ScalarEvolution.cpp revision d9cc749318cc9ab4f36efe8a44201a72adbda2b2
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/LoopInfo.h" 70#include "llvm/Assembly/Writer.h" 71#include "llvm/Transforms/Scalar.h" 72#include "llvm/Support/CFG.h" 73#include "llvm/Support/CommandLine.h" 74#include "llvm/Support/Compiler.h" 75#include "llvm/Support/ConstantRange.h" 76#include "llvm/Support/InstIterator.h" 77#include "llvm/Support/ManagedStatic.h" 78#include "llvm/Support/MathExtras.h" 79#include "llvm/Support/Streams.h" 80#include "llvm/ADT/Statistic.h" 81#include <ostream> 82#include <algorithm> 83#include <cmath> 84using namespace llvm; 85 86STATISTIC(NumBruteForceEvaluations, 87 "Number of brute force evaluations needed to " 88 "calculate high-order polynomial exit values"); 89STATISTIC(NumArrayLenItCounts, 90 "Number of trip counts computed with array length"); 91STATISTIC(NumTripCountsComputed, 92 "Number of loops with predictable loop counts"); 93STATISTIC(NumTripCountsNotComputed, 94 "Number of loops without predictable loop counts"); 95STATISTIC(NumBruteForceTripCountsComputed, 96 "Number of loops with trip counts computed by force"); 97 98static cl::opt<unsigned> 99MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 100 cl::desc("Maximum number of iterations SCEV will " 101 "symbolically execute a constant derived loop"), 102 cl::init(100)); 103 104static RegisterPass<ScalarEvolution> 105R("scalar-evolution", "Scalar Evolution Analysis", false, true); 106char ScalarEvolution::ID = 0; 107 108//===----------------------------------------------------------------------===// 109// SCEV class definitions 110//===----------------------------------------------------------------------===// 111 112//===----------------------------------------------------------------------===// 113// Implementation of the SCEV class. 114// 115SCEV::~SCEV() {} 116void SCEV::dump() const { 117 print(cerr); 118} 119 120uint32_t SCEV::getBitWidth() const { 121 if (const IntegerType* ITy = dyn_cast<IntegerType>(getType())) 122 return ITy->getBitWidth(); 123 return 0; 124} 125 126bool SCEV::isZero() const { 127 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 128 return SC->getValue()->isZero(); 129 return false; 130} 131 132 133SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {} 134 135bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 136 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 137 return false; 138} 139 140const Type *SCEVCouldNotCompute::getType() const { 141 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 142 return 0; 143} 144 145bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 146 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 147 return false; 148} 149 150SCEVHandle SCEVCouldNotCompute:: 151replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 152 const SCEVHandle &Conc, 153 ScalarEvolution &SE) const { 154 return this; 155} 156 157void SCEVCouldNotCompute::print(std::ostream &OS) const { 158 OS << "***COULDNOTCOMPUTE***"; 159} 160 161bool SCEVCouldNotCompute::classof(const SCEV *S) { 162 return S->getSCEVType() == scCouldNotCompute; 163} 164 165 166// SCEVConstants - Only allow the creation of one SCEVConstant for any 167// particular value. Don't use a SCEVHandle here, or else the object will 168// never be deleted! 169static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants; 170 171 172SCEVConstant::~SCEVConstant() { 173 SCEVConstants->erase(V); 174} 175 176SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) { 177 SCEVConstant *&R = (*SCEVConstants)[V]; 178 if (R == 0) R = new SCEVConstant(V); 179 return R; 180} 181 182SCEVHandle ScalarEvolution::getConstant(const APInt& Val) { 183 return getConstant(ConstantInt::get(Val)); 184} 185 186const Type *SCEVConstant::getType() const { return V->getType(); } 187 188void SCEVConstant::print(std::ostream &OS) const { 189 WriteAsOperand(OS, V, false); 190} 191 192// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any 193// particular input. Don't use a SCEVHandle here, or else the object will 194// never be deleted! 195static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 196 SCEVTruncateExpr*> > SCEVTruncates; 197 198SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty) 199 : SCEV(scTruncate), Op(op), Ty(ty) { 200 assert(Op->getType()->isInteger() && Ty->isInteger() && 201 "Cannot truncate non-integer value!"); 202 assert(Op->getType()->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits() 203 && "This is not a truncating conversion!"); 204} 205 206SCEVTruncateExpr::~SCEVTruncateExpr() { 207 SCEVTruncates->erase(std::make_pair(Op, Ty)); 208} 209 210void SCEVTruncateExpr::print(std::ostream &OS) const { 211 OS << "(truncate " << *Op << " to " << *Ty << ")"; 212} 213 214// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any 215// particular input. Don't use a SCEVHandle here, or else the object will never 216// be deleted! 217static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 218 SCEVZeroExtendExpr*> > SCEVZeroExtends; 219 220SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty) 221 : SCEV(scZeroExtend), Op(op), Ty(ty) { 222 assert(Op->getType()->isInteger() && Ty->isInteger() && 223 "Cannot zero extend non-integer value!"); 224 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits() 225 && "This is not an extending conversion!"); 226} 227 228SCEVZeroExtendExpr::~SCEVZeroExtendExpr() { 229 SCEVZeroExtends->erase(std::make_pair(Op, Ty)); 230} 231 232void SCEVZeroExtendExpr::print(std::ostream &OS) const { 233 OS << "(zeroextend " << *Op << " to " << *Ty << ")"; 234} 235 236// SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any 237// particular input. Don't use a SCEVHandle here, or else the object will never 238// be deleted! 239static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 240 SCEVSignExtendExpr*> > SCEVSignExtends; 241 242SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty) 243 : SCEV(scSignExtend), Op(op), Ty(ty) { 244 assert(Op->getType()->isInteger() && Ty->isInteger() && 245 "Cannot sign extend non-integer value!"); 246 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits() 247 && "This is not an extending conversion!"); 248} 249 250SCEVSignExtendExpr::~SCEVSignExtendExpr() { 251 SCEVSignExtends->erase(std::make_pair(Op, Ty)); 252} 253 254void SCEVSignExtendExpr::print(std::ostream &OS) const { 255 OS << "(signextend " << *Op << " to " << *Ty << ")"; 256} 257 258// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any 259// particular input. Don't use a SCEVHandle here, or else the object will never 260// be deleted! 261static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >, 262 SCEVCommutativeExpr*> > SCEVCommExprs; 263 264SCEVCommutativeExpr::~SCEVCommutativeExpr() { 265 SCEVCommExprs->erase(std::make_pair(getSCEVType(), 266 std::vector<SCEV*>(Operands.begin(), 267 Operands.end()))); 268} 269 270void SCEVCommutativeExpr::print(std::ostream &OS) const { 271 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 272 const char *OpStr = getOperationStr(); 273 OS << "(" << *Operands[0]; 274 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 275 OS << OpStr << *Operands[i]; 276 OS << ")"; 277} 278 279SCEVHandle SCEVCommutativeExpr:: 280replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 281 const SCEVHandle &Conc, 282 ScalarEvolution &SE) const { 283 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 284 SCEVHandle H = 285 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 286 if (H != getOperand(i)) { 287 std::vector<SCEVHandle> NewOps; 288 NewOps.reserve(getNumOperands()); 289 for (unsigned j = 0; j != i; ++j) 290 NewOps.push_back(getOperand(j)); 291 NewOps.push_back(H); 292 for (++i; i != e; ++i) 293 NewOps.push_back(getOperand(i)-> 294 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 295 296 if (isa<SCEVAddExpr>(this)) 297 return SE.getAddExpr(NewOps); 298 else if (isa<SCEVMulExpr>(this)) 299 return SE.getMulExpr(NewOps); 300 else if (isa<SCEVSMaxExpr>(this)) 301 return SE.getSMaxExpr(NewOps); 302 else if (isa<SCEVUMaxExpr>(this)) 303 return SE.getUMaxExpr(NewOps); 304 else 305 assert(0 && "Unknown commutative expr!"); 306 } 307 } 308 return this; 309} 310 311 312// SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular 313// input. Don't use a SCEVHandle here, or else the object will never be 314// deleted! 315static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>, 316 SCEVUDivExpr*> > SCEVUDivs; 317 318SCEVUDivExpr::~SCEVUDivExpr() { 319 SCEVUDivs->erase(std::make_pair(LHS, RHS)); 320} 321 322void SCEVUDivExpr::print(std::ostream &OS) const { 323 OS << "(" << *LHS << " /u " << *RHS << ")"; 324} 325 326const Type *SCEVUDivExpr::getType() const { 327 return LHS->getType(); 328} 329 330// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any 331// particular input. Don't use a SCEVHandle here, or else the object will never 332// be deleted! 333static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >, 334 SCEVAddRecExpr*> > SCEVAddRecExprs; 335 336SCEVAddRecExpr::~SCEVAddRecExpr() { 337 SCEVAddRecExprs->erase(std::make_pair(L, 338 std::vector<SCEV*>(Operands.begin(), 339 Operands.end()))); 340} 341 342SCEVHandle SCEVAddRecExpr:: 343replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 344 const SCEVHandle &Conc, 345 ScalarEvolution &SE) const { 346 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 347 SCEVHandle H = 348 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 349 if (H != getOperand(i)) { 350 std::vector<SCEVHandle> NewOps; 351 NewOps.reserve(getNumOperands()); 352 for (unsigned j = 0; j != i; ++j) 353 NewOps.push_back(getOperand(j)); 354 NewOps.push_back(H); 355 for (++i; i != e; ++i) 356 NewOps.push_back(getOperand(i)-> 357 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 358 359 return SE.getAddRecExpr(NewOps, L); 360 } 361 } 362 return this; 363} 364 365 366bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 367 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't 368 // contain L and if the start is invariant. 369 return !QueryLoop->contains(L->getHeader()) && 370 getOperand(0)->isLoopInvariant(QueryLoop); 371} 372 373 374void SCEVAddRecExpr::print(std::ostream &OS) const { 375 OS << "{" << *Operands[0]; 376 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 377 OS << ",+," << *Operands[i]; 378 OS << "}<" << L->getHeader()->getName() + ">"; 379} 380 381// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular 382// value. Don't use a SCEVHandle here, or else the object will never be 383// deleted! 384static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns; 385 386SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); } 387 388bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 389 // All non-instruction values are loop invariant. All instructions are loop 390 // invariant if they are not contained in the specified loop. 391 if (Instruction *I = dyn_cast<Instruction>(V)) 392 return !L->contains(I->getParent()); 393 return true; 394} 395 396const Type *SCEVUnknown::getType() const { 397 return V->getType(); 398} 399 400void SCEVUnknown::print(std::ostream &OS) const { 401 WriteAsOperand(OS, V, false); 402} 403 404//===----------------------------------------------------------------------===// 405// SCEV Utilities 406//===----------------------------------------------------------------------===// 407 408namespace { 409 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 410 /// than the complexity of the RHS. This comparator is used to canonicalize 411 /// expressions. 412 struct VISIBILITY_HIDDEN SCEVComplexityCompare { 413 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 414 return LHS->getSCEVType() < RHS->getSCEVType(); 415 } 416 }; 417} 418 419/// GroupByComplexity - Given a list of SCEV objects, order them by their 420/// complexity, and group objects of the same complexity together by value. 421/// When this routine is finished, we know that any duplicates in the vector are 422/// consecutive and that complexity is monotonically increasing. 423/// 424/// Note that we go take special precautions to ensure that we get determinstic 425/// results from this routine. In other words, we don't want the results of 426/// this to depend on where the addresses of various SCEV objects happened to 427/// land in memory. 428/// 429static void GroupByComplexity(std::vector<SCEVHandle> &Ops) { 430 if (Ops.size() < 2) return; // Noop 431 if (Ops.size() == 2) { 432 // This is the common case, which also happens to be trivially simple. 433 // Special case it. 434 if (SCEVComplexityCompare()(Ops[1], Ops[0])) 435 std::swap(Ops[0], Ops[1]); 436 return; 437 } 438 439 // Do the rough sort by complexity. 440 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare()); 441 442 // Now that we are sorted by complexity, group elements of the same 443 // complexity. Note that this is, at worst, N^2, but the vector is likely to 444 // be extremely short in practice. Note that we take this approach because we 445 // do not want to depend on the addresses of the objects we are grouping. 446 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 447 SCEV *S = Ops[i]; 448 unsigned Complexity = S->getSCEVType(); 449 450 // If there are any objects of the same complexity and same value as this 451 // one, group them. 452 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 453 if (Ops[j] == S) { // Found a duplicate. 454 // Move it to immediately after i'th element. 455 std::swap(Ops[i+1], Ops[j]); 456 ++i; // no need to rescan it. 457 if (i == e-2) return; // Done! 458 } 459 } 460 } 461} 462 463 464 465//===----------------------------------------------------------------------===// 466// Simple SCEV method implementations 467//===----------------------------------------------------------------------===// 468 469/// getIntegerSCEV - Given an integer or FP type, create a constant for the 470/// specified signed integer value and return a SCEV for the constant. 471SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) { 472 Constant *C; 473 if (Val == 0) 474 C = Constant::getNullValue(Ty); 475 else if (Ty->isFloatingPoint()) 476 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle : 477 APFloat::IEEEdouble, Val)); 478 else 479 C = ConstantInt::get(Ty, Val); 480 return getUnknown(C); 481} 482 483/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 484/// 485SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) { 486 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 487 return getUnknown(ConstantExpr::getNeg(VC->getValue())); 488 489 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(V->getType()))); 490} 491 492/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 493SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) { 494 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 495 return getUnknown(ConstantExpr::getNot(VC->getValue())); 496 497 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(V->getType())); 498 return getMinusSCEV(AllOnes, V); 499} 500 501/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 502/// 503SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS, 504 const SCEVHandle &RHS) { 505 // X - Y --> X + -Y 506 return getAddExpr(LHS, getNegativeSCEV(RHS)); 507} 508 509 510/// BinomialCoefficient - Compute BC(It, K). The result has width W. 511// Assume, K > 0. 512static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K, 513 ScalarEvolution &SE, 514 const IntegerType* ResultTy) { 515 // Handle the simplest case efficiently. 516 if (K == 1) 517 return SE.getTruncateOrZeroExtend(It, ResultTy); 518 519 // We are using the following formula for BC(It, K): 520 // 521 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 522 // 523 // Suppose, W is the bitwidth of the return value. We must be prepared for 524 // overflow. Hence, we must assure that the result of our computation is 525 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 526 // safe in modular arithmetic. 527 // 528 // However, this code doesn't use exactly that formula; the formula it uses 529 // is something like the following, where T is the number of factors of 2 in 530 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 531 // exponentiation: 532 // 533 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 534 // 535 // This formula is trivially equivalent to the previous formula. However, 536 // this formula can be implemented much more efficiently. The trick is that 537 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 538 // arithmetic. To do exact division in modular arithmetic, all we have 539 // to do is multiply by the inverse. Therefore, this step can be done at 540 // width W. 541 // 542 // The next issue is how to safely do the division by 2^T. The way this 543 // is done is by doing the multiplication step at a width of at least W + T 544 // bits. This way, the bottom W+T bits of the product are accurate. Then, 545 // when we perform the division by 2^T (which is equivalent to a right shift 546 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 547 // truncated out after the division by 2^T. 548 // 549 // In comparison to just directly using the first formula, this technique 550 // is much more efficient; using the first formula requires W * K bits, 551 // but this formula less than W + K bits. Also, the first formula requires 552 // a division step, whereas this formula only requires multiplies and shifts. 553 // 554 // It doesn't matter whether the subtraction step is done in the calculation 555 // width or the input iteration count's width; if the subtraction overflows, 556 // the result must be zero anyway. We prefer here to do it in the width of 557 // the induction variable because it helps a lot for certain cases; CodeGen 558 // isn't smart enough to ignore the overflow, which leads to much less 559 // efficient code if the width of the subtraction is wider than the native 560 // register width. 561 // 562 // (It's possible to not widen at all by pulling out factors of 2 before 563 // the multiplication; for example, K=2 can be calculated as 564 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 565 // extra arithmetic, so it's not an obvious win, and it gets 566 // much more complicated for K > 3.) 567 568 // Protection from insane SCEVs; this bound is conservative, 569 // but it probably doesn't matter. 570 if (K > 1000) 571 return new SCEVCouldNotCompute(); 572 573 unsigned W = ResultTy->getBitWidth(); 574 575 // Calculate K! / 2^T and T; we divide out the factors of two before 576 // multiplying for calculating K! / 2^T to avoid overflow. 577 // Other overflow doesn't matter because we only care about the bottom 578 // W bits of the result. 579 APInt OddFactorial(W, 1); 580 unsigned T = 1; 581 for (unsigned i = 3; i <= K; ++i) { 582 APInt Mult(W, i); 583 unsigned TwoFactors = Mult.countTrailingZeros(); 584 T += TwoFactors; 585 Mult = Mult.lshr(TwoFactors); 586 OddFactorial *= Mult; 587 } 588 589 // We need at least W + T bits for the multiplication step 590 // FIXME: A temporary hack; we round up the bitwidths 591 // to the nearest power of 2 to be nice to the code generator. 592 unsigned CalculationBits = 1U << Log2_32_Ceil(W + T); 593 // FIXME: Temporary hack to avoid generating integers that are too wide. 594 // Although, it's not completely clear how to determine how much 595 // widening is safe; for example, on X86, we can't really widen 596 // beyond 64 because we need to be able to do multiplication 597 // that's CalculationBits wide, but on X86-64, we can safely widen up to 598 // 128 bits. 599 if (CalculationBits > 64) 600 return new SCEVCouldNotCompute(); 601 602 // Calcuate 2^T, at width T+W. 603 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 604 605 // Calculate the multiplicative inverse of K! / 2^T; 606 // this multiplication factor will perform the exact division by 607 // K! / 2^T. 608 APInt Mod = APInt::getSignedMinValue(W+1); 609 APInt MultiplyFactor = OddFactorial.zext(W+1); 610 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 611 MultiplyFactor = MultiplyFactor.trunc(W); 612 613 // Calculate the product, at width T+W 614 const IntegerType *CalculationTy = IntegerType::get(CalculationBits); 615 SCEVHandle Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 616 for (unsigned i = 1; i != K; ++i) { 617 SCEVHandle S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType())); 618 Dividend = SE.getMulExpr(Dividend, 619 SE.getTruncateOrZeroExtend(S, CalculationTy)); 620 } 621 622 // Divide by 2^T 623 SCEVHandle DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 624 625 // Truncate the result, and divide by K! / 2^T. 626 627 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 628 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 629} 630 631/// evaluateAtIteration - Return the value of this chain of recurrences at 632/// the specified iteration number. We can evaluate this recurrence by 633/// multiplying each element in the chain by the binomial coefficient 634/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 635/// 636/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 637/// 638/// where BC(It, k) stands for binomial coefficient. 639/// 640SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It, 641 ScalarEvolution &SE) const { 642 SCEVHandle Result = getStart(); 643 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 644 // The computation is correct in the face of overflow provided that the 645 // multiplication is performed _after_ the evaluation of the binomial 646 // coefficient. 647 SCEVHandle Val = 648 SE.getMulExpr(getOperand(i), 649 BinomialCoefficient(It, i, SE, 650 cast<IntegerType>(getType()))); 651 Result = SE.getAddExpr(Result, Val); 652 } 653 return Result; 654} 655 656//===----------------------------------------------------------------------===// 657// SCEV Expression folder implementations 658//===----------------------------------------------------------------------===// 659 660SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op, const Type *Ty) { 661 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 662 return getUnknown( 663 ConstantExpr::getTrunc(SC->getValue(), Ty)); 664 665 // If the input value is a chrec scev made out of constants, truncate 666 // all of the constants. 667 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 668 std::vector<SCEVHandle> Operands; 669 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 670 // FIXME: This should allow truncation of other expression types! 671 if (isa<SCEVConstant>(AddRec->getOperand(i))) 672 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 673 else 674 break; 675 if (Operands.size() == AddRec->getNumOperands()) 676 return getAddRecExpr(Operands, AddRec->getLoop()); 677 } 678 679 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)]; 680 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty); 681 return Result; 682} 683 684SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op, const Type *Ty) { 685 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 686 return getUnknown( 687 ConstantExpr::getZExt(SC->getValue(), Ty)); 688 689 // FIXME: If the input value is a chrec scev, and we can prove that the value 690 // did not overflow the old, smaller, value, we can zero extend all of the 691 // operands (often constants). This would allow analysis of something like 692 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 693 694 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)]; 695 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty); 696 return Result; 697} 698 699SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op, const Type *Ty) { 700 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 701 return getUnknown( 702 ConstantExpr::getSExt(SC->getValue(), Ty)); 703 704 // FIXME: If the input value is a chrec scev, and we can prove that the value 705 // did not overflow the old, smaller, value, we can sign extend all of the 706 // operands (often constants). This would allow analysis of something like 707 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 708 709 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)]; 710 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty); 711 return Result; 712} 713 714/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion 715/// of the input value to the specified type. If the type must be 716/// extended, it is zero extended. 717SCEVHandle ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V, 718 const Type *Ty) { 719 const Type *SrcTy = V->getType(); 720 assert(SrcTy->isInteger() && Ty->isInteger() && 721 "Cannot truncate or zero extend with non-integer arguments!"); 722 if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits()) 723 return V; // No conversion 724 if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits()) 725 return getTruncateExpr(V, Ty); 726 return getZeroExtendExpr(V, Ty); 727} 728 729// get - Get a canonical add expression, or something simpler if possible. 730SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) { 731 assert(!Ops.empty() && "Cannot get empty add!"); 732 if (Ops.size() == 1) return Ops[0]; 733 734 // Sort by complexity, this groups all similar expression types together. 735 GroupByComplexity(Ops); 736 737 // If there are any constants, fold them together. 738 unsigned Idx = 0; 739 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 740 ++Idx; 741 assert(Idx < Ops.size()); 742 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 743 // We found two constants, fold them together! 744 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() + 745 RHSC->getValue()->getValue()); 746 Ops[0] = getConstant(Fold); 747 Ops.erase(Ops.begin()+1); // Erase the folded element 748 if (Ops.size() == 1) return Ops[0]; 749 LHSC = cast<SCEVConstant>(Ops[0]); 750 } 751 752 // If we are left with a constant zero being added, strip it off. 753 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 754 Ops.erase(Ops.begin()); 755 --Idx; 756 } 757 } 758 759 if (Ops.size() == 1) return Ops[0]; 760 761 // Okay, check to see if the same value occurs in the operand list twice. If 762 // so, merge them together into an multiply expression. Since we sorted the 763 // list, these values are required to be adjacent. 764 const Type *Ty = Ops[0]->getType(); 765 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 766 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 767 // Found a match, merge the two values into a multiply, and add any 768 // remaining values to the result. 769 SCEVHandle Two = getIntegerSCEV(2, Ty); 770 SCEVHandle Mul = getMulExpr(Ops[i], Two); 771 if (Ops.size() == 2) 772 return Mul; 773 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 774 Ops.push_back(Mul); 775 return getAddExpr(Ops); 776 } 777 778 // Now we know the first non-constant operand. Skip past any cast SCEVs. 779 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 780 ++Idx; 781 782 // If there are add operands they would be next. 783 if (Idx < Ops.size()) { 784 bool DeletedAdd = false; 785 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 786 // If we have an add, expand the add operands onto the end of the operands 787 // list. 788 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 789 Ops.erase(Ops.begin()+Idx); 790 DeletedAdd = true; 791 } 792 793 // If we deleted at least one add, we added operands to the end of the list, 794 // and they are not necessarily sorted. Recurse to resort and resimplify 795 // any operands we just aquired. 796 if (DeletedAdd) 797 return getAddExpr(Ops); 798 } 799 800 // Skip over the add expression until we get to a multiply. 801 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 802 ++Idx; 803 804 // If we are adding something to a multiply expression, make sure the 805 // something is not already an operand of the multiply. If so, merge it into 806 // the multiply. 807 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 808 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 809 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 810 SCEV *MulOpSCEV = Mul->getOperand(MulOp); 811 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 812 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) { 813 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 814 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 815 if (Mul->getNumOperands() != 2) { 816 // If the multiply has more than two operands, we must get the 817 // Y*Z term. 818 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 819 MulOps.erase(MulOps.begin()+MulOp); 820 InnerMul = getMulExpr(MulOps); 821 } 822 SCEVHandle One = getIntegerSCEV(1, Ty); 823 SCEVHandle AddOne = getAddExpr(InnerMul, One); 824 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]); 825 if (Ops.size() == 2) return OuterMul; 826 if (AddOp < Idx) { 827 Ops.erase(Ops.begin()+AddOp); 828 Ops.erase(Ops.begin()+Idx-1); 829 } else { 830 Ops.erase(Ops.begin()+Idx); 831 Ops.erase(Ops.begin()+AddOp-1); 832 } 833 Ops.push_back(OuterMul); 834 return getAddExpr(Ops); 835 } 836 837 // Check this multiply against other multiplies being added together. 