LLVM  6.0.0svn
ScalarEvolution.cpp
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1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
2 //
3 // The LLVM Compiler Infrastructure
4 //
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
7 //
8 //===----------------------------------------------------------------------===//
9 //
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
13 //
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. We only create one SCEV of a particular shape, so
18 // pointer-comparisons for equality are legal.
19 //
20 // One important aspect of the SCEV objects is that they are never cyclic, even
21 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
22 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
23 // recurrence) then we represent it directly as a recurrence node, otherwise we
24 // represent it as a SCEVUnknown node.
25 //
26 // In addition to being able to represent expressions of various types, we also
27 // have folders that are used to build the *canonical* representation for a
28 // particular expression. These folders are capable of using a variety of
29 // rewrite rules to simplify the expressions.
30 //
31 // Once the folders are defined, we can implement the more interesting
32 // higher-level code, such as the code that recognizes PHI nodes of various
33 // types, computes the execution count of a loop, etc.
34 //
35 // TODO: We should use these routines and value representations to implement
36 // dependence analysis!
37 //
38 //===----------------------------------------------------------------------===//
39 //
40 // There are several good references for the techniques used in this analysis.
41 //
42 // Chains of recurrences -- a method to expedite the evaluation
43 // of closed-form functions
44 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
45 //
46 // On computational properties of chains of recurrences
47 // Eugene V. Zima
48 //
49 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
50 // Robert A. van Engelen
51 //
52 // Efficient Symbolic Analysis for Optimizing Compilers
53 // Robert A. van Engelen
54 //
55 // Using the chains of recurrences algebra for data dependence testing and
56 // induction variable substitution
57 // MS Thesis, Johnie Birch
58 //
59 //===----------------------------------------------------------------------===//
60 
62 #include "llvm/ADT/APInt.h"
63 #include "llvm/ADT/ArrayRef.h"
64 #include "llvm/ADT/DenseMap.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"
81 #include "llvm/Analysis/LoopInfo.h"
85 #include "llvm/IR/Argument.h"
86 #include "llvm/IR/BasicBlock.h"
87 #include "llvm/IR/CFG.h"
88 #include "llvm/IR/CallSite.h"
89 #include "llvm/IR/Constant.h"
90 #include "llvm/IR/ConstantRange.h"
91 #include "llvm/IR/Constants.h"
92 #include "llvm/IR/DataLayout.h"
93 #include "llvm/IR/DerivedTypes.h"
94 #include "llvm/IR/Dominators.h"
95 #include "llvm/IR/Function.h"
96 #include "llvm/IR/GlobalAlias.h"
97 #include "llvm/IR/GlobalValue.h"
98 #include "llvm/IR/GlobalVariable.h"
99 #include "llvm/IR/InstIterator.h"
100 #include "llvm/IR/InstrTypes.h"
101 #include "llvm/IR/Instruction.h"
102 #include "llvm/IR/Instructions.h"
103 #include "llvm/IR/IntrinsicInst.h"
104 #include "llvm/IR/Intrinsics.h"
105 #include "llvm/IR/LLVMContext.h"
106 #include "llvm/IR/Metadata.h"
107 #include "llvm/IR/Operator.h"
108 #include "llvm/IR/PatternMatch.h"
109 #include "llvm/IR/Type.h"
110 #include "llvm/IR/Use.h"
111 #include "llvm/IR/User.h"
112 #include "llvm/IR/Value.h"
113 #include "llvm/Pass.h"
114 #include "llvm/Support/Casting.h"
116 #include "llvm/Support/Compiler.h"
117 #include "llvm/Support/Debug.h"
119 #include "llvm/Support/KnownBits.h"
122 #include <algorithm>
123 #include <cassert>
124 #include <climits>
125 #include <cstddef>
126 #include <cstdint>
127 #include <cstdlib>
128 #include <map>
129 #include <memory>
130 #include <tuple>
131 #include <utility>
132 #include <vector>
133 
134 using namespace llvm;
135 
136 #define DEBUG_TYPE "scalar-evolution"
137 
138 STATISTIC(NumArrayLenItCounts,
139  "Number of trip counts computed with array length");
140 STATISTIC(NumTripCountsComputed,
141  "Number of loops with predictable loop counts");
142 STATISTIC(NumTripCountsNotComputed,
143  "Number of loops without predictable loop counts");
144 STATISTIC(NumBruteForceTripCountsComputed,
145  "Number of loops with trip counts computed by force");
146 
147 static cl::opt<unsigned>
148 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
149  cl::desc("Maximum number of iterations SCEV will "
150  "symbolically execute a constant "
151  "derived loop"),
152  cl::init(100));
153 
154 // FIXME: Enable this with EXPENSIVE_CHECKS when the test suite is clean.
155 static cl::opt<bool>
156 VerifySCEV("verify-scev",
157  cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
158 static cl::opt<bool>
159  VerifySCEVMap("verify-scev-maps",
160  cl::desc("Verify no dangling value in ScalarEvolution's "
161  "ExprValueMap (slow)"));
162 
164  "scev-mulops-inline-threshold", cl::Hidden,
165  cl::desc("Threshold for inlining multiplication operands into a SCEV"),
166  cl::init(32));
167 
169  "scev-addops-inline-threshold", cl::Hidden,
170  cl::desc("Threshold for inlining addition operands into a SCEV"),
171  cl::init(500));
172 
174  "scalar-evolution-max-scev-compare-depth", cl::Hidden,
175  cl::desc("Maximum depth of recursive SCEV complexity comparisons"),
176  cl::init(32));
177 
179  "scalar-evolution-max-scev-operations-implication-depth", cl::Hidden,
180  cl::desc("Maximum depth of recursive SCEV operations implication analysis"),
181  cl::init(2));
182 
184  "scalar-evolution-max-value-compare-depth", cl::Hidden,
185  cl::desc("Maximum depth of recursive value complexity comparisons"),
186  cl::init(2));
187 
188 static cl::opt<unsigned>
189  MaxArithDepth("scalar-evolution-max-arith-depth", cl::Hidden,
190  cl::desc("Maximum depth of recursive arithmetics"),
191  cl::init(32));
192 
194  "scalar-evolution-max-constant-evolving-depth", cl::Hidden,
195  cl::desc("Maximum depth of recursive constant evolving"), cl::init(32));
196 
197 static cl::opt<unsigned>
198  MaxExtDepth("scalar-evolution-max-ext-depth", cl::Hidden,
199  cl::desc("Maximum depth of recursive SExt/ZExt"),
200  cl::init(8));
201 
202 static cl::opt<unsigned>
203  MaxAddRecSize("scalar-evolution-max-add-rec-size", cl::Hidden,
204  cl::desc("Max coefficients in AddRec during evolving"),
205  cl::init(16));
206 
207 //===----------------------------------------------------------------------===//
208 // SCEV class definitions
209 //===----------------------------------------------------------------------===//
210 
211 //===----------------------------------------------------------------------===//
212 // Implementation of the SCEV class.
213 //
214 
215 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
217  print(dbgs());
218  dbgs() << '\n';
219 }
220 #endif
221 
222 void SCEV::print(raw_ostream &OS) const {
223  switch (static_cast<SCEVTypes>(getSCEVType())) {
224  case scConstant:
225  cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
226  return;
227  case scTruncate: {
228  const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
229  const SCEV *Op = Trunc->getOperand();
230  OS << "(trunc " << *Op->getType() << " " << *Op << " to "
231  << *Trunc->getType() << ")";
232  return;
233  }
234  case scZeroExtend: {
235  const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
236  const SCEV *Op = ZExt->getOperand();
237  OS << "(zext " << *Op->getType() << " " << *Op << " to "
238  << *ZExt->getType() << ")";
239  return;
240  }
241  case scSignExtend: {
242  const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
243  const SCEV *Op = SExt->getOperand();
244  OS << "(sext " << *Op->getType() << " " << *Op << " to "
245  << *SExt->getType() << ")";
246  return;
247  }
248  case scAddRecExpr: {
249  const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
250  OS << "{" << *AR->getOperand(0);
251  for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
252  OS << ",+," << *AR->getOperand(i);
253  OS << "}<";
254  if (AR->hasNoUnsignedWrap())
255  OS << "nuw><";
256  if (AR->hasNoSignedWrap())
257  OS << "nsw><";
258  if (AR->hasNoSelfWrap() &&
260  OS << "nw><";
261  AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
262  OS << ">";
263  return;
264  }
265  case scAddExpr:
266  case scMulExpr:
267  case scUMaxExpr:
268  case scSMaxExpr: {
269  const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
270  const char *OpStr = nullptr;
271  switch (NAry->getSCEVType()) {
272  case scAddExpr: OpStr = " + "; break;
273  case scMulExpr: OpStr = " * "; break;
274  case scUMaxExpr: OpStr = " umax "; break;
275  case scSMaxExpr: OpStr = " smax "; break;
276  }
277  OS << "(";
278  for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
279  I != E; ++I) {
280  OS << **I;
281  if (std::next(I) != E)
282  OS << OpStr;
283  }
284  OS << ")";
285  switch (NAry->getSCEVType()) {
286  case scAddExpr:
287  case scMulExpr:
288  if (NAry->hasNoUnsignedWrap())
289  OS << "<nuw>";
290  if (NAry->hasNoSignedWrap())
291  OS << "<nsw>";
292  }
293  return;
294  }
295  case scUDivExpr: {
296  const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
297  OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
298  return;
299  }
300  case scUnknown: {
301  const SCEVUnknown *U = cast<SCEVUnknown>(this);
302  Type *AllocTy;
303  if (U->isSizeOf(AllocTy)) {
304  OS << "sizeof(" << *AllocTy << ")";
305  return;
306  }
307  if (U->isAlignOf(AllocTy)) {
308  OS << "alignof(" << *AllocTy << ")";
309  return;
310  }
311 
312  Type *CTy;
313  Constant *FieldNo;
314  if (U->isOffsetOf(CTy, FieldNo)) {
315  OS << "offsetof(" << *CTy << ", ";
316  FieldNo->printAsOperand(OS, false);
317  OS << ")";
318  return;
319  }
320 
321  // Otherwise just print it normally.
322  U->getValue()->printAsOperand(OS, false);
323  return;
324  }
325  case scCouldNotCompute:
326  OS << "***COULDNOTCOMPUTE***";
327  return;
328  }
329  llvm_unreachable("Unknown SCEV kind!");
330 }
331 
332 Type *SCEV::getType() const {
333  switch (static_cast<SCEVTypes>(getSCEVType())) {
334  case scConstant:
335  return cast<SCEVConstant>(this)->getType();
336  case scTruncate:
337  case scZeroExtend:
338  case scSignExtend:
339  return cast<SCEVCastExpr>(this)->getType();
340  case scAddRecExpr:
341  case scMulExpr:
342  case scUMaxExpr:
343  case scSMaxExpr:
344  return cast<SCEVNAryExpr>(this)->getType();
345  case scAddExpr:
346  return cast<SCEVAddExpr>(this)->getType();
347  case scUDivExpr:
348  return cast<SCEVUDivExpr>(this)->getType();
349  case scUnknown:
350  return cast<SCEVUnknown>(this)->getType();
351  case scCouldNotCompute:
352  llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
353  }
354  llvm_unreachable("Unknown SCEV kind!");
355 }
356 
357 bool SCEV::isZero() const {
358  if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
359  return SC->getValue()->isZero();
360  return false;
361 }
362 
363 bool SCEV::isOne() const {
364  if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
365  return SC->getValue()->isOne();
366  return false;
367 }
368 
369 bool SCEV::isAllOnesValue() const {
370  if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
371  return SC->getValue()->isMinusOne();
372  return false;
373 }
374 
376  const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
377  if (!Mul) return false;
378 
379  // If there is a constant factor, it will be first.
380  const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
381  if (!SC) return false;
382 
383  // Return true if the value is negative, this matches things like (-42 * V).
384  return SC->getAPInt().isNegative();
385 }
386 
389 
391  return S->getSCEVType() == scCouldNotCompute;
392 }
393 
397  ID.AddPointer(V);
398  void *IP = nullptr;
399  if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
400  SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
401  UniqueSCEVs.InsertNode(S, IP);
402  return S;
403 }
404 
406  return getConstant(ConstantInt::get(getContext(), Val));
407 }
408 
409 const SCEV *
410 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
411  IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
412  return getConstant(ConstantInt::get(ITy, V, isSigned));
413 }
414 
416  unsigned SCEVTy, const SCEV *op, Type *ty)
417  : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
418 
419 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
420  const SCEV *op, Type *ty)
421  : SCEVCastExpr(ID, scTruncate, op, ty) {
422  assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
423  (Ty->isIntegerTy() || Ty->isPointerTy()) &&
424  "Cannot truncate non-integer value!");
425 }
426 
427 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
428  const SCEV *op, Type *ty)
429  : SCEVCastExpr(ID, scZeroExtend, op, ty) {
430  assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
431  (Ty->isIntegerTy() || Ty->isPointerTy()) &&
432  "Cannot zero extend non-integer value!");
433 }
434 
435 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
436  const SCEV *op, Type *ty)
437  : SCEVCastExpr(ID, scSignExtend, op, ty) {
438  assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
439  (Ty->isIntegerTy() || Ty->isPointerTy()) &&
440  "Cannot sign extend non-integer value!");
441 }
442 
443 void SCEVUnknown::deleted() {
444  // Clear this SCEVUnknown from various maps.
445  SE->forgetMemoizedResults(this);
446 
447  // Remove this SCEVUnknown from the uniquing map.
448  SE->UniqueSCEVs.RemoveNode(this);
449 
450  // Release the value.
451  setValPtr(nullptr);
452 }
453 
454 void SCEVUnknown::allUsesReplacedWith(Value *New) {
455  // Remove this SCEVUnknown from the uniquing map.
456  SE->UniqueSCEVs.RemoveNode(this);
457 
458  // Update this SCEVUnknown to point to the new value. This is needed
459  // because there may still be outstanding SCEVs which still point to
460  // this SCEVUnknown.
461  setValPtr(New);
462 }
463 
464 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
465  if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
466  if (VCE->getOpcode() == Instruction::PtrToInt)
467  if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
468  if (CE->getOpcode() == Instruction::GetElementPtr &&
469  CE->getOperand(0)->isNullValue() &&
470  CE->getNumOperands() == 2)
471  if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
472  if (CI->isOne()) {
473  AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
474  ->getElementType();
475  return true;
476  }
477 
478  return false;
479 }
480 
481 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
482  if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
483  if (VCE->getOpcode() == Instruction::PtrToInt)
484  if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
485  if (CE->getOpcode() == Instruction::GetElementPtr &&
486  CE->getOperand(0)->isNullValue()) {
487  Type *Ty =
488  cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
489  if (StructType *STy = dyn_cast<StructType>(Ty))
490  if (!STy->isPacked() &&
491  CE->getNumOperands() == 3 &&
492  CE->getOperand(1)->isNullValue()) {
493  if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
494  if (CI->isOne() &&
495  STy->getNumElements() == 2 &&
496  STy->getElementType(0)->isIntegerTy(1)) {
497  AllocTy = STy->getElementType(1);
498  return true;
499  }
500  }
501  }
502 
503  return false;
504 }
505 
506 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
507  if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
508  if (VCE->getOpcode() == Instruction::PtrToInt)
509  if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
510  if (CE->getOpcode() == Instruction::GetElementPtr &&
511  CE->getNumOperands() == 3 &&
512  CE->getOperand(0)->isNullValue() &&
513  CE->getOperand(1)->isNullValue()) {
514  Type *Ty =
515  cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
516  // Ignore vector types here so that ScalarEvolutionExpander doesn't
517  // emit getelementptrs that index into vectors.
518  if (Ty->isStructTy() || Ty->isArrayTy()) {
519  CTy = Ty;
520  FieldNo = CE->getOperand(2);
521  return true;
522  }
523  }
524 
525  return false;
526 }
527 
528 //===----------------------------------------------------------------------===//
529 // SCEV Utilities
530 //===----------------------------------------------------------------------===//
531 
532 /// Compare the two values \p LV and \p RV in terms of their "complexity" where
533 /// "complexity" is a partial (and somewhat ad-hoc) relation used to order
534 /// operands in SCEV expressions. \p EqCache is a set of pairs of values that
535 /// have been previously deemed to be "equally complex" by this routine. It is
536 /// intended to avoid exponential time complexity in cases like:
537 ///
538 /// %a = f(%x, %y)
539 /// %b = f(%a, %a)
540 /// %c = f(%b, %b)
541 ///
542 /// %d = f(%x, %y)
543 /// %e = f(%d, %d)
544 /// %f = f(%e, %e)
545 ///
546 /// CompareValueComplexity(%f, %c)
547 ///
548 /// Since we do not continue running this routine on expression trees once we
549 /// have seen unequal values, there is no need to track them in the cache.
550 static int
551 CompareValueComplexity(SmallSet<std::pair<Value *, Value *>, 8> &EqCache,
552  const LoopInfo *const LI, Value *LV, Value *RV,
553  unsigned Depth) {
554  if (Depth > MaxValueCompareDepth || EqCache.count({LV, RV}))
555  return 0;
556 
557  // Order pointer values after integer values. This helps SCEVExpander form
558  // GEPs.
559  bool LIsPointer = LV->getType()->isPointerTy(),
560  RIsPointer = RV->getType()->isPointerTy();
561  if (LIsPointer != RIsPointer)
562  return (int)LIsPointer - (int)RIsPointer;
563 
564  // Compare getValueID values.
565  unsigned LID = LV->getValueID(), RID = RV->getValueID();
566  if (LID != RID)
567  return (int)LID - (int)RID;
568 
569  // Sort arguments by their position.
570  if (const auto *LA = dyn_cast<Argument>(LV)) {
571  const auto *RA = cast<Argument>(RV);
572  unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
573  return (int)LArgNo - (int)RArgNo;
574  }
575 
576  if (const auto *LGV = dyn_cast<GlobalValue>(LV)) {
577  const auto *RGV = cast<GlobalValue>(RV);
578 
579  const auto IsGVNameSemantic = [&](const GlobalValue *GV) {
580  auto LT = GV->getLinkage();
581  return !(GlobalValue::isPrivateLinkage(LT) ||
583  };
584 
585  // Use the names to distinguish the two values, but only if the
586  // names are semantically important.
587  if (IsGVNameSemantic(LGV) && IsGVNameSemantic(RGV))
588  return LGV->getName().compare(RGV->getName());
589  }
590 
591  // For instructions, compare their loop depth, and their operand count. This
592  // is pretty loose.
593  if (const auto *LInst = dyn_cast<Instruction>(LV)) {
594  const auto *RInst = cast<Instruction>(RV);
595 
596  // Compare loop depths.
597  const BasicBlock *LParent = LInst->getParent(),
598  *RParent = RInst->getParent();
599  if (LParent != RParent) {
600  unsigned LDepth = LI->getLoopDepth(LParent),
601  RDepth = LI->getLoopDepth(RParent);
602  if (LDepth != RDepth)
603  return (int)LDepth - (int)RDepth;
604  }
605 
606  // Compare the number of operands.
607  unsigned LNumOps = LInst->getNumOperands(),
608  RNumOps = RInst->getNumOperands();
609  if (LNumOps != RNumOps)
610  return (int)LNumOps - (int)RNumOps;
611 
612  for (unsigned Idx : seq(0u, LNumOps)) {
613  int Result =
614  CompareValueComplexity(EqCache, LI, LInst->getOperand(Idx),
615  RInst->getOperand(Idx), Depth + 1);
616  if (Result != 0)
617  return Result;
618  }
619  }
620 
621  EqCache.insert({LV, RV});
622  return 0;
623 }
624 
625 // Return negative, zero, or positive, if LHS is less than, equal to, or greater
626 // than RHS, respectively. A three-way result allows recursive comparisons to be
627 // more efficient.
629  SmallSet<std::pair<const SCEV *, const SCEV *>, 8> &EqCacheSCEV,
630  const LoopInfo *const LI, const SCEV *LHS, const SCEV *RHS,
631  DominatorTree &DT, unsigned Depth = 0) {
632  // Fast-path: SCEVs are uniqued so we can do a quick equality check.
633  if (LHS == RHS)
634  return 0;
635 
636  // Primarily, sort the SCEVs by their getSCEVType().
637  unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
638  if (LType != RType)
639  return (int)LType - (int)RType;
640 
641  if (Depth > MaxSCEVCompareDepth || EqCacheSCEV.count({LHS, RHS}))
642  return 0;
643  // Aside from the getSCEVType() ordering, the particular ordering
644  // isn't very important except that it's beneficial to be consistent,
645  // so that (a + b) and (b + a) don't end up as different expressions.
646  switch (static_cast<SCEVTypes>(LType)) {
647  case scUnknown: {
648  const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
649  const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
650 
652  int X = CompareValueComplexity(EqCache, LI, LU->getValue(), RU->getValue(),
653  Depth + 1);
654  if (X == 0)
655  EqCacheSCEV.insert({LHS, RHS});
656  return X;
657  }
658 
659  case scConstant: {
660  const SCEVConstant *LC = cast<SCEVConstant>(LHS);
661  const SCEVConstant *RC = cast<SCEVConstant>(RHS);
662 
663  // Compare constant values.
664  const APInt &LA = LC->getAPInt();
665  const APInt &RA = RC->getAPInt();
666  unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
667  if (LBitWidth != RBitWidth)
668  return (int)LBitWidth - (int)RBitWidth;
669  return LA.ult(RA) ? -1 : 1;
670  }
671 
672  case scAddRecExpr: {
673  const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
674  const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
675 
676  // There is always a dominance between two recs that are used by one SCEV,
677  // so we can safely sort recs by loop header dominance. We require such
678  // order in getAddExpr.
679  const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
680  if (LLoop != RLoop) {
681  const BasicBlock *LHead = LLoop->getHeader(), *RHead = RLoop->getHeader();
682  assert(LHead != RHead && "Two loops share the same header?");
683  if (DT.dominates(LHead, RHead))
684  return 1;
685  else
686  assert(DT.dominates(RHead, LHead) &&
687  "No dominance between recurrences used by one SCEV?");
688  return -1;
689  }
690 
691  // Addrec complexity grows with operand count.
692  unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
693  if (LNumOps != RNumOps)
694  return (int)LNumOps - (int)RNumOps;
695 
696  // Lexicographically compare.
697  for (unsigned i = 0; i != LNumOps; ++i) {
698  int X = CompareSCEVComplexity(EqCacheSCEV, LI, LA->getOperand(i),
699  RA->getOperand(i), DT, Depth + 1);
700  if (X != 0)
701  return X;
702  }
703  EqCacheSCEV.insert({LHS, RHS});
704  return 0;
705  }
706 
707  case scAddExpr:
708  case scMulExpr:
709  case scSMaxExpr:
710  case scUMaxExpr: {
711  const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
712  const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
713 
714  // Lexicographically compare n-ary expressions.
715  unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
716  if (LNumOps != RNumOps)
717  return (int)LNumOps - (int)RNumOps;
718 
719  for (unsigned i = 0; i != LNumOps; ++i) {
720  if (i >= RNumOps)
721  return 1;
722  int X = CompareSCEVComplexity(EqCacheSCEV, LI, LC->getOperand(i),
723  RC->getOperand(i), DT, Depth + 1);
724  if (X != 0)
725  return X;
726  }
727  EqCacheSCEV.insert({LHS, RHS});
728  return 0;
729  }
730 
731  case scUDivExpr: {
732  const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
733  const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
734 
735  // Lexicographically compare udiv expressions.
736  int X = CompareSCEVComplexity(EqCacheSCEV, LI, LC->getLHS(), RC->getLHS(),
737  DT, Depth + 1);
738  if (X != 0)
739  return X;
740  X = CompareSCEVComplexity(EqCacheSCEV, LI, LC->getRHS(), RC->getRHS(), DT,
741  Depth + 1);
742  if (X == 0)
743  EqCacheSCEV.insert({LHS, RHS});
744  return X;
745  }
746 
747  case scTruncate:
748  case scZeroExtend:
749  case scSignExtend: {
750  const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
751  const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
752 
753  // Compare cast expressions by operand.
