ScalarEvolution.cpp revision 70ff4cf1baf8cce04b38752ea485425782fb07b8
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 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 1484 /// (which may not be an immediate predecessor) which has exactly one 1485 /// successor from which BB is reachable, or null if no such block is 1486 /// found. 1487 BasicBlock* getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB); 1488 1489 /// executesAtLeastOnce - Test whether entry to the loop is protected by 1490 /// a conditional between LHS and RHS. 1491 bool executesAtLeastOnce(const Loop *L, bool isSigned, SCEV *LHS, SCEV *RHS); 1492 1493 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1494 /// in the header of its containing loop, we know the loop executes a 1495 /// constant number of times, and the PHI node is just a recurrence 1496 /// involving constants, fold it. 1497 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, 1498 const Loop *L); 1499 }; 1500} 1501 1502//===----------------------------------------------------------------------===// 1503// Basic SCEV Analysis and PHI Idiom Recognition Code 1504// 1505 1506/// deleteValueFromRecords - This method should be called by the 1507/// client before it removes an instruction from the program, to make sure 1508/// that no dangling references are left around. 1509void ScalarEvolutionsImpl::deleteValueFromRecords(Value *V) { 1510 SmallVector<Value *, 16> Worklist; 1511 1512 if (Scalars.erase(V)) { 1513 if (PHINode *PN = dyn_cast<PHINode>(V)) 1514 ConstantEvolutionLoopExitValue.erase(PN); 1515 Worklist.push_back(V); 1516 } 1517 1518 while (!Worklist.empty()) { 1519 Value *VV = Worklist.back(); 1520 Worklist.pop_back(); 1521 1522 for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end(); 1523 UI != UE; ++UI) { 1524 Instruction *Inst = cast<Instruction>(*UI); 1525 if (Scalars.erase(Inst)) { 1526 if (PHINode *PN = dyn_cast<PHINode>(VV)) 1527 ConstantEvolutionLoopExitValue.erase(PN); 1528 Worklist.push_back(Inst); 1529 } 1530 } 1531 } 1532} 1533 1534 1535/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1536/// expression and create a new one. 1537SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) { 1538 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!"); 1539 1540 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V); 1541 if (I != Scalars.end()) return I->second; 1542 SCEVHandle S = createSCEV(V); 1543 Scalars.insert(std::make_pair(V, S)); 1544 return S; 1545} 1546 1547/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 1548/// the specified instruction and replaces any references to the symbolic value 1549/// SymName with the specified value. This is used during PHI resolution. 1550void ScalarEvolutionsImpl:: 1551ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName, 1552 const SCEVHandle &NewVal) { 1553 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I); 1554 if (SI == Scalars.end()) return; 1555 1556 SCEVHandle NV = 1557 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, SE); 1558 if (NV == SI->second) return; // No change. 1559 1560 SI->second = NV; // Update the scalars map! 1561 1562 // Any instruction values that use this instruction might also need to be 1563 // updated! 1564 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1565 UI != E; ++UI) 1566 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 1567} 1568 1569/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1570/// a loop header, making it a potential recurrence, or it doesn't. 1571/// 1572SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) { 1573 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1574 if (const Loop *L = LI.getLoopFor(PN->getParent())) 1575 if (L->getHeader() == PN->getParent()) { 1576 // If it lives in the loop header, it has two incoming values, one 1577 // from outside the loop, and one from inside. 1578 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1579 unsigned BackEdge = IncomingEdge^1; 1580 1581 // While we are analyzing this PHI node, handle its value symbolically. 1582 SCEVHandle SymbolicName = SE.getUnknown(PN); 1583 assert(Scalars.find(PN) == Scalars.end() && 1584 "PHI node already processed?"); 1585 Scalars.insert(std::make_pair(PN, SymbolicName)); 1586 1587 // Using this symbolic name for the PHI, analyze the value coming around 1588 // the back-edge. 1589 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1590 1591 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1592 // has a special value for the first iteration of the loop. 1593 1594 // If the value coming around the backedge is an add with the symbolic 1595 // value we just inserted, then we found a simple induction variable! 1596 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1597 // If there is a single occurrence of the symbolic value, replace it 1598 // with a recurrence. 1599 unsigned FoundIndex = Add->getNumOperands(); 1600 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1601 if (Add->getOperand(i) == SymbolicName) 1602 if (FoundIndex == e) { 1603 FoundIndex = i; 1604 break; 1605 } 1606 1607 if (FoundIndex != Add->getNumOperands()) { 1608 // Create an add with everything but the specified operand. 1609 std::vector<SCEVHandle> Ops; 1610 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1611 if (i != FoundIndex) 1612 Ops.push_back(Add->getOperand(i)); 1613 SCEVHandle Accum = SE.getAddExpr(Ops); 1614 1615 // This is not a valid addrec if the step amount is varying each 1616 // loop iteration, but is not itself an addrec in this loop. 1617 if (Accum->isLoopInvariant(L) || 1618 (isa<SCEVAddRecExpr>(Accum) && 1619 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1620 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1621 SCEVHandle PHISCEV = SE.getAddRecExpr(StartVal, Accum, L); 1622 1623 // Okay, for the entire analysis of this edge we assumed the PHI 1624 // to be symbolic. We now need to go back and update all of the 1625 // entries for the scalars that use the PHI (except for the PHI 1626 // itself) to use the new analyzed value instead of the "symbolic" 1627 // value. 1628 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1629 return PHISCEV; 1630 } 1631 } 1632 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) { 1633 // Otherwise, this could be a loop like this: 1634 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 1635 // In this case, j = {1,+,1} and BEValue is j. 1636 // Because the other in-value of i (0) fits the evolution of BEValue 1637 // i really is an addrec evolution. 1638 if (AddRec->getLoop() == L && AddRec->isAffine()) { 1639 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1640 1641 // If StartVal = j.start - j.stride, we can use StartVal as the 1642 // initial step of the addrec evolution. 1643 if (StartVal == SE.getMinusSCEV(AddRec->getOperand(0), 1644 AddRec->getOperand(1))) { 1645 SCEVHandle PHISCEV = 1646 SE.getAddRecExpr(StartVal, AddRec->getOperand(1), L); 1647 1648 // Okay, for the entire analysis of this edge we assumed the PHI 1649 // to be symbolic. We now need to go back and update all of the 1650 // entries for the scalars that use the PHI (except for the PHI 1651 // itself) to use the new analyzed value instead of the "symbolic" 1652 // value. 1653 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1654 return PHISCEV; 1655 } 1656 } 1657 } 1658 1659 return SymbolicName; 1660 } 1661 1662 // If it's not a loop phi, we can't handle it yet. 1663 return SE.getUnknown(PN); 1664} 1665 1666/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 1667/// guaranteed to end in (at every loop iteration). It is, at the same time, 1668/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 1669/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 1670static uint32_t GetMinTrailingZeros(SCEVHandle S) { 1671 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 1672 return C->getValue()->getValue().countTrailingZeros(); 1673 1674 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 1675 return std::min(GetMinTrailingZeros(T->getOperand()), T->getBitWidth()); 1676 1677 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 1678 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 1679 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes; 1680 } 1681 1682 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 1683 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 1684 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes; 1685 } 1686 1687 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 1688 // The result is the min of all operands results. 