1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===// 2 // 3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. 4 // See https://llvm.org/LICENSE.txt for license information. 5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception 6 // 7 //===----------------------------------------------------------------------===// 8 // 9 // This file contains the implementation of the scalar evolution analysis 10 // engine, which is used primarily to analyze expressions involving induction 11 // variables in loops. 12 // 13 // There are several aspects to this library. First is the representation of 14 // scalar expressions, which are represented as subclasses of the SCEV class. 15 // These classes are used to represent certain types of subexpressions that we 16 // can handle. We only create one SCEV of a particular shape, so 17 // pointer-comparisons for equality are legal. 18 // 19 // One important aspect of the SCEV objects is that they are never cyclic, even 20 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If 21 // the PHI node is one of the idioms that we can represent (e.g., a polynomial 22 // recurrence) then we represent it directly as a recurrence node, otherwise we 23 // represent it as a SCEVUnknown node. 24 // 25 // In addition to being able to represent expressions of various types, we also 26 // have folders that are used to build the *canonical* representation for a 27 // particular expression. These folders are capable of using a variety of 28 // rewrite rules to simplify the expressions. 29 // 30 // Once the folders are defined, we can implement the more interesting 31 // higher-level code, such as the code that recognizes PHI nodes of various 32 // types, computes the execution count of a loop, etc. 33 // 34 // TODO: We should use these routines and value representations to implement 35 // dependence analysis! 36 // 37 //===----------------------------------------------------------------------===// 38 // 39 // There are several good references for the techniques used in this analysis. 40 // 41 // Chains of recurrences -- a method to expedite the evaluation 42 // of closed-form functions 43 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima 44 // 45 // On computational properties of chains of recurrences 46 // Eugene V. Zima 47 // 48 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization 49 // Robert A. van Engelen 50 // 51 // Efficient Symbolic Analysis for Optimizing Compilers 52 // Robert A. van Engelen 53 // 54 // Using the chains of recurrences algebra for data dependence testing and 55 // induction variable substitution 56 // MS Thesis, Johnie Birch 57 // 58 //===----------------------------------------------------------------------===// 59 60 #include "llvm/Analysis/ScalarEvolution.h" 61 #include "llvm/ADT/APInt.h" 62 #include "llvm/ADT/ArrayRef.h" 63 #include "llvm/ADT/DenseMap.h" 64 #include "llvm/ADT/DepthFirstIterator.h" 65 #include "llvm/ADT/EquivalenceClasses.h" 66 #include "llvm/ADT/FoldingSet.h" 67 #include "llvm/ADT/None.h" 68 #include "llvm/ADT/Optional.h" 69 #include "llvm/ADT/STLExtras.h" 70 #include "llvm/ADT/ScopeExit.h" 71 #include "llvm/ADT/Sequence.h" 72 #include "llvm/ADT/SetVector.h" 73 #include "llvm/ADT/SmallPtrSet.h" 74 #include "llvm/ADT/SmallSet.h" 75 #include "llvm/ADT/SmallVector.h" 76 #include "llvm/ADT/Statistic.h" 77 #include "llvm/ADT/StringRef.h" 78 #include "llvm/Analysis/AssumptionCache.h" 79 #include "llvm/Analysis/ConstantFolding.h" 80 #include "llvm/Analysis/InstructionSimplify.h" 81 #include "llvm/Analysis/LoopInfo.h" 82 #include "llvm/Analysis/ScalarEvolutionDivision.h" 83 #include "llvm/Analysis/ScalarEvolutionExpressions.h" 84 #include "llvm/Analysis/TargetLibraryInfo.h" 85 #include "llvm/Analysis/ValueTracking.h" 86 #include "llvm/Config/llvm-config.h" 87 #include "llvm/IR/Argument.h" 88 #include "llvm/IR/BasicBlock.h" 89 #include "llvm/IR/CFG.h" 90 #include "llvm/IR/Constant.h" 91 #include "llvm/IR/ConstantRange.h" 92 #include "llvm/IR/Constants.h" 93 #include "llvm/IR/DataLayout.h" 94 #include "llvm/IR/DerivedTypes.h" 95 #include "llvm/IR/Dominators.h" 96 #include "llvm/IR/Function.h" 97 #include "llvm/IR/GlobalAlias.h" 98 #include "llvm/IR/GlobalValue.h" 99 #include "llvm/IR/GlobalVariable.h" 100 #include "llvm/IR/InstIterator.h" 101 #include "llvm/IR/InstrTypes.h" 102 #include "llvm/IR/Instruction.h" 103 #include "llvm/IR/Instructions.h" 104 #include "llvm/IR/IntrinsicInst.h" 105 #include "llvm/IR/Intrinsics.h" 106 #include "llvm/IR/LLVMContext.h" 107 #include "llvm/IR/Metadata.h" 108 #include "llvm/IR/Operator.h" 109 #include "llvm/IR/PatternMatch.h" 110 #include "llvm/IR/Type.h" 111 #include "llvm/IR/Use.h" 112 #include "llvm/IR/User.h" 113 #include "llvm/IR/Value.h" 114 #include "llvm/IR/Verifier.h" 115 #include "llvm/InitializePasses.h" 116 #include "llvm/Pass.h" 117 #include "llvm/Support/Casting.h" 118 #include "llvm/Support/CommandLine.h" 119 #include "llvm/Support/Compiler.h" 120 #include "llvm/Support/Debug.h" 121 #include "llvm/Support/ErrorHandling.h" 122 #include "llvm/Support/KnownBits.h" 123 #include "llvm/Support/SaveAndRestore.h" 124 #include "llvm/Support/raw_ostream.h" 125 #include <algorithm> 126 #include <cassert> 127 #include <climits> 128 #include <cstddef> 129 #include <cstdint> 130 #include <cstdlib> 131 #include <map> 132 #include <memory> 133 #include <tuple> 134 #include <utility> 135 #include <vector> 136 137 using namespace llvm; 138 using namespace PatternMatch; 139 140 #define DEBUG_TYPE "scalar-evolution" 141 142 STATISTIC(NumArrayLenItCounts, 143 "Number of trip counts computed with array length"); 144 STATISTIC(NumTripCountsComputed, 145 "Number of loops with predictable loop counts"); 146 STATISTIC(NumTripCountsNotComputed, 147 "Number of loops without predictable loop counts"); 148 STATISTIC(NumBruteForceTripCountsComputed, 149 "Number of loops with trip counts computed by force"); 150 151 static cl::opt<unsigned> 152 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 153 cl::ZeroOrMore, 154 cl::desc("Maximum number of iterations SCEV will " 155 "symbolically execute a constant " 156 "derived loop"), 157 cl::init(100)); 158 159 // FIXME: Enable this with EXPENSIVE_CHECKS when the test suite is clean. 160 static cl::opt<bool> VerifySCEV( 161 "verify-scev", cl::Hidden, 162 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)")); 163 static cl::opt<bool> VerifySCEVStrict( 164 "verify-scev-strict", cl::Hidden, 165 cl::desc("Enable stricter verification with -verify-scev is passed")); 166 static cl::opt<bool> 167 VerifySCEVMap("verify-scev-maps", cl::Hidden, 168 cl::desc("Verify no dangling value in ScalarEvolution's " 169 "ExprValueMap (slow)")); 170 171 static cl::opt<bool> VerifyIR( 172 "scev-verify-ir", cl::Hidden, 173 cl::desc("Verify IR correctness when making sensitive SCEV queries (slow)"), 174 cl::init(false)); 175 176 static cl::opt<unsigned> MulOpsInlineThreshold( 177 "scev-mulops-inline-threshold", cl::Hidden, 178 cl::desc("Threshold for inlining multiplication operands into a SCEV"), 179 cl::init(32)); 180 181 static cl::opt<unsigned> AddOpsInlineThreshold( 182 "scev-addops-inline-threshold", cl::Hidden, 183 cl::desc("Threshold for inlining addition operands into a SCEV"), 184 cl::init(500)); 185 186 static cl::opt<unsigned> MaxSCEVCompareDepth( 187 "scalar-evolution-max-scev-compare-depth", cl::Hidden, 188 cl::desc("Maximum depth of recursive SCEV complexity comparisons"), 189 cl::init(32)); 190 191 static cl::opt<unsigned> MaxSCEVOperationsImplicationDepth( 192 "scalar-evolution-max-scev-operations-implication-depth", cl::Hidden, 193 cl::desc("Maximum depth of recursive SCEV operations implication analysis"), 194 cl::init(2)); 195 196 static cl::opt<unsigned> MaxValueCompareDepth( 197 "scalar-evolution-max-value-compare-depth", cl::Hidden, 198 cl::desc("Maximum depth of recursive value complexity comparisons"), 199 cl::init(2)); 200 201 static cl::opt<unsigned> 202 MaxArithDepth("scalar-evolution-max-arith-depth", cl::Hidden, 203 cl::desc("Maximum depth of recursive arithmetics"), 204 cl::init(32)); 205 206 static cl::opt<unsigned> MaxConstantEvolvingDepth( 207 "scalar-evolution-max-constant-evolving-depth", cl::Hidden, 208 cl::desc("Maximum depth of recursive constant evolving"), cl::init(32)); 209 210 static cl::opt<unsigned> 211 MaxCastDepth("scalar-evolution-max-cast-depth", cl::Hidden, 212 cl::desc("Maximum depth of recursive SExt/ZExt/Trunc"), 213 cl::init(8)); 214 215 static cl::opt<unsigned> 216 MaxAddRecSize("scalar-evolution-max-add-rec-size", cl::Hidden, 217 cl::desc("Max coefficients in AddRec during evolving"), 218 cl::init(8)); 219 220 static cl::opt<unsigned> 221 HugeExprThreshold("scalar-evolution-huge-expr-threshold", cl::Hidden, 222 cl::desc("Size of the expression which is considered huge"), 223 cl::init(4096)); 224 225 static cl::opt<bool> 226 ClassifyExpressions("scalar-evolution-classify-expressions", 227 cl::Hidden, cl::init(true), 228 cl::desc("When printing analysis, include information on every instruction")); 229 230 static cl::opt<bool> UseExpensiveRangeSharpening( 231 "scalar-evolution-use-expensive-range-sharpening", cl::Hidden, 232 cl::init(false), 233 cl::desc("Use more powerful methods of sharpening expression ranges. May " 234 "be costly in terms of compile time")); 235 236 //===----------------------------------------------------------------------===// 237 // SCEV class definitions 238 //===----------------------------------------------------------------------===// 239 240 //===----------------------------------------------------------------------===// 241 // Implementation of the SCEV class. 242 // 243 244 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP) 245 LLVM_DUMP_METHOD void SCEV::dump() const { 246 print(dbgs()); 247 dbgs() << '\n'; 248 } 249 #endif 250 251 void SCEV::print(raw_ostream &OS) const { 252 switch (getSCEVType()) { 253 case scConstant: 254 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false); 255 return; 256 case scPtrToInt: { 257 const SCEVPtrToIntExpr *PtrToInt = cast<SCEVPtrToIntExpr>(this); 258 const SCEV *Op = PtrToInt->getOperand(); 259 OS << "(ptrtoint " << *Op->getType() << " " << *Op << " to " 260 << *PtrToInt->getType() << ")"; 261 return; 262 } 263 case scTruncate: { 264 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this); 265 const SCEV *Op = Trunc->getOperand(); 266 OS << "(trunc " << *Op->getType() << " " << *Op << " to " 267 << *Trunc->getType() << ")"; 268 return; 269 } 270 case scZeroExtend: { 271 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this); 272 const SCEV *Op = ZExt->getOperand(); 273 OS << "(zext " << *Op->getType() << " " << *Op << " to " 274 << *ZExt->getType() << ")"; 275 return; 276 } 277 case scSignExtend: { 278 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this); 279 const SCEV *Op = SExt->getOperand(); 280 OS << "(sext " << *Op->getType() << " " << *Op << " to " 281 << *SExt->getType() << ")"; 282 return; 283 } 284 case scAddRecExpr: { 285 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this); 286 OS << "{" << *AR->getOperand(0); 287 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i) 288 OS << ",+," << *AR->getOperand(i); 289 OS << "}<"; 290 if (AR->hasNoUnsignedWrap()) 291 OS << "nuw><"; 292 if (AR->hasNoSignedWrap()) 293 OS << "nsw><"; 294 if (AR->hasNoSelfWrap() && 295 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW))) 296 OS << "nw><"; 297 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false); 298 OS << ">"; 299 return; 300 } 301 case scAddExpr: 302 case scMulExpr: 303 case scUMaxExpr: 304 case scSMaxExpr: 305 case scUMinExpr: 306 case scSMinExpr: { 307 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this); 308 const char *OpStr = nullptr; 309 switch (NAry->getSCEVType()) { 310 case scAddExpr: OpStr = " + "; break; 311 case scMulExpr: OpStr = " * "; break; 312 case scUMaxExpr: OpStr = " umax "; break; 313 case scSMaxExpr: OpStr = " smax "; break; 314 case scUMinExpr: 315 OpStr = " umin "; 316 break; 317 case scSMinExpr: 318 OpStr = " smin "; 319 break; 320 default: 321 llvm_unreachable("There are no other nary expression types."); 322 } 323 OS << "("; 324 ListSeparator LS(OpStr); 325 for (const SCEV *Op : NAry->operands()) 326 OS << LS << *Op; 327 OS << ")"; 328 switch (NAry->getSCEVType()) { 329 case scAddExpr: 330 case scMulExpr: 331 if (NAry->hasNoUnsignedWrap()) 332 OS << "<nuw>"; 333 if (NAry->hasNoSignedWrap()) 334 OS << "<nsw>"; 335 break; 336 default: 337 // Nothing to print for other nary expressions. 338 break; 339 } 340 return; 341 } 342 case scUDivExpr: { 343 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this); 344 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")"; 345 return; 346 } 347 case scUnknown: { 348 const SCEVUnknown *U = cast<SCEVUnknown>(this); 349 Type *AllocTy; 350 if (U->isSizeOf(AllocTy)) { 351 OS << "sizeof(" << *AllocTy << ")"; 352 return; 353 } 354 if (U->isAlignOf(AllocTy)) { 355 OS << "alignof(" << *AllocTy << ")"; 356 return; 357 } 358 359 Type *CTy; 360 Constant *FieldNo; 361 if (U->isOffsetOf(CTy, FieldNo)) { 362 OS << "offsetof(" << *CTy << ", "; 363 FieldNo->printAsOperand(OS, false); 364 OS << ")"; 365 return; 366 } 367 368 // Otherwise just print it normally. 369 U->getValue()->printAsOperand(OS, false); 370 return; 371 } 372 case scCouldNotCompute: 373 OS << "***COULDNOTCOMPUTE***"; 374 return; 375 } 376 llvm_unreachable("Unknown SCEV kind!"); 377 } 378 379 Type *SCEV::getType() const { 380 switch (getSCEVType()) { 381 case scConstant: 382 return cast<SCEVConstant>(this)->getType(); 383 case scPtrToInt: 384 case scTruncate: 385 case scZeroExtend: 386 case scSignExtend: 387 return cast<SCEVCastExpr>(this)->getType(); 388 case scAddRecExpr: 389 case scMulExpr: 390 case scUMaxExpr: 391 case scSMaxExpr: 392 case scUMinExpr: 393 case scSMinExpr: 394 return cast<SCEVNAryExpr>(this)->getType(); 395 case scAddExpr: 396 return cast<SCEVAddExpr>(this)->getType(); 397 case scUDivExpr: 398 return cast<SCEVUDivExpr>(this)->getType(); 399 case scUnknown: 400 return cast<SCEVUnknown>(this)->getType(); 401 case scCouldNotCompute: 402 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 403 } 404 llvm_unreachable("Unknown SCEV kind!"); 405 } 406 407 bool SCEV::isZero() const { 408 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 409 return SC->getValue()->isZero(); 410 return false; 411 } 412 413 bool SCEV::isOne() const { 414 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 415 return SC->getValue()->isOne(); 416 return false; 417 } 418 419 bool SCEV::isAllOnesValue() const { 420 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 421 return SC->getValue()->isMinusOne(); 422 return false; 423 } 424 425 bool SCEV::isNonConstantNegative() const { 426 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this); 427 if (!Mul) return false; 428 429 // If there is a constant factor, it will be first. 430 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0)); 431 if (!SC) return false; 432 433 // Return true if the value is negative, this matches things like (-42 * V). 434 return SC->getAPInt().isNegative(); 435 } 436 437 SCEVCouldNotCompute::SCEVCouldNotCompute() : 438 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute, 0) {} 439 440 bool SCEVCouldNotCompute::classof(const SCEV *S) { 441 return S->getSCEVType() == scCouldNotCompute; 442 } 443 444 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { 445 FoldingSetNodeID ID; 446 ID.AddInteger(scConstant); 447 ID.AddPointer(V); 448 void *IP = nullptr; 449 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 450 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V); 451 UniqueSCEVs.InsertNode(S, IP); 452 return S; 453 } 454 455 const SCEV *ScalarEvolution::getConstant(const APInt &Val) { 456 return getConstant(ConstantInt::get(getContext(), Val)); 457 } 458 459 const SCEV * 460 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) { 461 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 462 return getConstant(ConstantInt::get(ITy, V, isSigned)); 463 } 464 465 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, SCEVTypes SCEVTy, 466 const SCEV *op, Type *ty) 467 : SCEV(ID, SCEVTy, computeExpressionSize(op)), Ty(ty) { 468 Operands[0] = op; 469 } 470 471 SCEVPtrToIntExpr::SCEVPtrToIntExpr(const FoldingSetNodeIDRef ID, const SCEV *Op, 472 Type *ITy) 473 : SCEVCastExpr(ID, scPtrToInt, Op, ITy) { 474 assert(getOperand()->getType()->isPointerTy() && Ty->isIntegerTy() && 475 "Must be a non-bit-width-changing pointer-to-integer cast!"); 476 } 477 478 SCEVIntegralCastExpr::SCEVIntegralCastExpr(const FoldingSetNodeIDRef ID, 479 SCEVTypes SCEVTy, const SCEV *op, 480 Type *ty) 481 : SCEVCastExpr(ID, SCEVTy, op, ty) {} 482 483 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, const SCEV *op, 484 Type *ty) 485 : SCEVIntegralCastExpr(ID, scTruncate, op, ty) { 486 assert(getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && 487 "Cannot truncate non-integer value!"); 488 } 489 490 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID, 491 const SCEV *op, Type *ty) 492 : SCEVIntegralCastExpr(ID, scZeroExtend, op, ty) { 493 assert(getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && 494 "Cannot zero extend non-integer value!"); 495 } 496 497 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID, 498 const SCEV *op, Type *ty) 499 : SCEVIntegralCastExpr(ID, scSignExtend, op, ty) { 500 assert(getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && 501 "Cannot sign extend non-integer value!"); 502 } 503 504 void SCEVUnknown::deleted() { 505 // Clear this SCEVUnknown from various maps. 506 SE->forgetMemoizedResults(this); 507 508 // Remove this SCEVUnknown from the uniquing map. 509 SE->UniqueSCEVs.RemoveNode(this); 510 511 // Release the value. 512 setValPtr(nullptr); 513 } 514 515 void SCEVUnknown::allUsesReplacedWith(Value *New) { 516 // Remove this SCEVUnknown from the uniquing map. 517 SE->UniqueSCEVs.RemoveNode(this); 518 519 // Update this SCEVUnknown to point to the new value. This is needed 520 // because there may still be outstanding SCEVs which still point to 521 // this SCEVUnknown. 522 setValPtr(New); 523 } 524 525 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const { 526 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 527 if (VCE->getOpcode() == Instruction::PtrToInt) 528 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 529 if (CE->getOpcode() == Instruction::GetElementPtr && 530 CE->getOperand(0)->isNullValue() && 531 CE->getNumOperands() == 2) 532 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1))) 533 if (CI->isOne()) { 534 AllocTy = cast<PointerType>(CE->getOperand(0)->getType()) 535 ->getElementType(); 536 return true; 537 } 538 539 return false; 540 } 541 542 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const { 543 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 544 if (VCE->getOpcode() == Instruction::PtrToInt) 545 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 546 if (CE->getOpcode() == Instruction::GetElementPtr && 547 CE->getOperand(0)->isNullValue()) { 548 Type *Ty = 549 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 550 if (StructType *STy = dyn_cast<StructType>(Ty)) 551 if (!STy->isPacked() && 552 CE->getNumOperands() == 3 && 553 CE->getOperand(1)->isNullValue()) { 554 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2))) 555 if (CI->isOne() && 556 STy->getNumElements() == 2 && 557 STy->getElementType(0)->isIntegerTy(1)) { 558 AllocTy = STy->getElementType(1); 559 return true; 560 } 561 } 562 } 563 564 return false; 565 } 566 567 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const { 568 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 569 if (VCE->getOpcode() == Instruction::PtrToInt) 570 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 571 if (CE->getOpcode() == Instruction::GetElementPtr && 572 CE->getNumOperands() == 3 && 573 CE->getOperand(0)->isNullValue() && 574 CE->getOperand(1)->isNullValue()) { 575 Type *Ty = 576 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 577 // Ignore vector types here so that ScalarEvolutionExpander doesn't 578 // emit getelementptrs that index into vectors. 579 if (Ty->isStructTy() || Ty->isArrayTy()) { 580 CTy = Ty; 581 FieldNo = CE->getOperand(2); 582 return true; 583 } 584 } 585 586 return false; 587 } 588 589 //===----------------------------------------------------------------------===// 590 // SCEV Utilities 591 //===----------------------------------------------------------------------===// 592 593 /// Compare the two values \p LV and \p RV in terms of their "complexity" where 594 /// "complexity" is a partial (and somewhat ad-hoc) relation used to order 595 /// operands in SCEV expressions. \p EqCache is a set of pairs of values that 596 /// have been previously deemed to be "equally complex" by this routine. It is 597 /// intended to avoid exponential time complexity in cases like: 598 /// 599 /// %a = f(%x, %y) 600 /// %b = f(%a, %a) 601 /// %c = f(%b, %b) 602 /// 603 /// %d = f(%x, %y) 604 /// %e = f(%d, %d) 605 /// %f = f(%e, %e) 606 /// 607 /// CompareValueComplexity(%f, %c) 608 /// 609 /// Since we do not continue running this routine on expression trees once we 610 /// have seen unequal values, there is no need to track them in the cache. 611 static int 612 CompareValueComplexity(EquivalenceClasses<const Value *> &EqCacheValue, 613 const LoopInfo *const LI, Value *LV, Value *RV, 614 unsigned Depth) { 615 if (Depth > MaxValueCompareDepth || EqCacheValue.isEquivalent(LV, RV)) 616 return 0; 617 618 // Order pointer values after integer values. This helps SCEVExpander form 619 // GEPs. 620 bool LIsPointer = LV->getType()->isPointerTy(), 621 RIsPointer = RV->getType()->isPointerTy(); 622 if (LIsPointer != RIsPointer) 623 return (int)LIsPointer - (int)RIsPointer; 624 625 // Compare getValueID values. 626 unsigned LID = LV->getValueID(), RID = RV->getValueID(); 627 if (LID != RID) 628 return (int)LID - (int)RID; 629 630 // Sort arguments by their position. 631 if (const auto *LA = dyn_cast<Argument>(LV)) { 632 const auto *RA = cast<Argument>(RV); 633 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo(); 634 return (int)LArgNo - (int)RArgNo; 635 } 636 637 if (const auto *LGV = dyn_cast<GlobalValue>(LV)) { 638 const auto *RGV = cast<GlobalValue>(RV); 639 640 const auto IsGVNameSemantic = [&](const GlobalValue *GV) { 641 auto LT = GV->getLinkage(); 642 return !(GlobalValue::isPrivateLinkage(LT) || 643 GlobalValue::isInternalLinkage(LT)); 644 }; 645 646 // Use the names to distinguish the two values, but only if the 647 // names are semantically important. 648 if (IsGVNameSemantic(LGV) && IsGVNameSemantic(RGV)) 649 return LGV->getName().compare(RGV->getName()); 650 } 651 652 // For instructions, compare their loop depth, and their operand count. This 653 // is pretty loose. 654 if (const auto *LInst = dyn_cast<Instruction>(LV)) { 655 const auto *RInst = cast<Instruction>(RV); 656 657 // Compare loop depths. 658 const BasicBlock *LParent = LInst->getParent(), 659 *RParent = RInst->getParent(); 660 if (LParent != RParent) { 661 unsigned LDepth = LI->getLoopDepth(LParent), 662 RDepth = LI->getLoopDepth(RParent); 663 if (LDepth != RDepth) 664 return (int)LDepth - (int)RDepth; 665 } 666 667 // Compare the number of operands. 668 unsigned LNumOps = LInst->getNumOperands(), 669 RNumOps = RInst->getNumOperands(); 670 if (LNumOps != RNumOps) 671 return (int)LNumOps - (int)RNumOps; 672 673 for (unsigned Idx : seq(0u, LNumOps)) { 674 int Result = 675 CompareValueComplexity(EqCacheValue, LI, LInst->getOperand(Idx), 676 RInst->getOperand(Idx), Depth + 1); 677 if (Result != 0) 678 return Result; 679 } 680 } 681 682 EqCacheValue.unionSets(LV, RV); 683 return 0; 684 } 685 686 // Return negative, zero, or positive, if LHS is less than, equal to, or greater 687 // than RHS, respectively. A three-way result allows recursive comparisons to be 688 // more efficient. 689 // If the max analysis depth was reached, return None, assuming we do not know 690 // if they are equivalent for sure. 691 static Optional<int> 692 CompareSCEVComplexity(EquivalenceClasses<const SCEV *> &EqCacheSCEV, 693 EquivalenceClasses<const Value *> &EqCacheValue, 694 const LoopInfo *const LI, const SCEV *LHS, 695 const SCEV *RHS, DominatorTree &DT, unsigned Depth = 0) { 696 // Fast-path: SCEVs are uniqued so we can do a quick equality check. 697 if (LHS == RHS) 698 return 0; 699 700 // Primarily, sort the SCEVs by their getSCEVType(). 701 SCEVTypes LType = LHS->getSCEVType(), RType = RHS->getSCEVType(); 702 if (LType != RType) 703 return (int)LType - (int)RType; 704 705 if (EqCacheSCEV.isEquivalent(LHS, RHS)) 706 return 0; 707 708 if (Depth > MaxSCEVCompareDepth) 709 return None; 710 711 // Aside from the getSCEVType() ordering, the particular ordering 712 // isn't very important except that it's beneficial to be consistent, 713 // so that (a + b) and (b + a) don't end up as different expressions. 714 switch (LType) { 715 case scUnknown: { 716 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS); 717 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 718 719 int X = CompareValueComplexity(EqCacheValue, LI, LU->getValue(), 720 RU->getValue(), Depth + 1); 721 if (X == 0) 722 EqCacheSCEV.unionSets(LHS, RHS); 723 return X; 724 } 725 726 case scConstant: { 727 const SCEVConstant *LC = cast<SCEVConstant>(LHS); 728 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 729 730 // Compare constant values. 731 const APInt &LA = LC->getAPInt(); 732 const APInt &RA = RC->getAPInt(); 733 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth(); 734 if (LBitWidth != RBitWidth) 735 return (int)LBitWidth - (int)RBitWidth; 736 return LA.ult(RA) ? -1 : 1; 737 } 738 739 case scAddRecExpr: { 740 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS); 741 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 742 743 // There is always a dominance between two recs that are used by one SCEV, 744 // so we can safely sort recs by loop header dominance. We require such 745 // order in getAddExpr. 746 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop(); 747 if (LLoop != RLoop) { 748 const BasicBlock *LHead = LLoop->getHeader(), *RHead = RLoop->getHeader(); 749 assert(LHead != RHead && "Two loops share the same header?"); 750 if (DT.dominates(LHead, RHead)) 751 return 1; 752 else 753 assert(DT.dominates(RHead, LHead) && 754 "No dominance between recurrences used by one SCEV?"); 755 return -1; 756 } 757 758 // Addrec complexity grows with operand count. 759 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands(); 760 if (LNumOps != RNumOps) 761 return (int)LNumOps - (int)RNumOps; 762 763 // Lexicographically compare. 764 for (unsigned i = 0; i != LNumOps; ++i) { 765 auto X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, 766 LA->getOperand(i), RA->getOperand(i), DT, 767 Depth + 1); 768 if (X != 0) 769 return X; 770 } 771 EqCacheSCEV.unionSets(LHS, RHS); 772 return 0; 773 } 774 775 case scAddExpr: 776 case scMulExpr: 777 case scSMaxExpr: 778 case scUMaxExpr: 779 case scSMinExpr: 780 case scUMinExpr: { 781 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS); 782 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 783 784 // Lexicographically compare n-ary expressions. 785 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands(); 786 if (LNumOps != RNumOps) 787 return (int)LNumOps - (int)RNumOps; 788 789 for (unsigned i = 0; i != LNumOps; ++i) { 790 auto X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, 791 LC->getOperand(i), RC->getOperand(i), DT, 792 Depth + 1); 793 if (X != 0) 794 return X; 795 } 796 EqCacheSCEV.unionSets(LHS, RHS); 797 return 0; 798 } 799 800 case scUDivExpr: { 801 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS); 802 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 803 804 // Lexicographically compare udiv expressions. 805 auto X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getLHS(), 806 RC->getLHS(), DT, Depth + 1); 807 if (X != 0) 808 return X; 809 X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getRHS(), 810 RC->getRHS(), DT, Depth + 1); 811 if (X == 0) 812 EqCacheSCEV.unionSets(LHS, RHS); 813 return X; 814 } 815 816 case scPtrToInt: 817 case scTruncate: 818 case scZeroExtend: 819 case scSignExtend: { 820 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS); 821 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 822 823 // Compare cast expressions by operand. 824 auto X = 825 CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getOperand(), 826 RC->getOperand(), DT, Depth + 1); 827 if (X == 0) 828 EqCacheSCEV.unionSets(LHS, RHS); 829 return X; 830 } 831 832 case scCouldNotCompute: 833 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 834 } 835 llvm_unreachable("Unknown SCEV kind!"); 836 } 837 838 /// Given a list of SCEV objects, order them by their complexity, and group 839 /// objects of the same complexity together by value. When this routine is 840 /// finished, we know that any duplicates in the vector are consecutive and that 841 /// complexity is monotonically increasing. 842 /// 843 /// Note that we go take special precautions to ensure that we get deterministic 844 /// results from this routine. In other words, we don't want the results of 845 /// this to depend on where the addresses of various SCEV objects happened to 846 /// land in memory. 847 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 848 LoopInfo *LI, DominatorTree &DT) { 849 if (Ops.size() < 2) return; // Noop 850 851 EquivalenceClasses<const SCEV *> EqCacheSCEV; 852 EquivalenceClasses<const Value *> EqCacheValue; 853 854 // Whether LHS has provably less complexity than RHS. 855 auto IsLessComplex = [&](const SCEV *LHS, const SCEV *RHS) { 856 auto Complexity = 857 CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LHS, RHS, DT); 858 return Complexity && *Complexity < 0; 859 }; 860 if (Ops.size() == 2) { 861 // This is the common case, which also happens to be trivially simple. 862 // Special case it. 863 const SCEV *&LHS = Ops[0], *&RHS = Ops[1]; 864 if (IsLessComplex(RHS, LHS)) 865 std::swap(LHS, RHS); 866 return; 867 } 868 869 // Do the rough sort by complexity. 870 llvm::stable_sort(Ops, [&](const SCEV *LHS, const SCEV *RHS) { 871 return IsLessComplex(LHS, RHS); 872 }); 873 874 // Now that we are sorted by complexity, group elements of the same 875 // complexity. Note that this is, at worst, N^2, but the vector is likely to 876 // be extremely short in practice. Note that we take this approach because we 877 // do not want to depend on the addresses of the objects we are grouping. 878 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 879 const SCEV *S = Ops[i]; 880 unsigned Complexity = S->getSCEVType(); 881 882 // If there are any objects of the same complexity and same value as this 883 // one, group them. 884 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 885 if (Ops[j] == S) { // Found a duplicate. 886 // Move it to immediately after i'th element. 887 std::swap(Ops[i+1], Ops[j]); 888 ++i; // no need to rescan it. 889 if (i == e-2) return; // Done! 890 } 891 } 892 } 893 } 894 895 /// Returns true if \p Ops contains a huge SCEV (the subtree of S contains at 896 /// least HugeExprThreshold nodes). 897 static bool hasHugeExpression(ArrayRef<const SCEV *> Ops) { 898 return any_of(Ops, [](const SCEV *S) { 899 return S->getExpressionSize() >= HugeExprThreshold; 900 }); 901 } 902 903 //===----------------------------------------------------------------------===// 904 // Simple SCEV method implementations 905 //===----------------------------------------------------------------------===// 906 907 /// Compute BC(It, K). The result has width W. Assume, K > 0. 908 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 909 ScalarEvolution &SE, 910 Type *ResultTy) { 911 // Handle the simplest case efficiently. 912 if (K == 1) 913 return SE.getTruncateOrZeroExtend(It, ResultTy); 914 915 // We are using the following formula for BC(It, K): 916 // 917 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 918 // 919 // Suppose, W is the bitwidth of the return value. We must be prepared for 920 // overflow. Hence, we must assure that the result of our computation is 921 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 922 // safe in modular arithmetic. 923 // 924 // However, this code doesn't use exactly that formula; the formula it uses 925 // is something like the following, where T is the number of factors of 2 in 926 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 927 // exponentiation: 928 // 929 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 930 // 931 // This formula is trivially equivalent to the previous formula. However, 932 // this formula can be implemented much more efficiently. The trick is that 933 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 934 // arithmetic. To do exact division in modular arithmetic, all we have 935 // to do is multiply by the inverse. Therefore, this step can be done at 936 // width W. 937 // 938 // The next issue is how to safely do the division by 2^T. The way this 939 // is done is by doing the multiplication step at a width of at least W + T 940 // bits. This way, the bottom W+T bits of the product are accurate. Then, 941 // when we perform the division by 2^T (which is equivalent to a right shift 942 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 943 // truncated out after the division by 2^T. 944 // 945 // In comparison to just directly using the first formula, this technique 946 // is much more efficient; using the first formula requires W * K bits, 947 // but this formula less than W + K bits. Also, the first formula requires 948 // a division step, whereas this formula only requires multiplies and shifts. 949 // 950 // It doesn't matter whether the subtraction step is done in the calculation 951 // width or the input iteration count's width; if the subtraction overflows, 952 // the result must be zero anyway. We prefer here to do it in the width of 953 // the induction variable because it helps a lot for certain cases; CodeGen 954 // isn't smart enough to ignore the overflow, which leads to much less 955 // efficient code if the width of the subtraction is wider than the native 956 // register width. 957 // 958 // (It's possible to not widen at all by pulling out factors of 2 before 959 // the multiplication; for example, K=2 can be calculated as 960 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 961 // extra arithmetic, so it's not an obvious win, and it gets 962 // much more complicated for K > 3.) 963 964 // Protection from insane SCEVs; this bound is conservative, 965 // but it probably doesn't matter. 966 if (K > 1000) 967 return SE.getCouldNotCompute(); 968 969 unsigned W = SE.getTypeSizeInBits(ResultTy); 970 971 // Calculate K! / 2^T and T; we divide out the factors of two before 972 // multiplying for calculating K! / 2^T to avoid overflow. 973 // Other overflow doesn't matter because we only care about the bottom 974 // W bits of the result. 975 APInt OddFactorial(W, 1); 976 unsigned T = 1; 977 for (unsigned i = 3; i <= K; ++i) { 978 APInt Mult(W, i); 979 unsigned TwoFactors = Mult.countTrailingZeros(); 980 T += TwoFactors; 981 Mult.lshrInPlace(TwoFactors); 982 OddFactorial *= Mult; 983 } 984 985 // We need at least W + T bits for the multiplication step 986 unsigned CalculationBits = W + T; 987 988 // Calculate 2^T, at width T+W. 989 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T); 990 991 // Calculate the multiplicative inverse of K! / 2^T; 992 // this multiplication factor will perform the exact division by 993 // K! / 2^T. 994 APInt Mod = APInt::getSignedMinValue(W+1); 995 APInt MultiplyFactor = OddFactorial.zext(W+1); 996 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 997 MultiplyFactor = MultiplyFactor.trunc(W); 998 999 // Calculate the product, at width T+W 1000 IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 1001 CalculationBits); 1002 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 1003 for (unsigned i = 1; i != K; ++i) { 1004 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i)); 1005 Dividend = SE.getMulExpr(Dividend, 1006 SE.getTruncateOrZeroExtend(S, CalculationTy)); 1007 } 1008 1009 // Divide by 2^T 1010 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 1011 1012 // Truncate the result, and divide by K! / 2^T. 1013 1014 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 1015 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 1016 } 1017 1018 /// Return the value of this chain of recurrences at the specified iteration 1019 /// number. We can evaluate this recurrence by multiplying each element in the 1020 /// chain by the binomial coefficient corresponding to it. In other words, we 1021 /// can evaluate {A,+,B,+,C,+,D} as: 1022 /// 1023 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 1024 /// 1025 /// where BC(It, k) stands for binomial coefficient. 1026 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 1027 ScalarEvolution &SE) const { 1028 return evaluateAtIteration(makeArrayRef(op_begin(), op_end()), It, SE); 1029 } 1030 1031 const SCEV * 1032 SCEVAddRecExpr::evaluateAtIteration(ArrayRef<const SCEV *> Operands, 1033 const SCEV *It, ScalarEvolution &SE) { 1034 assert(Operands.size() > 0); 1035 const SCEV *Result = Operands[0]; 1036 for (unsigned i = 1, e = Operands.size(); i != e; ++i) { 1037 // The computation is correct in the face of overflow provided that the 1038 // multiplication is performed _after_ the evaluation of the binomial 1039 // coefficient. 1040 const SCEV *Coeff = BinomialCoefficient(It, i, SE, Result->getType()); 1041 if (isa<SCEVCouldNotCompute>(Coeff)) 1042 return Coeff; 1043 1044 Result = SE.getAddExpr(Result, SE.getMulExpr(Operands[i], Coeff)); 1045 } 1046 return Result; 1047 } 1048 1049 //===----------------------------------------------------------------------===// 1050 // SCEV Expression folder implementations 1051 //===----------------------------------------------------------------------===// 1052 1053 const SCEV *ScalarEvolution::getLosslessPtrToIntExpr(const SCEV *Op, 1054 unsigned Depth) { 1055 assert(Depth <= 1 && 1056 "getLosslessPtrToIntExpr() should self-recurse at most once."); 1057 1058 // We could be called with an integer-typed operands during SCEV rewrites. 1059 // Since the operand is an integer already, just perform zext/trunc/self cast. 1060 if (!Op->getType()->isPointerTy()) 1061 return Op; 1062 1063 // What would be an ID for such a SCEV cast expression? 1064 FoldingSetNodeID ID; 1065 ID.AddInteger(scPtrToInt); 1066 ID.AddPointer(Op); 1067 1068 void *IP = nullptr; 1069 1070 // Is there already an expression for such a cast? 1071 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) 1072 return S; 1073 1074 Type *IntPtrTy = getDataLayout().getIntPtrType(Op->getType()); 1075 1076 // We can only model ptrtoint if SCEV's effective (integer) type 1077 // is sufficiently wide to represent all possible pointer values. 1078 if (getDataLayout().getTypeSizeInBits(getEffectiveSCEVType(Op->getType())) != 1079 getDataLayout().getTypeSizeInBits(IntPtrTy)) 1080 return getCouldNotCompute(); 1081 1082 // If not, is this expression something we can't reduce any further? 1083 if (auto *U = dyn_cast<SCEVUnknown>(Op)) { 1084 // Perform some basic constant folding. If the operand of the ptr2int cast 1085 // is a null pointer, don't create a ptr2int SCEV expression (that will be 1086 // left as-is), but produce a zero constant. 1087 // NOTE: We could handle a more general case, but lack motivational cases. 1088 if (isa<ConstantPointerNull>(U->getValue())) 1089 return getZero(IntPtrTy); 1090 1091 // Create an explicit cast node. 1092 // We can reuse the existing insert position since if we get here, 1093 // we won't have made any changes which would invalidate it. 1094 SCEV *S = new (SCEVAllocator) 1095 SCEVPtrToIntExpr(ID.Intern(SCEVAllocator), Op, IntPtrTy); 1096 UniqueSCEVs.InsertNode(S, IP); 1097 addToLoopUseLists(S); 1098 return S; 1099 } 1100 1101 assert(Depth == 0 && "getLosslessPtrToIntExpr() should not self-recurse for " 1102 "non-SCEVUnknown's."); 1103 1104 // Otherwise, we've got some expression that is more complex than just a 1105 // single SCEVUnknown. But we don't want to have a SCEVPtrToIntExpr of an 1106 // arbitrary expression, we want to have SCEVPtrToIntExpr of an SCEVUnknown 1107 // only, and the expressions must otherwise be integer-typed. 1108 // So sink the cast down to the SCEVUnknown's. 1109 1110 /// The SCEVPtrToIntSinkingRewriter takes a scalar evolution expression, 1111 /// which computes a pointer-typed value, and rewrites the whole expression 1112 /// tree so that *all* the computations are done on integers, and the only 1113 /// pointer-typed operands in the expression are SCEVUnknown. 1114 class SCEVPtrToIntSinkingRewriter 1115 : public SCEVRewriteVisitor<SCEVPtrToIntSinkingRewriter> { 1116 using Base = SCEVRewriteVisitor<SCEVPtrToIntSinkingRewriter>; 1117 1118 public: 1119 SCEVPtrToIntSinkingRewriter(ScalarEvolution &SE) : SCEVRewriteVisitor(SE) {} 1120 1121 static const SCEV *rewrite(const SCEV *Scev, ScalarEvolution &SE) { 1122 SCEVPtrToIntSinkingRewriter Rewriter(SE); 1123 return Rewriter.visit(Scev); 1124 } 1125 1126 const SCEV *visit(const SCEV *S) { 1127 Type *STy = S->getType(); 1128 // If the expression is not pointer-typed, just keep it as-is. 1129 if (!STy->isPointerTy()) 1130 return S; 1131 // Else, recursively sink the cast down into it. 1132 return Base::visit(S); 1133 } 1134 1135 const SCEV *visitAddExpr(const SCEVAddExpr *Expr) { 1136 SmallVector<const SCEV *, 2> Operands; 1137 bool Changed = false; 1138 for (auto *Op : Expr->operands()) { 1139 Operands.push_back(visit(Op)); 1140 Changed |= Op != Operands.back(); 1141 } 1142 return !Changed ? Expr : SE.getAddExpr(Operands, Expr->getNoWrapFlags()); 1143 } 1144 1145 const SCEV *visitMulExpr(const SCEVMulExpr *Expr) { 1146 SmallVector<const SCEV *, 2> Operands; 1147 bool Changed = false; 1148 for (auto *Op : Expr->operands()) { 1149 Operands.push_back(visit(Op)); 1150 Changed |= Op != Operands.back(); 1151 } 1152 return !Changed ? Expr : SE.getMulExpr(Operands, Expr->getNoWrapFlags()); 1153 } 1154 1155 const SCEV *visitUnknown(const SCEVUnknown *Expr) { 1156 assert(Expr->getType()->isPointerTy() && 1157 "Should only reach pointer-typed SCEVUnknown's."); 1158 return SE.getLosslessPtrToIntExpr(Expr, /*Depth=*/1); 1159 } 1160 }; 1161 1162 // And actually perform the cast sinking. 1163 const SCEV *IntOp = SCEVPtrToIntSinkingRewriter::rewrite(Op, *this); 1164 assert(IntOp->getType()->isIntegerTy() && 1165 "We must have succeeded in sinking the cast, " 1166 "and ending up with an integer-typed expression!"); 1167 return IntOp; 1168 } 1169 1170 const SCEV *ScalarEvolution::getPtrToIntExpr(const SCEV *Op, Type *Ty) { 1171 assert(Ty->isIntegerTy() && "Target type must be an integer type!"); 1172 1173 const SCEV *IntOp = getLosslessPtrToIntExpr(Op); 1174 if (isa<SCEVCouldNotCompute>(IntOp)) 1175 return IntOp; 1176 1177 return getTruncateOrZeroExtend(IntOp, Ty); 1178 } 1179 1180 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, Type *Ty, 1181 unsigned Depth) { 1182 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 1183 "This is not a truncating conversion!"); 1184 assert(isSCEVable(Ty) && 1185 "This is not a conversion to a SCEVable type!"); 1186 Ty = getEffectiveSCEVType(Ty); 1187 1188 FoldingSetNodeID ID; 1189 ID.AddInteger(scTruncate); 1190 ID.AddPointer(Op); 1191 ID.AddPointer(Ty); 1192 void *IP = nullptr; 1193 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1194 1195 // Fold if the operand is constant. 1196 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1197 return getConstant( 1198 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty))); 1199 1200 // trunc(trunc(x)) --> trunc(x) 1201 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 1202 return getTruncateExpr(ST->getOperand(), Ty, Depth + 1); 1203 1204 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 1205 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1206 return getTruncateOrSignExtend(SS->getOperand(), Ty, Depth + 1); 1207 1208 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 1209 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 1210 return getTruncateOrZeroExtend(SZ->getOperand(), Ty, Depth + 1); 1211 1212 if (Depth > MaxCastDepth) { 1213 SCEV *S = 1214 new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), Op, Ty); 1215 UniqueSCEVs.InsertNode(S, IP); 1216 addToLoopUseLists(S); 1217 return S; 1218 } 1219 1220 // trunc(x1 + ... + xN) --> trunc(x1) + ... + trunc(xN) and 1221 // trunc(x1 * ... * xN) --> trunc(x1) * ... * trunc(xN), 1222 // if after transforming we have at most one truncate, not counting truncates 1223 // that replace other casts. 1224 if (isa<SCEVAddExpr>(Op) || isa<SCEVMulExpr>(Op)) { 1225 auto *CommOp = cast<SCEVCommutativeExpr>(Op); 1226 SmallVector<const SCEV *, 4> Operands; 1227 unsigned numTruncs = 0; 1228 for (unsigned i = 0, e = CommOp->getNumOperands(); i != e && numTruncs < 2; 1229 ++i) { 1230 const SCEV *S = getTruncateExpr(CommOp->getOperand(i), Ty, Depth + 1); 1231 if (!isa<SCEVIntegralCastExpr>(CommOp->getOperand(i)) && 1232 isa<SCEVTruncateExpr>(S)) 1233 numTruncs++; 1234 Operands.push_back(S); 1235 } 1236 if (numTruncs < 2) { 1237 if (isa<SCEVAddExpr>(Op)) 1238 return getAddExpr(Operands); 1239 else if (isa<SCEVMulExpr>(Op)) 1240 return getMulExpr(Operands); 1241 else 1242 llvm_unreachable("Unexpected SCEV type for Op."); 1243 } 1244 // Although we checked in the beginning that ID is not in the cache, it is 1245 // possible that during recursion and different modification ID was inserted 1246 // into the cache. So if we find it, just return it. 1247 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) 1248 return S; 1249 } 1250 1251 // If the input value is a chrec scev, truncate the chrec's operands. 1252 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 1253 SmallVector<const SCEV *, 4> Operands; 1254 for (const SCEV *Op : AddRec->operands()) 1255 Operands.push_back(getTruncateExpr(Op, Ty, Depth + 1)); 1256 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap); 1257 } 1258 1259 // Return zero if truncating to known zeros. 1260 uint32_t MinTrailingZeros = GetMinTrailingZeros(Op); 1261 if (MinTrailingZeros >= getTypeSizeInBits(Ty)) 1262 return getZero(Ty); 1263 1264 // The cast wasn't folded; create an explicit cast node. We can reuse 1265 // the existing insert position since if we get here, we won't have 1266 // made any changes which would invalidate it. 1267 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), 1268 Op, Ty); 1269 UniqueSCEVs.InsertNode(S, IP); 1270 addToLoopUseLists(S); 1271 return S; 1272 } 1273 1274 // Get the limit of a recurrence such that incrementing by Step cannot cause 1275 // signed overflow as long as the value of the recurrence within the 1276 // loop does not exceed this limit before incrementing. 1277 static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step, 1278 ICmpInst::Predicate *Pred, 1279 ScalarEvolution *SE) { 1280 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType()); 1281 if (SE->isKnownPositive(Step)) { 1282 *Pred = ICmpInst::ICMP_SLT; 1283 return SE->getConstant(APInt::getSignedMinValue(BitWidth) - 1284 SE->getSignedRangeMax(Step)); 1285 } 1286 if (SE->isKnownNegative(Step)) { 1287 *Pred = ICmpInst::ICMP_SGT; 1288 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) - 1289 SE->getSignedRangeMin(Step)); 1290 } 1291 return nullptr; 1292 } 1293 1294 // Get the limit of a recurrence such that incrementing by Step cannot cause 1295 // unsigned overflow as long as the value of the recurrence within the loop does 1296 // not exceed this limit before incrementing. 1297 static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step, 1298 ICmpInst::Predicate *Pred, 1299 ScalarEvolution *SE) { 1300 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType()); 1301 *Pred = ICmpInst::ICMP_ULT; 1302 1303 return SE->getConstant(APInt::getMinValue(BitWidth) - 1304 SE->getUnsignedRangeMax(Step)); 1305 } 1306 1307 namespace { 1308 1309 struct ExtendOpTraitsBase { 1310 typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *, 1311 unsigned); 1312 }; 1313 1314 // Used to make code generic over signed and unsigned overflow. 1315 template <typename ExtendOp> struct ExtendOpTraits { 1316 // Members present: 1317 // 1318 // static const SCEV::NoWrapFlags WrapType; 1319 // 1320 // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr; 1321 // 1322 // static const SCEV *getOverflowLimitForStep(const SCEV *Step, 1323 // ICmpInst::Predicate *Pred, 1324 // ScalarEvolution *SE); 1325 }; 1326 1327 template <> 1328 struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase { 1329 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW; 1330 1331 static const GetExtendExprTy GetExtendExpr; 1332 1333 static const SCEV *getOverflowLimitForStep(const SCEV *Step, 1334 ICmpInst::Predicate *Pred, 1335 ScalarEvolution *SE) { 1336 return getSignedOverflowLimitForStep(Step, Pred, SE); 1337 } 1338 }; 1339 1340 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits< 1341 SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr; 1342 1343 template <> 1344 struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase { 1345 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW; 1346 1347 static const GetExtendExprTy GetExtendExpr; 1348 1349 static const SCEV *getOverflowLimitForStep(const SCEV *Step, 1350 ICmpInst::Predicate *Pred, 1351 ScalarEvolution *SE) { 1352 return getUnsignedOverflowLimitForStep(Step, Pred, SE); 1353 } 1354 }; 1355 1356 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits< 1357 SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr; 1358 1359 } // end anonymous namespace 1360 1361 // The recurrence AR has been shown to have no signed/unsigned wrap or something 1362 // close to it. Typically, if we can prove NSW/NUW for AR, then we can just as 1363 // easily prove NSW/NUW for its preincrement or postincrement sibling. This 1364 // allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step + 1365 // Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the 1366 // expression "Step + sext/zext(PreIncAR)" is congruent with 1367 // "sext/zext(PostIncAR)" 1368 template <typename ExtendOpTy> 1369 static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty, 1370 ScalarEvolution *SE, unsigned Depth) { 1371 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType; 1372 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr; 1373 1374 const Loop *L = AR->getLoop(); 1375 const SCEV *Start = AR->getStart(); 1376 const SCEV *Step = AR->getStepRecurrence(*SE); 1377 1378 // Check for a simple looking step prior to loop entry. 1379 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start); 1380 if (!SA) 1381 return nullptr; 1382 1383 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV 1384 // subtraction is expensive. For this purpose, perform a quick and dirty 1385 // difference, by checking for Step in the operand list. 1386 SmallVector<const SCEV *, 4> DiffOps; 1387 for (const SCEV *Op : SA->operands()) 1388 if (Op != Step) 1389 DiffOps.push_back(Op); 1390 1391 if (DiffOps.size() == SA->getNumOperands()) 1392 return nullptr; 1393 1394 // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` + 1395 // `Step`: 1396 1397 // 1. NSW/NUW flags on the step increment. 1398 auto PreStartFlags = 1399 ScalarEvolution::maskFlags(SA->getNoWrapFlags(), SCEV::FlagNUW); 1400 const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags); 1401 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>( 1402 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap)); 1403 1404 // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies 1405 // "S+X does not sign/unsign-overflow". 1406 // 1407 1408 const SCEV *BECount = SE->getBackedgeTakenCount(L); 1409 if (PreAR && PreAR->getNoWrapFlags(WrapType) && 1410 !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount)) 1411 return PreStart; 1412 1413 // 2. Direct overflow check on the step operation's expression. 1414 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType()); 1415 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2); 1416 const SCEV *OperandExtendedStart = 1417 SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy, Depth), 1418 (SE->*GetExtendExpr)(Step, WideTy, Depth)); 1419 if ((SE->*GetExtendExpr)(Start, WideTy, Depth) == OperandExtendedStart) { 1420 if (PreAR && AR->getNoWrapFlags(WrapType)) { 1421 // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW 1422 // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then 1423 // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact. 1424 SE->setNoWrapFlags(const_cast<SCEVAddRecExpr *>(PreAR), WrapType); 1425 } 1426 return PreStart; 1427 } 1428 1429 // 3. Loop precondition. 1430 ICmpInst::Predicate Pred; 1431 const SCEV *OverflowLimit = 1432 ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE); 1433 1434 if (OverflowLimit && 1435 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) 1436 return PreStart; 1437 1438 return nullptr; 1439 } 1440 1441 // Get the normalized zero or sign extended expression for this AddRec's Start. 1442 template <typename ExtendOpTy> 1443 static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty, 1444 ScalarEvolution *SE, 1445 unsigned Depth) { 1446 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr; 1447 1448 const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE, Depth); 1449 if (!PreStart) 1450 return (SE->*GetExtendExpr)(AR->getStart(), Ty, Depth); 1451 1452 return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty, 1453 Depth), 1454 (SE->*GetExtendExpr)(PreStart, Ty, Depth)); 1455 } 1456 1457 // Try to prove away overflow by looking at "nearby" add recurrences. A 1458 // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it 1459 // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`. 1460 // 1461 // Formally: 1462 // 1463 // {S,+,X} == {S-T,+,X} + T 1464 // => Ext({S,+,X}) == Ext({S-T,+,X} + T) 1465 // 1466 // If ({S-T,+,X} + T) does not overflow ... (1) 1467 // 1468 // RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T) 1469 // 1470 // If {S-T,+,X} does not overflow ... (2) 1471 // 1472 // RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T) 1473 // == {Ext(S-T)+Ext(T),+,Ext(X)} 1474 // 1475 // If (S-T)+T does not overflow ... (3) 1476 // 1477 // RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)} 1478 // == {Ext(S),+,Ext(X)} == LHS 1479 // 1480 // Thus, if (1), (2) and (3) are true for some T, then 1481 // Ext({S,+,X}) == {Ext(S),+,Ext(X)} 1482 // 1483 // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T) 1484 // does not overflow" restricted to the 0th iteration. Therefore we only need 1485 // to check for (1) and (2). 1486 // 1487 // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T 1488 // is `Delta` (defined below). 1489 template <typename ExtendOpTy> 1490 bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start, 1491 const SCEV *Step, 1492 const Loop *L) { 1493 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType; 1494 1495 // We restrict `Start` to a constant to prevent SCEV from spending too much 1496 // time here. It is correct (but more expensive) to continue with a 1497 // non-constant `Start` and do a general SCEV subtraction to compute 1498 // `PreStart` below. 1499 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start); 1500 if (!StartC) 1501 return false; 1502 1503 APInt StartAI = StartC->getAPInt(); 1504 1505 for (unsigned Delta : {-2, -1, 1, 2}) { 1506 const SCEV *PreStart = getConstant(StartAI - Delta); 1507 1508 FoldingSetNodeID ID; 1509 ID.AddInteger(scAddRecExpr); 1510 ID.AddPointer(PreStart); 1511 ID.AddPointer(Step); 1512 ID.AddPointer(L); 1513 void *IP = nullptr; 1514 const auto *PreAR = 1515 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1516 1517 // Give up if we don't already have the add recurrence we need because 1518 // actually constructing an add recurrence is relatively expensive. 1519 if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2) 1520 const SCEV *DeltaS = getConstant(StartC->getType(), Delta); 1521 ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE; 1522 const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep( 1523 DeltaS, &Pred, this); 1524 if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1) 1525 return true; 1526 } 1527 } 1528 1529 return false; 1530 } 1531 1532 // Finds an integer D for an expression (C + x + y + ...) such that the top 1533 // level addition in (D + (C - D + x + y + ...)) would not wrap (signed or 1534 // unsigned) and the number of trailing zeros of (C - D + x + y + ...) is 1535 // maximized, where C is the \p ConstantTerm, x, y, ... are arbitrary SCEVs, and 1536 // the (C + x + y + ...) expression is \p WholeAddExpr. 1537 static APInt extractConstantWithoutWrapping(ScalarEvolution &SE, 1538 const SCEVConstant *ConstantTerm, 1539 const SCEVAddExpr *WholeAddExpr) { 1540 const APInt &C = ConstantTerm->getAPInt(); 1541 const unsigned BitWidth = C.getBitWidth(); 1542 // Find number of trailing zeros of (x + y + ...) w/o the C first: 1543 uint32_t TZ = BitWidth; 1544 for (unsigned I = 1, E = WholeAddExpr->getNumOperands(); I < E && TZ; ++I) 1545 TZ = std::min(TZ, SE.GetMinTrailingZeros(WholeAddExpr->getOperand(I))); 1546 if (TZ) { 1547 // Set D to be as many least significant bits of C as possible while still 1548 // guaranteeing that adding D to (C - D + x + y + ...) won't cause a wrap: 1549 return TZ < BitWidth ? C.trunc(TZ).zext(BitWidth) : C; 1550 } 1551 return APInt(BitWidth, 0); 1552 } 1553 1554 // Finds an integer D for an affine AddRec expression {C,+,x} such that the top 1555 // level addition in (D + {C-D,+,x}) would not wrap (signed or unsigned) and the 1556 // number of trailing zeros of (C - D + x * n) is maximized, where C is the \p 1557 // ConstantStart, x is an arbitrary \p Step, and n is the loop trip count. 1558 static APInt extractConstantWithoutWrapping(ScalarEvolution &SE, 1559 const APInt &ConstantStart, 1560 const SCEV *Step) { 1561 const unsigned BitWidth = ConstantStart.getBitWidth(); 1562 const uint32_t TZ = SE.GetMinTrailingZeros(Step); 1563 if (TZ) 1564 return TZ < BitWidth ? ConstantStart.trunc(TZ).zext(BitWidth) 1565 : ConstantStart; 1566 return APInt(BitWidth, 0); 1567 } 1568 1569 const SCEV * 1570 ScalarEvolution::getZeroExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) { 1571 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1572 "This is not an extending conversion!"); 1573 assert(isSCEVable(Ty) && 1574 "This is not a conversion to a SCEVable type!"); 1575 Ty = getEffectiveSCEVType(Ty); 1576 1577 // Fold if the operand is constant. 1578 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1579 return getConstant( 1580 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty))); 1581 1582 // zext(zext(x)) --> zext(x) 1583 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 1584 return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1); 1585 1586 // Before doing any expensive analysis, check to see if we've already 1587 // computed a SCEV for this Op and Ty. 1588 FoldingSetNodeID ID; 1589 ID.AddInteger(scZeroExtend); 1590 ID.AddPointer(Op); 1591 ID.AddPointer(Ty); 1592 void *IP = nullptr; 1593 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1594 if (Depth > MaxCastDepth) { 1595 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator), 1596 Op, Ty); 1597 UniqueSCEVs.InsertNode(S, IP); 1598 addToLoopUseLists(S); 1599 return S; 1600 } 1601 1602 // zext(trunc(x)) --> zext(x) or x or trunc(x) 1603 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) { 1604 // It's possible the bits taken off by the truncate were all zero bits. If 1605 // so, we should be able to simplify this further. 1606 const SCEV *X = ST->getOperand(); 1607 ConstantRange CR = getUnsignedRange(X); 1608 unsigned TruncBits = getTypeSizeInBits(ST->getType()); 1609 unsigned NewBits = getTypeSizeInBits(Ty); 1610 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains( 1611 CR.zextOrTrunc(NewBits))) 1612 return getTruncateOrZeroExtend(X, Ty, Depth); 1613 } 1614 1615 // If the input value is a chrec scev, and we can prove that the value 1616 // did not overflow the old, smaller, value, we can zero extend all of the 1617 // operands (often constants). This allows analysis of something like 1618 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 1619 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1620 if (AR->isAffine()) { 1621 const SCEV *Start = AR->getStart(); 1622 const SCEV *Step = AR->getStepRecurrence(*this); 1623 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1624 const Loop *L = AR->getLoop(); 1625 1626 if (!AR->hasNoUnsignedWrap()) { 1627 auto NewFlags = proveNoWrapViaConstantRanges(AR); 1628 setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), NewFlags); 1629 } 1630 1631 // If we have special knowledge that this addrec won't overflow, 1632 // we don't need to do any further analysis. 1633 if (AR->hasNoUnsignedWrap()) 1634 return getAddRecExpr( 1635 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1), 1636 getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags()); 1637 1638 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1639 // Note that this serves two purposes: It filters out loops that are 1640 // simply not analyzable, and it covers the case where this code is 1641 // being called from within backedge-taken count analysis, such that 1642 // attempting to ask for the backedge-taken count would likely result 1643 // in infinite recursion. In the later case, the analysis code will 1644 // cope with a conservative value, and it will take care to purge 1645 // that value once it has finished. 1646 const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L); 1647 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1648 // Manually compute the final value for AR, checking for overflow. 1649 1650 // Check whether the backedge-taken count can be losslessly casted to 1651 // the addrec's type. The count is always unsigned. 1652 const SCEV *CastedMaxBECount = 1653 getTruncateOrZeroExtend(MaxBECount, Start->getType(), Depth); 1654 const SCEV *RecastedMaxBECount = getTruncateOrZeroExtend( 1655 CastedMaxBECount, MaxBECount->getType(), Depth); 1656 if (MaxBECount == RecastedMaxBECount) { 1657 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1658 // Check whether Start+Step*MaxBECount has no unsigned overflow. 1659 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step, 1660 SCEV::FlagAnyWrap, Depth + 1); 1661 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul, 1662 SCEV::FlagAnyWrap, 1663 Depth + 1), 1664 WideTy, Depth + 1); 1665 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy, Depth + 1); 1666 const SCEV *WideMaxBECount = 1667 getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1); 1668 const SCEV *OperandExtendedAdd = 1669 getAddExpr(WideStart, 1670 getMulExpr(WideMaxBECount, 1671 getZeroExtendExpr(Step, WideTy, Depth + 1), 1672 SCEV::FlagAnyWrap, Depth + 1), 1673 SCEV::FlagAnyWrap, Depth + 1); 1674 if (ZAdd == OperandExtendedAdd) { 1675 // Cache knowledge of AR NUW, which is propagated to this AddRec. 1676 setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNUW); 1677 // Return the expression with the addrec on the outside. 1678 return getAddRecExpr( 1679 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, 1680 Depth + 1), 1681 getZeroExtendExpr(Step, Ty, Depth + 1), L, 1682 AR->getNoWrapFlags()); 1683 } 1684 // Similar to above, only this time treat the step value as signed. 1685 // This covers loops that count down. 1686 OperandExtendedAdd = 1687 getAddExpr(WideStart, 1688 getMulExpr(WideMaxBECount, 1689 getSignExtendExpr(Step, WideTy, Depth + 1), 1690 SCEV::FlagAnyWrap, Depth + 1), 1691 SCEV::FlagAnyWrap, Depth + 1); 1692 if (ZAdd == OperandExtendedAdd) { 1693 // Cache knowledge of AR NW, which is propagated to this AddRec. 1694 // Negative step causes unsigned wrap, but it still can't self-wrap. 1695 setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNW); 1696 // Return the expression with the addrec on the outside. 1697 return getAddRecExpr( 1698 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, 1699 Depth + 1), 1700 getSignExtendExpr(Step, Ty, Depth + 1), L, 1701 AR->getNoWrapFlags()); 1702 } 1703 } 1704 } 1705 1706 // Normally, in the cases we can prove no-overflow via a 1707 // backedge guarding condition, we can also compute a backedge 1708 // taken count for the loop. The exceptions are assumptions and 1709 // guards present in the loop -- SCEV is not great at exploiting 1710 // these to compute max backedge taken counts, but can still use 1711 // these to prove lack of overflow. Use this fact to avoid 1712 // doing extra work that may not pay off. 1713 if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards || 1714 !AC.assumptions().empty()) { 1715 1716 auto NewFlags = proveNoUnsignedWrapViaInduction(AR); 1717 setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), NewFlags); 1718 if (AR->hasNoUnsignedWrap()) { 1719 // Same as nuw case above - duplicated here to avoid a compile time 1720 // issue. It's not clear that the order of checks does matter, but 1721 // it's one of two issue possible causes for a change which was 1722 // reverted. Be conservative for the moment. 1723 return getAddRecExpr( 1724 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, 1725 Depth + 1), 1726 getZeroExtendExpr(Step, Ty, Depth + 1), L, 1727 AR->getNoWrapFlags()); 1728 } 1729 1730 // For a negative step, we can extend the operands iff doing so only 1731 // traverses values in the range zext([0,UINT_MAX]). 1732 if (isKnownNegative(Step)) { 1733 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 1734 getSignedRangeMin(Step)); 1735 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) || 1736 isKnownOnEveryIteration(ICmpInst::ICMP_UGT, AR, N)) { 1737 // Cache knowledge of AR NW, which is propagated to this 1738 // AddRec. Negative step causes unsigned wrap, but it 1739 // still can't self-wrap. 1740 setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNW); 1741 // Return the expression with the addrec on the outside. 