754  int X = CompareSCEVComplexity(EqCacheSCEV, LI, LC->getOperand(),
755  RC->getOperand(), DT, Depth + 1);
756  if (X == 0)
757  EqCacheSCEV.insert({LHS, RHS});
758  return X;
759  }
760 
761  case scCouldNotCompute:
762  llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
763  }
764  llvm_unreachable("Unknown SCEV kind!");
765 }
766 
767 /// Given a list of SCEV objects, order them by their complexity, and group
768 /// objects of the same complexity together by value. When this routine is
769 /// finished, we know that any duplicates in the vector are consecutive and that
770 /// complexity is monotonically increasing.
771 ///
772 /// Note that we go take special precautions to ensure that we get deterministic
773 /// results from this routine. In other words, we don't want the results of
774 /// this to depend on where the addresses of various SCEV objects happened to
775 /// land in memory.
777  LoopInfo *LI, DominatorTree &DT) {
778  if (Ops.size() < 2) return; // Noop
779 
781  if (Ops.size() == 2) {
782  // This is the common case, which also happens to be trivially simple.
783  // Special case it.
784  const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
785  if (CompareSCEVComplexity(EqCache, LI, RHS, LHS, DT) < 0)
786  std::swap(LHS, RHS);
787  return;
788  }
789 
790  // Do the rough sort by complexity.
791  std::stable_sort(Ops.begin(), Ops.end(),
792  [&EqCache, LI, &DT](const SCEV *LHS, const SCEV *RHS) {
793  return
794  CompareSCEVComplexity(EqCache, LI, LHS, RHS, DT) < 0;
795  });
796 
797  // Now that we are sorted by complexity, group elements of the same
798  // complexity. Note that this is, at worst, N^2, but the vector is likely to
799  // be extremely short in practice. Note that we take this approach because we
800  // do not want to depend on the addresses of the objects we are grouping.
801  for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
802  const SCEV *S = Ops[i];
803  unsigned Complexity = S->getSCEVType();
804 
805  // If there are any objects of the same complexity and same value as this
806  // one, group them.
807  for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
808  if (Ops[j] == S) { // Found a duplicate.
809  // Move it to immediately after i'th element.
810  std::swap(Ops[i+1], Ops[j]);
811  ++i; // no need to rescan it.
812  if (i == e-2) return; // Done!
813  }
814  }
815  }
816 }
817 
818 // Returns the size of the SCEV S.
819 static inline int sizeOfSCEV(const SCEV *S) {
820  struct FindSCEVSize {
821  int Size = 0;
822 
823  FindSCEVSize() = default;
824 
825  bool follow(const SCEV *S) {
826  ++Size;
827  // Keep looking at all operands of S.
828  return true;
829  }
830 
831  bool isDone() const {
832  return false;
833  }
834  };
835 
836  FindSCEVSize F;
838  ST.visitAll(S);
839  return F.Size;
840 }
841 
842 namespace {
843 
844 struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
845 public:
846  // Computes the Quotient and Remainder of the division of Numerator by
847  // Denominator.
848  static void divide(ScalarEvolution &SE, const SCEV *Numerator,
849  const SCEV *Denominator, const SCEV **Quotient,
850  const SCEV **Remainder) {
851  assert(Numerator && Denominator && "Uninitialized SCEV");
852 
853  SCEVDivision D(SE, Numerator, Denominator);
854 
855  // Check for the trivial case here to avoid having to check for it in the
856  // rest of the code.
857  if (Numerator == Denominator) {
858  *Quotient = D.One;
859  *Remainder = D.Zero;
860  return;
861  }
862 
863  if (Numerator->isZero()) {
864  *Quotient = D.Zero;
865  *Remainder = D.Zero;
866  return;
867  }
868 
869  // A simple case when N/1. The quotient is N.
870  if (Denominator->isOne()) {
871  *Quotient = Numerator;
872  *Remainder = D.Zero;
873  return;
874  }
875 
876  // Split the Denominator when it is a product.
877  if (const SCEVMulExpr *T = dyn_cast<SCEVMulExpr>(Denominator)) {
878  const SCEV *Q, *R;
879  *Quotient = Numerator;
880  for (const SCEV *Op : T->operands()) {
881  divide(SE, *Quotient, Op, &Q, &R);
882  *Quotient = Q;
883 
884  // Bail out when the Numerator is not divisible by one of the terms of
885  // the Denominator.
886  if (!R->isZero()) {
887  *Quotient = D.Zero;
888  *Remainder = Numerator;
889  return;
890  }
891  }
892  *Remainder = D.Zero;
893  return;
894  }
895 
896  D.visit(Numerator);
897  *Quotient = D.Quotient;
898  *Remainder = D.Remainder;
899  }
900 
901  // Except in the trivial case described above, we do not know how to divide
902  // Expr by Denominator for the following functions with empty implementation.
903  void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
904  void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
905  void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
906  void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
907  void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
908  void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
909  void visitUnknown(const SCEVUnknown *Numerator) {}
910  void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
911 
912  void visitConstant(const SCEVConstant *Numerator) {
913  if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
914  APInt NumeratorVal = Numerator->getAPInt();
915  APInt DenominatorVal = D->getAPInt();
916  uint32_t NumeratorBW = NumeratorVal.getBitWidth();
917  uint32_t DenominatorBW = DenominatorVal.getBitWidth();
918 
919  if (NumeratorBW > DenominatorBW)
920  DenominatorVal = DenominatorVal.sext(NumeratorBW);
921  else if (NumeratorBW < DenominatorBW)
922  NumeratorVal = NumeratorVal.sext(DenominatorBW);
923 
924  APInt QuotientVal(NumeratorVal.getBitWidth(), 0);
925  APInt RemainderVal(NumeratorVal.getBitWidth(), 0);
926  APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal);
927  Quotient = SE.getConstant(QuotientVal);
928  Remainder = SE.getConstant(RemainderVal);
929  return;
930  }
931  }
932 
933  void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
934  const SCEV *StartQ, *StartR, *StepQ, *StepR;
935  if (!Numerator->isAffine())
936  return cannotDivide(Numerator);
937  divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
938  divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
939  // Bail out if the types do not match.
940  Type *Ty = Denominator->getType();
941  if (Ty != StartQ->getType() || Ty != StartR->getType() ||
942  Ty != StepQ->getType() || Ty != StepR->getType())
943  return cannotDivide(Numerator);
944  Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
945  Numerator->getNoWrapFlags());
946  Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
947  Numerator->getNoWrapFlags());
948  }
949 
950  void visitAddExpr(const SCEVAddExpr *Numerator) {
952  Type *Ty = Denominator->getType();
953 
954  for (const SCEV *Op : Numerator->operands()) {
955  const SCEV *Q, *R;
956  divide(SE, Op, Denominator, &Q, &R);
957 
958  // Bail out if types do not match.
959  if (Ty != Q->getType() || Ty != R->getType())
960  return cannotDivide(Numerator);
961 
962  Qs.push_back(Q);
963  Rs.push_back(R);
964  }
965 
966  if (Qs.size() == 1) {
967  Quotient = Qs[0];
968  Remainder = Rs[0];
969  return;
970  }
971 
972  Quotient = SE.getAddExpr(Qs);
973  Remainder = SE.getAddExpr(Rs);
974  }
975 
976  void visitMulExpr(const SCEVMulExpr *Numerator) {
978  Type *Ty = Denominator->getType();
979 
980  bool FoundDenominatorTerm = false;
981  for (const SCEV *Op : Numerator->operands()) {
982  // Bail out if types do not match.
983  if (Ty != Op->getType())
984  return cannotDivide(Numerator);
985 
986  if (FoundDenominatorTerm) {
987  Qs.push_back(Op);
988  continue;
989  }
990 
991  // Check whether Denominator divides one of the product operands.
992  const SCEV *Q, *R;
993  divide(SE, Op, Denominator, &Q, &R);
994  if (!R->isZero()) {
995  Qs.push_back(Op);
996  continue;
997  }
998 
999  // Bail out if types do not match.
1000  if (Ty != Q->getType())
1001  return cannotDivide(Numerator);
1002 
1003  FoundDenominatorTerm = true;
1004  Qs.push_back(Q);
1005  }
1006 
1007  if (FoundDenominatorTerm) {
1008  Remainder = Zero;
1009  if (Qs.size() == 1)
1010  Quotient = Qs[0];
1011  else
1012  Quotient = SE.getMulExpr(Qs);
1013  return;
1014  }
1015 
1016  if (!isa<SCEVUnknown>(Denominator))
1017  return cannotDivide(Numerator);
1018 
1019  // The Remainder is obtained by replacing Denominator by 0 in Numerator.
1020  ValueToValueMap RewriteMap;
1021  RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
1022  cast<SCEVConstant>(Zero)->getValue();
1023  Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
1024 
1025  if (Remainder->isZero()) {
1026  // The Quotient is obtained by replacing Denominator by 1 in Numerator.
1027  RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
1028  cast<SCEVConstant>(One)->getValue();
1029  Quotient =
1030  SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
1031  return;
1032  }
1033 
1034  // Quotient is (Numerator - Remainder) divided by Denominator.
1035  const SCEV *Q, *R;
1036  const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
1037  // This SCEV does not seem to simplify: fail the division here.
1038  if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator))
1039  return cannotDivide(Numerator);
1040  divide(SE, Diff, Denominator, &Q, &R);
1041  if (R != Zero)
1042  return cannotDivide(Numerator);
1043  Quotient = Q;
1044  }
1045 
1046 private:
1047  SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
1048  const SCEV *Denominator)
1049  : SE(S), Denominator(Denominator) {
1050  Zero = SE.getZero(Denominator->getType());
1051  One = SE.getOne(Denominator->getType());
1052 
1053  // We generally do not know how to divide Expr by Denominator. We
1054  // initialize the division to a "cannot divide" state to simplify the rest
1055  // of the code.
1056  cannotDivide(Numerator);
1057  }
1058 
1059  // Convenience function for giving up on the division. We set the quotient to
1060  // be equal to zero and the remainder to be equal to the numerator.
1061  void cannotDivide(const SCEV *Numerator) {
1062  Quotient = Zero;
1063  Remainder = Numerator;
1064  }
1065 
1066  ScalarEvolution &SE;
1067  const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
1068 };
1069 
1070 } // end anonymous namespace
1071 
1072 //===----------------------------------------------------------------------===//
1073 // Simple SCEV method implementations
1074 //===----------------------------------------------------------------------===//
1075 
1076 /// Compute BC(It, K). The result has width W. Assume, K > 0.
1077 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
1078  ScalarEvolution &SE,
1079  Type *ResultTy) {
1080  // Handle the simplest case efficiently.
1081  if (K == 1)
1082  return SE.getTruncateOrZeroExtend(It, ResultTy);
1083 
1084  // We are using the following formula for BC(It, K):
1085  //
1086  // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
1087  //
1088  // Suppose, W is the bitwidth of the return value. We must be prepared for
1089  // overflow. Hence, we must assure that the result of our computation is
1090  // equal to the accurate one modulo 2^W. Unfortunately, division isn't
1091  // safe in modular arithmetic.
1092  //
1093  // However, this code doesn't use exactly that formula; the formula it uses
1094  // is something like the following, where T is the number of factors of 2 in
1095  // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
1096  // exponentiation:
1097  //
1098  // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
1099  //
1100  // This formula is trivially equivalent to the previous formula. However,
1101  // this formula can be implemented much more efficiently. The trick is that
1102  // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
1103  // arithmetic. To do exact division in modular arithmetic, all we have
1104  // to do is multiply by the inverse. Therefore, this step can be done at
1105  // width W.
1106  //
1107  // The next issue is how to safely do the division by 2^T. The way this
1108  // is done is by doing the multiplication step at a width of at least W + T
1109  // bits. This way, the bottom W+T bits of the product are accurate. Then,
1110  // when we perform the division by 2^T (which is equivalent to a right shift
1111  // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
1112  // truncated out after the division by 2^T.
1113  //
1114  // In comparison to just directly using the first formula, this technique
1115  // is much more efficient; using the first formula requires W * K bits,
1116  // but this formula less than W + K bits. Also, the first formula requires
1117  // a division step, whereas this formula only requires multiplies and shifts.
1118  //
1119  // It doesn't matter whether the subtraction step is done in the calculation
1120  // width or the input iteration count's width; if the subtraction overflows,
1121  // the result must be zero anyway. We prefer here to do it in the width of
1122  // the induction variable because it helps a lot for certain cases; CodeGen
1123  // isn't smart enough to ignore the overflow, which leads to much less
1124  // efficient code if the width of the subtraction is wider than the native
1125  // register width.
1126  //
1127  // (It's possible to not widen at all by pulling out factors of 2 before
1128  // the multiplication; for example, K=2 can be calculated as
1129  // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
1130  // extra arithmetic, so it's not an obvious win, and it gets
1131  // much more complicated for K > 3.)
1132 
1133  // Protection from insane SCEVs; this bound is conservative,
1134  // but it probably doesn't matter.
1135  if (K > 1000)
1136  return SE.getCouldNotCompute();
1137 
1138  unsigned W = SE.getTypeSizeInBits(ResultTy);
1139 
1140  // Calculate K! / 2^T and T; we divide out the factors of two before
1141  // multiplying for calculating K! / 2^T to avoid overflow.
1142  // Other overflow doesn't matter because we only care about the bottom
1143  // W bits of the result.
1144  APInt OddFactorial(W, 1);
1145  unsigned T = 1;
1146  for (unsigned i = 3; i <= K; ++i) {
1147  APInt Mult(W, i);
1148  unsigned TwoFactors = Mult.countTrailingZeros();
1149  T += TwoFactors;
1150  Mult.lshrInPlace(TwoFactors);
1151  OddFactorial *= Mult;
1152  }
1153 
1154  // We need at least W + T bits for the multiplication step
1155  unsigned CalculationBits = W + T;
1156 
1157  // Calculate 2^T, at width T+W.
1158  APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
1159 
1160  // Calculate the multiplicative inverse of K! / 2^T;
1161  // this multiplication factor will perform the exact division by
1162  // K! / 2^T.
1163  APInt Mod = APInt::getSignedMinValue(W+1);
1164  APInt MultiplyFactor = OddFactorial.zext(W+1);
1165  MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
1166  MultiplyFactor = MultiplyFactor.trunc(W);
1167 
1168  // Calculate the product, at width T+W
1169  IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
1170  CalculationBits);
1171  const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
1172  for (unsigned i = 1; i != K; ++i) {
1173  const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
1174  Dividend = SE.getMulExpr(Dividend,
1175  SE.getTruncateOrZeroExtend(S, CalculationTy));
1176  }
1177 
1178  // Divide by 2^T
1179  const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
1180 
1181  // Truncate the result, and divide by K! / 2^T.
1182 
1183  return SE.getMulExpr(SE.getConstant(MultiplyFactor),
1184  SE.getTruncateOrZeroExtend(DivResult, ResultTy));
1185 }
1186 
1187 /// Return the value of this chain of recurrences at the specified iteration
1188 /// number. We can evaluate this recurrence by multiplying each element in the
1189 /// chain by the binomial coefficient corresponding to it. In other words, we
1190 /// can evaluate {A,+,B,+,C,+,D} as:
1191 ///
1192 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1193 ///
1194 /// where BC(It, k) stands for binomial coefficient.
1196  ScalarEvolution &SE) const {
1197  const SCEV *Result = getStart();
1198  for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
1199  // The computation is correct in the face of overflow provided that the
1200  // multiplication is performed _after_ the evaluation of the binomial
1201  // coefficient.
1202  const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
1203  if (isa<SCEVCouldNotCompute>(Coeff))
1204  return Coeff;
1205 
1206  Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
1207  }
1208  return Result;
1209 }
1210 
1211 //===----------------------------------------------------------------------===//
1212 // SCEV Expression folder implementations
1213 //===----------------------------------------------------------------------===//
1214 
1216  Type *Ty) {
1217  assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
1218  "This is not a truncating conversion!");
1219  assert(isSCEVable(Ty) &&
1220  "This is not a conversion to a SCEVable type!");
1221  Ty = getEffectiveSCEVType(Ty);
1222 
1224  ID.AddInteger(scTruncate);
1225  ID.AddPointer(Op);
1226  ID.AddPointer(Ty);
1227  void *IP = nullptr;
1228  if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1229 
1230  // Fold if the operand is constant.
1231  if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1232  return getConstant(
1233  cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
1234 
1235  // trunc(trunc(x)) --> trunc(x)
1236  if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
1237  return getTruncateExpr(ST->getOperand(), Ty);
1238 
1239  // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1240  if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1241  return getTruncateOrSignExtend(SS->getOperand(), Ty);
1242 
1243  // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1244  if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1245  return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
1246 
1247  // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
1248  // eliminate all the truncates, or we replace other casts with truncates.
1249  if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
1251  bool hasTrunc = false;
1252  for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
1253  const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
1254  if (!isa<SCEVCastExpr>(SA->getOperand(i)))
1255  hasTrunc = isa<SCEVTruncateExpr>(S);
1256  Operands.push_back(S);
1257  }
1258  if (!hasTrunc)
1259  return getAddExpr(Operands);
1260  UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1261  }
1262 
1263  // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
1264  // eliminate all the truncates, or we replace other casts with truncates.
1265  if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
1267  bool hasTrunc = false;
1268  for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
1269  const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
1270  if (!isa<SCEVCastExpr>(SM->getOperand(i)))
1271  hasTrunc = isa<SCEVTruncateExpr>(S);
1272  Operands.push_back(S);
1273  }
1274  if (!hasTrunc)
1275  return getMulExpr(Operands);
1276  UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1277  }
1278 
1279  // If the input value is a chrec scev, truncate the chrec's operands.
1280  if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
1282  for (const SCEV *Op : AddRec->operands())
1283  Operands.push_back(getTruncateExpr(Op, Ty));
1284  return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
1285  }
1286 
1287  // The cast wasn't folded; create an explicit cast node. We can reuse
1288  // the existing insert position since if we get here, we won't have
1289  // made any changes which would invalidate it.
1290  SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
1291  Op, Ty);
1292  UniqueSCEVs.InsertNode(S, IP);
1293  addToLoopUseLists(S);
1294  return S;
1295 }
1296 
1297 // Get the limit of a recurrence such that incrementing by Step cannot cause
1298 // signed overflow as long as the value of the recurrence within the
1299 // loop does not exceed this limit before incrementing.
1300 static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
1301  ICmpInst::Predicate *Pred,
1302  ScalarEvolution *SE) {
1303  unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1304  if (SE->isKnownPositive(Step)) {
1305  *Pred = ICmpInst::ICMP_SLT;
1306  return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1307  SE->getSignedRangeMax(Step));
1308  }
1309  if (SE->isKnownNegative(Step)) {
1310  *Pred = ICmpInst::ICMP_SGT;
1311  return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1312  SE->getSignedRangeMin(Step));
1313  }
1314  return nullptr;
1315 }
1316 
1317 // Get the limit of a recurrence such that incrementing by Step cannot cause
1318 // unsigned overflow as long as the value of the recurrence within the loop does
1319 // not exceed this limit before incrementing.
1320 static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
1321  ICmpInst::Predicate *Pred,
1322  ScalarEvolution *SE) {
1323  unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1324  *Pred = ICmpInst::ICMP_ULT;
1325 
1326  return SE->getConstant(APInt::getMinValue(BitWidth) -
1327  SE->getUnsignedRangeMax(Step));
1328 }
1329 
1330 namespace {
1331 
1332 struct ExtendOpTraitsBase {
1333  typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *,
1334  unsigned);
1335 };
1336 
1337 // Used to make code generic over signed and unsigned overflow.
1338 template <typename ExtendOp> struct ExtendOpTraits {
1339  // Members present:
1340  //
1341  // static const SCEV::NoWrapFlags WrapType;
1342  //
1343  // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
1344  //
1345  // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1346  // ICmpInst::Predicate *Pred,
1347  // ScalarEvolution *SE);
1348 };
1349 
1350 template <>
1351 struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
1352  static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
1353 
1354  static const GetExtendExprTy GetExtendExpr;
1355 
1356  static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1357  ICmpInst::Predicate *Pred,
1358  ScalarEvolution *SE) {
1359  return getSignedOverflowLimitForStep(Step, Pred, SE);
1360  }
1361 };
1362 
1363 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1364  SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
1365 
1366 template <>
1367 struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
1368  static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
1369 
1370  static const GetExtendExprTy GetExtendExpr;
1371 
1372  static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1373  ICmpInst::Predicate *Pred,
1374  ScalarEvolution *SE) {
1375  return getUnsignedOverflowLimitForStep(Step, Pred, SE);
1376  }
1377 };
1378 
1379 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1380  SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
1381 
1382 } // end anonymous namespace
1383 
1384 // The recurrence AR has been shown to have no signed/unsigned wrap or something
1385 // close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1386 // easily prove NSW/NUW for its preincrement or postincrement sibling. This
1387 // allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1388 // Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1389 // expression "Step + sext/zext(PreIncAR)" is congruent with
1390 // "sext/zext(PostIncAR)"
1391 template <typename ExtendOpTy>
1392 static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
1393  ScalarEvolution *SE, unsigned Depth) {
1394  auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1395  auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1396 
1397  const Loop *L = AR->getLoop();
1398  const SCEV *Start = AR->getStart();
1399  const SCEV *Step = AR->getStepRecurrence(*SE);
1400 
1401  // Check for a simple looking step prior to loop entry.
1402  const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1403  if (!SA)
1404  return nullptr;
1405 
1406  // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1407  // subtraction is expensive. For this purpose, perform a quick and dirty
1408  // difference, by checking for Step in the operand list.
1410  for (const SCEV *Op : SA->operands())
1411  if (Op != Step)
1412  DiffOps.push_back(Op);
1413 
1414  if (DiffOps.size() == SA->getNumOperands())
1415  return nullptr;
1416 
1417  // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
1418  // `Step`:
1419 
1420  // 1. NSW/NUW flags on the step increment.
1421  auto PreStartFlags =
1423  const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags);
1424  const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1425  SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1426 
1427  // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
1428  // "S+X does not sign/unsign-overflow".
1429  //
1430 
1431  const SCEV *BECount = SE->getBackedgeTakenCount(L);
1432  if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
1433  !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
1434  return PreStart;
1435 
1436  // 2. Direct overflow check on the step operation's expression.
1437  unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1438  Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1439  const SCEV *OperandExtendedStart =
1440  SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy, Depth),
1441  (SE->*GetExtendExpr)(Step, WideTy, Depth));
1442  if ((SE->*GetExtendExpr)(Start, WideTy, Depth) == OperandExtendedStart) {
1443  if (PreAR && AR->getNoWrapFlags(WrapType)) {
1444  // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
1445  // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
1446  // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
1447  const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
1448  }
1449  return PreStart;
1450  }
1451 
1452  // 3. Loop precondition.
1453  ICmpInst::Predicate Pred;
1454  const SCEV *OverflowLimit =
1455  ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
1456 
1457  if (OverflowLimit &&
1458  SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit))
1459  return PreStart;
1460 
1461  return nullptr;
1462 }
1463 
1464 // Get the normalized zero or sign extended expression for this AddRec's Start.