838 for (unsigned OtherMulIdx = Idx+1; 839 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 840 ++OtherMulIdx) { 841 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 842 // If MulOp occurs in OtherMul, we can fold the two multiplies 843 // together. 844 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 845 OMulOp != e; ++OMulOp) 846 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 847 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 848 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 849 if (Mul->getNumOperands() != 2) { 850 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 851 MulOps.erase(MulOps.begin()+MulOp); 852 InnerMul1 = getMulExpr(MulOps); 853 } 854 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 855 if (OtherMul->getNumOperands() != 2) { 856 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 857 OtherMul->op_end()); 858 MulOps.erase(MulOps.begin()+OMulOp); 859 InnerMul2 = getMulExpr(MulOps); 860 } 861 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 862 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 863 if (Ops.size() == 2) return OuterMul; 864 Ops.erase(Ops.begin()+Idx); 865 Ops.erase(Ops.begin()+OtherMulIdx-1); 866 Ops.push_back(OuterMul); 867 return getAddExpr(Ops); 868 } 869 } 870 } 871 } 872 873 // If there are any add recurrences in the operands list, see if any other 874 // added values are loop invariant. If so, we can fold them into the 875 // recurrence. 876 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 877 ++Idx; 878 879 // Scan over all recurrences, trying to fold loop invariants into them. 880 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 881 // Scan all of the other operands to this add and add them to the vector if 882 // they are loop invariant w.r.t. the recurrence. 883 std::vector<SCEVHandle> LIOps; 884 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 885 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 886 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 887 LIOps.push_back(Ops[i]); 888 Ops.erase(Ops.begin()+i); 889 --i; --e; 890 } 891 892 // If we found some loop invariants, fold them into the recurrence. 893 if (!LIOps.empty()) { 894 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step } 895 LIOps.push_back(AddRec->getStart()); 896 897 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 898 AddRecOps[0] = getAddExpr(LIOps); 899 900 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 901 // If all of the other operands were loop invariant, we are done. 902 if (Ops.size() == 1) return NewRec; 903 904 // Otherwise, add the folded AddRec by the non-liv parts. 905 for (unsigned i = 0;; ++i) 906 if (Ops[i] == AddRec) { 907 Ops[i] = NewRec; 908 break; 909 } 910 return getAddExpr(Ops); 911 } 912 913 // Okay, if there weren't any loop invariants to be folded, check to see if 914 // there are multiple AddRec's with the same loop induction variable being 915 // added together. If so, we can fold them. 916 for (unsigned OtherIdx = Idx+1; 917 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 918 if (OtherIdx != Idx) { 919 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 920 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 921 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 922 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 923 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 924 if (i >= NewOps.size()) { 925 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 926 OtherAddRec->op_end()); 927 break; 928 } 929 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 930 } 931 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 932 933 if (Ops.size() == 2) return NewAddRec; 934 935 Ops.erase(Ops.begin()+Idx); 936 Ops.erase(Ops.begin()+OtherIdx-1); 937 Ops.push_back(NewAddRec); 938 return getAddExpr(Ops); 939 } 940 } 941 942 // Otherwise couldn't fold anything into this recurrence. Move onto the 943 // next one. 944 } 945 946 // Okay, it looks like we really DO need an add expr. Check to see if we 947 // already have one, otherwise create a new one. 948 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 949 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr, 950 SCEVOps)]; 951 if (Result == 0) Result = new SCEVAddExpr(Ops); 952 return Result; 953} 954 955 956SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) { 957 assert(!Ops.empty() && "Cannot get empty mul!"); 958 959 // Sort by complexity, this groups all similar expression types together. 960 GroupByComplexity(Ops); 961 962 // If there are any constants, fold them together. 963 unsigned Idx = 0; 964 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 965 966 // C1*(C2+V) -> C1*C2 + C1*V 967 if (Ops.size() == 2) 968 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 969 if (Add->getNumOperands() == 2 && 970 isa<SCEVConstant>(Add->getOperand(0))) 971 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 972 getMulExpr(LHSC, Add->getOperand(1))); 973 974 975 ++Idx; 976 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 977 // We found two constants, fold them together! 978 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() * 979 RHSC->getValue()->getValue()); 980 Ops[0] = getConstant(Fold); 981 Ops.erase(Ops.begin()+1); // Erase the folded element 982 if (Ops.size() == 1) return Ops[0]; 983 LHSC = cast<SCEVConstant>(Ops[0]); 984 } 985 986 // If we are left with a constant one being multiplied, strip it off. 987 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 988 Ops.erase(Ops.begin()); 989 --Idx; 990 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 991 // If we have a multiply of zero, it will always be zero. 992 return Ops[0]; 993 } 994 } 995 996 // Skip over the add expression until we get to a multiply. 997 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 998 ++Idx; 999 1000 if (Ops.size() == 1) 1001 return Ops[0]; 1002 1003 // If there are mul operands inline them all into this expression. 1004 if (Idx < Ops.size()) { 1005 bool DeletedMul = false; 1006 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1007 // If we have an mul, expand the mul operands onto the end of the operands 1008 // list. 1009 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 1010 Ops.erase(Ops.begin()+Idx); 1011 DeletedMul = true; 1012 } 1013 1014 // If we deleted at least one mul, we added operands to the end of the list, 1015 // and they are not necessarily sorted. Recurse to resort and resimplify 1016 // any operands we just aquired. 1017 if (DeletedMul) 1018 return getMulExpr(Ops); 1019 } 1020 1021 // If there are any add recurrences in the operands list, see if any other 1022 // added values are loop invariant. If so, we can fold them into the 1023 // recurrence. 1024 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1025 ++Idx; 1026 1027 // Scan over all recurrences, trying to fold loop invariants into them. 1028 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1029 // Scan all of the other operands to this mul and add them to the vector if 1030 // they are loop invariant w.r.t. the recurrence. 1031 std::vector<SCEVHandle> LIOps; 1032 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1033 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1034 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1035 LIOps.push_back(Ops[i]); 1036 Ops.erase(Ops.begin()+i); 1037 --i; --e; 1038 } 1039 1040 // If we found some loop invariants, fold them into the recurrence. 1041 if (!LIOps.empty()) { 1042 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step } 1043 std::vector<SCEVHandle> NewOps; 1044 NewOps.reserve(AddRec->getNumOperands()); 1045 if (LIOps.size() == 1) { 1046 SCEV *Scale = LIOps[0]; 1047 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1048 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1049 } else { 1050 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1051 std::vector<SCEVHandle> MulOps(LIOps); 1052 MulOps.push_back(AddRec->getOperand(i)); 1053 NewOps.push_back(getMulExpr(MulOps)); 1054 } 1055 } 1056 1057 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1058 1059 // If all of the other operands were loop invariant, we are done. 1060 if (Ops.size() == 1) return NewRec; 1061 1062 // Otherwise, multiply the folded AddRec by the non-liv parts. 1063 for (unsigned i = 0;; ++i) 1064 if (Ops[i] == AddRec) { 1065 Ops[i] = NewRec; 1066 break; 1067 } 1068 return getMulExpr(Ops); 1069 } 1070 1071 // Okay, if there weren't any loop invariants to be folded, check to see if 1072 // there are multiple AddRec's with the same loop induction variable being 1073 // multiplied together. If so, we can fold them. 1074 for (unsigned OtherIdx = Idx+1; 1075 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1076 if (OtherIdx != Idx) { 1077 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1078 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1079 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1080 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1081 SCEVHandle NewStart = getMulExpr(F->getStart(), 1082 G->getStart()); 1083 SCEVHandle B = F->getStepRecurrence(*this); 1084 SCEVHandle D = G->getStepRecurrence(*this); 1085 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D), 1086 getMulExpr(G, B), 1087 getMulExpr(B, D)); 1088 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep, 1089 F->getLoop()); 1090 if (Ops.size() == 2) return NewAddRec; 1091 1092 Ops.erase(Ops.begin()+Idx); 1093 Ops.erase(Ops.begin()+OtherIdx-1); 1094 Ops.push_back(NewAddRec); 1095 return getMulExpr(Ops); 1096 } 1097 } 1098 1099 // Otherwise couldn't fold anything into this recurrence. Move onto the 1100 // next one. 1101 } 1102 1103 // Okay, it looks like we really DO need an mul expr. Check to see if we 1104 // already have one, otherwise create a new one. 1105 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1106 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr, 1107 SCEVOps)]; 1108 if (Result == 0) 1109 Result = new SCEVMulExpr(Ops); 1110 return Result; 1111} 1112 1113SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS, const SCEVHandle &RHS) { 1114 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1115 if (RHSC->getValue()->equalsInt(1)) 1116 return LHS; // X udiv 1 --> x 1117 1118 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1119 Constant *LHSCV = LHSC->getValue(); 1120 Constant *RHSCV = RHSC->getValue(); 1121 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV)); 1122 } 1123 } 1124 1125 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow. 1126 1127 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)]; 1128 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS); 1129 return Result; 1130} 1131 1132 1133/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1134/// specified loop. Simplify the expression as much as possible. 1135SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start, 1136 const SCEVHandle &Step, const Loop *L) { 1137 std::vector<SCEVHandle> Operands; 1138 Operands.push_back(Start); 1139 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1140 if (StepChrec->getLoop() == L) { 1141 Operands.insert(Operands.end(), StepChrec->op_begin(), 1142 StepChrec->op_end()); 1143 return getAddRecExpr(Operands, L); 1144 } 1145 1146 Operands.push_back(Step); 1147 return getAddRecExpr(Operands, L); 1148} 1149 1150/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1151/// specified loop. Simplify the expression as much as possible. 1152SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands, 1153 const Loop *L) { 1154 if (Operands.size() == 1) return Operands[0]; 1155 1156 if (Operands.back()->isZero()) { 1157 Operands.pop_back(); 1158 return getAddRecExpr(Operands, L); // { X,+,0 } --> X 1159 } 1160 1161 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 1162 if (SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 1163 const Loop* NestedLoop = NestedAR->getLoop(); 1164 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) { 1165 std::vector<SCEVHandle> NestedOperands(NestedAR->op_begin(), 1166 NestedAR->op_end()); 1167 SCEVHandle NestedARHandle(NestedAR); 1168 Operands[0] = NestedAR->getStart(); 1169 NestedOperands[0] = getAddRecExpr(Operands, L); 1170 return getAddRecExpr(NestedOperands, NestedLoop); 1171 } 1172 } 1173 1174 SCEVAddRecExpr *&Result = 1175 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(), 1176 Operands.end()))]; 1177 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 1178 return Result; 1179} 1180 1181SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS, 1182 const SCEVHandle &RHS) { 1183 std::vector<SCEVHandle> Ops; 1184 Ops.push_back(LHS); 1185 Ops.push_back(RHS); 1186 return getSMaxExpr(Ops); 1187} 1188 1189SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) { 1190 assert(!Ops.empty() && "Cannot get empty smax!"); 1191 if (Ops.size() == 1) return Ops[0]; 1192 1193 // Sort by complexity, this groups all similar expression types together. 1194 GroupByComplexity(Ops); 1195 1196 // If there are any constants, fold them together. 1197 unsigned Idx = 0; 1198 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1199 ++Idx; 1200 assert(Idx < Ops.size()); 1201 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1202 // We found two constants, fold them together! 1203 ConstantInt *Fold = ConstantInt::get( 1204 APIntOps::smax(LHSC->getValue()->getValue(), 1205 RHSC->getValue()->getValue())); 1206 Ops[0] = getConstant(Fold); 1207 Ops.erase(Ops.begin()+1); // Erase the folded element 1208 if (Ops.size() == 1) return Ops[0]; 1209 LHSC = cast<SCEVConstant>(Ops[0]); 1210 } 1211 1212 // If we are left with a constant -inf, strip it off. 1213 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 1214 Ops.erase(Ops.begin()); 1215 --Idx; 1216 } 1217 } 1218 1219 if (Ops.size() == 1) return Ops[0]; 1220 1221 // Find the first SMax 1222 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 1223 ++Idx; 1224 1225 // Check to see if one of the operands is an SMax. If so, expand its operands 1226 // onto our operand list, and recurse to simplify. 1227 if (Idx < Ops.size()) { 1228 bool DeletedSMax = false; 1229 while (SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 1230 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 1231 Ops.erase(Ops.begin()+Idx); 1232 DeletedSMax = true; 1233 } 1234 1235 if (DeletedSMax) 1236 return getSMaxExpr(Ops); 1237 } 1238 1239 // Okay, check to see if the same value occurs in the operand list twice. If 1240 // so, delete one. Since we sorted the list, these values are required to 1241 // be adjacent. 