1689 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 1690 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1691 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 1692 return MinOpRes; 1693 } 1694 1695 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 1696 // The result is the sum of all operands results. 1697 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 1698 uint32_t BitWidth = M->getBitWidth(); 1699 for (unsigned i = 1, e = M->getNumOperands(); 1700 SumOpRes != BitWidth && i != e; ++i) 1701 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 1702 BitWidth); 1703 return SumOpRes; 1704 } 1705 1706 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 1707 // The result is the min of all operands results. 1708 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 1709 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1710 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 1711 return MinOpRes; 1712 } 1713 1714 if (SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 1715 // The result is the min of all operands results. 1716 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 1717 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 1718 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 1719 return MinOpRes; 1720 } 1721 1722 if (SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 1723 // The result is the min of all operands results. 1724 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 1725 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 1726 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 1727 return MinOpRes; 1728 } 1729 1730 // SCEVUDivExpr, SCEVUnknown 1731 return 0; 1732} 1733 1734/// createSCEV - We know that there is no SCEV for the specified value. 1735/// Analyze the expression. 1736/// 1737SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) { 1738 if (!isa<IntegerType>(V->getType())) 1739 return SE.getUnknown(V); 1740 1741 unsigned Opcode = Instruction::UserOp1; 1742 if (Instruction *I = dyn_cast<Instruction>(V)) 1743 Opcode = I->getOpcode(); 1744 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 1745 Opcode = CE->getOpcode(); 1746 else 1747 return SE.getUnknown(V); 1748 1749 User *U = cast<User>(V); 1750 switch (Opcode) { 1751 case Instruction::Add: 1752 return SE.getAddExpr(getSCEV(U->getOperand(0)), 1753 getSCEV(U->getOperand(1))); 1754 case Instruction::Mul: 1755 return SE.getMulExpr(getSCEV(U->getOperand(0)), 1756 getSCEV(U->getOperand(1))); 1757 case Instruction::UDiv: 1758 return SE.getUDivExpr(getSCEV(U->getOperand(0)), 1759 getSCEV(U->getOperand(1))); 1760 case Instruction::Sub: 1761 return SE.getMinusSCEV(getSCEV(U->getOperand(0)), 1762 getSCEV(U->getOperand(1))); 1763 case Instruction::Or: 1764 // If the RHS of the Or is a constant, we may have something like: 1765 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 1766 // optimizations will transparently handle this case. 1767 // 1768 // In order for this transformation to be safe, the LHS must be of the 1769 // form X*(2^n) and the Or constant must be less than 2^n. 1770 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 1771 SCEVHandle LHS = getSCEV(U->getOperand(0)); 1772 const APInt &CIVal = CI->getValue(); 1773 if (GetMinTrailingZeros(LHS) >= 1774 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) 1775 return SE.getAddExpr(LHS, getSCEV(U->getOperand(1))); 1776 } 1777 break; 1778 case Instruction::Xor: 1779 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 1780 // If the RHS of the xor is a signbit, then this is just an add. 1781 // Instcombine turns add of signbit into xor as a strength reduction step. 1782 if (CI->getValue().isSignBit()) 1783 return SE.getAddExpr(getSCEV(U->getOperand(0)), 1784 getSCEV(U->getOperand(1))); 1785 1786 // If the RHS of xor is -1, then this is a not operation. 1787 else if (CI->isAllOnesValue()) 1788 return SE.getNotSCEV(getSCEV(U->getOperand(0))); 1789 } 1790 break; 1791 1792 case Instruction::Shl: 1793 // Turn shift left of a constant amount into a multiply. 1794 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 1795 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 1796 Constant *X = ConstantInt::get( 1797 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 1798 return SE.getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 1799 } 1800 break; 1801 1802 case Instruction::LShr: 1803 // Turn logical shift right of a constant into a unsigned divide. 1804 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 1805 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 1806 Constant *X = ConstantInt::get( 1807 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 1808 return SE.getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 1809 } 1810 break; 1811 1812 case Instruction::Trunc: 1813 return SE.getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 1814 1815 case Instruction::ZExt: 1816 return SE.getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 1817 1818 case Instruction::SExt: 1819 return SE.getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 1820 1821 case Instruction::BitCast: 1822 // BitCasts are no-op casts so we just eliminate the cast. 1823 if (U->getType()->isInteger() && 1824 U->getOperand(0)->getType()->isInteger()) 1825 return getSCEV(U->getOperand(0)); 1826 break; 1827 1828 case Instruction::PHI: 1829 return createNodeForPHI(cast<PHINode>(U)); 1830 1831 case Instruction::Select: 1832 // This could be a smax or umax that was lowered earlier. 1833 // Try to recover it. 1834 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 1835 Value *LHS = ICI->getOperand(0); 1836 Value *RHS = ICI->getOperand(1); 1837 switch (ICI->getPredicate()) { 1838 case ICmpInst::ICMP_SLT: 1839 case ICmpInst::ICMP_SLE: 1840 std::swap(LHS, RHS); 1841 // fall through 1842 case ICmpInst::ICMP_SGT: 1843 case ICmpInst::ICMP_SGE: 1844 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 1845 return SE.getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 1846 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 1847 // ~smax(~x, ~y) == smin(x, y). 1848 return SE.getNotSCEV(SE.getSMaxExpr( 1849 SE.getNotSCEV(getSCEV(LHS)), 1850 SE.getNotSCEV(getSCEV(RHS)))); 1851 break; 1852 case ICmpInst::ICMP_ULT: 1853 case ICmpInst::ICMP_ULE: 1854 std::swap(LHS, RHS); 1855 // fall through 1856 case ICmpInst::ICMP_UGT: 1857 case ICmpInst::ICMP_UGE: 1858 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 1859 return SE.getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 1860 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 1861 // ~umax(~x, ~y) == umin(x, y) 1862 return SE.getNotSCEV(SE.getUMaxExpr(SE.getNotSCEV(getSCEV(LHS)), 1863 SE.getNotSCEV(getSCEV(RHS)))); 1864 break; 1865 default: 1866 break; 1867 } 1868 } 1869 1870 default: // We cannot analyze this expression. 1871 break; 1872 } 1873 1874 return SE.getUnknown(V); 1875} 1876 1877 1878 1879//===----------------------------------------------------------------------===// 1880// Iteration Count Computation Code 1881// 1882 1883/// getIterationCount - If the specified loop has a predictable iteration 1884/// count, return it. Note that it is not valid to call this method on a 1885/// loop without a loop-invariant iteration count. 