1742 return getAddRecExpr( 1743 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, 1744 Depth + 1), 1745 getSignExtendExpr(Step, Ty, Depth + 1), L, 1746 AR->getNoWrapFlags()); 1747 } 1748 } 1749 } 1750 1751 // zext({C,+,Step}) --> (zext(D) + zext({C-D,+,Step}))<nuw><nsw> 1752 // if D + (C - D + Step * n) could be proven to not unsigned wrap 1753 // where D maximizes the number of trailing zeros of (C - D + Step * n) 1754 if (const auto *SC = dyn_cast<SCEVConstant>(Start)) { 1755 const APInt &C = SC->getAPInt(); 1756 const APInt &D = extractConstantWithoutWrapping(*this, C, Step); 1757 if (D != 0) { 1758 const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth); 1759 const SCEV *SResidual = 1760 getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags()); 1761 const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1); 1762 return getAddExpr(SZExtD, SZExtR, 1763 (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW), 1764 Depth + 1); 1765 } 1766 } 1767 1768 if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) { 1769 setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNUW); 1770 return getAddRecExpr( 1771 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1), 1772 getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags()); 1773 } 1774 } 1775 1776 // zext(A % B) --> zext(A) % zext(B) 1777 { 1778 const SCEV *LHS; 1779 const SCEV *RHS; 1780 if (matchURem(Op, LHS, RHS)) 1781 return getURemExpr(getZeroExtendExpr(LHS, Ty, Depth + 1), 1782 getZeroExtendExpr(RHS, Ty, Depth + 1)); 1783 } 1784 1785 // zext(A / B) --> zext(A) / zext(B). 1786 if (auto *Div = dyn_cast<SCEVUDivExpr>(Op)) 1787 return getUDivExpr(getZeroExtendExpr(Div->getLHS(), Ty, Depth + 1), 1788 getZeroExtendExpr(Div->getRHS(), Ty, Depth + 1)); 1789 1790 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) { 1791 // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw> 1792 if (SA->hasNoUnsignedWrap()) { 1793 // If the addition does not unsign overflow then we can, by definition, 1794 // commute the zero extension with the addition operation. 1795 SmallVector<const SCEV *, 4> Ops; 1796 for (const auto *Op : SA->operands()) 1797 Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1)); 1798 return getAddExpr(Ops, SCEV::FlagNUW, Depth + 1); 1799 } 1800 1801 // zext(C + x + y + ...) --> (zext(D) + zext((C - D) + x + y + ...)) 1802 // if D + (C - D + x + y + ...) could be proven to not unsigned wrap 1803 // where D maximizes the number of trailing zeros of (C - D + x + y + ...) 1804 // 1805 // Often address arithmetics contain expressions like 1806 // (zext (add (shl X, C1), C2)), for instance, (zext (5 + (4 * X))). 1807 // This transformation is useful while proving that such expressions are 1808 // equal or differ by a small constant amount, see LoadStoreVectorizer pass. 1809 if (const auto *SC = dyn_cast<SCEVConstant>(SA->getOperand(0))) { 1810 const APInt &D = extractConstantWithoutWrapping(*this, SC, SA); 1811 if (D != 0) { 1812 const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth); 1813 const SCEV *SResidual = 1814 getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth); 1815 const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1); 1816 return getAddExpr(SZExtD, SZExtR, 1817 (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW), 1818 Depth + 1); 1819 } 1820 } 1821 } 1822 1823 if (auto *SM = dyn_cast<SCEVMulExpr>(Op)) { 1824 // zext((A * B * ...)<nuw>) --> (zext(A) * zext(B) * ...)<nuw> 1825 if (SM->hasNoUnsignedWrap()) { 1826 // If the multiply does not unsign overflow then we can, by definition, 1827 // commute the zero extension with the multiply operation. 1828 SmallVector<const SCEV *, 4> Ops; 1829 for (const auto *Op : SM->operands()) 1830 Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1)); 1831 return getMulExpr(Ops, SCEV::FlagNUW, Depth + 1); 1832 } 1833 1834 // zext(2^K * (trunc X to iN)) to iM -> 1835 // 2^K * (zext(trunc X to i{N-K}) to iM)<nuw> 1836 // 1837 // Proof: 1838 // 1839 // zext(2^K * (trunc X to iN)) to iM 1840 // = zext((trunc X to iN) << K) to iM 1841 // = zext((trunc X to i{N-K}) << K)<nuw> to iM 1842 // (because shl removes the top K bits) 1843 // = zext((2^K * (trunc X to i{N-K}))<nuw>) to iM 1844 // = (2^K * (zext(trunc X to i{N-K}) to iM))<nuw>. 1845 // 1846 if (SM->getNumOperands() == 2) 1847 if (auto *MulLHS = dyn_cast<SCEVConstant>(SM->getOperand(0))) 1848 if (MulLHS->getAPInt().isPowerOf2()) 1849 if (auto *TruncRHS = dyn_cast<SCEVTruncateExpr>(SM->getOperand(1))) { 1850 int NewTruncBits = getTypeSizeInBits(TruncRHS->getType()) - 1851 MulLHS->getAPInt().logBase2(); 1852 Type *NewTruncTy = IntegerType::get(getContext(), NewTruncBits); 1853 return getMulExpr( 1854 getZeroExtendExpr(MulLHS, Ty), 1855 getZeroExtendExpr( 1856 getTruncateExpr(TruncRHS->getOperand(), NewTruncTy), Ty), 1857 SCEV::FlagNUW, Depth + 1); 1858 } 1859 } 1860 1861 // The cast wasn't folded; create an explicit cast node. 1862 // Recompute the insert position, as it may have been invalidated. 1863 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1864 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator), 1865 Op, Ty); 1866 UniqueSCEVs.InsertNode(S, IP); 1867 addToLoopUseLists(S); 1868 return S; 1869 } 1870 1871 const SCEV * 1872 ScalarEvolution::getSignExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) { 1873 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1874 "This is not an extending conversion!"); 1875 assert(isSCEVable(Ty) && 1876 "This is not a conversion to a SCEVable type!"); 1877 Ty = getEffectiveSCEVType(Ty); 1878 1879 // Fold if the operand is constant. 1880 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1881 return getConstant( 1882 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty))); 1883 1884 // sext(sext(x)) --> sext(x) 1885 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1886 return getSignExtendExpr(SS->getOperand(), Ty, Depth + 1); 1887 1888 // sext(zext(x)) --> zext(x) 1889 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 1890 return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1); 1891 1892 // Before doing any expensive analysis, check to see if we've already 1893 // computed a SCEV for this Op and Ty. 1894 FoldingSetNodeID ID; 1895 ID.AddInteger(scSignExtend); 1896 ID.AddPointer(Op); 1897 ID.AddPointer(Ty); 1898 void *IP = nullptr; 1899 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1900 // Limit recursion depth. 1901 if (Depth > MaxCastDepth) { 1902 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), 1903 Op, Ty); 1904 UniqueSCEVs.InsertNode(S, IP); 1905 addToLoopUseLists(S); 1906 return S; 1907 } 1908 1909 // sext(trunc(x)) --> sext(x) or x or trunc(x) 1910 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) { 1911 // It's possible the bits taken off by the truncate were all sign bits. If 1912 // so, we should be able to simplify this further. 1913 const SCEV *X = ST->getOperand(); 1914 ConstantRange CR = getSignedRange(X); 1915 unsigned TruncBits = getTypeSizeInBits(ST->getType()); 1916 unsigned NewBits = getTypeSizeInBits(Ty); 1917 if (CR.truncate(TruncBits).signExtend(NewBits).contains( 1918 CR.sextOrTrunc(NewBits))) 1919 return getTruncateOrSignExtend(X, Ty, Depth); 1920 } 1921 1922 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) { 1923 // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw> 1924 if (SA->hasNoSignedWrap()) { 1925 // If the addition does not sign overflow then we can, by definition, 1926 // commute the sign extension with the addition operation. 1927 SmallVector<const SCEV *, 4> Ops; 1928 for (const auto *Op : SA->operands()) 1929 Ops.push_back(getSignExtendExpr(Op, Ty, Depth + 1)); 1930 return getAddExpr(Ops, SCEV::FlagNSW, Depth + 1); 1931 } 1932 1933 // sext(C + x + y + ...) --> (sext(D) + sext((C - D) + x + y + ...)) 1934 // if D + (C - D + x + y + ...) could be proven to not signed wrap 1935 // where D maximizes the number of trailing zeros of (C - D + x + y + ...) 1936 // 1937 // For instance, this will bring two seemingly different expressions: 1938 // 1 + sext(5 + 20 * %x + 24 * %y) and 1939 // sext(6 + 20 * %x + 24 * %y) 1940 // to the same form: 1941 // 2 + sext(4 + 20 * %x + 24 * %y) 1942 if (const auto *SC = dyn_cast<SCEVConstant>(SA->getOperand(0))) { 1943 const APInt &D = extractConstantWithoutWrapping(*this, SC, SA); 1944 if (D != 0) { 1945 const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth); 1946 const SCEV *SResidual = 1947 getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth); 1948 const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1); 1949 return getAddExpr(SSExtD, SSExtR, 1950 (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW), 1951 Depth + 1); 1952 } 1953 } 1954 } 1955 // If the input value is a chrec scev, and we can prove that the value 1956 // did not overflow the old, smaller, value, we can sign extend all of the 1957 // operands (often constants). This allows analysis of something like 1958 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 1959 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1960 if (AR->isAffine()) { 1961 const SCEV *Start = AR->getStart(); 1962 const SCEV *Step = AR->getStepRecurrence(*this); 1963 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1964 const Loop *L = AR->getLoop(); 1965 1966 if (!AR->hasNoSignedWrap()) { 1967 auto NewFlags = proveNoWrapViaConstantRanges(AR); 1968 setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), NewFlags); 1969 } 1970 1971 // If we have special knowledge that this addrec won't overflow, 1972 // we don't need to do any further analysis. 1973 if (AR->hasNoSignedWrap()) 1974 return getAddRecExpr( 1975 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1), 1976 getSignExtendExpr(Step, Ty, Depth + 1), L, SCEV::FlagNSW); 1977 1978 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1979 // Note that this serves two purposes: It filters out loops that are 1980 // simply not analyzable, and it covers the case where this code is 1981 // being called from within backedge-taken count analysis, such that 1982 // attempting to ask for the backedge-taken count would likely result 1983 // in infinite recursion. In the later case, the analysis code will 1984 // cope with a conservative value, and it will take care to purge 1985 // that value once it has finished. 1986 const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L); 1987 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1988 // Manually compute the final value for AR, checking for 1989 // overflow. 1990 1991 // Check whether the backedge-taken count can be losslessly casted to 1992 // the addrec's type. The count is always unsigned. 1993 const SCEV *CastedMaxBECount = 1994 getTruncateOrZeroExtend(MaxBECount, Start->getType(), Depth); 1995 const SCEV *RecastedMaxBECount = getTruncateOrZeroExtend( 1996 CastedMaxBECount, MaxBECount->getType(), Depth); 1997 if (MaxBECount == RecastedMaxBECount) { 1998 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1999 // Check whether Start+Step*MaxBECount has no signed overflow. 2000 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step, 2001 SCEV::FlagAnyWrap, Depth + 1); 2002 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul, 2003 SCEV::FlagAnyWrap, 2004 Depth + 1), 2005 WideTy, Depth + 1); 2006 const SCEV *WideStart = getSignExtendExpr(Start, WideTy, Depth + 1); 2007 const SCEV *WideMaxBECount = 2008 getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1); 2009 const SCEV *OperandExtendedAdd = 2010 getAddExpr(WideStart, 2011 getMulExpr(WideMaxBECount, 2012 getSignExtendExpr(Step, WideTy, Depth + 1), 2013 SCEV::FlagAnyWrap, Depth + 1), 2014 SCEV::FlagAnyWrap, Depth + 1); 2015 if (SAdd == OperandExtendedAdd) { 2016 // Cache knowledge of AR NSW, which is propagated to this AddRec. 2017 setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNSW); 2018 // Return the expression with the addrec on the outside. 2019 return getAddRecExpr( 2020 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, 2021 Depth + 1), 2022 getSignExtendExpr(Step, Ty, Depth + 1), L, 2023 AR->getNoWrapFlags()); 2024 } 2025 // Similar to above, only this time treat the step value as unsigned. 2026 // This covers loops that count up with an unsigned step. 2027 OperandExtendedAdd = 2028 getAddExpr(WideStart, 2029 getMulExpr(WideMaxBECount, 2030 getZeroExtendExpr(Step, WideTy, Depth + 1), 2031 SCEV::FlagAnyWrap, Depth + 1), 2032 SCEV::FlagAnyWrap, Depth + 1); 2033 if (SAdd == OperandExtendedAdd) { 2034 // If AR wraps around then 2035 // 2036 // abs(Step) * MaxBECount > unsigned-max(AR->getType()) 2037 // => SAdd != OperandExtendedAdd 2038 // 2039 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=> 2040 // (SAdd == OperandExtendedAdd => AR is NW) 2041 2042 setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNW); 2043 2044 // Return the expression with the addrec on the outside. 2045 return getAddRecExpr( 2046 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, 2047 Depth + 1), 2048 getZeroExtendExpr(Step, Ty, Depth + 1), L, 2049 AR->getNoWrapFlags()); 2050 } 2051 } 2052 } 2053 2054 auto NewFlags = proveNoSignedWrapViaInduction(AR); 2055 setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), NewFlags); 2056 if (AR->hasNoSignedWrap()) { 2057 // Same as nsw case above - duplicated here to avoid a compile time 2058 // issue. It's not clear that the order of checks does matter, but 2059 // it's one of two issue possible causes for a change which was 2060 // reverted. Be conservative for the moment. 2061 return getAddRecExpr( 2062 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1), 2063 getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags()); 2064 } 2065 2066 // sext({C,+,Step}) --> (sext(D) + sext({C-D,+,Step}))<nuw><nsw> 2067 // if D + (C - D + Step * n) could be proven to not signed wrap 2068 // where D maximizes the number of trailing zeros of (C - D + Step * n) 2069 if (const auto *SC = dyn_cast<SCEVConstant>(Start)) { 2070 const APInt &C = SC->getAPInt(); 2071 const APInt &D = extractConstantWithoutWrapping(*this, C, Step); 2072 if (D != 0) { 2073 const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth); 2074 const SCEV *SResidual = 2075 getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags()); 2076 const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1); 2077 return getAddExpr(SSExtD, SSExtR, 2078 (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW), 2079 Depth + 1); 2080 } 2081 } 2082 2083 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) { 2084 setNoWrapFlags(const_cast<SCEVAddRecExpr *>(AR), SCEV::FlagNSW); 2085 return getAddRecExpr( 2086 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1), 2087 getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags()); 2088 } 2089 } 2090 2091 // If the input value is provably positive and we could not simplify 2092 // away the sext build a zext instead. 2093 if (isKnownNonNegative(Op)) 2094 return getZeroExtendExpr(Op, Ty, Depth + 1); 2095 2096 // The cast wasn't folded; create an explicit cast node. 2097 // Recompute the insert position, as it may have been invalidated. 2098 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2099 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), 2100 Op, Ty); 2101 UniqueSCEVs.InsertNode(S, IP); 2102 addToLoopUseLists(S); 2103 return S; 2104 } 2105 2106 /// getAnyExtendExpr - Return a SCEV for the given operand extended with 2107 /// unspecified bits out to the given type. 2108 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 2109 Type *Ty) { 2110 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 2111 "This is not an extending conversion!"); 2112 assert(isSCEVable(Ty) && 2113 "This is not a conversion to a SCEVable type!"); 2114 Ty = getEffectiveSCEVType(Ty); 2115 2116 // Sign-extend negative constants. 2117 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 2118 if (SC->getAPInt().isNegative()) 2119 return getSignExtendExpr(Op, Ty); 2120 2121 // Peel off a truncate cast. 2122 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 2123 const SCEV *NewOp = T->getOperand(); 2124 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 2125 return getAnyExtendExpr(NewOp, Ty); 2126 return getTruncateOrNoop(NewOp, Ty); 2127 } 2128 2129 // Next try a zext cast. If the cast is folded, use it. 2130 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 2131 if (!isa<SCEVZeroExtendExpr>(ZExt)) 2132 return ZExt; 2133 2134 // Next try a sext cast. If the cast is folded, use it. 2135 const SCEV *SExt = getSignExtendExpr(Op, Ty); 2136 if (!isa<SCEVSignExtendExpr>(SExt)) 2137 return SExt; 2138 2139 // Force the cast to be folded into the operands of an addrec. 2140 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { 2141 SmallVector<const SCEV *, 4> Ops; 2142 for (const SCEV *Op : AR->operands()) 2143 Ops.push_back(getAnyExtendExpr(Op, Ty)); 2144 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW); 2145 } 2146 2147 // If the expression is obviously signed, use the sext cast value. 2148 if (isa<SCEVSMaxExpr>(Op)) 2149 return SExt; 2150 2151 // Absent any other information, use the zext cast value. 2152 return ZExt; 2153 } 2154 2155 /// Process the given Ops list, which is a list of operands to be added under 2156 /// the given scale, update the given map. This is a helper function for 2157 /// getAddRecExpr. As an example of what it does, given a sequence of operands 2158 /// that would form an add expression like this: 2159 /// 2160 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r) 2161 /// 2162 /// where A and B are constants, update the map with these values: 2163 /// 2164 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 2165 /// 2166 /// and add 13 + A*B*29 to AccumulatedConstant. 2167 /// This will allow getAddRecExpr to produce this: 2168 /// 2169 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 2170 /// 2171 /// This form often exposes folding opportunities that are hidden in 2172 /// the original operand list. 2173 /// 2174 /// Return true iff it appears that any interesting folding opportunities 2175 /// may be exposed. This helps getAddRecExpr short-circuit extra work in 2176 /// the common case where no interesting opportunities are present, and 2177 /// is also used as a check to avoid infinite recursion. 2178 static bool 2179 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 2180 SmallVectorImpl<const SCEV *> &NewOps, 2181 APInt &AccumulatedConstant, 2182 const SCEV *const *Ops, size_t NumOperands, 2183 const APInt &Scale, 2184 ScalarEvolution &SE) { 2185 bool Interesting = false; 2186 2187 // Iterate over the add operands. They are sorted, with constants first. 2188 unsigned i = 0; 2189 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 2190 ++i; 2191 // Pull a buried constant out to the outside. 2192 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero()) 2193 Interesting = true; 2194 AccumulatedConstant += Scale * C->getAPInt(); 2195 } 2196 2197 // Next comes everything else. We're especially interested in multiplies 2198 // here, but they're in the middle, so just visit the rest with one loop. 2199 for (; i != NumOperands; ++i) { 2200 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 2201 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 2202 APInt NewScale = 2203 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getAPInt(); 2204 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 2205 // A multiplication of a constant with another add; recurse. 2206 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1)); 2207 Interesting |= 2208 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 2209 Add->op_begin(), Add->getNumOperands(), 2210 NewScale, SE); 2211 } else { 2212 // A multiplication of a constant with some other value. Update 2213 // the map. 2214 SmallVector<const SCEV *, 4> MulOps(drop_begin(Mul->operands())); 2215 const SCEV *Key = SE.getMulExpr(MulOps); 2216 auto Pair = M.insert({Key, NewScale}); 2217 if (Pair.second) { 2218 NewOps.push_back(Pair.first->first); 2219 } else { 2220 Pair.first->second += NewScale; 2221 // The map already had an entry for this value, which may indicate 2222 // a folding opportunity. 2223 Interesting = true; 2224 } 2225 } 2226 } else { 2227 // An ordinary operand. Update the map. 2228 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 2229 M.insert({Ops[i], Scale}); 2230 if (Pair.second) { 2231 NewOps.push_back(Pair.first->first); 2232 } else { 2233 Pair.first->second += Scale; 2234 // The map already had an entry for this value, which may indicate 2235 // a folding opportunity. 2236 Interesting = true; 2237 } 2238 } 2239 } 2240 2241 return Interesting; 2242 } 2243 2244 bool ScalarEvolution::willNotOverflow(Instruction::BinaryOps BinOp, bool Signed, 2245 const SCEV *LHS, const SCEV *RHS) { 2246 const SCEV *(ScalarEvolution::*Operation)(const SCEV *, const SCEV *, 2247 SCEV::NoWrapFlags, unsigned); 2248 switch (BinOp) { 2249 default: 2250 llvm_unreachable("Unsupported binary op"); 2251 case Instruction::Add: 2252 Operation = &ScalarEvolution::getAddExpr; 2253 break; 2254 case Instruction::Sub: 2255 Operation = &ScalarEvolution::getMinusSCEV; 2256 break; 2257 case Instruction::Mul: 2258 Operation = &ScalarEvolution::getMulExpr; 2259 break; 2260 } 2261 2262 const SCEV *(ScalarEvolution::*Extension)(const SCEV *, Type *, unsigned) = 2263 Signed ? &ScalarEvolution::getSignExtendExpr 2264 : &ScalarEvolution::getZeroExtendExpr; 2265 2266 // Check ext(LHS op RHS) == ext(LHS) op ext(RHS) 2267 auto *NarrowTy = cast<IntegerType>(LHS->getType()); 2268 auto *WideTy = 2269 IntegerType::get(NarrowTy->getContext(), NarrowTy->getBitWidth() * 2); 2270 2271 const SCEV *A = (this->*Extension)( 2272 (this->*Operation)(LHS, RHS, SCEV::FlagAnyWrap, 0), WideTy, 0); 2273 const SCEV *B = (this->*Operation)((this->*Extension)(LHS, WideTy, 0), 2274 (this->*Extension)(RHS, WideTy, 0), 2275 SCEV::FlagAnyWrap, 0); 2276 return A == B; 2277 } 2278 2279 std::pair<SCEV::NoWrapFlags, bool /*Deduced*/> 2280 ScalarEvolution::getStrengthenedNoWrapFlagsFromBinOp( 2281 const OverflowingBinaryOperator *OBO) { 2282 SCEV::NoWrapFlags Flags = SCEV::NoWrapFlags::FlagAnyWrap; 2283 2284 if (OBO->hasNoUnsignedWrap()) 2285 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW); 2286 if (OBO->hasNoSignedWrap()) 2287 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW); 2288 2289 bool Deduced = false; 2290 2291 if (OBO->hasNoUnsignedWrap() && OBO->hasNoSignedWrap()) 2292 return {Flags, Deduced}; 2293 2294 if (OBO->getOpcode() != Instruction::Add && 2295 OBO->getOpcode() != Instruction::Sub && 2296 OBO->getOpcode() != Instruction::Mul) 2297 return {Flags, Deduced}; 2298 2299 const SCEV *LHS = getSCEV(OBO->getOperand(0)); 2300 const SCEV *RHS = getSCEV(OBO->getOperand(1)); 2301 2302 if (!OBO->hasNoUnsignedWrap() && 2303 willNotOverflow((Instruction::BinaryOps)OBO->getOpcode(), 2304 /* Signed */ false, LHS, RHS)) { 2305 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW); 2306 Deduced = true; 2307 } 2308 2309 if (!OBO->hasNoSignedWrap() && 2310 willNotOverflow((Instruction::BinaryOps)OBO->getOpcode(), 2311 /* Signed */ true, LHS, RHS)) { 2312 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW); 2313 Deduced = true; 2314 } 2315 2316 return {Flags, Deduced}; 2317 } 2318 2319 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and 2320 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of 2321 // can't-overflow flags for the operation if possible. 2322 static SCEV::NoWrapFlags 2323 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type, 2324 const ArrayRef<const SCEV *> Ops, 2325 SCEV::NoWrapFlags Flags) { 2326 using namespace std::placeholders; 2327 2328 using OBO = OverflowingBinaryOperator; 2329 2330 bool CanAnalyze = 2331 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr; 2332 (void)CanAnalyze; 2333 assert(CanAnalyze && "don't call from other places!"); 2334 2335 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; 2336 SCEV::NoWrapFlags SignOrUnsignWrap = 2337 ScalarEvolution::maskFlags(Flags, SignOrUnsignMask); 2338 2339 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. 2340 auto IsKnownNonNegative = [&](const SCEV *S) { 2341 return SE->isKnownNonNegative(S); 2342 }; 2343 2344 if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative)) 2345 Flags = 2346 ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask); 2347 2348 SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask); 2349 2350 if (SignOrUnsignWrap != SignOrUnsignMask && 2351 (Type == scAddExpr || Type == scMulExpr) && Ops.size() == 2 && 2352 isa<SCEVConstant>(Ops[0])) { 2353 2354 auto Opcode = [&] { 2355 switch (Type) { 2356 case scAddExpr: 2357 return Instruction::Add; 2358 case scMulExpr: 2359 return Instruction::Mul; 2360 default: 2361 llvm_unreachable("Unexpected SCEV op."); 2362 } 2363 }(); 2364 2365 const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt(); 2366 2367 // (A <opcode> C) --> (A <opcode> C)<nsw> if the op doesn't sign overflow. 2368 if (!(SignOrUnsignWrap & SCEV::FlagNSW)) { 2369 auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion( 2370 Opcode, C, OBO::NoSignedWrap); 2371 if (NSWRegion.contains(SE->getSignedRange(Ops[1]))) 2372 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW); 2373 } 2374 2375 // (A <opcode> C) --> (A <opcode> C)<nuw> if the op doesn't unsign overflow. 2376 if (!(SignOrUnsignWrap & SCEV::FlagNUW)) { 2377 auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion( 2378 Opcode, C, OBO::NoUnsignedWrap); 2379 if (NUWRegion.contains(SE->getUnsignedRange(Ops[1]))) 2380 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW); 2381 } 2382 } 2383 2384 return Flags; 2385 } 2386 2387 bool ScalarEvolution::isAvailableAtLoopEntry(const SCEV *S, const Loop *L) { 2388 return isLoopInvariant(S, L) && properlyDominates(S, L->getHeader()); 2389 } 2390 2391 /// Get a canonical add expression, or something simpler if possible. 2392 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 2393 SCEV::NoWrapFlags OrigFlags, 2394 unsigned Depth) { 2395 assert(!(OrigFlags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) && 2396 "only nuw or nsw allowed"); 2397 assert(!Ops.empty() && "Cannot get empty add!"); 2398 if (Ops.size() == 1) return Ops[0]; 2399 #ifndef NDEBUG 2400 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2401 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2402 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2403 "SCEVAddExpr operand types don't match!"); 2404 #endif 2405 2406 // Sort by complexity, this groups all similar expression types together. 2407 GroupByComplexity(Ops, &LI, DT); 2408 2409 // If there are any constants, fold them together. 2410 unsigned Idx = 0; 2411 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2412 ++Idx; 2413 assert(Idx < Ops.size()); 2414 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2415 // We found two constants, fold them together! 2416 Ops[0] = getConstant(LHSC->getAPInt() + RHSC->getAPInt()); 2417 if (Ops.size() == 2) return Ops[0]; 2418 Ops.erase(Ops.begin()+1); // Erase the folded element 2419 LHSC = cast<SCEVConstant>(Ops[0]); 2420 } 2421 2422 // If we are left with a constant zero being added, strip it off. 2423 if (LHSC->getValue()->isZero()) { 2424 Ops.erase(Ops.begin()); 2425 --Idx; 2426 } 2427 2428 if (Ops.size() == 1) return Ops[0]; 2429 } 2430 2431 // Delay expensive flag strengthening until necessary. 2432 auto ComputeFlags = [this, OrigFlags](const ArrayRef<const SCEV *> Ops) { 2433 return StrengthenNoWrapFlags(this, scAddExpr, Ops, OrigFlags); 2434 }; 2435 2436 // Limit recursion calls depth. 2437 if (Depth > MaxArithDepth || hasHugeExpression(Ops)) 2438 return getOrCreateAddExpr(Ops, ComputeFlags(Ops)); 2439 2440 if (SCEV *S = std::get<0>(findExistingSCEVInCache(scAddExpr, Ops))) { 2441 // Don't strengthen flags if we have no new information. 2442 SCEVAddExpr *Add = static_cast<SCEVAddExpr *>(S); 2443 if (Add->getNoWrapFlags(OrigFlags) != OrigFlags) 2444 Add->setNoWrapFlags(ComputeFlags(Ops)); 2445 return S; 2446 } 2447 2448 // Okay, check to see if the same value occurs in the operand list more than 2449 // once. If so, merge them together into an multiply expression. Since we 2450 // sorted the list, these values are required to be adjacent. 2451 Type *Ty = Ops[0]->getType(); 2452 bool FoundMatch = false; 2453 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i) 2454 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 2455 // Scan ahead to count how many equal operands there are. 2456 unsigned Count = 2; 2457 while (i+Count != e && Ops[i+Count] == Ops[i]) 2458 ++Count; 2459 // Merge the values into a multiply. 2460 const SCEV *Scale = getConstant(Ty, Count); 2461 const SCEV *Mul = getMulExpr(Scale, Ops[i], SCEV::FlagAnyWrap, Depth + 1); 2462 if (Ops.size() == Count) 2463 return Mul; 2464 Ops[i] = Mul; 2465 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count); 2466 --i; e -= Count - 1; 2467 FoundMatch = true; 2468 } 2469 if (FoundMatch) 2470 return getAddExpr(Ops, OrigFlags, Depth + 1); 2471 2472 // Check for truncates. If all the operands are truncated from the same 2473 // type, see if factoring out the truncate would permit the result to be 2474 // folded. eg., n*trunc(x) + m*trunc(y) --> trunc(trunc(m)*x + trunc(n)*y) 2475 // if the contents of the resulting outer trunc fold to something simple. 2476 auto FindTruncSrcType = [&]() -> Type * { 2477 // We're ultimately looking to fold an addrec of truncs and muls of only 2478 // constants and truncs, so if we find any other types of SCEV 2479 // as operands of the addrec then we bail and return nullptr here. 2480 // Otherwise, we return the type of the operand of a trunc that we find. 2481 if (auto *T = dyn_cast<SCEVTruncateExpr>(Ops[Idx])) 2482 return T->getOperand()->getType(); 2483 if (const auto *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 2484 const auto *LastOp = Mul->getOperand(Mul->getNumOperands() - 1); 2485 if (const auto *T = dyn_cast<SCEVTruncateExpr>(LastOp)) 2486 return T->getOperand()->getType(); 2487 } 2488 return nullptr; 2489 }; 2490 if (auto *SrcType = FindTruncSrcType()) { 2491 SmallVector<const SCEV *, 8> LargeOps; 2492 bool Ok = true; 2493 // Check all the operands to see if they can be represented in the 2494 // source type of the truncate. 2495 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 2496 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 2497 if (T->getOperand()->getType() != SrcType) { 2498 Ok = false; 2499 break; 2500 } 2501 LargeOps.push_back(T->getOperand()); 2502 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 2503 LargeOps.push_back(getAnyExtendExpr(C, SrcType)); 2504 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 2505 SmallVector<const SCEV *, 8> LargeMulOps; 2506 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 2507 if (const SCEVTruncateExpr *T = 2508 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 2509 if (T->getOperand()->getType() != SrcType) { 2510 Ok = false; 2511 break; 2512 } 2513 LargeMulOps.push_back(T->getOperand()); 2514 } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) { 2515 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType)); 2516 } else { 2517 Ok = false; 2518 break; 2519 } 2520 } 2521 if (Ok) 2522 LargeOps.push_back(getMulExpr(LargeMulOps, SCEV::FlagAnyWrap, Depth + 1)); 2523 } else { 2524 Ok = false; 2525 break; 2526 } 2527 } 2528 if (Ok) { 2529 // Evaluate the expression in the larger type. 2530 const SCEV *Fold = getAddExpr(LargeOps, SCEV::FlagAnyWrap, Depth + 1); 2531 // If it folds to something simple, use it. Otherwise, don't. 2532 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 2533 return getTruncateExpr(Fold, Ty); 2534 } 2535 } 2536 2537 // Skip past any other cast SCEVs. 2538 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 2539 ++Idx; 2540 2541 // If there are add operands they would be next. 2542 if (Idx < Ops.size()) { 2543 bool DeletedAdd = false; 2544 // If the original flags and all inlined SCEVAddExprs are NUW, use the 2545 // common NUW flag for expression after inlining. Other flags cannot be 2546 // preserved, because they may depend on the original order of operations. 2547 SCEV::NoWrapFlags CommonFlags = maskFlags(OrigFlags, SCEV::FlagNUW); 2548 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 2549 if (Ops.size() > AddOpsInlineThreshold || 2550 Add->getNumOperands() > AddOpsInlineThreshold) 2551 break; 2552 // If we have an add, expand the add operands onto the end of the operands 2553 // list. 2554 Ops.erase(Ops.begin()+Idx); 2555 Ops.append(Add->op_begin(), Add->op_end()); 2556 DeletedAdd = true; 2557 CommonFlags = maskFlags(CommonFlags, Add->getNoWrapFlags()); 2558 } 2559 2560 // If we deleted at least one add, we added operands to the end of the list, 2561 // and they are not necessarily sorted. Recurse to resort and resimplify 2562 // any operands we just acquired. 2563 if (DeletedAdd) 2564 return getAddExpr(Ops, CommonFlags, Depth + 1); 2565 } 2566 2567 // Skip over the add expression until we get to a multiply. 2568 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 2569 ++Idx; 2570 2571 // Check to see if there are any folding opportunities present with 2572 // operands multiplied by constant values. 2573 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 2574 uint64_t BitWidth = getTypeSizeInBits(Ty); 2575 DenseMap<const SCEV *, APInt> M; 2576 SmallVector<const SCEV *, 8> NewOps; 2577 APInt AccumulatedConstant(BitWidth, 0); 2578 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 2579 Ops.data(), Ops.size(), 2580 APInt(BitWidth, 1), *this)) { 2581 struct APIntCompare { 2582 bool operator()(const APInt &LHS, const APInt &RHS) const { 2583 return LHS.ult(RHS); 2584 } 2585 }; 2586 2587 // Some interesting folding opportunity is present, so its worthwhile to 2588 // re-generate the operands list. Group the operands by constant scale, 2589 // to avoid multiplying by the same constant scale multiple times. 2590 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 2591 for (const SCEV *NewOp : NewOps) 2592 MulOpLists[M.find(NewOp)->second].push_back(NewOp); 2593 // Re-generate the operands list. 2594 Ops.clear(); 2595 if (AccumulatedConstant != 0) 2596 Ops.push_back(getConstant(AccumulatedConstant)); 2597 for (auto &MulOp : MulOpLists) 2598 if (MulOp.first != 0) 2599 Ops.push_back(getMulExpr( 2600 getConstant(MulOp.first), 2601 getAddExpr(MulOp.second, SCEV::FlagAnyWrap, Depth + 1), 2602 SCEV::FlagAnyWrap, Depth + 1)); 2603 if (Ops.empty()) 2604 return getZero(Ty); 2605 if (Ops.size() == 1) 2606 return Ops[0]; 2607 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1); 2608 } 2609 } 2610 2611 // If we are adding something to a multiply expression, make sure the 2612 // something is not already an operand of the multiply. If so, merge it into 2613 // the multiply. 2614 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 2615 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 2616 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 2617 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 2618 if (isa<SCEVConstant>(MulOpSCEV)) 2619 continue; 2620 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 2621 if (MulOpSCEV == Ops[AddOp]) { 2622 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 2623 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 2624 if (Mul->getNumOperands() != 2) { 2625 // If the multiply has more than two operands, we must get the 2626 // Y*Z term. 2627 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 2628 Mul->op_begin()+MulOp); 2629 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 2630 InnerMul = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1); 2631 } 2632 SmallVector<const SCEV *, 2> TwoOps = {getOne(Ty), InnerMul}; 2633 const SCEV *AddOne = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1); 2634 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV, 2635 SCEV::FlagAnyWrap, Depth + 1); 2636 if (Ops.size() == 2) return OuterMul; 2637 if (AddOp < Idx) { 2638 Ops.erase(Ops.begin()+AddOp); 2639 Ops.erase(Ops.begin()+Idx-1); 2640 } else { 2641 Ops.erase(Ops.begin()+Idx); 2642 Ops.erase(Ops.begin()+AddOp-1); 2643 } 2644 Ops.push_back(OuterMul); 2645 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1); 2646 } 2647 2648 // Check this multiply against other multiplies being added together. 2649 for (unsigned OtherMulIdx = Idx+1; 2650 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 2651 ++OtherMulIdx) { 2652 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 2653 // If MulOp occurs in OtherMul, we can fold the two multiplies 2654 // together. 2655 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 2656 OMulOp != e; ++OMulOp) 2657 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 2658 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 2659 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 2660 if (Mul->getNumOperands() != 2) { 2661 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 2662 Mul->op_begin()+MulOp); 2663 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 2664 InnerMul1 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1); 2665 } 2666 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 2667 if (OtherMul->getNumOperands() != 2) { 2668 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 2669 OtherMul->op_begin()+OMulOp); 2670 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end()); 2671 InnerMul2 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1); 2672 } 2673 SmallVector<const SCEV *, 2> TwoOps = {InnerMul1, InnerMul2}; 2674 const SCEV *InnerMulSum = 2675 getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1); 2676 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum, 2677 SCEV::FlagAnyWrap, Depth + 1); 2678 if (Ops.size() == 2) return OuterMul; 2679 Ops.erase(Ops.begin()+Idx); 2680 Ops.erase(Ops.begin()+OtherMulIdx-1); 2681 Ops.push_back(OuterMul); 2682 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1); 2683 } 2684 } 2685 } 2686 } 2687 2688 // If there are any add recurrences in the operands list, see if any other 2689 // added values are loop invariant. If so, we can fold them into the 2690 // recurrence. 2691 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 2692 ++Idx; 2693 2694 // Scan over all recurrences, trying to fold loop invariants into them. 2695 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 2696 // Scan all of the other operands to this add and add them to the vector if 2697 // they are loop invariant w.r.t. the recurrence. 2698 SmallVector<const SCEV *, 8> LIOps; 2699 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 2700 const Loop *AddRecLoop = AddRec->getLoop(); 2701 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2702 if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) { 2703 LIOps.push_back(Ops[i]); 2704 Ops.erase(Ops.begin()+i); 2705 --i; --e; 2706 } 2707 2708 // If we found some loop invariants, fold them into the recurrence. 2709 if (!LIOps.empty()) { 2710 // Compute nowrap flags for the addition of the loop-invariant ops and 2711 // the addrec. Temporarily push it as an operand for that purpose. 2712 LIOps.push_back(AddRec); 2713 SCEV::NoWrapFlags Flags = ComputeFlags(LIOps); 2714 LIOps.pop_back(); 2715 2716 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 2717 LIOps.push_back(AddRec->getStart()); 2718 2719 SmallVector<const SCEV *, 4> AddRecOps(AddRec->operands()); 2720 // This follows from the fact that the no-wrap flags on the outer add 2721 // expression are applicable on the 0th iteration, when the add recurrence 2722 // will be equal to its start value. 2723 AddRecOps[0] = getAddExpr(LIOps, Flags, Depth + 1); 2724 2725 // Build the new addrec. Propagate the NUW and NSW flags if both the 2726 // outer add and the inner addrec are guaranteed to have no overflow. 2727 // Always propagate NW. 2728 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW)); 2729 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags); 2730 2731 // If all of the other operands were loop invariant, we are done. 2732 if (Ops.size() == 1) return NewRec; 2733 2734 // Otherwise, add the folded AddRec by the non-invariant parts. 2735 for (unsigned i = 0;; ++i) 2736 if (Ops[i] == AddRec) { 2737 Ops[i] = NewRec; 2738 break; 2739 } 2740 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1); 2741 } 2742 2743 // Okay, if there weren't any loop invariants to be folded, check to see if 2744 // there are multiple AddRec's with the same loop induction variable being 2745 // added together. If so, we can fold them. 2746 for (unsigned OtherIdx = Idx+1; 2747 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 2748 ++OtherIdx) { 2749 // We expect the AddRecExpr's to be sorted in reverse dominance order, 2750 // so that the 1st found AddRecExpr is dominated by all others. 2751 assert(DT.dominates( 2752 cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(), 2753 AddRec->getLoop()->getHeader()) && 2754 "AddRecExprs are not sorted in reverse dominance order?"); 2755 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 2756 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L> 2757 SmallVector<const SCEV *, 4> AddRecOps(AddRec->operands()); 2758 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 2759 ++OtherIdx) { 2760 const auto *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 2761 if (OtherAddRec->getLoop() == AddRecLoop) { 2762 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); 2763 i != e; ++i) { 2764 if (i >= AddRecOps.size()) { 2765 AddRecOps.append(OtherAddRec->op_begin()+i, 2766 OtherAddRec->op_end()); 2767 break; 2768 } 2769 SmallVector<const SCEV *, 2> TwoOps = { 2770 AddRecOps[i], OtherAddRec->getOperand(i)}; 2771 AddRecOps[i] = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1); 2772 } 2773 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 2774 } 2775 } 2776 // Step size has changed, so we cannot guarantee no self-wraparound. 2777 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap); 2778 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1); 2779 } 2780 } 2781 2782 // Otherwise couldn't fold anything into this recurrence. Move onto the 2783 // next one. 2784 } 2785 2786 // Okay, it looks like we really DO need an add expr. Check to see if we 2787 // already have one, otherwise create a new one. 2788 return getOrCreateAddExpr(Ops, ComputeFlags(Ops)); 2789 } 2790 2791 const SCEV * 2792 ScalarEvolution::getOrCreateAddExpr(ArrayRef<const SCEV *> Ops, 2793 SCEV::NoWrapFlags Flags) { 2794 FoldingSetNodeID ID; 2795 ID.AddInteger(scAddExpr); 2796 for (const SCEV *Op : Ops) 2797 ID.AddPointer(Op); 2798 void *IP = nullptr; 2799 SCEVAddExpr *S = 2800 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2801 if (!S) { 2802 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2803 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2804 S = new (SCEVAllocator) 2805 SCEVAddExpr(ID.Intern(SCEVAllocator), O, Ops.size()); 2806 UniqueSCEVs.InsertNode(S, IP); 2807 addToLoopUseLists(S); 2808 } 2809 S->setNoWrapFlags(Flags); 2810 return S; 2811 } 2812 2813 const SCEV * 2814 ScalarEvolution::getOrCreateAddRecExpr(ArrayRef<const SCEV *> Ops, 2815 const Loop *L, SCEV::NoWrapFlags Flags) { 2816 FoldingSetNodeID ID; 2817 ID.AddInteger(scAddRecExpr); 2818 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2819 ID.AddPointer(Ops[i]); 2820 ID.AddPointer(L); 2821 void *IP = nullptr; 2822 SCEVAddRecExpr *S = 2823 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2824 if (!S) { 2825 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2826 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2827 S = new (SCEVAllocator) 2828 SCEVAddRecExpr(ID.Intern(SCEVAllocator), O, Ops.size(), L); 2829 UniqueSCEVs.InsertNode(S, IP); 2830 addToLoopUseLists(S); 2831 } 2832 setNoWrapFlags(S, Flags); 2833 return S; 2834 } 2835 2836 const SCEV * 2837 ScalarEvolution::getOrCreateMulExpr(ArrayRef<const SCEV *> Ops, 2838 SCEV::NoWrapFlags Flags) { 2839 FoldingSetNodeID ID; 2840 ID.AddInteger(scMulExpr); 2841 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2842 ID.AddPointer(Ops[i]); 2843 void *IP = nullptr; 2844 SCEVMulExpr *S = 2845 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2846 if (!S) { 2847 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2848 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2849 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), 2850 O, Ops.size()); 2851 UniqueSCEVs.InsertNode(S, IP); 2852 addToLoopUseLists(S); 2853 } 2854 S->setNoWrapFlags(Flags); 2855 return S; 2856 } 2857 2858 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) { 2859 uint64_t k = i*j; 2860 if (j > 1 && k / j != i) Overflow = true; 2861 return k; 2862 } 2863 2864 /// Compute the result of "n choose k", the binomial coefficient. If an 2865 /// intermediate computation overflows, Overflow will be set and the return will 2866 /// be garbage. Overflow is not cleared on absence of overflow. 2867 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) { 2868 // We use the multiplicative formula: 2869 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 . 2870 // At each iteration, we take the n-th term of the numeral and divide by the 2871 // (k-n)th term of the denominator. This division will always produce an 2872 // integral result, and helps reduce the chance of overflow in the 2873 // intermediate computations. However, we can still overflow even when the 2874 // final result would fit. 2875 2876 if (n == 0 || n == k) return 1; 2877 if (k > n) return 0; 2878 2879 if (k > n/2) 2880 k = n-k; 2881 2882 uint64_t r = 1; 2883 for (uint64_t i = 1; i <= k; ++i) { 2884 r = umul_ov(r, n-(i-1), Overflow); 2885 r /= i; 2886 } 2887 return r; 2888 } 2889 2890 /// Determine if any of the operands in this SCEV are a constant or if 2891 /// any of the add or multiply expressions in this SCEV contain a constant. 2892 static bool containsConstantInAddMulChain(const SCEV *StartExpr) { 2893 struct FindConstantInAddMulChain { 2894 bool FoundConstant = false; 2895 2896 bool follow(const SCEV *S) { 2897 FoundConstant |= isa<SCEVConstant>(S); 2898 return isa<SCEVAddExpr>(S) || isa<SCEVMulExpr>(S); 2899 } 2900 2901 bool isDone() const { 2902 return FoundConstant; 2903 } 2904 }; 2905 2906 FindConstantInAddMulChain F; 2907 SCEVTraversal<FindConstantInAddMulChain> ST(F); 2908 ST.visitAll(StartExpr); 2909 return F.FoundConstant; 2910 } 2911 2912 /// Get a canonical multiply expression, or something simpler if possible. 2913 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 2914 SCEV::NoWrapFlags OrigFlags, 2915 unsigned Depth) { 2916 assert(OrigFlags == maskFlags(OrigFlags, SCEV::FlagNUW | SCEV::FlagNSW) && 2917 "only nuw or nsw allowed"); 2918 assert(!Ops.empty() && "Cannot get empty mul!"); 2919 if (Ops.size() == 1) return Ops[0]; 2920 #ifndef NDEBUG 2921 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2922 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2923 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2924 "SCEVMulExpr operand types don't match!"); 2925 #endif 2926 2927 // Sort by complexity, this groups all similar expression types together. 2928 GroupByComplexity(Ops, &LI, DT); 2929 2930 // If there are any constants, fold them together. 2931 unsigned Idx = 0; 2932 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2933 ++Idx; 2934 assert(Idx < Ops.size()); 2935 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2936 // We found two constants, fold them together! 2937 Ops[0] = getConstant(LHSC->getAPInt() * RHSC->getAPInt()); 2938 if (Ops.size() == 2) return Ops[0]; 2939 Ops.erase(Ops.begin()+1); // Erase the folded element 2940 LHSC = cast<SCEVConstant>(Ops[0]); 2941 } 2942 2943 // If we have a multiply of zero, it will always be zero. 2944 if (LHSC->getValue()->isZero()) 2945 return LHSC; 2946 2947 // If we are left with a constant one being multiplied, strip it off. 2948 if (LHSC->getValue()->isOne()) { 2949 Ops.erase(Ops.begin()); 2950 --Idx; 2951 } 2952 2953 if (Ops.size() == 1) 2954 return Ops[0]; 2955 } 2956 2957 // Delay expensive flag strengthening until necessary. 2958 auto ComputeFlags = [this, OrigFlags](const ArrayRef<const SCEV *> Ops) { 2959 return StrengthenNoWrapFlags(this, scMulExpr, Ops, OrigFlags); 2960 }; 2961 2962 // Limit recursion calls depth. 2963 if (Depth > MaxArithDepth || hasHugeExpression(Ops)) 2964 return getOrCreateMulExpr(Ops, ComputeFlags(Ops)); 2965 2966 if (SCEV *S = std::get<0>(findExistingSCEVInCache(scMulExpr, Ops))) { 2967 // Don't strengthen flags if we have no new information. 2968 SCEVMulExpr *Mul = static_cast<SCEVMulExpr *>(S); 2969 if (Mul->getNoWrapFlags(OrigFlags) != OrigFlags) 2970 Mul->setNoWrapFlags(ComputeFlags(Ops)); 2971 return S; 2972 } 2973 2974 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2975 if (Ops.size() == 2) { 2976 // C1*(C2+V) -> C1*C2 + C1*V 2977 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 2978 // If any of Add's ops are Adds or Muls with a constant, apply this 2979 // transformation as well. 2980 // 2981 // TODO: There are some cases where this transformation is not 2982 // profitable; for example, Add = (C0 + X) * Y + Z. Maybe the scope of 2983 // this transformation should be narrowed down. 2984 if (Add->getNumOperands() == 2 && containsConstantInAddMulChain(Add)) 2985 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0), 2986 SCEV::FlagAnyWrap, Depth + 1), 2987 getMulExpr(LHSC, Add->getOperand(1), 2988 SCEV::FlagAnyWrap, Depth + 1), 2989 SCEV::FlagAnyWrap, Depth + 1); 2990 2991 if (Ops[0]->isAllOnesValue()) { 2992 // If we have a mul by -1 of an add, try distributing the -1 among the 2993 // add operands. 2994 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { 2995 SmallVector<const SCEV *, 4> NewOps; 2996 bool AnyFolded = false; 2997 for (const SCEV *AddOp : Add->operands()) { 2998 const SCEV *Mul = getMulExpr(Ops[0], AddOp, SCEV::FlagAnyWrap, 2999 Depth + 1); 3000 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; 3001 NewOps.push_back(Mul); 3002 } 3003 if (AnyFolded) 3004 return getAddExpr(NewOps, SCEV::FlagAnyWrap, Depth + 1); 3005 } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) { 3006 // Negation preserves a recurrence's no self-wrap property. 3007 SmallVector<const SCEV *, 4> Operands; 3008 for (const SCEV *AddRecOp : AddRec->operands()) 3009 Operands.push_back(getMulExpr(Ops[0], AddRecOp, SCEV::FlagAnyWrap, 3010 Depth + 1)); 3011 3012 return getAddRecExpr(Operands, AddRec->getLoop(), 3013 AddRec->getNoWrapFlags(SCEV::FlagNW)); 3014 } 3015 } 3016 } 3017 } 3018 3019 // Skip over the add expression until we get to a multiply. 3020 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 3021 ++Idx; 3022 3023 // If there are mul operands inline them all into this expression. 3024 if (Idx < Ops.size()) { 3025 bool DeletedMul = false; 3026 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 3027 if (Ops.size() > MulOpsInlineThreshold) 3028 break; 3029 // If we have an mul, expand the mul operands onto the end of the 3030 // operands list. 3031 Ops.erase(Ops.begin()+Idx); 3032 Ops.append(Mul->op_begin(), Mul->op_end()); 3033 DeletedMul = true; 3034 } 3035 3036 // If we deleted at least one mul, we added operands to the end of the 3037 // list, and they are not necessarily sorted. Recurse to resort and 3038 // resimplify any operands we just acquired. 3039 if (DeletedMul) 3040 return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1); 3041 } 3042 3043 // If there are any add recurrences in the operands list, see if any other 3044 // added values are loop invariant. If so, we can fold them into the 3045 // recurrence. 3046 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 3047 ++Idx; 3048 3049 // Scan over all recurrences, trying to fold loop invariants into them. 3050 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 3051 // Scan all of the other operands to this mul and add them to the vector 3052 // if they are loop invariant w.r.t. the recurrence. 3053 SmallVector<const SCEV *, 8> LIOps; 3054 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 3055 const Loop *AddRecLoop = AddRec->getLoop(); 3056 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 3057 if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) { 3058 LIOps.push_back(Ops[i]); 3059 Ops.erase(Ops.begin()+i); 3060 --i; --e; 3061 } 3062 3063 // If we found some loop invariants, fold them into the recurrence. 3064 if (!LIOps.empty()) { 3065 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 3066 SmallVector<const SCEV *, 4> NewOps; 3067 NewOps.reserve(AddRec->getNumOperands()); 3068 const SCEV *Scale = getMulExpr(LIOps, SCEV::FlagAnyWrap, Depth + 1); 3069 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 3070 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i), 3071 SCEV::FlagAnyWrap, Depth + 1)); 3072 3073 // Build the new addrec. Propagate the NUW and NSW flags if both the 3074 // outer mul and the inner addrec are guaranteed to have no overflow. 3075 // 3076 // No self-wrap cannot be guaranteed after changing the step size, but 3077 // will be inferred if either NUW or NSW is true. 3078 SCEV::NoWrapFlags Flags = ComputeFlags({Scale, AddRec}); 3079 const SCEV *NewRec = getAddRecExpr( 3080 NewOps, AddRecLoop, AddRec->getNoWrapFlags(Flags)); 3081 3082 // If all of the other operands were loop invariant, we are done. 3083 if (Ops.size() == 1) return NewRec; 3084 3085 // Otherwise, multiply the folded AddRec by the non-invariant parts. 3086 for (unsigned i = 0;; ++i) 3087 if (Ops[i] == AddRec) { 3088 Ops[i] = NewRec; 3089 break; 3090 } 3091 return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1); 3092 } 3093 3094 // Okay, if there weren't any loop invariants to be folded, check to see 3095 // if there are multiple AddRec's with the same loop induction variable 3096 // being multiplied together. If so, we can fold them. 3097 3098 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L> 3099 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [ 3100 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z 3101 // ]]],+,...up to x=2n}. 3102 // Note that the arguments to choose() are always integers with values 3103 // known at compile time, never SCEV objects. 3104 // 3105 // The implementation avoids pointless extra computations when the two 3106 // addrec's are of different length (mathematically, it's equivalent to 3107 // an infinite stream of zeros on the right). 3108 bool OpsModified = false; 3109 for (unsigned OtherIdx = Idx+1; 3110 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 3111 ++OtherIdx) { 3112 const SCEVAddRecExpr *OtherAddRec = 3113 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]); 3114 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop) 3115 continue; 3116 3117 // Limit max number of arguments to avoid creation of unreasonably big 3118 // SCEVAddRecs with very complex operands. 3119 if (AddRec->getNumOperands() + OtherAddRec->getNumOperands() - 1 > 3120 MaxAddRecSize || hasHugeExpression({AddRec, OtherAddRec})) 3121 continue; 3122 3123 bool Overflow = false; 3124 Type *Ty = AddRec->getType(); 3125 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64; 3126 SmallVector<const SCEV*, 7> AddRecOps; 3127 for (int x = 0, xe = AddRec->getNumOperands() + 3128 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) { 3129 SmallVector <const SCEV *, 7> SumOps; 3130 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) { 3131 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow); 3132 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1), 3133 ze = std::min(x+1, (int)OtherAddRec->getNumOperands()); 3134 z < ze && !Overflow; ++z) { 3135 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow); 3136 uint64_t Coeff; 3137 if (LargerThan64Bits) 3138 Coeff = umul_ov(Coeff1, Coeff2, Overflow); 3139 else 3140 Coeff = Coeff1*Coeff2; 3141 const SCEV *CoeffTerm = getConstant(Ty, Coeff); 3142 const SCEV *Term1 = AddRec->getOperand(y-z); 3143 const SCEV *Term2 = OtherAddRec->getOperand(z); 3144 SumOps.push_back(getMulExpr(CoeffTerm, Term1, Term2, 3145 SCEV::FlagAnyWrap, Depth + 1)); 3146 } 3147 } 3148 if (SumOps.empty()) 3149 SumOps.push_back(getZero(Ty)); 3150 AddRecOps.push_back(getAddExpr(SumOps, SCEV::FlagAnyWrap, Depth + 1)); 3151 } 3152 if (!Overflow) { 3153 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRecLoop, 3154 SCEV::FlagAnyWrap); 3155 if (Ops.size() == 2) return NewAddRec; 3156 Ops[Idx] = NewAddRec; 3157 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 3158 OpsModified = true; 3159 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec); 3160 if (!AddRec) 3161 break; 3162 } 3163 } 3164 if (OpsModified) 3165 return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1); 3166 3167 // Otherwise couldn't fold anything into this recurrence. Move onto the 3168 // next one. 3169 } 3170 3171 // Okay, it looks like we really DO need an mul expr. Check to see if we 3172 // already have one, otherwise create a new one. 3173 return getOrCreateMulExpr(Ops, ComputeFlags(Ops)); 3174 } 3175 3176 /// Represents an unsigned remainder expression based on unsigned division. 3177 const SCEV *ScalarEvolution::getURemExpr(const SCEV *LHS, 3178 const SCEV *RHS) { 3179 assert(getEffectiveSCEVType(LHS->getType()) == 3180 getEffectiveSCEVType(RHS->getType()) && 3181 "SCEVURemExpr operand types don't match!"); 3182 3183 // Short-circuit easy cases 3184 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 3185 // If constant is one, the result is trivial 3186 if (RHSC->getValue()->isOne()) 3187 return getZero(LHS->getType()); // X urem 1 --> 0 3188 3189 // If constant is a power of two, fold into a zext(trunc(LHS)). 3190 if (RHSC->getAPInt().isPowerOf2()) { 3191 Type *FullTy = LHS->getType(); 3192 Type *TruncTy = 3193 IntegerType::get(getContext(), RHSC->getAPInt().logBase2()); 3194 return getZeroExtendExpr(getTruncateExpr(LHS, TruncTy), FullTy); 3195 } 3196 } 3197 3198 // Fallback to %a == %x urem %y == %x -<nuw> ((%x udiv %y) *<nuw> %y) 3199 const SCEV *UDiv = getUDivExpr(LHS, RHS); 3200 const SCEV *Mult = getMulExpr(UDiv, RHS, SCEV::FlagNUW); 3201 return getMinusSCEV(LHS, Mult, SCEV::FlagNUW); 3202 } 3203 3204 /// Get a canonical unsigned division expression, or something simpler if 3205 /// possible. 3206 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 3207 const SCEV *RHS) { 3208 assert(getEffectiveSCEVType(LHS->getType()) == 3209 getEffectiveSCEVType(RHS->getType()) && 3210 "SCEVUDivExpr operand types don't match!"); 3211 3212 FoldingSetNodeID ID; 3213 ID.AddInteger(scUDivExpr); 3214 ID.AddPointer(LHS); 3215 ID.AddPointer(RHS); 3216 void *IP = nullptr; 3217 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) 3218 return S; 3219 3220 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 3221 if (RHSC->getValue()->isOne()) 3222 return LHS; // X udiv 1 --> x 3223 // If the denominator is zero, the result of the udiv is undefined. Don't 3224 // try to analyze it, because the resolution chosen here may differ from 3225 // the resolution chosen in other parts of the compiler. 3226 if (!RHSC->getValue()->isZero()) { 3227 // Determine if the division can be folded into the operands of 3228 // its operands. 3229 // TODO: Generalize this to non-constants by using known-bits information. 3230 Type *Ty = LHS->getType(); 3231 unsigned LZ = RHSC->getAPInt().countLeadingZeros(); 3232 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1; 3233 // For non-power-of-two values, effectively round the value up to the 3234 // nearest power of two. 3235 if (!RHSC->getAPInt().isPowerOf2()) 3236 ++MaxShiftAmt; 3237 IntegerType *ExtTy = 3238 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 3239 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 3240 if (const SCEVConstant *Step = 3241 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) { 3242 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 3243 const APInt &StepInt = Step->getAPInt(); 3244 const APInt &DivInt = RHSC->getAPInt(); 3245 if (!StepInt.urem(DivInt) && 3246 getZeroExtendExpr(AR, ExtTy) == 3247 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 3248 getZeroExtendExpr(Step, ExtTy), 3249 AR->getLoop(), SCEV::FlagAnyWrap)) { 3250 SmallVector<const SCEV *, 4> Operands; 3251 for (const SCEV *Op : AR->operands()) 3252 Operands.push_back(getUDivExpr(Op, RHS)); 3253 return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW); 3254 } 3255 /// Get a canonical UDivExpr for a recurrence. 3256 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0. 3257 // We can currently only fold X%N if X is constant. 3258 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart()); 3259 if (StartC && !DivInt.urem(StepInt) && 3260 getZeroExtendExpr(AR, ExtTy) == 3261 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 3262 getZeroExtendExpr(Step, ExtTy), 3263 AR->getLoop(), SCEV::FlagAnyWrap)) { 3264 const APInt &StartInt = StartC->getAPInt(); 3265 const APInt &StartRem = StartInt.urem(StepInt); 3266 if (StartRem != 0) { 3267 const SCEV *NewLHS = 3268 getAddRecExpr(getConstant(StartInt - StartRem), Step, 3269 AR->getLoop(), SCEV::FlagNW); 3270 if (LHS != NewLHS) { 3271 LHS = NewLHS; 3272 3273 // Reset the ID to include the new LHS, and check if it is 3274 // already cached. 3275 ID.clear(); 3276 ID.AddInteger(scUDivExpr); 3277 ID.AddPointer(LHS); 3278 ID.AddPointer(RHS); 3279 IP = nullptr; 3280 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) 3281 return S; 3282 } 3283 } 3284 } 3285 } 3286 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 3287 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 3288 SmallVector<const SCEV *, 4> Operands; 3289 for (const SCEV *Op : M->operands()) 3290 Operands.push_back(getZeroExtendExpr(Op, ExtTy)); 3291 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 3292 // Find an operand that's safely divisible. 3293 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 3294 const SCEV *Op = M->getOperand(i); 3295 const SCEV *Div = getUDivExpr(Op, RHSC); 3296 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 3297 Operands = SmallVector<const SCEV *, 4>(M->operands()); 3298 Operands[i] = Div; 3299 return getMulExpr(Operands); 3300 } 3301 } 3302 } 3303 3304 // (A/B)/C --> A/(B*C) if safe and B*C can be folded. 3305 if (const SCEVUDivExpr *OtherDiv = dyn_cast<SCEVUDivExpr>(LHS)) { 3306 if (auto *DivisorConstant = 3307 dyn_cast<SCEVConstant>(OtherDiv->getRHS())) { 3308 bool Overflow = false; 3309 APInt NewRHS = 3310 DivisorConstant->getAPInt().umul_ov(RHSC->getAPInt(), Overflow); 3311 if (Overflow) { 3312 return getConstant(RHSC->getType(), 0, false); 3313 } 3314 return getUDivExpr(OtherDiv->getLHS(), getConstant(NewRHS)); 3315 } 3316 } 3317 3318 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 3319 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) { 3320 SmallVector<const SCEV *, 4> Operands; 3321 for (const SCEV *Op : A->operands()) 3322 Operands.push_back(getZeroExtendExpr(Op, ExtTy)); 3323 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 3324 Operands.clear(); 3325 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 3326 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 3327 if (isa<SCEVUDivExpr>(Op) || 3328 getMulExpr(Op, RHS) != A->getOperand(i)) 3329 break; 3330 Operands.push_back(Op); 3331 } 3332 if (Operands.size() == A->getNumOperands()) 3333 return getAddExpr(Operands); 3334 } 3335 } 3336 3337 // Fold if both operands are constant. 3338 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 3339 Constant *LHSCV = LHSC->getValue(); 3340 Constant *RHSCV = RHSC->getValue(); 3341 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 3342 RHSCV))); 3343 } 3344 } 3345 } 3346 3347 // The Insertion Point (IP) might be invalid by now (due to UniqueSCEVs 3348 // changes). Make sure we get a new one. 3349 IP = nullptr; 3350 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 3351 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator), 3352 LHS, RHS); 3353 UniqueSCEVs.InsertNode(S, IP); 3354 addToLoopUseLists(S); 3355 return S; 3356 } 3357 3358 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) { 3359 APInt A = C1->getAPInt().abs(); 3360 APInt B = C2->getAPInt().abs(); 3361 uint32_t ABW = A.getBitWidth(); 3362 uint32_t BBW = B.getBitWidth(); 3363 3364 if (ABW > BBW) 3365 B = B.zext(ABW); 3366 else if (ABW < BBW) 3367 A = A.zext(BBW); 3368 3369 return APIntOps::GreatestCommonDivisor(std::move(A), std::move(B)); 3370 } 3371 3372 /// Get a canonical unsigned division expression, or something simpler if 3373 /// possible. There is no representation for an exact udiv in SCEV IR, but we 3374 /// can attempt to remove factors from the LHS and RHS. We can't do this when 3375 /// it's not exact because the udiv may be clearing bits. 3376 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS, 3377 const SCEV *RHS) { 3378 // TODO: we could try to find factors in all sorts of things, but for now we 3379 // just deal with u/exact (multiply, constant). See SCEVDivision towards the 3380 // end of this file for inspiration. 3381 3382 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS); 3383 if (!Mul || !Mul->hasNoUnsignedWrap()) 3384 return getUDivExpr(LHS, RHS); 3385 3386 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) { 3387 // If the mulexpr multiplies by a constant, then that constant must be the 3388 // first element of the mulexpr. 3389 if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) { 3390 if (LHSCst == RHSCst) { 3391 SmallVector<const SCEV *, 2> Operands(drop_begin(Mul->operands())); 3392 return getMulExpr(Operands); 3393 } 3394 3395 // We can't just assume that LHSCst divides RHSCst cleanly, it could be 3396 // that there's a factor provided by one of the other terms. We need to 3397 // check. 3398 APInt Factor = gcd(LHSCst, RHSCst); 3399 if (!Factor.isIntN(1)) { 3400 LHSCst = 3401 cast<SCEVConstant>(getConstant(LHSCst->getAPInt().udiv(Factor))); 3402 RHSCst = 3403 cast<SCEVConstant>(getConstant(RHSCst->getAPInt().udiv(Factor))); 3404 SmallVector<const SCEV *, 2> Operands; 3405 Operands.push_back(LHSCst); 3406 Operands.append(Mul->op_begin() + 1, Mul->op_end()); 3407 LHS = getMulExpr(Operands); 3408 RHS = RHSCst; 3409 Mul = dyn_cast<SCEVMulExpr>(LHS); 3410 if (!Mul) 3411 return getUDivExactExpr(LHS, RHS); 3412 } 3413 } 3414 } 3415 3416 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) { 3417 if (Mul->getOperand(i) == RHS) { 3418 SmallVector<const SCEV *, 2> Operands; 3419 Operands.append(Mul->op_begin(), Mul->op_begin() + i); 3420 Operands.append(Mul->op_begin() + i + 1, Mul->op_end()); 3421 return getMulExpr(Operands); 3422 } 3423 } 3424 3425 return getUDivExpr(LHS, RHS); 3426 } 3427 3428 /// Get an add recurrence expression for the specified loop. Simplify the 3429 /// expression as much as possible. 