1242 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1243 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 1244 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1245 --i; --e; 1246 } 1247 1248 if (Ops.size() == 1) return Ops[0]; 1249 1250 assert(!Ops.empty() && "Reduced smax down to nothing!"); 1251 1252 // Okay, it looks like we really DO need an smax expr. Check to see if we 1253 // already have one, otherwise create a new one. 1254 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1255 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr, 1256 SCEVOps)]; 1257 if (Result == 0) Result = new SCEVSMaxExpr(Ops); 1258 return Result; 1259} 1260 1261SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS, 1262 const SCEVHandle &RHS) { 1263 std::vector<SCEVHandle> Ops; 1264 Ops.push_back(LHS); 1265 Ops.push_back(RHS); 1266 return getUMaxExpr(Ops); 1267} 1268 1269SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) { 1270 assert(!Ops.empty() && "Cannot get empty umax!"); 1271 if (Ops.size() == 1) return Ops[0]; 1272 1273 // Sort by complexity, this groups all similar expression types together. 1274 GroupByComplexity(Ops); 1275 1276 // If there are any constants, fold them together. 1277 unsigned Idx = 0; 1278 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1279 ++Idx; 1280 assert(Idx < Ops.size()); 1281 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1282 // We found two constants, fold them together! 1283 ConstantInt *Fold = ConstantInt::get( 1284 APIntOps::umax(LHSC->getValue()->getValue(), 1285 RHSC->getValue()->getValue())); 1286 Ops[0] = getConstant(Fold); 1287 Ops.erase(Ops.begin()+1); // Erase the folded element 1288 if (Ops.size() == 1) return Ops[0]; 1289 LHSC = cast<SCEVConstant>(Ops[0]); 1290 } 1291 1292 // If we are left with a constant zero, strip it off. 1293 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 1294 Ops.erase(Ops.begin()); 1295 --Idx; 1296 } 1297 } 1298 1299 if (Ops.size() == 1) return Ops[0]; 1300 1301 // Find the first UMax 1302 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 1303 ++Idx; 1304 1305 // Check to see if one of the operands is a UMax. If so, expand its operands 1306 // onto our operand list, and recurse to simplify. 1307 if (Idx < Ops.size()) { 1308 bool DeletedUMax = false; 1309 while (SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 1310 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 1311 Ops.erase(Ops.begin()+Idx); 1312 DeletedUMax = true; 1313 } 1314 1315 if (DeletedUMax) 1316 return getUMaxExpr(Ops); 1317 } 1318 1319 // Okay, check to see if the same value occurs in the operand list twice. If 1320 // so, delete one. Since we sorted the list, these values are required to 1321 // be adjacent. 1322 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1323 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y 1324 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1325 --i; --e; 1326 } 1327 1328 if (Ops.size() == 1) return Ops[0]; 1329 1330 assert(!Ops.empty() && "Reduced umax down to nothing!"); 1331 1332 // Okay, it looks like we really DO need a umax expr. Check to see if we 1333 // already have one, otherwise create a new one. 1334 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1335 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr, 1336 SCEVOps)]; 1337 if (Result == 0) Result = new SCEVUMaxExpr(Ops); 1338 return Result; 1339} 1340 1341SCEVHandle ScalarEvolution::getUnknown(Value *V) { 1342 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 1343 return getConstant(CI); 1344 SCEVUnknown *&Result = (*SCEVUnknowns)[V]; 1345 if (Result == 0) Result = new SCEVUnknown(V); 1346 return Result; 1347} 1348 1349 1350//===----------------------------------------------------------------------===// 1351// ScalarEvolutionsImpl Definition and Implementation 1352//===----------------------------------------------------------------------===// 1353// 1354/// ScalarEvolutionsImpl - This class implements the main driver for the scalar 1355/// evolution code. 1356/// 1357namespace { 1358 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl { 1359 /// SE - A reference to the public ScalarEvolution object. 1360 ScalarEvolution &SE; 1361 1362 /// F - The function we are analyzing. 1363 /// 1364 Function &F; 1365 1366 /// LI - The loop information for the function we are currently analyzing. 1367 /// 1368 LoopInfo &LI; 1369 1370 /// UnknownValue - This SCEV is used to represent unknown trip counts and 1371 /// things. 1372 SCEVHandle UnknownValue; 1373 1374 /// Scalars - This is a cache of the scalars we have analyzed so far. 1375 /// 1376 std::map<Value*, SCEVHandle> Scalars; 1377 1378 /// IterationCounts - Cache the iteration count of the loops for this 1379 /// function as they are computed. 1380 std::map<const Loop*, SCEVHandle> IterationCounts; 1381 1382 /// ConstantEvolutionLoopExitValue - This map contains entries for all of 1383 /// the PHI instructions that we attempt to compute constant evolutions for. 1384 /// This allows us to avoid potentially expensive recomputation of these 1385 /// properties. An instruction maps to null if we are unable to compute its 1386 /// exit value. 1387 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue; 1388 1389 public: 1390 ScalarEvolutionsImpl(ScalarEvolution &se, Function &f, LoopInfo &li) 1391 : SE(se), F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {} 1392 1393 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1394 /// expression and create a new one. 1395 SCEVHandle getSCEV(Value *V); 1396 1397 /// hasSCEV - Return true if the SCEV for this value has already been 1398 /// computed. 1399 bool hasSCEV(Value *V) const { 1400 return Scalars.count(V); 1401 } 1402 1403 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for 1404 /// the specified value. 1405 void setSCEV(Value *V, const SCEVHandle &H) { 1406 bool isNew = Scalars.insert(std::make_pair(V, H)).second; 1407 assert(isNew && "This entry already existed!"); 1408 } 1409 1410 1411 /// getSCEVAtScope - Compute the value of the specified expression within 1412 /// the indicated loop (which may be null to indicate in no loop). If the 1413 /// expression cannot be evaluated, return UnknownValue itself. 1414 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L); 1415 1416 1417 /// hasLoopInvariantIterationCount - Return true if the specified loop has 1418 /// an analyzable loop-invariant iteration count. 1419 bool hasLoopInvariantIterationCount(const Loop *L); 1420 1421 /// getIterationCount - If the specified loop has a predictable iteration 1422 /// count, return it. Note that it is not valid to call this method on a 1423 /// loop without a loop-invariant iteration count. 1424 SCEVHandle getIterationCount(const Loop *L); 1425 1426 /// deleteValueFromRecords - This method should be called by the 1427 /// client before it removes a value from the program, to make sure 1428 /// that no dangling references are left around. 1429 void deleteValueFromRecords(Value *V); 1430 1431 private: 1432 /// createSCEV - We know that there is no SCEV for the specified value. 1433 /// Analyze the expression. 1434 SCEVHandle createSCEV(Value *V); 1435 1436 /// createNodeForPHI - Provide the special handling we need to analyze PHI 1437 /// SCEVs. 1438 SCEVHandle createNodeForPHI(PHINode *PN); 1439 1440 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value 1441 /// for the specified instruction and replaces any references to the 1442 /// symbolic value SymName with the specified value. This is used during 1443 /// PHI resolution. 1444 void ReplaceSymbolicValueWithConcrete(Instruction *I, 1445 const SCEVHandle &SymName, 1446 const SCEVHandle &NewVal); 1447 1448 /// ComputeIterationCount - Compute the number of times the specified loop 1449 /// will iterate. 1450 SCEVHandle ComputeIterationCount(const Loop *L); 1451 1452 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1453 /// 'icmp op load X, cst', try to see if we can compute the trip count. 1454 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI, 1455 Constant *RHS, 1456 const Loop *L, 1457 ICmpInst::Predicate p); 1458 1459 /// ComputeIterationCountExhaustively - If the trip is known to execute a 1460 /// constant number of times (the condition evolves only from constants), 1461 /// try to evaluate a few iterations of the loop until we get the exit 1462 /// condition gets a value of ExitWhen (true or false). If we cannot 1463 /// evaluate the trip count of the loop, return UnknownValue. 1464 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond, 1465 bool ExitWhen); 1466 1467 /// HowFarToZero - Return the number of times a backedge comparing the 1468 /// specified value to zero will execute. If not computable, return 1469 /// UnknownValue. 1470 SCEVHandle HowFarToZero(SCEV *V, const Loop *L); 1471 1472 /// HowFarToNonZero - Return the number of times a backedge checking the 1473 /// specified value for nonzero will execute. If not computable, return 1474 /// UnknownValue. 1475 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L); 1476 1477 /// HowManyLessThans - Return the number of times a backedge containing the 1478 /// specified less-than comparison will execute. If not computable, return 1479 /// UnknownValue. isSigned specifies whether the less-than is signed. 1480 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, 1481 bool isSigned); 1482 1483 /// executesAtLeastOnce - Test whether entry to the loop is protected by 1484 /// a conditional between LHS and RHS. 1485 bool executesAtLeastOnce(const Loop *L, bool isSigned, SCEV *LHS, SCEV *RHS); 1486 1487 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1488 /// in the header of its containing loop, we know the loop executes a 1489 /// constant number of times, and the PHI node is just a recurrence 1490 /// involving constants, fold it. 1491 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, 1492 const Loop *L); 1493 }; 1494} 1495 1496//===----------------------------------------------------------------------===// 1497// Basic SCEV Analysis and PHI Idiom Recognition Code 1498// 1499 1500/// deleteValueFromRecords - This method should be called by the 1501/// client before it removes an instruction from the program, to make sure 1502/// that no dangling references are left around. 1503void ScalarEvolutionsImpl::deleteValueFromRecords(Value *V) { 1504 SmallVector<Value *, 16> Worklist; 1505 1506 if (Scalars.erase(V)) { 1507 if (PHINode *PN = dyn_cast<PHINode>(V)) 1508 ConstantEvolutionLoopExitValue.erase(PN); 1509 Worklist.push_back(V); 1510 } 1511 1512 while (!Worklist.empty()) { 1513 Value *VV = Worklist.back(); 1514 Worklist.pop_back(); 1515 1516 for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end(); 1517 UI != UE; ++UI) { 1518 Instruction *Inst = cast<Instruction>(*UI); 1519 if (Scalars.erase(Inst)) { 1520 if (PHINode *PN = dyn_cast<PHINode>(VV)) 1521 ConstantEvolutionLoopExitValue.erase(PN); 1522 Worklist.push_back(Inst); 1523 } 1524 } 1525 } 1526} 1527 1528 1529/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1530/// expression and create a new one. 1531SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) { 1532 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!"); 1533 1534 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V); 1535 if (I != Scalars.end()) return I->second; 1536 SCEVHandle S = createSCEV(V); 1537 Scalars.insert(std::make_pair(V, S)); 1538 return S; 1539} 1540 1541/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 1542/// the specified instruction and replaces any references to the symbolic value 1543/// SymName with the specified value. This is used during PHI resolution. 1544void ScalarEvolutionsImpl:: 1545ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName, 1546 const SCEVHandle &NewVal) { 1547 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I); 1548 if (SI == Scalars.end()) return; 1549 1550 SCEVHandle NV = 1551 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, SE); 1552 if (NV == SI->second) return; // No change. 1553 1554 SI->second = NV; // Update the scalars map! 1555 1556 // Any instruction values that use this instruction might also need to be 1557 // updated! 1558 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1559 UI != E; ++UI) 1560 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 1561} 1562 1563/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1564/// a loop header, making it a potential recurrence, or it doesn't. 1565/// 1566SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) { 1567 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1568 if (const Loop *L = LI.getLoopFor(PN->getParent())) 1569 if (L->getHeader() == PN->getParent()) { 1570 // If it lives in the loop header, it has two incoming values, one 1571 // from outside the loop, and one from inside. 1572 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1573 unsigned BackEdge = IncomingEdge^1; 1574 1575 // While we are analyzing this PHI node, handle its value symbolically. 1576 SCEVHandle SymbolicName = SE.getUnknown(PN); 1577 assert(Scalars.find(PN) == Scalars.end() && 1578 "PHI node already processed?"); 1579 Scalars.insert(std::make_pair(PN, SymbolicName)); 1580 1581 // Using this symbolic name for the PHI, analyze the value coming around 1582 // the back-edge. 1583 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1584 1585 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1586 // has a special value for the first iteration of the loop. 1587 1588 // If the value coming around the backedge is an add with the symbolic 1589 // value we just inserted, then we found a simple induction variable! 1590 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1591 // If there is a single occurrence of the symbolic value, replace it 1592 // with a recurrence. 1593 unsigned FoundIndex = Add->getNumOperands(); 1594 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1595 if (Add->getOperand(i) == SymbolicName) 1596 if (FoundIndex == e) { 1597 FoundIndex = i; 1598 break; 1599 } 1600 1601 if (FoundIndex != Add->getNumOperands()) { 1602 // Create an add with everything but the specified operand. 