1465 template <typename ExtendOpTy>
1466 static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
1467  ScalarEvolution *SE,
1468  unsigned Depth) {
1469  auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1470 
1471  const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE, Depth);
1472  if (!PreStart)
1473  return (SE->*GetExtendExpr)(AR->getStart(), Ty, Depth);
1474 
1475  return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty,
1476  Depth),
1477  (SE->*GetExtendExpr)(PreStart, Ty, Depth));
1478 }
1479 
1480 // Try to prove away overflow by looking at "nearby" add recurrences. A
1481 // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1482 // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1483 //
1484 // Formally:
1485 //
1486 // {S,+,X} == {S-T,+,X} + T
1487 // => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1488 //
1489 // If ({S-T,+,X} + T) does not overflow ... (1)
1490 //
1491 // RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1492 //
1493 // If {S-T,+,X} does not overflow ... (2)
1494 //
1495 // RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1496 // == {Ext(S-T)+Ext(T),+,Ext(X)}
1497 //
1498 // If (S-T)+T does not overflow ... (3)
1499 //
1500 // RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1501 // == {Ext(S),+,Ext(X)} == LHS
1502 //
1503 // Thus, if (1), (2) and (3) are true for some T, then
1504 // Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1505 //
1506 // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1507 // does not overflow" restricted to the 0th iteration. Therefore we only need
1508 // to check for (1) and (2).
1509 //
1510 // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1511 // is `Delta` (defined below).
1512 template <typename ExtendOpTy>
1513 bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
1514  const SCEV *Step,
1515  const Loop *L) {
1516  auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1517 
1518  // We restrict `Start` to a constant to prevent SCEV from spending too much
1519  // time here. It is correct (but more expensive) to continue with a
1520  // non-constant `Start` and do a general SCEV subtraction to compute
1521  // `PreStart` below.
1522  const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
1523  if (!StartC)
1524  return false;
1525 
1526  APInt StartAI = StartC->getAPInt();
1527 
1528  for (unsigned Delta : {-2, -1, 1, 2}) {
1529  const SCEV *PreStart = getConstant(StartAI - Delta);
1530 
1533  ID.AddPointer(PreStart);
1534  ID.AddPointer(Step);
1535  ID.AddPointer(L);
1536  void *IP = nullptr;
1537  const auto *PreAR =
1538  static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1539 
1540  // Give up if we don't already have the add recurrence we need because
1541  // actually constructing an add recurrence is relatively expensive.
1542  if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2)
1543  const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
1545  const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
1546  DeltaS, &Pred, this);
1547  if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1)
1548  return true;
1549  }
1550  }
1551 
1552  return false;
1553 }
1554 
1555 const SCEV *
1557  assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1558  "This is not an extending conversion!");
1559  assert(isSCEVable(Ty) &&
1560  "This is not a conversion to a SCEVable type!");
1561  Ty = getEffectiveSCEVType(Ty);
1562 
1563  // Fold if the operand is constant.
1564  if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1565  return getConstant(
1566  cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1567 
1568  // zext(zext(x)) --> zext(x)
1569  if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1570  return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
1571 
1572  // Before doing any expensive analysis, check to see if we've already
1573  // computed a SCEV for this Op and Ty.
1576  ID.AddPointer(Op);
1577  ID.AddPointer(Ty);
1578  void *IP = nullptr;
1579  if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1580  if (Depth > MaxExtDepth) {
1581  SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1582  Op, Ty);
1583  UniqueSCEVs.InsertNode(S, IP);
1584  addToLoopUseLists(S);
1585  return S;
1586  }
1587 
1588  // zext(trunc(x)) --> zext(x) or x or trunc(x)
1589  if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1590  // It's possible the bits taken off by the truncate were all zero bits. If
1591  // so, we should be able to simplify this further.
1592  const SCEV *X = ST->getOperand();
1593  ConstantRange CR = getUnsignedRange(X);
1594  unsigned TruncBits = getTypeSizeInBits(ST->getType());
1595  unsigned NewBits = getTypeSizeInBits(Ty);
1596  if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1597  CR.zextOrTrunc(NewBits)))
1598  return getTruncateOrZeroExtend(X, Ty);
1599  }
1600 
1601  // If the input value is a chrec scev, and we can prove that the value
1602  // did not overflow the old, smaller, value, we can zero extend all of the
1603  // operands (often constants). This allows analysis of something like
1604  // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1605  if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1606  if (AR->isAffine()) {
1607  const SCEV *Start = AR->getStart();
1608  const SCEV *Step = AR->getStepRecurrence(*this);
1609  unsigned BitWidth = getTypeSizeInBits(AR->getType());
1610  const Loop *L = AR->getLoop();
1611 
1612  if (!AR->hasNoUnsignedWrap()) {
1613  auto NewFlags = proveNoWrapViaConstantRanges(AR);
1614  const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
1615  }
1616 
1617  // If we have special knowledge that this addrec won't overflow,
1618  // we don't need to do any further analysis.
1619  if (AR->hasNoUnsignedWrap())
1620  return getAddRecExpr(
1621  getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1),
1622  getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
1623 
1624  // Check whether the backedge-taken count is SCEVCouldNotCompute.
1625  // Note that this serves two purposes: It filters out loops that are
1626  // simply not analyzable, and it covers the case where this code is
1627  // being called from within backedge-taken count analysis, such that
1628  // attempting to ask for the backedge-taken count would likely result
1629  // in infinite recursion. In the later case, the analysis code will
1630  // cope with a conservative value, and it will take care to purge
1631  // that value once it has finished.
1632  const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1633  if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1634  // Manually compute the final value for AR, checking for
1635  // overflow.
1636 
1637  // Check whether the backedge-taken count can be losslessly casted to
1638  // the addrec's type. The count is always unsigned.
1639  const SCEV *CastedMaxBECount =
1640  getTruncateOrZeroExtend(MaxBECount, Start->getType());
1641  const SCEV *RecastedMaxBECount =
1642  getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1643  if (MaxBECount == RecastedMaxBECount) {
1644  Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1645  // Check whether Start+Step*MaxBECount has no unsigned overflow.
1646  const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step,
1647  SCEV::FlagAnyWrap, Depth + 1);
1648  const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul,
1650  Depth + 1),
1651  WideTy, Depth + 1);
1652  const SCEV *WideStart = getZeroExtendExpr(Start, WideTy, Depth + 1);
1653  const SCEV *WideMaxBECount =
1654  getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
1655  const SCEV *OperandExtendedAdd =
1656  getAddExpr(WideStart,
1657  getMulExpr(WideMaxBECount,
1658  getZeroExtendExpr(Step, WideTy, Depth + 1),
1659  SCEV::FlagAnyWrap, Depth + 1),
1660  SCEV::FlagAnyWrap, Depth + 1);
1661  if (ZAdd == OperandExtendedAdd) {
1662  // Cache knowledge of AR NUW, which is propagated to this AddRec.
1663  const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1664  // Return the expression with the addrec on the outside.
1665  return getAddRecExpr(
1666  getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1667  Depth + 1),
1668  getZeroExtendExpr(Step, Ty, Depth + 1), L,
1669  AR->getNoWrapFlags());
1670  }
1671  // Similar to above, only this time treat the step value as signed.
1672  // This covers loops that count down.
1673  OperandExtendedAdd =
1674  getAddExpr(WideStart,
1675  getMulExpr(WideMaxBECount,
1676  getSignExtendExpr(Step, WideTy, Depth + 1),
1677  SCEV::FlagAnyWrap, Depth + 1),
1678  SCEV::FlagAnyWrap, Depth + 1);
1679  if (ZAdd == OperandExtendedAdd) {
1680  // Cache knowledge of AR NW, which is propagated to this AddRec.
1681  // Negative step causes unsigned wrap, but it still can't self-wrap.
1682  const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1683  // Return the expression with the addrec on the outside.
1684  return getAddRecExpr(
1685  getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1686  Depth + 1),
1687  getSignExtendExpr(Step, Ty, Depth + 1), L,
1688  AR->getNoWrapFlags());
1689  }
1690  }
1691  }
1692 
1693  // Normally, in the cases we can prove no-overflow via a
1694  // backedge guarding condition, we can also compute a backedge
1695  // taken count for the loop. The exceptions are assumptions and
1696  // guards present in the loop -- SCEV is not great at exploiting
1697  // these to compute max backedge taken counts, but can still use
1698  // these to prove lack of overflow. Use this fact to avoid
1699  // doing extra work that may not pay off.
1700  if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
1701  !AC.assumptions().empty()) {
1702  // If the backedge is guarded by a comparison with the pre-inc
1703  // value the addrec is safe. Also, if the entry is guarded by
1704  // a comparison with the start value and the backedge is
1705  // guarded by a comparison with the post-inc value, the addrec
1706  // is safe.
1707  if (isKnownPositive(Step)) {
1708  const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1709  getUnsignedRangeMax(Step));
1710  if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1711  (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1712  isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1713  AR->getPostIncExpr(*this), N))) {
1714  // Cache knowledge of AR NUW, which is propagated to this
1715  // AddRec.
1716  const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1717  // Return the expression with the addrec on the outside.
1718  return getAddRecExpr(
1719  getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1720  Depth + 1),
1721  getZeroExtendExpr(Step, Ty, Depth + 1), L,
1722  AR->getNoWrapFlags());
1723  }
1724  } else if (isKnownNegative(Step)) {
1725  const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1726  getSignedRangeMin(Step));
1727  if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1728  (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1729  isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1730  AR->getPostIncExpr(*this), N))) {
1731  // Cache knowledge of AR NW, which is propagated to this
1732  // AddRec. Negative step causes unsigned wrap, but it
1733  // still can't self-wrap.
1734  const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1735  // Return the expression with the addrec on the outside.
1736  return getAddRecExpr(
1737  getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1738  Depth + 1),
1739  getSignExtendExpr(Step, Ty, Depth + 1), L,
1740  AR->getNoWrapFlags());
1741  }
1742  }
1743  }
1744 
1745  if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
1746  const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1747  return getAddRecExpr(
1748  getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1),
1749  getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
1750  }
1751  }
1752 
1753  if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1754  // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
1755  if (SA->hasNoUnsignedWrap()) {
1756  // If the addition does not unsign overflow then we can, by definition,
1757  // commute the zero extension with the addition operation.
1759  for (const auto *Op : SA->operands())
1760  Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
1761  return getAddExpr(Ops, SCEV::FlagNUW, Depth + 1);
1762  }
1763  }
1764 
1765  // The cast wasn't folded; create an explicit cast node.
1766  // Recompute the insert position, as it may have been invalidated.
1767  if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1768  SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1769  Op, Ty);
1770  UniqueSCEVs.InsertNode(S, IP);
1771  addToLoopUseLists(S);
1772  return S;
1773 }
1774 
1775 const SCEV *
1777  assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1778  "This is not an extending conversion!");
1779  assert(isSCEVable(Ty) &&
1780  "This is not a conversion to a SCEVable type!");
1781  Ty = getEffectiveSCEVType(Ty);
1782 
1783  // Fold if the operand is constant.
1784  if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1785  return getConstant(
1786  cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1787 
1788  // sext(sext(x)) --> sext(x)
1789  if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1790  return getSignExtendExpr(SS->getOperand(), Ty, Depth + 1);
1791 
1792  // sext(zext(x)) --> zext(x)
1793  if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1794  return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
1795 
1796  // Before doing any expensive analysis, check to see if we've already
1797  // computed a SCEV for this Op and Ty.
1800  ID.AddPointer(Op);
1801  ID.AddPointer(Ty);
1802  void *IP = nullptr;
1803  if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1804  // Limit recursion depth.
1805  if (Depth > MaxExtDepth) {
1806  SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1807  Op, Ty);
1808  UniqueSCEVs.InsertNode(S, IP);
1809  addToLoopUseLists(S);
1810  return S;
1811  }
1812 
1813  // sext(trunc(x)) --> sext(x) or x or trunc(x)
1814  if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1815  // It's possible the bits taken off by the truncate were all sign bits. If
1816  // so, we should be able to simplify this further.
1817  const SCEV *X = ST->getOperand();
1818  ConstantRange CR = getSignedRange(X);
1819  unsigned TruncBits = getTypeSizeInBits(ST->getType());
1820  unsigned NewBits = getTypeSizeInBits(Ty);
1821  if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1822  CR.sextOrTrunc(NewBits)))
1823  return getTruncateOrSignExtend(X, Ty);
1824  }
1825 
1826  // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1827  if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1828  if (SA->getNumOperands() == 2) {
1829  auto *SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1830  auto *SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1831  if (SMul && SC1) {
1832  if (auto *SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1833  const APInt &C1 = SC1->getAPInt();
1834  const APInt &C2 = SC2->getAPInt();
1835  if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1836  C2.ugt(C1) && C2.isPowerOf2())
1837  return getAddExpr(getSignExtendExpr(SC1, Ty, Depth + 1),
1838  getSignExtendExpr(SMul, Ty, Depth + 1),
1839  SCEV::FlagAnyWrap, Depth + 1);
1840  }
1841  }
1842  }
1843 
1844  // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
1845  if (SA->hasNoSignedWrap()) {
1846  // If the addition does not sign overflow then we can, by definition,
1847  // commute the sign extension with the addition operation.
1849  for (const auto *Op : SA->operands())
1850  Ops.push_back(getSignExtendExpr(Op, Ty, Depth + 1));
1851  return getAddExpr(Ops, SCEV::FlagNSW, Depth + 1);
1852  }
1853  }
1854  // If the input value is a chrec scev, and we can prove that the value
1855  // did not overflow the old, smaller, value, we can sign extend all of the
1856  // operands (often constants). This allows analysis of something like
1857  // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1858  if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1859  if (AR->isAffine()) {
1860  const SCEV *Start = AR->getStart();
1861  const SCEV *Step = AR->getStepRecurrence(*this);
1862  unsigned BitWidth = getTypeSizeInBits(AR->getType());
1863  const Loop *L = AR->getLoop();
1864 
1865  if (!AR->hasNoSignedWrap()) {
1866  auto NewFlags = proveNoWrapViaConstantRanges(AR);
1867  const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
1868  }
1869 
1870  // If we have special knowledge that this addrec won't overflow,
1871  // we don't need to do any further analysis.
1872  if (AR->hasNoSignedWrap())
1873  return getAddRecExpr(
1874  getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
1875  getSignExtendExpr(Step, Ty, Depth + 1), L, SCEV::FlagNSW);
1876 
1877  // Check whether the backedge-taken count is SCEVCouldNotCompute.
1878  // Note that this serves two purposes: It filters out loops that are
1879  // simply not analyzable, and it covers the case where this code is
1880  // being called from within backedge-taken count analysis, such that
1881  // attempting to ask for the backedge-taken count would likely result
1882  // in infinite recursion. In the later case, the analysis code will
1883  // cope with a conservative value, and it will take care to purge
1884  // that value once it has finished.
1885  const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1886  if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1887  // Manually compute the final value for AR, checking for
1888  // overflow.
1889 
1890  // Check whether the backedge-taken count can be losslessly casted to
1891  // the addrec's type. The count is always unsigned.
1892  const SCEV *CastedMaxBECount =
1893  getTruncateOrZeroExtend(MaxBECount, Start->getType());
1894  const SCEV *RecastedMaxBECount =
1895  getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1896  if (MaxBECount == RecastedMaxBECount) {
1897  Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1898  // Check whether Start+Step*MaxBECount has no signed overflow.
1899  const SCEV *SMul = getMulExpr(CastedMaxBECount, Step,
1900  SCEV::FlagAnyWrap, Depth + 1);
1901  const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul,
1903  Depth + 1),
1904  WideTy, Depth + 1);
1905  const SCEV *WideStart = getSignExtendExpr(Start, WideTy, Depth + 1);
1906  const SCEV *WideMaxBECount =
1907  getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
1908  const SCEV *OperandExtendedAdd =
1909  getAddExpr(WideStart,
1910  getMulExpr(WideMaxBECount,
1911  getSignExtendExpr(Step, WideTy, Depth + 1),
1912  SCEV::FlagAnyWrap, Depth + 1),
1913  SCEV::FlagAnyWrap, Depth + 1);
1914  if (SAdd == OperandExtendedAdd) {
1915  // Cache knowledge of AR NSW, which is propagated to this AddRec.
1916  const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1917  // Return the expression with the addrec on the outside.
1918  return getAddRecExpr(
1919  getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this,
1920  Depth + 1),
1921  getSignExtendExpr(Step, Ty, Depth + 1), L,
1922  AR->getNoWrapFlags());
1923  }
1924  // Similar to above, only this time treat the step value as unsigned.
1925  // This covers loops that count up with an unsigned step.
1926  OperandExtendedAdd =
1927  getAddExpr(WideStart,
1928  getMulExpr(WideMaxBECount,
1929  getZeroExtendExpr(Step, WideTy, Depth + 1),
1930  SCEV::FlagAnyWrap, Depth + 1),
1931  SCEV::FlagAnyWrap, Depth + 1);
1932  if (SAdd == OperandExtendedAdd) {
1933  // If AR wraps around then
1934  //
1935  // abs(Step) * MaxBECount > unsigned-max(AR->getType())
1936  // => SAdd != OperandExtendedAdd
1937  //
1938  // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
1939  // (SAdd == OperandExtendedAdd => AR is NW)
1940 
1941  const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1942 
1943  // Return the expression with the addrec on the outside.
1944  return getAddRecExpr(
1945  getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this,
1946  Depth + 1),
1947  getZeroExtendExpr(Step, Ty, Depth + 1), L,
1948  AR->getNoWrapFlags());
1949  }
1950  }
1951  }
1952 
1953  // Normally, in the cases we can prove no-overflow via a
1954  // backedge guarding condition, we can also compute a backedge
1955  // taken count for the loop. The exceptions are assumptions and
1956  // guards present in the loop -- SCEV is not great at exploiting
1957  // these to compute max backedge taken counts, but can still use
1958  // these to prove lack of overflow. Use this fact to avoid
1959  // doing extra work that may not pay off.
1960 
1961  if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
1962  !AC.assumptions().empty()) {
1963  // If the backedge is guarded by a comparison with the pre-inc
1964  // value the addrec is safe. Also, if the entry is guarded by
1965  // a comparison with the start value and the backedge is
1966  // guarded by a comparison with the post-inc value, the addrec
1967  // is safe.
1968  ICmpInst::Predicate Pred;
1969  const SCEV *OverflowLimit =
1970  getSignedOverflowLimitForStep(Step, &Pred, this);
1971  if (OverflowLimit &&
1972  (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1973  (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1974  isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1975  OverflowLimit)))) {
1976  // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1977  const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1978  return getAddRecExpr(
1979  getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
1980  getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
1981  }
1982  }
1983 
1984  // If Start and Step are constants, check if we can apply this
1985  // transformation:
1986  // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1987  auto *SC1 = dyn_cast<SCEVConstant>(Start);
1988  auto *SC2 = dyn_cast<SCEVConstant>(Step);
1989  if (SC1 && SC2) {
1990  const APInt &C1 = SC1->getAPInt();
1991  const APInt &C2 = SC2->getAPInt();
1992  if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1993  C2.isPowerOf2()) {
1994  Start = getSignExtendExpr(Start, Ty, Depth + 1);
1995  const SCEV *NewAR = getAddRecExpr(getZero(AR->getType()), Step, L,
1996  AR->getNoWrapFlags());
1997  return getAddExpr(Start, getSignExtendExpr(NewAR, Ty, Depth + 1),
1998  SCEV::FlagAnyWrap, Depth + 1);
1999  }
2000  }
2001 
2002  if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
2003  const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
2004  return getAddRecExpr(
2005  getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
2006  getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
2007  }
2008  }
2009 
2010  // If the input value is provably positive and we could not simplify
2011  // away the sext build a zext instead.
2012  if (isKnownNonNegative(Op))
2013  return getZeroExtendExpr(Op, Ty, Depth + 1);
2014 
2015  // The cast wasn't folded; create an explicit cast node.
2016  // Recompute the insert position, as it may have been invalidated.
2017  if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2018  SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
2019  Op, Ty);
2020  UniqueSCEVs.InsertNode(S, IP);
2021  addToLoopUseLists(S);
2022  return S;
2023 }
2024 
2025 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
2026 /// unspecified bits out to the given type.
2028  Type *Ty) {
2029  assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
2030  "This is not an extending conversion!");
2031  assert(isSCEVable(Ty) &&
2032  "This is not a conversion to a SCEVable type!");
2033  Ty = getEffectiveSCEVType(Ty);
2034 
2035  // Sign-extend negative constants.
2036  if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
2037  if (SC->getAPInt().isNegative())
2038  return getSignExtendExpr(Op, Ty);
2039 
2040  // Peel off a truncate cast.
2041  if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
2042  const SCEV *NewOp = T->getOperand();
2043  if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
2044  return getAnyExtendExpr(NewOp, Ty);
2045  return getTruncateOrNoop(NewOp, Ty);
2046  }
2047 
2048  // Next try a zext cast. If the cast is folded, use it.
2049  const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
2050  if (!isa<SCEVZeroExtendExpr>(ZExt))
2051  return ZExt;
2052 
2053  // Next try a sext cast. If the cast is folded, use it.
2054  const SCEV *SExt = getSignExtendExpr(Op, Ty);
2055  if (!isa<SCEVSignExtendExpr>(SExt))
2056  return SExt;
2057 
2058  // Force the cast to be folded into the operands of an addrec.
2059  if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
2061  for (const SCEV *Op : AR->operands())
2062  Ops.push_back(getAnyExtendExpr(Op, Ty));
2063  return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
2064  }
2065 
2066  // If the expression is obviously signed, use the sext cast value.
2067  if (isa<SCEVSMaxExpr>(Op))
2068  return SExt;
2069 
2070  // Absent any other information, use the zext cast value.
2071  return ZExt;
2072 }
2073 
2074 /// Process the given Ops list, which is a list of operands to be added under
2075 /// the given scale, update the given map. This is a helper function for
2076 /// getAddRecExpr. As an example of what it does, given a sequence of operands
2077 /// that would form an add expression like this:
2078 ///
2079 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
2080 ///
2081 /// where A and B are constants, update the map with these values:
2082 ///
2083 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
2084 ///
2085 /// and add 13 + A*B*29 to AccumulatedConstant.
2086 /// This will allow getAddRecExpr to produce this:
2087 ///
2088 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
2089 ///
2090 /// This form often exposes folding opportunities that are hidden in
2091 /// the original operand list.
2092 ///
2093 /// Return true iff it appears that any interesting folding opportunities
2094 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
2095 /// the common case where no interesting opportunities are present, and
2096 /// is also used as a check to avoid infinite recursion.
2097 static bool
2100  APInt &AccumulatedConstant,
2101  const SCEV *const *Ops, size_t NumOperands,
2102  const APInt &Scale,
2103  ScalarEvolution &SE) {
2104  bool Interesting = false;
2105 
2106  // Iterate over the add operands. They are sorted, with constants first.
2107  unsigned i = 0;
2108  while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2109  ++i;
2110  // Pull a buried constant out to the outside.
2111  if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
2112  Interesting = true;
2113  AccumulatedConstant += Scale * C->getAPInt();
2114  }
2115 
2116  // Next comes everything else. We're especially interested in multiplies
2117  // here, but they're in the middle, so just visit the rest with one loop.
2118  for (; i != NumOperands; ++i) {
2119  const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
2120  if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
2121  APInt NewScale =
2122  Scale * cast<SCEVConstant>(Mul->getOperand(0))->getAPInt();
2123  if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
2124  // A multiplication of a constant with another add; recurse.
2125  const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
2126  Interesting |=
2127  CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2128  Add->op_begin(), Add->getNumOperands(),
2129  NewScale, SE);
2130  } else {
2131  // A multiplication of a constant with some other value. Update
2132  // the map.
2133  SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
2134  const SCEV *Key = SE.getMulExpr(MulOps);
2135  auto Pair = M.insert({Key, NewScale});
2136  if (Pair.second) {
2137  NewOps.push_back(Pair.first->first);
2138  } else {
2139  Pair.first->second += NewScale;
2140  // The map already had an entry for this value, which may indicate
2141  // a folding opportunity.
2142  Interesting = true;
2143  }
2144  }
2145  } else {
2146  // An ordinary operand. Update the map.