3430 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step, 3431 const Loop *L, 3432 SCEV::NoWrapFlags Flags) { 3433 SmallVector<const SCEV *, 4> Operands; 3434 Operands.push_back(Start); 3435 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 3436 if (StepChrec->getLoop() == L) { 3437 Operands.append(StepChrec->op_begin(), StepChrec->op_end()); 3438 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW)); 3439 } 3440 3441 Operands.push_back(Step); 3442 return getAddRecExpr(Operands, L, Flags); 3443 } 3444 3445 /// Get an add recurrence expression for the specified loop. Simplify the 3446 /// expression as much as possible. 3447 const SCEV * 3448 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 3449 const Loop *L, SCEV::NoWrapFlags Flags) { 3450 if (Operands.size() == 1) return Operands[0]; 3451 #ifndef NDEBUG 3452 Type *ETy = getEffectiveSCEVType(Operands[0]->getType()); 3453 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 3454 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy && 3455 "SCEVAddRecExpr operand types don't match!"); 3456 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 3457 assert(isLoopInvariant(Operands[i], L) && 3458 "SCEVAddRecExpr operand is not loop-invariant!"); 3459 #endif 3460 3461 if (Operands.back()->isZero()) { 3462 Operands.pop_back(); 3463 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X 3464 } 3465 3466 // It's tempting to want to call getConstantMaxBackedgeTakenCount count here and 3467 // use that information to infer NUW and NSW flags. However, computing a 3468 // BE count requires calling getAddRecExpr, so we may not yet have a 3469 // meaningful BE count at this point (and if we don't, we'd be stuck 3470 // with a SCEVCouldNotCompute as the cached BE count). 3471 3472 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags); 3473 3474 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 3475 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 3476 const Loop *NestedLoop = NestedAR->getLoop(); 3477 if (L->contains(NestedLoop) 3478 ? (L->getLoopDepth() < NestedLoop->getLoopDepth()) 3479 : (!NestedLoop->contains(L) && 3480 DT.dominates(L->getHeader(), NestedLoop->getHeader()))) { 3481 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->operands()); 3482 Operands[0] = NestedAR->getStart(); 3483 // AddRecs require their operands be loop-invariant with respect to their 3484 // loops. Don't perform this transformation if it would break this 3485 // requirement. 3486 bool AllInvariant = all_of( 3487 Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); }); 3488 3489 if (AllInvariant) { 3490 // Create a recurrence for the outer loop with the same step size. 3491 // 3492 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the 3493 // inner recurrence has the same property. 3494 SCEV::NoWrapFlags OuterFlags = 3495 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags()); 3496 3497 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags); 3498 AllInvariant = all_of(NestedOperands, [&](const SCEV *Op) { 3499 return isLoopInvariant(Op, NestedLoop); 3500 }); 3501 3502 if (AllInvariant) { 3503 // Ok, both add recurrences are valid after the transformation. 3504 // 3505 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if 3506 // the outer recurrence has the same property. 3507 SCEV::NoWrapFlags InnerFlags = 3508 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags); 3509 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags); 3510 } 3511 } 3512 // Reset Operands to its original state. 3513 Operands[0] = NestedAR; 3514 } 3515 } 3516 3517 // Okay, it looks like we really DO need an addrec expr. Check to see if we 3518 // already have one, otherwise create a new one. 3519 return getOrCreateAddRecExpr(Operands, L, Flags); 3520 } 3521 3522 const SCEV * 3523 ScalarEvolution::getGEPExpr(GEPOperator *GEP, 3524 const SmallVectorImpl<const SCEV *> &IndexExprs) { 3525 const SCEV *BaseExpr = getSCEV(GEP->getPointerOperand()); 3526 // getSCEV(Base)->getType() has the same address space as Base->getType() 3527 // because SCEV::getType() preserves the address space. 3528 Type *IntIdxTy = getEffectiveSCEVType(BaseExpr->getType()); 3529 // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP 3530 // instruction to its SCEV, because the Instruction may be guarded by control 3531 // flow and the no-overflow bits may not be valid for the expression in any 3532 // context. This can be fixed similarly to how these flags are handled for 3533 // adds. 3534 SCEV::NoWrapFlags OffsetWrap = 3535 GEP->isInBounds() ? SCEV::FlagNSW : SCEV::FlagAnyWrap; 3536 3537 Type *CurTy = GEP->getType(); 3538 bool FirstIter = true; 3539 SmallVector<const SCEV *, 4> Offsets; 3540 for (const SCEV *IndexExpr : IndexExprs) { 3541 // Compute the (potentially symbolic) offset in bytes for this index. 3542 if (StructType *STy = dyn_cast<StructType>(CurTy)) { 3543 // For a struct, add the member offset. 3544 ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue(); 3545 unsigned FieldNo = Index->getZExtValue(); 3546 const SCEV *FieldOffset = getOffsetOfExpr(IntIdxTy, STy, FieldNo); 3547 Offsets.push_back(FieldOffset); 3548 3549 // Update CurTy to the type of the field at Index. 3550 CurTy = STy->getTypeAtIndex(Index); 3551 } else { 3552 // Update CurTy to its element type. 3553 if (FirstIter) { 3554 assert(isa<PointerType>(CurTy) && 3555 "The first index of a GEP indexes a pointer"); 3556 CurTy = GEP->getSourceElementType(); 3557 FirstIter = false; 3558 } else { 3559 CurTy = GetElementPtrInst::getTypeAtIndex(CurTy, (uint64_t)0); 3560 } 3561 // For an array, add the element offset, explicitly scaled. 3562 const SCEV *ElementSize = getSizeOfExpr(IntIdxTy, CurTy); 3563 // Getelementptr indices are signed. 3564 IndexExpr = getTruncateOrSignExtend(IndexExpr, IntIdxTy); 3565 3566 // Multiply the index by the element size to compute the element offset. 3567 const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, OffsetWrap); 3568 Offsets.push_back(LocalOffset); 3569 } 3570 } 3571 3572 // Handle degenerate case of GEP without offsets. 3573 if (Offsets.empty()) 3574 return BaseExpr; 3575 3576 // Add the offsets together, assuming nsw if inbounds. 3577 const SCEV *Offset = getAddExpr(Offsets, OffsetWrap); 3578 // Add the base address and the offset. We cannot use the nsw flag, as the 3579 // base address is unsigned. However, if we know that the offset is 3580 // non-negative, we can use nuw. 3581 SCEV::NoWrapFlags BaseWrap = GEP->isInBounds() && isKnownNonNegative(Offset) 3582 ? SCEV::FlagNUW : SCEV::FlagAnyWrap; 3583 return getAddExpr(BaseExpr, Offset, BaseWrap); 3584 } 3585 3586 std::tuple<SCEV *, FoldingSetNodeID, void *> 3587 ScalarEvolution::findExistingSCEVInCache(SCEVTypes SCEVType, 3588 ArrayRef<const SCEV *> Ops) { 3589 FoldingSetNodeID ID; 3590 void *IP = nullptr; 3591 ID.AddInteger(SCEVType); 3592 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 3593 ID.AddPointer(Ops[i]); 3594 return std::tuple<SCEV *, FoldingSetNodeID, void *>( 3595 UniqueSCEVs.FindNodeOrInsertPos(ID, IP), std::move(ID), IP); 3596 } 3597 3598 const SCEV *ScalarEvolution::getAbsExpr(const SCEV *Op, bool IsNSW) { 3599 SCEV::NoWrapFlags Flags = IsNSW ? SCEV::FlagNSW : SCEV::FlagAnyWrap; 3600 return getSMaxExpr(Op, getNegativeSCEV(Op, Flags)); 3601 } 3602 3603 const SCEV *ScalarEvolution::getMinMaxExpr(SCEVTypes Kind, 3604 SmallVectorImpl<const SCEV *> &Ops) { 3605 assert(!Ops.empty() && "Cannot get empty (u|s)(min|max)!"); 3606 if (Ops.size() == 1) return Ops[0]; 3607 #ifndef NDEBUG 3608 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 3609 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 3610 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 3611 "Operand types don't match!"); 3612 #endif 3613 3614 bool IsSigned = Kind == scSMaxExpr || Kind == scSMinExpr; 3615 bool IsMax = Kind == scSMaxExpr || Kind == scUMaxExpr; 3616 3617 // Sort by complexity, this groups all similar expression types together. 3618 GroupByComplexity(Ops, &LI, DT); 3619 3620 // Check if we have created the same expression before. 3621 if (const SCEV *S = std::get<0>(findExistingSCEVInCache(Kind, Ops))) { 3622 return S; 3623 } 3624 3625 // If there are any constants, fold them together. 3626 unsigned Idx = 0; 3627 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 3628 ++Idx; 3629 assert(Idx < Ops.size()); 3630 auto FoldOp = [&](const APInt &LHS, const APInt &RHS) { 3631 if (Kind == scSMaxExpr) 3632 return APIntOps::smax(LHS, RHS); 3633 else if (Kind == scSMinExpr) 3634 return APIntOps::smin(LHS, RHS); 3635 else if (Kind == scUMaxExpr) 3636 return APIntOps::umax(LHS, RHS); 3637 else if (Kind == scUMinExpr) 3638 return APIntOps::umin(LHS, RHS); 3639 llvm_unreachable("Unknown SCEV min/max opcode"); 3640 }; 3641 3642 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 3643 // We found two constants, fold them together! 3644 ConstantInt *Fold = ConstantInt::get( 3645 getContext(), FoldOp(LHSC->getAPInt(), RHSC->getAPInt())); 3646 Ops[0] = getConstant(Fold); 3647 Ops.erase(Ops.begin()+1); // Erase the folded element 3648 if (Ops.size() == 1) return Ops[0]; 3649 LHSC = cast<SCEVConstant>(Ops[0]); 3650 } 3651 3652 bool IsMinV = LHSC->getValue()->isMinValue(IsSigned); 3653 bool IsMaxV = LHSC->getValue()->isMaxValue(IsSigned); 3654 3655 if (IsMax ? IsMinV : IsMaxV) { 3656 // If we are left with a constant minimum(/maximum)-int, strip it off. 3657 Ops.erase(Ops.begin()); 3658 --Idx; 3659 } else if (IsMax ? IsMaxV : IsMinV) { 3660 // If we have a max(/min) with a constant maximum(/minimum)-int, 3661 // it will always be the extremum. 3662 return LHSC; 3663 } 3664 3665 if (Ops.size() == 1) return Ops[0]; 3666 } 3667 3668 // Find the first operation of the same kind 3669 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < Kind) 3670 ++Idx; 3671 3672 // Check to see if one of the operands is of the same kind. If so, expand its 3673 // operands onto our operand list, and recurse to simplify. 3674 if (Idx < Ops.size()) { 3675 bool DeletedAny = false; 3676 while (Ops[Idx]->getSCEVType() == Kind) { 3677 const SCEVMinMaxExpr *SMME = cast<SCEVMinMaxExpr>(Ops[Idx]); 3678 Ops.erase(Ops.begin()+Idx); 3679 Ops.append(SMME->op_begin(), SMME->op_end()); 3680 DeletedAny = true; 3681 } 3682 3683 if (DeletedAny) 3684 return getMinMaxExpr(Kind, Ops); 3685 } 3686 3687 // Okay, check to see if the same value occurs in the operand list twice. If 3688 // so, delete one. Since we sorted the list, these values are required to 3689 // be adjacent. 3690 llvm::CmpInst::Predicate GEPred = 3691 IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE; 3692 llvm::CmpInst::Predicate LEPred = 3693 IsSigned ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE; 3694 llvm::CmpInst::Predicate FirstPred = IsMax ? GEPred : LEPred; 3695 llvm::CmpInst::Predicate SecondPred = IsMax ? LEPred : GEPred; 3696 for (unsigned i = 0, e = Ops.size() - 1; i != e; ++i) { 3697 if (Ops[i] == Ops[i + 1] || 3698 isKnownViaNonRecursiveReasoning(FirstPred, Ops[i], Ops[i + 1])) { 3699 // X op Y op Y --> X op Y 3700 // X op Y --> X, if we know X, Y are ordered appropriately 3701 Ops.erase(Ops.begin() + i + 1, Ops.begin() + i + 2); 3702 --i; 3703 --e; 3704 } else if (isKnownViaNonRecursiveReasoning(SecondPred, Ops[i], 3705 Ops[i + 1])) { 3706 // X op Y --> Y, if we know X, Y are ordered appropriately 3707 Ops.erase(Ops.begin() + i, Ops.begin() + i + 1); 3708 --i; 3709 --e; 3710 } 3711 } 3712 3713 if (Ops.size() == 1) return Ops[0]; 3714 3715 assert(!Ops.empty() && "Reduced smax down to nothing!"); 3716 3717 // Okay, it looks like we really DO need an expr. Check to see if we 3718 // already have one, otherwise create a new one. 3719 const SCEV *ExistingSCEV; 3720 FoldingSetNodeID ID; 3721 void *IP; 3722 std::tie(ExistingSCEV, ID, IP) = findExistingSCEVInCache(Kind, Ops); 3723 if (ExistingSCEV) 3724 return ExistingSCEV; 3725 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 3726 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 3727 SCEV *S = new (SCEVAllocator) 3728 SCEVMinMaxExpr(ID.Intern(SCEVAllocator), Kind, O, Ops.size()); 3729 3730 UniqueSCEVs.InsertNode(S, IP); 3731 addToLoopUseLists(S); 3732 return S; 3733 } 3734 3735 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, const SCEV *RHS) { 3736 SmallVector<const SCEV *, 2> Ops = {LHS, RHS}; 3737 return getSMaxExpr(Ops); 3738 } 3739 3740 const SCEV *ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 3741 return getMinMaxExpr(scSMaxExpr, Ops); 3742 } 3743 3744 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, const SCEV *RHS) { 3745 SmallVector<const SCEV *, 2> Ops = {LHS, RHS}; 3746 return getUMaxExpr(Ops); 3747 } 3748 3749 const SCEV *ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 3750 return getMinMaxExpr(scUMaxExpr, Ops); 3751 } 3752 3753 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 3754 const SCEV *RHS) { 3755 SmallVector<const SCEV *, 2> Ops = { LHS, RHS }; 3756 return getSMinExpr(Ops); 3757 } 3758 3759 const SCEV *ScalarEvolution::getSMinExpr(SmallVectorImpl<const SCEV *> &Ops) { 3760 return getMinMaxExpr(scSMinExpr, Ops); 3761 } 3762 3763 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 3764 const SCEV *RHS) { 3765 SmallVector<const SCEV *, 2> Ops = { LHS, RHS }; 3766 return getUMinExpr(Ops); 3767 } 3768 3769 const SCEV *ScalarEvolution::getUMinExpr(SmallVectorImpl<const SCEV *> &Ops) { 3770 return getMinMaxExpr(scUMinExpr, Ops); 3771 } 3772 3773 const SCEV * 3774 ScalarEvolution::getSizeOfScalableVectorExpr(Type *IntTy, 3775 ScalableVectorType *ScalableTy) { 3776 Constant *NullPtr = Constant::getNullValue(ScalableTy->getPointerTo()); 3777 Constant *One = ConstantInt::get(IntTy, 1); 3778 Constant *GEP = ConstantExpr::getGetElementPtr(ScalableTy, NullPtr, One); 3779 // Note that the expression we created is the final expression, we don't 3780 // want to simplify it any further Also, if we call a normal getSCEV(), 3781 // we'll end up in an endless recursion. So just create an SCEVUnknown. 3782 return getUnknown(ConstantExpr::getPtrToInt(GEP, IntTy)); 3783 } 3784 3785 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) { 3786 if (auto *ScalableAllocTy = dyn_cast<ScalableVectorType>(AllocTy)) 3787 return getSizeOfScalableVectorExpr(IntTy, ScalableAllocTy); 3788 // We can bypass creating a target-independent constant expression and then 3789 // folding it back into a ConstantInt. This is just a compile-time 3790 // optimization. 3791 return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy)); 3792 } 3793 3794 const SCEV *ScalarEvolution::getStoreSizeOfExpr(Type *IntTy, Type *StoreTy) { 3795 if (auto *ScalableStoreTy = dyn_cast<ScalableVectorType>(StoreTy)) 3796 return getSizeOfScalableVectorExpr(IntTy, ScalableStoreTy); 3797 // We can bypass creating a target-independent constant expression and then 3798 // folding it back into a ConstantInt. This is just a compile-time 3799 // optimization. 3800 return getConstant(IntTy, getDataLayout().getTypeStoreSize(StoreTy)); 3801 } 3802 3803 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy, 3804 StructType *STy, 3805 unsigned FieldNo) { 3806 // We can bypass creating a target-independent constant expression and then 3807 // folding it back into a ConstantInt. This is just a compile-time 3808 // optimization. 3809 return getConstant( 3810 IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo)); 3811 } 3812 3813 const SCEV *ScalarEvolution::getUnknown(Value *V) { 3814 // Don't attempt to do anything other than create a SCEVUnknown object 3815 // here. createSCEV only calls getUnknown after checking for all other 3816 // interesting possibilities, and any other code that calls getUnknown 3817 // is doing so in order to hide a value from SCEV canonicalization. 3818 3819 FoldingSetNodeID ID; 3820 ID.AddInteger(scUnknown); 3821 ID.AddPointer(V); 3822 void *IP = nullptr; 3823 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) { 3824 assert(cast<SCEVUnknown>(S)->getValue() == V && 3825 "Stale SCEVUnknown in uniquing map!"); 3826 return S; 3827 } 3828 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this, 3829 FirstUnknown); 3830 FirstUnknown = cast<SCEVUnknown>(S); 3831 UniqueSCEVs.InsertNode(S, IP); 3832 return S; 3833 } 3834 3835 //===----------------------------------------------------------------------===// 3836 // Basic SCEV Analysis and PHI Idiom Recognition Code 3837 // 3838 3839 /// Test if values of the given type are analyzable within the SCEV 3840 /// framework. This primarily includes integer types, and it can optionally 3841 /// include pointer types if the ScalarEvolution class has access to 3842 /// target-specific information. 3843 bool ScalarEvolution::isSCEVable(Type *Ty) const { 3844 // Integers and pointers are always SCEVable. 3845 return Ty->isIntOrPtrTy(); 3846 } 3847 3848 /// Return the size in bits of the specified type, for which isSCEVable must 3849 /// return true. 3850 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const { 3851 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 3852 if (Ty->isPointerTy()) 3853 return getDataLayout().getIndexTypeSizeInBits(Ty); 3854 return getDataLayout().getTypeSizeInBits(Ty); 3855 } 3856 3857 /// Return a type with the same bitwidth as the given type and which represents 3858 /// how SCEV will treat the given type, for which isSCEVable must return 3859 /// true. For pointer types, this is the pointer index sized integer type. 3860 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const { 3861 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 3862 3863 if (Ty->isIntegerTy()) 3864 return Ty; 3865 3866 // The only other support type is pointer. 3867 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"); 3868 return getDataLayout().getIndexType(Ty); 3869 } 3870 3871 Type *ScalarEvolution::getWiderType(Type *T1, Type *T2) const { 3872 return getTypeSizeInBits(T1) >= getTypeSizeInBits(T2) ? T1 : T2; 3873 } 3874 3875 const SCEV *ScalarEvolution::getCouldNotCompute() { 3876 return CouldNotCompute.get(); 3877 } 3878 3879 bool ScalarEvolution::checkValidity(const SCEV *S) const { 3880 bool ContainsNulls = SCEVExprContains(S, [](const SCEV *S) { 3881 auto *SU = dyn_cast<SCEVUnknown>(S); 3882 return SU && SU->getValue() == nullptr; 3883 }); 3884 3885 return !ContainsNulls; 3886 } 3887 3888 bool ScalarEvolution::containsAddRecurrence(const SCEV *S) { 3889 HasRecMapType::iterator I = HasRecMap.find(S); 3890 if (I != HasRecMap.end()) 3891 return I->second; 3892 3893 bool FoundAddRec = 3894 SCEVExprContains(S, [](const SCEV *S) { return isa<SCEVAddRecExpr>(S); }); 3895 HasRecMap.insert({S, FoundAddRec}); 3896 return FoundAddRec; 3897 } 3898 3899 /// Try to split a SCEVAddExpr into a pair of {SCEV, ConstantInt}. 3900 /// If \p S is a SCEVAddExpr and is composed of a sub SCEV S' and an 3901 /// offset I, then return {S', I}, else return {\p S, nullptr}. 3902 static std::pair<const SCEV *, ConstantInt *> splitAddExpr(const SCEV *S) { 3903 const auto *Add = dyn_cast<SCEVAddExpr>(S); 3904 if (!Add) 3905 return {S, nullptr}; 3906 3907 if (Add->getNumOperands() != 2) 3908 return {S, nullptr}; 3909 3910 auto *ConstOp = dyn_cast<SCEVConstant>(Add->getOperand(0)); 3911 if (!ConstOp) 3912 return {S, nullptr}; 3913 3914 return {Add->getOperand(1), ConstOp->getValue()}; 3915 } 3916 3917 /// Return the ValueOffsetPair set for \p S. \p S can be represented 3918 /// by the value and offset from any ValueOffsetPair in the set. 3919 ScalarEvolution::ValueOffsetPairSetVector * 3920 ScalarEvolution::getSCEVValues(const SCEV *S) { 3921 ExprValueMapType::iterator SI = ExprValueMap.find_as(S); 3922 if (SI == ExprValueMap.end()) 3923 return nullptr; 3924 #ifndef NDEBUG 3925 if (VerifySCEVMap) { 3926 // Check there is no dangling Value in the set returned. 3927 for (const auto &VE : SI->second) 3928 assert(ValueExprMap.count(VE.first)); 3929 } 3930 #endif 3931 return &SI->second; 3932 } 3933 3934 /// Erase Value from ValueExprMap and ExprValueMap. ValueExprMap.erase(V) 3935 /// cannot be used separately. eraseValueFromMap should be used to remove 3936 /// V from ValueExprMap and ExprValueMap at the same time. 3937 void ScalarEvolution::eraseValueFromMap(Value *V) { 3938 ValueExprMapType::iterator I = ValueExprMap.find_as(V); 3939 if (I != ValueExprMap.end()) { 3940 const SCEV *S = I->second; 3941 // Remove {V, 0} from the set of ExprValueMap[S] 3942 if (auto *SV = getSCEVValues(S)) 3943 SV->remove({V, nullptr}); 3944 3945 // Remove {V, Offset} from the set of ExprValueMap[Stripped] 3946 const SCEV *Stripped; 3947 ConstantInt *Offset; 3948 std::tie(Stripped, Offset) = splitAddExpr(S); 3949 if (Offset != nullptr) { 3950 if (auto *SV = getSCEVValues(Stripped)) 3951 SV->remove({V, Offset}); 3952 } 3953 ValueExprMap.erase(V); 3954 } 3955 } 3956 3957 /// Check whether value has nuw/nsw/exact set but SCEV does not. 3958 /// TODO: In reality it is better to check the poison recursively 3959 /// but this is better than nothing. 3960 static bool SCEVLostPoisonFlags(const SCEV *S, const Value *V) { 3961 if (auto *I = dyn_cast<Instruction>(V)) { 3962 if (isa<OverflowingBinaryOperator>(I)) { 3963 if (auto *NS = dyn_cast<SCEVNAryExpr>(S)) { 3964 if (I->hasNoSignedWrap() && !NS->hasNoSignedWrap()) 3965 return true; 3966 if (I->hasNoUnsignedWrap() && !NS->hasNoUnsignedWrap()) 3967 return true; 3968 } 3969 } else if (isa<PossiblyExactOperator>(I) && I->isExact()) 3970 return true; 3971 } 3972 return false; 3973 } 3974 3975 /// Return an existing SCEV if it exists, otherwise analyze the expression and 3976 /// create a new one. 3977 const SCEV *ScalarEvolution::getSCEV(Value *V) { 3978 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 3979 3980 const SCEV *S = getExistingSCEV(V); 3981 if (S == nullptr) { 3982 S = createSCEV(V); 3983 // During PHI resolution, it is possible to create two SCEVs for the same 3984 // V, so it is needed to double check whether V->S is inserted into 3985 // ValueExprMap before insert S->{V, 0} into ExprValueMap. 3986 std::pair<ValueExprMapType::iterator, bool> Pair = 3987 ValueExprMap.insert({SCEVCallbackVH(V, this), S}); 3988 if (Pair.second && !SCEVLostPoisonFlags(S, V)) { 3989 ExprValueMap[S].insert({V, nullptr}); 3990 3991 // If S == Stripped + Offset, add Stripped -> {V, Offset} into 3992 // ExprValueMap. 3993 const SCEV *Stripped = S; 3994 ConstantInt *Offset = nullptr; 3995 std::tie(Stripped, Offset) = splitAddExpr(S); 3996 // If stripped is SCEVUnknown, don't bother to save 3997 // Stripped -> {V, offset}. It doesn't simplify and sometimes even 3998 // increase the complexity of the expansion code. 3999 // If V is GetElementPtrInst, don't save Stripped -> {V, offset} 4000 // because it may generate add/sub instead of GEP in SCEV expansion. 4001 if (Offset != nullptr && !isa<SCEVUnknown>(Stripped) && 4002 !isa<GetElementPtrInst>(V)) 4003 ExprValueMap[Stripped].insert({V, Offset}); 4004 } 4005 } 4006 return S; 4007 } 4008 4009 const SCEV *ScalarEvolution::getExistingSCEV(Value *V) { 4010 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 4011 4012 ValueExprMapType::iterator I = ValueExprMap.find_as(V); 4013 if (I != ValueExprMap.end()) { 4014 const SCEV *S = I->second; 4015 if (checkValidity(S)) 4016 return S; 4017 eraseValueFromMap(V); 4018 forgetMemoizedResults(S); 4019 } 4020 return nullptr; 4021 } 4022 4023 /// Return a SCEV corresponding to -V = -1*V 4024 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V, 4025 SCEV::NoWrapFlags Flags) { 4026 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 4027 return getConstant( 4028 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 4029 4030 Type *Ty = V->getType(); 4031 Ty = getEffectiveSCEVType(Ty); 4032 return getMulExpr(V, getMinusOne(Ty), Flags); 4033 } 4034 4035 /// If Expr computes ~A, return A else return nullptr 4036 static const SCEV *MatchNotExpr(const SCEV *Expr) { 4037 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr); 4038 if (!Add || Add->getNumOperands() != 2 || 4039 !Add->getOperand(0)->isAllOnesValue()) 4040 return nullptr; 4041 4042 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1)); 4043 if (!AddRHS || AddRHS->getNumOperands() != 2 || 4044 !AddRHS->getOperand(0)->isAllOnesValue()) 4045 return nullptr; 4046 4047 return AddRHS->getOperand(1); 4048 } 4049 4050 /// Return a SCEV corresponding to ~V = -1-V 4051 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 4052 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 4053 return getConstant( 4054 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 4055 4056 // Fold ~(u|s)(min|max)(~x, ~y) to (u|s)(max|min)(x, y) 4057 if (const SCEVMinMaxExpr *MME = dyn_cast<SCEVMinMaxExpr>(V)) { 4058 auto MatchMinMaxNegation = [&](const SCEVMinMaxExpr *MME) { 4059 SmallVector<const SCEV *, 2> MatchedOperands; 4060 for (const SCEV *Operand : MME->operands()) { 4061 const SCEV *Matched = MatchNotExpr(Operand); 4062 if (!Matched) 4063 return (const SCEV *)nullptr; 4064 MatchedOperands.push_back(Matched); 4065 } 4066 return getMinMaxExpr(SCEVMinMaxExpr::negate(MME->getSCEVType()), 4067 MatchedOperands); 4068 }; 4069 if (const SCEV *Replaced = MatchMinMaxNegation(MME)) 4070 return Replaced; 4071 } 4072 4073 Type *Ty = V->getType(); 4074 Ty = getEffectiveSCEVType(Ty); 4075 return getMinusSCEV(getMinusOne(Ty), V); 4076 } 4077 4078 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS, 4079 SCEV::NoWrapFlags Flags, 4080 unsigned Depth) { 4081 // Fast path: X - X --> 0. 4082 if (LHS == RHS) 4083 return getZero(LHS->getType()); 4084 4085 // We represent LHS - RHS as LHS + (-1)*RHS. This transformation 4086 // makes it so that we cannot make much use of NUW. 4087 auto AddFlags = SCEV::FlagAnyWrap; 4088 const bool RHSIsNotMinSigned = 4089 !getSignedRangeMin(RHS).isMinSignedValue(); 4090 if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) { 4091 // Let M be the minimum representable signed value. Then (-1)*RHS 4092 // signed-wraps if and only if RHS is M. That can happen even for 4093 // a NSW subtraction because e.g. (-1)*M signed-wraps even though 4094 // -1 - M does not. So to transfer NSW from LHS - RHS to LHS + 4095 // (-1)*RHS, we need to prove that RHS != M. 4096 // 4097 // If LHS is non-negative and we know that LHS - RHS does not 4098 // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap 4099 // either by proving that RHS > M or that LHS >= 0. 4100 if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) { 4101 AddFlags = SCEV::FlagNSW; 4102 } 4103 } 4104 4105 // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS - 4106 // RHS is NSW and LHS >= 0. 4107 // 4108 // The difficulty here is that the NSW flag may have been proven 4109 // relative to a loop that is to be found in a recurrence in LHS and 4110 // not in RHS. Applying NSW to (-1)*M may then let the NSW have a 4111 // larger scope than intended. 4112 auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap; 4113 4114 return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags, Depth); 4115 } 4116 4117 const SCEV *ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty, 4118 unsigned Depth) { 4119 Type *SrcTy = V->getType(); 4120 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && 4121 "Cannot truncate or zero extend with non-integer arguments!"); 4122 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 4123 return V; // No conversion 4124 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 4125 return getTruncateExpr(V, Ty, Depth); 4126 return getZeroExtendExpr(V, Ty, Depth); 4127 } 4128 4129 const SCEV *ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, Type *Ty, 4130 unsigned Depth) { 4131 Type *SrcTy = V->getType(); 4132 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && 4133 "Cannot truncate or zero extend with non-integer arguments!"); 4134 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 4135 return V; // No conversion 4136 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 4137 return getTruncateExpr(V, Ty, Depth); 4138 return getSignExtendExpr(V, Ty, Depth); 4139 } 4140 4141 const SCEV * 4142 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) { 4143 Type *SrcTy = V->getType(); 4144 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && 4145 "Cannot noop or zero extend with non-integer arguments!"); 4146 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 4147 "getNoopOrZeroExtend cannot truncate!"); 4148 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 4149 return V; // No conversion 4150 return getZeroExtendExpr(V, Ty); 4151 } 4152 4153 const SCEV * 4154 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) { 4155 Type *SrcTy = V->getType(); 4156 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && 4157 "Cannot noop or sign extend with non-integer arguments!"); 4158 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 4159 "getNoopOrSignExtend cannot truncate!"); 4160 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 4161 return V; // No conversion 4162 return getSignExtendExpr(V, Ty); 4163 } 4164 4165 const SCEV * 4166 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) { 4167 Type *SrcTy = V->getType(); 4168 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && 4169 "Cannot noop or any extend with non-integer arguments!"); 4170 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 4171 "getNoopOrAnyExtend cannot truncate!"); 4172 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 4173 return V; // No conversion 4174 return getAnyExtendExpr(V, Ty); 4175 } 4176 4177 const SCEV * 4178 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) { 4179 Type *SrcTy = V->getType(); 4180 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && 4181 "Cannot truncate or noop with non-integer arguments!"); 4182 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 4183 "getTruncateOrNoop cannot extend!"); 4184 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 4185 return V; // No conversion 4186 return getTruncateExpr(V, Ty); 4187 } 4188 4189 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 4190 const SCEV *RHS) { 4191 const SCEV *PromotedLHS = LHS; 4192 const SCEV *PromotedRHS = RHS; 4193 4194 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 4195 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 4196 else 4197 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 4198 4199 return getUMaxExpr(PromotedLHS, PromotedRHS); 4200 } 4201 4202 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 4203 const SCEV *RHS) { 4204 SmallVector<const SCEV *, 2> Ops = { LHS, RHS }; 4205 return getUMinFromMismatchedTypes(Ops); 4206 } 4207 4208 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes( 4209 SmallVectorImpl<const SCEV *> &Ops) { 4210 assert(!Ops.empty() && "At least one operand must be!"); 4211 // Trivial case. 4212 if (Ops.size() == 1) 4213 return Ops[0]; 4214 4215 // Find the max type first. 4216 Type *MaxType = nullptr; 4217 for (auto *S : Ops) 4218 if (MaxType) 4219 MaxType = getWiderType(MaxType, S->getType()); 4220 else 4221 MaxType = S->getType(); 4222 assert(MaxType && "Failed to find maximum type!"); 4223 4224 // Extend all ops to max type. 4225 SmallVector<const SCEV *, 2> PromotedOps; 4226 for (auto *S : Ops) 4227 PromotedOps.push_back(getNoopOrZeroExtend(S, MaxType)); 4228 4229 // Generate umin. 4230 return getUMinExpr(PromotedOps); 4231 } 4232 4233 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) { 4234 // A pointer operand may evaluate to a nonpointer expression, such as null. 4235 if (!V->getType()->isPointerTy()) 4236 return V; 4237 4238 while (true) { 4239 if (const SCEVIntegralCastExpr *Cast = dyn_cast<SCEVIntegralCastExpr>(V)) { 4240 V = Cast->getOperand(); 4241 } else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) { 4242 const SCEV *PtrOp = nullptr; 4243 for (const SCEV *NAryOp : NAry->operands()) { 4244 if (NAryOp->getType()->isPointerTy()) { 4245 // Cannot find the base of an expression with multiple pointer ops. 4246 if (PtrOp) 4247 return V; 4248 PtrOp = NAryOp; 4249 } 4250 } 4251 if (!PtrOp) // All operands were non-pointer. 4252 return V; 4253 V = PtrOp; 4254 } else // Not something we can look further into. 4255 return V; 4256 } 4257 } 4258 4259 /// Push users of the given Instruction onto the given Worklist. 4260 static void 4261 PushDefUseChildren(Instruction *I, 4262 SmallVectorImpl<Instruction *> &Worklist) { 4263 // Push the def-use children onto the Worklist stack. 4264 for (User *U : I->users()) 4265 Worklist.push_back(cast<Instruction>(U)); 4266 } 4267 4268 void ScalarEvolution::forgetSymbolicName(Instruction *PN, const SCEV *SymName) { 4269 SmallVector<Instruction *, 16> Worklist; 4270 PushDefUseChildren(PN, Worklist); 4271 4272 SmallPtrSet<Instruction *, 8> Visited; 4273 Visited.insert(PN); 4274 while (!Worklist.empty()) { 4275 Instruction *I = Worklist.pop_back_val(); 4276 if (!Visited.insert(I).second) 4277 continue; 4278 4279 auto It = ValueExprMap.find_as(static_cast<Value *>(I)); 4280 if (It != ValueExprMap.end()) { 4281 const SCEV *Old = It->second; 4282 4283 // Short-circuit the def-use traversal if the symbolic name 4284 // ceases to appear in expressions. 4285 if (Old != SymName && !hasOperand(Old, SymName)) 4286 continue; 4287 4288 // SCEVUnknown for a PHI either means that it has an unrecognized 4289 // structure, it's a PHI that's in the progress of being computed 4290 // by createNodeForPHI, or it's a single-value PHI. In the first case, 4291 // additional loop trip count information isn't going to change anything. 4292 // In the second case, createNodeForPHI will perform the necessary 4293 // updates on its own when it gets to that point. In the third, we do 4294 // want to forget the SCEVUnknown. 4295 if (!isa<PHINode>(I) || 4296 !isa<SCEVUnknown>(Old) || 4297 (I != PN && Old == SymName)) { 4298 eraseValueFromMap(It->first); 4299 forgetMemoizedResults(Old); 4300 } 4301 } 4302 4303 PushDefUseChildren(I, Worklist); 4304 } 4305 } 4306 4307 namespace { 4308 4309 /// Takes SCEV S and Loop L. For each AddRec sub-expression, use its start 4310 /// expression in case its Loop is L. If it is not L then 4311 /// if IgnoreOtherLoops is true then use AddRec itself 4312 /// otherwise rewrite cannot be done. 4313 /// If SCEV contains non-invariant unknown SCEV rewrite cannot be done. 4314 class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> { 4315 public: 4316 static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE, 4317 bool IgnoreOtherLoops = true) { 4318 SCEVInitRewriter Rewriter(L, SE); 4319 const SCEV *Result = Rewriter.visit(S); 4320 if (Rewriter.hasSeenLoopVariantSCEVUnknown()) 4321 return SE.getCouldNotCompute(); 4322 return Rewriter.hasSeenOtherLoops() && !IgnoreOtherLoops 4323 ? SE.getCouldNotCompute() 4324 : Result; 4325 } 4326 4327 const SCEV *visitUnknown(const SCEVUnknown *Expr) { 4328 if (!SE.isLoopInvariant(Expr, L)) 4329 SeenLoopVariantSCEVUnknown = true; 4330 return Expr; 4331 } 4332 4333 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) { 4334 // Only re-write AddRecExprs for this loop. 4335 if (Expr->getLoop() == L) 4336 return Expr->getStart(); 4337 SeenOtherLoops = true; 4338 return Expr; 4339 } 4340 4341 bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; } 4342 4343 bool hasSeenOtherLoops() { return SeenOtherLoops; } 4344 4345 private: 4346 explicit SCEVInitRewriter(const Loop *L, ScalarEvolution &SE) 4347 : SCEVRewriteVisitor(SE), L(L) {} 4348 4349 const Loop *L; 4350 bool SeenLoopVariantSCEVUnknown = false; 4351 bool SeenOtherLoops = false; 4352 }; 4353 4354 /// Takes SCEV S and Loop L. For each AddRec sub-expression, use its post 4355 /// increment expression in case its Loop is L. If it is not L then 4356 /// use AddRec itself. 4357 /// If SCEV contains non-invariant unknown SCEV rewrite cannot be done. 4358 class SCEVPostIncRewriter : public SCEVRewriteVisitor<SCEVPostIncRewriter> { 4359 public: 4360 static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE) { 4361 SCEVPostIncRewriter Rewriter(L, SE); 4362 const SCEV *Result = Rewriter.visit(S); 4363 return Rewriter.hasSeenLoopVariantSCEVUnknown() 4364 ? SE.getCouldNotCompute() 4365 : Result; 4366 } 4367 4368 const SCEV *visitUnknown(const SCEVUnknown *Expr) { 4369 if (!SE.isLoopInvariant(Expr, L)) 4370 SeenLoopVariantSCEVUnknown = true; 4371 return Expr; 4372 } 4373 4374 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) { 4375 // Only re-write AddRecExprs for this loop. 4376 if (Expr->getLoop() == L) 4377 return Expr->getPostIncExpr(SE); 4378 SeenOtherLoops = true; 4379 return Expr; 4380 } 4381 4382 bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; } 4383 4384 bool hasSeenOtherLoops() { return SeenOtherLoops; } 4385 4386 private: 4387 explicit SCEVPostIncRewriter(const Loop *L, ScalarEvolution &SE) 4388 : SCEVRewriteVisitor(SE), L(L) {} 4389 4390 const Loop *L; 4391 bool SeenLoopVariantSCEVUnknown = false; 4392 bool SeenOtherLoops = false; 4393 }; 4394 4395 /// This class evaluates the compare condition by matching it against the 4396 /// condition of loop latch. If there is a match we assume a true value 4397 /// for the condition while building SCEV nodes. 4398 class SCEVBackedgeConditionFolder 4399 : public SCEVRewriteVisitor<SCEVBackedgeConditionFolder> { 4400 public: 4401 static const SCEV *rewrite(const SCEV *S, const Loop *L, 4402 ScalarEvolution &SE) { 4403 bool IsPosBECond = false; 4404 Value *BECond = nullptr; 4405 if (BasicBlock *Latch = L->getLoopLatch()) { 4406 BranchInst *BI = dyn_cast<BranchInst>(Latch->getTerminator()); 4407 if (BI && BI->isConditional()) { 4408 assert(BI->getSuccessor(0) != BI->getSuccessor(1) && 4409 "Both outgoing branches should not target same header!"); 4410 BECond = BI->getCondition(); 4411 IsPosBECond = BI->getSuccessor(0) == L->getHeader(); 4412 } else { 4413 return S; 4414 } 4415 } 4416 SCEVBackedgeConditionFolder Rewriter(L, BECond, IsPosBECond, SE); 4417 return Rewriter.visit(S); 4418 } 4419 4420 const SCEV *visitUnknown(const SCEVUnknown *Expr) { 4421 const SCEV *Result = Expr; 4422 bool InvariantF = SE.isLoopInvariant(Expr, L); 4423 4424 if (!InvariantF) { 4425 Instruction *I = cast<Instruction>(Expr->getValue()); 4426 switch (I->getOpcode()) { 4427 case Instruction::Select: { 4428 SelectInst *SI = cast<SelectInst>(I); 4429 Optional<const SCEV *> Res = 4430 compareWithBackedgeCondition(SI->getCondition()); 4431 if (Res.hasValue()) { 4432 bool IsOne = cast<SCEVConstant>(Res.getValue())->getValue()->isOne(); 4433 Result = SE.getSCEV(IsOne ? SI->getTrueValue() : SI->getFalseValue()); 4434 } 4435 break; 4436 } 4437 default: { 4438 Optional<const SCEV *> Res = compareWithBackedgeCondition(I); 4439 if (Res.hasValue()) 4440 Result = Res.getValue(); 4441 break; 4442 } 4443 } 4444 } 4445 return Result; 4446 } 4447 4448 private: 4449 explicit SCEVBackedgeConditionFolder(const Loop *L, Value *BECond, 4450 bool IsPosBECond, ScalarEvolution &SE) 4451 : SCEVRewriteVisitor(SE), L(L), BackedgeCond(BECond), 4452 IsPositiveBECond(IsPosBECond) {} 4453 4454 Optional<const SCEV *> compareWithBackedgeCondition(Value *IC); 4455 4456 const Loop *L; 4457 /// Loop back condition. 4458 Value *BackedgeCond = nullptr; 4459 /// Set to true if loop back is on positive branch condition. 4460 bool IsPositiveBECond; 4461 }; 4462 4463 Optional<const SCEV *> 4464 SCEVBackedgeConditionFolder::compareWithBackedgeCondition(Value *IC) { 4465 4466 // If value matches the backedge condition for loop latch, 4467 // then return a constant evolution node based on loopback 4468 // branch taken. 4469 if (BackedgeCond == IC) 4470 return IsPositiveBECond ? SE.getOne(Type::getInt1Ty(SE.getContext())) 4471 : SE.getZero(Type::getInt1Ty(SE.getContext())); 4472 return None; 4473 } 4474 4475 class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> { 4476 public: 4477 static const SCEV *rewrite(const SCEV *S, const Loop *L, 4478 ScalarEvolution &SE) { 4479 SCEVShiftRewriter Rewriter(L, SE); 4480 const SCEV *Result = Rewriter.visit(S); 4481 return Rewriter.isValid() ? Result : SE.getCouldNotCompute(); 4482 } 4483 4484 const SCEV *visitUnknown(const SCEVUnknown *Expr) { 4485 // Only allow AddRecExprs for this loop. 4486 if (!SE.isLoopInvariant(Expr, L)) 4487 Valid = false; 4488 return Expr; 4489 } 4490 4491 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) { 4492 if (Expr->getLoop() == L && Expr->isAffine()) 4493 return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE)); 4494 Valid = false; 4495 return Expr; 4496 } 4497 4498 bool isValid() { return Valid; } 4499 4500 private: 4501 explicit SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE) 4502 : SCEVRewriteVisitor(SE), L(L) {} 4503 4504 const Loop *L; 4505 bool Valid = true; 4506 }; 4507 4508 } // end anonymous namespace 4509 4510 SCEV::NoWrapFlags 4511 ScalarEvolution::proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR) { 4512 if (!AR->isAffine()) 4513 return SCEV::FlagAnyWrap; 4514 4515 using OBO = OverflowingBinaryOperator; 4516 4517 SCEV::NoWrapFlags Result = SCEV::FlagAnyWrap; 4518 4519 if (!AR->hasNoSignedWrap()) { 4520 ConstantRange AddRecRange = getSignedRange(AR); 4521 ConstantRange IncRange = getSignedRange(AR->getStepRecurrence(*this)); 4522 4523 auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion( 4524 Instruction::Add, IncRange, OBO::NoSignedWrap); 4525 if (NSWRegion.contains(AddRecRange)) 4526 Result = ScalarEvolution::setFlags(Result, SCEV::FlagNSW); 4527 } 4528 4529 if (!AR->hasNoUnsignedWrap()) { 4530 ConstantRange AddRecRange = getUnsignedRange(AR); 4531 ConstantRange IncRange = getUnsignedRange(AR->getStepRecurrence(*this)); 4532 4533 auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion( 4534 Instruction::Add, IncRange, OBO::NoUnsignedWrap); 4535 if (NUWRegion.contains(AddRecRange)) 4536 Result = ScalarEvolution::setFlags(Result, SCEV::FlagNUW); 4537 } 4538 4539 return Result; 4540 } 4541 4542 SCEV::NoWrapFlags 4543 ScalarEvolution::proveNoSignedWrapViaInduction(const SCEVAddRecExpr *AR) { 4544 SCEV::NoWrapFlags Result = AR->getNoWrapFlags(); 4545 4546 if (AR->hasNoSignedWrap()) 4547 return Result; 4548 4549 if (!AR->isAffine()) 4550 return Result; 4551 4552 const SCEV *Step = AR->getStepRecurrence(*this); 4553 const Loop *L = AR->getLoop(); 4554 4555 // Check whether the backedge-taken count is SCEVCouldNotCompute. 4556 // Note that this serves two purposes: It filters out loops that are 4557 // simply not analyzable, and it covers the case where this code is 4558 // being called from within backedge-taken count analysis, such that 4559 // attempting to ask for the backedge-taken count would likely result 4560 // in infinite recursion. In the later case, the analysis code will 4561 // cope with a conservative value, and it will take care to purge 4562 // that value once it has finished. 4563 const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L); 4564 4565 // Normally, in the cases we can prove no-overflow via a 4566 // backedge guarding condition, we can also compute a backedge 4567 // taken count for the loop. The exceptions are assumptions and 4568 // guards present in the loop -- SCEV is not great at exploiting 4569 // these to compute max backedge taken counts, but can still use 4570 // these to prove lack of overflow. Use this fact to avoid 4571 // doing extra work that may not pay off. 4572 4573 if (isa<SCEVCouldNotCompute>(MaxBECount) && !HasGuards && 4574 AC.assumptions().empty()) 4575 return Result; 4576 4577 // If the backedge is guarded by a comparison with the pre-inc value the 4578 // addrec is safe. Also, if the entry is guarded by a comparison with the 4579 // start value and the backedge is guarded by a comparison with the post-inc 4580 // value, the addrec is safe. 4581 ICmpInst::Predicate Pred; 4582 const SCEV *OverflowLimit = 4583 getSignedOverflowLimitForStep(Step, &Pred, this); 4584 if (OverflowLimit && 4585 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) || 4586 isKnownOnEveryIteration(Pred, AR, OverflowLimit))) { 4587 Result = setFlags(Result, SCEV::FlagNSW); 4588 } 4589 return Result; 4590 } 4591 SCEV::NoWrapFlags 4592 ScalarEvolution::proveNoUnsignedWrapViaInduction(const SCEVAddRecExpr *AR) { 4593 SCEV::NoWrapFlags Result = AR->getNoWrapFlags(); 4594 4595 if (AR->hasNoUnsignedWrap()) 4596 return Result; 4597 4598 if (!AR->isAffine()) 4599 return Result; 4600 4601 const SCEV *Step = AR->getStepRecurrence(*this); 4602 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 4603 const Loop *L = AR->getLoop(); 4604 4605 // Check whether the backedge-taken count is SCEVCouldNotCompute. 4606 // Note that this serves two purposes: It filters out loops that are 4607 // simply not analyzable, and it covers the case where this code is 4608 // being called from within backedge-taken count analysis, such that 4609 // attempting to ask for the backedge-taken count would likely result 4610 // in infinite recursion. In the later case, the analysis code will 4611 // cope with a conservative value, and it will take care to purge 4612 // that value once it has finished. 4613 const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L); 4614 4615 // Normally, in the cases we can prove no-overflow via a 4616 // backedge guarding condition, we can also compute a backedge 4617 // taken count for the loop. The exceptions are assumptions and 4618 // guards present in the loop -- SCEV is not great at exploiting 4619 // these to compute max backedge taken counts, but can still use 4620 // these to prove lack of overflow. Use this fact to avoid 4621 // doing extra work that may not pay off. 4622 4623 if (isa<SCEVCouldNotCompute>(MaxBECount) && !HasGuards && 4624 AC.assumptions().empty()) 4625 return Result; 4626 4627 // If the backedge is guarded by a comparison with the pre-inc value the 4628 // addrec is safe. Also, if the entry is guarded by a comparison with the 4629 // start value and the backedge is guarded by a comparison with the post-inc 4630 // value, the addrec is safe. 4631 if (isKnownPositive(Step)) { 4632 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 4633 getUnsignedRangeMax(Step)); 4634 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 4635 isKnownOnEveryIteration(ICmpInst::ICMP_ULT, AR, N)) { 4636 Result = setFlags(Result, SCEV::FlagNUW); 4637 } 4638 } 4639 4640 return Result; 4641 } 4642 4643 namespace { 4644 4645 /// Represents an abstract binary operation. This may exist as a 4646 /// normal instruction or constant expression, or may have been 4647 /// derived from an expression tree. 4648 struct BinaryOp { 4649 unsigned Opcode; 4650 Value *LHS; 4651 Value *RHS; 4652 bool IsNSW = false; 4653 bool IsNUW = false; 4654 4655 /// Op is set if this BinaryOp corresponds to a concrete LLVM instruction or 4656 /// constant expression. 4657 Operator *Op = nullptr; 4658 4659 explicit BinaryOp(Operator *Op) 4660 : Opcode(Op->getOpcode()), LHS(Op->getOperand(0)), RHS(Op->getOperand(1)), 4661 Op(Op) { 4662 if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(Op)) { 4663 IsNSW = OBO->hasNoSignedWrap(); 4664 IsNUW = OBO->hasNoUnsignedWrap(); 4665 } 4666 } 4667 4668 explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false, 4669 bool IsNUW = false) 4670 : Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW) {} 4671 }; 4672 4673 } // end anonymous namespace 4674 4675 /// Try to map \p V into a BinaryOp, and return \c None on failure. 4676 static Optional<BinaryOp> MatchBinaryOp(Value *V, DominatorTree &DT) { 4677 auto *Op = dyn_cast<Operator>(V); 4678 if (!Op) 4679 return None; 4680 4681 // Implementation detail: all the cleverness here should happen without 4682 // creating new SCEV expressions -- our caller knowns tricks to avoid creating 4683 // SCEV expressions when possible, and we should not break that. 4684 4685 switch (Op->getOpcode()) { 4686 case Instruction::Add: 4687 case Instruction::Sub: 4688 case Instruction::Mul: 4689 case Instruction::UDiv: 4690 case Instruction::URem: 4691 case Instruction::And: 4692 case Instruction::Or: 4693 case Instruction::AShr: 4694 case Instruction::Shl: 4695 return BinaryOp(Op); 4696 4697 case Instruction::Xor: 4698 if (auto *RHSC = dyn_cast<ConstantInt>(Op->getOperand(1))) 4699 // If the RHS of the xor is a signmask, then this is just an add. 4700 // Instcombine turns add of signmask into xor as a strength reduction step. 4701 if (RHSC->getValue().isSignMask()) 4702 return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1)); 4703 return BinaryOp(Op); 4704 4705 case Instruction::LShr: 4706 // Turn logical shift right of a constant into a unsigned divide. 4707 if (ConstantInt *SA = dyn_cast<ConstantInt>(Op->getOperand(1))) { 4708 uint32_t BitWidth = cast<IntegerType>(Op->getType())->getBitWidth(); 4709 4710 // If the shift count is not less than the bitwidth, the result of 4711 // the shift is undefined. Don't try to analyze it, because the 4712 // resolution chosen here may differ from the resolution chosen in 4713 // other parts of the compiler. 4714 if (SA->getValue().ult(BitWidth)) { 4715 Constant *X = 4716 ConstantInt::get(SA->getContext(), 4717 APInt::getOneBitSet(BitWidth, SA->getZExtValue())); 4718 return BinaryOp(Instruction::UDiv, Op->getOperand(0), X); 4719 } 4720 } 4721 return BinaryOp(Op); 4722 4723 case Instruction::ExtractValue: { 4724 auto *EVI = cast<ExtractValueInst>(Op); 4725 if (EVI->getNumIndices() != 1 || EVI->getIndices()[0] != 0) 4726 break; 4727 4728 auto *WO = dyn_cast<WithOverflowInst>(EVI->getAggregateOperand()); 4729 if (!WO) 4730 break; 4731 4732 Instruction::BinaryOps BinOp = WO->getBinaryOp(); 4733 bool Signed = WO->isSigned(); 4734 // TODO: Should add nuw/nsw flags for mul as well. 4735 if (BinOp == Instruction::Mul || !isOverflowIntrinsicNoWrap(WO, DT)) 4736 return BinaryOp(BinOp, WO->getLHS(), WO->getRHS()); 4737 4738 // Now that we know that all uses of the arithmetic-result component of 4739 // CI are guarded by the overflow check, we can go ahead and pretend 4740 // that the arithmetic is non-overflowing. 4741 return BinaryOp(BinOp, WO->getLHS(), WO->getRHS(), 4742 /* IsNSW = */ Signed, /* IsNUW = */ !Signed); 4743 } 4744 4745 default: 4746 break; 4747 } 4748 4749 // Recognise intrinsic loop.decrement.reg, and as this has exactly the same 4750 // semantics as a Sub, return a binary sub expression. 4751 if (auto *II = dyn_cast<IntrinsicInst>(V)) 4752 if (II->getIntrinsicID() == Intrinsic::loop_decrement_reg) 4753 return BinaryOp(Instruction::Sub, II->getOperand(0), II->getOperand(1)); 4754 4755 return None; 4756 } 4757 4758 /// Helper function to createAddRecFromPHIWithCasts. We have a phi 4759 /// node whose symbolic (unknown) SCEV is \p SymbolicPHI, which is updated via 4760 /// the loop backedge by a SCEVAddExpr, possibly also with a few casts on the 4761 /// way. This function checks if \p Op, an operand of this SCEVAddExpr, 4762 /// follows one of the following patterns: 4763 /// Op == (SExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) 4764 /// Op == (ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) 4765 /// If the SCEV expression of \p Op conforms with one of the expected patterns 4766 /// we return the type of the truncation operation, and indicate whether the 4767 /// truncated type should be treated as signed/unsigned by setting 4768 /// \p Signed to true/false, respectively. 4769 static Type *isSimpleCastedPHI(const SCEV *Op, const SCEVUnknown *SymbolicPHI, 4770 bool &Signed, ScalarEvolution &SE) { 4771 // The case where Op == SymbolicPHI (that is, with no type conversions on 4772 // the way) is handled by the regular add recurrence creating logic and 4773 // would have already been triggered in createAddRecForPHI. Reaching it here 4774 // means that createAddRecFromPHI had failed for this PHI before (e.g., 4775 // because one of the other operands of the SCEVAddExpr updating this PHI is 4776 // not invariant). 4777 // 4778 // Here we look for the case where Op = (ext(trunc(SymbolicPHI))), and in 4779 // this case predicates that allow us to prove that Op == SymbolicPHI will 4780 // be added. 4781 if (Op == SymbolicPHI) 4782 return nullptr; 4783 4784 unsigned SourceBits = SE.getTypeSizeInBits(SymbolicPHI->getType()); 4785 unsigned NewBits = SE.getTypeSizeInBits(Op->getType()); 4786 if (SourceBits != NewBits) 4787 return nullptr; 4788 4789 const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(Op); 4790 const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(Op); 4791 if (!SExt && !ZExt) 4792 return nullptr; 4793 const SCEVTruncateExpr *Trunc = 4794 SExt ? dyn_cast<SCEVTruncateExpr>(SExt->getOperand()) 4795 : dyn_cast<SCEVTruncateExpr>(ZExt->getOperand()); 4796 if (!Trunc) 4797 return nullptr; 4798 const SCEV *X = Trunc->getOperand(); 4799 if (X != SymbolicPHI) 4800 return nullptr; 4801 Signed = SExt != nullptr; 4802 return Trunc->getType(); 4803 } 4804 4805 static const Loop *isIntegerLoopHeaderPHI(const PHINode *PN, LoopInfo &LI) { 4806 if (!PN->getType()->isIntegerTy()) 4807 return nullptr; 4808 const Loop *L = LI.getLoopFor(PN->getParent()); 4809 if (!L || L->getHeader() != PN->getParent()) 4810 return nullptr; 4811 return L; 4812 } 4813 4814 // Analyze \p SymbolicPHI, a SCEV expression of a phi node, and check if the 4815 // computation that updates the phi follows the following pattern: 4816 // (SExt/ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) + InvariantAccum 4817 // which correspond to a phi->trunc->sext/zext->add->phi update chain. 4818 // If so, try to see if it can be rewritten as an AddRecExpr under some 4819 // Predicates. If successful, return them as a pair. Also cache the results 4820 // of the analysis. 4821 // 4822 // Example usage scenario: 4823 // Say the Rewriter is called for the following SCEV: 4824 // 8 * ((sext i32 (trunc i64 %X to i32) to i64) + %Step) 4825 // where: 4826 // %X = phi i64 (%Start, %BEValue) 4827 // It will visitMul->visitAdd->visitSExt->visitTrunc->visitUnknown(%X), 4828 // and call this function with %SymbolicPHI = %X. 4829 // 4830 // The analysis will find that the value coming around the backedge has 4831 // the following SCEV: 4832 // BEValue = ((sext i32 (trunc i64 %X to i32) to i64) + %Step) 4833 // Upon concluding that this matches the desired pattern, the function 4834 // will return the pair {NewAddRec, SmallPredsVec} where: 4835 // NewAddRec = {%Start,+,%Step} 4836 // SmallPredsVec = {P1, P2, P3} as follows: 4837 // P1(WrapPred): AR: {trunc(%Start),+,(trunc %Step)}<nsw> Flags: <nssw> 4838 // P2(EqualPred): %Start == (sext i32 (trunc i64 %Start to i32) to i64) 4839 // P3(EqualPred): %Step == (sext i32 (trunc i64 %Step to i32) to i64) 4840 // The returned pair means that SymbolicPHI can be rewritten into NewAddRec 4841 // under the predicates {P1,P2,P3}. 4842 // This predicated rewrite will be cached in PredicatedSCEVRewrites: 4843 // PredicatedSCEVRewrites[{%X,L}] = {NewAddRec, {P1,P2,P3)} 4844 // 4845 // TODO's: 4846 // 4847 // 1) Extend the Induction descriptor to also support inductions that involve 4848 // casts: When needed (namely, when we are called in the context of the 4849 // vectorizer induction analysis), a Set of cast instructions will be 4850 // populated by this method, and provided back to isInductionPHI. This is 4851 // needed to allow the vectorizer to properly record them to be ignored by 4852 // the cost model and to avoid vectorizing them (otherwise these casts, 4853 // which are redundant under the runtime overflow checks, will be 4854 // vectorized, which can be costly). 4855 // 4856 // 2) Support additional induction/PHISCEV patterns: We also want to support 4857 // inductions where the sext-trunc / zext-trunc operations (partly) occur 4858 // after the induction update operation (the induction increment): 4859 // 4860 // (Trunc iy (SExt/ZExt ix (%SymbolicPHI + InvariantAccum) to iy) to ix) 4861 // which correspond to a phi->add->trunc->sext/zext->phi update chain. 4862 // 4863 // (Trunc iy ((SExt/ZExt ix (%SymbolicPhi) to iy) + InvariantAccum) to ix) 4864 // which correspond to a phi->trunc->add->sext/zext->phi update chain. 4865 // 4866 // 3) Outline common code with createAddRecFromPHI to avoid duplication. 4867 Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>> 4868 ScalarEvolution::createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI) { 4869 SmallVector<const SCEVPredicate *, 3> Predicates; 4870 4871 // *** Part1: Analyze if we have a phi-with-cast pattern for which we can 4872 // return an AddRec expression under some predicate. 4873 4874 auto *PN = cast<PHINode>(SymbolicPHI->getValue()); 4875 const Loop *L = isIntegerLoopHeaderPHI(PN, LI); 4876 assert(L && "Expecting an integer loop header phi"); 4877 4878 // The loop may have multiple entrances or multiple exits; we can analyze 4879 // this phi as an addrec if it has a unique entry value and a unique 4880 // backedge value. 4881 Value *BEValueV = nullptr, *StartValueV = nullptr; 4882 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 4883 Value *V = PN->getIncomingValue(i); 4884 if (L->contains(PN->getIncomingBlock(i))) { 4885 if (!BEValueV) { 4886 BEValueV = V; 4887 } else if (BEValueV != V) { 4888 BEValueV = nullptr; 4889 break; 4890 } 4891 } else if (!StartValueV) { 4892 StartValueV = V; 4893 } else if (StartValueV != V) { 4894 StartValueV = nullptr; 4895 break; 4896 } 4897 } 4898 if (!BEValueV || !StartValueV) 4899 return None; 4900 4901 const SCEV *BEValue = getSCEV(BEValueV); 4902 4903 // If the value coming around the backedge is an add with the symbolic 4904 // value we just inserted, possibly with casts that we can ignore under 4905 // an appropriate runtime guard, then we found a simple induction variable! 4906 const auto *Add = dyn_cast<SCEVAddExpr>(BEValue); 4907 if (!Add) 4908 return None; 4909 4910 // If there is a single occurrence of the symbolic value, possibly 4911 // casted, replace it with a recurrence. 4912 unsigned FoundIndex = Add->getNumOperands(); 4913 Type *TruncTy = nullptr; 4914 bool Signed; 4915 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 4916 if ((TruncTy = 4917 isSimpleCastedPHI(Add->getOperand(i), SymbolicPHI, Signed, *this))) 4918 if (FoundIndex == e) { 4919 FoundIndex = i; 4920 break; 4921 } 4922 4923 if (FoundIndex == Add->getNumOperands()) 4924 return None; 4925 4926 // Create an add with everything but the specified operand. 4927 SmallVector<const SCEV *, 8> Ops; 4928 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 4929 if (i != FoundIndex) 4930 Ops.push_back(Add->getOperand(i)); 4931 const SCEV *Accum = getAddExpr(Ops); 4932 4933 // The runtime checks will not be valid if the step amount is 4934 // varying inside the loop. 4935 if (!isLoopInvariant(Accum, L)) 4936 return None; 4937 4938 // *** Part2: Create the predicates 4939 4940 // Analysis was successful: we have a phi-with-cast pattern for which we 4941 // can return an AddRec expression under the following predicates: 4942 // 4943 // P1: A Wrap predicate that guarantees that Trunc(Start) + i*Trunc(Accum) 4944 // fits within the truncated type (does not overflow) for i = 0 to n-1. 4945 // P2: An Equal predicate that guarantees that 4946 // Start = (Ext ix (Trunc iy (Start) to ix) to iy) 4947 // P3: An Equal predicate that guarantees that 4948 // Accum = (Ext ix (Trunc iy (Accum) to ix) to iy) 4949 // 4950 // As we next prove, the above predicates guarantee that: 4951 // Start + i*Accum = (Ext ix (Trunc iy ( Start + i*Accum ) to ix) to iy) 4952 // 4953 // 4954 // More formally, we want to prove that: 4955 // Expr(i+1) = Start + (i+1) * Accum 4956 // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum 4957 // 4958 // Given that: 4959 // 1) Expr(0) = Start 4960 // 2) Expr(1) = Start + Accum 4961 // = (Ext ix (Trunc iy (Start) to ix) to iy) + Accum :: from P2 4962 // 3) Induction hypothesis (step i): 4963 // Expr(i) = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum 4964 // 4965 // Proof: 4966 // Expr(i+1) = 4967 // = Start + (i+1)*Accum 4968 // = (Start + i*Accum) + Accum 4969 // = Expr(i) + Accum 4970 // = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum + Accum 4971 // :: from step i 4972 // 4973 // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy) + Accum + Accum 4974 // 4975 // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy) 4976 // + (Ext ix (Trunc iy (Accum) to ix) to iy) 4977 // + Accum :: from P3 4978 // 4979 // = (Ext ix (Trunc iy ((Start + (i-1)*Accum) + Accum) to ix) to iy) 4980 // + Accum :: from P1: Ext(x)+Ext(y)=>Ext(x+y) 4981 // 4982 // = (Ext ix (Trunc iy (Start + i*Accum) to ix) to iy) + Accum 4983 // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum 4984 // 4985 // By induction, the same applies to all iterations 1<=i<n: 4986 // 4987 4988 // Create a truncated addrec for which we will add a no overflow check (P1). 4989 const SCEV *StartVal = getSCEV(StartValueV); 4990 const SCEV *PHISCEV = 4991 getAddRecExpr(getTruncateExpr(StartVal, TruncTy), 4992 getTruncateExpr(Accum, TruncTy), L, SCEV::FlagAnyWrap); 4993 4994 // PHISCEV can be either a SCEVConstant or a SCEVAddRecExpr. 4995 // ex: If truncated Accum is 0 and StartVal is a constant, then PHISCEV 4996 // will be constant. 4997 // 4998 // If PHISCEV is a constant, then P1 degenerates into P2 or P3, so we don't 4999 // add P1. 5000 if (const auto *AR = dyn_cast<SCEVAddRecExpr>(PHISCEV)) { 5001 SCEVWrapPredicate::IncrementWrapFlags AddedFlags = 5002 Signed ? SCEVWrapPredicate::IncrementNSSW 5003 : SCEVWrapPredicate::IncrementNUSW; 5004 const SCEVPredicate *AddRecPred = getWrapPredicate(AR, AddedFlags); 5005 Predicates.push_back(AddRecPred); 5006 } 5007 5008 // Create the Equal Predicates P2,P3: 5009 5010 // It is possible that the predicates P2 and/or P3 are computable at 5011 // compile time due to StartVal and/or Accum being constants. 5012 // If either one is, then we can check that now and escape if either P2 5013 // or P3 is false. 5014 5015 // Construct the extended SCEV: (Ext ix (Trunc iy (Expr) to ix) to iy) 5016 // for each of StartVal and Accum 5017 auto getExtendedExpr = [&](const SCEV *Expr, 5018 bool CreateSignExtend) -> const SCEV * { 5019 assert(isLoopInvariant(Expr, L) && "Expr is expected to be invariant"); 5020 const SCEV *TruncatedExpr = getTruncateExpr(Expr, TruncTy); 5021 const SCEV *ExtendedExpr = 5022 CreateSignExtend ? getSignExtendExpr(TruncatedExpr, Expr->getType()) 5023 : getZeroExtendExpr(TruncatedExpr, Expr->getType()); 5024 return ExtendedExpr; 5025 }; 5026 5027 // Given: 5028 // ExtendedExpr = (Ext ix (Trunc iy (Expr) to ix) to iy 5029 // = getExtendedExpr(Expr) 5030 // Determine whether the predicate P: Expr == ExtendedExpr 5031 // is known to be false at compile time 5032 auto PredIsKnownFalse = [&](const SCEV *Expr, 5033 const SCEV *ExtendedExpr) -> bool { 5034 return Expr != ExtendedExpr && 5035 isKnownPredicate(ICmpInst::ICMP_NE, Expr, ExtendedExpr); 5036 }; 5037 5038 const SCEV *StartExtended = getExtendedExpr(StartVal, Signed); 5039 if (PredIsKnownFalse(StartVal, StartExtended)) { 5040 LLVM_DEBUG(dbgs() << "P2 is compile-time false\n";); 5041 return None; 5042 } 5043 5044 // The Step is always Signed (because the overflow checks are either 5045 // NSSW or NUSW) 5046 const SCEV *AccumExtended = getExtendedExpr(Accum, /*CreateSignExtend=*/true); 5047 if (PredIsKnownFalse(Accum, AccumExtended)) { 5048 LLVM_DEBUG(dbgs() << "P3 is compile-time false\n";); 5049 return None; 5050 } 5051 5052 auto AppendPredicate = [&](const SCEV *Expr, 5053 const SCEV *ExtendedExpr) -> void { 5054 if (Expr != ExtendedExpr && 5055 !isKnownPredicate(ICmpInst::ICMP_EQ, Expr, ExtendedExpr)) { 5056 const SCEVPredicate *Pred = getEqualPredicate(Expr, ExtendedExpr); 5057 LLVM_DEBUG(dbgs() << "Added Predicate: " << *Pred); 5058 Predicates.push_back(Pred); 5059 } 5060 }; 5061 5062 AppendPredicate(StartVal, StartExtended); 5063 AppendPredicate(Accum, AccumExtended); 5064 5065 // *** Part3: Predicates are ready. Now go ahead and create the new addrec in 5066 // which the casts had been folded away. The caller can rewrite SymbolicPHI 5067 // into NewAR if it will also add the runtime overflow checks specified in 5068 // Predicates. 5069 auto *NewAR = getAddRecExpr(StartVal, Accum, L, SCEV::FlagAnyWrap); 5070 5071 std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> PredRewrite = 5072 std::make_pair(NewAR, Predicates); 5073 // Remember the result of the analysis for this SCEV at this locayyytion. 5074 PredicatedSCEVRewrites[{SymbolicPHI, L}] = PredRewrite; 5075 return PredRewrite; 5076 } 5077 5078 Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>> 5079 ScalarEvolution::createAddRecFromPHIWithCasts(const SCEVUnknown *SymbolicPHI) { 5080 auto *PN = cast<PHINode>(SymbolicPHI->getValue()); 5081 const Loop *L = isIntegerLoopHeaderPHI(PN, LI); 5082 if (!L) 5083 return None; 5084 5085 // Check to see if we already analyzed this PHI. 5086 auto I = PredicatedSCEVRewrites.find({SymbolicPHI, L}); 5087 if (I != PredicatedSCEVRewrites.end()) { 5088 std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> Rewrite = 5089 I->second; 5090 // Analysis was done before and failed to create an AddRec: 5091 if (Rewrite.first == SymbolicPHI) 5092 return None; 5093 // Analysis was done before and succeeded to create an AddRec under 5094 // a predicate: 5095 assert(isa<SCEVAddRecExpr>(Rewrite.first) && "Expected an AddRec"); 5096 assert(!(Rewrite.second).empty() && "Expected to find Predicates"); 5097 return Rewrite; 5098 } 5099 5100 Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>> 5101 Rewrite = createAddRecFromPHIWithCastsImpl(SymbolicPHI); 5102 5103 // Record in the cache that the analysis failed 5104 if (!Rewrite) { 5105 SmallVector<const SCEVPredicate *, 3> Predicates; 5106 PredicatedSCEVRewrites[{SymbolicPHI, L}] = {SymbolicPHI, Predicates}; 5107 return None; 5108 } 5109 5110 return Rewrite; 5111 } 5112 5113 // FIXME: This utility is currently required because the Rewriter currently 5114 // does not rewrite this expression: 5115 // {0, +, (sext ix (trunc iy to ix) to iy)} 5116 // into {0, +, %step}, 5117 // even when the following Equal predicate exists: 5118 // "%step == (sext ix (trunc iy to ix) to iy)". 