1603 std::vector<SCEVHandle> Ops; 1604 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1605 if (i != FoundIndex) 1606 Ops.push_back(Add->getOperand(i)); 1607 SCEVHandle Accum = SE.getAddExpr(Ops); 1608 1609 // This is not a valid addrec if the step amount is varying each 1610 // loop iteration, but is not itself an addrec in this loop. 1611 if (Accum->isLoopInvariant(L) || 1612 (isa<SCEVAddRecExpr>(Accum) && 1613 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1614 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1615 SCEVHandle PHISCEV = SE.getAddRecExpr(StartVal, Accum, L); 1616 1617 // Okay, for the entire analysis of this edge we assumed the PHI 1618 // to be symbolic. We now need to go back and update all of the 1619 // entries for the scalars that use the PHI (except for the PHI 1620 // itself) to use the new analyzed value instead of the "symbolic" 1621 // value. 1622 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1623 return PHISCEV; 1624 } 1625 } 1626 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) { 1627 // Otherwise, this could be a loop like this: 1628 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 1629 // In this case, j = {1,+,1} and BEValue is j. 1630 // Because the other in-value of i (0) fits the evolution of BEValue 1631 // i really is an addrec evolution. 1632 if (AddRec->getLoop() == L && AddRec->isAffine()) { 1633 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1634 1635 // If StartVal = j.start - j.stride, we can use StartVal as the 1636 // initial step of the addrec evolution. 1637 if (StartVal == SE.getMinusSCEV(AddRec->getOperand(0), 1638 AddRec->getOperand(1))) { 1639 SCEVHandle PHISCEV = 1640 SE.getAddRecExpr(StartVal, AddRec->getOperand(1), L); 1641 1642 // Okay, for the entire analysis of this edge we assumed the PHI 1643 // to be symbolic. We now need to go back and update all of the 1644 // entries for the scalars that use the PHI (except for the PHI 1645 // itself) to use the new analyzed value instead of the "symbolic" 1646 // value. 1647 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1648 return PHISCEV; 1649 } 1650 } 1651 } 1652 1653 return SymbolicName; 1654 } 1655 1656 // If it's not a loop phi, we can't handle it yet. 1657 return SE.getUnknown(PN); 1658} 1659 1660/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 1661/// guaranteed to end in (at every loop iteration). It is, at the same time, 1662/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 1663/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 1664static uint32_t GetMinTrailingZeros(SCEVHandle S) { 1665 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 1666 return C->getValue()->getValue().countTrailingZeros(); 1667 1668 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 1669 return std::min(GetMinTrailingZeros(T->getOperand()), T->getBitWidth()); 1670 1671 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 1672 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 1673 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes; 1674 } 1675 1676 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 1677 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 1678 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes; 1679 } 1680 1681 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 1682 // The result is the min of all operands results. 1683 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 1684 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1685 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 1686 return MinOpRes; 1687 } 1688 1689 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 1690 // The result is the sum of all operands results. 1691 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 1692 uint32_t BitWidth = M->getBitWidth(); 1693 for (unsigned i = 1, e = M->getNumOperands(); 1694 SumOpRes != BitWidth && i != e; ++i) 1695 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 1696 BitWidth); 1697 return SumOpRes; 1698 } 1699 1700 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 1701 // The result is the min of all operands results. 1702 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 1703 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1704 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 1705 return MinOpRes; 1706 } 1707 1708 if (SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 1709 // The result is the min of all operands results. 1710 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 1711 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 1712 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 1713 return MinOpRes; 1714 } 1715 1716 if (SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 1717 // The result is the min of all operands results. 1718 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 1719 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 1720 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 1721 return MinOpRes; 1722 } 1723 1724 // SCEVUDivExpr, SCEVUnknown 1725 return 0; 1726} 1727 1728/// createSCEV - We know that there is no SCEV for the specified value. 1729/// Analyze the expression. 1730/// 1731SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) { 1732 if (!isa<IntegerType>(V->getType())) 1733 return SE.getUnknown(V); 1734 1735 unsigned Opcode = Instruction::UserOp1; 1736 if (Instruction *I = dyn_cast<Instruction>(V)) 1737 Opcode = I->getOpcode(); 1738 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 1739 Opcode = CE->getOpcode(); 1740 else 1741 return SE.getUnknown(V); 1742 1743 User *U = cast<User>(V); 1744 switch (Opcode) { 1745 case Instruction::Add: 1746 return SE.getAddExpr(getSCEV(U->getOperand(0)), 1747 getSCEV(U->getOperand(1))); 1748 case Instruction::Mul: 1749 return SE.getMulExpr(getSCEV(U->getOperand(0)), 1750 getSCEV(U->getOperand(1))); 1751 case Instruction::UDiv: 1752 return SE.getUDivExpr(getSCEV(U->getOperand(0)), 1753 getSCEV(U->getOperand(1))); 1754 case Instruction::Sub: 1755 return SE.getMinusSCEV(getSCEV(U->getOperand(0)), 1756 getSCEV(U->getOperand(1))); 1757 case Instruction::Or: 1758 // If the RHS of the Or is a constant, we may have something like: 1759 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 1760 // optimizations will transparently handle this case. 1761 // 1762 // In order for this transformation to be safe, the LHS must be of the 1763 // form X*(2^n) and the Or constant must be less than 2^n. 1764 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 1765 SCEVHandle LHS = getSCEV(U->getOperand(0)); 1766 const APInt &CIVal = CI->getValue(); 1767 if (GetMinTrailingZeros(LHS) >= 1768 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) 1769 return SE.getAddExpr(LHS, getSCEV(U->getOperand(1))); 1770 } 1771 break; 1772 case Instruction::Xor: 1773 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 1774 // If the RHS of the xor is a signbit, then this is just an add. 1775 // Instcombine turns add of signbit into xor as a strength reduction step. 1776 if (CI->getValue().isSignBit()) 1777 return SE.getAddExpr(getSCEV(U->getOperand(0)), 1778 getSCEV(U->getOperand(1))); 1779 1780 // If the RHS of xor is -1, then this is a not operation. 1781 else if (CI->isAllOnesValue()) 1782 return SE.getNotSCEV(getSCEV(U->getOperand(0))); 1783 } 1784 break; 1785 1786 case Instruction::Shl: 1787 // Turn shift left of a constant amount into a multiply. 1788 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 1789 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 1790 Constant *X = ConstantInt::get( 1791 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 1792 return SE.getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 1793 } 1794 break; 1795 1796 case Instruction::LShr: 1797 // Turn logical shift right of a constant into a unsigned divide. 1798 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 1799 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 1800 Constant *X = ConstantInt::get( 1801 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 1802 return SE.getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 1803 } 1804 break; 1805 1806 case Instruction::Trunc: 1807 return SE.getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 1808 1809 case Instruction::ZExt: 1810 return SE.getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 1811 1812 case Instruction::SExt: 1813 return SE.getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 1814 1815 case Instruction::BitCast: 1816 // BitCasts are no-op casts so we just eliminate the cast. 1817 if (U->getType()->isInteger() && 1818 U->getOperand(0)->getType()->isInteger()) 1819 return getSCEV(U->getOperand(0)); 1820 break; 1821 1822 case Instruction::PHI: 1823 return createNodeForPHI(cast<PHINode>(U)); 1824 1825 case Instruction::Select: 1826 // This could be a smax or umax that was lowered earlier. 1827 // Try to recover it. 1828 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 1829 Value *LHS = ICI->getOperand(0); 1830 Value *RHS = ICI->getOperand(1); 1831 switch (ICI->getPredicate()) { 1832 case ICmpInst::ICMP_SLT: 1833 case ICmpInst::ICMP_SLE: 1834 std::swap(LHS, RHS); 1835 // fall through 1836 case ICmpInst::ICMP_SGT: 1837 case ICmpInst::ICMP_SGE: 1838 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 1839 return SE.getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 1840 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 1841 // ~smax(~x, ~y) == smin(x, y). 1842 return SE.getNotSCEV(SE.getSMaxExpr( 1843 SE.getNotSCEV(getSCEV(LHS)), 1844 SE.getNotSCEV(getSCEV(RHS)))); 1845 break; 1846 case ICmpInst::ICMP_ULT: 1847 case ICmpInst::ICMP_ULE: 1848 std::swap(LHS, RHS); 1849 // fall through 1850 case ICmpInst::ICMP_UGT: 1851 case ICmpInst::ICMP_UGE: 1852 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 1853 return SE.getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 1854 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 1855 // ~umax(~x, ~y) == umin(x, y) 1856 return SE.getNotSCEV(SE.getUMaxExpr(SE.getNotSCEV(getSCEV(LHS)), 1857 SE.getNotSCEV(getSCEV(RHS)))); 1858 break; 1859 default: 1860 break; 1861 } 1862 } 1863 1864 default: // We cannot analyze this expression. 1865 break; 1866 } 1867 1868 return SE.getUnknown(V); 1869} 1870 1871 1872 1873//===----------------------------------------------------------------------===// 1874// Iteration Count Computation Code 1875// 1876 1877/// getIterationCount - If the specified loop has a predictable iteration 1878/// count, return it. Note that it is not valid to call this method on a 1879/// loop without a loop-invariant iteration count. 1880SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) { 1881 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L); 1882 if (I == IterationCounts.end()) { 1883 SCEVHandle ItCount = ComputeIterationCount(L); 1884 I = IterationCounts.insert(std::make_pair(L, ItCount)).first; 1885 if (ItCount != UnknownValue) { 1886 assert(ItCount->isLoopInvariant(L) && 1887 "Computed trip count isn't loop invariant for loop!"); 1888 ++NumTripCountsComputed; 1889 } else if (isa<PHINode>(L->getHeader()->begin())) { 1890 // Only count loops that have phi nodes as not being computable. 1891 ++NumTripCountsNotComputed; 1892 } 1893 } 1894 return I->second; 1895} 1896 1897/// ComputeIterationCount - Compute the number of times the specified loop 1898/// will iterate. 1899SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) { 1900 // If the loop has a non-one exit block count, we can't analyze it. 1901 SmallVector<BasicBlock*, 8> ExitBlocks; 1902 L->getExitBlocks(ExitBlocks); 1903 if (ExitBlocks.size() != 1) return UnknownValue; 1904 1905 // Okay, there is one exit block. Try to find the condition that causes the 1906 // loop to be exited. 1907 BasicBlock *ExitBlock = ExitBlocks[0]; 1908 1909 BasicBlock *ExitingBlock = 0; 1910 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 1911 PI != E; ++PI) 1912 if (L->contains(*PI)) { 1913 if (ExitingBlock == 0) 1914 ExitingBlock = *PI; 1915 else 1916 return UnknownValue; // More than one block exiting! 1917 } 1918 assert(ExitingBlock && "No exits from loop, something is broken!"); 1919 1920 // Okay, we've computed the exiting block. See what condition causes us to 1921 // exit. 1922 // 1923 // FIXME: we should be able to handle switch instructions (with a single exit) 1924 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 1925 if (ExitBr == 0) return UnknownValue; 1926 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 1927 1928 // At this point, we know we have a conditional branch that determines whether 1929 // the loop is exited. However, we don't know if the branch is executed each 1930 // time through the loop. If not, then the execution count of the branch will 1931 // not be equal to the trip count of the loop. 1932 // 1933 // Currently we check for this by checking to see if the Exit branch goes to 1934 // the loop header. If so, we know it will always execute the same number of 1935 // times as the loop. We also handle the case where the exit block *is* the 1936 // loop header. This is common for un-rotated loops. More extensive analysis 1937 // could be done to handle more cases here. 1938 if (ExitBr->getSuccessor(0) != L->getHeader() && 1939 ExitBr->getSuccessor(1) != L->getHeader() && 1940 ExitBr->getParent() != L->getHeader()) 1941 return UnknownValue; 1942 1943 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition()); 1944 1945 // If it's not an integer comparison then compute it the hard way. 1946 // Note that ICmpInst deals with pointer comparisons too so we must check 1947 // the type of the operand. 1948 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType())) 1949 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(), 1950 ExitBr->getSuccessor(0) == ExitBlock); 1951 1952 // If the condition was exit on true, convert the condition to exit on false 1953 ICmpInst::Predicate Cond; 1954 if (ExitBr->getSuccessor(1) == ExitBlock) 1955 Cond = ExitCond->getPredicate(); 1956 else 1957 Cond = ExitCond->getInversePredicate(); 1958 1959 // Handle common loops like: for (X = "string"; *X; ++X) 1960 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 1961 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 1962 SCEVHandle ItCnt = 1963 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond); 1964 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 1965 } 1966 1967 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 1968 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 1969 1970 // Try to evaluate any dependencies out of the loop. 1971 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 1972 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 1973 Tmp = getSCEVAtScope(RHS, L); 1974 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 1975 1976 // At this point, we would like to compute how many iterations of the 1977 // loop the predicate will return true for these inputs. 