2147  std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
2148  M.insert({Ops[i], Scale});
2149  if (Pair.second) {
2150  NewOps.push_back(Pair.first->first);
2151  } else {
2152  Pair.first->second += Scale;
2153  // The map already had an entry for this value, which may indicate
2154  // a folding opportunity.
2155  Interesting = true;
2156  }
2157  }
2158  }
2159 
2160  return Interesting;
2161 }
2162 
2163 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
2164 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
2165 // can't-overflow flags for the operation if possible.
2166 static SCEV::NoWrapFlags
2168  const SmallVectorImpl<const SCEV *> &Ops,
2169  SCEV::NoWrapFlags Flags) {
2170  using namespace std::placeholders;
2171 
2172  using OBO = OverflowingBinaryOperator;
2173 
2174  bool CanAnalyze =
2175  Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
2176  (void)CanAnalyze;
2177  assert(CanAnalyze && "don't call from other places!");
2178 
2179  int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2180  SCEV::NoWrapFlags SignOrUnsignWrap =
2181  ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
2182 
2183  // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2184  auto IsKnownNonNegative = [&](const SCEV *S) {
2185  return SE->isKnownNonNegative(S);
2186  };
2187 
2188  if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative))
2189  Flags =
2190  ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2191 
2192  SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
2193 
2194  if (SignOrUnsignWrap != SignOrUnsignMask && Type == scAddExpr &&
2195  Ops.size() == 2 && isa<SCEVConstant>(Ops[0])) {
2196 
2197  // (A + C) --> (A + C)<nsw> if the addition does not sign overflow
2198  // (A + C) --> (A + C)<nuw> if the addition does not unsign overflow
2199 
2200  const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt();
2201  if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
2203  Instruction::Add, C, OBO::NoSignedWrap);
2204  if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
2205  Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
2206  }
2207  if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
2209  Instruction::Add, C, OBO::NoUnsignedWrap);
2210  if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
2211  Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
2212  }
2213  }
2214 
2215  return Flags;
2216 }
2217 
2219  if (!isLoopInvariant(S, L))
2220  return false;
2221  // If a value depends on a SCEVUnknown which is defined after the loop, we
2222  // conservatively assume that we cannot calculate it at the loop's entry.
2223  struct FindDominatedSCEVUnknown {
2224  bool Found = false;
2225  const Loop *L;
2226  DominatorTree &DT;
2227  LoopInfo &LI;
2228 
2229  FindDominatedSCEVUnknown(const Loop *L, DominatorTree &DT, LoopInfo &LI)
2230  : L(L), DT(DT), LI(LI) {}
2231 
2232  bool checkSCEVUnknown(const SCEVUnknown *SU) {
2233  if (auto *I = dyn_cast<Instruction>(SU->getValue())) {
2234  if (DT.dominates(L->getHeader(), I->getParent()))
2235  Found = true;
2236  else
2237  assert(DT.dominates(I->getParent(), L->getHeader()) &&
2238  "No dominance relationship between SCEV and loop?");
2239  }
2240  return false;
2241  }
2242 
2243  bool follow(const SCEV *S) {
2244  switch (static_cast<SCEVTypes>(S->getSCEVType())) {
2245  case scConstant:
2246  return false;
2247  case scAddRecExpr:
2248  case scTruncate:
2249  case scZeroExtend:
2250  case scSignExtend:
2251  case scAddExpr:
2252  case scMulExpr:
2253  case scUMaxExpr:
2254  case scSMaxExpr:
2255  case scUDivExpr:
2256  return true;
2257  case scUnknown:
2258  return checkSCEVUnknown(cast<SCEVUnknown>(S));
2259  case scCouldNotCompute:
2260  llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
2261  }
2262  return false;
2263  }
2264 
2265  bool isDone() { return Found; }
2266  };
2267 
2268  FindDominatedSCEVUnknown FSU(L, DT, LI);
2270  ST.visitAll(S);
2271  return !FSU.Found;
2272 }
2273 
2274 /// Get a canonical add expression, or something simpler if possible.
2276  SCEV::NoWrapFlags Flags,
2277  unsigned Depth) {
2278  assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
2279  "only nuw or nsw allowed");
2280  assert(!Ops.empty() && "Cannot get empty add!");
2281  if (Ops.size() == 1) return Ops[0];
2282 #ifndef NDEBUG
2283  Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2284  for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2285  assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2286  "SCEVAddExpr operand types don't match!");
2287 #endif
2288 
2289  // Sort by complexity, this groups all similar expression types together.
2290  GroupByComplexity(Ops, &LI, DT);
2291 
2292  Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
2293 
2294  // If there are any constants, fold them together.
2295  unsigned Idx = 0;
2296  if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2297  ++Idx;
2298  assert(Idx < Ops.size());
2299  while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2300  // We found two constants, fold them together!
2301  Ops[0] = getConstant(LHSC->getAPInt() + RHSC->getAPInt());
2302  if (Ops.size() == 2) return Ops[0];
2303  Ops.erase(Ops.begin()+1); // Erase the folded element
2304  LHSC = cast<SCEVConstant>(Ops[0]);
2305  }
2306 
2307  // If we are left with a constant zero being added, strip it off.
2308  if (LHSC->getValue()->isZero()) {
2309  Ops.erase(Ops.begin());
2310  --Idx;
2311  }
2312 
2313  if (Ops.size() == 1) return Ops[0];
2314  }
2315 
2316  // Limit recursion calls depth.
2317  if (Depth > MaxArithDepth)
2318  return getOrCreateAddExpr(Ops, Flags);
2319 
2320  // Okay, check to see if the same value occurs in the operand list more than
2321  // once. If so, merge them together into an multiply expression. Since we
2322  // sorted the list, these values are required to be adjacent.
2323  Type *Ty = Ops[0]->getType();
2324  bool FoundMatch = false;
2325  for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
2326  if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
2327  // Scan ahead to count how many equal operands there are.
2328  unsigned Count = 2;
2329  while (i+Count != e && Ops[i+Count] == Ops[i])
2330  ++Count;
2331  // Merge the values into a multiply.
2332  const SCEV *Scale = getConstant(Ty, Count);
2333  const SCEV *Mul = getMulExpr(Scale, Ops[i], SCEV::FlagAnyWrap, Depth + 1);
2334  if (Ops.size() == Count)
2335  return Mul;
2336  Ops[i] = Mul;
2337  Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2338  --i; e -= Count - 1;
2339  FoundMatch = true;
2340  }
2341  if (FoundMatch)
2342  return getAddExpr(Ops, Flags);
2343 
2344  // Check for truncates. If all the operands are truncated from the same
2345  // type, see if factoring out the truncate would permit the result to be
2346  // folded. eg., n*trunc(x) + m*trunc(y) --> trunc(trunc(m)*x + trunc(n)*y)
2347  // if the contents of the resulting outer trunc fold to something simple.
2348  auto FindTruncSrcType = [&]() -> Type * {
2349  // We're ultimately looking to fold an addrec of truncs and muls of only
2350  // constants and truncs, so if we find any other types of SCEV
2351  // as operands of the addrec then we bail and return nullptr here.
2352  // Otherwise, we return the type of the operand of a trunc that we find.
2353  if (auto *T = dyn_cast<SCEVTruncateExpr>(Ops[Idx]))
2354  return T->getOperand()->getType();
2355  if (const auto *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2356  const auto *LastOp = Mul->getOperand(Mul->getNumOperands() - 1);
2357  if (const auto *T = dyn_cast<SCEVTruncateExpr>(LastOp))
2358  return T->getOperand()->getType();
2359  }
2360  return nullptr;
2361  };
2362  if (auto *SrcType = FindTruncSrcType()) {
2364  bool Ok = true;
2365  // Check all the operands to see if they can be represented in the
2366  // source type of the truncate.
2367  for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2368  if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2369  if (T->getOperand()->getType() != SrcType) {
2370  Ok = false;
2371  break;
2372  }
2373  LargeOps.push_back(T->getOperand());
2374  } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2375  LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2376  } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2377  SmallVector<const SCEV *, 8> LargeMulOps;
2378  for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2379  if (const SCEVTruncateExpr *T =
2380  dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2381  if (T->getOperand()->getType() != SrcType) {
2382  Ok = false;
2383  break;
2384  }
2385  LargeMulOps.push_back(T->getOperand());
2386  } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
2387  LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2388  } else {
2389  Ok = false;
2390  break;
2391  }
2392  }
2393  if (Ok)
2394  LargeOps.push_back(getMulExpr(LargeMulOps, SCEV::FlagAnyWrap, Depth + 1));
2395  } else {
2396  Ok = false;
2397  break;
2398  }
2399  }
2400  if (Ok) {
2401  // Evaluate the expression in the larger type.
2402  const SCEV *Fold = getAddExpr(LargeOps, Flags, Depth + 1);
2403  // If it folds to something simple, use it. Otherwise, don't.
2404  if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2405  return getTruncateExpr(Fold, Ty);
2406  }
2407  }
2408 
2409  // Skip past any other cast SCEVs.
2410  while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2411  ++Idx;
2412 
2413  // If there are add operands they would be next.
2414  if (Idx < Ops.size()) {
2415  bool DeletedAdd = false;
2416  while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2417  if (Ops.size() > AddOpsInlineThreshold ||
2418  Add->getNumOperands() > AddOpsInlineThreshold)
2419  break;
2420  // If we have an add, expand the add operands onto the end of the operands
2421  // list.
2422  Ops.erase(Ops.begin()+Idx);
2423  Ops.append(Add->op_begin(), Add->op_end());
2424  DeletedAdd = true;
2425  }
2426 
2427  // If we deleted at least one add, we added operands to the end of the list,
2428  // and they are not necessarily sorted. Recurse to resort and resimplify
2429  // any operands we just acquired.
2430  if (DeletedAdd)
2431  return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2432  }
2433 
2434  // Skip over the add expression until we get to a multiply.
2435  while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2436  ++Idx;
2437 
2438  // Check to see if there are any folding opportunities present with
2439  // operands multiplied by constant values.
2440  if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2441  uint64_t BitWidth = getTypeSizeInBits(Ty);
2444  APInt AccumulatedConstant(BitWidth, 0);
2445  if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2446  Ops.data(), Ops.size(),
2447  APInt(BitWidth, 1), *this)) {
2448  struct APIntCompare {
2449  bool operator()(const APInt &LHS, const APInt &RHS) const {
2450  return LHS.ult(RHS);
2451  }
2452  };
2453 
2454  // Some interesting folding opportunity is present, so its worthwhile to
2455  // re-generate the operands list. Group the operands by constant scale,
2456  // to avoid multiplying by the same constant scale multiple times.
2457  std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2458  for (const SCEV *NewOp : NewOps)
2459  MulOpLists[M.find(NewOp)->second].push_back(NewOp);
2460  // Re-generate the operands list.
2461  Ops.clear();
2462  if (AccumulatedConstant != 0)
2463  Ops.push_back(getConstant(AccumulatedConstant));
2464  for (auto &MulOp : MulOpLists)
2465  if (MulOp.first != 0)
2466  Ops.push_back(getMulExpr(
2467  getConstant(MulOp.first),
2468  getAddExpr(MulOp.second, SCEV::FlagAnyWrap, Depth + 1),
2469  SCEV::FlagAnyWrap, Depth + 1));
2470  if (Ops.empty())
2471  return getZero(Ty);
2472  if (Ops.size() == 1)
2473  return Ops[0];
2474  return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2475  }
2476  }
2477 
2478  // If we are adding something to a multiply expression, make sure the
2479  // something is not already an operand of the multiply. If so, merge it into
2480  // the multiply.
2481  for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2482  const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2483  for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2484  const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2485  if (isa<SCEVConstant>(MulOpSCEV))
2486  continue;
2487  for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2488  if (MulOpSCEV == Ops[AddOp]) {
2489  // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2490  const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2491  if (Mul->getNumOperands() != 2) {
2492  // If the multiply has more than two operands, we must get the
2493  // Y*Z term.
2494  SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2495  Mul->op_begin()+MulOp);
2496  MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2497  InnerMul = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
2498  }
2499  SmallVector<const SCEV *, 2> TwoOps = {getOne(Ty), InnerMul};
2500  const SCEV *AddOne = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
2501  const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV,
2502  SCEV::FlagAnyWrap, Depth + 1);
2503  if (Ops.size() == 2) return OuterMul;
2504  if (AddOp < Idx) {
2505  Ops.erase(Ops.begin()+AddOp);
2506  Ops.erase(Ops.begin()+Idx-1);
2507  } else {
2508  Ops.erase(Ops.begin()+Idx);
2509  Ops.erase(Ops.begin()+AddOp-1);
2510  }
2511  Ops.push_back(OuterMul);
2512  return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2513  }
2514 
2515  // Check this multiply against other multiplies being added together.
2516  for (unsigned OtherMulIdx = Idx+1;
2517  OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2518  ++OtherMulIdx) {
2519  const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2520  // If MulOp occurs in OtherMul, we can fold the two multiplies
2521  // together.
2522  for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2523  OMulOp != e; ++OMulOp)
2524  if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2525  // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2526  const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2527  if (Mul->getNumOperands() != 2) {
2528  SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2529  Mul->op_begin()+MulOp);
2530  MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2531  InnerMul1 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
2532  }
2533  const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2534  if (OtherMul->getNumOperands() != 2) {
2535  SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2536  OtherMul->op_begin()+OMulOp);
2537  MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2538  InnerMul2 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
2539  }
2540  SmallVector<const SCEV *, 2> TwoOps = {InnerMul1, InnerMul2};
2541  const SCEV *InnerMulSum =
2542  getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
2543  const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum,
2544  SCEV::FlagAnyWrap, Depth + 1);
2545  if (Ops.size() == 2) return OuterMul;
2546  Ops.erase(Ops.begin()+Idx);
2547  Ops.erase(Ops.begin()+OtherMulIdx-1);
2548  Ops.push_back(OuterMul);
2549  return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2550  }
2551  }
2552  }
2553  }
2554 
2555  // If there are any add recurrences in the operands list, see if any other
2556  // added values are loop invariant. If so, we can fold them into the
2557  // recurrence.
2558  while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2559  ++Idx;
2560 
2561  // Scan over all recurrences, trying to fold loop invariants into them.
2562  for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2563  // Scan all of the other operands to this add and add them to the vector if
2564  // they are loop invariant w.r.t. the recurrence.
2566  const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2567  const Loop *AddRecLoop = AddRec->getLoop();
2568  for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2569  if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
2570  LIOps.push_back(Ops[i]);
2571  Ops.erase(Ops.begin()+i);
2572  --i; --e;
2573  }
2574 
2575  // If we found some loop invariants, fold them into the recurrence.
2576  if (!LIOps.empty()) {
2577  // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2578  LIOps.push_back(AddRec->getStart());
2579 
2580  SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2581  AddRec->op_end());
2582  // This follows from the fact that the no-wrap flags on the outer add
2583  // expression are applicable on the 0th iteration, when the add recurrence
2584  // will be equal to its start value.
2585  AddRecOps[0] = getAddExpr(LIOps, Flags, Depth + 1);
2586 
2587  // Build the new addrec. Propagate the NUW and NSW flags if both the
2588  // outer add and the inner addrec are guaranteed to have no overflow.
2589  // Always propagate NW.
2590  Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2591  const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2592 
2593  // If all of the other operands were loop invariant, we are done.
2594  if (Ops.size() == 1) return NewRec;
2595 
2596  // Otherwise, add the folded AddRec by the non-invariant parts.
2597  for (unsigned i = 0;; ++i)
2598  if (Ops[i] == AddRec) {
2599  Ops[i] = NewRec;
2600  break;
2601  }
2602  return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2603  }
2604 
2605  // Okay, if there weren't any loop invariants to be folded, check to see if
2606  // there are multiple AddRec's with the same loop induction variable being
2607  // added together. If so, we can fold them.
2608  for (unsigned OtherIdx = Idx+1;
2609  OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2610  ++OtherIdx) {
2611  // We expect the AddRecExpr's to be sorted in reverse dominance order,
2612  // so that the 1st found AddRecExpr is dominated by all others.
2613  assert(DT.dominates(
2614  cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(),
2615  AddRec->getLoop()->getHeader()) &&
2616  "AddRecExprs are not sorted in reverse dominance order?");
2617  if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2618  // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2619  SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2620  AddRec->op_end());
2621  for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2622  ++OtherIdx) {
2623  const auto *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2624  if (OtherAddRec->getLoop() == AddRecLoop) {
2625  for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2626  i != e; ++i) {
2627  if (i >= AddRecOps.size()) {
2628  AddRecOps.append(OtherAddRec->op_begin()+i,
2629  OtherAddRec->op_end());
2630  break;
2631  }
2632  SmallVector<const SCEV *, 2> TwoOps = {
2633  AddRecOps[i], OtherAddRec->getOperand(i)};
2634  AddRecOps[i] = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
2635  }
2636  Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2637  }
2638  }
2639  // Step size has changed, so we cannot guarantee no self-wraparound.
2640  Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2641  return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2642  }
2643  }
2644 
2645  // Otherwise couldn't fold anything into this recurrence. Move onto the
2646  // next one.
2647  }
2648 
2649  // Okay, it looks like we really DO need an add expr. Check to see if we
2650  // already have one, otherwise create a new one.
2651  return getOrCreateAddExpr(Ops, Flags);
2652 }
2653 
2654 const SCEV *
2655 ScalarEvolution::getOrCreateAddExpr(SmallVectorImpl<const SCEV *> &Ops,
2656  SCEV::NoWrapFlags Flags) {
2658  ID.AddInteger(scAddExpr);
2659  for (const SCEV *Op : Ops)
2660  ID.AddPointer(Op);
2661  void *IP = nullptr;
2662  SCEVAddExpr *S =
2663  static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2664  if (!S) {
2665  const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2666  std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2667  S = new (SCEVAllocator)
2668  SCEVAddExpr(ID.Intern(SCEVAllocator), O, Ops.size());
2669  UniqueSCEVs.InsertNode(S, IP);
2670  addToLoopUseLists(S);
2671  }
2672  S->setNoWrapFlags(Flags);
2673  return S;
2674 }
2675 
2676 const SCEV *
2677 ScalarEvolution::getOrCreateMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2678  SCEV::NoWrapFlags Flags) {
2680  ID.AddInteger(scMulExpr);
2681  for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2682  ID.AddPointer(Ops[i]);
2683  void *IP = nullptr;
2684  SCEVMulExpr *S =
2685  static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2686  if (!S) {
2687  const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2688  std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2689  S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2690  O, Ops.size());
2691  UniqueSCEVs.InsertNode(S, IP);
2692  addToLoopUseLists(S);
2693  }
2694  S->setNoWrapFlags(Flags);
2695  return S;
2696 }
2697 
2698 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2699  uint64_t k = i*j;
2700  if (j > 1 && k / j != i) Overflow = true;
2701  return k;
2702 }
2703 
2704 /// Compute the result of "n choose k", the binomial coefficient. If an
2705 /// intermediate computation overflows, Overflow will be set and the return will
2706 /// be garbage. Overflow is not cleared on absence of overflow.
2707 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2708  // We use the multiplicative formula:
2709  // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2710  // At each iteration, we take the n-th term of the numeral and divide by the
2711  // (k-n)th term of the denominator. This division will always produce an
2712  // integral result, and helps reduce the chance of overflow in the
2713  // intermediate computations. However, we can still overflow even when the
2714  // final result would fit.
2715 
2716  if (n == 0 || n == k) return 1;
2717  if (k > n) return 0;
2718 
2719  if (k > n/2)
2720  k = n-k;
2721 
2722  uint64_t r = 1;
2723  for (uint64_t i = 1; i <= k; ++i) {
2724  r = umul_ov(r, n-(i-1), Overflow);
2725  r /= i;
2726  }
2727  return r;
2728 }
2729 
2730 /// Determine if any of the operands in this SCEV are a constant or if
2731 /// any of the add or multiply expressions in this SCEV contain a constant.
2732 static bool containsConstantInAddMulChain(const SCEV *StartExpr) {
2733  struct FindConstantInAddMulChain {
2734  bool FoundConstant = false;
2735 
2736  bool follow(const SCEV *S) {
2737  FoundConstant |= isa<SCEVConstant>(S);
2738  return isa<SCEVAddExpr>(S) || isa<SCEVMulExpr>(S);
2739  }
2740 
2741  bool isDone() const {
2742  return FoundConstant;
2743  }
2744  };
2745 
2746  FindConstantInAddMulChain F;
2748  ST.visitAll(StartExpr);
2749  return F.FoundConstant;
2750 }
2751 
2752 /// Get a canonical multiply expression, or something simpler if possible.
2754  SCEV::NoWrapFlags Flags,
2755  unsigned Depth) {
2756  assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2757  "only nuw or nsw allowed");
2758  assert(!Ops.empty() && "Cannot get empty mul!");
2759  if (Ops.size() == 1) return Ops[0];
2760 #ifndef NDEBUG
2761  Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2762  for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2763  assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2764  "SCEVMulExpr operand types don't match!");
2765 #endif
2766 
2767  // Sort by complexity, this groups all similar expression types together.
2768  GroupByComplexity(Ops, &LI, DT);
2769 
2770  Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2771 
2772  // Limit recursion calls depth.
2773  if (Depth > MaxArithDepth)
2774  return getOrCreateMulExpr(Ops, Flags);
2775 
2776  // If there are any constants, fold them together.
2777  unsigned Idx = 0;
2778  if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2779 
2780  // C1*(C2+V) -> C1*C2 + C1*V
2781  if (Ops.size() == 2)
2782  if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2783  // If any of Add's ops are Adds or Muls with a constant,
2784  // apply this transformation as well.
2785  if (Add->getNumOperands() == 2)
2786  // TODO: There are some cases where this transformation is not
2787  // profitable, for example:
2788  // Add = (C0 + X) * Y + Z.
2789  // Maybe the scope of this transformation should be narrowed down.
2791  return getAddExpr(getMulExpr(LHSC, Add->getOperand(0),
2792  SCEV::FlagAnyWrap, Depth + 1),
2793  getMulExpr(LHSC, Add->getOperand(1),
2794  SCEV::FlagAnyWrap, Depth + 1),
2795  SCEV::FlagAnyWrap, Depth + 1);
2796 
2797  ++Idx;
2798  while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2799  // We found two constants, fold them together!
2800  ConstantInt *Fold =
2801  ConstantInt::get(getContext(), LHSC->getAPInt() * RHSC->getAPInt());
2802  Ops[0] = getConstant(Fold);
2803  Ops.erase(Ops.begin()+1); // Erase the folded element
2804  if (Ops.size() == 1) return Ops[0];
2805  LHSC = cast<SCEVConstant>(Ops[0]);
2806  }
2807 
2808  // If we are left with a constant one being multiplied, strip it off.
2809  if (cast<SCEVConstant>(Ops[0])->getValue()->isOne()) {
2810  Ops.erase(Ops.begin());
2811  --Idx;
2812  } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2813  // If we have a multiply of zero, it will always be zero.
2814  return Ops[0];
2815  } else if (Ops[0]->isAllOnesValue()) {
2816  // If we have a mul by -1 of an add, try distributing the -1 among the
2817  // add operands.
2818  if (Ops.size() == 2) {
2819  if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2821  bool AnyFolded = false;
2822  for (const SCEV *AddOp : Add->operands()) {
2823  const SCEV *Mul = getMulExpr(Ops[0], AddOp, SCEV::FlagAnyWrap,
2824  Depth + 1);
2825  if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2826  NewOps.push_back(Mul);
2827  }
2828  if (AnyFolded)
2829  return getAddExpr(NewOps, SCEV::FlagAnyWrap, Depth + 1);
2830  } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2831  // Negation preserves a recurrence's no self-wrap property.