1886SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) { 1887 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L); 1888 if (I == IterationCounts.end()) { 1889 SCEVHandle ItCount = ComputeIterationCount(L); 1890 I = IterationCounts.insert(std::make_pair(L, ItCount)).first; 1891 if (ItCount != UnknownValue) { 1892 assert(ItCount->isLoopInvariant(L) && 1893 "Computed trip count isn't loop invariant for loop!"); 1894 ++NumTripCountsComputed; 1895 } else if (isa<PHINode>(L->getHeader()->begin())) { 1896 // Only count loops that have phi nodes as not being computable. 1897 ++NumTripCountsNotComputed; 1898 } 1899 } 1900 return I->second; 1901} 1902 1903/// ComputeIterationCount - Compute the number of times the specified loop 1904/// will iterate. 1905SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) { 1906 // If the loop has a non-one exit block count, we can't analyze it. 1907 SmallVector<BasicBlock*, 8> ExitBlocks; 1908 L->getExitBlocks(ExitBlocks); 1909 if (ExitBlocks.size() != 1) return UnknownValue; 1910 1911 // Okay, there is one exit block. Try to find the condition that causes the 1912 // loop to be exited. 1913 BasicBlock *ExitBlock = ExitBlocks[0]; 1914 1915 BasicBlock *ExitingBlock = 0; 1916 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 1917 PI != E; ++PI) 1918 if (L->contains(*PI)) { 1919 if (ExitingBlock == 0) 1920 ExitingBlock = *PI; 1921 else 1922 return UnknownValue; // More than one block exiting! 1923 } 1924 assert(ExitingBlock && "No exits from loop, something is broken!"); 1925 1926 // Okay, we've computed the exiting block. See what condition causes us to 1927 // exit. 1928 // 1929 // FIXME: we should be able to handle switch instructions (with a single exit) 1930 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 1931 if (ExitBr == 0) return UnknownValue; 1932 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 1933 1934 // At this point, we know we have a conditional branch that determines whether 1935 // the loop is exited. However, we don't know if the branch is executed each 1936 // time through the loop. If not, then the execution count of the branch will 1937 // not be equal to the trip count of the loop. 1938 // 1939 // Currently we check for this by checking to see if the Exit branch goes to 1940 // the loop header. If so, we know it will always execute the same number of 1941 // times as the loop. We also handle the case where the exit block *is* the 1942 // loop header. This is common for un-rotated loops. More extensive analysis 1943 // could be done to handle more cases here. 1944 if (ExitBr->getSuccessor(0) != L->getHeader() && 1945 ExitBr->getSuccessor(1) != L->getHeader() && 1946 ExitBr->getParent() != L->getHeader()) 1947 return UnknownValue; 1948 1949 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition()); 1950 1951 // If it's not an integer comparison then compute it the hard way. 1952 // Note that ICmpInst deals with pointer comparisons too so we must check 1953 // the type of the operand. 1954 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType())) 1955 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(), 1956 ExitBr->getSuccessor(0) == ExitBlock); 1957 1958 // If the condition was exit on true, convert the condition to exit on false 1959 ICmpInst::Predicate Cond; 1960 if (ExitBr->getSuccessor(1) == ExitBlock) 1961 Cond = ExitCond->getPredicate(); 1962 else 1963 Cond = ExitCond->getInversePredicate(); 1964 1965 // Handle common loops like: for (X = "string"; *X; ++X) 1966 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 1967 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 1968 SCEVHandle ItCnt = 1969 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond); 1970 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 1971 } 1972 1973 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 1974 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 1975 1976 // Try to evaluate any dependencies out of the loop. 1977 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 1978 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 1979 Tmp = getSCEVAtScope(RHS, L); 1980 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 1981 1982 // At this point, we would like to compute how many iterations of the 1983 // loop the predicate will return true for these inputs. 1984 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 1985 // If there is a loop-invariant, force it into the RHS. 1986 std::swap(LHS, RHS); 1987 Cond = ICmpInst::getSwappedPredicate(Cond); 1988 } 1989 1990 // FIXME: think about handling pointer comparisons! i.e.: 1991 // while (P != P+100) ++P; 1992 1993 // If we have a comparison of a chrec against a constant, try to use value 1994 // ranges to answer this query. 1995 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 1996 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 1997 if (AddRec->getLoop() == L) { 1998 // Form the comparison range using the constant of the correct type so 1999 // that the ConstantRange class knows to do a signed or unsigned 2000 // comparison. 2001 ConstantInt *CompVal = RHSC->getValue(); 2002 const Type *RealTy = ExitCond->getOperand(0)->getType(); 2003 CompVal = dyn_cast<ConstantInt>( 2004 ConstantExpr::getBitCast(CompVal, RealTy)); 2005 if (CompVal) { 2006 // Form the constant range. 2007 ConstantRange CompRange( 2008 ICmpInst::makeConstantRange(Cond, CompVal->getValue())); 2009 2010 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, SE); 2011 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 2012 } 2013 } 2014 2015 switch (Cond) { 2016 case ICmpInst::ICMP_NE: { // while (X != Y) 2017 // Convert to: while (X-Y != 0) 2018 SCEVHandle TC = HowFarToZero(SE.getMinusSCEV(LHS, RHS), L); 2019 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2020 break; 2021 } 2022 case ICmpInst::ICMP_EQ: { 2023 // Convert to: while (X-Y == 0) // while (X == Y) 2024 SCEVHandle TC = HowFarToNonZero(SE.getMinusSCEV(LHS, RHS), L); 2025 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2026 break; 2027 } 2028 case ICmpInst::ICMP_SLT: { 2029 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true); 2030 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2031 break; 2032 } 2033 case ICmpInst::ICMP_SGT: { 2034 SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS), 2035 SE.getNotSCEV(RHS), L, true); 2036 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2037 break; 2038 } 2039 case ICmpInst::ICMP_ULT: { 2040 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false); 2041 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2042 break; 2043 } 2044 case ICmpInst::ICMP_UGT: { 2045 SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS), 2046 SE.getNotSCEV(RHS), L, false); 2047 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2048 break; 2049 } 2050 default: 2051#if 0 2052 cerr << "ComputeIterationCount "; 2053 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 2054 cerr << "[unsigned] "; 2055 cerr << *LHS << " " 2056 << Instruction::getOpcodeName(Instruction::ICmp) 2057 << " " << *RHS << "\n"; 2058#endif 2059 break; 2060 } 2061 return ComputeIterationCountExhaustively(L, ExitCond, 2062 ExitBr->getSuccessor(0) == ExitBlock); 2063} 2064 2065static ConstantInt * 2066EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 2067 ScalarEvolution &SE) { 2068 SCEVHandle InVal = SE.getConstant(C); 2069 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE); 2070 assert(isa<SCEVConstant>(Val) && 2071 "Evaluation of SCEV at constant didn't fold correctly?"); 2072 return cast<SCEVConstant>(Val)->getValue(); 2073} 2074 2075/// GetAddressedElementFromGlobal - Given a global variable with an initializer 2076/// and a GEP expression (missing the pointer index) indexing into it, return 2077/// the addressed element of the initializer or null if the index expression is 2078/// invalid. 