5119 bool PredicatedScalarEvolution::areAddRecsEqualWithPreds( 5120 const SCEVAddRecExpr *AR1, const SCEVAddRecExpr *AR2) const { 5121 if (AR1 == AR2) 5122 return true; 5123 5124 auto areExprsEqual = [&](const SCEV *Expr1, const SCEV *Expr2) -> bool { 5125 if (Expr1 != Expr2 && !Preds.implies(SE.getEqualPredicate(Expr1, Expr2)) && 5126 !Preds.implies(SE.getEqualPredicate(Expr2, Expr1))) 5127 return false; 5128 return true; 5129 }; 5130 5131 if (!areExprsEqual(AR1->getStart(), AR2->getStart()) || 5132 !areExprsEqual(AR1->getStepRecurrence(SE), AR2->getStepRecurrence(SE))) 5133 return false; 5134 return true; 5135 } 5136 5137 /// A helper function for createAddRecFromPHI to handle simple cases. 5138 /// 5139 /// This function tries to find an AddRec expression for the simplest (yet most 5140 /// common) cases: PN = PHI(Start, OP(Self, LoopInvariant)). 5141 /// If it fails, createAddRecFromPHI will use a more general, but slow, 5142 /// technique for finding the AddRec expression. 5143 const SCEV *ScalarEvolution::createSimpleAffineAddRec(PHINode *PN, 5144 Value *BEValueV, 5145 Value *StartValueV) { 5146 const Loop *L = LI.getLoopFor(PN->getParent()); 5147 assert(L && L->getHeader() == PN->getParent()); 5148 assert(BEValueV && StartValueV); 5149 5150 auto BO = MatchBinaryOp(BEValueV, DT); 5151 if (!BO) 5152 return nullptr; 5153 5154 if (BO->Opcode != Instruction::Add) 5155 return nullptr; 5156 5157 const SCEV *Accum = nullptr; 5158 if (BO->LHS == PN && L->isLoopInvariant(BO->RHS)) 5159 Accum = getSCEV(BO->RHS); 5160 else if (BO->RHS == PN && L->isLoopInvariant(BO->LHS)) 5161 Accum = getSCEV(BO->LHS); 5162 5163 if (!Accum) 5164 return nullptr; 5165 5166 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap; 5167 if (BO->IsNUW) 5168 Flags = setFlags(Flags, SCEV::FlagNUW); 5169 if (BO->IsNSW) 5170 Flags = setFlags(Flags, SCEV::FlagNSW); 5171 5172 const SCEV *StartVal = getSCEV(StartValueV); 5173 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags); 5174 5175 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 5176 5177 // We can add Flags to the post-inc expression only if we 5178 // know that it is *undefined behavior* for BEValueV to 5179 // overflow. 5180 if (auto *BEInst = dyn_cast<Instruction>(BEValueV)) 5181 if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L)) 5182 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags); 5183 5184 return PHISCEV; 5185 } 5186 5187 const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) { 5188 const Loop *L = LI.getLoopFor(PN->getParent()); 5189 if (!L || L->getHeader() != PN->getParent()) 5190 return nullptr; 5191 5192 // The loop may have multiple entrances or multiple exits; we can analyze 5193 // this phi as an addrec if it has a unique entry value and a unique 5194 // backedge value. 5195 Value *BEValueV = nullptr, *StartValueV = nullptr; 5196 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 5197 Value *V = PN->getIncomingValue(i); 5198 if (L->contains(PN->getIncomingBlock(i))) { 5199 if (!BEValueV) { 5200 BEValueV = V; 5201 } else if (BEValueV != V) { 5202 BEValueV = nullptr; 5203 break; 5204 } 5205 } else if (!StartValueV) { 5206 StartValueV = V; 5207 } else if (StartValueV != V) { 5208 StartValueV = nullptr; 5209 break; 5210 } 5211 } 5212 if (!BEValueV || !StartValueV) 5213 return nullptr; 5214 5215 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() && 5216 "PHI node already processed?"); 5217 5218 // First, try to find AddRec expression without creating a fictituos symbolic 5219 // value for PN. 5220 if (auto *S = createSimpleAffineAddRec(PN, BEValueV, StartValueV)) 5221 return S; 5222 5223 // Handle PHI node value symbolically. 5224 const SCEV *SymbolicName = getUnknown(PN); 5225 ValueExprMap.insert({SCEVCallbackVH(PN, this), SymbolicName}); 5226 5227 // Using this symbolic name for the PHI, analyze the value coming around 5228 // the back-edge. 5229 const SCEV *BEValue = getSCEV(BEValueV); 5230 5231 // NOTE: If BEValue is loop invariant, we know that the PHI node just 5232 // has a special value for the first iteration of the loop. 5233 5234 // If the value coming around the backedge is an add with the symbolic 5235 // value we just inserted, then we found a simple induction variable! 5236 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 5237 // If there is a single occurrence of the symbolic value, replace it 5238 // with a recurrence. 5239 unsigned FoundIndex = Add->getNumOperands(); 5240 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 5241 if (Add->getOperand(i) == SymbolicName) 5242 if (FoundIndex == e) { 5243 FoundIndex = i; 5244 break; 5245 } 5246 5247 if (FoundIndex != Add->getNumOperands()) { 5248 // Create an add with everything but the specified operand. 5249 SmallVector<const SCEV *, 8> Ops; 5250 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 5251 if (i != FoundIndex) 5252 Ops.push_back(SCEVBackedgeConditionFolder::rewrite(Add->getOperand(i), 5253 L, *this)); 5254 const SCEV *Accum = getAddExpr(Ops); 5255 5256 // This is not a valid addrec if the step amount is varying each 5257 // loop iteration, but is not itself an addrec in this loop. 5258 if (isLoopInvariant(Accum, L) || 5259 (isa<SCEVAddRecExpr>(Accum) && 5260 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 5261 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap; 5262 5263 if (auto BO = MatchBinaryOp(BEValueV, DT)) { 5264 if (BO->Opcode == Instruction::Add && BO->LHS == PN) { 5265 if (BO->IsNUW) 5266 Flags = setFlags(Flags, SCEV::FlagNUW); 5267 if (BO->IsNSW) 5268 Flags = setFlags(Flags, SCEV::FlagNSW); 5269 } 5270 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) { 5271 // If the increment is an inbounds GEP, then we know the address 5272 // space cannot be wrapped around. We cannot make any guarantee 5273 // about signed or unsigned overflow because pointers are 5274 // unsigned but we may have a negative index from the base 5275 // pointer. We can guarantee that no unsigned wrap occurs if the 5276 // indices form a positive value. 5277 if (GEP->isInBounds() && GEP->getOperand(0) == PN) { 5278 Flags = setFlags(Flags, SCEV::FlagNW); 5279 5280 const SCEV *Ptr = getSCEV(GEP->getPointerOperand()); 5281 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr))) 5282 Flags = setFlags(Flags, SCEV::FlagNUW); 5283 } 5284 5285 // We cannot transfer nuw and nsw flags from subtraction 5286 // operations -- sub nuw X, Y is not the same as add nuw X, -Y 5287 // for instance. 5288 } 5289 5290 const SCEV *StartVal = getSCEV(StartValueV); 5291 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags); 5292 5293 // Okay, for the entire analysis of this edge we assumed the PHI 5294 // to be symbolic. We now need to go back and purge all of the 5295 // entries for the scalars that use the symbolic expression. 5296 forgetSymbolicName(PN, SymbolicName); 5297 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 5298 5299 // We can add Flags to the post-inc expression only if we 5300 // know that it is *undefined behavior* for BEValueV to 5301 // overflow. 5302 if (auto *BEInst = dyn_cast<Instruction>(BEValueV)) 5303 if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L)) 5304 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags); 5305 5306 return PHISCEV; 5307 } 5308 } 5309 } else { 5310 // Otherwise, this could be a loop like this: 5311 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 5312 // In this case, j = {1,+,1} and BEValue is j. 5313 // Because the other in-value of i (0) fits the evolution of BEValue 5314 // i really is an addrec evolution. 5315 // 5316 // We can generalize this saying that i is the shifted value of BEValue 5317 // by one iteration: 5318 // PHI(f(0), f({1,+,1})) --> f({0,+,1}) 5319 const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this); 5320 const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this, false); 5321 if (Shifted != getCouldNotCompute() && 5322 Start != getCouldNotCompute()) { 5323 const SCEV *StartVal = getSCEV(StartValueV); 5324 if (Start == StartVal) { 5325 // Okay, for the entire analysis of this edge we assumed the PHI 5326 // to be symbolic. We now need to go back and purge all of the 5327 // entries for the scalars that use the symbolic expression. 5328 forgetSymbolicName(PN, SymbolicName); 5329 ValueExprMap[SCEVCallbackVH(PN, this)] = Shifted; 5330 return Shifted; 5331 } 5332 } 5333 } 5334 5335 // Remove the temporary PHI node SCEV that has been inserted while intending 5336 // to create an AddRecExpr for this PHI node. We can not keep this temporary 5337 // as it will prevent later (possibly simpler) SCEV expressions to be added 5338 // to the ValueExprMap. 5339 eraseValueFromMap(PN); 5340 5341 return nullptr; 5342 } 5343 5344 // Checks if the SCEV S is available at BB. S is considered available at BB 5345 // if S can be materialized at BB without introducing a fault. 5346 static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S, 5347 BasicBlock *BB) { 5348 struct CheckAvailable { 5349 bool TraversalDone = false; 5350 bool Available = true; 5351 5352 const Loop *L = nullptr; // The loop BB is in (can be nullptr) 5353 BasicBlock *BB = nullptr; 5354 DominatorTree &DT; 5355 5356 CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT) 5357 : L(L), BB(BB), DT(DT) {} 5358 5359 bool setUnavailable() { 5360 TraversalDone = true; 5361 Available = false; 5362 return false; 5363 } 5364 5365 bool follow(const SCEV *S) { 5366 switch (S->getSCEVType()) { 5367 case scConstant: 5368 case scPtrToInt: 5369 case scTruncate: 5370 case scZeroExtend: 5371 case scSignExtend: 5372 case scAddExpr: 5373 case scMulExpr: 5374 case scUMaxExpr: 5375 case scSMaxExpr: 5376 case scUMinExpr: 5377 case scSMinExpr: 5378 // These expressions are available if their operand(s) is/are. 5379 return true; 5380 5381 case scAddRecExpr: { 5382 // We allow add recurrences that are on the loop BB is in, or some 5383 // outer loop. This guarantees availability because the value of the 5384 // add recurrence at BB is simply the "current" value of the induction 5385 // variable. We can relax this in the future; for instance an add 5386 // recurrence on a sibling dominating loop is also available at BB. 5387 const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop(); 5388 if (L && (ARLoop == L || ARLoop->contains(L))) 5389 return true; 5390 5391 return setUnavailable(); 5392 } 5393 5394 case scUnknown: { 5395 // For SCEVUnknown, we check for simple dominance. 5396 const auto *SU = cast<SCEVUnknown>(S); 5397 Value *V = SU->getValue(); 5398 5399 if (isa<Argument>(V)) 5400 return false; 5401 5402 if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB)) 5403 return false; 5404 5405 return setUnavailable(); 5406 } 5407 5408 case scUDivExpr: 5409 case scCouldNotCompute: 5410 // We do not try to smart about these at all. 5411 return setUnavailable(); 5412 } 5413 llvm_unreachable("Unknown SCEV kind!"); 5414 } 5415 5416 bool isDone() { return TraversalDone; } 5417 }; 5418 5419 CheckAvailable CA(L, BB, DT); 5420 SCEVTraversal<CheckAvailable> ST(CA); 5421 5422 ST.visitAll(S); 5423 return CA.Available; 5424 } 5425 5426 // Try to match a control flow sequence that branches out at BI and merges back 5427 // at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful 5428 // match. 5429 static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge, 5430 Value *&C, Value *&LHS, Value *&RHS) { 5431 C = BI->getCondition(); 5432 5433 BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0)); 5434 BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1)); 5435 5436 if (!LeftEdge.isSingleEdge()) 5437 return false; 5438 5439 assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()"); 5440 5441 Use &LeftUse = Merge->getOperandUse(0); 5442 Use &RightUse = Merge->getOperandUse(1); 5443 5444 if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) { 5445 LHS = LeftUse; 5446 RHS = RightUse; 5447 return true; 5448 } 5449 5450 if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) { 5451 LHS = RightUse; 5452 RHS = LeftUse; 5453 return true; 5454 } 5455 5456 return false; 5457 } 5458 5459 const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) { 5460 auto IsReachable = 5461 [&](BasicBlock *BB) { return DT.isReachableFromEntry(BB); }; 5462 if (PN->getNumIncomingValues() == 2 && all_of(PN->blocks(), IsReachable)) { 5463 const Loop *L = LI.getLoopFor(PN->getParent()); 5464 5465 // We don't want to break LCSSA, even in a SCEV expression tree. 5466 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) 5467 if (LI.getLoopFor(PN->getIncomingBlock(i)) != L) 5468 return nullptr; 5469 5470 // Try to match 5471 // 5472 // br %cond, label %left, label %right 5473 // left: 5474 // br label %merge 5475 // right: 5476 // br label %merge 5477 // merge: 5478 // V = phi [ %x, %left ], [ %y, %right ] 5479 // 5480 // as "select %cond, %x, %y" 5481 5482 BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock(); 5483 assert(IDom && "At least the entry block should dominate PN"); 5484 5485 auto *BI = dyn_cast<BranchInst>(IDom->getTerminator()); 5486 Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr; 5487 5488 if (BI && BI->isConditional() && 5489 BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) && 5490 IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) && 5491 IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent())) 5492 return createNodeForSelectOrPHI(PN, Cond, LHS, RHS); 5493 } 5494 5495 return nullptr; 5496 } 5497 5498 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 5499 if (const SCEV *S = createAddRecFromPHI(PN)) 5500 return S; 5501 5502 if (const SCEV *S = createNodeFromSelectLikePHI(PN)) 5503 return S; 5504 5505 // If the PHI has a single incoming value, follow that value, unless the 5506 // PHI's incoming blocks are in a different loop, in which case doing so 5507 // risks breaking LCSSA form. Instcombine would normally zap these, but 5508 // it doesn't have DominatorTree information, so it may miss cases. 5509 if (Value *V = SimplifyInstruction(PN, {getDataLayout(), &TLI, &DT, &AC})) 5510 if (LI.replacementPreservesLCSSAForm(PN, V)) 5511 return getSCEV(V); 5512 5513 // If it's not a loop phi, we can't handle it yet. 5514 return getUnknown(PN); 5515 } 5516 5517 const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I, 5518 Value *Cond, 5519 Value *TrueVal, 5520 Value *FalseVal) { 5521 // Handle "constant" branch or select. This can occur for instance when a 5522 // loop pass transforms an inner loop and moves on to process the outer loop. 5523 if (auto *CI = dyn_cast<ConstantInt>(Cond)) 5524 return getSCEV(CI->isOne() ? TrueVal : FalseVal); 5525 5526 // Try to match some simple smax or umax patterns. 5527 auto *ICI = dyn_cast<ICmpInst>(Cond); 5528 if (!ICI) 5529 return getUnknown(I); 5530 5531 Value *LHS = ICI->getOperand(0); 5532 Value *RHS = ICI->getOperand(1); 5533 5534 switch (ICI->getPredicate()) { 5535 case ICmpInst::ICMP_SLT: 5536 case ICmpInst::ICMP_SLE: 5537 std::swap(LHS, RHS); 5538 LLVM_FALLTHROUGH; 5539 case ICmpInst::ICMP_SGT: 5540 case ICmpInst::ICMP_SGE: 5541 // a >s b ? a+x : b+x -> smax(a, b)+x 5542 // a >s b ? b+x : a+x -> smin(a, b)+x 5543 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) { 5544 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType()); 5545 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType()); 5546 const SCEV *LA = getSCEV(TrueVal); 5547 const SCEV *RA = getSCEV(FalseVal); 5548 const SCEV *LDiff = getMinusSCEV(LA, LS); 5549 const SCEV *RDiff = getMinusSCEV(RA, RS); 5550 if (LDiff == RDiff) 5551 return getAddExpr(getSMaxExpr(LS, RS), LDiff); 5552 LDiff = getMinusSCEV(LA, RS); 5553 RDiff = getMinusSCEV(RA, LS); 5554 if (LDiff == RDiff) 5555 return getAddExpr(getSMinExpr(LS, RS), LDiff); 5556 } 5557 break; 5558 case ICmpInst::ICMP_ULT: 5559 case ICmpInst::ICMP_ULE: 5560 std::swap(LHS, RHS); 5561 LLVM_FALLTHROUGH; 5562 case ICmpInst::ICMP_UGT: 5563 case ICmpInst::ICMP_UGE: 5564 // a >u b ? a+x : b+x -> umax(a, b)+x 5565 // a >u b ? b+x : a+x -> umin(a, b)+x 5566 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) { 5567 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType()); 5568 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType()); 5569 const SCEV *LA = getSCEV(TrueVal); 5570 const SCEV *RA = getSCEV(FalseVal); 5571 const SCEV *LDiff = getMinusSCEV(LA, LS); 5572 const SCEV *RDiff = getMinusSCEV(RA, RS); 5573 if (LDiff == RDiff) 5574 return getAddExpr(getUMaxExpr(LS, RS), LDiff); 5575 LDiff = getMinusSCEV(LA, RS); 5576 RDiff = getMinusSCEV(RA, LS); 5577 if (LDiff == RDiff) 5578 return getAddExpr(getUMinExpr(LS, RS), LDiff); 5579 } 5580 break; 5581 case ICmpInst::ICMP_NE: 5582 // n != 0 ? n+x : 1+x -> umax(n, 1)+x 5583 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) && 5584 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) { 5585 const SCEV *One = getOne(I->getType()); 5586 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType()); 5587 const SCEV *LA = getSCEV(TrueVal); 5588 const SCEV *RA = getSCEV(FalseVal); 5589 const SCEV *LDiff = getMinusSCEV(LA, LS); 5590 const SCEV *RDiff = getMinusSCEV(RA, One); 5591 if (LDiff == RDiff) 5592 return getAddExpr(getUMaxExpr(One, LS), LDiff); 5593 } 5594 break; 5595 case ICmpInst::ICMP_EQ: 5596 // n == 0 ? 1+x : n+x -> umax(n, 1)+x 5597 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) && 5598 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) { 5599 const SCEV *One = getOne(I->getType()); 5600 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType()); 5601 const SCEV *LA = getSCEV(TrueVal); 5602 const SCEV *RA = getSCEV(FalseVal); 5603 const SCEV *LDiff = getMinusSCEV(LA, One); 5604 const SCEV *RDiff = getMinusSCEV(RA, LS); 5605 if (LDiff == RDiff) 5606 return getAddExpr(getUMaxExpr(One, LS), LDiff); 5607 } 5608 break; 5609 default: 5610 break; 5611 } 5612 5613 return getUnknown(I); 5614 } 5615 5616 /// Expand GEP instructions into add and multiply operations. This allows them 5617 /// to be analyzed by regular SCEV code. 5618 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 5619 // Don't attempt to analyze GEPs over unsized objects. 5620 if (!GEP->getSourceElementType()->isSized()) 5621 return getUnknown(GEP); 5622 5623 SmallVector<const SCEV *, 4> IndexExprs; 5624 for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index) 5625 IndexExprs.push_back(getSCEV(*Index)); 5626 return getGEPExpr(GEP, IndexExprs); 5627 } 5628 5629 uint32_t ScalarEvolution::GetMinTrailingZerosImpl(const SCEV *S) { 5630 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 5631 return C->getAPInt().countTrailingZeros(); 5632 5633 if (const SCEVPtrToIntExpr *I = dyn_cast<SCEVPtrToIntExpr>(S)) 5634 return GetMinTrailingZeros(I->getOperand()); 5635 5636 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 5637 return std::min(GetMinTrailingZeros(T->getOperand()), 5638 (uint32_t)getTypeSizeInBits(T->getType())); 5639 5640 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 5641 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 5642 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) 5643 ? getTypeSizeInBits(E->getType()) 5644 : OpRes; 5645 } 5646 5647 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 5648 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 5649 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) 5650 ? getTypeSizeInBits(E->getType()) 5651 : OpRes; 5652 } 5653 5654 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 5655 // The result is the min of all operands results. 5656 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 5657 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 5658 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 5659 return MinOpRes; 5660 } 5661 5662 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 5663 // The result is the sum of all operands results. 5664 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 5665 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 5666 for (unsigned i = 1, e = M->getNumOperands(); 5667 SumOpRes != BitWidth && i != e; ++i) 5668 SumOpRes = 5669 std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), BitWidth); 5670 return SumOpRes; 5671 } 5672 5673 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 5674 // The result is the min of all operands results. 5675 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 5676 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 5677 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 5678 return MinOpRes; 5679 } 5680 5681 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 5682 // The result is the min of all operands results. 5683 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 5684 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 5685 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 5686 return MinOpRes; 5687 } 5688 5689 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 5690 // The result is the min of all operands results. 5691 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 5692 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 5693 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 5694 return MinOpRes; 5695 } 5696 5697 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 5698 // For a SCEVUnknown, ask ValueTracking. 5699 KnownBits Known = computeKnownBits(U->getValue(), getDataLayout(), 0, &AC, nullptr, &DT); 5700 return Known.countMinTrailingZeros(); 5701 } 5702 5703 // SCEVUDivExpr 5704 return 0; 5705 } 5706 5707 uint32_t ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 5708 auto I = MinTrailingZerosCache.find(S); 5709 if (I != MinTrailingZerosCache.end()) 5710 return I->second; 5711 5712 uint32_t Result = GetMinTrailingZerosImpl(S); 5713 auto InsertPair = MinTrailingZerosCache.insert({S, Result}); 5714 assert(InsertPair.second && "Should insert a new key"); 5715 return InsertPair.first->second; 5716 } 5717 5718 /// Helper method to assign a range to V from metadata present in the IR. 5719 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) { 5720 if (Instruction *I = dyn_cast<Instruction>(V)) 5721 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range)) 5722 return getConstantRangeFromMetadata(*MD); 5723 5724 return None; 5725 } 5726 5727 void ScalarEvolution::setNoWrapFlags(SCEVAddRecExpr *AddRec, 5728 SCEV::NoWrapFlags Flags) { 5729 if (AddRec->getNoWrapFlags(Flags) != Flags) { 5730 AddRec->setNoWrapFlags(Flags); 5731 UnsignedRanges.erase(AddRec); 5732 SignedRanges.erase(AddRec); 5733 } 5734 } 5735 5736 ConstantRange ScalarEvolution:: 5737 getRangeForUnknownRecurrence(const SCEVUnknown *U) { 5738 const DataLayout &DL = getDataLayout(); 5739 5740 unsigned BitWidth = getTypeSizeInBits(U->getType()); 5741 const ConstantRange FullSet(BitWidth, /*isFullSet=*/true); 5742 5743 // Match a simple recurrence of the form: <start, ShiftOp, Step>, and then 5744 // use information about the trip count to improve our available range. Note 5745 // that the trip count independent cases are already handled by known bits. 5746 // WARNING: The definition of recurrence used here is subtly different than 5747 // the one used by AddRec (and thus most of this file). Step is allowed to 5748 // be arbitrarily loop varying here, where AddRec allows only loop invariant 5749 // and other addrecs in the same loop (for non-affine addrecs). The code 5750 // below intentionally handles the case where step is not loop invariant. 5751 auto *P = dyn_cast<PHINode>(U->getValue()); 5752 if (!P) 5753 return FullSet; 5754 5755 // Make sure that no Phi input comes from an unreachable block. Otherwise, 5756 // even the values that are not available in these blocks may come from them, 5757 // and this leads to false-positive recurrence test. 5758 for (auto *Pred : predecessors(P->getParent())) 5759 if (!DT.isReachableFromEntry(Pred)) 5760 return FullSet; 5761 5762 BinaryOperator *BO; 5763 Value *Start, *Step; 5764 if (!matchSimpleRecurrence(P, BO, Start, Step)) 5765 return FullSet; 5766 5767 // If we found a recurrence in reachable code, we must be in a loop. Note 5768 // that BO might be in some subloop of L, and that's completely okay. 5769 auto *L = LI.getLoopFor(P->getParent()); 5770 assert(L && L->getHeader() == P->getParent()); 5771 if (!L->contains(BO->getParent())) 5772 // NOTE: This bailout should be an assert instead. However, asserting 5773 // the condition here exposes a case where LoopFusion is querying SCEV 5774 // with malformed loop information during the midst of the transform. 5775 // There doesn't appear to be an obvious fix, so for the moment bailout 5776 // until the caller issue can be fixed. PR49566 tracks the bug. 5777 return FullSet; 5778 5779 // TODO: Extend to other opcodes such as mul, and div 5780 switch (BO->getOpcode()) { 5781 default: 5782 return FullSet; 5783 case Instruction::AShr: 5784 case Instruction::LShr: 5785 case Instruction::Shl: 5786 break; 5787 }; 5788 5789 if (BO->getOperand(0) != P) 5790 // TODO: Handle the power function forms some day. 5791 return FullSet; 5792 5793 unsigned TC = getSmallConstantMaxTripCount(L); 5794 if (!TC || TC >= BitWidth) 5795 return FullSet; 5796 5797 auto KnownStart = computeKnownBits(Start, DL, 0, &AC, nullptr, &DT); 5798 auto KnownStep = computeKnownBits(Step, DL, 0, &AC, nullptr, &DT); 5799 assert(KnownStart.getBitWidth() == BitWidth && 5800 KnownStep.getBitWidth() == BitWidth); 5801 5802 // Compute total shift amount, being careful of overflow and bitwidths. 5803 auto MaxShiftAmt = KnownStep.getMaxValue(); 5804 APInt TCAP(BitWidth, TC-1); 5805 bool Overflow = false; 5806 auto TotalShift = MaxShiftAmt.umul_ov(TCAP, Overflow); 5807 if (Overflow) 5808 return FullSet; 5809 5810 switch (BO->getOpcode()) { 5811 default: 5812 llvm_unreachable("filtered out above"); 5813 case Instruction::AShr: { 5814 // For each ashr, three cases: 5815 // shift = 0 => unchanged value 5816 // saturation => 0 or -1 5817 // other => a value closer to zero (of the same sign) 5818 // Thus, the end value is closer to zero than the start. 5819 auto KnownEnd = KnownBits::ashr(KnownStart, 5820 KnownBits::makeConstant(TotalShift)); 5821 if (KnownStart.isNonNegative()) 5822 // Analogous to lshr (simply not yet canonicalized) 5823 return ConstantRange::getNonEmpty(KnownEnd.getMinValue(), 5824 KnownStart.getMaxValue() + 1); 5825 if (KnownStart.isNegative()) 5826 // End >=u Start && End <=s Start 5827 return ConstantRange::getNonEmpty(KnownStart.getMinValue(), 5828 KnownEnd.getMaxValue() + 1); 5829 break; 5830 } 5831 case Instruction::LShr: { 5832 // For each lshr, three cases: 5833 // shift = 0 => unchanged value 5834 // saturation => 0 5835 // other => a smaller positive number 5836 // Thus, the low end of the unsigned range is the last value produced. 5837 auto KnownEnd = KnownBits::lshr(KnownStart, 5838 KnownBits::makeConstant(TotalShift)); 5839 return ConstantRange::getNonEmpty(KnownEnd.getMinValue(), 5840 KnownStart.getMaxValue() + 1); 5841 } 5842 case Instruction::Shl: { 5843 // Iff no bits are shifted out, value increases on every shift. 5844 auto KnownEnd = KnownBits::shl(KnownStart, 5845 KnownBits::makeConstant(TotalShift)); 5846 if (TotalShift.ult(KnownStart.countMinLeadingZeros())) 5847 return ConstantRange(KnownStart.getMinValue(), 5848 KnownEnd.getMaxValue() + 1); 5849 break; 5850 } 5851 }; 5852 return FullSet; 5853 } 5854 5855 /// Determine the range for a particular SCEV. If SignHint is 5856 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges 5857 /// with a "cleaner" unsigned (resp. signed) representation. 5858 const ConstantRange & 5859 ScalarEvolution::getRangeRef(const SCEV *S, 5860 ScalarEvolution::RangeSignHint SignHint) { 5861 DenseMap<const SCEV *, ConstantRange> &Cache = 5862 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges 5863 : SignedRanges; 5864 ConstantRange::PreferredRangeType RangeType = 5865 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED 5866 ? ConstantRange::Unsigned : ConstantRange::Signed; 5867 5868 // See if we've computed this range already. 5869 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S); 5870 if (I != Cache.end()) 5871 return I->second; 5872 5873 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 5874 return setRange(C, SignHint, ConstantRange(C->getAPInt())); 5875 5876 unsigned BitWidth = getTypeSizeInBits(S->getType()); 5877 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 5878 using OBO = OverflowingBinaryOperator; 5879 5880 // If the value has known zeros, the maximum value will have those known zeros 5881 // as well. 5882 uint32_t TZ = GetMinTrailingZeros(S); 5883 if (TZ != 0) { 5884 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) 5885 ConservativeResult = 5886 ConstantRange(APInt::getMinValue(BitWidth), 5887 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 5888 else 5889 ConservativeResult = ConstantRange( 5890 APInt::getSignedMinValue(BitWidth), 5891 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 5892 } 5893 5894 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 5895 ConstantRange X = getRangeRef(Add->getOperand(0), SignHint); 5896 unsigned WrapType = OBO::AnyWrap; 5897 if (Add->hasNoSignedWrap()) 5898 WrapType |= OBO::NoSignedWrap; 5899 if (Add->hasNoUnsignedWrap()) 5900 WrapType |= OBO::NoUnsignedWrap; 5901 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 5902 X = X.addWithNoWrap(getRangeRef(Add->getOperand(i), SignHint), 5903 WrapType, RangeType); 5904 return setRange(Add, SignHint, 5905 ConservativeResult.intersectWith(X, RangeType)); 5906 } 5907 5908 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 5909 ConstantRange X = getRangeRef(Mul->getOperand(0), SignHint); 5910 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 5911 X = X.multiply(getRangeRef(Mul->getOperand(i), SignHint)); 5912 return setRange(Mul, SignHint, 5913 ConservativeResult.intersectWith(X, RangeType)); 5914 } 5915 5916 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 5917 ConstantRange X = getRangeRef(SMax->getOperand(0), SignHint); 5918 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 5919 X = X.smax(getRangeRef(SMax->getOperand(i), SignHint)); 5920 return setRange(SMax, SignHint, 5921 ConservativeResult.intersectWith(X, RangeType)); 5922 } 5923 5924 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 5925 ConstantRange X = getRangeRef(UMax->getOperand(0), SignHint); 5926 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 5927 X = X.umax(getRangeRef(UMax->getOperand(i), SignHint)); 5928 return setRange(UMax, SignHint, 5929 ConservativeResult.intersectWith(X, RangeType)); 5930 } 5931 5932 if (const SCEVSMinExpr *SMin = dyn_cast<SCEVSMinExpr>(S)) { 5933 ConstantRange X = getRangeRef(SMin->getOperand(0), SignHint); 5934 for (unsigned i = 1, e = SMin->getNumOperands(); i != e; ++i) 5935 X = X.smin(getRangeRef(SMin->getOperand(i), SignHint)); 5936 return setRange(SMin, SignHint, 5937 ConservativeResult.intersectWith(X, RangeType)); 5938 } 5939 5940 if (const SCEVUMinExpr *UMin = dyn_cast<SCEVUMinExpr>(S)) { 5941 ConstantRange X = getRangeRef(UMin->getOperand(0), SignHint); 5942 for (unsigned i = 1, e = UMin->getNumOperands(); i != e; ++i) 5943 X = X.umin(getRangeRef(UMin->getOperand(i), SignHint)); 5944 return setRange(UMin, SignHint, 5945 ConservativeResult.intersectWith(X, RangeType)); 5946 } 5947 5948 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 5949 ConstantRange X = getRangeRef(UDiv->getLHS(), SignHint); 5950 ConstantRange Y = getRangeRef(UDiv->getRHS(), SignHint); 5951 return setRange(UDiv, SignHint, 5952 ConservativeResult.intersectWith(X.udiv(Y), RangeType)); 5953 } 5954 5955 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 5956 ConstantRange X = getRangeRef(ZExt->getOperand(), SignHint); 5957 return setRange(ZExt, SignHint, 5958 ConservativeResult.intersectWith(X.zeroExtend(BitWidth), 5959 RangeType)); 5960 } 5961 5962 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 5963 ConstantRange X = getRangeRef(SExt->getOperand(), SignHint); 5964 return setRange(SExt, SignHint, 5965 ConservativeResult.intersectWith(X.signExtend(BitWidth), 5966 RangeType)); 5967 } 5968 5969 if (const SCEVPtrToIntExpr *PtrToInt = dyn_cast<SCEVPtrToIntExpr>(S)) { 5970 ConstantRange X = getRangeRef(PtrToInt->getOperand(), SignHint); 5971 return setRange(PtrToInt, SignHint, X); 5972 } 5973 5974 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 5975 ConstantRange X = getRangeRef(Trunc->getOperand(), SignHint); 5976 return setRange(Trunc, SignHint, 5977 ConservativeResult.intersectWith(X.truncate(BitWidth), 5978 RangeType)); 5979 } 5980 5981 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 5982 // If there's no unsigned wrap, the value will never be less than its 5983 // initial value. 5984 if (AddRec->hasNoUnsignedWrap()) { 5985 APInt UnsignedMinValue = getUnsignedRangeMin(AddRec->getStart()); 5986 if (!UnsignedMinValue.isNullValue()) 5987 ConservativeResult = ConservativeResult.intersectWith( 5988 ConstantRange(UnsignedMinValue, APInt(BitWidth, 0)), RangeType); 5989 } 5990 5991 // If there's no signed wrap, and all the operands except initial value have 5992 // the same sign or zero, the value won't ever be: 5993 // 1: smaller than initial value if operands are non negative, 5994 // 2: bigger than initial value if operands are non positive. 5995 // For both cases, value can not cross signed min/max boundary. 5996 if (AddRec->hasNoSignedWrap()) { 5997 bool AllNonNeg = true; 5998 bool AllNonPos = true; 5999 for (unsigned i = 1, e = AddRec->getNumOperands(); i != e; ++i) { 6000 if (!isKnownNonNegative(AddRec->getOperand(i))) 6001 AllNonNeg = false; 6002 if (!isKnownNonPositive(AddRec->getOperand(i))) 6003 AllNonPos = false; 6004 } 6005 if (AllNonNeg) 6006 ConservativeResult = ConservativeResult.intersectWith( 6007 ConstantRange::getNonEmpty(getSignedRangeMin(AddRec->getStart()), 6008 APInt::getSignedMinValue(BitWidth)), 6009 RangeType); 6010 else if (AllNonPos) 6011 ConservativeResult = ConservativeResult.intersectWith( 6012 ConstantRange::getNonEmpty( 6013 APInt::getSignedMinValue(BitWidth), 6014 getSignedRangeMax(AddRec->getStart()) + 1), 6015 RangeType); 6016 } 6017 6018 // TODO: non-affine addrec 6019 if (AddRec->isAffine()) { 6020 const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(AddRec->getLoop()); 6021 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 6022 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 6023 auto RangeFromAffine = getRangeForAffineAR( 6024 AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount, 6025 BitWidth); 6026 ConservativeResult = 6027 ConservativeResult.intersectWith(RangeFromAffine, RangeType); 6028 6029 auto RangeFromFactoring = getRangeViaFactoring( 6030 AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount, 6031 BitWidth); 6032 ConservativeResult = 6033 ConservativeResult.intersectWith(RangeFromFactoring, RangeType); 6034 } 6035 6036 // Now try symbolic BE count and more powerful methods. 6037 if (UseExpensiveRangeSharpening) { 6038 const SCEV *SymbolicMaxBECount = 6039 getSymbolicMaxBackedgeTakenCount(AddRec->getLoop()); 6040 if (!isa<SCEVCouldNotCompute>(SymbolicMaxBECount) && 6041 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth && 6042 AddRec->hasNoSelfWrap()) { 6043 auto RangeFromAffineNew = getRangeForAffineNoSelfWrappingAR( 6044 AddRec, SymbolicMaxBECount, BitWidth, SignHint); 6045 ConservativeResult = 6046 ConservativeResult.intersectWith(RangeFromAffineNew, RangeType); 6047 } 6048 } 6049 } 6050 6051 return setRange(AddRec, SignHint, std::move(ConservativeResult)); 6052 } 6053 6054 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 6055 6056 // Check if the IR explicitly contains !range metadata. 6057 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue()); 6058 if (MDRange.hasValue()) 6059 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue(), 6060 RangeType); 6061 6062 // Use facts about recurrences in the underlying IR. Note that add 6063 // recurrences are AddRecExprs and thus don't hit this path. This 6064 // primarily handles shift recurrences. 6065 auto CR = getRangeForUnknownRecurrence(U); 6066 ConservativeResult = ConservativeResult.intersectWith(CR); 6067 6068 // See if ValueTracking can give us a useful range. 6069 const DataLayout &DL = getDataLayout(); 6070 KnownBits Known = computeKnownBits(U->getValue(), DL, 0, &AC, nullptr, &DT); 6071 if (Known.getBitWidth() != BitWidth) 6072 Known = Known.zextOrTrunc(BitWidth); 6073 6074 // ValueTracking may be able to compute a tighter result for the number of 6075 // sign bits than for the value of those sign bits. 6076 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT); 6077 if (U->getType()->isPointerTy()) { 6078 // If the pointer size is larger than the index size type, this can cause 6079 // NS to be larger than BitWidth. So compensate for this. 6080 unsigned ptrSize = DL.getPointerTypeSizeInBits(U->getType()); 6081 int ptrIdxDiff = ptrSize - BitWidth; 6082 if (ptrIdxDiff > 0 && ptrSize > BitWidth && NS > (unsigned)ptrIdxDiff) 6083 NS -= ptrIdxDiff; 6084 } 6085 6086 if (NS > 1) { 6087 // If we know any of the sign bits, we know all of the sign bits. 6088 if (!Known.Zero.getHiBits(NS).isNullValue()) 6089 Known.Zero.setHighBits(NS); 6090 if (!Known.One.getHiBits(NS).isNullValue()) 6091 Known.One.setHighBits(NS); 6092 } 6093 6094 if (Known.getMinValue() != Known.getMaxValue() + 1) 6095 ConservativeResult = ConservativeResult.intersectWith( 6096 ConstantRange(Known.getMinValue(), Known.getMaxValue() + 1), 6097 RangeType); 6098 if (NS > 1) 6099 ConservativeResult = ConservativeResult.intersectWith( 6100 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 6101 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1), 6102 RangeType); 6103 6104 // A range of Phi is a subset of union of all ranges of its input. 6105 if (const PHINode *Phi = dyn_cast<PHINode>(U->getValue())) { 6106 // Make sure that we do not run over cycled Phis. 6107 if (PendingPhiRanges.insert(Phi).second) { 6108 ConstantRange RangeFromOps(BitWidth, /*isFullSet=*/false); 6109 for (auto &Op : Phi->operands()) { 6110 auto OpRange = getRangeRef(getSCEV(Op), SignHint); 6111 RangeFromOps = RangeFromOps.unionWith(OpRange); 6112 // No point to continue if we already have a full set. 6113 if (RangeFromOps.isFullSet()) 6114 break; 6115 } 6116 ConservativeResult = 6117 ConservativeResult.intersectWith(RangeFromOps, RangeType); 6118 bool Erased = PendingPhiRanges.erase(Phi); 6119 assert(Erased && "Failed to erase Phi properly?"); 6120 (void) Erased; 6121 } 6122 } 6123 6124 return setRange(U, SignHint, std::move(ConservativeResult)); 6125 } 6126 6127 return setRange(S, SignHint, std::move(ConservativeResult)); 6128 } 6129 6130 // Given a StartRange, Step and MaxBECount for an expression compute a range of 6131 // values that the expression can take. Initially, the expression has a value 6132 // from StartRange and then is changed by Step up to MaxBECount times. Signed 6133 // argument defines if we treat Step as signed or unsigned. 6134 static ConstantRange getRangeForAffineARHelper(APInt Step, 6135 const ConstantRange &StartRange, 6136 const APInt &MaxBECount, 6137 unsigned BitWidth, bool Signed) { 6138 // If either Step or MaxBECount is 0, then the expression won't change, and we 6139 // just need to return the initial range. 6140 if (Step == 0 || MaxBECount == 0) 6141 return StartRange; 6142 6143 // If we don't know anything about the initial value (i.e. StartRange is 6144 // FullRange), then we don't know anything about the final range either. 6145 // Return FullRange. 6146 if (StartRange.isFullSet()) 6147 return ConstantRange::getFull(BitWidth); 6148 6149 // If Step is signed and negative, then we use its absolute value, but we also 6150 // note that we're moving in the opposite direction. 6151 bool Descending = Signed && Step.isNegative(); 6152 6153 if (Signed) 6154 // This is correct even for INT_SMIN. Let's look at i8 to illustrate this: 6155 // abs(INT_SMIN) = abs(-128) = abs(0x80) = -0x80 = 0x80 = 128. 6156 // This equations hold true due to the well-defined wrap-around behavior of 6157 // APInt. 6158 Step = Step.abs(); 6159 6160 // Check if Offset is more than full span of BitWidth. If it is, the 6161 // expression is guaranteed to overflow. 6162 if (APInt::getMaxValue(StartRange.getBitWidth()).udiv(Step).ult(MaxBECount)) 6163 return ConstantRange::getFull(BitWidth); 6164 6165 // Offset is by how much the expression can change. Checks above guarantee no 6166 // overflow here. 6167 APInt Offset = Step * MaxBECount; 6168 6169 // Minimum value of the final range will match the minimal value of StartRange 6170 // if the expression is increasing and will be decreased by Offset otherwise. 6171 // Maximum value of the final range will match the maximal value of StartRange 6172 // if the expression is decreasing and will be increased by Offset otherwise. 6173 APInt StartLower = StartRange.getLower(); 6174 APInt StartUpper = StartRange.getUpper() - 1; 6175 APInt MovedBoundary = Descending ? (StartLower - std::move(Offset)) 6176 : (StartUpper + std::move(Offset)); 6177 6178 // It's possible that the new minimum/maximum value will fall into the initial 6179 // range (due to wrap around). This means that the expression can take any 6180 // value in this bitwidth, and we have to return full range. 6181 if (StartRange.contains(MovedBoundary)) 6182 return ConstantRange::getFull(BitWidth); 6183 6184 APInt NewLower = 6185 Descending ? std::move(MovedBoundary) : std::move(StartLower); 6186 APInt NewUpper = 6187 Descending ? std::move(StartUpper) : std::move(MovedBoundary); 6188 NewUpper += 1; 6189 6190 // No overflow detected, return [StartLower, StartUpper + Offset + 1) range. 6191 return ConstantRange::getNonEmpty(std::move(NewLower), std::move(NewUpper)); 6192 } 6193 6194 ConstantRange ScalarEvolution::getRangeForAffineAR(const SCEV *Start, 6195 const SCEV *Step, 6196 const SCEV *MaxBECount, 6197 unsigned BitWidth) { 6198 assert(!isa<SCEVCouldNotCompute>(MaxBECount) && 6199 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth && 6200 "Precondition!"); 6201 6202 MaxBECount = getNoopOrZeroExtend(MaxBECount, Start->getType()); 6203 APInt MaxBECountValue = getUnsignedRangeMax(MaxBECount); 6204 6205 // First, consider step signed. 6206 ConstantRange StartSRange = getSignedRange(Start); 6207 ConstantRange StepSRange = getSignedRange(Step); 6208 6209 // If Step can be both positive and negative, we need to find ranges for the 6210 // maximum absolute step values in both directions and union them. 6211 ConstantRange SR = 6212 getRangeForAffineARHelper(StepSRange.getSignedMin(), StartSRange, 6213 MaxBECountValue, BitWidth, /* Signed = */ true); 6214 SR = SR.unionWith(getRangeForAffineARHelper(StepSRange.getSignedMax(), 6215 StartSRange, MaxBECountValue, 6216 BitWidth, /* Signed = */ true)); 6217 6218 // Next, consider step unsigned. 6219 ConstantRange UR = getRangeForAffineARHelper( 6220 getUnsignedRangeMax(Step), getUnsignedRange(Start), 6221 MaxBECountValue, BitWidth, /* Signed = */ false); 6222 6223 // Finally, intersect signed and unsigned ranges. 6224 return SR.intersectWith(UR, ConstantRange::Smallest); 6225 } 6226 6227 ConstantRange ScalarEvolution::getRangeForAffineNoSelfWrappingAR( 6228 const SCEVAddRecExpr *AddRec, const SCEV *MaxBECount, unsigned BitWidth, 6229 ScalarEvolution::RangeSignHint SignHint) { 6230 assert(AddRec->isAffine() && "Non-affine AddRecs are not suppored!\n"); 6231 assert(AddRec->hasNoSelfWrap() && 6232 "This only works for non-self-wrapping AddRecs!"); 6233 const bool IsSigned = SignHint == HINT_RANGE_SIGNED; 6234 const SCEV *Step = AddRec->getStepRecurrence(*this); 6235 // Only deal with constant step to save compile time. 6236 if (!isa<SCEVConstant>(Step)) 6237 return ConstantRange::getFull(BitWidth); 6238 // Let's make sure that we can prove that we do not self-wrap during 6239 // MaxBECount iterations. We need this because MaxBECount is a maximum 6240 // iteration count estimate, and we might infer nw from some exit for which we 6241 // do not know max exit count (or any other side reasoning). 6242 // TODO: Turn into assert at some point. 6243 if (getTypeSizeInBits(MaxBECount->getType()) > 6244 getTypeSizeInBits(AddRec->getType())) 6245 return ConstantRange::getFull(BitWidth); 6246 MaxBECount = getNoopOrZeroExtend(MaxBECount, AddRec->getType()); 6247 const SCEV *RangeWidth = getMinusOne(AddRec->getType()); 6248 const SCEV *StepAbs = getUMinExpr(Step, getNegativeSCEV(Step)); 6249 const SCEV *MaxItersWithoutWrap = getUDivExpr(RangeWidth, StepAbs); 6250 if (!isKnownPredicateViaConstantRanges(ICmpInst::ICMP_ULE, MaxBECount, 6251 MaxItersWithoutWrap)) 6252 return ConstantRange::getFull(BitWidth); 6253 6254 ICmpInst::Predicate LEPred = 6255 IsSigned ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE; 6256 ICmpInst::Predicate GEPred = 6257 IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE; 6258 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this); 6259 6260 // We know that there is no self-wrap. Let's take Start and End values and 6261 // look at all intermediate values V1, V2, ..., Vn that IndVar takes during 6262 // the iteration. They either lie inside the range [Min(Start, End), 6263 // Max(Start, End)] or outside it: 6264 // 6265 // Case 1: RangeMin ... Start V1 ... VN End ... RangeMax; 6266 // Case 2: RangeMin Vk ... V1 Start ... End Vn ... Vk + 1 RangeMax; 6267 // 6268 // No self wrap flag guarantees that the intermediate values cannot be BOTH 6269 // outside and inside the range [Min(Start, End), Max(Start, End)]. Using that 6270 // knowledge, let's try to prove that we are dealing with Case 1. It is so if 6271 // Start <= End and step is positive, or Start >= End and step is negative. 6272 const SCEV *Start = AddRec->getStart(); 6273 ConstantRange StartRange = getRangeRef(Start, SignHint); 6274 ConstantRange EndRange = getRangeRef(End, SignHint); 6275 ConstantRange RangeBetween = StartRange.unionWith(EndRange); 6276 // If they already cover full iteration space, we will know nothing useful 6277 // even if we prove what we want to prove. 6278 if (RangeBetween.isFullSet()) 6279 return RangeBetween; 6280 // Only deal with ranges that do not wrap (i.e. RangeMin < RangeMax). 6281 bool IsWrappedSet = IsSigned ? RangeBetween.isSignWrappedSet() 6282 : RangeBetween.isWrappedSet(); 6283 if (IsWrappedSet) 6284 return ConstantRange::getFull(BitWidth); 6285 6286 if (isKnownPositive(Step) && 6287 isKnownPredicateViaConstantRanges(LEPred, Start, End)) 6288 return RangeBetween; 6289 else if (isKnownNegative(Step) && 6290 isKnownPredicateViaConstantRanges(GEPred, Start, End)) 6291 return RangeBetween; 6292 return ConstantRange::getFull(BitWidth); 6293 } 6294 6295 ConstantRange ScalarEvolution::getRangeViaFactoring(const SCEV *Start, 6296 const SCEV *Step, 6297 const SCEV *MaxBECount, 6298 unsigned BitWidth) { 6299 // RangeOf({C?A:B,+,C?P:Q}) == RangeOf(C?{A,+,P}:{B,+,Q}) 6300 // == RangeOf({A,+,P}) union RangeOf({B,+,Q}) 6301 6302 struct SelectPattern { 6303 Value *Condition = nullptr; 6304 APInt TrueValue; 6305 APInt FalseValue; 6306 6307 explicit SelectPattern(ScalarEvolution &SE, unsigned BitWidth, 6308 const SCEV *S) { 6309 Optional<unsigned> CastOp; 6310 APInt Offset(BitWidth, 0); 6311 6312 assert(SE.getTypeSizeInBits(S->getType()) == BitWidth && 6313 "Should be!"); 6314 6315 // Peel off a constant offset: 6316 if (auto *SA = dyn_cast<SCEVAddExpr>(S)) { 6317 // In the future we could consider being smarter here and handle 6318 // {Start+Step,+,Step} too. 6319 if (SA->getNumOperands() != 2 || !isa<SCEVConstant>(SA->getOperand(0))) 6320 return; 6321 6322 Offset = cast<SCEVConstant>(SA->getOperand(0))->getAPInt(); 6323 S = SA->getOperand(1); 6324 } 6325 6326 // Peel off a cast operation 6327 if (auto *SCast = dyn_cast<SCEVIntegralCastExpr>(S)) { 6328 CastOp = SCast->getSCEVType(); 6329 S = SCast->getOperand(); 6330 } 6331 6332 using namespace llvm::PatternMatch; 6333 6334 auto *SU = dyn_cast<SCEVUnknown>(S); 6335 const APInt *TrueVal, *FalseVal; 6336 if (!SU || 6337 !match(SU->getValue(), m_Select(m_Value(Condition), m_APInt(TrueVal), 6338 m_APInt(FalseVal)))) { 6339 Condition = nullptr; 6340 return; 6341 } 6342 6343 TrueValue = *TrueVal; 6344 FalseValue = *FalseVal; 6345 6346 // Re-apply the cast we peeled off earlier 6347 if (CastOp.hasValue()) 6348 switch (*CastOp) { 6349 default: 6350 llvm_unreachable("Unknown SCEV cast type!"); 6351 6352 case scTruncate: 6353 TrueValue = TrueValue.trunc(BitWidth); 6354 FalseValue = FalseValue.trunc(BitWidth); 6355 break; 6356 case scZeroExtend: 6357 TrueValue = TrueValue.zext(BitWidth); 6358 FalseValue = FalseValue.zext(BitWidth); 6359 break; 6360 case scSignExtend: 6361 TrueValue = TrueValue.sext(BitWidth); 6362 FalseValue = FalseValue.sext(BitWidth); 6363 break; 6364 } 6365 6366 // Re-apply the constant offset we peeled off earlier 6367 TrueValue += Offset; 6368 FalseValue += Offset; 6369 } 6370 6371 bool isRecognized() { return Condition != nullptr; } 6372 }; 6373 6374 SelectPattern StartPattern(*this, BitWidth, Start); 6375 if (!StartPattern.isRecognized()) 6376 return ConstantRange::getFull(BitWidth); 6377 6378 SelectPattern StepPattern(*this, BitWidth, Step); 6379 if (!StepPattern.isRecognized()) 6380 return ConstantRange::getFull(BitWidth); 6381 6382 if (StartPattern.Condition != StepPattern.Condition) { 6383 // We don't handle this case today; but we could, by considering four 6384 // possibilities below instead of two. I'm not sure if there are cases where 6385 // that will help over what getRange already does, though. 6386 return ConstantRange::getFull(BitWidth); 6387 } 6388 6389 // NB! Calling ScalarEvolution::getConstant is fine, but we should not try to 6390 // construct arbitrary general SCEV expressions here. This function is called 6391 // from deep in the call stack, and calling getSCEV (on a sext instruction, 6392 // say) can end up caching a suboptimal value. 6393 6394 // FIXME: without the explicit `this` receiver below, MSVC errors out with 6395 // C2352 and C2512 (otherwise it isn't needed). 6396 6397 const SCEV *TrueStart = this->getConstant(StartPattern.TrueValue); 6398 const SCEV *TrueStep = this->getConstant(StepPattern.TrueValue); 6399 const SCEV *FalseStart = this->getConstant(StartPattern.FalseValue); 6400 const SCEV *FalseStep = this->getConstant(StepPattern.FalseValue); 6401 6402 ConstantRange TrueRange = 6403 this->getRangeForAffineAR(TrueStart, TrueStep, MaxBECount, BitWidth); 6404 ConstantRange FalseRange = 6405 this->getRangeForAffineAR(FalseStart, FalseStep, MaxBECount, BitWidth); 6406 6407 return TrueRange.unionWith(FalseRange); 6408 } 6409 6410 SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) { 6411 if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap; 6412 const BinaryOperator *BinOp = cast<BinaryOperator>(V); 6413 6414 // Return early if there are no flags to propagate to the SCEV. 6415 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap; 6416 if (BinOp->hasNoUnsignedWrap()) 6417 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW); 6418 if (BinOp->hasNoSignedWrap()) 6419 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW); 6420 if (Flags == SCEV::FlagAnyWrap) 6421 return SCEV::FlagAnyWrap; 6422 6423 return isSCEVExprNeverPoison(BinOp) ? Flags : SCEV::FlagAnyWrap; 6424 } 6425 6426 bool ScalarEvolution::isSCEVExprNeverPoison(const Instruction *I) { 6427 // Here we check that I is in the header of the innermost loop containing I, 6428 // since we only deal with instructions in the loop header. The actual loop we 6429 // need to check later will come from an add recurrence, but getting that 6430 // requires computing the SCEV of the operands, which can be expensive. This 6431 // check we can do cheaply to rule out some cases early. 6432 Loop *InnermostContainingLoop = LI.getLoopFor(I->getParent()); 6433 if (InnermostContainingLoop == nullptr || 6434 InnermostContainingLoop->getHeader() != I->getParent()) 6435 return false; 6436 6437 // Only proceed if we can prove that I does not yield poison. 6438 if (!programUndefinedIfPoison(I)) 6439 return false; 6440 6441 // At this point we know that if I is executed, then it does not wrap 6442 // according to at least one of NSW or NUW. If I is not executed, then we do 6443 // not know if the calculation that I represents would wrap. Multiple 6444 // instructions can map to the same SCEV. If we apply NSW or NUW from I to 6445 // the SCEV, we must guarantee no wrapping for that SCEV also when it is 6446 // derived from other instructions that map to the same SCEV. We cannot make 6447 // that guarantee for cases where I is not executed. So we need to find the 6448 // loop that I is considered in relation to and prove that I is executed for 6449 // every iteration of that loop. That implies that the value that I 6450 // calculates does not wrap anywhere in the loop, so then we can apply the 6451 // flags to the SCEV. 6452 // 6453 // We check isLoopInvariant to disambiguate in case we are adding recurrences 6454 // from different loops, so that we know which loop to prove that I is 6455 // executed in. 6456 for (unsigned OpIndex = 0; OpIndex < I->getNumOperands(); ++OpIndex) { 6457 // I could be an extractvalue from a call to an overflow intrinsic. 6458 // TODO: We can do better here in some cases. 6459 if (!isSCEVable(I->getOperand(OpIndex)->getType())) 6460 return false; 6461 const SCEV *Op = getSCEV(I->getOperand(OpIndex)); 6462 if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 6463 bool AllOtherOpsLoopInvariant = true; 6464 for (unsigned OtherOpIndex = 0; OtherOpIndex < I->getNumOperands(); 6465 ++OtherOpIndex) { 6466 if (OtherOpIndex != OpIndex) { 6467 const SCEV *OtherOp = getSCEV(I->getOperand(OtherOpIndex)); 6468 if (!isLoopInvariant(OtherOp, AddRec->getLoop())) { 6469 AllOtherOpsLoopInvariant = false; 6470 break; 6471 } 6472 } 6473 } 6474 if (AllOtherOpsLoopInvariant && 6475 isGuaranteedToExecuteForEveryIteration(I, AddRec->getLoop())) 6476 return true; 6477 } 6478 } 6479 return false; 6480 } 6481 6482 bool ScalarEvolution::isAddRecNeverPoison(const Instruction *I, const Loop *L) { 6483 // If we know that \c I can never be poison period, then that's enough. 6484 if (isSCEVExprNeverPoison(I)) 6485 return true; 6486 6487 // For an add recurrence specifically, we assume that infinite loops without 6488 // side effects are undefined behavior, and then reason as follows: 6489 // 6490 // If the add recurrence is poison in any iteration, it is poison on all 6491 // future iterations (since incrementing poison yields poison). If the result 6492 // of the add recurrence is fed into the loop latch condition and the loop 6493 // does not contain any throws or exiting blocks other than the latch, we now 6494 // have the ability to "choose" whether the backedge is taken or not (by 6495 // choosing a sufficiently evil value for the poison feeding into the branch) 6496 // for every iteration including and after the one in which \p I first became 6497 // poison. There are two possibilities (let's call the iteration in which \p 6498 // I first became poison as K): 6499 // 6500 // 1. In the set of iterations including and after K, the loop body executes 6501 // no side effects. In this case executing the backege an infinte number 6502 // of times will yield undefined behavior. 6503 // 6504 // 2. In the set of iterations including and after K, the loop body executes 6505 // at least one side effect. In this case, that specific instance of side 6506 // effect is control dependent on poison, which also yields undefined 6507 // behavior. 6508 6509 auto *ExitingBB = L->getExitingBlock(); 6510 auto *LatchBB = L->getLoopLatch(); 6511 if (!ExitingBB || !LatchBB || ExitingBB != LatchBB) 6512 return false; 6513 6514 SmallPtrSet<const Instruction *, 16> Pushed; 6515 SmallVector<const Instruction *, 8> PoisonStack; 6516 6517 // We start by assuming \c I, the post-inc add recurrence, is poison. Only 6518 // things that are known to be poison under that assumption go on the 6519 // PoisonStack. 6520 Pushed.insert(I); 6521 PoisonStack.push_back(I); 6522 6523 bool LatchControlDependentOnPoison = false; 6524 while (!PoisonStack.empty() && !LatchControlDependentOnPoison) { 6525 const Instruction *Poison = PoisonStack.pop_back_val(); 6526 6527 for (auto *PoisonUser : Poison->users()) { 6528 if (propagatesPoison(cast<Operator>(PoisonUser))) { 6529 if (Pushed.insert(cast<Instruction>(PoisonUser)).second) 6530 PoisonStack.push_back(cast<Instruction>(PoisonUser)); 6531 } else if (auto *BI = dyn_cast<BranchInst>(PoisonUser)) { 6532 assert(BI->isConditional() && "Only possibility!"); 6533 if (BI->getParent() == LatchBB) { 6534 LatchControlDependentOnPoison = true; 6535 break; 6536 } 6537 } 6538 } 6539 } 6540 6541 return LatchControlDependentOnPoison && loopHasNoAbnormalExits(L); 6542 } 6543 6544 ScalarEvolution::LoopProperties 6545 ScalarEvolution::getLoopProperties(const Loop *L) { 6546 using LoopProperties = ScalarEvolution::LoopProperties; 6547 6548 auto Itr = LoopPropertiesCache.find(L); 6549 if (Itr == LoopPropertiesCache.end()) { 6550 auto HasSideEffects = [](Instruction *I) { 6551 if (auto *SI = dyn_cast<StoreInst>(I)) 6552 return !SI->isSimple(); 6553 6554 return I->mayHaveSideEffects(); 6555 }; 6556 6557 LoopProperties LP = {/* HasNoAbnormalExits */ true, 6558 /*HasNoSideEffects*/ true}; 6559 6560 for (auto *BB : L->getBlocks()) 6561 for (auto &I : *BB) { 6562 if (!isGuaranteedToTransferExecutionToSuccessor(&I)) 6563 LP.HasNoAbnormalExits = false; 6564 if (HasSideEffects(&I)) 6565 LP.HasNoSideEffects = false; 6566 if (!LP.HasNoAbnormalExits && !LP.HasNoSideEffects) 6567 break; // We're already as pessimistic as we can get. 6568 } 6569 6570 auto InsertPair = LoopPropertiesCache.insert({L, LP}); 6571 assert(InsertPair.second && "We just checked!"); 6572 Itr = InsertPair.first; 6573 } 6574 6575 return Itr->second; 6576 } 6577 6578 bool ScalarEvolution::loopIsFiniteByAssumption(const Loop *L) { 6579 // A mustprogress loop without side effects must be finite. 6580 // TODO: The check used here is very conservative. It's only *specific* 6581 // side effects which are well defined in infinite loops. 6582 return isMustProgress(L) && loopHasNoSideEffects(L); 6583 } 6584 6585 const SCEV *ScalarEvolution::createSCEV(Value *V) { 6586 if (!isSCEVable(V->getType())) 6587 return getUnknown(V); 6588 6589 if (Instruction *I = dyn_cast<Instruction>(V)) { 6590 // Don't attempt to analyze instructions in blocks that aren't 6591 // reachable. Such instructions don't matter, and they aren't required 6592 // to obey basic rules for definitions dominating uses which this 6593 // analysis depends on. 6594 if (!DT.isReachableFromEntry(I->getParent())) 6595 return getUnknown(UndefValue::get(V->getType())); 6596 } else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 6597 return getConstant(CI); 6598 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 6599 return GA->isInterposable() ? getUnknown(V) : getSCEV(GA->getAliasee()); 6600 else if (!isa<ConstantExpr>(V)) 6601 return getUnknown(V); 6602 6603 Operator *U = cast<Operator>(V); 6604 if (auto BO = MatchBinaryOp(U, DT)) { 6605 switch (BO->Opcode) { 6606 case Instruction::Add: { 6607 // The simple thing to do would be to just call getSCEV on both operands 6608 // and call getAddExpr with the result. However if we're looking at a 6609 // bunch of things all added together, this can be quite inefficient, 6610 // because it leads to N-1 getAddExpr calls for N ultimate operands. 6611 // Instead, gather up all the operands and make a single getAddExpr call. 6612 // LLVM IR canonical form means we need only traverse the left operands. 6613 SmallVector<const SCEV *, 4> AddOps; 6614 do { 6615 if (BO->Op) { 6616 if (auto *OpSCEV = getExistingSCEV(BO->Op)) { 6617 AddOps.push_back(OpSCEV); 6618 break; 6619 } 6620 6621 // If a NUW or NSW flag can be applied to the SCEV for this 6622 // addition, then compute the SCEV for this addition by itself 6623 // with a separate call to getAddExpr. We need to do that 6624 // instead of pushing the operands of the addition onto AddOps, 6625 // since the flags are only known to apply to this particular 6626 // addition - they may not apply to other additions that can be 6627 // formed with operands from AddOps. 6628 const SCEV *RHS = getSCEV(BO->RHS); 6629 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op); 6630 if (Flags != SCEV::FlagAnyWrap) { 6631 const SCEV *LHS = getSCEV(BO->LHS); 6632 if (BO->Opcode == Instruction::Sub) 6633 AddOps.push_back(getMinusSCEV(LHS, RHS, Flags)); 6634 else 6635 AddOps.push_back(getAddExpr(LHS, RHS, Flags)); 6636 break; 6637 } 6638 } 6639 6640 if (BO->Opcode == Instruction::Sub) 6641 AddOps.push_back(getNegativeSCEV(getSCEV(BO->RHS))); 6642 else 6643 AddOps.push_back(getSCEV(BO->RHS)); 6644 6645 auto NewBO = MatchBinaryOp(BO->LHS, DT); 6646 if (!NewBO || (NewBO->Opcode != Instruction::Add && 6647 NewBO->Opcode != Instruction::Sub)) { 6648 AddOps.push_back(getSCEV(BO->LHS)); 6649 break; 6650 } 6651 BO = NewBO; 6652 } while (true); 6653 6654 return getAddExpr(AddOps); 6655 } 6656 6657 case Instruction::Mul: { 6658 SmallVector<const SCEV *, 4> MulOps; 6659 do { 6660 if (BO->Op) { 6661 if (auto *OpSCEV = getExistingSCEV(BO->Op)) { 6662 MulOps.push_back(OpSCEV); 6663 break; 6664 } 6665 6666 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op); 6667 if (Flags != SCEV::FlagAnyWrap) { 6668 MulOps.push_back( 6669 getMulExpr(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags)); 6670 break; 6671 } 6672 } 6673 6674 MulOps.push_back(getSCEV(BO->RHS)); 6675 auto NewBO = MatchBinaryOp(BO->LHS, DT); 6676 if (!NewBO || NewBO->Opcode != Instruction::Mul) { 6677 MulOps.push_back(getSCEV(BO->LHS)); 6678 break; 6679 } 6680 BO = NewBO; 6681 } while (true); 6682 6683 return getMulExpr(MulOps); 6684 } 6685 case Instruction::UDiv: 6686 return getUDivExpr(getSCEV(BO->LHS), getSCEV(BO->RHS)); 6687 case Instruction::URem: 6688 return getURemExpr(getSCEV(BO->LHS), getSCEV(BO->RHS)); 6689 case Instruction::Sub: { 6690 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap; 6691 if (BO->Op) 6692 Flags = getNoWrapFlagsFromUB(BO->Op); 6693 return getMinusSCEV(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags); 6694 } 6695 case Instruction::And: 6696 // For an expression like x&255 that merely masks off the high bits, 6697 // use zext(trunc(x)) as the SCEV expression. 6698 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) { 6699 if (CI->isZero()) 6700 return getSCEV(BO->RHS); 6701 if (CI->isMinusOne()) 6702 return getSCEV(BO->LHS); 6703 const APInt &A = CI->getValue(); 6704 6705 // Instcombine's ShrinkDemandedConstant may strip bits out of 6706 // constants, obscuring what would otherwise be a low-bits mask. 6707 // Use computeKnownBits to compute what ShrinkDemandedConstant 6708 // knew about to reconstruct a low-bits mask value. 6709 unsigned LZ = A.countLeadingZeros(); 6710 unsigned TZ = A.countTrailingZeros(); 6711 unsigned BitWidth = A.getBitWidth(); 6712 KnownBits Known(BitWidth); 6713 computeKnownBits(BO->LHS, Known, getDataLayout(), 6714 0, &AC, nullptr, &DT); 6715 6716 APInt EffectiveMask = 6717 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ); 6718 if ((LZ != 0 || TZ != 0) && !((~A & ~Known.Zero) & EffectiveMask)) { 6719 const SCEV *MulCount = getConstant(APInt::getOneBitSet(BitWidth, TZ)); 6720 const SCEV *LHS = getSCEV(BO->LHS); 6721 const SCEV *ShiftedLHS = nullptr; 6722 if (auto *LHSMul = dyn_cast<SCEVMulExpr>(LHS)) { 6723 if (auto *OpC = dyn_cast<SCEVConstant>(LHSMul->getOperand(0))) { 6724 // For an expression like (x * 8) & 8, simplify the multiply. 6725 unsigned MulZeros = OpC->getAPInt().countTrailingZeros(); 6726 unsigned GCD = std::min(MulZeros, TZ); 6727 APInt DivAmt = APInt::getOneBitSet(BitWidth, TZ - GCD); 6728 SmallVector<const SCEV*, 4> MulOps; 6729 MulOps.push_back(getConstant(OpC->getAPInt().lshr(GCD))); 6730 MulOps.append(LHSMul->op_begin() + 1, LHSMul->op_end()); 6731 auto *NewMul = getMulExpr(MulOps, LHSMul->getNoWrapFlags()); 6732 ShiftedLHS = getUDivExpr(NewMul, getConstant(DivAmt)); 6733 } 6734 } 6735 if (!ShiftedLHS) 6736 ShiftedLHS = getUDivExpr(LHS, MulCount); 6737 return getMulExpr( 6738 getZeroExtendExpr( 6739 getTruncateExpr(ShiftedLHS, 6740 IntegerType::get(getContext(), BitWidth - LZ - TZ)), 6741 BO->LHS->getType()), 6742 MulCount); 6743 } 6744 } 6745 break; 6746 6747 case Instruction::Or: 6748 // If the RHS of the Or is a constant, we may have something like: 6749 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 6750 // optimizations will transparently handle this case. 6751 // 6752 // In order for this transformation to be safe, the LHS must be of the 6753 // form X*(2^n) and the Or constant must be less than 2^n. 6754 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) { 6755 const SCEV *LHS = getSCEV(BO->LHS); 6756 const APInt &CIVal = CI->getValue(); 6757 if (GetMinTrailingZeros(LHS) >= 6758 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 6759 // Build a plain add SCEV. 6760 return getAddExpr(LHS, getSCEV(CI), 6761 (SCEV::NoWrapFlags)(SCEV::FlagNUW | SCEV::FlagNSW)); 6762 } 6763 } 6764 break; 6765 6766 case Instruction::Xor: 6767 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) { 6768 // If the RHS of xor is -1, then this is a not operation. 6769 if (CI->isMinusOne()) 6770 return getNotSCEV(getSCEV(BO->LHS)); 6771 6772 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 6773 // This is a variant of the check for xor with -1, and it handles 6774 // the case where instcombine has trimmed non-demanded bits out 6775 // of an xor with -1. 6776 if (auto *LBO = dyn_cast<BinaryOperator>(BO->LHS)) 6777 if (ConstantInt *LCI = dyn_cast<ConstantInt>(LBO->getOperand(1))) 6778 if (LBO->getOpcode() == Instruction::And && 6779 LCI->getValue() == CI->getValue()) 6780 if (const SCEVZeroExtendExpr *Z = 6781 dyn_cast<SCEVZeroExtendExpr>(getSCEV(BO->LHS))) { 6782 Type *UTy = BO->LHS->getType(); 6783 const SCEV *Z0 = Z->getOperand(); 6784 Type *Z0Ty = Z0->getType(); 6785 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 6786 6787 // If C is a low-bits mask, the zero extend is serving to 6788 // mask off the high bits. Complement the operand and 6789 // re-apply the zext. 6790 if (CI->getValue().isMask(Z0TySize)) 6791 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 6792 6793 // If C is a single bit, it may be in the sign-bit position 6794 // before the zero-extend. In this case, represent the xor 6795 // using an add, which is equivalent, and re-apply the zext. 6796 APInt Trunc = CI->getValue().trunc(Z0TySize); 6797 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() && 6798 Trunc.isSignMask()) 6799 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 6800 UTy); 6801 } 6802 } 6803 break; 6804 6805 case Instruction::Shl: 6806 // Turn shift left of a constant amount into a multiply. 