2833  for (const SCEV *AddRecOp : AddRec->operands())
2834  Operands.push_back(getMulExpr(Ops[0], AddRecOp, SCEV::FlagAnyWrap,
2835  Depth + 1));
2836 
2837  return getAddRecExpr(Operands, AddRec->getLoop(),
2838  AddRec->getNoWrapFlags(SCEV::FlagNW));
2839  }
2840  }
2841  }
2842 
2843  if (Ops.size() == 1)
2844  return Ops[0];
2845  }
2846 
2847  // Skip over the add expression until we get to a multiply.
2848  while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2849  ++Idx;
2850 
2851  // If there are mul operands inline them all into this expression.
2852  if (Idx < Ops.size()) {
2853  bool DeletedMul = false;
2854  while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2855  if (Ops.size() > MulOpsInlineThreshold)
2856  break;
2857  // If we have an mul, expand the mul operands onto the end of the
2858  // operands list.
2859  Ops.erase(Ops.begin()+Idx);
2860  Ops.append(Mul->op_begin(), Mul->op_end());
2861  DeletedMul = true;
2862  }
2863 
2864  // If we deleted at least one mul, we added operands to the end of the
2865  // list, and they are not necessarily sorted. Recurse to resort and
2866  // resimplify any operands we just acquired.
2867  if (DeletedMul)
2868  return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2869  }
2870 
2871  // If there are any add recurrences in the operands list, see if any other
2872  // added values are loop invariant. If so, we can fold them into the
2873  // recurrence.
2874  while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2875  ++Idx;
2876 
2877  // Scan over all recurrences, trying to fold loop invariants into them.
2878  for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2879  // Scan all of the other operands to this mul and add them to the vector
2880  // if they are loop invariant w.r.t. the recurrence.
2882  const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2883  const Loop *AddRecLoop = AddRec->getLoop();
2884  for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2885  if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
2886  LIOps.push_back(Ops[i]);
2887  Ops.erase(Ops.begin()+i);
2888  --i; --e;
2889  }
2890 
2891  // If we found some loop invariants, fold them into the recurrence.
2892  if (!LIOps.empty()) {
2893  // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2895  NewOps.reserve(AddRec->getNumOperands());
2896  const SCEV *Scale = getMulExpr(LIOps, SCEV::FlagAnyWrap, Depth + 1);
2897  for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2898  NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i),
2899  SCEV::FlagAnyWrap, Depth + 1));
2900 
2901  // Build the new addrec. Propagate the NUW and NSW flags if both the
2902  // outer mul and the inner addrec are guaranteed to have no overflow.
2903  //
2904  // No self-wrap cannot be guaranteed after changing the step size, but
2905  // will be inferred if either NUW or NSW is true.
2906  Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2907  const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2908 
2909  // If all of the other operands were loop invariant, we are done.
2910  if (Ops.size() == 1) return NewRec;
2911 
2912  // Otherwise, multiply the folded AddRec by the non-invariant parts.
2913  for (unsigned i = 0;; ++i)
2914  if (Ops[i] == AddRec) {
2915  Ops[i] = NewRec;
2916  break;
2917  }
2918  return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2919  }
2920 
2921  // Okay, if there weren't any loop invariants to be folded, check to see
2922  // if there are multiple AddRec's with the same loop induction variable
2923  // being multiplied together. If so, we can fold them.
2924 
2925  // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2926  // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2927  // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2928  // ]]],+,...up to x=2n}.
2929  // Note that the arguments to choose() are always integers with values
2930  // known at compile time, never SCEV objects.
2931  //
2932  // The implementation avoids pointless extra computations when the two
2933  // addrec's are of different length (mathematically, it's equivalent to
2934  // an infinite stream of zeros on the right).
2935  bool OpsModified = false;
2936  for (unsigned OtherIdx = Idx+1;
2937  OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2938  ++OtherIdx) {
2939  const SCEVAddRecExpr *OtherAddRec =
2940  dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2941  if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2942  continue;
2943 
2944  // Limit max number of arguments to avoid creation of unreasonably big
2945  // SCEVAddRecs with very complex operands.
2946  if (AddRec->getNumOperands() + OtherAddRec->getNumOperands() - 1 >
2947  MaxAddRecSize)
2948  continue;
2949 
2950  bool Overflow = false;
2951  Type *Ty = AddRec->getType();
2952  bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2953  SmallVector<const SCEV*, 7> AddRecOps;
2954  for (int x = 0, xe = AddRec->getNumOperands() +
2955  OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2956  const SCEV *Term = getZero(Ty);
2957  for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2958  uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2959  for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2960  ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2961  z < ze && !Overflow; ++z) {
2962  uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2963  uint64_t Coeff;
2964  if (LargerThan64Bits)
2965  Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2966  else
2967  Coeff = Coeff1*Coeff2;
2968  const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2969  const SCEV *Term1 = AddRec->getOperand(y-z);
2970  const SCEV *Term2 = OtherAddRec->getOperand(z);
2971  Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1, Term2,
2972  SCEV::FlagAnyWrap, Depth + 1),
2973  SCEV::FlagAnyWrap, Depth + 1);
2974  }
2975  }
2976  AddRecOps.push_back(Term);
2977  }
2978  if (!Overflow) {
2979  const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2981  if (Ops.size() == 2) return NewAddRec;
2982  Ops[Idx] = NewAddRec;
2983  Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2984  OpsModified = true;
2985  AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2986  if (!AddRec)
2987  break;
2988  }
2989  }
2990  if (OpsModified)
2991  return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2992 
2993  // Otherwise couldn't fold anything into this recurrence. Move onto the
2994  // next one.
2995  }
2996 
2997  // Okay, it looks like we really DO need an mul expr. Check to see if we
2998  // already have one, otherwise create a new one.
2999  return getOrCreateMulExpr(Ops, Flags);
3000 }
3001 
3002 /// Represents an unsigned remainder expression based on unsigned division.
3004  const SCEV *RHS) {
3005  assert(getEffectiveSCEVType(LHS->getType()) ==
3006  getEffectiveSCEVType(RHS->getType()) &&
3007  "SCEVURemExpr operand types don't match!");
3008 
3009  // Short-circuit easy cases
3010  if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
3011  // If constant is one, the result is trivial
3012  if (RHSC->getValue()->isOne())
3013  return getZero(LHS->getType()); // X urem 1 --> 0
3014 
3015  // If constant is a power of two, fold into a zext(trunc(LHS)).
3016  if (RHSC->getAPInt().isPowerOf2()) {
3017  Type *FullTy = LHS->getType();
3018  Type *TruncTy =
3019  IntegerType::get(getContext(), RHSC->getAPInt().logBase2());
3020  return getZeroExtendExpr(getTruncateExpr(LHS, TruncTy), FullTy);
3021  }
3022  }
3023 
3024  // Fallback to %a == %x urem %y == %x -<nuw> ((%x udiv %y) *<nuw> %y)
3025  const SCEV *UDiv = getUDivExpr(LHS, RHS);
3026  const SCEV *Mult = getMulExpr(UDiv, RHS, SCEV::FlagNUW);
3027  return getMinusSCEV(LHS, Mult, SCEV::FlagNUW);
3028 }
3029 
3030 /// Get a canonical unsigned division expression, or something simpler if
3031 /// possible.
3033  const SCEV *RHS) {
3034  assert(getEffectiveSCEVType(LHS->getType()) ==
3035  getEffectiveSCEVType(RHS->getType()) &&
3036  "SCEVUDivExpr operand types don't match!");
3037 
3038  if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
3039  if (RHSC->getValue()->isOne())
3040  return LHS; // X udiv 1 --> x
3041  // If the denominator is zero, the result of the udiv is undefined. Don't
3042  // try to analyze it, because the resolution chosen here may differ from
3043  // the resolution chosen in other parts of the compiler.
3044  if (!RHSC->getValue()->isZero()) {
3045  // Determine if the division can be folded into the operands of
3046  // its operands.
3047  // TODO: Generalize this to non-constants by using known-bits information.
3048  Type *Ty = LHS->getType();
3049  unsigned LZ = RHSC->getAPInt().countLeadingZeros();
3050  unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
3051  // For non-power-of-two values, effectively round the value up to the
3052  // nearest power of two.
3053  if (!RHSC->getAPInt().isPowerOf2())
3054  ++MaxShiftAmt;
3055  IntegerType *ExtTy =
3056  IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
3057  if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
3058  if (const SCEVConstant *Step =
3059  dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
3060  // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
3061  const APInt &StepInt = Step->getAPInt();
3062  const APInt &DivInt = RHSC->getAPInt();
3063  if (!StepInt.urem(DivInt) &&
3064  getZeroExtendExpr(AR, ExtTy) ==
3065  getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
3066  getZeroExtendExpr(Step, ExtTy),
3067  AR->getLoop(), SCEV::FlagAnyWrap)) {
3069  for (const SCEV *Op : AR->operands())
3070  Operands.push_back(getUDivExpr(Op, RHS));
3071  return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
3072  }
3073  /// Get a canonical UDivExpr for a recurrence.
3074  /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
3075  // We can currently only fold X%N if X is constant.
3076  const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
3077  if (StartC && !DivInt.urem(StepInt) &&
3078  getZeroExtendExpr(AR, ExtTy) ==
3079  getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
3080  getZeroExtendExpr(Step, ExtTy),
3081  AR->getLoop(), SCEV::FlagAnyWrap)) {
3082  const APInt &StartInt = StartC->getAPInt();
3083  const APInt &StartRem = StartInt.urem(StepInt);
3084  if (StartRem != 0)
3085  LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
3086  AR->getLoop(), SCEV::FlagNW);
3087  }
3088  }
3089  // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
3090  if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
3092  for (const SCEV *Op : M->operands())
3093  Operands.push_back(getZeroExtendExpr(Op, ExtTy));
3094  if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
3095  // Find an operand that's safely divisible.
3096  for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
3097  const SCEV *Op = M->getOperand(i);
3098  const SCEV *Div = getUDivExpr(Op, RHSC);
3099  if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
3100  Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
3101  M->op_end());
3102  Operands[i] = Div;
3103  return getMulExpr(Operands);
3104  }
3105  }
3106  }
3107  // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
3108  if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
3110  for (const SCEV *Op : A->operands())
3111  Operands.push_back(getZeroExtendExpr(Op, ExtTy));
3112  if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
3113  Operands.clear();
3114  for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
3115  const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
3116  if (isa<SCEVUDivExpr>(Op) ||
3117  getMulExpr(Op, RHS) != A->getOperand(i))
3118  break;
3119  Operands.push_back(Op);
3120  }
3121  if (Operands.size() == A->getNumOperands())
3122  return getAddExpr(Operands);
3123  }
3124  }
3125 
3126  // Fold if both operands are constant.
3127  if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
3128  Constant *LHSCV = LHSC->getValue();
3129  Constant *RHSCV = RHSC->getValue();
3130  return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
3131  RHSCV)));
3132  }
3133  }
3134  }
3135 
3137  ID.AddInteger(scUDivExpr);
3138  ID.AddPointer(LHS);
3139  ID.AddPointer(RHS);
3140  void *IP = nullptr;
3141  if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3142  SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
3143  LHS, RHS);
3144  UniqueSCEVs.InsertNode(S, IP);
3145  addToLoopUseLists(S);
3146  return S;
3147 }
3148 
3149 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
3150  APInt A = C1->getAPInt().abs();
3151  APInt B = C2->getAPInt().abs();
3152  uint32_t ABW = A.getBitWidth();
3153  uint32_t BBW = B.getBitWidth();
3154 
3155  if (ABW > BBW)
3156  B = B.zext(ABW);
3157  else if (ABW < BBW)
3158  A = A.zext(BBW);
3159 
3160  return APIntOps::GreatestCommonDivisor(std::move(A), std::move(B));
3161 }
3162 
3163 /// Get a canonical unsigned division expression, or something simpler if
3164 /// possible. There is no representation for an exact udiv in SCEV IR, but we
3165 /// can attempt to remove factors from the LHS and RHS. We can't do this when
3166 /// it's not exact because the udiv may be clearing bits.
3168  const SCEV *RHS) {
3169  // TODO: we could try to find factors in all sorts of things, but for now we
3170  // just deal with u/exact (multiply, constant). See SCEVDivision towards the
3171  // end of this file for inspiration.
3172 
3173  const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
3174  if (!Mul || !Mul->hasNoUnsignedWrap())
3175  return getUDivExpr(LHS, RHS);
3176 
3177  if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
3178  // If the mulexpr multiplies by a constant, then that constant must be the
3179  // first element of the mulexpr.
3180  if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
3181  if (LHSCst == RHSCst) {
3183  Operands.append(Mul->op_begin() + 1, Mul->op_end());
3184  return getMulExpr(Operands);
3185  }
3186 
3187  // We can't just assume that LHSCst divides RHSCst cleanly, it could be
3188  // that there's a factor provided by one of the other terms. We need to
3189  // check.
3190  APInt Factor = gcd(LHSCst, RHSCst);
3191  if (!Factor.isIntN(1)) {
3192  LHSCst =
3193  cast<SCEVConstant>(getConstant(LHSCst->getAPInt().udiv(Factor)));
3194  RHSCst =
3195  cast<SCEVConstant>(getConstant(RHSCst->getAPInt().udiv(Factor)));
3197  Operands.push_back(LHSCst);
3198  Operands.append(Mul->op_begin() + 1, Mul->op_end());
3199  LHS = getMulExpr(Operands);
3200  RHS = RHSCst;
3201  Mul = dyn_cast<SCEVMulExpr>(LHS);
3202  if (!Mul)
3203  return getUDivExactExpr(LHS, RHS);
3204  }
3205  }
3206  }
3207 
3208  for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
3209  if (Mul->getOperand(i) == RHS) {
3211  Operands.append(Mul->op_begin(), Mul->op_begin() + i);
3212  Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
3213  return getMulExpr(Operands);
3214  }
3215  }
3216 
3217  return getUDivExpr(LHS, RHS);
3218 }
3219 
3220 /// Get an add recurrence expression for the specified loop. Simplify the
3221 /// expression as much as possible.
3222 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
3223  const Loop *L,
3224  SCEV::NoWrapFlags Flags) {
3226  Operands.push_back(Start);
3227  if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
3228  if (StepChrec->getLoop() == L) {
3229  Operands.append(StepChrec->op_begin(), StepChrec->op_end());
3230  return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
3231  }
3232 
3233  Operands.push_back(Step);
3234  return getAddRecExpr(Operands, L, Flags);
3235 }
3236 
3237 /// Get an add recurrence expression for the specified loop. Simplify the
3238 /// expression as much as possible.
3239 const SCEV *
3241  const Loop *L, SCEV::NoWrapFlags Flags) {
3242  if (Operands.size() == 1) return Operands[0];
3243 #ifndef NDEBUG
3244  Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
3245  for (unsigned i = 1, e = Operands.size(); i != e; ++i)
3246  assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
3247  "SCEVAddRecExpr operand types don't match!");
3248  for (unsigned i = 0, e = Operands.size(); i != e; ++i)
3249  assert(isLoopInvariant(Operands[i], L) &&
3250  "SCEVAddRecExpr operand is not loop-invariant!");
3251 #endif
3252 
3253  if (Operands.back()->isZero()) {
3254  Operands.pop_back();
3255  return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
3256  }
3257 
3258  // It's tempting to want to call getMaxBackedgeTakenCount count here and
3259  // use that information to infer NUW and NSW flags. However, computing a
3260  // BE count requires calling getAddRecExpr, so we may not yet have a
3261  // meaningful BE count at this point (and if we don't, we'd be stuck
3262  // with a SCEVCouldNotCompute as the cached BE count).
3263 
3264  Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
3265 
3266  // Canonicalize nested AddRecs in by nesting them in order of loop depth.
3267  if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
3268  const Loop *NestedLoop = NestedAR->getLoop();
3269  if (L->contains(NestedLoop)
3270  ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
3271  : (!NestedLoop->contains(L) &&
3272  DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
3273  SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
3274  NestedAR->op_end());
3275  Operands[0] = NestedAR->getStart();
3276  // AddRecs require their operands be loop-invariant with respect to their
3277  // loops. Don't perform this transformation if it would break this
3278  // requirement.
3279  bool AllInvariant = all_of(
3280  Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); });
3281 
3282  if (AllInvariant) {
3283  // Create a recurrence for the outer loop with the same step size.
3284  //
3285  // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
3286  // inner recurrence has the same property.
3287  SCEV::NoWrapFlags OuterFlags =
3288  maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
3289 
3290  NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
3291  AllInvariant = all_of(NestedOperands, [&](const SCEV *Op) {
3292  return isLoopInvariant(Op, NestedLoop);
3293  });
3294 
3295  if (AllInvariant) {
3296  // Ok, both add recurrences are valid after the transformation.
3297  //
3298  // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
3299  // the outer recurrence has the same property.
3300  SCEV::NoWrapFlags InnerFlags =
3301  maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
3302  return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
3303  }
3304  }
3305  // Reset Operands to its original state.
3306  Operands[0] = NestedAR;
3307  }
3308  }
3309 
3310  // Okay, it looks like we really DO need an addrec expr. Check to see if we
3311  // already have one, otherwise create a new one.
3314  for (unsigned i = 0, e = Operands.size(); i != e; ++i)
3315  ID.AddPointer(Operands[i]);
3316  ID.AddPointer(L);
3317  void *IP = nullptr;
3318  SCEVAddRecExpr *S =
3319  static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
3320  if (!S) {
3321  const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
3322  std::uninitialized_copy(Operands.begin(), Operands.end(), O);
3323  S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
3324  O, Operands.size(), L);
3325  UniqueSCEVs.InsertNode(S, IP);
3326  addToLoopUseLists(S);
3327  }
3328  S->setNoWrapFlags(Flags);
3329  return S;
3330 }
3331 
3332 const SCEV *
3334  const SmallVectorImpl<const SCEV *> &IndexExprs) {
3335  const SCEV *BaseExpr = getSCEV(GEP->getPointerOperand());
3336  // getSCEV(Base)->getType() has the same address space as Base->getType()
3337  // because SCEV::getType() preserves the address space.
3338  Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType());
3339  // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
3340  // instruction to its SCEV, because the Instruction may be guarded by control
3341  // flow and the no-overflow bits may not be valid for the expression in any
3342  // context. This can be fixed similarly to how these flags are handled for
3343  // adds.
3346 
3347  const SCEV *TotalOffset = getZero(IntPtrTy);
3348  // The array size is unimportant. The first thing we do on CurTy is getting
3349  // its element type.
3350  Type *CurTy = ArrayType::get(GEP->getSourceElementType(), 0);
3351  for (const SCEV *IndexExpr : IndexExprs) {
3352  // Compute the (potentially symbolic) offset in bytes for this index.
3353  if (StructType *STy = dyn_cast<StructType>(CurTy)) {
3354  // For a struct, add the member offset.
3355  ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
3356  unsigned FieldNo = Index->getZExtValue();
3357  const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3358 
3359  // Add the field offset to the running total offset.
3360  TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3361 
3362  // Update CurTy to the type of the field at Index.
3363  CurTy = STy->getTypeAtIndex(Index);
3364  } else {
3365  // Update CurTy to its element type.
3366  CurTy = cast<SequentialType>(CurTy)->getElementType();
3367  // For an array, add the element offset, explicitly scaled.
3368  const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy);
3369  // Getelementptr indices are signed.
3370  IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
3371 
3372  // Multiply the index by the element size to compute the element offset.
3373  const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
3374 
3375  // Add the element offset to the running total offset.
3376  TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3377  }
3378  }
3379 
3380  // Add the total offset from all the GEP indices to the base.
3381  return getAddExpr(BaseExpr, TotalOffset, Wrap);
3382 }
3383 
3385  const SCEV *RHS) {
3386  SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
3387  return getSMaxExpr(Ops);
3388 }
3389 
3390 const SCEV *
3392  assert(!Ops.empty() && "Cannot get empty smax!");
3393  if (Ops.size() == 1) return Ops[0];
3394 #ifndef NDEBUG
3395  Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3396  for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3397  assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3398  "SCEVSMaxExpr operand types don't match!");
3399 #endif
3400 
3401  // Sort by complexity, this groups all similar expression types together.
3402  GroupByComplexity(Ops, &LI, DT);
3403 
3404  // If there are any constants, fold them together.
3405  unsigned Idx = 0;
3406  if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3407  ++Idx;
3408  assert(Idx < Ops.size());
3409  while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3410  // We found two constants, fold them together!
3411  ConstantInt *Fold = ConstantInt::get(
3412  getContext(), APIntOps::smax(LHSC->getAPInt(), RHSC->getAPInt()));
3413  Ops[0] = getConstant(Fold);
3414  Ops.erase(Ops.begin()+1); // Erase the folded element
3415  if (Ops.size() == 1) return Ops[0];
3416  LHSC = cast<SCEVConstant>(Ops[0]);
3417  }
3418 
3419  // If we are left with a constant minimum-int, strip it off.
3420  if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
3421  Ops.erase(Ops.begin());
3422  --Idx;
3423  } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
3424  // If we have an smax with a constant maximum-int, it will always be
3425  // maximum-int.
3426  return Ops[0];
3427  }
3428 
3429  if (Ops.size() == 1) return Ops[0];
3430  }
3431 
3432  // Find the first SMax
3433  while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
3434  ++Idx;
3435 
3436  // Check to see if one of the operands is an SMax. If so, expand its operands
3437  // onto our operand list, and recurse to simplify.
3438  if (Idx < Ops.size()) {
3439  bool DeletedSMax = false;
3440  while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
3441  Ops.erase(Ops.begin()+Idx);
3442  Ops.append(SMax->op_begin(), SMax->op_end());
3443  DeletedSMax = true;
3444  }
3445 
3446  if (DeletedSMax)
3447  return getSMaxExpr(Ops);
3448  }
3449 
3450  // Okay, check to see if the same value occurs in the operand list twice. If
3451  // so, delete one. Since we sorted the list, these values are required to
3452  // be adjacent.
3453  for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3454  // X smax Y smax Y --> X smax Y
3455  // X smax Y --> X, if X is always greater than Y
3456  if (Ops[i] == Ops[i+1] ||
3457  isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
3458  Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3459  --i; --e;
3460  } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
3461  Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3462  --i; --e;
3463  }
3464 
3465  if (Ops.size() == 1) return Ops[0];
3466 
3467  assert(!Ops.empty() && "Reduced smax down to nothing!");
3468 
3469  // Okay, it looks like we really DO need an smax expr. Check to see if we
3470  // already have one, otherwise create a new one.
3472  ID.AddInteger(scSMaxExpr);
3473  for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3474  ID.AddPointer(Ops[i]);
3475  void *IP = nullptr;
3476  if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3477  const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3478  std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3479  SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
3480  O, Ops.size());
3481  UniqueSCEVs.InsertNode(S, IP);
3482  addToLoopUseLists(S);
3483  return S;
3484 }
3485 
3487  const SCEV *RHS) {
3488  SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
3489  return getUMaxExpr(Ops);
3490 }
3491 
3492 const SCEV *
3494  assert(!Ops.empty() && "Cannot get empty umax!");
3495  if (Ops.size() == 1) return Ops[0];
3496 #ifndef NDEBUG
3497  Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3498  for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3499  assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3500  "SCEVUMaxExpr operand types don't match!");
3501 #endif
3502 
3503  // Sort by complexity, this groups all similar expression types together.
3504  GroupByComplexity(Ops, &LI, DT);
3505 
3506  // If there are any constants, fold them together.
3507  unsigned Idx = 0;
3508  if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3509  ++Idx;
3510  assert(Idx < Ops.size());
3511  while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3512  // We found two constants, fold them together!
3513  ConstantInt *Fold = ConstantInt::get(
3514  getContext(), APIntOps::umax(LHSC->getAPInt(), RHSC->getAPInt()));
3515  Ops[0] = getConstant(Fold);
3516  Ops.erase(Ops.begin()+1); // Erase the folded element
3517  if (Ops.size() == 1) return Ops[0];
3518  LHSC = cast<SCEVConstant>(Ops[0]);
3519  }
3520 
3521  // If we are left with a constant minimum-int, strip it off.