2079static Constant * 2080GetAddressedElementFromGlobal(GlobalVariable *GV, 2081 const std::vector<ConstantInt*> &Indices) { 2082 Constant *Init = GV->getInitializer(); 2083 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 2084 uint64_t Idx = Indices[i]->getZExtValue(); 2085 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 2086 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 2087 Init = cast<Constant>(CS->getOperand(Idx)); 2088 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 2089 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 2090 Init = cast<Constant>(CA->getOperand(Idx)); 2091 } else if (isa<ConstantAggregateZero>(Init)) { 2092 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 2093 assert(Idx < STy->getNumElements() && "Bad struct index!"); 2094 Init = Constant::getNullValue(STy->getElementType(Idx)); 2095 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 2096 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 2097 Init = Constant::getNullValue(ATy->getElementType()); 2098 } else { 2099 assert(0 && "Unknown constant aggregate type!"); 2100 } 2101 return 0; 2102 } else { 2103 return 0; // Unknown initializer type 2104 } 2105 } 2106 return Init; 2107} 2108 2109/// ComputeLoadConstantCompareIterationCount - Given an exit condition of 2110/// 'icmp op load X, cst', try to see if we can compute the trip count. 2111SCEVHandle ScalarEvolutionsImpl:: 2112ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS, 2113 const Loop *L, 2114 ICmpInst::Predicate predicate) { 2115 if (LI->isVolatile()) return UnknownValue; 2116 2117 // Check to see if the loaded pointer is a getelementptr of a global. 2118 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 2119 if (!GEP) return UnknownValue; 2120 2121 // Make sure that it is really a constant global we are gepping, with an 2122 // initializer, and make sure the first IDX is really 0. 2123 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 2124 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 2125 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 2126 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 2127 return UnknownValue; 2128 2129 // Okay, we allow one non-constant index into the GEP instruction. 2130 Value *VarIdx = 0; 2131 std::vector<ConstantInt*> Indexes; 2132 unsigned VarIdxNum = 0; 2133 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 2134 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 2135 Indexes.push_back(CI); 2136 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 2137 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 2138 VarIdx = GEP->getOperand(i); 2139 VarIdxNum = i-2; 2140 Indexes.push_back(0); 2141 } 2142 2143 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 2144 // Check to see if X is a loop variant variable value now. 2145 SCEVHandle Idx = getSCEV(VarIdx); 2146 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 2147 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 2148 2149 // We can only recognize very limited forms of loop index expressions, in 2150 // particular, only affine AddRec's like {C1,+,C2}. 2151 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 2152 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 2153 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 2154 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 2155 return UnknownValue; 2156 2157 unsigned MaxSteps = MaxBruteForceIterations; 2158 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 2159 ConstantInt *ItCst = 2160 ConstantInt::get(IdxExpr->getType(), IterationNum); 2161 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, SE); 2162 2163 // Form the GEP offset. 2164 Indexes[VarIdxNum] = Val; 2165 2166 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 2167 if (Result == 0) break; // Cannot compute! 2168 2169 // Evaluate the condition for this iteration. 2170 Result = ConstantExpr::getICmp(predicate, Result, RHS); 2171 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 2172 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 2173#if 0 2174 cerr << "\n***\n*** Computed loop count " << *ItCst 2175 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 2176 << "***\n"; 2177#endif 2178 ++NumArrayLenItCounts; 2179 return SE.getConstant(ItCst); // Found terminating iteration! 2180 } 2181 } 2182 return UnknownValue; 2183} 2184 2185 2186/// CanConstantFold - Return true if we can constant fold an instruction of the 2187/// specified type, assuming that all operands were constants. 2188static bool CanConstantFold(const Instruction *I) { 2189 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 2190 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 2191 return true; 2192 2193 if (const CallInst *CI = dyn_cast<CallInst>(I)) 2194 if (const Function *F = CI->getCalledFunction()) 2195 return canConstantFoldCallTo(F); 2196 return false; 2197} 2198 2199/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 2200/// in the loop that V is derived from. We allow arbitrary operations along the 2201/// way, but the operands of an operation must either be constants or a value 2202/// derived from a constant PHI. If this expression does not fit with these 2203/// constraints, return null. 2204static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 2205 // If this is not an instruction, or if this is an instruction outside of the 2206 // loop, it can't be derived from a loop PHI. 2207 Instruction *I = dyn_cast<Instruction>(V); 2208 if (I == 0 || !L->contains(I->getParent())) return 0; 2209 2210 if (PHINode *PN = dyn_cast<PHINode>(I)) { 2211 if (L->getHeader() == I->getParent()) 2212 return PN; 2213 else 2214 // We don't currently keep track of the control flow needed to evaluate 2215 // PHIs, so we cannot handle PHIs inside of loops. 2216 return 0; 2217 } 2218 2219 // If we won't be able to constant fold this expression even if the operands 2220 // are constants, return early. 2221 if (!CanConstantFold(I)) return 0; 2222 2223 // Otherwise, we can evaluate this instruction if all of its operands are 2224 // constant or derived from a PHI node themselves. 2225 PHINode *PHI = 0; 2226 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 2227 if (!(isa<Constant>(I->getOperand(Op)) || 2228 isa<GlobalValue>(I->getOperand(Op)))) { 2229 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 2230 if (P == 0) return 0; // Not evolving from PHI 2231 if (PHI == 0) 2232 PHI = P; 2233 else if (PHI != P) 2234 return 0; // Evolving from multiple different PHIs. 2235 } 2236 2237 // This is a expression evolving from a constant PHI! 2238 return PHI; 2239} 2240 2241/// EvaluateExpression - Given an expression that passes the 2242/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 2243/// in the loop has the value PHIVal. If we can't fold this expression for some 2244/// reason, return null. 2245static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 2246 if (isa<PHINode>(V)) return PHIVal; 2247 if (Constant *C = dyn_cast<Constant>(V)) return C; 2248 Instruction *I = cast<Instruction>(V); 2249 2250 std::vector<Constant*> Operands; 2251 Operands.resize(I->getNumOperands()); 2252 2253 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2254 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 2255 if (Operands[i] == 0) return 0; 2256 } 2257 2258 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2259 return ConstantFoldCompareInstOperands(CI->getPredicate(), 2260 &Operands[0], Operands.size()); 2261 else 2262 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2263 &Operands[0], Operands.size()); 2264} 2265 2266/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 2267/// in the header of its containing loop, we know the loop executes a 2268/// constant number of times, and the PHI node is just a recurrence 2269/// involving constants, fold it. 2270Constant *ScalarEvolutionsImpl:: 2271getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, const Loop *L){ 2272 std::map<PHINode*, Constant*>::iterator I = 2273 ConstantEvolutionLoopExitValue.find(PN); 2274 if (I != ConstantEvolutionLoopExitValue.end()) 2275 return I->second; 2276 2277 if (Its.ugt(APInt(Its.getBitWidth(),MaxBruteForceIterations))) 2278 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 2279 2280 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 2281 2282 // Since the loop is canonicalized, the PHI node must have two entries. One 2283 // entry must be a constant (coming in from outside of the loop), and the 2284 // second must be derived from the same PHI. 2285 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2286 Constant *StartCST = 2287 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2288 if (StartCST == 0) 2289 return RetVal = 0; // Must be a constant. 