1978 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) { 1979 // If there is a constant, force it into the RHS. 1980 std::swap(LHS, RHS); 1981 Cond = ICmpInst::getSwappedPredicate(Cond); 1982 } 1983 1984 // FIXME: think about handling pointer comparisons! i.e.: 1985 // while (P != P+100) ++P; 1986 1987 // If we have a comparison of a chrec against a constant, try to use value 1988 // ranges to answer this query. 1989 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 1990 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 1991 if (AddRec->getLoop() == L) { 1992 // Form the comparison range using the constant of the correct type so 1993 // that the ConstantRange class knows to do a signed or unsigned 1994 // comparison. 1995 ConstantInt *CompVal = RHSC->getValue(); 1996 const Type *RealTy = ExitCond->getOperand(0)->getType(); 1997 CompVal = dyn_cast<ConstantInt>( 1998 ConstantExpr::getBitCast(CompVal, RealTy)); 1999 if (CompVal) { 2000 // Form the constant range. 2001 ConstantRange CompRange( 2002 ICmpInst::makeConstantRange(Cond, CompVal->getValue())); 2003 2004 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, SE); 2005 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 2006 } 2007 } 2008 2009 switch (Cond) { 2010 case ICmpInst::ICMP_NE: { // while (X != Y) 2011 // Convert to: while (X-Y != 0) 2012 SCEVHandle TC = HowFarToZero(SE.getMinusSCEV(LHS, RHS), L); 2013 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2014 break; 2015 } 2016 case ICmpInst::ICMP_EQ: { 2017 // Convert to: while (X-Y == 0) // while (X == Y) 2018 SCEVHandle TC = HowFarToNonZero(SE.getMinusSCEV(LHS, RHS), L); 2019 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2020 break; 2021 } 2022 case ICmpInst::ICMP_SLT: { 2023 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true); 2024 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2025 break; 2026 } 2027 case ICmpInst::ICMP_SGT: { 2028 SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS), 2029 SE.getNotSCEV(RHS), L, true); 2030 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2031 break; 2032 } 2033 case ICmpInst::ICMP_ULT: { 2034 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false); 2035 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2036 break; 2037 } 2038 case ICmpInst::ICMP_UGT: { 2039 SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS), 2040 SE.getNotSCEV(RHS), L, false); 2041 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2042 break; 2043 } 2044 default: 2045#if 0 2046 cerr << "ComputeIterationCount "; 2047 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 2048 cerr << "[unsigned] "; 2049 cerr << *LHS << " " 2050 << Instruction::getOpcodeName(Instruction::ICmp) 2051 << " " << *RHS << "\n"; 2052#endif 2053 break; 2054 } 2055 return ComputeIterationCountExhaustively(L, ExitCond, 2056 ExitBr->getSuccessor(0) == ExitBlock); 2057} 2058 2059static ConstantInt * 2060EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 2061 ScalarEvolution &SE) { 2062 SCEVHandle InVal = SE.getConstant(C); 2063 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE); 2064 assert(isa<SCEVConstant>(Val) && 2065 "Evaluation of SCEV at constant didn't fold correctly?"); 2066 return cast<SCEVConstant>(Val)->getValue(); 2067} 2068 2069/// GetAddressedElementFromGlobal - Given a global variable with an initializer 2070/// and a GEP expression (missing the pointer index) indexing into it, return 2071/// the addressed element of the initializer or null if the index expression is 2072/// invalid. 2073static Constant * 2074GetAddressedElementFromGlobal(GlobalVariable *GV, 2075 const std::vector<ConstantInt*> &Indices) { 2076 Constant *Init = GV->getInitializer(); 2077 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 2078 uint64_t Idx = Indices[i]->getZExtValue(); 2079 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 2080 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 2081 Init = cast<Constant>(CS->getOperand(Idx)); 2082 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 2083 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 2084 Init = cast<Constant>(CA->getOperand(Idx)); 2085 } else if (isa<ConstantAggregateZero>(Init)) { 2086 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 2087 assert(Idx < STy->getNumElements() && "Bad struct index!"); 2088 Init = Constant::getNullValue(STy->getElementType(Idx)); 2089 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 2090 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 2091 Init = Constant::getNullValue(ATy->getElementType()); 2092 } else { 2093 assert(0 && "Unknown constant aggregate type!"); 2094 } 2095 return 0; 2096 } else { 2097 return 0; // Unknown initializer type 2098 } 2099 } 2100 return Init; 2101} 2102 2103/// ComputeLoadConstantCompareIterationCount - Given an exit condition of 2104/// 'icmp op load X, cst', try to see if we can compute the trip count. 2105SCEVHandle ScalarEvolutionsImpl:: 2106ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS, 2107 const Loop *L, 2108 ICmpInst::Predicate predicate) { 2109 if (LI->isVolatile()) return UnknownValue; 2110 2111 // Check to see if the loaded pointer is a getelementptr of a global. 2112 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 2113 if (!GEP) return UnknownValue; 2114 2115 // Make sure that it is really a constant global we are gepping, with an 2116 // initializer, and make sure the first IDX is really 0. 2117 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 2118 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 2119 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 2120 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 2121 return UnknownValue; 2122 2123 // Okay, we allow one non-constant index into the GEP instruction. 2124 Value *VarIdx = 0; 2125 std::vector<ConstantInt*> Indexes; 2126 unsigned VarIdxNum = 0; 2127 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 2128 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 2129 Indexes.push_back(CI); 2130 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 2131 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 2132 VarIdx = GEP->getOperand(i); 2133 VarIdxNum = i-2; 2134 Indexes.push_back(0); 2135 } 2136 2137 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 2138 // Check to see if X is a loop variant variable value now. 2139 SCEVHandle Idx = getSCEV(VarIdx); 2140 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 2141 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 2142 2143 // We can only recognize very limited forms of loop index expressions, in 2144 // particular, only affine AddRec's like {C1,+,C2}. 2145 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 2146 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 2147 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 2148 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 2149 return UnknownValue; 2150 2151 unsigned MaxSteps = MaxBruteForceIterations; 2152 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 2153 ConstantInt *ItCst = 2154 ConstantInt::get(IdxExpr->getType(), IterationNum); 2155 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, SE); 2156 2157 // Form the GEP offset. 2158 Indexes[VarIdxNum] = Val; 2159 2160 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 2161 if (Result == 0) break; // Cannot compute! 2162 2163 // Evaluate the condition for this iteration. 2164 Result = ConstantExpr::getICmp(predicate, Result, RHS); 2165 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 2166 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 2167#if 0 2168 cerr << "\n***\n*** Computed loop count " << *ItCst 2169 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 2170 << "***\n"; 2171#endif 2172 ++NumArrayLenItCounts; 2173 return SE.getConstant(ItCst); // Found terminating iteration! 2174 } 2175 } 2176 return UnknownValue; 2177} 2178 2179 2180/// CanConstantFold - Return true if we can constant fold an instruction of the 2181/// specified type, assuming that all operands were constants. 2182static bool CanConstantFold(const Instruction *I) { 2183 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 2184 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 2185 return true; 2186 2187 if (const CallInst *CI = dyn_cast<CallInst>(I)) 2188 if (const Function *F = CI->getCalledFunction()) 2189 return canConstantFoldCallTo(F); 2190 return false; 2191} 2192 2193/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 2194/// in the loop that V is derived from. We allow arbitrary operations along the 2195/// way, but the operands of an operation must either be constants or a value 2196/// derived from a constant PHI. If this expression does not fit with these 2197/// constraints, return null. 2198static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 2199 // If this is not an instruction, or if this is an instruction outside of the 2200 // loop, it can't be derived from a loop PHI. 2201 Instruction *I = dyn_cast<Instruction>(V); 2202 if (I == 0 || !L->contains(I->getParent())) return 0; 2203 2204 if (PHINode *PN = dyn_cast<PHINode>(I)) { 2205 if (L->getHeader() == I->getParent()) 2206 return PN; 2207 else 2208 // We don't currently keep track of the control flow needed to evaluate 2209 // PHIs, so we cannot handle PHIs inside of loops. 2210 return 0; 2211 } 2212 2213 // If we won't be able to constant fold this expression even if the operands 2214 // are constants, return early. 2215 if (!CanConstantFold(I)) return 0; 2216 2217 // Otherwise, we can evaluate this instruction if all of its operands are 2218 // constant or derived from a PHI node themselves. 2219 PHINode *PHI = 0; 2220 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 2221 if (!(isa<Constant>(I->getOperand(Op)) || 2222 isa<GlobalValue>(I->getOperand(Op)))) { 2223 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 2224 if (P == 0) return 0; // Not evolving from PHI 2225 if (PHI == 0) 2226 PHI = P; 2227 else if (PHI != P) 2228 return 0; // Evolving from multiple different PHIs. 2229 } 2230 2231 // This is a expression evolving from a constant PHI! 2232 return PHI; 2233} 2234 2235/// EvaluateExpression - Given an expression that passes the 2236/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 2237/// in the loop has the value PHIVal. If we can't fold this expression for some 2238/// reason, return null. 2239static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 2240 if (isa<PHINode>(V)) return PHIVal; 2241 if (Constant *C = dyn_cast<Constant>(V)) return C; 2242 Instruction *I = cast<Instruction>(V); 2243 2244 std::vector<Constant*> Operands; 2245 Operands.resize(I->getNumOperands()); 2246 2247 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2248 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 2249 if (Operands[i] == 0) return 0; 2250 } 2251 2252 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2253 return ConstantFoldCompareInstOperands(CI->getPredicate(), 2254 &Operands[0], Operands.size()); 2255 else 2256 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2257 &Operands[0], Operands.size()); 2258} 2259 2260/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 2261/// in the header of its containing loop, we know the loop executes a 2262/// constant number of times, and the PHI node is just a recurrence 2263/// involving constants, fold it. 2264Constant *ScalarEvolutionsImpl:: 2265getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, const Loop *L){ 2266 std::map<PHINode*, Constant*>::iterator I = 2267 ConstantEvolutionLoopExitValue.find(PN); 2268 if (I != ConstantEvolutionLoopExitValue.end()) 2269 return I->second; 2270 2271 if (Its.ugt(APInt(Its.getBitWidth(),MaxBruteForceIterations))) 2272 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 2273 2274 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 2275 2276 // Since the loop is canonicalized, the PHI node must have two entries. One 2277 // entry must be a constant (coming in from outside of the loop), and the 2278 // second must be derived from the same PHI. 2279 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2280 Constant *StartCST = 2281 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2282 if (StartCST == 0) 2283 return RetVal = 0; // Must be a constant. 2284 2285 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2286 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2287 if (PN2 != PN) 2288 return RetVal = 0; // Not derived from same PHI. 2289 2290 // Execute the loop symbolically to determine the exit value. 2291 if (Its.getActiveBits() >= 32) 2292 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 2293 2294 unsigned NumIterations = Its.getZExtValue(); // must be in range 2295 unsigned IterationNum = 0; 2296 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 2297 if (IterationNum == NumIterations) 2298 return RetVal = PHIVal; // Got exit value! 2299 2300 // Compute the value of the PHI node for the next iteration. 2301 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2302 if (NextPHI == PHIVal) 2303 return RetVal = NextPHI; // Stopped evolving! 2304 if (NextPHI == 0) 2305 return 0; // Couldn't evaluate! 2306 PHIVal = NextPHI; 2307 } 2308} 2309 2310/// ComputeIterationCountExhaustively - If the trip is known to execute a 2311/// constant number of times (the condition evolves only from constants), 2312/// try to evaluate a few iterations of the loop until we get the exit 2313/// condition gets a value of ExitWhen (true or false). If we cannot 2314/// evaluate the trip count of the loop, return UnknownValue. 2315SCEVHandle ScalarEvolutionsImpl:: 2316ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 2317 PHINode *PN = getConstantEvolvingPHI(Cond, L); 2318 if (PN == 0) return UnknownValue; 2319 2320 // Since the loop is canonicalized, the PHI node must have two entries. One 2321 // entry must be a constant (coming in from outside of the loop), and the 2322 // second must be derived from the same PHI. 2323 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2324 Constant *StartCST = 2325 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2326 if (StartCST == 0) return UnknownValue; // Must be a constant. 