3522  if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
3523  Ops.erase(Ops.begin());
3524  --Idx;
3525  } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
3526  // If we have an umax with a constant maximum-int, it will always be
3527  // maximum-int.
3528  return Ops[0];
3529  }
3530 
3531  if (Ops.size() == 1) return Ops[0];
3532  }
3533 
3534  // Find the first UMax
3535  while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
3536  ++Idx;
3537 
3538  // Check to see if one of the operands is a UMax. If so, expand its operands
3539  // onto our operand list, and recurse to simplify.
3540  if (Idx < Ops.size()) {
3541  bool DeletedUMax = false;
3542  while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
3543  Ops.erase(Ops.begin()+Idx);
3544  Ops.append(UMax->op_begin(), UMax->op_end());
3545  DeletedUMax = true;
3546  }
3547 
3548  if (DeletedUMax)
3549  return getUMaxExpr(Ops);
3550  }
3551 
3552  // Okay, check to see if the same value occurs in the operand list twice. If
3553  // so, delete one. Since we sorted the list, these values are required to
3554  // be adjacent.
3555  for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3556  // X umax Y umax Y --> X umax Y
3557  // X umax Y --> X, if X is always greater than Y
3558  if (Ops[i] == Ops[i+1] ||
3559  isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
3560  Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3561  --i; --e;
3562  } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
3563  Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3564  --i; --e;
3565  }
3566 
3567  if (Ops.size() == 1) return Ops[0];
3568 
3569  assert(!Ops.empty() && "Reduced umax down to nothing!");
3570 
3571  // Okay, it looks like we really DO need a umax expr. Check to see if we
3572  // already have one, otherwise create a new one.
3574  ID.AddInteger(scUMaxExpr);
3575  for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3576  ID.AddPointer(Ops[i]);
3577  void *IP = nullptr;
3578  if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3579  const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3580  std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3581  SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
3582  O, Ops.size());
3583  UniqueSCEVs.InsertNode(S, IP);
3584  addToLoopUseLists(S);
3585  return S;
3586 }
3587 
3589  const SCEV *RHS) {
3590  // ~smax(~x, ~y) == smin(x, y).
3591  return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3592 }
3593 
3595  const SCEV *RHS) {
3596  // ~umax(~x, ~y) == umin(x, y)
3597  return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3598 }
3599 
3600 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3601  // We can bypass creating a target-independent
3602  // constant expression and then folding it back into a ConstantInt.
3603  // This is just a compile-time optimization.
3604  return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy));
3605 }
3606 
3608  StructType *STy,
3609  unsigned FieldNo) {
3610  // We can bypass creating a target-independent
3611  // constant expression and then folding it back into a ConstantInt.
3612  // This is just a compile-time optimization.
3613  return getConstant(
3614  IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo));
3615 }
3616 
3618  // Don't attempt to do anything other than create a SCEVUnknown object
3619  // here. createSCEV only calls getUnknown after checking for all other
3620  // interesting possibilities, and any other code that calls getUnknown
3621  // is doing so in order to hide a value from SCEV canonicalization.
3622 
3624  ID.AddInteger(scUnknown);
3625  ID.AddPointer(V);
3626  void *IP = nullptr;
3627  if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3628  assert(cast<SCEVUnknown>(S)->getValue() == V &&
3629  "Stale SCEVUnknown in uniquing map!");
3630  return S;
3631  }
3632  SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3633  FirstUnknown);
3634  FirstUnknown = cast<SCEVUnknown>(S);
3635  UniqueSCEVs.InsertNode(S, IP);
3636  return S;
3637 }
3638 
3639 //===----------------------------------------------------------------------===//
3640 // Basic SCEV Analysis and PHI Idiom Recognition Code
3641 //
3642 
3643 /// Test if values of the given type are analyzable within the SCEV
3644 /// framework. This primarily includes integer types, and it can optionally
3645 /// include pointer types if the ScalarEvolution class has access to
3646 /// target-specific information.
3648  // Integers and pointers are always SCEVable.
3649  return Ty->isIntegerTy() || Ty->isPointerTy();
3650 }
3651 
3652 /// Return the size in bits of the specified type, for which isSCEVable must
3653 /// return true.
3655  assert(isSCEVable(Ty) && "Type is not SCEVable!");
3656  return getDataLayout().getTypeSizeInBits(Ty);
3657 }
3658 
3659 /// Return a type with the same bitwidth as the given type and which represents
3660 /// how SCEV will treat the given type, for which isSCEVable must return
3661 /// true. For pointer types, this is the pointer-sized integer type.
3663  assert(isSCEVable(Ty) && "Type is not SCEVable!");
3664 
3665  if (Ty->isIntegerTy())
3666  return Ty;
3667 
3668  // The only other support type is pointer.
3669  assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3670  return getDataLayout().getIntPtrType(Ty);
3671 }
3672 
3674  return getTypeSizeInBits(T1) >= getTypeSizeInBits(T2) ? T1 : T2;
3675 }
3676 
3678  return CouldNotCompute.get();
3679 }
3680 
3681 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3682  bool ContainsNulls = SCEVExprContains(S, [](const SCEV *S) {
3683  auto *SU = dyn_cast<SCEVUnknown>(S);
3684  return SU && SU->getValue() == nullptr;
3685  });
3686 
3687  return !ContainsNulls;
3688 }
3689 
3691  HasRecMapType::iterator I = HasRecMap.find(S);
3692  if (I != HasRecMap.end())
3693  return I->second;
3694 
3695  bool FoundAddRec = SCEVExprContains(S, isa<SCEVAddRecExpr, const SCEV *>);
3696  HasRecMap.insert({S, FoundAddRec});
3697  return FoundAddRec;
3698 }
3699 
3700 /// Try to split a SCEVAddExpr into a pair of {SCEV, ConstantInt}.
3701 /// If \p S is a SCEVAddExpr and is composed of a sub SCEV S' and an
3702 /// offset I, then return {S', I}, else return {\p S, nullptr}.
3703 static std::pair<const SCEV *, ConstantInt *> splitAddExpr(const SCEV *S) {
3704  const auto *Add = dyn_cast<SCEVAddExpr>(S);
3705  if (!Add)
3706  return {S, nullptr};
3707 
3708  if (Add->getNumOperands() != 2)
3709  return {S, nullptr};
3710 
3711  auto *ConstOp = dyn_cast<SCEVConstant>(Add->getOperand(0));
3712  if (!ConstOp)
3713  return {S, nullptr};
3714 
3715  return {Add->getOperand(1), ConstOp->getValue()};
3716 }
3717 
3718 /// Return the ValueOffsetPair set for \p S. \p S can be represented
3719 /// by the value and offset from any ValueOffsetPair in the set.
3721 ScalarEvolution::getSCEVValues(const SCEV *S) {
3722  ExprValueMapType::iterator SI = ExprValueMap.find_as(S);
3723  if (SI == ExprValueMap.end())
3724  return nullptr;
3725 #ifndef NDEBUG
3726  if (VerifySCEVMap) {
3727  // Check there is no dangling Value in the set returned.
3728  for (const auto &VE : SI->second)
3729  assert(ValueExprMap.count(VE.first));
3730  }
3731 #endif
3732  return &SI->second;
3733 }
3734 
3735 /// Erase Value from ValueExprMap and ExprValueMap. ValueExprMap.erase(V)
3736 /// cannot be used separately. eraseValueFromMap should be used to remove
3737 /// V from ValueExprMap and ExprValueMap at the same time.
3739  ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3740  if (I != ValueExprMap.end()) {
3741  const SCEV *S = I->second;
3742  // Remove {V, 0} from the set of ExprValueMap[S]
3743  if (SetVector<ValueOffsetPair> *SV = getSCEVValues(S))
3744  SV->remove({V, nullptr});
3745 
3746  // Remove {V, Offset} from the set of ExprValueMap[Stripped]
3747  const SCEV *Stripped;
3749  std::tie(Stripped, Offset) = splitAddExpr(S);
3750  if (Offset != nullptr) {
3751  if (SetVector<ValueOffsetPair> *SV = getSCEVValues(Stripped))
3752  SV->remove({V, Offset});
3753  }
3754  ValueExprMap.erase(V);
3755  }
3756 }
3757 
3758 /// Return an existing SCEV if it exists, otherwise analyze the expression and
3759 /// create a new one.
3761  assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3762 
3763  const SCEV *S = getExistingSCEV(V);
3764  if (S == nullptr) {
3765  S = createSCEV(V);
3766  // During PHI resolution, it is possible to create two SCEVs for the same
3767  // V, so it is needed to double check whether V->S is inserted into
3768  // ValueExprMap before insert S->{V, 0} into ExprValueMap.
3769  std::pair<ValueExprMapType::iterator, bool> Pair =
3770  ValueExprMap.insert({SCEVCallbackVH(V, this), S});
3771  if (Pair.second) {
3772  ExprValueMap[S].insert({V, nullptr});
3773 
3774  // If S == Stripped + Offset, add Stripped -> {V, Offset} into
3775  // ExprValueMap.
3776  const SCEV *Stripped = S;
3777  ConstantInt *Offset = nullptr;
3778  std::tie(Stripped, Offset) = splitAddExpr(S);
3779  // If stripped is SCEVUnknown, don't bother to save
3780  // Stripped -> {V, offset}. It doesn't simplify and sometimes even
3781  // increase the complexity of the expansion code.
3782  // If V is GetElementPtrInst, don't save Stripped -> {V, offset}
3783  // because it may generate add/sub instead of GEP in SCEV expansion.
3784  if (Offset != nullptr && !isa<SCEVUnknown>(Stripped) &&
3785  !isa<GetElementPtrInst>(V))
3786  ExprValueMap[Stripped].insert({V, Offset});
3787  }
3788  }
3789  return S;
3790 }
3791 
3792 const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
3793  assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3794 
3795  ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3796  if (I != ValueExprMap.end()) {
3797  const SCEV *S = I->second;
3798  if (checkValidity(S))
3799  return S;
3800  eraseValueFromMap(V);
3801  forgetMemoizedResults(S);
3802  }
3803  return nullptr;
3804 }
3805 
3806 /// Return a SCEV corresponding to -V = -1*V
3808  SCEV::NoWrapFlags Flags) {
3809  if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3810  return getConstant(
3811  cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3812 
3813  Type *Ty = V->getType();
3814  Ty = getEffectiveSCEVType(Ty);
3815  return getMulExpr(
3816  V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
3817 }
3818 
3819 /// Return a SCEV corresponding to ~V = -1-V
3821  if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3822  return getConstant(
3823  cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3824 
3825  Type *Ty = V->getType();
3826  Ty = getEffectiveSCEVType(Ty);
3827  const SCEV *AllOnes =
3828  getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3829  return getMinusSCEV(AllOnes, V);
3830 }
3831 
3832 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3833  SCEV::NoWrapFlags Flags,
3834  unsigned Depth) {
3835  // Fast path: X - X --> 0.
3836  if (LHS == RHS)
3837  return getZero(LHS->getType());
3838 
3839  // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
3840  // makes it so that we cannot make much use of NUW.
3841  auto AddFlags = SCEV::FlagAnyWrap;
3842  const bool RHSIsNotMinSigned =
3843  !getSignedRangeMin(RHS).isMinSignedValue();
3844  if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
3845  // Let M be the minimum representable signed value. Then (-1)*RHS
3846  // signed-wraps if and only if RHS is M. That can happen even for
3847  // a NSW subtraction because e.g. (-1)*M signed-wraps even though
3848  // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
3849  // (-1)*RHS, we need to prove that RHS != M.
3850  //
3851  // If LHS is non-negative and we know that LHS - RHS does not
3852  // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
3853  // either by proving that RHS > M or that LHS >= 0.
3854  if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
3855  AddFlags = SCEV::FlagNSW;
3856  }
3857  }
3858 
3859  // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
3860  // RHS is NSW and LHS >= 0.
3861  //
3862  // The difficulty here is that the NSW flag may have been proven
3863  // relative to a loop that is to be found in a recurrence in LHS and
3864  // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
3865  // larger scope than intended.
3866  auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3867 
3868  return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags, Depth);
3869 }
3870 
3871 const SCEV *
3873  Type *SrcTy = V->getType();
3874  assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3875  (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3876  "Cannot truncate or zero extend with non-integer arguments!");
3877  if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3878  return V; // No conversion
3879  if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3880  return getTruncateExpr(V, Ty);
3881  return getZeroExtendExpr(V, Ty);
3882 }
3883 
3884 const SCEV *
3886  Type *Ty) {
3887  Type *SrcTy = V->getType();
3888  assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3889  (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3890  "Cannot truncate or zero extend with non-integer arguments!");
3891  if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3892  return V; // No conversion
3893  if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3894  return getTruncateExpr(V, Ty);
3895  return getSignExtendExpr(V, Ty);
3896 }
3897 
3898 const SCEV *
3900  Type *SrcTy = V->getType();
3901  assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3902  (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3903  "Cannot noop or zero extend with non-integer arguments!");
3904  assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3905  "getNoopOrZeroExtend cannot truncate!");
3906  if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3907  return V; // No conversion
3908  return getZeroExtendExpr(V, Ty);
3909 }
3910 
3911 const SCEV *
3913  Type *SrcTy = V->getType();
3914  assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3915  (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3916  "Cannot noop or sign extend with non-integer arguments!");
3917  assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3918  "getNoopOrSignExtend cannot truncate!");
3919  if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3920  return V; // No conversion
3921  return getSignExtendExpr(V, Ty);
3922 }
3923 
3924 const SCEV *
3926  Type *SrcTy = V->getType();
3927  assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3928  (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3929  "Cannot noop or any extend with non-integer arguments!");
3930  assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3931  "getNoopOrAnyExtend cannot truncate!");
3932  if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3933  return V; // No conversion
3934  return getAnyExtendExpr(V, Ty);
3935 }
3936 
3937 const SCEV *
3939  Type *SrcTy = V->getType();
3940  assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3941  (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3942  "Cannot truncate or noop with non-integer arguments!");
3943  assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3944  "getTruncateOrNoop cannot extend!");
3945  if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3946  return V; // No conversion
3947  return getTruncateExpr(V, Ty);
3948 }
3949 
3951  const SCEV *RHS) {
3952  const SCEV *PromotedLHS = LHS;
3953  const SCEV *PromotedRHS = RHS;
3954 
3955  if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3956  PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3957  else
3958  PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3959 
3960  return getUMaxExpr(PromotedLHS, PromotedRHS);
3961 }
3962 
3964  const SCEV *RHS) {
3965  const SCEV *PromotedLHS = LHS;
3966  const SCEV *PromotedRHS = RHS;
3967 
3968  if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3969  PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3970  else
3971  PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3972 
3973  return getUMinExpr(PromotedLHS, PromotedRHS);
3974 }
3975 
3977  // A pointer operand may evaluate to a nonpointer expression, such as null.
3978  if (!V->getType()->isPointerTy())
3979  return V;
3980 
3981  if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3982  return getPointerBase(Cast->getOperand());
3983  } else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3984  const SCEV *PtrOp = nullptr;
3985  for (const SCEV *NAryOp : NAry->operands()) {
3986  if (NAryOp->getType()->isPointerTy()) {
3987  // Cannot find the base of an expression with multiple pointer operands.
3988  if (PtrOp)
3989  return V;
3990  PtrOp = NAryOp;
3991  }
3992  }
3993  if (!PtrOp)
3994  return V;
3995  return getPointerBase(PtrOp);
3996  }
3997  return V;
3998 }
3999 
4000 /// Push users of the given Instruction onto the given Worklist.
4001 static void
4003  SmallVectorImpl<Instruction *> &Worklist) {
4004  // Push the def-use children onto the Worklist stack.
4005  for (User *U : I->users())
4006  Worklist.push_back(cast<Instruction>(U));
4007 }
4008 
4009 void ScalarEvolution::forgetSymbolicName(Instruction *PN, const SCEV *SymName) {
4011  PushDefUseChildren(PN, Worklist);
4012 
4014  Visited.insert(PN);
4015  while (!Worklist.empty()) {
4016  Instruction *I = Worklist.pop_back_val();
4017  if (!Visited.insert(I).second)
4018  continue;
4019 
4020  auto It = ValueExprMap.find_as(static_cast<Value *>(I));
4021  if (It != ValueExprMap.end()) {
4022  const SCEV *Old = It->second;
4023 
4024  // Short-circuit the def-use traversal if the symbolic name
4025  // ceases to appear in expressions.
4026  if (Old != SymName && !hasOperand(Old, SymName))
4027  continue;
4028 
4029  // SCEVUnknown for a PHI either means that it has an unrecognized
4030  // structure, it's a PHI that's in the progress of being computed
4031  // by createNodeForPHI, or it's a single-value PHI. In the first case,
4032  // additional loop trip count information isn't going to change anything.
4033  // In the second case, createNodeForPHI will perform the necessary
4034  // updates on its own when it gets to that point. In the third, we do
4035  // want to forget the SCEVUnknown.
4036  if (!isa<PHINode>(I) ||
4037  !isa<SCEVUnknown>(Old) ||
4038  (I != PN && Old == SymName)) {
4039  eraseValueFromMap(It->first);
4040  forgetMemoizedResults(Old);
4041  }
4042  }
4043 
4044  PushDefUseChildren(I, Worklist);
4045  }
4046 }
4047 
4048 namespace {
4049 
4050 class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
4051 public:
4052  SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
4053  : SCEVRewriteVisitor(SE), L(L) {}
4054 
4055  static const SCEV *rewrite(const SCEV *S, const Loop *L,
4056  ScalarEvolution &SE) {
4057  SCEVInitRewriter Rewriter(L, SE);
4058  const SCEV *Result = Rewriter.visit(S);
4059  return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
4060  }
4061 
4062  const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4063  if (!SE.isLoopInvariant(Expr, L))
4064  Valid = false;
4065  return Expr;
4066  }
4067 
4068  const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
4069  // Only allow AddRecExprs for this loop.
4070  if (Expr->getLoop() == L)
4071  return Expr->getStart();
4072  Valid = false;
4073  return Expr;
4074  }
4075 
4076  bool isValid() { return Valid; }
4077 
4078 private:
4079  const Loop *L;
4080  bool Valid = true;
4081 };
4082 
4083 /// This class evaluates the compare condition by matching it against the
4084 /// condition of loop latch. If there is a match we assume a true value
4085 /// for the condition while building SCEV nodes.
4086 class SCEVBackedgeConditionFolder
4087  : public SCEVRewriteVisitor<SCEVBackedgeConditionFolder> {
4088 public:
4089  static const SCEV *rewrite(const SCEV *S, const Loop *L,
4090  ScalarEvolution &SE) {
4091  bool IsPosBECond = false;
4092  Value *BECond = nullptr;
4093  if (BasicBlock *Latch = L->getLoopLatch()) {
4094  BranchInst *BI = dyn_cast<BranchInst>(Latch->getTerminator());
4095  if (BI && BI->isConditional() &&
4096  BI->getSuccessor(0) != BI->getSuccessor(1)) {
4097  BECond = BI->getCondition();
4098  IsPosBECond = BI->getSuccessor(0) == L->getHeader();
4099  } else {
4100  return S;
4101  }
4102  }
4103  SCEVBackedgeConditionFolder Rewriter(L, BECond, IsPosBECond, SE);
4104  return Rewriter.visit(S);
4105  }
4106 
4107  const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4108  const SCEV *Result = Expr;
4109  bool InvariantF = SE.isLoopInvariant(Expr, L);
4110 
4111  if (!InvariantF) {
4112  Instruction *I = cast<Instruction>(Expr->getValue());
4113  switch (I->getOpcode()) {
4114  case Instruction::Select: {
4115  SelectInst *SI = cast<SelectInst>(I);
4117  compareWithBackedgeCondition(SI->getCondition());
4118  if (Res.hasValue()) {
4119  bool IsOne = cast<SCEVConstant>(Res.getValue())->getValue()->isOne();
4120  Result = SE.getSCEV(IsOne ? SI->getTrueValue() : SI->getFalseValue());
4121  }
4122  break;
4123  }
4124  default: {
4125  Optional<const SCEV *> Res = compareWithBackedgeCondition(I);
4126  if (Res.hasValue())
4127  Result = Res.getValue();
4128  break;
4129  }
4130  }
4131  }
4132  return Result;
4133  }
4134 
4135 private:
4136  explicit SCEVBackedgeConditionFolder(const Loop *L, Value *BECond,
4137  bool IsPosBECond, ScalarEvolution &SE)
4138  : SCEVRewriteVisitor(SE), L(L), BackedgeCond(BECond),
4139  IsPositiveBECond(IsPosBECond) {}
4140 
4141  Optional<const SCEV *> compareWithBackedgeCondition(Value *IC);
4142 
4143  const Loop *L;
4144  /// Loop back condition.
4145  Value *BackedgeCond = nullptr;
4146  /// Set to true if loop back is on positive branch condition.
4147  bool IsPositiveBECond;
4148 };
4149 
4151 SCEVBackedgeConditionFolder::compareWithBackedgeCondition(Value *IC) {
4152 
4153  // If value matches the backedge condition for loop latch,
4154  // then return a constant evolution node based on loopback
4155  // branch taken.
4156  if (BackedgeCond == IC)
4157  return IsPositiveBECond ? SE.getOne(Type::getInt1Ty(SE.getContext()))
4158  : SE.getZero(Type::getInt1Ty(SE.getContext()));
4159  return None;
4160 }
4161 
4162 class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
4163 public:
4164  SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
4165  : SCEVRewriteVisitor(SE), L(L) {}
4166 
4167  static const SCEV *rewrite(const SCEV *S, const Loop *L,
4168  ScalarEvolution &SE) {
4169  SCEVShiftRewriter Rewriter(L, SE);
4170  const SCEV *Result = Rewriter.visit(S);
4171  return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
4172  }
4173 
4174  const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4175  // Only allow AddRecExprs for this loop.
4176  if (!SE.isLoopInvariant(Expr, L))
4177  Valid = false;
4178  return Expr;
4179  }
4180 
4181  const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
4182  if (Expr->getLoop() == L && Expr->isAffine())
4183  return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE));
4184  Valid = false;
4185  return Expr;
4186  }
4187 
4188  bool isValid() { return Valid; }
4189 
4190 private:
4191  const Loop *L;
4192  bool Valid = true;
4193 };
4194 
4195 } // end anonymous namespace
4196 
4198 ScalarEvolution::proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR) {
4199  if (!AR->isAffine())
4200  return SCEV::FlagAnyWrap;
4201 
4202  using OBO = OverflowingBinaryOperator;
4203 
4205 
4206  if (!AR->hasNoSignedWrap()) {
4207  ConstantRange AddRecRange = getSignedRange(AR);
4208  ConstantRange IncRange = getSignedRange(AR->getStepRecurrence(*this));
4209 
4211  Instruction::Add, IncRange, OBO::NoSignedWrap);
4212  if (NSWRegion.contains(AddRecRange))
4213  Result = ScalarEvolution::setFlags(Result, SCEV::FlagNSW);
4214  }
4215 
4216  if (!AR->hasNoUnsignedWrap()) {
4217  ConstantRange AddRecRange = getUnsignedRange(AR);
4218  ConstantRange IncRange = getUnsignedRange(AR->getStepRecurrence(*this));
4219 
4221  Instruction::Add, IncRange, OBO::NoUnsignedWrap);
4222  if (NUWRegion.contains(AddRecRange))
4223  Result = ScalarEvolution::setFlags(Result, SCEV::FlagNUW);
4224  }
4225 
4226  return Result;
4227 }
4228 
4229 namespace {
4230 
4231 /// Represents an abstract binary operation. This may exist as a
4232 /// normal instruction or constant expression, or may have been
4233 /// derived from an expression tree.