2290 2291 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2292 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2293 if (PN2 != PN) 2294 return RetVal = 0; // Not derived from same PHI. 2295 2296 // Execute the loop symbolically to determine the exit value. 2297 if (Its.getActiveBits() >= 32) 2298 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 2299 2300 unsigned NumIterations = Its.getZExtValue(); // must be in range 2301 unsigned IterationNum = 0; 2302 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 2303 if (IterationNum == NumIterations) 2304 return RetVal = PHIVal; // Got exit value! 2305 2306 // Compute the value of the PHI node for the next iteration. 2307 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2308 if (NextPHI == PHIVal) 2309 return RetVal = NextPHI; // Stopped evolving! 2310 if (NextPHI == 0) 2311 return 0; // Couldn't evaluate! 2312 PHIVal = NextPHI; 2313 } 2314} 2315 2316/// ComputeIterationCountExhaustively - If the trip is known to execute a 2317/// constant number of times (the condition evolves only from constants), 2318/// try to evaluate a few iterations of the loop until we get the exit 2319/// condition gets a value of ExitWhen (true or false). If we cannot 2320/// evaluate the trip count of the loop, return UnknownValue. 2321SCEVHandle ScalarEvolutionsImpl:: 2322ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 2323 PHINode *PN = getConstantEvolvingPHI(Cond, L); 2324 if (PN == 0) return UnknownValue; 2325 2326 // Since the loop is canonicalized, the PHI node must have two entries. One 2327 // entry must be a constant (coming in from outside of the loop), and the 2328 // second must be derived from the same PHI. 2329 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2330 Constant *StartCST = 2331 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2332 if (StartCST == 0) return UnknownValue; // Must be a constant. 2333 2334 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2335 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2336 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 2337 2338 // Okay, we find a PHI node that defines the trip count of this loop. Execute 2339 // the loop symbolically to determine when the condition gets a value of 2340 // "ExitWhen". 2341 unsigned IterationNum = 0; 2342 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 2343 for (Constant *PHIVal = StartCST; 2344 IterationNum != MaxIterations; ++IterationNum) { 2345 ConstantInt *CondVal = 2346 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 2347 2348 // Couldn't symbolically evaluate. 2349 if (!CondVal) return UnknownValue; 2350 2351 if (CondVal->getValue() == uint64_t(ExitWhen)) { 2352 ConstantEvolutionLoopExitValue[PN] = PHIVal; 2353 ++NumBruteForceTripCountsComputed; 2354 return SE.getConstant(ConstantInt::get(Type::Int32Ty, IterationNum)); 2355 } 2356 2357 // Compute the value of the PHI node for the next iteration. 2358 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2359 if (NextPHI == 0 || NextPHI == PHIVal) 2360 return UnknownValue; // Couldn't evaluate or not making progress... 2361 PHIVal = NextPHI; 2362 } 2363 2364 // Too many iterations were needed to evaluate. 2365 return UnknownValue; 2366} 2367 2368/// getSCEVAtScope - Compute the value of the specified expression within the 2369/// indicated loop (which may be null to indicate in no loop). If the 2370/// expression cannot be evaluated, return UnknownValue. 2371SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) { 2372 // FIXME: this should be turned into a virtual method on SCEV! 2373 2374 if (isa<SCEVConstant>(V)) return V; 2375 2376 // If this instruction is evolved from a constant-evolving PHI, compute the 2377 // exit value from the loop without using SCEVs. 2378 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 2379 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 2380 const Loop *LI = this->LI[I->getParent()]; 2381 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 2382 if (PHINode *PN = dyn_cast<PHINode>(I)) 2383 if (PN->getParent() == LI->getHeader()) { 2384 // Okay, there is no closed form solution for the PHI node. Check 2385 // to see if the loop that contains it has a known iteration count. 2386 // If so, we may be able to force computation of the exit value. 2387 SCEVHandle IterationCount = getIterationCount(LI); 2388 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) { 2389 // Okay, we know how many times the containing loop executes. If 2390 // this is a constant evolving PHI node, get the final value at 2391 // the specified iteration number. 2392 Constant *RV = getConstantEvolutionLoopExitValue(PN, 2393 ICC->getValue()->getValue(), 2394 LI); 2395 if (RV) return SE.getUnknown(RV); 2396 } 2397 } 2398 2399 // Okay, this is an expression that we cannot symbolically evaluate 2400 // into a SCEV. Check to see if it's possible to symbolically evaluate 2401 // the arguments into constants, and if so, try to constant propagate the 2402 // result. This is particularly useful for computing loop exit values. 2403 if (CanConstantFold(I)) { 2404 std::vector<Constant*> Operands; 2405 Operands.reserve(I->getNumOperands()); 2406 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2407 Value *Op = I->getOperand(i); 2408 if (Constant *C = dyn_cast<Constant>(Op)) { 2409 Operands.push_back(C); 2410 } else { 2411 // If any of the operands is non-constant and if they are 2412 // non-integer, don't even try to analyze them with scev techniques. 2413 if (!isa<IntegerType>(Op->getType())) 2414 return V; 2415 2416 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 2417 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 2418 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(), 2419 Op->getType(), 2420 false)); 2421 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 2422 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 2423 Operands.push_back(ConstantExpr::getIntegerCast(C, 2424 Op->getType(), 2425 false)); 2426 else 2427 return V; 2428 } else { 2429 return V; 2430 } 2431 } 2432 } 2433 2434 Constant *C; 2435 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2436 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 2437 &Operands[0], Operands.size()); 2438 else 2439 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2440 &Operands[0], Operands.size()); 2441 return SE.getUnknown(C); 2442 } 2443 } 2444 2445 // This is some other type of SCEVUnknown, just return it. 2446 return V; 2447 } 2448 2449 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 2450 // Avoid performing the look-up in the common case where the specified 2451 // expression has no loop-variant portions. 2452 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 2453 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2454 if (OpAtScope != Comm->getOperand(i)) { 2455 if (OpAtScope == UnknownValue) return UnknownValue; 2456 // Okay, at least one of these operands is loop variant but might be 2457 // foldable. Build a new instance of the folded commutative expression. 2458 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 2459 NewOps.push_back(OpAtScope); 2460 2461 for (++i; i != e; ++i) { 2462 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2463 if (OpAtScope == UnknownValue) return UnknownValue; 2464 NewOps.push_back(OpAtScope); 2465 } 2466 if (isa<SCEVAddExpr>(Comm)) 2467 return SE.getAddExpr(NewOps); 2468 if (isa<SCEVMulExpr>(Comm)) 2469 return SE.getMulExpr(NewOps); 2470 if (isa<SCEVSMaxExpr>(Comm)) 2471 return SE.getSMaxExpr(NewOps); 2472 if (isa<SCEVUMaxExpr>(Comm)) 2473 return SE.getUMaxExpr(NewOps); 2474 assert(0 && "Unknown commutative SCEV type!"); 2475 } 2476 } 2477 // If we got here, all operands are loop invariant. 