6807 if (ConstantInt *SA = dyn_cast<ConstantInt>(BO->RHS)) { 6808 uint32_t BitWidth = cast<IntegerType>(SA->getType())->getBitWidth(); 6809 6810 // If the shift count is not less than the bitwidth, the result of 6811 // the shift is undefined. Don't try to analyze it, because the 6812 // resolution chosen here may differ from the resolution chosen in 6813 // other parts of the compiler. 6814 if (SA->getValue().uge(BitWidth)) 6815 break; 6816 6817 // We can safely preserve the nuw flag in all cases. It's also safe to 6818 // turn a nuw nsw shl into a nuw nsw mul. However, nsw in isolation 6819 // requires special handling. It can be preserved as long as we're not 6820 // left shifting by bitwidth - 1. 6821 auto Flags = SCEV::FlagAnyWrap; 6822 if (BO->Op) { 6823 auto MulFlags = getNoWrapFlagsFromUB(BO->Op); 6824 if ((MulFlags & SCEV::FlagNSW) && 6825 ((MulFlags & SCEV::FlagNUW) || SA->getValue().ult(BitWidth - 1))) 6826 Flags = (SCEV::NoWrapFlags)(Flags | SCEV::FlagNSW); 6827 if (MulFlags & SCEV::FlagNUW) 6828 Flags = (SCEV::NoWrapFlags)(Flags | SCEV::FlagNUW); 6829 } 6830 6831 Constant *X = ConstantInt::get( 6832 getContext(), APInt::getOneBitSet(BitWidth, SA->getZExtValue())); 6833 return getMulExpr(getSCEV(BO->LHS), getSCEV(X), Flags); 6834 } 6835 break; 6836 6837 case Instruction::AShr: { 6838 // AShr X, C, where C is a constant. 6839 ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS); 6840 if (!CI) 6841 break; 6842 6843 Type *OuterTy = BO->LHS->getType(); 6844 uint64_t BitWidth = getTypeSizeInBits(OuterTy); 6845 // If the shift count is not less than the bitwidth, the result of 6846 // the shift is undefined. Don't try to analyze it, because the 6847 // resolution chosen here may differ from the resolution chosen in 6848 // other parts of the compiler. 6849 if (CI->getValue().uge(BitWidth)) 6850 break; 6851 6852 if (CI->isZero()) 6853 return getSCEV(BO->LHS); // shift by zero --> noop 6854 6855 uint64_t AShrAmt = CI->getZExtValue(); 6856 Type *TruncTy = IntegerType::get(getContext(), BitWidth - AShrAmt); 6857 6858 Operator *L = dyn_cast<Operator>(BO->LHS); 6859 if (L && L->getOpcode() == Instruction::Shl) { 6860 // X = Shl A, n 6861 // Y = AShr X, m 6862 // Both n and m are constant. 6863 6864 const SCEV *ShlOp0SCEV = getSCEV(L->getOperand(0)); 6865 if (L->getOperand(1) == BO->RHS) 6866 // For a two-shift sext-inreg, i.e. n = m, 6867 // use sext(trunc(x)) as the SCEV expression. 6868 return getSignExtendExpr( 6869 getTruncateExpr(ShlOp0SCEV, TruncTy), OuterTy); 6870 6871 ConstantInt *ShlAmtCI = dyn_cast<ConstantInt>(L->getOperand(1)); 6872 if (ShlAmtCI && ShlAmtCI->getValue().ult(BitWidth)) { 6873 uint64_t ShlAmt = ShlAmtCI->getZExtValue(); 6874 if (ShlAmt > AShrAmt) { 6875 // When n > m, use sext(mul(trunc(x), 2^(n-m)))) as the SCEV 6876 // expression. We already checked that ShlAmt < BitWidth, so 6877 // the multiplier, 1 << (ShlAmt - AShrAmt), fits into TruncTy as 6878 // ShlAmt - AShrAmt < Amt. 6879 APInt Mul = APInt::getOneBitSet(BitWidth - AShrAmt, 6880 ShlAmt - AShrAmt); 6881 return getSignExtendExpr( 6882 getMulExpr(getTruncateExpr(ShlOp0SCEV, TruncTy), 6883 getConstant(Mul)), OuterTy); 6884 } 6885 } 6886 } 6887 break; 6888 } 6889 } 6890 } 6891 6892 switch (U->getOpcode()) { 6893 case Instruction::Trunc: 6894 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 6895 6896 case Instruction::ZExt: 6897 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 6898 6899 case Instruction::SExt: 6900 if (auto BO = MatchBinaryOp(U->getOperand(0), DT)) { 6901 // The NSW flag of a subtract does not always survive the conversion to 6902 // A + (-1)*B. By pushing sign extension onto its operands we are much 6903 // more likely to preserve NSW and allow later AddRec optimisations. 6904 // 6905 // NOTE: This is effectively duplicating this logic from getSignExtend: 6906 // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw> 6907 // but by that point the NSW information has potentially been lost. 6908 if (BO->Opcode == Instruction::Sub && BO->IsNSW) { 6909 Type *Ty = U->getType(); 6910 auto *V1 = getSignExtendExpr(getSCEV(BO->LHS), Ty); 6911 auto *V2 = getSignExtendExpr(getSCEV(BO->RHS), Ty); 6912 return getMinusSCEV(V1, V2, SCEV::FlagNSW); 6913 } 6914 } 6915 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 6916 6917 case Instruction::BitCast: 6918 // BitCasts are no-op casts so we just eliminate the cast. 6919 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 6920 return getSCEV(U->getOperand(0)); 6921 break; 6922 6923 case Instruction::PtrToInt: { 6924 // Pointer to integer cast is straight-forward, so do model it. 6925 const SCEV *Op = getSCEV(U->getOperand(0)); 6926 Type *DstIntTy = U->getType(); 6927 // But only if effective SCEV (integer) type is wide enough to represent 6928 // all possible pointer values. 6929 const SCEV *IntOp = getPtrToIntExpr(Op, DstIntTy); 6930 if (isa<SCEVCouldNotCompute>(IntOp)) 6931 return getUnknown(V); 6932 return IntOp; 6933 } 6934 case Instruction::IntToPtr: 6935 // Just don't deal with inttoptr casts. 6936 return getUnknown(V); 6937 6938 case Instruction::SDiv: 6939 // If both operands are non-negative, this is just an udiv. 6940 if (isKnownNonNegative(getSCEV(U->getOperand(0))) && 6941 isKnownNonNegative(getSCEV(U->getOperand(1)))) 6942 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1))); 6943 break; 6944 6945 case Instruction::SRem: 6946 // If both operands are non-negative, this is just an urem. 6947 if (isKnownNonNegative(getSCEV(U->getOperand(0))) && 6948 isKnownNonNegative(getSCEV(U->getOperand(1)))) 6949 return getURemExpr(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1))); 6950 break; 6951 6952 case Instruction::GetElementPtr: 6953 return createNodeForGEP(cast<GEPOperator>(U)); 6954 6955 case Instruction::PHI: 6956 return createNodeForPHI(cast<PHINode>(U)); 6957 6958 case Instruction::Select: 6959 // U can also be a select constant expr, which let fall through. Since 6960 // createNodeForSelect only works for a condition that is an `ICmpInst`, and 6961 // constant expressions cannot have instructions as operands, we'd have 6962 // returned getUnknown for a select constant expressions anyway. 6963 if (isa<Instruction>(U)) 6964 return createNodeForSelectOrPHI(cast<Instruction>(U), U->getOperand(0), 6965 U->getOperand(1), U->getOperand(2)); 6966 break; 6967 6968 case Instruction::Call: 6969 case Instruction::Invoke: 6970 if (Value *RV = cast<CallBase>(U)->getReturnedArgOperand()) 6971 return getSCEV(RV); 6972 6973 if (auto *II = dyn_cast<IntrinsicInst>(U)) { 6974 switch (II->getIntrinsicID()) { 6975 case Intrinsic::abs: 6976 return getAbsExpr( 6977 getSCEV(II->getArgOperand(0)), 6978 /*IsNSW=*/cast<ConstantInt>(II->getArgOperand(1))->isOne()); 6979 case Intrinsic::umax: 6980 return getUMaxExpr(getSCEV(II->getArgOperand(0)), 6981 getSCEV(II->getArgOperand(1))); 6982 case Intrinsic::umin: 6983 return getUMinExpr(getSCEV(II->getArgOperand(0)), 6984 getSCEV(II->getArgOperand(1))); 6985 case Intrinsic::smax: 6986 return getSMaxExpr(getSCEV(II->getArgOperand(0)), 6987 getSCEV(II->getArgOperand(1))); 6988 case Intrinsic::smin: 6989 return getSMinExpr(getSCEV(II->getArgOperand(0)), 6990 getSCEV(II->getArgOperand(1))); 6991 case Intrinsic::usub_sat: { 6992 const SCEV *X = getSCEV(II->getArgOperand(0)); 6993 const SCEV *Y = getSCEV(II->getArgOperand(1)); 6994 const SCEV *ClampedY = getUMinExpr(X, Y); 6995 return getMinusSCEV(X, ClampedY, SCEV::FlagNUW); 6996 } 6997 case Intrinsic::uadd_sat: { 6998 const SCEV *X = getSCEV(II->getArgOperand(0)); 6999 const SCEV *Y = getSCEV(II->getArgOperand(1)); 7000 const SCEV *ClampedX = getUMinExpr(X, getNotSCEV(Y)); 7001 return getAddExpr(ClampedX, Y, SCEV::FlagNUW); 7002 } 7003 case Intrinsic::start_loop_iterations: 7004 // A start_loop_iterations is just equivalent to the first operand for 7005 // SCEV purposes. 7006 return getSCEV(II->getArgOperand(0)); 7007 default: 7008 break; 7009 } 7010 } 7011 break; 7012 } 7013 7014 return getUnknown(V); 7015 } 7016 7017 //===----------------------------------------------------------------------===// 7018 // Iteration Count Computation Code 7019 // 7020 7021 const SCEV *ScalarEvolution::getTripCountFromExitCount(const SCEV *ExitCount) { 7022 // Get the trip count from the BE count by adding 1. Overflow, results 7023 // in zero which means "unknown". 7024 return getAddExpr(ExitCount, getOne(ExitCount->getType())); 7025 } 7026 7027 static unsigned getConstantTripCount(const SCEVConstant *ExitCount) { 7028 if (!ExitCount) 7029 return 0; 7030 7031 ConstantInt *ExitConst = ExitCount->getValue(); 7032 7033 // Guard against huge trip counts. 7034 if (ExitConst->getValue().getActiveBits() > 32) 7035 return 0; 7036 7037 // In case of integer overflow, this returns 0, which is correct. 7038 return ((unsigned)ExitConst->getZExtValue()) + 1; 7039 } 7040 7041 unsigned ScalarEvolution::getSmallConstantTripCount(const Loop *L) { 7042 auto *ExitCount = dyn_cast<SCEVConstant>(getBackedgeTakenCount(L, Exact)); 7043 return getConstantTripCount(ExitCount); 7044 } 7045 7046 unsigned 7047 ScalarEvolution::getSmallConstantTripCount(const Loop *L, 7048 const BasicBlock *ExitingBlock) { 7049 assert(ExitingBlock && "Must pass a non-null exiting block!"); 7050 assert(L->isLoopExiting(ExitingBlock) && 7051 "Exiting block must actually branch out of the loop!"); 7052 const SCEVConstant *ExitCount = 7053 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock)); 7054 return getConstantTripCount(ExitCount); 7055 } 7056 7057 unsigned ScalarEvolution::getSmallConstantMaxTripCount(const Loop *L) { 7058 const auto *MaxExitCount = 7059 dyn_cast<SCEVConstant>(getConstantMaxBackedgeTakenCount(L)); 7060 return getConstantTripCount(MaxExitCount); 7061 } 7062 7063 unsigned ScalarEvolution::getSmallConstantTripMultiple(const Loop *L) { 7064 SmallVector<BasicBlock *, 8> ExitingBlocks; 7065 L->getExitingBlocks(ExitingBlocks); 7066 7067 Optional<unsigned> Res = None; 7068 for (auto *ExitingBB : ExitingBlocks) { 7069 unsigned Multiple = getSmallConstantTripMultiple(L, ExitingBB); 7070 if (!Res) 7071 Res = Multiple; 7072 Res = (unsigned)GreatestCommonDivisor64(*Res, Multiple); 7073 } 7074 return Res.getValueOr(1); 7075 } 7076 7077 unsigned ScalarEvolution::getSmallConstantTripMultiple(const Loop *L, 7078 const SCEV *ExitCount) { 7079 if (ExitCount == getCouldNotCompute()) 7080 return 1; 7081 7082 // Get the trip count 7083 const SCEV *TCExpr = getTripCountFromExitCount(ExitCount); 7084 7085 const SCEVConstant *TC = dyn_cast<SCEVConstant>(TCExpr); 7086 if (!TC) 7087 // Attempt to factor more general cases. Returns the greatest power of 7088 // two divisor. If overflow happens, the trip count expression is still 7089 // divisible by the greatest power of 2 divisor returned. 7090 return 1U << std::min((uint32_t)31, 7091 GetMinTrailingZeros(applyLoopGuards(TCExpr, L))); 7092 7093 ConstantInt *Result = TC->getValue(); 7094 7095 // Guard against huge trip counts (this requires checking 7096 // for zero to handle the case where the trip count == -1 and the 7097 // addition wraps). 7098 if (!Result || Result->getValue().getActiveBits() > 32 || 7099 Result->getValue().getActiveBits() == 0) 7100 return 1; 7101 7102 return (unsigned)Result->getZExtValue(); 7103 } 7104 7105 /// Returns the largest constant divisor of the trip count of this loop as a 7106 /// normal unsigned value, if possible. This means that the actual trip count is 7107 /// always a multiple of the returned value (don't forget the trip count could 7108 /// very well be zero as well!). 7109 /// 7110 /// Returns 1 if the trip count is unknown or not guaranteed to be the 7111 /// multiple of a constant (which is also the case if the trip count is simply 7112 /// constant, use getSmallConstantTripCount for that case), Will also return 1 7113 /// if the trip count is very large (>= 2^32). 7114 /// 7115 /// As explained in the comments for getSmallConstantTripCount, this assumes 7116 /// that control exits the loop via ExitingBlock. 7117 unsigned 7118 ScalarEvolution::getSmallConstantTripMultiple(const Loop *L, 7119 const BasicBlock *ExitingBlock) { 7120 assert(ExitingBlock && "Must pass a non-null exiting block!"); 7121 assert(L->isLoopExiting(ExitingBlock) && 7122 "Exiting block must actually branch out of the loop!"); 7123 const SCEV *ExitCount = getExitCount(L, ExitingBlock); 7124 return getSmallConstantTripMultiple(L, ExitCount); 7125 } 7126 7127 const SCEV *ScalarEvolution::getExitCount(const Loop *L, 7128 const BasicBlock *ExitingBlock, 7129 ExitCountKind Kind) { 7130 switch (Kind) { 7131 case Exact: 7132 case SymbolicMaximum: 7133 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this); 7134 case ConstantMaximum: 7135 return getBackedgeTakenInfo(L).getConstantMax(ExitingBlock, this); 7136 }; 7137 llvm_unreachable("Invalid ExitCountKind!"); 7138 } 7139 7140 const SCEV * 7141 ScalarEvolution::getPredicatedBackedgeTakenCount(const Loop *L, 7142 SCEVUnionPredicate &Preds) { 7143 return getPredicatedBackedgeTakenInfo(L).getExact(L, this, &Preds); 7144 } 7145 7146 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L, 7147 ExitCountKind Kind) { 7148 switch (Kind) { 7149 case Exact: 7150 return getBackedgeTakenInfo(L).getExact(L, this); 7151 case ConstantMaximum: 7152 return getBackedgeTakenInfo(L).getConstantMax(this); 7153 case SymbolicMaximum: 7154 return getBackedgeTakenInfo(L).getSymbolicMax(L, this); 7155 }; 7156 llvm_unreachable("Invalid ExitCountKind!"); 7157 } 7158 7159 bool ScalarEvolution::isBackedgeTakenCountMaxOrZero(const Loop *L) { 7160 return getBackedgeTakenInfo(L).isConstantMaxOrZero(this); 7161 } 7162 7163 /// Push PHI nodes in the header of the given loop onto the given Worklist. 7164 static void 7165 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 7166 BasicBlock *Header = L->getHeader(); 7167 7168 // Push all Loop-header PHIs onto the Worklist stack. 7169 for (PHINode &PN : Header->phis()) 7170 Worklist.push_back(&PN); 7171 } 7172 7173 const ScalarEvolution::BackedgeTakenInfo & 7174 ScalarEvolution::getPredicatedBackedgeTakenInfo(const Loop *L) { 7175 auto &BTI = getBackedgeTakenInfo(L); 7176 if (BTI.hasFullInfo()) 7177 return BTI; 7178 7179 auto Pair = PredicatedBackedgeTakenCounts.insert({L, BackedgeTakenInfo()}); 7180 7181 if (!Pair.second) 7182 return Pair.first->second; 7183 7184 BackedgeTakenInfo Result = 7185 computeBackedgeTakenCount(L, /*AllowPredicates=*/true); 7186 7187 return PredicatedBackedgeTakenCounts.find(L)->second = std::move(Result); 7188 } 7189 7190 ScalarEvolution::BackedgeTakenInfo & 7191 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 7192 // Initially insert an invalid entry for this loop. If the insertion 7193 // succeeds, proceed to actually compute a backedge-taken count and 7194 // update the value. The temporary CouldNotCompute value tells SCEV 7195 // code elsewhere that it shouldn't attempt to request a new 7196 // backedge-taken count, which could result in infinite recursion. 7197 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 7198 BackedgeTakenCounts.insert({L, BackedgeTakenInfo()}); 7199 if (!Pair.second) 7200 return Pair.first->second; 7201 7202 // computeBackedgeTakenCount may allocate memory for its result. Inserting it 7203 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result 7204 // must be cleared in this scope. 7205 BackedgeTakenInfo Result = computeBackedgeTakenCount(L); 7206 7207 // In product build, there are no usage of statistic. 7208 (void)NumTripCountsComputed; 7209 (void)NumTripCountsNotComputed; 7210 #if LLVM_ENABLE_STATS || !defined(NDEBUG) 7211 const SCEV *BEExact = Result.getExact(L, this); 7212 if (BEExact != getCouldNotCompute()) { 7213 assert(isLoopInvariant(BEExact, L) && 7214 isLoopInvariant(Result.getConstantMax(this), L) && 7215 "Computed backedge-taken count isn't loop invariant for loop!"); 7216 ++NumTripCountsComputed; 7217 } else if (Result.getConstantMax(this) == getCouldNotCompute() && 7218 isa<PHINode>(L->getHeader()->begin())) { 7219 // Only count loops that have phi nodes as not being computable. 7220 ++NumTripCountsNotComputed; 7221 } 7222 #endif // LLVM_ENABLE_STATS || !defined(NDEBUG) 7223 7224 // Now that we know more about the trip count for this loop, forget any 7225 // existing SCEV values for PHI nodes in this loop since they are only 7226 // conservative estimates made without the benefit of trip count 7227 // information. This is similar to the code in forgetLoop, except that 7228 // it handles SCEVUnknown PHI nodes specially. 7229 if (Result.hasAnyInfo()) { 7230 SmallVector<Instruction *, 16> Worklist; 7231 PushLoopPHIs(L, Worklist); 7232 7233 SmallPtrSet<Instruction *, 8> Discovered; 7234 while (!Worklist.empty()) { 7235 Instruction *I = Worklist.pop_back_val(); 7236 7237 ValueExprMapType::iterator It = 7238 ValueExprMap.find_as(static_cast<Value *>(I)); 7239 if (It != ValueExprMap.end()) { 7240 const SCEV *Old = It->second; 7241 7242 // SCEVUnknown for a PHI either means that it has an unrecognized 7243 // structure, or it's a PHI that's in the progress of being computed 7244 // by createNodeForPHI. In the former case, additional loop trip 7245 // count information isn't going to change anything. In the later 7246 // case, createNodeForPHI will perform the necessary updates on its 7247 // own when it gets to that point. 7248 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) { 7249 eraseValueFromMap(It->first); 7250 forgetMemoizedResults(Old); 7251 } 7252 if (PHINode *PN = dyn_cast<PHINode>(I)) 7253 ConstantEvolutionLoopExitValue.erase(PN); 7254 } 7255 7256 // Since we don't need to invalidate anything for correctness and we're 7257 // only invalidating to make SCEV's results more precise, we get to stop 7258 // early to avoid invalidating too much. This is especially important in 7259 // cases like: 7260 // 7261 // %v = f(pn0, pn1) // pn0 and pn1 used through some other phi node 7262 // loop0: 7263 // %pn0 = phi 7264 // ... 7265 // loop1: 7266 // %pn1 = phi 7267 // ... 7268 // 7269 // where both loop0 and loop1's backedge taken count uses the SCEV 7270 // expression for %v. If we don't have the early stop below then in cases 7271 // like the above, getBackedgeTakenInfo(loop1) will clear out the trip 7272 // count for loop0 and getBackedgeTakenInfo(loop0) will clear out the trip 7273 // count for loop1, effectively nullifying SCEV's trip count cache. 7274 for (auto *U : I->users()) 7275 if (auto *I = dyn_cast<Instruction>(U)) { 7276 auto *LoopForUser = LI.getLoopFor(I->getParent()); 7277 if (LoopForUser && L->contains(LoopForUser) && 7278 Discovered.insert(I).second) 7279 Worklist.push_back(I); 7280 } 7281 } 7282 } 7283 7284 // Re-lookup the insert position, since the call to 7285 // computeBackedgeTakenCount above could result in a 7286 // recusive call to getBackedgeTakenInfo (on a different 7287 // loop), which would invalidate the iterator computed 7288 // earlier. 7289 return BackedgeTakenCounts.find(L)->second = std::move(Result); 7290 } 7291 7292 void ScalarEvolution::forgetAllLoops() { 7293 // This method is intended to forget all info about loops. It should 7294 // invalidate caches as if the following happened: 7295 // - The trip counts of all loops have changed arbitrarily 7296 // - Every llvm::Value has been updated in place to produce a different 7297 // result. 7298 BackedgeTakenCounts.clear(); 7299 PredicatedBackedgeTakenCounts.clear(); 7300 LoopPropertiesCache.clear(); 7301 ConstantEvolutionLoopExitValue.clear(); 7302 ValueExprMap.clear(); 7303 ValuesAtScopes.clear(); 7304 LoopDispositions.clear(); 7305 BlockDispositions.clear(); 7306 UnsignedRanges.clear(); 7307 SignedRanges.clear(); 7308 ExprValueMap.clear(); 7309 HasRecMap.clear(); 7310 MinTrailingZerosCache.clear(); 7311 PredicatedSCEVRewrites.clear(); 7312 } 7313 7314 void ScalarEvolution::forgetLoop(const Loop *L) { 7315 SmallVector<const Loop *, 16> LoopWorklist(1, L); 7316 SmallVector<Instruction *, 32> Worklist; 7317 SmallPtrSet<Instruction *, 16> Visited; 7318 7319 // Iterate over all the loops and sub-loops to drop SCEV information. 7320 while (!LoopWorklist.empty()) { 7321 auto *CurrL = LoopWorklist.pop_back_val(); 7322 7323 // Drop any stored trip count value. 7324 BackedgeTakenCounts.erase(CurrL); 7325 PredicatedBackedgeTakenCounts.erase(CurrL); 7326 7327 // Drop information about predicated SCEV rewrites for this loop. 7328 for (auto I = PredicatedSCEVRewrites.begin(); 7329 I != PredicatedSCEVRewrites.end();) { 7330 std::pair<const SCEV *, const Loop *> Entry = I->first; 7331 if (Entry.second == CurrL) 7332 PredicatedSCEVRewrites.erase(I++); 7333 else 7334 ++I; 7335 } 7336 7337 auto LoopUsersItr = LoopUsers.find(CurrL); 7338 if (LoopUsersItr != LoopUsers.end()) { 7339 for (auto *S : LoopUsersItr->second) 7340 forgetMemoizedResults(S); 7341 LoopUsers.erase(LoopUsersItr); 7342 } 7343 7344 // Drop information about expressions based on loop-header PHIs. 7345 PushLoopPHIs(CurrL, Worklist); 7346 7347 while (!Worklist.empty()) { 7348 Instruction *I = Worklist.pop_back_val(); 7349 if (!Visited.insert(I).second) 7350 continue; 7351 7352 ValueExprMapType::iterator It = 7353 ValueExprMap.find_as(static_cast<Value *>(I)); 7354 if (It != ValueExprMap.end()) { 7355 eraseValueFromMap(It->first); 7356 forgetMemoizedResults(It->second); 7357 if (PHINode *PN = dyn_cast<PHINode>(I)) 7358 ConstantEvolutionLoopExitValue.erase(PN); 7359 } 7360 7361 PushDefUseChildren(I, Worklist); 7362 } 7363 7364 LoopPropertiesCache.erase(CurrL); 7365 // Forget all contained loops too, to avoid dangling entries in the 7366 // ValuesAtScopes map. 7367 LoopWorklist.append(CurrL->begin(), CurrL->end()); 7368 } 7369 } 7370 7371 void ScalarEvolution::forgetTopmostLoop(const Loop *L) { 7372 while (Loop *Parent = L->getParentLoop()) 7373 L = Parent; 7374 forgetLoop(L); 7375 } 7376 7377 void ScalarEvolution::forgetValue(Value *V) { 7378 Instruction *I = dyn_cast<Instruction>(V); 7379 if (!I) return; 7380 7381 // Drop information about expressions based on loop-header PHIs. 7382 SmallVector<Instruction *, 16> Worklist; 7383 Worklist.push_back(I); 7384 7385 SmallPtrSet<Instruction *, 8> Visited; 7386 while (!Worklist.empty()) { 7387 I = Worklist.pop_back_val(); 7388 if (!Visited.insert(I).second) 7389 continue; 7390 7391 ValueExprMapType::iterator It = 7392 ValueExprMap.find_as(static_cast<Value *>(I)); 7393 if (It != ValueExprMap.end()) { 7394 eraseValueFromMap(It->first); 7395 forgetMemoizedResults(It->second); 7396 if (PHINode *PN = dyn_cast<PHINode>(I)) 7397 ConstantEvolutionLoopExitValue.erase(PN); 7398 } 7399 7400 PushDefUseChildren(I, Worklist); 7401 } 7402 } 7403 7404 void ScalarEvolution::forgetLoopDispositions(const Loop *L) { 7405 LoopDispositions.clear(); 7406 } 7407 7408 /// Get the exact loop backedge taken count considering all loop exits. A 7409 /// computable result can only be returned for loops with all exiting blocks 7410 /// dominating the latch. howFarToZero assumes that the limit of each loop test 7411 /// is never skipped. This is a valid assumption as long as the loop exits via 7412 /// that test. For precise results, it is the caller's responsibility to specify 7413 /// the relevant loop exiting block using getExact(ExitingBlock, SE). 7414 const SCEV * 7415 ScalarEvolution::BackedgeTakenInfo::getExact(const Loop *L, ScalarEvolution *SE, 7416 SCEVUnionPredicate *Preds) const { 7417 // If any exits were not computable, the loop is not computable. 7418 if (!isComplete() || ExitNotTaken.empty()) 7419 return SE->getCouldNotCompute(); 7420 7421 const BasicBlock *Latch = L->getLoopLatch(); 7422 // All exiting blocks we have collected must dominate the only backedge. 7423 if (!Latch) 7424 return SE->getCouldNotCompute(); 7425 7426 // All exiting blocks we have gathered dominate loop's latch, so exact trip 7427 // count is simply a minimum out of all these calculated exit counts. 7428 SmallVector<const SCEV *, 2> Ops; 7429 for (auto &ENT : ExitNotTaken) { 7430 const SCEV *BECount = ENT.ExactNotTaken; 7431 assert(BECount != SE->getCouldNotCompute() && "Bad exit SCEV!"); 7432 assert(SE->DT.dominates(ENT.ExitingBlock, Latch) && 7433 "We should only have known counts for exiting blocks that dominate " 7434 "latch!"); 7435 7436 Ops.push_back(BECount); 7437 7438 if (Preds && !ENT.hasAlwaysTruePredicate()) 7439 Preds->add(ENT.Predicate.get()); 7440 7441 assert((Preds || ENT.hasAlwaysTruePredicate()) && 7442 "Predicate should be always true!"); 7443 } 7444 7445 return SE->getUMinFromMismatchedTypes(Ops); 7446 } 7447 7448 /// Get the exact not taken count for this loop exit. 7449 const SCEV * 7450 ScalarEvolution::BackedgeTakenInfo::getExact(const BasicBlock *ExitingBlock, 7451 ScalarEvolution *SE) const { 7452 for (auto &ENT : ExitNotTaken) 7453 if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePredicate()) 7454 return ENT.ExactNotTaken; 7455 7456 return SE->getCouldNotCompute(); 7457 } 7458 7459 const SCEV *ScalarEvolution::BackedgeTakenInfo::getConstantMax( 7460 const BasicBlock *ExitingBlock, ScalarEvolution *SE) const { 7461 for (auto &ENT : ExitNotTaken) 7462 if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePredicate()) 7463 return ENT.MaxNotTaken; 7464 7465 return SE->getCouldNotCompute(); 7466 } 7467 7468 /// getConstantMax - Get the constant max backedge taken count for the loop. 7469 const SCEV * 7470 ScalarEvolution::BackedgeTakenInfo::getConstantMax(ScalarEvolution *SE) const { 7471 auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) { 7472 return !ENT.hasAlwaysTruePredicate(); 7473 }; 7474 7475 if (any_of(ExitNotTaken, PredicateNotAlwaysTrue) || !getConstantMax()) 7476 return SE->getCouldNotCompute(); 7477 7478 assert((isa<SCEVCouldNotCompute>(getConstantMax()) || 7479 isa<SCEVConstant>(getConstantMax())) && 7480 "No point in having a non-constant max backedge taken count!"); 7481 return getConstantMax(); 7482 } 7483 7484 const SCEV * 7485 ScalarEvolution::BackedgeTakenInfo::getSymbolicMax(const Loop *L, 7486 ScalarEvolution *SE) { 7487 if (!SymbolicMax) 7488 SymbolicMax = SE->computeSymbolicMaxBackedgeTakenCount(L); 7489 return SymbolicMax; 7490 } 7491 7492 bool ScalarEvolution::BackedgeTakenInfo::isConstantMaxOrZero( 7493 ScalarEvolution *SE) const { 7494 auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) { 7495 return !ENT.hasAlwaysTruePredicate(); 7496 }; 7497 return MaxOrZero && !any_of(ExitNotTaken, PredicateNotAlwaysTrue); 7498 } 7499 7500 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S) const { 7501 return Operands.contains(S); 7502 } 7503 7504 ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E) 7505 : ExactNotTaken(E), MaxNotTaken(E) { 7506 assert((isa<SCEVCouldNotCompute>(MaxNotTaken) || 7507 isa<SCEVConstant>(MaxNotTaken)) && 7508 "No point in having a non-constant max backedge taken count!"); 7509 } 7510 7511 ScalarEvolution::ExitLimit::ExitLimit( 7512 const SCEV *E, const SCEV *M, bool MaxOrZero, 7513 ArrayRef<const SmallPtrSetImpl<const SCEVPredicate *> *> PredSetList) 7514 : ExactNotTaken(E), MaxNotTaken(M), MaxOrZero(MaxOrZero) { 7515 assert((isa<SCEVCouldNotCompute>(ExactNotTaken) || 7516 !isa<SCEVCouldNotCompute>(MaxNotTaken)) && 7517 "Exact is not allowed to be less precise than Max"); 7518 assert((isa<SCEVCouldNotCompute>(MaxNotTaken) || 7519 isa<SCEVConstant>(MaxNotTaken)) && 7520 "No point in having a non-constant max backedge taken count!"); 7521 for (auto *PredSet : PredSetList) 7522 for (auto *P : *PredSet) 7523 addPredicate(P); 7524 } 7525 7526 ScalarEvolution::ExitLimit::ExitLimit( 7527 const SCEV *E, const SCEV *M, bool MaxOrZero, 7528 const SmallPtrSetImpl<const SCEVPredicate *> &PredSet) 7529 : ExitLimit(E, M, MaxOrZero, {&PredSet}) { 7530 assert((isa<SCEVCouldNotCompute>(MaxNotTaken) || 7531 isa<SCEVConstant>(MaxNotTaken)) && 7532 "No point in having a non-constant max backedge taken count!"); 7533 } 7534 7535 ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E, const SCEV *M, 7536 bool MaxOrZero) 7537 : ExitLimit(E, M, MaxOrZero, None) { 7538 assert((isa<SCEVCouldNotCompute>(MaxNotTaken) || 7539 isa<SCEVConstant>(MaxNotTaken)) && 7540 "No point in having a non-constant max backedge taken count!"); 7541 } 7542 7543 class SCEVRecordOperands { 7544 SmallPtrSetImpl<const SCEV *> &Operands; 7545 7546 public: 7547 SCEVRecordOperands(SmallPtrSetImpl<const SCEV *> &Operands) 7548 : Operands(Operands) {} 7549 bool follow(const SCEV *S) { 7550 Operands.insert(S); 7551 return true; 7552 } 7553 bool isDone() { return false; } 7554 }; 7555 7556 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each 7557 /// computable exit into a persistent ExitNotTakenInfo array. 7558 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo( 7559 ArrayRef<ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo> ExitCounts, 7560 bool IsComplete, const SCEV *ConstantMax, bool MaxOrZero) 7561 : ConstantMax(ConstantMax), IsComplete(IsComplete), MaxOrZero(MaxOrZero) { 7562 using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo; 7563 7564 ExitNotTaken.reserve(ExitCounts.size()); 7565 std::transform( 7566 ExitCounts.begin(), ExitCounts.end(), std::back_inserter(ExitNotTaken), 7567 [&](const EdgeExitInfo &EEI) { 7568 BasicBlock *ExitBB = EEI.first; 7569 const ExitLimit &EL = EEI.second; 7570 if (EL.Predicates.empty()) 7571 return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, EL.MaxNotTaken, 7572 nullptr); 7573 7574 std::unique_ptr<SCEVUnionPredicate> Predicate(new SCEVUnionPredicate); 7575 for (auto *Pred : EL.Predicates) 7576 Predicate->add(Pred); 7577 7578 return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, EL.MaxNotTaken, 7579 std::move(Predicate)); 7580 }); 7581 assert((isa<SCEVCouldNotCompute>(ConstantMax) || 7582 isa<SCEVConstant>(ConstantMax)) && 7583 "No point in having a non-constant max backedge taken count!"); 7584 7585 SCEVRecordOperands RecordOperands(Operands); 7586 SCEVTraversal<SCEVRecordOperands> ST(RecordOperands); 7587 if (!isa<SCEVCouldNotCompute>(ConstantMax)) 7588 ST.visitAll(ConstantMax); 7589 for (auto &ENT : ExitNotTaken) 7590 if (!isa<SCEVCouldNotCompute>(ENT.ExactNotTaken)) 7591 ST.visitAll(ENT.ExactNotTaken); 7592 } 7593 7594 /// Compute the number of times the backedge of the specified loop will execute. 7595 ScalarEvolution::BackedgeTakenInfo 7596 ScalarEvolution::computeBackedgeTakenCount(const Loop *L, 7597 bool AllowPredicates) { 7598 SmallVector<BasicBlock *, 8> ExitingBlocks; 7599 L->getExitingBlocks(ExitingBlocks); 7600 7601 using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo; 7602 7603 SmallVector<EdgeExitInfo, 4> ExitCounts; 7604 bool CouldComputeBECount = true; 7605 BasicBlock *Latch = L->getLoopLatch(); // may be NULL. 7606 const SCEV *MustExitMaxBECount = nullptr; 7607 const SCEV *MayExitMaxBECount = nullptr; 7608 bool MustExitMaxOrZero = false; 7609 7610 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts 7611 // and compute maxBECount. 7612 // Do a union of all the predicates here. 7613 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 7614 BasicBlock *ExitBB = ExitingBlocks[i]; 7615 7616 // We canonicalize untaken exits to br (constant), ignore them so that 7617 // proving an exit untaken doesn't negatively impact our ability to reason 7618 // about the loop as whole. 7619 if (auto *BI = dyn_cast<BranchInst>(ExitBB->getTerminator())) 7620 if (auto *CI = dyn_cast<ConstantInt>(BI->getCondition())) { 7621 bool ExitIfTrue = !L->contains(BI->getSuccessor(0)); 7622 if ((ExitIfTrue && CI->isZero()) || (!ExitIfTrue && CI->isOne())) 7623 continue; 7624 } 7625 7626 ExitLimit EL = computeExitLimit(L, ExitBB, AllowPredicates); 7627 7628 assert((AllowPredicates || EL.Predicates.empty()) && 7629 "Predicated exit limit when predicates are not allowed!"); 7630 7631 // 1. For each exit that can be computed, add an entry to ExitCounts. 7632 // CouldComputeBECount is true only if all exits can be computed. 7633 if (EL.ExactNotTaken == getCouldNotCompute()) 7634 // We couldn't compute an exact value for this exit, so 7635 // we won't be able to compute an exact value for the loop. 7636 CouldComputeBECount = false; 7637 else 7638 ExitCounts.emplace_back(ExitBB, EL); 7639 7640 // 2. Derive the loop's MaxBECount from each exit's max number of 7641 // non-exiting iterations. Partition the loop exits into two kinds: 7642 // LoopMustExits and LoopMayExits. 7643 // 7644 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it 7645 // is a LoopMayExit. If any computable LoopMustExit is found, then 7646 // MaxBECount is the minimum EL.MaxNotTaken of computable 7647 // LoopMustExits. Otherwise, MaxBECount is conservatively the maximum 7648 // EL.MaxNotTaken, where CouldNotCompute is considered greater than any 7649 // computable EL.MaxNotTaken. 7650 if (EL.MaxNotTaken != getCouldNotCompute() && Latch && 7651 DT.dominates(ExitBB, Latch)) { 7652 if (!MustExitMaxBECount) { 7653 MustExitMaxBECount = EL.MaxNotTaken; 7654 MustExitMaxOrZero = EL.MaxOrZero; 7655 } else { 7656 MustExitMaxBECount = 7657 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.MaxNotTaken); 7658 } 7659 } else if (MayExitMaxBECount != getCouldNotCompute()) { 7660 if (!MayExitMaxBECount || EL.MaxNotTaken == getCouldNotCompute()) 7661 MayExitMaxBECount = EL.MaxNotTaken; 7662 else { 7663 MayExitMaxBECount = 7664 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.MaxNotTaken); 7665 } 7666 } 7667 } 7668 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount : 7669 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute()); 7670 // The loop backedge will be taken the maximum or zero times if there's 7671 // a single exit that must be taken the maximum or zero times. 7672 bool MaxOrZero = (MustExitMaxOrZero && ExitingBlocks.size() == 1); 7673 return BackedgeTakenInfo(std::move(ExitCounts), CouldComputeBECount, 7674 MaxBECount, MaxOrZero); 7675 } 7676 7677 ScalarEvolution::ExitLimit 7678 ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock, 7679 bool AllowPredicates) { 7680 assert(L->contains(ExitingBlock) && "Exit count for non-loop block?"); 7681 // If our exiting block does not dominate the latch, then its connection with 7682 // loop's exit limit may be far from trivial. 7683 const BasicBlock *Latch = L->getLoopLatch(); 7684 if (!Latch || !DT.dominates(ExitingBlock, Latch)) 7685 return getCouldNotCompute(); 7686 7687 bool IsOnlyExit = (L->getExitingBlock() != nullptr); 7688 Instruction *Term = ExitingBlock->getTerminator(); 7689 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) { 7690 assert(BI->isConditional() && "If unconditional, it can't be in loop!"); 7691 bool ExitIfTrue = !L->contains(BI->getSuccessor(0)); 7692 assert(ExitIfTrue == L->contains(BI->getSuccessor(1)) && 7693 "It should have one successor in loop and one exit block!"); 7694 // Proceed to the next level to examine the exit condition expression. 7695 return computeExitLimitFromCond( 7696 L, BI->getCondition(), ExitIfTrue, 7697 /*ControlsExit=*/IsOnlyExit, AllowPredicates); 7698 } 7699 7700 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term)) { 7701 // For switch, make sure that there is a single exit from the loop. 7702 BasicBlock *Exit = nullptr; 7703 for (auto *SBB : successors(ExitingBlock)) 7704 if (!L->contains(SBB)) { 7705 if (Exit) // Multiple exit successors. 7706 return getCouldNotCompute(); 7707 Exit = SBB; 7708 } 7709 assert(Exit && "Exiting block must have at least one exit"); 7710 return computeExitLimitFromSingleExitSwitch(L, SI, Exit, 7711 /*ControlsExit=*/IsOnlyExit); 7712 } 7713 7714 return getCouldNotCompute(); 7715 } 7716 7717 ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCond( 7718 const Loop *L, Value *ExitCond, bool ExitIfTrue, 7719 bool ControlsExit, bool AllowPredicates) { 7720 ScalarEvolution::ExitLimitCacheTy Cache(L, ExitIfTrue, AllowPredicates); 7721 return computeExitLimitFromCondCached(Cache, L, ExitCond, ExitIfTrue, 7722 ControlsExit, AllowPredicates); 7723 } 7724 7725 Optional<ScalarEvolution::ExitLimit> 7726 ScalarEvolution::ExitLimitCache::find(const Loop *L, Value *ExitCond, 7727 bool ExitIfTrue, bool ControlsExit, 7728 bool AllowPredicates) { 7729 (void)this->L; 7730 (void)this->ExitIfTrue; 7731 (void)this->AllowPredicates; 7732 7733 assert(this->L == L && this->ExitIfTrue == ExitIfTrue && 7734 this->AllowPredicates == AllowPredicates && 7735 "Variance in assumed invariant key components!"); 7736 auto Itr = TripCountMap.find({ExitCond, ControlsExit}); 7737 if (Itr == TripCountMap.end()) 7738 return None; 7739 return Itr->second; 7740 } 7741 7742 void ScalarEvolution::ExitLimitCache::insert(const Loop *L, Value *ExitCond, 7743 bool ExitIfTrue, 7744 bool ControlsExit, 7745 bool AllowPredicates, 7746 const ExitLimit &EL) { 7747 assert(this->L == L && this->ExitIfTrue == ExitIfTrue && 7748 this->AllowPredicates == AllowPredicates && 7749 "Variance in assumed invariant key components!"); 7750 7751 auto InsertResult = TripCountMap.insert({{ExitCond, ControlsExit}, EL}); 7752 assert(InsertResult.second && "Expected successful insertion!"); 7753 (void)InsertResult; 7754 (void)ExitIfTrue; 7755 } 7756 7757 ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondCached( 7758 ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue, 7759 bool ControlsExit, bool AllowPredicates) { 7760 7761 if (auto MaybeEL = 7762 Cache.find(L, ExitCond, ExitIfTrue, ControlsExit, AllowPredicates)) 7763 return *MaybeEL; 7764 7765 ExitLimit EL = computeExitLimitFromCondImpl(Cache, L, ExitCond, ExitIfTrue, 7766 ControlsExit, AllowPredicates); 7767 Cache.insert(L, ExitCond, ExitIfTrue, ControlsExit, AllowPredicates, EL); 7768 return EL; 7769 } 7770 7771 ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondImpl( 7772 ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue, 7773 bool ControlsExit, bool AllowPredicates) { 7774 // Handle BinOp conditions (And, Or). 7775 if (auto LimitFromBinOp = computeExitLimitFromCondFromBinOp( 7776 Cache, L, ExitCond, ExitIfTrue, ControlsExit, AllowPredicates)) 7777 return *LimitFromBinOp; 7778 7779 // With an icmp, it may be feasible to compute an exact backedge-taken count. 7780 // Proceed to the next level to examine the icmp. 7781 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) { 7782 ExitLimit EL = 7783 computeExitLimitFromICmp(L, ExitCondICmp, ExitIfTrue, ControlsExit); 7784 if (EL.hasFullInfo() || !AllowPredicates) 7785 return EL; 7786 7787 // Try again, but use SCEV predicates this time. 7788 return computeExitLimitFromICmp(L, ExitCondICmp, ExitIfTrue, ControlsExit, 7789 /*AllowPredicates=*/true); 7790 } 7791 7792 // Check for a constant condition. These are normally stripped out by 7793 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to 7794 // preserve the CFG and is temporarily leaving constant conditions 7795 // in place. 7796 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) { 7797 if (ExitIfTrue == !CI->getZExtValue()) 7798 // The backedge is always taken. 7799 return getCouldNotCompute(); 7800 else 7801 // The backedge is never taken. 7802 return getZero(CI->getType()); 7803 } 7804 7805 // If it's not an integer or pointer comparison then compute it the hard way. 7806 return computeExitCountExhaustively(L, ExitCond, ExitIfTrue); 7807 } 7808 7809 Optional<ScalarEvolution::ExitLimit> 7810 ScalarEvolution::computeExitLimitFromCondFromBinOp( 7811 ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue, 7812 bool ControlsExit, bool AllowPredicates) { 7813 // Check if the controlling expression for this loop is an And or Or. 7814 Value *Op0, *Op1; 7815 bool IsAnd = false; 7816 if (match(ExitCond, m_LogicalAnd(m_Value(Op0), m_Value(Op1)))) 7817 IsAnd = true; 7818 else if (match(ExitCond, m_LogicalOr(m_Value(Op0), m_Value(Op1)))) 7819 IsAnd = false; 7820 else 7821 return None; 7822 7823 // EitherMayExit is true in these two cases: 7824 // br (and Op0 Op1), loop, exit 7825 // br (or Op0 Op1), exit, loop 7826 bool EitherMayExit = IsAnd ^ ExitIfTrue; 7827 ExitLimit EL0 = computeExitLimitFromCondCached(Cache, L, Op0, ExitIfTrue, 7828 ControlsExit && !EitherMayExit, 7829 AllowPredicates); 7830 ExitLimit EL1 = computeExitLimitFromCondCached(Cache, L, Op1, ExitIfTrue, 7831 ControlsExit && !EitherMayExit, 7832 AllowPredicates); 7833 7834 // Be robust against unsimplified IR for the form "op i1 X, NeutralElement" 7835 const Constant *NeutralElement = ConstantInt::get(ExitCond->getType(), IsAnd); 7836 if (isa<ConstantInt>(Op1)) 7837 return Op1 == NeutralElement ? EL0 : EL1; 7838 if (isa<ConstantInt>(Op0)) 7839 return Op0 == NeutralElement ? EL1 : EL0; 7840 7841 const SCEV *BECount = getCouldNotCompute(); 7842 const SCEV *MaxBECount = getCouldNotCompute(); 7843 if (EitherMayExit) { 7844 // Both conditions must be same for the loop to continue executing. 7845 // Choose the less conservative count. 7846 // If ExitCond is a short-circuit form (select), using 7847 // umin(EL0.ExactNotTaken, EL1.ExactNotTaken) is unsafe in general. 7848 // To see the detailed examples, please see 7849 // test/Analysis/ScalarEvolution/exit-count-select.ll 7850 bool PoisonSafe = isa<BinaryOperator>(ExitCond); 7851 if (!PoisonSafe) 7852 // Even if ExitCond is select, we can safely derive BECount using both 7853 // EL0 and EL1 in these cases: 7854 // (1) EL0.ExactNotTaken is non-zero 7855 // (2) EL1.ExactNotTaken is non-poison 7856 // (3) EL0.ExactNotTaken is zero (BECount should be simply zero and 7857 // it cannot be umin(0, ..)) 7858 // The PoisonSafe assignment below is simplified and the assertion after 7859 // BECount calculation fully guarantees the condition (3). 7860 PoisonSafe = isa<SCEVConstant>(EL0.ExactNotTaken) || 7861 isa<SCEVConstant>(EL1.ExactNotTaken); 7862 if (EL0.ExactNotTaken != getCouldNotCompute() && 7863 EL1.ExactNotTaken != getCouldNotCompute() && PoisonSafe) { 7864 BECount = 7865 getUMinFromMismatchedTypes(EL0.ExactNotTaken, EL1.ExactNotTaken); 7866 7867 // If EL0.ExactNotTaken was zero and ExitCond was a short-circuit form, 7868 // it should have been simplified to zero (see the condition (3) above) 7869 assert(!isa<BinaryOperator>(ExitCond) || !EL0.ExactNotTaken->isZero() || 7870 BECount->isZero()); 7871 } 7872 if (EL0.MaxNotTaken == getCouldNotCompute()) 7873 MaxBECount = EL1.MaxNotTaken; 7874 else if (EL1.MaxNotTaken == getCouldNotCompute()) 7875 MaxBECount = EL0.MaxNotTaken; 7876 else 7877 MaxBECount = getUMinFromMismatchedTypes(EL0.MaxNotTaken, EL1.MaxNotTaken); 7878 } else { 7879 // Both conditions must be same at the same time for the loop to exit. 7880 // For now, be conservative. 7881 if (EL0.ExactNotTaken == EL1.ExactNotTaken) 7882 BECount = EL0.ExactNotTaken; 7883 } 7884 7885 // There are cases (e.g. PR26207) where computeExitLimitFromCond is able 7886 // to be more aggressive when computing BECount than when computing 7887 // MaxBECount. In these cases it is possible for EL0.ExactNotTaken and 7888 // EL1.ExactNotTaken to match, but for EL0.MaxNotTaken and EL1.MaxNotTaken 7889 // to not. 7890 if (isa<SCEVCouldNotCompute>(MaxBECount) && 7891 !isa<SCEVCouldNotCompute>(BECount)) 7892 MaxBECount = getConstant(getUnsignedRangeMax(BECount)); 7893 7894 return ExitLimit(BECount, MaxBECount, false, 7895 { &EL0.Predicates, &EL1.Predicates }); 7896 } 7897 7898 ScalarEvolution::ExitLimit 7899 ScalarEvolution::computeExitLimitFromICmp(const Loop *L, 7900 ICmpInst *ExitCond, 7901 bool ExitIfTrue, 7902 bool ControlsExit, 7903 bool AllowPredicates) { 7904 // If the condition was exit on true, convert the condition to exit on false 7905 ICmpInst::Predicate Pred; 7906 if (!ExitIfTrue) 7907 Pred = ExitCond->getPredicate(); 7908 else 7909 Pred = ExitCond->getInversePredicate(); 7910 const ICmpInst::Predicate OriginalPred = Pred; 7911 7912 // Handle common loops like: for (X = "string"; *X; ++X) 7913 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 7914 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 7915 ExitLimit ItCnt = 7916 computeLoadConstantCompareExitLimit(LI, RHS, L, Pred); 7917 if (ItCnt.hasAnyInfo()) 7918 return ItCnt; 7919 } 7920 7921 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 7922 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 7923 7924 // Try to evaluate any dependencies out of the loop. 7925 LHS = getSCEVAtScope(LHS, L); 7926 RHS = getSCEVAtScope(RHS, L); 7927 7928 // At this point, we would like to compute how many iterations of the 7929 // loop the predicate will return true for these inputs. 7930 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) { 7931 // If there is a loop-invariant, force it into the RHS. 7932 std::swap(LHS, RHS); 7933 Pred = ICmpInst::getSwappedPredicate(Pred); 7934 } 7935 7936 // Simplify the operands before analyzing them. 7937 (void)SimplifyICmpOperands(Pred, LHS, RHS); 7938 7939 // If we have a comparison of a chrec against a constant, try to use value 7940 // ranges to answer this query. 7941 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 7942 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 7943 if (AddRec->getLoop() == L) { 7944 // Form the constant range. 7945 ConstantRange CompRange = 7946 ConstantRange::makeExactICmpRegion(Pred, RHSC->getAPInt()); 7947 7948 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 7949 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 7950 } 7951 7952 switch (Pred) { 7953 case ICmpInst::ICMP_NE: { // while (X != Y) 7954 // Convert to: while (X-Y != 0) 7955 ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit, 7956 AllowPredicates); 7957 if (EL.hasAnyInfo()) return EL; 7958 break; 7959 } 7960 case ICmpInst::ICMP_EQ: { // while (X == Y) 7961 // Convert to: while (X-Y == 0) 7962 ExitLimit EL = howFarToNonZero(getMinusSCEV(LHS, RHS), L); 7963 if (EL.hasAnyInfo()) return EL; 7964 break; 7965 } 7966 case ICmpInst::ICMP_SLT: 7967 case ICmpInst::ICMP_ULT: { // while (X < Y) 7968 bool IsSigned = Pred == ICmpInst::ICMP_SLT; 7969 ExitLimit EL = howManyLessThans(LHS, RHS, L, IsSigned, ControlsExit, 7970 AllowPredicates); 7971 if (EL.hasAnyInfo()) return EL; 7972 break; 7973 } 7974 case ICmpInst::ICMP_SGT: 7975 case ICmpInst::ICMP_UGT: { // while (X > Y) 7976 bool IsSigned = Pred == ICmpInst::ICMP_SGT; 7977 ExitLimit EL = 7978 howManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit, 7979 AllowPredicates); 7980 if (EL.hasAnyInfo()) return EL; 7981 break; 7982 } 7983 default: 7984 break; 7985 } 7986 7987 auto *ExhaustiveCount = 7988 computeExitCountExhaustively(L, ExitCond, ExitIfTrue); 7989 7990 if (!isa<SCEVCouldNotCompute>(ExhaustiveCount)) 7991 return ExhaustiveCount; 7992 7993 return computeShiftCompareExitLimit(ExitCond->getOperand(0), 7994 ExitCond->getOperand(1), L, OriginalPred); 7995 } 7996 7997 ScalarEvolution::ExitLimit 7998 ScalarEvolution::computeExitLimitFromSingleExitSwitch(const Loop *L, 7999 SwitchInst *Switch, 8000 BasicBlock *ExitingBlock, 8001 bool ControlsExit) { 8002 assert(!L->contains(ExitingBlock) && "Not an exiting block!"); 8003 8004 // Give up if the exit is the default dest of a switch. 8005 if (Switch->getDefaultDest() == ExitingBlock) 8006 return getCouldNotCompute(); 8007 8008 assert(L->contains(Switch->getDefaultDest()) && 8009 "Default case must not exit the loop!"); 8010 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L); 8011 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock)); 8012 8013 // while (X != Y) --> while (X-Y != 0) 8014 ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit); 8015 if (EL.hasAnyInfo()) 8016 return EL; 8017 8018 return getCouldNotCompute(); 8019 } 8020 8021 static ConstantInt * 8022 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 8023 ScalarEvolution &SE) { 8024 const SCEV *InVal = SE.getConstant(C); 8025 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 8026 assert(isa<SCEVConstant>(Val) && 8027 "Evaluation of SCEV at constant didn't fold correctly?"); 8028 return cast<SCEVConstant>(Val)->getValue(); 8029 } 8030 8031 /// Given an exit condition of 'icmp op load X, cst', try to see if we can 8032 /// compute the backedge execution count. 8033 ScalarEvolution::ExitLimit 8034 ScalarEvolution::computeLoadConstantCompareExitLimit( 8035 LoadInst *LI, 8036 Constant *RHS, 8037 const Loop *L, 8038 ICmpInst::Predicate predicate) { 8039 if (LI->isVolatile()) return getCouldNotCompute(); 8040 8041 // Check to see if the loaded pointer is a getelementptr of a global. 8042 // TODO: Use SCEV instead of manually grubbing with GEPs. 8043 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 8044 if (!GEP) return getCouldNotCompute(); 8045 8046 // Make sure that it is really a constant global we are gepping, with an 8047 // initializer, and make sure the first IDX is really 0. 8048 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 8049 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 8050 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 8051 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 8052 return getCouldNotCompute(); 8053 8054 // Okay, we allow one non-constant index into the GEP instruction. 8055 Value *VarIdx = nullptr; 8056 std::vector<Constant*> Indexes; 8057 unsigned VarIdxNum = 0; 8058 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 8059 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 8060 Indexes.push_back(CI); 8061 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 8062 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 8063 VarIdx = GEP->getOperand(i); 8064 VarIdxNum = i-2; 8065 Indexes.push_back(nullptr); 8066 } 8067 8068 // Loop-invariant loads may be a byproduct of loop optimization. Skip them. 8069 if (!VarIdx) 8070 return getCouldNotCompute(); 8071 8072 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 8073 // Check to see if X is a loop variant variable value now. 8074 const SCEV *Idx = getSCEV(VarIdx); 8075 Idx = getSCEVAtScope(Idx, L); 8076 8077 // We can only recognize very limited forms of loop index expressions, in 8078 // particular, only affine AddRec's like {C1,+,C2}<L>. 8079 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 8080 if (!IdxExpr || IdxExpr->getLoop() != L || !IdxExpr->isAffine() || 8081 isLoopInvariant(IdxExpr, L) || 8082 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 8083 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 8084 return getCouldNotCompute(); 8085 8086 unsigned MaxSteps = MaxBruteForceIterations; 8087 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 8088 ConstantInt *ItCst = ConstantInt::get( 8089 cast<IntegerType>(IdxExpr->getType()), IterationNum); 8090 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 8091 8092 // Form the GEP offset. 8093 Indexes[VarIdxNum] = Val; 8094 8095 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(), 8096 Indexes); 8097 if (!Result) break; // Cannot compute! 8098 8099 // Evaluate the condition for this iteration. 8100 Result = ConstantExpr::getICmp(predicate, Result, RHS); 8101 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 8102 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 8103 ++NumArrayLenItCounts; 8104 return getConstant(ItCst); // Found terminating iteration! 8105 } 8106 } 8107 return getCouldNotCompute(); 8108 } 8109 8110 ScalarEvolution::ExitLimit ScalarEvolution::computeShiftCompareExitLimit( 8111 Value *LHS, Value *RHSV, const Loop *L, ICmpInst::Predicate Pred) { 8112 ConstantInt *RHS = dyn_cast<ConstantInt>(RHSV); 8113 if (!RHS) 8114 return getCouldNotCompute(); 8115 8116 const BasicBlock *Latch = L->getLoopLatch(); 8117 if (!Latch) 8118 return getCouldNotCompute(); 8119 8120 const BasicBlock *Predecessor = L->getLoopPredecessor(); 8121 if (!Predecessor) 8122 return getCouldNotCompute(); 8123 8124 // Return true if V is of the form "LHS `shift_op` <positive constant>". 8125 // Return LHS in OutLHS and shift_opt in OutOpCode. 8126 auto MatchPositiveShift = 8127 [](Value *V, Value *&OutLHS, Instruction::BinaryOps &OutOpCode) { 8128 8129 using namespace PatternMatch; 8130 8131 ConstantInt *ShiftAmt; 8132 if (match(V, m_LShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt)))) 8133 OutOpCode = Instruction::LShr; 8134 else if (match(V, m_AShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt)))) 8135 OutOpCode = Instruction::AShr; 8136 else if (match(V, m_Shl(m_Value(OutLHS), m_ConstantInt(ShiftAmt)))) 8137 OutOpCode = Instruction::Shl; 8138 else 8139 return false; 8140 8141 return ShiftAmt->getValue().isStrictlyPositive(); 8142 }; 8143 8144 // Recognize a "shift recurrence" either of the form %iv or of %iv.shifted in 8145 // 8146 // loop: 8147 // %iv = phi i32 [ %iv.shifted, %loop ], [ %val, %preheader ] 8148 // %iv.shifted = lshr i32 %iv, <positive constant> 8149 // 8150 // Return true on a successful match. Return the corresponding PHI node (%iv 8151 // above) in PNOut and the opcode of the shift operation in OpCodeOut. 8152 auto MatchShiftRecurrence = 8153 [&](Value *V, PHINode *&PNOut, Instruction::BinaryOps &OpCodeOut) { 8154 Optional<Instruction::BinaryOps> PostShiftOpCode; 8155 8156 { 8157 Instruction::BinaryOps OpC; 8158 Value *V; 8159 8160 // If we encounter a shift instruction, "peel off" the shift operation, 8161 // and remember that we did so. Later when we inspect %iv's backedge 8162 // value, we will make sure that the backedge value uses the same 8163 // operation. 8164 // 8165 // Note: the peeled shift operation does not have to be the same 8166 // instruction as the one feeding into the PHI's backedge value. We only 8167 // really care about it being the same *kind* of shift instruction -- 8168 // that's all that is required for our later inferences to hold. 8169 if (MatchPositiveShift(LHS, V, OpC)) { 8170 PostShiftOpCode = OpC; 8171 LHS = V; 8172 } 8173 } 8174 8175 PNOut = dyn_cast<PHINode>(LHS); 8176 if (!PNOut || PNOut->getParent() != L->getHeader()) 8177 return false; 8178 8179 Value *BEValue = PNOut->getIncomingValueForBlock(Latch); 8180 Value *OpLHS; 8181 8182 return 8183 // The backedge value for the PHI node must be a shift by a positive 8184 // amount 8185 MatchPositiveShift(BEValue, OpLHS, OpCodeOut) && 8186 8187 // of the PHI node itself 8188 OpLHS == PNOut && 8189 8190 // and the kind of shift should be match the kind of shift we peeled 8191 // off, if any. 8192 (!PostShiftOpCode.hasValue() || *PostShiftOpCode == OpCodeOut); 8193 }; 8194 8195 PHINode *PN; 8196 Instruction::BinaryOps OpCode; 8197 if (!MatchShiftRecurrence(LHS, PN, OpCode)) 8198 return getCouldNotCompute(); 8199 8200 const DataLayout &DL = getDataLayout(); 8201 8202 // The key rationale for this optimization is that for some kinds of shift 8203 // recurrences, the value of the recurrence "stabilizes" to either 0 or -1 8204 // within a finite number of iterations. If the condition guarding the 8205 // backedge (in the sense that the backedge is taken if the condition is true) 8206 // is false for the value the shift recurrence stabilizes to, then we know 8207 // that the backedge is taken only a finite number of times. 8208 8209 ConstantInt *StableValue = nullptr; 8210 switch (OpCode) { 8211 default: 8212 llvm_unreachable("Impossible case!"); 8213 8214 case Instruction::AShr: { 8215 // {K,ashr,<positive-constant>} stabilizes to signum(K) in at most 8216 // bitwidth(K) iterations. 8217 Value *FirstValue = PN->getIncomingValueForBlock(Predecessor); 8218 KnownBits Known = computeKnownBits(FirstValue, DL, 0, &AC, 8219 Predecessor->getTerminator(), &DT); 8220 auto *Ty = cast<IntegerType>(RHS->getType()); 8221 if (Known.isNonNegative()) 8222 StableValue = ConstantInt::get(Ty, 0); 8223 else if (Known.isNegative()) 8224 StableValue = ConstantInt::get(Ty, -1, true); 8225 else 8226 return getCouldNotCompute(); 8227 8228 break; 8229 } 8230 case Instruction::LShr: 8231 case Instruction::Shl: 8232 // Both {K,lshr,<positive-constant>} and {K,shl,<positive-constant>} 8233 // stabilize to 0 in at most bitwidth(K) iterations. 8234 StableValue = ConstantInt::get(cast<IntegerType>(RHS->getType()), 0); 8235 break; 8236 } 8237 8238 auto *Result = 8239 ConstantFoldCompareInstOperands(Pred, StableValue, RHS, DL, &TLI); 8240 assert(Result->getType()->isIntegerTy(1) && 8241 "Otherwise cannot be an operand to a branch instruction"); 8242 8243 if (Result->isZeroValue()) { 8244 unsigned BitWidth = getTypeSizeInBits(RHS->getType()); 8245 const SCEV *UpperBound = 8246 getConstant(getEffectiveSCEVType(RHS->getType()), BitWidth); 8247 return ExitLimit(getCouldNotCompute(), UpperBound, false); 8248 } 8249 8250 return getCouldNotCompute(); 8251 } 8252 8253 /// Return true if we can constant fold an instruction of the specified type, 8254 /// assuming that all operands were constants. 8255 static bool CanConstantFold(const Instruction *I) { 8256 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 8257 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) || 8258 isa<LoadInst>(I) || isa<ExtractValueInst>(I)) 8259 return true; 8260 8261 if (const CallInst *CI = dyn_cast<CallInst>(I)) 8262 if (const Function *F = CI->getCalledFunction()) 8263 return canConstantFoldCallTo(CI, F); 8264 return false; 8265 } 8266 8267 /// Determine whether this instruction can constant evolve within this loop 8268 /// assuming its operands can all constant evolve. 8269 static bool canConstantEvolve(Instruction *I, const Loop *L) { 8270 // An instruction outside of the loop can't be derived from a loop PHI. 8271 if (!L->contains(I)) return false; 8272 8273 if (isa<PHINode>(I)) { 8274 // We don't currently keep track of the control flow needed to evaluate 8275 // PHIs, so we cannot handle PHIs inside of loops. 8276 return L->getHeader() == I->getParent(); 8277 } 8278 8279 // If we won't be able to constant fold this expression even if the operands 8280 // are constants, bail early. 8281 return CanConstantFold(I); 8282 } 8283 8284 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by 8285 /// recursing through each instruction operand until reaching a loop header phi. 8286 static PHINode * 8287 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L, 8288 DenseMap<Instruction *, PHINode *> &PHIMap, 8289 unsigned Depth) { 8290 if (Depth > MaxConstantEvolvingDepth) 8291 return nullptr; 8292 8293 // Otherwise, we can evaluate this instruction if all of its operands are 8294 // constant or derived from a PHI node themselves. 8295 PHINode *PHI = nullptr; 8296 for (Value *Op : UseInst->operands()) { 8297 if (isa<Constant>(Op)) continue; 8298 8299 Instruction *OpInst = dyn_cast<Instruction>(Op); 8300 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr; 8301 8302 PHINode *P = dyn_cast<PHINode>(OpInst); 8303 if (!P) 8304 // If this operand is already visited, reuse the prior result. 8305 // We may have P != PHI if this is the deepest point at which the 8306 // inconsistent paths meet. 8307 P = PHIMap.lookup(OpInst); 8308 if (!P) { 8309 // Recurse and memoize the results, whether a phi is found or not. 8310 // This recursive call invalidates pointers into PHIMap. 8311 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap, Depth + 1); 8312 PHIMap[OpInst] = P; 8313 } 8314 if (!P) 8315 return nullptr; // Not evolving from PHI 8316 if (PHI && PHI != P) 8317 return nullptr; // Evolving from multiple different PHIs. 8318 PHI = P; 8319 } 8320 // This is a expression evolving from a constant PHI! 8321 return PHI; 8322 } 8323 8324 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 8325 /// in the loop that V is derived from. We allow arbitrary operations along the 8326 /// way, but the operands of an operation must either be constants or a value 8327 /// derived from a constant PHI. If this expression does not fit with these 8328 /// constraints, return null. 8329 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 8330 Instruction *I = dyn_cast<Instruction>(V); 8331 if (!I || !canConstantEvolve(I, L)) return nullptr; 8332 8333 if (PHINode *PN = dyn_cast<PHINode>(I)) 8334 return PN; 8335 8336 // Record non-constant instructions contained by the loop. 8337 DenseMap<Instruction *, PHINode *> PHIMap; 8338 return getConstantEvolvingPHIOperands(I, L, PHIMap, 0); 8339 } 8340 8341 /// EvaluateExpression - Given an expression that passes the 8342 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 8343 /// in the loop has the value PHIVal. If we can't fold this expression for some 8344 /// reason, return null. 8345 static Constant *EvaluateExpression(Value *V, const Loop *L, 8346 DenseMap<Instruction *, Constant *> &Vals, 8347 const DataLayout &DL, 8348 const TargetLibraryInfo *TLI) { 8349 // Convenient constant check, but redundant for recursive calls. 8350 if (Constant *C = dyn_cast<Constant>(V)) return C; 8351 Instruction *I = dyn_cast<Instruction>(V); 8352 if (!I) return nullptr; 8353 8354 if (Constant *C = Vals.lookup(I)) return C; 8355 8356 // An instruction inside the loop depends on a value outside the loop that we 8357 // weren't given a mapping for, or a value such as a call inside the loop. 8358 if (!canConstantEvolve(I, L)) return nullptr; 8359 8360 // An unmapped PHI can be due to a branch or another loop inside this loop, 8361 // or due to this not being the initial iteration through a loop where we 8362 // couldn't compute the evolution of this particular PHI last time. 8363 if (isa<PHINode>(I)) return nullptr; 8364 8365 std::vector<Constant*> Operands(I->getNumOperands()); 8366 8367 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 8368 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i)); 8369 if (!Operand) { 8370 Operands[i] = dyn_cast<Constant>(I->getOperand(i)); 8371 if (!Operands[i]) return nullptr; 8372 continue; 8373 } 8374 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI); 8375 Vals[Operand] = C; 8376 if (!C) return nullptr; 8377 Operands[i] = C; 8378 } 8379 8380 if (CmpInst *CI = dyn_cast<CmpInst>(I)) 8381 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 8382 Operands[1], DL, TLI); 8383 if (LoadInst *LI = dyn_cast<LoadInst>(I)) { 8384 if (!LI->isVolatile()) 8385 return ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL); 8386 } 8387 return ConstantFoldInstOperands(I, Operands, DL, TLI); 8388 } 8389 8390 8391 // If every incoming value to PN except the one for BB is a specific Constant, 8392 // return that, else return nullptr. 8393 static Constant *getOtherIncomingValue(PHINode *PN, BasicBlock *BB) { 8394 Constant *IncomingVal = nullptr; 8395 8396 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 8397 if (PN->getIncomingBlock(i) == BB) 8398 continue; 8399 8400 auto *CurrentVal = dyn_cast<Constant>(PN->getIncomingValue(i)); 8401 if (!CurrentVal) 8402 return nullptr; 8403 8404 if (IncomingVal != CurrentVal) { 8405 if (IncomingVal) 8406 return nullptr; 8407 IncomingVal = CurrentVal; 8408 } 8409 } 8410 8411 return IncomingVal; 8412 } 8413 8414 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 8415 /// in the header of its containing loop, we know the loop executes a 8416 /// constant number of times, and the PHI node is just a recurrence 8417 /// involving constants, fold it. 8418 Constant * 8419 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 8420 const APInt &BEs, 8421 const Loop *L) { 8422 auto I = ConstantEvolutionLoopExitValue.find(PN); 8423 if (I != ConstantEvolutionLoopExitValue.end()) 8424 return I->second; 8425 8426 if (BEs.ugt(MaxBruteForceIterations)) 8427 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it. 8428 8429 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 8430 8431 DenseMap<Instruction *, Constant *> CurrentIterVals; 8432 BasicBlock *Header = L->getHeader(); 8433 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!"); 8434 8435 BasicBlock *Latch = L->getLoopLatch(); 8436 if (!Latch) 8437 return nullptr; 8438 8439 for (PHINode &PHI : Header->phis()) { 8440 if (auto *StartCST = getOtherIncomingValue(&PHI, Latch)) 8441 CurrentIterVals[&PHI] = StartCST; 8442 } 8443 if (!CurrentIterVals.count(PN)) 8444 return RetVal = nullptr; 8445 8446 Value *BEValue = PN->getIncomingValueForBlock(Latch); 8447 8448 // Execute the loop symbolically to determine the exit value. 8449 assert(BEs.getActiveBits() < CHAR_BIT * sizeof(unsigned) && 8450 "BEs is <= MaxBruteForceIterations which is an 'unsigned'!"); 8451 8452 unsigned NumIterations = BEs.getZExtValue(); // must be in range 8453 unsigned IterationNum = 0; 8454 const DataLayout &DL = getDataLayout(); 8455 for (; ; ++IterationNum) { 8456 if (IterationNum == NumIterations) 8457 return RetVal = CurrentIterVals[PN]; // Got exit value! 8458 8459 // Compute the value of the PHIs for the next iteration. 8460 // EvaluateExpression adds non-phi values to the CurrentIterVals map. 8461 DenseMap<Instruction *, Constant *> NextIterVals; 8462 Constant *NextPHI = 8463 EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI); 8464 if (!NextPHI) 8465 return nullptr; // Couldn't evaluate! 8466 NextIterVals[PN] = NextPHI; 8467 8468 bool StoppedEvolving = NextPHI == CurrentIterVals[PN]; 8469 8470 // Also evaluate the other PHI nodes. However, we don't get to stop if we 8471 // cease to be able to evaluate one of them or if they stop evolving, 8472 // because that doesn't necessarily prevent us from computing PN. 8473 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute; 8474 for (const auto &I : CurrentIterVals) { 8475 PHINode *PHI = dyn_cast<PHINode>(I.first); 8476 if (!PHI || PHI == PN || PHI->getParent() != Header) continue; 8477 PHIsToCompute.emplace_back(PHI, I.second); 8478 } 8479 // We use two distinct loops because EvaluateExpression may invalidate any 8480 // iterators into CurrentIterVals. 8481 for (const auto &I : PHIsToCompute) { 8482 PHINode *PHI = I.first; 8483 Constant *&NextPHI = NextIterVals[PHI]; 8484 if (!NextPHI) { // Not already computed. 8485 Value *BEValue = PHI->getIncomingValueForBlock(Latch); 8486 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI); 8487 } 8488 if (NextPHI != I.second) 8489 StoppedEvolving = false; 8490 } 8491 8492 // If all entries in CurrentIterVals == NextIterVals then we can stop 8493 // iterating, the loop can't continue to change. 8494 if (StoppedEvolving) 8495 return RetVal = CurrentIterVals[PN]; 8496 8497 CurrentIterVals.swap(NextIterVals); 8498 } 8499 } 8500 8501 const SCEV *ScalarEvolution::computeExitCountExhaustively(const Loop *L, 8502 Value *Cond, 8503 bool ExitWhen) { 8504 PHINode *PN = getConstantEvolvingPHI(Cond, L); 8505 if (!PN) return getCouldNotCompute(); 8506 8507 // If the loop is canonicalized, the PHI will have exactly two entries. 