4234 struct BinaryOp {
4235  unsigned Opcode;
4236  Value *LHS;
4237  Value *RHS;
4238  bool IsNSW = false;
4239  bool IsNUW = false;
4240 
4241  /// Op is set if this BinaryOp corresponds to a concrete LLVM instruction or
4242  /// constant expression.
4243  Operator *Op = nullptr;
4244 
4245  explicit BinaryOp(Operator *Op)
4246  : Opcode(Op->getOpcode()), LHS(Op->getOperand(0)), RHS(Op->getOperand(1)),
4247  Op(Op) {
4248  if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(Op)) {
4249  IsNSW = OBO->hasNoSignedWrap();
4250  IsNUW = OBO->hasNoUnsignedWrap();
4251  }
4252  }
4253 
4254  explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false,
4255  bool IsNUW = false)
4256  : Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW) {}
4257 };
4258 
4259 } // end anonymous namespace
4260 
4261 /// Try to map \p V into a BinaryOp, and return \c None on failure.
4263  auto *Op = dyn_cast<Operator>(V);
4264  if (!Op)
4265  return None;
4266 
4267  // Implementation detail: all the cleverness here should happen without
4268  // creating new SCEV expressions -- our caller knowns tricks to avoid creating
4269  // SCEV expressions when possible, and we should not break that.
4270 
4271  switch (Op->getOpcode()) {
4272  case Instruction::Add:
4273  case Instruction::Sub:
4274  case Instruction::Mul:
4275  case Instruction::UDiv:
4276  case Instruction::URem:
4277  case Instruction::And:
4278  case Instruction::Or:
4279  case Instruction::AShr:
4280  case Instruction::Shl:
4281  return BinaryOp(Op);
4282 
4283  case Instruction::Xor:
4284  if (auto *RHSC = dyn_cast<ConstantInt>(Op->getOperand(1)))
4285  // If the RHS of the xor is a signmask, then this is just an add.
4286  // Instcombine turns add of signmask into xor as a strength reduction step.
4287  if (RHSC->getValue().isSignMask())
4288  return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1));
4289  return BinaryOp(Op);
4290 
4291  case Instruction::LShr:
4292  // Turn logical shift right of a constant into a unsigned divide.
4293  if (ConstantInt *SA = dyn_cast<ConstantInt>(Op->getOperand(1))) {
4294  uint32_t BitWidth = cast<IntegerType>(Op->getType())->getBitWidth();
4295 
4296  // If the shift count is not less than the bitwidth, the result of
4297  // the shift is undefined. Don't try to analyze it, because the
4298  // resolution chosen here may differ from the resolution chosen in
4299  // other parts of the compiler.
4300  if (SA->getValue().ult(BitWidth)) {
4301  Constant *X =
4302  ConstantInt::get(SA->getContext(),
4303  APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4304  return BinaryOp(Instruction::UDiv, Op->getOperand(0), X);
4305  }
4306  }
4307  return BinaryOp(Op);
4308 
4309  case Instruction::ExtractValue: {
4310  auto *EVI = cast<ExtractValueInst>(Op);
4311  if (EVI->getNumIndices() != 1 || EVI->getIndices()[0] != 0)
4312  break;
4313 
4314  auto *CI = dyn_cast<CallInst>(EVI->getAggregateOperand());
4315  if (!CI)
4316  break;
4317 
4318  if (auto *F = CI->getCalledFunction())
4319  switch (F->getIntrinsicID()) {
4320  case Intrinsic::sadd_with_overflow:
4321  case Intrinsic::uadd_with_overflow:
4322  if (!isOverflowIntrinsicNoWrap(cast<IntrinsicInst>(CI), DT))
4323  return BinaryOp(Instruction::Add, CI->getArgOperand(0),
4324  CI->getArgOperand(1));
4325 
4326  // Now that we know that all uses of the arithmetic-result component of
4327  // CI are guarded by the overflow check, we can go ahead and pretend
4328  // that the arithmetic is non-overflowing.
4329  if (F->getIntrinsicID() == Intrinsic::sadd_with_overflow)
4330  return BinaryOp(Instruction::Add, CI->getArgOperand(0),
4331  CI->getArgOperand(1), /* IsNSW = */ true,
4332  /* IsNUW = */ false);
4333  else
4334  return BinaryOp(Instruction::Add, CI->getArgOperand(0),
4335  CI->getArgOperand(1), /* IsNSW = */ false,
4336  /* IsNUW*/ true);
4337  case Intrinsic::ssub_with_overflow:
4338  case Intrinsic::usub_with_overflow:
4339  if (!isOverflowIntrinsicNoWrap(cast<IntrinsicInst>(CI), DT))
4340  return BinaryOp(Instruction::Sub, CI->getArgOperand(0),
4341  CI->getArgOperand(1));
4342 
4343  // The same reasoning as sadd/uadd above.
4344  if (F->getIntrinsicID() == Intrinsic::ssub_with_overflow)
4345  return BinaryOp(Instruction::Sub, CI->getArgOperand(0),
4346  CI->getArgOperand(1), /* IsNSW = */ true,
4347  /* IsNUW = */ false);
4348  else
4349  return BinaryOp(Instruction::Sub, CI->getArgOperand(0),
4350  CI->getArgOperand(1), /* IsNSW = */ false,
4351  /* IsNUW = */ true);
4352  case Intrinsic::smul_with_overflow:
4353  case Intrinsic::umul_with_overflow:
4354  return BinaryOp(Instruction::Mul, CI->getArgOperand(0),
4355  CI->getArgOperand(1));
4356  default:
4357  break;
4358  }
4359  }
4360 
4361  default:
4362  break;
4363  }
4364 
4365  return None;
4366 }
4367 
4368 /// Helper function to createAddRecFromPHIWithCasts. We have a phi
4369 /// node whose symbolic (unknown) SCEV is \p SymbolicPHI, which is updated via
4370 /// the loop backedge by a SCEVAddExpr, possibly also with a few casts on the
4371 /// way. This function checks if \p Op, an operand of this SCEVAddExpr,
4372 /// follows one of the following patterns:
4373 /// Op == (SExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
4374 /// Op == (ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
4375 /// If the SCEV expression of \p Op conforms with one of the expected patterns
4376 /// we return the type of the truncation operation, and indicate whether the
4377 /// truncated type should be treated as signed/unsigned by setting
4378 /// \p Signed to true/false, respectively.
4379 static Type *isSimpleCastedPHI(const SCEV *Op, const SCEVUnknown *SymbolicPHI,
4380  bool &Signed, ScalarEvolution &SE) {
4381  // The case where Op == SymbolicPHI (that is, with no type conversions on
4382  // the way) is handled by the regular add recurrence creating logic and
4383  // would have already been triggered in createAddRecForPHI. Reaching it here
4384  // means that createAddRecFromPHI had failed for this PHI before (e.g.,
4385  // because one of the other operands of the SCEVAddExpr updating this PHI is
4386  // not invariant).
4387  //
4388  // Here we look for the case where Op = (ext(trunc(SymbolicPHI))), and in
4389  // this case predicates that allow us to prove that Op == SymbolicPHI will
4390  // be added.
4391  if (Op == SymbolicPHI)
4392  return nullptr;
4393 
4394  unsigned SourceBits = SE.getTypeSizeInBits(SymbolicPHI->getType());
4395  unsigned NewBits = SE.getTypeSizeInBits(Op->getType());
4396  if (SourceBits != NewBits)
4397  return nullptr;
4398 
4401  if (!SExt && !ZExt)
4402  return nullptr;
4403  const SCEVTruncateExpr *Trunc =
4404  SExt ? dyn_cast<SCEVTruncateExpr>(SExt->getOperand())
4405  : dyn_cast<SCEVTruncateExpr>(ZExt->getOperand());
4406  if (!Trunc)
4407  return nullptr;
4408  const SCEV *X = Trunc->getOperand();
4409  if (X != SymbolicPHI)
4410  return nullptr;
4411  Signed = SExt != nullptr;
4412  return Trunc->getType();
4413 }
4414 
4415 static const Loop *isIntegerLoopHeaderPHI(const PHINode *PN, LoopInfo &LI) {
4416  if (!PN->getType()->isIntegerTy())
4417  return nullptr;
4418  const Loop *L = LI.getLoopFor(PN->getParent());
4419  if (!L || L->getHeader() != PN->getParent())
4420  return nullptr;
4421  return L;
4422 }
4423 
4424 // Analyze \p SymbolicPHI, a SCEV expression of a phi node, and check if the
4425 // computation that updates the phi follows the following pattern:
4426 // (SExt/ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) + InvariantAccum
4427 // which correspond to a phi->trunc->sext/zext->add->phi update chain.
4428 // If so, try to see if it can be rewritten as an AddRecExpr under some
4429 // Predicates. If successful, return them as a pair. Also cache the results
4430 // of the analysis.
4431 //
4432 // Example usage scenario:
4433 // Say the Rewriter is called for the following SCEV:
4434 // 8 * ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
4435 // where:
4436 // %X = phi i64 (%Start, %BEValue)
4437 // It will visitMul->visitAdd->visitSExt->visitTrunc->visitUnknown(%X),
4438 // and call this function with %SymbolicPHI = %X.
4439 //
4440 // The analysis will find that the value coming around the backedge has
4441 // the following SCEV:
4442 // BEValue = ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
4443 // Upon concluding that this matches the desired pattern, the function
4444 // will return the pair {NewAddRec, SmallPredsVec} where:
4445 // NewAddRec = {%Start,+,%Step}
4446 // SmallPredsVec = {P1, P2, P3} as follows:
4447 // P1(WrapPred): AR: {trunc(%Start),+,(trunc %Step)}<nsw> Flags: <nssw>
4448 // P2(EqualPred): %Start == (sext i32 (trunc i64 %Start to i32) to i64)
4449 // P3(EqualPred): %Step == (sext i32 (trunc i64 %Step to i32) to i64)
4450 // The returned pair means that SymbolicPHI can be rewritten into NewAddRec
4451 // under the predicates {P1,P2,P3}.
4452 // This predicated rewrite will be cached in PredicatedSCEVRewrites:
4453 // PredicatedSCEVRewrites[{%X,L}] = {NewAddRec, {P1,P2,P3)}
4454 //
4455 // TODO's:
4456 //
4457 // 1) Extend the Induction descriptor to also support inductions that involve
4458 // casts: When needed (namely, when we are called in the context of the
4459 // vectorizer induction analysis), a Set of cast instructions will be
4460 // populated by this method, and provided back to isInductionPHI. This is
4461 // needed to allow the vectorizer to properly record them to be ignored by
4462 // the cost model and to avoid vectorizing them (otherwise these casts,
4463 // which are redundant under the runtime overflow checks, will be
4464 // vectorized, which can be costly).
4465 //
4466 // 2) Support additional induction/PHISCEV patterns: We also want to support
4467 // inductions where the sext-trunc / zext-trunc operations (partly) occur
4468 // after the induction update operation (the induction increment):
4469 //
4470 // (Trunc iy (SExt/ZExt ix (%SymbolicPHI + InvariantAccum) to iy) to ix)
4471 // which correspond to a phi->add->trunc->sext/zext->phi update chain.
4472 //
4473 // (Trunc iy ((SExt/ZExt ix (%SymbolicPhi) to iy) + InvariantAccum) to ix)
4474 // which correspond to a phi->trunc->add->sext/zext->phi update chain.
4475 //
4476 // 3) Outline common code with createAddRecFromPHI to avoid duplication.
4478 ScalarEvolution::createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI) {
4480 
4481  // *** Part1: Analyze if we have a phi-with-cast pattern for which we can
4482  // return an AddRec expression under some predicate.
4483 
4484  auto *PN = cast<PHINode>(SymbolicPHI->getValue());
4485  const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
4486  assert(L && "Expecting an integer loop header phi");
4487 
4488  // The loop may have multiple entrances or multiple exits; we can analyze
4489  // this phi as an addrec if it has a unique entry value and a unique
4490  // backedge value.
4491  Value *BEValueV = nullptr, *StartValueV = nullptr;
4492  for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
4493  Value *V = PN->getIncomingValue(i);
4494  if (L->contains(PN->getIncomingBlock(i))) {
4495  if (!BEValueV) {
4496  BEValueV = V;
4497  } else if (BEValueV != V) {
4498  BEValueV = nullptr;
4499  break;
4500  }
4501  } else if (!StartValueV) {
4502  StartValueV = V;
4503  } else if (StartValueV != V) {
4504  StartValueV = nullptr;
4505  break;
4506  }
4507  }
4508  if (!BEValueV || !StartValueV)
4509  return None;
4510 
4511  const SCEV *BEValue = getSCEV(BEValueV);
4512 
4513  // If the value coming around the backedge is an add with the symbolic
4514  // value we just inserted, possibly with casts that we can ignore under
4515  // an appropriate runtime guard, then we found a simple induction variable!
4516  const auto *Add = dyn_cast<SCEVAddExpr>(BEValue);
4517  if (!Add)
4518  return None;
4519 
4520  // If there is a single occurrence of the symbolic value, possibly
4521  // casted, replace it with a recurrence.
4522  unsigned FoundIndex = Add->getNumOperands();
4523  Type *TruncTy = nullptr;
4524  bool Signed;
4525  for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4526  if ((TruncTy =
4527  isSimpleCastedPHI(Add->getOperand(i), SymbolicPHI, Signed, *this)))
4528  if (FoundIndex == e) {
4529  FoundIndex = i;
4530  break;
4531  }
4532 
4533  if (FoundIndex == Add->getNumOperands())
4534  return None;
4535 
4536  // Create an add with everything but the specified operand.
4538  for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4539  if (i != FoundIndex)
4540  Ops.push_back(Add->getOperand(i));
4541  const SCEV *Accum = getAddExpr(Ops);
4542 
4543  // The runtime checks will not be valid if the step amount is
4544  // varying inside the loop.
4545  if (!isLoopInvariant(Accum, L))
4546  return None;
4547 
4548  // *** Part2: Create the predicates
4549 
4550  // Analysis was successful: we have a phi-with-cast pattern for which we
4551  // can return an AddRec expression under the following predicates:
4552  //
4553  // P1: A Wrap predicate that guarantees that Trunc(Start) + i*Trunc(Accum)
4554  // fits within the truncated type (does not overflow) for i = 0 to n-1.
4555  // P2: An Equal predicate that guarantees that
4556  // Start = (Ext ix (Trunc iy (Start) to ix) to iy)
4557  // P3: An Equal predicate that guarantees that
4558  // Accum = (Ext ix (Trunc iy (Accum) to ix) to iy)
4559  //
4560  // As we next prove, the above predicates guarantee that:
4561  // Start + i*Accum = (Ext ix (Trunc iy ( Start + i*Accum ) to ix) to iy)
4562  //
4563  //
4564  // More formally, we want to prove that:
4565  // Expr(i+1) = Start + (i+1) * Accum
4566  // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
4567  //
4568  // Given that:
4569  // 1) Expr(0) = Start
4570  // 2) Expr(1) = Start + Accum
4571  // = (Ext ix (Trunc iy (Start) to ix) to iy) + Accum :: from P2
4572  // 3) Induction hypothesis (step i):
4573  // Expr(i) = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum
4574  //
4575  // Proof:
4576  // Expr(i+1) =
4577  // = Start + (i+1)*Accum
4578  // = (Start + i*Accum) + Accum
4579  // = Expr(i) + Accum
4580  // = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum + Accum
4581  // :: from step i
4582  //
4583  // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy) + Accum + Accum
4584  //
4585  // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy)
4586  // + (Ext ix (Trunc iy (Accum) to ix) to iy)
4587  // + Accum :: from P3
4588  //
4589  // = (Ext ix (Trunc iy ((Start + (i-1)*Accum) + Accum) to ix) to iy)
4590  // + Accum :: from P1: Ext(x)+Ext(y)=>Ext(x+y)
4591  //
4592  // = (Ext ix (Trunc iy (Start + i*Accum) to ix) to iy) + Accum
4593  // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
4594  //
4595  // By induction, the same applies to all iterations 1<=i<n:
4596  //
4597 
4598  // Create a truncated addrec for which we will add a no overflow check (P1).
4599  const SCEV *StartVal = getSCEV(StartValueV);
4600  const SCEV *PHISCEV =
4601  getAddRecExpr(getTruncateExpr(StartVal, TruncTy),
4602  getTruncateExpr(Accum, TruncTy), L, SCEV::FlagAnyWrap);
4603 
4604  // PHISCEV can be either a SCEVConstant or a SCEVAddRecExpr.
4605  // ex: If truncated Accum is 0 and StartVal is a constant, then PHISCEV
4606  // will be constant.
4607  //
4608  // If PHISCEV is a constant, then P1 degenerates into P2 or P3, so we don't
4609  // add P1.
4610  if (const auto *AR = dyn_cast<SCEVAddRecExpr>(PHISCEV)) {
4614  const SCEVPredicate *AddRecPred = getWrapPredicate(AR, AddedFlags);
4615  Predicates.push_back(AddRecPred);
4616  }
4617 
4618  // Create the Equal Predicates P2,P3:
4619 
4620  // It is possible that the predicates P2 and/or P3 are computable at
4621  // compile time due to StartVal and/or Accum being constants.
4622  // If either one is, then we can check that now and escape if either P2
4623  // or P3 is false.
4624 
4625  // Construct the extended SCEV: (Ext ix (Trunc iy (Expr) to ix) to iy)
4626  // for each of StartVal and Accum
4627  auto GetExtendedExpr = [&](const SCEV *Expr) -> const SCEV * {
4628  assert(isLoopInvariant(Expr, L) && "Expr is expected to be invariant");
4629  const SCEV *TruncatedExpr = getTruncateExpr(Expr, TruncTy);
4630  const SCEV *ExtendedExpr =
4631  Signed ? getSignExtendExpr(TruncatedExpr, Expr->getType())
4632  : getZeroExtendExpr(TruncatedExpr, Expr->getType());
4633  return ExtendedExpr;
4634  };
4635 
4636  // Given:
4637  // ExtendedExpr = (Ext ix (Trunc iy (Expr) to ix) to iy
4638  // = GetExtendedExpr(Expr)
4639  // Determine whether the predicate P: Expr == ExtendedExpr
4640  // is known to be false at compile time
4641  auto PredIsKnownFalse = [&](const SCEV *Expr,
4642  const SCEV *ExtendedExpr) -> bool {
4643  return Expr != ExtendedExpr &&
4644  isKnownPredicate(ICmpInst::ICMP_NE, Expr, ExtendedExpr);
4645  };
4646 
4647  const SCEV *StartExtended = GetExtendedExpr(StartVal);
4648  if (PredIsKnownFalse(StartVal, StartExtended)) {
4649  DEBUG(dbgs() << "P2 is compile-time false\n";);
4650  return None;
4651  }
4652 
4653  const SCEV *AccumExtended = GetExtendedExpr(Accum);
4654  if (PredIsKnownFalse(Accum, AccumExtended)) {
4655  DEBUG(dbgs() << "P3 is compile-time false\n";);
4656  return None;
4657  }
4658 
4659  auto AppendPredicate = [&](const SCEV *Expr,
4660  const SCEV *ExtendedExpr) -> void {
4661  if (Expr != ExtendedExpr &&
4662  !isKnownPredicate(ICmpInst::ICMP_EQ, Expr, ExtendedExpr)) {
4663  const SCEVPredicate *Pred = getEqualPredicate(Expr, ExtendedExpr);
4664  DEBUG (dbgs() << "Added Predicate: " << *Pred);
4665  Predicates.push_back(Pred);
4666  }
4667  };
4668 
4669  AppendPredicate(StartVal, StartExtended);
4670  AppendPredicate(Accum, AccumExtended);
4671 
4672  // *** Part3: Predicates are ready. Now go ahead and create the new addrec in
4673  // which the casts had been folded away. The caller can rewrite SymbolicPHI
4674  // into NewAR if it will also add the runtime overflow checks specified in
4675  // Predicates.
4676  auto *NewAR = getAddRecExpr(StartVal, Accum, L, SCEV::FlagAnyWrap);
4677 
4678  std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> PredRewrite =
4679  std::make_pair(NewAR, Predicates);
4680  // Remember the result of the analysis for this SCEV at this locayyytion.
4681  PredicatedSCEVRewrites[{SymbolicPHI, L}] = PredRewrite;
4682  return PredRewrite;
4683 }
4684 
4687  auto *PN = cast<PHINode>(SymbolicPHI->getValue());
4688  const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
4689  if (!L)
4690  return None;
4691 
4692  // Check to see if we already analyzed this PHI.
4693  auto I = PredicatedSCEVRewrites.find({SymbolicPHI, L});
4694  if (I != PredicatedSCEVRewrites.end()) {
4695  std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> Rewrite =
4696  I->second;
4697  // Analysis was done before and failed to create an AddRec:
4698  if (Rewrite.first == SymbolicPHI)
4699  return None;
4700  // Analysis was done before and succeeded to create an AddRec under
4701  // a predicate:
4702  assert(isa<SCEVAddRecExpr>(Rewrite.first) && "Expected an AddRec");
4703  assert(!(Rewrite.second).empty() && "Expected to find Predicates");
4704  return Rewrite;
4705  }
4706 
4708  Rewrite = createAddRecFromPHIWithCastsImpl(SymbolicPHI);
4709 
4710  // Record in the cache that the analysis failed
4711  if (!Rewrite) {
4713  PredicatedSCEVRewrites[{SymbolicPHI, L}] = {SymbolicPHI, Predicates};
4714  return None;
4715  }
4716 
4717  return Rewrite;
4718 }
4719 
4720 /// A helper function for createAddRecFromPHI to handle simple cases.
4721 ///
4722 /// This function tries to find an AddRec expression for the simplest (yet most
4723 /// common) cases: PN = PHI(Start, OP(Self, LoopInvariant)).
4724 /// If it fails, createAddRecFromPHI will use a more general, but slow,
4725 /// technique for finding the AddRec expression.
4726 const SCEV *ScalarEvolution::createSimpleAffineAddRec(PHINode *PN,
4727  Value *BEValueV,
4728  Value *StartValueV) {
4729  const Loop *L = LI.getLoopFor(PN->getParent());
4730  assert(L && L->getHeader() == PN->getParent());
4731  assert(BEValueV && StartValueV);
4732 
4733  auto BO = MatchBinaryOp(BEValueV, DT);
4734  if (!BO)
4735  return nullptr;
4736 
4737  if (BO->Opcode != Instruction::Add)
4738  return nullptr;
4739 
4740  const SCEV *Accum = nullptr;
4741  if (BO->LHS == PN && L->isLoopInvariant(BO->RHS))
4742  Accum = getSCEV(BO->RHS);
4743  else if (BO->RHS == PN && L->isLoopInvariant(BO->LHS))
4744  Accum = getSCEV(BO->LHS);
4745 
4746  if (!Accum)
4747  return nullptr;
4748 
4750  if (BO->IsNUW)
4751  Flags = setFlags(Flags, SCEV::FlagNUW);
4752  if (BO->IsNSW)
4753  Flags = setFlags(Flags, SCEV::FlagNSW);
4754 
4755  const SCEV *StartVal = getSCEV(StartValueV);
4756  const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
4757 
4758  ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
4759 
4760  // We can add Flags to the post-inc expression only if we
4761  // know that it is *undefined behavior* for BEValueV to
4762  // overflow.
4763  if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
4764  if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
4765  (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
4766 
4767  return PHISCEV;
4768 }
4769 
4770 const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
4771  const Loop *L = LI.getLoopFor(PN->getParent());
4772  if (!L || L->getHeader() != PN->getParent())
4773  return nullptr;
4774 
4775  // The loop may have multiple entrances or multiple exits; we can analyze
4776  // this phi as an addrec if it has a unique entry value and a unique
4777  // backedge value.