2478 return Comm; 2479 } 2480 2481 if (SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 2482 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L); 2483 if (LHS == UnknownValue) return LHS; 2484 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L); 2485 if (RHS == UnknownValue) return RHS; 2486 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 2487 return Div; // must be loop invariant 2488 return SE.getUDivExpr(LHS, RHS); 2489 } 2490 2491 // If this is a loop recurrence for a loop that does not contain L, then we 2492 // are dealing with the final value computed by the loop. 2493 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 2494 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 2495 // To evaluate this recurrence, we need to know how many times the AddRec 2496 // loop iterates. Compute this now. 2497 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop()); 2498 if (IterationCount == UnknownValue) return UnknownValue; 2499 2500 // Then, evaluate the AddRec. 2501 return AddRec->evaluateAtIteration(IterationCount, SE); 2502 } 2503 return UnknownValue; 2504 } 2505 2506 //assert(0 && "Unknown SCEV type!"); 2507 return UnknownValue; 2508} 2509 2510/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 2511/// following equation: 2512/// 2513/// A * X = B (mod N) 2514/// 2515/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 2516/// A and B isn't important. 2517/// 2518/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 2519static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 2520 ScalarEvolution &SE) { 2521 uint32_t BW = A.getBitWidth(); 2522 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 2523 assert(A != 0 && "A must be non-zero."); 2524 2525 // 1. D = gcd(A, N) 2526 // 2527 // The gcd of A and N may have only one prime factor: 2. The number of 2528 // trailing zeros in A is its multiplicity 2529 uint32_t Mult2 = A.countTrailingZeros(); 2530 // D = 2^Mult2 2531 2532 // 2. Check if B is divisible by D. 2533 // 2534 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 2535 // is not less than multiplicity of this prime factor for D. 2536 if (B.countTrailingZeros() < Mult2) 2537 return new SCEVCouldNotCompute(); 2538 2539 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 2540 // modulo (N / D). 2541 // 2542 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 2543 // bit width during computations. 2544 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 2545 APInt Mod(BW + 1, 0); 2546 Mod.set(BW - Mult2); // Mod = N / D 2547 APInt I = AD.multiplicativeInverse(Mod); 2548 2549 // 4. Compute the minimum unsigned root of the equation: 2550 // I * (B / D) mod (N / D) 2551 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 2552 2553 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 2554 // bits. 2555 return SE.getConstant(Result.trunc(BW)); 2556} 2557 2558/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 2559/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 2560/// might be the same) or two SCEVCouldNotCompute objects. 2561/// 2562static std::pair<SCEVHandle,SCEVHandle> 2563SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 2564 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 2565 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 2566 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 2567 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 2568 2569 // We currently can only solve this if the coefficients are constants. 2570 if (!LC || !MC || !NC) { 2571 SCEV *CNC = new SCEVCouldNotCompute(); 2572 return std::make_pair(CNC, CNC); 2573 } 2574 2575 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 2576 const APInt &L = LC->getValue()->getValue(); 2577 const APInt &M = MC->getValue()->getValue(); 2578 const APInt &N = NC->getValue()->getValue(); 2579 APInt Two(BitWidth, 2); 2580 APInt Four(BitWidth, 4); 2581 2582 { 2583 using namespace APIntOps; 2584 const APInt& C = L; 2585 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 2586 // The B coefficient is M-N/2 2587 APInt B(M); 2588 B -= sdiv(N,Two); 2589 2590 // The A coefficient is N/2 2591 APInt A(N.sdiv(Two)); 2592 2593 // Compute the B^2-4ac term. 2594 APInt SqrtTerm(B); 2595 SqrtTerm *= B; 2596 SqrtTerm -= Four * (A * C); 2597 2598 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 2599 // integer value or else APInt::sqrt() will assert. 2600 APInt SqrtVal(SqrtTerm.sqrt()); 2601 2602 // Compute the two solutions for the quadratic formula. 2603 // The divisions must be performed as signed divisions. 2604 APInt NegB(-B); 2605 APInt TwoA( A << 1 ); 2606 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA)); 2607 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA)); 2608 2609 return std::make_pair(SE.getConstant(Solution1), 2610 SE.getConstant(Solution2)); 2611 } // end APIntOps namespace 2612} 2613 2614/// HowFarToZero - Return the number of times a backedge comparing the specified 2615/// value to zero will execute. If not computable, return UnknownValue 2616SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) { 2617 // If the value is a constant 2618 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2619 // If the value is already zero, the branch will execute zero times. 2620 if (C->getValue()->isZero()) return C; 2621 return UnknownValue; // Otherwise it will loop infinitely. 2622 } 2623 2624 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 2625 if (!AddRec || AddRec->getLoop() != L) 2626 return UnknownValue; 2627 2628 if (AddRec->isAffine()) { 2629 // If this is an affine expression, the execution count of this branch is 2630 // the minimum unsigned root of the following equation: 2631 // 2632 // Start + Step*N = 0 (mod 2^BW) 2633 // 2634 // equivalent to: 2635 // 2636 // Step*N = -Start (mod 2^BW) 2637 // 2638 // where BW is the common bit width of Start and Step. 2639 2640 // Get the initial value for the loop. 2641 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 2642 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 2643 2644 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop()); 2645 2646 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 2647 // For now we handle only constant steps. 2648 2649 // First, handle unitary steps. 2650 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 2651 return SE.getNegativeSCEV(Start); // N = -Start (as unsigned) 2652 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 2653 return Start; // N = Start (as unsigned) 2654 2655 // Then, try to solve the above equation provided that Start is constant. 2656 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 2657 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 2658 -StartC->getValue()->getValue(),SE); 2659 } 2660 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 2661 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 2662 // the quadratic equation to solve it. 2663 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec, SE); 2664 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2665 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2666 if (R1) { 2667#if 0 2668 cerr << "HFTZ: " << *V << " - sol#1: " << *R1 2669 << " sol#2: " << *R2 << "\n"; 2670#endif 2671 // Pick the smallest positive root value. 2672 if (ConstantInt *CB = 2673 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2674 R1->getValue(), R2->getValue()))) { 2675 if (CB->getZExtValue() == false) 2676 std::swap(R1, R2); // R1 is the minimum root now. 2677 2678 // We can only use this value if the chrec ends up with an exact zero 2679 // value at this index. When solving for "X*X != 5", for example, we 2680 // should not accept a root of 2. 