8508 // That's the only form we support here. 8509 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute(); 8510 8511 DenseMap<Instruction *, Constant *> CurrentIterVals; 8512 BasicBlock *Header = L->getHeader(); 8513 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!"); 8514 8515 BasicBlock *Latch = L->getLoopLatch(); 8516 assert(Latch && "Should follow from NumIncomingValues == 2!"); 8517 8518 for (PHINode &PHI : Header->phis()) { 8519 if (auto *StartCST = getOtherIncomingValue(&PHI, Latch)) 8520 CurrentIterVals[&PHI] = StartCST; 8521 } 8522 if (!CurrentIterVals.count(PN)) 8523 return getCouldNotCompute(); 8524 8525 // Okay, we find a PHI node that defines the trip count of this loop. Execute 8526 // the loop symbolically to determine when the condition gets a value of 8527 // "ExitWhen". 8528 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 8529 const DataLayout &DL = getDataLayout(); 8530 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){ 8531 auto *CondVal = dyn_cast_or_null<ConstantInt>( 8532 EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI)); 8533 8534 // Couldn't symbolically evaluate. 8535 if (!CondVal) return getCouldNotCompute(); 8536 8537 if (CondVal->getValue() == uint64_t(ExitWhen)) { 8538 ++NumBruteForceTripCountsComputed; 8539 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 8540 } 8541 8542 // Update all the PHI nodes for the next iteration. 8543 DenseMap<Instruction *, Constant *> NextIterVals; 8544 8545 // Create a list of which PHIs we need to compute. We want to do this before 8546 // calling EvaluateExpression on them because that may invalidate iterators 8547 // into CurrentIterVals. 8548 SmallVector<PHINode *, 8> PHIsToCompute; 8549 for (const auto &I : CurrentIterVals) { 8550 PHINode *PHI = dyn_cast<PHINode>(I.first); 8551 if (!PHI || PHI->getParent() != Header) continue; 8552 PHIsToCompute.push_back(PHI); 8553 } 8554 for (PHINode *PHI : PHIsToCompute) { 8555 Constant *&NextPHI = NextIterVals[PHI]; 8556 if (NextPHI) continue; // Already computed! 8557 8558 Value *BEValue = PHI->getIncomingValueForBlock(Latch); 8559 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI); 8560 } 8561 CurrentIterVals.swap(NextIterVals); 8562 } 8563 8564 // Too many iterations were needed to evaluate. 8565 return getCouldNotCompute(); 8566 } 8567 8568 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 8569 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = 8570 ValuesAtScopes[V]; 8571 // Check to see if we've folded this expression at this loop before. 8572 for (auto &LS : Values) 8573 if (LS.first == L) 8574 return LS.second ? LS.second : V; 8575 8576 Values.emplace_back(L, nullptr); 8577 8578 // Otherwise compute it. 8579 const SCEV *C = computeSCEVAtScope(V, L); 8580 for (auto &LS : reverse(ValuesAtScopes[V])) 8581 if (LS.first == L) { 8582 LS.second = C; 8583 break; 8584 } 8585 return C; 8586 } 8587 8588 /// This builds up a Constant using the ConstantExpr interface. That way, we 8589 /// will return Constants for objects which aren't represented by a 8590 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt. 8591 /// Returns NULL if the SCEV isn't representable as a Constant. 8592 static Constant *BuildConstantFromSCEV(const SCEV *V) { 8593 switch (V->getSCEVType()) { 8594 case scCouldNotCompute: 8595 case scAddRecExpr: 8596 return nullptr; 8597 case scConstant: 8598 return cast<SCEVConstant>(V)->getValue(); 8599 case scUnknown: 8600 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue()); 8601 case scSignExtend: { 8602 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V); 8603 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand())) 8604 return ConstantExpr::getSExt(CastOp, SS->getType()); 8605 return nullptr; 8606 } 8607 case scZeroExtend: { 8608 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V); 8609 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand())) 8610 return ConstantExpr::getZExt(CastOp, SZ->getType()); 8611 return nullptr; 8612 } 8613 case scPtrToInt: { 8614 const SCEVPtrToIntExpr *P2I = cast<SCEVPtrToIntExpr>(V); 8615 if (Constant *CastOp = BuildConstantFromSCEV(P2I->getOperand())) 8616 return ConstantExpr::getPtrToInt(CastOp, P2I->getType()); 8617 8618 return nullptr; 8619 } 8620 case scTruncate: { 8621 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V); 8622 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand())) 8623 return ConstantExpr::getTrunc(CastOp, ST->getType()); 8624 return nullptr; 8625 } 8626 case scAddExpr: { 8627 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V); 8628 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) { 8629 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) { 8630 unsigned AS = PTy->getAddressSpace(); 8631 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS); 8632 C = ConstantExpr::getBitCast(C, DestPtrTy); 8633 } 8634 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) { 8635 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i)); 8636 if (!C2) 8637 return nullptr; 8638 8639 // First pointer! 8640 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) { 8641 unsigned AS = C2->getType()->getPointerAddressSpace(); 8642 std::swap(C, C2); 8643 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS); 8644 // The offsets have been converted to bytes. We can add bytes to an 8645 // i8* by GEP with the byte count in the first index. 8646 C = ConstantExpr::getBitCast(C, DestPtrTy); 8647 } 8648 8649 // Don't bother trying to sum two pointers. We probably can't 8650 // statically compute a load that results from it anyway. 8651 if (C2->getType()->isPointerTy()) 8652 return nullptr; 8653 8654 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) { 8655 if (PTy->getElementType()->isStructTy()) 8656 C2 = ConstantExpr::getIntegerCast( 8657 C2, Type::getInt32Ty(C->getContext()), true); 8658 C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2); 8659 } else 8660 C = ConstantExpr::getAdd(C, C2); 8661 } 8662 return C; 8663 } 8664 return nullptr; 8665 } 8666 case scMulExpr: { 8667 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V); 8668 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) { 8669 // Don't bother with pointers at all. 8670 if (C->getType()->isPointerTy()) 8671 return nullptr; 8672 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) { 8673 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i)); 8674 if (!C2 || C2->getType()->isPointerTy()) 8675 return nullptr; 8676 C = ConstantExpr::getMul(C, C2); 8677 } 8678 return C; 8679 } 8680 return nullptr; 8681 } 8682 case scUDivExpr: { 8683 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V); 8684 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS())) 8685 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS())) 8686 if (LHS->getType() == RHS->getType()) 8687 return ConstantExpr::getUDiv(LHS, RHS); 8688 return nullptr; 8689 } 8690 case scSMaxExpr: 8691 case scUMaxExpr: 8692 case scSMinExpr: 8693 case scUMinExpr: 8694 return nullptr; // TODO: smax, umax, smin, umax. 8695 } 8696 llvm_unreachable("Unknown SCEV kind!"); 8697 } 8698 8699 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 8700 if (isa<SCEVConstant>(V)) return V; 8701 8702 // If this instruction is evolved from a constant-evolving PHI, compute the 8703 // exit value from the loop without using SCEVs. 8704 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 8705 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 8706 if (PHINode *PN = dyn_cast<PHINode>(I)) { 8707 const Loop *CurrLoop = this->LI[I->getParent()]; 8708 // Looking for loop exit value. 8709 if (CurrLoop && CurrLoop->getParentLoop() == L && 8710 PN->getParent() == CurrLoop->getHeader()) { 8711 // Okay, there is no closed form solution for the PHI node. Check 8712 // to see if the loop that contains it has a known backedge-taken 8713 // count. If so, we may be able to force computation of the exit 8714 // value. 8715 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(CurrLoop); 8716 // This trivial case can show up in some degenerate cases where 8717 // the incoming IR has not yet been fully simplified. 8718 if (BackedgeTakenCount->isZero()) { 8719 Value *InitValue = nullptr; 8720 bool MultipleInitValues = false; 8721 for (unsigned i = 0; i < PN->getNumIncomingValues(); i++) { 8722 if (!CurrLoop->contains(PN->getIncomingBlock(i))) { 8723 if (!InitValue) 8724 InitValue = PN->getIncomingValue(i); 8725 else if (InitValue != PN->getIncomingValue(i)) { 8726 MultipleInitValues = true; 8727 break; 8728 } 8729 } 8730 } 8731 if (!MultipleInitValues && InitValue) 8732 return getSCEV(InitValue); 8733 } 8734 // Do we have a loop invariant value flowing around the backedge 8735 // for a loop which must execute the backedge? 8736 if (!isa<SCEVCouldNotCompute>(BackedgeTakenCount) && 8737 isKnownPositive(BackedgeTakenCount) && 8738 PN->getNumIncomingValues() == 2) { 8739 8740 unsigned InLoopPred = 8741 CurrLoop->contains(PN->getIncomingBlock(0)) ? 0 : 1; 8742 Value *BackedgeVal = PN->getIncomingValue(InLoopPred); 8743 if (CurrLoop->isLoopInvariant(BackedgeVal)) 8744 return getSCEV(BackedgeVal); 8745 } 8746 if (auto *BTCC = dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 8747 // Okay, we know how many times the containing loop executes. If 8748 // this is a constant evolving PHI node, get the final value at 8749 // the specified iteration number. 8750 Constant *RV = getConstantEvolutionLoopExitValue( 8751 PN, BTCC->getAPInt(), CurrLoop); 8752 if (RV) return getSCEV(RV); 8753 } 8754 } 8755 8756 // If there is a single-input Phi, evaluate it at our scope. If we can 8757 // prove that this replacement does not break LCSSA form, use new value. 8758 if (PN->getNumOperands() == 1) { 8759 const SCEV *Input = getSCEV(PN->getOperand(0)); 8760 const SCEV *InputAtScope = getSCEVAtScope(Input, L); 8761 // TODO: We can generalize it using LI.replacementPreservesLCSSAForm, 8762 // for the simplest case just support constants. 8763 if (isa<SCEVConstant>(InputAtScope)) return InputAtScope; 8764 } 8765 } 8766 8767 // Okay, this is an expression that we cannot symbolically evaluate 8768 // into a SCEV. Check to see if it's possible to symbolically evaluate 8769 // the arguments into constants, and if so, try to constant propagate the 8770 // result. This is particularly useful for computing loop exit values. 8771 if (CanConstantFold(I)) { 8772 SmallVector<Constant *, 4> Operands; 8773 bool MadeImprovement = false; 8774 for (Value *Op : I->operands()) { 8775 if (Constant *C = dyn_cast<Constant>(Op)) { 8776 Operands.push_back(C); 8777 continue; 8778 } 8779 8780 // If any of the operands is non-constant and if they are 8781 // non-integer and non-pointer, don't even try to analyze them 8782 // with scev techniques. 8783 if (!isSCEVable(Op->getType())) 8784 return V; 8785 8786 const SCEV *OrigV = getSCEV(Op); 8787 const SCEV *OpV = getSCEVAtScope(OrigV, L); 8788 MadeImprovement |= OrigV != OpV; 8789 8790 Constant *C = BuildConstantFromSCEV(OpV); 8791 if (!C) return V; 8792 if (C->getType() != Op->getType()) 8793 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 8794 Op->getType(), 8795 false), 8796 C, Op->getType()); 8797 Operands.push_back(C); 8798 } 8799 8800 // Check to see if getSCEVAtScope actually made an improvement. 8801 if (MadeImprovement) { 8802 Constant *C = nullptr; 8803 const DataLayout &DL = getDataLayout(); 8804 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 8805 C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 8806 Operands[1], DL, &TLI); 8807 else if (const LoadInst *Load = dyn_cast<LoadInst>(I)) { 8808 if (!Load->isVolatile()) 8809 C = ConstantFoldLoadFromConstPtr(Operands[0], Load->getType(), 8810 DL); 8811 } else 8812 C = ConstantFoldInstOperands(I, Operands, DL, &TLI); 8813 if (!C) return V; 8814 return getSCEV(C); 8815 } 8816 } 8817 } 8818 8819 // This is some other type of SCEVUnknown, just return it. 8820 return V; 8821 } 8822 8823 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 8824 // Avoid performing the look-up in the common case where the specified 8825 // expression has no loop-variant portions. 8826 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 8827 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 8828 if (OpAtScope != Comm->getOperand(i)) { 8829 // Okay, at least one of these operands is loop variant but might be 8830 // foldable. Build a new instance of the folded commutative expression. 8831 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 8832 Comm->op_begin()+i); 8833 NewOps.push_back(OpAtScope); 8834 8835 for (++i; i != e; ++i) { 8836 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 8837 NewOps.push_back(OpAtScope); 8838 } 8839 if (isa<SCEVAddExpr>(Comm)) 8840 return getAddExpr(NewOps, Comm->getNoWrapFlags()); 8841 if (isa<SCEVMulExpr>(Comm)) 8842 return getMulExpr(NewOps, Comm->getNoWrapFlags()); 8843 if (isa<SCEVMinMaxExpr>(Comm)) 8844 return getMinMaxExpr(Comm->getSCEVType(), NewOps); 8845 llvm_unreachable("Unknown commutative SCEV type!"); 8846 } 8847 } 8848 // If we got here, all operands are loop invariant. 8849 return Comm; 8850 } 8851 8852 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 8853 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 8854 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 8855 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 8856 return Div; // must be loop invariant 8857 return getUDivExpr(LHS, RHS); 8858 } 8859 8860 // If this is a loop recurrence for a loop that does not contain L, then we 8861 // are dealing with the final value computed by the loop. 8862 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 8863 // First, attempt to evaluate each operand. 8864 // Avoid performing the look-up in the common case where the specified 8865 // expression has no loop-variant portions. 8866 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 8867 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L); 8868 if (OpAtScope == AddRec->getOperand(i)) 8869 continue; 8870 8871 // Okay, at least one of these operands is loop variant but might be 8872 // foldable. Build a new instance of the folded commutative expression. 8873 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(), 8874 AddRec->op_begin()+i); 8875 NewOps.push_back(OpAtScope); 8876 for (++i; i != e; ++i) 8877 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L)); 8878 8879 const SCEV *FoldedRec = 8880 getAddRecExpr(NewOps, AddRec->getLoop(), 8881 AddRec->getNoWrapFlags(SCEV::FlagNW)); 8882 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec); 8883 // The addrec may be folded to a nonrecurrence, for example, if the 8884 // induction variable is multiplied by zero after constant folding. Go 8885 // ahead and return the folded value. 8886 if (!AddRec) 8887 return FoldedRec; 8888 break; 8889 } 8890 8891 // If the scope is outside the addrec's loop, evaluate it by using the 8892 // loop exit value of the addrec. 8893 if (!AddRec->getLoop()->contains(L)) { 8894 // To evaluate this recurrence, we need to know how many times the AddRec 8895 // loop iterates. Compute this now. 8896 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 8897 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 8898 8899 // Then, evaluate the AddRec. 8900 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 8901 } 8902 8903 return AddRec; 8904 } 8905 8906 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 8907 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 8908 if (Op == Cast->getOperand()) 8909 return Cast; // must be loop invariant 8910 return getZeroExtendExpr(Op, Cast->getType()); 8911 } 8912 8913 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 8914 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 8915 if (Op == Cast->getOperand()) 8916 return Cast; // must be loop invariant 8917 return getSignExtendExpr(Op, Cast->getType()); 8918 } 8919 8920 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 8921 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 8922 if (Op == Cast->getOperand()) 8923 return Cast; // must be loop invariant 8924 return getTruncateExpr(Op, Cast->getType()); 8925 } 8926 8927 if (const SCEVPtrToIntExpr *Cast = dyn_cast<SCEVPtrToIntExpr>(V)) { 8928 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 8929 if (Op == Cast->getOperand()) 8930 return Cast; // must be loop invariant 8931 return getPtrToIntExpr(Op, Cast->getType()); 8932 } 8933 8934 llvm_unreachable("Unknown SCEV type!"); 8935 } 8936 8937 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 8938 return getSCEVAtScope(getSCEV(V), L); 8939 } 8940 8941 const SCEV *ScalarEvolution::stripInjectiveFunctions(const SCEV *S) const { 8942 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) 8943 return stripInjectiveFunctions(ZExt->getOperand()); 8944 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) 8945 return stripInjectiveFunctions(SExt->getOperand()); 8946 return S; 8947 } 8948 8949 /// Finds the minimum unsigned root of the following equation: 8950 /// 8951 /// A * X = B (mod N) 8952 /// 8953 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of 8954 /// A and B isn't important. 8955 /// 8956 /// If the equation does not have a solution, SCEVCouldNotCompute is returned. 8957 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const SCEV *B, 8958 ScalarEvolution &SE) { 8959 uint32_t BW = A.getBitWidth(); 8960 assert(BW == SE.getTypeSizeInBits(B->getType())); 8961 assert(A != 0 && "A must be non-zero."); 8962 8963 // 1. D = gcd(A, N) 8964 // 8965 // The gcd of A and N may have only one prime factor: 2. The number of 8966 // trailing zeros in A is its multiplicity 8967 uint32_t Mult2 = A.countTrailingZeros(); 8968 // D = 2^Mult2 8969 8970 // 2. Check if B is divisible by D. 8971 // 8972 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 8973 // is not less than multiplicity of this prime factor for D. 8974 if (SE.GetMinTrailingZeros(B) < Mult2) 8975 return SE.getCouldNotCompute(); 8976 8977 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 8978 // modulo (N / D). 8979 // 8980 // If D == 1, (N / D) == N == 2^BW, so we need one extra bit to represent 8981 // (N / D) in general. The inverse itself always fits into BW bits, though, 8982 // so we immediately truncate it. 8983 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 8984 APInt Mod(BW + 1, 0); 8985 Mod.setBit(BW - Mult2); // Mod = N / D 8986 APInt I = AD.multiplicativeInverse(Mod).trunc(BW); 8987 8988 // 4. Compute the minimum unsigned root of the equation: 8989 // I * (B / D) mod (N / D) 8990 // To simplify the computation, we factor out the divide by D: 8991 // (I * B mod N) / D 8992 const SCEV *D = SE.getConstant(APInt::getOneBitSet(BW, Mult2)); 8993 return SE.getUDivExactExpr(SE.getMulExpr(B, SE.getConstant(I)), D); 8994 } 8995 8996 /// For a given quadratic addrec, generate coefficients of the corresponding 8997 /// quadratic equation, multiplied by a common value to ensure that they are 8998 /// integers. 8999 /// The returned value is a tuple { A, B, C, M, BitWidth }, where 9000 /// Ax^2 + Bx + C is the quadratic function, M is the value that A, B and C 9001 /// were multiplied by, and BitWidth is the bit width of the original addrec 9002 /// coefficients. 9003 /// This function returns None if the addrec coefficients are not compile- 9004 /// time constants. 9005 static Optional<std::tuple<APInt, APInt, APInt, APInt, unsigned>> 9006 GetQuadraticEquation(const SCEVAddRecExpr *AddRec) { 9007 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 9008 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 9009 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 9010 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 9011 LLVM_DEBUG(dbgs() << __func__ << ": analyzing quadratic addrec: " 9012 << *AddRec << '\n'); 9013 9014 // We currently can only solve this if the coefficients are constants. 9015 if (!LC || !MC || !NC) { 9016 LLVM_DEBUG(dbgs() << __func__ << ": coefficients are not constant\n"); 9017 return None; 9018 } 9019 9020 APInt L = LC->getAPInt(); 9021 APInt M = MC->getAPInt(); 9022 APInt N = NC->getAPInt(); 9023 assert(!N.isNullValue() && "This is not a quadratic addrec"); 9024 9025 unsigned BitWidth = LC->getAPInt().getBitWidth(); 9026 unsigned NewWidth = BitWidth + 1; 9027 LLVM_DEBUG(dbgs() << __func__ << ": addrec coeff bw: " 9028 << BitWidth << '\n'); 9029 // The sign-extension (as opposed to a zero-extension) here matches the 9030 // extension used in SolveQuadraticEquationWrap (with the same motivation). 9031 N = N.sext(NewWidth); 9032 M = M.sext(NewWidth); 9033 L = L.sext(NewWidth); 9034 9035 // The increments are M, M+N, M+2N, ..., so the accumulated values are 9036 // L+M, (L+M)+(M+N), (L+M)+(M+N)+(M+2N), ..., that is, 9037 // L+M, L+2M+N, L+3M+3N, ... 9038 // After n iterations the accumulated value Acc is L + nM + n(n-1)/2 N. 9039 // 9040 // The equation Acc = 0 is then 9041 // L + nM + n(n-1)/2 N = 0, or 2L + 2M n + n(n-1) N = 0. 9042 // In a quadratic form it becomes: 9043 // N n^2 + (2M-N) n + 2L = 0. 9044 9045 APInt A = N; 9046 APInt B = 2 * M - A; 9047 APInt C = 2 * L; 9048 APInt T = APInt(NewWidth, 2); 9049 LLVM_DEBUG(dbgs() << __func__ << ": equation " << A << "x^2 + " << B 9050 << "x + " << C << ", coeff bw: " << NewWidth 9051 << ", multiplied by " << T << '\n'); 9052 return std::make_tuple(A, B, C, T, BitWidth); 9053 } 9054 9055 /// Helper function to compare optional APInts: 9056 /// (a) if X and Y both exist, return min(X, Y), 9057 /// (b) if neither X nor Y exist, return None, 9058 /// (c) if exactly one of X and Y exists, return that value. 9059 static Optional<APInt> MinOptional(Optional<APInt> X, Optional<APInt> Y) { 9060 if (X.hasValue() && Y.hasValue()) { 9061 unsigned W = std::max(X->getBitWidth(), Y->getBitWidth()); 9062 APInt XW = X->sextOrSelf(W); 9063 APInt YW = Y->sextOrSelf(W); 9064 return XW.slt(YW) ? *X : *Y; 9065 } 9066 if (!X.hasValue() && !Y.hasValue()) 9067 return None; 9068 return X.hasValue() ? *X : *Y; 9069 } 9070 9071 /// Helper function to truncate an optional APInt to a given BitWidth. 9072 /// When solving addrec-related equations, it is preferable to return a value 9073 /// that has the same bit width as the original addrec's coefficients. If the 9074 /// solution fits in the original bit width, truncate it (except for i1). 9075 /// Returning a value of a different bit width may inhibit some optimizations. 9076 /// 9077 /// In general, a solution to a quadratic equation generated from an addrec 9078 /// may require BW+1 bits, where BW is the bit width of the addrec's 9079 /// coefficients. The reason is that the coefficients of the quadratic 9080 /// equation are BW+1 bits wide (to avoid truncation when converting from 9081 /// the addrec to the equation). 9082 static Optional<APInt> TruncIfPossible(Optional<APInt> X, unsigned BitWidth) { 9083 if (!X.hasValue()) 9084 return None; 9085 unsigned W = X->getBitWidth(); 9086 if (BitWidth > 1 && BitWidth < W && X->isIntN(BitWidth)) 9087 return X->trunc(BitWidth); 9088 return X; 9089 } 9090 9091 /// Let c(n) be the value of the quadratic chrec {L,+,M,+,N} after n 9092 /// iterations. The values L, M, N are assumed to be signed, and they 9093 /// should all have the same bit widths. 9094 /// Find the least n >= 0 such that c(n) = 0 in the arithmetic modulo 2^BW, 9095 /// where BW is the bit width of the addrec's coefficients. 9096 /// If the calculated value is a BW-bit integer (for BW > 1), it will be 9097 /// returned as such, otherwise the bit width of the returned value may 9098 /// be greater than BW. 9099 /// 9100 /// This function returns None if 9101 /// (a) the addrec coefficients are not constant, or 9102 /// (b) SolveQuadraticEquationWrap was unable to find a solution. For cases 9103 /// like x^2 = 5, no integer solutions exist, in other cases an integer 9104 /// solution may exist, but SolveQuadraticEquationWrap may fail to find it. 9105 static Optional<APInt> 9106 SolveQuadraticAddRecExact(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 9107 APInt A, B, C, M; 9108 unsigned BitWidth; 9109 auto T = GetQuadraticEquation(AddRec); 9110 if (!T.hasValue()) 9111 return None; 9112 9113 std::tie(A, B, C, M, BitWidth) = *T; 9114 LLVM_DEBUG(dbgs() << __func__ << ": solving for unsigned overflow\n"); 9115 Optional<APInt> X = APIntOps::SolveQuadraticEquationWrap(A, B, C, BitWidth+1); 9116 if (!X.hasValue()) 9117 return None; 9118 9119 ConstantInt *CX = ConstantInt::get(SE.getContext(), *X); 9120 ConstantInt *V = EvaluateConstantChrecAtConstant(AddRec, CX, SE); 9121 if (!V->isZero()) 9122 return None; 9123 9124 return TruncIfPossible(X, BitWidth); 9125 } 9126 9127 /// Let c(n) be the value of the quadratic chrec {0,+,M,+,N} after n 9128 /// iterations. The values M, N are assumed to be signed, and they 9129 /// should all have the same bit widths. 9130 /// Find the least n such that c(n) does not belong to the given range, 9131 /// while c(n-1) does. 9132 /// 9133 /// This function returns None if 9134 /// (a) the addrec coefficients are not constant, or 9135 /// (b) SolveQuadraticEquationWrap was unable to find a solution for the 9136 /// bounds of the range. 9137 static Optional<APInt> 9138 SolveQuadraticAddRecRange(const SCEVAddRecExpr *AddRec, 9139 const ConstantRange &Range, ScalarEvolution &SE) { 9140 assert(AddRec->getOperand(0)->isZero() && 9141 "Starting value of addrec should be 0"); 9142 LLVM_DEBUG(dbgs() << __func__ << ": solving boundary crossing for range " 9143 << Range << ", addrec " << *AddRec << '\n'); 9144 // This case is handled in getNumIterationsInRange. Here we can assume that 9145 // we start in the range. 9146 assert(Range.contains(APInt(SE.getTypeSizeInBits(AddRec->getType()), 0)) && 9147 "Addrec's initial value should be in range"); 9148 9149 APInt A, B, C, M; 9150 unsigned BitWidth; 9151 auto T = GetQuadraticEquation(AddRec); 9152 if (!T.hasValue()) 9153 return None; 9154 9155 // Be careful about the return value: there can be two reasons for not 9156 // returning an actual number. First, if no solutions to the equations 9157 // were found, and second, if the solutions don't leave the given range. 9158 // The first case means that the actual solution is "unknown", the second 9159 // means that it's known, but not valid. If the solution is unknown, we 9160 // cannot make any conclusions. 9161 // Return a pair: the optional solution and a flag indicating if the 9162 // solution was found. 9163 auto SolveForBoundary = [&](APInt Bound) -> std::pair<Optional<APInt>,bool> { 9164 // Solve for signed overflow and unsigned overflow, pick the lower 9165 // solution. 9166 LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: checking boundary " 9167 << Bound << " (before multiplying by " << M << ")\n"); 9168 Bound *= M; // The quadratic equation multiplier. 9169 9170 Optional<APInt> SO = None; 9171 if (BitWidth > 1) { 9172 LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: solving for " 9173 "signed overflow\n"); 9174 SO = APIntOps::SolveQuadraticEquationWrap(A, B, -Bound, BitWidth); 9175 } 9176 LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: solving for " 9177 "unsigned overflow\n"); 9178 Optional<APInt> UO = APIntOps::SolveQuadraticEquationWrap(A, B, -Bound, 9179 BitWidth+1); 9180 9181 auto LeavesRange = [&] (const APInt &X) { 9182 ConstantInt *C0 = ConstantInt::get(SE.getContext(), X); 9183 ConstantInt *V0 = EvaluateConstantChrecAtConstant(AddRec, C0, SE); 9184 if (Range.contains(V0->getValue())) 9185 return false; 9186 // X should be at least 1, so X-1 is non-negative. 9187 ConstantInt *C1 = ConstantInt::get(SE.getContext(), X-1); 9188 ConstantInt *V1 = EvaluateConstantChrecAtConstant(AddRec, C1, SE); 9189 if (Range.contains(V1->getValue())) 9190 return true; 9191 return false; 9192 }; 9193 9194 // If SolveQuadraticEquationWrap returns None, it means that there can 9195 // be a solution, but the function failed to find it. We cannot treat it 9196 // as "no solution". 9197 if (!SO.hasValue() || !UO.hasValue()) 9198 return { None, false }; 9199 9200 // Check the smaller value first to see if it leaves the range. 9201 // At this point, both SO and UO must have values. 9202 Optional<APInt> Min = MinOptional(SO, UO); 9203 if (LeavesRange(*Min)) 9204 return { Min, true }; 9205 Optional<APInt> Max = Min == SO ? UO : SO; 9206 if (LeavesRange(*Max)) 9207 return { Max, true }; 9208 9209 // Solutions were found, but were eliminated, hence the "true". 9210 return { None, true }; 9211 }; 9212 9213 std::tie(A, B, C, M, BitWidth) = *T; 9214 // Lower bound is inclusive, subtract 1 to represent the exiting value. 9215 APInt Lower = Range.getLower().sextOrSelf(A.getBitWidth()) - 1; 9216 APInt Upper = Range.getUpper().sextOrSelf(A.getBitWidth()); 9217 auto SL = SolveForBoundary(Lower); 9218 auto SU = SolveForBoundary(Upper); 9219 // If any of the solutions was unknown, no meaninigful conclusions can 9220 // be made. 9221 if (!SL.second || !SU.second) 9222 return None; 9223 9224 // Claim: The correct solution is not some value between Min and Max. 9225 // 9226 // Justification: Assuming that Min and Max are different values, one of 9227 // them is when the first signed overflow happens, the other is when the 9228 // first unsigned overflow happens. Crossing the range boundary is only 9229 // possible via an overflow (treating 0 as a special case of it, modeling 9230 // an overflow as crossing k*2^W for some k). 9231 // 9232 // The interesting case here is when Min was eliminated as an invalid 9233 // solution, but Max was not. The argument is that if there was another 9234 // overflow between Min and Max, it would also have been eliminated if 9235 // it was considered. 9236 // 9237 // For a given boundary, it is possible to have two overflows of the same 9238 // type (signed/unsigned) without having the other type in between: this 9239 // can happen when the vertex of the parabola is between the iterations 9240 // corresponding to the overflows. This is only possible when the two 9241 // overflows cross k*2^W for the same k. In such case, if the second one 9242 // left the range (and was the first one to do so), the first overflow 9243 // would have to enter the range, which would mean that either we had left 9244 // the range before or that we started outside of it. Both of these cases 9245 // are contradictions. 9246 // 9247 // Claim: In the case where SolveForBoundary returns None, the correct 9248 // solution is not some value between the Max for this boundary and the 9249 // Min of the other boundary. 9250 // 9251 // Justification: Assume that we had such Max_A and Min_B corresponding 9252 // to range boundaries A and B and such that Max_A < Min_B. If there was 9253 // a solution between Max_A and Min_B, it would have to be caused by an 9254 // overflow corresponding to either A or B. It cannot correspond to B, 9255 // since Min_B is the first occurrence of such an overflow. If it 9256 // corresponded to A, it would have to be either a signed or an unsigned 9257 // overflow that is larger than both eliminated overflows for A. But 9258 // between the eliminated overflows and this overflow, the values would 9259 // cover the entire value space, thus crossing the other boundary, which 9260 // is a contradiction. 9261 9262 return TruncIfPossible(MinOptional(SL.first, SU.first), BitWidth); 9263 } 9264 9265 ScalarEvolution::ExitLimit 9266 ScalarEvolution::howFarToZero(const SCEV *V, const Loop *L, bool ControlsExit, 9267 bool AllowPredicates) { 9268 9269 // This is only used for loops with a "x != y" exit test. The exit condition 9270 // is now expressed as a single expression, V = x-y. So the exit test is 9271 // effectively V != 0. We know and take advantage of the fact that this 9272 // expression only being used in a comparison by zero context. 9273 9274 SmallPtrSet<const SCEVPredicate *, 4> Predicates; 9275 // If the value is a constant 9276 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 9277 // If the value is already zero, the branch will execute zero times. 9278 if (C->getValue()->isZero()) return C; 9279 return getCouldNotCompute(); // Otherwise it will loop infinitely. 9280 } 9281 9282 const SCEVAddRecExpr *AddRec = 9283 dyn_cast<SCEVAddRecExpr>(stripInjectiveFunctions(V)); 9284 9285 if (!AddRec && AllowPredicates) 9286 // Try to make this an AddRec using runtime tests, in the first X 9287 // iterations of this loop, where X is the SCEV expression found by the 9288 // algorithm below. 9289 AddRec = convertSCEVToAddRecWithPredicates(V, L, Predicates); 9290 9291 if (!AddRec || AddRec->getLoop() != L) 9292 return getCouldNotCompute(); 9293 9294 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 9295 // the quadratic equation to solve it. 9296 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { 9297 // We can only use this value if the chrec ends up with an exact zero 9298 // value at this index. When solving for "X*X != 5", for example, we 9299 // should not accept a root of 2. 9300 if (auto S = SolveQuadraticAddRecExact(AddRec, *this)) { 9301 const auto *R = cast<SCEVConstant>(getConstant(S.getValue())); 9302 return ExitLimit(R, R, false, Predicates); 9303 } 9304 return getCouldNotCompute(); 9305 } 9306 9307 // Otherwise we can only handle this if it is affine. 9308 if (!AddRec->isAffine()) 9309 return getCouldNotCompute(); 9310 9311 // If this is an affine expression, the execution count of this branch is 9312 // the minimum unsigned root of the following equation: 9313 // 9314 // Start + Step*N = 0 (mod 2^BW) 9315 // 9316 // equivalent to: 9317 // 9318 // Step*N = -Start (mod 2^BW) 9319 // 9320 // where BW is the common bit width of Start and Step. 9321 9322 // Get the initial value for the loop. 9323 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 9324 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop()); 9325 9326 // For now we handle only constant steps. 9327 // 9328 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the 9329 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap 9330 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step. 9331 // We have not yet seen any such cases. 9332 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step); 9333 if (!StepC || StepC->getValue()->isZero()) 9334 return getCouldNotCompute(); 9335 9336 // For positive steps (counting up until unsigned overflow): 9337 // N = -Start/Step (as unsigned) 9338 // For negative steps (counting down to zero): 9339 // N = Start/-Step 9340 // First compute the unsigned distance from zero in the direction of Step. 9341 bool CountDown = StepC->getAPInt().isNegative(); 9342 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start); 9343 9344 // Handle unitary steps, which cannot wraparound. 9345 // 1*N = -Start; -1*N = Start (mod 2^BW), so: 9346 // N = Distance (as unsigned) 9347 if (StepC->getValue()->isOne() || StepC->getValue()->isMinusOne()) { 9348 APInt MaxBECount = getUnsignedRangeMax(applyLoopGuards(Distance, L)); 9349 APInt MaxBECountBase = getUnsignedRangeMax(Distance); 9350 if (MaxBECountBase.ult(MaxBECount)) 9351 MaxBECount = MaxBECountBase; 9352 9353 // When a loop like "for (int i = 0; i != n; ++i) { /* body */ }" is rotated, 9354 // we end up with a loop whose backedge-taken count is n - 1. Detect this 9355 // case, and see if we can improve the bound. 9356 // 9357 // Explicitly handling this here is necessary because getUnsignedRange 9358 // isn't context-sensitive; it doesn't know that we only care about the 9359 // range inside the loop. 9360 const SCEV *Zero = getZero(Distance->getType()); 9361 const SCEV *One = getOne(Distance->getType()); 9362 const SCEV *DistancePlusOne = getAddExpr(Distance, One); 9363 if (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_NE, DistancePlusOne, Zero)) { 9364 // If Distance + 1 doesn't overflow, we can compute the maximum distance 9365 // as "unsigned_max(Distance + 1) - 1". 9366 ConstantRange CR = getUnsignedRange(DistancePlusOne); 9367 MaxBECount = APIntOps::umin(MaxBECount, CR.getUnsignedMax() - 1); 9368 } 9369 return ExitLimit(Distance, getConstant(MaxBECount), false, Predicates); 9370 } 9371 9372 // If the condition controls loop exit (the loop exits only if the expression 9373 // is true) and the addition is no-wrap we can use unsigned divide to 9374 // compute the backedge count. In this case, the step may not divide the 9375 // distance, but we don't care because if the condition is "missed" the loop 9376 // will have undefined behavior due to wrapping. 9377 if (ControlsExit && AddRec->hasNoSelfWrap() && 9378 loopHasNoAbnormalExits(AddRec->getLoop())) { 9379 const SCEV *Exact = 9380 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step); 9381 const SCEV *Max = getCouldNotCompute(); 9382 if (Exact != getCouldNotCompute()) { 9383 APInt MaxInt = getUnsignedRangeMax(applyLoopGuards(Exact, L)); 9384 APInt BaseMaxInt = getUnsignedRangeMax(Exact); 9385 if (BaseMaxInt.ult(MaxInt)) 9386 Max = getConstant(BaseMaxInt); 9387 else 9388 Max = getConstant(MaxInt); 9389 } 9390 return ExitLimit(Exact, Max, false, Predicates); 9391 } 9392 9393 // Solve the general equation. 9394 const SCEV *E = SolveLinEquationWithOverflow(StepC->getAPInt(), 9395 getNegativeSCEV(Start), *this); 9396 const SCEV *M = E == getCouldNotCompute() 9397 ? E 9398 : getConstant(getUnsignedRangeMax(E)); 9399 return ExitLimit(E, M, false, Predicates); 9400 } 9401 9402 ScalarEvolution::ExitLimit 9403 ScalarEvolution::howFarToNonZero(const SCEV *V, const Loop *L) { 9404 // Loops that look like: while (X == 0) are very strange indeed. We don't 9405 // handle them yet except for the trivial case. This could be expanded in the 9406 // future as needed. 9407 9408 // If the value is a constant, check to see if it is known to be non-zero 9409 // already. If so, the backedge will execute zero times. 9410 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 9411 if (!C->getValue()->isZero()) 9412 return getZero(C->getType()); 9413 return getCouldNotCompute(); // Otherwise it will loop infinitely. 9414 } 9415 9416 // We could implement others, but I really doubt anyone writes loops like 9417 // this, and if they did, they would already be constant folded. 9418 return getCouldNotCompute(); 9419 } 9420 9421 std::pair<const BasicBlock *, const BasicBlock *> 9422 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(const BasicBlock *BB) 9423 const { 9424 // If the block has a unique predecessor, then there is no path from the 9425 // predecessor to the block that does not go through the direct edge 9426 // from the predecessor to the block. 9427 if (const BasicBlock *Pred = BB->getSinglePredecessor()) 9428 return {Pred, BB}; 9429 9430 // A loop's header is defined to be a block that dominates the loop. 9431 // If the header has a unique predecessor outside the loop, it must be 9432 // a block that has exactly one successor that can reach the loop. 9433 if (const Loop *L = LI.getLoopFor(BB)) 9434 return {L->getLoopPredecessor(), L->getHeader()}; 9435 9436 return {nullptr, nullptr}; 9437 } 9438 9439 /// SCEV structural equivalence is usually sufficient for testing whether two 9440 /// expressions are equal, however for the purposes of looking for a condition 9441 /// guarding a loop, it can be useful to be a little more general, since a 9442 /// front-end may have replicated the controlling expression. 9443 static bool HasSameValue(const SCEV *A, const SCEV *B) { 9444 // Quick check to see if they are the same SCEV. 9445 if (A == B) return true; 9446 9447 auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) { 9448 // Not all instructions that are "identical" compute the same value. For 9449 // instance, two distinct alloca instructions allocating the same type are 9450 // identical and do not read memory; but compute distinct values. 9451 return A->isIdenticalTo(B) && (isa<BinaryOperator>(A) || isa<GetElementPtrInst>(A)); 9452 }; 9453 9454 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 9455 // two different instructions with the same value. Check for this case. 9456 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 9457 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 9458 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 9459 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 9460 if (ComputesEqualValues(AI, BI)) 9461 return true; 9462 9463 // Otherwise assume they may have a different value. 9464 return false; 9465 } 9466 9467 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred, 9468 const SCEV *&LHS, const SCEV *&RHS, 9469 unsigned Depth) { 9470 bool Changed = false; 9471 // Simplifies ICMP to trivial true or false by turning it into '0 == 0' or 9472 // '0 != 0'. 9473 auto TrivialCase = [&](bool TriviallyTrue) { 9474 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 9475 Pred = TriviallyTrue ? ICmpInst::ICMP_EQ : ICmpInst::ICMP_NE; 9476 return true; 9477 }; 9478 // If we hit the max recursion limit bail out. 9479 if (Depth >= 3) 9480 return false; 9481 9482 // Canonicalize a constant to the right side. 9483 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 9484 // Check for both operands constant. 9485 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 9486 if (ConstantExpr::getICmp(Pred, 9487 LHSC->getValue(), 9488 RHSC->getValue())->isNullValue()) 9489 return TrivialCase(false); 9490 else 9491 return TrivialCase(true); 9492 } 9493 // Otherwise swap the operands to put the constant on the right. 9494 std::swap(LHS, RHS); 9495 Pred = ICmpInst::getSwappedPredicate(Pred); 9496 Changed = true; 9497 } 9498 9499 // If we're comparing an addrec with a value which is loop-invariant in the 9500 // addrec's loop, put the addrec on the left. Also make a dominance check, 9501 // as both operands could be addrecs loop-invariant in each other's loop. 9502 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) { 9503 const Loop *L = AR->getLoop(); 9504 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) { 9505 std::swap(LHS, RHS); 9506 Pred = ICmpInst::getSwappedPredicate(Pred); 9507 Changed = true; 9508 } 9509 } 9510 9511 // If there's a constant operand, canonicalize comparisons with boundary 9512 // cases, and canonicalize *-or-equal comparisons to regular comparisons. 9513 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 9514 const APInt &RA = RC->getAPInt(); 9515 9516 bool SimplifiedByConstantRange = false; 9517 9518 if (!ICmpInst::isEquality(Pred)) { 9519 ConstantRange ExactCR = ConstantRange::makeExactICmpRegion(Pred, RA); 9520 if (ExactCR.isFullSet()) 9521 return TrivialCase(true); 9522 else if (ExactCR.isEmptySet()) 9523 return TrivialCase(false); 9524 9525 APInt NewRHS; 9526 CmpInst::Predicate NewPred; 9527 if (ExactCR.getEquivalentICmp(NewPred, NewRHS) && 9528 ICmpInst::isEquality(NewPred)) { 9529 // We were able to convert an inequality to an equality. 9530 Pred = NewPred; 9531 RHS = getConstant(NewRHS); 9532 Changed = SimplifiedByConstantRange = true; 9533 } 9534 } 9535 9536 if (!SimplifiedByConstantRange) { 9537 switch (Pred) { 9538 default: 9539 break; 9540 case ICmpInst::ICMP_EQ: 9541 case ICmpInst::ICMP_NE: 9542 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b. 9543 if (!RA) 9544 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS)) 9545 if (const SCEVMulExpr *ME = 9546 dyn_cast<SCEVMulExpr>(AE->getOperand(0))) 9547 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 && 9548 ME->getOperand(0)->isAllOnesValue()) { 9549 RHS = AE->getOperand(1); 9550 LHS = ME->getOperand(1); 9551 Changed = true; 9552 } 9553 break; 9554 9555 9556 // The "Should have been caught earlier!" messages refer to the fact 9557 // that the ExactCR.isFullSet() or ExactCR.isEmptySet() check above 9558 // should have fired on the corresponding cases, and canonicalized the 9559 // check to trivial case. 9560 9561 case ICmpInst::ICMP_UGE: 9562 assert(!RA.isMinValue() && "Should have been caught earlier!"); 9563 Pred = ICmpInst::ICMP_UGT; 9564 RHS = getConstant(RA - 1); 9565 Changed = true; 9566 break; 9567 case ICmpInst::ICMP_ULE: 9568 assert(!RA.isMaxValue() && "Should have been caught earlier!"); 9569 Pred = ICmpInst::ICMP_ULT; 9570 RHS = getConstant(RA + 1); 9571 Changed = true; 9572 break; 9573 case ICmpInst::ICMP_SGE: 9574 assert(!RA.isMinSignedValue() && "Should have been caught earlier!"); 9575 Pred = ICmpInst::ICMP_SGT; 9576 RHS = getConstant(RA - 1); 9577 Changed = true; 9578 break; 9579 case ICmpInst::ICMP_SLE: 9580 assert(!RA.isMaxSignedValue() && "Should have been caught earlier!"); 9581 Pred = ICmpInst::ICMP_SLT; 9582 RHS = getConstant(RA + 1); 9583 Changed = true; 9584 break; 9585 } 9586 } 9587 } 9588 9589 // Check for obvious equality. 9590 if (HasSameValue(LHS, RHS)) { 9591 if (ICmpInst::isTrueWhenEqual(Pred)) 9592 return TrivialCase(true); 9593 if (ICmpInst::isFalseWhenEqual(Pred)) 9594 return TrivialCase(false); 9595 } 9596 9597 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by 9598 // adding or subtracting 1 from one of the operands. 9599 switch (Pred) { 9600 case ICmpInst::ICMP_SLE: 9601 if (!getSignedRangeMax(RHS).isMaxSignedValue()) { 9602 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 9603 SCEV::FlagNSW); 9604 Pred = ICmpInst::ICMP_SLT; 9605 Changed = true; 9606 } else if (!getSignedRangeMin(LHS).isMinSignedValue()) { 9607 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 9608 SCEV::FlagNSW); 9609 Pred = ICmpInst::ICMP_SLT; 9610 Changed = true; 9611 } 9612 break; 9613 case ICmpInst::ICMP_SGE: 9614 if (!getSignedRangeMin(RHS).isMinSignedValue()) { 9615 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 9616 SCEV::FlagNSW); 9617 Pred = ICmpInst::ICMP_SGT; 9618 Changed = true; 9619 } else if (!getSignedRangeMax(LHS).isMaxSignedValue()) { 9620 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 9621 SCEV::FlagNSW); 9622 Pred = ICmpInst::ICMP_SGT; 9623 Changed = true; 9624 } 9625 break; 9626 case ICmpInst::ICMP_ULE: 9627 if (!getUnsignedRangeMax(RHS).isMaxValue()) { 9628 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 9629 SCEV::FlagNUW); 9630 Pred = ICmpInst::ICMP_ULT; 9631 Changed = true; 9632 } else if (!getUnsignedRangeMin(LHS).isMinValue()) { 9633 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS); 9634 Pred = ICmpInst::ICMP_ULT; 9635 Changed = true; 9636 } 9637 break; 9638 case ICmpInst::ICMP_UGE: 9639 if (!getUnsignedRangeMin(RHS).isMinValue()) { 9640 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS); 9641 Pred = ICmpInst::ICMP_UGT; 9642 Changed = true; 9643 } else if (!getUnsignedRangeMax(LHS).isMaxValue()) { 9644 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 9645 SCEV::FlagNUW); 9646 Pred = ICmpInst::ICMP_UGT; 9647 Changed = true; 9648 } 9649 break; 9650 default: 9651 break; 9652 } 9653 9654 // TODO: More simplifications are possible here. 9655 9656 // Recursively simplify until we either hit a recursion limit or nothing 9657 // changes. 9658 if (Changed) 9659 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1); 9660 9661 return Changed; 9662 } 9663 9664 bool ScalarEvolution::isKnownNegative(const SCEV *S) { 9665 return getSignedRangeMax(S).isNegative(); 9666 } 9667 9668 bool ScalarEvolution::isKnownPositive(const SCEV *S) { 9669 return getSignedRangeMin(S).isStrictlyPositive(); 9670 } 9671 9672 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 9673 return !getSignedRangeMin(S).isNegative(); 9674 } 9675 9676 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 9677 return !getSignedRangeMax(S).isStrictlyPositive(); 9678 } 9679 9680 bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 9681 return isKnownNegative(S) || isKnownPositive(S); 9682 } 9683 9684 std::pair<const SCEV *, const SCEV *> 9685 ScalarEvolution::SplitIntoInitAndPostInc(const Loop *L, const SCEV *S) { 9686 // Compute SCEV on entry of loop L. 9687 const SCEV *Start = SCEVInitRewriter::rewrite(S, L, *this); 9688 if (Start == getCouldNotCompute()) 9689 return { Start, Start }; 9690 // Compute post increment SCEV for loop L. 9691 const SCEV *PostInc = SCEVPostIncRewriter::rewrite(S, L, *this); 9692 assert(PostInc != getCouldNotCompute() && "Unexpected could not compute"); 9693 return { Start, PostInc }; 9694 } 9695 9696 bool ScalarEvolution::isKnownViaInduction(ICmpInst::Predicate Pred, 9697 const SCEV *LHS, const SCEV *RHS) { 9698 // First collect all loops. 9699 SmallPtrSet<const Loop *, 8> LoopsUsed; 9700 getUsedLoops(LHS, LoopsUsed); 9701 getUsedLoops(RHS, LoopsUsed); 9702 9703 if (LoopsUsed.empty()) 9704 return false; 9705 9706 // Domination relationship must be a linear order on collected loops. 9707 #ifndef NDEBUG 9708 for (auto *L1 : LoopsUsed) 9709 for (auto *L2 : LoopsUsed) 9710 assert((DT.dominates(L1->getHeader(), L2->getHeader()) || 9711 DT.dominates(L2->getHeader(), L1->getHeader())) && 9712 "Domination relationship is not a linear order"); 9713 #endif 9714 9715 const Loop *MDL = 9716 *std::max_element(LoopsUsed.begin(), LoopsUsed.end(), 9717 [&](const Loop *L1, const Loop *L2) { 9718 return DT.properlyDominates(L1->getHeader(), L2->getHeader()); 9719 }); 9720 9721 // Get init and post increment value for LHS. 9722 auto SplitLHS = SplitIntoInitAndPostInc(MDL, LHS); 9723 // if LHS contains unknown non-invariant SCEV then bail out. 9724 if (SplitLHS.first == getCouldNotCompute()) 9725 return false; 9726 assert (SplitLHS.second != getCouldNotCompute() && "Unexpected CNC"); 9727 // Get init and post increment value for RHS. 9728 auto SplitRHS = SplitIntoInitAndPostInc(MDL, RHS); 9729 // if RHS contains unknown non-invariant SCEV then bail out. 9730 if (SplitRHS.first == getCouldNotCompute()) 9731 return false; 9732 assert (SplitRHS.second != getCouldNotCompute() && "Unexpected CNC"); 9733 // It is possible that init SCEV contains an invariant load but it does 9734 // not dominate MDL and is not available at MDL loop entry, so we should 9735 // check it here. 9736 if (!isAvailableAtLoopEntry(SplitLHS.first, MDL) || 9737 !isAvailableAtLoopEntry(SplitRHS.first, MDL)) 9738 return false; 9739 9740 // It seems backedge guard check is faster than entry one so in some cases 9741 // it can speed up whole estimation by short circuit 9742 return isLoopBackedgeGuardedByCond(MDL, Pred, SplitLHS.second, 9743 SplitRHS.second) && 9744 isLoopEntryGuardedByCond(MDL, Pred, SplitLHS.first, SplitRHS.first); 9745 } 9746 9747 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 9748 const SCEV *LHS, const SCEV *RHS) { 9749 // Canonicalize the inputs first. 9750 (void)SimplifyICmpOperands(Pred, LHS, RHS); 9751 9752 if (isKnownViaInduction(Pred, LHS, RHS)) 9753 return true; 9754 9755 if (isKnownPredicateViaSplitting(Pred, LHS, RHS)) 9756 return true; 9757 9758 // Otherwise see what can be done with some simple reasoning. 9759 return isKnownViaNonRecursiveReasoning(Pred, LHS, RHS); 9760 } 9761 9762 Optional<bool> ScalarEvolution::evaluatePredicate(ICmpInst::Predicate Pred, 9763 const SCEV *LHS, 9764 const SCEV *RHS) { 9765 if (isKnownPredicate(Pred, LHS, RHS)) 9766 return true; 9767 else if (isKnownPredicate(ICmpInst::getInversePredicate(Pred), LHS, RHS)) 9768 return false; 9769 return None; 9770 } 9771 9772 bool ScalarEvolution::isKnownPredicateAt(ICmpInst::Predicate Pred, 9773 const SCEV *LHS, const SCEV *RHS, 9774 const Instruction *Context) { 9775 // TODO: Analyze guards and assumes from Context's block. 9776 return isKnownPredicate(Pred, LHS, RHS) || 9777 isBasicBlockEntryGuardedByCond(Context->getParent(), Pred, LHS, RHS); 9778 } 9779 9780 Optional<bool> 9781 ScalarEvolution::evaluatePredicateAt(ICmpInst::Predicate Pred, const SCEV *LHS, 9782 const SCEV *RHS, 9783 const Instruction *Context) { 9784 Optional<bool> KnownWithoutContext = evaluatePredicate(Pred, LHS, RHS); 9785 if (KnownWithoutContext) 9786 return KnownWithoutContext; 9787 9788 if (isBasicBlockEntryGuardedByCond(Context->getParent(), Pred, LHS, RHS)) 9789 return true; 9790 else if (isBasicBlockEntryGuardedByCond(Context->getParent(), 9791 ICmpInst::getInversePredicate(Pred), 9792 LHS, RHS)) 9793 return false; 9794 return None; 9795 } 9796 9797 bool ScalarEvolution::isKnownOnEveryIteration(ICmpInst::Predicate Pred, 9798 const SCEVAddRecExpr *LHS, 9799 const SCEV *RHS) { 9800 const Loop *L = LHS->getLoop(); 9801 return isLoopEntryGuardedByCond(L, Pred, LHS->getStart(), RHS) && 9802 isLoopBackedgeGuardedByCond(L, Pred, LHS->getPostIncExpr(*this), RHS); 9803 } 9804 9805 Optional<ScalarEvolution::MonotonicPredicateType> 9806 ScalarEvolution::getMonotonicPredicateType(const SCEVAddRecExpr *LHS, 9807 ICmpInst::Predicate Pred) { 9808 auto Result = getMonotonicPredicateTypeImpl(LHS, Pred); 9809 9810 #ifndef NDEBUG 9811 // Verify an invariant: inverting the predicate should turn a monotonically 9812 // increasing change to a monotonically decreasing one, and vice versa. 9813 if (Result) { 9814 auto ResultSwapped = 9815 getMonotonicPredicateTypeImpl(LHS, ICmpInst::getSwappedPredicate(Pred)); 9816 9817 assert(ResultSwapped.hasValue() && "should be able to analyze both!"); 9818 assert(ResultSwapped.getValue() != Result.getValue() && 9819 "monotonicity should flip as we flip the predicate"); 9820 } 9821 #endif 9822 9823 return Result; 9824 } 9825 9826 Optional<ScalarEvolution::MonotonicPredicateType> 9827 ScalarEvolution::getMonotonicPredicateTypeImpl(const SCEVAddRecExpr *LHS, 9828 ICmpInst::Predicate Pred) { 9829 // A zero step value for LHS means the induction variable is essentially a 9830 // loop invariant value. We don't really depend on the predicate actually 9831 // flipping from false to true (for increasing predicates, and the other way 9832 // around for decreasing predicates), all we care about is that *if* the 9833 // predicate changes then it only changes from false to true. 9834 // 9835 // A zero step value in itself is not very useful, but there may be places 9836 // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be 9837 // as general as possible. 9838 9839 // Only handle LE/LT/GE/GT predicates. 9840 if (!ICmpInst::isRelational(Pred)) 9841 return None; 9842 9843 bool IsGreater = ICmpInst::isGE(Pred) || ICmpInst::isGT(Pred); 9844 assert((IsGreater || ICmpInst::isLE(Pred) || ICmpInst::isLT(Pred)) && 9845 "Should be greater or less!"); 9846 9847 // Check that AR does not wrap. 9848 if (ICmpInst::isUnsigned(Pred)) { 9849 if (!LHS->hasNoUnsignedWrap()) 9850 return None; 9851 return IsGreater ? MonotonicallyIncreasing : MonotonicallyDecreasing; 9852 } else { 9853 assert(ICmpInst::isSigned(Pred) && 9854 "Relational predicate is either signed or unsigned!"); 9855 if (!LHS->hasNoSignedWrap()) 9856 return None; 9857 9858 const SCEV *Step = LHS->getStepRecurrence(*this); 9859 9860 if (isKnownNonNegative(Step)) 9861 return IsGreater ? MonotonicallyIncreasing : MonotonicallyDecreasing; 9862 9863 if (isKnownNonPositive(Step)) 9864 return !IsGreater ? MonotonicallyIncreasing : MonotonicallyDecreasing; 9865 9866 return None; 9867 } 9868 } 9869 9870 Optional<ScalarEvolution::LoopInvariantPredicate> 9871 ScalarEvolution::getLoopInvariantPredicate(ICmpInst::Predicate Pred, 9872 const SCEV *LHS, const SCEV *RHS, 9873 const Loop *L) { 9874 9875 // If there is a loop-invariant, force it into the RHS, otherwise bail out. 9876 if (!isLoopInvariant(RHS, L)) { 9877 if (!isLoopInvariant(LHS, L)) 9878 return None; 9879 9880 std::swap(LHS, RHS); 9881 Pred = ICmpInst::getSwappedPredicate(Pred); 9882 } 9883 9884 const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS); 9885 if (!ArLHS || ArLHS->getLoop() != L) 9886 return None; 9887 9888 auto MonotonicType = getMonotonicPredicateType(ArLHS, Pred); 9889 if (!MonotonicType) 9890 return None; 9891 // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to 9892 // true as the loop iterates, and the backedge is control dependent on 9893 // "ArLHS `Pred` RHS" == true then we can reason as follows: 9894 // 9895 // * if the predicate was false in the first iteration then the predicate 9896 // is never evaluated again, since the loop exits without taking the 9897 // backedge. 9898 // * if the predicate was true in the first iteration then it will 9899 // continue to be true for all future iterations since it is 9900 // monotonically increasing. 9901 // 9902 // For both the above possibilities, we can replace the loop varying 9903 // predicate with its value on the first iteration of the loop (which is 9904 // loop invariant). 9905 // 9906 // A similar reasoning applies for a monotonically decreasing predicate, by 9907 // replacing true with false and false with true in the above two bullets. 9908 bool Increasing = *MonotonicType == ScalarEvolution::MonotonicallyIncreasing; 9909 auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred); 9910 9911 if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS)) 9912 return None; 9913 9914 return ScalarEvolution::LoopInvariantPredicate(Pred, ArLHS->getStart(), RHS); 9915 } 9916 9917 Optional<ScalarEvolution::LoopInvariantPredicate> 9918 ScalarEvolution::getLoopInvariantExitCondDuringFirstIterations( 9919 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L, 9920 const Instruction *Context, const SCEV *MaxIter) { 9921 // Try to prove the following set of facts: 9922 // - The predicate is monotonic in the iteration space. 9923 // - If the check does not fail on the 1st iteration: 9924 // - No overflow will happen during first MaxIter iterations; 9925 // - It will not fail on the MaxIter'th iteration. 9926 // If the check does fail on the 1st iteration, we leave the loop and no 9927 // other checks matter. 9928 9929 // If there is a loop-invariant, force it into the RHS, otherwise bail out. 9930 if (!isLoopInvariant(RHS, L)) { 9931 if (!isLoopInvariant(LHS, L)) 9932 return None; 9933 9934 std::swap(LHS, RHS); 9935 Pred = ICmpInst::getSwappedPredicate(Pred); 9936 } 9937 9938 auto *AR = dyn_cast<SCEVAddRecExpr>(LHS); 9939 if (!AR || AR->getLoop() != L) 9940 return None; 9941 9942 // The predicate must be relational (i.e. <, <=, >=, >). 9943 if (!ICmpInst::isRelational(Pred)) 9944 return None; 9945 9946 // TODO: Support steps other than +/- 1. 9947 const SCEV *Step = AR->getStepRecurrence(*this); 9948 auto *One = getOne(Step->getType()); 9949 auto *MinusOne = getNegativeSCEV(One); 9950 if (Step != One && Step != MinusOne) 9951 return None; 9952 9953 // Type mismatch here means that MaxIter is potentially larger than max 9954 // unsigned value in start type, which mean we cannot prove no wrap for the 9955 // indvar. 9956 if (AR->getType() != MaxIter->getType()) 9957 return None; 9958 9959 // Value of IV on suggested last iteration. 9960 const SCEV *Last = AR->evaluateAtIteration(MaxIter, *this); 9961 // Does it still meet the requirement? 9962 if (!isLoopBackedgeGuardedByCond(L, Pred, Last, RHS)) 9963 return None; 9964 // Because step is +/- 1 and MaxIter has same type as Start (i.e. it does 9965 // not exceed max unsigned value of this type), this effectively proves 9966 // that there is no wrap during the iteration. To prove that there is no 9967 // signed/unsigned wrap, we need to check that 9968 // Start <= Last for step = 1 or Start >= Last for step = -1. 9969 ICmpInst::Predicate NoOverflowPred = 9970 CmpInst::isSigned(Pred) ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE; 9971 if (Step == MinusOne) 9972 NoOverflowPred = CmpInst::getSwappedPredicate(NoOverflowPred); 9973 const SCEV *Start = AR->getStart(); 9974 if (!isKnownPredicateAt(NoOverflowPred, Start, Last, Context)) 9975 return None; 9976 9977 // Everything is fine. 9978 return ScalarEvolution::LoopInvariantPredicate(Pred, Start, RHS); 9979 } 9980 9981 bool ScalarEvolution::isKnownPredicateViaConstantRanges( 9982 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) { 9983 if (HasSameValue(LHS, RHS)) 9984 return ICmpInst::isTrueWhenEqual(Pred); 9985 9986 // This code is split out from isKnownPredicate because it is called from 9987 // within isLoopEntryGuardedByCond. 9988 9989 auto CheckRanges = [&](const ConstantRange &RangeLHS, 9990 const ConstantRange &RangeRHS) { 9991 return RangeLHS.icmp(Pred, RangeRHS); 9992 }; 9993 9994 // The check at the top of the function catches the case where the values are 9995 // known to be equal. 9996 if (Pred == CmpInst::ICMP_EQ) 9997 return false; 9998 9999 if (Pred == CmpInst::ICMP_NE) 10000 return CheckRanges(getSignedRange(LHS), getSignedRange(RHS)) || 10001 CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS)) || 10002 isKnownNonZero(getMinusSCEV(LHS, RHS)); 10003 10004 if (CmpInst::isSigned(Pred)) 10005 return CheckRanges(getSignedRange(LHS), getSignedRange(RHS)); 10006 10007 return CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS)); 10008 } 10009 10010 bool ScalarEvolution::isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred, 10011 const SCEV *LHS, 10012 const SCEV *RHS) { 10013 // Match Result to (X + Y)<ExpectedFlags> where Y is a constant integer. 10014 // Return Y via OutY. 10015 auto MatchBinaryAddToConst = 10016 [this](const SCEV *Result, const SCEV *X, APInt &OutY, 10017 SCEV::NoWrapFlags ExpectedFlags) { 10018 const SCEV *NonConstOp, *ConstOp; 10019 SCEV::NoWrapFlags FlagsPresent; 10020 10021 if (!splitBinaryAdd(Result, ConstOp, NonConstOp, FlagsPresent) || 10022 !isa<SCEVConstant>(ConstOp) || NonConstOp != X) 10023 return false; 10024 10025 OutY = cast<SCEVConstant>(ConstOp)->getAPInt(); 10026 return (FlagsPresent & ExpectedFlags) == ExpectedFlags; 10027 }; 10028 10029 APInt C; 10030 10031 switch (Pred) { 10032 default: 10033 break; 10034 10035 case ICmpInst::ICMP_SGE: 10036 std::swap(LHS, RHS); 10037 LLVM_FALLTHROUGH; 10038 case ICmpInst::ICMP_SLE: 10039 // X s<= (X + C)<nsw> if C >= 0 10040 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) && C.isNonNegative()) 10041 return true; 10042 10043 // (X + C)<nsw> s<= X if C <= 0 10044 if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) && 10045 !C.isStrictlyPositive()) 10046 return true; 10047 break; 10048 10049 case ICmpInst::ICMP_SGT: 10050 std::swap(LHS, RHS); 10051 LLVM_FALLTHROUGH; 10052 case ICmpInst::ICMP_SLT: 10053 // X s< (X + C)<nsw> if C > 0 10054 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) && 10055 C.isStrictlyPositive()) 10056 return true; 10057 10058 // (X + C)<nsw> s< X if C < 0 10059 if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) && C.isNegative()) 10060 return true; 10061 break; 10062 10063 case ICmpInst::ICMP_UGE: 10064 std::swap(LHS, RHS); 10065 LLVM_FALLTHROUGH; 10066 case ICmpInst::ICMP_ULE: 10067 // X u<= (X + C)<nuw> for any C 10068 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNUW)) 10069 return true; 10070 break; 10071 10072 case ICmpInst::ICMP_UGT: 10073 std::swap(LHS, RHS); 10074 LLVM_FALLTHROUGH; 10075 case ICmpInst::ICMP_ULT: 10076 // X u< (X + C)<nuw> if C != 0 10077 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNUW) && !C.isNullValue()) 10078 return true; 10079 break; 10080 } 10081 10082 return false; 10083 } 10084 10085 bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred, 10086 const SCEV *LHS, 10087 const SCEV *RHS) { 10088 if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate) 10089 return false; 10090 10091 // Allowing arbitrary number of activations of isKnownPredicateViaSplitting on 10092 // the stack can result in exponential time complexity. 10093 SaveAndRestore<bool> Restore(ProvingSplitPredicate, true); 10094 10095 // If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L 10096 // 10097 // To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use 10098 // isKnownPredicate. isKnownPredicate is more powerful, but also more 10099 // expensive; and using isKnownNonNegative(RHS) is sufficient for most of the 10100 // interesting cases seen in practice. We can consider "upgrading" L >= 0 to 10101 // use isKnownPredicate later if needed. 10102 return isKnownNonNegative(RHS) && 10103 isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) && 10104 isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS); 10105 } 10106 10107 bool ScalarEvolution::isImpliedViaGuard(const BasicBlock *BB, 10108 ICmpInst::Predicate Pred, 10109 const SCEV *LHS, const SCEV *RHS) { 10110 // No need to even try if we know the module has no guards. 10111 if (!HasGuards) 10112 return false; 10113 10114 return any_of(*BB, [&](const Instruction &I) { 10115 using namespace llvm::PatternMatch; 10116 10117 Value *Condition; 10118 return match(&I, m_Intrinsic<Intrinsic::experimental_guard>( 10119 m_Value(Condition))) && 10120 isImpliedCond(Pred, LHS, RHS, Condition, false); 10121 }); 10122 } 10123 10124 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 10125 /// protected by a conditional between LHS and RHS. This is used to 10126 /// to eliminate casts. 10127 bool 10128 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 10129 ICmpInst::Predicate Pred, 10130 const SCEV *LHS, const SCEV *RHS) { 10131 // Interpret a null as meaning no loop, where there is obviously no guard 10132 // (interprocedural conditions notwithstanding). 10133 if (!L) return true; 10134 10135 if (VerifyIR) 10136 assert(!verifyFunction(*L->getHeader()->getParent(), &dbgs()) && 10137 "This cannot be done on broken IR!"); 10138 10139 10140 if (isKnownViaNonRecursiveReasoning(Pred, LHS, RHS)) 10141 return true; 10142 10143 BasicBlock *Latch = L->getLoopLatch(); 10144 if (!Latch) 10145 return false; 10146 10147 BranchInst *LoopContinuePredicate = 10148 dyn_cast<BranchInst>(Latch->getTerminator()); 10149 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() && 10150 isImpliedCond(Pred, LHS, RHS, 10151 LoopContinuePredicate->getCondition(), 10152 LoopContinuePredicate->getSuccessor(0) != L->getHeader())) 10153 return true; 10154 10155 // We don't want more than one activation of the following loops on the stack 10156 // -- that can lead to O(n!) time complexity. 10157 if (WalkingBEDominatingConds) 10158 return false; 10159 10160 SaveAndRestore<bool> ClearOnExit(WalkingBEDominatingConds, true); 10161 10162 // See if we can exploit a trip count to prove the predicate. 10163 const auto &BETakenInfo = getBackedgeTakenInfo(L); 10164 const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this); 10165 if (LatchBECount != getCouldNotCompute()) { 10166 // We know that Latch branches back to the loop header exactly 10167 // LatchBECount times. This means the backdege condition at Latch is 10168 // equivalent to "{0,+,1} u< LatchBECount". 