4778  Value *BEValueV = nullptr, *StartValueV = nullptr;
4779  for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
4780  Value *V = PN->getIncomingValue(i);
4781  if (L->contains(PN->getIncomingBlock(i))) {
4782  if (!BEValueV) {
4783  BEValueV = V;
4784  } else if (BEValueV != V) {
4785  BEValueV = nullptr;
4786  break;
4787  }
4788  } else if (!StartValueV) {
4789  StartValueV = V;
4790  } else if (StartValueV != V) {
4791  StartValueV = nullptr;
4792  break;
4793  }
4794  }
4795  if (!BEValueV || !StartValueV)
4796  return nullptr;
4797 
4798  assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
4799  "PHI node already processed?");
4800 
4801  // First, try to find AddRec expression without creating a fictituos symbolic
4802  // value for PN.
4803  if (auto *S = createSimpleAffineAddRec(PN, BEValueV, StartValueV))
4804  return S;
4805 
4806  // Handle PHI node value symbolically.
4807  const SCEV *SymbolicName = getUnknown(PN);
4808  ValueExprMap.insert({SCEVCallbackVH(PN, this), SymbolicName});
4809 
4810  // Using this symbolic name for the PHI, analyze the value coming around
4811  // the back-edge.
4812  const SCEV *BEValue = getSCEV(BEValueV);
4813 
4814  // NOTE: If BEValue is loop invariant, we know that the PHI node just
4815  // has a special value for the first iteration of the loop.
4816 
4817  // If the value coming around the backedge is an add with the symbolic
4818  // value we just inserted, then we found a simple induction variable!
4819  if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
4820  // If there is a single occurrence of the symbolic value, replace it
4821  // with a recurrence.
4822  unsigned FoundIndex = Add->getNumOperands();
4823  for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4824  if (Add->getOperand(i) == SymbolicName)
4825  if (FoundIndex == e) {
4826  FoundIndex = i;
4827  break;
4828  }
4829 
4830  if (FoundIndex != Add->getNumOperands()) {
4831  // Create an add with everything but the specified operand.
4833  for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4834  if (i != FoundIndex)
4835  Ops.push_back(SCEVBackedgeConditionFolder::rewrite(Add->getOperand(i),
4836  L, *this));
4837  const SCEV *Accum = getAddExpr(Ops);
4838 
4839  // This is not a valid addrec if the step amount is varying each
4840  // loop iteration, but is not itself an addrec in this loop.
4841  if (isLoopInvariant(Accum, L) ||
4842  (isa<SCEVAddRecExpr>(Accum) &&
4843  cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
4845 
4846  if (auto BO = MatchBinaryOp(BEValueV, DT)) {
4847  if (BO->Opcode == Instruction::Add && BO->LHS == PN) {
4848  if (BO->IsNUW)
4849  Flags = setFlags(Flags, SCEV::FlagNUW);
4850  if (BO->IsNSW)
4851  Flags = setFlags(Flags, SCEV::FlagNSW);
4852  }
4853  } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
4854  // If the increment is an inbounds GEP, then we know the address
4855  // space cannot be wrapped around. We cannot make any guarantee
4856  // about signed or unsigned overflow because pointers are
4857  // unsigned but we may have a negative index from the base
4858  // pointer. We can guarantee that no unsigned wrap occurs if the
4859  // indices form a positive value.
4860  if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
4861  Flags = setFlags(Flags, SCEV::FlagNW);
4862 
4863  const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
4864  if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
4865  Flags = setFlags(Flags, SCEV::FlagNUW);
4866  }
4867 
4868  // We cannot transfer nuw and nsw flags from subtraction
4869  // operations -- sub nuw X, Y is not the same as add nuw X, -Y
4870  // for instance.
4871  }
4872 
4873  const SCEV *StartVal = getSCEV(StartValueV);
4874  const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
4875 
4876  // Okay, for the entire analysis of this edge we assumed the PHI
4877  // to be symbolic. We now need to go back and purge all of the
4878  // entries for the scalars that use the symbolic expression.
4879  forgetSymbolicName(PN, SymbolicName);
4880  ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
4881 
4882  // We can add Flags to the post-inc expression only if we
4883  // know that it is *undefined behavior* for BEValueV to
4884  // overflow.
4885  if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
4886  if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
4887  (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
4888 
4889  return PHISCEV;
4890  }
4891  }
4892  } else {
4893  // Otherwise, this could be a loop like this:
4894  // i = 0; for (j = 1; ..; ++j) { .... i = j; }
4895  // In this case, j = {1,+,1} and BEValue is j.
4896  // Because the other in-value of i (0) fits the evolution of BEValue
4897  // i really is an addrec evolution.
4898  //
4899  // We can generalize this saying that i is the shifted value of BEValue
4900  // by one iteration:
4901  // PHI(f(0), f({1,+,1})) --> f({0,+,1})
4902  const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this);
4903  const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this);
4904  if (Shifted != getCouldNotCompute() &&
4905  Start != getCouldNotCompute()) {
4906  const SCEV *StartVal = getSCEV(StartValueV);
4907  if (Start == StartVal) {
4908  // Okay, for the entire analysis of this edge we assumed the PHI
4909  // to be symbolic. We now need to go back and purge all of the
4910  // entries for the scalars that use the symbolic expression.
4911  forgetSymbolicName(PN, SymbolicName);
4912  ValueExprMap[SCEVCallbackVH(PN, this)] = Shifted;
4913  return Shifted;
4914  }
4915  }
4916  }
4917 
4918  // Remove the temporary PHI node SCEV that has been inserted while intending
4919  // to create an AddRecExpr for this PHI node. We can not keep this temporary
4920  // as it will prevent later (possibly simpler) SCEV expressions to be added
4921  // to the ValueExprMap.
4922  eraseValueFromMap(PN);
4923 
4924  return nullptr;
4925 }
4926 
4927 // Checks if the SCEV S is available at BB. S is considered available at BB
4928 // if S can be materialized at BB without introducing a fault.
4929 static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S,
4930  BasicBlock *BB) {
4931  struct CheckAvailable {
4932  bool TraversalDone = false;
4933  bool Available = true;
4934 
4935  const Loop *L = nullptr; // The loop BB is in (can be nullptr)
4936  BasicBlock *BB = nullptr;
4937  DominatorTree &DT;
4938 
4939  CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
4940  : L(L), BB(BB), DT(DT) {}
4941 
4942  bool setUnavailable() {
4943  TraversalDone = true;
4944  Available = false;
4945  return false;
4946  }
4947 
4948  bool follow(const SCEV *S) {
4949  switch (S->getSCEVType()) {
4950  case scConstant: case scTruncate: case scZeroExtend: case scSignExtend:
4951  case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr:
4952  // These expressions are available if their operand(s) is/are.
4953  return true;
4954 
4955  case scAddRecExpr: {
4956  // We allow add recurrences that are on the loop BB is in, or some
4957  // outer loop. This guarantees availability because the value of the
4958  // add recurrence at BB is simply the "current" value of the induction
4959  // variable. We can relax this in the future; for instance an add
4960  // recurrence on a sibling dominating loop is also available at BB.
4961  const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
4962  if (L && (ARLoop == L || ARLoop->contains(L)))
4963  return true;
4964 
4965  return setUnavailable();
4966  }
4967 
4968  case scUnknown: {
4969  // For SCEVUnknown, we check for simple dominance.
4970  const auto *SU = cast<SCEVUnknown>(S);
4971  Value *V = SU->getValue();
4972 
4973  if (isa<Argument>(V))
4974  return false;
4975 
4976  if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
4977  return false;
4978 
4979  return setUnavailable();
4980  }
4981 
4982  case scUDivExpr:
4983  case scCouldNotCompute:
4984  // We do not try to smart about these at all.
4985  return setUnavailable();
4986  }
4987  llvm_unreachable("switch should be fully covered!");
4988  }
4989 
4990  bool isDone() { return TraversalDone; }
4991  };
4992 
4993  CheckAvailable CA(L, BB, DT);
4995 
4996  ST.visitAll(S);
4997  return CA.Available;
4998 }
4999 
5000 // Try to match a control flow sequence that branches out at BI and merges back
5001 // at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful
5002 // match.
5004  Value *&C, Value *&LHS, Value *&RHS) {
5005  C = BI->getCondition();
5006 
5007  BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
5008  BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
5009 
5010  if (!LeftEdge.isSingleEdge())
5011  return false;
5012 
5013  assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()");
5014 
5015  Use &LeftUse = Merge->getOperandUse(0);
5016  Use &RightUse = Merge->getOperandUse(1);
5017 
5018  if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
5019  LHS = LeftUse;
5020  RHS = RightUse;
5021  return true;
5022  }
5023 
5024  if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
5025  LHS = RightUse;
5026  RHS = LeftUse;
5027  return true;
5028  }
5029 
5030  return false;
5031 }
5032 
5033 const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
5034  auto IsReachable =
5035  [&](BasicBlock *BB) { return DT.isReachableFromEntry(BB); };
5036  if (PN->getNumIncomingValues() == 2 && all_of(PN->blocks(), IsReachable)) {
5037  const Loop *L = LI.getLoopFor(PN->getParent());
5038 
5039  // We don't want to break LCSSA, even in a SCEV expression tree.
5040  for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
5041  if (LI.getLoopFor(PN->getIncomingBlock(i)) != L)
5042  return nullptr;
5043 
5044  // Try to match
5045  //
5046  // br %cond, label %left, label %right
5047  // left:
5048  // br label %merge
5049  // right:
5050  // br label %merge
5051  // merge:
5052  // V = phi [ %x, %left ], [ %y, %right ]
5053  //
5054  // as "select %cond, %x, %y"
5055 
5056  BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
5057  assert(IDom && "At least the entry block should dominate PN");
5058 
5059  auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
5060  Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
5061 
5062  if (BI && BI->isConditional() &&
5063  BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) &&
5064  IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) &&
5065  IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent()))
5066  return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
5067  }
5068 
5069  return nullptr;
5070 }
5071 
5072 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
5073  if (const SCEV *S = createAddRecFromPHI(PN))
5074  return S;
5075 
5076  if (const SCEV *S = createNodeFromSelectLikePHI(PN))
5077  return S;
5078 
5079  // If the PHI has a single incoming value, follow that value, unless the
5080  // PHI's incoming blocks are in a different loop, in which case doing so
5081  // risks breaking LCSSA form. Instcombine would normally zap these, but
5082  // it doesn't have DominatorTree information, so it may miss cases.
5083  if (Value *V = SimplifyInstruction(PN, {getDataLayout(), &TLI, &DT, &AC}))
5084  if (LI.replacementPreservesLCSSAForm(PN, V))
5085  return getSCEV(V);
5086 
5087  // If it's not a loop phi, we can't handle it yet.
5088  return getUnknown(PN);
5089 }
5090 
5091 const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
5092  Value *Cond,
5093  Value *TrueVal,
5094  Value *FalseVal) {
5095  // Handle "constant" branch or select. This can occur for instance when a
5096  // loop pass transforms an inner loop and moves on to process the outer loop.
5097  if (auto *CI = dyn_cast<ConstantInt>(Cond))
5098  return getSCEV(CI->isOne() ? TrueVal : FalseVal);
5099 
5100  // Try to match some simple smax or umax patterns.
5101  auto *ICI = dyn_cast<ICmpInst>(Cond);
5102  if (!ICI)
5103  return getUnknown(I);
5104 
5105  Value *LHS = ICI->getOperand(0);
5106  Value *RHS = ICI->getOperand(1);
5107 
5108  switch (ICI->getPredicate()) {
5109  case ICmpInst::ICMP_SLT:
5110  case ICmpInst::ICMP_SLE:
5111  std::swap(LHS, RHS);
5113  case ICmpInst::ICMP_SGT:
5114  case ICmpInst::ICMP_SGE:
5115  // a >s b ? a+x : b+x -> smax(a, b)+x
5116  // a >s b ? b+x : a+x -> smin(a, b)+x
5117  if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
5118  const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
5119  const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
5120  const SCEV *LA = getSCEV(TrueVal);
5121  const SCEV *RA = getSCEV(FalseVal);
5122  const SCEV *LDiff = getMinusSCEV(LA, LS);
5123  const SCEV *RDiff = getMinusSCEV(RA, RS);
5124  if (LDiff == RDiff)
5125  return getAddExpr(getSMaxExpr(LS, RS), LDiff);
5126  LDiff = getMinusSCEV(LA, RS);
5127  RDiff = getMinusSCEV(RA, LS);
5128  if (LDiff == RDiff)
5129  return getAddExpr(getSMinExpr(LS, RS), LDiff);
5130  }
5131  break;
5132  case ICmpInst::ICMP_ULT:
5133  case ICmpInst::ICMP_ULE:
5134  std::swap(LHS, RHS);
5136  case ICmpInst::ICMP_UGT:
5137  case ICmpInst::ICMP_UGE:
5138  // a >u b ? a+x : b+x -> umax(a, b)+x
5139  // a >u b ? b+x : a+x -> umin(a, b)+x
5140  if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
5141  const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
5142  const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType());
5143  const SCEV *LA = getSCEV(TrueVal);
5144  const SCEV *RA = getSCEV(FalseVal);
5145  const SCEV *LDiff = getMinusSCEV(LA, LS);
5146  const SCEV *RDiff = getMinusSCEV(RA, RS);
5147  if (LDiff == RDiff)
5148  return getAddExpr(getUMaxExpr(LS, RS), LDiff);
5149  LDiff = getMinusSCEV(LA, RS);
5150  RDiff = getMinusSCEV(RA, LS);
5151  if (LDiff == RDiff)
5152  return getAddExpr(getUMinExpr(LS, RS), LDiff);
5153  }
5154  break;
5155  case ICmpInst::ICMP_NE:
5156  // n != 0 ? n+x : 1+x -> umax(n, 1)+x
5157  if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
5158  isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
5159  const SCEV *One = getOne(I->getType());
5160  const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
5161  const SCEV *LA = getSCEV(TrueVal);
5162  const SCEV *RA = getSCEV(FalseVal);
5163  const SCEV *LDiff = getMinusSCEV(LA, LS);
5164  const SCEV *RDiff = getMinusSCEV(RA, One);
5165  if (LDiff == RDiff)
5166  return getAddExpr(getUMaxExpr(One, LS), LDiff);
5167  }
5168  break;
5169  case ICmpInst::ICMP_EQ:
5170  // n == 0 ? 1+x : n+x -> umax(n, 1)+x
5171  if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
5172  isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
5173  const SCEV *One = getOne(I->getType());
5174  const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
5175  const SCEV *LA = getSCEV(TrueVal);
5176  const SCEV *RA = getSCEV(FalseVal);
5177  const SCEV *LDiff = getMinusSCEV(LA, One);
5178  const SCEV *RDiff = getMinusSCEV(RA, LS);
5179  if (LDiff == RDiff)
5180  return getAddExpr(getUMaxExpr(One, LS), LDiff);
5181  }
5182  break;
5183  default:
5184  break;
5185  }
5186 
5187  return getUnknown(I);
5188 }
5189 
5190 /// Expand GEP instructions into add and multiply operations. This allows them
5191 /// to be analyzed by regular SCEV code.
5192 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
5193  // Don't attempt to analyze GEPs over unsized objects.
5194  if (!GEP->getSourceElementType()->isSized())
5195  return getUnknown(GEP);
5196 
5197  SmallVector<const SCEV *, 4> IndexExprs;
5198  for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
5199  IndexExprs.push_back(getSCEV(*Index));
5200  return getGEPExpr(GEP, IndexExprs);
5201 }
5202 
5203 uint32_t ScalarEvolution::GetMinTrailingZerosImpl(const SCEV *S) {
5204  if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
5205  return C->getAPInt().countTrailingZeros();
5206 
5207  if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
5208  return std::min(GetMinTrailingZeros(T->getOperand()),
5209  (uint32_t)getTypeSizeInBits(T->getType()));
5210 
5211  if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
5212  uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
5213  return OpRes == getTypeSizeInBits(E->getOperand()->getType())
5214  ? getTypeSizeInBits(E->getType())
5215  : OpRes;
5216  }
5217 
5218  if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
5219  uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
5220  return OpRes == getTypeSizeInBits(E->getOperand()->getType())
5221  ? getTypeSizeInBits(E->getType())
5222  : OpRes;
5223  }
5224 
5225  if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
5226  // The result is the min of all operands results.
5227  uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
5228  for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
5229  MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
5230  return MinOpRes;
5231  }
5232 
5233  if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
5234  // The result is the sum of all operands results.
5235  uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
5236  uint32_t BitWidth = getTypeSizeInBits(M->getType());
5237  for (unsigned i = 1, e = M->getNumOperands();
5238  SumOpRes != BitWidth && i != e; ++i)
5239  SumOpRes =
5240  std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), BitWidth);
5241  return SumOpRes;
5242  }
5243 
5244  if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
5245  // The result is the min of all operands results.
5246  uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
5247  for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
5248  MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
5249  return MinOpRes;
5250  }
5251 
5252  if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
5253  // The result is the min of all operands results.
5254  uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
5255  for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
5256  MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
5257  return MinOpRes;
5258  }
5259 
5260  if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
5261  // The result is the min of all operands results.
5262  uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
5263  for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
5264  MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
5265  return MinOpRes;
5266  }
5267 
5268  if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
5269  // For a SCEVUnknown, ask ValueTracking.
5270  KnownBits Known = computeKnownBits(U->getValue(), getDataLayout(), 0, &AC, nullptr, &DT);
5271  return Known.countMinTrailingZeros();
5272  }
5273 
5274  // SCEVUDivExpr
5275  return 0;
5276 }
5277 
5279  auto I = MinTrailingZerosCache.find(S);
5280  if (I != MinTrailingZerosCache.end())
5281  return I->second;
5282 
5283  uint32_t Result = GetMinTrailingZerosImpl(S);
5284  auto InsertPair = MinTrailingZerosCache.insert({S, Result});
5285  assert(InsertPair.second && "Should insert a new key");
5286  return InsertPair.first->second;
5287 }
5288 
5289 /// Helper method to assign a range to V from metadata present in the IR.
5291  if (Instruction *I = dyn_cast<Instruction>(V))
5293  return getConstantRangeFromMetadata(*MD);
5294 
5295  return None;
5296 }
5297 
5298 /// Determine the range for a particular SCEV. If SignHint is
5299 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
5300 /// with a "cleaner" unsigned (resp. signed) representation.
5301 const ConstantRange &
5302 ScalarEvolution::getRangeRef(const SCEV *S,
5303  ScalarEvolution::RangeSignHint SignHint) {
5305  SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
5306  : SignedRanges;
5307 
5308  // See if we've computed this range already.
5310  if (I != Cache.end())
5311  return I->second;
5312 
5313  if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
5314  return setRange(C, SignHint, ConstantRange(C->getAPInt()));
5315 
5316  unsigned BitWidth = getTypeSizeInBits(S->getType());
5317  ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
5318 
5319  // If the value has known zeros, the maximum value will have those known zeros
5320  // as well.
5321  uint32_t TZ = GetMinTrailingZeros(S);
5322  if (TZ != 0) {
5323  if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
5324  ConservativeResult =
5326  APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
5327  else
5328  ConservativeResult = ConstantRange(
5329  APInt::getSignedMinValue(BitWidth),
5330  APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
5331  }
5332 
5333  if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
5334  ConstantRange X = getRangeRef(Add->getOperand(0), SignHint);
5335  for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
5336  X = X.add(getRangeRef(Add->getOperand(i), SignHint));
5337  return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
5338  }
5339 
5340  if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
5341  ConstantRange X = getRangeRef(Mul->getOperand(0), SignHint);
5342  for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
5343  X = X.multiply(getRangeRef(Mul->getOperand(i), SignHint));
5344  return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
5345  }
5346 
5347  if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
5348  ConstantRange X = getRangeRef(SMax->getOperand(0), SignHint);
5349  for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
5350  X = X.smax(getRangeRef(SMax->getOperand(i), SignHint));
5351  return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
5352  }
5353 
5354  if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
5355  ConstantRange X = getRangeRef(UMax->getOperand(0), SignHint);
5356  for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
5357  X = X.umax(getRangeRef(UMax->getOperand(i), SignHint));
5358  return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
5359  }
5360 
5361  if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
5362  ConstantRange X = getRangeRef(UDiv->getLHS(), SignHint);
5363  ConstantRange Y = getRangeRef(UDiv->getRHS(), SignHint);
5364  return setRange(UDiv, SignHint,
5365  ConservativeResult.intersectWith(X.udiv(Y)));
5366  }
5367 
5368  if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
5369  ConstantRange X = getRangeRef(ZExt->getOperand(), SignHint);
5370  return setRange(ZExt, SignHint,
5371  ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
5372  }
5373 
5374  if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
5375  ConstantRange X = getRangeRef(SExt->getOperand(), SignHint);
5376  return setRange(SExt, SignHint,
5377  ConservativeResult.intersectWith(X.signExtend(BitWidth)));
5378  }
5379 
5380  if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
5381  ConstantRange X = getRangeRef(Trunc->getOperand(), SignHint);
5382  return setRange(Trunc, SignHint,
5383  ConservativeResult.intersectWith(X.truncate(BitWidth)));
5384  }
5385 
5386  if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
5387  // If there's no unsigned wrap, the value will never be less than its
5388  // initial value.
5389  if (AddRec->hasNoUnsignedWrap())
5390  if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
5391  if (!C->getValue()->isZero())
5392  ConservativeResult = ConservativeResult.intersectWith(
5393  ConstantRange(C->getAPInt(), APInt(BitWidth, 0)));
5394 
5395  // If there's no signed wrap, and all the operands have the same sign or
5396  // zero, the value won't ever change sign.
5397  if (AddRec->hasNoSignedWrap()) {
5398  bool AllNonNeg = true;
5399  bool AllNonPos = true;
5400  for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5401  if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
5402  if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
5403  }
5404  if (AllNonNeg)
5405  ConservativeResult = ConservativeResult.intersectWith(
5406  ConstantRange(APInt(BitWidth, 0),
5407  APInt::getSignedMinValue(BitWidth)));
5408  else if (AllNonPos)
5409  ConservativeResult = ConservativeResult.intersectWith(
5411  APInt(BitWidth, 1)));
5412  }
5413 
5414  // TODO: non-affine addrec
5415  if (AddRec->isAffine()) {
5416  const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
5417  if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
5418  getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
5419  auto RangeFromAffine = getRangeForAffineAR(
5420  AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
5421  BitWidth);
5422  if (!RangeFromAffine.isFullSet())
5423  ConservativeResult =
5424  ConservativeResult.intersectWith(RangeFromAffine);
5425 
5426  auto RangeFromFactoring = getRangeViaFactoring(
5427  AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
5428  BitWidth);
5429  if (!RangeFromFactoring.isFullSet())
5430  ConservativeResult =
5431  ConservativeResult.intersectWith(RangeFromFactoring);
5432  }
5433  }
5434 
5435  return setRange(AddRec, SignHint, std::move(ConservativeResult));
5436  }
5437 
5438  if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
5439  // Check if the IR explicitly contains !range metadata.
5440  Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
5441  if (MDRange.hasValue())
5442  ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
5443 
5444  // Split here to avoid paying the compile-time cost of calling both
5445  // computeKnownBits and ComputeNumSignBits. This restriction can be lifted
5446  // if needed.
5447  const DataLayout &DL = getDataLayout();
5448  if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
5449  // For a SCEVUnknown, ask ValueTracking.
5450  KnownBits Known = computeKnownBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
5451  if (Known.One != ~Known.Zero + 1)
5452  ConservativeResult =
5453  ConservativeResult.intersectWith(ConstantRange(Known.One,
5454  ~Known.Zero + 1));
5455  } else {
5456  assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
5457  "generalize as needed!");
5458  unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
5459  if (NS > 1)
5460  ConservativeResult = ConservativeResult.intersectWith(
5461  ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
5462