2681 SCEVHandle Val = AddRec->evaluateAtIteration(R1, SE); 2682 if (Val->isZero()) 2683 return R1; // We found a quadratic root! 2684 } 2685 } 2686 } 2687 2688 return UnknownValue; 2689} 2690 2691/// HowFarToNonZero - Return the number of times a backedge checking the 2692/// specified value for nonzero will execute. If not computable, return 2693/// UnknownValue 2694SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) { 2695 // Loops that look like: while (X == 0) are very strange indeed. We don't 2696 // handle them yet except for the trivial case. This could be expanded in the 2697 // future as needed. 2698 2699 // If the value is a constant, check to see if it is known to be non-zero 2700 // already. If so, the backedge will execute zero times. 2701 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2702 if (!C->getValue()->isNullValue()) 2703 return SE.getIntegerSCEV(0, C->getType()); 2704 return UnknownValue; // Otherwise it will loop infinitely. 2705 } 2706 2707 // We could implement others, but I really doubt anyone writes loops like 2708 // this, and if they did, they would already be constant folded. 2709 return UnknownValue; 2710} 2711 2712/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 2713/// (which may not be an immediate predecessor) which has exactly one 2714/// successor from which BB is reachable, or null if no such block is 2715/// found. 2716/// 2717BasicBlock * 2718ScalarEvolutionsImpl::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 2719 // If the block has a unique predecessor, the predecessor must have 2720 // no other successors from which BB is reachable. 2721 if (BasicBlock *Pred = BB->getSinglePredecessor()) 2722 return Pred; 2723 2724 // A loop's header is defined to be a block that dominates the loop. 2725 // If the loop has a preheader, it must be a block that has exactly 2726 // one successor that can reach BB. This is slightly more strict 2727 // than necessary, but works if critical edges are split. 2728 if (Loop *L = LI.getLoopFor(BB)) 2729 return L->getLoopPreheader(); 2730 2731 return 0; 2732} 2733 2734/// executesAtLeastOnce - Test whether entry to the loop is protected by 2735/// a conditional between LHS and RHS. 2736bool ScalarEvolutionsImpl::executesAtLeastOnce(const Loop *L, bool isSigned, 2737 SCEV *LHS, SCEV *RHS) { 2738 BasicBlock *Preheader = L->getLoopPreheader(); 2739 BasicBlock *PreheaderDest = L->getHeader(); 2740 2741 // Starting at the preheader, climb up the predecessor chain, as long as 2742 // there are predecessors that can be found that have unique successors 2743 // leading to the original header. 2744 for (; Preheader; 2745 PreheaderDest = Preheader, 2746 Preheader = getPredecessorWithUniqueSuccessorForBB(Preheader)) { 2747 2748 BranchInst *LoopEntryPredicate = 2749 dyn_cast<BranchInst>(Preheader->getTerminator()); 2750 if (!LoopEntryPredicate || 2751 LoopEntryPredicate->isUnconditional()) 2752 continue; 2753 2754 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition()); 2755 if (!ICI) continue; 2756 2757 // Now that we found a conditional branch that dominates the loop, check to 2758 // see if it is the comparison we are looking for. 2759 Value *PreCondLHS = ICI->getOperand(0); 2760 Value *PreCondRHS = ICI->getOperand(1); 2761 ICmpInst::Predicate Cond; 2762 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest) 2763 Cond = ICI->getPredicate(); 2764 else 2765 Cond = ICI->getInversePredicate(); 2766 2767 switch (Cond) { 2768 case ICmpInst::ICMP_UGT: 2769 if (isSigned) continue; 2770 std::swap(PreCondLHS, PreCondRHS); 2771 Cond = ICmpInst::ICMP_ULT; 2772 break; 2773 case ICmpInst::ICMP_SGT: 2774 if (!isSigned) continue; 2775 std::swap(PreCondLHS, PreCondRHS); 2776 Cond = ICmpInst::ICMP_SLT; 2777 break; 2778 case ICmpInst::ICMP_ULT: 2779 if (isSigned) continue; 2780 break; 2781 case ICmpInst::ICMP_SLT: 2782 if (!isSigned) continue; 2783 break; 2784 default: 2785 continue; 2786 } 2787 2788 if (!PreCondLHS->getType()->isInteger()) continue; 2789 2790 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS); 2791 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS); 2792 if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) || 2793 (LHS == SE.getNotSCEV(PreCondRHSSCEV) && 2794 RHS == SE.getNotSCEV(PreCondLHSSCEV))) 2795 return true; 2796 } 2797 2798 return false; 2799} 2800 2801/// HowManyLessThans - Return the number of times a backedge containing the 2802/// specified less-than comparison will execute. If not computable, return 2803/// UnknownValue. 2804SCEVHandle ScalarEvolutionsImpl:: 2805HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) { 2806 // Only handle: "ADDREC < LoopInvariant". 2807 if (!RHS->isLoopInvariant(L)) return UnknownValue; 2808 2809 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 2810 if (!AddRec || AddRec->getLoop() != L) 2811 return UnknownValue; 2812 2813 if (AddRec->isAffine()) { 2814 // FORNOW: We only support unit strides. 2815 SCEVHandle One = SE.getIntegerSCEV(1, RHS->getType()); 2816 if (AddRec->getOperand(1) != One) 2817 return UnknownValue; 2818 2819 // We know the LHS is of the form {n,+,1} and the RHS is some loop-invariant 2820 // m. So, we count the number of iterations in which {n,+,1} < m is true. 2821 // Note that we cannot simply return max(m-n,0) because it's not safe to 2822 // treat m-n as signed nor unsigned due to overflow possibility. 2823 2824 // First, we get the value of the LHS in the first iteration: n 2825 SCEVHandle Start = AddRec->getOperand(0); 2826 2827 if (executesAtLeastOnce(L, isSigned, 2828 SE.getMinusSCEV(AddRec->getOperand(0), One), RHS)) { 2829 // Since we know that the condition is true in order to enter the loop, 2830 // we know that it will run exactly m-n times. 2831 return SE.getMinusSCEV(RHS, Start); 2832 } else { 2833 // Then, we get the value of the LHS in the first iteration in which the 2834 // above condition doesn't hold. This equals to max(m,n). 2835 SCEVHandle End = isSigned ? SE.getSMaxExpr(RHS, Start) 2836 : SE.getUMaxExpr(RHS, Start); 2837 2838 // Finally, we subtract these two values to get the number of times the 2839 // backedge is executed: max(m,n)-n. 2840 return SE.getMinusSCEV(End, Start); 2841 } 2842 } 2843 2844 return UnknownValue; 2845} 2846 2847/// getNumIterationsInRange - Return the number of iterations of this loop that 2848/// produce values in the specified constant range. Another way of looking at 2849/// this is that it returns the first iteration number where the value is not in 2850/// the condition, thus computing the exit count. If the iteration count can't 2851/// be computed, an instance of SCEVCouldNotCompute is returned. 2852SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 2853 ScalarEvolution &SE) const { 2854 if (Range.isFullSet()) // Infinite loop. 2855 return new SCEVCouldNotCompute(); 2856 2857 // If the start is a non-zero constant, shift the range to simplify things. 2858 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 2859 if (!SC->getValue()->isZero()) { 2860 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 2861 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 2862 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop()); 2863 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 2864 return ShiftedAddRec->getNumIterationsInRange( 2865 Range.subtract(SC->getValue()->getValue()), SE); 2866 // This is strange and shouldn't happen. 2867 return new SCEVCouldNotCompute(); 2868 } 2869 2870 // The only time we can solve this is when we have all constant indices. 2871 // Otherwise, we cannot determine the overflow conditions. 2872 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 2873 if (!isa<SCEVConstant>(getOperand(i))) 2874 return new SCEVCouldNotCompute(); 2875 2876 2877 // Okay at this point we know that all elements of the chrec are constants and 2878 // that the start element is zero. 2879 2880 // First check to see if the range contains zero. If not, the first 2881 // iteration exits. 