10169 Type *Ty = LatchBECount->getType(); 10170 auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW); 10171 const SCEV *LoopCounter = 10172 getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags); 10173 if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter, 10174 LatchBECount)) 10175 return true; 10176 } 10177 10178 // Check conditions due to any @llvm.assume intrinsics. 10179 for (auto &AssumeVH : AC.assumptions()) { 10180 if (!AssumeVH) 10181 continue; 10182 auto *CI = cast<CallInst>(AssumeVH); 10183 if (!DT.dominates(CI, Latch->getTerminator())) 10184 continue; 10185 10186 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false)) 10187 return true; 10188 } 10189 10190 // If the loop is not reachable from the entry block, we risk running into an 10191 // infinite loop as we walk up into the dom tree. These loops do not matter 10192 // anyway, so we just return a conservative answer when we see them. 10193 if (!DT.isReachableFromEntry(L->getHeader())) 10194 return false; 10195 10196 if (isImpliedViaGuard(Latch, Pred, LHS, RHS)) 10197 return true; 10198 10199 for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()]; 10200 DTN != HeaderDTN; DTN = DTN->getIDom()) { 10201 assert(DTN && "should reach the loop header before reaching the root!"); 10202 10203 BasicBlock *BB = DTN->getBlock(); 10204 if (isImpliedViaGuard(BB, Pred, LHS, RHS)) 10205 return true; 10206 10207 BasicBlock *PBB = BB->getSinglePredecessor(); 10208 if (!PBB) 10209 continue; 10210 10211 BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator()); 10212 if (!ContinuePredicate || !ContinuePredicate->isConditional()) 10213 continue; 10214 10215 Value *Condition = ContinuePredicate->getCondition(); 10216 10217 // If we have an edge `E` within the loop body that dominates the only 10218 // latch, the condition guarding `E` also guards the backedge. This 10219 // reasoning works only for loops with a single latch. 10220 10221 BasicBlockEdge DominatingEdge(PBB, BB); 10222 if (DominatingEdge.isSingleEdge()) { 10223 // We're constructively (and conservatively) enumerating edges within the 10224 // loop body that dominate the latch. The dominator tree better agree 10225 // with us on this: 10226 assert(DT.dominates(DominatingEdge, Latch) && "should be!"); 10227 10228 if (isImpliedCond(Pred, LHS, RHS, Condition, 10229 BB != ContinuePredicate->getSuccessor(0))) 10230 return true; 10231 } 10232 } 10233 10234 return false; 10235 } 10236 10237 bool ScalarEvolution::isBasicBlockEntryGuardedByCond(const BasicBlock *BB, 10238 ICmpInst::Predicate Pred, 10239 const SCEV *LHS, 10240 const SCEV *RHS) { 10241 if (VerifyIR) 10242 assert(!verifyFunction(*BB->getParent(), &dbgs()) && 10243 "This cannot be done on broken IR!"); 10244 10245 // If we cannot prove strict comparison (e.g. a > b), maybe we can prove 10246 // the facts (a >= b && a != b) separately. A typical situation is when the 10247 // non-strict comparison is known from ranges and non-equality is known from 10248 // dominating predicates. If we are proving strict comparison, we always try 10249 // to prove non-equality and non-strict comparison separately. 10250 auto NonStrictPredicate = ICmpInst::getNonStrictPredicate(Pred); 10251 const bool ProvingStrictComparison = (Pred != NonStrictPredicate); 10252 bool ProvedNonStrictComparison = false; 10253 bool ProvedNonEquality = false; 10254 10255 auto SplitAndProve = 10256 [&](std::function<bool(ICmpInst::Predicate)> Fn) -> bool { 10257 if (!ProvedNonStrictComparison) 10258 ProvedNonStrictComparison = Fn(NonStrictPredicate); 10259 if (!ProvedNonEquality) 10260 ProvedNonEquality = Fn(ICmpInst::ICMP_NE); 10261 if (ProvedNonStrictComparison && ProvedNonEquality) 10262 return true; 10263 return false; 10264 }; 10265 10266 if (ProvingStrictComparison) { 10267 auto ProofFn = [&](ICmpInst::Predicate P) { 10268 return isKnownViaNonRecursiveReasoning(P, LHS, RHS); 10269 }; 10270 if (SplitAndProve(ProofFn)) 10271 return true; 10272 } 10273 10274 // Try to prove (Pred, LHS, RHS) using isImpliedViaGuard. 10275 auto ProveViaGuard = [&](const BasicBlock *Block) { 10276 if (isImpliedViaGuard(Block, Pred, LHS, RHS)) 10277 return true; 10278 if (ProvingStrictComparison) { 10279 auto ProofFn = [&](ICmpInst::Predicate P) { 10280 return isImpliedViaGuard(Block, P, LHS, RHS); 10281 }; 10282 if (SplitAndProve(ProofFn)) 10283 return true; 10284 } 10285 return false; 10286 }; 10287 10288 // Try to prove (Pred, LHS, RHS) using isImpliedCond. 10289 auto ProveViaCond = [&](const Value *Condition, bool Inverse) { 10290 const Instruction *Context = &BB->front(); 10291 if (isImpliedCond(Pred, LHS, RHS, Condition, Inverse, Context)) 10292 return true; 10293 if (ProvingStrictComparison) { 10294 auto ProofFn = [&](ICmpInst::Predicate P) { 10295 return isImpliedCond(P, LHS, RHS, Condition, Inverse, Context); 10296 }; 10297 if (SplitAndProve(ProofFn)) 10298 return true; 10299 } 10300 return false; 10301 }; 10302 10303 // Starting at the block's predecessor, climb up the predecessor chain, as long 10304 // as there are predecessors that can be found that have unique successors 10305 // leading to the original block. 10306 const Loop *ContainingLoop = LI.getLoopFor(BB); 10307 const BasicBlock *PredBB; 10308 if (ContainingLoop && ContainingLoop->getHeader() == BB) 10309 PredBB = ContainingLoop->getLoopPredecessor(); 10310 else 10311 PredBB = BB->getSinglePredecessor(); 10312 for (std::pair<const BasicBlock *, const BasicBlock *> Pair(PredBB, BB); 10313 Pair.first; Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { 10314 if (ProveViaGuard(Pair.first)) 10315 return true; 10316 10317 const BranchInst *LoopEntryPredicate = 10318 dyn_cast<BranchInst>(Pair.first->getTerminator()); 10319 if (!LoopEntryPredicate || 10320 LoopEntryPredicate->isUnconditional()) 10321 continue; 10322 10323 if (ProveViaCond(LoopEntryPredicate->getCondition(), 10324 LoopEntryPredicate->getSuccessor(0) != Pair.second)) 10325 return true; 10326 } 10327 10328 // Check conditions due to any @llvm.assume intrinsics. 10329 for (auto &AssumeVH : AC.assumptions()) { 10330 if (!AssumeVH) 10331 continue; 10332 auto *CI = cast<CallInst>(AssumeVH); 10333 if (!DT.dominates(CI, BB)) 10334 continue; 10335 10336 if (ProveViaCond(CI->getArgOperand(0), false)) 10337 return true; 10338 } 10339 10340 return false; 10341 } 10342 10343 bool ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L, 10344 ICmpInst::Predicate Pred, 10345 const SCEV *LHS, 10346 const SCEV *RHS) { 10347 // Interpret a null as meaning no loop, where there is obviously no guard 10348 // (interprocedural conditions notwithstanding). 10349 if (!L) 10350 return false; 10351 10352 // Both LHS and RHS must be available at loop entry. 10353 assert(isAvailableAtLoopEntry(LHS, L) && 10354 "LHS is not available at Loop Entry"); 10355 assert(isAvailableAtLoopEntry(RHS, L) && 10356 "RHS is not available at Loop Entry"); 10357 10358 if (isKnownViaNonRecursiveReasoning(Pred, LHS, RHS)) 10359 return true; 10360 10361 return isBasicBlockEntryGuardedByCond(L->getHeader(), Pred, LHS, RHS); 10362 } 10363 10364 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS, 10365 const SCEV *RHS, 10366 const Value *FoundCondValue, bool Inverse, 10367 const Instruction *Context) { 10368 // False conditions implies anything. Do not bother analyzing it further. 10369 if (FoundCondValue == 10370 ConstantInt::getBool(FoundCondValue->getContext(), Inverse)) 10371 return true; 10372 10373 if (!PendingLoopPredicates.insert(FoundCondValue).second) 10374 return false; 10375 10376 auto ClearOnExit = 10377 make_scope_exit([&]() { PendingLoopPredicates.erase(FoundCondValue); }); 10378 10379 // Recursively handle And and Or conditions. 10380 const Value *Op0, *Op1; 10381 if (match(FoundCondValue, m_LogicalAnd(m_Value(Op0), m_Value(Op1)))) { 10382 if (!Inverse) 10383 return isImpliedCond(Pred, LHS, RHS, Op0, Inverse, Context) || 10384 isImpliedCond(Pred, LHS, RHS, Op1, Inverse, Context); 10385 } else if (match(FoundCondValue, m_LogicalOr(m_Value(Op0), m_Value(Op1)))) { 10386 if (Inverse) 10387 return isImpliedCond(Pred, LHS, RHS, Op0, Inverse, Context) || 10388 isImpliedCond(Pred, LHS, RHS, Op1, Inverse, Context); 10389 } 10390 10391 const ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue); 10392 if (!ICI) return false; 10393 10394 // Now that we found a conditional branch that dominates the loop or controls 10395 // the loop latch. Check to see if it is the comparison we are looking for. 10396 ICmpInst::Predicate FoundPred; 10397 if (Inverse) 10398 FoundPred = ICI->getInversePredicate(); 10399 else 10400 FoundPred = ICI->getPredicate(); 10401 10402 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 10403 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 10404 10405 return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS, Context); 10406 } 10407 10408 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS, 10409 const SCEV *RHS, 10410 ICmpInst::Predicate FoundPred, 10411 const SCEV *FoundLHS, const SCEV *FoundRHS, 10412 const Instruction *Context) { 10413 // Balance the types. 10414 if (getTypeSizeInBits(LHS->getType()) < 10415 getTypeSizeInBits(FoundLHS->getType())) { 10416 // For unsigned and equality predicates, try to prove that both found 10417 // operands fit into narrow unsigned range. If so, try to prove facts in 10418 // narrow types. 10419 if (!CmpInst::isSigned(FoundPred)) { 10420 auto *NarrowType = LHS->getType(); 10421 auto *WideType = FoundLHS->getType(); 10422 auto BitWidth = getTypeSizeInBits(NarrowType); 10423 const SCEV *MaxValue = getZeroExtendExpr( 10424 getConstant(APInt::getMaxValue(BitWidth)), WideType); 10425 if (isKnownPredicate(ICmpInst::ICMP_ULE, FoundLHS, MaxValue) && 10426 isKnownPredicate(ICmpInst::ICMP_ULE, FoundRHS, MaxValue)) { 10427 const SCEV *TruncFoundLHS = getTruncateExpr(FoundLHS, NarrowType); 10428 const SCEV *TruncFoundRHS = getTruncateExpr(FoundRHS, NarrowType); 10429 if (isImpliedCondBalancedTypes(Pred, LHS, RHS, FoundPred, TruncFoundLHS, 10430 TruncFoundRHS, Context)) 10431 return true; 10432 } 10433 } 10434 10435 if (CmpInst::isSigned(Pred)) { 10436 LHS = getSignExtendExpr(LHS, FoundLHS->getType()); 10437 RHS = getSignExtendExpr(RHS, FoundLHS->getType()); 10438 } else { 10439 LHS = getZeroExtendExpr(LHS, FoundLHS->getType()); 10440 RHS = getZeroExtendExpr(RHS, FoundLHS->getType()); 10441 } 10442 } else if (getTypeSizeInBits(LHS->getType()) > 10443 getTypeSizeInBits(FoundLHS->getType())) { 10444 if (CmpInst::isSigned(FoundPred)) { 10445 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 10446 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 10447 } else { 10448 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 10449 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 10450 } 10451 } 10452 return isImpliedCondBalancedTypes(Pred, LHS, RHS, FoundPred, FoundLHS, 10453 FoundRHS, Context); 10454 } 10455 10456 bool ScalarEvolution::isImpliedCondBalancedTypes( 10457 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, 10458 ICmpInst::Predicate FoundPred, const SCEV *FoundLHS, const SCEV *FoundRHS, 10459 const Instruction *Context) { 10460 assert(getTypeSizeInBits(LHS->getType()) == 10461 getTypeSizeInBits(FoundLHS->getType()) && 10462 "Types should be balanced!"); 10463 // Canonicalize the query to match the way instcombine will have 10464 // canonicalized the comparison. 10465 if (SimplifyICmpOperands(Pred, LHS, RHS)) 10466 if (LHS == RHS) 10467 return CmpInst::isTrueWhenEqual(Pred); 10468 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS)) 10469 if (FoundLHS == FoundRHS) 10470 return CmpInst::isFalseWhenEqual(FoundPred); 10471 10472 // Check to see if we can make the LHS or RHS match. 10473 if (LHS == FoundRHS || RHS == FoundLHS) { 10474 if (isa<SCEVConstant>(RHS)) { 10475 std::swap(FoundLHS, FoundRHS); 10476 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 10477 } else { 10478 std::swap(LHS, RHS); 10479 Pred = ICmpInst::getSwappedPredicate(Pred); 10480 } 10481 } 10482 10483 // Check whether the found predicate is the same as the desired predicate. 10484 if (FoundPred == Pred) 10485 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS, Context); 10486 10487 // Check whether swapping the found predicate makes it the same as the 10488 // desired predicate. 10489 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 10490 // We can write the implication 10491 // 0. LHS Pred RHS <- FoundLHS SwapPred FoundRHS 10492 // using one of the following ways: 10493 // 1. LHS Pred RHS <- FoundRHS Pred FoundLHS 10494 // 2. RHS SwapPred LHS <- FoundLHS SwapPred FoundRHS 10495 // 3. LHS Pred RHS <- ~FoundLHS Pred ~FoundRHS 10496 // 4. ~LHS SwapPred ~RHS <- FoundLHS SwapPred FoundRHS 10497 // Forms 1. and 2. require swapping the operands of one condition. Don't 10498 // do this if it would break canonical constant/addrec ordering. 10499 if (!isa<SCEVConstant>(RHS) && !isa<SCEVAddRecExpr>(LHS)) 10500 return isImpliedCondOperands(FoundPred, RHS, LHS, FoundLHS, FoundRHS, 10501 Context); 10502 if (!isa<SCEVConstant>(FoundRHS) && !isa<SCEVAddRecExpr>(FoundLHS)) 10503 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS, Context); 10504 10505 // There's no clear preference between forms 3. and 4., try both. 10506 return isImpliedCondOperands(FoundPred, getNotSCEV(LHS), getNotSCEV(RHS), 10507 FoundLHS, FoundRHS, Context) || 10508 isImpliedCondOperands(Pred, LHS, RHS, getNotSCEV(FoundLHS), 10509 getNotSCEV(FoundRHS), Context); 10510 } 10511 10512 // Unsigned comparison is the same as signed comparison when both the operands 10513 // are non-negative. 10514 if (CmpInst::isUnsigned(FoundPred) && 10515 CmpInst::getSignedPredicate(FoundPred) == Pred && 10516 isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS)) 10517 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS, Context); 10518 10519 // Check if we can make progress by sharpening ranges. 10520 if (FoundPred == ICmpInst::ICMP_NE && 10521 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) { 10522 10523 const SCEVConstant *C = nullptr; 10524 const SCEV *V = nullptr; 10525 10526 if (isa<SCEVConstant>(FoundLHS)) { 10527 C = cast<SCEVConstant>(FoundLHS); 10528 V = FoundRHS; 10529 } else { 10530 C = cast<SCEVConstant>(FoundRHS); 10531 V = FoundLHS; 10532 } 10533 10534 // The guarding predicate tells us that C != V. If the known range 10535 // of V is [C, t), we can sharpen the range to [C + 1, t). The 10536 // range we consider has to correspond to same signedness as the 10537 // predicate we're interested in folding. 10538 10539 APInt Min = ICmpInst::isSigned(Pred) ? 10540 getSignedRangeMin(V) : getUnsignedRangeMin(V); 10541 10542 if (Min == C->getAPInt()) { 10543 // Given (V >= Min && V != Min) we conclude V >= (Min + 1). 10544 // This is true even if (Min + 1) wraps around -- in case of 10545 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)). 10546 10547 APInt SharperMin = Min + 1; 10548 10549 switch (Pred) { 10550 case ICmpInst::ICMP_SGE: 10551 case ICmpInst::ICMP_UGE: 10552 // We know V `Pred` SharperMin. If this implies LHS `Pred` 10553 // RHS, we're done. 10554 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(SharperMin), 10555 Context)) 10556 return true; 10557 LLVM_FALLTHROUGH; 10558 10559 case ICmpInst::ICMP_SGT: 10560 case ICmpInst::ICMP_UGT: 10561 // We know from the range information that (V `Pred` Min || 10562 // V == Min). We know from the guarding condition that !(V 10563 // == Min). This gives us 10564 // 10565 // V `Pred` Min || V == Min && !(V == Min) 10566 // => V `Pred` Min 10567 // 10568 // If V `Pred` Min implies LHS `Pred` RHS, we're done. 10569 10570 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min), 10571 Context)) 10572 return true; 10573 break; 10574 10575 // `LHS < RHS` and `LHS <= RHS` are handled in the same way as `RHS > LHS` and `RHS >= LHS` respectively. 10576 case ICmpInst::ICMP_SLE: 10577 case ICmpInst::ICMP_ULE: 10578 if (isImpliedCondOperands(CmpInst::getSwappedPredicate(Pred), RHS, 10579 LHS, V, getConstant(SharperMin), Context)) 10580 return true; 10581 LLVM_FALLTHROUGH; 10582 10583 case ICmpInst::ICMP_SLT: 10584 case ICmpInst::ICMP_ULT: 10585 if (isImpliedCondOperands(CmpInst::getSwappedPredicate(Pred), RHS, 10586 LHS, V, getConstant(Min), Context)) 10587 return true; 10588 break; 10589 10590 default: 10591 // No change 10592 break; 10593 } 10594 } 10595 } 10596 10597 // Check whether the actual condition is beyond sufficient. 10598 if (FoundPred == ICmpInst::ICMP_EQ) 10599 if (ICmpInst::isTrueWhenEqual(Pred)) 10600 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS, Context)) 10601 return true; 10602 if (Pred == ICmpInst::ICMP_NE) 10603 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 10604 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS, 10605 Context)) 10606 return true; 10607 10608 // Otherwise assume the worst. 10609 return false; 10610 } 10611 10612 bool ScalarEvolution::splitBinaryAdd(const SCEV *Expr, 10613 const SCEV *&L, const SCEV *&R, 10614 SCEV::NoWrapFlags &Flags) { 10615 const auto *AE = dyn_cast<SCEVAddExpr>(Expr); 10616 if (!AE || AE->getNumOperands() != 2) 10617 return false; 10618 10619 L = AE->getOperand(0); 10620 R = AE->getOperand(1); 10621 Flags = AE->getNoWrapFlags(); 10622 return true; 10623 } 10624 10625 Optional<APInt> ScalarEvolution::computeConstantDifference(const SCEV *More, 10626 const SCEV *Less) { 10627 // We avoid subtracting expressions here because this function is usually 10628 // fairly deep in the call stack (i.e. is called many times). 10629 10630 // X - X = 0. 10631 if (More == Less) 10632 return APInt(getTypeSizeInBits(More->getType()), 0); 10633 10634 if (isa<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) { 10635 const auto *LAR = cast<SCEVAddRecExpr>(Less); 10636 const auto *MAR = cast<SCEVAddRecExpr>(More); 10637 10638 if (LAR->getLoop() != MAR->getLoop()) 10639 return None; 10640 10641 // We look at affine expressions only; not for correctness but to keep 10642 // getStepRecurrence cheap. 10643 if (!LAR->isAffine() || !MAR->isAffine()) 10644 return None; 10645 10646 if (LAR->getStepRecurrence(*this) != MAR->getStepRecurrence(*this)) 10647 return None; 10648 10649 Less = LAR->getStart(); 10650 More = MAR->getStart(); 10651 10652 // fall through 10653 } 10654 10655 if (isa<SCEVConstant>(Less) && isa<SCEVConstant>(More)) { 10656 const auto &M = cast<SCEVConstant>(More)->getAPInt(); 10657 const auto &L = cast<SCEVConstant>(Less)->getAPInt(); 10658 return M - L; 10659 } 10660 10661 SCEV::NoWrapFlags Flags; 10662 const SCEV *LLess = nullptr, *RLess = nullptr; 10663 const SCEV *LMore = nullptr, *RMore = nullptr; 10664 const SCEVConstant *C1 = nullptr, *C2 = nullptr; 10665 // Compare (X + C1) vs X. 10666 if (splitBinaryAdd(Less, LLess, RLess, Flags)) 10667 if ((C1 = dyn_cast<SCEVConstant>(LLess))) 10668 if (RLess == More) 10669 return -(C1->getAPInt()); 10670 10671 // Compare X vs (X + C2). 10672 if (splitBinaryAdd(More, LMore, RMore, Flags)) 10673 if ((C2 = dyn_cast<SCEVConstant>(LMore))) 10674 if (RMore == Less) 10675 return C2->getAPInt(); 10676 10677 // Compare (X + C1) vs (X + C2). 10678 if (C1 && C2 && RLess == RMore) 10679 return C2->getAPInt() - C1->getAPInt(); 10680 10681 return None; 10682 } 10683 10684 bool ScalarEvolution::isImpliedCondOperandsViaAddRecStart( 10685 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, 10686 const SCEV *FoundLHS, const SCEV *FoundRHS, const Instruction *Context) { 10687 // Try to recognize the following pattern: 10688 // 10689 // FoundRHS = ... 10690 // ... 10691 // loop: 10692 // FoundLHS = {Start,+,W} 10693 // context_bb: // Basic block from the same loop 10694 // known(Pred, FoundLHS, FoundRHS) 10695 // 10696 // If some predicate is known in the context of a loop, it is also known on 10697 // each iteration of this loop, including the first iteration. Therefore, in 10698 // this case, `FoundLHS Pred FoundRHS` implies `Start Pred FoundRHS`. Try to 10699 // prove the original pred using this fact. 10700 if (!Context) 10701 return false; 10702 const BasicBlock *ContextBB = Context->getParent(); 10703 // Make sure AR varies in the context block. 10704 if (auto *AR = dyn_cast<SCEVAddRecExpr>(FoundLHS)) { 10705 const Loop *L = AR->getLoop(); 10706 // Make sure that context belongs to the loop and executes on 1st iteration 10707 // (if it ever executes at all). 10708 if (!L->contains(ContextBB) || !DT.dominates(ContextBB, L->getLoopLatch())) 10709 return false; 10710 if (!isAvailableAtLoopEntry(FoundRHS, AR->getLoop())) 10711 return false; 10712 return isImpliedCondOperands(Pred, LHS, RHS, AR->getStart(), FoundRHS); 10713 } 10714 10715 if (auto *AR = dyn_cast<SCEVAddRecExpr>(FoundRHS)) { 10716 const Loop *L = AR->getLoop(); 10717 // Make sure that context belongs to the loop and executes on 1st iteration 10718 // (if it ever executes at all). 10719 if (!L->contains(ContextBB) || !DT.dominates(ContextBB, L->getLoopLatch())) 10720 return false; 10721 if (!isAvailableAtLoopEntry(FoundLHS, AR->getLoop())) 10722 return false; 10723 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, AR->getStart()); 10724 } 10725 10726 return false; 10727 } 10728 10729 bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow( 10730 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, 10731 const SCEV *FoundLHS, const SCEV *FoundRHS) { 10732 if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT) 10733 return false; 10734 10735 const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(LHS); 10736 if (!AddRecLHS) 10737 return false; 10738 10739 const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(FoundLHS); 10740 if (!AddRecFoundLHS) 10741 return false; 10742 10743 // We'd like to let SCEV reason about control dependencies, so we constrain 10744 // both the inequalities to be about add recurrences on the same loop. This 10745 // way we can use isLoopEntryGuardedByCond later. 10746 10747 const Loop *L = AddRecFoundLHS->getLoop(); 10748 if (L != AddRecLHS->getLoop()) 10749 return false; 10750 10751 // FoundLHS u< FoundRHS u< -C => (FoundLHS + C) u< (FoundRHS + C) ... (1) 10752 // 10753 // FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C) 10754 // ... (2) 10755 // 10756 // Informal proof for (2), assuming (1) [*]: 10757 // 10758 // We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**] 10759 // 10760 // Then 10761 // 10762 // FoundLHS s< FoundRHS s< INT_MIN - C 10763 // <=> (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C [ using (3) ] 10764 // <=> (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ] 10765 // <=> (FoundLHS + INT_MIN + C + INT_MIN) s< 10766 // (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ] 10767 // <=> FoundLHS + C s< FoundRHS + C 10768 // 10769 // [*]: (1) can be proved by ruling out overflow. 10770 // 10771 // [**]: This can be proved by analyzing all the four possibilities: 10772 // (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and 10773 // (A s>= 0, B s>= 0). 10774 // 10775 // Note: 10776 // Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C" 10777 // will not sign underflow. For instance, say FoundLHS = (i8 -128), FoundRHS 10778 // = (i8 -127) and C = (i8 -100). Then INT_MIN - C = (i8 -28), and FoundRHS 10779 // s< (INT_MIN - C). Lack of sign overflow / underflow in "FoundRHS + C" is 10780 // neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS + 10781 // C)". 10782 10783 Optional<APInt> LDiff = computeConstantDifference(LHS, FoundLHS); 10784 Optional<APInt> RDiff = computeConstantDifference(RHS, FoundRHS); 10785 if (!LDiff || !RDiff || *LDiff != *RDiff) 10786 return false; 10787 10788 if (LDiff->isMinValue()) 10789 return true; 10790 10791 APInt FoundRHSLimit; 10792 10793 if (Pred == CmpInst::ICMP_ULT) { 10794 FoundRHSLimit = -(*RDiff); 10795 } else { 10796 assert(Pred == CmpInst::ICMP_SLT && "Checked above!"); 10797 FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - *RDiff; 10798 } 10799 10800 // Try to prove (1) or (2), as needed. 10801 return isAvailableAtLoopEntry(FoundRHS, L) && 10802 isLoopEntryGuardedByCond(L, Pred, FoundRHS, 10803 getConstant(FoundRHSLimit)); 10804 } 10805 10806 bool ScalarEvolution::isImpliedViaMerge(ICmpInst::Predicate Pred, 10807 const SCEV *LHS, const SCEV *RHS, 10808 const SCEV *FoundLHS, 10809 const SCEV *FoundRHS, unsigned Depth) { 10810 const PHINode *LPhi = nullptr, *RPhi = nullptr; 10811 10812 auto ClearOnExit = make_scope_exit([&]() { 10813 if (LPhi) { 10814 bool Erased = PendingMerges.erase(LPhi); 10815 assert(Erased && "Failed to erase LPhi!"); 10816 (void)Erased; 10817 } 10818 if (RPhi) { 10819 bool Erased = PendingMerges.erase(RPhi); 10820 assert(Erased && "Failed to erase RPhi!"); 10821 (void)Erased; 10822 } 10823 }); 10824 10825 // Find respective Phis and check that they are not being pending. 10826 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) 10827 if (auto *Phi = dyn_cast<PHINode>(LU->getValue())) { 10828 if (!PendingMerges.insert(Phi).second) 10829 return false; 10830 LPhi = Phi; 10831 } 10832 if (const SCEVUnknown *RU = dyn_cast<SCEVUnknown>(RHS)) 10833 if (auto *Phi = dyn_cast<PHINode>(RU->getValue())) { 10834 // If we detect a loop of Phi nodes being processed by this method, for 10835 // example: 10836 // 10837 // %a = phi i32 [ %some1, %preheader ], [ %b, %latch ] 10838 // %b = phi i32 [ %some2, %preheader ], [ %a, %latch ] 10839 // 10840 // we don't want to deal with a case that complex, so return conservative 10841 // answer false. 10842 if (!PendingMerges.insert(Phi).second) 10843 return false; 10844 RPhi = Phi; 10845 } 10846 10847 // If none of LHS, RHS is a Phi, nothing to do here. 10848 if (!LPhi && !RPhi) 10849 return false; 10850 10851 // If there is a SCEVUnknown Phi we are interested in, make it left. 10852 if (!LPhi) { 10853 std::swap(LHS, RHS); 10854 std::swap(FoundLHS, FoundRHS); 10855 std::swap(LPhi, RPhi); 10856 Pred = ICmpInst::getSwappedPredicate(Pred); 10857 } 10858 10859 assert(LPhi && "LPhi should definitely be a SCEVUnknown Phi!"); 10860 const BasicBlock *LBB = LPhi->getParent(); 10861 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS); 10862 10863 auto ProvedEasily = [&](const SCEV *S1, const SCEV *S2) { 10864 return isKnownViaNonRecursiveReasoning(Pred, S1, S2) || 10865 isImpliedCondOperandsViaRanges(Pred, S1, S2, FoundLHS, FoundRHS) || 10866 isImpliedViaOperations(Pred, S1, S2, FoundLHS, FoundRHS, Depth); 10867 }; 10868 10869 if (RPhi && RPhi->getParent() == LBB) { 10870 // Case one: RHS is also a SCEVUnknown Phi from the same basic block. 10871 // If we compare two Phis from the same block, and for each entry block 10872 // the predicate is true for incoming values from this block, then the 10873 // predicate is also true for the Phis. 10874 for (const BasicBlock *IncBB : predecessors(LBB)) { 10875 const SCEV *L = getSCEV(LPhi->getIncomingValueForBlock(IncBB)); 10876 const SCEV *R = getSCEV(RPhi->getIncomingValueForBlock(IncBB)); 10877 if (!ProvedEasily(L, R)) 10878 return false; 10879 } 10880 } else if (RAR && RAR->getLoop()->getHeader() == LBB) { 10881 // Case two: RHS is also a Phi from the same basic block, and it is an 10882 // AddRec. It means that there is a loop which has both AddRec and Unknown 10883 // PHIs, for it we can compare incoming values of AddRec from above the loop 10884 // and latch with their respective incoming values of LPhi. 10885 // TODO: Generalize to handle loops with many inputs in a header. 10886 if (LPhi->getNumIncomingValues() != 2) return false; 10887 10888 auto *RLoop = RAR->getLoop(); 10889 auto *Predecessor = RLoop->getLoopPredecessor(); 10890 assert(Predecessor && "Loop with AddRec with no predecessor?"); 10891 const SCEV *L1 = getSCEV(LPhi->getIncomingValueForBlock(Predecessor)); 10892 if (!ProvedEasily(L1, RAR->getStart())) 10893 return false; 10894 auto *Latch = RLoop->getLoopLatch(); 10895 assert(Latch && "Loop with AddRec with no latch?"); 10896 const SCEV *L2 = getSCEV(LPhi->getIncomingValueForBlock(Latch)); 10897 if (!ProvedEasily(L2, RAR->getPostIncExpr(*this))) 10898 return false; 10899 } else { 10900 // In all other cases go over inputs of LHS and compare each of them to RHS, 10901 // the predicate is true for (LHS, RHS) if it is true for all such pairs. 10902 // At this point RHS is either a non-Phi, or it is a Phi from some block 10903 // different from LBB. 10904 for (const BasicBlock *IncBB : predecessors(LBB)) { 10905 // Check that RHS is available in this block. 10906 if (!dominates(RHS, IncBB)) 10907 return false; 10908 const SCEV *L = getSCEV(LPhi->getIncomingValueForBlock(IncBB)); 10909 // Make sure L does not refer to a value from a potentially previous 10910 // iteration of a loop. 10911 if (!properlyDominates(L, IncBB)) 10912 return false; 10913 if (!ProvedEasily(L, RHS)) 10914 return false; 10915 } 10916 } 10917 return true; 10918 } 10919 10920 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 10921 const SCEV *LHS, const SCEV *RHS, 10922 const SCEV *FoundLHS, 10923 const SCEV *FoundRHS, 10924 const Instruction *Context) { 10925 if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS)) 10926 return true; 10927 10928 if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS)) 10929 return true; 10930 10931 if (isImpliedCondOperandsViaAddRecStart(Pred, LHS, RHS, FoundLHS, FoundRHS, 10932 Context)) 10933 return true; 10934 10935 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 10936 FoundLHS, FoundRHS); 10937 } 10938 10939 /// Is MaybeMinMaxExpr an (U|S)(Min|Max) of Candidate and some other values? 10940 template <typename MinMaxExprType> 10941 static bool IsMinMaxConsistingOf(const SCEV *MaybeMinMaxExpr, 10942 const SCEV *Candidate) { 10943 const MinMaxExprType *MinMaxExpr = dyn_cast<MinMaxExprType>(MaybeMinMaxExpr); 10944 if (!MinMaxExpr) 10945 return false; 10946 10947 return is_contained(MinMaxExpr->operands(), Candidate); 10948 } 10949 10950 static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE, 10951 ICmpInst::Predicate Pred, 10952 const SCEV *LHS, const SCEV *RHS) { 10953 // If both sides are affine addrecs for the same loop, with equal 10954 // steps, and we know the recurrences don't wrap, then we only 10955 // need to check the predicate on the starting values. 10956 10957 if (!ICmpInst::isRelational(Pred)) 10958 return false; 10959 10960 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS); 10961 if (!LAR) 10962 return false; 10963 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS); 10964 if (!RAR) 10965 return false; 10966 if (LAR->getLoop() != RAR->getLoop()) 10967 return false; 10968 if (!LAR->isAffine() || !RAR->isAffine()) 10969 return false; 10970 10971 if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE)) 10972 return false; 10973 10974 SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ? 10975 SCEV::FlagNSW : SCEV::FlagNUW; 10976 if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW)) 10977 return false; 10978 10979 return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart()); 10980 } 10981 10982 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max 10983 /// expression? 10984 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE, 10985 ICmpInst::Predicate Pred, 10986 const SCEV *LHS, const SCEV *RHS) { 10987 switch (Pred) { 10988 default: 10989 return false; 10990 10991 case ICmpInst::ICMP_SGE: 10992 std::swap(LHS, RHS); 10993 LLVM_FALLTHROUGH; 10994 case ICmpInst::ICMP_SLE: 10995 return 10996 // min(A, ...) <= A 10997 IsMinMaxConsistingOf<SCEVSMinExpr>(LHS, RHS) || 10998 // A <= max(A, ...) 10999 IsMinMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS); 11000 11001 case ICmpInst::ICMP_UGE: 11002 std::swap(LHS, RHS); 11003 LLVM_FALLTHROUGH; 11004 case ICmpInst::ICMP_ULE: 11005 return 11006 // min(A, ...) <= A 11007 IsMinMaxConsistingOf<SCEVUMinExpr>(LHS, RHS) || 11008 // A <= max(A, ...) 11009 IsMinMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS); 11010 } 11011 11012 llvm_unreachable("covered switch fell through?!"); 11013 } 11014 11015 bool ScalarEvolution::isImpliedViaOperations(ICmpInst::Predicate Pred, 11016 const SCEV *LHS, const SCEV *RHS, 11017 const SCEV *FoundLHS, 11018 const SCEV *FoundRHS, 11019 unsigned Depth) { 11020 assert(getTypeSizeInBits(LHS->getType()) == 11021 getTypeSizeInBits(RHS->getType()) && 11022 "LHS and RHS have different sizes?"); 11023 assert(getTypeSizeInBits(FoundLHS->getType()) == 11024 getTypeSizeInBits(FoundRHS->getType()) && 11025 "FoundLHS and FoundRHS have different sizes?"); 11026 // We want to avoid hurting the compile time with analysis of too big trees. 11027 if (Depth > MaxSCEVOperationsImplicationDepth) 11028 return false; 11029 11030 // We only want to work with GT comparison so far. 11031 if (Pred == ICmpInst::ICMP_ULT || Pred == ICmpInst::ICMP_SLT) { 11032 Pred = CmpInst::getSwappedPredicate(Pred); 11033 std::swap(LHS, RHS); 11034 std::swap(FoundLHS, FoundRHS); 11035 } 11036 11037 // For unsigned, try to reduce it to corresponding signed comparison. 11038 if (Pred == ICmpInst::ICMP_UGT) 11039 // We can replace unsigned predicate with its signed counterpart if all 11040 // involved values are non-negative. 11041 // TODO: We could have better support for unsigned. 11042 if (isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS)) { 11043 // Knowing that both FoundLHS and FoundRHS are non-negative, and knowing 11044 // FoundLHS >u FoundRHS, we also know that FoundLHS >s FoundRHS. Let us 11045 // use this fact to prove that LHS and RHS are non-negative. 11046 const SCEV *MinusOne = getMinusOne(LHS->getType()); 11047 if (isImpliedCondOperands(ICmpInst::ICMP_SGT, LHS, MinusOne, FoundLHS, 11048 FoundRHS) && 11049 isImpliedCondOperands(ICmpInst::ICMP_SGT, RHS, MinusOne, FoundLHS, 11050 FoundRHS)) 11051 Pred = ICmpInst::ICMP_SGT; 11052 } 11053 11054 if (Pred != ICmpInst::ICMP_SGT) 11055 return false; 11056 11057 auto GetOpFromSExt = [&](const SCEV *S) { 11058 if (auto *Ext = dyn_cast<SCEVSignExtendExpr>(S)) 11059 return Ext->getOperand(); 11060 // TODO: If S is a SCEVConstant then you can cheaply "strip" the sext off 11061 // the constant in some cases. 11062 return S; 11063 }; 11064 11065 // Acquire values from extensions. 11066 auto *OrigLHS = LHS; 11067 auto *OrigFoundLHS = FoundLHS; 11068 LHS = GetOpFromSExt(LHS); 11069 FoundLHS = GetOpFromSExt(FoundLHS); 11070 11071 // Is the SGT predicate can be proved trivially or using the found context. 11072 auto IsSGTViaContext = [&](const SCEV *S1, const SCEV *S2) { 11073 return isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGT, S1, S2) || 11074 isImpliedViaOperations(ICmpInst::ICMP_SGT, S1, S2, OrigFoundLHS, 11075 FoundRHS, Depth + 1); 11076 }; 11077 11078 if (auto *LHSAddExpr = dyn_cast<SCEVAddExpr>(LHS)) { 11079 // We want to avoid creation of any new non-constant SCEV. Since we are 11080 // going to compare the operands to RHS, we should be certain that we don't 11081 // need any size extensions for this. So let's decline all cases when the 11082 // sizes of types of LHS and RHS do not match. 11083 // TODO: Maybe try to get RHS from sext to catch more cases? 11084 if (getTypeSizeInBits(LHS->getType()) != getTypeSizeInBits(RHS->getType())) 11085 return false; 11086 11087 // Should not overflow. 11088 if (!LHSAddExpr->hasNoSignedWrap()) 11089 return false; 11090 11091 auto *LL = LHSAddExpr->getOperand(0); 11092 auto *LR = LHSAddExpr->getOperand(1); 11093 auto *MinusOne = getMinusOne(RHS->getType()); 11094 11095 // Checks that S1 >= 0 && S2 > RHS, trivially or using the found context. 11096 auto IsSumGreaterThanRHS = [&](const SCEV *S1, const SCEV *S2) { 11097 return IsSGTViaContext(S1, MinusOne) && IsSGTViaContext(S2, RHS); 11098 }; 11099 // Try to prove the following rule: 11100 // (LHS = LL + LR) && (LL >= 0) && (LR > RHS) => (LHS > RHS). 11101 // (LHS = LL + LR) && (LR >= 0) && (LL > RHS) => (LHS > RHS). 11102 if (IsSumGreaterThanRHS(LL, LR) || IsSumGreaterThanRHS(LR, LL)) 11103 return true; 11104 } else if (auto *LHSUnknownExpr = dyn_cast<SCEVUnknown>(LHS)) { 11105 Value *LL, *LR; 11106 // FIXME: Once we have SDiv implemented, we can get rid of this matching. 11107 11108 using namespace llvm::PatternMatch; 11109 11110 if (match(LHSUnknownExpr->getValue(), m_SDiv(m_Value(LL), m_Value(LR)))) { 11111 // Rules for division. 11112 // We are going to perform some comparisons with Denominator and its 11113 // derivative expressions. In general case, creating a SCEV for it may 11114 // lead to a complex analysis of the entire graph, and in particular it 11115 // can request trip count recalculation for the same loop. This would 11116 // cache as SCEVCouldNotCompute to avoid the infinite recursion. To avoid 11117 // this, we only want to create SCEVs that are constants in this section. 11118 // So we bail if Denominator is not a constant. 11119 if (!isa<ConstantInt>(LR)) 11120 return false; 11121 11122 auto *Denominator = cast<SCEVConstant>(getSCEV(LR)); 11123 11124 // We want to make sure that LHS = FoundLHS / Denominator. If it is so, 11125 // then a SCEV for the numerator already exists and matches with FoundLHS. 11126 auto *Numerator = getExistingSCEV(LL); 11127 if (!Numerator || Numerator->getType() != FoundLHS->getType()) 11128 return false; 11129 11130 // Make sure that the numerator matches with FoundLHS and the denominator 11131 // is positive. 11132 if (!HasSameValue(Numerator, FoundLHS) || !isKnownPositive(Denominator)) 11133 return false; 11134 11135 auto *DTy = Denominator->getType(); 11136 auto *FRHSTy = FoundRHS->getType(); 11137 if (DTy->isPointerTy() != FRHSTy->isPointerTy()) 11138 // One of types is a pointer and another one is not. We cannot extend 11139 // them properly to a wider type, so let us just reject this case. 11140 // TODO: Usage of getEffectiveSCEVType for DTy, FRHSTy etc should help 11141 // to avoid this check. 11142 return false; 11143 11144 // Given that: 11145 // FoundLHS > FoundRHS, LHS = FoundLHS / Denominator, Denominator > 0. 11146 auto *WTy = getWiderType(DTy, FRHSTy); 11147 auto *DenominatorExt = getNoopOrSignExtend(Denominator, WTy); 11148 auto *FoundRHSExt = getNoopOrSignExtend(FoundRHS, WTy); 11149 11150 // Try to prove the following rule: 11151 // (FoundRHS > Denominator - 2) && (RHS <= 0) => (LHS > RHS). 11152 // For example, given that FoundLHS > 2. It means that FoundLHS is at 11153 // least 3. If we divide it by Denominator < 4, we will have at least 1. 11154 auto *DenomMinusTwo = getMinusSCEV(DenominatorExt, getConstant(WTy, 2)); 11155 if (isKnownNonPositive(RHS) && 11156 IsSGTViaContext(FoundRHSExt, DenomMinusTwo)) 11157 return true; 11158 11159 // Try to prove the following rule: 11160 // (FoundRHS > -1 - Denominator) && (RHS < 0) => (LHS > RHS). 11161 // For example, given that FoundLHS > -3. Then FoundLHS is at least -2. 11162 // If we divide it by Denominator > 2, then: 11163 // 1. If FoundLHS is negative, then the result is 0. 11164 // 2. If FoundLHS is non-negative, then the result is non-negative. 11165 // Anyways, the result is non-negative. 11166 auto *MinusOne = getMinusOne(WTy); 11167 auto *NegDenomMinusOne = getMinusSCEV(MinusOne, DenominatorExt); 11168 if (isKnownNegative(RHS) && 11169 IsSGTViaContext(FoundRHSExt, NegDenomMinusOne)) 11170 return true; 11171 } 11172 } 11173 11174 // If our expression contained SCEVUnknown Phis, and we split it down and now 11175 // need to prove something for them, try to prove the predicate for every 11176 // possible incoming values of those Phis. 11177 if (isImpliedViaMerge(Pred, OrigLHS, RHS, OrigFoundLHS, FoundRHS, Depth + 1)) 11178 return true; 11179 11180 return false; 11181 } 11182 11183 static bool isKnownPredicateExtendIdiom(ICmpInst::Predicate Pred, 11184 const SCEV *LHS, const SCEV *RHS) { 11185 // zext x u<= sext x, sext x s<= zext x 11186 switch (Pred) { 11187 case ICmpInst::ICMP_SGE: 11188 std::swap(LHS, RHS); 11189 LLVM_FALLTHROUGH; 11190 case ICmpInst::ICMP_SLE: { 11191 // If operand >=s 0 then ZExt == SExt. If operand <s 0 then SExt <s ZExt. 11192 const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(LHS); 11193 const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(RHS); 11194 if (SExt && ZExt && SExt->getOperand() == ZExt->getOperand()) 11195 return true; 11196 break; 11197 } 11198 case ICmpInst::ICMP_UGE: 11199 std::swap(LHS, RHS); 11200 LLVM_FALLTHROUGH; 11201 case ICmpInst::ICMP_ULE: { 11202 // If operand >=s 0 then ZExt == SExt. If operand <s 0 then ZExt <u SExt. 11203 const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(LHS); 11204 const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(RHS); 11205 if (SExt && ZExt && SExt->getOperand() == ZExt->getOperand()) 11206 return true; 11207 break; 11208 } 11209 default: 11210 break; 11211 }; 11212 return false; 11213 } 11214 11215 bool 11216 ScalarEvolution::isKnownViaNonRecursiveReasoning(ICmpInst::Predicate Pred, 11217 const SCEV *LHS, const SCEV *RHS) { 11218 return isKnownPredicateExtendIdiom(Pred, LHS, RHS) || 11219 isKnownPredicateViaConstantRanges(Pred, LHS, RHS) || 11220 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) || 11221 IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS) || 11222 isKnownPredicateViaNoOverflow(Pred, LHS, RHS); 11223 } 11224 11225 bool 11226 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 11227 const SCEV *LHS, const SCEV *RHS, 11228 const SCEV *FoundLHS, 11229 const SCEV *FoundRHS) { 11230 switch (Pred) { 11231 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 11232 case ICmpInst::ICMP_EQ: 11233 case ICmpInst::ICMP_NE: 11234 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 11235 return true; 11236 break; 11237 case ICmpInst::ICMP_SLT: 11238 case ICmpInst::ICMP_SLE: 11239 if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 11240 isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 11241 return true; 11242 break; 11243 case ICmpInst::ICMP_SGT: 11244 case ICmpInst::ICMP_SGE: 11245 if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 11246 isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 11247 return true; 11248 break; 11249 case ICmpInst::ICMP_ULT: 11250 case ICmpInst::ICMP_ULE: 11251 if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 11252 isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 11253 return true; 11254 break; 11255 case ICmpInst::ICMP_UGT: 11256 case ICmpInst::ICMP_UGE: 11257 if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 11258 isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 11259 return true; 11260 break; 11261 } 11262 11263 // Maybe it can be proved via operations? 11264 if (isImpliedViaOperations(Pred, LHS, RHS, FoundLHS, FoundRHS)) 11265 return true; 11266 11267 return false; 11268 } 11269 11270 bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred, 11271 const SCEV *LHS, 11272 const SCEV *RHS, 11273 const SCEV *FoundLHS, 11274 const SCEV *FoundRHS) { 11275 if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS)) 11276 // The restriction on `FoundRHS` be lifted easily -- it exists only to 11277 // reduce the compile time impact of this optimization. 11278 return false; 11279 11280 Optional<APInt> Addend = computeConstantDifference(LHS, FoundLHS); 11281 if (!Addend) 11282 return false; 11283 11284 const APInt &ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getAPInt(); 11285 11286 // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the 11287 // antecedent "`FoundLHS` `Pred` `FoundRHS`". 11288 ConstantRange FoundLHSRange = 11289 ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS); 11290 11291 // Since `LHS` is `FoundLHS` + `Addend`, we can compute a range for `LHS`: 11292 ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(*Addend)); 11293 11294 // We can also compute the range of values for `LHS` that satisfy the 11295 // consequent, "`LHS` `Pred` `RHS`": 11296 const APInt &ConstRHS = cast<SCEVConstant>(RHS)->getAPInt(); 11297 // The antecedent implies the consequent if every value of `LHS` that 11298 // satisfies the antecedent also satisfies the consequent. 11299 return LHSRange.icmp(Pred, ConstRHS); 11300 } 11301 11302 bool ScalarEvolution::canIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride, 11303 bool IsSigned) { 11304 assert(isKnownPositive(Stride) && "Positive stride expected!"); 11305 11306 unsigned BitWidth = getTypeSizeInBits(RHS->getType()); 11307 const SCEV *One = getOne(Stride->getType()); 11308 11309 if (IsSigned) { 11310 APInt MaxRHS = getSignedRangeMax(RHS); 11311 APInt MaxValue = APInt::getSignedMaxValue(BitWidth); 11312 APInt MaxStrideMinusOne = getSignedRangeMax(getMinusSCEV(Stride, One)); 11313 11314 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow! 11315 return (std::move(MaxValue) - MaxStrideMinusOne).slt(MaxRHS); 11316 } 11317 11318 APInt MaxRHS = getUnsignedRangeMax(RHS); 11319 APInt MaxValue = APInt::getMaxValue(BitWidth); 11320 APInt MaxStrideMinusOne = getUnsignedRangeMax(getMinusSCEV(Stride, One)); 11321 11322 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow! 11323 return (std::move(MaxValue) - MaxStrideMinusOne).ult(MaxRHS); 11324 } 11325 11326 bool ScalarEvolution::canIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride, 11327 bool IsSigned) { 11328 11329 unsigned BitWidth = getTypeSizeInBits(RHS->getType()); 11330 const SCEV *One = getOne(Stride->getType()); 11331 11332 if (IsSigned) { 11333 APInt MinRHS = getSignedRangeMin(RHS); 11334 APInt MinValue = APInt::getSignedMinValue(BitWidth); 11335 APInt MaxStrideMinusOne = getSignedRangeMax(getMinusSCEV(Stride, One)); 11336 11337 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow! 11338 return (std::move(MinValue) + MaxStrideMinusOne).sgt(MinRHS); 11339 } 11340 11341 APInt MinRHS = getUnsignedRangeMin(RHS); 11342 APInt MinValue = APInt::getMinValue(BitWidth); 11343 APInt MaxStrideMinusOne = getUnsignedRangeMax(getMinusSCEV(Stride, One)); 11344 11345 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow! 11346 return (std::move(MinValue) + MaxStrideMinusOne).ugt(MinRHS); 11347 } 11348 11349 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, 11350 const SCEV *Step) { 11351 const SCEV *One = getOne(Step->getType()); 11352 Delta = getAddExpr(Delta, getMinusSCEV(Step, One)); 11353 return getUDivExpr(Delta, Step); 11354 } 11355 11356 const SCEV *ScalarEvolution::computeMaxBECountForLT(const SCEV *Start, 11357 const SCEV *Stride, 11358 const SCEV *End, 11359 unsigned BitWidth, 11360 bool IsSigned) { 11361 11362 assert(!isKnownNonPositive(Stride) && 11363 "Stride is expected strictly positive!"); 11364 // Calculate the maximum backedge count based on the range of values 11365 // permitted by Start, End, and Stride. 11366 const SCEV *MaxBECount; 11367 APInt MinStart = 11368 IsSigned ? getSignedRangeMin(Start) : getUnsignedRangeMin(Start); 11369 11370 APInt StrideForMaxBECount = 11371 IsSigned ? getSignedRangeMin(Stride) : getUnsignedRangeMin(Stride); 11372 11373 // We already know that the stride is positive, so we paper over conservatism 11374 // in our range computation by forcing StrideForMaxBECount to be at least one. 11375 // In theory this is unnecessary, but we expect MaxBECount to be a 11376 // SCEVConstant, and (udiv <constant> 0) is not constant folded by SCEV (there 11377 // is nothing to constant fold it to). 11378 APInt One(BitWidth, 1, IsSigned); 11379 StrideForMaxBECount = APIntOps::smax(One, StrideForMaxBECount); 11380 11381 APInt MaxValue = IsSigned ? APInt::getSignedMaxValue(BitWidth) 11382 : APInt::getMaxValue(BitWidth); 11383 APInt Limit = MaxValue - (StrideForMaxBECount - 1); 11384 11385 // Although End can be a MAX expression we estimate MaxEnd considering only 11386 // the case End = RHS of the loop termination condition. This is safe because 11387 // in the other case (End - Start) is zero, leading to a zero maximum backedge 11388 // taken count. 11389 APInt MaxEnd = IsSigned ? APIntOps::smin(getSignedRangeMax(End), Limit) 11390 : APIntOps::umin(getUnsignedRangeMax(End), Limit); 11391 11392 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart) /* Delta */, 11393 getConstant(StrideForMaxBECount) /* Step */); 11394 11395 return MaxBECount; 11396 } 11397 11398 ScalarEvolution::ExitLimit 11399 ScalarEvolution::howManyLessThans(const SCEV *LHS, const SCEV *RHS, 11400 const Loop *L, bool IsSigned, 11401 bool ControlsExit, bool AllowPredicates) { 11402 SmallPtrSet<const SCEVPredicate *, 4> Predicates; 11403 11404 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS); 11405 bool PredicatedIV = false; 11406 11407 if (!IV && AllowPredicates) { 11408 // Try to make this an AddRec using runtime tests, in the first X 11409 // iterations of this loop, where X is the SCEV expression found by the 11410 // algorithm below. 11411 IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates); 11412 PredicatedIV = true; 11413 } 11414 11415 // Avoid weird loops 11416 if (!IV || IV->getLoop() != L || !IV->isAffine()) 11417 return getCouldNotCompute(); 11418 11419 auto WrapType = IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW; 11420 bool NoWrap = ControlsExit && IV->getNoWrapFlags(WrapType); 11421 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT; 11422 11423 const SCEV *Stride = IV->getStepRecurrence(*this); 11424 11425 bool PositiveStride = isKnownPositive(Stride); 11426 11427 // Avoid negative or zero stride values. 11428 if (!PositiveStride) { 11429 // We can compute the correct backedge taken count for loops with unknown 11430 // strides if we can prove that the loop is not an infinite loop with side 11431 // effects. Here's the loop structure we are trying to handle - 11432 // 11433 // i = start 11434 // do { 11435 // A[i] = i; 11436 // i += s; 11437 // } while (i < end); 11438 // 11439 // The backedge taken count for such loops is evaluated as - 11440 // (max(end, start + stride) - start - 1) /u stride 11441 // 11442 // The additional preconditions that we need to check to prove correctness 11443 // of the above formula is as follows - 11444 // 11445 // a) IV is either nuw or nsw depending upon signedness (indicated by the 11446 // NoWrap flag). 11447 // b) loop is single exit with no side effects. 11448 // 11449 // 11450 // Precondition a) implies that if the stride is negative, this is a single 11451 // trip loop. The backedge taken count formula reduces to zero in this case. 11452 // 11453 // Precondition b) implies that the unknown stride cannot be zero otherwise 11454 // we have UB. 11455 // 11456 // The positive stride case is the same as isKnownPositive(Stride) returning 11457 // true (original behavior of the function). 11458 // 11459 // We want to make sure that the stride is truly unknown as there are edge 11460 // cases where ScalarEvolution propagates no wrap flags to the 11461 // post-increment/decrement IV even though the increment/decrement operation 11462 // itself is wrapping. The computed backedge taken count may be wrong in 11463 // such cases. This is prevented by checking that the stride is not known to 11464 // be either positive or non-positive. For example, no wrap flags are 11465 // propagated to the post-increment IV of this loop with a trip count of 2 - 11466 // 11467 // unsigned char i; 11468 // for(i=127; i<128; i+=129) 11469 // A[i] = i; 11470 // 11471 if (PredicatedIV || !NoWrap || isKnownNonPositive(Stride) || 11472 !loopIsFiniteByAssumption(L)) 11473 return getCouldNotCompute(); 11474 } else if (!Stride->isOne() && !NoWrap) { 11475 auto isUBOnWrap = [&]() { 11476 // Can we prove this loop *must* be UB if overflow of IV occurs? 11477 // Reasoning goes as follows: 11478 // * Suppose the IV did self wrap. 11479 // * If Stride evenly divides the iteration space, then once wrap 11480 // occurs, the loop must revisit the same values. 11481 // * We know that RHS is invariant, and that none of those values 11482 // caused this exit to be taken previously. Thus, this exit is 11483 // dynamically dead. 11484 // * If this is the sole exit, then a dead exit implies the loop 11485 // must be infinite if there are no abnormal exits. 11486 // * If the loop were infinite, then it must either not be mustprogress 11487 // or have side effects. Otherwise, it must be UB. 11488 // * It can't (by assumption), be UB so we have contradicted our 11489 // premise and can conclude the IV did not in fact self-wrap. 11490 // From no-self-wrap, we need to then prove no-(un)signed-wrap. This 11491 // follows trivially from the fact that every (un)signed-wrapped, but 11492 // not self-wrapped value must be LT than the last value before 11493 // (un)signed wrap. Since we know that last value didn't exit, nor 11494 // will any smaller one. 11495 11496 if (!isLoopInvariant(RHS, L)) 11497 return false; 11498 11499 auto *StrideC = dyn_cast<SCEVConstant>(Stride); 11500 if (!StrideC || !StrideC->getAPInt().isPowerOf2()) 11501 return false; 11502 11503 if (!ControlsExit || !loopHasNoAbnormalExits(L)) 11504 return false; 11505 11506 return loopIsFiniteByAssumption(L); 11507 }; 11508 11509 // Avoid proven overflow cases: this will ensure that the backedge taken 11510 // count will not generate any unsigned overflow. Relaxed no-overflow 11511 // conditions exploit NoWrapFlags, allowing to optimize in presence of 11512 // undefined behaviors like the case of C language. 11513 if (canIVOverflowOnLT(RHS, Stride, IsSigned) && !isUBOnWrap()) 11514 return getCouldNotCompute(); 11515 } 11516 11517 const SCEV *Start = IV->getStart(); 11518 const SCEV *End = RHS; 11519 // When the RHS is not invariant, we do not know the end bound of the loop and 11520 // cannot calculate the ExactBECount needed by ExitLimit. However, we can 11521 // calculate the MaxBECount, given the start, stride and max value for the end 11522 // bound of the loop (RHS), and the fact that IV does not overflow (which is 11523 // checked above). 11524 if (!isLoopInvariant(RHS, L)) { 11525 const SCEV *MaxBECount = computeMaxBECountForLT( 11526 Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned); 11527 return ExitLimit(getCouldNotCompute() /* ExactNotTaken */, MaxBECount, 11528 false /*MaxOrZero*/, Predicates); 11529 } 11530 // If the backedge is taken at least once, then it will be taken 11531 // (End-Start)/Stride times (rounded up to a multiple of Stride), where Start 11532 // is the LHS value of the less-than comparison the first time it is evaluated 11533 // and End is the RHS. 11534 const SCEV *BECountIfBackedgeTaken = 11535 computeBECount(getMinusSCEV(End, Start), Stride); 11536 // If the loop entry is guarded by the result of the backedge test of the 11537 // first loop iteration, then we know the backedge will be taken at least 11538 // once and so the backedge taken count is as above. If not then we use the 11539 // expression (max(End,Start)-Start)/Stride to describe the backedge count, 11540 // as if the backedge is taken at least once max(End,Start) is End and so the 11541 // result is as above, and if not max(End,Start) is Start so we get a backedge 11542 // count of zero. 11543 const SCEV *BECount; 11544 if (isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) 11545 BECount = BECountIfBackedgeTaken; 11546 else { 11547 // If we know that RHS >= Start in the context of loop, then we know that 11548 // max(RHS, Start) = RHS at this point. 11549 if (isLoopEntryGuardedByCond( 11550 L, IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE, RHS, Start)) 11551 End = RHS; 11552 else 11553 End = IsSigned ? getSMaxExpr(RHS, Start) : getUMaxExpr(RHS, Start); 11554 BECount = computeBECount(getMinusSCEV(End, Start), Stride); 11555 } 11556 11557 const SCEV *MaxBECount; 11558 bool MaxOrZero = false; 11559 if (isa<SCEVConstant>(BECount)) 11560 MaxBECount = BECount; 11561 else if (isa<SCEVConstant>(BECountIfBackedgeTaken)) { 11562 // If we know exactly how many times the backedge will be taken if it's 11563 // taken at least once, then the backedge count will either be that or 11564 // zero. 11565 MaxBECount = BECountIfBackedgeTaken; 11566 MaxOrZero = true; 11567 } else { 11568 MaxBECount = computeMaxBECountForLT( 11569 Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned); 11570 } 11571 11572 if (isa<SCEVCouldNotCompute>(MaxBECount) && 11573 !isa<SCEVCouldNotCompute>(BECount)) 11574 MaxBECount = getConstant(getUnsignedRangeMax(BECount)); 11575 11576 return ExitLimit(BECount, MaxBECount, MaxOrZero, Predicates); 11577 } 11578 11579 ScalarEvolution::ExitLimit 11580 ScalarEvolution::howManyGreaterThans(const SCEV *LHS, const SCEV *RHS, 11581 const Loop *L, bool IsSigned, 11582 bool ControlsExit, bool AllowPredicates) { 11583 SmallPtrSet<const SCEVPredicate *, 4> Predicates; 11584 // We handle only IV > Invariant 11585 if (!isLoopInvariant(RHS, L)) 11586 return getCouldNotCompute(); 11587 11588 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS); 11589 if (!IV && AllowPredicates) 11590 // Try to make this an AddRec using runtime tests, in the first X 11591 // iterations of this loop, where X is the SCEV expression found by the 11592 // algorithm below. 11593 IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates); 11594 11595 // Avoid weird loops 11596 if (!IV || IV->getLoop() != L || !IV->isAffine()) 11597 return getCouldNotCompute(); 11598 11599 auto WrapType = IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW; 11600 bool NoWrap = ControlsExit && IV->getNoWrapFlags(WrapType); 11601 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT : ICmpInst::ICMP_UGT; 11602 11603 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this)); 11604 11605 // Avoid negative or zero stride values 11606 if (!isKnownPositive(Stride)) 11607 return getCouldNotCompute(); 11608 11609 // Avoid proven overflow cases: this will ensure that the backedge taken count 11610 // will not generate any unsigned overflow. Relaxed no-overflow conditions 11611 // exploit NoWrapFlags, allowing to optimize in presence of undefined 11612 // behaviors like the case of C language. 11613 if (!Stride->isOne() && !NoWrap) 11614 if (canIVOverflowOnGT(RHS, Stride, IsSigned)) 11615 return getCouldNotCompute(); 11616 11617 const SCEV *Start = IV->getStart(); 11618 const SCEV *End = RHS; 11619 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) { 11620 // If we know that Start >= RHS in the context of loop, then we know that 11621 // min(RHS, Start) = RHS at this point. 11622 if (isLoopEntryGuardedByCond( 11623 L, IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE, Start, RHS)) 11624 End = RHS; 11625 else 11626 End = IsSigned ? getSMinExpr(RHS, Start) : getUMinExpr(RHS, Start); 11627 } 11628 11629 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride); 11630 11631 APInt MaxStart = IsSigned ? getSignedRangeMax(Start) 11632 : getUnsignedRangeMax(Start); 11633 11634 APInt MinStride = IsSigned ? getSignedRangeMin(Stride) 11635 : getUnsignedRangeMin(Stride); 11636 11637 unsigned BitWidth = getTypeSizeInBits(LHS->getType()); 11638 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1) 11639 : APInt::getMinValue(BitWidth) + (MinStride - 1); 11640 11641 // Although End can be a MIN expression we estimate MinEnd considering only 11642 // the case End = RHS. This is safe because in the other case (Start - End) 11643 // is zero, leading to a zero maximum backedge taken count. 11644 APInt MinEnd = 11645 IsSigned ? APIntOps::smax(getSignedRangeMin(RHS), Limit) 11646 : APIntOps::umax(getUnsignedRangeMin(RHS), Limit); 11647 11648 const SCEV *MaxBECount = isa<SCEVConstant>(BECount) 11649 ? BECount 11650 : computeBECount(getConstant(MaxStart - MinEnd), 11651 getConstant(MinStride)); 11652 11653 if (isa<SCEVCouldNotCompute>(MaxBECount)) 11654 MaxBECount = BECount; 11655 11656 return ExitLimit(BECount, MaxBECount, false, Predicates); 11657 } 11658 11659 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(const ConstantRange &Range, 11660 ScalarEvolution &SE) const { 11661 if (Range.isFullSet()) // Infinite loop. 11662 return SE.getCouldNotCompute(); 11663 11664 // If the start is a non-zero constant, shift the range to simplify things. 11665 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 11666 if (!SC->getValue()->isZero()) { 11667 SmallVector<const SCEV *, 4> Operands(operands()); 11668 Operands[0] = SE.getZero(SC->getType()); 11669 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(), 11670 getNoWrapFlags(FlagNW)); 11671 if (const auto *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 11672 return ShiftedAddRec->getNumIterationsInRange( 11673 Range.subtract(SC->getAPInt()), SE); 11674 // This is strange and shouldn't happen. 11675 return SE.getCouldNotCompute(); 11676 } 11677 11678 // The only time we can solve this is when we have all constant indices. 11679 // Otherwise, we cannot determine the overflow conditions. 11680 if (any_of(operands(), [](const SCEV *Op) { return !isa<SCEVConstant>(Op); })) 11681 return SE.getCouldNotCompute(); 11682 11683 // Okay at this point we know that all elements of the chrec are constants and 11684 // that the start element is zero. 11685 11686 // First check to see if the range contains zero. If not, the first 11687 // iteration exits. 11688 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 11689 if (!Range.contains(APInt(BitWidth, 0))) 11690 return SE.getZero(getType()); 11691 11692 if (isAffine()) { 11693 // If this is an affine expression then we have this situation: 11694 // Solve {0,+,A} in Range === Ax in Range 11695 11696 // We know that zero is in the range. If A is positive then we know that 11697 // the upper value of the range must be the first possible exit value. 11698 // If A is negative then the lower of the range is the last possible loop 11699 // value. Also note that we already checked for a full range. 11700 APInt A = cast<SCEVConstant>(getOperand(1))->getAPInt(); 11701 APInt End = A.sge(1) ? (Range.getUpper() - 1) : Range.getLower(); 11702 11703 // The exit value should be (End+A)/A. 11704 APInt ExitVal = (End + A).udiv(A); 11705 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 11706 11707 // Evaluate at the exit value. If we really did fall out of the valid 11708 // range, then we computed our trip count, otherwise wrap around or other 11709 // things must have happened. 11710 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 11711 if (Range.contains(Val->getValue())) 11712 return SE.getCouldNotCompute(); // Something strange happened 11713 11714 // Ensure that the previous value is in the range. This is a sanity check. 11715 assert(Range.contains( 11716 EvaluateConstantChrecAtConstant(this, 11717 ConstantInt::get(SE.getContext(), ExitVal - 1), SE)->getValue()) && 11718 "Linear scev computation is off in a bad way!"); 11719 return SE.getConstant(ExitValue); 11720 } 11721 11722 if (isQuadratic()) { 11723 if (auto S = SolveQuadraticAddRecRange(this, Range, SE)) 11724 return SE.getConstant(S.getValue()); 11725 } 11726 11727 return SE.getCouldNotCompute(); 11728 } 11729 11730 const SCEVAddRecExpr * 11731 SCEVAddRecExpr::getPostIncExpr(ScalarEvolution &SE) const { 11732 assert(getNumOperands() > 1 && "AddRec with zero step?"); 11733 // There is a temptation to just call getAddExpr(this, getStepRecurrence(SE)), 11734 // but in this case we cannot guarantee that the value returned will be an 11735 // AddRec because SCEV does not have a fixed point where it stops 11736 // simplification: it is legal to return ({rec1} + {rec2}). For example, it 11737 // may happen if we reach arithmetic depth limit while simplifying. So we 11738 // construct the returned value explicitly. 11739 SmallVector<const SCEV *, 3> Ops; 11740 // If this is {A,+,B,+,C,...,+,N}, then its step is {B,+,C,+,...,+,N}, and 11741 // (this + Step) is {A+B,+,B+C,+...,+,N}. 11742 for (unsigned i = 0, e = getNumOperands() - 1; i < e; ++i) 11743 Ops.push_back(SE.getAddExpr(getOperand(i), getOperand(i + 1))); 11744 // We know that the last operand is not a constant zero (otherwise it would 11745 // have been popped out earlier). This guarantees us that if the result has 11746 // the same last operand, then it will also not be popped out, meaning that 11747 // the returned value will be an AddRec. 11748 const SCEV *Last = getOperand(getNumOperands() - 1); 11749 assert(!Last->isZero() && "Recurrency with zero step?"); 11750 Ops.push_back(Last); 11751 return cast<SCEVAddRecExpr>(SE.getAddRecExpr(Ops, getLoop(), 11752 SCEV::FlagAnyWrap)); 11753 } 11754 11755 // Return true when S contains at least an undef value. 11756 static inline bool containsUndefs(const SCEV *S) { 11757 return SCEVExprContains(S, [](const SCEV *S) { 11758 if (const auto *SU = dyn_cast<SCEVUnknown>(S)) 11759 return isa<UndefValue>(SU->getValue()); 11760 return false; 11761 }); 11762 } 11763 11764 namespace { 11765 11766 // Collect all steps of SCEV expressions. 11767 struct SCEVCollectStrides { 11768 ScalarEvolution &SE; 11769 SmallVectorImpl<const SCEV *> &Strides; 11770 11771 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S) 11772 : SE(SE), Strides(S) {} 11773 11774 bool follow(const SCEV *S) { 11775 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S)) 11776 Strides.push_back(AR->getStepRecurrence(SE)); 11777 return true; 11778 } 11779 11780 bool isDone() const { return false; } 11781 }; 11782 11783 // Collect all SCEVUnknown and SCEVMulExpr expressions. 11784 struct SCEVCollectTerms { 11785 SmallVectorImpl<const SCEV *> &Terms; 11786 11787 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T) : Terms(T) {} 11788 11789 bool follow(const SCEV *S) { 11790 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S) || 11791 isa<SCEVSignExtendExpr>(S)) { 11792 if (!containsUndefs(S)) 11793 Terms.push_back(S); 11794 11795 // Stop recursion: once we collected a term, do not walk its operands. 11796 return false; 11797 } 11798 11799 // Keep looking. 11800 return true; 11801 } 11802 11803 bool isDone() const { return false; } 11804 }; 11805 11806 // Check if a SCEV contains an AddRecExpr. 11807 struct SCEVHasAddRec { 11808 bool &ContainsAddRec; 11809 11810 SCEVHasAddRec(bool &ContainsAddRec) : ContainsAddRec(ContainsAddRec) { 11811 ContainsAddRec = false; 11812 } 11813 11814 bool follow(const SCEV *S) { 11815 if (isa<SCEVAddRecExpr>(S)) { 11816 ContainsAddRec = true; 11817 11818 // Stop recursion: once we collected a term, do not walk its operands. 11819 return false; 11820 } 11821 11822 // Keep looking. 11823 return true; 11824 } 11825 11826 bool isDone() const { return false; } 11827 }; 11828 11829 // Find factors that are multiplied with an expression that (possibly as a 11830 // subexpression) contains an AddRecExpr. In the expression: 11831 // 11832 // 8 * (100 + %p * %q * (%a + {0, +, 1}_loop)) 11833 // 11834 // "%p * %q" are factors multiplied by the expression "(%a + {0, +, 1}_loop)" 11835 // that contains the AddRec {0, +, 1}_loop. %p * %q are likely to be array size 11836 // parameters as they form a product with an induction variable. 