Pred, 3309 SCEV *LHS, SCEV *RHS) { 3310 return ((ScalarEvolutionsImpl*)Impl)->isLoopGuardedByCond(L, Pred, 3311 LHS, RHS); 3312} 3313 3314SCEVHandle ScalarEvolution::getBackedgeTakenCount(const Loop *L) const { 3315 return ((ScalarEvolutionsImpl*)Impl)->getBackedgeTakenCount(L); 3316} 3317 3318bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) const { 3319 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 3320} 3321 3322void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) { 3323 return ((ScalarEvolutionsImpl*)Impl)->forgetLoopBackedgeTakenCount(L); 3324} 3325 3326SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const { 3327 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L); 3328} 3329 3330void ScalarEvolution::deleteValueFromRecords(Value *V) const { 3331 return ((ScalarEvolutionsImpl*)Impl)->deleteValueFromRecords(V); 3332} 3333 3334static void PrintLoopInfo(raw_ostream &OS, const ScalarEvolution *SE, 3335 const Loop *L) { 3336 // Print all inner loops first 3337 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 3338 PrintLoopInfo(OS, SE, *I); 3339 3340 OS << "Loop " << L->getHeader()->getName() << ": "; 3341 3342 SmallVector<BasicBlock*, 8> ExitBlocks; 3343 L->getExitBlocks(ExitBlocks); 3344 if (ExitBlocks.size() != 1) 3345 OS << "<multiple exits> "; 3346 3347 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 3348 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 3349 } else { 3350 OS << "Unpredictable backedge-taken count. "; 3351 } 3352 3353 OS << "\n"; 3354} 3355 3356void ScalarEvolution::print(raw_ostream &OS, const Module* ) const { 3357 Function &F = ((ScalarEvolutionsImpl*)Impl)->F; 3358 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI; 3359 3360 OS << "Classifying expressions for: " << F.getName() << "\n"; 3361 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 3362 if (I->getType()->isInteger()) { 3363 OS << *I; 3364 OS << " --> "; 3365 SCEVHandle SV = getSCEV(&*I); 3366 SV->print(OS); 3367 OS << "\t\t"; 3368 3369 if (const Loop *L = LI.getLoopFor((*I).getParent())) { 3370 OS << "Exits: "; 3371 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop()); 3372 if (isa<SCEVCouldNotCompute>(ExitValue)) { 3373 OS << "<<Unknown>>"; 3374 } else { 3375 OS << *ExitValue; 3376 } 3377 } 3378 3379 3380 OS << "\n"; 3381 } 3382 3383 OS << "Determining loop execution counts for: " << F.getName() << "\n"; 3384 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I) 3385 PrintLoopInfo(OS, this, *I); 3386} 3387 3388void ScalarEvolution::print(std::ostream &o, const Module *M) const { 3389 raw_os_ostream OS(o); 3390 print(OS, M); 3391} 3392