2327 2328 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2329 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2330 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 2331 2332 // Okay, we find a PHI node that defines the trip count of this loop. Execute 2333 // the loop symbolically to determine when the condition gets a value of 2334 // "ExitWhen". 2335 unsigned IterationNum = 0; 2336 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 2337 for (Constant *PHIVal = StartCST; 2338 IterationNum != MaxIterations; ++IterationNum) { 2339 ConstantInt *CondVal = 2340 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 2341 2342 // Couldn't symbolically evaluate. 2343 if (!CondVal) return UnknownValue; 2344 2345 if (CondVal->getValue() == uint64_t(ExitWhen)) { 2346 ConstantEvolutionLoopExitValue[PN] = PHIVal; 2347 ++NumBruteForceTripCountsComputed; 2348 return SE.getConstant(ConstantInt::get(Type::Int32Ty, IterationNum)); 2349 } 2350 2351 // Compute the value of the PHI node for the next iteration. 2352 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2353 if (NextPHI == 0 || NextPHI == PHIVal) 2354 return UnknownValue; // Couldn't evaluate or not making progress... 2355 PHIVal = NextPHI; 2356 } 2357 2358 // Too many iterations were needed to evaluate. 2359 return UnknownValue; 2360} 2361 2362/// getSCEVAtScope - Compute the value of the specified expression within the 2363/// indicated loop (which may be null to indicate in no loop). If the 2364/// expression cannot be evaluated, return UnknownValue. 2365SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) { 2366 // FIXME: this should be turned into a virtual method on SCEV! 2367 2368 if (isa<SCEVConstant>(V)) return V; 2369 2370 // If this instruction is evolved from a constant-evolving PHI, compute the 2371 // exit value from the loop without using SCEVs. 2372 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 2373 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 2374 const Loop *LI = this->LI[I->getParent()]; 2375 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 2376 if (PHINode *PN = dyn_cast<PHINode>(I)) 2377 if (PN->getParent() == LI->getHeader()) { 2378 // Okay, there is no closed form solution for the PHI node. Check 2379 // to see if the loop that contains it has a known iteration count. 2380 // If so, we may be able to force computation of the exit value. 2381 SCEVHandle IterationCount = getIterationCount(LI); 2382 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) { 2383 // Okay, we know how many times the containing loop executes. If 2384 // this is a constant evolving PHI node, get the final value at 2385 // the specified iteration number. 2386 Constant *RV = getConstantEvolutionLoopExitValue(PN, 2387 ICC->getValue()->getValue(), 2388 LI); 2389 if (RV) return SE.getUnknown(RV); 2390 } 2391 } 2392 2393 // Okay, this is an expression that we cannot symbolically evaluate 2394 // into a SCEV. Check to see if it's possible to symbolically evaluate 2395 // the arguments into constants, and if so, try to constant propagate the 2396 // result. This is particularly useful for computing loop exit values. 2397 if (CanConstantFold(I)) { 2398 std::vector<Constant*> Operands; 2399 Operands.reserve(I->getNumOperands()); 2400 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2401 Value *Op = I->getOperand(i); 2402 if (Constant *C = dyn_cast<Constant>(Op)) { 2403 Operands.push_back(C); 2404 } else { 2405 // If any of the operands is non-constant and if they are 2406 // non-integer, don't even try to analyze them with scev techniques. 2407 if (!isa<IntegerType>(Op->getType())) 2408 return V; 2409 2410 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 2411 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 2412 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(), 2413 Op->getType(), 2414 false)); 2415 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 2416 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 2417 Operands.push_back(ConstantExpr::getIntegerCast(C, 2418 Op->getType(), 2419 false)); 2420 else 2421 return V; 2422 } else { 2423 return V; 2424 } 2425 } 2426 } 2427 2428 Constant *C; 2429 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2430 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 2431 &Operands[0], Operands.size()); 2432 else 2433 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2434 &Operands[0], Operands.size()); 2435 return SE.getUnknown(C); 2436 } 2437 } 2438 2439 // This is some other type of SCEVUnknown, just return it. 2440 return V; 2441 } 2442 2443 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 2444 // Avoid performing the look-up in the common case where the specified 2445 // expression has no loop-variant portions. 2446 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 2447 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2448 if (OpAtScope != Comm->getOperand(i)) { 2449 if (OpAtScope == UnknownValue) return UnknownValue; 2450 // Okay, at least one of these operands is loop variant but might be 2451 // foldable. Build a new instance of the folded commutative expression. 2452 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 2453 NewOps.push_back(OpAtScope); 2454 2455 for (++i; i != e; ++i) { 2456 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2457 if (OpAtScope == UnknownValue) return UnknownValue; 2458 NewOps.push_back(OpAtScope); 2459 } 2460 if (isa<SCEVAddExpr>(Comm)) 2461 return SE.getAddExpr(NewOps); 2462 if (isa<SCEVMulExpr>(Comm)) 2463 return SE.getMulExpr(NewOps); 2464 if (isa<SCEVSMaxExpr>(Comm)) 2465 return SE.getSMaxExpr(NewOps); 2466 if (isa<SCEVUMaxExpr>(Comm)) 2467 return SE.getUMaxExpr(NewOps); 2468 assert(0 && "Unknown commutative SCEV type!"); 2469 } 2470 } 2471 // If we got here, all operands are loop invariant. 2472 return Comm; 2473 } 2474 2475 if (SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 2476 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L); 2477 if (LHS == UnknownValue) return LHS; 2478 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L); 2479 if (RHS == UnknownValue) return RHS; 2480 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 2481 return Div; // must be loop invariant 2482 return SE.getUDivExpr(LHS, RHS); 2483 } 2484 2485 // If this is a loop recurrence for a loop that does not contain L, then we 2486 // are dealing with the final value computed by the loop. 2487 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 2488 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 2489 // To evaluate this recurrence, we need to know how many times the AddRec 2490 // loop iterates. Compute this now. 2491 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop()); 2492 if (IterationCount == UnknownValue) return UnknownValue; 2493 2494 // Then, evaluate the AddRec. 2495 return AddRec->evaluateAtIteration(IterationCount, SE); 2496 } 2497 return UnknownValue; 2498 } 2499 2500 //assert(0 && "Unknown SCEV type!"); 2501 return UnknownValue; 2502} 2503 2504/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 2505/// following equation: 2506/// 2507/// A * X = B (mod N) 2508/// 2509/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 2510/// A and B isn't important. 2511/// 2512/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 2513static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 2514 ScalarEvolution &SE) { 2515 uint32_t BW = A.getBitWidth(); 2516 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 2517 assert(A != 0 && "A must be non-zero."); 2518 2519 // 1. D = gcd(A, N) 2520 // 2521 // The gcd of A and N may have only one prime factor: 2. The number of 2522 // trailing zeros in A is its multiplicity 2523 uint32_t Mult2 = A.countTrailingZeros(); 2524 // D = 2^Mult2 2525 2526 // 2. Check if B is divisible by D. 2527 // 2528 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 2529 // is not less than multiplicity of this prime factor for D. 2530 if (B.countTrailingZeros() < Mult2) 2531 return new SCEVCouldNotCompute(); 2532 2533 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 2534 // modulo (N / D). 2535 // 2536 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 2537 // bit width during computations. 2538 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 2539 APInt Mod(BW + 1, 0); 2540 Mod.set(BW - Mult2); // Mod = N / D 2541 APInt I = AD.multiplicativeInverse(Mod); 2542 2543 // 4. Compute the minimum unsigned root of the equation: 2544 // I * (B / D) mod (N / D) 2545 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 2546 2547 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 2548 // bits. 2549 return SE.getConstant(Result.trunc(BW)); 2550} 2551 2552/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 2553/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 2554/// might be the same) or two SCEVCouldNotCompute objects. 2555/// 2556static std::pair<SCEVHandle,SCEVHandle> 2557SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 2558 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 2559 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 2560 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 2561 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 2562 2563 // We currently can only solve this if the coefficients are constants. 2564 if (!LC || !MC || !NC) { 2565 SCEV *CNC = new SCEVCouldNotCompute(); 2566 return std::make_pair(CNC, CNC); 2567 } 2568 2569 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 2570 const APInt &L = LC->getValue()->getValue(); 2571 const APInt &M = MC->getValue()->getValue(); 2572 const APInt &N = NC->getValue()->getValue(); 2573 APInt Two(BitWidth, 2); 2574 APInt Four(BitWidth, 4); 2575 2576 { 2577 using namespace APIntOps; 2578 const APInt& C = L; 2579 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 2580 // The B coefficient is M-N/2 2581 APInt B(M); 2582 B -= sdiv(N,Two); 2583 2584 // The A coefficient is N/2 2585 APInt A(N.sdiv(Two)); 2586 2587 // Compute the B^2-4ac term. 2588 APInt SqrtTerm(B); 2589 SqrtTerm *= B; 2590 SqrtTerm -= Four * (A * C); 2591 2592 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 2593 // integer value or else APInt::sqrt() will assert. 2594 APInt SqrtVal(SqrtTerm.sqrt()); 2595 2596 // Compute the two solutions for the quadratic formula. 2597 // The divisions must be performed as signed divisions. 2598 APInt NegB(-B); 2599 APInt TwoA( A << 1 ); 2600 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA)); 2601 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA)); 2602 2603 return std::make_pair(SE.getConstant(Solution1), 2604 SE.getConstant(Solution2)); 2605 } // end APIntOps namespace 2606} 2607 2608/// HowFarToZero - Return the number of times a backedge comparing the specified 2609/// value to zero will execute. If not computable, return UnknownValue 2610SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) { 2611 // If the value is a constant 2612 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2613 // If the value is already zero, the branch will execute zero times. 2614 if (C->getValue()->isZero()) return C; 2615 return UnknownValue; // Otherwise it will loop infinitely. 2616 } 2617 2618 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 2619 if (!AddRec || AddRec->getLoop() != L) 2620 return UnknownValue; 2621 2622 if (AddRec->isAffine()) { 2623 // If this is an affine expression, the execution count of this branch is 2624 // the minimum unsigned root of the following equation: 2625 // 2626 // Start + Step*N = 0 (mod 2^BW) 2627 // 2628 // equivalent to: 2629 // 2630 // Step*N = -Start (mod 2^BW) 2631 // 2632 // where BW is the common bit width of Start and Step. 2633 2634 // Get the initial value for the loop. 2635 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 2636 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 2637 2638 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop()); 2639 2640 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 2641 // For now we handle only constant steps. 2642 2643 // First, handle unitary steps. 2644 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 2645 return SE.getNegativeSCEV(Start); // N = -Start (as unsigned) 2646 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 2647 return Start; // N = Start (as unsigned) 2648 2649 // Then, try to solve the above equation provided that Start is constant. 2650 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 2651 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 2652 -StartC->getValue()->getValue(),SE); 2653 } 2654 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 2655 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 2656 // the quadratic equation to solve it. 2657 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec, SE); 2658 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2659 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2660 if (R1) { 2661#if 0 2662 cerr << "HFTZ: " << *V << " - sol#1: " << *R1 2663 << " sol#2: " << *R2 << "\n"; 2664#endif 2665 // Pick the smallest positive root value. 2666 if (ConstantInt *CB = 2667 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2668 R1->getValue(), R2->getValue()))) { 2669 if (CB->getZExtValue() == false) 2670 std::swap(R1, R2); // R1 is the minimum root now. 2671 2672 // We can only use this value if the chrec ends up with an exact zero 2673 // value at this index. When solving for "X*X != 5", for example, we 2674 // should not accept a root of 2. 2675 SCEVHandle Val = AddRec->evaluateAtIteration(R1, SE); 2676 if (Val->isZero()) 2677 return R1; // We found a quadratic root! 2678 } 2679 } 2680 } 2681 2682 return UnknownValue; 2683} 2684 2685/// HowFarToNonZero - Return the number of times a backedge checking the 2686/// specified value for nonzero will execute. If not computable, return 2687/// UnknownValue 2688SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) { 2689 // Loops that look like: while (X == 0) are very strange indeed. We don't 2690 // handle them yet except for the trivial case. This could be expanded in the 2691 // future as needed. 2692 2693 // If the value is a constant, check to see if it is known to be non-zero 2694 // already. If so, the backedge will execute zero times. 2695 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2696 if (!C->getValue()->isNullValue()) 2697 return SE.getIntegerSCEV(0, C->getType()); 2698 return UnknownValue; // Otherwise it will loop infinitely. 