11837 // 11838 // This collector expects all array size parameters to be in the same MulExpr. 11839 // It might be necessary to later add support for collecting parameters that are 11840 // spread over different nested MulExpr. 11841 struct SCEVCollectAddRecMultiplies { 11842 SmallVectorImpl<const SCEV *> &Terms; 11843 ScalarEvolution &SE; 11844 11845 SCEVCollectAddRecMultiplies(SmallVectorImpl<const SCEV *> &T, ScalarEvolution &SE) 11846 : Terms(T), SE(SE) {} 11847 11848 bool follow(const SCEV *S) { 11849 if (auto *Mul = dyn_cast<SCEVMulExpr>(S)) { 11850 bool HasAddRec = false; 11851 SmallVector<const SCEV *, 0> Operands; 11852 for (auto Op : Mul->operands()) { 11853 const SCEVUnknown *Unknown = dyn_cast<SCEVUnknown>(Op); 11854 if (Unknown && !isa<CallInst>(Unknown->getValue())) { 11855 Operands.push_back(Op); 11856 } else if (Unknown) { 11857 HasAddRec = true; 11858 } else { 11859 bool ContainsAddRec = false; 11860 SCEVHasAddRec ContiansAddRec(ContainsAddRec); 11861 visitAll(Op, ContiansAddRec); 11862 HasAddRec |= ContainsAddRec; 11863 } 11864 } 11865 if (Operands.size() == 0) 11866 return true; 11867 11868 if (!HasAddRec) 11869 return false; 11870 11871 Terms.push_back(SE.getMulExpr(Operands)); 11872 // Stop recursion: once we collected a term, do not walk its operands. 11873 return false; 11874 } 11875 11876 // Keep looking. 11877 return true; 11878 } 11879 11880 bool isDone() const { return false; } 11881 }; 11882 11883 } // end anonymous namespace 11884 11885 /// Find parametric terms in this SCEVAddRecExpr. We first for parameters in 11886 /// two places: 11887 /// 1) The strides of AddRec expressions. 11888 /// 2) Unknowns that are multiplied with AddRec expressions. 11889 void ScalarEvolution::collectParametricTerms(const SCEV *Expr, 11890 SmallVectorImpl<const SCEV *> &Terms) { 11891 SmallVector<const SCEV *, 4> Strides; 11892 SCEVCollectStrides StrideCollector(*this, Strides); 11893 visitAll(Expr, StrideCollector); 11894 11895 LLVM_DEBUG({ 11896 dbgs() << "Strides:\n"; 11897 for (const SCEV *S : Strides) 11898 dbgs() << *S << "\n"; 11899 }); 11900 11901 for (const SCEV *S : Strides) { 11902 SCEVCollectTerms TermCollector(Terms); 11903 visitAll(S, TermCollector); 11904 } 11905 11906 LLVM_DEBUG({ 11907 dbgs() << "Terms:\n"; 11908 for (const SCEV *T : Terms) 11909 dbgs() << *T << "\n"; 11910 }); 11911 11912 SCEVCollectAddRecMultiplies MulCollector(Terms, *this); 11913 visitAll(Expr, MulCollector); 11914 } 11915 11916 static bool findArrayDimensionsRec(ScalarEvolution &SE, 11917 SmallVectorImpl<const SCEV *> &Terms, 11918 SmallVectorImpl<const SCEV *> &Sizes) { 11919 int Last = Terms.size() - 1; 11920 const SCEV *Step = Terms[Last]; 11921 11922 // End of recursion. 11923 if (Last == 0) { 11924 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) { 11925 SmallVector<const SCEV *, 2> Qs; 11926 for (const SCEV *Op : M->operands()) 11927 if (!isa<SCEVConstant>(Op)) 11928 Qs.push_back(Op); 11929 11930 Step = SE.getMulExpr(Qs); 11931 } 11932 11933 Sizes.push_back(Step); 11934 return true; 11935 } 11936 11937 for (const SCEV *&Term : Terms) { 11938 // Normalize the terms before the next call to findArrayDimensionsRec. 11939 const SCEV *Q, *R; 11940 SCEVDivision::divide(SE, Term, Step, &Q, &R); 11941 11942 // Bail out when GCD does not evenly divide one of the terms. 11943 if (!R->isZero()) 11944 return false; 11945 11946 Term = Q; 11947 } 11948 11949 // Remove all SCEVConstants. 11950 erase_if(Terms, [](const SCEV *E) { return isa<SCEVConstant>(E); }); 11951 11952 if (Terms.size() > 0) 11953 if (!findArrayDimensionsRec(SE, Terms, Sizes)) 11954 return false; 11955 11956 Sizes.push_back(Step); 11957 return true; 11958 } 11959 11960 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter. 11961 static inline bool containsParameters(SmallVectorImpl<const SCEV *> &Terms) { 11962 for (const SCEV *T : Terms) 11963 if (SCEVExprContains(T, [](const SCEV *S) { return isa<SCEVUnknown>(S); })) 11964 return true; 11965 11966 return false; 11967 } 11968 11969 // Return the number of product terms in S. 11970 static inline int numberOfTerms(const SCEV *S) { 11971 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S)) 11972 return Expr->getNumOperands(); 11973 return 1; 11974 } 11975 11976 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) { 11977 if (isa<SCEVConstant>(T)) 11978 return nullptr; 11979 11980 if (isa<SCEVUnknown>(T)) 11981 return T; 11982 11983 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) { 11984 SmallVector<const SCEV *, 2> Factors; 11985 for (const SCEV *Op : M->operands()) 11986 if (!isa<SCEVConstant>(Op)) 11987 Factors.push_back(Op); 11988 11989 return SE.getMulExpr(Factors); 11990 } 11991 11992 return T; 11993 } 11994 11995 /// Return the size of an element read or written by Inst. 11996 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) { 11997 Type *Ty; 11998 if (StoreInst *Store = dyn_cast<StoreInst>(Inst)) 11999 Ty = Store->getValueOperand()->getType(); 12000 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst)) 12001 Ty = Load->getType(); 12002 else 12003 return nullptr; 12004 12005 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty)); 12006 return getSizeOfExpr(ETy, Ty); 12007 } 12008 12009 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms, 12010 SmallVectorImpl<const SCEV *> &Sizes, 12011 const SCEV *ElementSize) { 12012 if (Terms.size() < 1 || !ElementSize) 12013 return; 12014 12015 // Early return when Terms do not contain parameters: we do not delinearize 12016 // non parametric SCEVs. 12017 if (!containsParameters(Terms)) 12018 return; 12019 12020 LLVM_DEBUG({ 12021 dbgs() << "Terms:\n"; 12022 for (const SCEV *T : Terms) 12023 dbgs() << *T << "\n"; 12024 }); 12025 12026 // Remove duplicates. 12027 array_pod_sort(Terms.begin(), Terms.end()); 12028 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end()); 12029 12030 // Put larger terms first. 12031 llvm::sort(Terms, [](const SCEV *LHS, const SCEV *RHS) { 12032 return numberOfTerms(LHS) > numberOfTerms(RHS); 12033 }); 12034 12035 // Try to divide all terms by the element size. If term is not divisible by 12036 // element size, proceed with the original term. 12037 for (const SCEV *&Term : Terms) { 12038 const SCEV *Q, *R; 12039 SCEVDivision::divide(*this, Term, ElementSize, &Q, &R); 12040 if (!Q->isZero()) 12041 Term = Q; 12042 } 12043 12044 SmallVector<const SCEV *, 4> NewTerms; 12045 12046 // Remove constant factors. 12047 for (const SCEV *T : Terms) 12048 if (const SCEV *NewT = removeConstantFactors(*this, T)) 12049 NewTerms.push_back(NewT); 12050 12051 LLVM_DEBUG({ 12052 dbgs() << "Terms after sorting:\n"; 12053 for (const SCEV *T : NewTerms) 12054 dbgs() << *T << "\n"; 12055 }); 12056 12057 if (NewTerms.empty() || !findArrayDimensionsRec(*this, NewTerms, Sizes)) { 12058 Sizes.clear(); 12059 return; 12060 } 12061 12062 // The last element to be pushed into Sizes is the size of an element. 12063 Sizes.push_back(ElementSize); 12064 12065 LLVM_DEBUG({ 12066 dbgs() << "Sizes:\n"; 12067 for (const SCEV *S : Sizes) 12068 dbgs() << *S << "\n"; 12069 }); 12070 } 12071 12072 void ScalarEvolution::computeAccessFunctions( 12073 const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts, 12074 SmallVectorImpl<const SCEV *> &Sizes) { 12075 // Early exit in case this SCEV is not an affine multivariate function. 12076 if (Sizes.empty()) 12077 return; 12078 12079 if (auto *AR = dyn_cast<SCEVAddRecExpr>(Expr)) 12080 if (!AR->isAffine()) 12081 return; 12082 12083 const SCEV *Res = Expr; 12084 int Last = Sizes.size() - 1; 12085 for (int i = Last; i >= 0; i--) { 12086 const SCEV *Q, *R; 12087 SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R); 12088 12089 LLVM_DEBUG({ 12090 dbgs() << "Res: " << *Res << "\n"; 12091 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n"; 12092 dbgs() << "Res divided by Sizes[i]:\n"; 12093 dbgs() << "Quotient: " << *Q << "\n"; 12094 dbgs() << "Remainder: " << *R << "\n"; 12095 }); 12096 12097 Res = Q; 12098 12099 // Do not record the last subscript corresponding to the size of elements in 12100 // the array. 12101 if (i == Last) { 12102 12103 // Bail out if the remainder is too complex. 12104 if (isa<SCEVAddRecExpr>(R)) { 12105 Subscripts.clear(); 12106 Sizes.clear(); 12107 return; 12108 } 12109 12110 continue; 12111 } 12112 12113 // Record the access function for the current subscript. 12114 Subscripts.push_back(R); 12115 } 12116 12117 // Also push in last position the remainder of the last division: it will be 12118 // the access function of the innermost dimension. 12119 Subscripts.push_back(Res); 12120 12121 std::reverse(Subscripts.begin(), Subscripts.end()); 12122 12123 LLVM_DEBUG({ 12124 dbgs() << "Subscripts:\n"; 12125 for (const SCEV *S : Subscripts) 12126 dbgs() << *S << "\n"; 12127 }); 12128 } 12129 12130 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and 12131 /// sizes of an array access. Returns the remainder of the delinearization that 12132 /// is the offset start of the array. The SCEV->delinearize algorithm computes 12133 /// the multiples of SCEV coefficients: that is a pattern matching of sub 12134 /// expressions in the stride and base of a SCEV corresponding to the 12135 /// computation of a GCD (greatest common divisor) of base and stride. When 12136 /// SCEV->delinearize fails, it returns the SCEV unchanged. 12137 /// 12138 /// For example: when analyzing the memory access A[i][j][k] in this loop nest 12139 /// 12140 /// void foo(long n, long m, long o, double A[n][m][o]) { 12141 /// 12142 /// for (long i = 0; i < n; i++) 12143 /// for (long j = 0; j < m; j++) 12144 /// for (long k = 0; k < o; k++) 12145 /// A[i][j][k] = 1.0; 12146 /// } 12147 /// 12148 /// the delinearization input is the following AddRec SCEV: 12149 /// 12150 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k> 12151 /// 12152 /// From this SCEV, we are able to say that the base offset of the access is %A 12153 /// because it appears as an offset that does not divide any of the strides in 12154 /// the loops: 12155 /// 12156 /// CHECK: Base offset: %A 12157 /// 12158 /// and then SCEV->delinearize determines the size of some of the dimensions of 12159 /// the array as these are the multiples by which the strides are happening: 12160 /// 12161 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes. 12162 /// 12163 /// Note that the outermost dimension remains of UnknownSize because there are 12164 /// no strides that would help identifying the size of the last dimension: when 12165 /// the array has been statically allocated, one could compute the size of that 12166 /// dimension by dividing the overall size of the array by the size of the known 12167 /// dimensions: %m * %o * 8. 12168 /// 12169 /// Finally delinearize provides the access functions for the array reference 12170 /// that does correspond to A[i][j][k] of the above C testcase: 12171 /// 12172 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>] 12173 /// 12174 /// The testcases are checking the output of a function pass: 12175 /// DelinearizationPass that walks through all loads and stores of a function 12176 /// asking for the SCEV of the memory access with respect to all enclosing 12177 /// loops, calling SCEV->delinearize on that and printing the results. 12178 void ScalarEvolution::delinearize(const SCEV *Expr, 12179 SmallVectorImpl<const SCEV *> &Subscripts, 12180 SmallVectorImpl<const SCEV *> &Sizes, 12181 const SCEV *ElementSize) { 12182 // First step: collect parametric terms. 12183 SmallVector<const SCEV *, 4> Terms; 12184 collectParametricTerms(Expr, Terms); 12185 12186 if (Terms.empty()) 12187 return; 12188 12189 // Second step: find subscript sizes. 12190 findArrayDimensions(Terms, Sizes, ElementSize); 12191 12192 if (Sizes.empty()) 12193 return; 12194 12195 // Third step: compute the access functions for each subscript. 12196 computeAccessFunctions(Expr, Subscripts, Sizes); 12197 12198 if (Subscripts.empty()) 12199 return; 12200 12201 LLVM_DEBUG({ 12202 dbgs() << "succeeded to delinearize " << *Expr << "\n"; 12203 dbgs() << "ArrayDecl[UnknownSize]"; 12204 for (const SCEV *S : Sizes) 12205 dbgs() << "[" << *S << "]"; 12206 12207 dbgs() << "\nArrayRef"; 12208 for (const SCEV *S : Subscripts) 12209 dbgs() << "[" << *S << "]"; 12210 dbgs() << "\n"; 12211 }); 12212 } 12213 12214 bool ScalarEvolution::getIndexExpressionsFromGEP( 12215 const GetElementPtrInst *GEP, SmallVectorImpl<const SCEV *> &Subscripts, 12216 SmallVectorImpl<int> &Sizes) { 12217 assert(Subscripts.empty() && Sizes.empty() && 12218 "Expected output lists to be empty on entry to this function."); 12219 assert(GEP && "getIndexExpressionsFromGEP called with a null GEP"); 12220 Type *Ty = GEP->getPointerOperandType(); 12221 bool DroppedFirstDim = false; 12222 for (unsigned i = 1; i < GEP->getNumOperands(); i++) { 12223 const SCEV *Expr = getSCEV(GEP->getOperand(i)); 12224 if (i == 1) { 12225 if (auto *PtrTy = dyn_cast<PointerType>(Ty)) { 12226 Ty = PtrTy->getElementType(); 12227 } else if (auto *ArrayTy = dyn_cast<ArrayType>(Ty)) { 12228 Ty = ArrayTy->getElementType(); 12229 } else { 12230 Subscripts.clear(); 12231 Sizes.clear(); 12232 return false; 12233 } 12234 if (auto *Const = dyn_cast<SCEVConstant>(Expr)) 12235 if (Const->getValue()->isZero()) { 12236 DroppedFirstDim = true; 12237 continue; 12238 } 12239 Subscripts.push_back(Expr); 12240 continue; 12241 } 12242 12243 auto *ArrayTy = dyn_cast<ArrayType>(Ty); 12244 if (!ArrayTy) { 12245 Subscripts.clear(); 12246 Sizes.clear(); 12247 return false; 12248 } 12249 12250 Subscripts.push_back(Expr); 12251 if (!(DroppedFirstDim && i == 2)) 12252 Sizes.push_back(ArrayTy->getNumElements()); 12253 12254 Ty = ArrayTy->getElementType(); 12255 } 12256 return !Subscripts.empty(); 12257 } 12258 12259 //===----------------------------------------------------------------------===// 12260 // SCEVCallbackVH Class Implementation 12261 //===----------------------------------------------------------------------===// 12262 12263 void ScalarEvolution::SCEVCallbackVH::deleted() { 12264 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 12265 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 12266 SE->ConstantEvolutionLoopExitValue.erase(PN); 12267 SE->eraseValueFromMap(getValPtr()); 12268 // this now dangles! 12269 } 12270 12271 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) { 12272 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 12273 12274 // Forget all the expressions associated with users of the old value, 12275 // so that future queries will recompute the expressions using the new 12276 // value. 12277 Value *Old = getValPtr(); 12278 SmallVector<User *, 16> Worklist(Old->users()); 12279 SmallPtrSet<User *, 8> Visited; 12280 while (!Worklist.empty()) { 12281 User *U = Worklist.pop_back_val(); 12282 // Deleting the Old value will cause this to dangle. Postpone 12283 // that until everything else is done. 12284 if (U == Old) 12285 continue; 12286 if (!Visited.insert(U).second) 12287 continue; 12288 if (PHINode *PN = dyn_cast<PHINode>(U)) 12289 SE->ConstantEvolutionLoopExitValue.erase(PN); 12290 SE->eraseValueFromMap(U); 12291 llvm::append_range(Worklist, U->users()); 12292 } 12293 // Delete the Old value. 12294 if (PHINode *PN = dyn_cast<PHINode>(Old)) 12295 SE->ConstantEvolutionLoopExitValue.erase(PN); 12296 SE->eraseValueFromMap(Old); 12297 // this now dangles! 12298 } 12299 12300 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 12301 : CallbackVH(V), SE(se) {} 12302 12303 //===----------------------------------------------------------------------===// 12304 // ScalarEvolution Class Implementation 12305 //===----------------------------------------------------------------------===// 12306 12307 ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI, 12308 AssumptionCache &AC, DominatorTree &DT, 12309 LoopInfo &LI) 12310 : F(F), TLI(TLI), AC(AC), DT(DT), LI(LI), 12311 CouldNotCompute(new SCEVCouldNotCompute()), ValuesAtScopes(64), 12312 LoopDispositions(64), BlockDispositions(64) { 12313 // To use guards for proving predicates, we need to scan every instruction in 12314 // relevant basic blocks, and not just terminators. Doing this is a waste of 12315 // time if the IR does not actually contain any calls to 12316 // @llvm.experimental.guard, so do a quick check and remember this beforehand. 12317 // 12318 // This pessimizes the case where a pass that preserves ScalarEvolution wants 12319 // to _add_ guards to the module when there weren't any before, and wants 12320 // ScalarEvolution to optimize based on those guards. For now we prefer to be 12321 // efficient in lieu of being smart in that rather obscure case. 12322 12323 auto *GuardDecl = F.getParent()->getFunction( 12324 Intrinsic::getName(Intrinsic::experimental_guard)); 12325 HasGuards = GuardDecl && !GuardDecl->use_empty(); 12326 } 12327 12328 ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg) 12329 : F(Arg.F), HasGuards(Arg.HasGuards), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT), 12330 LI(Arg.LI), CouldNotCompute(std::move(Arg.CouldNotCompute)), 12331 ValueExprMap(std::move(Arg.ValueExprMap)), 12332 PendingLoopPredicates(std::move(Arg.PendingLoopPredicates)), 12333 PendingPhiRanges(std::move(Arg.PendingPhiRanges)), 12334 PendingMerges(std::move(Arg.PendingMerges)), 12335 MinTrailingZerosCache(std::move(Arg.MinTrailingZerosCache)), 12336 BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)), 12337 PredicatedBackedgeTakenCounts( 12338 std::move(Arg.PredicatedBackedgeTakenCounts)), 12339 ConstantEvolutionLoopExitValue( 12340 std::move(Arg.ConstantEvolutionLoopExitValue)), 12341 ValuesAtScopes(std::move(Arg.ValuesAtScopes)), 12342 LoopDispositions(std::move(Arg.LoopDispositions)), 12343 LoopPropertiesCache(std::move(Arg.LoopPropertiesCache)), 12344 BlockDispositions(std::move(Arg.BlockDispositions)), 12345 UnsignedRanges(std::move(Arg.UnsignedRanges)), 12346 SignedRanges(std::move(Arg.SignedRanges)), 12347 UniqueSCEVs(std::move(Arg.UniqueSCEVs)), 12348 UniquePreds(std::move(Arg.UniquePreds)), 12349 SCEVAllocator(std::move(Arg.SCEVAllocator)), 12350 LoopUsers(std::move(Arg.LoopUsers)), 12351 PredicatedSCEVRewrites(std::move(Arg.PredicatedSCEVRewrites)), 12352 FirstUnknown(Arg.FirstUnknown) { 12353 Arg.FirstUnknown = nullptr; 12354 } 12355 12356 ScalarEvolution::~ScalarEvolution() { 12357 // Iterate through all the SCEVUnknown instances and call their 12358 // destructors, so that they release their references to their values. 12359 for (SCEVUnknown *U = FirstUnknown; U;) { 12360 SCEVUnknown *Tmp = U; 12361 U = U->Next; 12362 Tmp->~SCEVUnknown(); 12363 } 12364 FirstUnknown = nullptr; 12365 12366 ExprValueMap.clear(); 12367 ValueExprMap.clear(); 12368 HasRecMap.clear(); 12369 BackedgeTakenCounts.clear(); 12370 PredicatedBackedgeTakenCounts.clear(); 12371 12372 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage"); 12373 assert(PendingPhiRanges.empty() && "getRangeRef garbage"); 12374 assert(PendingMerges.empty() && "isImpliedViaMerge garbage"); 12375 assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!"); 12376 assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!"); 12377 } 12378 12379 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 12380 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 12381 } 12382 12383 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 12384 const Loop *L) { 12385 // Print all inner loops first 12386 for (Loop *I : *L) 12387 PrintLoopInfo(OS, SE, I); 12388 12389 OS << "Loop "; 12390 L->getHeader()->printAsOperand(OS, /*PrintType=*/false); 12391 OS << ": "; 12392 12393 SmallVector<BasicBlock *, 8> ExitingBlocks; 12394 L->getExitingBlocks(ExitingBlocks); 12395 if (ExitingBlocks.size() != 1) 12396 OS << "<multiple exits> "; 12397 12398 if (SE->hasLoopInvariantBackedgeTakenCount(L)) 12399 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L) << "\n"; 12400 else 12401 OS << "Unpredictable backedge-taken count.\n"; 12402 12403 if (ExitingBlocks.size() > 1) 12404 for (BasicBlock *ExitingBlock : ExitingBlocks) { 12405 OS << " exit count for " << ExitingBlock->getName() << ": " 12406 << *SE->getExitCount(L, ExitingBlock) << "\n"; 12407 } 12408 12409 OS << "Loop "; 12410 L->getHeader()->printAsOperand(OS, /*PrintType=*/false); 12411 OS << ": "; 12412 12413 if (!isa<SCEVCouldNotCompute>(SE->getConstantMaxBackedgeTakenCount(L))) { 12414 OS << "max backedge-taken count is " << *SE->getConstantMaxBackedgeTakenCount(L); 12415 if (SE->isBackedgeTakenCountMaxOrZero(L)) 12416 OS << ", actual taken count either this or zero."; 12417 } else { 12418 OS << "Unpredictable max backedge-taken count. "; 12419 } 12420 12421 OS << "\n" 12422 "Loop "; 12423 L->getHeader()->printAsOperand(OS, /*PrintType=*/false); 12424 OS << ": "; 12425 12426 SCEVUnionPredicate Pred; 12427 auto PBT = SE->getPredicatedBackedgeTakenCount(L, Pred); 12428 if (!isa<SCEVCouldNotCompute>(PBT)) { 12429 OS << "Predicated backedge-taken count is " << *PBT << "\n"; 12430 OS << " Predicates:\n"; 12431 Pred.print(OS, 4); 12432 } else { 12433 OS << "Unpredictable predicated backedge-taken count. "; 12434 } 12435 OS << "\n"; 12436 12437 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 12438 OS << "Loop "; 12439 L->getHeader()->printAsOperand(OS, /*PrintType=*/false); 12440 OS << ": "; 12441 OS << "Trip multiple is " << SE->getSmallConstantTripMultiple(L) << "\n"; 12442 } 12443 } 12444 12445 static StringRef loopDispositionToStr(ScalarEvolution::LoopDisposition LD) { 12446 switch (LD) { 12447 case ScalarEvolution::LoopVariant: 12448 return "Variant"; 12449 case ScalarEvolution::LoopInvariant: 12450 return "Invariant"; 12451 case ScalarEvolution::LoopComputable: 12452 return "Computable"; 12453 } 12454 llvm_unreachable("Unknown ScalarEvolution::LoopDisposition kind!"); 12455 } 12456 12457 void ScalarEvolution::print(raw_ostream &OS) const { 12458 // ScalarEvolution's implementation of the print method is to print 12459 // out SCEV values of all instructions that are interesting. Doing 12460 // this potentially causes it to create new SCEV objects though, 12461 // which technically conflicts with the const qualifier. This isn't 12462 // observable from outside the class though, so casting away the 12463 // const isn't dangerous. 12464 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 12465 12466 if (ClassifyExpressions) { 12467 OS << "Classifying expressions for: "; 12468 F.printAsOperand(OS, /*PrintType=*/false); 12469 OS << "\n"; 12470 for (Instruction &I : instructions(F)) 12471 if (isSCEVable(I.getType()) && !isa<CmpInst>(I)) { 12472 OS << I << '\n'; 12473 OS << " --> "; 12474 const SCEV *SV = SE.getSCEV(&I); 12475 SV->print(OS); 12476 if (!isa<SCEVCouldNotCompute>(SV)) { 12477 OS << " U: "; 12478 SE.getUnsignedRange(SV).print(OS); 12479 OS << " S: "; 12480 SE.getSignedRange(SV).print(OS); 12481 } 12482 12483 const Loop *L = LI.getLoopFor(I.getParent()); 12484 12485 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 12486 if (AtUse != SV) { 12487 OS << " --> "; 12488 AtUse->print(OS); 12489 if (!isa<SCEVCouldNotCompute>(AtUse)) { 12490 OS << " U: "; 12491 SE.getUnsignedRange(AtUse).print(OS); 12492 OS << " S: "; 12493 SE.getSignedRange(AtUse).print(OS); 12494 } 12495 } 12496 12497 if (L) { 12498 OS << "\t\t" "Exits: "; 12499 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 12500 if (!SE.isLoopInvariant(ExitValue, L)) { 12501 OS << "<<Unknown>>"; 12502 } else { 12503 OS << *ExitValue; 12504 } 12505 12506 bool First = true; 12507 for (auto *Iter = L; Iter; Iter = Iter->getParentLoop()) { 12508 if (First) { 12509 OS << "\t\t" "LoopDispositions: { "; 12510 First = false; 12511 } else { 12512 OS << ", "; 12513 } 12514 12515 Iter->getHeader()->printAsOperand(OS, /*PrintType=*/false); 12516 OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, Iter)); 12517 } 12518 12519 for (auto *InnerL : depth_first(L)) { 12520 if (InnerL == L) 12521 continue; 12522 if (First) { 12523 OS << "\t\t" "LoopDispositions: { "; 12524 First = false; 12525 } else { 12526 OS << ", "; 12527 } 12528 12529 InnerL->getHeader()->printAsOperand(OS, /*PrintType=*/false); 12530 OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, InnerL)); 12531 } 12532 12533 OS << " }"; 12534 } 12535 12536 OS << "\n"; 12537 } 12538 } 12539 12540 OS << "Determining loop execution counts for: "; 12541 F.printAsOperand(OS, /*PrintType=*/false); 12542 OS << "\n"; 12543 for (Loop *I : LI) 12544 PrintLoopInfo(OS, &SE, I); 12545 } 12546 12547 ScalarEvolution::LoopDisposition 12548 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) { 12549 auto &Values = LoopDispositions[S]; 12550 for (auto &V : Values) { 12551 if (V.getPointer() == L) 12552 return V.getInt(); 12553 } 12554 Values.emplace_back(L, LoopVariant); 12555 LoopDisposition D = computeLoopDisposition(S, L); 12556 auto &Values2 = LoopDispositions[S]; 12557 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) { 12558 if (V.getPointer() == L) { 12559 V.setInt(D); 12560 break; 12561 } 12562 } 12563 return D; 12564 } 12565 12566 ScalarEvolution::LoopDisposition 12567 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) { 12568 switch (S->getSCEVType()) { 12569 case scConstant: 12570 return LoopInvariant; 12571 case scPtrToInt: 12572 case scTruncate: 12573 case scZeroExtend: 12574 case scSignExtend: 12575 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L); 12576 case scAddRecExpr: { 12577 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 12578 12579 // If L is the addrec's loop, it's computable. 12580 if (AR->getLoop() == L) 12581 return LoopComputable; 12582 12583 // Add recurrences are never invariant in the function-body (null loop). 12584 if (!L) 12585 return LoopVariant; 12586 12587 // Everything that is not defined at loop entry is variant. 12588 if (DT.dominates(L->getHeader(), AR->getLoop()->getHeader())) 12589 return LoopVariant; 12590 assert(!L->contains(AR->getLoop()) && "Containing loop's header does not" 12591 " dominate the contained loop's header?"); 12592 12593 // This recurrence is invariant w.r.t. L if AR's loop contains L. 12594 if (AR->getLoop()->contains(L)) 12595 return LoopInvariant; 12596 12597 // This recurrence is variant w.r.t. L if any of its operands 12598 // are variant. 12599 for (auto *Op : AR->operands()) 12600 if (!isLoopInvariant(Op, L)) 12601 return LoopVariant; 12602 12603 // Otherwise it's loop-invariant. 12604 return LoopInvariant; 12605 } 12606 case scAddExpr: 12607 case scMulExpr: 12608 case scUMaxExpr: 12609 case scSMaxExpr: 12610 case scUMinExpr: 12611 case scSMinExpr: { 12612 bool HasVarying = false; 12613 for (auto *Op : cast<SCEVNAryExpr>(S)->operands()) { 12614 LoopDisposition D = getLoopDisposition(Op, L); 12615 if (D == LoopVariant) 12616 return LoopVariant; 12617 if (D == LoopComputable) 12618 HasVarying = true; 12619 } 12620 return HasVarying ? LoopComputable : LoopInvariant; 12621 } 12622 case scUDivExpr: { 12623 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 12624 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L); 12625 if (LD == LoopVariant) 12626 return LoopVariant; 12627 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L); 12628 if (RD == LoopVariant) 12629 return LoopVariant; 12630 return (LD == LoopInvariant && RD == LoopInvariant) ? 12631 LoopInvariant : LoopComputable; 12632 } 12633 case scUnknown: 12634 // All non-instruction values are loop invariant. All instructions are loop 12635 // invariant if they are not contained in the specified loop. 12636 // Instructions are never considered invariant in the function body 12637 // (null loop) because they are defined within the "loop". 12638 if (auto *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) 12639 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant; 12640 return LoopInvariant; 12641 case scCouldNotCompute: 12642 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 12643 } 12644 llvm_unreachable("Unknown SCEV kind!"); 12645 } 12646 12647 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) { 12648 return getLoopDisposition(S, L) == LoopInvariant; 12649 } 12650 12651 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) { 12652 return getLoopDisposition(S, L) == LoopComputable; 12653 } 12654 12655 ScalarEvolution::BlockDisposition 12656 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) { 12657 auto &Values = BlockDispositions[S]; 12658 for (auto &V : Values) { 12659 if (V.getPointer() == BB) 12660 return V.getInt(); 12661 } 12662 Values.emplace_back(BB, DoesNotDominateBlock); 12663 BlockDisposition D = computeBlockDisposition(S, BB); 12664 auto &Values2 = BlockDispositions[S]; 12665 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) { 12666 if (V.getPointer() == BB) { 12667 V.setInt(D); 12668 break; 12669 } 12670 } 12671 return D; 12672 } 12673 12674 ScalarEvolution::BlockDisposition 12675 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) { 12676 switch (S->getSCEVType()) { 12677 case scConstant: 12678 return ProperlyDominatesBlock; 12679 case scPtrToInt: 12680 case scTruncate: 12681 case scZeroExtend: 12682 case scSignExtend: 12683 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB); 12684 case scAddRecExpr: { 12685 // This uses a "dominates" query instead of "properly dominates" query 12686 // to test for proper dominance too, because the instruction which 12687 // produces the addrec's value is a PHI, and a PHI effectively properly 12688 // dominates its entire containing block. 12689 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 12690 if (!DT.dominates(AR->getLoop()->getHeader(), BB)) 12691 return DoesNotDominateBlock; 12692 12693 // Fall through into SCEVNAryExpr handling. 12694 LLVM_FALLTHROUGH; 12695 } 12696 case scAddExpr: 12697 case scMulExpr: 12698 case scUMaxExpr: 12699 case scSMaxExpr: 12700 case scUMinExpr: 12701 case scSMinExpr: { 12702 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 12703 bool Proper = true; 12704 for (const SCEV *NAryOp : NAry->operands()) { 12705 BlockDisposition D = getBlockDisposition(NAryOp, BB); 12706 if (D == DoesNotDominateBlock) 12707 return DoesNotDominateBlock; 12708 if (D == DominatesBlock) 12709 Proper = false; 12710 } 12711 return Proper ? ProperlyDominatesBlock : DominatesBlock; 12712 } 12713 case scUDivExpr: { 12714 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 12715 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS(); 12716 BlockDisposition LD = getBlockDisposition(LHS, BB); 12717 if (LD == DoesNotDominateBlock) 12718 return DoesNotDominateBlock; 12719 BlockDisposition RD = getBlockDisposition(RHS, BB); 12720 if (RD == DoesNotDominateBlock) 12721 return DoesNotDominateBlock; 12722 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ? 12723 ProperlyDominatesBlock : DominatesBlock; 12724 } 12725 case scUnknown: 12726 if (Instruction *I = 12727 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) { 12728 if (I->getParent() == BB) 12729 return DominatesBlock; 12730 if (DT.properlyDominates(I->getParent(), BB)) 12731 return ProperlyDominatesBlock; 12732 return DoesNotDominateBlock; 12733 } 12734 return ProperlyDominatesBlock; 12735 case scCouldNotCompute: 12736 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 12737 } 12738 llvm_unreachable("Unknown SCEV kind!"); 12739 } 12740 12741 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) { 12742 return getBlockDisposition(S, BB) >= DominatesBlock; 12743 } 12744 12745 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) { 12746 return getBlockDisposition(S, BB) == ProperlyDominatesBlock; 12747 } 12748 12749 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const { 12750 return SCEVExprContains(S, [&](const SCEV *Expr) { return Expr == Op; }); 12751 } 12752 12753 void 12754 ScalarEvolution::forgetMemoizedResults(const SCEV *S) { 12755 ValuesAtScopes.erase(S); 12756 LoopDispositions.erase(S); 12757 BlockDispositions.erase(S); 12758 UnsignedRanges.erase(S); 12759 SignedRanges.erase(S); 12760 ExprValueMap.erase(S); 12761 HasRecMap.erase(S); 12762 MinTrailingZerosCache.erase(S); 12763 12764 for (auto I = PredicatedSCEVRewrites.begin(); 12765 I != PredicatedSCEVRewrites.end();) { 12766 std::pair<const SCEV *, const Loop *> Entry = I->first; 12767 if (Entry.first == S) 12768 PredicatedSCEVRewrites.erase(I++); 12769 else 12770 ++I; 12771 } 12772 12773 auto RemoveSCEVFromBackedgeMap = 12774 [S](DenseMap<const Loop *, BackedgeTakenInfo> &Map) { 12775 for (auto I = Map.begin(), E = Map.end(); I != E;) { 12776 BackedgeTakenInfo &BEInfo = I->second; 12777 if (BEInfo.hasOperand(S)) 12778 Map.erase(I++); 12779 else 12780 ++I; 12781 } 12782 }; 12783 12784 RemoveSCEVFromBackedgeMap(BackedgeTakenCounts); 12785 RemoveSCEVFromBackedgeMap(PredicatedBackedgeTakenCounts); 12786 } 12787 12788 void 12789 ScalarEvolution::getUsedLoops(const SCEV *S, 12790 SmallPtrSetImpl<const Loop *> &LoopsUsed) { 12791 struct FindUsedLoops { 12792 FindUsedLoops(SmallPtrSetImpl<const Loop *> &LoopsUsed) 12793 : LoopsUsed(LoopsUsed) {} 12794 SmallPtrSetImpl<const Loop *> &LoopsUsed; 12795 bool follow(const SCEV *S) { 12796 if (auto *AR = dyn_cast<SCEVAddRecExpr>(S)) 12797 LoopsUsed.insert(AR->getLoop()); 12798 return true; 12799 } 12800 12801 bool isDone() const { return false; } 12802 }; 12803 12804 FindUsedLoops F(LoopsUsed); 12805 SCEVTraversal<FindUsedLoops>(F).visitAll(S); 12806 } 12807 12808 void ScalarEvolution::addToLoopUseLists(const SCEV *S) { 12809 SmallPtrSet<const Loop *, 8> LoopsUsed; 12810 getUsedLoops(S, LoopsUsed); 12811 for (auto *L : LoopsUsed) 12812 LoopUsers[L].push_back(S); 12813 } 12814 12815 void ScalarEvolution::verify() const { 12816 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 12817 ScalarEvolution SE2(F, TLI, AC, DT, LI); 12818 12819 SmallVector<Loop *, 8> LoopStack(LI.begin(), LI.end()); 12820 12821 // Map's SCEV expressions from one ScalarEvolution "universe" to another. 12822 struct SCEVMapper : public SCEVRewriteVisitor<SCEVMapper> { 12823 SCEVMapper(ScalarEvolution &SE) : SCEVRewriteVisitor<SCEVMapper>(SE) {} 12824 12825 const SCEV *visitConstant(const SCEVConstant *Constant) { 12826 return SE.getConstant(Constant->getAPInt()); 12827 } 12828 12829 const SCEV *visitUnknown(const SCEVUnknown *Expr) { 12830 return SE.getUnknown(Expr->getValue()); 12831 } 12832 12833 const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) { 12834 return SE.getCouldNotCompute(); 12835 } 12836 }; 12837 12838 SCEVMapper SCM(SE2); 12839 12840 while (!LoopStack.empty()) { 12841 auto *L = LoopStack.pop_back_val(); 12842 llvm::append_range(LoopStack, *L); 12843 12844 auto *CurBECount = SCM.visit( 12845 const_cast<ScalarEvolution *>(this)->getBackedgeTakenCount(L)); 12846 auto *NewBECount = SE2.getBackedgeTakenCount(L); 12847 12848 if (CurBECount == SE2.getCouldNotCompute() || 12849 NewBECount == SE2.getCouldNotCompute()) { 12850 // NB! This situation is legal, but is very suspicious -- whatever pass 12851 // change the loop to make a trip count go from could not compute to 12852 // computable or vice-versa *should have* invalidated SCEV. However, we 12853 // choose not to assert here (for now) since we don't want false 12854 // positives. 12855 continue; 12856 } 12857 12858 if (containsUndefs(CurBECount) || containsUndefs(NewBECount)) { 12859 // SCEV treats "undef" as an unknown but consistent value (i.e. it does 12860 // not propagate undef aggressively). This means we can (and do) fail 12861 // verification in cases where a transform makes the trip count of a loop 12862 // go from "undef" to "undef+1" (say). The transform is fine, since in 12863 // both cases the loop iterates "undef" times, but SCEV thinks we 12864 // increased the trip count of the loop by 1 incorrectly. 12865 continue; 12866 } 12867 12868 if (SE.getTypeSizeInBits(CurBECount->getType()) > 12869 SE.getTypeSizeInBits(NewBECount->getType())) 12870 NewBECount = SE2.getZeroExtendExpr(NewBECount, CurBECount->getType()); 12871 else if (SE.getTypeSizeInBits(CurBECount->getType()) < 12872 SE.getTypeSizeInBits(NewBECount->getType())) 12873 CurBECount = SE2.getZeroExtendExpr(CurBECount, NewBECount->getType()); 12874 12875 const SCEV *Delta = SE2.getMinusSCEV(CurBECount, NewBECount); 12876 12877 // Unless VerifySCEVStrict is set, we only compare constant deltas. 12878 if ((VerifySCEVStrict || isa<SCEVConstant>(Delta)) && !Delta->isZero()) { 12879 dbgs() << "Trip Count for " << *L << " Changed!\n"; 12880 dbgs() << "Old: " << *CurBECount << "\n"; 12881 dbgs() << "New: " << *NewBECount << "\n"; 12882 dbgs() << "Delta: " << *Delta << "\n"; 12883 std::abort(); 12884 } 12885 } 12886 12887 // Collect all valid loops currently in LoopInfo. 12888 SmallPtrSet<Loop *, 32> ValidLoops; 12889 SmallVector<Loop *, 32> Worklist(LI.begin(), LI.end()); 12890 while (!Worklist.empty()) { 12891 Loop *L = Worklist.pop_back_val(); 12892 if (ValidLoops.contains(L)) 12893 continue; 12894 ValidLoops.insert(L); 12895 Worklist.append(L->begin(), L->end()); 12896 } 12897 // Check for SCEV expressions referencing invalid/deleted loops. 12898 for (auto &KV : ValueExprMap) { 12899 auto *AR = dyn_cast<SCEVAddRecExpr>(KV.second); 12900 if (!AR) 12901 continue; 12902 assert(ValidLoops.contains(AR->getLoop()) && 12903 "AddRec references invalid loop"); 12904 } 12905 } 12906 12907 bool ScalarEvolution::invalidate( 12908 Function &F, const PreservedAnalyses &PA, 12909 FunctionAnalysisManager::Invalidator &Inv) { 12910 // Invalidate the ScalarEvolution object whenever it isn't preserved or one 12911 // of its dependencies is invalidated. 12912 auto PAC = PA.getChecker<ScalarEvolutionAnalysis>(); 12913 return !(PAC.preserved() || PAC.preservedSet<AllAnalysesOn<Function>>()) || 12914 Inv.invalidate<AssumptionAnalysis>(F, PA) || 12915 Inv.invalidate<DominatorTreeAnalysis>(F, PA) || 12916 Inv.invalidate<LoopAnalysis>(F, PA); 12917 } 12918 12919 AnalysisKey ScalarEvolutionAnalysis::Key; 12920 12921 ScalarEvolution ScalarEvolutionAnalysis::run(Function &F, 12922 FunctionAnalysisManager &AM) { 12923 return ScalarEvolution(F, AM.getResult<TargetLibraryAnalysis>(F), 12924 AM.getResult<AssumptionAnalysis>(F), 12925 AM.getResult<DominatorTreeAnalysis>(F), 12926 AM.getResult<LoopAnalysis>(F)); 12927 } 12928 12929 PreservedAnalyses 12930 ScalarEvolutionVerifierPass::run(Function &F, FunctionAnalysisManager &AM) { 12931 AM.getResult<ScalarEvolutionAnalysis>(F).verify(); 12932 return PreservedAnalyses::all(); 12933 } 12934 12935 PreservedAnalyses 12936 ScalarEvolutionPrinterPass::run(Function &F, FunctionAnalysisManager &AM) { 12937 // For compatibility with opt's -analyze feature under legacy pass manager 12938 // which was not ported to NPM. This keeps tests using 12939 // update_analyze_test_checks.py working. 12940 OS << "Printing analysis 'Scalar Evolution Analysis' for function '" 12941 << F.getName() << "':\n"; 12942 AM.getResult<ScalarEvolutionAnalysis>(F).print(OS); 12943 return PreservedAnalyses::all(); 12944 } 12945 12946 INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution", 12947 "Scalar Evolution Analysis", false, true) 12948 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker) 12949 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass) 12950 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass) 12951 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass) 12952 INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution", 12953 "Scalar Evolution Analysis", false, true) 12954 12955 char ScalarEvolutionWrapperPass::ID = 0; 12956 12957 ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) { 12958 initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry()); 12959 } 12960 12961 bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) { 12962 SE.reset(new ScalarEvolution( 12963 F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(F), 12964 getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F), 12965 getAnalysis<DominatorTreeWrapperPass>().getDomTree(), 12966 getAnalysis<LoopInfoWrapperPass>().getLoopInfo())); 12967 return false; 12968 } 12969 12970 void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); } 12971 12972 void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const { 12973 SE->print(OS); 12974 } 12975 12976 void ScalarEvolutionWrapperPass::verifyAnalysis() const { 12977 if (!VerifySCEV) 12978 return; 12979 12980 SE->verify(); 12981 } 12982 12983 void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const { 12984 AU.setPreservesAll(); 12985 AU.addRequiredTransitive<AssumptionCacheTracker>(); 12986 AU.addRequiredTransitive<LoopInfoWrapperPass>(); 12987 AU.addRequiredTransitive<DominatorTreeWrapperPass>(); 12988 AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>(); 12989 } 12990 12991 const SCEVPredicate *ScalarEvolution::getEqualPredicate(const SCEV *LHS, 12992 const SCEV *RHS) { 12993 FoldingSetNodeID ID; 12994 assert(LHS->getType() == RHS->getType() && 12995 "Type mismatch between LHS and RHS"); 12996 // Unique this node based on the arguments 12997 ID.AddInteger(SCEVPredicate::P_Equal); 12998 ID.AddPointer(LHS); 12999 ID.AddPointer(RHS); 13000 void *IP = nullptr; 13001 if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP)) 13002 return S; 13003 SCEVEqualPredicate *Eq = new (SCEVAllocator) 13004 SCEVEqualPredicate(ID.Intern(SCEVAllocator), LHS, RHS); 13005 UniquePreds.InsertNode(Eq, IP); 13006 return Eq; 13007 } 13008 13009 const SCEVPredicate *ScalarEvolution::getWrapPredicate( 13010 const SCEVAddRecExpr *AR, 13011 SCEVWrapPredicate::IncrementWrapFlags AddedFlags) { 13012 FoldingSetNodeID ID; 13013 // Unique this node based on the arguments 13014 ID.AddInteger(SCEVPredicate::P_Wrap); 13015 ID.AddPointer(AR); 13016 ID.AddInteger(AddedFlags); 13017 void *IP = nullptr; 13018 if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP)) 13019 return S; 13020 auto *OF = new (SCEVAllocator) 13021 SCEVWrapPredicate(ID.Intern(SCEVAllocator), AR, AddedFlags); 13022 UniquePreds.InsertNode(OF, IP); 13023 return OF; 13024 } 13025 13026 namespace { 13027 13028 class SCEVPredicateRewriter : public SCEVRewriteVisitor<SCEVPredicateRewriter> { 13029 public: 13030 13031 /// Rewrites \p S in the context of a loop L and the SCEV predication 13032 /// infrastructure. 13033 /// 13034 /// If \p Pred is non-null, the SCEV expression is rewritten to respect the 13035 /// equivalences present in \p Pred. 13036 /// 13037 /// If \p NewPreds is non-null, rewrite is free to add further predicates to 13038 /// \p NewPreds such that the result will be an AddRecExpr. 13039 static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE, 13040 SmallPtrSetImpl<const SCEVPredicate *> *NewPreds, 13041 SCEVUnionPredicate *Pred) { 13042 SCEVPredicateRewriter Rewriter(L, SE, NewPreds, Pred); 13043 return Rewriter.visit(S); 13044 } 13045 13046 const SCEV *visitUnknown(const SCEVUnknown *Expr) { 13047 if (Pred) { 13048 auto ExprPreds = Pred->getPredicatesForExpr(Expr); 13049 for (auto *Pred : ExprPreds) 13050 if (const auto *IPred = dyn_cast<SCEVEqualPredicate>(Pred)) 13051 if (IPred->getLHS() == Expr) 13052 return IPred->getRHS(); 13053 } 13054 return convertToAddRecWithPreds(Expr); 13055 } 13056 13057 const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) { 13058 const SCEV *Operand = visit(Expr->getOperand()); 13059 const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand); 13060 if (AR && AR->getLoop() == L && AR->isAffine()) { 13061 // This couldn't be folded because the operand didn't have the nuw 13062 // flag. Add the nusw flag as an assumption that we could make. 13063 const SCEV *Step = AR->getStepRecurrence(SE); 13064 Type *Ty = Expr->getType(); 13065 if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNUSW)) 13066 return SE.getAddRecExpr(SE.getZeroExtendExpr(AR->getStart(), Ty), 13067 SE.getSignExtendExpr(Step, Ty), L, 13068 AR->getNoWrapFlags()); 13069 } 13070 return SE.getZeroExtendExpr(Operand, Expr->getType()); 13071 } 13072 13073 const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) { 13074 const SCEV *Operand = visit(Expr->getOperand()); 13075 const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand); 13076 if (AR && AR->getLoop() == L && AR->isAffine()) { 13077 // This couldn't be folded because the operand didn't have the nsw 13078 // flag. Add the nssw flag as an assumption that we could make. 13079 const SCEV *Step = AR->getStepRecurrence(SE); 13080 Type *Ty = Expr->getType(); 13081 if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNSSW)) 13082 return SE.getAddRecExpr(SE.getSignExtendExpr(AR->getStart(), Ty), 13083 SE.getSignExtendExpr(Step, Ty), L, 13084 AR->getNoWrapFlags()); 13085 } 13086 return SE.getSignExtendExpr(Operand, Expr->getType()); 13087 } 13088 13089 private: 13090 explicit SCEVPredicateRewriter(const Loop *L, ScalarEvolution &SE, 13091 SmallPtrSetImpl<const SCEVPredicate *> *NewPreds, 13092 SCEVUnionPredicate *Pred) 13093 : SCEVRewriteVisitor(SE), NewPreds(NewPreds), Pred(Pred), L(L) {} 13094 13095 bool addOverflowAssumption(const SCEVPredicate *P) { 13096 if (!NewPreds) { 13097 // Check if we've already made this assumption. 13098 return Pred && Pred->implies(P); 13099 } 13100 NewPreds->insert(P); 13101 return true; 13102 } 13103 13104 bool addOverflowAssumption(const SCEVAddRecExpr *AR, 13105 SCEVWrapPredicate::IncrementWrapFlags AddedFlags) { 13106 auto *A = SE.getWrapPredicate(AR, AddedFlags); 13107 return addOverflowAssumption(A); 13108 } 13109 13110 // If \p Expr represents a PHINode, we try to see if it can be represented 13111 // as an AddRec, possibly under a predicate (PHISCEVPred). If it is possible 13112 // to add this predicate as a runtime overflow check, we return the AddRec. 13113 // If \p Expr does not meet these conditions (is not a PHI node, or we 13114 // couldn't create an AddRec for it, or couldn't add the predicate), we just 13115 // return \p Expr. 13116 const SCEV *convertToAddRecWithPreds(const SCEVUnknown *Expr) { 13117 if (!isa<PHINode>(Expr->getValue())) 13118 return Expr; 13119 Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>> 13120 PredicatedRewrite = SE.createAddRecFromPHIWithCasts(Expr); 13121 if (!PredicatedRewrite) 13122 return Expr; 13123 for (auto *P : PredicatedRewrite->second){ 13124 // Wrap predicates from outer loops are not supported. 13125 if (auto *WP = dyn_cast<const SCEVWrapPredicate>(P)) { 13126 auto *AR = cast<const SCEVAddRecExpr>(WP->getExpr()); 13127 if (L != AR->getLoop()) 13128 return Expr; 13129 } 13130 if (!addOverflowAssumption(P)) 13131 return Expr; 13132 } 13133 return PredicatedRewrite->first; 13134 } 13135 13136 SmallPtrSetImpl<const SCEVPredicate *> *NewPreds; 13137 SCEVUnionPredicate *Pred; 13138 const Loop *L; 13139 }; 13140 13141 } // end anonymous namespace 13142 13143 const SCEV *ScalarEvolution::rewriteUsingPredicate(const SCEV *S, const Loop *L, 13144 SCEVUnionPredicate &Preds) { 13145 return SCEVPredicateRewriter::rewrite(S, L, *this, nullptr, &Preds); 13146 } 13147 13148 const SCEVAddRecExpr *ScalarEvolution::convertSCEVToAddRecWithPredicates( 13149 const SCEV *S, const Loop *L, 13150 SmallPtrSetImpl<const SCEVPredicate *> &Preds) { 13151 SmallPtrSet<const SCEVPredicate *, 4> TransformPreds; 13152 S = SCEVPredicateRewriter::rewrite(S, L, *this, &TransformPreds, nullptr); 13153 auto *AddRec = dyn_cast<SCEVAddRecExpr>(S); 13154 13155 if (!AddRec) 13156 return nullptr; 13157 13158 // Since the transformation was successful, we can now transfer the SCEV 13159 // predicates. 13160 for (auto *P : TransformPreds) 13161 Preds.insert(P); 13162 13163 return AddRec; 13164 } 13165 13166 /// SCEV predicates 13167 SCEVPredicate::SCEVPredicate(const FoldingSetNodeIDRef ID, 13168 SCEVPredicateKind Kind) 13169 : FastID(ID), Kind(Kind) {} 13170 13171 SCEVEqualPredicate::SCEVEqualPredicate(const FoldingSetNodeIDRef ID, 13172 const SCEV *LHS, const SCEV *RHS) 13173 : SCEVPredicate(ID, P_Equal), LHS(LHS), RHS(RHS) { 13174 assert(LHS->getType() == RHS->getType() && "LHS and RHS types don't match"); 13175 assert(LHS != RHS && "LHS and RHS are the same SCEV"); 13176 } 13177 13178 bool SCEVEqualPredicate::implies(const SCEVPredicate *N) const { 13179 const auto *Op = dyn_cast<SCEVEqualPredicate>(N); 13180 13181 if (!Op) 13182 return false; 13183 13184 return Op->LHS == LHS && Op->RHS == RHS; 13185 } 13186 13187 bool SCEVEqualPredicate::isAlwaysTrue() const { return false; } 13188 13189 const SCEV *SCEVEqualPredicate::getExpr() const { return LHS; } 13190 13191 void SCEVEqualPredicate::print(raw_ostream &OS, unsigned Depth) const { 13192 OS.indent(Depth) << "Equal predicate: " << *LHS << " == " << *RHS << "\n"; 13193 } 13194 13195 SCEVWrapPredicate::SCEVWrapPredicate(const FoldingSetNodeIDRef ID, 13196 const SCEVAddRecExpr *AR, 13197 IncrementWrapFlags Flags) 13198 : SCEVPredicate(ID, P_Wrap), AR(AR), Flags(Flags) {} 13199 13200 const SCEV *SCEVWrapPredicate::getExpr() const { return AR; } 13201 13202 bool SCEVWrapPredicate::implies(const SCEVPredicate *N) const { 13203 const auto *Op = dyn_cast<SCEVWrapPredicate>(N); 13204 13205 return Op && Op->AR == AR && setFlags(Flags, Op->Flags) == Flags; 13206 } 13207 13208 bool SCEVWrapPredicate::isAlwaysTrue() const { 13209 SCEV::NoWrapFlags ScevFlags = AR->getNoWrapFlags(); 13210 IncrementWrapFlags IFlags = Flags; 13211 13212 if (ScalarEvolution::setFlags(ScevFlags, SCEV::FlagNSW) == ScevFlags) 13213 IFlags = clearFlags(IFlags, IncrementNSSW); 13214 13215 return IFlags == IncrementAnyWrap; 13216 } 13217 13218 void SCEVWrapPredicate::print(raw_ostream &OS, unsigned Depth) const { 13219 OS.indent(Depth) << *getExpr() << " Added Flags: "; 13220 if (SCEVWrapPredicate::IncrementNUSW & getFlags()) 13221 OS << "<nusw>"; 13222 if (SCEVWrapPredicate::IncrementNSSW & getFlags()) 13223 OS << "<nssw>"; 13224 OS << "\n"; 13225 } 13226 13227 SCEVWrapPredicate::IncrementWrapFlags 13228 SCEVWrapPredicate::getImpliedFlags(const SCEVAddRecExpr *AR, 13229 ScalarEvolution &SE) { 13230 IncrementWrapFlags ImpliedFlags = IncrementAnyWrap; 13231 SCEV::NoWrapFlags StaticFlags = AR->getNoWrapFlags(); 13232 13233 // We can safely transfer the NSW flag as NSSW. 13234 if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNSW) == StaticFlags) 13235 ImpliedFlags = IncrementNSSW; 13236 13237 if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNUW) == StaticFlags) { 13238 // If the increment is positive, the SCEV NUW flag will also imply the 13239 // WrapPredicate NUSW flag. 13240 if (const auto *Step = dyn_cast<SCEVConstant>(AR->getStepRecurrence(SE))) 13241 if (Step->getValue()->getValue().isNonNegative()) 13242 ImpliedFlags = setFlags(ImpliedFlags, IncrementNUSW); 13243 } 13244 13245 return ImpliedFlags; 13246 } 13247 13248 /// Union predicates don't get cached so create a dummy set ID for it. 13249 SCEVUnionPredicate::SCEVUnionPredicate() 13250 : SCEVPredicate(FoldingSetNodeIDRef(nullptr, 0), P_Union) {} 13251 13252 bool SCEVUnionPredicate::isAlwaysTrue() const { 13253 return all_of(Preds, 13254 [](const SCEVPredicate *I) { return I->isAlwaysTrue(); }); 13255 } 13256 13257 ArrayRef<const SCEVPredicate *> 13258 SCEVUnionPredicate::getPredicatesForExpr(const SCEV *Expr) { 13259 auto I = SCEVToPreds.find(Expr); 13260 if (I == SCEVToPreds.end()) 13261 return ArrayRef<const SCEVPredicate *>(); 13262 return I->second; 13263 } 13264 13265 bool SCEVUnionPredicate::implies(const SCEVPredicate *N) const { 13266 if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N)) 13267 return all_of(Set->Preds, 13268 [this](const SCEVPredicate *I) { return this->implies(I); }); 13269 13270 auto ScevPredsIt = SCEVToPreds.find(N->getExpr()); 13271 if (ScevPredsIt == SCEVToPreds.end()) 13272 return false; 13273 auto &SCEVPreds = ScevPredsIt->second; 13274 13275 return any_of(SCEVPreds, 13276 [N](const SCEVPredicate *I) { return I->implies(N); }); 13277 } 13278 13279 const SCEV *SCEVUnionPredicate::getExpr() const { return nullptr; } 13280 13281 void SCEVUnionPredicate::print(raw_ostream &OS, unsigned Depth) const { 13282 for (auto Pred : Preds) 13283 Pred->print(OS, Depth); 13284 } 13285 13286 void SCEVUnionPredicate::add(const SCEVPredicate *N) { 13287 if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N)) { 13288 for (auto Pred : Set->Preds) 13289 add(Pred); 13290 return; 13291 } 13292 13293 if (implies(N)) 13294 return; 13295 13296 const SCEV *Key = N->getExpr(); 13297 assert(Key && "Only SCEVUnionPredicate doesn't have an " 13298 " associated expression!"); 13299 13300 SCEVToPreds[Key].push_back(N); 13301 Preds.push_back(N); 13302 } 13303 13304 PredicatedScalarEvolution::PredicatedScalarEvolution(ScalarEvolution &SE, 13305 Loop &L) 13306 : SE(SE), L(L) {} 13307 13308 const SCEV *PredicatedScalarEvolution::getSCEV(Value *V) { 13309 const SCEV *Expr = SE.getSCEV(V); 13310 RewriteEntry &Entry = RewriteMap[Expr]; 13311 13312 // If we already have an entry and the version matches, return it. 13313 if (Entry.second && Generation == Entry.first) 13314 return Entry.second; 13315 13316 // We found an entry but it's stale. Rewrite the stale entry 13317 // according to the current predicate. 13318 if (Entry.second) 13319 Expr = Entry.second; 13320 13321 const SCEV *NewSCEV = SE.rewriteUsingPredicate(Expr, &L, Preds); 13322 Entry = {Generation, NewSCEV}; 13323 13324 return NewSCEV; 13325 } 13326 13327 const SCEV *PredicatedScalarEvolution::getBackedgeTakenCount() { 13328 if (!BackedgeCount) { 13329 SCEVUnionPredicate BackedgePred; 13330 BackedgeCount = SE.getPredicatedBackedgeTakenCount(&L, BackedgePred); 13331 addPredicate(BackedgePred); 13332 } 13333 return BackedgeCount; 13334 } 13335 13336 void PredicatedScalarEvolution::addPredicate(const SCEVPredicate &Pred) { 13337 if (Preds.implies(&Pred)) 13338 return; 13339 Preds.add(&Pred); 13340 updateGeneration(); 13341 } 13342 13343 const SCEVUnionPredicate &PredicatedScalarEvolution::getUnionPredicate() const { 13344 return Preds; 13345 } 13346 13347 void PredicatedScalarEvolution::updateGeneration() { 13348 // If the generation number wrapped recompute everything. 13349 if (++Generation == 0) { 13350 for (auto &II : RewriteMap) { 13351 const SCEV *Rewritten = II.second.second; 13352 II.second = {Generation, SE.rewriteUsingPredicate(Rewritten, &L, Preds)}; 13353 } 13354 } 13355 } 13356 13357 void PredicatedScalarEvolution::setNoOverflow( 13358 Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) { 13359 const SCEV *Expr = getSCEV(V); 13360 const auto *AR = cast<SCEVAddRecExpr>(Expr); 13361 13362 auto ImpliedFlags = SCEVWrapPredicate::getImpliedFlags(AR, SE); 13363 13364 // Clear the statically implied flags. 13365 Flags = SCEVWrapPredicate::clearFlags(Flags, ImpliedFlags); 13366 addPredicate(*SE.getWrapPredicate(AR, Flags)); 13367 13368 auto II = FlagsMap.insert({V, Flags}); 13369 if (!II.second) 13370 II.first->second = SCEVWrapPredicate::setFlags(Flags, II.first->second); 13371 } 13372 13373 bool PredicatedScalarEvolution::hasNoOverflow( 13374 Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) { 13375 const SCEV *Expr = getSCEV(V); 13376 const auto *AR = cast<SCEVAddRecExpr>(Expr); 13377 13378 Flags = SCEVWrapPredicate::clearFlags( 13379 Flags, SCEVWrapPredicate::getImpliedFlags(AR, SE)); 13380 13381 auto II = FlagsMap.find(V); 13382 13383 if (II != FlagsMap.end()) 13384 Flags = SCEVWrapPredicate::clearFlags(Flags, II->second); 13385 13386 return Flags == SCEVWrapPredicate::IncrementAnyWrap; 13387 } 13388 13389 const SCEVAddRecExpr *PredicatedScalarEvolution::getAsAddRec(Value *V) { 13390 const SCEV *Expr = this->getSCEV(V); 13391 SmallPtrSet<const SCEVPredicate *, 4> NewPreds; 13392 auto *New = SE.convertSCEVToAddRecWithPredicates(Expr, &L, NewPreds); 13393 13394 if (!New) 13395 return nullptr; 13396 13397 for (auto *P : NewPreds) 13398 Preds.add(P); 13399 13400 updateGeneration(); 13401 RewriteMap[SE.getSCEV(V)] = {Generation, New}; 13402 return New; 13403 } 13404 13405 PredicatedScalarEvolution::PredicatedScalarEvolution( 13406 const PredicatedScalarEvolution &Init) 13407 : RewriteMap(Init.RewriteMap), SE(Init.SE), L(Init.L), Preds(Init.Preds), 13408 Generation(Init.Generation), BackedgeCount(Init.BackedgeCount) { 13409 for (auto I : Init.FlagsMap) 13410 FlagsMap.insert(I); 13411 } 13412 13413 void PredicatedScalarEvolution::print(raw_ostream &OS, unsigned Depth) const { 13414 // For each block. 13415 for (auto *BB : L.getBlocks()) 13416 for (auto &I : *BB) { 13417 if (!SE.isSCEVable(I.getType())) 13418 continue; 13419 13420 auto *Expr = SE.getSCEV(&I); 13421 auto II = RewriteMap.find(Expr); 13422 13423 if (II == RewriteMap.end()) 13424 continue; 13425 13426 // Don't print things that are not interesting. 13427 if (II->second.second == Expr) 13428 continue; 13429 13430 OS.indent(Depth) << "[PSE]" << I << ":\n"; 13431 OS.indent(Depth + 2) << *Expr << "\n"; 13432 OS.indent(Depth + 2) << "--> " << *II->second.second << "\n"; 13433 } 13434 } 13435 13436 // Match the mathematical pattern A - (A / B) * B, where A and B can be 13437 // arbitrary expressions. Also match zext (trunc A to iB) to iY, which is used 13438 // for URem with constant power-of-2 second operands. 13439 // It's not always easy, as A and B can be folded (imagine A is X / 2, and B is 13440 // 4, A / B becomes X / 8). 13441 bool ScalarEvolution::matchURem(const SCEV *Expr, const SCEV *&LHS, 13442 const SCEV *&RHS) { 13443 // Try to match 'zext (trunc A to iB) to iY', which is used 13444 // for URem with constant power-of-2 second operands. Make sure the size of 13445 // the operand A matches the size of the whole expressions. 13446 if (const auto *ZExt = dyn_cast<SCEVZeroExtendExpr>(Expr)) 13447 if (const auto *Trunc = dyn_cast<SCEVTruncateExpr>(ZExt->getOperand(0))) { 13448 LHS = Trunc->getOperand(); 13449 // Bail out if the type of the LHS is larger than the type of the 13450 // expression for now. 13451 if (getTypeSizeInBits(LHS->getType()) > 13452 getTypeSizeInBits(Expr->getType())) 13453 return false; 13454 if (LHS->getType() != Expr->getType()) 13455 LHS = getZeroExtendExpr(LHS, Expr->getType()); 13456 RHS = getConstant(APInt(getTypeSizeInBits(Expr->getType()), 1) 13457 << getTypeSizeInBits(Trunc->getType())); 13458 return true; 13459 } 13460 const auto *Add = dyn_cast<SCEVAddExpr>(Expr); 13461 if (Add == nullptr || Add->getNumOperands() != 2) 13462 return false; 13463 13464 const SCEV *A = Add->getOperand(1); 13465 const auto *Mul = dyn_cast<SCEVMulExpr>(Add->getOperand(0)); 13466 13467 if (Mul == nullptr) 13468 return false; 13469 13470 const auto MatchURemWithDivisor = [&](const SCEV *B) { 13471 // (SomeExpr + (-(SomeExpr / B) * B)). 13472 if (Expr == getURemExpr(A, B)) { 13473 LHS = A; 13474 RHS = B; 13475 return true; 13476 } 13477 return false; 13478 }; 13479 13480 // (SomeExpr + (-1 * (SomeExpr / B) * B)). 13481 if (Mul->getNumOperands() == 3 && isa<SCEVConstant>(Mul->getOperand(0))) 13482 return MatchURemWithDivisor(Mul->getOperand(1)) || 13483 MatchURemWithDivisor(Mul->getOperand(2)); 13484 13485 // (SomeExpr + ((-SomeExpr / B) * B)) or (SomeExpr + ((SomeExpr / B) * -B)). 13486 if (Mul->getNumOperands() == 2) 13487 return MatchURemWithDivisor(Mul->getOperand(1)) || 13488 MatchURemWithDivisor(Mul->getOperand(0)) || 13489 MatchURemWithDivisor(getNegativeSCEV(Mul->getOperand(1))) || 13490 MatchURemWithDivisor(getNegativeSCEV(Mul->getOperand(0))); 13491 return false; 13492 } 13493 13494 const SCEV * 13495 ScalarEvolution::computeSymbolicMaxBackedgeTakenCount(const Loop *L) { 13496 SmallVector<BasicBlock*, 16> ExitingBlocks; 13497 L->getExitingBlocks(ExitingBlocks); 13498 13499 // Form an expression for the maximum exit count possible for this loop. We 13500 // merge the max and exact information to approximate a version of 13501 // getConstantMaxBackedgeTakenCount which isn't restricted to just constants. 13502 SmallVector<const SCEV*, 4> ExitCounts; 13503 for (BasicBlock *ExitingBB : ExitingBlocks) { 13504 const SCEV *ExitCount = getExitCount(L, ExitingBB); 13505 if (isa<SCEVCouldNotCompute>(ExitCount)) 13506 ExitCount = getExitCount(L, ExitingBB, 13507 ScalarEvolution::ConstantMaximum); 13508 if (!isa<SCEVCouldNotCompute>(ExitCount)) { 13509 assert(DT.dominates(ExitingBB, L->getLoopLatch()) && 13510 "We should only have known counts for exiting blocks that " 13511 "dominate latch!"); 13512 ExitCounts.push_back(ExitCount); 13513 } 13514 } 13515 if (ExitCounts.empty()) 13516 return getCouldNotCompute(); 13517 return getUMinFromMismatchedTypes(ExitCounts); 13518 } 13519 13520 /// This rewriter is similar to SCEVParameterRewriter (it replaces SCEVUnknown 13521 /// components following the Map (Value -> SCEV)), but skips AddRecExpr because 13522 /// we cannot guarantee that the replacement is loop invariant in the loop of 13523 /// the AddRec. 13524 class SCEVLoopGuardRewriter : public SCEVRewriteVisitor<SCEVLoopGuardRewriter> { 13525 ValueToSCEVMapTy ⤅ 13526 13527 public: 13528 SCEVLoopGuardRewriter(ScalarEvolution &SE, ValueToSCEVMapTy &M) 13529 : SCEVRewriteVisitor(SE), Map(M) {} 13530 13531 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) { return Expr; } 13532 13533 const SCEV *visitUnknown(const SCEVUnknown *Expr) { 13534 auto I = Map.find(Expr->getValue()); 13535 if (I == Map.end()) 13536 return Expr; 13537 return I->second; 13538 } 13539 }; 13540 13541 const SCEV *ScalarEvolution::applyLoopGuards(const SCEV *Expr, const Loop *L) { 13542 auto CollectCondition = [&](ICmpInst::Predicate Predicate, const SCEV *LHS, 13543 const SCEV *RHS, ValueToSCEVMapTy &RewriteMap) { 13544 // If we have LHS == 0, check if LHS is computing a property of some unknown 13545 // SCEV %v which we can rewrite %v to express explicitly. 13546 const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS); 13547 if (Predicate == CmpInst::ICMP_EQ && RHSC && 13548 RHSC->getValue()->isNullValue()) { 13549 // If LHS is A % B, i.e. A % B == 0, rewrite A to (A /u B) * B to 13550 // explicitly express that. 13551 const SCEV *URemLHS = nullptr; 13552 const SCEV *URemRHS = nullptr; 13553 if (matchURem(LHS, URemLHS, URemRHS)) { 13554 if (const SCEVUnknown *LHSUnknown = dyn_cast<SCEVUnknown>(URemLHS)) { 13555 Value *V = LHSUnknown->getValue(); 13556 auto Multiple = 13557 getMulExpr(getUDivExpr(URemLHS, URemRHS), URemRHS, 13558 (SCEV::NoWrapFlags)(SCEV::FlagNUW | SCEV::FlagNSW)); 13559 RewriteMap[V] = Multiple; 13560 return; 13561 } 13562 } 13563 } 13564 13565 if (!isa<SCEVUnknown>(LHS)) { 13566 std::swap(LHS, RHS); 13567 Predicate = CmpInst::getSwappedPredicate(Predicate); 13568 } 13569 13570 // For now, limit to conditions that provide information about unknown 13571 // expressions. 13572 auto *LHSUnknown = dyn_cast<SCEVUnknown>(LHS); 13573 if (!LHSUnknown) 13574 return; 13575 13576 // Check whether LHS has already been rewritten. In that case we want to 13577 // chain further rewrites onto the already rewritten value. 13578 auto I = RewriteMap.find(LHSUnknown->getValue()); 13579 const SCEV *RewrittenLHS = I != RewriteMap.end() ? I->second : LHS; 13580 13581 // TODO: use information from more predicates. 13582 switch (Predicate) { 13583 case CmpInst::ICMP_ULT: 13584 if (!containsAddRecurrence(RHS)) 13585 RewriteMap[LHSUnknown->getValue()] = getUMinExpr( 13586 RewrittenLHS, getMinusSCEV(RHS, getOne(RHS->getType()))); 13587 break; 13588 case CmpInst::ICMP_ULE: 13589 if (!containsAddRecurrence(RHS)) 13590 RewriteMap[LHSUnknown->getValue()] = getUMinExpr(RewrittenLHS, RHS); 13591 break; 13592 case CmpInst::ICMP_UGT: 13593 if (!containsAddRecurrence(RHS)) 13594 RewriteMap[LHSUnknown->getValue()] = 13595 getUMaxExpr(RewrittenLHS, getAddExpr(RHS, getOne(RHS->getType()))); 13596 break; 13597 case CmpInst::ICMP_UGE: 13598 if (!containsAddRecurrence(RHS)) 13599 RewriteMap[LHSUnknown->getValue()] = getUMaxExpr(RewrittenLHS, RHS); 13600 break; 13601 case CmpInst::ICMP_EQ: 13602 if (isa<SCEVConstant>(RHS)) 13603 RewriteMap[LHSUnknown->getValue()] = RHS; 13604 break; 13605 case CmpInst::ICMP_NE: 13606 if (isa<SCEVConstant>(RHS) && 13607 cast<SCEVConstant>(RHS)->getValue()->isNullValue()) 13608 RewriteMap[LHSUnknown->getValue()] = 13609 getUMaxExpr(RewrittenLHS, getOne(RHS->getType())); 13610 break; 13611 default: 13612 break; 13613 } 13614 }; 13615 // Starting at the loop predecessor, climb up the predecessor chain, as long 13616 // as there are predecessors that can be found that have unique successors 13617 // leading to the original header. 13618 // TODO: share this logic with isLoopEntryGuardedByCond. 13619 ValueToSCEVMapTy RewriteMap; 13620 for (std::pair<const BasicBlock *, const BasicBlock *> Pair( 13621 L->getLoopPredecessor(), L->getHeader()); 13622 Pair.first; Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { 13623 13624 const BranchInst *LoopEntryPredicate = 13625 dyn_cast<BranchInst>(Pair.first->getTerminator()); 13626 if (!LoopEntryPredicate || LoopEntryPredicate->isUnconditional()) 13627 continue; 13628 13629 bool EnterIfTrue = LoopEntryPredicate->getSuccessor(0) == Pair.second; 13630 SmallVector<Value *, 8> Worklist; 13631 SmallPtrSet<Value *, 8> Visited; 13632 Worklist.push_back(LoopEntryPredicate->getCondition()); 13633 while (!Worklist.empty()) { 13634 Value *Cond = Worklist.pop_back_val(); 13635 if (!Visited.insert(Cond).second) 13636 continue; 13637 13638 if (auto *Cmp = dyn_cast<ICmpInst>(Cond)) { 13639 auto Predicate = 13640 EnterIfTrue ? Cmp->getPredicate() : Cmp->getInversePredicate(); 13641 CollectCondition(Predicate, getSCEV(Cmp->getOperand(0)), 13642 getSCEV(Cmp->getOperand(1)), RewriteMap); 13643 continue; 13644 } 13645 13646 Value *L, *R; 13647 if (EnterIfTrue ? match(Cond, m_LogicalAnd(m_Value(L), m_Value(R))) 13648 : match(Cond, m_LogicalOr(m_Value(L), m_Value(R)))) { 13649 Worklist.push_back(L); 13650 Worklist.push_back(R); 13651 } 13652 } 13653 } 13654 13655 // Also collect information from assumptions dominating the loop. 13656 for (auto &AssumeVH : AC.assumptions()) { 13657 if (!AssumeVH) 13658 continue; 13659 auto *AssumeI = cast<CallInst>(AssumeVH); 13660 auto *Cmp = dyn_cast<ICmpInst>(AssumeI->getOperand(0)); 13661 if (!Cmp || !DT.dominates(AssumeI, L->getHeader())) 13662 continue; 13663 CollectCondition(Cmp->getPredicate(), getSCEV(Cmp->getOperand(0)), 13664 getSCEV(Cmp->getOperand(1)), RewriteMap); 13665 } 13666 13667 if (RewriteMap.empty()) 13668 return Expr; 13669 SCEVLoopGuardRewriter Rewriter(*this, RewriteMap); 13670 return Rewriter.visit(Expr); 13671 } 13672