2882 if (!Range.contains(APInt(getBitWidth(),0))) 2883 return SE.getConstant(ConstantInt::get(getType(),0)); 2884 2885 if (isAffine()) { 2886 // If this is an affine expression then we have this situation: 2887 // Solve {0,+,A} in Range === Ax in Range 2888 2889 // We know that zero is in the range. If A is positive then we know that 2890 // the upper value of the range must be the first possible exit value. 2891 // If A is negative then the lower of the range is the last possible loop 2892 // value. Also note that we already checked for a full range. 2893 APInt One(getBitWidth(),1); 2894 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 2895 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 2896 2897 // The exit value should be (End+A)/A. 2898 APInt ExitVal = (End + A).udiv(A); 2899 ConstantInt *ExitValue = ConstantInt::get(ExitVal); 2900 2901 // Evaluate at the exit value. If we really did fall out of the valid 2902 // range, then we computed our trip count, otherwise wrap around or other 2903 // things must have happened. 2904 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 2905 if (Range.contains(Val->getValue())) 2906 return new SCEVCouldNotCompute(); // Something strange happened 2907 2908 // Ensure that the previous value is in the range. This is a sanity check. 2909 assert(Range.contains( 2910 EvaluateConstantChrecAtConstant(this, 2911 ConstantInt::get(ExitVal - One), SE)->getValue()) && 2912 "Linear scev computation is off in a bad way!"); 2913 return SE.getConstant(ExitValue); 2914 } else if (isQuadratic()) { 2915 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 2916 // quadratic equation to solve it. To do this, we must frame our problem in 2917 // terms of figuring out when zero is crossed, instead of when 2918 // Range.getUpper() is crossed. 2919 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 2920 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 2921 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 2922 2923 // Next, solve the constructed addrec 2924 std::pair<SCEVHandle,SCEVHandle> Roots = 2925 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 2926 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2927 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2928 if (R1) { 2929 // Pick the smallest positive root value. 2930 if (ConstantInt *CB = 2931 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2932 R1->getValue(), R2->getValue()))) { 2933 if (CB->getZExtValue() == false) 2934 std::swap(R1, R2); // R1 is the minimum root now. 2935 2936 // Make sure the root is not off by one. The returned iteration should 2937 // not be in the range, but the previous one should be. When solving 2938 // for "X*X < 5", for example, we should not return a root of 2. 2939 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 2940 R1->getValue(), 2941 SE); 2942 if (Range.contains(R1Val->getValue())) { 2943 // The next iteration must be out of the range... 2944 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1); 2945 2946 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 2947 if (!Range.contains(R1Val->getValue())) 2948 return SE.getConstant(NextVal); 2949 return new SCEVCouldNotCompute(); // Something strange happened 2950 } 2951 2952 // If R1 was not in the range, then it is a good return value. Make 2953 // sure that R1-1 WAS in the range though, just in case. 2954 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1); 2955 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 2956 if (Range.contains(R1Val->getValue())) 2957 return R1; 2958 return new SCEVCouldNotCompute(); // Something strange happened 2959 } 2960 } 2961 } 2962 2963 // Fallback, if this is a general polynomial, figure out the progression 2964 // through brute force: evaluate until we find an iteration that fails the 2965 // test. This is likely to be slow, but getting an accurate trip count is 2966 // incredibly important, we will be able to simplify the exit test a lot, and 2967 // we are almost guaranteed to get a trip count in this case. 2968 ConstantInt *TestVal = ConstantInt::get(getType(), 0); 2969 ConstantInt *EndVal = TestVal; // Stop when we wrap around. 2970 do { 2971 ++NumBruteForceEvaluations; 2972 SCEVHandle Val = evaluateAtIteration(SE.getConstant(TestVal), SE); 2973 if (!isa<SCEVConstant>(Val)) // This shouldn't happen. 2974 return new SCEVCouldNotCompute(); 2975 2976 // Check to see if we found the value! 2977 if (!Range.contains(cast<SCEVConstant>(Val)->getValue()->getValue())) 2978 return SE.getConstant(TestVal); 2979 2980 // Increment to test the next index. 2981 TestVal = ConstantInt::get(TestVal->getValue()+1); 2982 } while (TestVal != EndVal); 2983 2984 return new SCEVCouldNotCompute(); 2985} 2986 2987 2988 2989//===----------------------------------------------------------------------===// 2990// ScalarEvolution Class Implementation 2991//===----------------------------------------------------------------------===// 2992 2993bool ScalarEvolution::runOnFunction(Function &F) { 2994 Impl = new ScalarEvolutionsImpl(*this, F, getAnalysis<LoopInfo>()); 2995 return false; 2996} 2997 2998void ScalarEvolution::releaseMemory() { 2999 delete (ScalarEvolutionsImpl*)Impl; 3000 Impl = 0; 3001} 3002 3003void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 3004 AU.setPreservesAll(); 3005 AU.addRequiredTransitive<LoopInfo>(); 3006} 3007 3008SCEVHandle ScalarEvolution::getSCEV(Value *V) const { 3009 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V); 3010} 3011 3012/// hasSCEV - Return true if the SCEV for this value has already been 3013/// computed. 3014bool ScalarEvolution::hasSCEV(Value *V) const { 3015 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V); 3016} 3017 3018 3019/// setSCEV - Insert the specified SCEV into the map of current SCEVs for 3020/// the specified value. 3021void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) { 3022 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H); 3023} 3024 3025 3026SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const { 3027 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L); 3028} 3029 3030bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const { 3031 return !isa<SCEVCouldNotCompute>(getIterationCount(L)); 3032} 3033 3034SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const { 3035 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L); 3036} 3037 3038void ScalarEvolution::deleteValueFromRecords(Value *V) const { 3039 return ((ScalarEvolutionsImpl*)Impl)->deleteValueFromRecords(V); 3040} 3041 3042static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE, 3043 const Loop *L) { 3044 // Print all inner loops first 3045 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 3046 PrintLoopInfo(OS, SE, *I); 3047 3048 OS << "Loop " << L->getHeader()->getName() << ": "; 3049 3050 SmallVector<BasicBlock*, 8> ExitBlocks; 3051 L->getExitBlocks(ExitBlocks); 3052 if (ExitBlocks.size() != 1) 3053 OS << "<multiple exits> "; 3054 3055 if (SE->hasLoopInvariantIterationCount(L)) { 3056 OS << *SE->getIterationCount(L) << " iterations! "; 3057 } else { 3058 OS << "Unpredictable iteration count. "; 3059 } 3060 3061 OS << "\n"; 3062} 3063 3064void ScalarEvolution::print(std::ostream &OS, const Module* ) const { 3065 Function &F = ((ScalarEvolutionsImpl*)Impl)->F; 3066 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI; 3067 3068 OS << "Classifying expressions for: " << F.getName() << "\n"; 3069 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 3070 if (I->getType()->isInteger()) { 3071 OS << *I; 3072 OS << " --> "; 3073 SCEVHandle SV = getSCEV(&*I); 3074 SV->print(OS); 3075 OS << "\t\t"; 3076 3077 if (const Loop *L = LI.getLoopFor((*I).getParent())) { 3078 OS << "Exits: "; 3079 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop()); 3080 if (isa<SCEVCouldNotCompute>(ExitValue)) { 3081 OS << "<<Unknown>>"; 3082 } else { 3083 OS << *ExitValue; 3084 } 3085 } 3086 3087 3088 OS << "\n"; 3089 } 3090 3091 OS << "Determining loop execution counts for: " << F.getName() << "\n"; 3092 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I) 3093 PrintLoopInfo(OS, this, *I); 3094} 3095