2699 } 2700 2701 // We could implement others, but I really doubt anyone writes loops like 2702 // this, and if they did, they would already be constant folded. 2703 return UnknownValue; 2704} 2705 2706/// executesAtLeastOnce - Test whether entry to the loop is protected by 2707/// a conditional between LHS and RHS. 2708bool ScalarEvolutionsImpl::executesAtLeastOnce(const Loop *L, bool isSigned, 2709 SCEV *LHS, SCEV *RHS) { 2710 BasicBlock *Preheader = L->getLoopPreheader(); 2711 BasicBlock *PreheaderDest = L->getHeader(); 2712 if (Preheader == 0) return false; 2713 2714 BranchInst *LoopEntryPredicate = 2715 dyn_cast<BranchInst>(Preheader->getTerminator()); 2716 if (!LoopEntryPredicate) return false; 2717 2718 // This might be a critical edge broken out. If the loop preheader ends in 2719 // an unconditional branch to the loop, check to see if the preheader has a 2720 // single predecessor, and if so, look for its terminator. 2721 while (LoopEntryPredicate->isUnconditional()) { 2722 PreheaderDest = Preheader; 2723 Preheader = Preheader->getSinglePredecessor(); 2724 if (!Preheader) return false; // Multiple preds. 2725 2726 LoopEntryPredicate = 2727 dyn_cast<BranchInst>(Preheader->getTerminator()); 2728 if (!LoopEntryPredicate) return false; 2729 } 2730 2731 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition()); 2732 if (!ICI) return false; 2733 2734 // Now that we found a conditional branch that dominates the loop, check to 2735 // see if it is the comparison we are looking for. 2736 Value *PreCondLHS = ICI->getOperand(0); 2737 Value *PreCondRHS = ICI->getOperand(1); 2738 ICmpInst::Predicate Cond; 2739 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest) 2740 Cond = ICI->getPredicate(); 2741 else 2742 Cond = ICI->getInversePredicate(); 2743 2744 switch (Cond) { 2745 case ICmpInst::ICMP_UGT: 2746 if (isSigned) return false; 2747 std::swap(PreCondLHS, PreCondRHS); 2748 Cond = ICmpInst::ICMP_ULT; 2749 break; 2750 case ICmpInst::ICMP_SGT: 2751 if (!isSigned) return false; 2752 std::swap(PreCondLHS, PreCondRHS); 2753 Cond = ICmpInst::ICMP_SLT; 2754 break; 2755 case ICmpInst::ICMP_ULT: 2756 if (isSigned) return false; 2757 break; 2758 case ICmpInst::ICMP_SLT: 2759 if (!isSigned) return false; 2760 break; 2761 default: 2762 return false; 2763 } 2764 2765 if (!PreCondLHS->getType()->isInteger()) return false; 2766 2767 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS); 2768 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS); 2769 return (LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) || 2770 (LHS == SE.getNotSCEV(PreCondRHSSCEV) && 2771 RHS == SE.getNotSCEV(PreCondLHSSCEV)); 2772} 2773 2774/// HowManyLessThans - Return the number of times a backedge containing the 2775/// specified less-than comparison will execute. If not computable, return 2776/// UnknownValue. 2777SCEVHandle ScalarEvolutionsImpl:: 2778HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) { 2779 // Only handle: "ADDREC < LoopInvariant". 2780 if (!RHS->isLoopInvariant(L)) return UnknownValue; 2781 2782 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 2783 if (!AddRec || AddRec->getLoop() != L) 2784 return UnknownValue; 2785 2786 if (AddRec->isAffine()) { 2787 // FORNOW: We only support unit strides. 2788 SCEVHandle One = SE.getIntegerSCEV(1, RHS->getType()); 2789 if (AddRec->getOperand(1) != One) 2790 return UnknownValue; 2791 2792 // We know the LHS is of the form {n,+,1} and the RHS is some loop-invariant 2793 // m. So, we count the number of iterations in which {n,+,1} < m is true. 2794 // Note that we cannot simply return max(m-n,0) because it's not safe to 2795 // treat m-n as signed nor unsigned due to overflow possibility. 2796 2797 // First, we get the value of the LHS in the first iteration: n 2798 SCEVHandle Start = AddRec->getOperand(0); 2799 2800 if (executesAtLeastOnce(L, isSigned, 2801 SE.getMinusSCEV(AddRec->getOperand(0), One), RHS)) { 2802 // Since we know that the condition is true in order to enter the loop, 2803 // we know that it will run exactly m-n times. 2804 return SE.getMinusSCEV(RHS, Start); 2805 } else { 2806 // Then, we get the value of the LHS in the first iteration in which the 2807 // above condition doesn't hold. This equals to max(m,n). 2808 SCEVHandle End = isSigned ? SE.getSMaxExpr(RHS, Start) 2809 : SE.getUMaxExpr(RHS, Start); 2810 2811 // Finally, we subtract these two values to get the number of times the 2812 // backedge is executed: max(m,n)-n. 2813 return SE.getMinusSCEV(End, Start); 2814 } 2815 } 2816 2817 return UnknownValue; 2818} 2819 2820/// getNumIterationsInRange - Return the number of iterations of this loop that 2821/// produce values in the specified constant range. Another way of looking at 2822/// this is that it returns the first iteration number where the value is not in 2823/// the condition, thus computing the exit count. If the iteration count can't 2824/// be computed, an instance of SCEVCouldNotCompute is returned. 2825SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 2826 ScalarEvolution &SE) const { 2827 if (Range.isFullSet()) // Infinite loop. 2828 return new SCEVCouldNotCompute(); 2829 2830 // If the start is a non-zero constant, shift the range to simplify things. 2831 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 2832 if (!SC->getValue()->isZero()) { 2833 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 2834 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 2835 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop()); 2836 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 2837 return ShiftedAddRec->getNumIterationsInRange( 2838 Range.subtract(SC->getValue()->getValue()), SE); 2839 // This is strange and shouldn't happen. 2840 return new SCEVCouldNotCompute(); 2841 } 2842 2843 // The only time we can solve this is when we have all constant indices. 2844 // Otherwise, we cannot determine the overflow conditions. 2845 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 2846 if (!isa<SCEVConstant>(getOperand(i))) 2847 return new SCEVCouldNotCompute(); 2848 2849 2850 // Okay at this point we know that all elements of the chrec are constants and 2851 // that the start element is zero. 2852 2853 // First check to see if the range contains zero. If not, the first 2854 // iteration exits. 2855 if (!Range.contains(APInt(getBitWidth(),0))) 2856 return SE.getConstant(ConstantInt::get(getType(),0)); 2857 2858 if (isAffine()) { 2859 // If this is an affine expression then we have this situation: 2860 // Solve {0,+,A} in Range === Ax in Range 2861 2862 // We know that zero is in the range. If A is positive then we know that 2863 // the upper value of the range must be the first possible exit value. 2864 // If A is negative then the lower of the range is the last possible loop 2865 // value. Also note that we already checked for a full range. 2866 APInt One(getBitWidth(),1); 2867 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 2868 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 2869 2870 // The exit value should be (End+A)/A. 2871 APInt ExitVal = (End + A).udiv(A); 2872 ConstantInt *ExitValue = ConstantInt::get(ExitVal); 2873 2874 // Evaluate at the exit value. If we really did fall out of the valid 2875 // range, then we computed our trip count, otherwise wrap around or other 2876 // things must have happened. 2877 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 2878 if (Range.contains(Val->getValue())) 2879 return new SCEVCouldNotCompute(); // Something strange happened 2880 2881 // Ensure that the previous value is in the range. This is a sanity check. 2882 assert(Range.contains( 2883 EvaluateConstantChrecAtConstant(this, 2884 ConstantInt::get(ExitVal - One), SE)->getValue()) && 2885 "Linear scev computation is off in a bad way!"); 2886 return SE.getConstant(ExitValue); 2887 } else if (isQuadratic()) { 2888 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 2889 // quadratic equation to solve it. To do this, we must frame our problem in 2890 // terms of figuring out when zero is crossed, instead of when 2891 // Range.getUpper() is crossed. 2892 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 2893 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 2894 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 2895 2896 // Next, solve the constructed addrec 2897 std::pair<SCEVHandle,SCEVHandle> Roots = 2898 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 2899 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2900 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2901 if (R1) { 2902 // Pick the smallest positive root value. 2903 if (ConstantInt *CB = 2904 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2905 R1->getValue(), R2->getValue()))) { 2906 if (CB->getZExtValue() == false) 2907 std::swap(R1, R2); // R1 is the minimum root now. 2908 2909 // Make sure the root is not off by one. The returned iteration should 2910 // not be in the range, but the previous one should be. When solving 2911 // for "X*X < 5", for example, we should not return a root of 2. 2912 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 2913 R1->getValue(), 2914 SE); 2915 if (Range.contains(R1Val->getValue())) { 2916 // The next iteration must be out of the range... 2917 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1); 2918 2919 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 2920 if (!Range.contains(R1Val->getValue())) 2921 return SE.getConstant(NextVal); 2922 return new SCEVCouldNotCompute(); // Something strange happened 2923 } 2924 2925 // If R1 was not in the range, then it is a good return value. Make 2926 // sure that R1-1 WAS in the range though, just in case. 2927 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1); 2928 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 2929 if (Range.contains(R1Val->getValue())) 2930 return R1; 2931 return new SCEVCouldNotCompute(); // Something strange happened 2932 } 2933 } 2934 } 2935 2936 // Fallback, if this is a general polynomial, figure out the progression 2937 // through brute force: evaluate until we find an iteration that fails the 2938 // test. This is likely to be slow, but getting an accurate trip count is 2939 // incredibly important, we will be able to simplify the exit test a lot, and 2940 // we are almost guaranteed to get a trip count in this case. 2941 ConstantInt *TestVal = ConstantInt::get(getType(), 0); 2942 ConstantInt *EndVal = TestVal; // Stop when we wrap around. 2943 do { 2944 ++NumBruteForceEvaluations; 2945 SCEVHandle Val = evaluateAtIteration(SE.getConstant(TestVal), SE); 2946 if (!isa<SCEVConstant>(Val)) // This shouldn't happen. 2947 return new SCEVCouldNotCompute(); 2948 2949 // Check to see if we found the value! 2950 if (!Range.contains(cast<SCEVConstant>(Val)->getValue()->getValue())) 2951 return SE.getConstant(TestVal); 2952 2953 // Increment to test the next index. 2954 TestVal = ConstantInt::get(TestVal->getValue()+1); 2955 } while (TestVal != EndVal); 2956 2957 return new SCEVCouldNotCompute(); 2958} 2959 2960 2961 2962//===----------------------------------------------------------------------===// 2963// ScalarEvolution Class Implementation 2964//===----------------------------------------------------------------------===// 2965 2966bool ScalarEvolution::runOnFunction(Function &F) { 2967 Impl = new ScalarEvolutionsImpl(*this, F, getAnalysis<LoopInfo>()); 2968 return false; 2969} 2970 2971void ScalarEvolution::releaseMemory() { 2972 delete (ScalarEvolutionsImpl*)Impl; 2973 Impl = 0; 2974} 2975 2976void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 2977 AU.setPreservesAll(); 2978 AU.addRequiredTransitive<LoopInfo>(); 2979} 2980 2981SCEVHandle ScalarEvolution::getSCEV(Value *V) const { 2982 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V); 2983} 2984 2985/// hasSCEV - Return true if the SCEV for this value has already been 2986/// computed. 2987bool ScalarEvolution::hasSCEV(Value *V) const { 2988 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V); 2989} 2990 2991 2992/// setSCEV - Insert the specified SCEV into the map of current SCEVs for 2993/// the specified value. 2994void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) { 2995 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H); 2996} 2997 2998 2999SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const { 3000 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L); 3001} 3002 3003bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const { 3004 return !isa<SCEVCouldNotCompute>(getIterationCount(L)); 3005} 3006 3007SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const { 3008 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L); 3009} 3010 3011void ScalarEvolution::deleteValueFromRecords(Value *V) const { 3012 return ((ScalarEvolutionsImpl*)Impl)->deleteValueFromRecords(V); 3013} 3014 3015static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE, 3016 const Loop *L) { 3017 // Print all inner loops first 3018 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 3019 PrintLoopInfo(OS, SE, *I); 3020 3021 OS << "Loop " << L->getHeader()->getName() << ": "; 3022 3023 SmallVector<BasicBlock*, 8> ExitBlocks; 3024 L->getExitBlocks(ExitBlocks); 3025 if (ExitBlocks.size() != 1) 3026 OS << "<multiple exits> "; 3027 3028 if (SE->hasLoopInvariantIterationCount(L)) { 3029 OS << *SE->getIterationCount(L) << " iterations! "; 3030 } else { 3031 OS << "Unpredictable iteration count. "; 3032 } 3033 3034 OS << "\n"; 3035} 3036 3037void ScalarEvolution::print(std::ostream &OS, const Module* ) const { 3038 Function &F = ((ScalarEvolutionsImpl*)Impl)->F; 3039 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI; 3040 3041 OS << "Classifying expressions for: " << F.getName() << "\n"; 3042 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 3043 if (I->getType()->isInteger()) { 3044 OS << *I; 3045 OS << " --> "; 3046 SCEVHandle SV = getSCEV(&*I); 3047 SV->print(OS); 3048 OS << "\t\t"; 3049 3050 if (const Loop *L = LI.getLoopFor((*I).getParent())) { 3051 OS << "Exits: "; 3052 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop()); 3053 if (isa<SCEVCouldNotCompute>(ExitValue)) { 3054 OS << "<<Unknown>>"; 3055 } else { 3056 OS << *ExitValue; 3057 } 3058 } 3059 3060 3061 OS << "\n"; 3062 } 3063 3064 OS << "Determining loop execution counts for: " << F.getName() << "\n"; 3065 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I) 3066 PrintLoopInfo(OS, this, *I); 3067} 3068